We cannot but be somewhat surprised that, among the many attempts which have been made by the philosophers of Britain to explain the wonderful phenomena which are clasped under this name, no author of eminence, besides the Hon. Mr Cavendish and Lord Mahon, have availed themselves of their susceptibility of mathematical discussion; and our wonder is the greater, because it was by a mathematical view of the subject, in the phenomena of attraction and repulsion, that the celebrated philosopher Franklin was led to the only knowledge of electricity that deserves the name of science; for we had scarcely any leading facts, by which we could clas the phenomena, till he published his theory of positive and negative, or plus and minus, electricity. This is founded entirely on the phenomena of attraction and repulsion. These furnish us with all the indications of the presence of the mighty agent, and the marks of its kind, and the measures of its force. Mechanical force accompanies every other appearance; and this accompaniment is regulated in a determinate manner. Many of the effects of electricity are strictly mechanical, producing local motion in the same manner as magnetism or gravitation produce it. One should have expected that the countrymen of Newton, prompted by his success and his fame, would take to this mode of examination, and would have endeavoured to deduce, from the laws observed in the action of this motive force, an explanation of other wonderful phenomena, which are inseparably connected with those of attraction and repulsion.

But this has not been the case, if we except the labours of the two philosophers above mentioned, and a few very obvious positions which must occur to all the inventors and improvers of electrometers, batteries, and other things of measurable nature.

This view has, however, been taken of the subject by a philosopher of unquestioned merit, Mr Aepinus of the Imperial Academy of St Petersburg. This gentleman, struck with the resemblance of the electrical properties of the tourmaline to the properties of a magnet, which have always been considered as the subject of mathematical discussion, fortunately remarked a wonderful wonderful similarity in the whole series of electrical and magnetic attractions and repulsions, and set himself seriously to the classification of them. Having done this with great success, and having maturely reflected on Dr Franklin's happy thought of plus and minus electricity, and his consequent theory of the Leyden phial, he at last hit on a mode of conceiving the whole subject of magnetism and electricity, that bids fair for leading us to a full explanation of all the phenomena; in as far, at least, as it enables us to class them with precision, and to predict what will be the result of any proposed treatment. He candidly gives it the modest name of a hypothesis.

This was published at St Petersburg in 1759, under the title of *Theoria Electritatis et Magnetismi*, and is unquestionably one of the most ingenious and brilliant performances of this century. It is indeed most surprising that it is so little known in this country. This, we imagine, has been chiefly owing to the very slight and almost unintelligible account which Dr Priestley has given of it in his history of electricity; a work which professes to comprehend every thing that has been done by the philosophers of Europe and America for the advancement of this part of natural science, and which indeed contains a great deal of instructive information, and, at the same time, so many loose conjectures and insignificant observations, that the reader (especially if acquainted with the Doctor's character as an unwearyed bookmaker) reasonably believes that he has let nothing slip that was worthy of notice. We do not pretend to account for the manner in which Dr Priestley has mentioned this work so much, and so deservedly celebrated on the continent. We cannot think that he has read it so as to comprehend it, and imagine, that seeing so much algebraic notation in every page, and being at that time a novice in mathematical learning, he contented himself with a few scattered paragraphs which were free of those embarrassments; and thus could only get a very imperfect notion of the system. The Hon. Mr Cavendish has done it more justice in the 6th volume of the Philosophical Transactions, and considers his own most excellent dissertation only as an extention and more accurate application of Epinus's Theory. That we have not an account of this exposition of the Franklinian theory of electricity in our language, is a material want in British literature; and we trust, therefore, that our readers will be highly pleased with having the ingenious discoveries of the great American philosopher put into a form so nearly approaching to a system of demonstrative science.

We propose, therefore, in this place, to give such a brief account of Epinus's theory of electricity, as will enable the reader to reduce to a very simple and easily remembered law all the phenomena of electricity which have any close dependence on the mechanical effects of this powerful agent of nature; referring for a demonstration of what is purely mathematical to Sir Isaac Newton's Principia, and the Dissertation by Mr Cavendish already mentioned, except in such important articles as we think ourselves able to present in a new, and, we hope, a more familiar form. We do not mean, in this place, to give a system of philosophical electricity, nor even to narrate and explain the more remarkable phenomena. Of these we have already given a vast collection in the article Electricity, Encycl.

We confine ourselves to the phenomena which may be called mechanical, producing measurable motion as their immediate effect; and thus giving us a principle for the mathematical examination of the cause of electrical phenomena. We shall consider the reader as acquainted with the other physical effects of electricity, and shall frequently refer to them for proofs.

Moreover, as our intention is merely to give a synoptical view of this elaborate and copious performance of Mr Epinus, hoping that it will excite our countrymen to a careful perusal of so valuable a work, we shall omit most of the algebraic investigations contained in it, and present the conclusions in a more familiar, and not less convincing, form. At the same time we will insert the valuable additions made by Mr Cavendish, and many important particulars not noticed by either of those gentlemen.

**Hypothesis of Epinus.**

The phenomena of electricity are produced by a hypothetical fluid of peculiar nature, and therefore called the electric fluid, having the following properties:

1. Its particles repel each other, with a force decreasing as the distances increase. 2. Its particles attract the particles of some ingredient in all other bodies, with a force decreasing, according to the same law, with an increase of distance; and this attraction is mutual. 3. The electric fluid is dispersed in the pores of other bodies, and moves with various degrees of facility through the pores of different kinds of matter. In those bodies which we call non-electric, such as water or metals, it moves without any perceivable obstruction; but in glaas, resins, and all bodies called electric, it moves with very great difficulty, or is altogether immoveable. 4. The phenomena of electricity are of two kinds: 1. Such as arise from the actual motion of the fluid from a body containing more into one containing less of it. 2. Such as do not immediately arise from this transference, but are instances of its attraction and repulsion.

These things being supposed, certain consequences necessarily result from them, which ought to be analogous to the observed phenomena of electricity, if this hypothesis be complete, or some farther modification of the assumed properties is necessary, in order to make the analogy perfect.

Suppose the body A (fig. 1.) to contain a certain quantity of fluid. Its particles adjoining to the surface, such as P, are attracted by the particles of common matter in the body, but repelled by the other particles of the fluid. The totality of the attractive forces acting on P may be equal to the totality of the repulsive forces, or may be unequal. If these two sums are equal, P is in equilibrium, and has no tendency to change its place. But there may be such a quantity of fluid in the body, that the repulsions of the fluid exceed the attractions of the common matter. In this case, P has a tendency to quit the body, or there is an expulsive force acting on it, and it will quit the body if it be moveable. Because the same must be admitted in respect of every other particle of moveable fluid, it is plain that there will be an efflux, till the attraction of the common matter for the particles of fluid is equal. equal to the repulsion of the remaining fluid. On the other hand, if the primitive repulsion of the fluid acting on the particle P be less than the attractions of the common matter, there will be the same, or at least a similar, superiority of attraction acting on the fluid residing in the circumambient bodies; and there will be an influx from all hands, till an equilibrium be restored.

Hence it follows, that there may always be affixed to any body such a quantity of fluid that there shall be no tendency either to efflux or influx. But if the quantity be increased, and nothing prevent the motion, the redundant fluid will flow out; and if the proper quantity be diminished, there will be an influx of the surrounding fluid, if not prevented by some external force. This may be called the body's natural quantity; because the body, when left to itself, will always be reduced to this state.

If two bodies, A and B, contain each its natural quantity, they will not exert any sensible action on each other; for, because the fluid contained in B is united by attraction to the common matter, and is also repelled by the fluid in A, it necessarily follows, that the whole body B is repelled by the fluid in A. But, on the other hand, the matter in A attracts the fluid in B, and consequently attracts the whole body B: Similar action is exerted by B on A. These contrary forces are either equal, and destroy each other, or unequal, and one of them prevails. This equality or inequality evidently depends on the quantity of fluid contained in one or both of the bodies (no. 7.). Now it is known that bodies left entirely to themselves neither attract nor repel; and it follows from the hypothetical properties of the fluid, that if there be either a redundancy or deficiency of fluid, there will be an efflux or influx, till the attractions and repulsions balance each other. Therefore the internal state of two bodies which neither attract nor repel each other, is that where each contains its natural quantity of electric fluid.

In order, therefore, to conceive distinctly the state of a body containing its natural quantity, and to have a distinct notion of this natural quantity, we must suppose that the quantity of fluid competent to a particle of matter in A repels the fluid competent to a particle of matter in B, just as much as it attracts that particle of matter; and also, that the fluid belonging to a particle of matter in A, repels the fluid belonging to a particle of matter in B, just as much as the particle of matter in A attracts it. Thus the whole fluid in the one repels the whole fluid in the other as much as it attracts the whole matter.

Since this must be conceived of every particle of common matter in a body, we must admit, that when a body is in its natural state, the quantity of electric fluid in it is proportional to the quantity of matter, every particle being united with an equal quantity of fluid. This, however, does not necessarily require that different kinds of matter, in their natural or saturated state, shall contain the same proportion of fluid. It is sufficient that each contains such a quantity, uniformly distributed among its particles, that its repulsion for the fluid in another body is equal to its attraction for the common matter in it. It is, however, more probable, for reasons to be given afterwards, that the quantity of electric fluid attached, or competent, to a particle of all kinds of matter is the same.

We shall now consider more particularly the immediate results of this hypothesis, in the most simple cases, from which we may derive some elementary propositions.

Since our hypothesis is accommodated to the fact, Electric that bodies in their natural state, having their natural quantity of electric fluid, are altogether inactive on each other, by making this natural quantity such, that its mutual repulsion exactly balances its attraction for the common matter—it follows, that we must deduce all total or partial electric phenomena from a redundancy or deficiency of electric fluid. This accordingly is the Franklinian doctrine. The redundant state of a body is called by Dr Franklin positive or plus electricity, and the deficient state is called negative or minus electricity.

A body may contain more than its natural quantity, or less, in every part, or it may be redundant in one place and deficient in another. These different conditions will exhibit different appearances, which must be considered first of all.

Let the body A (fig. 1.) be supposed in its natural state throughout, which we shall generally express by the redundancy that it is saturated; and let us express the fluid quantity of fluid required for its saturation by the symbol Q. Let P be a superficial particle of the fluid. It is attracted by the common matter of the body (which we shall in future call simply the matter), and it is repelled equally by the fluid. Let us call the attraction a, and the repulsion r. Then the force with which the superficial particle is attracted by the body, must be \(a - r\), and \(a - r\) must be = 0, because \(a = r\). Let the quantity \(f\) of fluid be added to the body, and uniformly distributed through its substance. Then, because we must admit that the action is in proportion to the quantity of acting fluid, and this is now \(Q + f\), we have \(Q : Q + f = r : \frac{Q + f}{Q} \times r\); and therefore

\[P \text{ is repelled by the whole fluid with the force } \frac{Q + f}{Q} \times r,\]

or \(\frac{Q}{Q} + \frac{fr}{Q}\), or \(r + \frac{fr}{Q}\). But it is attracted by the common matter in the same manner as before, that is, with a force \(= a\). Therefore the whole action on P is \(a - r - \frac{fr}{Q}\). But \(a - r = 0\). Therefore the whole action on P is \(-\frac{fr}{Q}\); that is, P is repelled with the force \(\frac{fr}{Q}\).

This will perhaps be as distinctly conceived by recollecting, that as much of the fluid as was necessary for saturation, that is, the quantity Q, puts the particle P in equilibrium; and therefore we need only consider the action of the redundant fluid \(f\). To find the repulsive force of this, say \(Q : f = r : \frac{fr}{Q}\), and prefix the sign \(-\); because we are to consider attractions as positive, and repulsions as negative quantities.

Unless, therefore, the particle P be withheld by some other

States of a body causing efflux or influx.

And as every superficial particle is in a similar situation, we see that there will be an efflux from an overcharged body, till all the redundant fluid has quitted it. This efflux will indeed gradually diminish as the expelling force diminishes; that is, as \( f \) diminishes, but will never cease till \( f \) be reduced to nothing. But if there be either an external force acting on the superficial fluid in the opposite direction, or some internal obstruction to its motion, the efflux will stop when the remaining expelling force is just in equilibrium with this external force, or this obstruction.

On the other hand, if the body contains less than its natural quantity of fluid, there will be an influx from without; for if there be a deficiency of fluid \( = f \), the particle \( P \) will be repelled with the force

\[ \frac{Q - f \times r}{Q} \]

\( = r - \frac{f}{Q} \). It is attracted with the force \( a \); and therefore the whole action is \( = a - r + \frac{f}{Q} = + \frac{f}{Q} \) (because \( a - r = 0 \)); that is, \( P \) is attracted with the force \( \frac{f}{Q} \). Fluid will therefore enter from all quarters, as long as there is any deficiency of the quantity necessary for saturation, unless it be opposed by some external force, or hindered by some internal obstruction.

When there is a deficiency of fluid, there is a redundancy of matter, such that its attraction for external fluid is equal to the repulsion of a quantity \( f \) of fluid. This confirms the assumption in no. 10, that the action of a body on the electric fluid depends entirely on the redundant fluid, or the redundant matter of the body.

The efflux or influx may be prevented, either by surrounding the body with substances, through the pores of which the fluid cannot move at all, or by the body itself being of this constitution. And thus we see, that the very circumstance of being impervious to the fluid, or completely permeable, renders the body capable or incapable of permanently exhibiting electrical phenomena, if surrounded by permeable bodies. This circumstance alone, therefore, is sufficient to constitute the difference between electrics per se, and non-electrics.

Here, then, is a numerous class of phenomena, which receive an explanation by this hypothetical constitution of the electric fluid. All electrics per se are bodies fit for containing electricity in bodies which are rendered capable (by whatever means) of producing electrical phenomena; and no conductor, or substance which allows the electricity to pass through it, can be made electric by any of the means which produce that effect in insulators. And it is well known, that the electricity of electrics is vastly more durable than that of non-electrics in similar situations. It is true, indeed, that an electric, which has been excited so as to exhibit electric phenomena with great vivacity, loses this power very quickly if plunged into water, or any other conducting body. But this is owing to the redundancy or deficiency being quite superficial, so that the parts which are disposed to give out or to take in the fluid are in immediate contact with the conducting matter. That the redundancy or deficiency is superficial, follows from this hypothesis; for when the surface is overcharged by the means employed for exciting, the impermeability of the electric per se prevents this redundant fluid from penetrating to any depth; and when the surface has been rendered deficient in fluid, the same impermeability prevents the fluid from expanding from the interior parts, so as to contribute to the replenishing the superficial stratum with fluid. If, indeed, we could fall on any way of overcharging the interior parts of a glass ball, or of withdrawing the natural quantity from them, it is highly probable, that it would continue to attract or repel even after it had been plunged in water. Although the surrounding water would instantly take off the fluid redundant contained in the very surface, the repulsion of the fluid in the internal parts would still be sensible; nay, if a very small permeability be supposed, the body would again become overcharged at the surface; just as we see, that when we plunge a red hot ball of iron into water, and take it out again immediately, it is black on the surface, and may be touched with the finger; but in half a minute after, it again becomes red hot. Perhaps this may be accomplished with a globe of sealing wax, which is permeable while liquid, by electrifying it in a particular way while in that state, and allowing it to freeze. But the reader is not far enough advanced in the hypothesis to understand the process which must be followed. He cannot but recollect, however, many examples in coated glass, &c., where the electricity is most pertinaciously retained by a surface in very close contact with conductors.

Let us now suppose a body NS (fig. 2.), containing in the half NA a quantity \( f \) of redundant fluid, and in the half AS let there be a deficiency \( g \) of fluid; that is, let there be a quantity of matter unfatuated, and such as will attract fluid as much as the quantity \( g \) of fluid would repel it. Let the fluid necessary for the saturation of each half of NS be \( Q \), as before. Let the attraction of the whole matter of NA for a particle of fluid at N be \( a \); and let \( r \) be the repulsion exerted on the same particle N by the whole uniformly distributed fluid in NA and let \( r' \) be the repulsion exerted by the same quantity of fluid in the remote part SA. Then the force with which the particle N or S is attracted by the merely saturated body NS must be \( = a - r - r' \). This is evidently nothing, if the body be in its natural state. But as NA contains the redundant fluid \( f \), and SA is deficient by the quantity \( g \), the whole action must be \( = \frac{Q + f \times r}{Q} \)

\[ = \frac{Q - g \times r'}{Q}. \]

But because \( a - r - r' = 0 \), the action becomes \( = \frac{g \times r'}{Q} \), or because \( r \) is greater than \( r' \), the particle N is repelled with the force \( \frac{f - g \times r'}{Q} \).

In like manner, the particle S is attracted with the force \( \frac{g \times r'}{Q} \).

In the mean time, a particle C, situated at the middle, must be in equilibrium, if the body be in its natural state, being equally attracted, and also equally repelled, on both sides. But as we suppose that NA is overcharged...

ged with the quantity \( f \), C must be repelled in the direction CS with the force \( \frac{f}{Q} \). And if we also suppose that AS is deficient by the quantity \( g \), C is attracted in the direction CS with a force \( \frac{g}{Q} \). Therefore, on the whole, it is urged in the direction CS with the force \( \frac{f + g}{Q} \) or \( \frac{f + g \times r}{Q} \).

Hence we learn, that as long as there is any redundancy in AN, and deficiency in AS, there is a tendency of the redundant fluid to move from N toward S; and, if the body be altogether permeable by the electric fluid, we cannot have a permanent state till the fluid is similarly distributed, and equally divided, between the two halves of NS. Therefore a state like that assumed in this example cannot be permanent in a conducting body, unless an external force act on it; but it may subsist in a non-conductor, and in a lesser degree, in all imperfect conductors.

It is necessary, in this place, to consider a little the nature of that resistance which must be assigned to the motion of the electric fluid through the pores of the body. If it resemble the resistance opposed by a perfect fluid, arising solely from the inertia of its particles, then there is no inequality of force to minute but that it will operate a uniform distribution of the fluid, or at least a dilution which will make the excess of the mutual attractions and repulsions precisely equal and opposite to the external force which keeps it in any state of unequal distribution. But it may resemble the resistance to the deflection of a parcel of small shot disseminated among a quantity of grain, or the resistance to motion through the pores of a plastic or ductile body, such as clay or lead. Here, in order that a particle may change its place, it must overcome the tenacity of the adjoining particles of the body. Therefore, when an unequal distribution has been produced by an external force, the removal or alteration of that force will not be followed by an equable distribution of the fluid. In every part there will remain such an inequality of distribution, that the want of equilibrium between the electric attractions or repulsions is balanced by the tenacity of the parts.

We learn farther from the foregoing propositions, that a particle at N is less repelled than if the part AS were overcharged as AN is: for in that case, it would be expelled by a force \( \frac{f \times r + r}{Q} \), which is much greater than \( \frac{f - g}{Q} \). And, in like manner, the particle S is attracted with less force than it would be if NA were equally undercharged with SA.

The condition of the body now described may be changed by different methods. The redundant fluid in AN may flow into AS, where it is deficient, till the whole be uniformly distributed; or fluid may escape from AN, and fluid may enter into AS, till the body be in its natural state. The first method will be so much the slower as the body is less permeable, or more remarkably electric per se; and the second method will be slower than if the whole body were overcharged or undercharged.

What we have been now saying of a body NS that is overcharged at one end, and undercharged at the other, and capable of retaining this state, is applicable, in every particular, to two conducting bodies NA and SA, having a non-conducting body Z interposed between them, as in fig. 3. All the formulas, or expressions of the forces which tend to expel or to draw in fluids, are the same as before. Perhaps this is the best way of forming to ourselves a distinct notion of the body that is redundant in fluid at one end, and deficient at the other. And we perceive, that the state of the two bodies, separated by the electric Z, will be more permanent when one is overcharged, and the other undercharged, than if both are either over or undercharged.

It must be remarked, that the quantities \( f \) and \( g \) were A body taken at random. They may be so taken, that the intensity with which the fluid tends to escape at N, or to enter at S, may be nothing, or may even be changed where it is to their opposite. Thus, in order that there may be redundant no tendency to escape from N, we have only to suppose or deficient.

\[ g \times r - f \times r = 0, \quad \text{or} \quad g : f = r : r', \quad \text{and} \quad g = \frac{f}{r}. \]

In this case, the particle at N is as much attracted by the redundant matter in SA as it is repelled by the redundant fluid in NA.

When the extremity N is rendered inactive in this manner, the condition of the other extremity S is considerably changed. To discover this condition, put for this:

\[ \frac{f}{r} \] in place of \( g \) in the formula \( \frac{g \times r - f \times r}{Q} \), which expresses the attraction for a particle at S, and we obtain

\[ \frac{f \times r^2 - r^2}{Q}. \]

On the other hand, we may have the redundancy and deficiency so balanced, that there shall be no tendency to influx at S. For this purpose, we must make

\[ g = \frac{f}{r}. \]

When this obtains at S, the action at N will be had by putting \( \frac{f}{r} \) in place of \( g \) in the formula \( \frac{f \times r^2 - r^2}{Q} \), and this will give us \( \frac{f \times r^2 - r^2}{Q} \) for the force repelling a particle at N.

When the tendency to efflux or influx is induced in this manner, by a due proportion of the redundancy and deficiency of electric fluid, the part of the body where this obtains is by no means in its natural state, and may contain either more or less than its natural quantity. But it neither acts like an overcharged nor like an undercharged body, and may therefore be called neutral. The reader who is conversant with electrical experiments, will recollect numberless instances of this, and will also recollect that they are important ones. Such, for example, is the case with the plates and covers of the electrophorus. These circumstances, therefore, claim particular attention.

As the quantities \( f \) and \( g \) may be so chosen, that the apparatus shall be neutral, either at S or at N; they may likewise be so, that either end shall exhibit either the appearance of redundancy or deficiency. Thus, instead of neutrality at N, we may have repulsion, as at the first, by making \( g \) less in any degree than \( \frac{f}{r} \). If, on the contrary, \( g \) be greater than \( \frac{f}{r} \), the extremity N, tho' overcharged, will attract fluid. In like manner, if \( g \) be less than \( \frac{f}{r} \), the extremity S, although undercharged, will repel fluid.—We may make the following general remarks.

1. Both extremities N and S cannot be neutral at the same time: for since the neutrality arises from the increased quantity of redundancy or deficiency at the other extremity, so as to compensate for its greater distance, the activity of that extremity must be proportionally greater on the fluid adjoining to its surface, whether externally or internally. When an overcharged extremity is rendered neutral, the other extremity attracts fluid more strongly; and when a deficient extremity is rendered neutral, the other repels fluid more strongly. All these elementary corollaries will be fully verified afterwards, and give clear explanations of the most curious phenomena.

2. We have been supposing, that the redundant fluid is uniformly spread, and that the body is divided into equal portions; but this was merely to simplify the procedure and the formulae. The reader must see, that the general conclusions are not affected by this, and that similar formulae will be obtained, whatever is the disposition of the fluid. We cannot tell in what manner the redundant fluid is disposed, even in a body of the simplest form, till we know what is the variation of its attraction and repulsion by a change of distance; and even when this has been discovered, we find it difficult in most cases, and impossible in many, to ascertain the mode of distribution. We shall learn it in some important cases, by means of various phenomena judiciously selected.

A body may be considered in many divisions, in some of which the fluid is redundant, and in others deficient. We may express the repulsion of the whole of this body in the same way as we express that of a body considered in two divisions, using the letters f, g, h, &c., to express the quantities of redundant or deficient fluid in each portion, while Q expresses the quantity necessary for saturating each of them; and the repulsion at different distances may be expressed by r, r', r'', &c., as they are more and more remote; and we may express their action as attractive or repulsive by prefixing the sign + or —. Thus the attraction may be

\[ \left( \frac{f}{r} - \frac{g}{r'} + \frac{h}{r''} - i \right) Q, \]

Having obtained the expressions of the invisible actions of electrified bodies on the fluid within them, or surrounding them, let us now consider their sensible actions on other bodies, producing motion, or tendencies to motion.

Here it is obvious, that the mechanical phenomena exhibited are what may be called *remote effects* of the acting forces. The immediate effects, or the mutual actions of the particles, are not observed, but hypothetically inferred. The tangible matter of the body is put in motion, in consequence of its connection with the fluid residing in the body, which fluid is the only subject of the action of the other body.

In considering these phenomena, we shall content ourselves with a more general view of the actions which take place between the fluid or tangible matter of the one body, and the fluid or matter of the other, so as to gain our purpose by more simple formulæ than those hitherto employed. They were premised, however, because we must have recourse to them on many very important particular occasions.

Let there be two bodies, A and B, in their natural state. Let the tangible matter in A be called M, and let m and f be the tangible matter and the fluid in B. Let the mutual action between a single particle of fluid and the matter necessary for its saturation be expressed by the indeterminate symbol z, because it varies by a change of distance.

The actions are mutual and equal. Therefore when the motion of B by the action of A is determined, the motion of A is also ascertained. We shall therefore only consider how A is affected. 1. Every particle of fluid in A tends toward every particle of matter in B, with the force z. The whole tendency of A toward B may therefore be expressed by z, multiplied by the product of F and m. 2. Every particle of fluid in A is repelled by every particle of fluid in B, with the same force z. 3. Every particle of matter in A is attracted by every particle of fluid in B, with the same force. We may express this more purely and briefly thus:

1. F tends toward m with the force \( + Fmz \) 2. F tends from f with the force \( - Ffz \) 3. M tends toward f with the force \( + Mfz \)

Therefore the sensible tendency of A to or from B will be \( = z \times Fm + Mf - Ff \). But, by the hypothesis, the attraction of a particle of the fluid in A for a particle of the matter in B, is equal to its repulsion for the particle or parcel of the fluid attached or competent to that particle of matter. Therefore the attraction \( Fmz \) is balanced by the repulsion \( Ffz \). Therefore there remains the attraction of the matter in A for the fluid in B unbalanced, and the body A will tend toward the body B with the force \( Mfz \), or B attracts A with the force \( Mfz \). A must therefore move toward B. And, by the 3rd law of motion, B must move toward A with equal force.

But the fact is, that no tendency of any kind is observed between bodies in their natural state. The hypothesis, therefore, is not complete. If we abide by it as far as it is already expressed, we must further suppose, that there is some repulsive force exerted between the bodies to balance the attraction of M for f. Mr. Epinus, therefore, supposes, that every particle of tangible matter repels another particle as much as it attracts the fluid necessary for its saturation. The whole action of B on A will now be \( = z \times Fm - Ff - Mm + Mf \). Fmz is balanced by Ffz, and Mmz by Mfz, and no excess remains on either side.

Epinus acknowledges, that this circumstance appeared to himself to be hardly admissible; it seeming inconceivable, that a particle in A shall repel a particle in B, or tend from it, electrically, while it attracts it, or tends toward it, by planetary gravitation. We cannot conceive this; but more attentive consideration showed him, that there is nothing in it contrary to the observed analogy of natural operations. We must acknowledge, that we see innumerable influences of inherent forces of attraction and repulsion; and nothing hinders us from referring this lately discovered power to the class of primitive and fundamental powers of nature. Nor is there any difficulty in reconciling this repulsion with universal gravitation; for while bodies are in their natural state,

state, the electric attractions and repulsions precisely balance each other; and there is nothing to disturb the phenomena of planetary gravitation; and when bodies are not in their natural electrical state, it is a fact that their gravitation is disturbed. Although we cannot conceive a body to have a tendency to another body, and at the same time a tendency from it, when we derive our notion of these tendencies entirely from our own consciousness of effort, endeavour, constancy, nay, even accedingi seu recedendi, nothing is more certain than that bodies exhibit at once the appearances which we endeavour to express by these words. We can bring the north poles of two magnets near each other, in which case they recede from each other; and if this be prevented by some obstacle, they press on this obstacle, and seem to endeavour to separate. If, while they are in this state, we electrify one of them, we find that they will now approach each other; and we have a distinct proof that both tendencies are in actual exertion by varying their distances, so that one or other force may prevail; or by placing a third body, which shall be affected by the one but not by the other, &c. We do not understand, nor can conceive in the least, how either force, or how gravity, resides in a body; but the effects are past contradiction. It must be granted, therefore, that this additional circumstance of Ampère's hypothesis has nothing in it that is repugnant to the observed phenomena of nature.

N.B. It is not necessary to suppose (although Mr Ampère does suppose it), that every atom of tangible matter repels every other atom. It will equally explain all the phenomena, if we suppose that every particle contains an atom or ingredient having this property, and that it is this atom alone which attracts the particles of electrical fluid. The material atoms having this property, and their corresponding atoms of fluid, may be very few in comparison with the number of atoms which compose the tangible matter. Their mutual specific action being very great in comparison with the attraction of gravitation (as we certainly observe in the action of light), all the phenomena of electricity will be produced without any sensible effect on the phenomena of gravitation, even although neither the electric fluid nor its ally, this ingredient of tangible matter, should not gravitate. But this supposition is by no means necessary.

Since we call that the natural electrical state of bodies in which they do not affect each other, and the hypothetical powers of the fluid are accommodated to this condition, we may consider any body that has more than its natural quantity as consisting of a quantity of matter saturated with fluid, and a quantity of redundant fluid superadded; and an undercharged body may be considered as consisting of a quantity of matter superadded. The saturated matter of these two bodies will be totally inactive on another body in its natural state, and will neither attract nor repel it, nor be attracted nor repelled by it; therefore the action of the overcharged body will depend entirely on the redundant fluid; and that of the undercharged body will depend entirely on the redundant matter; therefore we need only consider them as consisting of this redundant fluid or matter, agreeably to what was said in more vague terms in no. 10. and 13. This will free us from the complicated formulae which would otherwise be necessary for expressing all the actions of the fluid and tangible matter of two bodies on each other. The results will be sufficiently particular for distinguishing the sensible action of bodies in the chief general cases; but in some particular and important cases, it is absolutely necessary to employ every term.

1. Suppose two bodies A and B, containing the quantities F' and f' of redundant fluid, it is plain that their mutual action is expressed by $F' \times f' + z$, and that (symbol) it is a repulsion; for since every particle of redundant fluid in A repels every particle of redundant fluid in B, with the force $z$; and since $F'$ and $f'$ are the numbers of such particles in each, the whole repulsion must be expressed by the product of these numbers.

2. In like manner, two bodies A and B, containing the redundant matter M and m', will repel each other with the force $M' \times m' \times z$.

3. And two bodies A and B, one of which A contains the redundant fluid F', and the other B contains the redundant matter m', will attract each other with the force $F' \times m' \times z$.

4. It follows from these premises, that if either of the bodies be in its natural state, they will neither attract nor repel each other; for, in such a case, one of the factors $F'$, or $f'$, or $M'$, or $m'$, which is necessary for making a product, is wanting. This may be perceived independent of the mathematical formula; for if A contain redundant fluid, and B be in its natural state, every particle of the redundant fluid in A is as much repelled by the natural fluid in B as it is attracted by the tangible matter.

The three first propositions agree perfectly with the known phenomena of electricity; for bodies repel each other, whether both are positively or both are negatively electrified, and bodies always attract each other when the one is positively and the other negatively electrified. But the fourth case seems very inconsistent with the most familiar phenomena. Dr Franklin and all his followers assert, on the contrary, that electrified bodies, whether positive or negative, always attract, and are attracted, by all bodies which are in their natural state of electricity. But it will be clearly shown presently, that they are mistaken, and that Franklin's theory necessarily supposes the truth of the fourth proposition, otherwise two bodies in their natural state could not be neutral or inactive, as any one may perceive on a very slight examination by the Franklinian principles. It will presently appear, with the fullest evidence; and, in the mean time, we proceed to explain the action of bodies which are overcharged in some part, and undercharged in another.

Let the body B (fig. 4.) be overcharged in the part Bn, and undercharged in the part Bt, and let $f'$ and $m'$ be the redundant fluid and common matter in those parts; let A be overcharged, and contain the redundant fluid F; let $z$ and $z'$ express the intensity of action corresponding with the distances of A from the overcharged and undercharged parts of B; the part Bn repels A with the force $F' \times f' \times z$, while the part Bt attracts it with the force $F' \times m' \times z$: A will therefore be attracted or repelled by B, according as $F' \times m' \times z$ is greater or less than $F' \times f' \times z'$; that is, according as $m'/f'$ is greater or less than $f'/z'$. This, again, depends on the proportion of $f'$ to $m'$, and on the proportion of $z'$ to $z$. The first depends on many external circumstances, which may occasion a greater or less redundancy or deficiency of electrical fluid; the second de-

pends entirely on the law of electric attraction and repulsion, or the change produced in its intensity by a change of distance. As we are, at present, only aiming at very general notions, it is enough to recollect, that all the electric phenomena, and indeed the general analogy of nature, concur in shewing that the intensity of both forces (attraction and repulsion) decreases by an increase of distance; and to combine this with that circumstance of the hypothesis which states the repulsion to be equal to the attraction at the same distance; therefore both forces vary by the same law, and we have z always greater than z'. The visible action of B on A (which, by the 3d law of motion, is accompanied by a similar action of A on B) may be various, even with one position of B, and will be changed by changing this position.

1. We may suppose that B contains, on the whole, its natural quantity, but that part of it is abstracted from B, and is crowded into B. This is a very common case, as we shall see presently, and it will be expressed in our formula by making f' = m'. In this case, therefore, we have Ff' > greater than F'm'z, because z is greater than z'. A will therefore be repelled by B, and will repel it; and the repulsion will be

\[ Ff' \times z = z'. \]

It is evident, that if A be placed on the other side of B, the appearances will be reversed, and the bodies will attract each other with the force \( Ff' \times z = z'. \)

It is also plain, that if A be as much undercharged as we have supposed it overcharged, all the appearances will be reversed; if on the undercharged side of B, it will be repelled; and if on the overcharged side of B, it will be attracted.

2. If the redundancy and deficiency in the two portions of B be inversely proportional to the forces, so that \( F : m' = z : z', \) we shall have \( f' = m'z, \) and \( m' = \frac{f'z}{z}. \) In this case these two actions balance each other, and A is neither attracted nor repelled when at this precise distance from the overcharged side of B. B may be said to be neutral with respect to A, although A and the adjoining side of B are both overcharged.

But if A be placed at the same distance on the other side of B, the effect will be very different: For because \( m' = \frac{f'z}{z}, \) and \( m'z' \) is now changed into \( m'z, \) and \( f'z \) into \( f'z', \) we have the action on A = \( F \times \left( \frac{f'z}{z} - f'z' \right), = Ff' \times \frac{z^2 - z'^2}{z}; \) that is, A is strongly attracted.

In like manner, \( f' \) and \( m' \) may be so proportioned, that when A, containing redundant fluid, is placed near the undercharged end of B, it shall neither be attracted nor repelled, B becoming neutral with regard to A at that precise distance. For this purpose \( m' \) must be \( = \frac{f'z'}{z}. \) And if A be now placed at the same distance on the other side of B, it will be repelled with the force \( Ff' \times \frac{z^2 - z'^2}{z}. \)

Thus, when the overcharged end is rendered neutral to an overcharged body, the other end strongly attracts it; and when the undercharged end is rendered neutral to the same body, the overcharged end strongly repels it.

Similar appearances are exhibited when A is undercharged.

These cases are of frequent occurrence, and are important, as will appear afterwards.

It is easy now to see what changes will be made on the action of B on A, by changing the proportion of \( f' \) and \( m'. \) If \( m' \) be made greater than \( \frac{f'z}{z}, \) A will be attracted in the situation where it was formerly neutral; and if \( m' \) be made less, A will be repelled, &c. &c.

Therefore, when we observe B to be neutral, or attractive, or repulsive, we must conclude that \( m' \) is equal to \( \frac{f'z}{z}, \) or greater or less than it, &c.

We have been thus minute, that the reader may perceive the agreement between this action on a body containing redundant fluid, and the action on the superfluous fluid formerly considered in no. 21, 22, 23, 24. When these things are attended to, we shall explain, with great ease, all the curious phenomena of the electrophorus.

There is another circumstance to be attended to here, which will also explain some electrical appearances that seem very puzzling. We limited the inactivity of B to a certain precise distance of the body A. This inactivity required that \( m' \) should be \( = \frac{f'z}{z}. \) If A be brought nearer, both \( z \) and \( z' \) are increased. If they are both increased in the same proportion, the value of \( \frac{z}{z'} \) will be the same as before, and the body A will neither be attracted nor repelled at this new distance. But if \( z \) increase faster than \( z', \) we shall have \( f'z \) greater than \( m'z', \) and A will be repelled; and if \( z \) increases more slowly than \( z', \) A will be attracted by bringing it nearer. The contrary effects will be observed if A be removed farther from the overcharged end of B. This explains many curious phenomena; and those phenomena become instructive, because they enable us to discover the law of electric action, by shewing us the manner in which it diminishes by a change of distance. Electricians cannot but recollect many instances, in which the motion of the electrometer appeared very capricious. The general fact is, that when an overcharged pith ball is situated near the overcharged side of the electrophorus as to be neutral, it is repelled when brought nearer, but attracted when removed to a greater distance. This shews that \( z \) increases faster than \( z' \) when A is brought nearer to B. Now, since the bodies may be again rendered neutral at a greater distance than before, and the same appearances are still observed, it follows, that the law of action is such, that every diminution of distance causes \( z \) to increase faster than \( z'. \)

We shall find this to be valuable information.

Let us, in the last place, inquire into the sensible effects on A when it also is partly overcharged and partly undercharged. This is a much more complicated case, and is susceptible of great variety of external appearances, according to the degrees of redundancy and deficiency, and according to the kind of electricity (positive or negative) of the ends which front each other. First, then, let the overcharged end of A (fig. 5.) from the undercharged end of B, they being overcharged in N and n, but undercharged in S and s. Let F and f be the quantity of fluid natural to each; and let F' and f' be the redundancy in N and n, and M' and m' the deficiency in S and s. Moreover, let Z and Z' represent the intensity of actions of a particle in N on a particle in n; and let z and z' represent the actions of a particle in S on a particle in s; or, in other words, let Z, Z', z, z', represent the intensity of action between particle and particle, corresponding to the distances Ns, Nn, Ss, Sn.

Proceeding in the same manner as in the former examples, we easily see, that the action of B on A is

\[ \frac{F'f'Z - FfZ'}{Ff} = \frac{M'm'z + M'f'z'}{Ff}; \]

the attractions are considered as positive quantities, having the sign + prefixed to them, and the repulsions are negative, having the sign −.

This action will be either attractive or repulsive, according as the sum of the first and last terms of the numerator exceeds or falls short of the sum of the second and third: And the value of each term will be greater or less, according to the quantity of redundant fluid and matter, and also according to the intensity of the electric action. It would require several pages to state all those possible varieties. We shall therefore content ourselves at present with stating the simplest case; because a clear conception of this will enable the reader to form a pretty distinct notion of the other possible cases; and also, because this case is very frequent, and is the most useful for the explanation of phenomena.

We shall suppose, that the redundant part of each body is just as much overcharged as the deficient part is undercharged; so that F = M', and f = m'. In this case, the formula becomes

\[ \frac{F'f(Z - Z') - z + z'}{Ff}. \]

Here we see that the sensible or external effect on A depends entirely on the law of electric action, or the variation of its intensity by a change of distance. If the sum of Z and z exceed the sum of Z' and z, A will be attracted; but if Z + z be less than Z' + z, A will be repelled. This circumstance suggests to us a very perspicuous method of expressing these actions between particle and particle, so that the imagination shall have a ready conception of the circumstance which determines the external complicated effect of this internal action. This will be obtained by measuring off from a fixed point of a straight line portions respectively equal to the distances Ns, Nn, Ss, and Sn, between the points of the two bodies A and B, where we suppose the forces of the redundant fluid and redundant matter to be concentrated, and erect ordinates having the proportion of those forces. If the law of action be known, even though very imperfectly, we shall see, with one glance, of which kind the movements or tendencies of the bodies will be. Thus, in fig. 5, drawing the line Cz, take Cρ = Ns, Cq = Nn, Cr = Ss, and Ct = Sn, and erect the ordinates Pρ, Qq, Rr, and Tt. If the electric action be like all the other attractions and repulsions which we are familiarly acquainted with, decreasing with an increase of distance, and decreasing more slowly as the distances are greater, these ordinates will be bounded by a curve PQRTZ, which has its convexity turned toward the axis. We shall presently get full proof that this is the case here; but we premise this general view of the subject, that we may avoid the more tedious, but more philosophical, process of deducing the nature of the curve from the phenomena now under consideration.

This construction evidently makes the pair of ordinates Pρ, Qq, equidistant with the pair Rr, Tt, of the scale Alfo, Pρ, Rr, and Qq, Tt, are equidistant pairs. It is no less clear, that the sum of Pρ and Tt, exceeds, force, the sum of Qq and Rr. For if Cz be bisected in V, and Vv be drawn perpendicular to it, cutting the straight lines PT and QR in x and y, then xv is the half sum of Pρ and Tt, and yv is the half sum of Qq and Rr. Moreover, if Qm and Tn are drawn parallel to the base, we see that Pm exceeds Rr; and, in general, that if any pair of equidistant ordinates are brought nearer to C, their difference increases, and vice versa. Also, if two pairs of equidistant ordinates be brought nearer to C, each pair by the same quantity, the difference of the nearest pair will increase more than the difference of the more remote pair. And this will hold true, although the first of the remote pair should stand between the two ordinates of the first pair. If the reader will take the trouble of considering these simple consequences with a little attention, he will have a notion of all the effects that are to be expected in the mutual actions of the two bodies, sufficiently precise for our present purpose. We shall give a much more accurate account of these mathematical truths in treating the article MAGNETISM, where precision is absolutely necessary, and where it will be attended with the greatest success in the explanation of phenomena.

Now let us apply this to our present purpose. First, when the overcharged end of A is turned toward the undercharged end of B, A must be attracted; for Pρ + Tt is greater than Qq + Rr.

Secondly, This attraction must increase by bringing the bodies nearer; for this will increase the difference between Pm and Rn.

Thirdly, The attraction will increase by increasing the length either of A or of B (the distance Ns remaining the same); for by increasing the length of A, which is represented by ρr or qt, Rr is more diminished than Tt is. In like manner, by increasing B, whose length is represented by q or rt, we diminish Qt more than Tt.

On the other hand, if the overcharged end of B from the overcharged end of A, their mutual action will be picture of

\[ \frac{F'f(-Pρ + Qq + Rr - Tt)}{Ff}, \]

and A will be repelled, and the repulsion will increase or diminish, by change of distance or magnitude, precisely in the same manner that the attractions did. It is hardly necessary to observe, that all these consequences will result equally from bringing an apparatus similar to that represented in fig. 3, near to another of the same kind; and that they will be various according to the position and the redundancy or deficiency of the two parts of each apparatus.

If the body B of fig. 5, is not at liberty to approach which toward A, nor to recede from it, and can only turn itself round its centre B, it will arrange itself in a certain indeterminate position with respect to that of A. For instance, example, if the centre B (fig. 7.) be placed in the line resembling passing passing through S and N of the body A, B will arrange itself in the same straight line; for if we forcibly give it another position, such as \( x \) B \( n' \), N will attract \( x \) and repel \( n' \), and these actions will concur in putting B into the position \( x' \) B \( n' \). S, however, will repel \( x \) and attract \( n' \); and these forces tend to give the contrary position. But S being more remote than N, the former forces will prevail, and B will take the position \( x' \) B \( n' \).

If the centre B be placed somewheres on the line AD, drawn through a certain point of the body NAS (which will be determined afterwards), at right angles to NAS, the body B will assume the position \( x' \) B \( r' \), parallel to NAS, but subcontrary. For if we forcibly give it any other position \( x' \) B \( r' \), it is plain that N repels \( x \) and attracts \( r' \), while S attracts \( x \) and repels \( r' \). These four forces evidently combine to turn the body round its centre, and cannot balance each other till B assume the position \( x' \) B \( r' \), where \( x' \) is next to S, and \( r' \) is next to N.

If the centre of B have any other situation, such as \( x' \) B \( r' \), the body will arrange itself in some such position as \( x' \) B \( r' \). It may be demonstrated, that if B be infinitely small, so that the action of the end of A on each of its extremities may be considered as equal, B will arrange itself in the tangent \( B'P \) of a curve NB'S, such that if we draw NB', SB, and from any point T of the tangent draw TE parallel to BN, and TP parallel to B'S, we shall have BE to BF, as the force of S to the force of N. This arrangement of B will be still more remarkable and distinct if N be an overcharged sphere, and S an undercharged one, and both be insulated. We must leave it to the reader's reflection to see the changes which will arise from the inequality of the redundancy and deficiency in A or B, or both, and proceed to consider the consequences of the mobility of the electric fluid. There will remove all the difficulty and paradox that appears in some of the foregoing propositions.

Let the body A (fig. 4.) contain redundant fluid, and let B be in its natural state, but let the fluid in A be fixed, and that in B perfectly moveable; it is evident that the redundant fluid in A will repel the moveable fluid in B, toward its remote extremity \( n' \), and leave it undercharged in \( x \). The fluid will be rarefied in \( x \), and conflagitated in \( n' \). We need only consider the mutual actions of the redundant fluid and redundant matter. It is plain that things are now in the situation described in \( n' \) fig. 5.: A must be attracted by B, because \( f' = m' \), and \( z' \) is greater than \( z \). The attractive force is \( F'f' \times (z - z') \).

Thus we see that the hypothesis is accommodated to the phenomena in the case in which it appeared to differ so widely from it. Had the fluid been immoveable, the mutual actions would have balanced each other so that no external effects would have appeared. But now the greater vicinity of the redundant matter prevails, A is attracted by B, and, the actions being all mutual, B is attracted by A, and approaches it.

We have supposed that the fluid in A is immoveable; but this was for the sake of greater simplicity. Suppose it moveable. Then, as soon as the uniform distribution of the fluid in B is changed, and B becomes undercharged at \( x \), and overcharged at \( n' \), there are forces acting on the fluid in A, and tending to change its state of distribution. The redundant matter in S attracts the redundant fluid in A more than the more remote redundant fluid in \( n' \) repels it, because \( z' \) is less than \( z \). This tends to conflagitate the redundant fluid of A in the nearer parts, and render N more redundant, and S less redundant in fluid than before. It is plain, that this must increase their mutual action, without changing its nature. It can be distinctly demonstrated, that however small the redundancy in A may be, it can never be rendered deficient in its remote extremity by the action of the unequally disposed fluid in B, if the fluid in B be no more nor less than its natural quantity. It is also plain, that this change in the disposition of the fluid in A must increase the similar change in B. It will be still more rarefied in \( x \), and condensed in \( n' \); and this will go on in both till all is in equilibrium. When things are in this state, a particle of fluid in B is in equilibrium by the combined action of several forces. The particle B is propelled toward \( n' \) by the action of the redundant fluid in A. But it is urged toward S by the repulsion of the redundant fluid on the side of \( n' \), and also by the attraction of the redundant matter on the side of \( x \); and the repulsion of the redundant fluid in A must be conceived as balancing the united action of those two forces residing in B.

Hence we may conclude, that the density of the fluid General in B will increase gradually from \( x \) to \( n' \). It will be extremely difficult to obtain any more precise idea of its density in the different parts of B, even although we knew the law of action between single particles.

This must depend very much on the form and dimensions of B; for any individual particle suffers the sensible action of all the redundant fluid and redundant matter in it, since we suppose it affected by the more remote fluid in A. All that we can say of it in general is, that the density in the vicinity of \( x \) is less than the natural density; but in the vicinity of \( n' \) it is greater; and therefore there must be some point between \( x \) and \( n' \) where the fluid will have its natural density. This point may be called a neutral point. We do not mean by this that a particle of superficial fluid will neither be attracted nor repelled in this place. This will not always be the case (although it will never be greatly otherwise); nor will the variation of the density in the different parts of B be proportional to the force of A on those parts. Some eminent naturalists have been of this opinion; and, having made experiments in which it appeared to be otherwise, they have rejected the whole theory. But a little reflection will convince the mathematician, that the sum of the internal forces which tend to urge a particle of fluid from its place, and which are balanced by the action of A, are not proportional to the variations of density, although they increase and decrease together. We shall take the proper opportunity of explaining those experiments; and will also consider some simple, but important cases, where we think the law of distribution of the fluid ascertained with tolerable precision.

If we suppose, on the other hand, that A is undercharged, the redundant matter in A will attract the moveable fluid in B, and will abstract it from the remote extremity, and crowd it into the adjacent extremity. Moreover, the fluid now becoming redundant in the nearer extremity of B, will act more strongly on the moveable fluid in A than the more remote redundant matter of B; and thus fluid will be propelled toward the remote side of A, which will become now undercharged. charged in its nearer side, and less undercharged in its remote side than if B were taken away. This must increase the inequality of distribution of the fluid in B; and both will be put farther from their natural state; but A will never become overcharged in its remote extremity.

Things being in this state, it is plain that A and B will mutually attract each other in the same manner, and with the same force, as when A was as much overcharged as it is now undercharged.

Thus, then, we see how the attraction obtains, whether A be over or undercharged. A fact which Dr. Franklin could never explain to his own satisfaction; nor will it ever be explained consistently with the acknowledged principles and observed laws of mechanics by any person who employs elastic atmospheres for this purpose. It is indeed a sufficient objection to the employment of such electric or other atmospheres, that the same extent of attraction and repulsion between the particles of the atmosphere is necessary, as is employed here between the particles of the fluid residing in the body; and therefore they cease to give any explanation, even although their supposed actions were legitimately deduced from their constitution. This is by no means the case. Let any person examine seriously the modes operandi of the electric atmospheres employed by Lord Mahon (the only person who has written mathematically on the subject), and he will see, that the whole is nothing but figurative language, without any distinct perception of what is meant by these atmospheres, as distinct from the fluid moveable in the conducting bodies, or any perception how the unequal density of these atmospheres protrudes the fluid along the conductor. Besides, it is well known that a conducting wire becomes positive at one end, and negative at the other, by the mere vicinity of an overcharged or undercharged body, and this in an instant, although it be surrounded with sealing wax, or other nonconductors, to any thickness: in this case there can be no atmospheres to operate on the included fluid. To this we may add Dr. Franklin's judicious experiment of whirling an electrified ball many times round his head, with great rapidity, by means of a silk line, without any sensible diminution of its electricity. It is not conceivable that an electric atmosphere could remain attached to the ball; nor could it be instantaneously formed round the ball, in every point of its motion, so as to be operative the moment he stopped it and tried it; for this would have exhausted or greatly diminished the electricity of the ball; whereas that sagacious philosopher affirms (and any person will find it true), that when the air is dry, he did not observe the electricity more diminished than that of another ball which remained all the while in the same place.

Let the overcharged body A (fig. 6.) be brought near the ends of two oblong conductors B and C in their natural state, and lying parallel to each other; the fluid will be propelled toward their remote ends N, where it will be condensed, while it will be rarefied in the ends S and r, adjacent to A. Both will be attracted by A, and will attract it. But the redundant fluid in NB will repel the redundant fluid in rC; and the redundant matter in SB will repel the redundant matter in rC. For this reason the bodies B and C will repel each other, and will separate; but SB attracts nC, and NB attracts rC; and on this account the bodies should approach: but the distances of the attracting parts being greater than those of the repelling parts, the repulsions must prevail, and the bodies must really separate.

It is equally clear that the very same sensible appearance will result from bringing an undercharged body near the ends of B and C, although the internal motions are just the opposite to the former.

If another body D, electrified in the same way with A, be brought near the opposite ends of B and C, it will prevent or diminish the internal motions, and it should therefore prevent or diminish the external effects.

If another conducting body be brought near to the end s of C, that fronts A, it will be affected as C is, and the end f will repel r; but if it be brought near the remote end, as is the case with the body F, it will attract this remote end. As the body A, containing more or less than its natural share of electric fluid, affects every other body, while they do not (when out of its neighbourhood) affect each other, it is usually said to be the electrified body, and the others are said to be conductors, cannot retain their power of exhibiting electrical appearances (see no. 17.), it will be convenient to distinguish this last electrical state by a particular name. We shall call it ELECTRICITY BY POSITION, or INDUCED ELECTRICITY. It is induced by position with regard to the permanently electrical body.

We have supposed, in these last propositions, that consequently the fluid was perfectly moveable in B, and, at last also, in A: but let us examine the consequences of some obstruction to this motion. Without entering into a minute enquiry on this head, we may state the obstruction as uniform, and such that a certain small force is necessary for causing a particle of fluid to get through between two particles of the common matter, just as we conceive to happen in tenacious bodies of uniform texture (see no. 18.).

It is evident, that when an overcharged body A (fig. 4. or 5.) is brought near such an imperfect conductor B, the fluid cannot be so copiously propelled to the remote extremity n. We may conceive the state of distribution by taking a constant quantity from the intensities of the force of A at every point of B. This circumstance alone shows us, that there will not be so unequal a distribution of the fluid, and therefore there will not be such a strong attraction between imperfect as between perfect conductors. But besides this, we see that an incomparably longer time must elapse before things come to a state of equilibrium. Each particle of fluid employs time to overcome the obstacle to its motion, and it cannot advance till after the succeeding ones, each escaping in its turn, have again come up with the foremost. An important consequence results from this. The neutral point, where the fluid is of the natural density, will not be so far from the other body as it would have been without these obstructions; and this point will be a considerable while of advancing along the imperfect conductor. At the first approach of the overcharged electric, the near extremity of the imperfect conductor becomes a little undercharged, and the neutral point advances from the very extremity a small way, the displaced fluid being crowded a little before it, and giving way by degrees.

as its foremost particles get past the obstructions. The motion forward takes place over a considerable extent at the very first; namely, in that part of the conductor where the propelling power of the neighbouring electric is just able to push a particle over the obstruction. As the propulsion goes on, the neutral point must gradually advance, and at last reach a certain distance determined by the degree of the obstruction. It is plain, that the final accumulation at the remote end of the imperfect conductor will be less than in a perfect conductor, and the neutral point will be nearer to the other end.

There is another remarkable consequence of the obstruction. It must always happen that, at the beginning of the action, the greatest conflagration will not be towards the remote extremity, but in a place much nearer to the disturbing cause. Beyond this, the conflagration will diminish. As time elapses during this operation, this constituted fluid acts on the fluid beyond it by repulsion, and may do this with sufficient force to displace some of it, and render a part of the imperfect conductor deficient, with a small conflagration beyond it. This may, in like manner, produce a rarefaction farther on, followed by another condensation; and this may be frequently repeated when the obstruction is very great, and the repulsion of the overcharged body very great also. This can be strictly demonstrated in some very simple cases, but the demonstration is very tedious: As the result, however, is of the first importance in the theory of electricity, and serves to explain some of the most abstruse phenomena, we wish the reader to have some stronger ground of confidence than the above bare assertion. He may observe similar effects of causes precisely similar. If we dip the end of a flat ruler into water, and if, after allowing the water to become perfectly still, we move the ruler gently along in a direction perpendicular to the face, we shall observe a single wave heap up before the ruler, and keep before it, all the rest of the water before it remaining still: but if we do the same thing in a vessel of clammy fluid, especially if the clammy part is swimming on the surface of a more perfect fluid, like a cream, we shall observe a series of such waves to curl up before the ruler, and form before it in succession; and if we have previously spotted the surface of the cream, we shall see that it is not the same individual waves that are pushed before the ruler, but that they are successively formed out of different parts of the surface, and that the particles which, at one time, form the summit of a wave, are, immediately after, at the bottom, &c. In like manner, when a cannon is fired in clear air, at no great distance, we hear a single snap; but, in a thick fog, we hear the snap both preceded and followed by a quivering noise, resembling the rushing of a fluttering wind, which lasts perhaps half a second. A slight reflection on these facts will show that they are necessary results of the mechanical laws of such obstruction.

The consequence of this mode of action must be, that an imperfect conductor may have more than one neutral point, and more than one overcharged and undercharged portion, so that its action on distant bodies may be extremely various. The formula of no. 28, was accommodated to this case, and will be found to have very curious results. Another body may be placed in the direction of the axis, and will be attracted at one distance, repelled when this distance is increased, and again attracted when at a still greater distance, &c. &c.

Suppose the obstruction not to be considerable: The immediate operation of the neighbouring overcharged body will be the production of an undercharged part in the adjoining extremity, an overcharged part beyond this, an undercharged portion farther on, &c. In a little while these will shift along the conductor; one after another will disappear at the farther end, and the body will have at last but one neutral point. A greater obstruction will leave the body, finally, with more than one neutral point, and their ultimate number will be greater in proportion as the obstruction to the fluid's motion is supposed greater.

Now, let the overcharged body, the cause of this unequal distribution, be removed. We have seen, n° 7, lecture that when a body contains its natural quantity of fluid, evenly but unequally distributed, there is a force acting on every particle, and tending to restore the original equal distribution; and that such a force remains as long as there is any inequality in this respect. If, therefore, there be no obstruction, the uniform distribution will take place immediately; for it is well known, that the speed with which electricity is propagated is immense. The elasticity, or the attractive and repulsive forces, must be very great indeed when compared with any that we know, except, perhaps, the force which impels the particles of light. The electricity, therefore, of a perfect conductor, that is, its power of acting on other bodies in the same way that an original electric acts on them, must be quite momentary, and cease as soon as the inducing cause is removed. The conductor is electrical merely in consequence of its position. Hence the propriety of our denominations. Nothing material is supposed in this theory to be communicated from the overcharged body: Nay, this theory teaches, that the sensible electricity of the overcharged body is augmented in some respects; for it becomes more overcharged in the part nearest to the conductor. Indeed it becomes less overcharged on the other end, and will act less forcibly on that side than if the conductor were away. It may be remarked here (it should have been mentioned in n° 55.), that when F is presented in the manner shown in fig. 6, the body B becomes more strongly overcharged at the end remote from A, and more strongly undercharged at the end next to A, than when F is away. The contrary may happen, by presenting a body in the manner of E. We wish these particulars to be kept in mind. In the mean time, all these circumstances are necessary consequences of the supposition, that nothing is communicated from A to B or C. The electricity induced on perfect conductors is momentary, requiring the continual presence of a body that is electrified in some way or other.

But the case is quite otherwise in imperfect conductors. When the overcharged, or otherwise electrical body A is removed, the forces which tend to restore the uniform distribution of the fluid immediately operate, and must restore it in part. They cannot, however, do it completely: For when the force which urges any particle from an overcharged to an undercharged part is just in equilibrium with the obstruction, it will remain, just as a number of grains of small shot may lie, uniformly mixed with a mass of clammy fluid, or,

as such fluids retain heavy mud, in a state of equable or unequal diffusion. If the resistance arise merely from the inertia of the tangible matter, there is no force so small but it will in time restore the uniform distribution. But this cannot be the case in solid bodies. Their particles exert lateral forces, by which they maintain themselves in particular situations; these must be overcome by superior forces.

We should therefore expect, that imperfect conductors will retain part of their unequal constitution; and, in consequence of this, their power of affecting other bodies like electric; that is, their ELECTRICITY. For we must observe (having neglected to do it in the beginning), that the term electricity is as often used to express this power of producing electrical phenomena as it is used for expressing a substance supposed to be the original cause of all these appearances. It is necessary to keep this distinction in mind; because there are many phenomena which clearly indicate the difference of this cause, and they must not be confounded with others, where the exhibition of electric phenomena is evidently propagated to a distance. We must not always suppose, that when the electric appearances are exhibited in an instant at the far end of a wire 4½ miles long, the same numerical particles of the electric fluid have moved over this space. We must distinguish those cases where this must be granted from those in which it certainly has not happened. Of these there are innumerable instances.

We have now to observe, that by this theory the single circumstance of perfect and imperfect conducting power is sufficient for establishing the whole difference between idio-electrics and non-electrics. The idio-electrics are susceptible of excitation in various ways, and retain their electricity; and this may be done in any part of them without affecting the rest in any remarkable degree. This cannot be done in perfect conductors, plainly because they are perfect conductors. Any inequality of distribution of the electric fluid, which is all that is necessary for rendering them electric, is immediately destroyed by its uniform diffusion. We can have no direct proof of their incapability of excitation; but if they can be excited, they cannot shew it. We doubt, however, their excitability; because the appearances in the excitation of electrics seem to indicate, that opposite states of two bodies are necessary previous to the appearance of electricity. This is impossible in perfect conductors. By this theory, therefore, perfect conductors are necessarily non-electrics; and non-conductors are necessarily (if excitable) idio-electrics.

With respect to the particular phenomena which may be expected on the removal of the original electric; it may just be remarked, that the electric appearances of the imperfect conductor will go off in the contrary order to that of their indication. The accumulation and deficiency will diminish gradually, and the neutral point or points will gradually approach the end which had fronted the original electric. The imperfect conductor will be finally left with one or more neutral points, according to the magnitude of the obstructions, and the force which had been employed in its electrification: And their final state will be so much the more unequal, and consequently they will retain to much the greater electric powers, as they are less perfect conductors.

The last observation which we shall make on this head at present is, that whether electrified by induction, or by friction, or most other modes of excitation, superficial electrification will be nearly superficial in bodies also, which conduct very imperfectly; and bodies which are altogether impervious (if there be any such) must have the accumulation or deficiency altogether at their surface. If a glass globe be such a body, it will hardly be possible to electrify it to any depth; and all that we can expect is alternate strata of overcharged and undercharged glass. If these strata are once formed, they tend greatly to make the body retain its superficial electricity. A superficial stratum of redundant fluid, tending, by the mutual repulsion of its particles, to escape, is retained by the stratum of redundant matter immediately below it: And the almost insuperable obstruction prevents the fluid of the stratum beyond this from coming up to supply the vacancy. If we can fall on any contrivance to produce such deficient strata within the glass, we shall make it much more retentive, and capable of holding a much greater quantity. We have already mentioned something of this in no. 14; and we recommend the case to the attentive consideration of the reader.

Thus have we given a sketch of the leading doctrines of this elegant theory of Mr. Epinus, all legitimately founded on the deduced from the circumstances assumed in the hypothesis with this concerning the mechanical properties of that sub-existence which he calls the electric fluid. Let us now see what with what success this hypothesis may be applied to account for the phenomena. It would have been more philosophical to have arranged the phenomena, and from the comparison to have deduced the hypothesis. But this would have required much more room than can be afforded in a Work like ours.

We presume, that many of our readers, namely, all such as are already conversant with electrical phenomena and with electric experiments, have seen, as we went along, the perfect agreement of the hypothesis with the various phenomena of attraction and repulsion, and all those which are usually called under the name of electric atmospheres; and we are confident, that when they compare the consequences that should necessarily result from such a fluid with the legitimate consequences of the mechanical action of elastic atmospheres, they will acknowledge the great superiority of this hypothesis in point of simplicity, perspicuity, and analogy with other general operations of nature. To such readers it would not be necessary to state any farther comparison; but there are many who have not yet formed any distinct system of view of the appearances called electrical. We do not know any way of giving such a view of them as by means of this hypothesis; and we may venture to say, that it will enable the student of Nature to clasps them all, with hardly a single exception. After which, the hypothesis may be thrown aside by the fatidic philosopher; and the useful classification, and general laws of the electric phenomena, will remain ready foundations for a more perfect theory. For the sake of such readers, therefore, we shall take a short review of those general appearances which are accompanied by attractions and repulsions, and compare them with this Epinian theory.

We shall not at present consider the various modes of excitation, although this theory also affords much in-

friction on the subject, but confine ourselves entirely to the facts which are most immediately dependent on it, and should be employed to support or overturn it; and we shall suppose the reader acquainted with most parts of the common apparatus; such as electrometers, inflation, &c. We also presume he knows, that when a small pith-ball has been electrified by touching a piece of glass which has been excited by rubbing with dry flannel, it will repel another body to electrified; and that balls, which have received their electricity in this manner from sealing-wax excited by the same rubber, also repel each other; but that balls, thus electrified by glass, attract those which are electrified by sealing wax.

The following simple apparatus will serve for all the experiments which are necessary for establishing the theory:

1. Two slender glass rods A (fig. 8.), having a brass ball B at the end, about a quarter of an inch in diameter, suspending a very small and delicate pith-ball electrometer C.

2. Some electrometers (fig. 9.), consisting of two pieces of rush pith, about four inches long, nicely suspended, and hanging parallel, and almost in contact with each other. It is proper to have them as smooth as possible, and neatly rounded at the ends, to prevent unnecessary dissipation.

3. Some pith-ball electrophoreses (fig. 10.), whose threads are of silk, about four inches long, and some with flaxen threads moistened with a solution of some deliquescent salt, that they may be always in a good conducting state.

4. Several brass conductors (fig. 11.), each supported on an insulating stalk and foot. They should be about an inch and half or two inches long, and about three-fourths of an inch in diameter, with round ends, and well polished, to prevent all dissipation. The foot must be so narrow as to allow them to touch each other at the ends.

5. Two balls (fig. 12.), one of glass, and the other of glass coated with sealing wax, each furnished with an insulating handle, the other end of which may be occasionally stuck into a foot, or into the side of a block of wood, which can be slid up or down on a wooden pillar, and fixed at any height. These balls should be about three inches in diameter. They must be excited by rubbing with dry warm flannel.

6. Some little pieces of gilt card (fig. 13.), about two inches long, half an inch broad, and rounded at the ends, and made as smooth as possible. Each must have a dimple struck in the middle with a polished blunt point, so that it will traverse freely like a mariner's needle when set on a glass point, rounded in the flame of a lamp. More artificial needles may be made of some light wood, having small cork balls at the ends, all gilt and polished, and turning, in like manner, on glass stalks; also some similar needles made of sealing wax, one end of each being black, and the other red.

The mechanical phenomena of electricity may be expressed in a few simple propositions. The most general fact that we know, and from which all the rest may be deduced, is the following:

If any body A is electrified, by any means whatever, and if another body B is brought into its neighbourhood, the last becomes electrical by position.

Set the brass conductors in a row, touching each other, as represented in fig. 11. by A, B, C; and let a pith-ball electrometer, having silk threads, be set near one end of the conductors. Excite one of the globes, caused by rubbing it with dry flannel. When this is brought near the end of the conductor, the pith-ball will approach the other end. But the globe must not be brought so near as to cause the pith-ball to strike against the other end. On removing the globe, the pith-ball will move off and hang perpendicularly. The same effect is produced by both globes.

Thus the mere vicinity of the electric renders the conductor electric, and the electricity ceases on removing the globe. This is perfectly conformable to the theory, whether we suppose the fluid to be made redundant or deficient at the remote end of the conductor. If one should ascribe the approach of the pith-ball to the immediate action of the globe, it is sufficient to observe, that if the ball be suspended near the side of the conductor, it will approach the conductor, shewing that it is affected by the conductor, and not by the globe.

Let the globe be held in the position D (fig. 12.), about six inches from the conductor, and a little above the line of its axis. Take the glass rod (fig. 8.), and bring its knob into contact with the under side of the remote tally, end c of the conductor. The balls of the electrometer will separate, shewing that they are electrified in the same manner, and repel each other. Slide the brass knob along the under side of the conductors, quite to the end a. The balls will gradually collapse as the knob approaches a point near the middle of the conductors, where they will hang parallel. Paffing this point, they will again separate, and most of all when the knob is at a. In this situation they will deviate toward the globe, and will be directed straight toward it, if it be held too near, or in the direction of the axis. This would disturb the experiment, and must be avoided. These phenomena are conformable to the account given of the disposition of the fluid in the conductor. The electrometer may be considered as making a part of the conductor; and when its threads hang parallel, it is in its natural state, having its fluid of its natural density. This, however, cannot be strictly true, according to the theory; because the balls of the electrometer must be considered as more remote from the electric, and their electrical state must correspond to a point of the conductor more remote than that where the knob of the electrometer touches it. This will be more remarkably the case as the threads are longer. Accordingly, an electrometer with very long threads will never collapse. The place of the neutral point cannot be accurately ascertained in this way. Lord Mahon imagined, that its situation B was determined (in his experiments with a long conductor) to be such, that D was harmonically divided in B and a; and he finds this to be agreeable to the result of an electric atmosphere whose density is inversely proportional to the square of the distance. But we cannot deduce this from his narration of the experiment. He gives no reason for his selection of the point D, nor tells us the form and dimensions of the electric employed, nor takes into account the action of the fluid in the long conductor. It is evident that no computation can be instituted, even on his Lordship's principles, till all this be done. We have have always found, that the neutral point was farther from the electric, in proportion as the conductor was smaller; and when the electricity was stronger; and that the differences in this respect were so very considerable, that no dependence could be had on this experiment for determining the law of action. It should be so, both according to Lord Mahon's and Mr. Epinus's theory. But to proceed with our examination:

Having touched the end c of the conductor with the knob of the electroscope, bring it away. The balls will continue to repel each other, and they are attracted by any body that is in its natural state. Touch the same end with the knob of the other electroscope, and bring it also away; the balls of the two electrometers will be found to repel each other; but if one has touched the conductor at c, and the other has touched it at a, the electrometers will strongly attract each other. All this is quite conformable to the theory. If the fluid has been compressed at c, and therefore the balls of that electroscope are overcharged, they must repel each other, and repel any other body electrified in the same way. They must attract and be attracted by any natural body. But the balls of the other electroscope having touched the conductor at a, must be undercharged, and the redundant fluid of the one must attract the redundant matter of the other.

If the conductor has been electrified by the vicinity of excited glass, the electroscope which touched it in the remote end c, will be repelled by a piece of excited glass, but attracted by excited sealing wax. The electroscope which touched the conductor in a will be attracted by excited glass, and repelled by excited sealing wax. The contrary will be observed if the conductor has had its electricity induced on it by the vicinity of the globe covered with sealing wax. This is a complete proof that Mr. Dufuy's doctrine of vitreous and resinous electricity is unfounded. Both kinds of electricity are produced in a conducting body, without any material communication, by mere juxtaposition to a body possessed of either the vitreous or the resinous electricity.

We have not yet mentioned any reasons which indicate which end of the conductor is electrical by the redundancy of electric fluid, nor is the reader prepared for seeing their force. It is generally believed, that the remote end of a conductor which is electrified by glass, excited by rubbing it with flannel or amalgamated leather, is electrical by redundancy. No difference has been observed in the attractions and repulsions. But there are other marks of distinction which are constant, and undoubtedly arise from a difference in the mode of action of those mechanical forces. If, while the excited glass globe remains at D, a glass mirror, foiled as usual with tin-leaf, be made to touch the remote end of the conductor, and slowly drawn transversely, so that the conductor draws a line as it were across it—this mirror being laid down with the foiled side underneath, the dust, which settles on it in the course of a day or two, will be chiefly collected along this line, somewhat in the form of the fibres of a feather. But if the conductor was rendered electrical by the globe covered with sealing-wax, the dust will be collected along this line in little spots like a row of beads. The appearances will be reversed if the mirror has been passed across the end of the conductor which is nearest to the excited glass. In short, in whatever way the drawing point has been electrified, if it repel a ball which has touched excited glass, the line will be feathered; but if it attract such a ball, the line will be spotted. There are many ways of making this appearance much more remarkable (see Electricity, Encycl. Sect. viii. n° 48.) than this; but we have mentioned it on this occasion, because the circumstances which occasion the difference, whatever it is, are the most simple possible. Nothing is communicated; and therefore the effect must arise from the unnatural state of a substance or power residing in the body. If it be a substance sui generis, the electric action must arise from a different distribution of this substance; from a redundancy and deficiency of it in the different portions of the conductor. Without pretending as yet to say which is redundant, we shall suppose, with Dr Franklin, that the electricity of excited glass is so; and we shall use the words redundant and positive to distinguish this electricity from the other. This is merely that we may, on many occasions, considerably abbreviate language.

The different electrical states of the different portions of the conductor may be seen in another way, which is perhaps more simple and unexceptionable than that already narrated. While the globe remains at D, take the two extreme pieces A and C aside; or, if only two pieces have been used, draw the remote piece farther away. Now remove the excited globe. When we examine A separately, we shall find it wholly negative, or undercharged, strongly repelling a ball electrified by sealing wax, and attracting a ball electrified by glass. The other piece C exhibits positive electricity, attracting and repelling what A repelled and attracted. If only three pieces of the conductor have been employed, the middle piece B is generally positive; but this in a very faint degree.

If all the pieces be again joined, they are void of electricity. If, instead of such conductors, a row of metal balls, suspended by silk lines, are employed, one of them may generally be found without any sensible electricity, when separated from the rest, having been the neutral part of the row while united.

These very simple facts show, as completely as can be wished, that if the electric phenomena depend on a fluid moveable in the pores of the body, the constitution given it by Mr. Epinus is adequate to the explanation. We may now venture to assert, that every other phenomenon of attraction and repulsion will be found in exact conformity with the legitimate consequences of this constitution of the electric fluid.

That nothing is communicated from the electric will in the appearance will more forcibly by the following experiment: Let a conductor be rendered electrical in the way now described, and touch either extremity of it with the common little electroscope, and observe attentively the divergence of its threads. Now approach its remote extremity with another conducting body, such as a single piece of those conductors, it will be rendered electrical; as may be discovered by a delicate electroscope. Observe carefully whether the electroscope in contact with the first conductor be affected;—it will generally be found to spread its threads wider. It will certainly be thus affected if the other conductor be very long and bulky, or touched by the hand; or if, instead of this second conductor, we approach the first with the extended palm.

palm of the hand. As the second conductor was rendered electrical, fo, undoubtedly, is the hand also; and its electrification has not deprived the first conductor of any of its electric power, but, on the contrary, has increased it. And this augmentation of its power is equally sensible at both ends: For an electrometer at the other end will also diverge more when the hand is brought near the remote end. This theory explains this in the most satisfactory manner. The first conductor renders the second electric, by propelling its fluid to a greater distance. The second conductor now acts on the fluid that is moveable in the first, and causes a greater accumulation in its end which is farthest from the electric; that is, renders it more electric.

Suppose that, instead of employing an excited globe of glass, we had made use of a conducting body, slightly overcharged. Thus if we employ the conductor A, overcharged, to induce electricity on C; this will produce the same general effect on our set of conductors. But if we have previously examined the force of the redundant body, by suspending a pith-ball near it, and observing its deviation from the perpendicular, we may sometimes be led to think, that it has imparted something to the other body. For if the other body and the pith-ball be on opposite sides of the redundant body, the pith-ball will fall a little; indicating a diminution of electric force. But this should happen according to the theory; for it was shewn, in no. 52, that the constitution in the remote end of the overcharged body will be diminished, and along with this, its action on the pith-ball. We should find the electricity of the other end, next the conductor, increased, could we find an easy way of examining it; but an electrometer applied there will be too much affected by the conductor.

The same conclusions may be drawn from the following facts: Hang up a ruff-pith electrometer. Approach it below with a body slightly electrified. The legs of the electrometer immediately diverge, though attracted by the electrified body. Hold the hand above the electrometer, and they will diverge still more; touch the top of it, and they spread yet farther. Hold the electrified body (very weakly electrified) above the electrometer, so that its legs may diverge a little. Hold the hand above the electrified body; the legs of the electrometer will come nearer each other.

These appearances are observed whether the electric be positive or negative. We need not take up time in explaining this by the theory, its agreement is so obvious.

Lastly, on this head, if, in place of a fixed conductor, we use one of the needles of gilt card, set on its pivot, and if we then approach it with another conducting body, in the manner represented by F and C of fig. 6, we shall observe that end of the needle to avoid the other body; but if we bring them together, in the manner represented by F and B, they will attract each other. The attraction will be greater when the body F is long; and most of all when it communicates with the ground. These phenomena are therefore in perfect conformity with the theory; but it may sometimes happen that E will attract the end of C that is nearest to A, and E will be electrified positively if A be positive. This seems inconsistent with the theory; and, accordingly, it has been adduced by Volta against Lord Mahon's account of the electrical state of a conductor in a situation similar to that of C. But the theory of Ampère shows the possibility of this case. When E is very long, or when it is held in the hand, it is rendered much more undercharged than the adjacent part of C; and the fluid in the remotest, but not much remotest, part of C is strongly attracted by the copious redundant matter in the near end of E, and is brought back again, and passes over into E, in the way to be described immediately. The case is rare, and it will not happen at any considerable distance from the neutral point of C. If, indeed, E touch the near end of C before A is brought near, the approach of A will cause fluid to pass into E immediately, and C will be left undercharged on the whole.

The reader, who is at all conversant with electrical experiments, will be sensible, that these experiments are delicate, requiring the greatest dryness of air, and every attention to prevent the dissipation of electricity during the performance. This, by changing the state of the conductors and electrometers, will frequently occasion irregularities. The electrometers are most apt to change in this respect, it being scarcely possible to make them perfectly smooth and free from sharp angles. It may therefore happen, that when the conductors have affected them for some time, by the action of the disturbing electric, the removal of this electric will not cause the electrometers to hang perpendicular; they will often be attracted by the conductors, and often repelled; but the intelligent experimenter, aware of these circumstances, will know what allowances to make.

The theory obtains a full more complete support from a comparison with similar experiments made with imperfect conductors. If, in place of the series A, B, C, of metallic conductors, we employ cylinders of glass or sealing wax, or even dry wood or marble, and electrometers with silk threads in place of the ruff-pith, the electrometers, we shall find all the appearances to be such as the theory enables us to predict. If, for example, we use a single cylinder A of glass, we shall find that the neighbourhood of the electric D scarcely induces any electricity on A. The electrometer will hardly exhibit the smallest attraction, and its motions will be almost entirely such as arise from the immediate influence of the electric body D. A cylinder of very dry wood will be more affected by the electric D; and a circumstance of theoretical importance is very distinctly observed, namely, the gradual shifting of the neutral point. It will be found to advance along the cylinder for a very long while, when every circumstance is very favourable, the air very dry, and the wood almost a nonconductor; and its final situation will be found much nearer to the electric than in the brass conductor. Several instructive experiments of this kind may be found in a treatise published in 1783 by Dr Thomas Milner at Maidstone in Kent, entitled, "Experiments and Observations on Electricity." The author does not profess to advance any new doctrines, but only to exhibit experiments scientifically arranged for forming a system. He supports the Franklinian system as it was generally understood at that time; but is much embarrassed for the explanation of the repulsion of negative electrics. The Epiphanian correction of this theory did not offer itself to his mind.

We need not go over the same ground again with imperfect conductors. It is well known that such bodies

The balls of an electrometer with linen threads diverge vastly more when an electrified body is held below it, than if the threads are silk: that such electrometers frequently exhibit very capricious appearances from the flow but real progres of the electricity along the threads. These anomalies will be better understood when we explain the diffusion of electricity along imperfect conductors.

A very essential deduction from the theory is, that the electricity induced on an imperfect conductor must have some permanency. This is fully confirmed by experiment. But the remarkable instances of this particular cannot be produced till we be better acquainted with the methods of producing great accumulations of fluid. It is enough to observe at present, that a permanent electricity may always be observed, at the junction of the conductors with their insulating stalks. The brass conductor A ceases to be electric as soon as the excited globe is removed; but the very top of the glass stalk on which it is supported will sensibly affect a delicate electrometer for a long while after. The following pretty experiment shews this permanency very distinctly. Set one of the sealing-wax needles on its pivot, and place it between two inflated metal spheres of considerable size, at such a distance from both as not to receive a spark. Electrify these balls moderately, one of them positively, and the other negatively, and keep them thus electrified for some hours by renewing their electrification. The needle quickly arranges itself in the line adjoining the two spheres, just as a magnetic needle will do when placed between two magnets whose dissimilar poles front each other. Any gentle force will derange the needle; but it will vibrate like a magnetic needle, and finally settle in its former position. When this has been continued some time, that end of the needle which pointed to the positive globe will be found negative, and the other end will be found positive, if examined with an electroscope. And now, if the two globes be removed, this little needle will remain electrical for entire days in dry frosty weather, and its ends will approach any body that is brought near it (taking care not to come too close); and the end which pointed to the positive globe will avoid a piece of rubbed sealing wax, but will approach a piece of rubbed glass; but the other end will be affected in the opposite way. In short, it proves an electric needle with a positive and negative pole.

If two small inflated balls are moderately electrified, and placed about six inches asunder, this needle, when carried round them, will arrange itself exactly as a magnetic needle does when carried round a magnet of the same length. If the same trial be made with the needle of gilt card, it will arrange itself in the same manner that a soft iron needle arranges itself near a magnet, but either end will turn indifferently to either globe.

If a thin glass plate, coated with red sealing wax, be set on the positive and negative globes, and we sprinkle (from a considerable height) a fine powder of black sealing wax, and then pat the plate gently with a glass rod so as to agitate it a little, the particles of wax powder will gradually arrange themselves into curve lines, diverging from the point over one of the globes, and converging to the point over the other, precisely like the curves formed by iron filings sprinkled on a paper held over a magnet. Each little rag of wax becomes electrical by position, acquires two poles, and the positive pole of one attracts the negative pole of another; and they adhere in a certain determinate position, nearly a tangent to the curve, which was mentioned in no. 50, and indicates the law of magnetic action. When in this state, if a hot brick be held over the plate till the wax soften a little, the particles of black wax will adhere to the red coating, and give us a permanent specimen of the action.

It is well known that liquid sealing wax is a conductor. The writer of this article filled a glass tube with powdered sealing wax, and melted it, and then exposed it, in its melted state, to the influence of a positive and negative globe, hoping to make a powerful and permanent electric needle, which should have two poles, and exhibit a set of phenomena resembling those of magnetism. Accordingly he, in some measure, succeeded, by keeping the globes continually electrified for several hours, till the wax was quite cold. It had two distinct poles, and preserved this property, even though plunged in water, and while immersed in the water; but he was greatly disappointed as to the degree of its electricity. It just affected a sensible electrometer at the distance of six inches from either pole. It was considerably stronger than if it had not been melted during the impregnation, but by no means in the degree that he expected. It retained some electricity for about six weeks, although lying neglected among conducting bodies. After its power seemed quite extinct, he was melting it again in order to renew it. Some light fibrous things chanced to be near it. While it was softening, it became very sensibly electrical, causing these fibres to bend towards it, and even to cling to the tube. We shall see by and bye, that he was mistaken in expecting more remarkable appearances, and that the theory, when properly applied, does not promise them. Having thus established (as we think) this theory on insufficient foundations for making it a very perspicuous way of explaining the phenomena of induced electricity, we proceed to compare it with the second general fact in electricity.

PROP. II. When an inflated body B is brought very near an electrified body A, a spark is observed to be communicated between them, accompanied with a noise (which we shall call the electric snap), and B is now electrified permanently, and the electricity of A is diminished.

Although this be one of the most familiar facts in electricity, it will be proper to consider its attending circumstances in a way that connects it with what we have now learned concerning electricity by position.

Let the inflated body A (fig. i4.) be furnished with a cork ball, hanging by a silk thread from a glass stalk connected with A; let B be fitted up in the same manner; let A be electrified weakly, and its degree of electricity be estimated by the inclination of the ball towards A; since B is not electrified, its electrometer will hang perpendicular; but when it approaches A (keeping the electrometers on the remote sides of both), its electrometer will approach it, and the electrometer of A will gradually approach the perpendicular. When the bodies are brought very near, a spark is seen between them; and, at that instant, the electrometer of B comes... B comes much nearer to it, and that of A drops farther from it. If they be now separated, their electrometers will retain their new positions with very little change, and B will now manifest the same kind of electricity with A.

Such is the appearance when A has been but weakly electrified. Bringing B near A, the fluid in B is drawn to the remote side, if A be overcharged, or drawn to the side nearest to A, if A has been undercharged. B acts on its electrometer in consequence of the change made in the disposition of its fluid. The electrometer is attracted. In the mean time, the change made in the disposition of the fluid in B affects the moveable fluid in A. If A was overcharged, the adjacent side of B becomes undercharged, and its redundant matter, attracting the fluid in A, condenses it in the adjacent side, abstracting part of the redundant fluid from that side which is next to the pith-ball. Then the joint action of the whole redundant fluid in A on the pith-ball is diminished.

As there is now an attraction in the redundant fluid in A for the redundant matter on the adjacent side of B, it is reasonable to suppose, that when this attraction, joined to the repulsion of the redundant fluid behind it, is able to overcome the attraction which connects it with the superficial particles of the matter, it will then escape and fly into B; but this will not happen gradually, but at once, as soon as the expelling force has arisen to a very considerable intensity. We cannot say what is the precise augmentation that is necessary; but we can clearly see, that however great the attraction for the adjoining particles may be, while the particle is surrounded by them on all sides, it will yield to the smallest inequality of force, because the particles before it attract as much as those behind it; but when it is just about to quit the last or superficial particles of A, a much greater force is now necessary. It can be strictly demonstrated, that when the mutual tendency is inversely as the square of the distance, the action of a particle placed immediately without a sphere of such matter is double of its action when situated in the very surface*. A fallus of this kind must obtain whatever be the law of electric attraction. We shall see other causes which should prevent the escape of redundant fluid, and also its admission, till the impelling force is increased in a certain abrupt degree.

These observations must suffice at present to explain the delusive nature of this transference, if there be really a transference. That this has happened, may be confidently inferred from the sudden diminution of the electricity of A, indicated by the sudden fall of its electrometer; but it is more expressly established, that there has been a transference by the change produced on B. It is now permanently electrified, and its electricity is of the same kind with that of A, positive or negative according as A is positive or negative. And now we are enabled to explain the third general fact in electricity.

**Prop. III.** When a body has imparted electricity to another, it constantly repels it, unless that other has afterwards imparted all its electricity to other bodies. This fact, from which there is no exception, is an immediate consequence of the theory. Before the transference supposed by it, B was in its natural state; after the transference, both bodies contain redundant fluid, or redundant matter; therefore they must mutually repel.

We may now take another form of the experiment, which will be much more convincing and instructive. Let A be electrified positively, or by redundancy, and let its electrometer be attached to it by a conducting stalk, and have a flaxen thread; let this be the case also with the electrometer of B; then the appearances should happen in the following order: When A is made to approach B, the electrometer of B must gradually rise, diverging from B; because the fluid condensed on the side remote from A, and in the electrometer, will act more strongly on it than the deserted matter on the other side of B; and when the sudden transference is made, and B is wholly overcharged, its electrometer will immediately rise much higher, and must remain at that height, nearly, when A is removed. On the other hand, the electrometer attached to the remote side of A must descend, by reason of the change made in the disposition of the fluid in A by the induced electrical state of B; and when a considerable portion of the redundant fluid in A passes into B, the electrometer of A must suddenly sink much lower, and remain in that state when B is removed.

Many circumstances of this phenomenon corroborate our belief of a real transference of matter. The cause of a peculiar substance resides formerly in A alone; it now resides also in B. The larger that B is, the greater is the diminution of A's electric power, and the smaller is the power acquired by B. It perfectly resembles, in this respect, the communication of salts, sweetens, &c., by mixing a solution of salt or sugar with different quantities of water; and the evidence of a transference of a substance, the cause of electric attractions and repulsions, is at least as cogent as the evidence of the transference of heat, when we mix hot water with a quantity of cold, or when a hot solid body is applied to the side of a cold one. We also see so many chemical and other changes produced by this communication of electricity, that we can hardly refuse admitting that some material substance passes from one body to another, and, in its new situation, exerts its attractions and repulsions, and produces all their effects.

We may deduce the following corollaries; all of which are exactly conformable to the phenomena, serving still more to confirm the justness of the theory.

1. A certain quantity of what possesses these powers of attraction and repulsion is necessary for giving a determined vivacity to the appearances. Another spark must pass between the bodies, only if they be brought quite fill nearer, and their electrometers must rise and fall imperceptibly farther. For by the first transference of electric fluid into B, the expelling power of A is diminished, and the superior attraction of the redundant matter in the adjacent side of B is also counteracted by the repulsion of the fluid which has entered into it; therefore no more will follow unless these forces be increased, at least to their former degree. When this addition has been made to B, and this abstraction from A, their respective electrometers must be affected. All this is in perfect conformity to experience.

2. All the phenomena of communicated electricity must be more remarkable in proportion to the conducting power of the bodies. A very imperfect conductor, too,

The middle conductor B (fig. 11.), and hang in its place a cork ball by a long silk thread. As soon as the electric body D is brought near to A, the ball is attracted by its remote end, comes into contact, is repelled by it, and attracted by the adjacent end of C, touches it, is faintly repelled by it, and again attracted by A; and the operation is repeated several times. When all has ceased, remove C, and also the electric D. C is found to have the same electricity with D, and A has the opposite electricity. The process is too obvious to need any detailed application of the theory. The cork ball was the carrier of fluid from A to C if D was electric by redundancy, or from C to A if D was undercharged. If instead of removing C when the vibrations of the ball have ceased, we bring D a little nearer, they will be renewed, and, after some time, will again cease. The reason is plain. The carrier will have brought the conductor A into a state of equilibrium with the action of D. But this action is now increased, and the effects are renewed. If we now remove D, the ball will vibrate between A and C with great rapidity for a considerable time before the vibrations come to an end; and we shall find their number to be the same as before. The cause of this is also obvious from the theory. We may suppose A to be negative, and C positive. One of them will attract the ball into contact, and will repel it, having put it into an electric state opposite to that of the other conductor. It now becomes a carrier of fluid from the positive to the negative conductor, till it nearly restore both to their primitive state of neutrality.

There is frequently a seeming capriciousness in those irregular attractions and repulsions. A pith ball, or a down feather, hung by silk, will cling to the conductor, or otherwise electrified body, and will not fly off again, at least for a long while. This only happens when those bodies are so dry as to be almost non-conductors. They acquire a positive and negative pole, like an iron nail adhering to a magnet, and are not repelled till they become almost wholly positive or negative. It never happens with conducting light bodies.

It should follow from the theory, that the electric attractions and repulsions will not be prevented by the intervention of non-conducting substances in their neutral state. Accordingly, it is a fact, that the insertion of a thin pane of glass, let it be ever so extensive, does not hinder the electrometer from being affected. Also, if an insulated electric be covered with a glass bell, an electrometer on the outside will be affected. Nay, a metal ball, covered to any thickness with sealing wax, when electrified, will affect an electrometer in the same way as when naked. We cannot see how these facts can be explained by the action of electric atmospheres. It is indeed said, that the atmosphere on one side of the glass produces an atmosphere on the other; but we have no explanation of this production. If the interposed plate be a non-conductor, how does the one atmosphere produce the other? It must produce this effect by acting at a distance on the particles which are to form this atmosphere. Of what use, then, is the atmosphere, even if those atmospheres could affect the observed motions of the electrometer in conformity with the laws of mechanics? The atmospheres only substitute millions of attractions or repulsions in place of one. We must observe, however, that the motions of the electrometer are modified, and sometimes greatly changed, by the interposed non-conducting plate; but this is owing to the electricity induced on the plate. If the electric is positive, the adjacent surface of the plate becomes faintly negative, and the side next the electrometer slightly positive. This affects the electrometer even more than the more remote electric does. That this is the cause of the difference between the state of the electrometer when the plate is there and when it is removed, will appear plainly by breathing gently on the glass plate to damp it, and give it a small conducting power. This will make some change in the position of the electrometer. Continue this more and more, till the plate will no longer inflate. The changes produced on the electrometer's position will form a regular series, till it is seen to assume the very position which it would have taken had the plate been brass.

Then, considering those changes in a contrary order, and supposing the series continued a little farther, we shall always find that it leads to the position which it would have taken when no plate whatever is interposed. We consider this as an important fact, shewing that the electric action is similar to gravitation, and that there is no more occasion for the intervention of an atmosphere for explaining the phenomena of electricity than for explaining those of gravitation.

6. Since non-electrics are conductors, and since electrics may be excited by friction with a non-electric, it follows, that if this non-electric be insulated, and separated from the electric, it will exhibit signs of electricity; but when they are together, there must not appear any marks of it, however strong the excitation may be. We do not pretend to comprehend distinctly the manner in which friction, or the other modes of excitation, operate in changing the connection between the particles of the fluid and those of the tangible matter; nor is this explained in any electric theory that we know; but if we are satisfied with the evidences which we have for the existence of a substance, whose presence or absence is the cause of the electric phenomena, we must grant that its usual connection with the tangible matter of bodies is changed in the act of excitation, by friction, or by any other means. In the case of friction producing positive electricity on the surface of the electric, we must suppose that the act of friction causes one body to emit or absorb the fluid more copiously than the other, or perhaps the one to emit, and the other to absorb. Which ever is the case, the adjoining surfaces must be in opposite states, and the one must be as much overcharged as the other is undercharged. When the bodies (which we may suppose to have the form of plates) are joined, and the one exactly covers the other, the assemblage must be inactive; for a particle of moveable fluid, situated anywhere on the side of the overcharged plate, will be as much attracted by the undercharged surface of the remote plate as it is repelled by the overcharged surface of the near plate. The surfaces are equal, and equally electric, and act on either side with equal intensity; and they are coincident. Therefore their actions balance. The action is expressed by the formula of n° 43; namely, $F' = \frac{m}{x} - \frac{m}{x'}$; and $x = x'$ is $= 0$, by reason of the equal distances of these surfaces from the particle of exterior fluid.

But let the plates be separated. Part, and probably the greatest part, of the redundant fluid on one of the rubbed surfaces will fly back to the other, being urged both by the attraction of the redundant matter and the repulsion of its own particles. But the electric, being electric because, and only because, it is a non conductor, must retain some, or will remain deprived of some, in a stratum a little within the surface. The two plates must therefore be left in opposite states, and the conducting, or non-electric plate, if insulated before separation, must now exhibit electric action.

All this is exactly agreeable to fact. We also know, that electrics may be excited by rubbing on each other; and if of equal extent, and equally rubbed, they exhibit no electric powers while joined together; but when parted, they are always in opposite states. The same thing happens when sulphur is melted in a metal dish, or when Newton's metal is melted in a glass dish. While joined, they are most perfectly neutral; but manifest very strong opposite electricities when they are separated. This completely disappears when they are joined again, and reappears on their separation, even after being kept for months or years in favourable circumstances. We have observed the plates of tale, and other laminated foils, exhibit very vivid electricity when split asunder.

Attention to these particulars enables us to construct machines for quickly exciting vivid electricity on the surface of bodies, and for afterwards exhibiting it with continued dispatch. The whirling globe, cylinder, or plate, first employed by Mr Hauksbee, for the solitary purpose of examining the electricity of the globe, was most ingeniously converted by Haufen, a German professor, into a rapid collector and dispenser of electricity to other bodies, by placing an insulated prime conductor close to that part of the surface of the globe which had been excited by friction. Did our limits give us room, we should gladly enlarge on this subject, which is full of most curious particulars, highly meriting the attention of the philosopher. But it might easily occupy a whole volume; and we have still before us the most interesting parts of the mechanical department of electricity, and shall hardly find room for what is essentially requisite for a clear and useful comprehension of it. We must, therefore, request our readers to have recourse to the original authors, who have considered the excitation by friction minutely. And we particularly recommend the very careful perusal of Becaria's Dissertations on it, comparing the phenomena, in every step, with this theory of Epimus. Much valuable information is also obtained from Mr Nicholson's Observations, of which an abstract is given in the article Electricity Encycl. Britan. The Epimian theory will be found to connect many things, which, to an ordinary reader, must appear solitary and accidental.

Seeing that this very simple hypothesis of Epimus evidently so perfectly coincides in its legitimate consequences with all the general phenomena of attraction and repulsion, and not only with those that are simple, but even such fluids as are compounded of many others—we may listen, without the imputation of levity, to the other evidences which may be offered for the materiality and mobility of the cause of those mechanical phenomena. Such evidences are very numerous, and very persuasive. We have said, that the transference of electricity is defunctory, and that the change made in the electric state of the communicating communicating bodies is always considerable. It appears to keep some settled ratio to the whole electric power of the body. When the form of the parts where the communication takes place, and other circumstances, remain the same, the transference increases with the size of the bodies; and all the phenomena are more vivid in proportion. When the conductor is very large, the spark is very bright, and the snap very loud.

1. This snap alone indicates some material agent. It is occasioned by a foworous undulation of the air, or of some elastic fluid, which suddenly expands, and as suddenly collapses again. But such is the rapidity of the undulation, that when it is made in close vessels it does not exist long enough, in a very expanded state, to affect the column of water, supported in a tube by the elasticity of the air, for the purpose of a delicate thermometer or barometer; just as a musket ball will pass through a loose hanging sheet of paper without causing any sensible agitation.

2. The spark is accompanied by intense heat, which will kindle inflammable bodies, will melt, explode, and calcine metals.

3. The spark produces some very remarkable chemical effects. It calcines metals even under water or oil; it renders Bolognian phosphorus luminous: it decomposes water, and makes new compositions and decompositions of many gaseous fluids; it affects vegetable colours; it blackens the calces of bismuth, lead, tin, luna cornes; it communicates a very peculiar smell to the air of a room, which is distinct from all others; and in the calcination of metals, it changes remarkably the smells with which this operation is usually accompanied: it affects the tongue with an acidulous taste; it agitates the nervous system.—When we compare these appearances with similar chemical and physiological phenomena, which naturalists never hesitate in ascribing to the action of material substances, transferable from one body, or one state of combination, to another, we can see no greater reason for hesitating in ascribing the electric phenomena to the action of a material substance; which we may call a fluid, on account of its connected mobility, and the electric fluid, on account of its distinguishing effects. We are well aware, that these evidences do not amount to demonstration; and that it is possible that the electric phenomena, as well as many chemical changes, may result from the mere difference of arrangement, or position, of the ultimate particles of bodies, and may be considered as the result of a change of modes, and not of things. But in the instances we have mentioned, this is extremely improbable.

We therefore venture to affirm the existence of this substance, which philosophers have called the electric fluid, as a proposition abundantly demonstrated; and to affirm, on the authority of all the above-mentioned facts, that its mechanical character is such as is expressed in Mr. Epinus's hypothesis.

We proceed, therefore, to explain the most interesting phenomena of electricity from these principles.

We have seen that, in a perfect conductor, in its natural state, the electric fluid is uniformly distributed, and cannot remain in any other condition. We are particularly interested to know how it is distributed in an overcharged or undercharged body, and how this is affected by the circumambient non-conducting air. It is evident that much depends on this. The tendency to escape, and, particularly, the tendency to transference from one body to another, must be greatest where the fluid is most concentrated. We know that it tends remarkably to dilate from all protuberances, edges, and long bodies, and that it is impossible to confine it in a body having very acute far-projecting points; and, what is more paradoxical, it is hardly possible to prevent its entering into a body furnished with a sharp point. The smallest reflection must suggest to our imagination, that a perfectly moveable fluid, whose particles mutually repel, even at considerable distances, and which is confined in a vessel from which it cannot escape, must be compressed against the sides of the vessel, and be denser there than in the middle of the vessel. But in what proportion its density will diminish as we recede from the walls of the vessel, must depend on the change of electric repulsion by an increase of distance. The intensity varies in the proportion of some function of the distance, and may be expressed by the ordinates of a curve, on whose axis the distances are measured. But we are ignorant of this function. We must therefore endeavour to discover it, by observing a proper distribution of phenomena. Having made some approximation to this discovery, such as shall give rise to a probable conjecture concerning the function which expresses the intensity of electric repulsion, mathematics will then enable us to say how the fluid must be distributed (at least in some simple and instructive cases) in a perfectly conducting body surrounded by the air, and what will be its action on another body. Thus we shall obtain offensive results, which we can compare with experiments. The writer of this article made many experiments with this view above 30 years ago, and flatters himself that he has not been unsuccessful in his attempts. These were conducted in the most obvious and simple manner, suggested by the reasonings of Mr. Epinus; and it was with singular pleasure that, some years after, he perused the excellent dissertation of Mr. Cavendish in the Philosophical Transactions, vol. 61, where he obtained a much fuller conviction of the truth of the conclusion which he had drawn, in a ruder way, from more familiar appearances. Mr. Cavendish has, with singular sagacity and address, employed his mathematical knowledge in a way that opened the road to a much farther and more scientific prosecution of the discovery, if it can be called by that name. After this, Mr. Coulomb, a distinguished member of the French academy of sciences, engaged in the same research in a way still more refined; and supported his conclusions by some of the most valuable experiments that have been offered to the public. We shall now give a very brief account of this argument: and have premised these historical remarks; because the writer, although he had established the general conclusion, and had read an account of his investigation in a public society in 1769, in which it was applied to the most remarkable facts then known in electricity, has no claim to the more elaborate proofs of the same doctrine, which is given in some of the following paragraphs. These are but an application of Mr. Cavendish's more cautious and general mathematical procedure, to the function which the writer apprehends to be sufficiently established by observation.

The most unexceptionable experiments with which we can begin, seem to be the repulsions observable between

Whatever be the law of distribution of the particles in a sphere, the general action of its particles on the particles of another sphere will follow a law which will not differ much from the law of action between two particles, if the diameters of the spheres be small in proportion to their distance from each other. The investigation was therefore begun with them. But the subject required an electrometer susceptible of comparison with others, and that could exhibit absolute measures. The one employed was made in the following manner; and we give it to the public as a valuable philosophical instrument.

Fig. 15. represents the electrometer in front. A is a polished brass ball, 1/4th of an inch in diameter. It is fixed on the point of a needle three inches long, as slender as can be had of that length. The other end of the needle passes through a ball of amber or glass, or other firm non-conducting substance, about half or three-fourths of an inch in diameter; but the end must not reach quite to the surface, although the ball is completely perforated. From this ball rises a slender glass rod FEL, three inches long from F to E, where it bends at right angles, and is continued on to L, immediately over the centre of the ball A. At J, is fixed a piece of amber C, formed into two parallel cheeks, between which hangs the stalk DCB of the electrometer. This is formed by dipping a strong and dry silk thread, or fine cord, in melted sealing wax, and holding it perpendicular till it remain covered with a thin coating, and be fully penetrated by it. It must be kept extended, that it may be very straight; and it must be rendered smooth, by holding it before a clear fire. This stalk is fastened into a small cube of amber, perforated on purpose, and having five holes drilled in two of its opposite sides. The cheeks of the piece C are wide enough to allow this cube to move freely between them, round two fine pins, which are thrust through the holes in the cheeks, and reach about half way to the stalk. The lower part of the stalk is about three inches long, and terminates in a gilt and burnished cork-ball (or made of thin metal), a quarter of an inch in diameter. The upper part CD is of the same length, and passes through (with some friction) a small cork-ball. This part of the instrument is so proportioned, that when FE is perpendicular to the horizon, and DCB hangs freely, the balls B and A just touch each other. Fig. 16. gives a side perspective view of the instrument. The ball F is fixed on the end of the glass rod FI, which passes perpendicularly through the centre of a graduated circle GHO, and has a knob handle of boxwood on the farther end I. This glass rod turns stiffly, but smoothly, in the head of the pillar HK, &c., and has an index NH, which turns round it. This index is set parallel to the line LA, drawn through the centre of the fixed ball of the electrometer. The circle is divided into 360 degrees, and O is placed uppermost, and 90 on the right hand. Thus the index will point out the angle which LA makes with the vertical. It will be convenient to have another index, turning stiffly on the same axis, and extending a good way beyond the circle.

This instrument is used in the following manner: A connection is made with the body whose electricity is to be examined, by sticking the point of the connecting wire into the hole at F, till it touch the end of the needle; or, if we would merely electrify the balls A and B, and then leave them inflated, we have only to touch one of them with an electrified body. Now, take hold of the handle I, and turn it to the right till the index reach 90. In this position, the line LA is horizontal, and so is CB; and the moveable ball B is resting on A, and is carried by it. Now electrify the balls, and gently turn the handle backwards, bringing the index back toward 0, &c., noticing carefully the two balls. It will happen that, in some particular position of the index, they will be observed to separate. Bring them together again, and again cause them to separate, till the exact position at separation is ascertained. This will show their repulsive force in contact, or at the distance of their centres, equal to the sum of their radii. Having determined this point, turn the instrument still more toward the vertical position. The balls will now separate more and more. Let an assistant turn the long index so as to make it parallel to the stalk of the electrometer, by making the one hide the other from his view. The mathematical reader will see that this electrometer has the properties ascribed to it. It will give absolute measures; for by poising the stalk, by laying some grains weight on the cork-ball D, till it becomes horizontal and perfectly balanced, and computing for the proportional lengths of BC and DC, we know exactly the number of grains with which the balls must repel each other (when the stalk is in a horizontal position), in order merely to separate. Then a very simple computation will tell us the grains of repulsion when they separate in any oblique position of the stalk; and another computation, by the resolution of forces, will show us the repulsion exerted between them when AL is oblique, and BC makes any given angle with it. All this is too obvious to need any farther explanation. The reason for giving the connection between A and C such a circuitous form, was to avoid all action between the fixed and the moveable part of the electrometer, except what is exerted between the two balls A and B. The needle AF, indeed, may act a little, and might have been avoided, by making the horizontal axis FI to join with A; but as it was wanted to make the instrument of more general use, and frequently to connect it with an electrical machine, a battery, or a large body, no mode of connection offered itself which would not have been more faulty in this respect. The neatest and most commodious form would have been to attach the axis FI to C, and to make CA and CB stiff metallic wires, in the same manner as Mr Brooke's electrometer is made. But as the whole of their lengths would have acted, this construction would have been very improper in the investigation of the law of electric repulsion. As it now stands, we imagine that it has considerable advantages over Mr Brooke's construction; and also over Mr De Luc's incomparable electrometer, described in his Essays on Meteorology. It has even advantages over Mr Coulomb's incomparably more delicate electrometer, which is sensible, and can measure repulsions which do not exceed the 50,000 of a grain; for the instrument which we have described will measure the attractions of the oppositely electrified bodies; a thing which Mr Coulomb could not do without a great circuit of experiments. For instead of making the ball B above A, by inclining the instrument to the right hand, we may incline it to

the left; and then, by electrifying one of the balls positively, and the other negatively, when at a great distance from each other, their mutual attraction will cause them to approach; CB will deviate from the vertical toward A; and we can compute the force by means of this deviation.

We must remind the person who would make observations with this instrument, that every part of it must be secured against dissipation as much as possible, by varnishing all its parts, by having all angles, points, and roughnesses removed, and by choosing a dry state of the air, and a warm room; and, because it is impossible to prevent dissipation altogether, we must make a previous course of experiments, in a variety of circumstances, in order to determine the diminution per minute corresponding to the circumstances of the experiments that are to be made with further views.

We trust that the reader will accept of this particular account of an instrument which promises to be of considerable service to the curious naturalist; and we now proceed with an account of the conclusions which have been drawn from observations made with it.

Here we could give a particular narration of some of the experiments, and the computations made from them; but we omit this, because it is really unnecessary. It suffices to say, that the writer has made many hundreds, with different instruments, of different sizes, some of them with balls of an inch diameter, and radii of 18 inches. Their coincidence with each other was far beyond his expectation, and he has not one in his notes which deviates from the medium of the whole force, and but few that have deviated. The deviations were as frequently in excess as in defect. His custom was to measure all the forces by a linear scale, and express them by straight lines erected as ordinates to a base, on which he let off the distances from a fixed point; he then drew the most regular curve that he could through the summits of these ordinates. This method shows, in the most palpable manner, the coincidence or irregularity of the experiments.

The result of the whole was, that the mutual repulsion of two spheres, electrified positively or negatively, was very nearly in the inverse proportion of the squares of the distances of their centres, or rather in a proportion somewhat greater, approaching to \( \frac{1}{x^2} \). No difference was observed, although one of the spheres was much larger than the other; and this circumstance enables us to make a considerable improvement on the electrometer. Let the ball A be made an inch in diameter, while B is but \( \frac{1}{4} \) of an inch. This greatly diminishes the proportion of the irregular actions of the rest of the apparatus to the whole force, and also diminishes the dissipation when the general intensity is the same.

When the experiments were repeated with balls having opposite electricities, and which therefore attracted each other, the results were not altogether so regular, and a few irregularities amounted to \( \frac{1}{3} \) of the whole; but these anomalies were as often on one side of the medium as on the other. This series of experiments gave a result which deviated as little as the former (or rather less) from the inverse duplicate ratio of the distances; but the deviation was in defect as the other was in excess.

We therefore think that it may be concluded, that the action between two spheres is exactly in the inverse duplicate ratio of the distance of their centres, and that this difference between the observed attractions and repulsions is owing to some unperceived cause in the form of the experiment.

It must be observed also, that the attractions and repulsions, with the same density and the same distances, and repulsions, to all senses, equal, except in the aforementioned cases of anomalous experiments. The mathematical reader will quickly perceive, that the above-mentioned irregularities are imperfections of experiment, and that the gradations of this function of the distances are too great to be much affected by such small anomalies. The indication of the law is precise enough to make it worth while to adopt it, in the mean time, as a hypothesis, and then to select, with judgment, some legitimate consequences which will admit of an exact comparison with experiment, on so large a scale, that the unavoidable errors of observation shall bear but an insignificant proportion to the whole quantity. We shall attempt this: and it is peculiarly fortunate, that this observed law of action between two spheres gives the most easy access to the law of action between the particles which compose them; for Sir Isaac Newton has demonstrated (and it is one of his most precious theorems), that if the particles of matter act on each other with a force which varies in the inverse duplicate ratio of the distances, then spheres, consisting of such particles, and of equal density at equal distances from the centre, also act on each other with forces varying in the same proportion of the distances of their centres. He demonstrates the same thing of hollow spherical shells. He demonstrates that they act on each other with the same force as if all their matter were collected in their centres. And, lastly, he demonstrates that if the law of action between the particles be different from this, the sensible action of spheres, or of hollow spherical shells, will also be different (see Principia, I. Prop. 74, &c., also Astronomy, Encycl. 307).

Therefore we may conclude, that the law of electric attraction and repulsion is similar to that of gravitation; and that each of those forces diminishes in the same proportion that the square of the distance between the particles increase. We have obtained much useful information from this discovery. We have now full confirmation of the propositions concerning the mutual action of two bodies, each overcharged at one end and undercharged at the other. Their evidence before given amounted only to a reasonable probability; but we now see, that the curve line, whose ordinates represent the forces, is really convex to the abscissa, and that \( Z + z \) is always greater than \( Z' + z' \); from which circumstance all the rest follows of course.

Let us now enquire into the manner in which the redundant fluid, or redundant matter, is distributed in such bodies; the proportion in which it subsists in bodies fluid when communicating with each other; the tendencies to escape; the forces which produce a transference, &c. &c.

In the course of this enquiry, a continual reference will be made to the following elementary proposition:

Let ABD (fig. 17.) be the base of a cone or pyramid, whose vertex is P, and axis PC; and let \( a b d \) be another section of it by a plane parallel to the base; let these two circles, or similar polygons, consist of matter or fluid of equal and uniform density; and let P be a particle of fluid or matter; the attraction or repulsion of this particle for the whole matter or fluid in the figure ABD is equal to its attraction or repulsion for the

The whole matter or fluid in \( abd \). For the attraction for a particle in \( ABD \) is to the attraction for a particle similarly placed in \( abd \) as \( P^2 \) to \( PC^2 \); and the number of particles in \( ABD \) is to that of those in \( abd \) as \( PC^2 \) to \( P^2 \); therefore the whole attraction for \( ABD \) is to that for \( abd \) as \( P^2 \times PC^2 \) to \( PC^2 \times P^2 \), or in the ratio of equality.

Cor. 1. The same will be true of the action of plates of equal thickness and equal density; or, in general, having such thickness and density as to contain quantities of matter or fluid proportional to their areas.

2. The action of all such sections made by parallel planes, or by planes equally inclined to their axis, are equal.

3. The tendency of a particle \( P \) to a plane, or plate of uniform thickness and density, and infinitely extended, or to a portion of it bounded by the same pyramid, is the same, at whatever distance it be placed from the plate, and it is always perpendicular to it.

4. This tendency is proportional to the density and thickness of the plate or plates jointly.

It is only in two or three simple cases that we can propose to state with precision what will be the disposition and action of the electric fluid in bodies; but we shall select those that are most instructive, and connected with the most remarkable and important phenomena.

Let \( Aa'dD \) (fig. 18.) and \( Eb'c'H \) represent the sections of a part of two infinitely extended parallel plates (which we shall call \( A \) and \( E \)), consisting of solid conducting matter, in which the electric fluid can move without any obstruction, but from which it cannot escape.

Firstly, let them be both overcharged, \( A \) containing the quantity \( r \) of redundant fluid, and \( E \) containing the quantity \( s \), and let \( r \) be greater than \( s \).

The fluid will be disposed in the following manner:

1. There will be two strata, \( Aa'bB \) and \( Gg'bH \), adjoining to the remote surfaces, in each of which the quantity \( \frac{r+s}{2} \) will be crowded together as close as possible.

2. Adjoining to the interior surface (that is, the surface nearest to \( E \)) of the plate \( A \), there will be a stratum \( Cc'd'D \), containing the quantity \( \frac{r-s}{2} \), crowded together.

3. The adjacent side of \( E \) will have a stratum \( Ef'fF \), just sufficient for containing the quantity \( \frac{r-s}{2} \) at its natural density. This stratum will be entirely exhausted of fluid.

4. The spaces \( Bb'c'C \) and \( Ff'g'G \) will be in their natural state.

For a particle of fluid in the space \( Bb'c'C \) is urged in the direction \( ad \) by the force \( \frac{r+s}{2} \) (\( n^9 \) 97, 3.), and in the direction \( da \) by the force \( \frac{r-s}{2} \), therefore it is, on the whole, urged in the direction \( ad \) with the force \( r \), which will balance the repulsion of the redundant fluid in the other plate. A particle of fluid in the space \( Ff'g'G \) is repelled in the direction \( bc \) by a force \( \frac{r+s}{2} \) by the fluid in \( Gg'bH \), and it is attracted in the same direction by the redundant matter in \( Ef'fF \), with the force \( \frac{r-s}{2} \). These make a force \( r \) which balances the repulsion \( r \) of the other plate. No other disposition will be permanent; for if a particle be taken out from either stratum \( Aa'bB \) or \( Cc'd'D \) into the space between them, the repulsion from that stratum which it quitted is lessened, and the repulsion of the opposite stratum, joined to that of the other plate, will drive it back again. The same thing holds with respect to the fluid in the other plate.

Cor. 1. If the two plates be equally overcharged, all the redundant fluid will be crowded on the remote surfaces, and the adjacent surfaces will be in the natural state.

In the second place, let the plates be undercharged, when \( r \) and \( s \) be the fluid wanting in \( A \), and \( r \) the fluid wanting in \( E \), and let \( r \) be greater than \( s \); then,

1. The strata adjoining to \( Aa'bB \) and \( Gg'bH \) will be completely exhausted of fluid, and the redundant matter in each will be such as would be saturated by \( \frac{r+s}{2} \).

2. The stratum \( Cc'd'D \) will contain redundant fluid \( \frac{r-s}{2} \), crowded close.

3. The stratum \( Ef'fF \) will be deprived of fluid, and the quantity abstracted is \( \frac{r-s}{2} \).

4. The spaces \( Bb'c'C \) and \( Ff'g'G \) are in the natural state.

The demonstration is the same as in the former case.

Thirdly, let \( A \) be overcharged, and \( E \) undercharged, \( A \) containing the redundant fluid \( r \), and \( E \) wanting in the fluid \( s \); and let \( r \) be greater than \( s \). Then,

1. The strata \( Aa'bB \) and \( Gg'bH \) contain the redundant fluid \( \frac{r-s}{2} \), crowded close.

2. The stratum \( Cc'd'D \) contains the quantity \( \frac{r+s}{2} \), crowded close.

3. The stratum \( Ef'fF \) is exhausted, and wants the quantity \( \frac{r-s}{2} \).

4. The rest is in the natural state.

Cor. 2. If the redundant fluid in \( A \) be just sufficient to saturate the redundant matter in \( E \), the two remote surfaces will be in their natural state, all the redundant fluid in \( A \) being crowded into the stratum \( Cc'd'D \), and all the redundant matter being in \( Ef'fF \).

This disposition will be the same, whatever is the distance or thickness of the plates, unless the redundant fluid in \( A \) be more than can be contained in the whole of \( E \) when crowded close.

When the two plates are overcharged, the fluid presses their remote surfaces with the force \( \frac{r+s}{2} \), and escapes with that force if a passage were opened. It would enter the remote surfaces of two undercharged plates with the same force; and, in either case, it would run from the inner surface of one to the adjacent surface of the other, with the force \( \frac{r-s}{2} \).

If one be overcharged and the other undercharged, fluid would escape from the remote surface with the force...

force \( \frac{r}{4} \), and would run through a canal between them with the force \( \frac{r+1}{4} \).

They repel or attract each other with the force \( r+2 \), according as they are both over or undercharged, or as one is overcharged and the other undercharged.

This example of parallel plates, infinitely extended, is the simplest that can be supposed. But it cannot obtain under our observation; and in all cases which we can observe, the fluid cannot be uniformly spread in any stratum, but must be denser near the edges, or near the centre, as they are overcharged or undercharged.

Let ABD (fig. 19.) represent a sphere of perfectly conducting matter, overcharged with electric fluid, which is perfectly moveable in its pores, but cannot escape from the sphere. Let it be surrounded by conducting matter saturated with moveable fluid. It is required to determine the disposition of the fluid within and without this sphere.

Sir Isaac Newton has demonstrated (Princ. I. 70.) that a particle \( p \) placed anywhere within this sphere, is not affected by any matter that is without the concentric spherical surface \( pqr \) in which itself is situated, therefore not affected by what is between the surfaces ABD and \( pqr \). He also demonstrates, that the matter within the surface \( pqr \) acts on the particle \( p \) in the same manner as if the whole of it were collected in the centre C.

Hence it follows, that the redundant fluid will be all confipated as close as possible within the external surface of the sphere, forming a shell of a certain minute thickness, between the spherical surfaces ABD and \( abd \); and all that is within this (that is, nearer the centre C) will be in its natural state.

With respect to the distribution of the fluid in the surrounding matter, which we suppose to be infinitely extended, we must recollect that this shell of confipated redundant fluid repels any external particle of fluid in the same manner as if all were collected at C. Hence it is evident, that the fluid in the surrounding matter will be repelled, and, being moveable, it will recede from this centre; and there will be a space all round the sphere ABD which is undercharged, forming a shell between the concentric surfaces ABD and \( abd \). This shell will contain such a quantity of redundant matter, that its attraction for a particle of fluid is equal to the repulsion of the shell of fluid crowded internally on the surface ABD. All beyond this surface \( abd \) will be in its natural state; for this redundant matter acts on a particle of fluid, situated farther from the centre, in the same manner as if all this redundant matter were collected in the centre C. So does the redundant fluid in the confipated shell. Therefore their actions balance each other, and there is no force exerted on any particle of fluid beyond this deficient shell. This deficient shell will not affect the fluid in the sphere \( abd \) by Newton's demonstration. No other disposition will be permanent. But farther: This undercharged shell must be completely exhausted: for a particle of fluid placed between ABD and \( abd \) will be more repelled by the fluid in the crowded shell within the surface ABD, than it is attracted by the redundant matter of its own shell that is less remote from the centre; and it is not affected by what is more remote from the centre. Therefore the fluid without the sphere ABD cannot be in equilibrium, unless the shell between ABD and \( abd \) be not only rarefied, but altogether exhausted of fluid.

If the sphere be undercharged, the space between ABD and \( abd \) will be entirely exhausted of fluid, and there will be a shell \( abd \) of redundant matter surrounding the sphere. All within \( abd \), and all without \( abd \), will be in its natural state. It is unnecessary to repeat the steps of the same demonstration.

This valuable proposition is by the Hon. Mr Cavendish.

This would be the disposition in and about a glass globe filled and surrounded with an ocean of water, of this and having redundant fluid within it, on the supposition that glass is impervious to the electric fluid. But it would not affect an electrometer, even supposing that the movements of the electrometer could be affected under water. Suppose the globe of water to be surrounded with air, and that the fluid is disposed in both in the manner here described; it will be perfectly neutral in its action on any electrometer situated in the air. But, by reason of the almost total immobility of the fluid in pure dry air, this state cannot soon obtain; and, till it obtain, the confipated shell within the glass must repel the fluid in an electrometer more than the partially rarefied shell of air, which surrounds the glass, attracts it. By the gradual retiring of the fluid in the surrounding air from the globe, the attraction of the deserted matter will come nearer to equality with the repulsion of the confipated shell within the glass, and the globe will appear to have lost fluid. Yet it may retain all the redundant fluid which it had at the first. Therefore we are not to imagine that a body similar to this globe has no redundant electric fluid, or only a small quantity, because we observe it inactive, or nearly so.

Thus we see, as we proceed, that the Egyptian theory is adequate to the explanation of the phenomena, by the phenomena. But we see it much more remarkably in a very familiar and amusing experiment, usually called the ELECTRIC WELL.

To see it in perfection, make a glass vessel of globular shape, with a narrow mouth, sufficiently wide, however, to admit an electrometer suspended to the end of a glass rod of a crooked form, so that the electrometer can be presented to any part of the inside. Smear the outside of the globe with some transparent clammy fluid, such as syrup. Set it on an insulating stand (a wine glass), and electrify it positively. Hold the electrometer near it, anywhere without, and it will be strongly affected. Its deviations from the perpendicular (if the ball of the electrometer has also been electrified) will indicate a force inversely as the square of the distance from the centre of the globe, pretty exactly, if the thread of the electrometer is of silk. Now let down the electrometer into the inside of the globe. It will not be affected in any sensible degree, nor approach or avoid any body that is lying within the globe. The electrometer may be held in all parts of the globe, and when brought out again, is perfectly inactive and neutral. But if the balls of the electrometer be touched with a wire, while hanging free within the globe, they will, on withdrawing the wire, repel each other; and when taken out, they will be found negatively electrified. The experiment succeeds as well with a metal globe; nay, even although the mouth be pretty wide; in which case, there is not a perfect balance of action in every direction. The electrometer may be made to touch the bottom of the globe, or anywhere not too near the mouth, without acquiring any sensible electricity; but if we touch the outside with the electrometer, it will instantly be electrified and strongly repelled. Deep cylinders, and all round vessels with narrow mouths, exhibit the same faintness of electricity within, except near the brims, although strongly electric without; and even open metal cups have the interior electricity much diminished.

Reflecting on this valuable proposition of Mr Cavendish, we see clearly why an overcharged electric is only superficially so; and that this will be the case even although we attempt to accumulate a great quantity of electricity in it, by melting it in a thin glass globe, and electrifying it while liquid, and keeping up the accumulating force till it becomes quite cold. The present writer, not having considered the subject with that judicious accuracy that Mr Cavendish exerted, had hopes of producing a powerful and permanent electric in this way, and was mortified and puzzled by the disappointment, till he saw his mistake on reading Mr Cavendish's dissertation.

These observations also point out a thing which should be attended to in our experiments for discovering the electricity excited in the spontaneous operations of nature, as in chemical composition and decomposition, congelation, fusion, evaporation, &c. It has been usual to put the substances into glasses, or other non-conducting vessels, or into vessels which conduct very imperfectly. In this last case especially, the very faint electricity which is produced, instantly forms a compensation to itself in the substance of the vessel, and the apparatus becomes almost neutral, although there may have been a great deal of electricity excited. It will be proper to consider whether the nature of the experiment will admit of metallic vessels. In the experiments on metallic foliation, the best method seems to be, to make the vessel itself the substance that is to be dissolved.

For similar reasons we may collect, without a more minute examination, that bodies of all shapes, when overcharged, will have the redundant fluid much denser near the surface than in the interior parts; and denser in all elevations, bumps, projections, angles, and near the ends of oblong bodies; and that, in general, the quantity of redundant fluid, or redundant matter, will be much more nearly proportional to the surfaces of bodies than to their quantities of matter. All this is fully proved by experience. The experiment of the electrified chain is a very beautiful one. Lay a long metal chain in an insulated metal dish furnished with an electrometer. Let one end be held an inch or two above the coil by a silk thread. Electrify the whole, and observe the divergency of the electrometer; then, gradually drawing up the chain from the coil, the electrometer will gradually fall lower, and lowering the chain again will gradually raise it.

We now see with how little reason Lord Mahon concluded that the point of his conductor, observed to be neutral, corresponded with his theory; namely, one of the media of a harmonic division. We see no reason for beginning the computation at the extremity of the prime conductor. It certainly should not have been from the extremity. Had the prime conductor been a single globe, it should have begun from the centre of this globe. If it was of the usual form, with an outstanding wire, terminated by a large ball, the action of the body of the conductor should certainly have been taken into the account. In short, almost any point of the long conductor might have been accommodated to his Lordship's theory.

We might now proceed to investigate the distribution of the electric fluid in bodies exposed to the action of others, and particularly in the oblong conductors made use of in our preparatory propositions. The problem is determinate, when the length and diameter of cylindric conductors are given; but even when the electric employed for inducing the electricity is in the form of a globe, we must employ functions of the distances that are pretty complex, and oblige us to have recourse to second fluxions. The mutual actions of two oblong conductors, of considerable diameters, give a problem that will occupy the first mathematicians; but which is quite improper for this scanty abstract. Nor is a minute knowledge of the disposition of the fluid of very important service. We may therefore content ourselves with a general representation of the state of the fluid in the following manner, which will give us a pretty distinct notion how it will act in most cases:

Let A (fig. 20.) be an overcharged sphere, and BC a conducting cylindric or prismatic body; draw bc parallel to BC, and erect perpendiculars Bb, Cc, Pp, &c., to represent the equable density of the fluid, when the conductor is in its natural state; but let Bb, Cc, Pp, &c., represent the unequal densities in its different points, while in the vicinity of the overcharged sphere. These ordinates must be bounded by a line dnr, which will cut the line bc in the point n of the perpendicular, drawn from the neutral point N of the conductor. The whole quantity of fluid in the conductor is represented by the parallelogram BCcb; which must therefore be equal to the space BCrad: the redundant fluid in any portion CP or PN is represented by the spaces rtp, or tpn; and the redundant matter, or deficient fluid, in any portion BQ, is represented by bdvq. The action of this body on any body placed near it, depends entirely on the area contained between this curve line and its axis bc. The only circumstance that we can ascertain with respect to this curve is, that the variations of curvature in every point are proportional to the forces exerted by the sphere A; and are therefore inversely as the squares of the distances from A. This property will be demonstrated by and bye. The place of n, and the magnitude of the ordinates, will vary as the diameter of the conductor varies. We shall consider this a little more particularly in some cases which will occur afterwards. We may consider the simplest case that can occur; namely, when the conductor is, like a wire, of no sensible diameter, nay, as containing only one row of particles.

Let AE (fig. 21.) be such a slender conducting ca. In a natural; and let Bb, Cc, Ee, &c., represent the density of the fluid which occupies it, being kept in this state of inequable density by the repulsion for some overcharged body. A particle in C is impelled in the direction CE by all the fluid on the side of A, and in the direction... direction CA by all the fluid on the side of E. The moving force, therefore, arises from the difference of these repulsions. When the diameter of the canal is constant, this arises only from the difference of density. The force of the element adjacent to E may therefore be expressed by the excess of D above C, and the action at the distance CD jointly. Therefore, drawing \( \frac{d}{c} \) parallel to AE, this force of the element E will be expressed by \( \frac{f}{c} \), repelling the particle in the direction CA. If CF be taken equal to CD, the force of the element at F will be expressed by \( \frac{f}{c} \), or \( \frac{f}{c} \), also impelling the particle in the direction CA. The joint action of these two elements therefore is \( \frac{d}{c} + \frac{f}{c} \).

If bce were a straight line, we should have \( \frac{d}{c} + \frac{f}{c} \), always proportional to \( \frac{c}{c} \); and it might be expressed by \( m \times c \), \( m \) being a number expressing what part of \( c \) the sum of \( d \) and \( f \) amounts to (perhaps \( \frac{1}{2} \), or \( \frac{1}{3} \), or \( \frac{1}{4} \), &c.). But in the case expressed in the figure, \( d \) does not increase so fast as \( c \), and \( f \) increases faster than \( c \). However, in the immediate neighbourhood of any point C, we may express the accelerating force tending towards A by \( \frac{m}{c} \), without any sensible error; that is, by \( \frac{m}{c} \); that is, by

the fluxion of the area of a hyperbola HD'G', having CC and CK for its asymptotes; and the whole action of the fluid between F and D, on the particle C, will be expressed by the area CDD'H'. Hence it follows, that the action of the smallest conceivable portion of the canal immediately adjoining to C on both sides, or the difference of the actions of the two adjoining elements, is equal to the action of all beyond it. This shows, that the state of compression is hardly affected by anything that is at a sensible distance from C; and that the density of the fluid, in an indefinitely slender canal, is, to all sensible uniform. The geometrical will also see, that the second fluxion of D'd is proportional to the force of the distant body. We learn, therefore, to much of the nature of the curve bce.

We are now in a condition to examine the communication of electricity by means of conducting canals (which is one of the most important articles of the study), having found that the fluid, in a very slender canal, is very nearly of uniform density throughout.

There can be no doubt but that, if a body B (fig. 22.) be overcharged or undercharged, any other body C, which communicates with it by a conducting canal, will also be overcharged or undercharged. It is evident, that if a body, in any state of electricity, be in the neighbourhood of an overcharged or undercharged body A, while it communicates with C by a canal leading from the side most remote from A, fluid will be driven from B into C, or attracted from C into B.

It is not, however, so clear, that when the canal leads from the side nearest to A (as in fig. 23.), fluid will be driven from B into C. We conceive the fluid to be moveable in the body and in this canal, but not to escape from it. Its motion, therefore, in this case, should, in the opinion of Mr Cavendish, resemble the running of water in a syphon by the pressure of the air. While the repulsion of the redundant fluid in A allows the bend of the syphon nearest to A to retain fluid, a current should take place from B along the short legs, in consequence of the superior action on the fluid in the long leg. But if the repulsion of A can drive the fluid out of the bend between E and F, Mr Cavendish thinks, that it does not appear that fluid will come up from B in opposition to the repulsion of A, and then run along to D. But fluid does not move, in either of these cases, on the principle of a syphon; because there is nothing to hinder the fluid from expanding in the part EDF. And we are rather disposed to think, that it will always move from B, over the bend, to C: For even if the fluid can be completely driven out of the bend EF, it must be done by degrees, and the fluid in the long leg will, from the very beginning of the action of A, be more moved from its place than that in the short leg; and therefore will yield to the compression, which acts transversely, and, by thus yielding more toward F than toward E, the fluid will rush through the contracted part, and go into C. We do not say this with full confidence; but are thus particular, on account of an important use that may be made of the experiment. For if the body A be undercharged, fluid will certainly be attracted from C, and passing round over the bend into B, however great the action of A may be. Perhaps this may be contrived, therefore, fluid, as to decide the long agitated question, Whether the electricity of excited glass be plus or minus? If it be found that this apparatus, being presented to the rubber of an electrical machine, diminishes the positive electricity of C, and increases that of B; but that, presenting the same apparatus to the prime conductor, makes little change—we may conclude, that the electricity of the prime conductor is positive. We have tried the experiment, paying attention to every circumstance that seemed likely to insure success; but we have always found hitherto, that the apparatus was equally affected by both electricities.

We must now consider the action of electrified bodies on the canals of communication; because this will give us the easiest method of ascertaining the proportion in which the expelling fluid is distributed between them. For when two bodies communicate by a canal, and have attained a permanent state, we must conceive that their opposite actions on the fluid moveable along this canal are in equilibrium, or are equal. This will generally be a much easier problem than their action on each other, since we have seen a little ago, that the fluid in a slender canal is of uniform density very nearly. A very few examples of the most important of the simple cases must suffice.

Therefore let AC a (fig. 24.) represent the edge of Action of a thin conducting circular plate, to which the slender plate on a canal CP is perpendicular in the centre. It is required to determine the action of the matter or fluid, uniformly spread over this plate, on the fluid moveable in the canal PC?

1. Required the action of a particle in A on the fluid in the whole canal? Join AP; and call CP \( x \), AP \( y \), and AC \( r \); and let \( f \) express the intensity of action at the distance \( r \), or the unit of the scale on which the lines are measured.

The action of A on P, in the direction AP, is \( \frac{f}{r^2} \). This, when estimated in the direction CD, is reduced to \( \frac{f}{y} \times \frac{x}{y} \); and is therefore \( f \times \frac{x}{y} \). Therefore the fluxion of the action, in the direction CP, on the whole canal, is \( f \times \frac{x}{y} \times \frac{x}{y} = f \times \frac{x^2}{y^2} \) (because \( x : y = y : x \)) \( = f \times \frac{x^2}{y^2} \). The variable part of the fluent is \( f \times \frac{1}{y} \), and the complete fluent is \( f \left( C - \frac{1}{y} \right) \), where \( C \) is a constant quantity, accommodated to the nature of the case. Now, the action must vanish when the canal vanishes, or when \( x = 0 \), and \( y = r \). Therefore \( C - \frac{1}{r} = 0 \), and \( C = \frac{1}{r} \); and the general expression of the action is \( f \left( \frac{1}{r} - \frac{1}{y} \right) = f \times \frac{y - r}{ry} \), expressing the action of a particle in the circumference of the plate on the fluid in the whole canal CP.

2. Required the action of the plate, whose diameter is \( A_a \), on the particle P?

Let \( a \) represent the area of a circle, whose diameter is \( = 1 \). Then \( a \times r \) is the area of the plate, and \( 2a \times r \) is the fluxion of this area; because \( r : y = y : r \), \( 2a \times r \) is \( = 2ayy \). Therefore the fluxion of the action of the plate on the particle P is \( f \times 2ayy \times \frac{x}{y} = 2fa \times \frac{x}{y} \). The fluent of this has for its variable part \( 2fa \times \frac{1}{y} \) (for when the particle P is given, \( x \) does not vary). This is \( 2fa \times \frac{x}{y} \). To complete this fluent, we must add a constant quantity, which shall make the fluent \( = 0 \) when the particle P is at an infinite distance; and therefore when \( x = y \). Therefore \( \frac{y}{y} - \frac{x}{y} = 0 \), or \( 1 - \frac{x}{y} = 0 \), or \( C = 1 \); and the complete fluent for the whole plate is \( 2fa \left( 1 - \frac{x}{y} \right) \).

The meaning of this expression may not occur to the reader: For \( 1 - \frac{x}{y} \) is evidently an abstract number; so is \( a \). Therefore the expression appears to have no reference to the size of the plate. But this agrees with the observation in n° 91, where it was shewn, that provided the angle of the cone or pyramid remained the same, the magnitude of the base made no change in its attraction or repulsion for a particle in the vertex.

It will appear by and bye, that \( 1 - \frac{x}{y} \) is a measure or function of a certain angle of a cone.

Cor. If PC be very small in proportion to AC, the action is nearly the same as if the plate were infinite:

For when the plate is infinite, \( \frac{x}{y} \) is \( = 0 \), and the action is \( = 1 \), whatever is the distance (see n° 91—93). Therefore, when \( x \) is very small in comparison of \( r \), and consequently of \( y \), \( 1 - \frac{x}{y} \) is very nearly \( = 1 \).

3. To find the action of the plate on the whole column?

The fluxion of this must be \( 2fa \times \left( 1 - \frac{x}{y} \right) \), or \( 2fa \left( \frac{x}{y} - \frac{x}{y} \right) \), or \( 2fa \times \left( x - y \right) \); because \( y = \frac{x}{y} \). The fluent of this has for its variable part \( 2fa \times \left( x - y \right) \). A constant quantity must be added, which shall make it \( = 0 \) when the column \( = 0 \); that is, when \( y = r \), and \( x = 0 \); that is, \( C - r = 0 \), and \( C = r \). Therefore the complete fluent is \( 2fa \left( x + r - y \right) \).

Thus have we arrived at a most simple expression of the attraction or repulsion of a plate for such a column, or portions of such a column. And it is most easy to easily constructed geometrically, so as to give us a sensible image of this action of easy conception and remembrance. It is as follows: Produce PC till CK = CA, and about the centre P describe the arch AI, cutting CK in L. Then \( 2fa \times IK \) is evidently the geometrical expression of the attraction or repulsion. This is plainly a cylinder, whose radius is a unit of the scale, and whose height is twice HK.

In like manner, by describing the arch AI round the centre P, we have \( 2fa \times IK \) for the action of the plate on the small column CP; and \( 2fa \times LI \) is the action of the plate on the portion PP.

The general meaning of the expression \( 2fa \times IK \) is, that the action of the whole plate on the column PC is the same as if all the fluid in the cylinder \( a \times 2IK \), were placed at the distance 1 from the acting particle.

From this proposition may be easily deduced some very useful corollaries by the help of the geometrical construction.

1. If PC be very great in comparison with AC, the action is nearly the same as if the column were infinitely extended; for in this case IK is very nearly \( = CK \), the difference being to the whole nearly as AC to twice AP.

2. If, in addition to this last condition, another column \( \rho C \) be very small in comparison of AC, then the action on PC is to that on \( \rho C \) very nearly as \( \rho C \) to AC. For it will appear that \( IK : IK = \rho C : AC \) very nearly. It is exactly so when \( CP : CA = CA : CP \); and it will always be in a greater proportion than that of \( \rho C \) to IK.

This will be found to be a very important observation.

The redundant fluid has hitherto been supposed to be uniformly spread over the plate; but this cannot be; because its mutual repulsion will cause it to be denser near the circumference. We have not determined, by a formula of easy application, what will be the variation of density. Therefore let us consider the result of the extreme case, and suppose the whole redundant fluid to be crowded into the circumference of the plate, as we saw that it must be on the surface of a globe.

In this case the action on the fluid in the canal will be \( fa \left( r - \frac{r^2}{y} \right) \). For the area of the plate is \( a \times r \), and the action of a particle in the circumference on the whole canal was shown (no. 129.) to be \( f \left( \frac{y - r}{r} \right) \). Therefore the action of the whole fluid crowded into the circumference is \( f a r \times \frac{y - r}{r} = f a r \frac{y - r}{r} \). It may be represented as follows: Describe the quadrant CBE, cutting AP and A in B and L. Draw BD and b parallel to PC. Then PB = y - r, and DC = r - y. Therefore the action is represented by \( f \) multiplying a cylinder, whose radius is 1 and height is DC. In like manner, dC is the height of the cylinder corresponding to the column CP, and Dd the height corresponding to PP.

Cor. 1. When CP is very great in comparison with CA, the point D is very near to A, and I is very near to C, and CD is to IK nearly in the ratio of equality. In this case the action of the fluid, uniformly spread over the plate, is nearly double of the action of the same fluid crowded round the circumference; for they are as cylinders, having the same bases and heights in the ratio of 2 IK to DC, which is nearly the ratio of 2 to 1.

2. On the other hand, when the column PC is very short, the action of the fluid spread uniformly over the plate is to its action, when crowded round the circumference, nearly in the ratio of AC to PC. For these actions are in the ratio of \( 2 f a \times i K \) to \( f a \times d C \), or as \( 2 f K \) to \( d C \), or nearly as \( 2 f C \) to \( d C \), or more nearly as \( 2 b d \) to \( d C \). But \( C d : b d = b d : 2 A + A d \), or nearly as \( b d : 2 C \). Therefore \( C d : b d = 2 C : 4 CA \) nearly.

Hence we see that the action on short columns is much more diminished by the receipt of the redundant fluid toward the circumference than that on long columns. Therefore, any external electric force which tends to send fluid along this canal, and from thence to spread it over the plate, will find into the plate a greater quantity of fluid than if the fluid remained ultimately in a state of uniform distribution over its surface; and that the odds will be greater when the canal is short.

Lastly, on this subject, if KL be taken equal to AP, or PL be equal to KL, the repulsion which all the fluid in the plate, collected in K, would exert on the fluid in the canal CL, is equal to the repulsion which the same fluid, constricted in the circumference, would exert on the column CP. For we have seen that the action of a particle in A on the whole column PC, when estimated in the direction PC, is \( \frac{y - r}{r} \); and it is well known that the action of a particle in K for the column CL is \( \frac{1}{KC} - \frac{1}{KL} \), or \( \frac{1}{r} - \frac{1}{y} = \frac{y - r}{ry} \).

Therefore the action of the whole fluid, collected in the circumference, on the column CP is equal to that of the same fluid, collected in K, on the columns CL.

Cor. 1. If the column CP is very long in proportion to AC or KC, the actions of the fluids in these two different situations are very nearly the same. The action of the fluid collected in K exceeds its action when collected in A only by its action on the small and remote column LP. The action of all the fluid collected at K on the column CP, is easily had by taking \( C = KP \). It is equal to the action of the same fluid placed in A on the column CL.

Cor. 2. The action of all the fluid uniformly spread, exerted on the column CP, is to the action of the same fluid collected in K, exerted on the column CL, as 2 IK to CD.

If the column CP is very great in proportion to AC, the half breadth of the plate, the action in the first case is very nearly double of the action in the other case, and is exactly in this proportion if CP is of infinite extent.

Cor. 3. If CNO be a spherical surface or shell of the same thickness and diameter as the plate Aa, and surface, containing redundant fluid of the same uniform density, field, or the action of this fluid on the column CL is double of that on the action of the fluid uniformly spread over the plate, on the column CP, and quadruple of the action of the fluid collected in the circumference: for the action is the same as if all were collected in the centre K, and the surface of the sphere is four times that of the plate, and therefore they are as 1K to 2 CD.

Let us now consider the comparative actions of different plates or spheres on the canals.

If two circular plates, DE, de (fig. 25.), or two Actions of spherical shells, ABO, abo, of equal diameters and two thicknesses with the plates, and containing redundant spheres, are fluid of equal density, communicate with infinitely extended straight canals OP, op, passing through their centres perpendicular to their surfaces, also containing fluid uniformly distributed and of equal density—the infinitely repulsions will be as the diameters. For the repulsion long of the spherical surfaces is the same as if all the fluid were collected at their centres; and the repulsion of the fluid uniformly forced over the surfaces of the plates is double of its repulsion if collected at the centres of these spheres; it follows, that the repulsions of the plates are proportional to those of the spheres. But because the repulsion of a plate whose radius is r was shown to be \( 2 a \times r + x - y \), and when the column is infinitely extended, x is equal to y, and \( r + x - y = r \), it follows, that the repulsions of the plates are as \( 2 a \times R \) and \( 2 a \times r \), or proportional to their diameters. Therefore the repulsions of the spheres are in the same proportion.

Cor. 1. If the canals are very long in proportion to the diameters of the plates or spheres, the repulsions are nearly in the same proportion.

Cor. 2. But as the lengths of the canals diminish, the repulsions approach to equality; for it was shown, that portion of the greatest repulsion was very small, the repulsion was to that for an infinite column as the length of the canal is to the radius of the plate. Therefore if the radius of the greater plate be (for example) double of that of the smaller, and the little column be \( \frac{1}{8} \)th of the radius, it will be \( \frac{1}{8} \)th of the radius of the smaller plate. Now \( \frac{1}{8} \)th of half the repulsion is equal to \( \frac{1}{8} \)th of the double repulsion. Also, in the case of the spheres, the repulsion of a particle at the surface, is as the quantity of fluid directly, and as the square of the radius inversely; but when the density is the same in both fluids, the quantity is as the surface, or as the square of the radius. Therefore the repulsions are equal.

Cor. 3. If the density of the fluid in two spherical shells be inversely as the diameters, the repulsions for an infinitely infinitely extended column of fluid are equal; for each action of repulsion as if all the fluid was collected in the centre.

Therefore, if the density, and consequently the quantity of redundant fluid be varied in any proportion, the repulsion will vary inversely in the same proportion. The repulsions will now be as the diameters:

\[ \text{as } CO \times \frac{1}{CO} \text{ to } co \times \frac{1}{co}, \text{ or in the ratio of equality.} \]

Cor. 4. When the quantities of redundant fluid in two spheres are proportional to their diameters, their repulsions for an infinitely extended canal are equal; for if this redundant fluid is confounded in the surfaces of the spheres, as it always will be when they consist of conducting matter, the densities are as the diameters inversely, because the surfaces are as the squares of the diameters. Therefore, by the last corollary, their actions on an infinitely extended canal are equal. But in spheres of non-conducting matter it may be differently disposed, in concentric shells of uniform density. This makes no change in the action on the fluid that is without the sphere, because each shell acts on it as if it were all collected in the centre. Therefore the repulsions are still equal.

Cor. 5. Two overcharged spheres, or spherical shells, OAB, oab (fig. 26.), communicating by an infinitely extended canal of conducting matter, contain quantities of redundant fluid proportional to their diameters; for their actions on the fluid in the interjacent canal must be in equilibrium, and therefore equal. This will be the case only when the quantities of fluid are in the proportion of their diameters.

When the canals are very long in proportion to the diameters of the spheres, the proportion of the quantities of redundant fluid will not greatly differ from that of the diameters.

Cor. 6. When the spheres of conducting matter are thus in equilibrium, the pressures of the fluid on their surfaces are inversely as their diameters; for the repulsion of a particle at the surface is the same with the tendency of that particle from the centre of the sphere, the actions being mutual. Now this is proportional to the quantity of redundant fluid directly, and to the square of the distance from the centre inversely, that is, to the diameter directly, and to the square of the diameter inversely.

Hence it follows, that the tendency to escape from the fluid the spheres is inversely as the diameter, all other circumstances being the same; for in as far as the escape proceeds from mere electric repulsion, it must follow this proportion. But there are evident proofs of the cooperation of other physical causes. We observe chemical compositions and decompositions accompanying the escape of electric fluid, and its influx into bodies; we are ignorant how far, and in what manner, these operations are affected by distance. Boscovich shows most convincingly, that the action of a particle (of whatever order of composition), on external atoms and particles, is surprisingly changed by a change in the distance and arrangement of its component atoms. A confounding, therefore, to a certain determined degree and lineal magnitude, may be necessary for giving occasion to some of those chemical operations that accompany, and perhaps occasion, the escape of the electric fluid. If this be the case (and it is demonstrable to be possible, if the operations of Nature be owing to attractions and repulsions), the escape must be defultory. It is actually so; and this confirms the opinion.

The public is indebted to Mr Cavendish for the preceding theorems on the action of spheres and circular plates. He has given them in a more abstract and general form, applicable to any law of electric action which experience may warrant. We have accommodated them to the inverse duplicate ratio of the distances, as a point sufficiently established; and we hope that we have rendered them more simple and perspicuous. We have availed ourselves of Mr Coulomb's demonstration of the uniform density in the canal, without which the theorems could not have been demonstrated. The minute quantity of the fluid in the canal can have no sensible effect on the disposition or proportion of the fluid in the plates or spheres.

It may be thought that the last corollary, respecting the equilibrium of two spheres, is not agreeable to hydrodynamical principles, which require the equality of the two forces which balance each other at the orifices of a slender cylindrical canal; whereas, in that corollary, the forces at the extremities of the canal are inversely as the diameters of the spheres or plates. This would be a valid objection, if the compelling forces acted only on the extremities of the canals; but they act on every particle through their whole length. It is not, therefore, the pressure at one end of the canal that is in equilibrium with the pressure at the other end, by the interpolation of the fluid. It is the pressure at one end, together with the sum of all the intermediate pressures in that direction, that is in equilibrium with all the pressure in the opposite direction. The pressures at the ends are only parts of the whole opposite pressures; they are the first in each account. In this manner a slender pipe, having a ball at each end, may be kept filled with mercury, while lying horizontal, if the air in each ball is of equal density. But if it be raised perpendicular to the horizon, it cannot remain filled from end to end, unless the air of the ball below be made so elastic by condensation, that its pressure on the lower orifice of the pipe exceed the pressure of the air in the upper ball on the other orifice by a force equal to the weight of the mercury, that is, to the aggregate of the action of gravity on each particle of mercury in the pipe. Therefore the repulsions of the spheres that we are speaking of are in equilibrium by the intervention of the fluid in the canal, in perfect conformity with the laws of hydrostatical pressure.

Mr Cavendish has pursued this subject much farther, and has considered the mutual action of more than two bodies, communicating with each other by canals of moveable fluid uniformly dense. But as we have not room for the whole of his valuable propositions, we selected those which were elementary and leading theorems, or such as will enable us to explain the most important phenomena. They are also such, as that the attentive reader will find no difficulty in the investigation of those which we have omitted.

Mr Cavendish's most general proposition is as follows: General

When an overcharged body communicates, by a canal of very great length, straight or crooked, with two or more similar bodies, also at a very great distance from each other, and all are in electric equilibrium, and consequently... consequently each body overcharged in a certain determined proportion, depending on its magnitude; if any two of these bodies are made to communicate in the same manner, their degrees of electricity are such, that no fluid will pass from one to the other; their mutual actions on the fluid in this canal being also in equilibrium. He brings out this by induction and combination of the single cases, each of which he demonstrates by means of the following theorem:

The action of an overcharged sphere ACB (fig. 25.) on the fluid in the whole of a canal dfP that is oblique, tending to impel the fluids in the direction of that canal, is equal to its action on the fluid in the whole of the rectilineal canal CP. Let bi be a minute portion of the straight canal, and df the portion of the crooked canal which is equidistant from the centre C of the sphere; draw the radii Cf, Cd, and the concentric arches bf, id, cutting fC in g; and draw ge perpendicular to df; the force acting on id, impelling it toward P, may be represented by bi. The same force acting on df, in the direction ef, must therefore be expressed by gf. This, when eliminated in the direction of the canal df, is reduced to ef; but it is exerted on each particle of df. Now df × ef = gf × ef; and df × ef = gf × ef = gf × bi; therefore the whole force on df, in the direction df, is equal to the force on id, in the direction id. Hence the truth of the proposition is manifest.

We beg the curious reader to apply this to the case in hand, and he will find, that the most complicated cases may all be reduced to the simple ones which we have demonstrated to be strictly true when the bodies are spheres or plates, and the canals infinitely long, and which are very nearly true when the canals are very long, and the bodies similar: And we now proceed to one compound case more, which includes all the most remarkable phenomena of electricity.

Let HK, AB, DF, and LM (fig. 27.), be four parallel and equal circular plates, two of which, HK and AB, communicate by a canal GC of indefinite extent, joining their centres, and perpendicular to their planes; let DF and LM be connected in the same manner, and let the two canals be in one straight line; let the plate HK be overcharged, and the plate LM just saturated. It is required to determine the disposition and proportion of the electric fluid in the plates which will make this condition of HK and LM possible and permanent, every thing being in equilibrium.

The plate HK being overcharged, and communicating with AB, AB must be overcharged in the same manner; and being also equal to HK, it must be overcharged in the same degree, containing an equal quantity of redundant fluid disposed in the same manner. To simplify the investigation, we shall first suppose that the redundant fluid is uniformly spread over the surfaces of both.

When the plates HK and AB are in this state, let the plates DF and LM be brought near them, as is represented in the figure, CE being the distance of the centres of AB and DF. It is evident, that the redundant fluid in AB will act on the natural moveable fluid in DF, and drive some of it along the canal EN, and render LM overcharged. Take off this redundant fluid in LM. This will diminish or annihilate the repulsion which it was beginning to exert on the canal EN; therefore more fluid will come out of DF, and again render LM overcharged. The redundant fluid in LM may again be taken off, in less quantity than before, as is plain. Do this repeatedly till no more can be taken off. But this will undoubtedly render DF undercharged, and it will now contain redundant matter. This will act on the fluid in the canal GC, and abstract it from G; therefore fluid will come out of HK into AB. HK will be less overcharged than before, and AB will be more overcharged. But the now increased quantity of redundant fluid in AB will act more strongly on the moveable fluid in DF, and drive more out of it. This will leave more redundant matter in it than before, and this will act as before on the fluid in the canal GC. This will go on, by repeatedly touching LM, till at last all is in equilibrium. Or this ultimate state may be produced at once by allowing LM to communicate with the ground. And now, in this permanent state of things, HK contains a certain quantity of redundant fluid; AB contains a greater quantity; DF contains redundant matter; and LM contains its natural quantity. The demand of the problem therefore is to determine the proportion of the redundant fluid in HK to that in AB, and the proportion of the redundant fluid in AB to the deficiency of fluid in DF. The dynamical considerations which determine these proportions are, &c. The repulsion of the redundant fluid in AB, for the fluid in the canal EN, must be precisely equal to the attraction of the redundant matter in DF for the same fluid in the canal; for LM, being saturated, is neutral. 2d, The repulsion of the redundant fluid in HK, for the whole fluid in the canal GC, must balance the excess of the repulsion of the redundant fluid in AB above the attraction of the redundant matter in DF for the same.

Let the redundant fluid in AB be = f. the redundant matter in DF = m. the redundant fluid in HK. = F.

Because HK and AB are equal, there can be no doubt; but that the fluid in those plates would be similarly disposed; and it is highly probable, that if AB be very near DF, the redundant fluid in AB, and the redundant matter in DF, will also be disposed nearly in the same manner. This will appear plainly when we consider with attention the forces acting between a very small portion of AB and the corresponding portion of DF. The probability that this is the case is so evident, that we apprehend it unnecessary to detail the proofs. We shall afterwards consider some circumstances which show that the disposition in the three plates will (though nearly similar) be nearer to a state of uniform distribution than if only AB and HK had been in action. Assuming therefore this similarity of distribution, it follows, that their actions on the fluid in the canals will be similar, and nearly proportional to their quantities.

Therefore let n be to n as the repulsion of the fluid in AB, for the fluid that would occupy CE, is to its repulsion for the fluid in EN or CG.

Then the action of AB on EN is \( f \times n - r \), and the action of DF on EN is \( mn \); therefore, because the plate LM is inactive, the actions of AB and DF on EN must balance each other, and \( f \times n - r = mn \), and \( m = f \times \frac{n}{n} \). The repulsion of \( f \) for the fluid in CG is \( fn \). The attraction of \( m \) for it is \( m \times n - 1 \); and because \( m = f \times \frac{n-1}{n} \), the attraction of \( m \) for the fluid in CG is \( f \times \frac{n-1}{n} \times n - 1 \). Therefore the repulsion of \( f \) is to the attraction of \( m \) as \( fn \) to \( f \times \frac{n-1}{n} \), or as \( fn^2 \) to \( f \times \frac{n-1}{n} \), or as \( n^2 \) to \( n - 1 \).

Call the repulsion of \( f \), and the attraction of \( m \) \( a \).

We have \( r : a = n^2 : n - 1 \)

and \( r : r - a = n^2 : (n - 1)^2 = n^2 : 2n - 1 \).

Therefore, because the repulsion of \( F \) is equal to this excess of \( r \) above \( a \), we have \( n^2 : 2n - 1 = f : F_1 \) and \( F = f \times \frac{2n - 1}{n^2} \), or \( f = F \times \frac{n^2}{2n - 1} \). Therefore, if \( n^2 \) is much greater than \( 2n - 1 \), the quantity of redundant fluid in AB will be much greater than the quantity in HK.

Now, when the electric action is inversely as the square of the distance, and EC is very small in comparison with AC, we have seen \( n^2 : 15 \) that \( 1 : n \) nearly \( ly = CE : CA \), or that \( n \) is nearly \( \frac{AC}{EC} \). When this is the case, and consequently \( n \) is a considerable number, we may take the number \( \frac{n^2}{2n - 1} \) without any great error. In this case \( f \) is equal to \( F \times \frac{n^2}{2n - 1} \) very nearly. Suppose CA to be six inches, and CE to be \( \frac{1}{6} \) of an inch; this will give \( n = 120 \), and \( f = 60 F \); or, more exactly, \( F = \frac{n^2}{2n - 1} = \frac{14400}{239} = 60 \).

If, instead of the plate HK, we employ a globe of the same diameter, \( f \) will be but half of this quantity, or \( f = F \times \frac{n^2}{4} \) (\( n^2 = 123, 124 \)).

It also appears, that when the plates AB and DF are very near to each other, and consequently \( n \) a large number, the deficiency in DF is very nearly equal to the redundancy in AB. In the example now given, \( m = \frac{59}{60} \) of \( f \), being \( f \times n - 1 \).

Yet this great deficiency in DF does not make it electrical on the side toward LM. It is just so much evacuated, that a particle of fluid at its surface has no tendency to enter or to quit it.

Lastly, this great quantity of fluid collected in AB does not render it more electrical than HK.

In general, things are in the condition treated of in \( n^2 22, 23 \), &c.

The attentive reader will readily see, that this account of the apparatus of four plates is only an approximation to the condition that really obtains under our observation. Our canals are not of indefinite length, nor occupied by fluid that is distributed with perfect uniformity; nor is the fluid uniformly spread over the surface of the plates. He will also see, that the real state of things, as they occur in our experiments, tends to diminish the great disproportion which this imaginary statement determines. But when the canals are very long, in comparison with the diameters of the plates, and AB is very near to DK, the difference from this determination is inconsiderable. We shall note these differences when we consider the remarkable phenomena that are explained by them.

In the mean time, we shall just mention some simple consequences of the present combination of plates.

Suppose AB touched by a body. Electric fluid will Method be communicated; but by no means all the redundant fluid contained in AB; only as much will quit it as will reduce it to a neutral state, if the body which touches it communicates with the ground; that is, till \( r \). By the attraction of the redundant matter in DF attracts fluid on the remote side of AB as much as the redundant fluid left in AB repels it. When this has been done, DF is no longer neutral; for the repulsion of AB for the fluid in EN is now diminished, and therefore the attraction of DF will prevail. If we now touch DF, it may again become neutral with respect to EN; but AB will now repel again the fluid in CG, and again be electric on that side by redundancy. Touching AB a second time takes more fluid from it, and DF again becomes electric by deficiency, and attracts fluid on that side.—And thus, by repeatedly touching AB and DF alternately, the great accumulation of fluid in AB may be exhausted, and the nearly equal deficiency in DF may be made up.

But this may be done in a much more expeditious way. Suppose a slender conducting canal \( abd \) brought near to the outsides of the plates, the end \( a \) being near to A, and the end \( d \) to D. The vicinity of \( a \) to A causes the fluid in \( ab \) to recede a little from \( a \) by the repulsion of the redundant fluid in AB. This will leave redundant matter in \( a \), which will strongly attract the redundant fluid from A, and \( a \) may receive a spark. But the consequence, even of a nearer approach of the fluid to the outward surface of A, will render the corresponding part of DF more attractive, and the retiring of fluid from \( a \) along \( ab \) will push some of its natural fluid toward \( d \); and thus A becomes more disposed to give out, and \( a \) to take it in, while \( d \) is disposed to emit, and D to attract. Thus every circumstance favours the passage of the whole, or almost the whole, redundant fluid to quit AB at A, to go along \( abd \), and to enter into DF at D.

It is plain, that there must be a strong tendency in the fluid in AB to go into DF, and that the plates must strongly attract each other. A particle of fluid situated between them tends toward DF with a force, which is to the sole repulsion of AB nearly as twice the redundant fluid in it to what it would contain if electrified to the same degree while standing alone.

With this particular and remarkable case of induced electricity, we shall conclude our explanation of Mr. Ampère's Theory of Electric Attraction and Repulsion. The reader will recollect, that we began the consideration of the disposition of the electric fluid in bodies, in order to deduce such legitimate consequences of the hypothetical law of action as we could compare with the phenomena.

These comparisons are abundantly supplied by the preceding paragraphs, particularly by \( n^2 74, 75, 76 \), by \( n^2 130 \), and by \( n^2 134 \).

Let a smooth metal sphere be electrified positively in any manner whatever, and then touch it with a small

The redundant fluid is divided between them in a proportion which the theory determines with accuracy. By the theory also the redundant fluid in both acts as if collected in the centre. Therefore the proportion of the repulsions is determined. These can be examined by our electrometer. But, as this measurement may be said to depend on the truth of the theory, we may examine this independent of it. Let the balls be equal. Then the redundant fluid is divided equally between the bodies, whatever be the law of action. Therefore observe the electrometer, as it is affected by the electrified body, both before and after the communication. This will give the positions of the electrometer which correspond to the quantities 2 and 1.

Take off the electricity of one of the balls by touching it, and then touch the other ball with it. This will reduce to \( \frac{1}{4} \) the original quantity \( \frac{1}{2} \), and therefore to \( \frac{1}{4} \)th of the original quantity. This will determine the value of another position of the electrometer. In like manner, we obtain \( \frac{1}{8} \)th, \( \frac{1}{16} \)th, &c. &c. Then, by touching a ball containing 1 with a ball containing \( \frac{1}{2} \), we get a position for \( \frac{1}{4} \), \( \frac{1}{8} \), &c. Proceeding in this way, we graduate our electrometer independently of all theory, and can now examine the electricity of bodies with confidence. The writer of this article took this method of examining his electrometer, not having then seen Mr Cavendish's dissertation, which gives another mode of measurement. He had the satisfaction of observing, in the first place, that the positions of the instrument which unquestionably indicated 1, \( \frac{1}{2} \), \( \frac{1}{4} \), &c. were precisely those which should indicate them if electric repulsion be inversely as the squares of the distances.

Having thus examined the electrometer, it was easy to give to balls any proposed degree of electricity, and then make a communication between balls of very different diameters. The electrometer informed us when the repeated abstractions by a small ball reduced the electricity of a large ball to \( \frac{1}{4} \), \( \frac{1}{8} \), &c. This showed the proportion of electricity contained in balls of different diameters. This was also found to be such as resulted from an action in the inverse duplicate ratio of the distances.

Long after this, Mr Cavendish's investigation pointed out the proportion of the redundant electric fluid in balls of different sizes joined by long wires; in no. 130, &c., these were examined—and found to be such as were so indicated by the electrometer.

And, lastly, the mode of accumulating great quantities of fluid by means of parallel plates, gave a third way of confronting the hypothetical law with experiment. The argument was no less satisfactory in this case; but the examination required attention to particulars not yet mentioned, which made the proportions between the fluid in HK and AB (fig. 27.) widely different from those mentioned in the preceding paragraphs. These circumstances are among the most curious and important in the whole study, and will be considered in their place.

We rest therefore with confidence on the truth of the law of electric action, assumed by us as a principle of explanation and investigation. It is quite needless and unprofitable to give any detail of the numerous experiments in which we confronted it with the phenomena. The scrupulous reader will get ample satisfaction from the excellent experiments of Mr Coulomb with his delicate electrometer. He will find them in the Memoirs of the Academy of Sciences of Paris for 1784, 1785, 1786, and 1787. Some of them are of the same kind with those employed by the writer of this article; others are of a different kind; and many are directed to another object, extremely curious and important in this study, namely, to discover how the electric fluid is disposed in bodies; and a third set are directed to an examination of the manner in which the electric fluid is diffused along imperfect conductors.

But we have already drawn this article to a great length, and must bring it to an end, by explaining some very remarkable phenomena, namely, the operation of the Leyden phial, the operation of the electrophorus, and the diffusion of electricity by sharp points and by imperfect conductors.

The observations of Mr Watson on the necessity of connecting the rubber of an electrical machine with the ground, might have suggested to philosophers the doctrine of plus and minus electricity, especially after the valuable discoveries of Mr Symmer and Cigna. A serious consideration of these general facts would have led to the theory of coated glass almost at its first appearance. But the historical fact was otherwise; and a considerable time elapsed between the first experiments with charged glass by Kleist, and the clear and satisfactory account given by Dr Franklin, of all the essential parts of the apparatus, and the probable procedure of nature in the phenomenon. The impermeability of glass by the electric fluid, and the consequent abstraction of it from the one side while it was accumulated on the other, suggested to his acute mind the leading principle of electrical philosophy; namely, that all the phenomena arise from the redundancy or deficiency of electric fluid, and that a certain quantity of it resides naturally in all bodies in a state of uniform distribution, and, in this state, produces no sensible effect. This was, in his hands, the inlet to the whole science; and the greatest part of what has been since added is a more difficult explanation how the redundancy or deficiency of electric fluid produces the observed phenomena. Dr Franklin deduced this leading principle from observing, that as fast as one side of a glass plate was electrified positively, the other side appeared negative, and that, unless the electricity of that side was communicated to other bodies, the other side could be no farther electrified. Having formed this opinion, the old observations of Watson, Symmer, and Cigna, were explained at once, and the explanation of the Leyden phial would have come in course. It is for these reasons, as much as for the important discovery of the fameses of electricity and of thunder, that Dr Franklin stands so high in the rank of philosophers, and is justly considered as the author of this department of natural science. Whatever credit may be due to the chemical speculations of De Luc, Wilcke, Winkler, and many others, who have attempted to affixate electricity with other operations of nature, by resolving the electric fluid into its constituent parts, all their explanations presuppose a mathematical and mechanical doctrine concerning the mode of action of the ingredients, which will either account for the total inactivity of the compound, or which will explain, in the very same manner, the action of the compound itself; yet all seem to content themselves with a vague and indistinct notion of this preliminary step, and have allowed themselves to speak of electrical atmospheres, and spheres of activity, and such other creatures of the mind, without once taking the trouble of considering whether those assumptions afforded any real explanation. How different was Newton's conduct. When he discovered that the planets attracted each other in the inverse duplicate ratio of the distances, and that terrestrial gravity was an instance of the same force, and that therefore the deflection of the earth was the effect of the accumulated weight of all its parts; he did not rashly affirm this of the planets, till he examined what would be the effect of the accumulated attraction in the abovementioned proportion.

Mr Epinus has the honour of first treading in the steps of our illustrious countryman; and he has done it with singular success in the explanation of the phenomena of attraction and repulsion, as we have already seen. In no part of the study has his success been so conspicuous as in the explanation of the curious and important phenomena of the Leyden phial. It only remained for him to account for the accumulation of such a prodigious quantity of this agent as was competent to the production of effects which seemed to exceed the similar effects in other cases, out of all proportion. Indeed, the disproportion is so great, as to make them appear to be of a different and incomparable nature. Dr Wilson's experiments in the pantheon are therefore precious, by shewing that nothing was wanted for the production of all the effects of the Leyden phial but a surface sufficiently extensive for containing a vast quantity of fluid, and so perfectly conducting as to admit of its simultaneous and rapid transference. Therefore we assert, that one of the chief merits of Mr Epinus's theory is the satisfactory explanation of the accumulation of this vast quantity of fluid in a small space. We trust, therefore, that our readers will peruse it with pleasure. But we must here observe, that Mr Epinus has not expressly done this in the work which we have already made so much use of, nor in any other that we know of. He has gone no farther than to point out to the mathematicians, that his hypothesis is adequate to the accounting for any degree of accumulation whatever. This he does in that part of his work which contains the formulæ of n° 38, 39, 40, 41, &c. And he afterwards shews, that all the phenomena of attraction and repulsion which are observed in the charged jar are precisely such as are necessary consequences of his theory.

It is to the Hon. Mr Cavendish that we are indebted for the satisfactory, the complete (and we may call it the popular), explanation of all the phenomena. Forming to himself the same notion of the mechanical properties of the electric fluid with Mr Epinus, he examined, with the patience, and much of the address, of a Newton, the action of such a fluid on the fluid around it, and the sensible effects on the bodies in which it resided; the disposition of it in a considerable variety of cases; and particularly its action on the fluid contained in slender canals and in parallel plates—till he arrived at a situation of things similar to the Leyden phial. And he then pointed out the precise degree of accumulation that was attainable, on different suppositions concerning the law of electric action in general.

We have given an abstract of this investigation accommodated to the inverse duplicate ratio of the distances. From this it appears (n° 135), that whatever quantity of electric fluid we can put into a circular plate 12 inches in diameter, by simple communication with the prime conductor of an electrical machine, we can accumulate 60 times as much in it by bringing the plate within 1/5th of an inch of another equal plate which communicates with the ground; and it appears in n° 139, that all this accumulated fluid may be transferred in an instant to the other plate (which is shown to be almost equally deprived of fluid), by connecting the two plates by a small wire.

But as it was also shown in that paragraph, that the force with which the accumulated fluid was attracted by the redundant matter in the other plate was exceedingly great, and consequently its tendency to escape was proportionally increased; this accumulation cannot be obtained unless we can prevent this spontaneous transference.

Here the non-conducting power of idio-electrics, inexplicable by means of the term "spheres," without any diminution, the action of the electric fluid on fluid or matter on the other side of them, comes to our aid, and we at once think of interpolating a plate of glass, or wax, or resin, or any other electric, between our conducting plates. Such is the immediate suggestion of a person's mind who entertains the Epinian notion of the electric fluid; and such, we are convinced, is the thought of all who imagine that they understand the phenomena of the Leyden phial. But those who attempt to explain electric action by means of what they call electric atmospheres of variable density or intensity, are not intitled to make any such inference, nor to expect any such phenomena as the Leyden phial exhibits. Electricity, they say, acts by the intervention of atmospheres: Therefore, whatever allows the propagation of this action (conceive it in any manner whatever), allows the propagation of these agents; and whatever does not conduct electric action, does not conduct the agents. Interpolated glass should therefore prevent all action on the other plate. This is true, even although it were possible (which we think it is not) to form a clear notion of the free passage of this material atmosphere in an instant, and this without any diminution of its quantity, and consequently of its action, by the displacement of so much of it by the solid matter of the body which it penetrates. Yet without this undiminished action of the electrified plate on the fluid, and on the matter, beyond the glass, and on the canal by which its fluid may be driven off into the general mass—no such accumulation can take place; and if the phenomena of the Leyden phial are agreeable to the results of the Epinian hypothesis, all explanation by atmospheres must be abandoned. Indeed when the partisans of the atmospheres attempt to explain their conceptions of them, they do not appear to differ from what are called "spheres of activity" (a phrase first used by Dr Gilbert of Colchester, in his celebrated work De Magnete et Corporibus Magneticis); and spheres of activity will be found nothing more than a figurative expression of some indistinct conception of action in every direction. When we use the words attraction and repulsion, we do not speak a whit more figuratively than when we use the general word action. These terms are all figurative, only attraction and repulsion have the advantage... vantage of specifying the direction in which we conceive the action to be exerted.

It therefore becomes still more interesting to the philosopher to compare the phenomena of charged glass with the Epiphanian theory. They afford an experimentum crucis in the question about electric atmospheres.

Let G (fig. 28.) represent the end of a prime conductor, furnished with Henley's electrometer. Let AB represent a round plate of tinfoil, pasted on a pane of glass which exceeds the tinfoil about two inches all round. The pane is fixed in a wooden foot, that it may stand upright and be shifted to any distance from the conductor. DF represents another plate of the same dimensions as AB, in the centre of which is a wire EN, having a small ball on the end N, to which is attached a Canton's electrometer. This wire passes through the wooden ball O, fastened to the insulating stand P. The glass pane must be very clean, dry, and warm. Connect the conductor G with AB by a wire reaching to the centre C. Turn the cylinder of the electrical machine slowly, till the electrometer rises to 30° or 40°, and note the number of turns. Take off the electricity, and having taken away the connecting wire GC, turn the machine again till the electrometer rises to the same height. The difference in the number of turns will give some notion of the expenditure of fluid necessary for electrifying the plate of tinfoil alone. This will be found to be very trifling when the electricity is in so moderate a degree. It is proper, however, to keep to this moderate degree of electrification, because when it is much higher, the dissipation from the edges of the plate is very great. Replace the wire, and again raise the electrometer to 30°. Now bring forward the plate DF, keeping it duly opposite and parallel to AB, and taking care not to touch it. It will produce no sensible change on the position of the electrometer till it come within four or three inches of the glass pane; and even when we bring it much nearer (if a spark do not fly from the glass pane to DF), the electrometer HG will sink but two or three degrees, and the electrometer at N will be little affected. Now remove the plate DF again to the distance of two or three feet, and attach to its ball N a bit of chain, or silver or gold thread, which will trail on the table. Again, raise the electrometer to 30°, and bring DF gradually forward to AB. The electrometer HG will gradually fall down, but will rise to its former height, if DF be withdrawn to its first situation. It is scarcely necessary to shew the conformity of this to the theory contained in n° 134, 135, &c. As the plate DF approaches, the redundant fluid in AB acts on the fluid in DF, and drives it to the remote end of the wire EN, as was shewn by the divergency of the balls at N; and then an accumulation begins in AB, and the electrometer HG falls, in the same manner as if part of the fluid in the prime conductor were communicated to AB. When DF communicates with the ground, the electrometer at N cannot shew any electricity, but much more fluid is now driven out of DF, in proportion as it is brought nearer to AB. Instead of connecting AB immediately with the prime conductor, let the wire GC have a plate at the end G, of the same dimensions as AB, having an electrometer attached to the side next to AB. Let this apparatus of two plates be electrified any how, and note the divergency of the electrometer at H, before DF, communicating with the ground, is brought near it, and then attend to the changes. We shall find the divergency of this electrometer correspond with the distance of DF very nearly as the theory requires.

While the plates AB and DF are near each other, especially when DF communicates with the ground, if we hang a pith-pall between them by a silk thread, it will be strongly attracted by the plate which is nearest to it, whether DF or AB; and having touched it, it will be briskly repelled, and attracted by the glass pane, which will repel it after contact, to be again attracted and repelled by DF; and thus bandied between the plates till all electricity disappear in both, the electrometer attached to H descending gradually all the while.

As all these phenomena are more remarkable in proportion as the plates are brought nearer, they are most of all when DF is applied close to the glass pane. And if, in this situation, we take any accurate method for measuring the intensity of the electricity in the plate HG, before the approach of DF, we shall find the diminution, occasioned by its coming into full contact with the pane, considerably greater than what is pointed out in n° 135. When we employed plates of 12 inches diameter, pasted on a pane one-fortieth of an inch in thickness, we found the diminution not less than 199 parts of 200; and we found that it required at least 200 times the revolution of the cylinder to raise the electrometer to the same height as before. This comparison is not susceptible of great accuracy, by reason of many circumstances, which will occur to an electrician. But in all the trials we have made, we are certain that the accumulation greatly exceeded that pointed out by the Epiphanian theory as improved by Mr Cavendish. And we must here observe, that we found this superiority more remarkable in some kinds of glass than others, and more remarkable in some other idio-electrics. We think that in general it was most remarkable in the coarse kinds of glass, provided they were uniformly transparent. We found it most remarkable in some common glasses which had exfoliated greatly by the weather; but we also found that such glasses were very apt to be burnt by the charge. The hardest and best London crown-glass seemed to accumulate less than any other; and a coloured glass, which when viewed by reflection seemed quite opaque, but appeared brown by transmitted light, admitted an accumulation greatly exceeding all that we have tried; but it could not be charged much higher without the certainty of being burnt. This diversity in the accumulation, which may be made in different kinds of glass, hinders us from comparing the absolute accumulations affixed by the theory with those which experiment gives us. But though we cannot make this comparison, we can make others which are equally satisfactory. We can discover what proportion there is between the accumulation in glasses of the same kind, as it may differ in thickness and in extent of surface. Using mirror glasses, which is of uniform and measurable thickness, and very flat plates, which come into accurate or equable contact—we found that the accumulation is inversely as the thickness of the plates; but with this exception, that when two plates were used instead of a plate of double thickness, the diminution by the increase of thickness was not nearly in the proportion of this increase. Instead

stead of being reduced to one-half, it was more than two thirds; and in the kind called Dutch plate, the diminution was inconsiderable.

The experiments with the Dutch and other double plates, suggested another instructive and pretty experiment. Observing these plates to cohere with considerable force, it was thought worth while to measure it; which was attempted in this manner: Two very flat brass plates A.B., DF (fig. 29.), furnished with wires and balls, were suspended, about three inches asunder, by silk threads, as represented in the figure. At G was attached a very fine silver wire, which hung very loose between it and the prime conductor, without coming near the table. Another was attached to N, which touched the table. A plate of mirror glass was set between them, as shown by Q.R. When this apparatus was electrified, the threads of suspension immediately began to deviate from the perpendicular, and the plates to approach the glass pane and each other. The pane was carefully shifted, so as to be kept in the exact middle between them. This result showed very plainly the pressure of the fluid on one of the plates, and the mutual attraction of the redundant matter and redundant fluid. This increased as the accumulation increased; and it was attempted to compare the attraction with the accumulation, by comparing the deviation of the suspending threads with that of the electrometer attached to the prime conductor; but we could not reconcile the series (which, however, was extremely regular) with the law of electric action. This harmony was probably disturbed by the force employed in raising the silver wires. When more flexible silver threads were used, much was lost by diffusion from the roughness of the thread. We did not think of employing a fine flaxen thread moistened; but, indeed, an agreement was hardly to be expected; because theory teaches us, that the distribution of the redundant fluid in A.B. will be extremely different from the distribution of the redundant matter in D.F., till the plates come very near each other. The accumulation in A.B. depends greatly on the law of distribution, being less (with any degree of redundancy) when the fluid is denser near the centre of the plate. Other circumstances concurred to disturb this trial; but the theory was abundantly confirmed by the experiment, which showed the strong attraction arising from the accumulation. This was so great, that although the plates were only three inches in diameter, and the glass pane was 1/4 of an inch thick, and the threads deviated about 18 degrees from the perpendicular—it required above an ounce weight, hung on the wire E.N., to separate the plates from the glass.

The experienced electrician need not be told, that by bringing the two ends of a bent wire in contact with the two plates (first touching D.F. with it) discharges the apparatus, and causes the plates to drop off from the pane. But he may farther observe, that if there be attached to each end of the discharging wire a downy feather, and if he first bring the end near the plate D.F., and observe the feather to be not at all, or but a very little, affected, and if he then bend round the other end toward the plate A.B., both feathers will immediately stretch out their fibres to the plates, and cling fast to them, long before the discharging spark is seen. This is a fine proof of the process of discharge, which begins by the induction of electricity on the ends of the discharging wire; first, negative electricity on the end that approaches A, and, in the same instant, opposite electricities at D and the adjoining end of the wire.

The following observation of Professor Richmann of St Peterburgh (the gentleman who fell a sacrifice to electrical studies by a thunder stroke from his apparatus) is extremely instructive and amusing. Let a glass pane be coated on both sides, and furnished with a small Richmann electrometer attached to the coatings. It is represented as if seen edgewise in fig. 30. Let it be charged positively (that is, by redundancy) by the coating A.B., while D.F. communicates with the ground. The electrometer A.a will stand out from the plate, and D.d will hang down close by its coating, as long as D.F. communicates with the ground. But as the electricity gradually diffuses by communication to the contiguous air, the ball a will gradually, but very slowly, fall down. We may judge of the intensity of the remaining electricity by the deviation of the electrometer, and we may conceive this deviation divided into degrees, indicating, not angles, but intensities, which we conceive as proportional to the redundancy or deficiency which occasion them.

If we take away the communication with the ground, we shall observe the ball a fall down very speedily, and then more slowly, till it reach about half of its first elevation. The ball d will at the same time rise to nearly the same height; the angle between the two electrometers continuing nearly the same as at first. When d has ceased to rise, both balls will very slowly descend, till the charge is lost by diffusion. If we touch D.F. during this descent, d will immediately fall down, and a will as suddenly rise nearly as much; the angle between the electrometers continuing nearly the same. Remove the finger from D.F.; and a will fall, and d will rise, to nearly their former places; and the slow descent of both will again continue. The same thing will happen if we touch A.B.; a will fall down close to the plate, and d will rise, &c. And this alternate touching of the coatings may be repeated some hundreds of times before the plate be discharged. If we suspend a crooked wire v.w., having two pith balls v and w from an inflated point m above the plate, it will vibrate with great rapidity, the balls striking the coatings alternately; and thus restoring the equilibrium by steps. Each stroke is accompanied by a spark.

All these phenomena are not only consequences of the theory, but their measures agree precisely with the computations deduced from the formulae in n° 22, 23, 24, accommodated to the case by means of n° 135 and 136, as we have verified by repeated trials. But it would occupy much room to trace the agreement here, and would fatigue such readers as are not familiarly conversant with fluxionary calculations. The inquisitive reader will get full conviction by perusing Répinus's Essay, Appendix i. A very distinct notion may be conceived of the whole process, by supposing that in a minute A.B. loses 1/9th of the unbalanced redundancy actually in it, and consequently diminishes as much in its action. It will be proved afterwards, that the dilutions in equal times are really in proportion to the superficial repulsions then exerted. We may also suppose, that the action of the redundant fluid, or redundant matter, in either coating, on the external fluid contiguous to it, is to its action on the fluid contiguous to the the other coating in the constant proportion of 10 to 9. We select this proportion for the simplicity of the computation. Then the difference of these actions is always 1/10th of the full action on the fluid contiguous to it. This is also an exact supposition in some particular cases, depending on the breadth of the coating and the thickness of the pane.

Now, let the primitive unbalanced repulsion between AB and the contiguous fluid of the electrometer be 100, while DF communicates with the ground. The ball a will stand at 100; the ball d will hang touching DF. Then a, by losing 1/10th, retains only 92, and would sink to 92. But as this destroys the equilibrium on the other side, fluid will enter into DF, so as to reduce the deficiency 1/10th. Therefore nine degrees of fluid will enter; and its action on a will be the same as if 1/10th of o, or 8.1, had been restored to AB. Therefore a will rise from 92 to 98.1; or it will sink in one minute from 100 to 98.1.

But if we have cut off the communication of DF with the ground, this quantity of fluid cannot come into DF; and the quantity which really comes into it from the air will be to that which escapes from A as the attraction on the side of DF to the repulsion on the side of AB. By the diminution of the repulsion 1/10th, and the want of 9 degrees of fluid in DF to balance it, DF acquires an attraction for fluid, which may be called q. Therefore, since 1/10th of the primitive repulsion of AB has diffused 10 measures of fluid in the minute, the attraction of DF will cause it to acquire 1/10th of q, or 0.9, from the air in the same minute. At the end of the minute, therefore, there remains an unbalanced attraction for fluid = 8.1; and consequently an unbalanced repulsion between the redundant matter in DF, and that in the ball d. Therefore d will rise to 8.1. But a cannot now be at 98.1; because DF has not acquired q measures of fluid, but only 1/10th of one measure. Therefore a, instead of rising from 92 to 98.1, will only rise to 90 + 1/10th × 1/10th; that is, to 90.81.

At the close of the minute, therefore, a is at 90.81, and d is at 8.1, and their distance is 98.91. In the next minute, AB will lose 1/10th of the remaining unbalanced electricity of that side, and DF will now acquire a greater proportion than before; because its former unbalanced attraction gets an addition equal to 1/10th of the loss of AB. This will make a larger compensation in the action on a, and a will not fall so much as before. And because in the succeeding minutes the attraction of DF for fluid is increasing, and the repulsion of AB is diminishing, the compensation in the action on a, by the increased attraction of DF, continues to increase, and the descent of a grows continually slower; consequently a time must come, when the repulsion of AB for fluid is to the attraction of DF for it, nearly in the proportion of 10 to 9. When this state obtains, d will rise no more; because the receipt of fluid by DF, being now 1/10th of the loss by AB, it will exactly compensate the additional attraction of DF for fluid, occasioned by that loss. The next loss by AB not being so great, and the next receipt by DF continuing the same, by reason of its undiminished attraction, there will be a greater compensation in the action on a, which will prevent its descending so fast; and there will be more than a compensation for the additional attraction of DF for fluid; that is, the fluid which has now come into DF will render it, and also the ball d, less negative than before; and therefore they will not repel so strongly. Therefore d must now descend. It is evident, that similar reasons will still subsist for the flow deficient of a, and the slower descent of d, till all redundancy and deficiency are at an end.

This maximum of the elevation of d happens when a has descended about one-half of its elevation; that is, when the unbalanced repulsion of AB is reduced to about one half. For if one half of the unbalanced fluid be really taken out of AB, and if DF can get no supply whatever, it must acquire an attraction corresponding to 1/10th of this; and if the supply by the air be now opened to it, things will go on in the way already described, till all is discharged.

This account of the process is only an approximation; because we have supposed the changes to happen in a deftory manner, as in the popular way of explaining the acceleration of gravity. The rise of d is not at an end till the attraction of DF for fluid is to the repulsion of AB as 19 to 20.

But if we interrupt this progress in any period of it, by touching DF, we immediately render it neutral, and d falls quite down, in consequence of receiving a complete supply of fluid. But this must change the state of AB, and cause it to rise 1/10th of the descent of d. As a and d were nearly at an equal height before DF was touched, it is plain that a will rise to nearly twice its present height; after which, the same series of phenomena will be repeated as soon as the finger is removed from DF.

If, instead of touching DF, we touch AB, the same things must happen; a must fall down, and d must rise to nearly twice its present height, and all will go on as before, after removing the finger. Lastly, if instead of allowing either side to touch the ground alternately, we only touch it with a small insulated body, such as the wire with the balls v and u, the ball attached to the side touched sinks, till the electricity is shared between the coating and the wire with balls. The ball attached to the other coating rises 1/10th of the sinking of the first ball. The crooked wire ball is now repelled by the coating which it touched, and the other ball is brought near to the other coating, and must be attracted by it, because the electricities are opposite. This operation evidently tends to transfer the redundant fluid by degrees to the side where it is deficient. It needs no explanation. We shall only mention a thing which we have always observed, without being able to account for it. The vibration of the wire acquires a certain rapidity, which continues for a long while, and suddenly accelerates greatly, and immediately afterwards ceases altogether.

This pretty experiment of Professor Richmann will be found very instructive; and will enable us to understand the operation of the electrophorus, and to see the great mistake of those who say that it is perfectly similar to a discharged glass plate.

Thus, then, we see, that all the classes of phenomena, connected with attraction and repulsion, are precisely such as would result from the action of a fluid so demonstrated. The complete undiminished action of the charged cause of those phenomena on the other side of the imposed non-conductor of that cause is demonstrated, and... all explanation by the mechanical action of material elastic atmospheres of variable density must be abandoned, and the infinitely simpler explanation by the attractive and repulsive forces of the fluid itself must be preferred.

So happily does the Franklinian theory of positive and negative electricity explain the phenomena, when a suitable notion is formed of the manner of action of this fluid. We cannot but think that this is attained, when, to the general doctrine of Epinus, we add the specification of the law of action, so fully verified by the experiments of Mr Coulomb, which are in the hands of the public; and are of that simple nature, that any careful experimenter can convince himself of their accuracy (See n° 144.). We may therefore proceed with some confidence, and apply this doctrine even to cases where experiment does not offer itself for proof.

Dr Franklin affirms that electric fluid cannot be thrown into one side of the coated pane unless it be abstracted from the other; and that therefore the charged glass contains no more than it did before charging. We indeed find, that we cannot charge the inside, if the outside do not communicate with the ground. He proves it also by saying, that if a person, when insulated, discharges a glass through his own body, he is not found electrified: And he infers, as a necessary consequence of this, that a series of any number of jars may be charged by the same turns of a machine, if we make the outside of the first communicate with the inside of the second, and the outside of the second with the inside of the third; and so on; and the outside of the last communicate with the ground. Having made the trial, and having found that more turns of the machine were necessary, he attributes this to dissipation into the air by the communication. But our theory teaches us otherwise. We learn from it, that the redundant matter in the plate DF is less than the redundant fluid in AB, in the proportion of \( \frac{n}{n-1} \) to \( \frac{n}{n} \); and therefore the redundant fluid in the overcharged side of the next plate is no greater. The charge or redundancy in the nth jar of the series will therefore be \( \frac{n-1}{n} \). Thus,

if \( n \), or the charge of the 1st jar, be 60, the charge of the 10th jar will be nearly 51. Although a coated plate cannot be charged, unless one of the coatings communicate with the ground, it may be electrified as much as one of the coatings can be alone. And this is seen in our attempt to charge it: For as soon as we attempt to electrify one side, the other is electrified also; for it gives a spark, which no electrified body will do. Also, when we discharge a jar by an insulated discharger, we always leave it electrical in the same way with the body from which it was charged. If a man is not found electrified after having discharged a jar through his own body, it is owing to the great surface of his body, which reduces the simple electrification of a side of the jar to a very insignificant and inensible quantity.

Wilcke (and we believe Franklin before him) maintains, that when the jar has been charged, by connecting one side with the prime conductor and the other with the rubber, it is neutral and inactive on both sides. But this is not so; and a slight reflection might have convinced them that it cannot be so: if it were, the jar could not be discharged. Each side, while connected with the machine, must be in the condition of the part with which it is connected, and in a disposition to take or give. If the trial be carefully made, it will be found to be equally active on both sides; and the discharging rod, having down on its ends, will shew this in an unequivocal manner, and shew that its condition differs in this respect from that of a jar charged in the ordinary way. It is in the maximum state of Richman's plate, described in n° 156. when it rises no more.

In discharging a jar A, if instead of the outside communicating with the inside by a wire, we make it communicate with the inside of a second jar B, while the outside of B is made to communicate with the inside of A, we shall find B charged by the discharge of A; and that the discharge of A is not complete, the charge always remaining, whatever may have been the magnitude of \( n \).

We may infer from this experiment, that when a shock is given to a number of persons, \( a, b, c, \ldots \), we infer are not to conclude, that the fluid which comes into the deficient side of the jar is the same which came out of the redundant side. The whole, or perhaps only a part, of the moveable fluid in the person \( a \) goes into \( b \), replacing as much as has passed from \( b \) into \( c \), &c. Indeed, where the canal is a slender wire, we may grant that great part of the individual particles of fluid which were accumulated on the inside of the jar have gone into the outside. Perhaps the quantity transferred, even in what we call a very great discharge, may be but a small proportion of what naturally belongs to a body. This may be the reason why a charge will not melt more than a certain length of wire. Mr Cavendish ascribes this to the greater obstruction in a longer wire; but this does not appear too probable. A greater obstruction would occasion a longer delay of the transference; and therefore the action of the same quantity would be longer continued. He proves, that a metal wire conducts many hundred times faster than water; yet, when water is dissipated by a discharge, it is found to have actually conducted a much greater proportion of the whole charge. We ascribe it chiefly to this, that, in a short wire, the quantity transferred exceeds the whole quantity belonging to the wire.

It is purely needless to prove that the theory of Leyden Leyden phial is the same with that of the coated pane. The only difference is, that we are not so able to tell the disposition of the accumulated fluid, and the evacuated matter, in every figure. When the phial is of a globular form, and of uniform thickness, with an exceedingly small neck, we then know the disposition more accurately than in a plate. The redundant fluid is then uniformly distributed. If we could insure the uniformity of thickness, such a phial would be an excellent unit for measuring all other charges by; but we can neither insure this (by the manner of working glasses), nor measure its want of uniformity: whereas we can have mirror plates made of precisely equal thickness, and measure it. This, therefore, must be taken as our unit.

And here we remark, that this gives us the most perfect of all methods for comparing our theory with experiment. We must take two plates, of the same verifying glasses and the same thickness, but of different dimensions of coated surface. We must charge both by very long conducting wires on both sides, and then measure how... how often the charge of the one is contained in the other. Mr Cavendish has given an unexceptionable method of doing this independent of all theory. As it applies equally to jars, however irregular, we shall take it altogether.

When a jar is charged, observe the electrometer connected with it, and immediately communicate the charge to another equal jar (the perfect equality being previously ascertained by the methods, which will appear immediately). Again note the electrometer. This will give the elevation, which indicates one-half, independent of all theory. Now electrify a jar, or a row of equal jars, to the same degree with the first, and communicate the charge to a coated mirror plate, discharging the plate after each communication, till the electrometer reaches the degree which indicates one-half. This shews how often the charge of the plate is contained in that of the jar or row of jars.

Let the charge of the plate be to that of the jars as $x$ to 1. Then, by each communication, the electricity is diminished in the proportion of $\frac{1+x}{1}$. If $m$ communications have been made, it will be reduced in the proportion of $\frac{1+x^m}{1}$ to 1. Therefore $1+x^m = 2$, and $1+x = \sqrt{2}$, and $x = \sqrt{2} - 1$.

When $x$ is small in proportion to 1, we shall be very near the truth, by multiplying the number of communications by 1444, and subtracting 0.5 from the product. The remainder shews how often the charge of the plate is contained in that of the jars, or $\frac{1}{x}$.

Thus may the perfect equality of two jars be ascertained; and the one which exceeds, on trial, may be reduced to equality by cutting off a little of the coating. An electrician should have a pair of small jars or phials so adjusted. It will serve to discover in a minute or two the mark of one-half electricity for any electrometer, and for any degree; as also for measuring jars, batteries, shocks, &c. much more accurately than any other method: because such phials, constructed as we shall describe immediately, may be made so neutral, and so retentive, that the quantity which dissipates during the handling becomes quite insignificant in proportion to the quantity remaining; whereas, in all experiments with electrometers, constructed with the most curious attention, the dissipations are great in proportion to the whole, and are capricious.

It was chiefly by this method that the writer of this article, having read Mr Cavendish's paper, compared the measures given by experiment with those which result from an action in the inverse duplicate ratio of the distance. When the charges were moderate, the coincidence was perfect; when the charges were great, the large plates contained a little more. This is plainly owing to their being less disposed to dissipate from the edges.

We may now follow with some confidence the practical maxims deducible from the theory for the construction of this accumulating apparatus. The theory prescribes a very conducting coating, in close and uninterrupted contact: it prescribes an extensive surface, and a thin plate of idi-electric substance. Accordingly, all these are in fact attended by a more powerful effect. Metal is found to be far preferable to water, which was first employed, having been suggested by the original experiments of Gray, Klenz, and Cuneus. A continuous plating is prescribed, in preference to some methods commonly practised; such as filling the jar with brass dust, or gold leaf, or covering its surface with filings stuck on with gum water, or coating the inside with an amalgam of mercury and tin. This last appears, by reflection from the outside, to give a very continuous coating; but if we hold the jar between the eye and the light, we may perceive that it is only like the covering with a cobweb. Yet there are cases where these imperfect coatings only are practicable, and some rare ones where they are preferable. In the Hint for medical exhibition of electricity, where the purpose intended is supposed to require the transfusion of a great quantity of the electric fluid, any thing that can diminish the irritating smartness of the spark is desirable. This is greatly affected by those imperfect coatings. Small shocks, which convey the same quantity of fluid with the sharp pungent and alarming spark from a large surface, are quite soft and inoffensive, greatly resembling the spasmodic quivering, sometimes felt in the lip or eyelid, and will not alarm the most fearful patient.

Close contact of the metallic coating is observed to how to increase the effect of the charge. But it is also found, prevent the that it greatly increases the risk of bursting the glass bursting by spontaneous discharge through its substance. An experienced electrician (we think it is Mr Brookes of Norwich) says, that since he has employed paper covered with tinfoil, with the paper next the glass, instead of the foil itself, he has never had a jar burst; whereas the accident had been very frequent before. The theory justifies this observation. Paper is an imperfect conductor, even when soaked with flour paste; and the transfusion, though rapid, is not instantaneous nor defective, but begins faintly, and swells to a maximum. It operates on the glass, like gradual warming instead of the sudden application of great heat.

Mr Cuthbertson, an excellent artist in all electrical apparatus, and inventor of the best air-pump, has made a curious observation on this subject. He says that he has uniformly observed, that jars take a much greater charge (nearly one-third), if the inside be considerably damped, by blowing into it with a tube reaching to the bottom (Nicholson's Journal, March 1799).—We must acknowledge, that we can form no distinct conception of what Mr Cuthbertson calls an undulation of the elastic atmosphere. We do not know whether he means that the atmosphere is actually undulating as water, or as air in the production of sound, its parts being in a reciprocating motion; or whether he only means that this atmosphere consists of quiescent strata, alternately denser and rarer. Nor can we form any notion how either of these undulations contributes to the explosion, or prevents it. We are really but very imperfectly acquainted with that part of the science which should determine the precise accumulation that produces the defective transference. We mentioned one necessary consequence of the action inversely as the square of the distance, which has some relation to this question, viz., that a particle, making part of a spherical surface, is twice as much repelled when it has just quitted the surface as when it made part of it, provided its place be immediately supplied. And another circumstance has been frequently mentioned, viz., that a greater, and perhaps much greater, force is necessary for enabling a particle

particle of fluid to quit the last series of particles of the solid matter than for producing almost any conflagration. But we are not certain that these circumstances are of sufficient influence to explain the whole of the event. Valens quantum valere possit. Yet we are of opinion that Mr Cuthbertson has assigned the true cause, namely, the imperfect coating of the inside of the glass. When we come to the explanation of the escape of electricity along imperfect conductors, we hope that it will appear, that the disposition to escape must be greatly diminished by a charge, which diffuses the fluid so, that in no place the conflagration is remarkably greater than in another part very near it, and the density changes everywhere slowly.

With respect to the form of the coated glass, the theory prefers that which will occasion such a distribution of the electric fluid as shall make its repulsion for the fluid in the canal which connects it with the prime conductor as little as possible. In this respect, it would seem that a plate is the best, and a globe the worst; but if both are very thin, the difference cannot be considerable. Our experience, however, seems to indicate the opposite maxim as the most proper. We have uniformly found a globe to be far preferable to a plate of the same thickness, and that a plate was generally the weakest form. It must be owned, that we have not yet been able to ascertain by the theory what is the exact distribution of the redundant fluid in a plate. In a sphere, it must be uniformly spread over the surface. We must also attribute part of the inferiority of the plate to its greater tendency to dissipation from the edges. If a plate be coated in a star-like form, with slender projecting points, we shall observe them luminous in the dark, almost at the beginning of the accumulation; and the plate will discharge itself by these points, over the uncoated part, before it has attained any considerable strength. These forms are least exposed to this deterioration which have the least circumference to the same quantity of surface. We have always found, that a square coating will not receive a more powerful charge without exploding than a circular one of the same breadth, although it contains a fourth more surface; and this although any visible escape from the angles be prevented by covering the outline with sealing wax. Of all forms, therefore, a globe, with a very narrow, but long neck, is the most retentive. But it is very difficult to coat the inside of such a vessel. The balloons used in chemical distillations make excellent jars, and can be easily coated internally when the neck will admit the hand. The thinnest of tinfoil may be used, by first pasting it on paper, and then applying it either with the foil or the paper next the glass. It should be cut into guttlets, as in the covering of terrestrial globes; and they should be put on overlapping about half an inch. The middle of the bottom is then coated with a circular piece. The great bottles for holding the mineral acids are also good jars, but inferior to the balloons, because they are very thick in the bottom, and for some distance from it. A box of balloons contains more effective surface than an equal box of jars of the same diameter and height of coating.

The most compendious battery may be made in the following manner: Choose some very flat and thin panes of the best crown glass, coat a circle (a b c d), (fig. 31.) in the middle of both surfaces, so as to leave a sufficient border uncoated for preventing a spontaneous discharge; let each of them have a narrow lip of tinfoil reaching from the coating to the edge on one side; and a similar lip leading to the opposite edge on the other side. Lay them on each other, so that the lips of two adjoining plates may coincide. Connect all the ends of these lips on one side together by a slip of the same foil, or a wire which touches them all. Then, connecting one of these collecting slips with the prime conductor, and the other with the ground, we may charge and discharge the whole together. If the panes be round, or exact squares, we may employ as few of them together as we please, by letting the whole in an open frame, like an old-fashioned plate-warmer; and then turning the set which we would employ together at right angles to the rest. This evidently detaches the two parcels from each other. This battery may be varied in many ways; and if the whole is always to be employed together, we may make it extremely retentive, by covering the uncoated border of the plate with melted pitch, and, while it is soft, pressing down its neighbour on it till the metallic coatings touch. For greater variability this may be done in parcels of the whole.

On the same principle, a most compendious battery may be made by alternate layers of tinfoil and hard varnish, or by coating plates of very clear and dry Muscovy glass. But these must be used with caution, lest they be burst by a spontaneous discharge; in which case we cannot discover where the flaw has happened. They make a surprising accumulation, without shewing any vivid electricity.

We have made a very fine electric phial for carrying about, by forming tin-plate (iron plate tinned) into somewhat of a phial shape, with a long neck. We then covered this with a coating of fine sealing wax, about \(\frac{1}{10}\)th of an inch thick, quite to the end of the neck, and coated the sealing wax, all but the neck, with tinfoil. It is plain that the sealing wax is the coated idio-electric, and that the tin-plate phial serves for an inner coating and wire. The dissipation is almost nothing if the neck be very small; and it only requires a little caution to avoid bursting by too high a charge. Even this may be prevented by coating the sealing wax so near to the end of the neck, that a spontaneous discharge must happen before the accumulation is too great.

It is well known that the discharge happens when the discharging balls are at a considerable distance from each other; therefore only as much is discharged as corresponds to that distance. This is one cause of the residuum of a discharge which sometimes is pretty considerable. Some experiments require the very utmost force of the charge. It is therefore proper to make the discharge as close and abrupt as possible. But the most rapid approach that we can make of the discharger is nothing in comparison with the velocity with which the fluid seems to fly off, and will therefore have but small influence in making a more instantaneous and complete discharge. Theory points out the following method: Let a very thick plate of glass (half an inch), of several inches diameter, be put between the discharging balls, which should, in this case, be small, and let these balls be strongly pressed against it by a spring. While the charge is going on, a very small part of the glass plate, round round the points of contact, will receive a weak and useless charge; but this will not hinder the battery from acquiring the same intensity of charge. When this is completed, let the intervening glass plate be briskly withdrawn. The discharge will begin with an intensity which is unattainable in the ordinary manner of proceeding.

Much has been said of the lateral explosion. It appears, that in some of the prodigious transferences of electricity that have taken place in the discharge of great surfaces through wires barely sufficient to conduct them, flashes of light are thrown off laterally; but the most delicate electrometer, it is said, is not affected. The fact is not accurately narrated; we have always observed a very delicate electrometer to be affected. The passage of such a quantity of fluid is almost equivalent to the co-existence of it in any given section of the wire; but it remains there for so short a time, that, acting as an accelerating force, it cannot produce a very sensible motion. It is like the discharging a pistol ball through a sheet of paper hanging loosely. It goes through it without very sensibly agitating it.

It has sometimes appeared to us probable, that, by means of this lateral explosion, the direction of the current may be discovered. Let the jar a b (fig. 32.) be discharged by a wire a c d e f, interrupted at c d by the coating of a very thin plate of talc; let the coating also be very thin. There must be some obstruction to the motion, which must cause the fluid to press on the sides or surfaces of the coating, just as the obstruction to the motion of water in a pipe (arising from friction, or even from material obstacles in the pipe) causes the water to press on the sides of the pipe. Therefore if a wire connect the other coating with the ground, we should expect that fluid will be expelled along this wire, and a charge be given to the plate of talc. Now whether the course in this apparatus be from b to a, or from a to b, if any charge be acquired by c d, it will probably be positive in c d, and negative in a b; for it is electric fluid that is supposed to pass; therefore we should always have one species of electricity, whether a has been charged by glass or by sealing wax; and this species will indicate which is positive. We have said "probably"—for it is not impossible that it may be otherwise. If the abstraction at d be supposed more powerful than the supplying force at c, the same obstruction may perhaps keep the plate c d in an adsorbing state, just as water descending in a vertical pipe, into which it is pressed by a very small head of water in the cistern, instead of pressing the sides of the pipe, rather draws them inwards, as is well known. This seems, at any rate, an interesting experiment; for we must acknowledge, that there still hangs a mysterious curtain before a theory which deduces so much from the presence of a substance which we have never been able to exhibit alone, and where we do not know when it abounds and when it is deficient. It is like the phlogiston of Stahl, or the caloric of Lavoisier. It will be proper to use the thinnest plate of talc to be charged, and to connect it with another coated plate of half the diameter, or less, in order to increase the accumulation. It seems by no means a desperate case.

The theory of coated glass now explained, might have been treated with more precision, and the formulæ deduced in the beginning of this article might have been employed for stating the sum total of the acting forces, and thus demonstrating with precision the truth of the general result; and indeed it was with such a view that they were premised: but they would have been considerably complicated in the present case; for however thin we suppose the tinfoil coatings to be, it is evident from n° 92, &c. that each coating will consist of three strata; of which the two outermost are active, and must have their forces stated, and the statement of the force of each stratum would have consisted of three terms. This would have been very embarrassing to some readers; and the force of the conclusion would not, after all, have been much more convincing than we hope the above more loose and popular account has been.

We have hitherto considered the non-electric coatings only, and have not attended to what may chance charge result in the substance of the coated electrica them. May not part, at least, of the redundant fluid be lodged in one superficial stratum of the glass? or, if it do not penetrate it, may it not adhere to the surface, and drive off from the other surface, or stratum, a part of what naturally adheres to it? Till Dr Franklin's notions on the subject became prevalent, no person doubted this. The electric was supposed to contain or to accumulate in its surface all the electricity that we know. But the first suggestion of Dr Franklin's experiments certainly was, that the electric plate or vessel acted merely as an obstacle, preventing the fluid from flying from the body where it was redundant to that where it was deficient. It is therefore an important question in the science, whether the glass or electric concerned in these phenomena serve any other purpose besides the mere prevention of the redundant fluid from flying to the negative plate?

Now it appears, at the very first, that this is the case. For if a glass be coated only on one side, and be electrified on that side, we obtain a strong spark from the other side by bringing the knuckle near it; and this may be obtained for some time from one spot of that surface; and, after this, we get no more from that spot; but get sparks, with the same vivacity, and in the same number, from any other spot that is opposite to the coating on the other side. In this manner we can obtain a succession of sparks from every inch of surface opposite to the coating, and from no other part. But what puts this question beyond all doubt is, that if we now lay a metal coating on the surface from which the sparks have been drawn in this manner, and make a communication between the two metallic coatings, by means of a bent wire, we obtain a perfect discharge. To complete the proof, we need only observe, that this experiment succeeds whether the glass has been electrified by excited glass or by excited sealing wax. Therefore the coated surface may receive the electric fluid by the coating, as we see plainly that it is attracted by the coating. The use of the coatings may be nothing more than than to act as conductors to every part of the surface of the electric. None of these thoughts escaped the penetrating and sagacious mind of Dr Franklin. He immediately put it to the test of experiment; and, laying a moveable metallic coating on both surfaces, he found the glass charge perfectly well. He lifted off the coatings; which operation was accompanied by flashes. flashes of light between the metallic coverings and the glass from which he separated them. Having removed the coatings, he applied others, completed the circle, and obtained a perfect discharge, not distinguishable from what he would have obtained from the first coatings.

Thus was it demonstrated, that the glass plate itself acquired by charging a redundant stratum on one side, and a deficient stratum on the other side; and we now see, at once, the reason why the accumulation turns out greater than what is determined by the theory. The distance between the redundant and deficient stratum is less than the thickness of the glass; and this, perhaps, in an unknown proportion.

This precious experiment of Dr Franklin was repeated by every electrician, and varied in a thousand ways. No philosopher has carried this research farther than Becaria; and he has given ground for a most important discovery in the mechanical theory, namely, that the charged glass has several strata, of inconceivable thinness, alternately redundant and deficient in electric fluid; and that by continuing the electrification, these strata penetrate deeper into the glass, and probably increase in number. We have not room here to give even an account of his experiments, and must refer the philosophical and curious reader to that part of his valuable Treatise where he treats of what he calls vindicating or recovering electricity; as also to a paper by Mr Henry in Phil. Trans. for 1766, giving account of experiments on Dutch plates by Mr Lane. The general form of the experiment is this. He puts two plates together; he coats the outer surfaces, and charges and discharges them as one thick plate. Their inner touching surfaces are found strongly electrical after the discharge, having opposite electricities, and changing these electricities, by repeated separations and replacements, in a way seemingly very capricious at first sight, but which the attentive reader will find to be according to fixed laws, and agreeably to the supposition that the strata gradually shift their places within the glass, very much resembling what we observe on a long glass rod which we would render electric by induction. In this case, as was observed in no. 57, there are observed more than one neutral point, &c.

Mr Cavendish endeavours to give us some notion of the disposition of the fluid in the substance of the glass in the following manner: Having separated the coated plate from the machine and from the ground, suppose a little of the redundant fluid in B b D (fig. 33.) equal to the fluid wanting in E e F. If we now suppose all the redundant fluid to be lodged in b b d d, and e e f f to hold all the redundant matter, and the two coatings to be in their natural state, a particle p, placed in the middle of the surface b d, will be nearly as much attracted by e e f f as it is repelled by b b d d (exactly so if the plates were infinitely extended); and if the coating be removed, keeping parallel and opposite to the surface that it quits, there will be very little, if any, tendency to fly from the glass to the coating; there will rather be some disposition in the fluid to quit the coating and fly to the glass; because the repulsion of b b d d is more diminished than the attraction of e e f f (no. 42.). But the difference will be very small indeed. (N.B. the result would be very different if electric action followed a different law. Were it as \( \frac{I}{d^2} \), the coating would be much overcharged; and were it as \( \frac{I}{d^3} \), it would be very much undercharged). Now the fact is, that when the coating is carefully removed, it is possessed of very little electricity, not more than may reasonably be supposed to run into it by bringing away one part before another. It is impossible to keep it mathematically parallel.

Hence we may conclude that the greatest part of the redundant fluid is lodged in the glass if the plates be thin, and the redundant fluid bear but a small proportion to the natural quantity. Similar reasoning shows that the greatest part of the deficiency is in the other side of the glass; and that therefore the coatings are very nearly in their natural state, and merely serve the purpose of conducting.

We have employed coatings of considerable thicknesses, having holes through them, opposite to which was some gold leaf of the heaviest sort, and almost free of cracks. We have examined the state of the bottom of those pits in Mr Coulomb's manner, and always found them void of electricity.

Thus we learn that glasses, and probably all other conductors, acquire redundant and deficient strata as well as about the most perfect conductors, at the same time that they may be impervious to the fluid; and we get some mode of conceiving how the rupture happens by a strong charge. This may very probably happen when the strata have formed, in alternate order, so deep in the glass, that a stratum, in which the fluid is crowded close together, may become contiguous to one deprived altogether of fluid. We cannot, however, say with confidence, what should be the effect of this state of things; or of one contiguity stratum coming in contact with another.

This view of the condition of charged glasses explains (we think) several phenomena which seem not well understood by electricians.

The residuum of a discharge is frequently owing to a charge extending beyond the coating, where the accumulation is considerably irregular, or different from what it would be if the plates were infinitely extended. This outline charge is taken up by the coated part after a very little while, and may again be discharged. But it also frequently arises from another stratum (much thinner, as it will always be) than the exterior one, coming to the surface some time after the first discharge, and being now in a condition for being discharged. It explains the sparkling that is perceived in succession between the parts of a jar that is coated in spots, during the charge, and the very sensible residuum of the charge of such a vessel. It explains the phenomena of Becaria's Electrica Vindix (see Electricity, Encycl. § 48.), and the great difference that may be found in the different kinds of glass in this respect. It explains the great difference between the tension occasioned by a spark from a perfectly conducting surface of considerable extent, and that occasioned by a shock, which conveys the same quantity of fluid accumulated in a small surface of glass. The discharge of the first is almost instantaneous, while that of the last requires a small moment of time, and is therefore less defunctory and and abrupt. The one is pungent and startling; but the other is softer in the first instant, and swells to a maximum. Therefore, in the medical employment of electricity, when the purpose is to be effected by the translation of a great quantity of electric fluid, we should recommend very small shocks from a very large surface of coated glass, very faintly electrified, in place of strong sparks. Patients of irritable constitutions are frequently alarmed by the quickness and pungency of strong sparks; but if the balls of Lane's shock-measurer be set so close as to give four or five shocks in each turn of a seven inch cylinder, the shocks are not even disagreeable. The balls should be made of fine expelled silver; in which case, the surface will never be hurt by the greatest discharge; whereas the discharge of four square feet of coated glass will raise such a roughness on the surface of brass as will cause it to foul, and destroy entirely the regularity of the expenditure of fluid. The same consideration should make us prefer a jar coated internally with amalgam. This cobweb coating gives a greater softness to the shock. Lastly, we see why a powerful and permanent electricity was not produced in the tube filled with melted sealing wax, and treated as mentioned in no. 101. The redundancy and deficiency intended to be produced could only be superficial. And because the wax cooled by degrees from the surface to the axis, and the wax is a conductor while liquid, it must have taken a charge at last; and therefore must appear but faintly electrical.

This account of the state of charged glass promises us some assistance in our attempts to conceive what passes in the excitation of glass by friction. It appears from Beccaria's experiments, that the redundant fluid is lodged in the same manner in both cases; for by rubbing one side of a glass tumbler, while points were presented to the opposite surface, and were connected with a wire that communicated with the ground, he gave it a powerful charge.

It is observed, that when the laminae of a piece of Muscovy glass are separated, by pulling them asunder without inserting any instrument between them, they are electrical when separated; one being positive, and the other negative. Must we not conclude from this, that when conjoined they were in the state of charged glass? If we take this view of it, a body may contain a prodigious quantity of electric fluid without exhibiting any appearance of it. Mr Nicholson found, by a very fair computation from his experiments, that a cubic inch of tale, when split into plates of 0.011 of an inch in thickness, and coated with gold leaf, gave a shock equal to the emptying 45 conductors, each seven inches in diameter and three feet long, electrified so that each gave a spark at nine inches distance. Now, the whole of this was moveable fluid, and no more than what the tale contains when unelectrified; for no more comes into the positive side than goes out of the negative side. Nay, there is no probability that the quantity moveable in our experiments bears a considerable proportion to the natural quantity. The quantity of moveable fluid in a man's body is therefore very great; and Lord Mahon is well authorized to say, that the sudden displacing of this quantity in a returning stroke, which has been occasioned by a discharge of a cloud in a very distant place, is fully adequate to the production of the most violent effects. But his Lordship has not attended

We have now seen in what sense the idioelectric may be said to be impervious to the electric fluid. It is moved in them only to very small and imperceptible distances. When a considerable stratum is discharged, the fluid does not come from the extremity of it to the point of discharge through the glass, but through the coating. And when alternate strata of redundant fluid and redundant matter are formed, the particles in each shift their places very little, moving perpendicularly to the stratum.

Even this degree of obstruction has been denied by some very active electricians, who have multiplied experiments to prove that the fluid passes freely through glass, and that the theory of coated electricity is totally different from what Franklin imagines. Mr Lyons of Dover has published a numerous list of singular experiments, which he has made with this view, with much trouble, and no small expense. They may all be reduced to this: A wire is brought from the outside of a phial, charged by the knob, and terminates in a sharp point at a small distance from a thin glass plate (it is commonly introduced into a glass tube, having a ball at the end, and the point of the wire reaches to the centre of the ball); and another wire is connected with the discharging rod, and also comes very near (and frequently close) to the other side of the glass, opposite to the pointed wire. With this apparatus he obtains a discharge; and therefore says, that the glass is permeable to electricity. But he does not narrate all the circumstances of the experiment. We have repeated all of them that have any real difference (for most of them are the same fact in different forms), and we have obtained discharges: But they were all very incomplete, except when the glass was perforated, which happened very frequently. The discharge was never made with a full, bright, undivided spark, and loud snap; but with sputtering, and trains of sparks, continued for a very sensible time; and the phial was never deprived of a considerable part of its charge: and (which Mr Lyons has taken no notice of) the glass is found to be charged, negative on the side connected with the positive side of the phial, and positive on the other. This charge was communicated to the glass over a pretty considerable surface round the points immediately opposite to the wires. This is quite conformable to the experiments of Dr Franklin and Beccaria, who charged a tumbler by grasping it with the hand, and presenting the inside to a point electrified by the prime conductor. The whole experiment is analogous to the one narrated in no. 176.

We may conclude our observations on coated glasses by mentioning a curious experiment. A flat stick of fine sealing wax, warmed till it bent pretty readily, was rendered permanently electrical, with a positive and negative pole, in a manner analogous to the double touch of magnets. A small jar was taken, having a hemisphere on the end of its inside wire, and another on the end of a stiff wire projecting from the outer coating, and then turned up parallel to the inside wire; so that the two hemispheres stood equally high, and about three inches asunder. This jar was electrified too weakly, as to run no risk of a spontaneous discharge. The flat faces of the two hemispheres were now applied to the flat side of the sealing wax, and were moved to and fro along it, overpassing both ends about an inch with each hemisphere. The experiment was very troublesome; for the phial often discharged itself along the surface of the sealing wax, and all was to begin again. But, by continuing this operation till the sealing wax grew quite cold and hard, it acquired a very sensible electricity, which lasted several weeks when kept with care; but still it was not much more sensible than that of the sealing wax, which congealed between two globes oppositely electrified.

After this application of the theory to the phenomena of coated glass, it will not be necessary to employ much time in its application to the electrophorus. The general propositions from n° 14. to 21., and their companions in n° 38—43., will enable us to state with precision (when combined with the law of electric action) the actions of every part of this apparatus; and considerable assistance will be derived from a careful consideration of our analysis of Professor Richmann's experiment in n° 156. But we must content ourselves with a general, popular view of these particulars, which may be sufficient for making us understand what will be the kind, and somewhat of the intensity, of the action of its different parts.

The electrophorus consists of three parts. The chief part is the cake ABCD (fig. 34.) of some electric; such as gum lac, sealing wax, pitch, or other resinous composition. This is melted on some conducting plate, DCFE, and allowed to congeal; in which state it is found to be negatively electric. Another conducting plate GHBA is laid on it, and may be raised up by silk lines, or any insulating handle. We shall call ABCD the cake, DCFE the sole, and GHBA the cover.

The general appearances not having been so scientifically classified in the article Electricity as could be wished, we shall here narrate them, very briefly, in a way more suited to our purpose. In comparing the theory with observation, it will be proper to make all the three parts of considerable thickness, and of no great breadth. Although this diminishes greatly the most remarkable of the actions, it leaves them sufficiently vivid, and it greatly increases the smaller changes which are instructive in the comparison. The general facts are,

1. If the sole has been insulated during the congelation of the electric, till all is cold and hard, the whole is found negatively electric, and the finger draws a spark from any part of it, especially from the sole. If allowed to remain in this situation, its electricity grows gradually weaker, and at last disappears; but it may be excited again by rubbing the cake with dry warm flannel, or, which is the best, with dry and warm cat or hare fur. If the cover be now set on the cake by its insulating handle, but without touching the cover, and again separated from the cake, no electricity whatever is observed in the cover.

2. But if it be touched while on the cake, a sharp pungent spark is obtained from it; and if, at the same time, the sole be touched with the thumb, a very sensible shock is felt in the finger and thumb.

3. After this, the electrophorus appears quite inactive, and is said to be dead; neither sole nor cover giving any sign of electricity. But,

4. When the cover is raised to some distance from the cake (keeping it parallel therewith), if it be touched while in this situation, a smart spark flies, to some distance, between it and the finger, more remarkably from the upper side, and still more from its edge, which will even throw off sparks into the air, if it be not rounded off. As this diminishes the deflected effects, it is proper to have the edge so rounded. This spark is not so sharp as the former, and resembles that from any electrified conductor.

5. The electricity of the cover, while thus raised, is of the opposite kind to that of the cake, or is positive.

6. The electricity of the cover while lying on the cake is the same with that of the cake, or negative.

7. The appearances n° 2, 3, 4, may be repeated for a very long time without any sensible diminution of their vivacity. The instrument has been known to retain its power undiminished even for months. This makes it a sort of magazine of electricity, and we can take off the electricity of the cake and of the cover as charges for separate jars, the cover, when raised, charging like the prime conductor of an ordinary electrical machine; and, when set on the cake, charging it like the rubber. This caused the inventor, Mr Volta, to give it the name of Electrophorus.

8. If the sole be insulated before putting on the cover, the spark obtained from the cover is not of that cutting kind it was before; but the same shock will be felt if both cake and cover be touched together.

9. If the cover be again raised to a considerable height, the sole will be found electrical, and its electricity is that of the cake, and opposite to that of the cover.

10. After touching both cover and sole, if the cover be raised and again let down, without touching it while aloft, the whole is again inactive.

11. If both cover and sole be made inactive when joined, they show opposite electricities when separated, the sole having the electricity of the cake.

12. If both cover and sole be made inactive when separate, they both show the opposite to the electricity of the cake when joined.

Let us now attend to the disposition of the electrical fluid in the different parts of the instrument in their various situations, and to the forces which operate mutually between them. N.B. Experiments for examining this instrument are best made by setting the three plates vertically, supported on glass stalks, with leaden feet, to steady them. A very small electrometer may be attached to the outer surfaces of the cover and sole.

If the extent of the plates were incomparably greater than their thickness, we may infer from n° 92., &c. that the redundant fluid and matter would be disposed in parallel strata, and that the actions would be the same at all distances. But since this is not the case, the disposition of the fluid will be somewhat different; and whatever it is, the action of any stratum will be diminished by an increase of distance. The following description cannot be very different from the truth:

1. The cake grows negative by cooling; and if it were were alone, it would have a negative superficial stratum on both sides, of greater thickness near the edges; and the fluid would probably grow denser by degrees to the middle, where it would have its natural density. This disposition may be inferred from n° 92, 93, and 98. But it cools in conjunction with the sole, and the attraction of the redundant matter in the cake for the moveable fluid in the sole disturbs its uniform diffusion in the sole, and causes it to approach the cake. And because this, in all probability, happens while the cake is still a conductor, the disposition of its fluid will be different from that described above, and the final disposition of the fluid in the cake and sole will resemble that described in n° 95, where the plates E and A represent the cake and sole. But because we do not know precisely the gradation of density, and aim only at general notions at present, it will be sufficient to consider the cake and sole as divided into two strata only; one redundant in fluid, and the other deficient, neglecting the neutral stratum that is interposed between them in each. The cake, then, consists of a stratum A B b a containing redundant matter, and a stratum a b CD containing redundant fluid; and the sole has a stratum DC m containing redundant fluid, namely, all that belongs naturally to the space DCFE, and a stratum m n FE containing redundant matter. This may be called the primitive state of the cake and sole; and if once changed by communication with unelectrified bodies, it can never be recovered again without some new excitement.

II. If the sole be touched by any body communicating with the ground, fluid will come in, till the repulsion of the redundant fluid in the sole for a superficial particle y is equal to the attraction of the redundant matter in the cake for the same particle. What has been said concerning infinitely extended plates, rendered neutral on one side, may suffice to give us a notion of the present disposition of the fluid in the sole. The under surface will be neutral, and the fluid will increase in density toward the surface DC. The sole contains more than its natural quantity of fluid, but is neutral by the balance of opposite forces. Let it now be insulated. This disposition of fluid may be called the common state of the electrophorus.

III. Let the cover GH BA be laid on it. The particle z, at the upper surface of the cover, must be more attracted by the redundant matter in the stratum A B b a than it is repelled by the redundant fluid in the remote strata; for the fluid in the cake is less than what belongs to it in its natural state, and therefore z is attracted by the cake. The redundant fluid which has come into the remote side of the sole is less than what would saturate the redundant matter of the cake, because it only balances the excess of the remote action of this matter above the nearer action of the compressed fluid in the sole; and this smaller quantity of redundant fluid acts on z at a greater distance than that of the redundant matter in the cake. On the whole, therefore, the particle z, lying immediately within the surface GH, is attracted; therefore some will move toward the cake, and its natural state of uniform diffusion through the cover will be changed into a violent state, in which it will be compressed on the surface AB, being attracted from the surface GH. It will now have a stratum G g p H, containing redundant matter, and another g p BA, containing redundant fluid. But this will disturb the arrangement which had taken place in the sole, and had rendered it neutral on the under surface. We do not attend to the fluid in the cake, but consider it as immovable, for any motion which it can get will be so small, that the variations of its action will be altogether insignificant. The particle y, situated in that surface, will be more repelled by the compressed fluid in the stratum g p CA than it is attracted by the equivalent, but more remote redundant matter in G H p g. Fluid is therefore disposed to quit the surface EF, and the sole appears positively electric; very little indeed, if the cover be thin. All this may be observed by attaching a small Canton's electrometer to the lower surface of the sole, or by touching the sole with the electrometer of fig. 8, and then trying its electricity by rubbed wax or glass.

IV. A particle of fluid z, placed immediately without the surface GH, will be more attracted by the deficient stratum G H p g and by A B b a than it is repelled by the redundant strata beyond them, and the cover must be sensibly negative. This is the common state of the whole instrument after setting on the cover. It is slightly positive on the lower surface of the sole, and much more sensibly negative on the upper surface of the cover. A smart spark will therefore be seen between it and the finger, fluid will enter, till the attraction of the redundant matter in A B b a is balanced by the repulsion of the redundant fluid in DCFE.

V. A spark will now be obtained from the sole, because it was faintly positive before, and there has been added the action of the fluid which has entered into the cover. The fluid in the sole is therefore disposed to fly to any body presented to it. But when this has happened, the equilibrium at the surface GH is destroyed, and that surface again becomes negative, and will attract fluid, although the cover already contains more than its natural quantity. A small spark will therefore be seen between the cover and any conducting body presented to it. By touching it, the neutrality or equilibrium is restored at GH; but it is destroyed again at EF, which will again give a positive spark, which, in its turn, again leaves GH negative. This will go on for ever, in a series of communications continually diminishing, so as soon to become insensible, if the three parts of the electrophorus be thin. This makes it proper to make them otherwise, if the instrument be intended for illustrating the theory.

At last the equilibrium is completed at the surfaces GH and EF, and both are neutral in relation to surrounding bodies, although both the cover and sole contain more than their natural share of electric fluid. We may call this the neutral or dead state of the electrophorus.

This state may be produced at once, instead of doing it by these alternate touches of GH and EF. If we touch at once both these surfaces, we have a bright, pungent spark, and a small shock. It this be the object of the experiment, the state N° IV. which gives occasion to it, may be called the charged state of the electrophorus.

When the instrument has thus been rendered neutral in relation to surrounding bodies, it is plain that it may continue in this state for any length of time without any diminution of its capability of producing the other phenomena. phenomena, provided only that no fluid pass from the cover to the cake. We do not fully understand what prevents this communication, nor indeed what prevents the rapid escape from an overcharged body into the air. This cause, whatever it be, operates here; and the best way of preventing the dissipation, or the absorption by the cake, is to keep the electrophorus with its cover on. It will come into this neutral state by dissipation from the sole, and absorption by the cover, in no very long time; and after this, will remain neutral, retaining its power with great obstinacy, especially if the cake and plates are very thin.

VI. If the cover be now removed to a distance, both parts of the apparatus will show strong marks of electricity. The cover contains much redundant fluid, and must appear strongly positive, and will give a bright spark, which may be employed for any purpose. It may be employed for charging a jar positively by the knob, if we just touch the cover with the knob. The sole will attract fluid, or be negative, although it contain more than its natural quantity of fluid, and it will take a spark. The sole therefore, in the absence of the cover, may be employed to charge a jar negatively by the knob. By touching it with the finger, or with the knob of a jar held in the hand, it is reduced to the common state described in No II.; and now all the former experiments may be repeated. We may call this the active or the charging state.

This state of the apparatus has caused it to get the name Electrophorus. Volta, its undoubted inventor, called it Electroforo perpetuo; for it appears, as has been already observed, to contain a magazine of electricity. The cover, when removed, will charge a jar held in the hand positively; and having done this service, it will charge a jar negatively when again set on the cake. The sole, in the absence of the cover, will charge a third jar negatively; and then, when the cover, after being touched, is set down again, it will charge a fourth jar positively. It will not be difficult to contrive a simple mechanism, connected with the motion of the cover, which shall connect the joined parts with two jars, and shall connect them, when separated, with two others; and thus charge all the four with great expedition. All this is done without any new excitation of the electrophorus. But it is by no means a magazine of electricity which it gradually expends: it is a collector of electricity from the surrounding bodies, which it afterwards imparts to others, and may be employed to discharge jars in the same gradual manner as to charge them.

VII. If the electrophorus is not insulated, a shock may still be obtained, by first touching the sole, and then, without removing the finger, touching the cover: but this will not be so smart as when the negative cover is touched at the same time that we touch the sole, more highly positive, than when it communicates with the ground. The difference must, however, be almost imperceptible when the pieces are thin.

VIII. If the electrophorus is not insulated, the cover, when put on, will give a spark in the manner already mentioned, and it will be somewhat stronger than when it is insulated; because the fluid is allowed to escape from the sole, and does not obstruct the entry into the cover. If we then, without removing the finger from the cover, touch the sole, nothing is felt; but if we first touch the sole, and, without removing the finger from it, touch the cover, we obtain a shock. This is evident from the theory. By this series of alternate touches, the period of the electrophorus is completed. The electrophorus is charged, or rendered neutral, by touching the plates when joined; then, by touching both when separated, the whole is reduced to the common state. When separated, from being in the neutral state, they have opposite electricities, the sole shewing that of the cake. When brought together, each in the common state, they have opposite electricities, the cover shewing that of the cake.

IX. When, by long exposure to the air without its cover, the electrophorus has lost its virtue, it may be brought again into an active state in a variety of ways. Its surface may be rendered negative by friction with dry cat or hare skin, or warm flannel. It may be rendered negative by setting on it a jar charged negatively on the inside, and then touching the knob with anything communicating with the ground. This is the most expedient method, and will give it a high degree of excitement, if the jar be of size, and if the electrophorus be covered with a plate of tinfoil which comes into contact all over its surface. This however requires the previous charging of the jar; therefore it will be as expedient and effectual to connect this surface with the rubber of an electrical machine. We had almost forgotten to remark, that the effects of bringing the cover edgewise to the cake follow clearly from the theory, as will appear to the attentive reader without further explanation.

The electrophorus has been compared to a charged plate of coated glass. It is true that it may be brought into an external state which very much resembles a charged pane; namely, when the cover, in its natural state, is set on the electrophorus in its natural state; and accordingly it gives a shock, and the two exterior surfaces become neutral; but the internal constitution, and the acting forces, are totally and essentially different. The two coatings of the pane would not, when separated, exhibit the appearances of the electrophorus; nor, when touched in their disjoined state, will they produce the same effects when joined. In the operation of coated glass, the constant or invariable part, the glass is not the agent, it is merely the occasion of the action, by allowing the accumulation. In the electrophorus, the electric, which is the constant invariable part, is the agent producing the accumulation. The electrophorus is an original, and a very ingenious and curious electrical machine. Nothing has so much contributed to spread some general, though slight, acquaintance with the mechanical principles of electricity. The numerous dabblers in natural knowledge had been diverted from scientific pursuit by the variety of the singular and amusing effects of electricity, and had really attained very little connected knowledge. The effects of the electrophorus forced this knowledge on them; because no use can be made of it without a pretty clear conception of the disposition of the electricity, and the kind and intensity of the actions. It is therefore most ungrateful in the experimenters who have attained better views, to attempt to rob Mr Volta of the real merit of discovery, by shewing that its effects are similar to those of Mr Symmer's stockings, or of Cigna's plates, or of Franklin's charged or discharged glass panes. And the attempt destroys itself: for it shews the ignorance or inattention of its author; for the similarity is not real, as will appear clear to any person who will examine things minutely and scientifically, proceeding in this examination on suppositions similar to those which we employed in the analysis of Richmann's experiment. It was indeed in subterfuge to this examination that we entered into the detail of that experiment, it being a simpler case. The accurate examination of Richmann's experiment requires the fluxionary calculus in its refined form. In the present question five acting strata are to be considered, which renders the formula very complicated, and indeed intractable, unless we make the plates extremely thin; which, fortunately, is the best form of the instrument. We have completed this mathematical analysis; and the popular view here given is the result of that computation.

The electricians are no less obliged to Mr Volta for another machine, or instrument, from which the study of Nature's operations has derived, or may derive, immense advantages. We mean the condenser, or collector of electricity. We refer to the article Electricity in the Encyclopedia for a description of the instrument, and some account of its effects and properties. The general effect is to render sensible an accumulation or deficiency of electric fluid so slight that it will not affect the most delicate electrometer; and it produces (at least in the opinion of Mr Volta) this effect, by employing for the sole of an electrophorus a body which is an imperfect conductor, such as a plate of well dried marble, or well dried, but not baked, wood; or even a conducting body, covered with a bit of dry taffety or other silk. Mr Volta, Cavallo, and others, who have written a great deal on the subject, have attempted to show how these substances are preferable (and they certainly are preferable in a high degree) to more perfect insulators; but not having taken pains to form precise notions of the disposition and action of the electric fluid in the situations afforded by the instrument, their reasonings have not been very clear. We think that an adequate conception of the essentials of the proposed instrument may be acquired by means of the following considerations:

Furnish the cover of an electrophorus with a graduated electrometer, which indicates the proportional degree of electricity: electrify it positively to any degree, suppose six, while held in the hand, at some distance, right over a metal plate lying on a wine glass as an insulating stand, but communicating with the ground by a wire. Bring it gradually down toward the plate. Theory teaches, and we know it by experiment, that the electrometer will gradually subside, and perhaps will reach to zero before the electricity is communicated in a spark. Stop it before this happens. In this state the attraction of the lying plate produces a compensation of four degrees of the mutual repulsion of the parts of the cover, by confining the fluid on its under surface, and forming a deficient stratum above. This needs no farther explanation after what has been said on the charging of coated glass plates. Now we can suppose that the escape of the fluid from this body into the air begins, as soon as electrified to the degree six, and that it will fly to the lying plate with the degree two, if brought nearer. If we can prevent this communication to the lying plate, by interpolating an electric, we may electrify the cover again, while so near the metal plate, to the degree six, before it will stream off into the air. If it be now removed from the lying plate, the fluid would raise the electrometer to ten, did it not immediately stream off; and an electric excitement of any kind which could only raise this body to the degree six by its intensity, will, by this apparatus, raise it to the degree ten, if only copious enough in extent. If we do the same thing when the wire is taken away which connects the lying plate with the ground, we know that the same diminution of the electricity of the other plate cannot be produced by bringing it down into the neighbourhood of the lying plate (see no. 134, &c., 151, &c.).

Here we see the whole theory of Mr Volta's condenser. He seems to have obscured his conceptions of it therewith having his thoughts running upon the electrophorus lately invented by him, and is led into fruitless attempts to explain the advantages of the imperfect conductor above the perfect insulator. But the apparatus is altogether different from an electrophorus, and is more analogous in its operations to a coated plate not charged nor insulated on the opposite side; and such a coated plate lying on a table is a complete condenser, if the upper coating be of the same size with the plate of the condenser. All the directions given by Mr Volta for the preparation of the imperfect conductors shew, that the effect produced is to make them as perfect conductors as possible for any degree of electricity that exceeds a certain small intensity, but such as shall not suffer this very weak electricity to clear the first step of the conduit. The marble must be thoroughly dried, and even heated in an oven, and either used in this warm state, or varnished, so as to prevent the reabsorption of moisture. We know that marble of slender dimensions, so as to be completely dried throughout, will not conduct till it has again become moist. A thick piece of marble is rendered so superficially only, and still conducts internally. It is then in the best possible state. The same may be said of dry unbaked wood. Varnishing the upper surface of a piece of marble or wood is equivalent to laying a thin glass plate on it. Now this method, or covering the top of the marble, or of a book, or even the table, with a piece of clean dry silk, makes them all the most perfect condensers. This just view of the matter has great advantages. It takes away the mysterious indistinctness and obscurity which kept the instrument a quackish tool, incapable of improvement. We can now make one incomparably better and more simple than any proposed by the very ingenious inventor. We need only the simple moveable plate. Let this be varnished on the under side with a moderately thick coat of the purest and hardest vernis de Martin, or coach-painters varnish; and we have a complete condenser by laying this on a table. If it be connected by a wire with the substance in which the weak and imperceptible electricity is excited, it will be raised (provided there be enough of it of that small intensity) in the proportion of the thickness of the varnish to the fourth part of the diameter of the plate. This degree of condensation will be procured by detaching the connecting wire from the insulating handle of the condenser, and then raising the condenser from the table. It will then give sparks, though the original electricity could not sensibly affect a flaxen fibre. It must be particularly noted, that it can produce this condensation only when there is fluid to condense; that is, only when the weak electricity is diffused over a greater space than the plate of the condenser. In this way it is a most excellent collector of the weak atmospheric electricity, and of all diffused electricity. But to derive the same advantage from it in many very interesting cases, such as the inquiry into the electricity excited in many operations of Nature on small quantities of matter, we must have condensers of various sizes, some not larger than a silver penny. To construct these in perfection, we must use the purest and hardest varnish, of a kind not apt to crack, and highly coercive. This requires experiment to discover it. Spirit varnishes are the most coercive; but by their difference of contraction by cold from that of metals, they soon appear frosted, and when viewed through a lens, they appear all shivered: They are then useless. Oil varnishes have the requisite toughness, but are much inferior in coercion. We have found amber varnish inferior to copal varnish in this respect, contrary to our expectation.

On the whole, we should prefer the finest coach-painters varnish, new from the shop, into which a pencil has never been dipped: and we must be particularly careful to clear our pencils of moisture and all conducting matter, which never fails to taint the varnish. We scarcely need remark, that the coat of varnish on these small condensers should be very thin, otherwise we lose all the advantage of their smallness.

Mr. Cavalli has ingeniously improved Volta's condenser by connecting the moveable plate, after removal, with a smaller condenser. The effect of this is evident from n° 130. But the same thing would have been generally obtained by using the small condenser at first, or by using a still thinner coat of varnish.

It will readily occur to the reader, that this instrument is not instantaneous in its operation, and that the application must be continued for some time, in order to collect the minute electricity which may be excited in the operations of nature. He will also be careful that the experiment be so conducted that no useless accumulation is made anywhere else. When we expect electricity from any chemical mixture, it never should be made in a glass vessel, for this will take a charge, and thus may absorb the whole excited electricity, accumulating it in a neutral or insensible state. Let the mixture be made in vessels of a conducting substance, insulated with as little contact as possible with the inflating support; for here will also be something like a charge. Suspend it by silk threads, or let it rest on the tops of three glass rods, &c.

After this account of the Leyden phial, electrophorus, and condenser, it is surely unnecessary to employ any time in explaining Mr. Bennet's most ingenious and useful instrument called the doubler of electricity. The explanation offers itself spontaneously to any person who understands what has been said already. Mr. Cavalli has with industry searched out all its imperfections, and has done something to remove them, by several very ingenious contrivances, minutely described in his Treatise on Electricity. Mr. Bennet's original instrument may be freed, we imagine, as far as seems possible, by using a plate of air as the intermediate between the three plates of the doubler. Stick on one of the plates three very small spherules made from a capillary tube of glass, or from a thread of sealing wax. The other plate being laid on them, rests on mere points, and can scarcely receive any friction, which will disturb the experiment. Mr. Nicholson's beautiful mechanism for expediting the multiplication has the inconvenience of bringing the plates towards each other edgewise, which will bring on a spark or communication sooner than may be desired: but this is no inconvenience whatever in any philosophical research; because, before this happens, the electricity has become very distinguishable as to its kind, and the degree of multiplication is little more than an amusement. The spark may even serve to give an indication of the original intensity, by means of the number of turns necessary for producing it. If the fine wires, which form the alternate connections in ingenious manner, could be tipped with little balls to prevent the dissipation, it would be a great improvement indeed. An alternate motion, like that of a pump-handle, might be adopted with advantage. This would allow the plates to approach each other face to face, and admit a greater multiplication, if thought necessary.

One of the most remarkable facts in electricity is the rapid dissipation by sharp points, and the impossibility of making any considerable accumulation in a body which has any such projecting beyond other parts of its surface. The dissipation is attended with many remarkable circumstances, which have greatly the appearance of the actual escape of some material substance. A stream of wind blows from such a point, and quickly electrifies the air of a room to such a degree, that an electrometer in the farthest corner of the room is affected by it. This dissipation in a dark place is, in many instances, accompanied by a bright train of light diverging from the point like a firework. Dr Franklin therefore was very anxious to reconcile this appearance with his theory of plus and minus electricity, but does not express himself well satisfied with any explanation which had occurred to him. From the beginning, he saw that he could not consider the stream of wind as a proof of the escape of the electric fluid, because the same stream is observed to issue from a sharp negative point; which, according to his theory, is not dispersing, but absorbing it. Mr. Cavendish has, in our opinion, given the first satisfactory account of this phenomenon.

To see this in its full force, the phenomenon itself must be carefully observed. The stream of wind is plainly produced by the escape of something from the point itself, which hurries the air along with it; and this draws along with it a great deal of the surrounding air, especially from behind, in the same manner as the very slender thread of air from a blowpipe hurries along with it the surrounding air and flame from a considerable surface on all sides. It is in this manner that it gathers the whole of a large flame into one mass, and, at last, into a very point. If the smoke of a little rosin thrown on a bit of live coal be made to rise quietly round a point projecting from an electrified body, continually supplied from an electrical machine, the vortices of this smoke may be observed to curl in from all sides, along the wire, forming a current of which the wire is the axis, and it goes off completely by the point. But if the wire be made to pass through a cork fixed in the bottom of a wide glass tube, and if its point project not beyond the mouth of the tube, the afflux of the air from behind is prevented, and we have no stream; but if the cork be removed, and the wire fill occupy the axis of the tube, but without touching the sides, we have the stream very distinctly; and smoke which rises round the far end of the tube is drawn into it, and goes off at the point of the wire.

Now it is of importance to observe, that whatever prevents the formation of this stream of wind prevents the dissipation of electricity (for we shall not say escape of electric fluid) from the point. If the point project a quarter of an inch beyond the tube, or if the tube be open behind, the stream is strong, and the dissipation so rapid, that even a very good machine is not able to raise a Henry's electrometer, standing on the conductor, a very few degrees. If the tube be flipped forward, so that the point is just even with its mouth, the dissipation of electricity is next to nothing, and does not exceed what might be produced by such air as can be collected by a superficial point. If the tube be made to advance half an inch beyond the point which it surrounds, the dissipation becomes insensible. All these facts put it beyond a doubt that the air is the cause, or, at least, the occasion of the dissipation, and carries the electricity off with it, in this manner rendering electrical the whole air of a room. The problem is reduced to explain how the air contiguous to a sharp electrified point is electrified and thrown off.

It was demonstrated in n° 130, that two spheres, connected by an infinitely extended, but slender conducting canal, are in electrical equilibrium, if their surfaces contain fluid in the proportion of their diameters. In this case, the superficial density of the fluid and its tendency to escape are inversely as the diameters (n° 130). Now if, in imagination, we gradually diminish the diameter of one of the spheres, the tendency to escape will increase in a greater proportion than any that we can name. We know, that when the prime conductor of a powerful table-machine has a wire of a few inches in length projecting from its end, and terminating in a ball of half an inch in diameter, we cannot electrify it beyond a certain degree; for when arrived at this degree, the electricity flies off in successive bursts from this ball. Being much more overcharged than any other part of the body, the air surrounding the ball becomes more overcharged by communication, and is repelled, and its place supplied by other air, not so much overcharged, which surrounded the other parts of the body, and is pressed forwards into this space by the general repulsion of the conductor and the confining pressure of the atmosphere; otherwise, being also overcharged, it would have no tendency to come to this place. Half a turn of the cylinder is sufficient to accumulate to a degree sufficient for producing one of these explosions, and we have two of them for every turn of the cylinder. A point may be compared to an incomparably smaller ball. The condensation of the fluid, and its tendency to escape, must be greater in the same unmeasurable proportion. This density and mutual repulsion cannot be diminished, and must even be increased, by the matter of the wire forming a cone, of which the point is the apex; therefore, if there were no other cause, we must see that it is almost impossible to confine a collection of particles, mutually repelling, and condensed, as these are in a fine point.

But the chief cause seems to be a certain chemical union which takes place between the electric fluid and a corresponding ingredient of the air. In this state of electricity condensation, almost completely surrounded by the air, mutually the little mass of fluid must attract and be attracted with air, with very great force, and more readily overcome the force which keeps the electrified fluid attached to the last series of particles of the wire. It unites with the air, rendering it electric in the highest degree of redundancy. It is therefore strongly repelled by the mass of condensed fluid which succeeds it within the point. Thus the electrified air continually thrown off, in a state of electrification, that must rapidly diminish the electricity of the conductor. Hence the uninterrupted flow, without noise or much light, when the point is made very fine. When the point is blunt, a little accumulation is necessary before it attains the degree necessary for even this minute explosion; but this is soon done, and these little explosions succeed each other rapidly, accompanied by a fluttering noise, and trains of bright sparks. The noise is undoubtedly owing to the atoms of the highly electrified fluid. These are, in all probability, rarefied of a sudden, in the act of electrification, and immediately collapse again in the act of chemical union, which causes a sonorous agitation of the air. This electrified air is thus thrown off, and its place is immediately supplied by air from behind, not yet electrified, and therefore strongly drawn forward to the point, from which they are thrown off in their turn. This rapid expansion and subsequent collapsing of the air is verified by the experiments of Mr. Kinnersly, related by Dr. Franklin, and is seen in numberless experiments made with other views in later times, and not attended to. Perhaps it is produced by the great heat which accompanies, or is generated in the transference of electricity, and it is of the same kind with what occasions the bursting of stones, splitting of trees, exploding of metals, &c. by electricity. The expansion is either inconsiderable, or it is successively produced in very small portions of the substance expanded; for when metal is exploded in close vessels, or under water, there is but a minute portion of gaseous matter produced; and in the dissipation by a very fine point, sufficiently great to give full employment to a powerful machine, the stream of wind is but very faint, and nine-tenths of this has been dragged along by the really electrified thread of wind in the middle.

From a collation of all the appearances of electricity, we must form the same conception of the forces which operate round a point that is negatively electrified, not dispersing, but drawing in electric fluid. It is more completely undercharged than any other part of a body, and attracts the fluid in the surrounding air, and the air in which it is retained, with incomparably greater force. It therefore deprives the contiguous air of its fluid, and then repels it; and then produces a stream like the overcharged point.

If a conducting body be brought near to any part of an overcharged body, the fronting part of the first is rendered undercharged; and this increases the charge of the opposite part of the overcharged body. It becomes more overcharged in that part, and sooner attains that degree of condensation that enables the fluid to quit the superficial series of particles, and to electrify strongly the contiguous air. The explosion is therefore made in this part in preference to any other; and the air thus exploded is strongly attracted by the fronting part of the other body, and must fly thither in preference to any other point. If, moreover, the fronting part of A be prominent or pointed, this effect will be produced in a superior degree; and the current of electrified air, which will begin very early, will increase this disposition to transference in this way by rarefying the air; a change which the whole course of electric phenomena shews to be highly favourable to this transference, although we cannot perhaps form any very adequate notion how it contributes to this effect. This seems to be the reason why a great explosion and snap, with a copious transference of electricity, is generally preceded by a hissing noise like the rushing of wind, which swells to a maximum in the loud snap itself.

If two prominences, precisely similar, and electrified in the contrary way to the same degree, are presented to each other, we cannot say from which the current should take its commencement, or whether it should not equally begin from both, and a general dispersion of air laterally be the effect; but such a situation is barely possible, and must be infinitely rare. The current will begin from the side which has some superiority of propelling force. We are disposed to think that this current of material electrified substance must suffer great change during its passage, by mixing with the current in an opposite electrical state coming from the other body. Any little mass of the one current must strongly attract a contiguous mass of the other, and certain changes should surely arise from this mixture. These may, in their turn, make a great change in the mechanical motions of the air; and, instead of producing a quasimodo dispersion of air from between the bodies, as should result from the meeting of opposite streams, it may even produce a collapsing of the air by the mutual strong attractions of the little masses. Many valuable experiments offer themselves to the curious inquirer. Two little balls may be thus presented to each other, and a smoke may be made with resin to occupy the interval between them. Motions may be observed which have certain analogies that would afford useful information to the mechanical inquirer. There must be something of this mixture of currents in all such transfers, and the most minute differences in the condition of a little parcel of the air may greatly affect the future motions. The most promising form of such experiment would be to use two points of the same substance, shape, and size, and electrified to the same degree in opposite senses.

After all care has been taken to insure similarity, there remains one essential difference, that the one current is redundant in electric fluid, and the other deficient. This circumstance must produce characteristic differences of appearance. And are there not such differences? Is not the pencil and the star of light a characteristic difference? And does not this well-supported fact greatly corroborate the opinion of Dr Franklin, that the electric phenomena result from the redundancy and deficiency of one substance, and not from two distinct substances operating in a similar manner? For the distinction in appearance is a mechanical distinction. Motion, direction, velocity, are perceivable in it. Locomotive forces are concerned in it; but they are so implicated with forces which probably resemble chemical affinities, hardly operating beyond contact, that to extricate their effects from the complicated phenomenon seems a desperate problem. There is some hitherto inexplicable chemical composition and decomposition taking place in the transference of electricity. Of this a numerous train of observations made since the dawn of the pneumatic chemistry leaves us no room to doubt. The emission or production of light and heat is a remarkable sign and proof. Now this takes place along the whole path of transference; therefore the process is by no means completed at the point from which the active cause proceeds; and although there be certain appearances that are pretty regular, they are still mixed with others of the most capricious anomaly. The zigzag form of the most condensed spark, totally unlike, by its sharp angles, to any motions producible by accelerating forces, which motions are, without exception, curvilinear, makes us doubt exceedingly whether the luminous lines which we observe are successive appearances of the same matter in different places, or whether they be not rather simultaneous, or nearly simultaneous, corollaries of different parcels of matter in different places, indicating chemical compositions taking place almost at once; and this becomes more probable, when we reflect on what has been laid already of the jumbling of opposite currents; such mixtures should be expected. We have seen a darted flash of lightning which reached (in a direction nearly parallel to the horizon) above three miles from right to left; and it seemed to us to be co-extensive; we could not say at which end it began. The thunder began with a loud crack, and continued with a most irregular rumbling noise about fifteen seconds, and seemed equal on both hands. We imagine that it was really a simultaneous snap, in the whole extent of the spark, but of different strength in different places; different portions of the fowery agitation were propagated to the ear in succession by the fowery undulations of air, causing it to seem a lengthened sound. Such would be the appearance to a person standing at one end of a long line of soldiers who discharge their firelocks at one instant. It will seem a running fire, of different strength in different parts of the line, if the muskets have been unequally loaded. It is inconceivable that this long zigzag spark can mark the track of an individual mass of electrified air. The velocity and momentum would be enormous, and would sweep off every thing in its way, and its path could not be angular. The same must be affected of the streams of light in our experiments. The velocity is so unmeasurable that we cannot tell its direction. There may be very little local motion, just as in the propagation of sound, or of a wave on the surface of water. That particular change of mutual situation among the adjoining atoms which occasions chemical solution or precipitation may be produced in an instant, over a great extent, as we know that a parcel of iron filings, lying at random on the surface of quicksilver, will, in one instant, be arranged in a certain manner by the mere neighbourhood of a magnet. Is not this like the simultaneous precipitation of water along the whole path of a discharge?

But still there must be some cause which gives these simultaneous corollaries a situation with respect to each other, that has a certain regularity. Now the luminous trains (for they are not uniform lines of light) of almost continuous sparks which are arranged between

a positive and a negative point, seem to us to indicate emanation from the positive, and reception by the neg- ative point. The general line has a considerable re- semblance to the path of a body projected from the po- sitive point, repelled by it, and attracted by the nega- tive point. This will appear to the mechanician on a very little reflection. If the curve were completely vi- sible, it would somewhat resemble those drawn between P and N in fig. 35. PABN overpasses the point N, and comes to it from behind; PabN lies within the other, and arrives in a direction nearly perpendicular to the axis; P = BN describes a straight line, and arrives in the direction PN. As the chemical composition ad- vances; the light is diffused or produced; and there- fore the appearances are more rare as we advance far- ther in the direction in which they are produced; and there would perhaps be no appearance at all at the point where the motion ends, were it not that the few remaining parcels, where the compositions or decompo- sitions have not been completed, are crowded together at the negative point, incomparably more than in any other part of the track. We think that these considerations offer some explanation of the appearance of the pencil and star, which are so uniformly characteristic of the positive and negative electricities; but we see many grounds of uncertainty and doubt, and offer it with due diffidence.

The curious figures observed by Mr Lichtenberg, formed by the dust which settles on a line drawn on the face of a mirror by the positive, and by the nega- tive knobs of a charged jar, are also uniformly charac- teristic of the two electricities. These are mechanical distinctions, indicating certain differences of acceler- ating forces. We must refer the curious reader to Lichtenberg's Dissertations in the Gottingen Commen- taries; to the Publication of the Haarlem Society; to the Gotha Magazine; to Dissertations by Speth at Alt- dorff, and other German writers.

It only remains for us to take notice of the general laws of the diffusion of electricity into the air, and along imperfect insulators. On this subject we have some valuable experiments of Mr Coulomb, published in the Memoirs of the Academy of Sciences of Paris for 1785.

These experiments were made with the assistance of an electrometer of a particular construction, which shall be described under the article ELECTROMETER.

The general result of Mr Coulomb's experiments was, that the momentary diffusion of moderate de- grees of electricity is proportional to the degree of electricity at the moment. He found that the diffu- sion is not sensibly affected by the state of the baro- meter or thermometer; nor is there any sensible dif- ference in bodies of different sizes or different substances, or even different figures, provided that the electricity is very weak.

But he found the diffusion greatly affected by the different states of humidity of the air. Saussure's hy- grometer has its scale distinctly related to the quantity of water dissolved in a cubic foot of the air. The fol- lowing little table shows an evident relation to this in the diffusion of electricity:

| Hygrometer | Grains water in cubic feet | Diffusion per minute | |------------|--------------------------|---------------------| | 69 | 6,197 | | | 75 | 7,295 | | | 80 | 8,045 | | | 87 | 9,221 | |

Hence it follows, that the diffusion is very nearly in the triplicate ratio of the moisture of the air. Thus if we consider as \( \frac{7,167}{6,180} \) we have \( m = 2,764 \). \( \frac{8,045}{6,180} \) gives \( m = 2,76 \). \( \frac{9,221}{6,180} \) gives \( m = 3,61 \).

Hence, at a medium, \( m = 3,30 \).

We should have observed, that the ingenious author took care to separate this diffusion by immediate con- tact with the air, from what was occasioned by the im- perfect insulation afforded by the supports.

It must also be remarked here, that the immediate object of observation in the experiments is the diminu- tion of repulsion. This is found to be, in any given state of the air, a certain proportion of the whole re- pulsion at the moment of diminution; but this is double of the proportion of the density of the electric fluid; for it must be recollected, that the repulsions by which we judge of the diffusion are mutual, exerted by every particle of fluid in the ball t of Coulomb's electrometer, on every particle in the ball a. It is therefore propor- tional to the electric density of each; and therefore, dur- ing the whole diffusion, the densities retain their primi- tive proportion; therefore, the diminution of the repul- sion being as the diminution of the products of the den- sities, it is as the diminution of the squares of either. If therefore the density be represented by \( d \), the mutual re- pulsion is representable by \( d^2 \); and its momentary dimi- nution by the fluxion of \( d^2 \); that is, by \( 2d \times d \), or \( 2d^2 \times d \).

Now \( z \times d^2 \) is to \( d^2 \) as \( 2d \) is to \( d \); and therefore the di- minution of repulsion observed in our experiment bears to the whole repulsion twice as great a proportion as the diminution of density, or the quantity of fluid diffused, bears to the whole quantity at the moment. For ex- ample, if we observe the repulsion diminished \( \frac{1}{2} \), we conclude that \( \frac{1}{2} \) of the fluid has escaped.

Mr Coulomb has not examined the proportion be- tween the diffusions from bodies of different sizes. A great and a small sphere, communicating by a very long canal, have superficial densities, and tendencies to escape, inversely proportional to the diameters. A body of twice the diameter has four times the surface; and though the tendency to escape be twice as small, the surface is four times as great. Perhaps the greater sur- face may compensate for the smaller density, and the quantity of fluid actually gone off may be greater in a large sphere. This may be made the subject of trial.

It must be kept in mind, that the law of diffusion ascertained by these experiments, relates to one given de- pendent state of the air, and that it does not follow that in the state of another state, containing perhaps the same quantity of the air, water, the diffusion shall be the same. The air is such a heterogeneous and variable compound, that it may have very different affinities with the electric fluid. Mr Coulomb thought that he should infer from his numerous experiments, that the diffusion did not increase in the ratio of the cube of the water dissolved in the air, unless it was nearly as much as it could dissolve in that temperature. This indeed is conformable to general observation: for air is thought dry when it dries quickly any thing exposed to it; that is, when not nearly saturated with moisture. Now it is well known, that what is thought dry air is favourable to electricity.

The diffusion along imperfect insulators is brought about in a way somewhat different from the manner of its escaping by electrifying the contiguous air and going off with it. It seems to be chiefly, if not solely, along the surface of the insulating support that the electricity is diffused, and that the diffusion is produced there chiefly by the moisture which adheres to it. It is not very easy to form a clear notion of the manner, but Mr Coulomb's explanation seems as satisfactory as any we have seen.

Water adheres to all bodies, sticking to their surfaces. This adhesion prevents it from going off when electrified; and it is therefore susceptible of a higher degree of electrification. If we suppose that the particles of moisture are uniformly disposed along the surface, leaving spaces between them, the electricity communicated to one particle must attain a certain density before it can fly across the insulating interval to the next. Therefore, when such an imperfect conductor is electrified at one end, the electricity, in passing to the other, will be weakened at every step. If we take three adjacent particles \(a, b, c\) of this conducting matter, we learn, from n° 105, that the motion of \(b\) is sensibly affected only by the difference of \(a\) to \(c\); and therefore that the passage of electricity from \(b\) to \(c\) requires that this difference be superior or equal to the force necessary for clearing this coercive interval. Let a particle pass over. The electric density of the particle \(b\) of conducting matter is diminished, while the density of the particle on the other side of \(b\) remains as before. Therefore some will pass from \(a\) to \(b\), and from the particle preceding \(a\) to \(a\); and so on, till we come to the electrified end of this imperfect insulator. It is plain from this consideration, that we must arrive at last at a particle beyond \(c\), where the whole repulsion of the preceding particle is just sufficient to clear this interval. Some will come over, whose repulsion, now acting in the opposite direction, will hinder any fluid from supplying its place in the particle which it has quitted. Here the transference will stop, and beyond this the infusing is complete. There is therefore a mathematical relation between the insulating power and the length of the canal, which may be ascertained by our theory; and thus another opportunity obtained for comparing it with observation. That this investigation may be as simple as possible, we may take a very probable case, namely, where the insulating, or, to name it more graphically, the coercive, interval is equal in every part of the canal.

Let \(R\) be the coercive power of the insulator; that is, let \(R\) be the force necessary for clearing the coercive interval. Let a ball \(C\) (fig. 36.) be suspended by a silk thread \(AB\), and let \(C\) represent the quantity of its redundant fluid; and let the density in the different points of the canal be as the ordinates \(AD, PD, \&c.\) of some curve line \(DdB\), which cuts the axis in \(B\) where the thread begins to infuse completely. Let \(Pp\) be an element of the axis. Draw the ordinate \(fF\), the tangent \(dfF\), and the normal \(dE\), and \(fe\) perpendicular to \(PD\). Let \(AC = r, AP = x, PD = y\). Then \(Pp = x\), and \(de = -y\). We have seen, that the only sensible action on the particle of fluid in \(P\) is

\[ \frac{xy}{x} \quad \text{(see n° 105)}, \]

when the action of the redundant fluid in the globe on the particle \(P\) having the density \(y\), is represented by

\[ \frac{Cy}{(r + x)}. \]

Therefore we have

\[ \frac{xy}{x} = R, \]

the coercive power of the thread. This is supposed to be constant. Therefore

\[ \frac{Pd \times de}{Pp} = \text{equal to some constant line } R. \]

But \(Pp, \text{or } fe : de = Pd : PE\).

Therefore the subnormal \(PE\) is a constant line. But this is the property of the parabola alone; and the curve of density \(DdB\) is a parabola, of which the parameter is \(2PE\), or \(2R\).

Cor. 1. The densities in different points of an imperfect insulator are as the square roots of their distance from the point of complete insulation: For \(Pd : AD = BP : BA\).

2. The length of canal required for insulating different densities of electricity are as the squares of the densities. For \(AB = \frac{AD^2}{2PE}\); and \(PE\) has been shown to be a constant quantity. Indeed we see in the demonstration, that \(BP\) would infuse a ball, whose electric density is \(PD\), and \(BA : BP = AD^2 : PD^2\).

3. The length necessary for insulation is inversely as the coercive force of the canal, and may be represented generally by \(R\). For \(AB = \frac{DA^2}{2PE} = \frac{D^2}{2R}\).

Mr Coulomb has verified these conclusions by a very satisfactory series of experiments, by the assistance of his delicate electrometer, which is admirably fitted for this trial. The subject is so interesting to every zealous student of electricity, that Mr Canton, Dr B. Wilson, Mr Waitz, Wilcke, and others, have made experiments for establishing some measure of the conducting powers of different substances. It was one of the first things that made the writer of this article suppose that electric action was in the inverse duplicate ratio of the distances: for, as early as 1763, he had found, that the lengths of capillary tubes necessary for infusing were as the squares of the repulsions of the ball which they infusible. The mode of reasoning offers itself, and the fluxionary expression of the infusing power,

\[ \frac{dd}{x} \quad \text{led immediately to a force proportional to } \frac{1}{x^2}. \]

Numerous experiments were made, which we do not give here, because the public are already possessed of those of Mr Coulomb.

This discussion explains, in a satisfactory manner, the operation of the condenser, as described by Mr Volta. The weak degrees of electricity, which are rendered sufficiently sensible by the infusion of the plate of dry marble, are completely infusible by the perhaps thin stratum that has been sufficiently dried, while the rest conducts with an efficacy sufficient for permitting the accumulation. When we reflect on the theory now delivered, we see that the formulae determine the distribution of the fluid along an imperfect conductor in a certain manner, on the supposition that a certain determinate dose has been imparted to the ball; because this dose, by diffusing itself from particle to particle of the conducting matter, will diffuse itself all the way to B, in such a manner that the repulsion shall everywhere be in equilibrium with the maximum of the coercive force of the insulating interval. But it must be farther noticed, that this resistance is not active, but coercitive, and we may compare it to friction or viscosity. Any repulsion of electric fluid, which falls short of this, will not disturb the stability of the fluid spread along the canal, according to any law whatever. So that if AD represent the electric density of the globe, and remain constant, any curve of density will answer, if \( \frac{d^2}{dx^2} \) be everywhere less than R. It is therefore an indeterminate problem to assign, in general, the disposition of fluid in the canal.

The density is as the ordinates of a parabola only on the supposition that the maximum of R is everywhere the same. And, in this case, the distance AB is a minimum; for, in other cases of density, we must have \( \frac{d^2}{dx^2} \) less than R. If, therefore, we vary a single element of the curve DdB, in order that the stability of the fluid may not be disturbed, having d constant, we must necessarily have x larger, that \( \frac{d^2}{dx^2} \) may still be less than R; that is, we must lengthen the axis.

We see also, that to ascertain the distribution in a conducting canal is a determinate problem; whereas, in imperfect conductors, it is indeterminate, but limited by the state of the fluid, when it is disposed that in every point the action of the fluid is in equilibrium with the maximum of resistance. This consideration will be applied to a valuable purpose in the article MAGNETISM.

This doctrine gives, in our opinion, a very satisfactory explanation of the curious observations of Mr Brookes and Mr Cuthbertson, mentioned in n° 167, namely, that damping the inside of a coated jar diminishes the risk of explosion, and enables it to hold a higher charge. We learn here, that there is no density so great but that the least imperfect conductor will inflate it, if long enough; and that the coercive quality of an imperfect conductor may be conceived to constitute from A towards B, that the densities shall diminish in any ratio that we please, so that the variation of density (the cause of motion) may everywhere, even to the inflating point B, be very small. However great the constitution at the edge of the metallic coating may be, an imperfect conductor may be continued outward from that edge, and may be so constituted, that the constitution shall diminish by such gentle gradations, that an explosion shall be impossible. An uniform dampness will not do this, but it will diminish the abruptness of the variation of density. The state of density beyond the edge of the coating of a charged jar, very clean and dry, may be represented by the parabolic arch Dina. This may be changed by damping, or properly dirtying (to use Mr Brookes's phrase), to DfB; which is evidently preferable. We think it by no means difficult to contrive such a continuation of imperfectly-conducting coating. Thus, if gold leaf can be ground to an impalpable powder, it may be mixed with an oil varnish in various proportions. Zones of this gold varnish may be drawn parallel to the edge of the coating, decreasing in metal as they recede from the edge. By such contrivances it may be possible to increase the retentive power to a great degree.

This doctrine farther teaches us, that many precautions must be taken when we are making experiments deducing from which measures are to be deduced; and it points measures out to the mathematician. In particular, when experiments, bodies, supported by insulators, are electrified to a high degree, the supports may receive a quantity of fluid, which may greatly disturb the results; and this quantity, by exerting but a weak action on the parts of the canal, may continue for a very long time, and not be removed but with great difficulty. In such cases, it will be necessary to use new supports in every experiment. Not knowing, or not attending to this circumstance, many erroneous opinions have been formed in some delicate departments of electrical research.

Mr Coulomb's experiments on this subject are chiefly valuable for having stated the relation between the intensity of the electricity, or, as he expresses it, the electric density, and the lengths of support necessary for the complete insulation. But, as the absolute intensities have all been measured by his electrometer, and he has not given its particular scale, we cannot make much use of them till this be done by some electrician.

Mr Coulomb found, that a thread of gum lac was the most perfect of all insulators, and is not less than powers of ten times better than a silk thread as dry as it can be various made, if we measure its excellence by its thinness. In substances of a considerable number of experiments, he found that a thread of gum lac, of 15 inches long, insulated as well as a fine silk thread of 15 inches. When the thread of silk was dipped in fine sealing wax, it was equal to the pure lac, if six inches long, or four times its length. If we measure their excellence by the intensities with which they insulate, lac is three times better than the dry thread, and twice as good as the thread dipped in sealing wax; so that a fibre of silk, even when included in the lac, diminishes its insulating power. We also learn, that the diffusion along these substances is not entirely owing to moisture condensed or adherent on their surfaces, but to a small degree of conducting power. We have repeated many of these experiments, and find that the conducting power of silk thread depends greatly on its colour. When of a brilliant white, or if black, its conducting power seems to be the greatest, and a high golden yellow, or a nut brown, seemed to be the best insulators; doubtless the dyeing drug is as much concerned as the fibre.

Glass, even in its dryest state, and in situations where moisture could have no access to it, viz: in vessels containing caustic alkali dried by red heat, or holding fresh made quicklime, appeared in our experiments to be considerably better than silk; and where drawn into a slender thread, and covered with gum lac (melted), insulated when three times the length of a thread of lac; but we found at the same time, that extreme fineness was necessary, and that it dissipated in proportion to the square of its diameter. It was remarkably hurt by having a bore, however fine, unless the bore could also be coated with lac. Human hair, when completely freed from every thing that water could wash out of it, and then dried by lime, and coated with lac, was equal to silk. Fir, and cedar, and larch, and the rose-tree, when split into filaments, and first dried by lime, and afterwards baked in an oven which just made paper become faintly brown, seemed hardly inferior to gum lac.

The white woods, as they are called, and mahogany, were much inferior. Fir baked, and coated with melted lac, seems therefore the best support when strength is required. The lac may be rendered less brittle by a minute portion of pure turpentine, which has been cleared of water by a little boiling, without sensibly increasing its conducting power. Lac, or sealing wax, dissolved in spirits, is far inferior to its liquid state by heat.

These observations may be of use for the construction of electrical machines of other electrics than glass.

General reflections. We have now given a comparison of the hypothesis of Mr. Epinus with the chief facts observed in electricity, diversified by every circumstance that seemed likely to influence the result, or which is of importance to be known. We trust that the reader will agree with us in saying that the agreement is as complete as can be expected in a theory of this kind; and that the application not only seems to explain the phenomena, but is practically useful for directing us to the procedures which are likely to produce the effect we wish. Thus, should our physiological opinions suggest that copious transference of fluid is proper, our hypothesis points out the most effectual and the most convenient methods for producing it. We learn how to constitute the fluid in a quiescent state, or how to abstract as much of it as possible from any part of a patient; we can do this even in the internal parts of the body. We had once an opportunity of seeing what we thought the cure of a paralysis of the gullet. Electricity was tried, first in the way of sparks, and then small shocks taken across the trachea. These could not be tolerated by the patient. The surgeon wished to give a shock to the oesophagus without affecting the trachea. We recommended a leaden pistol bullet at the end of a strong wire, the whole dipped in melted sealing wax. This was introduced a little way, we think not more than three inches, into the gullet, which the patient permitted. A very slight charge was given to it in a few seconds; and the first shock produced a convulsion in the muscle, and the second removed the disorder completely. Here the ball formed the inner, and the gullet the outer, coating of the little Leyden phial.

Notwithstanding the flattering testimony given by the great conformity of this doctrine with the phenomena, we still choose to present it under the title of a hypothesis. We have never seen the electric fluid in a separate state; nor have we been able to say in what cases it abounds, or when it is deficient. After what we have seen in the late experiments of that philanthropic philosopher Count Rumford on the production of heat by friction, we think that we cannot be too cautious on what grounds we admit invisible agents to perform the operations of Nature. We think that all must acknowledge that those experiments tend very much to stagger our belief in the existence of a fluid sui generis, a fire, heat, caloric, or what we please to call it; and all will acknowledge, that no better proofs can be urged for the existence of an electric fluid.

Accordingly, many acute and ingenious persons have rejected the notion of the existence of an electric fluid, and have attempted to shew that the phenomena proceed, not from the presence of a peculiar substance, but from peculiar modes; as we know that found, and some concomitant motions and other mechanical appearances, are the results of the elastic undulations of air; and as Lord Bacon and others have explained the effects of fire by elastic undulations of the integrant particles of tangible matter.

We have seen nothing, however, of this kind that appears to give any explanation of the motions, forces, and other mechanical appearances of electricity. We peremptorily require, that every doctrine which claims the name of an explanation, shall be perfectly consistent with the acknowledged laws of mechanism; and that the explanation shall consist in pointing out those mechanical laws of which the facts in electricity are particular instances. It is no difficult matter to present an intricate or complex phenomenon to our view, in such a form, that it shall have some resemblance to some other complex physical fact, more familiar, perhaps, but not better understood. The specious appearance of similarity, and the more familiar acquaintance with the other phenomena, dispose us to consider the comparison as a sort of explanation, or, at least, an illustration, and to have a sort of indolent acquiescence in it as a theory.

But this will not do in the present question: For we have here selected a particular circumstance, the observed motions occasioned by electricity, and called attractions and repulsions—a circumstance which admits of the most accurate examination and comparison with any explanation that is attempted. In such a case, a vague picture would speedily vanish into air, and prove to be nothing but figurative expressions.

Many philosophers, and among them some respectable mathematicians, have supported the doctrine of Du Fay, Symmer, Cigusa, &c., who employ two fluids as agents in all electrical operations. It must be granted that there are some appearances, where the explanation by means of two fluids seems, at first sight, more palpable and easier conceived. But whenever we attempt to obtain measures, and to say what will be the precise kind and degree of the action, we find ourselves obliged to assign to the particles of those fluids acting mechanical forces precisely equivalent to those assigned by Epinus to his single fluid. Then we have to add some mysterious unexplained connections, both with each other and with the other particles of tangible matter. If we except Mr Prevost, in his Essai sur les Forces Magnétiques et Électriques, we do not recollect an author who has ventured to subject his system to strict examination, by pointing out to us the laws of action according to which he conceives the particles influence each other. We shall have a proper opportunity, in the article MAGNETISM, to give this author's theory the attention it really merits. We venture to say, that all the chemical theories of electricity labour under these inconveniences, and have acquired their influence merely from the inattention of their partisans.

tians to the laws of mechanical motion, and require, in order to reconcile them with those laws, the adoption of powers similar to Epinus's attractions and repulsions. Slight resemblances to phenomena, which stand equally in need of explanation, have contented the partisans of such theories, and figurative language and metaphorical conceptions have taken place of precise discussion. It would be endless to examine them all.

The most specious of any that we know was published by Mr James Ruffell, Professor of natural philosophy; a person of the most acute discernment, and an excellent reasoner. It was delivered to his pupils, not as a theory, but as a conjecture, founded on Lord Kames's theory of spontaneous evaporation, which had obtained a very general reception; a conjecture, said the Professor, founded on such resemblances as made a similarity of operation very probable, and was an incitement and direction to the philosopher to a proper train of experimental discussion. We say this on the authority of his pupils in the years 1767, 1768, and 1769, and of some notes in his own hand writing now in our possession.

Mr Ruffell considered the electrical phenomena as the results of the action of a substance which may be called the electrical fluid, which is connected with bodies by attractive and repulsive forces acting at a distance, and diminishing as the distance increases.

Mr Ruffell speaks of the electric fluid as a compound of several others; and, particularly, as containing elementary fire, and deriving from it a great elasticity, or mutual repulsion of its particles. This, however, is different from the elasticity or mutual repulsion of the particles of air, because it acts at a distance; whereas the particles of air act only on the adjoining particles. By this constitution, bodies containing more electric fluid than the spaces around them repel each other.

The particles of this electric fluid attract the particles of other bodies with a force which diminishes by distance.

The characteristic ingredient of this fluid is electricity properly so called. This is united with the elastic fluid by chemical affinity, which Mr Ruffell calls elective attraction, a term introduced into chemistry by Dr Cullen and Dr Black. This extends to all distances, but not precisely by the same law as the mutual repulsion of the particles of the other fluid, and in general, it represents the repulsions of that fluid while in this state of composition. This electricity, moreover, attracts the particles of other bodies, but with certain exceptions. Non-electric or conducting bodies are attracted by it at all distances; but electrics act on it only at very small and insensible distances. At such distances its particles also attract each other.

By this constitution, the compound electric fluid repels its own particles at all considerable distances, but attracts at very small distances. It attracts conducting bodies at all distances, but non-conductors, only at very small distances. The phenomena of light and heat are considered as marks of partial decomposition, and as proofs of the presence of elementary fire in the compound: the smell peculiar to electricity, and the effect on the organ of taste, are proofs of decomposition and of the complex nature of the fluid.

Bodies (conductors) containing electric fluid, repel each other at considerable distances, but, if forced very near, attract each other. Electrics can contain it only in consequence of the electricity in the compound. Part of this electricity must be attached to the surface in a non-elastic stage; because when it is brought to near as to be attracted, its particles are within the spheres of each other's action, and this redoubled attraction overcomes the repulsion occasioned by its union with the other ingredient; and the electric fluid is partly decomposed, and the electricity, properly so called, adheres to the surface of the electric, as the water of damp air adheres to a cold pane of glass in our windows. Also, by this constitution, electric fluid may appear in two states; elastic, like air, when entire; and unelastic, like water, when partly decomposed by the attraction of electrics.

Electricity may be forced into this unelastic union by various means; by friction, which forces the electric fluid contained in the air into close contact, and thus occasions this decomposition of the fluid and the union of its electricity with the surface. This operation is compared by Mr Ruffell to the forcible wetting of some powders, such as lycopodium, which cannot be wetted without some difficulty and mechanical compression; after which it adheres to water strongly. It may be thus united in some natural operations, as is observed in the melting and freezing of some substances in contact with electrics; and it may be thus forced into union by means of metallic coatings, into which the electric fluid is forced by an artful employment of its mutual repulsions. This operation is compared to the condensation of the moisture of damp air by a cold pane of the window; and the evacuation of the other side of the coated pane is compared to the evaporation of the moisture from the other side of the window pane, in consequence of the heat which must emerge from the condensed vapour. We find in the Professor's notes above-mentioned many such partial analogies, employed to shew the students that such things are seen in the operations of Nature, and that his conjecture merits attention.

The intelligent reader will see that the general results of this constitution of the electric fluid will tally pretty well with the ordinary electrical phenomena; and, accordingly, this conjecture was received with great satisfaction. We remember the being much pleased with it, as we heard it applied by Mr Ruffell's pupils, many of whom will recollect what is here put on record. But the attentive reader will also see, that all this intricate combination of different kinds of attraction and repulsion is nothing but mere accommodations, of hypothetical forces to the phenomena. How incomparably more beautiful is the simple hypothesis of Epinus, which, without any such accommodations, tallies so precisely with all the phenomena that have yet been observed? Here no distinction of action is necessary, and all the varieties are consequences of a circumstance perfectly agreeable to general laws; namely, that the internal structure of some substances may be such as obstructs the motion of the electric fluid through the pores—Nothing is more likely.

Several years after the death of the Scotch Professor in 1773, a theory very much resembling this of acquired great authority, being proposed to the philosophers by the celebrated naturalist Mr de Luc. This gentleman having long cultivated the study of meteorology with unwearied assiduity and great success, and having been so familiarly conversant with expansive fluids, and the affinities of their compounds, was disposed to see their operations in almost all the changes on the surface of this globe. Electricity was too busy an actor in our atmosphere to escape his particular notice. While the mechanical philosophers endeavoured to explain its effects by accelerating forces attracting and repelling, Mr de Luc endeavoured to explain them by means of the expansive properties of aeriform fluids and gases, and by their chemical affinities, compositions, and decompositions. He had formed to himself a peculiar opinion concerning the constitution of our atmosphere, and had explained the condensation of moisture, whether of steam or of damp aeriform fluids, in a way much more refined than the simple theory of Dr Hooke, viz. solution in air. He considers the compound of air and fire as the carrier of the water held in solution in damp air, and the fire as the general carrier of both the air and the moisture. Even fire is considered by him as a vapour, of which light is the carrier.

When this damp air or steam is applied to a cold surface, such as that of a glass pane, it is decomposed. The water is attracted by the pane by chemical affinity, and attaches itself to the surface. The fire, thus set at liberty, acts on the pane in another way, producing the equilibrium of temperature, and the expansion of the pane. Acting in the same manner on the moisture which chances to adhere to the other side, in a proportion suited to its temperature, it destroys their union, enters into chemical combination with the moisture, and fits it for uniting with the air on the other side, or carries it off.

Having read Mr Volta's theory of electric influences, by which that philosopher was enabled to give a scientific narration and arrangement of the phenomena of the electrophorus newly invented by himself, and which is called an explanation of those phenomena, Mr de Luc imagined that he saw a close analogy between those influences on the plates of the electrophorus and the hygroscopic phenomena of the condensation and evaporation of moisture. In short, he was struck with the resemblance between the condensation of moisture on one side of a glass pane, and its evaporation from the other; and the accumulation of electric fluid on one side of a coated pane, and the abstraction of it from the other. Subsequent examination pointed out to him the same analogy between all other hygroscopic and electric phenomena.

He therefore immediately formed a similar opinion concerning the electric operations. It may be expressed briefly as follows:

The electrical phenomena are the operations of an expansive substance, called the electric fluid. This consists of two parts: 1. Electric matter, which is the gravitating part of the compound; and electric deferent fluid, or carrying fluid, by which alone the electric matter seems to be carried from one body to another. The resemblance between the hygroscopic and electrical phenomena are affirmed to be:

1. As watery vapour or steam is composed of fire, the deferent fluid, and water, the gravitating part, so electric fluid is composed of the electric deferent fluid, and electric matter.

2. As vapours are partly decomposed when too dense for their temperature, and then their deferent fluid becomes free, and shows itself as fire; so electric fluid

that is too dense is decomposed, and its deferent fluid manifests itself in the phosphoric and fiery phenomena of electricity.

3. As fire quits the water of vapour, to unite itself with a body less warm; so the electric deferent quits the electric matter, in part, to go to other bodies which have proportionally less of it.

In this analogy, however, there is a distinction. Fire, in quitting the water in vapour, remains actuated by nothing but its expansive force; remains free, and extends itself till the equilibrium of temperature is restored; but the electric deferent, when disengaged from electric matter, in order to restore its peculiar equilibrium, is actuated by tendencies to distinct bodies, and acts by this tendency in thus restoring the electric equilibrium; and it is only in consequence of this tendency that it quitted the electric matter. This tendency is then directed to some body in the vicinity.

4. As the fire of vapour pervades all bodies, to restore the equilibrium of temperature, depositing the water; so the electric deferent quits the electric matter, to restore the electric equilibrium in an instant, and for this purpose pervades all bodies, depositing on them the electric matter which it carried, but differently, according to their natures.

5. As fire and water, while composing vapour, retain their tendencies and affinities by which they produce the hygroscopic phenomena; so the ingredients of the electric fluid, even in their state of union, retain their tendencies and affinities, which produce the greatest part of the electric phenomena.

6. In particular, the electric matter retains its tendencies and affinities; and farther, the electric affinities are, like the hygroscopic, without any choice.

Here, however, there is a farther distinction. The affinities of water respect only hygroscopic substances; but those of electric matter respect all substances, and therefore respect the common atmospheric fluids.

7. When fire quits the water of vapour, to form the equilibrium of temperature, it remains in the place where vapour most abounds, but is partly latent, not exerting its powers; so in the restoration of the equilibrium of the electric deferent among neighbouring bodies, those which have proportionally most electric matter also retain most deferent fluid, but in a latent state.

8. As two masses of vapour may be in expansive equilibrium (which others call balancing each other's facility) although the vapours contain very different proportions of fire and water; so two masses of electric fluid may be in expansive equilibrium, although one contains much more electric matter in the same bulk, provided that the electric deferent be also more copious.

The chief distinction that mingles with these analogies is, that the affinity of water to hygroscopic substances operates only in contact; whereas electric matter tends to distant bodies; and these distances are very different in regard to different bodies.

Such is the resemblance which has appeared so strong to Mr de Luc. It is evidently the same which furnished the conjecture to Mr Ruffell, and which he considered mechanically, in order to explain the phenomena of electric motions to students of mechanical philosophy. The only resemblance seems to us to appear in the condensation of moisture contained in damp air.

Mr de Luc, led by the habits of his former studies, attempts

Attempts to explain every thing by the relations which were most familiar to him, affinities and expansive forces. Let us attend a little to the manner in which he explains one or two of the most general facts.

1. The conditions of conductors and non-conductors.

This distinction depends on the differences in the tendency to distant bodies: there are great differences in these distances according to the nature of the bodies; and from this arise great differences of phenomena, independent of insulation or non-insulation, which are only the sensible distinctions of these classes of bodies. Electric matter tends to conductors at great distances; but having reached them, it does not adhere, and remains free to move round them, being dragged by the different fluid; but its tendency to non-conductors is only at small and insensible distances; and having come into contact, it adheres, and can no longer be dragged by the different fluid.

Hence the operation of conductors and non-conductors; and there is no other foundation for the notion of ido-electrics and non-electrics, or electric by communication. A part of a non-conductor takes as much electric matter as it can from the substance furnishing it; but cannot communicate it to another part, except very slowly; therefore, to communicate it to the whole surface, we must cover it with a conductor (Surely this is a distinction in the body, independent of the distance of mutual tendency!).

Hence, too, the property of non-conductors by which the electric fluid is benumbed (engorged) or cramped; therefore we can accumulate a great deal in them; and it will remain long, being benumbed; and if it be determined to quit them at once, the current will be much more dense than when quitting an equal conducting surface.

Since conductors do not fix the electric fluid, it must circulate round them. It is urged to this motion by its expansive power, by which it would disperse from a body with inconceivable velocity, and perhaps the rapidity of its motion would decompose it, and cause some light to emerge; but it is at the same time impelled by its tendency to bodies. Thus, by these two forces, it runs to a conducting body, and must circulate round it as the planets do round the sun. In this circulation, if it come to any great projection, it cannot follow the outline, because so abrupt; it therefore flies off at all points and protuberances. It will be the more difficult to keep to an abrupt outline as the stratum in circulation is more copious or deeper, because a greater mass is with greater difficulty turned round a sharp angle. It is more inclined to escape if another body be near, and it immediately becomes a satellite to that body.

Thus all bodies get a share of electric fluid, circulating round conductors, and benumbed or cramped in non-conductors. Bodies of this last class receive their portion by the air as hygroscopic substances receive their water by the fire.

All the differences in the tendencies to bodies proceed from the electric matter. The different fluid follows other laws; namely, 1. Its tendency to all substances is greater than that of the electric matter to any one. 2. The tendency (and also that of the electric matter) is always from the body which contains most of it to that which contains least. 3. The body which contains most of the one also contains most of the other. 4. The different fluid has a particular affinity (chemical) with the electric matter. 5. All these tendencies are lessened by an increase of distance. 6. The electric matter, when composing electric fluid, has more or less expansive force as it is united to more or less different fluid.

Explanation of Charged Plates.

Mr de Luc says (§ 286.), that his system was suggested by Volta's Theory of Electric Influences. These (says he) had been pretty well generalized before, but with little improvement to the science, till Mr Volta discovered a circumstance which, in his opinion, connected by a general theory many phenomena which had formerly no observed relation to any thing. This was, that when a body electrified positively brings a neighbouring body communicating with the ground into the negative state, its own positive electricity is weakened while it remains in that neighbourhood, but is recovered when the other body is removed. "Such is the distinguishing law of Mr Volta's theory, which brings all the phenomena of electric influences under his theory, beginning with those of coated glass, which were formerly so obscure, because they were not referred to their true cause, &c.

"My System (Mr de Luc says) concerning the nature of the electric fluid explains the laws of Mr Volta's theory; and of consequence explains, like it, all the phenomena which it comprehends; but it reaches much farther, seeing that more general laws comprehend a greater number of phenomena.

"In the phenomena of coated glass, I plainly saw one of the procedures of watery vapour. Suppose a glass pane, moistened on both sides, and having the temperature of the surrounding bodies. Suppose that warmer vapour comes to one side. It is condensed on the surface; that is, it is decomposed; the water adheres to the surface, and the fire penetrates the glass, heats it, and increases the evaporation from the other side, by entering into combination with the water and carrying it off with it. More vapour is condensed on the side A; more fire reaches the side B, and carries off more water. But as this happens only because the fire also raises the temperature of the pane, it is evident that the condensation on the side A, and the evaporation from B, must gradually slacken, and the maximum of accumulation in A, and of evaporation from B, will take place when the temperature of the pane is the same with that of the hot vapour.

"The electrical phenomena of coated glass are perfectly similar. The electric fluid reaches the side A, is decomposed, and the electric matter is there benumbed and fixed. The different fluid penetrates the pane, and carries off the electric matter from the side B. This goes on, but slackens; and the maximum of accumulation and evacuation obtains when the side A has acquired the same intensity of electricity with the charging machine. More is accumulated in A than is attracted from B; because B is farther from the source (he might have added, that part of the fire is expended in raising the temperature of the pane); but the accumulation is inactive, because the electric matter is benumbed and fixed. Though the electric matter is much diminished in B, yet the electric fluid in its coating has as much expansive force as that of the ground; because...

because it has a surplus of electric fluid. The absolute quantity of electric matter in both sides is somewhat augmented."

This explanation of the Leyden phial comprehends the whole of Mr de Luc's theory; and the constitution of the electric fluid, and its various affinities, expansive powers and tendencies, are all assigned to it in subfervency to this explanation, or deduced from those phenomena. As the author, in all his writings, claims some superiority over other naturalists for more general and comprehensive views, and for more scrupulous attention to precision and measurement, and particularly for more solicitude that no natural agent be omitted that has any share in the procedure, he surely will not be offended, although we should state such difficulties and objections as occur to us in the consideration of this System (as he chooses to call it) of electricity.

We with that it had been expressed in the plain and precise language of mechanical and chemical science; for he reasons entirely from the nature of expansive forces, tendencies, and affinities. His language will appear to some readers, as it does to us, rather to express the conduct of intelligent beings, acting with choice, and for a purpose, than the laws of life itself. His account would have been less agreeable, it is true, but more instructive, and less apt to be mistaken. Metaphorical language is seldom used without the risk of metaphorical conceptions; and the reader is very apt to think that he has acquired a notion of the subject, while he is really thinking of a thing of a different nature. We apprehend that a great deal of this happens in this instance, and that when the narration is stripped of its figurative language, it will be found without that connection and analogy which it seems to possess.

We also wish that the explanation had been derived from some well-established principle. The whole of it is professedly founded on a resemblance between the phenomena of electricity and some things said of watery vapour; but these are not the phenomena of watery vapour, but Mr de Luc's hypothesis (he will pardon us the term, which we prefer to system) concerning watery vapours. We do not think it philosophic to explain one hypothesis by another. Our illustrious countrymen Bacon and Newton, disapproved of this practice; and their rules of philosophizing have still currency among philosophers. Explanation, in our opinion, is the pointing out some acknowledged general fact in nature, and shewing that the particular phenomenon is an example of it. We do not see this in Mr de Luc's explanation; because we do not see the facts in the case of watery vapours to which the phenomena of electricity are said to have a resemblance. The phenomena we mean are chiefly the motions, and the transference of the powers producing such motions; we do not speak of the light, and some other phenomena, because Mr de Luc does not speak of them in this explanation. We shall even admit the transference as a phenomenon, although we do not see any substance transferred; but we see a power of producing certain motions, where that power did not formerly appear; and the appearance of this power is all the authority adduced, even by Mr de Luc, for the transference. We must now add, that the electric phenomena, which Mr de Luc calls like the phenomena of watery vapour, are all suppositions; and that therefore the explanation is a system of suppositions, framed so as to be like the system of watery vapour. For Mr de Luc will grant, that, on the one hand, we see nothing like the water in the electric phenomena; and, on the other hand, there is nothing in watery vapour like the motions of the electrometers, which are the only phenomena from which Mr de Luc professes to reason.

We also fear that the very curious experiments of Count Rumford on the melting of ice, and the propagation of heat through liquids, will oblige Mr de Luc to change the talk of the ingredients, both of vapour and of electric fluid. Water, and not fire, seems to be the carrier or electric fluid; and we think that Franklin and Ampère have made it highly probable that electricity, and not air, is the carrier.

We have also great difficulty in conceiving (indeed we cannot conceive) how the electric fluid, from which the electric matter has been detached by its superior affinity with the side A, can overcome the same superior affinity of the electric matter with the side B (a), and carry it off; how the electric fluid penetrates the non-conducting pane, in order to carry off the electric matter in the form of fluid; and how it cannot do this, except by means of a conducting canal, into which it is expressly said that it does not penetrate. It must not be said that it runs along the surface of this canal: for the smallest wire will be a sufficient conductor, covered a foot thick with sealing wax. This indeed, according to Mr de Luc, allows the electric fluid to pass; but it must also, according to him, drain it pretty clear of all electric matter. For we cannot help thinking, that the process (although purely ideal) has a closer resemblance to what we should observe in a stream of muddy water poured on a strainer, both sides of which are previously foul. If we were disposed to amuse ourselves with a figurative hypothesis, we could give one on the principle of filtration that is very pretty, and put to the purpose, of glass coated, and charged and discharged by conducting canals.

With respect to the suggestion of this theory by Volta's theory of electric influences, and the ignorance of naturalists before that time of the true state of things, we must observe, that Mr Ruffel proposed the same analogy to the consideration of his hearers many years before; and it was very generally known. The electric influences had been fully detailed by Ampère and Wilcke in 1759, and applied with peculiar address and force of evidence by Mr Cavendish before 1771; and they were described nearly in the same way by Lenz, Lichtenberg, and others.

And with respect to Mr Volta's general principle, which Mr de Luc prizes so highly, and by which he explains every thing, we must observe, that it is not true as a phenomenon in electricity; but, on the contrary, the positive state of a body is rendered stronger, or more remarkable, by inducing the negative state on a neighbouring body. See no. 52 and 66. Mr Volta was misled by the appearances of the electrophorus, which had engaged all his attention, and modelled all his notions on these subjects.

(a) We may here ask, How comes there to be such a quantity of electric matter already lodged in B?—Is it benumbed? or in what state is it? His observations had been confined to disks; and though these are excellent instruments for producing very sensible effects, they are quite unfit for examining the general nature of electric influences. Even without much knowledge of dynamics, a person must perceive that the action of their different parts on the electrometer may be very different, by reason of their different positions and distances from it. Besides, the electrometers of the apparatus described by Mr de Luc in fact, 440, &c., did not indicate the real condition of the disks to which they were attached, but the condition of the remote ends of overcharged conductors of considerable length. Therefore, although all the electrometers fell lower when the other group of disks was brought near, the positive state of the nearest disk was greatly augmented. The most unexceptionable apparatus for this purpose would be a row of polished balls on insulating stands, placed in contact, the whole charged positively; and when another such group, or a long body, is brought near, let the balls be separated at once, and examined apart by a very small electrometer, made in the form of our figure 8. We presume to say that, if the other group is properly managed, and made to communicate thoroughly with the ground, the positive electricity of the balls nearest it will be found greatly augmented, and that every one of them will be found in that precise state of electrification that is pointed out by the Epiphanian theory. Mr de Luc has made and narrated the experiments with the disks, and the curious figures observed by Lichtenberg, with great judgment and fidelity; and they are classical and valuable experiments for the examination of the theory. We may here mention a very neat way of executing the apparatus of balls, which was practised by a young friend, who was so kind as to make the experiments for us, when our thoughts were turned to Mr de Luc's theory. Each ball was mounted on a slender glass rod varnished. The lower end of the stalk was fixed in a little block of wood which had a square hole through it, by which it fitted tightly along a horizontal bar of mahogany, supported at the ends about an inch from the table. The balls were made to separate at once, and equally, from each other, by a chequer-jointed frame, such as is seen in the toyshops, carrying a company of foot soldiers, who open and close their ranks and files by pulling or pushing the ends of the frame. Taking out the pins of the middle joints of this chequered framework, and widening the holes for receiving the glass stalks, it is plain that all the balls will separate at once, in the very state of electricity in which they were when in the neighbourhood of the non-insulated group. This apparatus consisted of six balls. We found the ball next the other group much more strongly positive than before bringing that group near; and it was generally the third ball which seemed equally electric in both situations. We added nine balls more, connecting the whole by a similar contrivance; and found it a most instructive apparatus for the theory of the distribution of the electric fluid. We wish that it had occurred to us when the n°62, &c., were under consideration.

With respect to the condition in which the electric matter is said to be lodged in the side A of the coated pane, where Mr de Luc says that it is fixed, engourdi, in the non-conducting surface (which condition Mr de Luc considers as characteristic of such substances), we must say that the description of its state is by no means agreeable to what we have observed. The powers of this electric matter are no more benumbed or enervated (it is a very unphilosophical phrase), than if it were in a conducting body at the same distance from the opposite coating. If coatings be applied to a block of glass of two or three inches in thickness, and if the electrification be so moderate that it would not fly from the one coating to the other when the glass is removed—no sensible difference will be found between the electricity of the two coatings with or without the glass. The electric matter in the side A has not its powers engourdi; they are balanced by the powers of the side B.

But how will Mr de Luc explain the charging a pane negatively? How will he bring off a quantity of electric matter, greater (according to his own account) than what will be benumbed on the other side? Nay, we must ask, where does he find it? Is there a quantity already benumbed there? What is to revive it?

Let us now consider a little the constitution of the ingredients of this electric fluid, by which all these things are brought about. And in doing this, let us banish, when possible, all figurative language; and, in the precise and dry phraseology of dynamics, let us speak of the motion of single particles of the electric fluid, different fluid, and electric matter. By expansive power, must certainly be meant such a power as that by which air, gases, inflamed gunpowder, steam, and the like, enlarge their bulk, and which is clearly manifested as a mechanical pressure, by bursting vessels, impelling bullets or pithons, &c., as well as by the actual enlargement of the bulk of the fluid. We have no other indications of its being a force; and therefore our notions of its mode of acting must be derived solely from what we understand of this power in air or the other fluids. Newton's Principia are our authority for saying, that all that we know of it is, that it acts as a number of corpuses would act, which repel each other with a force inversely proportional to their distances; this action not extending beyond the adjoining corpuses, not even to the second. We know a good deal of the propagation of pressure and progressive motion through such a fluid, when it is confined in a vessel, or system of vessels, of any form, and some few simple circumstances which take place in the elastic undulations which may be excited and propagated through it. We have but a very indistinct notion of the motions which one mass of such a fluid will produce in another mass, when both are at liberty to expand. This is very indistinct; but we are certain that it will be like the motion of two masses of air blown or driven against each other. Now these electric fluids, by their expansive powers, must act like those others with which we are more familiarly acquainted. And here we venture to say, that the appearances in electricity are so far from being like these, that we cannot imagine anything more remarkably different. We shall mention but one thing. Every mark that we have for the presence of electric fluid obliges us to grant, that in an overcharged body it is crowded into the external surface, so that the quantity has little or no relation to the quantity of matter in any body, but merely to its surface. This is quite unlike air, or any other expansive fluid, which is uniformly distributed through the whole space comprehended by the surface which bounds it. We never saw anything like like streams of this electric fluid, impelling or any way acting on each other, except in the transference by sparks; and there it was indeed like the motions of air, for it was not electric fluid, nor electric matter, but electrified air.

Let us next consider the tendencies by which the relations of these expansive fluids to other bodies are produced, and the electric motions are said to be explained. We observe that Mr de Luc avoids the use of the words attraction and repulsion, so much employed by the British philosophers. He considers these tendencies as determinate impulsions, and adopts the doctrine of Le Sage of Geneva, who has not only laid Newton under great obligations, by a mechanical explanation of gravity, but has also explained expansion, elasticity, chemical affinity, and all specific tendencies, to the satisfaction of the most eminent mathematicians. To such only Mr de Luc professes to address himself, who are not contented with a doctrine which supposes bodices to act where they are not. But, unfortunately, Mr le Sage has never obliged the world with this explanation. We are not most eminent mathematicians; but we are able to prove, that Mr le Sage's favourite theorem, mentioned by Mr de Luc in § 157, 158, as demonstrated by Mr Prevost, the editor of Laurence Newtonian, is a complete detraction of the first principles of Mr le Sage, and is also incompatible with mechanical laws. Mr de Luc should have given a demonstration of the theorem on which all his system relied; otherwise it is only reviving "dixit philosophus, ergo verum."

But let us see what these tendencies perform. Mr de Luc says, that the fluid, setting out from a body by its expansive power, would move in a straight line with inconceivable velocity, and would immediately deflect even this globe, were it not deflected by its tendency to other bodies. We do not see whence this immense velocity is derived. But let it go off; it is deflected from its rectilinear course by its tendency to some conducting body, which it reaches, but cannot, or does not, enter; and therefore must continually circulate round it, as the planets circulate round the sun, following its outline, if not too abrupt, but flying off from all points in the direction of the axis of the point, &c. Here we are at home; for this is a plain dynamical problem of central forces. All that we shall say on this head is, that Mr de Luc has certainly not considered the planetary motions with attention, when he hazarded this very comprehensive proposition. If he will take the trouble to do this, he will see that every part of it is inconsistent with the acknowledged laws of mechanism, and that the motions are absolutely impossible. Besides, we know that it will not fly off from a hundred points placed together, which is a still more abrupt outline, if they do not project beyond the brim of a pit in which they stand; yet this pit only makes the outline more abrupt. We farther believe, that no person can form to himself any distinct notion of such circulations round every conducting body; they will be more numerous, and infinitely more confused and jarring, than all the vortices of Des Cartes. How can such motions take place round a bunch of braids wire buried in sealing wax? Yet he must grant that they really happen there; or what prevents the electric fluid from being strained clear of all electric matter in passing thro' the air?

We would also ask, why the tendency is always from the body containing most of the fluid to that containing least? It is not enough to say that it is so; this would only be contriving a thing to suit a purpose; a reason should be given if we pretend to explain. Now the tendency to a distant body is to the matter in that body, without any relation to the fluid in it, or in the body from which it came.

On the whole, we cannot think this theory is anything but telling a story of ideal beings, in very figurative language, which gives it some animation and interest. The different affinities, tendencies, and powers, are only ways of expressing certain supposed events, and suited to those events; but it gives no explanation of the observed mechanical phenomena of electricity, flowing from acknowledged principles that they must be so.

What a difference between this laboured and intricate mechanism and the simple, perspicuous, and distinct theory of Epinus! Even Mr Ruffell's explanation is more intelligible, and more applicable to the motions which are really observed. That gentleman saw the necessity of considering them as the subjects of mechanical diffusion, and that all that was wanted was to find out what law of distant action would tally with the phenomena. The Scotch philosopher was careful to warn his hearers that he only proposed a conjecture. The Swede calls his performance Tentamen Theoriae, &c., and begins and concludes it with expressly saying, that it is only a hypothesis. The English nobleman calls his dissertation an Attempt to explain some of the phenomena, &c. None of these philosophers call their works a system, which comprehends all theories, whether that of Volta or of any other successful inquirer.

We hope to be excused for treating so largely of this subject. It struck us as a very proper example of the bad consequences of indulging in figurative language. It must be very seducing; when so scrupulous and so eminent a philosopher as Mr de Luc is led astray by it.

We conclude this long article by observing, that whatever may be the fate of Mr Epinus's hypothetical theory, his classification of the facts, and his precise determination of the mechanical phenomena to be expected from any proposed situation and condition of the substances, will ever remain, and be an unerring direction in future experiments; and the whole is an illustrious specimen of ingenuity, address, and good reasoning. We hope to make this still more evident, when we apply it to the quiet and manageable phenomena of Magnetism.

Pondere et mensura,

In page 580, col. 2, line 8th from the bottom, for "incomparable," read "comparable."

APPENDIX;

CONTAINING AN ABSTRACT OF MR COULOMB'S EXPERIMENTS.

Mr Coulomb in the Mem. de l'Acad. de Paris for 1786; relates several experiments made for ascertaining the disposition or distribution of the electric fluid in an overcharged body. Their general results were,

1. That the fluid is distributed among bodies according to their figure, without any elective affinity to any kind of substance.

For when a ball, or body of conducting matter, and of any shape, is electrified to any particular degree, as indica-

The preceding propositions are quite analogous to propositions in Mr Cavendish's dissertation in the Philosophical Transactions for 1771.

In the Memoirs of the same Academy for 1787, Mr Coulomb endeavours to ascertain the density of the fluid in different bodies which touch each other. When the bodies do not differ extremely in magnitude, he determines this by the immediate application of them to the electrometer; but when one is extremely small in comparison with the other, he first determines the force of the large body, and then touches it 20 or 40 times with the small one, till the force of the large body is reduced to \( \frac{1}{3} \), \( \frac{1}{5} \), etc. The general result was, that when the surfaces of the spheres had the proportion expressed in the first column of the following table, then the density in the small one had the proportion expressed by the numbers of the second column, and never attained the magnitude 2.

| Distance | Density | |----------|---------| | 1 | 1 | | 4 | 1.08 | | 10 | 1.3 | | 64 | 1.65 | | Infinite | 2 |

This is extremely different from the proportions which obtain when the two spheres communicate by very long slender canals, which he found exactly conformable to the determinations of the theory: but in Mr Coulomb's experiments the spheres touched each other, and had no other communication.

He then endeavours to ascertain the density of the fluid in the different parts of the surface of their touching spheres, in order to obtain some experimental knowledge of the distribution. He touched them (while in mutual contact) with the little paper circle, and examined its electricity by his electrometer, and made his estimation, on the supposition that it brought off one-half of the electricity of the touched part.

When the globes were equal, he found the density to be 0 at the point of contact, and scarcely sensible till he took the paper 30 degrees from the point of contact. From this it increased rapidly to 60°; slowly from thence to 90°; and from thence to 180° it was almost uniform. The densities were nearly:

| Distance | Density | |----------|---------| | 0 | 0 | | 1 | 30 | | 4 | 60 | | 5 | 90 | | 6 | 180 |

He also found, that the more the globes differed in bulk, the more is the density changed in the small globe, and it is the more uniform in the great one, increasing rapidly from 0, at the point of contact, to about 7, and beyond this being sensibly uniform.

Hence we may conclude, that the electricity is diffused with almost perfect uniformity in a globe communicating with another at a great distance by a slender canal (as Mr Cavendish has demonstrated); while, from the reasoning employed before, it is probable that it is also uniformly diffused all along the canal; and therefore, that the quantities in two such globes are very nearly as the diameters, and the densities inversely as the diameters, as Mr Cavendish demonstrated, on the supposition that the fluid in the canal is incomprehensible.

He found that a small globe, placed between two equally large ones, showed electricities of the same kind...

with that of the other two, when the radius of the great one was not more than five times that of the middle one, but showed no electricity when the disproportion was greater.

When three equal globes were in contact, the density of fluid in the middle globe was $\frac{1}{134}$ of that of the other two. A small globe being removed to a very small distance from an overcharged great one, after having been in contact, showed opposite electricity in the fronting point; when a little farther off, it was neutral; and beyond this, it was overcharged.

The diameters being 11 and 8, the fronting point of the small one was negative till the distance was 1; here it was neutral, and when it was removed farther, it was positive. When the diameters were 11 and 4, the small globe was negative till their distance was 2, where it was neutral. When the diameters were 11 and 2, the distance which rendered the small globe neutral in the fronting point was 2.

All these facts are perfectly conformable to a mathematical deduction, from the supposition that the redundant fluid is spread over the surface, and that the inferior points are neutral. If any sort of doubt should remain in the minds of those who are not conversant in such discussions, it must be greatly removed by the fact, that it is quite indifferent whether one or both globes be solid, or be an extremely thin shell.

When an electrified body is touched with a long wire, and by another of equal diameter and length, coated to any thickness with lac or sealing wax, the two wires take off precisely the same quantity of electricity. This was demonstrated by touching a globe repeatedly till the electricity was reduced to $\frac{1}{4}$.

Hence we must conclude, that the electric fluid does not form active atmospheres around bodies, by the action of whose particles in contact (mathematical or physical) the phenomena of attraction and repulsion are produced, but by the action of the fluid in the body, agreeable to the theory of Alpina.

Such are the observations of Mr Coulomb. They are extremely valuable, because they confirm in the completest manner the legitimate consequences of the theory.

We think that the materiality of that which is transferred from place to place in the exhibition of electric phenomena, is greatly confirmed by some observations of Mr Wilson's in the Pantheon. When a spark was taken from the whole of the long wire extended in that vast theatre, the sensation was so different from a spark which conveyed even a much greater quantity of fluid from a pretty large, but compact, surface, that they could hardly be compared. The last was like the abrupt twitch with the point of a hooked pin, as if pulling off a point of the skin; the spark from the long wire was more like the forcible piercing with a needle, not very sharp, breaking the skin, and pushing it inward. We had this account from the Doctor in conversation. He ascribed it, with seeming justice, to the momentum acquired by the fluid accelerated along that great extent of wire.