philosophising; for we rarely find them forming general propositions on copious inductions of facts in the conduct of men. They always proceed in the synthetic method, as if they were fully conversant in the first principles of human nature, and had nothing to do but to make the application, according to the established forms of logic. While we admire, therefore, the sagacity, the penetration, the candid observation, and the happy illustration, to be found in the works of the ancient moralists and writers on jurisprudence and politics, we cannot but lament that such great men, frequently engaged in public affairs, and therefore having the finest opportunities for deducing general laws, have done so little in this way; and that their writings, however engaging and precious, cannot be considered as anything more refined than the observations of judicious and worthy men, with all the diffuseness and repetition of ordinary conversation. All this has arisen from the want of a just notion of what is attainable in this department of science, namely, the laws of intellectual and moral nature; and of the only possible method of attaining this knowledge, viz. observation and experiment, and the formation of general laws by the induction of particular facts.

We have been led into these reflections by the attention of the ancients to the curious phenomena of magnetism; which must have occurred in considerable antiquity and entertaining variety to any person who had turned to the experimental method. And we have hazarded these free remarks, expecting the acquiescence of our readers, because the superior knowledge which we, in these later days, have acquired of the magnetic phenomena, were the first fruits of the true method of philosophising. This was pointed out to the learned world in 1592 by our celebrated countryman Chancellor Bacon, in his two great works, the Novum Organum Scientiarum, and De Argumentis Scientiarum. Dr Gilbert of Colchester, a philosopher of eminence in many respects, but chiefly because he had the same just views of philosophy with his noble countryman, published about the same time his Physiologia Nova, seu Tractatus de Magnete et Corporibus magnetici. In the introduction, he recounts all the knowledge of the ancients on the subject, and their supine inattention to what was so entirely in their hands; and the impossibility of ever adding to the stock of useful knowledge, so long as men imagined themselves to be philosophising while they were only repeating a few easy words, and the unmeaning phrases of the Aristotelian school. It is curious to remark the almost perfect sameness of Dr Gilbert's sentiments and language with those of Lord Bacon. They both charge, in a peremptory manner, all those who pretend to inform others, to give over their dialectic labours, which are nothing but ringing changes on a few trite truths, and many unfounded conjectures, and immediately to betake themselves to experiment. He has pursued this method on the subject of magnetism with wonderful ardour, and with equal genius and success; for Dr Gilbert was possessed both of great ingenuity, and a mind fitted for general views of things. The work contains a prodigious number and variety of observations and experiments, collected with eagerness from the writings of others, and instituted by himself with considerable expense and labour. It would indeed be a miracle, if all Dr Gilbert's general inferences were just, or all his experiments accurate. It was untrammelled ground. But, on the whole, this performance contains more real information than any writing of the age in which he lived, and is scarcely exceeded by any that has appeared since. We may hold it with justice as the first fruits of the Baconian or experimental philosophy.

This work of Dr Gilbert's relates chiefly to the lodestone, and what we call magnets, that is, pieces of steel which have acquired properties similar to those of the lodestone. But he extends the term magnetism, and the epithet magnetic, to all bodies which are affected by lodestones and magnets in a manner similar to that in which they affect each other. In the course of his investigation, indeed, he finds that these bodies are only such as contain iron in some state or other; and in proving this limitation he mentions a great variety of phenomena which have a considerable resemblance to those which he allows to be magnetic, namely, those which he called electrical, because they were produced in the same way that amber is made to attract and repel light bodies. He marks with care the distinctions between these and the characteristic phenomena of magnets. He seems to have known, that all bodies may be rendered electrical, while ferruginous substances alone can be made magnetic.

It is not saying too much of this work of Dr Gilbert's to affirm, that it contains almost every thing that we know about magnetism. His unwearied diligence in searching every writing on the subject, and in getting information from navigators, and his incessant occupation in experiments, have left very few facts unknown to him. We meet with many things in the writings of posterior inquirers, some of them of high reputation, and of the present day, which are published and received as notable discoveries, but are contained in the rich collection of Dr Gilbert. We by no means ascribe all this to mean plagiarism, although we know traders in experimental knowledge who are not free from this charge. We ascribe it to the general indolence of mankind, who do not like the trouble of consulting originals, where things are mixed with others which they do not want, or treated in a way, and with a painful minuteness, which are no longer in fashion. Dr Gilbert's book, although one of those which does the highest honour to our country, is less known in Britain than on the continent. Indeed we know but of two British editions of it, which are both in Latin; and we have seen five editions published in Germany and Holland before 1648. We carefully recommend it to the perusal of the curious reader. He will (besides the sound philosophy) find more facts in it than in the two large folios of Scarlatti.

After this most deserved eulogy on the parent of magnetic philosophy, it is time to enter on the subject.

In mechanical philosophy, a phenomenon is not to be considered as explained, unless we can show that it is the certain result of the laws of motion applied to matter. It is in this way that the general propositions in physical astronomy, in the theory of machines, in hydraulics, &c. are demonstrated. But the phenomena called magnetic have not as yet obtained such an explanation. We do not see their immediate cause, nor can we say with confidence that they are the effects of any any particular kind of matter, acting on the bodies either by impulsion or pressure.

All that can be done here is to clas the phenomena in the most distinct manner, according to their generality. In this we obtain a two-fold advantage. We may take it for granted that the most general phenomenon is the nearest allied to the general cause. But, farther, we obtain by this method a true theory of all the subordinate phenomena. For a just theory is only the pointing out the general fact of which the phenomenon under consideration is a particular instance. Beginning therefore with the phenomenon which comprehends all the particular cases, we explain those cases in shewing in what manner they are included in the general phenomenon, and thus we shall be able to predict what will be the result of putting the body under consideration into any particular situation. And perhaps we may find, in them all, coincidences which will enable us to shew that they are all modifications of a fact still more general. If we gain this point, we shall have established a complete theory of them, having discovered the general fact in which they are all comprehended. Should we ever remain ignorant of the cause of this general fact, we have nevertheless rendered this a complete branch of mechanical theory. Nay, we may perhaps discover such circumstances of resemblance between this general fact and others, with which we are better acquainted, that we shall, with great probability at least, be able to assign the cause of the general fact itself, by shewing the law of which it is a particular instance.

We shall attempt this method on the present occasion.

The leading facts in magnetism are the two following:

1. If any oblong piece of iron, such as a bar, rod, or wire, be so fitted, that it can assume any direction, it will arrange itself in a certain determinate direction with respect to the axis of the earth. Thus, if, in any part of Britain, an iron or steel wire be thrust through a piece of cork, as represented in fig. 1, so as that the whole may swim level in water, and if it be laid in the water nearly north-west and south-east, it will slowly change its position, and finally settle in a direction making an angle of about 25 degrees with the meridian.

This experiment, which we owe to Dr Gilbert (see B. I. ch. i.), is delicate, and requires attention to many circumstances. The force with which the iron tends toward this final position is extremely weak, and will be balanced by very minute and otherwise insensible resistances; but we have never found it fail when executed as here directed. An iron wire of the size of an ordinary quill, and about eight or ten inches long, is very fit for the purpose. It should be thrust through the cork at right angles to its axis; and so adjusted, by repeated trials, as to swim level or parallel to the horizon. The experiment must also be made at a great distance from all iron; therefore in a basin of some other metal or earthen ware. It may sometimes require a very long while before the motion begins; and if the wire has been placed at right angles to the direction which we have mentioned as final, it will never change its position; therefore we have directed it to be laid in a direction not too remote, yet very sensibly different from the final direction.

But this is not the true position affected by the iron rod. If it be thrust through a piece of wood or cork perfectly spherical, in such a manner that it passes through its centre, and if the centre of gravity coincide with this centre, and the whole be of such weight as to remain in any part of the water, without either ascending or descending, then it will finally settle in a plane inclined to the meridian about 25°, and the north end will be depressed about 73° below the horizon.

All this is equivalent with saying, that if any oblong piece of iron or steel be very nicely poised on its centre of gravity, and at perfect liberty to turn round that centre in every direction, it will finally take the position now mentioned.

We have farther to observe with regard to this experiment, that it is indifferent which end of the rod be placed toward the north in the beginning of the experiment. That end will finally settle toward the north; and if the experiment be repeated with the same rod, but with the other end north, it will finally settle in this new attitude. It is, however, not always that we find pieces of iron thus perfectly indifferent. Very frequently one end affects the northerly position, and we cannot make the other end assume its place; the causes of this difference will be clearly seen by and bye.

The position thus affected by a rod of iron is called Magnetism by Dr Gilbert the MAGNETICAL POSITION OF DIRECTION. It is not the same, nor parallel, in all parts of the earth, as will be more particularly noticed afterwards.

2. The other leading fact is this: When a piece of iron, lying in the magnetical position, or nearly so, and at perfect liberty to move in every direction, is approached by another oblong piece of iron, held nearly in the same position, it is attracted by it; that is, the moveable piece of iron will gradually approach to the one that is presented to it, and will at last come into contact with it, and may then be slowly drawn along by it.

This phenomenon, although not so delicate as the former, is still very nice, because the attraction is so weak that it is balanced by almost insensible obstructions. But the experiment will scarcely fail if conducted as follows: Let a strong iron wire be made to float on water by means of a piece of cork, in the manner already described, having one end under water. See fig. 1, B.

When it is nearly in the magnetical position, bring the end of a pretty big iron rod, such as the point of a new poker, within a quarter of an inch of its southern end (holding the poker in a position not very different from the magnetical position), and hold it there for some time, not exactly southward from it, but a little to one side. The floating iron will be observed to turn towards it with an accelerated motion; will touch it, and may then be drawn by it through the water in any direction. We shall have the same result by approaching the northern extremity of the floating iron with the upper end of the poker.

The same phenomenon may be observed by suspending the first piece of iron by its middle by a long and slender hair or thread. The suspension must be long, otherwise the stiffness of the hair or thread may be sufficient for balancing the very small force with which the pieces of iron tend toward each other. The phenomenon non may also be observed in a piece of iron which turns freely on a fine point, like the needle of the mariner's compass.

In this, as in the former experiment, the ends of the pieces of iron are observed, in general, to be indifferent; that is, either end of the one will attract either end of the other. It often happens, however, that the ends are not thus indifferent, and that the end of the moveable piece of iron, instead of approaching the other, will be observed to recede from it, and appear to avoid it. We shall soon learn the cause of this difference in the states of iron.

It is scarcely necessary to remark, that we must infer from these experiments, that the action is mutual between the two pieces of iron. Either of them may be the moveable piece which approaches the other, manifesting the attraction of that other. This reciprocity of action will be abundantly verified and explained in its proper place.

These two facts were long thought to be peculiar to loadstones and artificial magnets, that is, pieces of iron loaded with certain substances by certain treatment with loadstones; but they were discovered by Dr Gilbert to be inherent in all iron in its metallic state; and were thought by him to be necessary consequences of a general principle in the constitution of this globe. These phenomena are indeed much more conspicuous in loadstones and magnets; and it is therefore with such that experiments are best made for learning their various modifications.

But there is another circumstance, besides the degree of viscosity, in which the magnetism of common iron and steel remarkably differs from that of a loadstone or magnet. When a loadstone or magnet is so supported as to be at liberty to take any position, it arranges itself in the magnetic direction, and one determined end of it settles in the northern quarter; and if it be placed so that the other end is in that situation, it does not remain there, but gradually turns round, and, after a few oscillations, the same end ultimately settles in the north. This is distinctly seen in the needle of the mariner's compass, which is just a small magnet prepared in the same way with all other magnets. The several ends of loadstones or magnets are thus permanently the north or the south ends; whereas we said that either end of a piece of common iron being turned to the northern quarter, it finally settles there.

It is this circumstance which has rendered magnetism so precious a discovery to mankind, by furnishing us with the compass, an instrument by which we learn the different quarters of the horizon, and which thus tells the direction of a ship's course through the pathless ocean (see Compass and Variation, Encyc.). And also shows us the directions of the veins and workings in the deepest mines. It was natural therefore to call those the north and south ends of the mariner's needle, or of a loadstone or magnet. Dr Gilbert called them the poles of the loadstone or magnet. He had found it convenient for the proposed train of his experiments to form his loadstones into spheres, which he called terrella, from their resemblance to this globe; in which case the north and south ends of his loadstones were the poles of the terrella. He therefore gave the name pole to that part of any loadstone or magnet which thus turned to the north or south. The denomination was adopted by all subsequent writers, and now makes a term in the language of magnetism.

Also, when we approach either end of a piece of iron A to either end of another B, these ends mutually attract; or if either end of a magnet A be brought near either end of a piece of common iron, they mutually attract each other. But if we bring that end of a magnet A which turns to the north near to the similar end of another magnet B, these ends will not attract each other, but, on the contrary, will repel. If the two magnets are made to float on pieces of wood, and have their north poles facing each other, the magnets will retire from each other; and in doing so, they generally turn round their axes, till the north pole of one fronts the south pole of the other, and then they run together. This is a very notable distinction between the magnetism of magnets and that of common iron; and whenever we see a piece of iron shew this prominent distinction of its ends, we must consider it as a magnet, and conclude that it has met with some peculiar treatment.

It is not, however, strictly true, that the poles of loadstones or magnets are so fixed in particular parts of their substance, nor that the poles of the same name do constantly repel each other; for if a small or weak magnet A have its pole brought near the similar pole of a large or strong magnet B, they are often found to attract when almost touching, although at more considerable distances they repel each other. But this is not an exception to the general proposition; for when the north pole of A is thus attracted by the north pole of B, it will be found, by other trials, to have all the qualities of a south pole, while thus in the neighbourhood of the north pole of B.

The magnetic properties and phenomena are conveniently distinguished into those of force and polarity. Those of the first class only were known to the ancients, and even of them their knowledge was extremely scanty and imperfect. They may all be classified under the following general propositions:

1. The similar poles of two magnets repel each other with a force decreasing as the distances increase. 2. The dissimilar poles of two magnets attract each other with a force decreasing as the distances increase. 3. Magnets arrange themselves in a certain determinate position with respect to each other.

The first object of research in our farther examination of these properties is the relation which is observed to obtain between the distances of the acting poles and their force of action. This has accordingly occupied much attention of the philosophers, and numerous experiments have been made in order to ascertain the law of variation, both of the attraction and the repulsion. A great number of these have been narrated in the article Magnetism of the Encyc., from which it appears that it has been a matter of great difficulty, and had not been ascertained with certainty or precision when that article was published. It is obvious, from the nature of the thing, that the determination is very difficult, and the investigation very complicated. We can only observe the simultaneous motion of the whole magnet; yet we know that there are four separate actions coexisting and contributing in different directions, and with different forces, to the sensible effect. The force which we measure, in any way whatever, is com- pounded of four different forces, which we cannot separate and measure apart; for the north pole of A repels the north pole of B, and attracts its south pole, while the south pole of A exerts the opposite forces on the same poles of B. The attraction which we observe is the excess of two unequal attractions above two unequal repulsions. The same might be said of an observed repulsion. Nay, the matter is incomparably more complicated than this; because, for any thing that we know, every particle of A acts on every particle of B, and is acted on by it; and the intensity of those actions may be different at the same distances, and is certainly different when the distances are so. Thus there is a combination of an unknown number of actions, each of which is unknown individually, both in direction and intensity. The precise determination is therefore, in all probability, impossible. By precise determination, we mean the law of mutual action between two magnetic particles, or that precise function of the distance which defines the intensity of the force; so that measuring the distance of the acting particles on the axis of a curve, the ordinates of the curve may have the proportions of the attractions and repulsions.

It is almost needless to attempt any deduction of the law of variation from the numerous experiments which have been published by different philosophers. An ample collection of them may be seen in Scarelli's treatise. Mr Mutenbruck has made a prodigious number; but all are so anomalous, and exhibit such different laws of diminution by an increase of distance, that we may be certain that the experiments have been injudicious. Attention has not been paid to the proper objects. Magnets of most improper shapes have been employed, and of most diffuse polarity. No notice has been taken of a circumstance which, one should think, ought to have occupied the chief attention; namely, the joint action of four poles, of which the experiment exhibits only the complex result. A very slight reflection might have made the enquirer perceive, that the attractions or repulsions are not the most proper phenomena for declaring the precise law of variation; because what we observe is only the excess of a small difference of attractions and repulsions above another small difference. Mr Hawking and Dr Brook Taylor employed a much better method, by observing the deviations from the meridian which a magnet occasioned in a compass needle at different distances. This is occasioned by the difference of the two sums of the same forces; and this difference may be made a hundred times greater than the other. But they employed magnets of most improper shapes.

We must except from this criticism the experiments of Mr Lambert, recorded in the Memoirs of the Academy of Berlin for 1756, published in 1758. This most sagacious philosopher (for he highly merits that name) placed a mariner's needle at various distances from a magnet, in the direction of its axis, and observed the declination from the magnetic meridian produced by the magnet, and the obliquity of the magnet to the axis of the needle. Thus, was the action of the magnet set in opposition and equilibrium with the natural polarity of the needle. But the difficulty was to discover in what proportion each of those forces was changed by their obliquity of action on this little lever.

No man excelled Mr Lambert in address in devising methods of mathematical investigation. He observed, that when the obliquity of the magnet to the axis of the needle was 30°, it caused it to decline 1°. When the obliquity was 75°, the distance being the same, it declined 30°. Call the obliquity \( \theta \), and the declination \( d \), and let \( f \) be that function of the angle which is proportional to the action. Also let \( p \) be the natural polarity of the needle, and \( m \) the force of the magnet. It is evident that

\[ p \times f_1 \cdot 15 = m \times f_3 \cdot 30 \]

And \( p : m = f_1 \cdot 30 : f_3 \cdot 15 \); for the same reason

\[ p : m = f_1 \cdot 75 : f_3 \cdot 30 \]

Therefore \( f_1 \cdot 15 : f_3 \cdot 30 = f_1 \cdot 30 : f_3 \cdot 75 \).

But it is well known that

\[ \text{Sine } 15 : \text{Sine } 30 = \text{Sine } 30 : \text{Sine } 75. \]

Hence Mr Lambert was led to conjecture, that the sine was that function of the angle which was proportional to the action of magnetism on a lever. But one experiment was insufficient for determining this point. He made a similar comparison of several other obliquities and declinations with the same distances of the magnet, and also with other distances; and he put it past all dispute, that his conjecture was just.

Had Mr Lambert's experiments terminated here, it must be granted that he has made a notable discovery in the theory of the intimate nature of magnetism. It completely refutes all the theories which pretend to explain the action of a magnet by the impulsion of a stream of fluid, or by pressure arising from the motion of such a stream; for in this case the pressure on the needle must have diminished in the duplicate ratio of the sine. The directive power with the angle 90° must be 4 times greater than with the angle 30°; whereas it was observed to be only twice as great. Magnetism does not act therefore by the impulsion or prelure of a stream of fluid, but in the manner of a simple incitement, as we conceive attraction or repulsion to act.

Having ascertained the effect of obliquity, Mr Lambert proceeded to examine the effect of distance; and, by a most ingenious analysis of his observations, he discovered, that if we represent the force of the magnet by \( f \), and the distance of the nearest pole of the magnet from the centre of the needle by \( s \), and if \( a \) be a constant quantity, nearly equal to two-thirds of the length of the needle, we have \( f \) proportional to \( \frac{s}{a} \).

Mr Lambert found this hold with very great exactness with magnets ten times larger, and needles twice as short. But he acknowledges, that it gives a very singular result, as if the action of a magnet were exerted from a centre beyond itself. He attributes this to its true cause, the still great complication of the result, arising from the action of the remote pole of the magnet. He therefore takes another method of examination, which we shall understand by and bye, when we consider the directive power of a magnet. We have mentioned this imperfect attempt chiefly on account of the unquestionable manner in which he has ascertained the effect of obliquity, and the importance of this determination.

We have attempted this investigation in a very simple manner. We got some magnets made, consisting of two balls connected by a slender rod. By a very particular mode of impregnation, we gave them a pretty good magne- magnetism; and the force of each pole seemed to reside almost in the centre of the ball. This was our object in giving them this shape. It reduced the examination both of the attractive and of the directive power to a very easy computation. The result was, that the force of each pole varied in the inverse duplicate ratio of the distance. The error of this hypothesis in no case amounted to 1/4th of the whole. In computing for the phenomena of the directive power, the irregularities and deviations from this ratio were much smaller.

The previous knowledge of this function would greatly expedite and facilitate our farther investigation: but we must content ourselves with a very imperfect approximation, and with arriving at the desired determination by degrees, and by a very circuitous route.

It is a matter of experience, that when two magnets are taken, each of which is as nearly equal as possible in the strength of both poles, then, if they are placed with their axes in one straight line, and the north pole of one fronting the south pole of the other, they attract each other with a force which diminishes as the distance increases; and this variation of force is regular, that is, without any sudden changes of intensity, till it becomes insensible. No influence has occurred of its breaking suddenly off when of any sensible force, but it appears to diminish continually like gravity. No influence occurs in which attraction is changed into repulsion.

But it is, moreover, to be particularly remarked, that, having made this observation with the north pole of A fronting the south pole of B, if the experiment be repeated with the south pole of A fronting the north pole of B, the results will be precisely the same. And, lastly, it is a matter of unexpected experience, that the sensible action of A on B, measured by the force which is necessary for preventing the farther approach of B, is precisely equal to the action of B on A. This is the case, however unequal the force of the two magnets may be; that is, although A may support ten pounds of iron, and B only ten ounces.

Now, the simplest view we can take of this experiment is, by supposing the whole action of one end or pole of a magnet to be exerted at one point of it. This will give us four actions of A on B, accompanied by as many equal and opposite actions of B on A. It is plain that we may content ourselves with the investigation of one only of these sets of actions.

What we observe is the excess of the attractions of the poles of A for the dissimilar poles of B above the repulsions of the same poles of A for the similar poles of B. At all distances there is such an excess. The sum of the attractions exceeds the sum of the repulsions competent to every distance.

Now this will really happen, if we suppose that the poles of a magnet are of equal strength, and that, however these different magnets differ in strength, they have the same law of diminution by an increase of distance. The first circumstance is a very possible thing, and the last is demonstrated by the observed equality of action and reaction. Every thing will now appear very plain, by representing (as we did in Electricity, Suppl. p. 44, &c.) the intensities of attraction and repulsion by the ordinates of a curve, of which the abscissae represent the distances of the acting poles.

Therefore let A and B (fig. 2.) represent the two magnets, placed with their four poles S, N, s, n, in a straight line. In the straight line Oq take Om, Op, On, Os, respectively equal to Nr, Nn, Sr, Sn; and let MPNQ be a curve line, having Oq for its axis and asymptote; and let the curve, in every part, be convex towards its axis. Then draw the ordinates mM, pP, nN, qQ, to the curve. These ordinates will represent the intensities of the forces exerted between the poles of the magnets, in such a manner as to fulfill all the conditions that are really observed: For mM represents the attraction of the north pole N of the magnet A for the south pole s of the magnet B; pP represents the repulsion of N for n; nN represents the repulsion of S for s; and qQ represents the attraction of S for n. The distance between m and n, or between p and q, is equal to the length of the magnet A; and mp, or nq, is equal to that of B. Mm, Pp, and Nn, Qq, are pairs of equidistant ordinates. It surely requires only the inspection of the figure to see that, in whatever situation along the axis we place those pairs of equidistant ordinates, the sum of Mm and Qq will always exceed the sum of Pp and Nn; that is, the sum of the attractions will always exceed that of the repulsions. This will not be the case if the curve, whose ordinates are proportional to the forces, have a point Z of contrary flexure, as is represented by the dotted curve PZQ. For this curve, having Oq for its asymptote (in order to correspond with forces which diminish continually by an increase of distance, but do not abruptly cease) must have its convexity turned toward this asymptote in the remote parts. But there will be an arch MPZ between Z and O, which is concave toward the asymptote. In which case, it is possible that Mm + Qq shall be less than Pp + Nn; and then the repulsions will exceed the attractions; which is contrary to the whole train of observation.

It may be thought, that if the repulsion exerted between two particles be always less than the attraction at the same distance, the phenomena will be accounted for, although the law of action be not represented by such a curve as has been assumed. Undoubtedly they will, while the dissimilar poles front each other. But the results of such a supposition will not agree with the phenomena while the similar poles front each other: For it is an undoubted fact, that when two fine hard magnets, whose poles are nearly or exactly of equal vigour, have their similar poles fronting each other, the repulsions fall very little short of the attractions at the same distances when their position is changed: When the distances are considerable, scarcely any difference can be observed in the beginning of the experiment. The differences, also, which are observed at smaller distances, are observed to augment by continuing the magnets in their places without changing their distances; and therefore seem to arise from some change produced by each on the magnetism of the other. And, accordingly, if we invert one of the magnets, we shall find that the attractions have been diminished as much as the repulsions. Now, the consequences of magnetic repulsion, being always weaker than attraction, would be the reverse of this. The differences would appear most remarkable in the greater distances, and magnets might be found which repel at small distances, and attract at greater distances; which is contrary to all observation.

From all this it follows, with sufficient evidence for our present purpose, that the function of the distance which expresses the law of magnetic action must be represented by the ordinates of a curve of the hyperbolic kind, referred to its asymptote as an axis; and therefore always convex toward this axis. We think it also sufficiently clear, that the consequences which we have deduced from the simple supposition of four acting points, instead of the combined action of every particle, may be adopted with safety. For they would be just, if there were only those four particles; they would be just with respect to another four particles—therefore they would be just when these are joined; and so on of any number. Therefore the curves, whose ordinates express the mean action of each pole, as if exerted by its centre of effort, will have the same general form: It will be convex toward its asymptotic axis.

It will greatly aid our conceptions of the combined actions of the four magnetic poles, if we notice some of the primary properties of a curve of this kind, limited by no other condition.

Draw the chords MQ, FN, MP, NQ. Bisection them in B, D, E, F, and join EF. Draw the ordinates Ec, Pf, and BD & (cutting EF in C). Draw Pu parallel to the axis, cutting Ec in t. Draw also Qi parallel to the axis, cutting Pf in r. Also draw FHL parallel to the axis, and Po parallel to QN; and draw Plz, and Pe v, cutting Mm in l and x.

Let each ordinate be represented by the letter at its intersection with the axis. Thus, the ordinates Mm and Qq may be represented by m and q, &c.

Because MP is bisected in E, Mt is double of Ec; Mt is double of EL; Mx is double of Ec. Also, because Pt is parallel to QN, and Pu to Qi, we have tu = Ni. From these premises, it is easy to perceive, that,

1. Bb = \(\frac{m + q}{2}\) 2. Db = \(\frac{\rho + n}{2}\) 3. BD = \(\frac{m + q - \rho + n}{2}\) 4. Mu = \(m - \rho\) 5. ut = \(n - q\) 6. Mt = \(m + \rho - n - q\) 7. Ec = \(\frac{m + \rho}{2}\) 8. Pf = \(\frac{n + q}{2}\) 9. Ml = \(m + \rho - n + q\) 10. EL = \(m + \rho - n + q\) 11. CD = \(\frac{m + q - \rho + n}{2}\) 12. CH = \(m + \rho - n + q\)

These combinations will suggest to the attentive reader the explanation of many modifications of the combined action of the four poles of two magnets. They are all comprehended in one proposition, which it will be convenient to render familiar to the thought; namely, if two pairs of equidistant ordinates be taken, the sum of the two extremes exceeds that of the intermediate ones. \(m + q\) is greater than \(\rho + n\). Also, the difference between the pair nearest to O exceeds the difference between the remote pair.

Now, conceiving these ordinates to represent the mutual actions of the magnetic poles, we see that their tendency to or from each other, or their sensible attractions or repulsions, are expressed by \(m + q - \rho + n\); that is, by the excess of the sum of the actions of the nearest and most remote poles above the sum of the actions of the intermediate distant poles. It will also be frequently convenient to consider this tendency as represented by \(m - \rho - n - q\); that is, by the excess of the difference of the actions of the nearest pole of A on the two poles of B, above the difference of the actions of its remote pole on the same poles of B.

Let us now consider some of the chief modifications of these actions.

1. Let the dissimilar poles front each other. It is explained that \(m + q\) represent attractions, and that \(\rho + n\) represent repulsions. Also \(m + q\) is greater than \(\rho + n\). Therefore the magnets will attract each other. This attraction is also represented by \(m - \rho - n - q\).

Now \(m + q - \rho + n\) is evidently equal to Mt, or to twice Ec, or to twice BD, or to four times CD.

This action will be increased,

1. By increasing the strength of either of the magnets. The action of the magnets is the combined action of each acting particle of the one on each acting particle of the other; and it is mutual. Therefore all the ordinates will increase in the ratio of the strength of each magnet, and their sums and differences will increase in the same ratio.

2. By diminishing the distance between the magnets. For this brings all the ordinates nearer to O, while their distances \(mp, pn, ng, rq\) remain as before. In this case it is plain, that Mu, the difference of Mm and Pp, will increase faster than tu or Ni, the difference between Na and Qq. Therefore Mt will increase; that is, the attraction will increase.

3. By increasing the length of A, while the distance between them remains the same. For Om remaining the same, as also mp and ng, while rq is only removed farther from mp, it is plain Mu remains the same, and that Ni and tu are diminished; therefore Mt must increase, or the attraction must increase.

4. By increasing the length of B, the distance between them remaining the same. For this increases mp and ng; and consequently increases Mu and tu. But Mu increases more than tu; and therefore Mt is increased, and the attraction or tendency is increased.

All these consequences of our original supposition, that the magnetic action may be represented by the ordinates of a curve everywhere convex to an asymptotic axis, are strictly conformable to observation.

If we place the magnets with their similar poles And of frothing each other, it is evident that the ordinates which expressed attractions in the former case, will now express repulsions; and that the forces with which the magnets now repel each other, are equal to those with which they attracted when at the same distances. When the experiments are made with good lodestones, or very fine magnets, tempered extremely hard, and having the energy of their poles sensibly residing in a small space very near the extremities, the results are also very near- ly conformable to this mathematical theory; but there is generally a weaker action. The magnets seldom repel as strongly as they attract at the same distance; at least when their distances are small. If one or both of the magnets is felt, or if one of them be much more vigorous than the other, there are observed much greater deviations from this theory. The repulsions are considerably weaker than the attractions at the same distance, and the law of variation becomes extremely different. When placed at very considerable distances, they repel. As the magnet B is brought nearer to A, the repulsion increases, agreeably to the theory, but not so fast. Bringing them still nearer, the repulsion ceases to increase, then gradually diminishes, and frequently vanishes altogether, before the magnets are in contact; and when brought still nearer, it is changed into attraction.

But more careful observation shows, that this anomaly does not invalidate the theory. It is found that the vigour of the magnets is permanently changed by this process. The magnets act on each other in such a way as to weaken each other's magnetism. Nay, it frequently happens, that the weaker or the softer of the two has had its magnetism changed, and that the pole nearest to the other has changed its nature. While they are lying in contact, or at such a distance that they attract, although their similar poles face each other, it is found that the pole of one of them is really changed; although it may sometimes recover its former species again, but never so vigorously as when the other magnet is removed. In short, it is observed, that the magnetism is diminished in all experiments in which the magnets repel each other, and that it is improved in all experiments in which they attract.

We have hitherto supposed the magnets placed with their axes in one straight line. If they are differently placed, we cannot ascertain by this single circumstance of the law of magnetic action, whether they will attract or repel—we must know somewhat more of the variation of force by a change of distance.

If the magnet B be not at liberty to approach toward A, or recede from it, but be so supported at its centre B that it can turn round it, it is very plain that it will retain the position in which it is drawn in the figure. For its south pole s being more attracted by N than it is repelled by S, is, on the whole, attracted by the magnet A; and, by this attraction, it would vibrate like a pendulum that is supported at the centre B. In like manner, its north pole n is more repelled by N than it is attracted by S, and is, on the whole, repelled. The part B n would therefore also vibrate like a pendulum round B. Thus each half of it is urged into the very position which it now has; and if this position be changed a little, the attraction of sB toward A, and the repulsion of nB from it, would impel it toward the position sBn.

This will be very evident, if we put the magnet B into the position sBa', at right angles to the line AB. The pole s and the pole n are urged in opposite, and therefore conflicting, directions with equal forces, very nearly at right angles to s' n', if the magnet B be small. In any oblique position, the forces will be somewhat unequal, and account must be had of the obliquity of the action, in order to know the precise rotative momentum of the actions.

Dr Gilbert has given to this modification of the action of A on B, the name of vis dispontens; which we may translate by directive power or force. Also, that modification of the tendency of B to or from A is called by him the verticitas of B. We might call it the verticity of B; but we think that the name polarity is sufficiently expressive of the phenomenon; and as it has come into general use, we shall abide by it.

It is not easy to give a general, and at the same time its measure, precise measure of the directive power of A and polarity of B. The magnet B must be considered as a lever; and then the force tending to bring it into its ultimate position as depends both on the distance of its poles from N and S, and also on the angle which the axis of B makes with the line AB. When the axis of B coincides with AB, the force acting on its poles, tending to keep them in that situation, is evidently $m + p - n + q$, and therefore may be represented by ML (in fig. 2.), or by twice EL, or by four times CH. If B has the position aB', perpendicular to AB, let the ordinates Ex and Ff cut the curve on I and K; and draw KL parallel to the axis (our figure causes this line almost to coincide with QL, and in all important cases it will be nearly the same). In this case IL will express one half of this force. Either of these estimations of this modification of the mutual action of the magnets, will be sufficient for the objects we have in view.

The directive power of A, and the polarity of B, are how increased,

1. By increasing the strength of one or both of the magnets. This is evident.

2. By diminishing the distance of the magnets. For this, by increasing the sum of Mm and Pp more than the sum of Na and Qq, must increase EL or ML.

3. By increasing the length of A. For this, by removing m and q farther from m and p, must depress the points L and I, and increase EL, or IL, or ML.

4. By diminishing the length of B, while the distance Na between the magnets remains the same. For this, by bringing p and q nearer to m and n, must increase Mm + Pp more than Na + Qq. Or, by bringing Ex and Ff nearer to Mm and Na, it must increase EL and ML.

If the distance Na between the pole of A and the remote pole of B remain the same, the directive force of A, and polarity of B, are diminished by diminishing the length of B, as is easily seen from what has been just now said. It is also diminished, but in a very small degree, by diminishing the length of B, when the distance between the centres of A and B remain the same. For, in this case, the ordinates Ie and Kf retain their places; but the points m and p approach to e; and this brings the intersection E of the ordinate and chord nearer to I, and diminishes EL, because the point L is not so much depressed by the approach of E to K as E is depressed.

But in all cases, the ratio of the directive power of A to its attractive force, or of the polarity of B to its distance affecting tendency to A, is increased by diminishing the length of B. For it is plain, that by diminishing m.p and n.q, while the ordinates Ie and Kf keep their places, the point o is raised, and the point L is depressed; and therefore the ratio of directive EL to Eo, or of ML to Mt, is increased. We even perceive that, by diminishing the length of B continually and and without end, the ratio of $M_1$ to $M_t$ may be made to exceed any ratio that can be assigned.

Now, since diminishing the length of $B$ increases the ratio of the directive power of $A$ to its attractive power, while increasing the length of $A$ increases both, and also increases the ratio of $E_L$ to $E_O$ (as is very easily seen), and since this increase may be as great as we please, it necessarily follows, that if the same very small magnet $B$ be placed at such distances from a large and strong magnet $A$, and from a smaller and less vigorous one $C$, as to have equal polarities to both, its tendency to $A$ will be less than its tendency to $C$. It may even be less in any ratio we please, by sufficiently diminishing the length of $B$.

Dr Gilbert observed this; and he expresses his observation by saying, that the directive power extends to greater distances than the attracting power. We must just conclude, that the law becomes insensible at smaller distances than the first. This will be found a very important observation. It may be of use to keep in mind, that the directive power of a magnet $A$ on another magnet $B$, is the difference of the sums of the actions of each pole of $A$ on both poles of $B$; and the attractive power of $A$ for another magnet $B$, is the difference of the differences of these actions.

It may be also remarked just now, that the directive force of $A$ always exceeds its attractive force by the quantity $2(\rho - q)$. For their difference may be expressed by $\rho t$, which is equal to twice $o L$. Now $ce$ is equal to $P_p$, or to $p$; and $ce$ is equal to $P_p - F_f$, or to $P_p - Q_q - F_f$, or to $P_p - Q_q - F_f$. Therefore $o L = P_p - Q_q$, and $\rho t = 2(P_p - Q_q)$.

By inspecting this figure with attention, we obtain indications of many interesting particulars. If the lengths of the magnets $A$ and $B$ are the same, the point $n$ in the axis of the curve will coincide with $p$. As the length of $A$ increases, the part $ag$ is removed farther from the part $mp$. The line $Pt$ becomes less inclined to the axis, and is ultimately parallel to it, when $a$ is infinitely remote. At this time $L$ falls on $e$; so that the ultimate ratio of the attraction to the polarity is that of $E_c$ to $E_e$, when the magnet $A$ is infinitely long. It is then the ratio of the difference of the actions of the nearest pole of $A$ on the two poles of $B$ to the sum of these actions. Hence it follows, that when $A$ is very great and $B$ very small, the polarity of $B$ is vastly greater than its tendency to $A$. It may have a great polarity when its tendency is insensible.

The ratio of the polarity to the attraction also increases by increasing the distance of the magnets while their dimensions continue the same. This will appear, by remarking that the chords $MP$ and $NQ$ must intersect in some point $w$; and that when the four points $m$, $p$, $n$, and $q$, move off from $O$, keeping the same distances from each other, $EO$ will diminish farther than $EL$, and the ratio of $EL$ to $EO$ will continually increase.

Therefore when a small magnet $B$ is placed at such a distance from a great magnet $A$, and from a smaller one $C$, as to have equal polarity to both, its tendency to $C$ will exceed its tendency to $A$. For the polarities being equal, it must be farther from the great magnet; in which case the ratio of its polarity to its attraction is increased.

And this will also obtain if the magnets differ also in strength. For, to have equal polarities, $B$ must be still farther from the great and powerful magnet.

For all these reasons, a large and powerful magnet may exert a strong directive power, while its attractive power is insensible.

We have hitherto supposed the magnet $B$ to be placed in the direction of the axis of $A$, and only at liberty to turn round its centre $B$. But let its centre be placed on the centre of $A$, as in fig. 3; it must evidently take a position which may be called contrary to that of $A$, the north pole of $B$ turning toward the south pole of $A$, and its south pole turning toward the north pole of $A$.

The same thing must happen when the centre of $B$ is placed in $B$, anywhere in the line $AE$ perpendicular to $NS$. $S$ attracts $n$ with a force $nb$, while $N$ repels $n$ with a force $na$, somewhat smaller than $nb$. These two compose the force $nd$. In like manner, the two forces $ce$ and $sf$, exerted by $N$ and $S$ on the pole $s$, compose the force $sq$. Now if the axis of the magnet $B$ be parallel to $NS$, but the poles in a contrary position, and if each magnet be equally vigorous in both poles, the magnet $B$ will retain this position; because the forces $nb$ and $ce$ are equal, as also the forces $na$ and $sf$. These must compose two forces $nd$ and $sq$, which are equal, and equally inclined to $ns$; and they will therefore be in equilibrium on this lever.

Let us now place the centre of the small magnet in $C$, neither in the axis of the other, nor in the perpendicular $AE$. Let its north pole $n$ point toward the centre of $A$. It cannot remain in this position; for $N$ repels $n$ with a force $nc$, while $S$ attracts it with a force $nb$ (smaller than $nc$, because the distance is greater). These two compose a force $nd$ considerably different from the direction $ce$ of its axis. In like manner, the south pole $s$ of the small magnet is acted on by two forces $ce$ and $sf$, exerted by the two poles of $A$, which compose a force $sq$ nearly equal and parallel to $nd$, but in a nearly opposite direction. It is plain that these forces must turn the small magnet round its centre $C$, and that it cannot rest but in a position nearly parallel to $nd$ or $sq$. Its position is better represented by fig. 4, with its south pole turned toward the north pole of the other magnet, and its north pole in the opposite direction.

What the precise position will be, depends on that function of the distance which is always proportional to the intensity of the action; on the force of each of the poles of $A$, and on the length of the magnet $B$. Nay, even when we know this function, the problem is still very intricate.

There are methods by which we may approximate to the function with success. If the magnet $B$ be indefinitely small, so that we may consider the actions on near its two poles as equal, the investigation is greatly simplified. For, in this case, each pole of the small magnet $B$ (fig. 5.) may be conceived as coinciding with its centre. Then, drawing $NB$, $SB$, and taking $Bb$ toward $N$, to represent the force with which $N$ attracts the south pole of $B$, and taking $Be$, in $SB$ produced, to represent the force with which $S$ repels the same pole, the compound force acting on this pole is $Bd$, the diagonal of a parallelogram $Bb$, $dc$. In like manner, we must take $Be$, in $Nb$ produced, and equal to $Bb$, to to represent the repulsion of N for the north pole of B, and Bf equal to Bc, to represent the attraction of S for this pole. The compound force will be Bg, equal and opposite to Bd. It follows evidently from this investigation, that the small magnet will not rest in any position but dg. In this supposition, therefore, of extreme minuteness of the magnet B, one of the parallelograms is sufficient. We may farther remark, that we have this approximation secure against any error arising from the supposition that all the action of each pole of B is exerted by one point. Although we suppose it diffused over a considerable portion of the magnet, still the extreme minuteness of the whole makes the action, even on its extreme points, very nearly equal.

Hence may be derived a construction for ascertaining the position of the needle, when the function m of the distance is given, or for discovering this function by observation of the position of the needle.

Let NS (fig. 5, n° 2.) meet the direction of the needle in K. Make BG = BN, and draw NF, GE, SH perpendicular to BK. It is evident that Bb is to Bc, or bd, as the fine of the angle HBS to the fine of KBN. Therefore, because BG and BN are equal, we have Bb : Bc = GE : NF.

Therefore GE : NF = BS : BN

But SH : GE = BS : BN

Therefore SH : NF = BS : BN

And SK : NK = BS : BN

If magnetic action be inversely as the distance, we have SK : NK = BS : BN, and B is in the circumference of a circle which passes through S and N, and has BK for a tangent, as is plain by elementary geometry. If the action be inversely as the square of the distance, we have SK : NK = BS : BN, and B is in the circumference of a curve of more difficult investigation. But, as in the circle, the sum of the angles BSN and BNS is a constant angle; so, in this curve, the sum of the cosines of those angles is a constant quantity. This suggests a very simple construction of the curve.

Let it pass through the point T of the line AT, drawn from the centre of the magnet, perpendicular to its axis. Describe the semicircle SPQN, cutting ST and NT in P and Q. Then, in order to find the point where any line SB cuts the curve, let it cut the semicircle in p, and apply the line Nq = SP + NQ = SP, and produce it till it meet the line SB in B, which is a point in the curve; for it is evident that Sp and Nq are the cosines of BSN and BNS. We hope to give, by the help of a learned friend, the complete construction of curves for every value of m, in an Appendix to this article. It will form a new and curious class, arranged by the functions of the angles at N and S.

But, in the mean time, we have determined the position of an indefinitely small needle, in respect of a magnet of which we may conceive the polar activity concentrated in two points; and we may, on the other hand, make use of the observed positions of such a needle and magnet for discovering the value of m. For, since

\[ \frac{SK}{NK} = \frac{BS}{NB} \]

it is plain that \( m = \frac{\log_{10} SK}{\log_{10} SB} \).

Thus, in an observation which the writer of this article made on a very small needle, and a magnet having globular poles, and 8 inches between their centres, he found SB = 57, NB = 7, SK = 1149, and NK = 337. This gives \( m = 1.97 \), which differs from 2 only \( \frac{1}{6} \)th part.

Finding it so very near the inverse duplicate ratio of the distance, a circle VUZ was described, the circumference of which is the locus of SB : BN = 8 : 5333. When the centre of the needle was placed anywhere in the circumference of this circle, it scarcely deviated from the point K, except when far removed from the magnet that its natural polarity prevailed over the directive power of the magnet, or to near its middle that the action of the cylindrical part became very sensible.

It is plain that the length of the needle must occasion some deviation from the magnetic direction, by destroying the perfect equality of action on its two poles. He therefore employed three needles of \( \frac{1}{4}, \frac{1}{2}, \) and \( \frac{3}{4} \) of an inch in length; and by noticing the differences of direction, he inferred what would be the direction, if the forces on each pole were precisely equal. He had the pleasure of feeling that the deviation from the inverse duplicate ratio of the distances was scarcely perceptible.

Mr Lambert's experiments on the directive power of the magnet, narrated in his second dissertation in the 2nd volume of the Memoirs of the Academy of Berlin, are the most valuable of all that are on record; and the ingenious address with which they are conducted, and the inferences are drawn, would have done credit to Newton himself. We earnestly recommend the careful perusal of that Essay, as the most instructive of any that we have read. The writer of this found himself obliged to repeat all his former experiments, mentioned above, in Mr Lambert's manner; and with his precaution of keeping the needle in its natural position; a circumstance to which he had not sufficiently attended before. The new results were still more conformable to his conjecture as to the law of variation. Mr Lambert closes his dissertation with an hypothesis, "that the force of each transverse element of a magnet is as its distance from the centre, and its action on a particle of another magnet is inversely as the square of the distance." On this supposition, he calculates the position of a very small needle, and draws three of the curves to which it should be the tangent. These are very exactly coincident with some that he observed. We tried this with several magnetic bars, and found it very conformable to observation in some magnets; but deviating too far in the case of other magnets, that we are convinced that there is no rule for the force of each transverse element of a magnet, and that the magnetism is differently disposed in different magnets. It was chiefly this which induced us to form the magnets employed in this research of two balls united by a slender rod. Lichtenberg, in his notes on Erxleben's Natural Philosophy, says, that there is a Ms. of the celebrated Tobias Mayer in the library of the Academy of Göttingen, in which he affirms the hypothesis above-mentioned, and gives a construction of the magnetic curves founded on it, making them a kind of catenaria. The interior curves do indeed resemble the catenaries, but the exterior are totally unlike. But there is no occasion for much argument to convince us, that the first part of this hypothesis is not only gratuitous, but unwarranted by any general phenomena. We know that a magnetic bar may have its magnetism very differently disposed; for it may have more than two poles, and the intermediate poles cannot have this disposition of the magnetism. Magnetism.

Such a disposition is perhaps possible; but is by no means general, or even frequent. We are disposed to think, that permanent magnetism must have its intensity diminishing in the very extremity of the bar. The reader may guess at our reasons from what is said in Electricity, Suppl. p. 222.

The following very curious and instructive phenomenon was the first thing which greatly excited the curiosity of the writer of this article, and long puzzled him to explain it. Indeed it was his endeavor to explain it which gradually opened up to him the theory of the mutual action of magnets contained in these paragraphs, and first gave him occasion to admire the sagacity of Dr. Gilbert, and to see the connecting principle of the vast variety of observations and experiments which that philosopher had made. It seems owing to the want of this connecting principle, that a book so rich in facts should be so little read, and that so many of Dr. Gilbert's observations have been published by others as new discoveries.

Amusing himself in the summer 1758 with magnetic experiments, two large and strong magnets A and B (fig. 6), were placed with their dissimilar poles facing each other, and about three inches apart. A small needle, supported on a point, was placed between them at D, and it arranged itself in the same manner as the great magnets. Happening to set it off to a good distance on the table, as at F, he was surprised to see it immediately turn round on its pivot, and arrange itself nearly in the opposite direction. Bringing it back to D restored it to its former position. Carrying it gradually out along DF, perpendicular to NS, he observed it to become sensibly more feeble, vibrating more slowly; and when in a certain point E, it had no polarity whatever towards A and B, but retained any position that was given it. Carrying it farther out, it again acquired polarity to A and B, but in the opposite direction; for it now arranged itself in a position that was parallel to NS, but its north pole was next to N, and its south pole to S.

This singular appearance naturally excited his attention. The line on which the magnets A and B were placed had been marked on the table, as also the line DF perpendicular to the former. The point E was now marked as an important one. The experiments were interrupted by a friend coming in, to whom such things were no entertainment. Next day, wishing to repeat them to some friends, the magnets A and B were again laid on the line on which they had been placed the day before, and the needle was placed at E, expecting it to be neutral. But it was found to have considerable vorticity, turning its north pole toward the magnet B; and it required to be taken farther out, toward F, before it became neutral. While standing there, something chanced to joggle the magnets A and B, and they instantly rushed together. At the same instant, the little magnet or needle turned itself briskly, and arranged itself as it had done the day before, at F, quivering very briskly, and thus shewing great vorticity. This naturally surprised the beholders; and we now found that, by gradually withdrawing the magnets A and B from each other, the needle became weaker—then became neutral—and then turned round on its pivot, and took the contrary position. It was very amusing to observe how the simply separating the magnets A and B, or bringing them together, made the needle assume such a variety of positions and degrees of vorticity in each.

The needle was now put in various situations, in respect to the two great magnets; namely, off at a side, and not in the perpendicular DF. In these situations, it took an inconceivable variety of positions, which could not be reduced to any rule; and in most of them, it required only a motion of one of the great magnets for an inch or two, to make the needle turn briskly round on its pivot, and assume a position nearly opposite to what it had before.

But all this was very puzzling, and it was not till after several months, that the writer of this article, having conceived the notion of the magnetic curves, was in a condition to explain the phenomena. With this assistance, however, they are very clear, and very instructive.

Nothing hinders us from supposing the magnets A and B perfectly equal in every respect. Let NHM, NEL, be two magnetic curves belonging to A; that is, such that the needle arranges itself along the tangent of the curve. Then the magnet B has two curves SGK, SEI, perfectly equal, and similar to the other two. Let the curves NHM and SGK intersect in C and F. Let the curves NEL and SEI touch each other in E.

The needle being placed at C, would arrange itself in the tangent of the curve KGS, by the action of B alone, having its north pole turned toward the south pole S of B. But, by the action of A alone, it would be a tangent to the curve NHM, having its north pole turned away from N. Therefore, by the combined action of both magnets, it will take neither of these positions, but an intermediate one, nearly bisecting the angle formed by the two curves, having its north pole turned toward B.

But remove the needle to F. Then, by the action of the magnet A, it would be a tangent to the curve FM, having its north pole toward M. By the action of B, it would be a tangent to the curve KFG, having its north pole in the angle MFG, or turned toward A. By their joint action, it takes a position nearly bisecting the angle GFM, with its north pole toward A.

Let the needle be placed in E. Then, by the action of the magnet A, it would be a tangent to the curve NEL, with its north pole pointing to F. But, by the action of B, it will be a tangent to SEI, with its north pole pointing to D. These actions being supposed equal and opposite, it will have no vorticity, or will be neutral, and retain any position that is given to it.

The curve SEI intersects the curve NHM in P and Q. The same reasoning shows, that when the needle is placed at P, it will arrange itself with its north pole on the angle SPH; but, when taken to Q, it will stand with its north pole in the angle EQM.

From these facts and reasonings we must infer, that, for every distance of the magnets A and B, there will be a series of curves, to which the indefinitely short needle will always be a tangent. They will rise from the adjoining poles on both sides, crossing diagonally the lozenges formed by the primary or simple curves, as in fig. 6. These may be called compound or secondary magnetic curves. Moreover, these fe- Secondary curves will be of two kinds, according as they pass through the first or second intersections of the primary curves, and the needle will have opposite positions when placed on them. These two sets of curves will be separated by a curve GEH, in the circumference of which the needle will be neutral. This curve passes through the points where the primary curves touch each other. We may call this the line of neutrality or inactivity.

We now see distinctly the effect of bringing the magnets A and B nearer together, or separating them farther from each other. By bringing them nearer to each other, the point E, which is now a point of neutrality, may be found in the second intersection (such as F) of two magnetic curves, and the needle will take a contrary position. By drawing them farther from each other, E may be in the first intersection of two magnetic curves, and the needle will take a position similar to that of C.

If the magnets A and B are not placed so as to form a straight line with their four poles, but have their axes making an angle with each other, the contacts and intersections of their attending curves may be very different from those now represented; and the positions of the needle will differ accordingly. But it is plain, from what has been laid, that if we knew the law of action, and consequently the form of the primary curves, we should always be able to say what will be the position of the needle. Indeed, the consideration of the simple curves, although it was the mean of suggesting to the writer of this article the explanation of those more complicated phenomena, is by no means necessary for this purpose. Having the law of magnetic action, we must know each of the eight forces by which the needle is affected, both in respect of direction and intensity; and are therefore able to ascertain the single force arising from their composition.

When the similar poles of A and B are opposed to each other, it is easy to see, that the position of the needle must be extremely different from what we have been describing. When placed anywhere in the line DF, between two magnets, whose north poles face each other in N and S, its north pole will always point away from the middle point D. There will be no neutral point E. If the needle be placed at P or Q, its north pole will be within the angle EPH, or FQI. This position of the magnets gives another set of secondary curves, which also cross the primary curves, passing diagonally through the lozenges formed by their intersection. But it is the other diagonal of each lozenge which is a chord to those secondary curves. They will, therefore, have a form totally different from the former species.

The consideration of this compounded magnetism is important in the science, both for explaining complex phenomena, and for advancing our knowledge of the great deaderatum, the law of magnetic action. It serves this purpose remarkably. By employing a very small needle, the points of neutrality ascertain very nearly where the magnetic curves have a common tangent, and shows the position of this tangent. By placing the two magnets so as to form various angles with each other, we can, by means of these neutral points, know the position of the tangent in every point of the curve, and thus can ascertain the form of the curve, and the law of action, with considerable accuracy. The writer of this article took this method; and the result confirmed him in the opinion, that it was in the inverse duplicate ratio of the distances. The chief (perhaps the only) ground of error seemed to be the difficulty of procuring large magnets, having the action of each pole very much concentrated. Large magnets must be employed. He attempted to make such, consisting of two spherical balls, joined by a slender rod. But he could not give a strong magnetism to magnets of this form, and was forced to make use of common bars, the poles of which are considerably diffused. This diffusion of the pole renders it very difficult to select with propriety the points from which the distances are to be estimated, in the investigation of the relation between the forces and distances.

He tried another method for ascertaining this so much desired law, which had also the same result. Having made a needle consisting of two balls joined by a slender rod, and having touched it with great care, so that the whole strength of its poles seemed very little removed from the centres of the balls, he counted the number of horizontal vibrations which it made in a given time by the force of terrestrial magnetism. He then placed it on the middle of a very fine and large magnet, placed with its poles in the magnetic meridian, the north pole pointing south. In this situation he counted the vibrations made in a given time. He then raised it up above the centre of the large magnet, till the distance of its poles from those of the great magnet were changed in a certain proportion. In this situation its vibrations were again counted. It was tried in the same way in a third situation, considerably more remote from the great magnet. Then, having made the proper reduction of the forces corresponding to the obliquity of their action, the force of the poles of the great magnet was computed from the number of vibrations. To state here the circumstances of the experiment, the necessary reductions, and the whole computations, would occupy several pages, and to an intelligent reader would answer little purpose. Mr Lambert's excellent dissertation in the 2nd vol. of the Mem. de l'Acad. de Berlin, will show the prolixity and intricacy of this investigation. Suffice it to say, that these experiments were the most consistent with each other of any made by the writer of this article, with the view of ascertaining the law of magnetic action; and it is chiefly from their result that he thinks himself authorized to say, with some confidence, that it is inversely as the square of the distance. These experiments were first made in a rough way in 1769 and 1770. In 1775, observing that Mr Epinus seemed to think the action inversely as the distance (see his Tentam. Theor. Elec. et Magn. § 301, &c.), they were repeated with very great care; and to these were added another set of experiments, made with the same magnet and the same needle, placed not above the magnet, but at one side (but always in the line through the centre, perpendicular to the axis, so that the actions of the two poles might be equal). This disposition evidently simplifies the process exceedingly. The result of the whole was still more satisfactory. This conclusion is also confirmed by the experiments of Mr Coulomb in the Memoirs of the Academy of Sciences at Paris for 1786 and 1787. It would seem therefore to be pretty well established. Another method, which seems susceptible of considerable considerable accuracy, still remains to be tried. It will be mentioned in due time.

Such then are the general laws observed in the mutual action of magnets. We think it scarcely necessary to enter into a further detail of their consequences, corresponding to the innumerable varieties of positions in which they may be placed with respect to each other. We are confident, that the sensible actions will always be found agreeable to the legitimate consequences of the general propositions which we have established in the preceding paragraphs. We proceed therefore to consider some physical facts not yet taken notice of, which have great influence on the phenomena, and greatly assist us in our endeavours to understand something of their remote cause.

Magnetism, in all its modifications of attraction, repulsion, and direction, is, in general, of a temporary or perishable nature. The best lodestones and magnets, unless kept with care, and with attention to certain circumstances, are observed to diminish in their power. Natural lodestones, and magnets made of steel, tempered as hard as possible, retain their virtue with greatest obstinacy, and seldom lose it altogether, unless in situations which our knowledge of magnetism teaches us to be unfavourable to its durability. Magnets of tempered steel, such as are used for watch-springs, are much sooner weakened, part with a greater proportion of their force by simple keeping, and finally retain little or none. Soft steel and iron lose their magnetism almost as soon as its producing cause is removed, and cannot be made to retain any sensible portion of it, unless their metallic state suffer some change.

1. Nothing tends so much to impair the power of a magnet as the keeping it in an improper position. If its axis be placed in the magnetic direction, but in a contrary position, that is, with the north pole of it where the south pole tends to settle, it will grow weaker from day to day; and unless it be a natural lodestone, or be of hard tempered steel, it will, after no very long time, lose its power altogether.

2. This dissipation of a strong magnetic power is greatly promoted by heat. Even the heat of boiling water affects it sensibly; and if it be made red hot, it is entirely destroyed. This last fact has long been known. Dr Gilbert tried it with many degrees of violent heat, and found the consequences as now stated; but having no thermometers in that dawn of science, he could not say anything precise. He only observed, that it is destroyed by a heat not sufficient to make it visible in a dark room. Mr Canton found even boiling water to weaken it; but on cooling again the greatest part was recovered.

3. What is more remarkable, magnetism is impaired by any rough usage. Dr Gilbert found, that a magnet which he had impregnated very strongly, was very much impaired by a single fall on the floor; and it has been observed since his time, that falling on stones, or receiving any concussion which causes the magnet to ring or sound, hurts it much more than beating it with anything soft and yielding. Grinding a natural lodestone with coarse powders, to bring it into shape, weakens it much; and lodestones should therefore be reduced into a shape as little different from their natural form as possible; and this should be done briskly, cutting them with the thin disks of the lapidary's wheel, cutting off only what is necessary for leaving their most active parts or poles as near their extremities as we can.

All these causes of the diminution of magnetism are more operative if the magnet be all the while in an improper position.

4. Lastly, magnetism is impaired and destroyed by placing the magnet near another magnet, with their similar poles facing each other. We have had occasion to remark this already, when mentioning the experiments made with magnets in this position, for attaining the general laws or variations of their repulsion. We there observed, that magnets so situated always weakened each other, and that a powerful magnet often changed the species of the nearest pole of one less powerful. This change is recovered, in part at least, when it has taken place in a lodestone or a magnet of hard steel; but in spring tempered steel the change is generally permanent, and almost to the full extent of its condition while the magnets are together. It is to be remarked, that this change is gradual; and is expedited by any of the other causes, particularly by heat or by knocking.

On the other hand, magnetism is acquired by the same means, when some other circumstances are attended to.

1. A bar of iron, which has long stood in the magnetic direction, or nearly so, will gradually acquire magnetic polarity, and the ends will acquire the polarity corresponding to their situation. In this country, and the north of Europe, the old spindles of turret vases, old bars of windows, &c., acquire a sensible magnetism; their lower extremity becoming a north pole, and the other end a south pole. Gilbert says, that this was first observed in Mantua, in the vase spindle of the Augustinian church—"Vesto flexa (says he) de prompta, et apothecario cuidam concepsa, attrabebat ferrea ramenta, vi perquam infirma." The upper bar of a hand rail to a stair on the north side of the highest part of the steeple of St Giles's church in Edinburgh is very magnetic; and the upper end of it, where it is lodged in the stone, is a vigorous south pole. It is worth noticing, that the parts of such old bars acquire the strongest magnetism when their metallic state is changed by exposure to the air, becoming foliated and friable. It would be worth while to try, whether the ethiops martialis, produced by steam in the experiments for decomposing water, will acquire magnetism during its production. The pipe and the wires, which are converted into the thinning ethiops, should be placed in the magnetic direction.

2. If a bar of steel be long hammered while lying in the magnetic direction, it acquires a sensible magnetism (See Dr Gilbert's plate, representing a blacksmith hammering a bar of iron in the magnetic direction). The points of drills, especially the great ones, which are urged by very great pressure; and broaches, worked by a long lever, so as to cut the iron very fast, acquire a strong magnetism; and the lower end always becomes the north pole (Phil. Trans. xx. 417.) Even driving a hard steel punch into a piece of iron, gives it magnetism by a single blow. In short, any very violent squeeze given to a piece of tempered steel renders it magnetic, and its polarity corresponds with its position during the experiment. We can scarcely take up a cutting or boring tool in a smith's shop that is not magnetic. Even soft soft steel and iron acquire permanent magnetism in this way. Iron also acquires it by twisting and breaking. It is therefore difficult to procure pieces of iron or steel totally void of determinate and permanent magnetism; and this frequently mars the experiments mentioned in the first paragraphs of this article. The way therefore to ensure success in these experiments is to deprive the rods of their accidental magnetism, by some of the methods mentioned a little ago. Let them be heated red hot, and allowed to cool while lying in a direction perpendicular to the magnetic direction (nearly E.N.E. and W.S.W. in this country).

3. As heat is observed to destroy magnetism, so it may also be employed to induce it on substances that are susceptible of magnetism. Dr Gilbert makes this observation in many parts of his work. He says, that the ores of iron which are in that particular metallic state which he considers as most susceptible of magnetism, will acquire it by long continuance in a red heat, if laid in the magnetic direction, and that their polarity is conformable to their position, that end of the mass which is next the north becoming the north pole. He also made many experiments on iron and steel bars exposed to strong heats in the magnetical direction. Such experiments have been made since Gilbert's time in great number. Dr Hooke, in 1684, made experiments on rods of iron and steel one-fifth of an inch in diameter, and seven inches long. He found them to acquire permanent magnetism by exposure to strong heat in the magnetic direction, and if allowed to cool in that direction. But the magnetism thus acquired by steel rods was much stronger, and more permanent, if they were suddenly quenched with cold water, so as to temper them very hard. He found, that the end which was next to the north, or the lower end of a vertical bar, was always its permanent north pole. Even quenching the upper end, while the rest was suffered to cool gradually, became a very sensible south pole. No magnetism was acquired if this operation was performed on a rod lying at right angles to the magnetical direction.

In these trials the polarity was always estimated by the action on a mariner's needle, and the intensity of the magnetism was estimated by the deviation caused in this needle from its natural position. Dr Gilbert made a very remarkable observation, which has since been repeated by Mr Cavalli, and published in the Philosophical Transactions as a remarkable discovery. Dr Gilbert says, p. 69. "Bacillum ferrum, valde ignitum apud se veriorum excitio; sed veriorum, nec ad tale ferrum convertitur; sed statim ut primum de candore aliquantum remissum, confinit illius." In several other parts of his treatise he repeats the same thing with different circumstances. It appears, therefore, that while iron is red hot, it is not susceptible of magnetism, and that it is during the cooling in the magnetic direction that it acquires it. Gilbert endeavoured to mark the degree of heat most favourable for this purpose; but being unprovided with thermometers, he could not determine anything with precision. He says, that the veriorum, or mariner's needle, was most deranged from its natural position a little while after the bar of iron ceased to shine in daylight, but was still pretty bright in a dark room. But there are other experiments which we have made, and which will be mentioned by and bye; by which it appears, that although a bright red or a white heat makes iron unsusceptible of magnetism while in that state, it predisposes it for becoming magnetic. When a bar of steel was made to acquire magnetism by tempering it in the magnetical direction, we found that the acquired magnetism was much stronger when the bar was made first of all very hot, even although allowed to come to its most magnetic state before quenching, than if it had been heated only to that degree; may, we always found it stronger when it was quenched when red hot. We offer no explanation at present; our sole business just now being to state facts, and to generalize them, in the hopes of finding some fact which shall contain all the others.

4. The most distinct acquisitions and changes of magnetism are by juxtaposition to other magnets and to iron, separation. As the magnetism of a lodestone or magnet is weakened by bringing its pole near the similar pole of another magnet, it is improved by bringing it near the other pole; and it is always improved by bringing it near any piece of iron or soft steel.

But this action, and the mutual relation of magnets and common iron, being the most general, and the most curious and instructive of all the phenomena of magnetism, they merit a very particular consideration.

Of the communication of Magnetism.

This whole may be comprehended in one proposition, which may be said to contain a complete theory of magnetism.

Fundamental proposition:

Any piece of iron, when in the neighbourhood of a magnet, is a magnet, and its polarity is so disposed that the magnet and it mutually attract each other.

The phenomena which result from this fundamental principle are infinitely various, and we must content ourselves with describing a simple case or two, which will sufficiently enable the reader to explain every other.

Take a large and strong magnet N S (fig. 7.), of which N is the north, and S the south pole. Let it be properly supported in a horizontal position, with its unmarked poles free, and at a distance from iron or other bodies. Take any small piece of common iron, not exceeding two or three inches in length, such as a small key. Take also another piece of iron, such as another smaller key, or a bit of wire about the thickness of an ordinary quill.

1. Hold the key horizontally, near one of the poles, (as shown at n° 1.), taking care not to touch the pole with it; and then bring the other piece of iron to the other end of the key (it is indifferent which pole is thus approached with the key, and which end of the key is held near the pole). The wire will hang by the key, and will continue to hang by it, when we gradually withdraw the key horizontally from the magnet, till, at a certain distance, the wire will drop from the key, because the magnetism imparted from this distance is too weak. That this is the sole reason of its dropping, will appear by taking a shorter, or rather a flenderer, bit of wire, and touch the remote end of the key with it: it will be supported, even though we remove the key still farther from the magnet.

2. Hold the key below one of the poles, as at n° 2. or 3, and touch its remote end with the wire. It will be suspended in like manner, till we remove the key too far from the magnet.

3. Hold Hold the key above the poles, as at fig. 4 or 5, and touch its adjacent end with the wire (taking care that the wire do not also touch the magnet). The wire will still be supported by the key, till both are removed too far from the magnet.

Thus it appears, that in all these situations the key has shewn the characteristic phenomenon of magnetism, namely, attraction for iron. In the experiment with the key held above the pole, the wire is in the same situation in respect to magnetism as the key is when held below the pole; but the actions are mutual. As the key attracts the wire, so the wire attracts the key.

If the magnet be supported in a vertical position, as in fig. 8, the phenomena will be the same; and when the key is held directly above or directly below the pole, it will carry rather a heavier wire than in the horizontal position of the magnet and key.

Instead of approaching the magnet with the key and wire, we may bring the magnet toward them, and the phenomena will be still more palpable. Thus, if the bit of wire be lying on the table, and we touch one end of it with the key, they will shew no connection whatever. While we hold the key very near one end of the wire, bring down the pole of a magnet toward the key, and we shall then see the end of the wire rise up and stick to the key, which will now support it. In like manner, if we lay a quantity of iron filings on the table, and touch them with the key, in the absence of the magnet, we find the key totally inactive. But, on bringing the magnet anyhow near the key, it immediately attracts the iron filings, and gathers up a heap of them.

In the next place, this vicinity of a magnet to a piece of iron gives it a directive power. Let NAS (fig. 9) be a magnet, and BC (fig. 1.) a key held near the north pole, and in the direction of the axis. Bring a very small mariner's needle, supported on a sharp point, near the end C of the key which is farthest from N. We shall see this needle immediately turn its south pole towards C, and its north pole away from C. This position of the needle is indicated at e, by marking its north pole with a dart, and its south with a cross. Thus it appears that the key has got a directive power like a magnet, and that the end C is performing the office of a north pole, attracting the south pole of the needle, and repelling its north pole. It may indeed be said, that the needle at e arranges itself in this manner by the directive power of the magnet; for it would take the same position although the key were away. But if we place the needle at b, it will arrange itself as there represented, shewing that it is influenced by the key, and not (wholly at least) by the magnet. In like manner, if we place the needle at a, we shall see it turn its north pole toward B, notwithstanding the action of the magnet on it. This action evidently tends to turn its north pole quite another way; but it is influenced by B, and B is performing the office of a south pole.

In like manner, if we place the key as at fig. 2, we shall observe the end B attract the south pole of the needle placed at a, and the end C attract the north pole of a needle placed in b. In this situation of the key, we see that B performs the office of a north pole, and C performs the office of a south pole.

Thus it appears that the key in both situations has become a magnet, possessed of both an attractive and a directive power. It has acquired two poles.

Lastly, the magnetism of the key is disposed, that the two magnets NAS and BC must mutually attract each other; for their dissimilar poles front each other. Now, it is a matter of uniform and uncontradicted observation, that when a piece of iron is thus placed near our own magnet, and the disposition of its magnetism is thus examined by means of a mariner's needle, the disposition is such that two permanent magnets with their poles so disposed must attract each other. The piece of iron, therefore, having the same magnetic relation to the magnet that a similar and similarly disposed magnet has, must be affected in the same manner. We cannot, by any knowledge yet contained in this article, give any precise intimation in what way the polarity of the piece of iron will be disposed. This depends on its shape as much as on its position. By describing two or three examples, a notion is obviously enough suggested, which, although extremely gratuitous, and perhaps erroneous, is of service, because it has a general analogy with the observed appearances.

If one end of a slender rod or wire be held near the north pole of the magnet, while the rod is held in the direction of the axis (like the key in fig. 7, n° 1.), the near end becomes a south, and the remote end a north pole. Keeping this south pole in its place, and turning the rod in any direction from thence, as from a centre, the remote end is always a north pole. And, in general, the end of any oblong piece of iron which is nearest to the pole of a magnet becomes a pole of the opposite name, while the remote end becomes a pole of the same name with that of the magnet.

If the iron rod be held perpendicularly to the axis, with its middle very near the north pole of the magnet, the two extremities of the iron become north poles, and the middle is a south pole.

If the north pole of a magnet be held perpendicular to the centre of a round iron plate, and very near it, this plate will have a south pole in its centre, and every part of its circumference will have the virtue of a north pole.

If the plate be shaped with points like a star, each of these points will be a very distinct and vigorous north pole.

Something like this will be observed in a piece of iron of any irregular shape. The part immediately adjoining to the north pole of the magnet will have the virtue of a south pole, and all the remote protuberances will be north poles.

The notion naturally suggested by these appearances is, that the virtue of a north pole seems to reside in something that is moveable, and that is protruded by the north pole of the magnet toward the remote parts of the iron; and is thus constituted in all the remote edges, points, and protuberances, much in the same manner as electricity is observed to be protruded to the remote parts and protuberances of a conducting body by the presence of an overcharged body. This notion will greatly assist the imagination; and its consequences very much resemble what we observe.

As a further mark of the complete communication of every magnetic power by mere vicinity to a magnet, we may here observe, that the wire D, of fig. 7, n° 2, and 3, will support another wire, and this another; and so Magnetism.

on, to a number depending on the strength of the magnet. The key has therefore become a true magnet in every respect; for it induces complete magnetism on the appended wire. That this is not the same operation of the great magnet (at least not wholly so), appears by examining the magnetism of D with the needle, which will be seen to be more influenced by D than by A. This fact has been long known. The ancients speak of it: They observe, that a lodestone causes an iron ring to carry another ring, and that a third; and so on, till the string of rings appears like a chain.

What has now been said will explain a seeming exception to the universality of the proposition. If the key be held in the situation and position represented by fig. 10, the bit of wire will not be attracted by it; and we may imagine that it has acquired no magnetism: But if we bring a mariner's needle, or a bit of wire, near to its remote end B, it will be strongly attracted, and show B to be a north pole. The needle held near to C will also show C to be a south pole. Also, if held near to D, it will show D to be a north pole. Now the ends C, both of the key and of the wire, being south poles, they cannot attract each other, but, on the contrary, they will repel; and therefore the wire will not adhere to the key. And if the key of fig. 17, n° 4, with the wire hanging to it, be gradually carried outward, beyond the north pole of the magnet, and then brought down till its lower end be level with the pole, the wire will drop off.

There is, however, one exception to the proposition. If the key in fig. 7, with its appending wire D, be gradually carried from any of the situations 2, 3, 4, or 5, toward the middle of the magnet, the wire will drop off whenever it arrives very near the middle. If we suppose a plane to pass through the magnetic centre A, perpendicular to the axis (which plane is very properly called the magnetic equatorial plane by Gilbert), a slender piece of iron, held anywhere in this plane, acquires no sensible magnetism. It gives no indication of any polarity, and it is not attracted by the magnet. It is well known, that the activity of a lodestone or magnet resides chiefly in two parts of it, which have been called its poles; and that those are the best magnets or lodestones in which this activity is least diffused; and that a certain circumference of every lodestone or magnet is wholly inactive. When a lodestone or magnet of any shape is laid among iron filings, it collects them on two parts only of its surface; and between these there is a space all round, to which no filings attach themselves.

We presume that the reader already explains this appearance to himself. Many things show a contrariety of action of the two poles of a magnet. We have already observed, that the north pole of a strong magnet will produce a strong northern polarity in the remote end of a small steel bar; and, if it be then applied near to that end in the opposite direction, it will destroy this polarity, and produce a southern polarity. In whatever these actions may consist, there is something not only different but opposite. They do not blend their effects, as the yellow and blue making rays do in producing green. They oppose each other, like mechanical pressures or impulsions. We have every mark of mechanical action; we have local motion, though unseen, except in the gradual progression of the magnetic faculties along the bar; but we have it distinctly in the ultimate effect, the approach or recess of the magnets: and in these phenomena we see plainly, that the forces, in producing their effects, act in opposite directions. Whatever the internal invisible motions may be, they are composed of motions whose equivalents are the same with the equivalents of the ultimate, external, sensible motions; therefore the internal motions are opposite and equal if the sensible motions are so, and conversely.

Adopting this principle, therefore, that the actions of the two poles are not only different but opposite, it follows, that if they are also equal and act similarly, each must prevent the action of the other; and that there will be a mechanical equilibrium—it may even be called a magnetical equilibrium. Therefore if every part of a slender rod, or of a thin plate of iron, lie in the plane of the magnetic equator, the magnetic state (in whatever it may consist) cannot be produced in it. It will exhibit no magnetism; have no polar faculties; and we can see no reason why it should be attracted by the magnet, or should attract iron. We must not forget to observe in this place, that iron in a state of incandescence acquires no magnetism by juxtaposition. We have already remarked, that iron in this state does not affect the magnet. If a bar of red hot iron be set near a mariner's needle, it does not affect it in the smallest degree till it almost ceases to appear red hot in daylight, as has been observed by Dr Gilbert. All actions that we know are accompanied by equal and opposite reactions; and we should expect what really happens in the present case, namely, that red hot iron should not be rendered magnetical and attractive.

There is a very remarkable circumstance which encompasses the whole of this communication of magnetism to a piece of iron. It does not impair the power of the magnet; but, on the contrary, improves it. This fact was observed, and particularly attended to, by Dr Gilbert. He remarks, that a magnet, in the hands of a judicious philosopher, may be made to impart more magnetism than it possesses to each of ten thousand bars of steel, and that it will be more vigorous than when the operations began. A magnet (says he) may be spoiled by injudicious treatment with other magnets, but never can touch a piece of common iron without being improved by it. He gives a more direct proof. Let a magnet carry as heavy a lump of iron as possible by its lower pole. Bring a great lump of iron close to its upper pole, and it will now carry more. Let it be loaded with as much as it can carry while the lump of iron touches its upper pole. Remove this lump, and the load will instantly drop off. But the following experiment shows this truth in the most convincing manner:

Let NAS (fig. 11.) be a magnet, not very large, nor of extreme hardness. Let CD be a strong iron wire, hanging perpendicularly from a hook by a short thread or loop. The magnet, by its action on CD, renders D a north pole and C a south pole, and the polarity of D's magnetism fits it for being attracted. Let it assume the position C, and let this be very carefully marked. Now bring a great bar of iron B near to the other end of the magnet. We shall instantly perceive the wire C approach to the south pole of the magnet, taking a position C. Withdraw the bar of iron, and C will fall back into the position C. As we bring the iron bar gradually nearer to the magnet, the wire will deviate farther from the perpendicular, and when the bar B touches the magnet CD, will start a great way forward. It is also farther to be observed, that the larger the bar of iron is, the more will CD deviate from the perpendicular.

Now this must be ascribed to the action of the bar on the magnet. For if the magnet be removed, the bar alone will make no sensible change on the position of the wire. We know that the bar of iron becomes magnetic by the vicinity of the magnet. If we doubt this, we need only examine it by means of a piece of iron or a mariner's needle. This will show us that it has become a south, and a north pole. Here then are two magnets with their dissimilar poles facing each other. In conformity with the whole train of magnetic phenomena, we must conclude that they attract each other, and must improve each other's magnetism.

This is a most important circumstance in the theory of magnetism. For it shows us, that, in rendering a piece of iron magnetic, there is no material communication. There is no indication of the transference of any substance residing in the magnet into the piece of iron; nor is there even any transference of a power or quality. Were this the case, or if the substance or quality which was in A be now transferred to B, it can no longer be in A; and therefore the phenomena resulting from its presence and agency must be diminished. We must say that the magnet has excited powers inherent, but dormant, in the iron; or is, at least, the occasion of this excitement, by disturbing, in some adequate manner, the primitive condition of the iron. We must also say, that the competency of the magnet and of the iron to produce the phenomena, is owing to the same circumstances in both; because we see nothing in the phenomena which authorizes us to make any distinction between them. Whatever therefore causes one magnet to attract another, is also the reason why a piece of iron in the neighborhood of a magnet attracts another piece of iron; and we must say that the cause of polarity, or the origin of the directive power, is the same in both. Now we understand perfectly the directive power of a magnet, as exerted on another magnet. We see that it arises from a combination and mechanical composition of attractions and repulsions. It must be the same in this magnetism now inherent in the iron. The piece of iron directs a mariner's needle, as a magnet would direct it; therefore, as there is something in a piece of iron which now attracts something in another piece of iron, so there is something in the first which repels something in the last.

It may indeed be said that it is not a piece of iron, but a mariner's needle, or magnet, that is thus directed by our iron magnetized by vicinity to a magnet. This objection is completely removed by the most curious of all the facts which occur in this manner of producing magnetism. Take a piece of common iron, fashion it, and fit it up precisely like a mariner's needle, and carefully avoid every treatment that can make it magnetic. Set it on its pivot, and bring it near the north pole of a magnet, placing the end, made like the south pole of the needle, next to the north pole of the magnet. In short, place it by hand exactly as a real mariner's needle would arrange itself. It will retain that position. Now carry it round the magnet, along the circumference of a magnetic curve, or in any regular and continuous route. This piece of iron will, in every situation, assume the very same position or attitude which the real magnetic needle would assume if in the same place, and it will oscillate precisely in the same way.

Here then it is plain, that there is no distinction of power between the magnetism of the iron and of the real needle. To complete the proof: Instead of approaching the magnet with this iron needle, bring it into the vicinity of a piece of iron, which is itself magnetic only by vicinity to a magnet, it will arrange itself just as the real needle would do, with the sole difference, that it does not indicate the kind of polarity existing in the extremities of the iron, because either end of it will be attracted by them. And this circumstance leads us to the consideration of the only distinction between the magnetism of a loadstone or magnet and that of common iron.

The magnetism of common iron is momentary, and therefore indifferent; whereas that of a magnet is permanent and determinate. When iron becomes magnetic in the way now mentioned, it remains so only rent; but while the magnet remains in its place; and when that is removed, the iron exhibits no signs of magnetism. Therefore when the north pole of a magnet has produced a south pole in the nearest end of an iron wire, and a north pole at its remote end, if we turn the magnet, and present its south pole, the nearest end of the wire instantly becomes a north pole, and the other a south pole; and this change may be made as often, and as rapidly, as we please. This is the reason which made us direct the experimenter on the iron needle to begin his operation, by placing the end marked for a south pole next to the north pole of the magnet. It becomes a real south pole in an instant, and acts as such during its perpetration round the magnet. But in any one of its situations, if we turn it half round with the finger, the end which formerly turned away from a pole of the magnet, will now turn as vigorously toward it. Therefore, in carrying the iron needle round the magnet, we directed the progress to be made in a continuous line, to avoid all chance of mistaking the polarities.

For all the reasons now adduced, we think ourselves obliged to say, that the magnetism produced on common iron by mere juxtaposition to a magnet, is generated without any communication of substance or faculty. The power of producing magnetic phenomena is not shared between the magnet and the iron. We shall call it INDUCED MAGNETISM; MAGNETISM BY INDUCTION.

We have said that induced magnetism of common iron is quite momentary. This must be understood with careful limitations. It is strictly true only in the case of the finest and purest soft iron, free of all knots and hard veins, and therefore in its most metallic state. Iron is rarely found in a state so very pure and metallic; and even this iron will acquire permanent and determinate magnetism by induction, if it has been twisted or hammered violently, although not in the magnetic direction; also the changes produced (we imagine) on the purest iron by the action of the atmosphere make it susceptible of fixed magnetism. But the magnetism thus inducible on good iron is scarcely sensible, and of no duration, unless it has lain in the neighborhood of a magnet for a very long while.

What has now been said of common iron, is also true of it when in the state of soft steel. But any degree of temper that is given to steel makes a very important change in this respect. In the first place, it acquires magnetism more slowly by induction than an equal and similar piece of common iron, and finally acquires less. These differences are easily examined by the deviations which it causes in the mariner's needle from the magnetic meridian, and by its attraction.

When the inducing magnet is removed, some magnetism remains in the steel bar, which retains the polarity which it had in the neighbourhood of the magnet.

Steel tempered to the degree fit for watch springs acquires a strong magnetism, which it exhibits immediately on the removal of the magnet. But it dissipates very fast; and, in a very few minutes, it is reduced to less than one-half of its intensity while in contact with the magnet, and not two-thirds of what it was immediately on removal from it. It continues to dissipate for some days, though the bar be kept with care; but the dissipation diminishes fast, and it retains at least one-third of its greatest power for any length of time, unless carefully kept or injudiciously treated.

Steel tempered for strong cutting tools, such as chisels, punches, and drills for metal, acquires magnetism still more slowly by induction, and acquires less of it while in contact with the magnet; but it retains it more firmly, and finally retains a greater proportion of what it had acquired.

Steel made as hard as possible, is much longer in acquiring all the magnetism which simple juxtaposition can give to it. It acquires less than the former; but it retains it with great firmness, and finally retains a much greater proportion.

Such ores of iron as are susceptible of magnetism, are nearly like hard steel in these respects; that is, in the time necessary for their greatest impregnation, and in the durability of the acquired magnetism. They differ exceedingly in respect to the degree of power which they can attain by mere juxtaposition, and the varieties seem to depend on heterogeneous mixture. We must observe, that few ores of iron are susceptible of magnetism in their natural state. The ordinary ores, consisting of the metal in the state of an oxide, and combined with sulphur, are not magnetizable while remaining in that state. Most ores require roasting, and a sort of cementation, in contact with inflammable substances. This matter is not well understood; but it would seem that complete metallization is far from being the most favourable condition, and that a certain degree of oxidation, and perhaps some other composition, yet unknown, make the best lodestones. But all this is extremely obscure. The late Dr Gowin Knight made a composition which acquired a very strong and permanent magnetism, but the secret died with him. Dr Gilbert speaks of similar compositions, in which ferruginous clays were ingredients; but we know nothing of the state of the metal in them, nor their mode of acquiring magnetism.

It is of peculiar importance to remark that the acquisition of magnetism is gradual and progressive, and that the gradation is the more perceptible in proportion as the steel is of a harder temper. When a magnet is brought to one end of a bar of common iron, its remote extremity, unless exceedingly long, acquires its utmost magnetism immediately. But when the north pole of a magnet is applied to one end of a bar of hard steel, the part in contact immediately becomes a south pole, and the far end is not yet affected. We observe a north pole formed at some distance from the contact, and beyond this a faint south pole. These gradually advance along the bar. The remote extremity becomes first a faint south pole, and it is not till after a very long while (if ever) that it becomes a simple, vigorous, north pole. More frequently it remains a diffused and feeble north pole: nay, if the bar be very long, it often happens that we have a succession of north and south poles, which never make their way to the far end of the bar. This phenomenon was first observed (we think) by Dr Brook Taylor, who gives an account of his observations in the Philosophical Transactions, no. 344.

From the account we have given of these phenomena it is evident that induced magnetism is always so disposed that the sum of the mutual attractions of the dissimilar poles exceeds the magnetic, sum of the repulsions between the similar poles, and that therefore the two magnets tend to each other. This is evidently equivalent to saying, that a piece of unmagnetic iron is always attracted by a magnet. No exception has ever been observed to this fact; for Pliny's story of a Thaumedes, or lodestone, which repels iron, is allowed by all to have been a fable.

We think ourselves authorized to say that this attraction of the lodestone for iron, or this tendency of iron to the lodestone, is a secondary phenomenon, and is the consequence of the proper disposition of the induced magnetism. The proofs already given of the compound nature of this phenomenon, namely, that it arises from the excess of two attractions above two repulsions, need (we imagine) no addition. But the following considerations place the matter beyond doubt:

1. The magnetism of the two poles is evidently of an opposite nature; the one repelling what the other attracts. If the one attracts iron, therefore, the other should repel it. But each pole, by inducing a magnetism opposite to its own, on the nearest end of the iron, and the same with its own on the remote end, and its action diminishing with an increase of distance, there must always be an excess of attraction, and the iron must be attracted.

2. Each of the magnets A and B, in either of the positions represented in fig. 12, would alone attract the piece of common iron C. But when placed together, the south pole of A tends to render the upper end of C a north pole; while the north pole of B tends to make it a south pole. If their actions be nearly equal, the weight of C cannot be supported by the magnetism induced by any difference of action that may remain. While C is hanging by B alone, let A be gradually brought near; it gradually destroys the action of the north pole of B, so that C gradually loses its magnetism and polarity, and its weight prevails.

3. In all those cases where the induction of magnetism is slow, the attraction is weak in proportion. This is particularly remarked by Dr Gilbert. If we take pieces of common iron, and of steel of different tempers, but all of the same size and form, we shall find that the iron is much more strongly attracted than any of the rest, and that the attraction for each of them is weaker in proportion as they are harder. This diversity is so accurately observed, that when the piece is thoroughly susceptible of magnetism, we can tell, with considerable precision, what degree will be ultimately acquired, and how much will be finally retained. Also, the attraction of the magnet for any of those pieces of steel increases exactly in proportion as their acquired magnetism increases.

4. An ore of iron incapable of acquiring magnetism is not attracted by a magnet. But we know that, by cementation with charcoal dust, they may be rendered susceptible of magnetism. In this state they are attracted. It is an universal fact, that any substance that is attracted by a magnet may be rendered magnetic, and that none else can. We have already observed that red hot iron is not attracted; nor does it acquire any directive power while in that state. From all this we must conclude, that the previous induction of magnetism is the mean of the observed attraction of magnets for iron, and that this is not a primary fact in magnetism.

These observations also complete the proof that magnetic attraction and repulsion are equal at the same distance, and follow the same law. Dr Gilbert seems to think, that the repulsion is always weaker than the attraction; and this is almost the only mistake in conception into which that excellent philosopher has fallen. But it only requires a fair comparison of facts to convince a good logician, that since, in every case, and at every distance, either pole of a magnet attracts either end of a piece of common iron, it is impossible that one of these forces can exceed the other. It might be so, were it not that induced magnetism is durable in proper substances. And if we take magnets which have been made such by induction, and present them to each other with their similar poles facing each other, they never fail to repel each other at considerable distances, and even at very small distances for a few moments; and this is the case whichever poles are next each other. This cannot be on any other supposition. Cases would occur of polarity without attraction, or of attraction without polarity. Such have never been seen, any more than the Thracians, always repelling iron.

Let a great number of small oblong pieces of iron lying very near each other on the surface of quicksilver. Bring a strong magnet into the midst of them. It immediately renders them all magnetic by induction. The one nearest the north pole of the magnet immediately turns one end toward it, and the other end away from it. The same effect is produced on the one that is just beyond this nearest one. Thus the remote end of the first becomes a north pole, and the nearest end of the second becomes a south pole. These, being very near each other, must mutually attract. The same thing may be said of a third, a fourth; and so on. And thus it appears, that not only is magnetism induced on them all, but also, that the magnetism of each is so disposed, that both ends of it are in a state of attraction for the ends of some of its neighbours; and that they will therefore arrange themselves by coalescence in some particular manner. Should a parcel of them chance to be standing with their centres in a magnetic curve, with their heads and points turned in any ways whatever, the moment that the magnet is brought among them, and set in the axis of that magnetic curve, the whole pieces of this row will instantly turn towards each other, and their ends will adhere together, if they are near enough; otherwise they will only point toward each other, forming a set of tangents to the magnetic curve, reaching from one pole of the magnet to the other.

Or, suppose a vast number of small bits of iron, each shaped like a grain of barley, a little oblong. Let them be scattered over the surface of a table, so near each other as just to have room to turn round. Let a magnet be placed in the midst of them. They will all have magnetism induced on them in an instant; and such as are not already touching others, will turn round (because they rest on the table by one point only), and each will turn its ends to the ends of its neighbours; and thus they will arrange themselves in curves, which will not differ greatly from true magnetic curves (because each grain is very short), issuing from one pole of the magnet, and terminating in the other.

Does not this suggest to the reflecting reader an explanation of that curious arrangement of iron filings round a magnet, which has so long entertained and puzzled both the philosophers and the unlearned, and which has given rise to the Cartesian and other theories of magnetism? The particles of iron filings are little rags of soft iron torn off by the file, and generally a little oblong. These must have magnetism induced on them by a magnet, and, while falling through the air from the hand that threw them about the magnet, they are at perfect liberty to arrange themselves magnetically; and must therefore so arrange themselves, forming on the table curves, which differ very little indeed from the true magnetic curves. Suppose them scattered about the table before the magnet is laid on it. If we pat the table a little, so as to throw it into tremors, this will allow the particles to dance, and turn round on their points of support, till they coalesce by their ends in the manner already described.

All this is the genuine and inevitable consequence of what Dr Gilbert has taught us of induced magnetism. It must be so; and cannot be otherwise. This curious arrangement of iron filings round a magnet is therefore not a primary fact, and a foundation for a theory, but the result of principles much more general.

Most of our readers know that this disposition of iron filings has given rise to the chief mechanical theories which have been propounded by ingenious men for the explanation of all the phenomena of magnetism. An invisible fluid has been supposed to circulate through the pores of a magnet, running along its axis, issuing from one pole, streaming round the magnet, and entering again by the other pole. This is thought to be indicated by those lines formed by the filings. The stream, running also through them, or around them, arranges them in the direction of its motion, just as we observe a stream of water arrange the flotsam and jetsam. It would require a volume to detail the different manners in which those mechanicians attempt to account for the attraction, repulsion, and polarity of magnetic bodies, by the mechanical impulsion of this fluid. Let it suffice to say, that almost every step of their theories is in contradiction to the acknowledged laws of impulsion. Nay, the whole attempt is against the first rule of all philosophical discussion, never to admit for an explanation of phenomena the agency of any cause which we do not know to exist, and to operate in the very phenomenon. We know of no such fluid; and we can demonstrate, that the genuine effects of its impulsion would be totally unlike the phenomena. moment of magnetism. But the proper refutation of these theories would fill volumes. Let it suffice (and to every logician it will abundantly suffice) to remark, that this phenomenon is but a secondary fact, depending on, and resulting from, principles much more general, viz. the induction of magnetism, and the attraction of dissimilar, and repulsion of similar, poles.

The above explanation of the curious disposition of iron filings round a magnet, occurred to the writer of this article while studying natural philosophy, on seeing the Professor exhibit Mr Henshaw's beautiful experiment in proof of terrestrial magnetism*. He at that time imagined himself the author, and promised himself some credit for the thought. But having seen the Physiologia Nova de Magnete by Dr Gilbert, he found that it had not escaped the notice of that sagacious philosopher; as will appear past dispute from the following passage, as well as some others, let's pointed, in that work:

"Magnetica frusta (that is, substances susceptible of magnetism) bene et convenienter intra vires poita, mutuo coherent. Ferramenta, prefente magnete (etiam si magnetem non attinrent), concurrent, fociet se mutuo querant, et amplexantur, et, conjuncta, quasiferrumina-

tur. Scobs ferrea, vel in pulverem redacta, fitulis imposita chartaceis—supra lapidem meridianiter locata, vel propius tantum adnotato, in usu coaelect corpus; et subito tam multae partes concrecunt et combinantur; ferrumque aliud affectat conjuratorum turma et attrahit, ac si unum tantum et integrum effect ferri bacillum; dirigiturque supra lapidem in septentriones et meridiem. Sed cum longius a magnete removeretur (tangam folia rufus) separantur, et diffundunt singula corpucula." B. ii. c. 23.

Mr Epiphan also had taken the same view of the subject*. It is also very clearly conceived and expressed by the celebrated David Gregory, Savilian Professor of astronomy in the University of Oxford, in a MS. volume of notes and commentaries, written by him in 1693, on Newton's Principia, and used by Newton in improving the second edition. The M.S. is now in the library of the university of Edinburgh. Gregory's words are as follow: "Mihi semper dubium vidum est num magnetica virtus mechanicæ, i.e. per impulsum, producatur. Minum est, effluvis, qua ferrum agitare valent, braeas aureas interpositas ne vel minimum a loco movere. Lucretii et Cartesi theoriam, de fugato intermedio aere, refutat experimentum infra aquam in-stitutum. Sucti in limatura ferri, magneti in plano ensu- vis meridian circumposita, non sunt ab effluvis secundum illas canales motis, sed ex inde, quod ipsa ramenta, mag- netice excitata, seque secundum longitudinem et secundum po- lot disponunt. Ex altera vero parte exinde quod vis magnetica, interveniente flamma aut calore, interrumpat, quod virga ferrea, vel diuturno fitu perpendiculari, vel in eo fitu frigescendo, virtutem magneticae a tel- lure acquirat, ut nos docet perficacissimus Gilbertus. Quod mallei super incudem iecu forti ad alterum extrellum, virtute acquirat magneticae; quod iecu forti vel faltem fortiori ad alterum extremum poli perma- tantur, ut qui prius septentriones respiciat nunc austrum respicit; quod iecu forti ad medium, virtutem illam proflus amittat. Haec inquam, et familia, mecha- nicam ejus qualitates ortum argument. Hugenius, pre- ter gravitatem, etiam magneticae, et electricae virtu- tem, aliaque plures experimento novit vires naturales, ut mihi ipfi narravit hac eflate anni 1693. Qualis ut haec forsan quod cyba papyracea, prope labra vasis aquae, cui innatet, continentis, poita, labrum viciniflum continuo, et cum impetu petat (A)." Nat. MS. in Prop. 23. ii. Prim.

Not only the mere arrangement of the filings in curve lines follows of necessity from the properties of induced magnetism, but all the subordinate circumstances of this phenomenon are included in the same explanation. By continuing to tap the table, and throw it into tremors, the filings are observed to approach gradually, but very slowly, to the poles of the magnet. Each particle is a very small temporary magnet. The attractive power of the great magnet, \(m - p = n - q\), is therefore extremely small in proportion to its directive power, \(m + p = n + q\). And we observe that the accumulation of the filings round the poles of the magnet is so much the slower as the filings are finer.

If a paper be laid above the magnet, and the filings be sprinkled on it, we observe them to conflagate along its edges, while none remain immediately above its substance; they are all beyond, or on the outside of its outline, and they are observed not to be lying flat on the paper, but to be standing obliquely on one point. They move off from the paper immediately above the magnet, because they repel each other. They stand obliquely from the edges, because that is the direction of a magnetic meridian at its parting from the pole. If the magnet be at some distance below the paper, then tapping the paper will cause the filings to move away from the magnet laterally. This singular and unexpected appearance is owing to the combination of gravity with the magnetic action. A particle, such as \(n\) (fig. 13.), rests on the paper by the point \(n\), which is a temporary north pole (\(S\) being supposed the south pole of the magnet). The particle takes a position \(n\) nearer to the horizon than the position \(n\), which it would take if its centre of gravity \(b\) were supported. The position is such, that its weight, acting vertically at \(b\), is in equilibrium with the magnetic repulsion \(s d\), exerted between \(S\) and \(n\). When the paper is tapped, it is beaten down, or withdrawn from \(n\), and the particle of iron is left for a moment in the air. It therefore turns quickly round \(b\), in order to assume a position parallel to \(n\), and it meets the paper, as that rises again after the stroke, in a point farther removed from the magnet, and again deflected by its weight (turning round the newly supported point \(n\)), till it again takes a position parallel to \(n\), but farther off, as represented by the dotted line. Thus it travels gradually outwards from the magnet, appearing to be repelled, although it is really attracted by it. If the magnet be held above the paper, at a little distance, the filings, when we repeatedly pat the paper, gradually collect into a heap under it. This will appear very plainly to one who considers the situation of a particle in the manner now explained.

(A) Perhaps it may be proper to observe, that Dr Gregory expresses his differing in his opinion from Newton about magnetism. Newton, in this proposition, thinks, that the law of magnetic action approaches to the inverse triplicate ratio of the distances. Dr Gregory invalidates the argument used by Newton. The curve lines formed by very fine filings approach very nearly to the form of the primary curve which indicates the law of magnetic action in the way already explained. If the magnet be placed under water, and if filings be sprinkled copiously on the surface of it from a gauze screen, held at some distance above it, the resistance to their motion through the water gives them time to arrange themselves magnetically before they reach the bottom, and the lines become more accurate. But they were so much deranged by any method that we could take for removing the water, and measuring them, that we were disappointed in our expectations of obtaining a very near approximation to the law of action.

We took notice of some very singular phenomena of a compass needle in the neighbourhood of two magnets, and we observed that, in this case also, the needle was always a tangent to a curve of another kind, and which we called secondary and compound magnetic curves. These are produced in the same way, by throwing iron filings round the magnets. Many representations have been given of these curves by different authors, particularly by Muenchenbroek, in his Essais de Physique; and by Fuss in the Comment. Petropolit. Great use has been made of these arrangements of filings by two magnets in the theories of magnetism proposed by those who insist on explaining all motion by impulse. When the dissimilar poles of two magnets A and B (fig. 14.) face each other, the curves formed by the filings considerably resemble those which surround a single magnet, and give the whole somewhat of the appearance of a magnet with very diffused poles. The arranging fluid, which streams from one pole of a magnet, is supposed to meet with no obstruction to its entry into the adjoining pole of the other magnet, but, on the contrary, to be impelled into it; and therefore (say the proponents) it circulates round both as one magnet, and by its vortex brings the magnets together; which phenomenon we call the attraction of the magnets. But when the similar poles front each other; for example, the poles from which the arranging fluid issues, then the two streams meet, obstruct each other, accumulate, and, by this accumulation, cause the magnets to recede from each other; which we call the repulsion of the magnets. This is the only explanation of this kind that can make any pretensions to probability, or indeed, that can be conceived. For how the free circulation in the former case can bring the two magnets together, no person can form to himself any conception. We see nothing like this produced by any vortex that we are acquainted with. All such vortices cause bodies to separate. But even this explanation of magnetic repulsion is inadmissible. It will not apply to the repulsion of the receiving poles; and the phenomena of the filings are inconsistent with the notion of accumulation. The filings indeed accumulate, and they look not unlike two streams which oppose each other, and deflect to the sides (See fig. 15.). But, unfortunately, by tapping the paper gently, the filings do not move off from the magnets, but approach them much faster than in any other experiment. The phenomenon receives a complete and palpable explanation from the principles we have established. Both magnets concur in giving the same polarity to every particle of the filings. Thus, if the fronting poles are north poles, each particle has its nearest end made a vigorous south pole; and its remote end a north pole; and it is therefore strongly attracted towards both magnets while it is arranged in the tangent to the secondary curve of that class, which crosses the others nearly at right angles.

Since it is found, that the magnetism, even of natural lodestones and hard steel, are continually tending to decay; and since we find that it may be induced by mere approach to a magnet; and since we know that magnets may oppose each other in producing it—it is reasonable to suppose, that when a piece of iron has acquired a slight, though permanent magnetism, by the vicinity of a magnet, a magnet applied in the opposite direction will destroy it, and afterwards produce the opposite magnetism.

Accordingly, we may change the poles of soft magnets at pleasure.

Farther; since we find that lodestones and hard tempered steel bars are distinguished from soft ones only by the degree of obstinacy with which they retain their present condition, we should also expect that hard magnets will even affect each other. It must therefore happen, that a powerful magnet applied to a weak one, so that their similar poles are in contact, shall weaken, destroy, and even change the magnetism of the weaker. Dr Knight's famous magazine of magnets enabled him to change the poles of the greatest and the strongest natural lodestone, or artificial magnet, that could be given him, in the space of one minute.

We now see clearly the reason why magnetic repulsion is weaker than attraction at the same distance. When magnets are placed with their similar poles fronting each other, in order to make trials of their repulsion, they really do weaken each other, and are not in the same magnetical condition as before. For similar reasons, we see how experiments with magnets attracting each other rather improve them, and make their attractive powers appear greater than they are. All these effects must be most remarkable in soft magnets, especially when long.

We also see, that the observed law of attraction and repulsion between two magnets must be different from the real law of magnetic action. For, in the experiments made on attraction at different distances, beginning with the greatest distance, the magnetism is continually increasing, and the attraction will appear to increase in a higher rate than the just one; the contrary may happen, if we begin with the smaller distances. The results of experiments on repulsion must be still more erroneous; because it is easier to diminish any accumulation which required an exertion to produce it, than to push it still farther.

We have now a complete explanation of the remarkable fact, that the induction of magnetism does not improve the magnet employed; but, on the contrary, improves it. The magnetism induced on the iron causes it to act on the magnet employed in the very same manner that a permanent magnet of the same shape, size, and strength, would do. Nay, it will have even a greater effect; for as it improves the magnet, its own induced magnetism will improve; and will therefore still farther improve the magnet.

Hence it is, that, in whatever manner a magnet touches a piece of iron, it improves by it. It may be hurt by a magnet in an improper position; but it always puts common iron into a state which increases its own magnetism. magnetism. This has been known as long as magnetism itself; and the ancients conceived the notion, that the magnet somehow fed upon the iron (a).

We think that these observations authorise us to say, that in reducing a loadstone into a convenient shape, as much as possible of the operation should be performed by grinding them with emery, in cavities made in large blocks of hammered iron. The magnetism induced on the iron must be favourable to the conservation of that in the loadstone; which, we are persuaded, is rapidly dissipated by the tremors into which this very elastic substance is thrown by the grinding with coarse powders in any mould but iron. We imagine, that the cutting off slices by the lapidaries wheel has the same bad effect.

Not only will a magnet lift a greater lump of iron by its north pole, when another lump is applied to its south pole, but it will lift a greater piece of iron from an anvil than from a wooden table: for the magnet induces the properly disposed polarity, not only in the iron which it lifts, but also in the anvil, or any piece of iron immediately beyond it. This is so disposed as to increase the magnetism of the piece of iron between them; and therefore to increase their attraction. The magnetism induced on the anvil is also in part, and perhaps chiefly, induced by the intervening iron. These experiments are extremely variable in their results.—Sometimes a small magnet will pull an iron wire from a large and strong one. Sometimes this will be done even by a piece of unmagnetic iron; and the results appear quite capricious. But they are accurately fixed, depending on the induced compound magnetism. Mr. Agrippa has stated some of the more simple cases, in which we can tell which magnet shall prevail. But the unfolding even of these cases would take a great deal of room, and must be omitted here. Besides, we are too imperfectly acquainted with the degree of magnetism induced on the various parts of an iron rod, and the degree of magnetism inherent in the various parts of the magnets, to be able to say, with certainty, even in those simple cases, on which side the superiority of attraction will remain.

We may now proceed to deduce from this theory (for so it may justly be called, since all is reduced to one fact) the process for communicating magnetism to bodies fitted for receiving and retaining it; that is, the method of making artificial magnets. We shall not employ much time on this, because the most approved methods have been delivered at length in the article Magnetism of the Encyclopaedia Britannica; and therefore we shall just make such observations on them as serve to confirm, or to perfect them by the theory. We acknowledge, that we do not know the internal process by which magnetism is induced, nor even in what this magnetism consists. All that we know is, that the bringing the pole of a magnet near to any magnetifiable matter, produces a magnetism of the kind opposite to that of the pole employed. We know that this is the case with both poles, and that it obtains at all the distances where magnetism is observed. We know that the action of one pole is contrary to that of the other; that is, it counteracts the other, prevents it from producing its effect, and destroys it when already produced; and we know, that the production of these effects resembles in its result the protrusion of something fluid through the pores of the body, constituting it in all remote parts; as if the virtue of a pole resided in this moveable matter. This is nearly all that we know of it; and by these facts and notions we must judge of the propriety and effect of all the processes for magnetising bodies.

The most simple method of magnetising a steel bar, is to apply the north pole of a magnet to that end which we wish to render a south pole. Attention to the effects of this application is very instructive. Have in readiness a very small compass needle, turning on its pivot. It should not exceed half an inch in length, and should be as hard tempered as possible, and strongly impregnated. Immediately after the application of the magnet, carry the needle along the side of the bar. If the bar be long, and very hard, we shall observe a fourth polarity at the place of contact; a north polarity at a small distance from it; beyond this a weak south polarity; then a weak and diffused north polarity, &c.; toward the remote end the polarity will be found very uncertain. The same thing may be discovered by laying a stiff paper on the bar, and sprinkling iron filings over it, and then gently tapping the paper, to make them arrange themselves in curve lines; which will point out the various poles, and show whether they are diffused or constricted. It is very amusing and instructive to observe the progress of this impregnation. In a few minutes after the first application of the magnet, we shall perceive the state of magnetism very sensibly changed. The north pole will be farther from the magnet, and will be more distinct; the southern polarity will also be protruded, and may appear for a moment at the remote extremity. The change advances; but the progress is more slow, and at last is intangible. When the bar is not harder than the temper of a cutting tool, the process is soon over; and if the bar is but six or eight inches long, the remote end shows the north polarity in a very few minutes. When the bar is very hard, the progress of impregnation is greatly expedited by striking it so as to make it sound. If it be suspended by a string in a vertical position, and the magnet applied to its lower end, the striking it with a key will make it ring; and in this way make the progress of magnetization very quick: but it does not allow it to acquire all the magnetism that can be given it by a very strong magnet.

But this is a bad way of impregnation. It is seldom that uniform magnetism, with only two poles, and those

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(a) So Claudian. ——"Nam ferro nurunt vitam, ferrique vigore Veficitur, hoc dulces epulas, hoc pabula novit Hinc proprias renovat vire, hinc fusa per artus Aspera feceretum servant alimenta vigorem Hoc absente perit, tristi morientia torpent Membra fame, venasque sitis confunxit apertas."

Pliny says, "Sola haec materia (ferrum) vires ab eo lapide, accipit retinetque Jongo tempore, aliud apprehendens ferrum, ut annulorum catena spectetur interdum, quod imperitum vulgus ferrum appellat vivum." of equal strength, can be given. Even when there are but two, the remote pole is generally diffused, and therefore feeble. It is much improved by employing two magnets, one at each end. And if the bar is not more than six or eight inches long, and good magnets are employed, the magnetism is abundantly regular.

This, accordingly, is practised for the impregnation of dipping needles, which must not be touched, lest we disturb the centre of gravity of the needle. But in all cases, this method is tedious, and does not give strong magnetism.

The method which was usually practised before we had obtained a pretty clear knowledge of magnetism, was to apply the pole of a magnet to one end of the bar, and pass it along to the other end, pressing moderately. This was repeated several times on both sides of the bar, always beginning the stroke at the same end as at first, and, in bringing the magnet back to that end, keeping it at a distance from the bar. The effect of this operation was to leave the end at which we began the stroke possessed of the polarity of the pole employed.

A general notion of the process may be given as follows, observing, however, that there occur very many great and capricious anomalies. When the north pole N (fig. 16.) of the magnet A is set on the end C of the bar CBD, a south pole is produced at C; and a north pole at D, when the length of the bar is moderate. As the magnet advances slowly along the bar, the southern polarity at C first increases, then diminishes, and vanishes entirely when N has arrived at a certain point a; after which, a northern polarity appears at C, and increases during the whole progress of the magnet. In the mean time, the northern polarity first produced at D increases till the magnet reaches a certain point e, then diminishes, vanishes when the magnet reaches a certain point f; after which, a southern polarity appears at D, which increases till the magnet reaches D.

Mr Brugmann, who first attended minutely to these particulars (for Gilbert speaks of them pointedly), calls a and f points of indifference, and e the culminating point of the pole D, and i the culminating point of the pole C. Hardly can any general rule be given for the situation of these points, nor even for the order in which they stand; so great and capricious are the anomalies in an amazing series of experiments narrated by Brugmann and by Van Swinden. Repeating the operation, and beginning at C, the northern polarity there is weakened (sometimes destroyed); then restored, and continually increased during the rest of the stroke. The southern polarity at D is also first weakened, and sometimes destroyed; then restored, and finally augmented. The points i, a, e, f, change their situations, and frequently their order.

Van Swinden has attempted to deduce some general laws from his immense list of experiments, avoiding every consideration of a hypothesis, or the least conjecture by what means these faculties are excited. But though we have perused his investigation with care and candor, we must acknowledge, that we have not derived any knowledge which can help us to predict the result of particular modes of treatment with any greater precision than is suggested by a sort of common sense, aided (or perhaps perverted) by a vague notion, that these energies reside in something, which avoids the pole of the same name, carrying along with it this distinctive energy or polarity. This conception tallies perfectly with these observations of Brugmann and Van Swinden; and admits of all the anomalies in the situation of Bergmann's indifferent and culminating points, if we only suppose that this motion is obstructed by the particles of the body. We must leave this to the reflection of the reader, who will guess how, when the magnet is between C and i, this substance, avoiding the pole N of the magnet, escapes below it, and goes toward the farther end. As the magnet advances, it drives some of this back again, &c. &c. This is gratuitous; but it aids the fancy, which, without some conception of this kind, has no object of steady contemplation. We have no thought when we speak of the generating at C, or a, or e, a faculty of some kind, by the exertion of the same faculty in N. The conception is too abstracted, and much too complex. We must content ourselves with knowing, that N produces a south pole immediately under it, and a north pole everywhere else, or endeavours to do so. It is unnecessary to insist longer on this method: Common sense shows it to be a very injudicious one.

This method was greatly improved by beginning the friction at the centre. Apply the north pole at the centre or middle of the bar, and draw it over the end intended for the south pole. Having done this several times to one end on both sides, turn the magnet, applying its south pole to the middle of the bar, and drawing it several times over the end intended for the north pole.

It was still more improved by employing two magnets at once, placed as in fig. 17., on the middle B of the bar, and drawing them away from each other, over the ends of it, as shown by the directing darts, and repeating this operation. It is plain that, as far as we understand anything of this matter, this process must be much preferable to either of the former two. The magnets A and E certainly concur in producing a properly disposed magnetism on all that lies between them; and therefore on the whole bar at the end of each stroke. The end C must become a north, and D a south pole. Still, however, as the stroke goes on to the point of indifference, each magnet tends to weaken the polarity of the parts situated beyond it.

This method continued to be practised till about the year 1750. Mr Canton, availing himself of the experiments of Mr Mitchell of Cambridge, published his method by the double touch as it is called. See Monthly Review for 1785.

We need not repeat what has been detailed in the Method Encyclopaedia, Magnetism, p. 440, &c. and shall only touch make some observations on the peculiar advantages of this process, as prescribed by Mitchell, Canton, and improved by Mr Anthamme, in his memoir sur les Aimants artificiels, 1766, which was crowned by the Academy of Sciences. (See also dissertations on the subject by Le Maire and Du Hamel, 1745.)

There is an evident propriety in the arrangement invented by Mr Mitchell, represented in fig. 18. The magnetism induced on the two pieces of soft iron AD and BC is an excellent method for securing every accession of magnetism to either of the bars. A good deal depends on the proper size and length of these pieces; and our ignorance of the interior process obliges us to have recourse to experiment alone for ascertaining this. Whatever circumstances induce the strongest magnetism on those pieces of iron, will cause them to produce the greatest effect on the steel bars; and this will be indicated by a greater attraction. Therefore that distance will be the best which enables two bars AB and DC to lift the greatest weight hung on the piece AD or BC. When we impregnated bars whose breadth was about one-tenth of their length, and their thickness about one-half of their breadth, we found, that if AD was about one-fourth, or nearly one-third, of AB, they carried more than if it was either much longer or much shorter. Mr Anthaume's addition of the two great bars of iron E and F makes a sensible improvement of the beginning of the impregnation, when very weak magnets are employed; but did not seem to us to be of any farther service on the table. This is agreeable to any theory which can be established by what we have said hitherto.

The method of employing the magnets A and E (fig. 19), prescribed by Mitchell and Canton, is extremely judicious. The meeting of the dissimilar poles at top increases the magnetism of each. The two dissimilar poles F and G, certainly tend to give a regular and proper magnetism to the part FG of the bar which lies between them; and this is the case on whatever part of the bar they are placed. But each pole tends to destroy the present magnetism of what lies between it and the pole of the bar on that side. But mark—they tend to produce the desired magnetism on what lies between them with the sum of their forces; while each tends to destroy the magnetism of the part without it by the difference only of their forces. Therefore, on the whole, as they are moved to and fro along the bar, and the foremost one even made to pass over the end of it a little way, they always add to the magnetism already acquired. This consideration seems to justify setting F and G extremely near each other; for this seems to increase the sum, and to diminish the difference of their action. But it may be a question, Whether we gain more by strongly magnetizing a very small part during the very short while that the magnets pass over it, or by acting on more of the bar at once, and continuing a weaker action for a longer while on this larger portion. Mr Epinus adds another consideration depending on his notion of the internal process; but we defer this to another opportunity. The safest direction seems to be, to place them at the distance which enables them to lift the greatest weight. They are then undoubtedly acting with the greatest effect.

Mr Anthaume directs to place the touching magnets as in fig. 20, for a reason to be mentioned afterwards. Mr Epinus also recommends it for reasons founded on his own hypothesis. We must say, that, in our trials, we have found this method very sensibly superior, especially in the latter parts of the operation, when the resistance to farther impregnation becomes nearly a balance for the accumulating power of the magnets; and we consider this as no inconsiderable argument for the justice of Mr Epinus's hypothesis.

The great advantage of this method is the regularity of the magnetism which it produces. We never find more than two poles; and when the bars are hard, and of uniform texture, the polarity is very little diffused, and seemingly confined to a very small space at the very extremities of the bar. This is indeed a prodigious advantage in point of strength. It is no less so in order to fit the magnets for experiments on the law of magnetic action; for the latitude which the diffused condition of the poles gives in the selection of the points from which the distances are to be computed, has hitherto hindered us from pronouncing on the law of magnetic action with the precision of which we think it fully susceptible. This method also is the only one by which we have been able to impregnate two bars joined end to end, considering them as one bar. We have sometimes (though very rarely) succeeded in this; so that when filings were thrown over them, the appearance could not be distinguished from a single bar.

N.B. Yet even in this case, in one experiment with two bars of six inches long, treated as one, when it could not be distinguished, either by the appearance of the filings, or by going round it very near with a compass needle, a very small compass needle discovered a neutral point, and a reversal of polarity similar to fig. 14, at F, shewing that it was really acting as two bars. Perhaps it must always be so; and this question is of considerable importance in the establishment of any theory of the internal process.

It deserves remark, that, in order to succeed in this attempt, a very considerable precaution is necessary. We were obliged to clean the ends of the bars very carefully, and to force the frame of bars and soft pieces of iron strongly together by wedges, in the manner of a form of types. We thought that wetting the ends of the bars with pure water aided the experiment; and we are very certain that oil not only greatly obstructed it, but even sensibly impeded the common process. We had put a single drop of oil on a pair of bars which we were touching in the common Cantonian method, that the magnets might be more easily drawn along them; but we were surprised at finding that we could not give a strong impregnation. The oil undoubtedly prevents the close contact. We found the finest gold leaf produce the same effect in a great degree; as also tallow, of which a square inch weighed 1/5th of a grain. We do not infer anything like obstruction to the passage of something material, but rather ascribe it to mere dilution; although we are of opinion, that in the impregnation of two contiguous bars, so that the magnetism (whatever it is) is disposed precisely as in one bar, there is a material transference. But we shall speak of this in its due place.

It is not unworthy of remark, that we found bars to acquire more powerful magnetism when pretty well polished than when rough. But we also found, that bars considerably rough acquired the first degrees of it much more expeditiously than those which are smooth; although we never could bring them to that high degree of magnetism that the same bars acquired after they had been polished. We think it probable, that the tremors, occasioned by the rough and harsh surfaces of the hard steel, are the causes of this phenomenon.

Some more observations on this method of the double touch will be made afterwards, when we consider the hypothesis of Mr Epinus; and we conclude the present subject, by attempting to explain some puzzling appearances which frequently occur in making artificial magnets.

A bar touched by a very strong magnet has been said by Munchenbroek to be impaired by going over it explained with a weaker magnet. If it had been made as strong as possible, the weaker magnet, when passed over it in the way practised by Mulchenbroek, must first destroy part of this magnetism; and having done so, it is unable to raise it anew to the same degree of vigour.

Yet (says Mulchenbroek with surprise) a large bar of common iron has greatly improved the magnet. A very large piece of iron may do this (especially if shaped like a horseshoe, and applied with both heels), if the bar be not already at its maximum.

It was thought wonderful, that, in the method of double touch, not only was the magnetism of the magnets employed not impaired, but, beginning with two magnets, whose power is almost insensible, and repeating the operations in the precise manner described by Mitchell or Canton, not only the bars intended to be made magnetic, but also the magnets employed, may be brought to their highest possible state of magnetism. This is in evident conformity to the general facts of induced magnetism, and affords the strongest proof that nothing is communicated in this operation, but that powers residing in the bars are excited, or brought into action. The manipulation merely gives occasion to this action, as a spark of fire kindles a city.

There still remain some circumstances of this method, as practised by Savery, Canton, and Antheaume, which are extremely curious and important.

Mr Savery had observed a small bit of steel acquire very sensible magnetism by lying long in contact with the lower end of a great window bar. Telling this to a friend, he was, for the first time, informed, that this had been long observed, and that Dr Gilbert had made some curious inferences from it. Mr Savery wanted some magnets, and was at a distance from town. Reflecting, like a philosopher, on what he had heard and observed, he saw here a source of magnetism which he could increase, in the manner commonly practised in making magnets. He placed the bar AB (fig. 21.) to be magnetized between two great bars of common iron C and D, placing all the three in the magnetic direction. He took another bar EF, and put two little pieces of iron, like the armour of a loadstone, on its ends; and with those ends he rubbed the bar AB, rubbing the upper half of it with the end F, and the lower with the end E. The result of this was a very brisk magnetism in a few minutes, which, by various well devised alternations, he brought to its highest degree. His numerous experiments published in the Philosophical Transactions in 1746, contain much curious information, highly deserving the attention of the philosophers. Mr Canton, proceeding on the same principle, that bars of iron, which have been long in a vertical position, acquire an efficient magnetism, begins his operations by placing his steel bar on the head of a kitchen poker, and rubs it with the lower end of a pair of kitchen tongs. Mr Antheaume adheres more strictly to the inferences from the principle of terrestrial magnetism, and repeats precisely the previous disposition of things practised by Mr Savery, placing his little steel bar AB (fig. 22.) between two great bars C and D of common iron, and arranging the whole in the magnetic direction. Then, proceeding most judiciously on the same principle, he greatly improves the process, by employing two bars EF and GH for the touch, holding them about an inch apart, inclined about 15° to the bar AB. It is plain, that the lower end of each of these five bars is a north pole, and the upper end a south pole. Therefore the poles F and G concur in giving the proper magnetism to the portion FG of the steel bar which is between them; and by rubbing it with these poles up and down, overpowering each extremity about half an inch, he must soon give to the bar AB a regular magnetism; weak, perhaps, but to be afterwards increased in the Cantonian method, on a horizontal table. In this manner did Mr Antheaume make magnets of very great strength in 1766. See his Dissertation already quoted.

These observations naturally bring us to the Physio-Logia Nova de Magnete et Corporibus Magneticius of Dr Gilbert; a discovery which the sagacious Kepler classes among the greatest in the annals of science.

It could not be that a phenomenon so general, and so interesting and important as the natural polarity of magnetic bodies, would be long known without exciting curiosity about its cause. Accordingly the philosophers of the 16th century speculated much about it, and entertained a variety of opinion, if that can be called an opinion which can hardly be said to express a thought. We have in Maraldi's Fisica a short notice of many of these opinions. Some maintained that the needle was directed by a certain point in the heavens, as if that were saying more than that it always pointed one way. Others, with more appearance of reasoning, ascribed the direction to vast magnetic rocks. But all this was without giving themselves the trouble of trying to ascertain what situation of such rocks would produce the direction that is observed. Fracastor was, if I mistake not, the first who thought this trouble at all necessary; and he observes very sensibly, that if those rocks are supposed to be in any place yet visited by navigators, and if they act as lodestones do (a circumstance which he says must be admitted, if we attempt to explain), the direction of the needle will be very different from what we know it to be. He therefore places them in the inaccessible polar regions, but not in the very pole. Norman, the discoverer of the dip of the mariner's needle, or of the true magnetic direction, was naturally led by his discovery to conceive the directing cause as placed in the earth; because the north point of the needle, in every part of Europe, points very far below the horizon. But although he calls the treatise in which he announces his discovery the New Attraction, he does not express himself as supposing the needle to be attracted by any point within the earth, but only that it is always directed to that point.

It is to Dr Gilbert of Colchester that we owe the opinion now universally admitted, that magnetic polarity is a part of the constitution of this globe. Norman had, not long before, discovered, that if a steel needle be very exactly balanced on a horizontal axis, like the beam of a common balance, so that it would retain any position given it, and if it be then touched with a magnet, and placed on its axis in the magnetic meridian, it is no longer in equilibrium, but (at London) the north point of it will dip 72 or 73 degrees below the horizon. He did not, however, publish his discovery till he had obtained information how it stood in other parts of the world. The differences in the variation in different places naturally suggested the necessity of this to him. Being a maker of mariners' compasses, require for their exhibition a dipping needle, and the attention to circumstances which can occur only to a mathematician. A dipping needle is to this day, notwithstanding all our improvements in the arts, one of the most delicate and difficult tasks that an instrument maker can take in hand, and a good one cannot be had for less than twenty guineas. We are confident that such as even Norman could make were far inferior to what are now made, and quite unfit for use at sea while the ship is under sail, although they may be tolerably exact for an observation of the dip in any port; and we presume that it was such observations only that Norman confined in. Our readers will readily conceive the difficulty of poising a needle with such a perfect coincidence of its centre of gravity and axis of motion, and perfect roundness of this axis, that it shall remain in any position that is given it. Add to this, that a grain of dust, invisible to the nicest eye, getting under one side of this axis, may be sufficient for making it assume another position. It must also be a difficult matter to preserve this delicate thing, so as that no change can happen to it. Besides, all this must be performed on a piece of tempered steel which we are certain has no magnetism. Where can this be got, or what can insure us against magnetism? Nor is there less difficulty in making the observations without great risk of error. If the needle, moveable only in a vertical plane, be not set in the plane of a magnetic meridian, it will always dip too much. At London, where the magnetic direction is inclined 73° to the horizon, if it be in a plane 20° from the magnetic meridian, it will stand almost perpendicular; for it is easy to see, by the mechanical revolution of forces, that it will take the position which brings it nearest to the true magnetic direction. This, we think, is confirmed by several of Norman's and other old observations of dip. They are much greater than they have been since found in the same places.

Mr Daniel Bernoulli has given a very ingenious principle, by which we can make a dipping needle which will give a very accurate observation on shore; and being so easily executed, it deserves to be generally known. Let a dipping needle be made in the best manner that can be done by a workman of the place, and balanced with some care before impregnation, so that we may be certain that when touched it will take nearly the true dip. Touch it, and observe the dip. Destroy its magnetism, and then alter its balance in such a manner that, without any magnetism, it will arrange itself in the inclination of the observed dip. Now touch it again, giving it the same poles as before. It is plain that it will now approach exceedingly near indeed to the true dip, because its want of perfect equilibrium de-ranged it but a few degrees from the proper direction. If this second observation of the dip should differ several degrees from the first, by the inaccurate first formation of the needle, it will be proper to repeat the operation. Very rarely indeed will the third observation of the dip vary from the truth half a degree.

Mr Bernoulli makes this simple contrivance answer the purpose of an universal instrument in the following ingenious manner. A very light brass graduated circle EFG (fig. 25.) is fixed to one side of the needle, concentric with its axis, and the whole is balanced as nicely as possible before impregnation. A very light index CD is then fitted on the axis, so as to turn rather stiffly on it. This will destroy the equilibrium of the needle. If the needle has been made with perfect accuracy, and perfectly balanced, the addition of this index would cause it always to settle with the index perpendicular to the horizon, whatever degree of the circle it may chance to point at. But as this is scarcely to be expected, set the index at various degrees of the circle, and note what inclination the unmagnetic needle takes for each place of the index, and record them all in a table. Suppose, for example, that when the index is at 30°, the needle inclines 46° from the horizon. If in any place we observe that the needle (rendered magnetic by lying between two strong magnets), having the index at 50°, inclines 46°, we may be certain that this is the dip at that place; for the needle is not changed by the magnetism from the position which gravity alone would give it. As we generally know something of the dip that is to be expected in any place, we must set the index accordingly. If the needle does not show the expected dip, alter the position of the index, and again observe the dip. See whether this second position of the index and this dip form a pair which is in the table. If they do, we have got the true dip. If not, we must try another position of the index. Noticing whether the agreement of this last pair be greater or less than that of the former pair, we learn whether to change the position of the index in the same direction as before, or in the opposite. The writer of this article has a dipping needle of this kind, made by a person totally unacquainted with the making of philosophical instruments. It has been used at Leith, at Cronstadt in Russia, at Scarborough, and at New York, and the dip indicated by it did not in any single trial differ 14 degrees from other trials, or from the dip observed by the finest instruments. He tried it himself in Leith Roads, in a rough sea; and does not think it inferior, either in certainty or dispatch, to a needle of the most elaborate construction. It is worthy of its most ingenious author, and of the public notice, because it can be made for a moderate expense, and therefore may be the means of multiplying the observations of the dip, which are of immense consequence in the theory of magnetism, and for giving us an accurate knowledge of the magnetic constitution of this globe.

This knowledge is still very imperfect, owing to the want of a very numerous collection of observations of the dip. They are of more importance than those of the horizontal deviations from the meridian. All that we can say is, that the earth acts on the mariner's needle as a great loadstone would do. But we do not think that the appearances resemble the effects of what we would call a good loadstone, having the regular magnetism of two vigorous poles. The dips of the needle in various parts of the earth seem to be such as would result from the action of an extremely irregular loadstone, having its poles exceedingly diffused. The increase of the dip, as we recede from those places where the needle is horizontal, is too rapid to agree with the supposition of two poles of constituted magnetism, whether we suppose the magnetic action in the inverse simple or duplicate ratio of the distances, unless the great terrestrial magnet be of much smaller dimensions than what some other appearances oblige us to suppose. If there be four poles, as Dr Halley imagined, it will be next to impossible to ascertain the positions of the dipping needle. It will be a tangent to one of the secondary magnetic curves, and these will be of a very intricate species. We cannot but consider the discovery of the magnetic constitution of this globe as a point of very great importance, both to the philosopher and to society. We have considered it with some care; but hitherto we have not been able to form a systematic view of the appearances which gives us any satisfaction. The well-informed reader is sensible, that the attempt by means of the horizontal or variation needle is extremely tedious in its application, and is very unlikely to succeed; at the same time it must be well understood. The two dissertations by Euler, in the 13th and 17th volumes of the Memoirs of the Royal Academy at Berlin, are most excellent performances, and give a true notion of the difficulty of the subject. Yet, even in these, a circumstance is overlooked, which, for anything we know to the contrary, may have a very great effect. If the magnetic axis be far removed from the axis of revolution, as far, for example, as Mr Churchman places it, the magnetic meridians will be (generally) much inclined to the horizon; and we shall err very far, if we suppose (as in Euler's calculus) that the dipping needle will arrange itself in the vertical plane, passing through the direction of the horizontal or variation needle; or if we imagine that the poles of the great magnet are in that plane. We even presume to think that Mr Euler's assumption of the place of his fictitious poles (namely, where the needle is vertical), in order to obtain a manageable calculus, is erroneous. The introduction of this circumstance of inclination of the magnetic meridians to the horizon, complicates the calculation to such a degree as to make it almost unmanageable, except in some selected situations. Fortunately, they are important ones for ascertaining the places of the poles. But the investigation by the positions of the dipping needle is incomparably more simple, and more likely to give us a knowledge of a multiplicity of poles. The consideration of the magnetic curves (in the sense used in the present article), teaches us that we are not to imagine the poles immediately under those parts of the surface where the needle stands perpendicular to the horizon, nor the magnetic equator to be in those places where the needle is horizontal; a notion commonly and plausibly entertained. Unfortunately our most numerous observations of the dip are not in places where they are the most instructive. A series should be obtained, extending from New Zealand northward, across the Pacific Ocean to Cape Fairweather on the west coast of North America, and continued through that part of the continent. Another series should extend from the Cape of Good Hope, up along the west coast of Africa to the tropic of Capricorn; from thence across the interior of Africa (where it would be of great importance to mark the place of its horizontality) through Sicily, Italy, Dalmatia, the east of Germany, the Gulf of Bothnia, Lapland, and the west point of Greenland. This would be nearly a plane passing through the probable situations of the poles. Another series should be made at right angles to this, forming a small circle, crossing the other near Cape Fairweather. This would pass near Japan, through Borneo, and the west end of New Holland; also near Mexico, and a few degrees west of Easter Island. In this place, and at Borneo, the inclination of the magnetic plane to the horizon would be considerable, but we cannot find this out. It may, however, be discovered in other points of this circle, where the dip is considerable. We have not room in this short account to illustrate the advantages derived from these series; but the reflecting reader will be very sensible of them, if he only supposes the great magnet to be accompanied by its magnetic curves, to which the needle is always a tangent. He will then see that the first series from New Zealand to Cape Fairweather, and the second from Cape Fairweather round the other side of the globe, being in one plane, and at very different distances from the magnetic axis, must contain very instructive positions of the needle. But we still confess, that when we compare the dips already known with the variations, they appear so irreconcilable with the results of an uniform regular magnetism, that we despair of success. Everything seems to indicate a multiplicity of poles, or, what is still more adverse to all calculation, an irregular magnetism with very diffused polarity.

Much instruction may surely be expected from the observations of the Russian academicians and their eleves, who are employed in surveying that vast empire; yet we do not meet with a single observation of the dip of the needle in all the bygone publications of that academy, nor indeed are there many of the variation.

For want of such information, philosophers are extremely divided in their opinions of the situation of the magnetic poles of this globe. Professor Knutti, in the 17th volume of the Peterburgh Commentaries, places the north pole in lat. 75° N. and long. 23° W. from London; and the south pole in lat. 50° S. and long. 92° E.

Wilcke of Stockholm, in his indication chart (Sved. Mem. tom. xxx. p. 28.), places the north pole in N. Lat. 75°, near Baffin's Bay, in the longitude of California. The south pole is in the Pacific Ocean, in lat. 70° S.

Churchman places the north pole in lat. 59° N. and long. 135° W., a little way inland from Cape Fairweather; and the south pole in lat. 39° S. Long. 165° E., due south from New Zealand.

A planisphere by the Academy of Sciences at Paris for 1786, places the magnetic equator so as to intersect the earth's equator in long. 75° and 155° from Ferro Canary Island, with an inclination of 12 degrees nearly, making it a great circle very nearly. But we are not informed on what authority this is done; and it does not accord with many observations of the dip which we have collected from the voyages of several British navigators, and from some voyages between Stockholm and Canton. Mr Churchman has given a sketch of a planisphere with lines, which may be called parallels of the dip. Those parts of each parallel that have been ascertained by observation are marked by dots, so that we can judge of his authority for the whole construction. It is but a sketch, but gives more synoptical information than any thing yet published.

The magnetic equator cuts the earth's equator in long. 15° and 105° E. from Greenwich, in an angle of nearly 17 degrees. The circles of magnetic inclination are not parallel, being considerably nearer to each other on the short meridian than on its opposite. This circumstance, being founded on observation, is one of the strongest arguments for the existence of a magnet of tolerable regularity, as the cause of all the positions of the compass needle; for such must be the positions of the circles of equal dip, if the axis of this magnet is far removed from the axis of rotation, and does not interfere.

Now, if the situation of the poles be anything near the average or medium of these determinations, and if we form all our notions by analogy, comparing the positions of the compass needle in relation to the great terrestrial magnet, with the positions assumed by a small needle in the neighbourhood of a magnet, we must conclude, that the magnetical constitution of this globe has little or no reference to its regular external form. The axis of the magnet is very far removed from that of the globe (at least 1,000 miles), and is not nearly parallel to it, nor in the same plane. It required the sagacity and the skill of a Euler to subject such anomalous magnetism to any rules of computation; and every person qualified to judge of the subject must allow his dissertation in the 13th volume of the Berlin Memoirs to be a work of wonderful research. It is a very agreeable thing to see such a conformity between the lines which express the regular magnetism of Euler's dissertation, and the lines drawn by Dr Halley from observation, and which appeared to himself so capricious, that he despaired (notwithstanding his consummate skill in geometry) of their ever being reduced to a mathematical and precise system.

Without detracting from the merit of Dr Gilbert, we may presume to say that his notion of the earth's being a great magnet was not, in his mind, more than Gilbert's sagacious conjecture, formed from a very general and even vague comparison. Yet the comparison was sufficiently good to give him great confidence in his opinion that the action of this great magnet, in perfect conformity to what we observe in our experiments with magnets, is the source of all the magnetism that we observe. If there was nothing else in proof of the justness of his theory, it is abundantly proved by the beautiful experiment of Mr Henshaw, mentioned in the article Variation, Encycl. p. 621, col. 2. An iron bar held nearly upright, attracts the south end of a compass needle with its lower end; and if that end of the bar be kept in its place, and the bar turned round till it becomes the upper end, the south point of the needle immediately turns away from it, and the north end is now attracted. This experiment may be perfectly imitated with artificial magnetism.

Having supported a large magnet SAN (fig. 24.), so that its ends are detached from surrounding bodies, place a small needle B (poised on its pivot) about three inches below the north pole N of the magnet, and in such a situation that its polarity to the magnet may be very weak. Take now a small piece of common iron, and hold it in the position represented at C. Its lower end becomes a north pole, attracting the fourth pole of the needle. Keeping this in its place, turn round the piece of iron into the position D; the fourth pole of B will now avoid it, and the north pole will be attracted. We directed the needle to be so placed, that its polarity, in relation to the magnet, may be weak. If it be strong, it may act on the end of C or D like a magnet, and counteract the magnetism induced on C or D by vicinity to A. An anonymous writer in the Philosophical Transactions, No. 177, Vol. XV., relates several observations made during a voyage to the East Indies, which are quite conformable to this. A few leagues northwest from the island Ascension, the south point of the compass needle hardly showed any tendency to or from the lower end of an iron bar. It seemed rather to avoid the upper end; it was not in the least affected by the middle of the bar; but when the bar was laid horizontal, in the magnetic direction, its two ends affected the similar ends of the compass needle very strongly; but when horizontal, and lying at right angles to the magnetic direction, its polarity was altogether indifferent.

As the other phenomena of induced artificial magnetism have the same resemblance to the phenomena of natural magnetism, a bar which has remained long in the vicinity of a magnet acquires magnetism (permanent) in the same way, and modified by the same circumstances, as in natural magnetism. Hammering a bit of common iron in the immediate vicinity of a magnet, gives it very good magnetism. Exposing a red hot bar to cool in the neighborhood of a magnet has the same effect. Also quenching it suddenly has the same effect. Quenching a small red hot steel bar between two magnets, was found by us to communicate a much stronger magnetism than we could give it by any other method. Its form indeed was very unfavorable for the ordinary method of touching; for it consisted of two little spheres connected by a slender rod, and could scarcely be impregnated in any other way than by placing it for a very long while between magnets. In all these experiments, the polarity acquired is precisely similar to that acquired by the same treatment in relation to this supposed great terrestrial magnet. In short, in whatever manner we pursue this analogy in our experiments, we find the resemblance most perfect in the phenomena.

We cannot but think, therefore, that this new physiology of the magnet by Dr. Gilbert is well established; and we think ourselves authorized to affirm it as a proposition fully demonstrated, that the earth is a great magnet, or contains a great magnet, the agency of which produces the direction of the magnetic needle, and all the magnetism which iron acquires by long continuance in a proper position. It is this which made us say, in the beginning of this article, that attraction and polarity were not confined to magnets, but were properties belonging to all iron in its metallic state. We now see the reason why any piece of iron brought very near to another piece will attract it—both become magnetic, in consequence of the agency of the great magnet; and their magnetism is so disposed, that their mutual attractions exceed their repulsions. Also, why an iron rod, placed nearly in the magnetical direction, will finally arrange itself in that direction. Also, why the terrestrial polarity of common iron is indifferent, and either end of the rod will settle in the north, if it have nearly that position at first. The magnetism induced by mere momentary position is so feeble as to yield to any artificial magnetism. As a moment was sufficient for imparting it, a moment suffices for destroying it; and another moment will impair the opposite magnetism. But artificial magnetism requires more force for its production, and some of it remains when the producing cause is removed, and it does not yield at once to the contrary magnetism. That there is no farther difference appears from this, that long continued polition gives determined and permanent magnetism, and that it is destroyed by an equally long continuance in the contrary position. It seems to be very generally true, that a magnet will carry more by its north than by its south pole. It should be so in this part of the world, because the terrestrial magnetism induced on the iron conspires with the magnetism induced by the north pole of a magnet, but counteracts the magnetism induced by the south pole.

The propriety of Mr Savery's, Mr Canton's, and Mr Anthoine's processes for beginning the impregnation of hard steel bars is now plain, and the superior effect of the two great bars of common iron in the proposed method of Mr Anthoine. We cannot but take this opportunity of paying the proper tribute of praise to the ingenuity of Mr Savery. Every circumstance of his process was selected in consequence of an accurate conception of magnetism, and the combination of this science with Dr. Gilbert's theory. His process is the same with Anthoine's in every respect, except the circumstance of the double touch borrowed from Mitchell and Canton. These observations do not detract from the discernment of Mitchell and Canton, who saw in those experiments what had escaped the attention of hundreds of readers.

But there occurs an objection to this theory of Dr. Gilbert, which was urged against it with great force. We observe no tendency in the magnet or compass-needle toward this supposed magnet. An iron or steel bar is not found to increase its tendency downwards, that is, is not sensibly heavier, when its south pole is up-traction, permott in this part of the world. A needle set afloat on a piece of cork arranges itself quickly in the proper direction; but if continued ever so long afloat, it has never been observed to approach the north side of the vessel. This is quite unlike what we observe in the mutual actions of magnets, or the action of magnets on iron. This objection appears to have given Dr. Gilbert some concern; and he mentions many experiments which have been tried on purpose to discover some magnetical tendency. He gets rid of it as well as he can, by saying, that the directive power of a magnet extends much farther than its attractive power. He confirms this by several experiments. But Dr. Gilbert had not studied the simultaneous actions of the four poles, nor explained, by the principles of compound motion, how these produced all the possible positions of the needle. Indeed, the composition of mechanical forces was by no means familiar with philosophers at the end of the 16th century. We see it now very distinctly. The polarity of the needle, or the force with which it turns itself into the magnetical position, depends on the difference between the sums of the actions of each pole of the magnet on both the poles of the needle; whereas its tendency towards the magnet depends on the difference of the differences of those actions (see n° 22, 25.) The first may thus be very great when the other is almost insensible. We see, that coarse iron filings heap about the magnet very fast, and that very fine filings approach it very slowly. Now, the largest magnet that we can employ, when compared with the great magnet in the earth, is but as a particle of the finest filings that can be conceived. This surely diminishes exceedingly, if it does not entirely annihilate the objection: but as we have have heard it urged by many as an improbable thing, that a long magnet, kept afloat for many months (which has been done) shall not show the smallest tendency towards the pole of the terrestrial magnet; we think it deserves to be considered with accuracy, and the question decided in a way which will admit of no doubt.

Let the very small magnet C (fig. 25.) be placed near a great magnet A, and then near a smaller magnet B, in such a manner that its polarity to both shall be the same; and then let us determine the proportion between the attractions of A and B for the small magnet C.

This will evidently depend on the law of magnetic action. For greater simplicity of investigation, we shall content ourselves with supposing the action to be inversely as the distance.

Let AN = AS = a; BN = b; CN = c; AC = d; BC = e; and let the absolute force of A be to that of B at the same distance as m to 1.

The magnetic action being supposed proportional to \( \frac{1}{d} \), we have,

1. Action of AN on C \( = \frac{m}{d-a-c} \).

2. AN on CN \( = \frac{m}{d-a+c} \).

3. AS on C \( = \frac{m}{d+a-e} \).

4. AS on CN \( = \frac{m}{d+a+c} \).

5. The whole action \( = \frac{8ma cd}{(d^2-a^2)^2} \times \frac{d^2-a^2}{d^2-a^2} \).

6. If c be very small in comparison with a or b, the whole action of A is very nearly \( \frac{8ma cd}{d^2-a^2} \).

7. And the tendency of C to B is, in like manner, \( \frac{8bc cd}{(b^2-a^2)^2} \).

The directive powers of A and B are at their maximum state when C is placed with its axis at right angles to the lines AC or BC. In which case we have,

8. The directive power of A \( = \frac{4ma}{d^2-a^2} \).

9. The directive power of B \( = \frac{4b}{b^2-a^2} \).

When these directive powers are made equal, by placing C at the proper distances from A and B, we have,

10. \( 4ma : 4b \); or \( ma : b = d^2-a^2 : b^2-a^2 \).

And \( ma^2 - ma b^2 = b^2 - b^2 + ma b^2 \).

\( ma^2 = b^2(d^2-a^2) + ma b^2 \).

11. \( b^2 = \frac{b}{ma}(d^2-a^2) + b^2 \).

12. \( b = \sqrt{\frac{b}{ma}(d^2-a^2)} + b^2 \).

Let the attractions of A and B for the very small magnet C, when its polarity to both is the same, be expressed by the symbols \( \alpha \) and \( \beta \). We have

\( \alpha : \beta = \frac{8ma cd}{(d^2-a^2)^2} : \frac{8bc cd}{(b^2-a^2)^2} \), which, by no 10, is

\( \frac{8(d^2-a^2)cd}{(d^2-a^2)^2} : \frac{8(b^2-a^2)cd}{(b^2-a^2)^2} = \frac{d^2-a^2}{b^2-a^2} \).

\( = bd : ma^2 \); that is,

13. Attractions of A : attraction of B \( = bd : ma^2 \).

As an example of this comparison, let us suppose the great terrestrial magnet to be a thousand times larger and stronger than the magnet whose attraction we are comparing with that of terrestrial magnetism. Let us also suppose the distance from the pole of the great magnet to be small, so that its attraction may be considerable. Let us make \( d = 1200 \), \( a = 1000 \), and \( b = 1 \). These are all very reasonable suppositions.

Substituting these values in the formula, we have attraction of A : attraction of B \( = 1 : 1000 \) very nearly; and therefore when the needle, when placed near a magnet, vibrates by its polarity as fast as it does by natural magnetism, its tendency toward that magnet must be altogether insensible; for the disproportion is incomparably greater than that of 1 to 1000, in the largest magnets with which we can make experiments. Observe also, that we have taken the case where the attractions are the strongest, viz., when the magnet C is placed in the axis of A or B. In the oblique positions, tangents to the magnetic curves, the attractions are smaller, almost in any ratio.

We took the inverse ratio of the distances for the law of action, only because the analysis was very simple. It is very evident, that the disproportion will be still more remarkable if the action be inversely as the square of the distance.

The objection therefore to the origin of the polarity of the compass needle, and of all other magnets, namely, the action of a great magnet contained in the earth, appears plainly to be of no force. We rather think that the want of all sensible attraction, where there is a brisk polarity, is a proof of the justness of the conjecture; for if the compass needle were arranged by the action of magnetic rocks, or even extensive strata, near the surface of the earth, the attractions would bear a greater proportion to the polarities. We have even observed this. A considerable mass of magnetic stratum was found to derange the needle of a surveyor's theodolite at a considerable distance all around (about 140 yards). The writer placed the needle on a thin dish, which just floated it on water in a large wooden dish, and set it in a place where it was drawn about 15 degrees from the magnetic meridian. It was left in that situation a whole night, well defended from the wind by a board laid on the dish. Next morning it was found applied to that side of the dish which was nearest to the disturbing rocks. It had moved about six inches. This was repeated three times, and each time it moved in the same direction (nearly), which differed considerably from the direction of the needle itself.

It is now plain that we may, with confidence, assume Dr Gilbert's theory of terrestrial magnetism as sufficiently established. And, since we must certainly call that the north pole of the great magnet which is situated in the northern parts of the earth, and since those poles of magnets which attract each other have opposite polarities, we must say, that what we call the north pole of a mariner's needle, or of any other magnet, has the southern polarity.

We may now venture to go farther with Dr Gilbert, and and to say that all the magnetism which we observe, whether in nature or art, is either the immediate or the remote effect of the action of the great magnet. As soft bars soon acquire a transient magnetism; as hard bars, after long exposure, acquire a sensible and permanent magnetism—we must infer, that ores of iron, which are in a state fit for impregnation, must acquire a sensible and permanent magnetism by continuing, for a series of ages, in the bowels of the earth. And thus the magnetism of loadstones, which, till the discovery of the natural magnetism acquired by position, were the sources of all our magnetical phenomena, is now proved to be a necessary consequence of the existence and agency of a great magnet contained in the bowels of the earth.

It seems to result from this theory, that, in these northern parts of the world, that part of every natural loadstone that is at the extremity of the line drawn through the stone in the magnetic direction should be its pole; and that the loadstone, when properly poised, should of itself assume the very position which it had in the mine. Dr Gilbert complains of the inattention of miners (rude hominum genus, luxu polos quam physicis confulentes) to this important circumstance. Once, however, he had the good fortune to be advertised of a great magnetic mass lying in its matrix. He repaired quickly to the mine, examined it, and marked its points which were in the extremities of the magnetic line. When it was detached from its matrix, he had the pleasure of finding its poles in the very places he expected. The loadstone was of considerable size, weighing about 20 pounds.—Mr Wicke gives in the Swedish Commentaries several instances of the same kind.

But should this always be the case? By no means. There are many circumstances which may give the magnetism of a loadstone a very different direction. We have found, that simple juxtaposition to a magnet will sometimes give a succession of poles to a long bar of hard steel. The same thing may happen to an extensive vein of magnetizable matter. The loadstone taken out of this vein may have been placed like that of a soft bar placed in the magnetic line, if lying in one part of the vein; if taken from another part of it, its polarity may be the very reverse; and in another part it may have no magnetism, although completely fitted for acquiring it. It may have its poles placed in a direction different from all these, in consequence of the vicinity of a greater loadstone. As loadstones possessed of vigorous magnetism are always found only in small pieces, and in pieces of various sizes and force, we must expect every position of their poles. The only thing that we can expect by theory is, that adjoining loadstones will have their friendly poles turned toward each other, and a general prevalence of or tendency to a polarity symmetrical with that of the earth. The reader will find some more observations to this purpose in the article Variation, Encycl. p. 623; as also in Gilbert's treatise, B. III. c. 2. p. 121.

Nor should all strata or masses of iron ore be magnetic. We know that none are susceptible of induced magnetism, but such as are, to a certain degree, in the metallic state. Such ores are not abundant. Nay, even all of such strata do not necessarily acquire magnetism by the action of the great magnet. If their principal dimensions lie nearly perpendicular to the magnetic direction, they will not acquire any sensible quantity. A stratum in this country, rising about 17 degrees to the N. N. W. will scarcely acquire magnetism. It may also happen, that the influence of the great magnet is counteracted by that of some extensive stratum inaccessible to man, by reason of its great depth.

Thus we see, that all the appearances of the original magnetism of loadstones are perfectly consistent with the notion that they are effects of one general cosmical cause, the action of the great magnet contained in the earth, and that there is no occasion to suppose this great magnet to differ, in its constitution or manner of action, from the small masses of similar matter called loadstone. The only difficulty that presents itself is the great superiority of magnetic force observable in some loadstones over other masses of ores circumjacent, which are not distinguishable by us by any other circumstance. We acknowledge ourselves unable to solve this difficulty; for the magnetism of such pieces is sometimes incomparably stronger than what a bar of iron acquires by position; yet this bar is much more susceptible than the ores which are fit for becoming loadstones. Perhaps there is some chemical change which occurs gradually in certain masses, which aids the impregnation, in the same way that we know that being red hot destroys all magnetism, whether in a metal bar or in an ore. This seems to be confirmed by what we see in some old iron stanchions, which acquire the strongest magnetism in those parts of their substance which are combining themselves with ingredients floating in the atmosphere. That part which is casted in the flume, and exfoliates and splits with rust, being converted into something like what is called finery cinder, becomes highly and permanently magnetic. Such peculiarities as these, operating for ages, may allow a degree of magnetical impregnation (in whatever this may consist) to take place, to which we can see no resemblance in our experiments. It would be worth while to place iron wires in a tube in the magnetic direction, which could be kept of a proper red heat, while it is converted into athiops by fleam. It is not unlikely that it would acquire a sensible and permanent magnetism in this way. It may be, that the little atoms, as they arrange themselves in a form of crystalline or symmetrical form, may also arrange so as to favour magnetism. Were this tried in the vicinity of a strong magnet, the effect might be more remarkable and precise. Perhaps, too, while iron is precipitated in a metallic form from its solutions by another metal, something of the same kind may happen. We know, that proper ores of iron, exposed to cementation in a low red heat, in the magnetic direction, becomes magnetic.

Notice has been taken in the Encycl. art. Variation, of the attempts of ingenious men to explain the cause of the change which is observed in all parts of the globe, on the change of the direction of the mariner's needle, the gradual change of the variation. The hypothesis of Dr Halley, that the globe which we inhabit is hollow, and includes a magnetic nucleus, moving round another axis, is not inconsistent with any natural law, if he did not suppose the interval filled up with some fluid. The action of the nucleus and shell on the intervening fluid would gradually bring the two to one common motion of rotation, as may be inferred from the reasonings employed by Newton in his remarks on the Cartelian vortices. Leaving out this circumstance, there is only another cause which can affect, and must affect, the rotation of both; namely, the mutual action of the magnetic nucleus, and the masses of magnetic matter in the shell. If the axis of rotation of this nucleus be different from the line joining its magnetic poles, these poles will have a motion relative to the shell; and this motion may easily be conceived such as will produce the changes of magnetic direction which we observe. It may even produce a motion of the northern magnetic pole in one direction, and of the southern pole in the opposite direction, and this with the appearance of different periods of rotation, as supposed by Mr Churchman. We may here observe, by the way, that the change of magnetic direction in this country is not nearly so great as is commonly imagined. The horizontal needle has shifted its position about 35° at London since 1783; but the point of the dipping needle has not changed 1°. We may also observe, that when the pole of the central magnet changes its place, the magnetism of an extensive stratum, influenced by it, may so alter its disposition, as to change the position of the compass needle in the opposite direction to that of the change which the central magnet alone would induce on it.

But as motions have not yet been affixed to this nucleus, which quadrates with the observed positions of the needle, and as the very existence of it is hypothetical, it may not be amiss to examine, whether such a change of variation may not be explained by what we know of the laws of magnetism, and of the internal constitution of this earth?

1. It is pretty certain, that the veins in which lead-stones are found are not parts of the great magnet. This appears from their having two poles while in the mine, and also from the very small depth to which man has been able to penetrate. When we compare the positions of the dipping needle with those of a small needle near a magnet, we must infer, that the poles are very far below the surface.

Yet we know, that there are magnetifiable strata of very great extent occupying a very considerable portion of the external covering. Though their bulk and absolute power may be small, when compared with those of the great magnet, yet their greater vicinity to the needles on which observations are made, may give them a very sensible influence. In this way may a great deal of the observed irregularities of the positions of the needle be accounted for. In the Lagoon at Teneriffe, Feuille observed the variation 13° 30' west in 1724, while at the head of the island it was only 5°. The dip at the Lagoon was 63° 30', greatly surpassing what was observed in the neighbourhood. Muller found, in the mountains of Bohemia, great and destitute differences of declination, amounting sometimes to 30°. At Mantua, the variation in 1758 was 12°; while at Bononia and Brixia it was nearly 18°. Great irregularities were observed by Goëte in the Gulph of Finland, especially near the island of Suurari, among some rocks; on one of these, the needle showed no polarity. Captain Cook and Captain Phipps observed differences of 1°, extending to a considerable distance, on the west coasts of North America. In the neighbourhood of the island Elba in the Mediterranean, the position of the needle is greatly affected by the iron strata, in which that island so much abounds. In this country, there are also observed small deviations, which extend over considerable tracts of country, indicating a great extent of strata that are weakly magnetic. Since such strata receive their magnetism by induction, in a manner similar to a bar of hard steel, and since we know that this receives it gradually, it may very probably happen, that a long series of years may elapse before the magnetism attains its ultimate disposition.

Here, then, is a necessary change of the magnetic direction; and although it may be very different in different places, according to the disposition and the power of those strata, there must be a general vergency of it one way.

2. It is well known that all metals, and particularly iron, are in a process of continual production and demetallization. The veins of metals, and more particularly those of iron, are evidently of posterior date to that of the rocks in which they are lodged. Chemistry teaches us, by the very nature of the substances which compose them, that they are in a state of continual change. This is another cause of change in the magnetic direction. Nay, we know that some of them have suddenly changed their situation by earthquakes and volcanoes. Some of the streams of lava from Vesuvius and Etna abound in iron. This has greatly changed its situation; and if the strata from which it proceeded were magnetic, the needle in its neighbourhood must be affected. Nay, subterranean heat alone will effect a change, by changing the magnetism of the strata. Mr Lievog, royal astronomer at Bellfleldt in Iceland, writes, that the great eruption from Hecla in 1783, changed the direction of the needle nine degrees in the immediate neighbourhood. This change was produced at a mile's distance from the frozen lava; and it diminished to two degrees at the distance of 2½ miles. He could not approach any nearer, on account of the heat still remaining in the lava, after an interval of 14 months.

All these causes of change in the direction of the mariner's needle must be partial and irregular. But there is another cause, which is comical and universal, Dr Halley's supposition of four poles, or, at least, the supposition of irregular and diffused poles, seems the only thing that will agree with the observations of declination. We know that all magnetism of this kind (that is, disposed in this manner) has a natural tendency to change. The two northern poles may have the same or opposite polarities. If they are the same, their action on each other tends to diminish the general magnetism, and to cause the centre of effort to approach the centre of the magnet. If they have opposite polarities, the contrary effect will be produced. The general magnetism of each will increase, and the pole (or its centre of effort) will approach to the surface. In either of these cases, the compound magnetism of the whole may change exceedingly, by a change by no means considerable in the magnetism of each pair of poles. It is difficult to subject this to calculation; but the reader may have very convincing proof of it, by taking a strong and a weaker magnet of the same length, and one of them, at least, of steel not harder than spring temper. Lay them across each other like an acute letter X; and then place a compass needle, so that its plane of rotation may be perpendicular to the plane of the X. Note exactly the position in which the needle settles. In a few minutes after, it will be found to change considerably. We flatter ourselves, that our readers will grant that the preceding pages contain what may justly be called a theory of magnetism, in as much as we have been able to include every phenomenon in one general fact, the induction of magnetism; and have given such a description of that fact and its modifications, that we can accurately predict what will be the appearances of magnets and iron put into any defined situation with respect to each other. If our notions of philosophical disquisition (delivered in art. Philosophy, Encycl. Brit.) be just, we have explained the subordinate phenomena, or have given a theory of magnetism.

But it is not easy to satisfy human curiosity. Men have even investigated, or sought for causes of the perseverance of matter in its present condition. We have not been contented with Newton's theory of the celestial motions, and have sought for the cause of that mutual tendency which he called gravitation, and of which all the motions are particular instances.

Philosophers have been no less inquisitive after what may be the cause of that mutual attraction of the similar poles, and the repulsion of the similar poles, and that faculty of mutual impregnation, or excitement, which so remarkably distinguishes iron, in its various states, from all other substances. The action of bodies on each other at a distance, has appeared to them an absurdity, and all have had recourse to some material intermediate.

The phenomenon of the arrangement of iron filings is extremely curious, and naturally engages the attention. It is hardly possible to look at it without the thought arising in the mind of a stream issuing from one pole of the magnet, moving round it, entering by the other pole, and again issuing from the former outlet. Accordingly, this notion has been entertained from the earliest times, and different speculations have had different ways of conceiving how this stream operated the effects which we observe.

The simplest and most obvious was just to make it act like any other stream of fluid matter, by impulsion. Impulsion is the thing aimed at by all the speculators. They have a notion, that we conceive this way of communicating motion with intuitive clearness, and that a thing is fully explained when it can be shown that it is a case of impulsion. We have considered the authority of these explanations in the article Impulsion of this Supplement, and need not repeat our reasons for refusing it any pre-eminence. But even when we have shown the phenomena to be cases of impulsion by such a stream, the greatest difficulty, the most curious and the most embarrassing, is to ascertain the sources of this impulsive motion of the fluid—how, and from what cause does it begin? What forces bend it in curves round the magnet? Those philosophers, whose principle obliges them to explain gravitation also by impulse, must have another stream to impel this into its curves. Acting by impulsion, this magnetic stream must lose a quantity of motion equal to what it communicates. What is to restore this? What directs it in a particular course thro' the magnet? And what is it that can totally alter that course—in a moment—in all the phenomena of induced magnetism? How does it impel? Lucretius, either of himself, or speaking after the Greek philosophers, makes it impel, not the iron, but the surrounding air, sweeping it out of the way; and thus giving occasion for the surrounding air to rush around the magnet, and to hurry the bits of iron toward it. There is, perhaps, more ingenious refinement in this thought than in any of the impulsive theories adopted since his day by Des Cartes, Euler, and other great philosophers. But it is fascinatingly remarked by D. Gregory, in his MS. notes on Newton, that this theory of Lucretius falls to the ground; because the experiments succeed just as well under water as in the air. As to the explanations, or descriptions, of the canals and their dock gates, opening in one direction, and shutting in the other, constructions that are changed in an instant in a bar of iron, by changing the position of the magnet, we only wonder that men who have a reputation to lose, should ever hazard such crude and unmechanical dreams before the public eye. The mind of man cannot conceive the possibility of their formation; and if they are really formed, the effects should be the very opposite of those that are observed: the stream should move those bodies least which afford ready channels for its passage. If a rag of iron filings be arranged by the impulsion of such a stream, it should be carried along by it; and if it is impelled toward one end of the magnet, it should be impelled from the other end. Since we now know, that each particle of filings is a momentary magnet, we must allow a similar stream whirling round each. Is that an explanation which exceeds all power of conception?

But has it ever been shown, that there is any impulsion at all in these phenomena? Where is the impelling substance? The only argument ever offered for its existence is, that we are resolved that the phenomena of magnetism shall be produced by impulsion, and the arrangement of iron filings looks somewhat like a stream. But enough of this. We trust that we have shown the way in which this arrangement obtains in the clearest manner. Every particle becomes magnetic by induction. This is a fact, which sets all reasoning at defiance. The polarity of each rag is so disputed, that their adjoining ends turn to each other. This is another incontrovertible fact. And these two facts explain the whole. The arrangement of iron filings, therefore, is a secondary fact, depending on principles more general; and therefore cannot, consistently with just logic, be assumed as the foundation of a theory.

Had magnetism exhibited no phenomena besides the attraction and repulsion of magnets, it is likely that we should not have proceeded very far in our theories, and would have contented ourselves with reducing these phenomena to their most general laws. But the communication of magnetism seems a great mystery. The simple approach of a magnet communicates these powers to a piece of iron; and this without any diminution of its own powers. On the contrary, beginning with magnets which have hardly any sensible power, we can, by a proper alternation of the manipulations, communicate the strongest magnetism to as many hard steel bars as we please; and the original magnets shall be brought to their highest degree of magnetism. We have no notion of powers or faculties, but as qualities of some substances in which they are inherent. Yet here is no appearance of something abstracted from one body, and communicated to, or shared with another. The process is like kindling a great fire by a simple spark; here Is no communication, but only occasion given to the exertion of powers inherent in the combustible matter. It appears probable, that the case is the same in magnetism; and that all that is performed in making a magnet is the excitement of powers already in the steel, or the giving occasion for their exertion; as burning the thread which ties together the two ends of a bow, allows it to unbind. This notion did not escape the sagacity of Dr. Gilbert; and he is at much pains to shew, that the *coitus magneticus* is a quality inherent in all magnetical bodies, and only requires the proper circumstance for its exertion. He is not very fortunate in his attempts to explain how it is developed by the vicinity of a magnet, and how this faculty, or actual exertion of this power, becomes permanent in one body, while in another it requires the constant presence of the magnet.

It is to Mr. Epinus, of the Imperial Academy of St. Petersburg, that we are indebted for the first really philosophical attempt to explain all these mysteries. We mentioned, in the article ELECTRICITY, Suppl., the circumstance which suggested the first hint of this theory to Epinus, viz., the resemblance between the attractions and repulsions of the tourmaline and of a magnet. A material cause of the electric phenomena had long been thought familiar to the philosophers. They had attributed them to a fluid which they called an electric fluid, and which they conceived to be fixed among bodies in different proportions, and to be transferable from one to another. Dr. Franklin's theory of the Leyden phial, which led him to think that the faculty of producing the electrical phenomena depended on the deficiency as well as the redundancy of this fluid, combined with the phenomena of induced electricity, suggested to Epinus a very perilous method of stating the analogy of the tourmaline and the magnet; which he published in 1758 in a paper read to the academy.

Reflecting more deeply on these things, Mr. Epinus came by degrees to perceive the perfect similarity between all the phenomena of electricity by position and those of magnetism; and this led him to account for them in the same manner. As the phenomena of the Leyden phial, explained in Franklin's manner, shews that a body may appear electrical all over, by having less than its natural quantity of the electric fluid, as well as by having more, it seemed to follow, that it may also be so in respect to different parts of the same body; and therefore a body may become electrified in opposite ways at its two extremities, merely by abstracting the fluid from one end, and condensing it in the other; and thus may be explained the phenomena of induced electricity, where nothing appears to have been communicated from one body to the other. If this be the case, the two ends of a body rendered electric by induction should exhibit the same distinctions of phenomena that are exhibited by bodies wholly redundant and wholly deficient. The redundant ends should repel each other; so should the deficient ends; and a redundant part should attract a deficient. All these results of the conjecture tally exactly with observation, and give a high degree of probability to the conjecture. The similarity of these phenomena to the attractions of the dissimilar poles of a magnet, and the repulsions of the similar poles, is so striking, that the same mode of explanation forces itself on the mind, and led Mr. Epinus to think, that the faculty of producing the magnetical phenomena belong to a magnetical fluid, residing in all bodies susceptible of magnetism; and that the exertion of this faculty require nothing but the abstraction of the fluid from one end of the magnetic bar, and its condensation in the other. And this conjecture was confirmed by observing, that in the induction of magnetism on a piece of iron, the power of the magnet is not diminished.

All these circumstances led Mr. Epinus to frame the following hypothesis:

1. There exists a substance in all magnetic bodies, which may be called the magnetic fluid; the particles of which repel each other with a force decreasing as the distance increases.

2. The particles of magnetic fluid attract, and are attracted by the particles of iron, with a force that varies according to the same law.

3. The particles of iron repel each other according to the same law.

4. The magnetic fluid moves, without any considerable obstruction, through the pores of iron and soft steel; but is more and more obstructed in its motion as the steel is tempered harder; and in hard tempered steel, and in the ores of iron, it is moved with the greatest difficulty.

In consequence of this supposed attraction for iron, the fluid may be contained in it in a certain determinate quantity. This quantity will be such, that the accumulated attraction of a particle for all the iron balances, or is equal to, the repulsion of all the fluid which the iron contains. The quantity of fluid competent to a particle of iron is supposed to be such, that the repulsion exerted between it and the fluid competent to another particle of iron is also equal to its attraction for that particle of iron; and therefore the attraction between the fluid in an iron bar A for the iron of another bar B, is just equal to its repulsion for the fluid in B; it is also equal to the repulsion of the iron in A for the iron in B. This quantity of fluid residing in the iron may be called its NATURAL QUANTITY.

In consequence of the mobility through the pores of the iron, the magnetic fluid may be abstracted from one end of a bar, and condensed in the other, by the agency of a proper external force. But this is a violent state. The mutual repulsion of the particles of condensed fluid, and the attraction of the iron which it has quitted, tend to produce a more uniform distribution. If we reflect on the law of action, we shall clearly perceive, that somewhat of this tendency must obtain in every state of condensation and rarefaction, and that there can be a perfect equilibrium only when the fluid is diffused with perfect uniformity. This, therefore, may be called the NATURAL STATE of the iron.

If the resistance opposed by the iron to the motion of the magnetic fluid be like that of perfect fluids to the motion of solid bodies, arising entirely from the communication of motion, there is no tendency to uniform diffusion so weak as not to overcome such resistance, and finally to produce this uniform distribution. But (as is more probable) if the obstruction resembles that of a clammy fluid, or of a soft plastic body like clay, some of the accumulation, produced by the agency of an external force, may remain when the force is removed; the diffusion will cease whenever the equilibrising force is just in equilibrium with the obstruction.

All the preceding circumstances of the hypothesis are are so perfectly analogous to the hypothesis of Mr. Aepinus for explaining the electrical phenomena, which is given in detail in the article Electricity of this Supplement, that it would be superfluous to enter into a minute discussion of their immediate results. We therefore beg the reader to peruse that part of the article Electricity where the elements of Aepinus's hypothesis are delivered, and the phenomena of induced electricity explained (viz., from no 11. to 63, inclusive), and to suppose the discourse to relate to the magnetic fluid.

Let N, S, n, r, be considered as the overcharged and undercharged parts of a magnetical body, or the poles of a magnet, and of iron rendered magnetical by induction. We shall confine our observations in this place to those circumstances in which the mechanical phenomena of magnetism are limited by the circumstance, that magnets always contain their natural quantity of fluid; so that their action on iron, and on each other, depends entirely on its unequal distribution; as is the case with induced electricity.

Let the magnet NAS (fig. 26.), having its north pole NA overcharged, be let near to the bar B of common iron, and let their axes form one straight line. Then (as in the case of electrics) the overcharged pole NA acts on the bar B only by means of the redundant fluid which it contains. For that portion of its fluid, which is just sufficient for saturating the iron, will repel the fluid in B, just as much as the iron in NA attracts it; and therefore the fluid in B suffers no change from this portion of the fluid in NA. In like manner, the pole SA acts on B only in consequence of the iron in SA, which is not saturated or attended by its equivalent fluid.

If the fluid in B is immovable, even the redundant fluid in NA, and redundant iron in SA, will produce no sensible effect on it: For every particle of iron in B is accompanied by as much fluid as will balance, by its repulsions and attractions, the attractions and repulsions of the equidistant particle of iron. But as the magnetical fluid in B is supposed to be easily moveable, it will be repelled by the redundant fluid in AN toward the remote extremity n, till the resistance that it meets with, joined to its own tendency to uniform diffusion, just balances the repulsion of AN. This tendency to uniform diffusion obtains as soon as any fluid quits its place; as has been sufficiently explained in the Supplementary article Electricity, no 16. 17. &c.

But, at the same time, the redundant iron in AS attracts the fluid in B, and would attract it from B, and condense it into B. This attraction opposes the repulsion now mentioned. But, because AS is more remote from every point of B than AN is from the same point, the repulsions of the redundant fluid in AN will prevail; and, on the whole, fluid will be propelled toward n, and will be rarefied on the part B. But as to what will be the law of dilution, both in the redundant and deficient parts of B, it is plain that nothing can be said with precision. This must depend on the distribution of the fluid in the magnet NAS. The more diffused that we suppose the redundant fluid and matter in the magnet, the farther removed will the centres of effort of its poles be from their extremities; the smaller will be the action of AN and AS, the smaller will be their difference of action; and therefore the smaller will be the condensation in B, and the rarefaction in B. Hence we learn, in the outset of this attempt to explanation, that the action of a magnet will be so much the greater as its poles are more concentrated. This is agreeable to observation, and gives some credit to the hypothesis. We can just see, in a very general manner, that the fluid will be rarer than its natural state in s, and denser in r; and that the change of density is gradual, and that the density may be represented by the ordinates of some line c b d (fig. 27.), while the natural density is represented by the ordinates to the line C b D, parallel to s n. There will be some point B of the iron bar, where the fluid will be of its natural density, and the ordinate B b will meet the line c b d in the point of its intersection with CD.

All this action is internal and imperceptible. Let us inquire what will be the sensible external action. There is a superiority of attraction towards the magnet: For since the magnetic action is supposed to diminish continually by an increase of distance, the curve whose ordinates represent the forces, has its convexity toward the axis. Also, the force of the poles AN, AS are equal at equal distances: For, by the hypothesis, the attraction and repulsion of an individual particle are equal at equal distances; and the condensation in AN is equal to the deficiency in AS, by the same hypothesis; because NAS still contains its natural quantity of fluid. Therefore the action of both poles may be expressed by the ordinates of the same curve, and they will differ only by reason of their distances. We may therefore express the actions by the four ordinates M m, P p, N n, Q q, of fig. 2.; of which the property (deduced from the single circumstance of its being convex toward the axis) is, that M m + Q q is greater than P p + N n. There is therefore a surplus of attraction. It is only this surplus that is perceived. The fluid, moveable in B, but retained by it so as not to be allowed to escape, is pressed towards its remote end n by the excess P p - Q q of the repulsion of the redundant fluid in AN, above the attraction of the redundant iron in AS. This excess on every particle of the fluid is transmitted, by the common laws of hydrostatics, to the stratum immediately incumbent on the extremity n, and B is thus pressed away from A. But every particle of the solid matter in B is attracted towards A by the excess M m - N n of the attraction of the redundant fluid in AN above the repulsion of the redundant iron in AS; and this excess is greater than the other; for m + q is greater than p + n.

The piece of common iron n B is therefore attracted, in consequence of the fluid in it having been propelled towards its remote extremity, and distributed in a manner somewhat resembling its distribution in NAS. Now, in this hypothesis, magnetism is held to depend entirely on the distribution of the fluid. B has therefore become a magnet, has magnetism induced on it, and, only in consequence of this induction, is attracted by A.

Had we supposed the deficient, or south pole of A, to have been nearest to B, the redundant matter in AN would have attracted the moveable fluid in B more than the remoter redundant fluid in AS repels it; and, on this account, the magnetic fluid would have been concupitated in B, and rarefied in B n. It would, in this case also, have been distributed in a manner similar to Magnetism.

Its situation in the magnet. And B would therefore have been a momentary magnet, having its redundant pole facing the deficient or dissimilar pole of A. It is plain, that there would be the same surplus of attraction in this as in the former instance, and B would (on the whole) be attracted in consequence, and only in consequence, of having had a properly disposed magnetism induced on it by juxtaposition. The sensible attraction, in this case, is a consequence of the distribution now described; because, since the fluid confounded in the end next to A cannot quit B, the tendency of this fluid toward A must press the solid matter of B in this direction (by hydrostatic laws) more than this solid matter is repelled in the opposite direction.

Thus it appears, that the hypothesis tallies precisely with the induction of magnetism. We do not call this an explanation of the phenomenon; for the fact is, that it is the hypothesis that is explained by the phenomenon: That is, if any person be told that induced magnetism is produced by the action of a fluid, in consequence of its situation being changed, he will find, that in order to agree with the attraction of dissimilar, and the repulsion of similar poles, he must accommodate the fluid to the phenomena, by giving it the properties assigned to it by Epicurus.

But the agreement with this simplest possible case of the most simple example of induced magnetism, is not enough to make us adopt the hypothesis as adequate to the explanation of all the magnetic phenomena. We must confront the hypothesis with a variety of observations, to see whether the coincidence will be without exception.

When the key CB, in fig. 8, is brought below the confounded north pole N of the magnet SAN, its own moveable fluid is propelled from C towards B, and is disposed in CB nearly after the same manner as in SAN. Therefore the redundant fluid in the lower end of the key repels the moveable fluid in the wire BD more than the redundant matter in the upper end C attracts it; and thus the fluid is raised in the upper end of the wire BD, and condensed in its lower end D. CB and BD therefore are two temporary magnets, having their dissimilar poles in contact, or nearest to each other. This is all that is required for their attraction. This effect is promoted by the action of N on the wire BD, also propelling the fluid toward D; and thus increasing the mutual attraction of CB and BD. In like manner, when the key CB is held above the magnet, the moveable fluid in it is more attracted by the redundant matter in SA than it is repelled by the more remote redundant fluid in AN. The same thing happens to the fluid in the wire BD. Therefore CB and BD must attract each other; and the key will carry the wire, although the magnet is below it, and also attracts it. This singularity proceeds from the almost perfect mobility of the fluid in the two pieces of common iron, which renders their poles extremely confounded; whereas the hardness required for the fixed magnetism of the magnet prevents this complete confounding and rarefaction. This can be strictly demonstrated in the case of slender rods of iron; but we can show, and experience confirms it, that in other cases, depending on the shape and the temper of the pieces, the wire will not adhere to the key, but to the magnet.

In the various situations and positions of the key and wire represented in fig. 7, the actions of some of the poles on the moveable fluid in the iron are oblique in regard to the length of the pieces; but, since the moveable matter is supposed to be a fluid, it will still be propelled along the pieces, notwithstanding their obliquity, in the same manner as gravity makes water occupy the lower end of a pipe lying obliquely. If indeed the magnetic fluid could escape from the iron without any obstruction by the propulsion of the magnet, it could produce no attraction, or sensible motion, any more than light does in a transparent body. What is demonstrated of the electric fluid in the Supplemental article Electricity, n° 133, is equally true here. Why the fluid does not escape when it is so perfectly moveable, is a question of another kind, and will be considered afterwards; at present, the hypothesis is, that it does not escape.

If the key and wire have the position fig. 10, n° 1, the fluid is expelled from the parts in contact, and is condensed in the remote ends. So far from attracting each other, the key and wire must repel. They are temporary magnets, having their similar poles facing each other. They must repel each other, if presented in a similar manner to the south pole of the magnet.

If they be presented as in n° 2, fig. 16, where the actions of both poles of the magnet are equal, the state of the fluid in them will not be affected. The redundant pole of the magnet repels the moveable fluid in both the key and the wire toward the upper ends; but the deficient pole acts equally on it in the opposite direction. It therefore remains uniformly distributed through their substance; and therefore they can exhibit no appearance of magnetism.

But if the key and wire be presented to the same part of the magnet, but in another position, as shown in fig. 8, n° 3, the fluid of the key will be attracted from C, and condensed in B, by the joint action of both poles of the magnet. The same thing will happen in the wire BD. Here, therefore, we have two magnets with their dissimilar poles touching. They will attract each other strongly; and if carried gradually toward the upper or lower end of the magnet, they will separate before the point B arrives abreast of N or S. For similar reasons, the pieces of iron presented to the middle of the magnet, as in fig. 10, will have one side a weak north pole, and the other side a weak south pole; but this will not be conspicuous, unless the pieces be broad.

This experiment shows, in a very perspicuous manner, the competency of the hypothesis to the explanation of the phenomena. When the fluid is not moved, magnetism is not induced, even on the most susceptible substance.

When a piece of iron A (fig. 10), nearly as large as the magnet can carry, hangs at either pole, a large piece of iron B, brought near to the pole on the other side, should cause it immediately to fall. If S be the deficient pole, it causes the fluid in A to ascend to the top, and A is attracted; but, for the same reason, it causes the fluid in B to accumulate in its lower end. This redundant fluid must evidently counteract the redundant matter in S, in the induction of the magnetic state on A. Being more remote from A than S is, it cannot wholly prevent the accumulation in the upper end of A; but it renders it so trifling, that the remaining attraction thence arising cannot support the weight of A. This is a very instructive experiment.

But if, on the contrary, we bring a large piece of iron C below the heavy key A, this piece C will have its fluid accumulated in its upper end, both by the action of A on it, and by the action of the magnet. The attraction of the magnet for A should therefore be augmented; and a magnet should carry a heavier lump of iron when a great lump is beyond it. And it is clear (we think), for similar reasons, that the magnetism of the magnet itself in fig. 17. should be increased by bringing a great lump of iron near its opposite pole: for the magnet differs from common iron only in the degree of the mobility of its fluid.

When a compass needle is placed opposite to the redundant pole N of a magnet AN (fig. 28.), it arranges itself magnetically. If a piece of common iron be now presented laterally to the near point of the needle, the redundant matter in the adjoining parts of the needle and the iron should make them repel; but if presented to the remote end, the redundant matter in the iron should attract the redundant fluid in that end of the needle, and that end should turn toward the iron.

A parcel of slender iron wires, carried by the pole of a magnet, as in fig. 29., should avoid each other. If N be the redundant pole, the fluid in each wire will be driven to the remote end, where it must repel the similarly situated fluid of its neighbour. The same external appearance must be exhibited by pieces of wire hanging at the deficient pole of the magnet.

The redundant pole of a magnet A (fig. 30.) being held vertically above the centre of two pieces of common iron, movable round a slender pin, renders the middle of each deficient, and their extremities redundant; therefore they should repel each other, and spread out. The same effect should be produced by the undercharged pole of A.

The redundant pole of a magnet A being applied to one branch of the piece of forked iron NC (fig. 31.), should drive the fluid into its remote parts C, and then the branch NC should be able to induce the magnetic state on a bit of iron D. But if the deficient pole S of another magnet B be applied to the other branch, these two actions should counteract each other at C, and the iron should remain indifferent, and fall.—Yet the magnet B alone would equally cause C to carry the piece of iron.

It is surely unnecessary to demonstrate, that the consequence of this hypothesis must be, that when a magnet puts any piece of iron into the magnetic state, its own magnetism is improved. For the induced magnetism of the iron is always so disposed as to give the fluid in the magnet a greater conglomeration where already condensed, and to abstract more fluid from the parts already deficient. If magnetism be produced by such a fluid, a magnet must always improve by lying anyhow among pieces of iron.

But the case may be very different when magnets are kept in each other's neighbourhood. When the overcharged poles of two magnets are placed facing each other, the redundant fluid in each repels that in the other more than it attracts the remoter redundant iron. The magnets must therefore repel each other. Moreover, in rendering them magnetic, the repulsion of redundant fluid, or the attraction of redundant matter of some other magnet, had been employed; and when the magnet was removed, some of the conglomitated fluid overcame the obstruction to its uniform diffusion, and escaped into the deficient pole; what remains is withheld by the obstruction, and the restoring forces are just in equilibrium with this obstruction. If we now add to them the repulsion of redundant fluid, directed toward the deficient pole, some more of the conglomitated fluid must be driven that way, and the magnet must be weakened. Nay, it may be destroyed, and even reversed, if one of the magnets be very powerful, and have its own magnetism very fixed; that is, if its fluid be very redundant, and meet with very great obstruction to its motion. Hence it also should follow, that the repulsion observed between two magnets should be weaker at the same distance than their attraction, and should follow a different law. For, in the course of the experiments, the situation of the fluid in the magnets is continually changing, and approaching to a state of uniform diffusion.

Let us now examine into the sensible effect of this fluid on a magnet which cannot move from its place, but can turn on its centre like a compass needle. This scarcely requires any discussion. We should only be repeating, with regard to the redundant fluid and redundant matter, what we formerly said in regard of north pole and south pole; the little magnet must arrange itself nearly in the tangent of a magnetic curve. But it requires a more minute investigation to determine what the sensible phenomenon should be when the fluid of the little magnet is perfectly moveable.

Suppose therefore a particle C (fig. 32.) of magnetic fluid, at perfect liberty to move in every direction, and acted on by the redundant and deficient poles of a magnet NAS. The redundant iron in S attracts C in the direction and with the force CF, while the redundant fluid in N repels it in the direction and with the force CD. By their joint action it must be urged in the direction and with the force CE, the diagonal of the parallelogram CDEF, which must be accurately a tangent to a magnetic curve. If this particle of fluid belong to the piece of iron n C s, which lies in that very direction, it will unquestionably be pulled towards the extremity n. The same must happen to other particles. Hence it appears that a piece of common iron in this situation and position must become a magnet, and must retain this position; only the mechanical energy of the lever may change the equilibrium of the magnetic forces a little; because when the piece of iron n C s has any sensible magnitude, the action on its different points will be a little unequal, and may compose diagonals which divide a little from the tangent.

Should the iron needle chance not to have the exact position, but not deviate very far from it, it is also clear that the fluid, not being able to escape, will press on the side toward which it is impelled; and thus will cause the needle to turn on its pivot, and finally arrange itself in magnetical and mechanical equilibrium, deviating so much the less from a tangent to a magnetic curve as the piece of iron is smaller. Any piece of common iron, held in the neighbourhood of a magnet, will become more overcharged at one end and undercharged at the other, in proportion as the position of its length comes nearer to the tangent of a magnetic curve. A slender wire held perpendicular to this position, that is, perpendicular to the curve, should not acquire any sensible magnetism, either attractive or directive.

We surely need not now employ many words to shew that a parcel of iron filings, fixed round a magnet, should arrange themselves in the primary magnetic curves, or that when fixed round two magnets they should form the secondary or composite curves.

Let us now enquire more particularly into the modifications of this accumulation of magnetic fluid which may result from the nature of the piece of iron, as it is put into the magnetic state. The propelling force of A acts against the mutual repulsion of the particles of fluid in B, and also against the obstruction to its motion through the pores of B. The greater this obstruction, the smaller will be the accumulation which suffices, in conjunction with the obstruction and the attraction of the deflected iron, to balance the propulsive force of the redundant fluid in the overcharged pole of A. This circumstance therefore must limit the accumulation that can be produced in a given time. Therefore the magnetism produced on soft steel or iron should be greater than that produced in hard steel at the same distance. Hence the great advantage of soft poles, or of armour, or of capping, to a loadstone, or to a bundle of hard bars. The best form and dimensions of this armour is certainly determinable by mathematical principles, if we knew the law of magnetical action, and the disposition of the magnetism in our loadstone; but these are too imperfectly known in all cases for us to pretend to give any exact rules. We must decide experimentally by making the caps large at first, and reducing them till we find the loadstone carry less; then make them a small matter larger. The chief things to be minded are the purity, the uniformity, and the softness of the iron, and the closest possible contact.

If the obstruction resemble that to motion through a clammy fluid, the final accumulation in hard steel may be nearly equal to that in iron, but will require much longer time. Also, because such obstruction to the motion of the fluid will nearly balance the propelling force in parts that are far removed from the magnet, the accumulation will begin thereabouts, while the bar beyond is not yet affected. A redundant pole will be formed in that place. This will operate on what is immediately beyond it, driving the fluid farther on, and occasioning another accumulation at a still further distance. This may produce a similar effect in a still smaller degree farther on. Thus the steel bar will have the fluid alternately condensed and rarefied, and contain alternate north and south poles. This state of distribution will not be permanent; fluid will be gradually changing its place; these poles will gradually advance along the bar, the remoter poles becoming gradually more diffuse and faint; and it will not be till after a very long time that a regular magnetism with two poles will be produced. To state mathematically the procedure of this mechanism would require many pages. Yet it may be done in some simple cases, as Newton has stated the process of aerial undulation. But we cannot enter upon the task in this limited dissertation. What is said in the Supplementary article Electricity (no. 217, 218.) on the distribution of the electric fluid in an imperfect insulator, will assist the reader to form a notion of the state of magnetism during its induction. That such alternations proceed from such mechanism, we have sufficient proof in the instances mentioned in the former part of this article. The wave, or curl, produced on the surface of a clammy fluid, is a phenomenon of the same kind, answering to similar causes.

When the magnet which has produced all these changes is removed, it is evident that a part of this accumulation will be undone again. The repulsion of the condensed fluid, and the attraction of the deflected iron, will bring back some of the fluid. But it is very evident, that a part of the accumulation will remain, by reason of the obstruction to its motion in returning; and this remainder must be so much the greater as the obstruction to the change of situation is greater. In short, we cannot doubt but that the magnetism which remains will be greater in hard than in spring tempered steel.

Thus have we traced the hypothesis in a great variety of circumstances and situations, and pointed out what the process should be the external appearance in each. We did not, in each instance, mention the perfect coincidence of these consequences with what is really observed, but left it to the recollection of the reader. The coincidence is indeed so complete, that it seems hardly possible to refuse granting that nature operates in this or some very similar manner. We get some confidence in the conjecture, and may even proceed to explain complicated phenomena by this hypothetical theory. We might proceed to show, that the effects of all the methods practised by the artists in making artificial magnets are only consequences of the hypothesis; but this is hardly necessary. We shall just mention some facts in those processes which have puzzled the naturalists.

1. A strong magnet is known to communicate the greatest magnetism to a bar of hard steel; but Mutchenerbroek frequently found, that a weak magnet would communicate more to a soft than to a hard bar.

Explanation. When the magnet is strong enough to impregnate both as highly as they are capable of, the hard bar must be the strongest; but if it can saturate neither, the spring-tempered bar must be left the most magnetical.

2. A strong magnet has sometimes communicated no higher magnetism than a weaker one; both have been able to saturate the bar.

3. A weak magnet has often impaired a strong one by simply passing along it two or three times; but a piece of iron always improves a magnet by the same treatment.

Explanation. When the north pole of a weak but hard magnet is set on the north pole of a strong one, it must certainly repel part of the fluid towards the other end, and thus it must weaken the magnet. When it is carried forward, it cannot repel this back again, because it is not of itself supposed capable of making the magnet so strong. But the end of a piece of iron, always acquiring a magnetism opposite to that of the part which it touches, must increase the accumulation of fluid where it is already condensed, and must expel more from those parts which are already deficient.

4. All the parts of the process of the double touch, as practised by Melsa Mitchell and Canton, are easily explained by this hypothesis. A particle of fluid p (fig. 33.), situated in the middle between the two magnets, is repelled in the direction p e by the redundant pole of the magnet AN, whose centre of effort is supposed to be at C. It is attracted with an equal force in the direction \( p \) toward the centre of effort of the deficient pole of AS. By these combined actions it is impelled in the direction \( p'f \). Now it is plain that, although by increasing the distance between N and S, the forces with which these poles act on \( p \) are diminished, yet the compound force \( p'f \) may increase by the diminution of the angle \( dp'f \). If the action is as \( \frac{1}{\pi} \), \( p'f \) will be greatest when \( \text{Cof. } dp'f \times \text{Cof. } dp'f \) is a maximum; or (nearly) when

\[ \sin^2 dp'f \times \text{Cof. } dp'f \] is a maximum; but this depends on the place of the centre of effort. We can, however, gather from this observation, that the nearer we suppose the centres of effort of the poles N and S to the extremities of the magnets, the nearer must they be placed to each other. But we must also attend to another circumstance; that by bringing the poles nearer together, although we produce a greater action on the intervening fluid, this action is exerted on a smaller quantity of it, and therefore a less effect may be produced. This makes a wider position preferable; but we have too imperfect a knowledge of the circumstances to be able to determine this with accuracy. The unfavourable action on the fluid beyond the magnets must also be considered. Yet all this may be ascertained with precision in some very simple instances, and the determination might be of service, if we had not a better method, independent of all hypotheses or theory; namely, to place the magnets at the distance where they are observed to lift the heaviest bar of iron; then we are certain that their action is most favourable, all circumstances being combined.

We also see a sufficient reason for preferring the position of the magnets employed by Mr. Anthamum (and before him by Mr. Servington Savery), in his process for making artificial magnets. The form of the parallelogram \( dp'f \) is then much more favourable, the diagonal \( p'f \) being much longer.

We also see, in general, that, by the method of double touch, a much greater accumulation of fluid may be produced than by any other known process.

And, lastly, since no appearances indicate any difference between natural and artificial magnetism, this hypothesis is equally applicable to the explanation of the phenomena of natural magnetism; such as the position of the horizontal, and of the dipping needle, and the impregnation of natural lodestones.

Having such a body of evidence for the aptitude of this hypothesis for the explanation of phenomena, it will surely be agreeable to meet with any circumstances which render the hypothesis itself more probable. These are not wanting; although it must be acknowledged that nothing has yet appeared, besides the phenomena of magnetism, to give us any indication of the existence of such a fluid; but there are many particulars in their appearance which greatly resemble the mechanical properties of a fluid.

Heating a rod of iron, and allowing it to cool in a position perpendicular to the magnetic direction, destroys its magnetism. Iron is expanded by heat. If the particles of the magnetic fluid are retained between those of the iron, notwithstanding the forces which tend to diffuse them uniformly, they may thus escape from between the ferruginous particles which with-held them.

For similar reasons, magnetism should be acquired by heating a bar and letting it cool in the magnetic direction. But, besides this evident mechanical opportunity of motion, the union of fire (or whatever name the neologists may choose to give to the cause of expansion and of heat) with the particles of iron may totally change the action of those particles on the particles of fluid in immediate contact with them; nay, it may even change the sensible law of action between magnet and magnet. Of this no one can doubt who understands the application of mathematical science to corporeal attraction (See Boscovich, Suppl.) A change may be produced in the action between magnets without any remarkable change happening in the actions within the magnet, and it may be just the reverse. The union of fire with the magnetic fluid may increase the mutual repulsion of its parts, as it does in all aerial fluids or gases. This alone would produce a diffusion of some magnetism. It may increase the attraction (at infinitesimal distances) between the fluid and the iron, as it does in numberless cases in chemistry.

It is well known that violently knocking or hammering a magnet weakens its force, and that hammering a piece of iron in the magnetic direction will give it some magnetism. By this treatment the parts of the iron are put into a tremulous motion, alternately approaching and receding from each other. In the infants of their recepts, the pent-up particles of the fluid may make their escape. A quantity of small shot may be uniformly mixed with a quantity of wheat, and will remain so forever, if nothing disturb the vessel; but continue to tap it smartly with a stick for a long time, and the grains of small shot will escape from their confinements, and will all go to the bottom. We may conceive the particles of magnetic fluid to be affected in the same way. The same effect is produced by grinding or filing magnets and lodestones. The latter are frequently made worthless by grinding them into the proper shape. This should be avoided as much as possible, and it should always be done in moulds made of soft iron and very massive; but this will not always prevent the diffusion of strong magnetism. As a farther reason for assigning this cause for the diffusion in such cases, it must be observed (Mitschenbroek takes notice of it), that a magnet or lodestone may be ground at its neutral point without much damage. But we had the following most distinct example of the process. A very fine artificial magnet was suspended by a thread, with its south pole down. A person was employed to knock it incessantly with a piece of pebble, in such a manner as to make it ring very clearly, being extremely hard and elastic. Its magnetism was examined from time to time with a very small compass needle. In three quarters of an hour, its magnetism was not only destroyed, but the lower end shewed signs of a north pole. The same magnet was again touched, and made as strong as before, and was then wound about very tight with wetted whipscord, leaving a small part bare in the middle. It was again knocked with the pebble, but could no longer ring. At the end of three quarters of an hour its magnetism was still vigorous, and was not near gone after two hours and a quarter. We discharged a Leyden jar (coated with gold leaf) in the same way. It stood on the top of an axis; and while this was turned round, the edge was rubbed with a very dry cork filled with rosin, and fastened to the end of a glass rod. This made the jar found like the glass of a harmonica. One of them was split in this operation.

A small bar of steel was heated red hot and tempered hard between two strong magnets lying in shallow boxes filled with water, and was more strongly impregnated in this way than in any other that we could think of for a bar of that shape. It has not yet been ascertained what temperature it is most susceptible of magnetism, but it was considerably hotter than to be just visible in a dark place. It is no objection to our way of conceiving magnetism, that the fluid is immovable or inactive when the iron is red hot. Either of these, or both of them, may result from the union with the cause of heat. Even a particular degree of expansion may so change the law of action as to make it immovable; or the union with caloric may render it inactive at all sensible distances. We cannot but think, that some very instructive facts might be obtained by experiments made on iron in the moment of its production, and changes in various chemical processes. All magnetism is gone when it is united with sulphur and arsenic in the greatest number of ores; and when it is in the state of an ochre, rust, ochreous, or solution in acids; and when united with astringent substances, such as galls. When, and in what state, does it become magnetic? And whence comes the fluid of Aepinus? It were worth while to try, whether magnets have any influence in the formation or crystallization of the martial salts; and what will be their effect on iron when precipitated from its solutions by another metal, &c. &c.

There remains one remarkable fact to be taken notice of, which, in one point of view, is a confirmation of the hypothesis, but in another presents considerable difficulties. It is well known, that no magnet has ever been seen which has but one pole; that is, on the hypothesis of Aepinus, which is wholly redundant, or wholly deficient. If all magnetism be either the immediate or the remote effect of the great magnet contained in the earth, and if it be produced by induction, without any communication of substance, but only by changing the disposition of the fluid already in the iron, we never should see a magnet with only one pole. It must be owned, that we never can make such a magnet by any of the processes hitherto described; but the existence of such does not seem impossible. Supposing a magnet, of the most regular magnetism, having only two poles; and that we cut it through at the neutral point, or that we cut or break off any part of it—the fact is, (for the experiment has been tried ever since men began to speculate about magnetism), that each part becomes an ordinary magnet, with two poles, one of which is of the same kind as before the separation. The question now is, What should happen according to the theory maintained by Aepinus?—Tentam. Theor. Elett. et Magnetismi, p. 164, &c.

Let NAS (fig. 34.) be a magnet, of which N is the overcharged pole. Let the ordinates of the curve DAE express the difference between the natural density of the fluid, in a state of uniform diffusion, and its density as it is really disposed in the magnet. The area pND will there express the quantity of redundant fluid in the part nN, and the area qESm expresses the fluid wanting in the part Sm. The intersection A marks that part of the magnet where the fluid is of its natural density. Suppose the part Na to be separated from the rest, containing the redundant fluid NDpa. The tendency of this fluid to escape from the iron with which it is connected will be greater (Mr Aepinus thinks) than before; because its tendency to quit the magnet formerly was repelled by the attractions of the redundant matter contained in AS. This is certainly true of the extremity N; say, perhaps of all the old external surface. Fluid will therefore escape. Suppose that so much has quitted the iron that the point n has the fluid of its natural density, as is represented in n'3, there is still a force operating at n, tending to escape, arising from the repulsion of all the redundant fluid ndDN. If this be sufficient for overcoming the obstruction, it will really escape, and the iron will be left in the state represented by n'4, with an overcharged part fN, and an undercharged part fn.

In like manner, the tendency of the magnetic fluid surrounding the magnet to enter into its deficient pole, will be greater when it is separated from the other, not being checked by the repulsion of the redundant fluid in that other.

Mr Aepinus relates some experiments which he made on this subject. The general result of them was, that the moment the parts were separated, each had two poles, and that the neutral point of each magnet was much nearer to the place of their former union than to their other ends. In a quarter of an hour afterward, the neutral points had advanced nearer to their middle, and continued to do so, by very small steps, for some hours, and sometimes days, and finally were stationary in their middles.

We acknowledge, that this reasoning does not altogether satisfy us, and that the gradual progress of the neutral point toward the middle of each piece, although agreeable to what should result from an escape of fluid, is not a proof of it. We know already, that the induction of magnetism is a progressive thing; and we should have expected this change of the situation of the neutral point, whatever be the nature of magnetism. There is something similar to this, and perhaps equally puzzling, in the immediate recovery of magnetism which has been weakened by heat; it is partly recovered on cooling.

But our chief difficulty is this: At the point A (fig. 34.) everything is in equilibrium before the fracture. The particle A is repelled by the redundant fluid in AN, and attracted by the redundant matter in AS; yet it does not move, for the magnetism is supposed to have permanency. Therefore the obstruction at A cannot be overcome by the united repulsion of AN and attraction of AS. Nor can the obstruction at N be overcome by the difference of these two forces. Now suppose AS annihilated. The change made on the state of things at A is surely greater than that at N, because the force attracted is greater, the distance being less. It does not clearly appear, therefore, that the removal of AS should occasion an efflux at N. This, however, is not impossible; because the fluid may be dispersed; by great conflagration near N, and no great excess of density near A, that a smaller change at N may produce an efflux there. But surely the tendency to escape at A must now be diminished; instead of being greater after the fracture. And if any escape from N, this will still more diminish that tendency to escape from... from A. It does not therefore appear a clear consequence of the general theory, that the constricted fluid should escape; and more particularly, that A should become deficient. And with respect to the entry of fluid into the other fragment, and its becoming overcharged at m, the reasoning seems still less convincing. The steps of the physical process in the two parts of the original magnet are by no means convertible or counterparts of each other. There is nothing in the part AS to resemble the force of repulsion really exerting itself in the corresponding point of AN. There would be, if there were a particle of fluid in that place; but there is not. The tendency therefore of external fluid to enter there, does not resemble the tendency of the internal fluid to expand and dissipate. It is true, indeed, the discourse should be confined to points of the surface. But the internal motion must also be considered; and the great objection always remains, namely, that the obstruction at A (n° 1.) or at n (n° 3.) is sufficient to prevent the passage of a particle of fluid from the pole AN into the pole AS, when urged by the repulsion of the fluid in the one and the attraction of the iron in the other; and yet will not prevent the escape of a particle when one of those causes of motion is removed. Add to this, that the whole hypothesis assumes as a principle, that the resistance to escape from any point is greater than the obstruction to motion through the pores. This is readily granted; for how ever great we suppose the attraction, in the limits of physical contact, it will be no obstruction to motion through the pores, because the particle is equally affected by the opposite sides of the pores; whereas, in quitting the body altogether, there is nothing beyond the body to counteract the attraction by which it is retained.

There seems something wanting to accommodate this beautiful hypothesis of Mr Æpinus to this remarkable phenomenon; and the coincidence is otherwise to complete, that we are almost obliged to conclude that it is merely a deficiency, arising from our not having a sufficient knowledge of the law of magnetic action. This is quite sufficient: For it may be strictly demonstrated, that if the magnetic action decreases in higher ratio than that of the squares of the distances, the permanency of the fluid in any particular disposition has scarcely any dependence on the particles at any sensible distance, and is affected only by the variations of its density (See Electricity, Suppl. n° 217, for a case somewhat similar). Therefore, if the fluid be disposed, that its density may be represented by the ordinates of such a curve as is drawn in fig. 34, having its two extremities concave toward the axis, and a point of contrary flexure at A, the tendency to escape at A will be the greatest possible; and when the magnet is broken at A (n° 1.), or when the fluid has taken the arrangement represented by n° 3, it cannot flop there, and will become deficient in that part. Now, it must be acknowledged, that we are not absolutely certain that the magnetic action is in the precise inverse duplicate ratio of the distance. All that we are certain of is, that it is much nearer to it than to either the inverse simple or inverse triplicate ratio. We own ourselves rather disposed to ascribe the present difficulty to our ignorance of some circumstance, purely mathematical, overlooked, or mistaken, than to think a conjecture unfounded, which tallies so accurately with such a variety of phenomena.

We may here observe, that we are not altogether satisfied with Æpinus's form of the experiment. He did not break a magnet; he let two fixed bars end to end, and touched them as one bar, making the magnetism perfectly regular; he then separated them, and found that each had two poles. But was he certain that, when joined, they made but one magnet? We have sometimes succeeded in doing this, as we thought, by the curves of iron filings; but on putting the needle with which we were examining their polarity into proper situations, we sometimes found it in the second intersection of the secondary curves, shewing that the bars were really two magnets, and not one.

On the other hand, when a piece is broken off from a magnet, the incrustation and elastic tremor into which the parts are thrown, and even the bending previous to the fracture, may give opportunity to a dissipation, which could not otherwise happen. The parts should be separated by corrosion in an acid, and the gradual change of magnetism should be carefully noted. The writer of this article has made some experiments of this nature, the results of which present some curious observations: but they are not yet brought to a conclusion that is fit to be laid before the public.

Mr Prevôt of Geneva, in a dissertation on the origin Hypothesis of magnetic forces, endeavours to give a theory which obviates the only difficulty in that of Æpinus; but it is incomparably more complex, employing two fluids, which by their union compose a third, which he calls combined fluid. There is much ingenuity, and even mathematical address, in adjusting the relative properties of those fluids. But some of them are palpably incompatible; e.g., the particles of each attract each other, but those of the other kind most strongly; yet they are both elastic like air. This is surely inconceivable.—Granting this, however, he finds his different attractions, so that a strong elective attraction of the combined fluid for iron decomposes part of the fluid in the iron, and each of its ingredients occupies opposite ends of the bar: then will the bars approach or recede, according as the near ends contain a different or the same ingredient. All this is operated without repulsion.

But the whole of this is mere accommodation, like Æpinus's, but to much more complex, that it requires very intense contemplation to follow the author through the consequences. Add to this, that his attractions are operated by another fluid, infinitely more subtle than either of those already mentioned, every particle of these being, as it were, a world in comparison of those of the other. In short, he adopts all the extravagant suppositions of Le Sage of Geneva, and everything is ultimately impulsion. Nor is the contrivance for obviating the difficulty (so often mentioned) at all clear and convincing; and it is equally gratuitous with the rest. We cannot think this hypothesis is all entitled to the name of explanation.

This must serve for an account of the hypothesis of Mr Æpinus. The philosophical reader will see, that however exactly it may tally with every phenomenon, it cannot be called an explanation of the phenomena; because it is the phenomena which explain the hypothesis, or give us the characters of the magnetic fluid, if such Magnetism.

Such fluid exists. But we are not obliged to admit this existence, as we admit that to be the true deciphering of a letter which makes sense of it. In that case we know both parts of the subject—the characters and the sounds; but are ignorant which corresponds to which. Did we see a fluid abstracted from one part of a bar and constricted in another, and perceive the abstraction and constriction always accompanied by the observed attractions and repulsions, the rules of philosophical discussion, nay, the constitution of our own mind, would oblige us to assign the one as the cause or occasion of the other. But this important circumstance is wanting in the present case. We think, however, that it merits a close attention; and we entertain great hopes of its being one day completed, by including this single exception.

At the same time, it must be owned, that it gives no extension of knowledge; for it can have no greater extension than the phenomena on which it is founded, and cannot, without risk of error, be applied to an untried case, of a kind dissimilar in its nature to the phenomena on which it is founded. We doubt not but that its ingenious author would have said, that a hit broken off from the north pole of a magnet would be wholly a north pole, if he had not known that the fact was otherwise.

But this hypothesis greatly aids the imagination in conceiving the process of the magnetic phenomena. The more we study them, the more do they appear to resemble the protrusion of a fluid through the parts of an obstructing body. It proceeds gradually. It may be, as it were, overdone, and regorges when the propelling cause is removed. The motion is aided by what we know to aid other obstructed motions. As a fluid would be constricted in all protuberances, so the faculty of producing the phenomena is greater in all such situations, &c. &c. This, joined to the imposibility of speaking, with clearness of conception, of the propagation of powers without the protrusion of something in which they inhere, gives it a hold of the imagination which is not easily shaken off.

To say that nothing is explained when the attraction of the fluid is not explained, and that this is the main question, gives us little concern. We offer no explanation of this attraction, more than of the attraction of gravity. There is nothing contrary to the laws of human intellect, nothing inconsistent with the rules of reasoning, in saying, that things are so constituted, that when two particles are together, they separate, although we are ignorant of the immediate cause of their separation. Those who think that all motion is performed by impulsion, and who explain magnetism by a stream of fluid circulating round the magnet, must have another fluid to impel this fluid into its curvilinear path; for they insist, that the planets are so impelled. Then they must have a third fluid to deflect the vertical motions of the second, and so on without end. This is evident, and it is absurd. But we have said enough in the article Impulsion, Suppl., to show that all hypotheses framed on purpose to explain action by impulsion by impulsion are illogical; because impulsion requires explanation as much as the other, and neither the one nor the other will ever be resolved into anything but the fiat of the Allwise Author of the universe.

Suppl. Vol. II. Part I.

We conclude with desiring the reader to remark, that the explanation which we have given of the magnetic phenomena is independent of the hypothesis of Æpinus, or any hypothesis whatever. We have narrated a plethora of very distinguishing facts, and have marked their distinctions. We have been able to reduce them to general classes; and even to group those classes into others still more general; and at last, to point out one which is discoverable in them all. This is giving a philosophical theory, in the strictest sense of the word, because we show, in every case, the modification of the general fact which allots it this or that particular place in the classification. Thus we have shown that the polarity or directive power of magnets is only a modification of the general fact of attraction and repulsion.

Dr Gilbert's theory of terrestrial magnetism is indeed a hypothesis, and we enunciate it as such. It only claims probability, and we apprehend that a very high degree of credit will be given to it.

We hope that many of our readers will have their curiosity excited by the account we have given of Æpinus's theory. To such we earnestly recommend the perusal of his book Tentamen Theoria Electricitatis et Magnetismi, Auct. F. Æpine, Petropolis, 1759. Van Swinden has included a very good abstract of it in his 2d volume Sur l'Electricité, written by Professor Steiglitz of Ratibon or Ingolstadt. The mathematical part is greatly simplified, and the whole is presented in a very clear and accurate manner. Mr Van Swinden is a professed foe to all hypotheses; but he is not moderate, and we wish that we could say that he is candid. He attacks everything; and takes the opportunity of every analogy pointed out by Æpinus between magnetism and electricity to repeat the full sentence of his dissertation, namely, that magnetism and electricity are not the same; a thing that Æpinus also maintains. But he even charges Æpinus with a mistake in his fundamental arguments, which invalidates his whole theory. He says that Æpinus has omitted one of the acting forces assumed in his hypothesis. This is a most groundless charge; and we own that we cannot conceive how Van Swinden could fall into such a mistake. We are unwilling to call it intentional, for the mere purpose of raising a man of straw to knock him down again. Abbé Haüy of the French Academy has also published an abridgment of Æpinus's theory, with many excellent remarks, tending to clear the theory of the only defect that has been found in it. This work was much approved of, and recommended by the Academy. We have not had the good fortune to see a copy of it.

The reader cannot but have remarked the close analogy between the magnetic phenomena and those of induced electricity; indeed, all the phenomena of attraction and repulsion are the same in both. The mechanical composition of those actions produces a directive power and a polarity, in electrical as well as in magnetic bodies. We can make an electrical needle which will arrange itself, with respect to the overcharged and undercharged ends of a body electrified by mere position, just as a compass needle is arranged by a magnet. We can touch a thick of sealing wax in the manner of the double touch, so as to give it poles of considerable force and durability. As a red hot steel bar acquires permanent poles by quenching it near a magnet, so melted wax acquires them by freezing in the neighbourhood of a positive positive and negative electric. Some have inferred a sameness of origin of these two species of powers from those various circumstances of resemblance; but the original causes seem to be distinct on many accounts.

Electricity is common to all bodies. The cause of magnetism can operate only on iron. Although lightning or an electrical shock gives polarity to a needle, we need not infer the identity of the cause, because the polarity which it gives is always the same with that given by great heat; and there is always intense heat in this operation. The phenomenon which looks the most like an indication of identity of the origin of electricity and magnetism is the direction of the rays of the aurora borealis—they converge to the same point of the heavens to which the elevated pole of the dipping needle directs itself. But this is by no means a sufficient foundation for establishing a sameness. Electricity and magnetism may, however, be related by means of some powers hitherto unknown. But we are decidedly of opinion, that the electric and magnetic fluid are totally different, although their mechanical actions are so like that there is hardly a phenomenon in the one which has not an exact counterpart in the other. But we see them both operating, with all their marks of distinction, in the same body; for iron and lodestones may be electrified, like any other body, and their magnetism suffers no change or modification. We can set these two forces in opposition or composition, just as we can oppose or compound gravity with either. While the iron filings are arranging themselves round a magnet, the mechanical action of electricity may be employed either to promote or hinder the arrangement. They are therefore distinct powers, inherent in different subjects.

But there are abundance of other phenomena which shew this diversity. There is nothing in magnetism like a body overcharged or undercharged in toto. There is nothing which indicates the presence of the fluid to the other senses—nothing like the spark, the snap, the visible efflorescence; because the magnetic fluid enters into no union with air, or anything but iron. There is nothing resembling that inconceivably rapid motion which we see in electricity; the quickest motion of magnetism seems inferior (even beyond comparison) with the flow of motion along any electric conductor. Therefore there is no possibility of discharging a magnet as we discharge a coated plate. Indeed, the resemblance between a magnet and a coated plate of glass is exceedingly slight. The only resemblance is between the magnet and an inconceivably thin stratum of the glass, which stratum is positive in one side and negative in the other. The only perfect resemblance is between the induced magnetism of common iron, and the induced electricity of a conductor.

The following seem the most instructive dissertations on magnetism, either as valuable collections of observations, or as judicious reasonings from them, or as the speculations of eminent or ingenious men concerning the nature of magnetism.

Gilbertus de Magnete, Lond. 1600, fol. Æpinii Tentamen Theorie Magn. et Electr. Eberhardi Tentam. Theor. Magnetismi, 1720. Dissertations sur l'aimant, par du Fay, 1728. Münchenbrock Dissert. Physico Experimentalis de Magnete. Pièces qui ont emporté le prix de l'Acad. des Sciences à Paris sur la meilleure construction des Bouffées de déclinaison. Recueil des pièces couronnées, tom. v. Euleri opuscula, tom. iii. continens Theoriam Magnetis, Berlino, 1751. Æpinii Oratio Academica, 1758. Æpinii item Comment. Petrop. nov. tom. x. Anton. Brugmanni tentam. Phil. de materia Magnetica, Francofurtæ, 1765.

There is a German translation of this work by Effenbach, with many very valuable additions.

Scarletta de Magnete, 2 tom fol. Van Swinden Tentamina Magnetices, 4to. Van Swinden sur l'Analogie entre les phénomènes Électriques et Magnétiques, 3 tom. 8vo. Dissertation sur les Aimans artificielles par Antheaume. Expériences sur les Aimans artificielles par Nicholas, Futs, 1782. Essai sur l'Origine des Forces Magnétiques par Mr Prevost. Sur les Aimans artificielles par Rivoir, Paris 1752. Dissertatio de Magnetismo par Sam. Klingendler et Jo. Brandt, Holm. 1752. Description des Courants Magnétiques, Strasbourg, 1753. Traité de l'Aimant par Dalancé, Amit. 1687.

Besides these original works, we have several dissertations on magnetic vortices by Des Cartes, Bernoulli, Euler, Du Tour, &c. published in the collections of the works of those authors, and many dissertations in the memoirs of different academies; and there are many popular treatises by the traders in experimental philosophy in London and Paris. Dr Gowen Knight, the person in Europe who was most eminently skilled in the knowledge of the phenomena, also published a dissertation intitled, An attempt to explain the Phenomena of Nature by two principles, Attraction and Repulsion, Lond. 1748, 4to., in which he has included a theory of magnetism. It is a very curious work, and should be studied by all those who have recourse without scruple to the agency of invisible fluids, when they are tired of patient thinking. They would there see what thought and combination are necessary before an invisible fluid can be really fitted for performing any office we choose to assign it. And they will get real instruction as to what services we may expect of such agents, and from what talks they must be excluded. The Doctor's theory of magnetism is very unlike the rest of the performance; for he does not avail himself of the vast apparatus of propositions which he had established, and adopts without any nice adjustment the most common notions of an impulsive vortex. Both the production and maintenance of this vortex, and its mode of operation, are irreconcilable with the acknowledged laws of imulsion.

Si quid novi fit rectius illius, candidatus imperit—si non—bis utere vicum.

APPENDIX.

We have been favoured with the following investigation of the curves, to which a needle of indefinite motion of the nutentis will be a tangent, by Mr Playfair, Professor of Mathematics in the University of Edinburgh. Two magnetical poles being given in position, the force of each of which is supposed to be as the nth power of the distance from it reciprocally, it is required to find a curve, in any point of which a needle (indefinitely short) being placed, its direction, when at rest, may be a tangent to the curve?

1. Let A and B (fig. 35.) be the poles of a magnet, C any point in the curve required; then we may suppose the one of these poles to act on the needle only by repulsion, and the other only by attraction, and the direction of the needle, when at rest, will be the diagonal of a parallelogram, the sides of which represent these forces. Therefore, having joined AC and BC, let AD be drawn parallel to BC, and make \( \frac{AC}{AD} = \frac{BC}{EC} = AC : AD \); join CD, then CDF will touch the curve in C.

2. Hence an expression for AF may be obtained.

For, by the construction, \( AD = BC \), and since BC : AD :: BF : FA, and BC - AD : AD :: AB : AF, we have \( AF = \frac{AB \times AC}{BC + AC} \).

3. A fluxionary expression for AF may also be found in terms of the angles CAB, ABC. In CF take the indefinitely small part CH, draw AH, BH, and from C draw CL perpendicular to AH and CK to BH. Draw also BC and AM at right angles to FH. Let the angles CAB = \( \alpha \), and CBA = \( \beta \); then CAH = \( \alpha \), and CBH = \( \beta \); also CL = AC \( \times \alpha \), and CK = BC \( \times \beta \). Now HC : CL :: AC : AM = \( \frac{AC \times \alpha}{HC} \); and for the same reason BC = \( \frac{BC \times \beta}{HC} \).

Therefore since AF : FB :: AM : DC, AF : FB :: \( \frac{AC \times \alpha}{HC} : \frac{BC \times \beta}{HC} \), and AF : AB :: \( \frac{\sin \alpha}{\sin \beta} : \frac{\sin \beta}{\sin \alpha} \); therefore if \( AB = a \), \( AF = \frac{a \sin \alpha}{\sin \beta} + \frac{a \sin \beta}{\sin \alpha} \).

4. If this value of AF be put equal to that already found, a fluxionary equation will be obtained, by the integration of which the curve may be constructed. Because \( AF = \frac{AB \times AC}{BC + AC} \); and since AC = \( \frac{a \sin \alpha}{\sin \beta} \), and BC = \( \frac{a \sin \beta}{\sin \alpha} \), we have by substitution \( AF = \frac{a \sin \alpha}{\sin \beta} + \frac{a \sin \beta}{\sin \alpha} \).

Hence, \( \sin \alpha \times \sin \beta + \sin \beta \times \sin \alpha = C \).

5. These fluxions are easily found when \( m \) is any whole positive number.

If \( m = 1 \), we have \( \sin \alpha + \sin \beta = 0 \). \( m = 2 \), \( \sin \alpha + \sin \beta = 0 \). \( m = 3 \), \( \sin \alpha + \sin \beta = 0 \). \( m = 4 \), \( \sin \alpha + \sin \beta = 0 \), &c.

Therefore, &c.

Also if \( m = 1 \), \( \cos \alpha + \cos \beta = C \). \( m = 2 \), \( \cos \alpha + \cos \beta = C \). \( m = 3 \), \( \cos \alpha + \cos \beta = C \). \( m = 4 \), \( \cos \alpha + \cos \beta = C \).

We omitted the inserting in its proper place, no. 65. Addition to a hypothesis of the celebrated astronomer Tobias Mayer of Gottingen, by which the direction of the mariner's needle in all parts of the earth may be determined. He supposes that the earth contains a very powerful magnet of considerable dimensions, which arranges the needle according to the known laws of magnetism. The centre of this magnet was distant from the centre of the earth about 480 English miles in 1756, and a line joining these centres intersected the earth's surface in a point situated in 17° N. Lat. and 183° E. Long., from London. The axis of the magnet is perpendicular to this line, and the plane in which it lies is inclined about 11° to the plane of the meridian, the north end of the axis lying on the east side of that meridian. Magnetism.

From these data, it will be found that the axis of this magnet cuts the surface of the earth about the middle of the eastern shore of Baffin's Bay, and in another point about 800 miles S.S.W. of the southern point of New Zealand. Professor Lichtenberg of Gottingen, who gives this extract from the manuscript, says, that the hypothesis is accompanied by a considerable list of variations and dips calculated by it, and compared with observations, and that the agreement is very remarkable. He gives indeed a dozen instances in very different regions of the earth. But we suspect that there is some error or defect in the data given by him, because the annual changes, which he also gives, are such as are inconsistent with the data, and even with each other. He says, that the distance from the centre increases about four miles annually, and that thence arises an annual diminution of 8 minutes in the latitude and 14 in the longitude of that point where the straight line joining the centres meets the surface. It can have no such consequence. He says also, that the above mentioned inclination of the places increases 8 minutes annually. The compound force of the magnet is said to be as the square root of the distance inversely. We are at a loss to understand the meaning of this circumstance; because Mayer's hypothesis concerning the law of magnetic attraction is exceedingly different, as related by Mr. Lichtenberg from the same manuscript. But it was our duty to communicate this notice, though imperfect, of the speculations of this celebrated mathematician. See Exliber's Elem. of Nat. Phil., published by Lichtenberg 1784, p. 645.

Let HZOF (fig. 37.) be the plane of a magnetic meridian, H'O the plane of the horizon, and NS the position of the magnetic needle in any place, when it is at liberty to settle in the true magnetic direction. The angle HON is the inclination or dip of the needle. Let Z'F be a vertical circle, in which a well constructed dipping needle can freely play up and down. This needle cannot place itself in the magnetic direction, because it can only move in a vertical plane. Its north point is impelled in the direction n'o, and its south point in the direction s'o, both of which are parallel to NS. By the laws of mechanical equilibrium, it cannot rest, except in such a position that the forces n'o and s'o are in a plane perpendicular to the plane Z'F. In any other position, there would be a force impelling the needle toward that side on which n'o makes an acute angle with the tangent r't of the vertical circle. Therefore the spherical triangle N'F is right angled in n', and Cof. NF n : R = Tan. n F : Tan. NF = Tan. HN : Tan. n'. Therefore

\[ \tan. n' = \frac{\tan. HN}{\cot. H'} \]

Therefore, in any place, the real inclination of the magnetic direction to the horizon is different from what is pointed out by a dipping needle when it is in a plane which declines from the magnetic meridian; and the tangent of the observed dip of the needle exceeds that of the inclination of the magnetic direction in the proportion of radius to the cosine of the deviation H'C'n, or the proportion of the secant of this angle to the radius. If therefore the dipping needle play in a magnetic east and west circle, it will stand perpendicular to the horizon.

M A L.