ABDC

ABDC (fig. 11.) represents a glass cylinder, twelve inches in diameter and the same in height, covered by a glass plate fitted to it by a projecting fillet on the under surface. This cover is pierced with two round holes one inch and three-fourths in diameter. One of them f is in the centre, and receives the lower end of the glass tube f h, of twenty four inches height, which is fixed in the hole with a cement made of sealing-wax, or other electric substance. The top of this tube receives the brass collar H, (fig. 12. N^o 3.) bored truly cylindrical with a small shoulder, which rests on the top of the tube. This collar is fastened with cement, and receives the hollow cylinder $\backslash phi$ (fig. 12. N^o 2.), to which is joined the circular plate a b, divided on the edge into 360 degrees. It is also pierced with a round hole G in the centre, which receives the cylindrical pin i (fig. 12. N^o 1.) having a milled head b, and furnished with an index i o, whose point is bent down so as to mark the divisions on the circle a b. This pin turns stiffly in the hole G, and the cylinder $\backslash phi$ moves steadily in the collar H. To the lower end of the centre pin is fastened a little pincer, q, formed like the end of a port-crayon, and tightened by the ring q, so as to hold fast the suspension wire, the lower end of which is grasped by a similar pincer, P o (fig. 13.) tightened by the ring $\backslash phi$. The lower end $\backslash phi\; o$ is cylindrical, and is of such a weight, as to draw the wire perfectly straight, but without any risk of breaking it. It may be made equal to half of the weight that will just break it.

This pincer is enlarged at C, and pierced with a hole, which tightly receives the arm g C q of the electrometer. This arm is eight inches long; and consists of a dry silk thread, or a slender straw completely dried, and dipped in melted lac or fine sealing-wax, and held perpendicularly before a clear fire, till it become a slender cylinder of about one-tenth of an inch in diameter. This occupies six of the eight inches, from g to q: the remaining two inches consist of a fine thread of the lac or sealing-wax, as it drains off in forming the arm. At a, is a ball of pith or fine cork,

one-fourth or one-half of an inch in diameter, made very smooth, and gilded. It is balanced by a vertical circle of paper g, of large dimensions, made stiff with varnish. The resistance of the air to this plane soon checks the oscillations of the arm.

The whole instrument is seen in its place in fig. 11, where the arm hangs horizontally about the middle of the height of the great cylinder. In its oscillations the ball a moves round in a circle, whose centre is in the axis of the whole instrument. Its situation is indicated by a graduated circle $\backslash propto\; o\; q$, drawn on a slip of paper, and made to adhere to the glass by varnish. The electrified body whose action is to be observed, is another small ball of cork t, also gilt, or a brass ball well polished. This is carried by a stalk of lac m o, enclosing a dry silk thread. This stalk is grasped by a clamp of cleft deal, or any similar contrivance, which is made to lie firm on the glass cover. When this ball is let down through the hole m, it stands so as to touch the ball a on the arm, when that ball is opposite to o on the graduated circle.

In order to electrify the ball t, we are to employ the insulating handle, fig. 14, which is a slender stick of sealing-wax or lac, holding a metal wire that carries a small polished metallic ball. This is to be touched with some electrified body, such as the prime conductor of a machine, the knob of a jar, &c. This electrified ball is to be introduced cautiously into the hole m, and the ball t is to be touched with it. The ball a is immediately repelled to a distance, twisting the suspension wire, till the force of twist exerted by the wire balances the mutual repulsion of the balls t and a.

This is the process for examining the law of electric action. When it is desired to examine the action of different bodies in different states, another apparatus is wanted. This is represented by the piece c A d (fig. 15.) consisting of a plug of sealing-wax A, fitting tightly into the hole m, and pierced by the wire c d, hooked at c, to receive a wire to connect it occasionally with an electrified body, and having below a polished metal ball d.

The instrument is fitted for observation in the following manner: The milled button b is turned at top, till the twist index i o is at the mark o of the twist circle. Then the whole is turned in the collar H, till the ball a stand opposite to the mark o of the paper circle $\backslash propto\; o\; q$, and at the same time the ball t or d is touched. The observation is thus made. The ball t is first electrified as just described, and thus a is repelled, and retiring twists the wire, settling, after a few oscillations, at such a distance as is proportional to the repulsion. The twist-index is now turned so as to force a nearer to t. The repulsion thus produced is estimated by adding the motion of the index to the angle at which the ball first stopped. Giving the index another turn, we have another repulsion, which is estimated in a similar way, and thus we obtain as many measures as required.

It is not necessary to make this instrument of very large dimensions; one 14 inches high, and five in diameter, of which the arm a g should occupy two inches and a half, will be sufficiently large for most purposes. The diameter of the glass cylinder must always be double the length of the arm a g, that the position of this may not be disturbed by the action of the glass.

Dr Robison considered this electrometer as one of the

the most valuable instruments that have been made, as it is not only extremely delicate, but gives absolute measures with the greatest accuracy. For all purposes in which only repulsions were to be measured, he preferred it to his own instrument described in ELECTRICITY, N^o 206.

He, however, suggested several improvements in it, which are deserving of attention.

The bottom should be furnished with a round hole, admitting the lower end of the cylinder C belonging to the lower pincer (when the wire is strained at both ends) to hang freely, by which means much tedious oscillation will be prevented. It is much more convenient to have the suspension wire strained at both ends; and it should extend as far below the arms as above it, and the lower extremity should be grasped by a pincer that turns by a milled head in a hole at the end of a slender spring. The instrument may then be speedily adjusted by placing the twist index at o, and gently turning the lower button till the ball a point exactly at o on the paper circle.

The instrument will be greatly improved, if, in place of the apparatus with the ball t, we substitute the piece represented at fig. 15, making some little changes in its construction. Thus, instead of the wire c d, is used the smallest glass tube that will admit of being varnished on the inside, which is done by drawing through it a silk thread dipped in varnish, made of lac.

The outside of the tube must also be varnished, and a brass ball d fixed at its lower end, and a slender wire surmounted by a ball, is to be inserted into the tube, so as to touch the ball below. The position of the ball d will not be liable to alteration, when the hole m is once stopped with the plug. In making delicate experiments, the upper ball c must be touched with the charger, represented at fig. 14, by which means the ball d is electrified. Then drawing out C by means of the forceps, the ball d is left completely insulated. In examining the electricity of the atmosphere, to which purpose this instrument is well adapted, the wire must be allowed to remain in the tube.

It was by means of this incomparable instrument, that M. Coulomb made the valuable experiments, to which we alluded in the article ELECTRICITY, when treating of the law of action of the electric fluid. By means of this electrometer, he also made his experiments on the dissipation of electricity into the air, and along imperfect conductors. He ascertained the law of dissipation into the air from bodies in contact, and the relation which this bore to the original repulsion, by first observing the gradual approach of the ball a towards t, in proportion as the electricity dissipated from both, and then slackening the twist index till the ball a resumed its original situation.

The following was the general result of Mr Coulomb's experiments.

That the momentary dissipation of moderate degrees of electricity is proportional to the degree of electricity at the moment. He found that the dissipation is not sensibly affected by the state of the barometer or thermometer; nor is there any sensible difference of bodies of different sizes or different substances, or even different figures, provided that the electricity is very weak.

But he found that the dissipation was greatly affect-

ed by the different states of humidity of the air. In the Electrometer-scale of Saussure's hygrometer, the relation to the quantity of water which a cubic foot of air is capable of holding in solution is distinctly marked; the relation of this solution to the dissipation of electricity in Coulomb's experiments, may hence be seen in the following table, the first column of which marks the degrees of Saussure's hygrometer, the second how many grains of water are dissolved in a cubic foot of air at each degree, and the third column shows the corresponding dissipation per minute.

Hence it follows, that the dissipation is very nearly in the triplicate ratio of the moisture of the air. Thus

if we make $\backslash frac\{69\}\{75\}\; =\; \backslash frac\{7,197\}\{6,180\}$; $m$ will be = 2,764. If we

make $\backslash frac\{69\}\{80\}\; =\; \backslash frac\{8,045\}\{6,180\}$; $m$ will be = 2,76; and if we

make $\backslash frac\{69\}\{87\}\; =\; \backslash frac\{9,240\}\{6,180\}$; $m$ will be = 3,61; or at a medium $m$ will be = 3,40.

The immediate object that M. Coulomb had in view in his experiments, was to ascertain the diminution of repulsion. He found that this, in a given state of the air, was a certain proportion of the whole repulsion taken at the moment of diminution, which is double the proportion of the density of the fluid; for the repulsions by which we judge of the dissipation are reciprocal, being exerted by every particle of fluid in the ball t of the electrometer, on every particle of fluid in the ball a. The diminution of repulsion is therefore proportional to the density of the electric fluid in each ball; and, as during the whole dissipation, the densities continue to have their original proportion, and as the diminution of repulsion is directly proportional to the diminution of the products of the densities, it is consequently directly proportional to the square of either. If we put d for the density, the mutual repulsion will be represented by d², and its momentary diminution by the fluxion of d², or $2d\; \backslash times\; d$. But $2d\; \backslash times\; d\; :\; d^2\; =\; 2\; :\; d$. The diminution of the repulsion observed by experiment will be to the whole repulsion, in double the proportion that the diminution of density, or the dissipation of fluid will have to the whole quantity of fluid at the moment of observation. Let us, for instance, suppose the observed diminution of repulsion to be $\backslash frac\{1\}\{60\}$; we may conclude, that the quantity of fluid lost by dissipation is $\backslash frac\{1\}\{120\}$. M. Coulomb did not examine the proportion of the dissipations from bodies of various sizes. But we know, that if two spheres communicate by a very long canal, their superficial densities, and the tendencies of fluid to escape from them, are inversely as the diameters of the spheres. Now, in a body that has twice the diameter of another body, the surface of the former is quadruple of that of the latter; and though the tendency of fluid to escape from the former is only the half of its tendency to escape from the latter, yet the greater surface of the former may so far make up for its smaller density, that the

the dissipation of fluid from a large sphere may in fact be greater than that from a small one in the same given time.

We have remarked above, that these experiments were made in a particular state of the air; and the law of dissipation ascertained by them is of course adapted only to that given state. In a different state of the air, even if this should be impregnated with the same proportion of moisture, the law of dissipation may be different. The inference which M. Coulomb expected to draw from his experiments was, that the ratio of dissipation would prove to be less than the cube of the quantity of water held in solution, except when that quantity of water was what the air was capable of holding in solution at the given temperature.

This is agreeable to observation; for we know that air which is considered as dry, that is, when it is not nearly saturated with moisture, is the most favourable to electrical phenomena.

Such is the general result of Coulomb's experiments on the dissipation of electricity into the air.

The method in which M. Coulomb examined the dissipation along imperfect conductors, by means of this instrument, was, by completely insulating the ball $t$, and then after observing the loss sustained by a body in contact with it from the air, sliding a metallic rod down the insulating stalk, till the dissipation began to exceed what took place only by the air.

From his experiments respecting the dissipation along imperfect conductors, he found that this took place in a different manner from that in which electricity escaped by communication with the contiguous air. The electricity seems to be diffused chiefly along the surface of the insulator, and appears principally to be produced by the moisture that is more or less attached to it. M. Coulomb illustrates this in the following manner.

Water is found to adhere to the surface of all bodies from which it is prevented by adhesion from escaping when the bodies are electrified, and is thus rendered capable of receiving a greater degree of electric power. Let us suppose that the particles of moisture are disposed uniformly over the surface, with intervals between them; the electricity that is communicated to one particle, must acquire a certain degree of density, before it can fly from this particle to the next, across the intervening insulating space. When an imperfect conductor of this kind is electrified at one extremity, the communicated electricity, in passing to the other extremity, must be weakened every step in passing from particle to particle.

Suppose we have three adjacent particles, which we may call $a$, $b$, and $c$; we infer from N^o 374. of the article ELECTRICITY, that the motion of $b$ is sensibly effected, only by the difference of $a$ and $c$: and therefore the passage of electric fluid from $b$ to $c$, requires that this difference be superior, or at least equal to the force necessary for clearing this coercive interval. Let a particle pass over. The density of fluid of the particle $b$ is diminished, while the density of the particle on the other side of $a$ remains as before. Therefore some fluid 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 insulator. It is plain, from this consideration, that we must at last arrive at a particle beyond $c$, where the whole repulsion of the preceding

particle is just sufficient to clear the coercive interval. Some fluid will come over; and the repulsion of this, acting now in the opposite direction, will prevent any fluid from coming to supply its place in the particle which it has just quitted; the transference of fluid will therefore stop here, and beyond this point the insulation will be complete. Hence we perceive that there is a mathematical relation between the insulating power, and the length of the canal; and this may be ascertained by the theory which we adopted in the article ELECTRICITY. We shall here give an instance of this investigation; and, for the sake of simplicity, we shall take a very probable case, viz. where the insulating interval, or, as we may more properly call it, the coercive interval, is equal in every part of the canal.

Let $R$ represent the coercive power of the insulator, or the degree of force required to clear the coercive interval between two particles. Suppose a ball $C$, fig. 16. suspended by a silken thread $AB$; and let us denote the quantity of a redundant fluid in the ball by $C$, and let the densities at the different points of the canal be denoted by $AD$, $Pd$, &c. ordinates to some curve $DdB$, cutting the axis in $B$, the point where the thread $AB$ begins to insulate completely. Let $Pp$ be an element of the axis; draw the ordinate $pf$, a tangent to the curve $d/f$, the normal $dE$, and draw $fe$ perpendicular to $Pd$. Suppose $AC=r$, $AP=x$, and $Pd=y$. Then we shall have $Pp=x$, and $de=-y$. It was shown in N^o 374. of the article ELECTRICITY, that the

only sensible action of the fluid on a particle at $P$ is $-\backslash frac\{yy\}\{x\}$, when the action of the redundant fluid in the globe on the particle at $P$, having the density $y$, is denoted by $\backslash frac\{Cy\}\{(r+x)^2\}$. Therefore $\backslash frac\{yy\}\{x\}\; =\; R$, the coercive power of

the thread, which is supposed to be constant, $\backslash frac\{Pd\; \backslash times\; dc\}\{Pp\}$ is therefore equal to some constant line $R$. But $Pp$ (or $fe$) : $dc\; =\; Pd\; :\; PE$. The subnormal, $PE$, is therefore a constant line. But as this is the property of a parabola, the curve of density $DdB$ must be a parabola, of which $2PE\; =\; 2R$, is the parameter.

COR. 1.—The densities at different points of an imperfect insulator are in the subduplicate ratio of their distances from the point of complete insulation: for $Pd^2\; :\; AD^2\; =\; BP\; :\; BA$.

COR. 2.—The lengths of canal requisite for insulating different densities of the electric fluid are in the duplicate ratio of their densities; for $AB\; =\; \backslash frac\{AD^2\}\{2PE\}$, and $PE$ is a constant quantity.

COR. 3.—The length of canal requisite for insulation is inversely as its coercive power, and may be represented by $\backslash frac\{D^2\}\{R\}$. For $AB\; =\; \backslash frac\{DA^2\}\{2PE\}\; =\; \backslash frac\{D^2\}\{2R\}$.

If we reflect on this theory, we shall perceive, that our formulæ determine the distribution of fluid along the surface of an imperfect conductor, only in a certain manner, supposing that the ball $C$ has received a certain determinate portion of fluid, for this portion diffusing itself, particle by particle, through the conducting matter, will extend to $b$ in such a manner, as that

Electrometer. the repulsion shall be everywhere in equilibrio with the coercive power of the insulating interval, taken at a maximum.

We must here remark that this resistance is not active, but only coercive, and may be compared to the resistance afforded by viscosity or friction. Any repulsion of electric fluid, which falls short of this, will not disturb the stability of the fluid that is 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 or density will answer,

provided that $\backslash frac\{dd\}\{x\}$ 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 on this supposition only, 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 $\backslash frac\{dd\}\{x\}$ 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 $\backslash frac\{dd\}\{x\}$ may still be less than R; that is, we

must lengthen the axis.

The reasonings which have thus been deduced from theory, were confirmed by M. Coulomb in a numerous set of experiments. These are chiefly valuable for having stated the relation that subsists between the electric density, and the length of support necessary for complete insulation. But as M. Coulomb has not given us the scale of his electrometer, according to which the absolute measures of the densities were determined, the experiments can be of but little use till this be known.

We hinted, at the end of the theoretical part of ELECTRICITY, that the theory of Volta's condenser might be more satisfactorily explained after we had considered the above experiments of Coulomb. The account which we gave of the condenser in Chap. xiii. of that article, (chiefly from Cavallo), was the only one we could properly give in that early part of our view of the science. We are now prepared for a more scientific account of the effects of that instrument. The following is nearly the manner in which Dr Robison considered the subject.

Let the cover of an electrophorus be furnished with a graduated electrometer, such as may indicate the proportional degrees of electricity; electricity it positively to any degree, we shall suppose six, while it is held in the hand, at a little distance, directly over a metallic plate lying on a wire glass, or such like insulating stand, but made to communicate with the ground by a wire. Now bring it gradually down towards the plate. Theory teaches, and we see it confirmed by experiment, that the electrometer will gradually subside, and will perhaps fall to 2°, before the electricity is communicated in a spark: but let us stop it before this happens; the attraction of the lying plate produces a compensation of four degrees of the mutual repulsion of the parts of the cover, by condensing the fluid on its inferior surface, and forming a deficient stratum above. This needs no further explanation, after what we said under ELECTRICITY, on

the charging of coated glass plates. Now we may suppose that the escape of the fluid from this body into the air, begins as soon as it is electrified to 6°, and that it will fly to the insulated plate with the degree 2, if it be brought nearer. But if we can prevent this communication to the insulated plate, by interposing an electric, we may electrify the cover again, while so near the metallic plate, to 6°, before it will pass off into the air. If now it be removed from the lying plate, the fluid would cause the electrometer to rise to 10°, if it did not immediately pass off; and an electric excitement of any kind which could raise this body only to 6° by its intensity, will, by means of this apparatus, raise it to the degree 10, if it be sufficiently copious in extent. If we do the same thing when the wire which connects the lying plate with the ground is taken away, we know that the same diminution of the electricity of the other plate cannot be produced by bringing it down near the lying insulated plate.

The theory of Volta's condenser now becomes very simple. M. Volta seems to have obscured his conceptions of it, by being intent on the electrophorus which he had lately invented, and was thus led into fruitless attempts to explain the advantages of the imperfect conductor above the perfect insulator. But the condensing apparatus is wholly different from an electrophorus; its operations are more analogous to those of a coated plate not charged, and insulated only on one side; and such a coated plate lying on a table will be a complete condenser, if the upper coating be of the same dimensions as the plate of the condenser. All the directions given by M. Volta for preparing the imperfect conductors prove, 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 conducting space. The marble must be thoroughly dried, and even heated in an oven, and either used in this warm state, or must be 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 electricity till it has again become moist. A thick piece of marble is rendered dry only superficially, and still conducts internally. It is then in the best possible state for a condenser. The same is the case with dry unbaked wood. Varnishing the upper surface of a piece of marble or wood is equivalent to covering it with a thin glass plate. Now by this method of covering the top of the marble, a book, or even the table, with a piece of clean dry silk, they all become most perfect condensers. This view of the matter has great advantage. We learn from it how to form a condensing apparatus much more simple and at the same time much more efficacious. We require only the simple moveable plate, which must be covered on the under side with a very thin coating of the finest coach-painters varnish. By connecting this, by a wire, with the substance whose weak electricity is to be examined, this electricity will be raised in the proportion of the thickness of the varnish to the fourth of the plate's diameter. This condensation will be produced by detaching the wire from the insulating handle of the condensing plate, and then lifting this from the table on which it was lying. It will then afford sparks, though the original electricity