MAGNETISM

THE word magnetism is derived from the Greek word μαγνη, a name given to the loadstone or native magnet, an ore of iron well known to the ancients. The term μαγνη itself is said to be derived from one Magnes, a Greek shepherd, who observed on Mount Ida the attractive power which the loadstone exercised upon his iron crook. The most probable supposition however is, that it took its name from Magnesia, a country in Lydia, where it was first discovered; and this conjecture is confirmed by the fact that the magnet was often called by the ancients Lapis Heraclæus, from Heraclæa, the capital of Magnesia.

The science of magnetism treats of the phenomena exhibited by magnets, whether natural like the loadstone, or artificial like bars of steel to which magnetism has been permanently communicated;—of their reciprocal action upon each other; of the laws of the forces which they develop; of the methods of making artificial magnets; and of the magnetic phenomena exhibited by the globe which we inhabit.

In giving an account of this interesting science, which has made rapid progress in modern times, we shall adopt the following arrangement:

1. 1. On the history of magnetical discovery.
2. 2. On the general phenomena and principles of natural and artificial magnets.
3. 3. On the magnetism of bodies not ferruginous.
4. 4. On the development of magnetism in bodies by rotation.
5. 5. On the influence of heat on magnetism.
6. 6. On the action of iron spheres on the needle.
7. 7. On the influence of magnetism on chemical action.
8. 8. On the laws of magnetic forces.
9. 9. On terrestrial magnetism.
10. 10. On the different methods of making artificial magnets.
11. 11. On magnetical instruments and apparatus.
12. 12. On the theories of magnetism.

The attractive power of the natural magnet or loadstone over small pieces of iron seems to have been known from the remotest antiquity. It is distinctly referred to by Homer, Pythagoras, and Aristotle. Pliny mentions a chain of iron rings suspended from one another, the first being upheld by the loadstone; and he relates that Dinoscares proposed to Ptolemy Philadelphus to build, at Alexandria, a temple, the vault of which, crowned with loadstones, should suspend in the air an iron statue of Queen Arsinoë. St Augustin likewise makes mention of a statue suspended in the air in the middle of the temple of Serapis at Alexandria. From references made to the magnet by Euripides, Claudian, and others, and from the experiment with the rings mentioned by Pliny,¹ it is not very improbable that the ancients were acquainted with the communicability of magnetism to iron bodies. The magnetical properties of the loadstone, like the electrical ones of amber, were supposed to be miraculous. Medical qualities of various kinds were ascribed to it; and even Hippocrates ranks it amongst the number of purgatives.

In order to explain the properties of the loadstone, Thales, Anaxagoras, and others, supposed it to have a soul; while some conceived that it was surrounded with an emanation, capable of creating a vacuum, into which the iron precipitated itself.

In his description of China, Duhalde has stated that the Invention directive power, or polarity, of the magnet, was known to the Chinese in the earliest ages, and that the needle had been employed to guide travellers by land a thousand years before Christ; and it is stated by Humboldt, that, according to the Peuthsaoyani, a treatise on Medical Natural History, written under the Saong dynasty, 400 years before Columbus, the Chinese suspended the needle by a thread, and found it to decline to the south-east, and never to rest at the true south point.

Although the common properties of the loadstone were known to the ancients, and were no doubt studied even during the dark ages, yet, notwithstanding the claims of the Chinese and Arabians, the directive power of the loadstone, or of a needle touched or rubbed by it, seems to be the discovery of modern times. Are Frode, an Icelandic historian, who was born in the year 1068, and who must have written his Landnamabok, or history of the discovery of Iceland, about the end of the eleventh century, mentions, in the most unequivocal manner, the directive power of the loadstone as known in his day. He states that Floke Vilgerderson, a renowned viking or pirate, departed from Rogoland in Norway, to seek Gadersholm or Iceland, some time in the year 868. He carried with him three ravens as guides, and, to consecrate them for this purpose, he offered up a sacrifice in Smörsund, where his ship lay. "For," says Frode, "in those times seamen had no loadstone² in the northern countries."

That the mariner's compass was known in the twelfth century, about the year 1150, is proved by notices of it in various authors, particularly in an old French poem called La Bible Guyot, which is contained in a curious quarto manuscript of the thirteenth century, still existing in the Royal Library at Paris. Guyot of Provins, the author of this poem, was alive in 1181. After referring to the ways by which navigators are guided in their course, and mentioning the pole star, he adds,

Un art font qui mentir ne peut,
Par la vertu de la marinière,
Un pierre laide et brunière
Où le fers volontiers se joint,
Ont regardent lor droit point.

That is, "they possess a never-failing method, by the virtue of the marinière, an ugly and brown stone, to which iron adheres of its own accord." The author next adds, that this art consists in rubbing a needle on the marinière; and that the point of this needle turns just against the pole-star in dark nights, when neither star nor moon are seen.

Quant il nuit est ténèbre et brune,
Quand ne voit estole ne lune,
Lor font à l'aiguille allumer,
Puiz ne peut ils assorer,
Contre l'estole va le pointe,
Par se sont il mariner cointe,
De la droit voie tems:
C'est un art qui ne peut mentir.

¹ Sola hæc materia (ferrum) vires ab eo lapide accipit, retinetque longo tempore, aliud apprehendens ferrum, ut annulorum catena spectetur interdum, quod imperitum vulgus ferrum appellat vivum.

² Leidarstein, or Leading Stone, from which our word Loadstone is derived.

History. Cardinal James de Vitri, who flourished about the year 1200, mentions the magnetic needle in his History of Jerusalem; and he adds, that it was of indispensable utility to those who travelled by sea.

That the mariner's compass was known to the northern nations in 1266, appears from Torficus's History of Norway, where it is mentioned that Jarl Sturla's poem on the death of the Swedish count Byrgers was rewarded with a mariner's compass. The directive property of the magnet is also distinctly mentioned in an epistle of Petrus Peregrinus de Marcourt, written about the latter end of the thirteenth century. This letter was addressed "Ad Sigerium de Foueancourt militem de magnete." This epistle contains a description of the loadstone, the means of finding its poles, and its property of attracting iron; and it proves that the part of the magnet which is turned to the north attracts that which is turned to the south.

A Neapolitan named Flavio Gioia, who lived in the thirteenth century, has been regarded by many as the inventor of the compass. Dr Gilbert affirms that Paulus Venetus brought the compass from China to Italy in 1260.

Paulus Venetus. Ludis Vestomannus asserts, that about 1500 he saw a pilot in the East Indies direct his course by a magnetic needle like those now in use. One of the earliest treatises on magnetism is a Latin letter of Peter Adsiger, contained in a volume of manuscripts in the library of the university of Leyden. This letter, which appears to have been written for the instruction of a friend, is in reality a methodical treatise, in two parts, the first of which is subdivided into ten, and the second into three chapters. In the second chapter of the second part, the mariner's compass, and the method of constructing it, are clearly described; and, what is still more interesting, the author not only mentions the declination of the magnetic needle, but had observed its actual deviation from the meridian. "Take notice," says he, "that the magnet, as well as the needle which has been touched by it, does not point exactly to the poles; but that part of it which is reckoned to point to the south inclines a little to the west, and that part which looks towards the north inclines as much to the east. The exact quantity of this declination I have found, after numerous experiments, to be five degrees. However, this declination is no obstacle to our guidance, because we make the needle itself decline from the true south by nearly one point and a half towards the west. A point, then, contains five degrees." Mr Christie seems to consider the authenticity of this manuscript as doubtful, because no new observation of the declination seems to have been made for two centuries afterwards; and because the declination should be westerly in place of easterly in 1269, according to the best law of the change which can be deduced from subsequent observations.

The declination or the variation of the needle, thus distinctly described by Adsiger, if his manuscript is authentic, must be considered as well known before the time of Columbus, to whom the discovery of it has been generally ascribed. His son Ferdinand states, that on the 14th of September (13th according to Mr Irving) 1492, his father, when about two hundred leagues from the island of Ferro, noticed for the first time the variation of the needle; "a phenomenon," says Washington Irving, "which had never before been remarked." "He perceived," adds this author, "about nightfall, that the needle, instead of pointing to the north star, varied but half a point, or between five and six degrees to the north-west, and still more on the following morning. Struck with this circumstance, he observed it attentively for three days, and found that the variation increased as he advanced. He at first made no mention of this phenomenon, knowing how ready his people were to take alarm; but it soon attracted the attention of the pilots, and filled them with consternation. It seemed as if the laws of nature were changing as they advanced, and that they were entering another world, subject to unknown influences. They apprehended that the compass was about to lose its mysterious virtues; and, without this guide, what was to become of them in a vast and trackless ocean? Columbus tasked his science and ingenuity for reasons with which to allay their terrors. He told them that the direction of the needle was not to the polar star, but to some fixed and invisible point. The variation was not caused by any failing in the compass, which, like the other heavenly bodies, had its changes and revolutions, and every day described a circle round the pole. The high opinion that the pilots entertained of Columbus as a profound astronomer gave weight to his theory, and their alarm subsided."¹ Although the details which we have already given afford sufficient proof that the variation of the needle had been discovered two hundred years before the time of Columbus, yet it is evident, from the above passage, that he had discovered the variation of the variation, or that the variation was not a constant quantity, but varied in different latitudes.

Notwithstanding these casual observations on the variation of the compass, no accurate measures of its amount were made till about the middle of the 16th century. In 1541 it was found that the declination of the needle from the meridian of Paris was about 7° or 8° easterly. In 1550 it was 8° or 9°, and in 1580 11½° easterly. Norman,² who first observed the variation in London, made it 11° 15' easterly; and Mr Burrough,³ comptroller of the navy, in 1580 found it to be at an average 11° 19' E. at Limehouse. The following observations made at other places will show the gradual change in the variation.

Columbus. His son Ferdinand states, that on the 14th of September (13th according to Mr Irving) 1492, his father, when about two hundred leagues from the island of Ferro, noticed for the first time the variation of the needle; "a phenomenon," says Washington Irving, "which had never before been remarked." "He perceived," adds this author, "about nightfall, that the needle, instead of pointing to the north star, varied but half a point, or be-

between five and six degrees to the north-west, and still more on the following morning. Struck with this circumstance, he observed it attentively for three days, and found that the variation increased as he advanced. He at first made no mention of this phenomenon, knowing how ready his people were to take alarm; but it soon attracted the attention of the pilots, and filled them with consternation. It seemed as if the laws of nature were changing as they advanced, and that they were entering another world, subject to unknown influences. They apprehended that the compass was about to lose its mysterious virtues; and, without this guide, what was to become of them in a vast and trackless ocean? Columbus tasked his science and ingenuity for reasons with which to allay their terrors. He told them that the direction of the needle was not to the polar star, but to some fixed and invisible point. The variation was not caused by any failing in the compass, which, like the other heavenly bodies, had its changes and revolutions, and every day described a circle round the pole. The high opinion that the pilots entertained of Columbus as a profound astronomer gave weight to his theory, and their alarm subsided."¹ Although the details which we have already given afford sufficient proof that the variation of the needle had been discovered two hundred years before the time of Columbus, yet it is evident, from the above passage, that he had discovered the variation of the variation, or that the variation was not a constant quantity, but varied in different latitudes.

Notwithstanding these casual observations on the variation of the compass, no accurate measures of its amount were made till about the middle of the 16th century. In 1541 it was found that the declination of the needle from the meridian of Paris was about 7° or 8° easterly. In 1550 it was 8° or 9°, and in 1580 11½° easterly. Norman,² who first observed the variation in London, made it 11° 15' easterly; and Mr Burrough,³ comptroller of the navy, in 1580 found it to be at an average 11° 19' E. at Limehouse. The following observations made at other places will show the gradual change in the variation.

The important discovery of the dip or inclination of the Dip of the needle was made in 1576, by Robert Norman, whom we have already mentioned. Having constructed many compasses, and having always balanced the needles for them before he touched them with the magnet, he invariably found, that after they were touched, the north point always inclined below the horizon, so that he was obliged to make the card of the compass level, by putting some small pieces of wire on the end of it. Having mentioned this discovery to some of his friends, he was advised to construct an instrument which would enable him to measure the greatest angle which it would make with the horizon. With this instrument, which is the dipping needle in its first and rudest form, he found the dip to be at 71° 50'; an observation which, according to Bond, must have been made about 1576.

That ferruginous substances always possess a greater or

¹ Irving's Life and Voyages of Columbus, vol. i. p. 201.

² The New Attractive, by Robert Norman, Lond. 1596.

³ A Discourse on the Variation of the Compass. Lond. 1581. Gellibrand found that the north-east of the needle was gradually moving to the westward.

a less degree of magnetism, has been long known. One Julius Caesar, a surgeon of Rimini, first observed the conversion of iron into a magnet. In 1590 he noticed this effect on a bar of iron which had supported a piece of brick-work on the top of a tower of the church of St Augustin. The very same fact was observed about 1630, by Gassendi, on the cross of the church of St John at Aix, which had fallen down in consequence of having been struck with lightning. He found the foot of it wasted with rust, and possessing all the properties of a loadstone.

While magnetism was making slow advances by means of insulated observations, it was destined to receive a vigorous impulse from the pen of Dr Gilbert of Colchester. This eminent individual, who was physician in ordinary to Queen Elizabeth, published, in 1600, his Physiologia Nova, seu Tractatus de Magnete et Corporibus Magneticis, a work which contains almost all the information concerning magnetism which was known during the two following centuries. It relates chiefly to the natural loadstone, and to artificial magnets, or bars of steel which have acquired similar properties. He applies the term magnetic to all bodies which are acted upon by loadstones and magnets, in the same manner as they act upon each other, and he finds that all such bodies contain iron in some state or other. He considers the phenomena of electricity as having a considerable resemblance to those of magnetism, though he points out the differences by which the two classes of phenomena are marked. In treating of the directive power of the needle, he supposed, "that the earth itself being in all its parts magnetic, and the water not, wherever the land was, there would the needle turn, as to the greater quantity of magnetic matter." He regarded the earth as acting upon a magnetised bar, and upon iron, like a magnet, the directive power of the needle being produced by the action of magnetism of a contrary kind to that which exists at the extremity of the needle directed towards the pole of the globe. He gave the name of pole to the extremities of the needle which pointed towards the poles of the earth, conformably to his views of terrestrial magnetism, calling the extremity that pointed towards the north the south pole of the needle, and that which pointed to the south the north pole.

About the year 1650, Mr Bond, a teacher of mathematics in London, who had been employed to superintend the publication of the popular treatises on navigation, published a work called the Seaman's Calendar, in which he maintains that he has discovered the true progress of the deviation of the compass; and in another book, called The Longitude Found, and in the Phil. Trans. 1668, he published a table of the computed variations for London for many years to come, extending from 1663 to 1716. The results which his table contains agree very nearly with those which were observed for the next twenty-five years, but after that the differences became very great. In a subsequent paper in the Phil. Trans. for 1673, Bond attempted to account for the change in the variation and dip of the needle, by supposing that the two magnetic poles revolved round the poles of the earth. He asserted that he knew the period of this revolution, as well as its cause; and he proposed to determine the longitude by means of the dip of the needle. He did not, however, think proper to communicate either his views or method to the public.

Newton, Huygens, Hooke, and some of the other philosophers who flourished about the end of the seventeenth century, were occupied, though not to a great degree, with the subject of magnetism. Some of their observations and discoveries are referred to in a manuscript volume of notes and commentaries, written by David Gregory in 1693, in a copy of Newton's Principia, and used by Newton in improving the second edition. Newton had supposed that the law of magnetic action approaches to the inverse triplicate ratio

of the distance; but Gregory did not adopt this opinion, and invalidates the arguments which were used in its support. Newton committed another mistake in asserting, as we shall afterwards see, that red hot iron has no magnetic property.

Several interesting experiments had been made by Dr Dr Hooke. Gilbert, on the effects of heat in destroying magnetism, and also in inducing it in substances susceptible of being impregnated. He likewise made numerous experiments with bars of iron and steel placed in the magnetic meridian and exposed to great heats. Dr Hooke took up this subject in 1684. He used rods of iron and steel about seven inches long and one fifth of an inch in diameter, and he found that they acquired permanent magnetism when strongly heated in the magnetic meridian, and allowed to cool in the same position. The permanency of the effect was greater, and the magnetism stronger, when the rods were suddenly cooled in cold water, so as to give them a very hard temper. He found that the end which was next to the north, or the lower end of a vertical bar, was invariably a permanent north pole. Even when the upper end alone was quenched, while the rest of the bar cooled slowly, that end became a sensible south pole. If the same process was adopted when the steel bar lay at right angles to the magnetic meridian, no magnetism was acquired.

The subject of terrestrial magnetism now occupied the Dr Halley. attention of our eminent countryman Dr Edmund Halley; and in 1683 he published his Theory of Magnetism, which to a certain extent forms the nucleus of more modern hypotheses. He regarded the earth's magnetism as caused by four poles of attraction, two of them near each pole of the earth; and he supposes "that in those parts of the world which lie nearly adjacent to any one of these magnetic poles, the needle is governed thereby, the nearest pole being always predominant over that more remote." He supposes that the magnetic pole, which was in his time nearest Britain, was situated near the meridian of the land's end, and not above 7° from the north pole; the other north magnetic pole being in the meridian of California, and about 15° from the north pole of the earth. He placed one of the two south poles about 16° from the south pole of the globe, and 95° west from London; and the other, or the most powerful of the four, about 20° from the south pole, and 120° east of London.

In order to account for the change in the variation, Dr Dr Halley, some years afterwards, added to these reasonable suppositions the very extraordinary one, that our globe was a hollow shell, and that within it a solid globe revolved, in nearly the same time as the outer one, and about the same centre of gravity, and with a fluid medium between them. To this inner globe he assigned two magnetic poles, and to the outer one other two; and he conceived the change in the variation of the needle to be caused by a want of coincidence in the times of rotation of the inner globe and the external shell. "Now, supposing," says he, "such an external sphere having such a motion, we may solve the two great difficulties in every former hypothesis; for if this exterior shell of earth be a magnet, having its poles at a distance from the poles of diurnal rotation, and if the internal nucleus be likewise a magnet, having its poles in two other places, distant also from its axis, and these latter, by a gradual and slow motion, change their places in respect of the external, we may then give a reasonable account of the four magnetic poles, as also of the changes of the needle's variation." From some reasons which Dr Halley then states, he concludes "that the two poles of the external globe are fixed in the earth, and that if the needle were wholly governed by them, the variation would be always the same, with some little irregularities; but the internal sphere, having such a gradual translation of its poles, influences the needle, and directs it va-

History. riously, according to the result of the attractive and directive power of each pole, and consequently there must be a period of revolution of this internal ball, after which the variation will return as before."

This theory excited so much notice, that an application was made to William and Mary, for a ship, "in order to seek, by observation, the discovery of the rule for the variation of the compass." The command of a ship of the royal navy was in consequence given to Dr Halley; and, in the accomplishment of the object which he had in view, he performed two voyages, one in 1698 and the other in 1699, in which he traversed various parts of the Pacific and Atlantic Oceans, and obtained such a number of valuable results, that he completed a chart of the variation of the needle, which exhibited to the eye the general law of its phenomena.

Graham. The very important discovery of the daily variation of the needle was made in 1722, by Mr Graham, a celebrated mathematical instrument maker in London. While the

Daily variation discovered. needle was advancing by an annual motion to the westward, Mr Graham found that its north extremity moved westward during the early part of the day, and returned again in the evening to the eastward, to the same position which it occupied in the morning, remaining nearly stationary during the night. Mr Graham at first ascribed these changes to defects in the form of his needles; but, by numerous and careful observations, repeated under every variation of the weather and of the heat and pressure of the atmosphere, he concluded that the daily variation was a regular phenomenon, of which he could not find the cause. It was generally a maximum between ten o'clock A.M. and 4 o'clock P.M., and a minimum between six and seven o'clock P.M. Between the 6th February and the 12th May 1722, he made a thousand observations in the same place, from which he found that the greatest westerly variation was $14^\{\backslash circ\}\; 45\text{'}$, and the least $13^\{\backslash circ\}\; 50\text{'}$; but in general it varied between $14^\{\backslash circ\}\; 35\text{'}$ and $14^\{\backslash circ\}$, giving $35\text{'}$ for the amount of the daily variation.

The law of the magnetic force, or the rate at which it varies with the distance, had, as we have seen, occupied the attention of Sir Isaac Newton and David Gregory. Numerous experiments were made by various authors for the same purpose, a large collection of which have been published by Scarella, in his treatise De Magnete, published at Brescia in 1759. Muschenbroeck made a great number of experiments with the same view; but as the joint action of the four poles was never considered, the precise law of variation remained unknown. Mr Hauksbee and Dr Brooke Taylor employed a much better method, namely, the deviation of a compass-needle from the meridian, produced by the action of a magnet at different distances; but the magnets which they used had improper shapes, and the conclusion which they drew from their experiments was, that the magnetic force decreased much quicker at great distances than at small ones, and that it is different in different loadstones.¹

Notwithstanding this strange conclusion, the observations to which we have referred were of great value; and Mr Michell² succeeded in deducing from them, in 1750, the true law of magnetic action. "There have been," says Mr Michell, "some who have imagined that the decrease of the magnetic attraction and repulsion is inversely as the cubes of the distances; others, as the squares; and others, that it follows no certain ratio at all, but that it is much quicker at great distances than at small ones, and that it is different in different stones. Among the last is Dr Brooke Taylor and Muschenbroeck, who seem to have been pretty

accurate in their experiments. The conclusions of these gentlemen were drawn from their experiments, without their being aware of the third property of magnets just mentioned, which, if they had made proper allowances for, together with the increase and diminution of power in the magnets they tried their experiments with, all the irregularities they complained of (as far as appears from their relations of them) might very well be accounted for, and the whole of their experiments coincide with the squares of the distances inversely."

It is to Mr Michell also that we owe the introduction of the torsion balance, for measuring small forces; an instrument which, as we shall see, was employed with singular success and dexterity by Coulomb in his electrical, magnetic, and hydrodynamical researches; and the science of magnetism is no less indebted to Mr Michell for his invention of the method of double touch, as it is called, by which artificial magnets may be made with greater strength than could have been obtained from the previous method of Duhamel.

The hypothesis of Descartes, who explained the polarity of the needle by means of currents moving rapidly from the equator to the poles, was adopted and defended by Euler and Daniel Bernoulli; but we cannot afford any space for such useless speculations. Euler afterwards occupied himself more advantageously for science in attempting to investigate mathematically the direction of the needle on every part of the earth's surface.³ Perceiving the intricacy which would arise from the adoption of four poles, as imagined by Halley, he tried the effect of employing two poles not diametrically opposite; and he found, that when a proper position was given them, the variation under the same meridian might be both easterly and westerly, as in Halley's chart. The solution which he has given is founded on the principle, "that the magnetic direction on the earth follows always the small circle which passes through the given place, and the two magnetic poles of the earth; or that the horizontal needle is a tangent to the circle passing through the place of observation, and through the two points on the earth's surface where the dipping needle becomes vertical, or the horizontal needle loses its directive power. In the application of this principle, Euler makes four different suppositions respecting the magnetic poles: 1. That they are diametrically opposite to each other; 2. that they are in opposite meridians, but not in opposite parallels; 3. that they are on the same meridian; and, 4. that they have every other situation whatever. The first of these suppositions he finds to be quite irreconcilable with the observed phenomena, but in the other three he finds that the variation may be both easterly and westerly in the same meridian. By successive approximations he finds the position of the two magnetic poles in 1757 to be as follows: The north pole in latitude $76^\{\backslash circ\}$ north, and longitude $96^\{\backslash circ\}$ west from Teneriffe; and the south pole in latitude $58^\{\backslash circ\}$ south, and longitude $158^\{\backslash circ\}$ west from Teneriffe. To this dissertation Euler has added a chart of the curves of equal variation, calculated on the preceding principles, and suited to 1757; and their general accordance with observation is very surprising. In a subsequent dissertation Euler endeavoured to improve his theory, by supposing the two magnetic poles to be at the surface of the earth. The chord joining these poles he calls the magnetic axis, and the middle point of that chord its magnetic centre. Then, if we draw a line from the place of observation to the magnetic centre, and consider this as the base of an isosceles triangle, one of whose sides is the magnetic axis, the other side will be the direction of a freely suspended needle. This hypo-

the torsion balance, for measuring small forces; an instrument which, as we shall see, was employed with singular success and dexterity by Coulomb in his electrical, magnetic, and hydrodynamical researches; and the science of magnetism is no less indebted to Mr Michell for his invention of the method of double touch, as it is called, by which artificial magnets may be made with greater strength than could have been obtained from the previous method of Duhamel.

The hypothesis of Descartes, who explained the polarity of the needle by means of currents moving rapidly from the equator to the poles, was adopted and defended by Euler and Daniel Bernoulli; but we cannot afford any space for such useless speculations. Euler afterwards occupied himself more advantageously for science in attempting to investigate mathematically the direction of the needle on every part of the earth's surface.³ Perceiving the intricacy which would arise from the adoption of four poles, as imagined by Halley, he tried the effect of employing two poles not diametrically opposite; and he found, that when a proper position was given them, the variation under the same meridian might be both easterly and westerly, as in Halley's chart. The solution which he has given is founded on the principle, "that the magnetic direction on the earth follows always the small circle which passes through the given place, and the two magnetic poles of the earth; or that the horizontal needle is a tangent to the circle passing through the place of observation, and through the two points on the earth's surface where the dipping needle becomes vertical, or the horizontal needle loses its directive power. In the application of this principle, Euler makes four different suppositions respecting the magnetic poles: 1. That they are diametrically opposite to each other; 2. that they are in opposite meridians, but not in opposite parallels; 3. that they are on the same meridian; and, 4. that they have every other situation whatever. The first of these suppositions he finds to be quite irreconcilable with the observed phenomena, but in the other three he finds that the variation may be both easterly and westerly in the same meridian. By successive approximations he finds the position of the two magnetic poles in 1757 to be as follows: The north pole in latitude $76^\{\backslash circ\}$ north, and longitude $96^\{\backslash circ\}$ west from Teneriffe; and the south pole in latitude $58^\{\backslash circ\}$ south, and longitude $158^\{\backslash circ\}$ west from Teneriffe. To this dissertation Euler has added a chart of the curves of equal variation, calculated on the preceding principles, and suited to 1757; and their general accordance with observation is very surprising. In a subsequent dissertation Euler endeavoured to improve his theory, by supposing the two magnetic poles to be at the surface of the earth. The chord joining these poles he calls the magnetic axis, and the middle point of that chord its magnetic centre. Then, if we draw a line from the place of observation to the magnetic centre, and consider this as the base of an isosceles triangle, one of whose sides is the magnetic axis, the other side will be the direction of a freely suspended needle. This hypo-

thesis, though it has various defects, fulfils, as has been well remarked, certain conditions that are essential to a good theory. 1. It gives the needle the approximately accurate positions at the equator, the needle and the axis being then parallel; 2. it fulfils the condition of the needle and axis, forming a continuous line at the poles; 3. it furnishes two points at which the needle would be vertical; and, 4. it gives a series of positions, single for each place, and having a certain, and oftentimes pretty close, approach to the true position.¹

The law of magnetic action occupied the particular attention of M. Lambert, the celebrated Prussian philosopher, who has published an account of his labours in the Memoirs of the Academy of Berlin for 1756. Having placed a mariner's compass at various distances from a magnet, and in the direction of its axis, he observed the declination of the needle produced by the magnet, and the obliquity of the magnet to the needle's axis. From several observations at different obliquities, he found that the action of magnetism on a lever was proportional to the sine of the angle of its obliquity to the axis of the lever or needle. M. Lambert then proceeded to study the effect of distance, and he discovered that the force of a magnet is proportional to the distance of the nearest pole of the magnet from the centre of the needle, diminished by the square of a constant quantity, nearly equal to two thirds of the length of the needle. This result he found to be true with magnets ten times larger, and needles twice as short; but as the law led him to a strange result, as if the action on a magnet were exerted from a centre beyond itself, he was therefore obliged to take another method of determining the law of action, namely, by a series of experiments on the directive power of the magnet,² from which he inferred, "that the force of each transverse element of a magnet is as its distance from the centre, and its action as a particle of another magnet inversely as the square of the distance." By means of this law he calculates the position of a very small needle, and draws three of the curves to which it should be a tangent, and these coincide very accurately with some of those which he had observed.

Our learned countryman Dr Robison had been pursuing similar inquiries before he had seen Lambert's experiments. He got some magnets made, composed of two balls connected by a slender rod; and after magnetising them strongly, he found that the force of each pole resided nearly in the centre of the ball. In this way the attractive and the directive powers of the magnets were easily computed, and the result was, that the force of each pole was inversely as the square of the distance. In no case did the error of this hypothesis amount to one fifteenth of the whole, and in the calculation for the phenomena of the directive power the errors were still smaller. When Dr Robison had seen Lambert's second memoir, he repeated all his former experiments in Lambert's manner, taking the precaution of keeping the needle in its natural position, which he had not previously attended to; and the results which he now obtained were still more conformable to his conjecture as to the law of variation. Dr Robison tried another method of ascertaining the law of magnetic action. In 1769 or 1770 he constructed a needle of two balls joined by a slender rod, and having touched it with great care, so as to keep the whole strength of the poles near the centre of the balls, he counted the number of oscillations which it performed horizontally in a given time by the force of the earth's 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 a large magnet, till the distance of its poles from those of the great magnet was 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." The results of these experiments were the most consistent with each other of any that Dr Robison made for determining the law of the magnetic force, and it was chiefly from them that he thought himself authorized to say with some confidence, that it is inversely as the square of the distance. When Dr Robison, however, observed, some years afterwards, that Æpinus, in 1777, conceived the force to vary inversely as the simple distance, he repeated the experiments with great care, and added another set made with the same magnet, and the same needle placed at one side of the magnet instead of above it. By this arrangement, which greatly simplified the process, the result of the whole was still more satisfactory. The inverse law of the square of the distance was therefore well established.

Various speculations respecting the cause of the phenomena of magnetism had been hazarded by different authors; but it was reserved for M. Æpinus to devise a rational hypothesis, which embraced and explained almost all the phenomena which had been observed by previous authors. This hypothesis, which he has explained at great length in his Tentamen Theoriæ Electricitatis et Magnetismi, published in 1759, may be stated in the following manner.

1. 1. In all magnetic bodies there exists a substance which may be called the magnetic fluid, whose particles repel each other with a force inversely as the distance.
2. 2. The particles of this fluid attract the particles of iron, and are attracted by them in return with a similar force.
3. 3. The particles of iron repel each other according to the same law.

1. 4. The magnetic fluid moves through the pores of iron and soft steel with very little obstruction; but its motion is more and more obstructed as the steel increases in hardness and temper, and it moves with the greatest difficulty in hard-tempered steel and the ores of iron.

The method of making artificial magnets, which was practised by the philosophers of the seventeenth century, of making a very simple but a very inefficacious one. It consisted in merely rubbing the steel bar to be magnetised, upon one of the poles of a natural or artificial magnet, in a direction at right angles to the line joining the poles of the magnet. Towards the middle of the eighteenth century, however, the art of making artificial magnets had excited general attention; and it is to Dr Gowin Knight, an English physician, that we are indebted for the discovery of a method of making powerful magnets. This method he kept secret from the public, but it was afterwards published by Dr Wilson. Duhamel, Canton, Michell, Antheaume, Savery, Æpinus, Robison, Coulomb, Biot, Scoresby, and others, made various improvements on this art, as will be minutely described when we arrive at that part of our subject.

The science of magnetism owes many obligations to Mr Experiment John Canton, one of the most active experimental philosophers who adorned the middle of the eighteenth century. In or previous to the year 1756, he made no fewer than 4000 observations on the diurnal variation of the needle, with the view of determining its amount, and investigating its origin. He found the daily change differ-

¹ See an excellent paper on Terrestrial Magnetism, in the Magazine of Popular Science, May 1836, No. iv. p. 223, 224.

² Memoirs of the Berlin Academy, vol. xxii.

History. ent in different seasons of the year, as shown in the following table.

He found also that the time of minimum westerly variation at London was between eight and nine o'clock A. M., and the time of maximum between one and two o'clock P. M., the needle returning to its morning position about eight or nine in the evening. A series of similar observations were made with nearly the same results by Mr Van Swinden; but this excellent observer discovered, that some time before the hour in the morning when the westerly minimum took place, and after the same hour in the evening, a motion of the needle both to the eastward and westward took place; that is, the morning westerly variation is sometimes preceded by a small easterly variation, and the principal easterly variation in the evening is followed by a small westerly variation.

Canton explained the westerly variation of the needle, and the subsequent easterly motion, by supposing that the heat of the sun, acting upon the eastern parts of the earth, weakens their influence, as heat is known to do that of a magnet, and consequently the needle will move to the westward. In the same way, as the sun warms the western side of the earth in the afternoon, the needle will then take a contrary direction.

Discovery of Coulomb. One of the ablest cultivators of the science of magnetism was the celebrated Coulomb, who, by the application of the principle of torsion, first used by Michell, determined the correct law of magnetic attractions and repulsions.¹ After measuring with great nicety, by the torsion balance, the force requisite to make a magnetic bar suspended horizontally deviate any number of degrees from a given position, he was enabled to verify the discovery of Lambert already mentioned, that the effect of terrestrial magnetism is proportional to the sine of the angle which the magnetic meridian forms with the axis of the magnet upon which it acts. By making the homologous poles of two magnetised wires repel each other, he observed the force of torsion which was necessary to overcome certain quantities of their mutual repulsion, and, at the distances 12°, 17°, and 24°, he found that the repulsive forces were as the numbers 3312, 1692, and 864, deviating little from 3312, 1650, and 828, which they would have been had the repulsive force varied in the inverse ratio of the square of the distance. The excess of 42 and 36 in the experimental numbers was owing to the circumstance that it was not a particle, but a portion, of each wire, from which the repulsive force emanated, so that the force of the other particles being exerted less obliquely, and therefore being stronger at greater distances, ought to produce an excess such as that actually observed. A similar result was obtained when the contrary poles of the magnetised wires were made to attract each other; so that Coulomb concluded that the attractive and repulsive forces exercised by two magnetic particles are inversely as the square of their distances, a result which he confirmed by several other methods than that which we have noticed.

Distribution of magnetism. Provided with such a delicate instrument as the torsion balance, Coulomb was enabled to apply it with singular advantage to almost every branch of the science. His first object was to determine the law according to which magnetism is distributed in a magnetic bar. It was of course well known that the magnetism in the middle of

the bar was imperceptible, and that it increased according to a regular law, and with great rapidity, towards each of its poles. By suspending a small proof needle with a silk fibre, and causing it to oscillate horizontally, opposite different points of a magnetic bar placed vertically, Coulomb computed the part of the effect which was due to terrestrial magnetism, and the part which was due to the action of the bar; and in this way he obtained the following results, which show the extreme rapidity with which magnetism is increased towards the poles.

In examining the distribution of electricity in a circular plane, Coulomb found that the thickness of the electric stratum was almost constant from the centre to within a very small distance of the circumference, when it increased all on a sudden with great rapidity. He conceived that a similar distribution of magnetism took place in the transverse section of a magnetic bar; and, by a series of nice experiments with the torsion balance, he found this to be the case, and established the important fact, that the magnetic power resides on the surface of iron bodies, and is entirely independent of their mass.

The effect of temperature on magnets was another subject to which Coulomb directed his powerful mind; but he did not live to give an account of his experiments, which were published after his death by his friend M. Biot. Coulomb found that the magnetism of a bar magnetised to saturation diminished greatly by raising its temperature from 12° of Reaumur to 680°; and that when a magnetic bar was tempered at 780°, 860°, and 950°, of Reaumur, the development of its magnetism was gradually increased, being more than double at 900° of what it was at 780°. He found also that the directive force of the bar reached its maximum when it was tempered at a bright cherry-red heat at 900°; and that at higher temperatures the force diminished. It is to Mr Barlow, however, as we shall presently see, that we are indebted for the complete investigation of the influence of temperature on the development of magnetism.

Coulomb made many valuable experiments on the best methods of making artificial magnets, and he subjected all the various processes that had been previously employed to the test of accurate measurement. His experiments on the best forms of magnetic needles are equally valuable; but the most interesting of his researches, and the last to which he devoted his great talents, were those which relate to the action of magnets upon all natural bodies. Hitherto, iron, steel, nickel, and cobalt, had been regarded as the only magnetic bodies; but, in the year 1802, Coulomb announced to the Institute of France, that all bodies whatever are subject to the magnetic influence, even to such a degree as to be capable of accurate measurement. The substances employed by Coulomb were in the form of a cylinder or small bar, about one third of an inch in length and one thirtieth in thickness, and they were suspended by a single fibre of silk between the opposite poles of two powerful steel magnets, placed in the same straight line, and having their opposite poles at a distance exceeding by a quarter of an inch the length of the cylinders. The cylinders were then made to oscillate between the poles of the magnets, and were

¹ See our article ELECTRICITY, p. 586, where the torsion balance is minutely described.

protected from all motions of the air by a glass receiver. The result of these experiments was, that whatever was the substance of the cylinders, they always arranged themselves in a line joining the poles of the magnets, and returned to that position whenever they were deflected from it. These experiments were made with cylinders of gold, silver, copper, lead, tin, glass, wood, chalk, bone, and every variety of substance, organic and inorganic. The only explanation which Coulomb could give of these phenomena was, either that all bodies whatever were susceptible of magnetism, or that they contained small portions of iron or other magnetic metals, which communicated to them the property of obeying the magnet. In order to investigate this subject, MM. Sage and Guyton prepared highly purified needles of the different metals, and M. Coulomb found that the momenta of the forces with which they were solicited by the magnets were as follows:—

the momentum of torsion alone, for all the needles, being 0.00136, a little more than a fourth of the action which the magnets exert upon the needles.

In order to determine if these phenomena were owing to particles of iron disseminated through the bodies, Coulomb fabricated needles out of three different mixtures of white wax and iron filings, and he found that the forces exerted by magnets upon these needles were proportional to the absolute quantities of iron which they contain. Coulomb now tried a needle of silver, purified by upellation, and another needle of silver alloyed with $\backslash frac\{1\}\{20\}$th part of iron, and he found that the action of the magnet upon the former was 415 times less than upon the latter. Hence there will be 415 times less iron in the pure than in the impure silver; and since the latter contains $\backslash frac\{1\}\{20\}$th part of its weight of iron, the first will contain $\backslash frac\{1\}\{20\}$th of $\backslash frac\{1\}\{20\}$th, or $\backslash frac\{1\}\{400\}$th, or it will contain 32799 parts of pure silver and one of iron, a quantity of alloy beyond the reach of chemical detection.

Amongst the scientific travellers who contributed to our knowledge of terrestrial magnetism, Baron Alexander Humboldt was one of the most distinguished. Himself an accurate and scientific observer, and possessed of nice instruments and methods of observation, he made numerous accurate observations on the dip and variation of the needle in various parts of the earth, and particularly near the magnetic equator; and, by means of these valuable data, M. Biot was enabled to throw much light on the subject of terrestrial magnetism. Hitherto the magnetic poles had been considered as either on or very near the surface of the earth; but as it had been found impossible to deduce the phenomena of the variation and dip of the needle, philosophers were led to consider the situation of these poles as indeterminate. M. Biot was the first to adopt this view of the subject; and after numerous comparisons, he came to the conclusion, that the nearer these poles were placed to each other, the greater was the agreement between the computed and observed results; and by considering the two poles as indefinitely near each other in the centre of the earth, the computed and observed measures approximated as closely as could be expected. Hence it was inferred that the phenomena of terrestrial magnetism were not such as are produced by permanently magnetic bodies, but those rather that arise from simple iron or ferruginous masses, which are only

temporarily magnetic. In this manner M. Biot was led to express the law of terrestrial magnetism in a complicated formula, which represented the observations with wonderful accuracy.

In the year 1809, Professor Krafft of St Petersburg undertook the very same inquiry, and after comparing the same observations which were used by Biot, with the respective situations of the places where they were obtained, he arrived at the following simple law: "If we suppose a circle circumscribed about the earth, having the two extremities of the magnetic axis for its poles, and if we consider this circle as a magnetic equator, the tangent of the dip of the needle, in any magnetic latitude, will be equal to double the tangent of this latitude." Upon re-examining his former formula, M. Biot found that it was reducible to the above simple law, a coincidence which may be considered as giving it additional confirmation.

One of the most zealous and successful cultivators of Professor magnetical science is Professor Hansteen of Christiania, who published, in 1817, an able work on the magnetism of the earth.¹ The Royal Society of Denmark proposed, in 1811, the prize question, "Is the supposition of one magnetical axis sufficient to account for the magnetical phenomena of the earth, or are two necessary?" Professor Hansteen's attention had been previously drawn to this subject by seeing a terrestrial globe, on which was drawn an elliptical line round the south pole, and marked Regio Polaris magnetica, one of the foci being called Regio fortior, and the other Regio debilior. As this figure professed to be drawn by Wilcke, from the observations of Cook and Furneaux, Hansteen was led to compare it with the facts; and the result of the comparison being favourable, he was induced to study the theory of Halley, which had previously appeared to him wild and extravagant. The result of his researches, however, was favourable to that part of Halley's theory which assumes the existence of four poles and two magnetic axes. Hansteen's Memoir, which was crowned by the Danish Society, forms the groundwork of the larger volume which he published in 1817. In his fifth chapter, on the Mathematical Theory of the Magnet, he deduces the law of magnetic action from a series of experiments similar to those of Hauksbee and Lambert. Assuming that the attraction or repulsion between any two magnetic particles is directly as the intensity of the force, and inversely as some unknown power $t$ of the mutual distance of these particles, and supposing that the magnetic intensity of any particle is proportional to some power $r$ of its distance $a$ from the centre of the magnet, he finds the following expression for the effect $F$, which a linear magnet would have upon a magnetic point situated anywhere upon the axis produced:

$x$ being the length of half the axis of the linear magnet, and $F$ (multiplied by a constant quantity, depending on the degrees of magnetism which the point and line possess) representing the force. In conducting the experiments, Hansteen placed a very sensible compass upon a horizontal table, so that the needle pointed to $0^\backslash circ$. From beneath the centre of this needle, and perpendicular to its direction, or to the magnetic meridian, he drew a straight line upon the table, and divided it into portions, so that ten of them were equal to the half axis $a$ of the artificial magnet. This magnet was then placed on the line at different distances from the needle, and the deviation of the needle from the magnetic meridian which it produced was accurately observed for each distance. Upon com-

¹ Untersuchungen über den Magnetismus der Erde, 4to. Christiania, 1817.

History. Comparing the results, and calculating them by the formula, upon the supposition that $t$ was 1 or 3, the differences were very great; but by making $t=2$, the calculated and observed results agreed remarkably well, as the following table shows:

From this remarkable coincidence between the observed and the computed results, Hansteen concludes that "the attractive or repulsive force with which two magnetic particles affect each other, is always directly as their intensities, and inversely as the squares of their mutual distance." He shows that the undetermined value of $r$ produces almost no effect at considerable distances; and he is inclined to think that $r=2$, or that the absolute intensity of any magnetic particle, situated in the axis, is proportional to the square of its distance from the middle point of that axis. Mr Hansteen has also demonstrated that the distance from the middle of a magnet being the same, the force opposite the poles, or in the direction of the axis, is double of the force in the magnetic equator. If a globe contains at its centre an infinitely small magnet, Hansteen shows that, near the magnetic equator, the dip must increase twice as rapidly as the magnetic latitude, and, near the pole, half as rapidly; and that the increment of the dip must be equal to the alteration of the latitude of that part of the globe where the dip is $54^\{\backslash circ\}\; 44\text{'}$. Our author also states, that if the earth had only one magnetic axis, whose centre coincided with that of the earth, the lines of equal dip would coincide with those of equal intensity; but as this is far from being the case, his opinion that there are two magnetic axes becomes more probable.

The most valuable part, however, of Professor Hansteen's work is that which relates to the number, position, and revolution of the magnetic poles. Having collected all the observations of value that had been made on the variation of the needle, he proved that there were four points of convergence among the lines of variation, viz. a weaker and a stronger point in the vicinity of each pole of the globe. The strongest poles N, S, lie almost diametrically opposite to each other, and the same is true of the weaker poles $n$, $s$. These four poles he found to have a regular motion obliquely, the two northern ones N, $n$, from west to east, and the two southern ones S, $s$, from east to west. The following he found to be their periods of revolution, and their positions, in 1830:—

Since the publication of these results, Professor Hansteen had access to the valuable series of magnetical observations made during the British voyages of discovery to the

arctic regions; and, after a diligent comparison of them, he obtained new and more accurate determinations of the positions and periods of revolution of the four magnetic poles, but still differing so little from his previous determinations, as to give a high degree of probability to the correctness of the results. He finds from Captain Parry's observations, that in 1819 the pole N must have been situated in north lat. $71^\{\backslash circ\}\; 27\text{'}$, and the time of its revolution 1890 (in place of 1740, as formerly calculated). The period of revolution of S he changed from 4609 to 4605, and that of $s$ from 1304 to 1303, that of $n$ remaining at 860 as before. Professor Hansteen considers N and S as the terminating points of one magnetic axis, and $n$ and $s$ those of the other axis; and he remarks that these two axes cross each other without intersection, or without passing through the centre of the earth. In reference to the causes of these singular changes, our author considers it possible that the illumination and heating of the earth, during one revolution about its axis, may produce a magnetic tension, as it produces the electrical phenomena. In support of his hypothesis of four poles, Professor Hansteen has shown very clearly that the changes in the variation and dip of the needle in both hemispheres may be well explained by their motion; but we cannot here enter into these details.

With the view of discovering the nature of the forces by which the phenomena of terrestrial magnetism are produced, Professor Hansteen resolved to ascertain, at different parts of the earth's surface, the intensity of its magnetism, and to determine the form of the lines of equal intensity, or, as he calls them, the isodynamical magnetic lines. By means of the same needle intrusted to different philosophers, he had observations on the number of its oscillations in a given time made in every part of Europe; and he afterwards undertook a journey to Siberia to make the observations himself in that interesting magnetical region. From these observations he deduced the following law, according to which the magnetic intensity varies with the dip of the needle:—

Professor Hansteen's journey to Siberia was attended with secondary consequences of great value to science. The attention of the Russian government, and the Academy of Sciences at St Petersburg, was thus called to the subject of magnetism; and, on the recommendation of Baron Humboldt, the emperor liberally agreed to erect magnetic observatories in suitable stations, for determining, every ten years, the exact position of the two lines of the variation which pass through his empire.

In determining the intensity of terrestrial magnetism, Professor Hansteen observed that the time of vibration of a horizontal needle varied during the day. Graham had previously suspected a change of this kind, but his methods were not accurate enough to prove it. Hansteen, however, found that the minimum intensity took place between 10 and 11 A. M., and the maximum between 4 and 5 P. M. He concluded also that there was an annual variation, the intensity being considerably greater in winter near the perihelion, than in summer near the aphelion; that the greatest monthly variation was a maximum when the earth is in its perihelion or aphelion, and a minimum near the equinoxes; and that the greatest daily variation

is least in winter and greatest in summer. He found also that the aurora borealis weakened the magnetic force, and that the magnetic intensity is always weakest when the moon crosses the equator. In making experiments in the round tower at Copenhagen, he found that the magnetic intensity increased regularly towards the top, where it was a maximum; and having extended his observations, he obtained the general result, that at the foot of any vertical object the needle oscillates quicker at the north side of it, and slower at the south side; whereas at the upper end it oscillates quicker at the south side, and slower at the north side.

In the aerostatic ascent of MM. Gay-Lussac and Biot, they were unable to detect any change in the intensity of terrestrial magnetism at the height of 4000 metres. Sausure, however, had found that the intensity was considerably less on the Col du Géant than at Chamouni and Geneva, the difference in the levels of these places being in the one case 10,000 and in the other 7800 feet, but his observations contradict his conclusion. M. Kupffer has more recently obtained a similar result by observations on Mount Elbrouz, having found a decrease of intensity in rising 4500 feet above his first station; and he explains the result obtained by MM. Gay-Lussac and Biot by supposing that an increase of intensity was produced by the diminution of temperature. Mr Henwood, on the other hand, has made observations at the surface of Dolcoath mine, at 1320 feet beneath its surface, and on a hill 710 feet above the level of the sea, without being able to detect any difference in the intensity. To the late Captain Foster¹ we owe many valuable observations on the magnetic intensity made at Spitzbergen and elsewhere. From these he concluded, that the diurnal change in the horizontal intensity is principally, if not wholly, owing to a small change in the amount of the dip. The maximum took place at about 3h. 30' A. M., and the minimum at 2h. 47' P. M., its greatest change amounting to one eighty-third of its mean value. Captain Foster is of opinion that these changes have the sun for their primary agent, and that his action is such as to produce a constant inflexion of the pole towards the sun during the 24 hours, an idea which Mr Christie had previously stated.²

About the year 1818, Professor Barlow of Woolwich turned his attention to the subject of magnetism, with the view principally of calculating the effect of a ship's guns on the compass. In trying the effects of different iron balls, he was led to the curious facts, that there exists round every globe and mass of iron a great circle inclined to the horizon at an angle equal to the complement of the dip of the needle; that the plane of this circle is a plane of no attraction upon a needle whose centre is in that plane; that if we regard this circle as the magnetic equator, the tangent of the deviation of the needle from its north or south pole will be proportional to the rectangle of the sine of the double latitude, and cosine of the longitude; that when the distance of the needle is variable, the tangent of deviation will be reciprocally proportional to the cube of the distance; and that, all things else being the same, the tangents of deviation will be proportional to the cubes of the diameters of the balls or shells, whatever be their masses, provided their thickness exceed a certain quantity.

These results were published in the first edition of Mr Barlow's Essay on Magnetic Attractions; but in the second edition of that work, he has published some curious results respecting the relative magnetic power of different descriptions of iron and steel, and on the effect of tempe-

rature on the quality and quantity of the attractive power of iron. The results of the first of these series of experiments were as follow, the numbers expressing the proportional magnetic power of the different descriptions of iron and steel.

In his experiments on the effects of temperature, Mr Barlow found that every kind of iron and steel possessed a greater capacity for the development of its magnetism when softened by heat than when cold; from which he concludes that its complete development when cold is prevented only by the hardness or resisting power of the metal. At a white heat he found that iron lost entirely its magnetic power, a result apparently inconsistent with the preceding conclusion; but, what was a still more extraordinary circumstance, when the white heat, at which there was no magnetism, began to subside into a bright red, or red heat, an attractive power showed itself, the reverse of what it had when cold; and after it had passed through these two shades of colour, it resumed the same attractive power which it had when cold, the passage from the negative attraction of red passing into the positive attraction of the cold metal at the point of a red heat, the maximum, however, taking place at a blood-red heat.

The experimental laws of attraction of an iron shell or sphere, obtained by Mr Barlow, were first examined theoretically by Mr Charles Bonnycastle, who deduced them mathematically from the theory of Æpinus, which supposes the two magnetic fluids to be accumulated in the poles of magnets. This theory, however, led to some improbable consequences, and therefore Mr Barlow was induced to adopt that of Coulomb and Biot, with the modification, that the magnetic power all resides on the surface of iron bodies, and is independent of the mass; a modification which enabled Mr Barlow to obtain a general analytical expression of the disturbing power of an iron ball at its surface, as compared with that of the earth, and from which he deduced theoretically all his experimental laws.

These important discoveries enabled Mr Barlow to invent a most ingenious method of correcting the error of the compass, arising from the attraction of all the iron on board ships. This source of error had been noticed by Mr Wales, Mr Downie in 1794, and by Captain Flinders; but it is to Mr Bain⁴ that we owe the distinct establishment and explanation of this source of error. As a hollow shell of iron about four pounds in weight acts as powerfully at the same distance as a solid iron ball of 200 pounds weight, Mr Barlow happily conceived that a plate of five or six pounds weight might be made to represent and counteract the amount of the attraction of all the iron on board a vessel, and therefore leave the needle as free to obey the action of terrestrial magnetism as if there were no iron in the ship at all. After this ingenious contrivance had been submitted to the admiralty, it was tried in every part of the world; and even in the regions which surround the magnetic pole, where the compass becomes useless, it never failed to indicate the true magnetic direction when the connecting plate was properly applied. At Port Bowen, where the dip is 88°, and the magnetic intensity which acts upon a horizontal needle extremely weak, the azimuth compass on board Captain Parry's ship gave the very same variation as that observed on shore. "Such an invention as this," says Captain Parry, "so sound in principle, so easy of application, and so universally beneficial

¹ The height of the tower is 126 feet.

² Phil. Trans. 1828.

³ Phil. Trans. 1827, pp. 345-349.

⁴ Treatise on the Variation of the Compass.

History. in practice, needs no testimony of mine to establish its merits; but when I consider the many anxious days and sleepless nights which the uselessness of the compass in these seas had formerly occasioned me, I really should have esteemed it a kind of personal ingratitude to Mr Barlow, as well as great injustice to so memorable a discovery, not to have stated my opinion of its merits, under circumstances so well calculated to put them to a satisfactory trial." For this beautiful invention, the Board of Longitude conferred upon Mr Barlow the highest reward of £500; and the Emperor of Russia, who was never inattentive to the interests of science, sent him a fine gold watch and a rich dress chain, for the same contrivance.

Magnetism of rotation. A series of beautiful discoveries was made about this time by M. Arago, Mr Christie, and Mr Barlow, on the influence of rotation on bodies both magnetic and non-magnetic. Mr Barlow, so early as 1818 or 1819, had found, that when a plate of iron was made to turn upon its centre, different parts of its circumference had different degrees of magnetic action on the compass; but here there was no effect discovered as due to rotation. In 1821, Mr Christie, in a series of experiments on iron plates, not only found that different parts in the circumference of the same plate had different attracting powers; but that the same part had a different influence, according as the same plate was made to revolve to the right or left hand. Mr Christie therefore discovered that there was a deviation due to rotation, and that magnetical effects were produced which were nearly independent of the velocity of rotation, and which continued after the rotation had ceased. When the rotation was very rapid, the forces exerted upon the needle were always in the same direction as the forces derived from the slowest rotation, and which continue to act after the rotation has ceased, the former being to the latter nearly as three to two. From all the observations made by Mr Christie, he considers that the direction of the magnetic polarity acquired by rotation, whether at right angles to the line of the dip or not, has always a reference to the direction of the terrestrial magnetic force; and he infers that this magnetism is communicated to it from the earth. "It does not therefore appear from this," says Mr Christie, "that a body can become polarised by rotation alone, independently of the action of another body; so that, if from these experiments we might be led to attribute the magnetic polarity of the earth to its rotation, we must at the same time suppose a source from which magnetic influence is derived. Is it not, then, possible that the sun may be the centre of such influence, as well as the source of light and heat, and that, by their rotation, the earth and other planets may receive polarity from it?" When these experiments were repeated at Port Bowen in 1825 by Captain Foster, the phenomena were exhibited on a more striking scale.

Mr Christie. In December 1824, Mr Barlow began a series of experiments, with the view of ascertaining whether magnetism, as produced by various processes with iron, could be excited or disturbed by rapid rotation. They were completed in January, but their publication was delayed till June, that an account of them might appear along with those of Mr Christie above mentioned. Mr Barlow's first experiments were made on a 13-inch shell attached to a lathe turned by a steam-engine, the mean speed of which was about 640 revolutions in a minute. The deviation of a needle exposed to its action increased with the velocity, and remained constant while the velocity continued constant, the needle always returning exactly to its original position the moment the motion of the ball ceased. This, therefore, is a phenomenon different from that observed by Mr Christie; a temporary effect wholly dependent on the velocity of rotation, whereas that observed by Mr Christie was permanent, and nearly independent of

Mr Barlow. the number of revolutions. In examining the direction of the new force impressed upon the iron shell, he found it to be in every case equivalent to a polarisation at right angles to the axis of rotation.

History. Previous to the publication of these experiments, and without any knowledge of them, M. Arago had made the remarkable discovery, that if plates of copper and other substances are put into rapid rotation beneath a magnetised horizontal needle freely suspended, the rotatory plate will first cause the needle to deviate from its true direction; and by increasing the velocity, the deviation will increase, till the needle passes the opposite point, when it will continue to revolve, and at last with such velocity that the eye is unable to distinguish it.

M. Arago was led to this beautiful discovery by a previous series of experiments of great interest. He found that a magnetic needle oscillating above or near any body whatever, such as a plate of metal or a surface of water, gradually oscillated in arcs of less and less amplitude, as if it had been placed in a resisting medium; and, what was particularly remarkable, the number of oscillations performed in a given time was not changed. This curious fact was announced to the Academy of Sciences in Paris on the 22d of November 1824; and he was hence conducted to the still more remarkable discovery of the effects of rotation which we have already mentioned.

M. Seebeck of Berlin repeated the experiments of M. Arago on the influence of plates of metal and other substances in diminishing the amplitude of oscillation; but we must reserve our account of them till we come to the chapter on that subject.

The experiments of M. Arago on the rotation of metallic plates were described and repeated by M. Gay-Lussac and Babbage in London in the month of March or April 1825; and they excited so much attention, from their connection with the effects observed by Mr Barlow, that Mr Babbage and Mr Herschel immediately erected an apparatus for repeating them. In their first trial, the deviation of the needle did not exceed $10^\{\backslash circ\}$ or $11^\{\backslash circ\}$ with a revolving plate of copper. In order to enlarge the visible effect, they reversed the experiment, in order to try whether discs of copper and other non-magnetic substances might not be set in motion if suspended over a revolving magnet. A horse-shoe magnet, capable of lifting twenty pounds, was made to revolve rapidly about its axis of symmetry placed vertically. A circular disc of copper, six inches in diameter and one twenty-fifth of an inch thick, was suspended centrally over it, by a silk thread just capable of supporting it. A sheet of paper being interposed, and the magnet set in motion, the copper began revolving in the same direction, at first slowly, but with an accelerating velocity. On reversing the motion of the magnet, the velocity of the copper was destroyed gradually. It stopped for an instant, and then immediately began to revolve in the opposite direction. Screens of paper, glass, wood, copper, tin, zinc, lead, bismuth, were interposed betwixt the magnet and the copper, but they exerted no sensible interceptive power. But when tinned iron plate was interposed, the magnetic influence was greatly diminished by one plate, and almost annihilated by two thicknesses of it. A piece of iron connecting the two poles of the revolving magnet produced the same effect. The substances in which signs of magnetism were developed by the revolving magnet were copper, zinc, silver, tin, lead, antimony, mercury, gold, bismuth, and carbon in the state in which it is precipitated from carburetted hydrogen in gasworks. By getting plates of different metals cast in the same mould, they found that the proportional intensity of magnetic action for each respectively was as follows:

M. Arago had observed the very remarkable fact, that if the disc of copper be cut from the circumference towards the centre, like radii, but without taking away the metal, the action upon the needle is greatly diminished. After verifying this result, Messrs Babbage and Herschel ascertained that re-establishing the metallic contact with other metals, restored, either wholly or very nearly, the original power of the plate, even though the soldering metal had a very feeble magnetic power. The law of the force, with a decrease of distance, they found to vary between the square and the cube. "The rationale," says Messrs Babbage and Herschel, "of these phenomena, as well as of those observed by Mr Barlow in the rotation of iron, which form only a particular case (though certainly the most prominent of any) of the class in question, seems to depend on a principle which, whether it has or has not been before entertained, or distinctly stated in words, it may be as well, once for all, to assume here, as a postulatum, viz. that in the induction of magnetism, time enters as an essential element, and that no finite degree of magnetic polarity can be communicated to or taken from any body whatever, susceptible of magnetism, in an instant."

The preceding results were verified by Mr Christie, who found, that when a thick plate of copper revolved under a small magnet, the force which deflected the needle varied inversely as the fourth power of the distance; but when the copper discs were small, and the magnets large, the power of the distance was between the square and the cube; when the plates were of different weights, the force was nearly in the ratio of the weights at small distances, but at smaller distances it varied in a higher ratio.

The discovery of two poles of maximum cold on opposite sides of the north pole of the earth, which was announced by Sir David Brewster in 1820, led him and other authors to the opinion that there might be some connection between the magnetic poles and those of maximum cold. "Imperfect," says he, "as the analogy is between the isothermal and magnetic centres, it is yet too important to be passed over without notice. Their local coincidence is sufficiently remarkable, and it would be to overstep the limits of philosophical caution to maintain that they have no other connection but that of accidental locality; and if we had as many measures of the mean temperature as we have of the variation of the needle, we might determine whether the isothermal poles were fixed or moveable." And he concludes his paper on the mean temperature of the globe with the following paragraph: "Having thus endeavoured to establish a new law of the distribution of heat over the surface of the globe, it might be no uninteresting inquiry to investigate the causes which have modified in so remarkable a manner the influence of the solar rays. The subject, however, is too comprehensive and too hypothetical to be discussed at present. How far the general form and position of the continents and seas of the northern hemisphere may disturb the natural parallelism of the isothermal lines to the equator, to what extent the current through Behring's Strait, transporting the waters of warmer climates across the polar seas, may produce a warm meridian in the direction of its motion, and throw the coldest parts of the globe to a distance from the pole,—whether or not the magnetic, or galvanic, or chemical poles of the globe (as the important discoveries of Mr Oersted entitle us to call them), may have their operations accompanied with the production of cold, one of the most ordinary effects of chemical action,—or whether the great metallic mass which crosses the globe, and on which its magnetic phenomena have been supposed to depend, may not occasion a greater radiation of heat in those points where it develops its magnetic influence,—are a few points which we may at-

tempt to discuss when the progress of science has accumulated a greater number of facts, and made us better acquainted with the superficial condition as well as the internal organization of the globe."¹

The two poles of maximum cold, which will likely perform an important part in the future history of terrestrial magnetism, are situated, according to Sir David Brewster, as follows, according to the best observations made both near them and at a distance. The American pole is situated in latitude 73° north, and longitude 100° west from Greenwich, a little to the east of Cape Walker; and the Asiatic pole in latitude 73° north, and longitude 80° east, between Siberia and Cape Matzol on the Gulf of Oby. Hence the two warm meridians will be in west longitude 10° and east longitude 170°, the latter passing through Lord Mulgrave's range, and the former between St Helena and Ascension Island. The two cold meridians, or those which pass through the poles of maximum cold, will be in west longitude 100° and east longitude 80°, the latter passing near Mexico and through Bathurst Island, and the former through Colombo in Ceylon, Berar in Hindustan, and crossing the Oby a little to the west of Narym in Siberia. The following is the formula which the same author has given for the mean temperature at any point of the globe, $T$ being the mean temperature required, $t$ the maximum equatorial temperature, $\backslash tau$ the minimum temperature at each of the cold poles, and $\backslash delta,\; \backslash vartheta$ the distances of the place from the two cold poles.

The distances $\backslash delta,\; \backslash vartheta$ are found from the formulae

in which $L$ is the colatitude of the pole of maximum cold, $t$ the colatitude of the place, and $M$ the difference of longitude between the place and the pole of maximum cold. The values of $t$ and $\backslash tau$ have been determined with considerable accuracy, $t$ being nearly 82°·8 Fahrenheit, and $\backslash tau$ from 0° to -33°. The exponent $n$ is nearly $\backslash frac\{1\}\{4\}$ths, but future observations may induce us to increase or diminish it.

Now it is a remarkable circumstance that the same formula, mutatis mutandis, expresses the magnetic intensity of magnetism at any point of the earth's surface, the intensity at the two magnetic poles being supposed equal. If we call $S$ the maximum number of seconds in which any number $n$ of oscillations are performed which takes place at the island of St Thomas on the west coast of Africa, and $s$ the minimum number of seconds in which $n$ oscillations are performed which takes place at the magnetic poles, then the intensity $I$ will be

$\backslash delta$ and $\backslash vartheta$ being determined by the formulae already given, adopting the position of the poles in the preceding page. The values of $S$ and $s$, according to Captain Sabine and Hansteen, will be about 370° and 262°. This formula will give for the isodynamical lines, or those of equal intensity, a series of returning curves of the nature of Lemniscates, almost similar to those drawn by Captain Sabine, and given in a future figure, and exactly like the polar isothermal lines.

The connection thus indicated between the heat and the magnetism of the earth has been studied by succeeding authors, and the general principle has been adopted by many distinguished philosophers. Dr Traill expressed the opinion, "that the disturbance of the equilibrium of the temperature of our planet by the continual action of the sun's rays on its intertropical regions, and by the polar ices, must convert the earth into a vast thermo-magnetic apparatus."

¹ Edinburgh Transactions, 1820.

History. tus;" and "that the disturbance of the equilibrium of temperature even in stony strata may elicit some degree of magnetism." Mr Christie thinks it "not improbable that difference of temperature may be the primary cause of the polarity of the earth, though its influence may be modified by other circumstances." M. Ampère, who ascribes magnetism to transverse electrical currents, thinks that the strata of our globe may form considerable galvanic arrangements, and that the electric currents may be affected by the rotation of the earth. M. Oersted remarks, in a recent treatise on thermo-electricity, "that the most efficacious excitation of electricity upon the earth appears to be produced by the sun producing daily evaporation, deoxidation, and heat, all of which excite electrical currents." After stating that the sun daily produces electric currents, and these currents magnetism, he observes, that "thus the earth seems to have a constant magnetic polarity, produced in the course of time by the electrical currents which surround it, and a variable magnetism, produced immediately by the same current." As the sun produces different effects on water and solid bodies, Oersted supposes that the intensity will vary in the same parallel, and the direction of the needle will be oblique to the equator, in consequence of the lines of equal electro-magnetic intensity being twice bent by the influence of the two great masses of continent. "The yearly and daily change," he observes, "must occasion yearly and daily variations. As to the variations comprehended in greater periods, we might perhaps attribute them to a motion of the coolest points in such continents, which, it appears, cannot remain the same for ever, because the currents of warmer air must principally be directed to such points." Analogous views have been recently stated by M. Kupffer, in a memoir read in 1829 to the Russian Academy, in which he adopts explicitly Sir David Brewster's opinions of the existence of two cold poles distant from the pole of revolution. "But this distribution of temperature," says he, "appears also to have a great influence on the distribution of the intensity of terrestrial magnetism. This would no doubt be the case if it is true, as I have tried to show in another memoir, that terrestrial magnetism resides at the surface of the globe. We have here the choice between two hypotheses; either the earth should be considered as a magnet existing by itself, and then the intensity of its magnetism will be the inverse of its temperature; or it receives its influence from without, and is only like a piece of soft iron, to which the presence of a distant body communicates magnetism, and then the intensity of its magnetism will increase with its temperature. Though the first of these hypotheses has been hitherto generally adopted, yet the second acquires some probability from the discovery of the magnetic influence of the solar rays, and of the known relation between the diurnal variations of the declination of the needle and the course of the sun." The connection between the poles of maximum cold and those to which the isodynamical magnetic lines are related, is considered by Dr Dalton as a probable supposition. "If the idea," says he, "suggested by Sir David Brewster in the Transactions of the Royal Society of Edinburgh, vol. ix. 1821, be correct (and there seems great reason to believe it to be so), namely, that there are two poles of greatest cold in the northern hemisphere, the above observation will enable us to see the natural cause of this remarkable fact. The lands within the arctic circle, in the absence of the sun, must depend upon the south-west winds from the two great oceans for their winter heat. Those parts of the eastern and western continents which are most remote from the ocean, as measured along the curvilinear tracts of the

current of air, must receive that air in great measure deprived both of its vapour and its temperature. Accordingly it is found that the temperature of the north-east parts of such continents exhibits the extreme of cold. Probably a latitude of 75° north, and a longitude of 90° east and 90° west, would be found nearly equally cold, and to exceed any other place on the surface of the globe in this respect; and it would be a curious coincidence if Professor Hansteen's two supposed northern magnetic poles should be found in the same positions as the two poles of extreme cold."

In a general history of magnetical discoveries, it may be proper to take some notice of the very curious experiments which have been made respecting the influence of the solar rays in the production of permanent magnetism, although, according to the generally received opinion, the existence of such an influence has not been established; but if the propriety of doing this had been doubtful, the observation just made by M. Kupffer, as connecting this supposed property of violet light with terrestrial magnetism, would have removed the doubt. Dr Morichini, an eminent physician in Rome, was the first who announced it as an experimental fact, that an unmagnetised needle could be rendered magnetic by the action of the violet rays of the sun. His experiments were successfully repeated by Dr Carpi at Rome, and the Marquis Ridolfi at Florence; but M. d'Hombre Firmas at Alais in France, Professor Configliachi of Pavia, and M. Bérard of Montpellier, failed in obtaining decided magnetic effects from the violet rays. In 1814 Dr Morichini exhibited the actual experiment to Sir Humphry Davy, and in 1817 Dr Carpi showed it to Professor Playfair. A few months after Sir Humphry witnessed the experiment, the writer of this article met him at Geneva, and learned from him the fact, that he had paid the most diligent attention to one of Morichini's experiments, and that he saw, with his own eyes, an unmagnetised needle rendered magnetic by violet light. The following account of the experiment made by Dr Carpi was given to us verbally by Professor Playfair, who approved of the statement of it which we drew up at the time. "The violet light was obtained in the usual manner, by means of a common prism, and was collected into a focus by a lens of a sufficient size. The needle was made of soft wire, and was found upon trial to possess neither polarity nor any power of attracting iron filings. It was fixed horizontally upon a support, by means of wax, and in such a direction as to cut the magnetic meridian at right angles. The focus of violet rays was carried slowly along the needle, proceeding from the centre towards one of the extremities, care being taken never to go back in the same direction, and never to touch the other half of the needle. At the end of half an hour after the needle was exposed to the action of the violet rays, it was carefully examined, and it had acquired neither polarity nor any force of attraction; but after continuing the operation twenty-five minutes longer, when it was taken off and placed on its pivot, it traversed with great alacrity, and settled in the direction of the magnetical meridian, with the end over which the rays had passed turned towards the north. It also attracted and suspended a fringe of iron filings. The extremity of the needle that was exposed to the action of the violet rays repelled the north pole of a compass-needle. This effect was so distinctly marked as to leave no doubt in the minds of any who were present, that the needle had received its magnetism from the action of the violet rays." In this state of the subject, Mrs Somerville made some simple and well-conducted experiments, which seemed to set the question at rest, from the distinct and decided

character of the results. A sewing needle, an inch long, and devoid of magnetism, had one half of it covered with paper, and the other exposed to the violet rays of the spectrum, five feet distant from the prism. In two hours it acquired magnetism, the exposed end exhibiting north polarity. The indigo rays produced an equal effect, and the blue and green the same in a less degree. The yellow, orange, and red rays had no effect even after three days' exposure to their action. Pieces of blue watch-springs received a higher magnetism. When the sun's light fell upon the exposed end through blue coloured glass, or through blue or green riband, the same magnetic effects were produced.

The experiments of Mr Christie, an account of which was read to the Royal Society a short time before Mrs Somerville's, confirmed her results to a certain degree, by a different mode of observation. He found that the compound solar rays possessed magnetic influence, and exhibited it in their effect of diminishing the vibrations of magnetised and unmagnetised steel needles, and also needles of copper or of glass, by making them oscillate in the sun's white ray. Mr Christie, however, has recently remarked, that as his experiments have not succeeded on repetition by Mr Snow Harris, when made in a vacuum, his results must have been owing to currents of air. In justice to Mr Christie, however, we must mention, that Professor Zantedeschi repeated Mr Christie's experiments at Pavia, under an Italian sun, with a needle a Paris foot long, and obtained a striking result. This needle, when drawn from its position of equilibrium, through an area of $90^\backslash circ$, performed four oscillations in $30^\backslash circ$, the last of which had a semiamplitude of $70^\backslash circ$. In the solar rays it performed in $30^\backslash circ$ four oscillations, the last of which had only a semiamplitude of $60^\backslash circ$. When he exposed to the sun the north pole, the semiamplitude of the last oscillation was $6^\backslash circ$ less than that of the first, while by exposing the south pole this last oscillation became greater than the first. The experiments of Baumgartner and Barlocci tended to confirm these results. The former found that iron wires polished on a part of their length are magnetised by white solar light, exhibiting a north pole on the polished part; and the latter has shown that an armed natural loadstone, which carried $1\backslash frac\{1\}\{2\}$ Roman pound, exhibited, after three hours' exposure to the strong light of the sun, an increase of energy equivalent to 2 ounces or $\backslash frac\{1\}\{4\}$th of a pound, while another larger one, which carried 5 pounds 5 ounces, had its strength nearly doubled by two days' exposure. Zantedeschi tried an artificial horse-shoe loadstone, which carried 13$\backslash frac\{1\}\{2\}$ ounces; after three days' exposure to the sun it carried 3$\backslash frac\{1\}\{2\}$ ounces more, and by continuing its exposure its power increased to 31 ounces. An oxidated magnet gained most power, and a polished one none. He found also that the north pole of a loadstone exposed to the sun's rays concentrated by a lens acquires strength, while its south pole, similarly exposed, loses it.

Notwithstanding all these results, the general opinion seems now to be, that light does not exercise any decided effect in producing magnetism. The experiments of MM. P. Ries and Moser were made with needles both polished and oxidated, and also with wires half-polished; and polarised as well as common light was made to fall upon them in a concentrated state, but no decided effect upon their number of oscillations could be observed; and they state that they think themselves justly entitled to reject totally a discovery which, for seventeen years, has at different times disturbed science.

In 1827, Mr Snow Harris communicated to the Royal Society of Edinburgh his Experimental Inquiries concerning the Laws of Magnetic Forces, made with a beautiful and accurate instrumental apparatus, invented by the author for examining the phenomena of induced magnetism. With

this apparatus he found that the magnetic development in masses of iron by induction is, ceteris paribus, directly proportional to the power of the inductive force, and inversely as the distance; and that the forces which magnets develop in a mass of iron at a given distance, within certain limits, may be taken as a fair measure of their respective intensities. From another series of experiments he has shown, that the absolute force of attraction exerted between a magnet and a piece of iron, varies with the power of the magnet, and consequently with the force induced in the iron, ceteris paribus; and that when the force induced in the iron is a constant quantity, while its distance from a temporary or permanent magnet is variable, the absolute force varies with the distance. This result was not only apparent when the magnetic force was varied by induction, but was also satisfactorily shown when varied by magnets of which the relative powers of induction were previously ascertained. Mr Harris made a number of nice experiments on the absolute force of attraction and repulsion between two magnetised bodies, which he found to be in the inverse ratio of the square of the distance. When, in the case of attraction, the magnets, however, were nearly approximated in relation to their respective intensities, the increments in the forces began to decline, and in some instances at near approximations the absolute force was in the simple inverse ratio of the distance. In the experiments with the repelling poles, the deviations from the regular force were still more considerable, and, what is curious in this case, the force became less and less, until the polarity of the weaker magnet appeared to be so counteracted by induction, that the repulsion was at length superseded by attraction. Mr Harris next proceeded to determine the law according to which the forces are developed in different points of the longitudinal magnetic axis between the centre and poles of a magnet, and he found that it varied directly as the square of the distance from the magnetic centre; a law which is uniform in bars of steel regularly hardened and magnetised throughout. This law of distribution is exactly the same as that which has been given by Hansteen.

Mr Harris has also published other two memoirs in the Philosophical Transactions for 1831, the first On the Influence of Screens in arresting the progress of Magnetic Action, and the second On the Power of Masses of Iron to control the Attractive Force of a Magnet, of both of which some account will be found in a subsequent section. In his latest paper, On the Investigation of Magnetic Intensity by the Oscillations of the Magnetic Needle, he exposed an oscillating magnetic bar to a bright sunshine; and though he observed the effect observed by Mr Christie, which that philosopher ascribed to the influence of the sun's rays, yet he found that they all disappeared when the needle was made to oscillate in an exhausted receiver.

M. Haldat of Nancy communicated, in 1830, to the so-M. Haldat. ciety of that city, the results of some interesting researches A. D. 1830. on the incoercibility of the magnetic fluid, or its power of exerting its influence through all bodies, even the most dense; a property which is not possessed by light, heat, or electricity. In this research he adopted various methods of observation, and interposed a great variety of substances; and from the numerous experiments which he made, he has drawn the following conclusions: 1. That the agent or fluid by which the magnetic phenomena are explained is incoercible in the present state of the science; 2. that iron, considered as presenting an exception to this law, coerces the magnetic influences only by acquiring itself the magnetic state; 3. that incandescence does not give to bodies the power of coercing the magnetic influence. In a previous memoir, M. Haldat had obtained some interesting results on the production of magnetism by friction. He found that all hard bodies may, by means of friction, assist in the decomposition of the magnetic fluid, if their action

History. is promoted by the combined action of magnets which, by themselves, are incapable of producing it. If a piece of soft wire, for example, four inches long, and 1-25th of an inch in diameter, is placed horizontally between two bar-magnets, with their opposite poles facing each other, and at such a distance that the wire cannot be magnetised, it will receive distinct magnetism by friction with all hard bodies, such as copper, brass, zinc, glass, hard woods, &c. M. Haldat employed the ingenious process of M. Gay-Lussac, of magnetising soft iron by torsion, in neutralising the wires before they were magnetised. If they are twisted after receiving magnetism, they will preserve the magnetism which they had received before torsion; but if, after being twisted, they are twisted in an opposite direction, they will become perfectly neutral.

M. Haldat likewise made some interesting experiments on the effect of the coercive force in steel on the magnetism produced by rotation, and he found that the force with which a revolving steel disc dragged round a magnetic needle was in the inverse ratio of the coercive force of the steel. When the discs were not hot, they had the same effect as those at the ordinary temperature. We owe also to M. Haldat an interesting paper on magnetic figures. Figures of any kind, when traced by the pole of a magnet on a plate of steel, are rendered visible by sifting upon the invisible tracings filings of steel, which arrange themselves in the most beautiful manner along the outlines of the figure which has been traced.

A series of very interesting experiments have been recently published by M. Quetelet of Brussels, On the successive degrees of Magnetic Force which a Steel Needle receives during the multiple frictions which are employed to magnetise it. These experiments were made principally before 1830, but they were not given to the public till 1833. The following are the general results which were obtained by the author.

1. When a needle or bar that had never been magnetised, is magnetised to saturation by the method of separate contact, the magnetic force acquired is a maximum in relation to the forces which can be given to the same needle or bar by the subsequent reversals of its poles.

2. The magnetic force which a needle can acquire becomes weaker in proportion as the reversal of its poles, has been multiplied. The series of frictions which tend to bring back the poles to their primitive state are more efficacious than the others.

3. This difference between the forces which the needle acquires after the successive reversal of its poles, goes on continually diminishing, and converges towards a limit. It depends in general on the size of the needle in relation to that of the rubbing bars, as well as in its force of coercion.

4. A needle cannot receive all the magnetic force which it can acquire, if the frictions do not take place over all its surface; this becomes particularly sensible in the reversal of the poles.

5. The rubbing bars give (ceteris paribus) to bars of the same dimensions as themselves a magnetic force equal to that which they possess, and in bars of different dimensions the forces acquired are as the cubes of their homologous dimensions. The last part of this proposition was long ago established by Coulomb.

6. When we rub magnetic bars with other bars weaker than themselves, the force of the first diminishes in place of increasing; and it appears that the force becomes that which those latter bars would be capable of giving at the first by directly magnetising them.

7. The relation which exists between the forces which a needle or a bar receives by successive frictions, and the number of these frictions, may be expressed by an exponential formula of three constants.

One of these constants appears to change its value with the size of the bars which are magnetised, at least while these bars have a magnitude which does not exceed that of the rubbing bars, and while they are of the same quality of steel.

In this way we know beforehand the successive degrees of force which a bar takes at each friction, if we have previously determined the law of these augmentations for the same rubbing bars, and for any other bar which we get to serve as the modulus. If the bar which is rubbed has begun to be magnetised, we must calculate first the number of frictions to which this force corresponds, in order to be able to assign the rank of the subsequent frictions, and the magnitude of the corresponding magnetical forces.

8. When the rubbing bars are greater than the bar to be magnetised, from the first complete friction the force of magnetism is very nearly one half of the force which the magnetised bar will finally possess.

After the twelfth complete friction, the magnetic force differs little from that which the rubbing bars can communicate.

We owe also to M. Quetelet two interesting memoirs on the magnetic intensity of different places in Switzerland, Italy, Germany, and the Low Countries.

The influence of the aurora borealis on the magnetic needle, which was observed by Hiorter at Upsal in 1741, and by Wargent in 1750, had long induced philosophers to regard it as a magnetic phenomenon; and this was greatly confirmed by the fact that the south end of the dipping needle points to that part of the heavens to which the rays of the aurora appear to converge. "The aurora borealis," says Dr Robison, "is observed in Europe to disturb the needle exceedingly, sometimes drawing it several degrees from its position. It is always observed to increase its deviation from the meridian, that is, an aurora borealis makes the needle point more westerly. This disturbance sometimes amounts to six or seven degrees, and is generally observed to be greatest when the aurora borealis is most remarkable.

"This is a very curious phenomenon, and we have not been able to find any connection between this meteor and the position of a magnetic needle. It is to be observed, that a needle of copper or wood, or any substance besides iron, is not affected. We long thought it an electric phenomenon, and that the needle was affected as any other body balanced in the same manner would be; but a copper needle would then be affected. Indeed, it may still be doubted whether the aurora borealis be an electric phenomenon. They are very frequent and remarkable in Sweden, and yet Bergman says that he never observed any electric symptoms about them, though in the mean time the magnetic needle was greatly affected.

"We see the needle frequently disturbed, both from its general annual position, and from the change made on it by the diurnal variations. This is probably the effect of auroræ boreales which are invisible, either on account of thick weather or daylight. Van Swinden says he seldom or Van Swinden never failed to observe auroræ boreales immediately after any anomalous motion of the needle; and concluded that there had been one at the time, though he could not see it. Since no needle but a magnetic one is affected by the aurora borealis, we may conclude that there is some natural connection between this meteor and magnetism. This should farther incite us to observe the circumstance formerly mentioned, viz. that the south end of the dipping needle points to that part of the heavens where the rays of the aurora appear to converge. We wish that this were diligently observed in places which have very different variations and dips of the mariner's needle."

A valuable series of observations on the influence of the Dr. Dalton aurora borealis on the magnetic needle was made by Dr.

Dalton, at Kendal and Keswick, during seven years from May 1786 to May 1793, and has been published in his Meteorological Observations and Essays, which appeared in 1793. During these observations he noticed the effect which they produced on the magnetic needle, and he was thus led to study the phenomena of the aurora, and to establish beyond a doubt the relation of all its phenomena to the magnetic poles and equator. His views and speculations on this subject we shall detail at some length in a future part of this article; but we shall at present give our readers a specimen of the observations which he made on the magnetic needle during the changes of an aurora.

Feb. 12. The aurora appeared at Kendal after 6h. p. m. flaming over two thirds of the hemisphere. The beams converged to a point in the magnetic meridian, about $15^\{\backslash circ\}$ or $20^\{\backslash circ\}$ to the south of the zenith. The following were the changes which he observed in the needle and in the aurora:—

In these observations, the deviation produced by the aurora was $53^\{\backslash circ\}$. In some cases during the prevalence of auroras Dr Dalton did not observe any perceptible disturbance of the needle.

Professor Hansteen observes, that large extraordinary movements of the needle, in which it traverses frequently with a shivering motion an arc of several degrees on both sides of its usual position, are seldom, perhaps never, exhibited, unless when the aurora borealis is visible; and that this disturbance of the needle seems to operate at the same time in places the most widely separate. "The extent of such extraordinary movements," he adds, "may, in less than twenty-four hours, amount to $5^\{\backslash circ\}$ or $5\backslash frac\{1\}\{2\}^\{\backslash circ\}$. In most cases, the disturbance is also communicated to the dipping needle; and so soon as the crown of the aurora quits the usual place (the points where the dipping needle produced would meet the sky), the instrument moves several degrees forward, and seems to follow it. After such disorders, the mean variation of the needle is wont to change, and not to re-

cover its previous magnitude till after a new and similar disturbance." History.

From an extensive series of accurate observations made by M. Arago, by M. Arago at Paris since 1818, the needle was almost invariably found to be affected by auroræ that were seen in Scotland; and so striking was the connection between the two classes of facts, that the existence of the aurora could be inferred from the derangements of the needle. M. Arago has likewise discovered, that, early in the morning, often ten or twelve hours before the aurora is developed in a very distant place, its appearance is announced by a particular form of the curve which exhibits the diurnal variation of the needle, that is, by the value of the morning and evening maxima of elongation. From a number of corresponding observations on the hourly declination made by M. Arago and M. Kupffer, who established at Kasan, near the eastern limit of Europe, one of Gambe's compasses, similar to that used at Paris, these philosophers were convinced that, notwithstanding a difference of longitude of above $47^\{\backslash circ\}$, the disturbances produced upon the needle by the aurora took place at the same instant. It is a curious fact, however, and one yet unexplained, that during the frequent occurrence of the aurora at Port Bowen, Captain Foster did not observe any peculiar changes in the direction of the needle, although, from his great proximity to the magnetic pole, the diurnal change sometimes amounted to $4^\{\backslash circ\}$ or $5^\{\backslash circ\}$; and, under such circumstances, the influence of the aurora ought to have been particularly conspicuous. Mr Christie is of opinion that the direction of the needle may be influenced by the electrical state of the clouds; and he found it to be so in a very distinct experiment which he made for the purpose. Captain Sir Everard Home had observed the same effect produced during thunder storms; Home, and, in two instances, he found that a needle came sooner to rest during a thunder storm than it had done either previous or subsequent to it, the number of oscillations having been reduced in one case from 100 to 40, and in another from 200 to 120.

During the late journey of Captain Back to the polar regions in 1833, 1834, and 1835, he found that the needle was generally affected by the aurora; and on one occasion the deviation which it produced was $8^\{\backslash circ\}$. "For nearly a month, however" (previous to the 7th January 1834), he remarks, "the needle had not been perceived to be affected by the aurora, which, it may be proper to observe, was always very faint, apparently high, and generally confined to one point of the heavens." Captain Back repeatedly observed, that when the aurora was concentrated in individual beams, the needle was powerfully affected; but that it generally returned to its mean position when the aurora became generally diffused. On several occasions the needle was restless, and exhibited the vibrating action produced by the aurora when this motion was not visible; and Captain Back states that he could not account for this, except by supposing the invisible presence of the aurora in full day.

The only metals which were supposed to have a distinct and decided power, and were therefore called magnetic metals, are iron, nickel, and cobalt. Mr David Lyon² has lately endeavoured to show that these metals resemble one another, not only in their principal qualities, but in the numerical values of their qualities; and he adds, that whilst these three magnetic substances have the values above referred to near each other, there are no other substances in which the same values come very near or fall within those of the three magnetic substances. The values to which Mr Lyon alludes are the following:³

¹ Appendix to Captain Back's Narrative of the Arctic Land Expedition, &c. p. 601.

² London and Edinburgh Phil. Mag. December 1834, p. 415.

³ M. Pouillet, in his Éléments de Physique, tom. iii. p. 89, refers to some remarkable analogies which he has observed between the distance of the atoms of bodies and their magnetic properties.

The preceding speculation, though ingenious, and deserving of attention, has however been overturned by some very recent observations of M. Faraday. "Cobalt and chromium," says he, "are said to be both magnetic metals. I cannot find that either of them is so, in its pure state, at any temperatures. When the property was present in specimens supposed to be pure, I have traced it to iron or nickel."¹

Mr Faraday has very recently published some interesting observations² On the General Magnetic Relations and Characters of the Metals. He is of opinion that all the metals are magnetic, in the same manner as iron, though not at common temperatures, or under ordinary circumstances. He does not allude to a feeble magnetism, uncertain in its existence and source, but to a distinct and decided power, such as that possessed by iron and nickel; and his impression is, that there is a certain temperature for each metal (well known in the case of iron, beneath which it is magnetic, but above which it loses all power), and that there is some relation between this point of temperature and the intensity of magnetic force, which the body, when reduced beneath it, can acquire. Iron and nickel would then be no more exceptions from the metals in regard to magnetism, than mercury is in regard to liquefaction.

In order to investigate this point, Mr Faraday subjected various metals in their pure state to a temperature from 60° to 70° below the zero of Fahrenheit, but he could not detect in them the least indication of magnetism. The metals tried were the following:

Mr Faraday next proceeded to compare iron and nickel with respect to the points of temperature at which they ceased to be magnetic. Iron loses all magnetic properties at an orange heat, and is then to a magnet the same as a piece of copper. Mr Faraday found that the point at which nickel lost its magnetic relations was very much lower than with iron, but equally defined and distinct. If heated and then cooled, it remained unmagnetic long after it had fallen below a heat visible in the dark; and almond oil can bear and give that heat which makes nickel indifferent to a magnet, its demagnetising temperature being about 630° or 640° Fahr. In order to determine what relation the temperature which took from a magnet its power over soft iron had to that which would take from soft iron or steel its power relative to a magnet, Mr Faraday gradually raised the temperature of a magnet, and found that it lost its polarity rather suddenly when scarcely at the boiling point of almond oil, and then acted with a magnet as cold soft iron. It required to be raised to a full orange heat before it lost its power as soft iron. "Hence he concludes, the force of the steel to retain that condition of its particles which renders it a permanent magnet, gives way to heat at a far lower temperature than that which is necessary to prevent its particles assuming the

same state by the inductive action of a neighbouring magnet. Hence, at one temperature, its particles can of themselves retain a permanent state; whilst, at a higher temperature, that state, though it can be induced from without, will continue only as long as the inductive action lasts, and at a still higher temperature all capability of assuming this condition is lost. The temperature at which polarity was destroyed appeared to vary with the hardness and condition of the steel. Fragments of loadstone of very high power were then experimented with. These preserved their polarity at higher temperatures than the steel magnet; the heat of boiling oil was not sufficient to injure it. Just below visible ignition in the dark they lost their polarity, but from that to a temperature a little higher, being very dull ignition, they acted as soft iron would do, and then suddenly lost that power also. Thus the loadstone retained its polarity longer than the steel magnet, but lost its capability of becoming a magnet by induction much sooner. When magnetic polarity was given to it with a magnet, it retained this power up to the same degree of temperature as that at which it held its first and natural magnetism."

Some of the results observed by M. Pouillet³ stand in opposition to some of the preceding statements. M. Pouillet considers it as certain that there are five simple magnetic bodies, viz.

and in consequence of having observed some remarkable analogies between the distance of the atoms of bodies and their magnetic properties, he was led to suppose that the magnetic limit of different bodies ought to be found at very different temperatures. "I have indeed," says he, "demonstrated by experiment, 1. that cobalt never ceases to be magnetic, or rather that its magnetic limit is at a temperature higher than the brightest white heat; 2. that chrome has its magnetic limit a little below the temperature of dark blood-red heat; 3. that nickel has its magnetic limit about 350° centigrade nearly at the melting point of zinc; and, 4. that manganese has its magnetic limit at the temperature of from 20° to 25° below zero." Experiments, continues he, "on these five magnetic bodies seem to prove, 1st, that heat acts upon magnetism only in consequence of the greater or less distance which it occasions between the atoms of bodies; and, 2d, that all bodies would become magnetic if we could by any action whatever make their atoms approach within a suitable distance."

Among the latest researches on magnetism are those of Professor Gauss of Göttingen, who has published an account of them in a treatise entitled Intensitas vis Magneticae Terrestris ad absolutam mensuram revocatis. His object is to impart to magnetical observations the accuracy of astronomical ones. By observing the oscillations of a magnetised bar, he finds the product of the horizontal intensity of the earth's magnetism, and the static momentum of the free magnetism of the bar; and by eliminating the latter from the two equations, he obtains an absolute measure of the former, independent of the magnetism of the bar. The horizontal intensity thus found is then to be multiplied by the secant of the dip of the needle, in order to give the absolute intensity. In this inquiry Professor Gauss found it necessary to deduce from observation the true law of magnetic action, which, from a number of consistent and carefully made experiments, he found to be in the inverse ratio of the square of the distance. From a series of accurate experiments

¹ London and Edinburgh Phil. Mag. March 1836, p. 178.

² Ibid. p. 177.

³ M. Pouillet remarks elsewhere, that manganese does not become magnetic till it is cooled down to 15° or 20° below zero. (El. Phys. iii. p. 18.)

⁴ Éléments de Physique, 2d. edit. tom. iii. p. 89, Paris, 1832.

Professor Gauss found the horizontal intensity at Göttingen, on the 18th September 1832, to be 1.7821; and taking the exponent of gravity in moving bodies at the place of observation as the unit of force, and using the Paris line and the Berlin pound, he found the absolute horizontal intensity to be 0.0039131; and as he found the dip at Göttingen on the 23d June 1832 to be $68^\{\backslash circ\}\; 22\text{'}\; 52\text{'}\text{'}$, the absolute intensity of terrestrial magnetism will be

Professor Gauss has proposed, and put in practice, a very accurate method of observing the daily variation of the needle, and of determining the time of vibration of a needle or magnetised bar. He fixes a plane mirror on the end of the bar, and perpendicularly to its axis, and by observing the reflected image of the divisions of a scale, by the aid of a theodolite placed at a distance, he is able to observe and to measure the minutest changes.

The magnetised bar employed by Gauss is of much larger dimensions than the bar of Prony's magnetic telescope; the small ones, which he uses as magnetometers, being four pounds weight, and the large ones twenty-five pounds; two of which, when fastened together, form the apparatus or multiplier of induction for rendering sensible and measuring the oscillatory movements predicted by a theory founded on Mr Faraday's great discovery. By this valuable invention of Professor Gauss, the observer is not under the necessity of approaching the magnetised bar, so that no disturbance is occasioned by the currents of air produced by the proximity of the observer's body, so that observations may be made in the smallest intervals of time.

With apparatus similar to that of Professor Gauss, simultaneous observations have been made in 1834 and 1836, at intervals of five or ten minutes, at Göttingen, Copenhagen, Altona, Brunswick, Leipzig, Berlin, Milan, and Rome. It appears, from the graphic representation of the results, that the smallest inflexions of the horary curves are parallel, and consequently the disturbing causes which produce them simultaneous at Milan and Copenhagen, two of the places of observation, which have a difference of latitude of $10^\{\backslash circ\}\; 13\text{'}$.

In giving an account of Professor Hansteen's labours, we have briefly noticed his journey in Siberia, and the erection of magnetic observatories by the emperor of Russia, on the recommendation of Baron Humboldt; and we have also referred to the early researches of this distinguished philosopher. When travelling in the equinoctial regions of America during the years 1799-1804, Baron Humboldt had devoted much attention to the determination of the intensity of the magnetic forces, and of the dip and variation of the needle. Upon his arrival in Europe, he conceived the design of examining the progress of the horary changes of the variation, and the perturbations to which it is subject, by employing a method which had never been adopted on an extended scale. In a large garden at Berlin, he measured, particularly at the period of the equinoxes in 1806 and 1807, the angular alterations of the magnetic meridian, at intervals of an hour, often of half an hour, without interruption, during four, five, or six days, and as many nights. The instrument employed was Prony's magnetic telescope, suspended according to the method of Coulomb, and capable of being reversed upon its axis. It was placed in a glass frame, and directed towards a very distant meridian mark, the illuminated divisions of which indicated six or seven seconds of hourly variation. In these researches Baron Humboldt was struck with the frequency of oscillations whose amplitude extended beyond all the divisions of the scale, and which repeatedly took place at the same hours before sunrise. "These vagaries of the needle," says the baron, "the almost periodical return of which has recently been confirmed by M. Kupffer, in the account of his travels in the Caucasus, appeared to

me the effect of a re-action of the interior of the earth towards the surface; I should venture to say, of magnetic storms, which indicate a rapid change of tension." With the view of investigating the causes of these disturbances, Baron Humboldt proposed to erect similar apparatus on both sides of the meridian of Berlin; but the political tempest of Germany, and his mission to France by the government, delayed the execution of his plan. M. Arago, however, as we have already seen, began and prosecuted his inquiry with singular success.

When Baron Humboldt again fixed his residence in Germany in 1827, he erected one of Gambey's compasses in a magnetic pavilion, without any iron, in the middle of a garden, and began a series of regular observations in the autumn of 1828. At his request, the Imperial Academy and the curator of the university of Kasan erected magnetic observatories at St Petersburg and Kasan; and the imperial department for mines has established similar stations at Moscow, Barnaul, and Nertschinsk. The academy, too, has sent Mr George Fuss to Pekin, where he has procured the erection of a magnetic pavilion in the convent garden of the monks of the Greek church. Since Mr G. Fuss's return, M. Kowanko, a young officer of mines, continues the horary observations corresponding to those made in Germany and Russia. Admiral Greig has established one of Gambey's compasses in the Crimea at Nicolaeff. Baron Humboldt has procured the establishment of a magnetic apparatus at the depth of thirty-five fathoms, in an adit in the mines of Freiberg in Saxony. Baron Von Wrangel has been provided with one of Gambey's compasses at Sitka, in one of the Russian settlements. M. Arago has caused to be erected, at his own expense, one of Gambey's compasses in the interior of Mexico, where the soil is 6000 feet above the sea. The French minister of marine has established a magnetic station in Iceland, and the necessary instruments will be sent this summer (1836) to Reikavik; and Baron Humboldt, at the desire of Admiral de Laborde, has sent instruments to the Havannah in Cuba, to furnish a magnetic observatory under the tropic of Cancer.

Some years ago, the writer of this article urged a distinguished and influential member of the British government to establish magnetic observatories in England and the colonies, but no steps were taken in consequence of this application. Baron Humboldt has, however, addressed an interesting letter to his Royal Highness the Duke of Sussex, as president of the Royal Society, soliciting this body to extend, in the colonies of Great Britain, the line of simultaneous observations, and to establish permanent magnetic stations, either in the tropical regions on each side of the magnetic equator, or in the high latitudes of the southern hemisphere, and in Canada. We hope that the Royal Society will use its influence with the British government to have this proposal carried into effect, and that this country shall not be exposed to the humiliation of being indifferent to the progress of those branches of scientific inquiry which its extensive influence in various regions of the globe enables it effectually to advance.

CHAP. II.—ON THE GENERAL PHENOMENA AND PROPERTIES OF MAGNETIC BODIES.

A body is said to be magnetic when it has the power of attracting soft iron, either in the subdivided state of iron filings, or in large portions; or of attracting and repelling other magnetic bodies like itself: of taking a particular position when freely suspended, or moving on a pivot: and of communicating magnetism either temporarily to soft or permanently to hard iron in the form of steel. Hence we may arrange the general properties of magnetic bodies under the following heads.

1. 1. On the attractive power of magnetic bodies upon soft iron.
2. 2. On the attractive and repulsive power of magnets over each other, or over iron either temporarily or permanently magnetised.
3. 3. On the effect of masses of iron on the attractive force of a magnet.
4. 4. On the polarity of magnetic bodies.
5. 5. On the power of magnets to communicate magnetism to other bodies.
6. 6. On the distribution of magnetism in artificial magnets.
7. 7. On the effect of division and fracture on the distribution of magnetism.
8. 8. On magnetic figures.

The natural magnet or loadstone was for a long time the only body considered as possessing magnetic properties. It is an ore of iron, of a grey colour, and a dark metallic lustre. Its specific gravity is about four and a half times that of water. It crystallizes in the form of the regular octahedron, and it consists of from 85 to 75 parts of iron, and from 15 to 25 parts of oxygen. It is found in almost every part of the world,¹ and often forms rocks of considerable magnitude; but different specimens of it possess very different powers of attraction.

The smallest loadstones generally have a greater attractive power in proportion to their size than larger ones. They have been found of such strength, that though weighing only about twenty-five grains, they could lift a piece of iron about forty-five times heavier than themselves. A small magnet set in a ring, and worn by Sir Isaac Newton, is said to have been capable of lifting 746 grains, or 250 times its own weight; and it is stated by Cavallo, that he has seen a loadstone which weighed only about six and a half grains, which lifted a weight of 300 grains.

Natural loadstones often possess unequal powers of attraction in different parts of their mass, in consequence of want of homogeneity of structure and composition; and hence a portion has often been cut from a large loadstone which could lift a greater weight of iron than the large one itself, the portion detached having possessed the most suitable structure, and the other part having weakened the action of the powerful part by keeping the body to be lifted at a greater distance from those points where the magnetism was strongest. It is no doubt from a similar cause that small magnets have a greater proportional power than large ones, or that those of two pounds weight have seldom been found capable of lifting more than ten times their own weight of iron.

If we now take a natural loadstone L, however shapeless, and, after rolling it in a quantity of iron filings, afterwards withdraw it, we shall find that the filings are accumulated more abundantly in two opposite points A, B, than in any other, as shown in fig. 1. These two points A, B are called the poles of the magnet, and are the points of greatest attraction. When either of these poles is held at a distance from the iron filings, the filings will be attracted to it, and will adhere with such force that it is difficult to brush them off.

If we suspend a small needle of iron or steel by a fine linen or silken fibre, or balance it on a pivot, and bring

the poles of the loadstone L near it, it will be attracted to it in the first case, or will oscillate on its pivot in the second case.

If we make the needle float on water in a glass tumbler, and bring any pole of L on the outside of the tumbler, the needle will be attracted towards the pole, notwithstanding the interposition of the glass; and by using the needle upon a pivot, it will be found that the attractive force of the loadstone is in no respect diminished by the interposition of any substance whatever, except iron, conductors and non-conductors of electricity having no effect whatever in stopping or diminishing the action of the loadstone, unless the interposed body be iron, or contains iron in any of its metallic states.

While the loadstone thus attracts iron, and all bodies containing it in a metallic state, these same bodies exercise a reciprocal attraction upon the loadstone, action and re-action being equal and opposite. The truth of this may be exhibited by suspending a magnet, and bringing into the vicinity of its poles a piece of soft iron. The magnet will be gradually attracted by the iron, in the same manner as if the iron had been suspended and a pole of the magnet held near it.

If we suspend near each other two loadstones, AB, A'B', like that shown in fig. 1, by two threads T, T', we shall find, by changing the relative position of their poles, A, B, A', B', that there are certain positions in which these poles attract each other, and others in which they are repelled. By marking the poles which attract each other, such as A, B' and A', B, we shall find that the poles which repel each other are A, A' and B, B', and that this mutual attraction and repulsion takes place under every change of circumstances.

If we suspend a piece of soft iron ab from a loadstone AB, we shall find that the end b of the iron exercises the same attractive and repulsive power upon the poles A', B' (fig. 2) of a suspended magnet that B did; and in like manner, if the piece of iron a'b' is suspended from the pole A', the end a' will exercise the same attraction and repulsion upon the poles of a suspended magnet that A did.

If we suspend a piece of iron C from the arm of a balance, it will be attracted by the pole P of a magnet A, and will descend towards P in virtue of this attraction. If we now place a mass of iron I close to A, the suspended iron C will rise, as if the attractive force of P were diminished. This power of the mass of iron I seems only to extend to a given point within the magnet A, the distance between the magnet and the iron remaining the same;

¹ According to Norman, the best loadstones were those brought from China and Bengal.

for if the iron C is suspended above a point $x$ at some distance from P, the action of I will not be felt at the point $x$, except by diminishing the distance between P and C, or by increasing the neutralising power of the mass I.

Mr Snow Harris, to whom we owe this experiment, has shown that a similar effect is produced when the iron I is placed between the magnet PA and the suspended iron C, and also when I is placed below P. In the first of these cases I stops the attraction of P upon C, and acts as a screen.

SECT. IV.—On the Polarity of Magnetic Bodies.

If we suspend a loadstone, as in fig. 2, or make it float upon water or mercury, by placing it on a thin plate of cork or wood, it will gradually change its place till it rests in a position where a line joining the poles A, B is nearly north and south. This is, generally speaking, the case in Europe, the end A, which points northward, deviating in some places from the meridian to the west, in some places to the east; while in other parts of the globe it points exactly to the north. The deviation of the loadstone from the meridian is called its declination or variation. This property of the magnet is called its polarity, or directive power; and the pole A, which turns to the north, is called its north pole; and the pole B, which turns to the south, its south pole. It will now be found that the poles and magnets A, A', or B, B', which repel each other, are either both north or both south poles; and that the north and south poles attract each other. Hence there is in magnetism, as there is in electricity, two opposite powers or principles, namely, the northern and the southern, or boreal and austral magnetism; and, as in electricity, a repulsion takes place between the two powers of the same name, and attraction between the two powers of an opposite name.

The magnetism from which loadstones derive their polarity, or their tendency to direct themselves to particular points of the compass, is obviously derived in some way or other from the earth or its atmosphere; and hence it is called the Magnetism of the Earth, or Terrestrial Magnetism, which will be treated more fully in a future part of this article.

SECT. V.—On the Power of Magnets to communicate Magnetism to other Bodies.

We have already seen, that if a piece of soft iron is suspended to a magnet by the attraction of one of its poles, the iron becomes magnetic, but only during the time that it is in contact with the loadstone. But if we use a piece of hardened iron, or steel, $a\; b$, and suspend it as in fig. 3, it will be found to have acquired a permanent magnetism, the strength of which will depend on the power of the natural magnet A B, and on the time which the steel bar has been suspended. The pole $a$ will be a north pole similar to A, and the pole $b$ a south pole similar to B; and the little magnet $a\; b$ will possess all the properties of the natural magnet, such as attraction for soft iron, and polarity; and its action upon another little steel magnet $a\text{'}\; b\text{'}$, made in a similar manner, will be the same as the action of two natural magnets upon each other. A steel magnet thus made is called an artificial magnet; and we shall in the sequel consider the magnets of which we speak as steel bars rendered permanently magnetic.

A little magnet $a\; b$ has been made by a very simple process, namely, that of contact with the pole of a natural magnet; but there are more complex and efficacious methods, by which a very high degree of permanent magnetism can be communicated to steel, which will be fully explained in the practical part of this treatise.

In order to communicate magnetism from a natural or artificial magnet to unmagnetised iron or steel, it is not necessary that the two bodies be in contact. The communication is effected as perfectly, though more feebly, when the bodies are separated by space.

If the north pole N of an artificial steel magnet A is placed near the extremity $s$ of a piece

of soft iron B, the end $s$ will instantly acquire the properties of a south pole, and the opposite end $n$ those of a north pole. The opposite poles would have been produced at $n$ and $s$ if the south pole S of the magnet A had been placed near the iron B.

In like manner, the iron B, though only temporarily magnetic, will render another piece of iron C, and this again another piece D, temporarily magnetic, north and south poles being produced at $n\text{'}$, $s\text{'}$, and $n\text{'}\text{'}$, $s\text{'}\text{'}$.

The magnetism inherent in B, C, and D, is said to be induced by the presence of the real magnet A, and the phenomena are exactly analogous to the communication of electricity to unelectrified bodies by induction, the positive state inducing the negative, and the negative the positive, in the parts of a conductor placed in a state of insulation near an electrified body.

In order to show by simple experiments that soft iron is itself a magnet while placed near a magnet, let A be a magnet, and K a key held near its lower edge. A nail N will remain suspended by virtue of its induced magnetism; but if A is withdrawn, or K removed from A, the nail N will instantly fall, the induced magnetism diminishing with the distance.

If we hold the key K above a portion of iron filings, they will not be attracted by it; but if we then bring the magnet A near the ring of the key, as in the figure, the iron filings will instantly start up, and be attracted by the key.

We have already noticed, in Sect. I., that the iron attracted by a magnet re-acts upon the magnet, and attracts it in return. The same is the case with a bar of iron on which magnetism is induced. It re-acts on the magnet which induces its magnetism, and increases its magnetic intensity. Hence we derive a distinct explanation of the remarkable facts, that a magnet has its power increased by having a bar of iron placed in contact with one of its poles, and that we can gradually add more weight to that which is carried by a magnet, provided we make the addition slowly and in small quantities, the power of the magnet being increased by the re-action of each separate piece of iron that it is made to carry.

If the bar of iron on which magnetism is induced is consecutively long, and the strength of the magnet great, a succession of poles is produced along its length, a north pole always following a south pole, and vice versa.

These facts enable us to explain the phenomena of magnetic attraction and repulsion, which are necessary consequences of magnetic induction. The magnet attracts a piece of iron by inducing an opposite polarity at the end in contact with it, and the two opposite principles attract each other. In like manner, the north pole of one magnet attracts the south pole of another, and the north and south poles repel each other, in consequence of the attraction and repulsion of the opposite or similar principles. The attraction of iron filings is explained in the same manner. The particle of iron next the magnet has magnetism induced upon it, and it becomes a minute mag-

net, like B in fig. 5. This particle again makes the next particle a magnet, like C, and so on, the opposite polarities in each particle of the filings attracting one another, as if they were real magnets.

In comparing the amount of the attractive force of two dissimilar poles of two magnets, with the amount of the repulsive force of the two similar poles, it has been found that the former force is considerably greater than the latter. This result is a necessary consequence of the inductive process above described. When the two attracting poles are in contact, each magnet tends to increase the power of the other, by developing the opposite magnetisms in the adjacent halves, and thus increasing their mutual attraction. But when the two repelling poles are brought into contact, the action of each half brought into contact has a tendency to develop in that half a magnetism opposite to that which it really possesses, and thus to diminish the two similar principles, and weaken their repulsive power. This injurious influence of opposite poles upon the repulsive power of the magnets in action, is finely exhibited when one of the magnets is very powerful, and the other very weak. When the two similar poles are held at a moderate distance, a repulsion is distinctly exhibited; but when they are brought into contact, the stronger attracts the weaker magnet, an effect which is produced by its actually destroying the similar weak magnetism in the half next it, and inducing in that half the opposite magnetism, which, of course, occasions attraction.

When the magnet A and the piece of iron B are placed in the same straight line, as in fig. 5, the pole N acts favourably in inducing south polar magnetism at n, and north polar at s; but it is evident that the remote pole S must tend to weaken the inductive force of N, by inducing, though in a feeble degree, north polar magnetism at n and south polar at s. If the soft iron B is placed as in fig. 7, the induced magnetism will be nearly as strong as before, the greater proximity of N tending to produce south polar magnetism in n, being compensated by the increased proximity of S tending to produce north polar magnetism in n. In the inclined position C the induced magnetism is still stronger, as S acts more powerfully upon n; and when the two are parallel, as in fig. 8, the two bars or magnets are in the position most favourable for developing and sustaining the magnetism which they receive or possess.

Hitherto we have considered the natural and artificial magnet as producing magnetism in soft or hard iron, distributed in the same manner as in the inducing magnet; but by the action of one or more magnets, we can distribute the magnetism in various ways, as follows:

In the case of bars, we may have a north pole in the middle of it, and a south pole at each extremity. Thus, in fig. 9, if the magnet NS has its north pole N placed opposite the middle of the soft iron bar mn, this bar will have a south pole at s and north poles at n, n. The very same effect will be produced if, as in fig. 10, we place the soft iron bar B between two magnets A, C, whose north poles N, N are nearest the bar. These north poles N, N tend to produce south poles at s, s, and consequently northern polarity in the middle at n. In the preceding case a south pole may be produced in the

middle, and north poles at the ends of the bar, by placing the south poles of the magnets where the north poles are placed.

In like manner, a piece of soft iron ss, ss, of the form of a cross, will have south poles at s, s, s, s, if the south pole S of a magnet A is placed on or near its centre, as in fig. 11, as it may be conceived to consist of two bars ss, ss. For the same reason, if a circular plate of soft iron is substituted in place of the cross ss, ss, and the south pole S of the magnet placed upon or near its centre, that centre will be a north pole, and every point of the circumference of the plate will be a south pole.

A very instructive experiment, founded on magnetic induction, is exhibited in fig. 12, where several soft iron wires or slender bars sn, sn, sn are suspended at the north pole N of a magnet N. Each of the ends s, s, s becomes a south pole by induction from the action of the north, and consequently the lower ends n, n, n north poles. The south poles s, s, s have a tendency to repel each other, but are prevented from yielding to their repulsive forces in consequence of their strong adhesion to the north pole N. The north poles n, n, n, however, are free from this restraint, and exhibit their mutual repulsion by their diverging, as shown in the figure. Hence we see the reason why rows of iron filings adhering to each other, when attracted by a magnet, keep separate from each other by the repulsive forces of the similar poles.

In the following form of the experiment given by Cavallo, the repulsion of both poles is well illustrated. If we suspend two short pieces of soft iron wire ns, ns by threads, they will hang in contact in a vertical position. If we now bring the north pole N of a magnet A to a moderate distance from the wires, they will recede from each other, as in fig. 13. The ends s, s, being made south poles by induction from the north pole N, will repel each other, and so will the north poles n, n. This separation of the wires will increase as the magnet A approaches nearer them; but there will be a particular distance at which the attractive force of N overcomes the repulsive force of the poles s, s, and causes the wires to converge, as in fig. 14, the north poles n, n still exhibiting their mutual repulsion.

The neutralisation or destruction of induced magnetism, by two equal and opposite magnetic actions, is shown in the following experiment, given by Dr Robison. If we take a forked piece of soft iron CDE, and suspend it by the branch D from the north pole of a magnet B, it will be magnetised by induction, and will carry a key at its lower end E, which will be a north pole. If we now apply to the other branch C the south pole S of another and equal magnet A, the key will instantly drop off. This obviously arises from the south pole S inducing a south pole at E, which either destroys or neutralizes the north polar magnetism previously induced by N.

It is very obvious, from the preceding experiments, that in regular magnets, with a north pole at one end and a south pole at the other, the two kinds of magnetism, north polar and south polar, are equally and regularly distributed, the one occupying one half of the magnet, and the other the other half. It is obvious also that each kind of magnetism has no intensity at the centre of the magnet, or its middle part, and that it increases, according to some regular law, from that point towards the two poles at the extremities of the magnet.

The first person who determined the law of distribution which we have now mentioned was M. Coulomb. The magnet which he employed for this purpose was a cylinder two lines in diameter, twenty-seven inches long, and its weight 1946 grains; and he ascertained the intensity of magnetism at each point, from its middle to its extremity, by observing the number of oscillations which a small magnetic needle performed in a minute, when it was made to oscillate before different points of the wire. He had previously observed the number of oscillations which the same needle performed out of the sphere of the magnet, and he considered the magnetic intensity as proportional to the difference of the squares of those two numbers of oscillations. The first needle which he employed was three lines in diameter and six lines long, and it was made of such a size, and of such hardness, that its magnetism should not be perceptibly altered by the action of the wire during the experiments; for if any change did take place, the results obtained at different points of the magnet could not be compared. The great length of twenty-seven inches was given to the magnet, in order that its remotest pole might be so distant from the needle that it would be unnecessary to make any allowance for its action upon the oscillations of the needle. In this way Coulomb obtained the following results:—

The distribution of the magnetism is exhibited in fig. 16, where AN is half of the magnet, and N its north

pole; and the ordinates to the curves represent the intensities in the preceding table.

These experiments were repeated by Coulomb, with magnets of the same shape and diameter, but of a less length, all other circumstances being unchanged, and he obtained nearly the same results for the three inches of the magnet nearest N; and hence he concluded, that what-

ever was the length of the magnet, provided it was greater than six or seven inches, the three inches at both its north and south poles gave always the same results as the twenty-seven inch magnet. From this point towards the centre the magnetism became weak and insensible in all of them; and in very long magnets he even found that the ordinates sometimes passed from positive to negative.

M. Biot has remarked that the curve of intensity, as determined by Coulomb, results from the combination of two logarithmic curves ACB, A'CB, which, setting out from each pole A, B of the magnet AB, would have their ordinates equal and in an opposite direction, as shown in fig. 17. The intensities calculated upon this supposition agree exactly with the observed results.

As Coulomb had examined the distribution of magnetism only in magnets of considerable size, M. Becquerel¹ was desirous of ascertaining if the law was observed in steel wires of a small diameter, such as $\backslash frac\{1\}\{100\}$th of a millimetre, or $\backslash frac\{1\}\{1000\}$th of an inch. In order to procure such wires, he encased a steel wire one millimetre in diameter in a cylinder of silver, and having drawn out the whole into a wire, the silver was removed by means of boiling mercury. He employed the method used by Coulomb in determining the law of distribution; but, on account of the fineness of the wires, and the weakness of the magnetism which they acquired, he was obliged to make some changes in the method. He obtained, however, the very same results as those given by Coulomb.

A number of interesting experiments on the distribution of magnetism have been made by M. Kupffer of Kasan,² by means of the method of Coulomb. He employed a flat and very narrow needle, twelve millimetres long, and he placed it at a horizontal distance of three decimetres from a cylindrical bar magnet of cast steel not tempered, 607 millimetres long and 12$\backslash frac\{1\}\{2\}$ millimetres thick. He began his experiments with magnets that possess a weak degree of magnetism. In magnetising them, he rubbed the steel bar perpendicularly on the north pole of a very strong artificial magnet, and he replaced the bar vertically before the needle, the north pole of the former being uppermost. He found that the south pole was stronger than the north pole, and that the point of indifference, or the neutral point, was nearer the stronger pole than the other. Upon reversing the magnet, the magnetic intensities of its different points increased, and the neutral point approached the middle of the magnet. These changes were produced successively, and the magnet did not attain its final state till it had remained some time in the same position. Kupffer observed, that whenever the magnetic intensities of the bar increased, the neutral point slowly approached the middle point; that this point was always nearer the stronger pole; that a bar magnetised vertically was always more powerful when its north pole was downwards; and that a bar magnetised by the method mentioned above was always strongest in the pole immediately produced by that of the magnet.

After detailing his observations with a bar magnetised to saturation, he proceeds to determine the influence exercised by the form of the extremities of the bar on the magnetic intensity, and on the position of the neutral point. A cylindrical bar of steel, cast but not tempered, having been rounded at one of its ends, and magnetised to saturation, was placed fourteen centimetres from a magnetic needle, and in the line of its direction. When its

¹ Ann. de Chimie, tom. xxii. p. 115; Becquerel, Traité Expérimental de l'Électricité et de Magnétisme, tom. i. p. 365.

² Ibid. tom. xxvi. p. 59.

General Properties of Magnetic Bodies. north pole was directed to the south, the force of the rounded north pole was 2.0319, and that of the south pole was 2.1558. In the opposite position of the bar, the magnetic force of the north pole was 2.2198, and that of the south pole 2.3006, the neutral point being in the middle.

The rounded end of the bar was now filed to a point, and made sharper and sharper in every successive experiment, after being each time magnetised to saturation. The force of the sharpened pole diminished with its acuteness. The neutral point receded always from this extremity.

Distribution of magnetism in the interior of magnets. Coulomb formed sixteen rectangular magnets out of the same piece of steel. Each was six inches long, nine and a half lines wide, and 382 grains in weight. They were annealed at a white heat, without being tempered, in order that he might be certain of having them always in the same state. He magnetised them all to saturation, and formed bundles with a certain number of them, similar poles being placed together. The magnets in each bundle were bound tightly together with a strong silk thread. Each bundle was then placed in a torsion balance, and placed 30° out of the magnetic meridian. The force of torsion necessary to retain it in this position was a measure of its magnetic intensity. The following were the forces or degrees of torsion necessary to keep the different bundles at rest.

Hence it follows that the magnetic force of each bundle increases in a ratio much less than that of the number of plates.

Coulomb next determined the magnetic state of each of the magnets composing the bundles of eight and sixteen magnets; and he found that the two outermost magnets, those which formed the surface of the bundles, had a much greater force than the rest.

The first had a force which measured.....46

The second.....48

And the mean force of all the rest was.....30

A single magnet had its directing force 82°, while for sixteen of them united the mean directing force of each was only 14°3, that is, about the sixth part of the other.

In examining the bundle of eight magnets by the method of oscillation, he found that the two outermost performed twenty oscillations in 90½ minutes, while all the rest performed the same number in from 211 to 278 nearly, showing the weakness of their magnetism. It is curious that the outermost but one had its poles reversed.

Coulomb also found that a bundle of magnets will take nearly the same degree of magnetism as a single magnet of the same shape and weight; which leads us to believe that, in magnets of one piece, the magnetism diminishes from the surface to the centre, as in the preceding bundles of magnets.

SECT. VII.—On the Effect of Division and Fracture in the Distribution of Magnetism.

Effects produced by breaking magnets. As no natural or artificial magnet has ever been seen with only one pole, or one kind of magnetism, it became interesting to determine experimentally the distribution of magnetism in a part of a magnet cut from its north or south extremity. This experiment has been often made,

both by cutting it through at the middle or neutral point, or by cutting or breaking off a portion from the end of it. If NS, for example, is a magnet, N its north and S its south pole, and ACB the curve representing the intensity of its magnetism; then, if we cut it through the middle C, each half ns, n's will be a complete magnet, with a north pole at n, and a south one at s, and their neutral points at c, c'; the curves at acb, ac'b, representing the distribution of their north and south polar magnetism, being similar to the curve ACB of the large magnet of which they are the halves.

When Epinus made this curious experiment, he did not divide the magnet in two, but he set two steel bars end to end, and magnetised them as one magnet, so that this compound magnet had its magnetism distributed as in a single bar, like NS, fig. 18. He then separated them, and found that each bar was a perfect magnet, with two poles. Dr Robison repeated this experiment successfully on some occasions; but he sometimes found indications of the compound magnet acting as two magnets. We are persuaded that this arose from an imperfect union of the two bars, and not from any defect in Epinus's experiment. The united ends of the bars should be ground together, so as to be kept in perfect contact, and preserved in this state by a powerful pressure during the time that they are magnetised. If thus be done, we have no doubt that they will act on iron filings, and throw them into curves, as if they were a single bar, and will, by examination with a fine needle, exhibit the same regular distribution of magnetism which takes place in the most perfect magnet.

Upon the separation of the magnets thus united, Epinus found that two poles were instantly developed in each half, but that the neutral points c, c', fig. 18, were nearer the interior poles s, n', or, what is the same thing, nearer the original neutral point C, than to n and s'. In the space of about a quarter of an hour it had, however, advanced nearer to the middle points c, c', and continued for some hours, and sometimes for days, to advance to these points, which it finally reached, thus completing the regular distribution of the two opposite magnetisms.

Some observations, but not very accurate ones, have been made on the division of magnets in the direction of their lengths. According to Dr Derham, the two portions sometimes have contrary, and sometimes the same poles, as when they were united. When one portion was much thinner than the other, the thinner portion had generally its poles reversed. This experiment does not possess much interest; for it can scarcely be doubted that, if we could divide a magnet in the direction of its length without any violence or concussion, each portion, whether thinner or thicker, would have, when separate, the same polarities as when combined. The experiment would be easily made by pressing two equal steel bars into close contact, magnetising them in this state, and then separating them.

A very remarkable analogy has been pointed out by Sir David Brewster, between the preceding results and those between which he has obtained with parallelpipeds of glass which received the doubly refracting structure by being quickly cooled on all their surfaces from a state of red heat. This change is analogous to that of temper in a magnet; and the effect of it is to produce a certain development of positive and negative double refraction throughout the whole of the parallelpipeds of glass. These phenomena will be minutely explained in our article on OPTICS; but we may

state at present, that the structure of the glass modifies the action of the ether which it contains, just as the structure of the tempered steel keeps the two magnetisms in an uncombined state. This is shown in fig. 19, where

AB is a thick plate of glass quickly cooled. The middle portion of it P has positive, and the external portions N, N, negative double refraction. The density of the ether in each of these portions varies according to a regular law; and the intensity of the doubly refracting force, at different points both of the positive and negative structures, is represented by a curve formed by the superposition of a straight line and a parabola. If we now cut the

parallelopiped of glass into two halves, through the dotted line AB, fig. 19, each half will have the same structure as the whole, as shown in fig. 20; the parts that were formerly positive being now negative, and vice versa; and the intensity of the doubly refracting force in each half will be represented by the ordinates of a curve formed by the superposition of a straight line and a parabola. This fact is in perfect analogy with the magnetic one, and there are many other remarkable points of resemblance which we have not space to describe at present.

SECT. VIII.—On Magnetic Figures.

In our article on ELECTRICITY we have given an account of the beautiful electrical figures discovered by M. Lichtenberg, and which form one of the most interesting popular experiments in that science. We are indebted to M. Haldat of Nancy for the analogous discovery of magnetic figures, which may be easily produced. For this purpose he employs plates of steel from eight to twelve inches square, and from one twentieth to one eighth of an inch thick. The plates which he used were of that kind of steel which is used for the manufacture of cuirasses, so that it did not require to be tempered, being sufficiently hard to preserve the magnetism communicated to it. Figures of any kind may be traced on the surface of the steel plate, either by one magnet or by several combined; and the best form for this purpose is that in which the poles are rounded. In this way we may write upon a steel plate the name of a friend, or sketch a flower or a figure, with the extremity of a magnet. If it is a south pole that we use, all the traces which it makes will have north polar magnetism; and if we shake steel filings upon the plate out of a gauze bag, the filings will arrange themselves in the empty spaces between the lines traced by the pole of the magnet, and thus represent in vacant steel the name which has been written, or the flower or figure which has been sketched. "These figures," says M. Haldat, "have a perfect resemblance to those which are formed on the surface of non-magnetic plates, viz. wood, card, glass, or paper, under which a magnet is placed. The resemblance between the

two sorts of figures, when the magnets and the parts magnetised have the same form, is not only exact in the whole figure, but even in the smallest details. The filings collect at the parts where the magnetism is most intense, they arrange themselves in pencils and radii, and form the same curves which we have represented in fig. 1, page 702. These curves, and pencils, and rays, so similar at the two poles of the same magnet, have such a resemblance that they do not allow us to distinguish the two parts from one another."

M. Haldat has likewise produced these curves by interposing between the tracing magnets and the steel plates solid non-magnetic bodies, such as cards, glass, and even metallic plates that are not ferruginous. This method of producing magnetism in the steel plate by induction gives the same figures; but, in order to be efficacious, the magnet must have its pole carried parallel to and at a small distance from the plate of steel, and must repeat its traces, in order that the magnetism may be sufficiently developed. For rectilinear figures, M. Haldat employs rules with grooves, which keep the motion and distance of the bar invariable; for curvilinear figures he interposes some thin and uniform plate, and he can vary the distinctness of the figures by varying the distance of the tracing pole of the magnet.

In sifting the iron filings upon the steel plate, a gentle vibration of the plate, by tapping its edge with the ring of a small key, will assist the filings in taking their proper places; but we must avoid such vibrations as will produce regular acoustic figures, unless we wish, as M. Haldat has found to be practicable, to unite the magnetic with the acoustic figures, which produces very interesting and varied forms.

M. Haldat has found that the magnetic figures will continue for six months. In order to remove the magnetism which produces them, he recommends the heating of the plate upon red-hot charcoal, till it is brought to the straw-yellow temperature. In order to render the repolishing of the plate unnecessary, M. Haldat tins it, and the temperature at which the tin melts, when it is required to efface the magnetism, indicates the necessary heat. M. Haldat employs also another method, which is perhaps the best. He places the steel plate upon a block of wood, and by repeated and violent blows of a wooden hammer he removes the magnetism of the plate, the figures gradually becoming weaker and weaker when the experiment is tried with it in different stages. The effect is often produced in three or four minutes.

As the figures traced on the steel are nothing more than magnets of different forms, and are surrounded on all sides with a substance capable of acquiring the magnetism which may be developed by communication, we might expect, as M. Haldat remarks, that this means of communication between the opposite poles of the magnets would bring them into a neutral state. This, however, is not the case, and the portion of the metal which surrounds the magnetic figure performs the part of the armature of a loadstone, and the magnetism is thus kept up. If the figure be a simple rectangle, like that of a bar-magnet, the state of the plate, examined with a small needle, is exactly the same as a bar-magnet, and the parts which surround this magnetic portion are in a neutral state, as if unconnected with the rectangular space; from which it follows that the magnetic virtue, which communicates itself so easily by influence, ceases to communicate itself between the continuous parts of a magnetisable body, of which one portion is magnetic, and the rest in a neutral state.

In carrying into effect the preceding method of making improvements on magnetic figures, a very great difficulty must be experienced in recollecting the invisible traces made by the pole of the magnet, so as to complete a regular figure or drawing. When the figures are made immediately, as M. Haldat ex-

presses it, that is, by the actual contact of the pole of the magnet, without any intermediate body, the best method would be to cover the plate of steel with the slightest coating of grease, and sift upon the surface, through a linen bag, some of the finest flour. The pole of the magnet, while tracing the figures on the steel, will remove the flour, and thus exhibit to the eye an accurate picture of what it has traced; and it will thus be easy to make the magnetic figures more distinct by repeating the traces with the magnet. The same thing may be done by putting an etching ground upon the steel plate, and tracing the figure as before. When the figure is completed, the coating of grease and flour, or the etching ground, must be removed previous to the application of the iron filings.

When the figures are to be produced mediately, or by the intervention of a non-magnetic substance, such as paper, card, wood, or glass, a fine dust may in like manner be laid upon the surface; but when the interposed substance will receive the mark of a pencil or sharp point, it would be preferable to attach to the cylindrical pole of the tracing magnet a very short point of a non-magnetic substance, which would make a visible mark on the paper, card, or wood, without strewing any fine dust on their surfaces. By the use of such a point, indeed, we may dispense altogether with the interposed substance, and communicate the magnetism by induction to the steel plate, in the very same way as if it had been done by the intervention of a non-magnetic plate whose thickness is equal to the length of the short point or tracer affixed to the pole of the magnet.

The magnetic figures might be rendered permanent by covering the steel plate either with a gummy or balsamic solution, which will indurate by exposure to the air; or with a coating of some easily melted substance, which becomes fixed at ordinary temperatures. If we sift the iron filings on the steel plate when covered with such a fluid, the filings will take their magnetic position round the traced lines, and will become fixed by the induration or solidification of the fluid coating.

CHAP. III.—ON THE MAGNETISM OF BODIES NOT FERRUGINOUS.

SECT. I.—On the Magnetism of Metals, Minerals, and other Bodies.

Iron was long regarded as the only body endowed with the property of acting and of being acted upon as a magnet; and though other metals and substances have been recently found to possess the same property, and though all substances whatever have been found by Coulomb to obey the power of a strong magnet, yet it is still a matter of doubt whether the magnetic effects thus produced are owing to a magnetism residing in the proper substance of the body, or are owing to a minute quantity of iron which enters into their composition.

The most magnetic metal next to iron is nickel. It receives and retains communicated magnetism longer than any other metal, and needles of nickel have a distinct polarity. These properties have been found in nickel after it has been repeatedly purified, though some authors have stated that they could not detect this property in certain specimens. A very decisive and instructive experiment on the magnetic qualities of nickel was made by M. Biot. He possessed a needle of nickel which had been purified by M. Thénard. It was 212 millimetres long, six broad, and 5.178 grains in weight. Having made a needle of steel of exactly the same dimensions, and which weighed 4.586

grains, he magnetised them both to saturation, and caused them to oscillate in the magnetic meridian. The nickel needle performed ten oscillations in eighty-seven seconds, and the steel one the same number in forty-five and a half seconds. As the shape of the needles was the same, the moments of their directive forces were directly as their weights, and inversely as the squares of eighty-seven seconds and forty-five and a half seconds, that is, as 0.3088 to 1, that is, the directive force of the needle of nickel was nearly one third of that of the steel needle. Now it is impossible to suppose that purified nickel could contain such a large proportion of iron as is necessary to produce such a degree of magnetic polarity, without its being easily recognised by the chemist; and M. Biot supposes that the magnetic power of the nickel might have been still farther increased by the means which are used to modify the coercive power of steel and iron.

A series of careful experiments were made by M. Cavallo, on the magnetism of brass when hammered. He found that brass, whether old or new, British or foreign, was made magnetic when placed between two pieces of card and hammered on an anvil with a common hammer; and that the magnetism thus imparted was always removed by making the brass red hot, and could be again communicated to it. Lest it might be supposed that ferruginous matter might pass to the brass through rents or openings in the card, he hardened a piece of brass by beating it between two large flints, using one piece as a hammer, and the other as an anvil. The hammered brass became magnetic, but not so strongly as before; which arose probably from the rough and irregular surfaces of the flints, which prevented the brass from being hardened as uniformly as it was with the steel hammer. The flints, before and after the experiment, did not possess the slightest magnetism.

The degree of magnetism communicated to brass by hammering is vaguely stated by Cavallo to have been such "as to attract either pole of the needle from about a quarter of an inch distance." The following are the conclusions which M. Cavallo has drawn from these and other experiments:

"1st, That most brass becomes magnetic by hammering, and loses its magnetism by annealing or softening in the fire, or at least its magnetism is so far weakened by it, as afterwards to be only discoverable when set to float on quicksilver.

"2d, The acquired magnetism is not owing to particles of iron or steel imparted to the brass by the tools employed, or naturally mixed with the brass.

"3d, Those pieces of brass which have that property, retain it without any diminution after a great number of repeated trials, viz. after having been repeatedly hardened and softened.

"4th, A large piece of brass has generally a magnetic power somewhat stronger than a smaller piece, and the flat surface of the piece draws the needle more forcibly than the edge or corner of it.

"5th, If only one end of a large piece of brass be hammered, then that end alone will disturb the magnetic needle, and not the rest.

"6th, The magnetic power which brass acquires by hammering has a certain limit, beyond which it cannot be increased by farther hammering. This limit is various in pieces of brass of different thicknesses, and likewise of different qualities.

"7th, Though there are some pieces of brass which have not the power of being rendered magnetic by hammering, yet all the pieces of magnetic brass that I have tried lose their magnetism, so as no longer to affect the needle, by

being made red hot, excepting indeed when some pieces of iron are concealed in them, which sometimes occurs; but in this case the piece of brass, after having been made red hot and cooled, will attract the needle more forcibly with one part of its surface than with the rest of it; and hence, by turning the piece of brass about, and presenting every part of it successively to the suspended magnetic needle, one may easily discover in what part of it the iron is lodged.

"8th, In the course of my experiments on the magnetism of brass, I have twice observed the following remarkable circumstance: A piece of brass which had the property of becoming magnetic by hammering, and of losing the magnetism by softening, having been left in the fire till it was partially melted, I found upon trial that it had lost the property of becoming magnetic by hammering; but having been afterwards fairly fused in a crucible, it thereby acquired the property it had originally, viz. that of becoming magnetic by hammering.

"9th, I have likewise often observed, that a long continuance of a fire so strong as to be little short of melting hot, generally diminishes, and sometimes quite destroys, the property of becoming magnetic in brass. At the same time the texture of the metal is considerably altered, becoming what some workmen call rotten. From this it appears, that the property of becoming magnetic in brass by hammering, is rather owing to some particular configuration of its parts, than to the admixture of any iron; which is confirmed still farther by observing that Dutch plate brass (which is made, not by melting the copper, but by keeping it in a strong degree of heat whilst surrounded by lapis calaminaris) also possesses that property, at least all the pieces of it which I have tried have that property. From these observations it follows, that when brass is to be used for the construction of instruments wherein a magnetic needle is concerned, as dipping needles, variation compasses, &c. &c. the brass should be either left quite soft, or it should be chosen of such a sort as will not be made magnetic by hammering, which sort, however, does not occur very frequently."

These judicious suggestions of M. Cavallo respecting the condition of the brass parts of azimuth compasses were not attended to as they ought, and we have no doubt that various grave errors have arisen from their neglect. Many examples have recently occurred, in which the errors were detected; and it is now the invariable practice of well-informed instrument-makers to reject hammered brass bowls for compasses, and to use those which are cast and turned for the purpose.

M. Cavallo and others have observed, that cobalt, zinc, copper, and bismuth, as well as their ores, are attracted by the magnet and antimony when gently heated. Minerals which are not metallic are almost all acted upon by the magnet, particularly where they have experienced the action of fire. The pure earths, and particularly silix, are found to have the same property. Among minerals, the following table shows those which are attracted and those which are not attracted by the magnet; but we place little faith in their accuracy.

Some accurate experiments have been made on mica by M. Biot. The chemical composition and optical structure of different varieties of this mineral vary greatly. M. Biot

examined particularly mica from Siberia and mica from Zinwald in Bohemia. Though both were highly pellucid, yet chemical re-agents indicated in each the existence of oxide of iron. In the Bohemian mica it was greatest, and, according to an accurate analysis by Vauquelin, amounted to 20 per cent. Before the Siberian mica was analysed, M. Biot tried their magnetic properties. He cut out of each, thin rectangular plates of the same form, which he subdivided into smaller similar pieces, and having united them in a bundle, he suspended each bundle by a silk fibre, and caused each bundle to oscillate in succession between the poles of two strong magnets. The bundle of Zinwald mica performed twelve oscillations in fifty-five seconds, and that of the Siberian mica only seven in the same time. Hence the magnetic powers of the two micas were as 6.8 to 20, the ratio of 49 and 14 to the squares of the number of oscillations. If the oxide of iron, then, be the cause of their magnetic virtue, it should exist in the above proportions of 6.8 to 20; and as it was found to be 20 per cent. in the Zinwald mica, it ought to be 6.8 in the Siberian. It is very remarkable that the result of Vauquelin's analysis gave exactly this per centage of the oxide of iron, though it was not known to M. Biot till his experiment had been made.

The existence of magnetism in brass, while there was Magnetism of Bodies not Ferruginous. not the least trace of it either in the copper or zinc of which it is composed, led philosophers to investigate the effects produced by the union of different metals, or by their combined metals. Iron itself is a simple chemical body. Steel is a combination of iron and carbon. The loadstone is a combination of iron and oxygen; and as no magnetism is found either in carbon or oxygen, we are naturally led to believe, as M. Pouillet has remarked, that the magnetic fluid resides in the substance of the iron, and that it is carried with the atoms of that metal into all the chemical combinations which they form. We may therefore expect to find magnetic properties more or less developed in all ferruginous bodies, whether the iron be an accidental or an essential ingredient; and indeed cast iron, plumbago, and the oxides and sulphurets of iron, exert a sensible action on the magnetic needle.

These views, however, are not in unison with facts which seem to have been well ascertained. Dr Matthew Young found, that the smallest admixture of antimony was capable of destroying the polarity of iron; and M. Seebeck states, that an alloy of one part of iron and four parts of antimony was so completely destitute of magnetic action, that, even when it was put into rotation, it exerted no power over the magnetic needle. The magnetic qualities of nickel also are destroyed by a mixture with it of other metals. Chenevix found that a very small proportion of arsenic deprived a mass of nickel which had previously exhibited a strong magnetic power, of the whole of its magnetism; and Dr Seebeck found that an alloy of two parts of copper with one of nickel was entirely devoid of magnetism, and on this account he recommends it as well suited for the manufacture of compass boxes. On the other hand, Mr Hatchet ascertained, that when a large proportion of carbon, or sulphur, or phosphorus, was combined with iron, the iron was enabled fully to receive and retain its magnetic properties; but he at the same time found that there was a limit beyond which an excess of any of these three substances rendered the compound wholly incapable of receiving magnetism.

Animal and vegetable substances, after combination, are said to be attracted by the magnet. The flesh, and particularly blood, are acted upon more powerfully than other parts, and bone less powerfully. Burned vegetables have the same property, and also soot and atmospheric dust; and M. Cavallo has maintained, that brisk chemical effervescence acted upon the magnetic needle.

SECT. II.—Account of the Experiments of Coulomb, Becquerel, Arago, and Seebeck, on the Existence of Universal Magnetism.

These various experiments on the magnetic power of so many classes of bodies, differing essentially in their composition, and in many of which it could not be reasonably supposed that iron existed, led some philosophers to believe that almost all substances gave indications of magnetism. M. Cavallo announced this opinion, but Mr Bennett questioned the accuracy of the experiments, and ascribed the movements observed in the needle to the agitation of the air in the receiver, arising from changes of temperature produced by the proximity of the observer's body, or from other causes.

Coulomb's experiments. It was not therefore till 1802, that the supposition of universal magnetism was put to the test of rigorous experiment. The apparatus which Coulomb employed for this purpose is shown in fig. 21,

Fig. 21.

where AA is a glass receiver perforated at its top, and having a tube AB, with a cork B, which could be raised and lowered with facility. Through this cork passed a rod u of wood or metal, to which was attached a silk fibre, which suspended a ring of very fine paper, on which the small needle ns (about the third of an inch long and $\backslash frac\{1\}\{10\}$th thick) was placed. The receiver was then placed so as to enclose the opposite poles N, S of the powerful magnets M, M, each formed of four bars of steel tempered to a white heat. Each bar was seventeen inches long, three fifths of an inch wide, and one sixth of an inch thick, each bundle of four bars being one and three eighths of an inch wide, and one third of an inch thick. The distance NS of their poles was eight tenths of an inch. In making the experiments, the rod u was turned till the needle ns was removed from the influence of the magnets; and after the number of its oscillations was observed, the rod u was turned till the needle descended between the poles N, S of the magnets, when the number of oscillations of the needle was again counted, or the time in which a given number of oscillations was performed. If the needle performed the same number of oscillations in the same time, whether it oscillated between the poles N, S, or beyond their influence, it is obvious that the magnets exercised no power over them; but this was never the case, and Coulomb found that all substances whatever, when formed into small needles, turned themselves in the direction of the poles N, S, and, after a few oscillations, finally settled in that position. When these bodies were moved a very little way out of their position of equilibrium, they immediately began to oscillate round it, the oscillations being always performed more rapidly in the presence of the magnets than when they were removed out of their influence. Gold, silver, glass, wood, and all substances, whether organic or inorganic, thus obey the power of the magnets. Hence we cannot avoid the conclusion, either that all bodies are susceptible of magnetism, or that they contain minute quantities of iron, or other magnetic metals, which give them that susceptibility. M. Biot does not consider this alternative so inevitable as it appears, and throws out the conjecture, that the action may not be magnetic, but may

be owing to some small force similar or analogous to the electrical forces developed by the simple contact of heterogeneous bodies. This no doubt might be, if there was any contact; and, in the absence of any reasons whatever for ascribing the observed effects to another cause, we cannot but rest between the alternative opinions above mentioned, giving a preference to that which ascribes the phenomenon to the existence in all bodies of a slight susceptibility to magnetic action.

This opinion derives considerable support from the experiments made by Coulomb on the comparative magnetic susceptibilities of cylindrical needles of gold, silver, lead, copper, and tin, which had been purified with the greatest care by MM. Sage and Guyton, and the results of which we have already given in our history of magnetism. M. Coulomb made a number of experiments on the effects experienced by needles of white wax, containing different proportions of iron filings, and he found that the intensities of the action which they experienced when oscillating between two magnets, was proportional to the absolute quantities of iron which they contained, the distribution and chemical state of the ferruginous particles being the same.

Since the time of Coulomb, methods different from his have been employed in developing magnetism in all bodies whatever. In order to detect small quantities of iron in minerals, M. Hauy employed the process of what he calls double magnetism. For this purpose, he placed a small bar-magnet in the direction of the needle, and in the same horizontal plane, the two similar poles being placed towards each other. The magnet being now brought slowly towards the needle, the latter deviates from the direction of the magnetic meridian, and takes a position perpendicular to it; an effect arising from the combined action of the poles of the magnet and the earth upon the magnetism of the needle. In this position, a very feeble magnetic action is sufficient to make the needle turn round and place its south pole opposite the north pole of the needle.

When the magnet is above the plane of the needle, and their opposite poles placed near each other, the needle does not change its direction while the point of suspension is beyond the bar, and at a suitable distance; but it is not so when the distance changes, for it tends continually to place itself perpendicular to the line of the poles.

This important subject has been investigated by M. Becquerel, who obtained the following results.¹ His bar-magnet consisted of six united bars, each eight decimetres long and two centimetres broad. The needle was placed at different heights within and without the bar, and he sought to determine for each height the horizontal distance from the point of suspension (which is always in the line of the poles) to the nearest extremity of the needle, in order that its direction might be perpendicular to that line. The results were as follow:

Hence it appears, that when the centre of suspension is

¹ Traité Exp. de l'Electricité, 5e. tom. ii. p. 367.

above the bar, the perpendicular position is obtained by increasing the vertical and diminishing the horizontal distance; and that both these distances are increased while the centre of suspension is below the bar; and the direction of the deviation depends on accidental causes, and is often determined by the simple motion of the apparatus.

When M. Becquerel substituted for his magnetic needle a needle of soft iron, the results were exactly the same, differing only in their intensity. We come now to the original part of M. Becquerel's inquiry. Instead of a needle he used a small paper case filled with deutoxide of iron, or a mixture of deutoxide and tritoxide. With the former the effects were the same as with the steel needle; but it was different with the latter, in which one part of deutoxide was mixed with thirty parts of tritoxide.

If the centre of suspension be placed as near as possible to the north pole of the bar-magnet, and in the line of the poles, the paper case will take immediately a direction perpendicular to this line, instead of one coincident with it, as a soft iron needle would have done. If we put it out of this direction, it will return to it by a series of oscillations, whose velocity depends on the quantity of the deutoxide. From this it follows, that all the south polar magnetism of the paper case is situated on the side of it next the bar-magnet, while the north polar magnetism is on the other side, as may be exhibited by carrying a small magnetic needle along the paper case. Such a distribution of magnetism is impossible in soft iron or tempered steel.

If the centre of suspension be above the bar, the paper case will deviate from the position which it had at first, and tend to place itself in the direction of the line of the poles; an effect quite opposite to that produced by a steel or iron needle. The following were the experimental results:

The transverse magnetism acquired by the paper case is permanent for some time, however small may be the proportion of deutoxide which it contains.

M. Becquerel next filled the paper case with very pure tritoxide, obtained by calcining nitrate of iron. The effect was much weaker than before. When the point of suspension was very near one of the extremities of the bar, the paper case still placed itself in a position perpendicular to the line of the poles; but if this point was placed above or below the bar, changing at the same time the vertical distance, the paper case deviated from its primitive direction, without, however, taking a direction perpendicular to that which it commonly takes when the centre of suspension is very near the extremity. It might be possible, M. Becquerel thinks, to attain the perpendicular direction by employing much stronger magnets. The following were the experimental results:—

Whenever the tritoxide contains the smallest quantity of the deutoxide, the velocity of the oscillations increases very powerfully. If, for example, we take two paper cases, one filled with tritoxide, and the other with tritoxide mixed with one thirtieth of the deutoxide, the first will perform twelve oscillations in thirty seconds, round a direction perpendicular to the line of the poles, while the other will execute twenty-five in the same time. Hence we may by this means readily determine the quantity of the deutoxide of iron contained in the tritoxide.

M. Becquerel next employed needles of wood, gum-lac, With and other substances, which have still a feeble magnetism than the tritoxide of iron. He placed a needle of white wood, n s, four centimetres long and two millimetres in diameter, above the interval between the opposite poles of two bar-magnets, as in fig. 21, the distance between N and S being three or four millimetres. The point of suspension was as near as possible to N S. The needle placed itself perpendicular to the line of the poles N, S, in place of the position observed by Coulomb, coincident with N S. It comport itself therefore like the mixture of deutoxide and tritoxide of iron, or like the tritoxide alone. But if we separate gradually the extremities N, S of the bars, the wooden needle will place itself in the line N S, joining the poles, as shown in the figure. The deviations were as follow:

When the bars are very close, and the needle in the perpendicular position, if we draw it out of this position, and keep it some instants in the direction of this line, it will remain there; but the smallest motion will cause it to return into its primitive direction, which it takes in preference to any other.

If we use only one bar-magnet, and place the wooden needle precisely opposite one of its poles, and as near as possible to the end of the bar, it will still direct itself perpendicularly to it; but if, while the point of suspension remains always in this line, we advance it within the bar, the needle will deviate from its direction, without, however, reaching the position of 90°, as will be seen from the following results:

Beyond ten millimetres the deviations increase insensibly and irregularly, so that they cannot be measured.

General conclusion. From these interesting experiments, M. Becquerel concludes that the magnetic effects produced by a strong bar-magnet upon a magnetic needle, or one of soft iron, differ essentially from those which take place in all bodies where the magnetism is very weak. In the former, whatever be their positions and directions, the magnetism is always distributed in the direction of their length, to the exclusion of every other direction; whereas in the tritoxide of iron, wood, and gum-lac, it is distributed in a direction which depends on the distance of the body from the poles of the magnet, so that the distribution varies with the direction which the magnet causes these needles to take, in virtue of the action which it exercises over them.

Discoveries of M. Arago. The universal prevalence of magnetism in all bodies whatever has been established by a beautiful discovery of M. Arago. This distinguished philosopher conceived the idea of studying the oscillations of a magnetic needle when placed above or near any body whatever. Having suspended a magnetic needle above metal, or even water, and caused it to deviate a certain number of degrees from its position, it began, when left to itself, to oscillate in arcs of less and less amplitude, as if it had been placed in a resisting medium; and, what was peculiarly curious in these experiments, this diminution in the amplitude of the oscillations did not alter the number of oscillations which were performed in a given time. The following were some of M. Arago's experiments with water, ice, and glass, the semi-amplitude of the oscillations being at the instant 43°. The distance of the water from the needle

was.....0.65 millim.

The amplitude lost 10° in.....30 oscillations.

When the distance was.....52.2 millim.

A loss of 10° of amplitude required.....60 oscillations.

That is, the number of oscillations required to diminish the amplitude 10° was twice as great when the distance of the needle from the water was 52.2 millimetres, as when it was 0.65.

By placing the same needle upon ice, M. Arago obtained the following results:

By placing another needle near a plate of crown glass, he obtained the following results:

Plates of metal afforded M. Arago similar results; but he nevertheless observed that those metals which act with more energy than glass, wood, &c. have a mode of action different from that of these substances. From all these results, it is manifest that all bodies, when placed near a magnetic needle in a state of oscillation, exercise over it an action, the effect of which is to diminish the amplitude of its oscillations, without altering their number; and hence the doctrine of the universal prevalence of magnetism in all bodies derives a new confirmation.

When Dr Seebeck of Berlin heard of the discovery of

M. Arago, he made a magnetic needle two and an eighth inches long oscillate at a distance of three lines above plates of various bodies, and counted the number of oscillations which were required in each case to reduce the amplitude from 45° to 10°.

Dr Seebeck found, that in alloying magnetic with non-magnetic substances, he formed compounds which exercised no action on the magnetic needle. The alloys which had particularly this singular property were those consisting of four parts of antimony and one of iron, or two parts of copper and one of nickel. In these cases the magnetism of the two ingredients must have been neutralized by their opposite actions.

CHAP. IV.—ON THE DEVELOPMENT OF MAGNETISM IN ALL BODIES BY ROTATION.

When M. Arago was engaged in the experiments described in the preceding chapter, the idea occurred to him of trying if the magnetic needle would be dragged along by the rotatory plates which had the power of diminishing the amplitude of its oscillation. This happy conjecture was immediately confirmed by experiment, and one of the most beautiful discoveries added to the science of magnetism.

The apparatus which he used for this purpose is shown in Plate CCCXXV. fig. 3, where H is a clock made of copper, with the exception of two or three pivots, which are of steel. It is supported on a tripod stand TT, which can be levelled by screws S, S at the end of its three feet; and the object of it is to give a rapid rotatory motion by a vertical

Fig. 22.

axis, on which is fitted a piece a, b, c, fig. 4, with three branches, upon which the revolving discs are to be placed. These discs are perforated at their centre by a small hole which receives the prolongation of the axis of rotation, and they are kept upon the branches a, b, c, by the pressure of a screw. Wings w, w (fig. 4), which can be inclined at any angle, are applied for the purpose of retarding the velocity of the discs. A plate PP, with an opening in its centre a little larger than the diameter of the discs, rests upon the table TT, and a sheet of paper ff, shown in fig. 22 (which is an enlarged view of that part of the apparatus)

is pasted to the lower face of PP. A glass receiver RR rests upon the upper face of PP, and within it is suspended the magnetic needle aa', by a fibre of silk attached to the axis and button mn, by which the needle can be raised or depressed. A weight W gives motion to the clock, and a hand indicates upon the dial-plate the number of revolutions performed by the disc in a given time.

When a disc of copper was placed on the support a, b, c, Plate CCCXXV. fig. 4, as shown at PP, fig. 22, and the copper made to revolve beneath the needle aa', with the sheet of paper ff intervening, the needle aa' is drawn out of the magnetic meridian the instant that the copper begins to revolve, and with a degree of force proportional to the velocity of rotation. As the force with which the needle is dragged from its place is opposed to the magnetic action of the earth, which tends to keep the needle in the magnetic meridian, the needle will take a position of equilibrium depending on the ratio of these forces. When the motion of the copper disc, however, is very rapid, the magnetism of the earth is overpowered by that of the revolving plate, and the needle does not stop, but continues to turn. The action of the revolving disc decreases in proportion as the distance of the needle from the plate PP is increased, the velocity being the same; so that if the motion of the needle be continuous when the two bodies are separated only by a sheet of paper, the needle will take a fixed position by increasing its distance from the plate; and its deviation from the magnetic meridian becomes less and less as it is removed to a greater height above the disc. When the plates have portions cut out in the direction of their radii, their action on the needle is diminished.

In trying plates of various metals, M. Arago found the results so dependent on the alloy which the metals contained, that he did not publish the results which he obtained. He devoted his attention to the determination of the directions of the force which is developed in the revolving discs, and for this purpose he sought the components of this force in the direction of three lines parallel to three co-ordinate planes perpendicular to each other. The component perpendicular to the plate he found to be a repulsive force, which may be rendered sensible by means of a very long magnet suspended by a thread vertically to the extremity of the arms of a balance kept in equilibrium by a weight at the other extremity. The moment that the plate begins to revolve, the magnet is repelled, and the beam of the balance inclines to the other side. The second component is horizontal and perpendicular to a vertical plane which contains the radius abutting against the projection of the pole of the needle. This is the force which gives a motion of rotation to the needle, and it acts in the direction of a tangent to the circle. The third component is parallel to the radius which abuts against the projection of the pole of the needle. It may be determined with a dipping needle placed vertically, so that its axis of rotation is continued in a plane perpendicular to one of the radii of the disc. A similar needle placed at the centre of the disc experiences no action. There is also a second point, nearer the margin than the centre, where a needle experiences no change in its position; but between these points the lower pole is constantly attract-

ed towards the centre, while it is repelled beyond that point.

No sooner were M. Arago's experiments announced to the Institute, which was done at the sitting of the 7th March 1825, than philosophers in every part of Europe repeated them, and succeeded in adding several important facts to those discovered by M. Arago. MM. Babbage, Herschel, Barlow, Nobili, Baccelli, Christie, and MM. Prevost and Colladon, took a prominent part in these researches. The results obtained by Messrs Babbage and Herschel were the most important, and the experiments were made in a manner different from those of M. Arago. A horse-shoe magnet, which lifted twenty pounds, was made to revolve rapidly round its axis of symmetry, placed vertically, with its poles uppermost. A circular disc of copper, six inches in diameter and $\backslash frac\{1\}\{2\}$th of an inch thick, was suspended above the revolving magnet. As soon as the rotation of the magnet commenced, the copper began to turn in the same direction, at first slowly, but afterwards with an increasing velocity. When the magnet was made to turn in the opposite direction, the disc of copper changed the direction of its motion also, and exhibited the same phenomena. Metallic plates, ten inches in diameter and half an inch thick, when interposed between the magnet and the copper disc, did not sensibly modify the results, as M. Arago had observed. Glass produced no effect, but a sheet of tin-plate iron diminished greatly the influence of the magnet, while two such plates almost destroyed it. They also found that a disc of copper ten inches in diameter, and half an inch thick, and revolving with a velocity of seven revolutions in a second, did not communicate any motion to a similar disc freely suspended above it.

In comparing the influence of different metals, each disc had the same diameter and the same velocity; and the following were the results which were obtained by this and another method of observation.

The second method of observation by which the results in the last column were obtained was more expeditious than the first. Portions of different bodies of the same form and dimensions were suspended above a revolving magnet, and the time of successive oscillations and the points of equilibrium were observed.

Our authors next sought to determine the effect produced by a solution of continuity in the metallic disc upon which the revolving magnet acted. For this purpose a disc of lead twelve inches in diameter and one tenth of an inch thick was suspended at a given distance from a horse-shoe magnet revolving with the ordinary rapidity, first in its entire state, and afterwards in the state shown in the annexed figures, the black lines in the direction of the radii be-

Developing the planes where the lead was cut through. The accelerating forces, represented by $\backslash frac\{s\}\{t^2\}$, where $s$ is the number of revolutions, and $t$ the time employed, are as follow:

Effects similar, but differing in degree, were obtained with other metals. With soft tinned iron the cutting produced a very slight diminution of effect, whilst in copper the same operation reduced the accelerating force in the ratio of five to one.

Messrs Babbage and Herschel next tried the effect of filling up the cuts with other metals. A light upper disc, suspended at a given distance above a revolving magnet, performed six revolutions in 54¹/₈. When it was cut as in fig. 27, its magnetic action was so weakened that it took 121¹/₃ to perform six revolutions. When the eight open radial spaces were filled up with tin, its magnetic action was restored to such a degree that it made six revolutions in 57¹/₃. This fact is very interesting, as tin has less than half the energy of copper. The following results were obtained from other experiments, the numbers representing the accelerating forces or the magnetic energies developed in the plates.

Law of the force. In determining the law of the force in relation to the distance, Messrs Babbage and Herschel found it to vary between the ratio of the square and the cube of the distance. Mr Christie found, that when the revolving disc was thick and the needle delicate, the force which produced the deviation of the needle increased directly as the velocity of rotation, and inversely as the fourth power of the distance. MM. Prevost and Colladon found that the angles of deviation, and not their sines, increased in the direct ratio of the velocity, at least within certain limits; and that the sines of the angles of deviation were in the inverse ratio of the two and a half power of the distance.¹

Experiments of M. Haldat. M. Haldat made some interesting experiments on this subject. He found that every needle, however weak was its magnetism, obeyed the action of the revolving disc; but that this action disappeared entirely when its polarity disappeared. He found it impossible to magnetise needles by the action of the revolving disc, however rapid; and, in consequence of ascribing this effect to the want of coercive power, he employed discs of iron and steel, both soft and hardened.

A disc of soft iron acted with more energy than one of copper, and with the same velocity it dragged the needle twice the distance that a disc of brass did. Iron strongly hammered acted like soft iron, and was unable to give polarity to a steel needle. But a disc of untempered steel one twenty-fifth of an inch thick did not produce any appreciable effect on the magnetic needle, which, after a few irregular oscillations, maintained its ordinary position of equilibrium. Hence our author concluded that the force which acted upon it was in the inverse ratio of the coercive force. M. Haldat also found that discs in a state of incandescence exercised the same action as those at the ordinary temperature.

of Mr Barlow. We have already seen, in our historical detail, that about six months previous to the announcement of M. Arago's discoveries, Mr Barlow had announced to the Royal Society

of London the result of a series of experiments on the magnetic effects produced by iron in rotation. Having found that an iron ball performing 640 revolutions in a minute caused a magnetic needle to deviate several degrees, and to take a fixed position during the continuance of the motion; that the needle deviated in an opposite direction when the motion of the ball was reversed; that there were certain positions in which a bomb twelve inches in diameter, moved by a steam-engine, occasioned no deviation in the needle; that in some positions the deviation was in one direction, and in other positions in another; and that the deviation varied between 0° and 80°; he constructed a regular apparatus for determining the laws of these phenomena, and in which the iron which formed part of it should not influence the results. This apparatus is shown in Plate CCCXXV. fig. 2, where S is an iron sphere, made to revolve on a horizontal axis AB, by means of two wheels, like an electrical machine, their diameters being as six to one, so as to perform 720 revolutions in a minute. A table LM was placed near the sphere, for holding the needle, so that the needle could be placed in any position, either above or below the sphere. The table LM being brought to the height of the axis AB, the needle was placed successively in different positions round the sphere. The influence of the earth's magnetism on the needle being destroyed or neutralised by the action of a magnet properly placed for this purpose, and shown at NS standing vertically, Mr Barlow found, that whatever was the azimuth of the needle, its north pole approached the sphere S when the upper part of the sphere was moving towards the needle, and that its south pole approached the sphere when the upper part moved from the needle.

Having placed the axis of rotation sometimes in the magnetic meridian, sometimes in the direction of east and west, and sometimes in intermediate positions, he found, that whatever was the direction of the axis of rotation, the needle being always a tangent to the sphere, the north end of the needle was attracted when the sphere moved towards the needle, and repelled when its motion was from the needle. When the needle was carried round the revolving sphere in the semicircle, where the motion was directed towards the needle, its north extremity approached the sphere, and in the other semicircle it receded from it. The points where the sphere exercised upon it no action were at the two extremities of the axis, and those where the effect was a maximum were at the two extremities of an axis at right angles to this. In this case the direction of the needle was towards the centre of the ball.

The different positions of the needle are shown in fig. 28, where s is the sphere, ab its axis of rotation, and

ed its equator. The lines $ns$, $ns\text{'}$, &c. show the primitive position of the needle, and the dotted lines $n\text{'}s\text{'}$, $n\text{'}s\text{'}\text{'}$, &c. those assumed by it when the motion is made from $c$ to $d$. The effects are reversed when the motion is made from $d$ to $c$.

If we carry the needle, when perfectly neutralised, round the sphere, and parallel to its axis, it has a tendency to place itself at right angles to the axis, and takes opposite directions at certain parts of the circle. If, for example, the axis be in the magnetic meridian, and the motion directed from the west to the east point of the horizon, the needle will direct itself to the west, and will do the same at all points between the horizon and an altitude of $60^\backslash circ$. Beyond this the north end will direct itself to the east till it has passed the zenith $30^\backslash circ$ to the west; and then from his point to the west horizon, the north extremity will direct itself to the west, and similar changes will take place under the sphere. The same effects are produced, whatever be the direction of the axis and that of motion.

When a magnetic needle not neutralised is placed in different positions round the sphere whose axis is in the magnetic direction, the effects produced are as shown in fig. 29, where AB is the axis of rotation, the black lines

representing the natural deviations of the needle, and the dotted ones those which it assumes when the sphere is in motion. Beginning at the point A, if the motion be from left to right, that is, from west to east, the needle moves from $n$ to $n\text{'}$ in the same direction till it arrives at $30^\backslash circ$. It then remains in its natural direction. The needle moves in a contrary direction from right to left at $60^\backslash circ$, $75^\backslash circ$, and at $90^\backslash circ$.

Mr Barlow was next desirous of ascertaining the different effects produced by a solid and a hollow ball of iron, and with this view he put in motion a solid ball 7.87 inches in diameter, and weighing sixty-eight pounds, and also a hollow sphere of iron, weighing only about thirty-four pounds. Both of them performed 640 revolutions in a minute, and the following were the average results:—

When the two balls were at rest, the difference of their action was nothing.

Mr Barlow's paper on rotation was communicated to the Royal Society on the 14th April 1825, and on the 20th Mr Christie communicated one On the Magnetism of Iron arising from its Rotation. Mr Christie's experiments were made with circular plates of iron put in motion by an ingenious piece of machinery, by which he could make the plate revolve in every possible plane in reference to the magnetic meridian. From a great body of well-devised experiments, he obtained the following general law of the deviation due to rotation, so that the direction of the rotation being given, he could tell the direction of the deviation. This law we must give in his own words.

"I refer the deviations of the horizontal needle to the

deviations of magnetic particles in the direction of the dip, or to those of a dipping needle passing through its centre; so that, in whatever direction this imaginary dipping needle would deviate by the action of the iron, the horizontal needle would deviate in such a manner as to be in the same vertical plane with it: thus, when the north end of the horizontal needle deviates towards the west, and consequently the south end towards the east, I consider that it has obeyed the deviation of the axis of the imaginary dipping needle, whose northern extremity has deviated towards the west, and its southern towards the east; so that the western side of the equator of this dipping needle has deviated towards the south pole of the sphere, and its eastern side towards the north pole. It would follow from this, that if the north and south sides of the equator of the dipping needle (referring to these points in the horizon) deviated towards the poles, no corresponding deviations would be observed in the horizontal needle; the effect, in this case, taking place in the meridian, would only be observable in the angle which the dipping needle made with the horizon. As it is not my intention at present to advance any hypothesis on the subject, I wish this to be considered only as a method of connecting all the phenomena under one general view. Assuming it then for this purpose, it will be found that the deviations of the horizontal needle due to rotation are always such as would be produced by the sides of the equator of this imaginary dipping needle deviating in directions contrary to the directions in which the edges of the plate move, that edge of the plate nearest to either edge of the equator producing the greatest effect on it."

From another set of experiments, Mr Christie also found that the effect produced on the iron by its rotation is permanent so long as the plate remains stationary; that it is independent of friction; that it is so far independent of velocity, that the iron can scarcely be moved so slowly that the whole effect shall not be produced; and that the whole effect is produced by making it perform one fourth of a revolution. After Mr Christie had discovered these peculiar effects, he exhibited some of the phenomena to Mr Barlow, who conceived that the effect would be increased by rapid rotation, and who was thus led to make the experiments of which we have already given an account; but the phenomena differ essentially from those observed by Mr Christie, the former being temporary and dependent on velocity, while the latter are permanent, and independent of the rapidity of rotation.

In comparing the magnetic forces produced by rapid and slow rotation, Mr Christie found that the forces exerted on the needle during the rapid rotation of the plate are always in the same direction as the forces which are derived from the slowest rotation, and which continue to act after the rotation has ceased; but that the former forces are greater than the latter. From a mean of all the observations, the forces seem to be in the ratio of seventeen to thirteen, or very nearly of three to two. Hence Mr Christie conceives that the polarising of the iron in the same direction will account for the phenomena in both cases; but that the intensity of the polarity during the rapid rotation is greater than of that which appears to be permanent after the rotation, whether slow or rapid, has ceased; and that the phenomena observed during rapid rotation are such as should be expected from what have been described as arising from rotation, without regard to its velocity.

We have already seen that Messrs Babbage and Herschel interposed plates of various metals between the remnants of a revolving magnet and the copper disc, and found no perceptible effect to be produced. Mr Snow Harris, however,

Influence of Heat on Magnetism. has recently shown that several substances not supposed to contain iron have the power of intercepting the influence of a revolving magnet. A circular magnetic disc being delicately balanced on a fine central point by means of a rim of lead, was put into a state of rotation on a small agate cup, at the rate of 600 revolutions in a minute; and a light ring of tinned iron, also finely balanced on a central pivot, was placed immediately over it, at about four inches distance, by means of a thin plate of glass, on which its pivot rested. When the ring of tinned iron began to move slowly on its pivot by the influence of the magnet revolving below, a large mass of copper, about three inches thick, and consisting of plates a foot square, was carefully interposed between the magnet and the iron ring. The interposition of the copper soon sensibly diminished the motion of the iron disc, and at length arrested it altogether. On again withdrawing the copper, the motion of the disc was restored; and the same effects were repeatedly obtained. In this experiment both the magnet and the disc were enclosed by glass shades, and supported on a firm base.

The same effects were produced by a mass of silver and zinc; but when their thickness was considerably diminished by removing the central plates, the motion of the disc was not impeded. A very great thickness of lead was necessary to stop the disc, in consequence, as Mr Harris supposes, of its magnetic energy being so much less than that of copper.

CHAP. V.—ON THE INFLUENCE OF HEAT ON MAGNETISM.

Influence of heat on magnetism. This interesting department of magnetism divides itself into three parts: 1st, On the effect of heat on the development of free magnetism; 2dly, on the anomalous attraction observed during the bright red and red heats; and, 3dly, on the effect of heat on the distribution of magnetism in magnets.

SECT. I.—On the Effect of Heat on the development of Magnetism in Cast and Malleable Iron.

In cast and malleable iron. In the course of his experiments on the relative magnetic powers of different kinds of iron and steel, already given in the history of magnetism, Mr Barlow was led to the conclusion, that the harder the metal was, the less it exhibited of a magnetic quality; a result which was highly favourable to the hypothesis, that the cohesive power of hardened steel not only prevented the entire development of its magnetism, but also the re-combination of the two kinds of magnetism when they were displaced by the action of a powerful magnet. With the view of establishing this hypothesis, Mr Barlow found it necessary to ascertain whether these different kinds of iron and steel would exhibit the same magnetic powers when reduced to the same degree of softness, which could only be done by heating them in a furnace, and trying their magnetic qualities in that state.

Having procured a bar of soft iron twenty-five inches long and an inch and a quarter square, and a cast-iron one of nearly the same dimensions, he inclined the bars in the direction of the dip; and having placed a magnetic needle nearly on a level with the upper extremity, and at the distance of six inches from it, he observed the deviations produced by the bars in different states of heat. Thus,

These experiments were often repeated with the same results. It deserves to be remarked as a singular result, that cast iron is decidedly inferior in its action when cold, and when hot possesses a superior power to malleable iron.

Mr Barlow now compared malleable iron with soft and hard shear steel. The bars were twenty-four inches long and an inch and a quarter square, and the following were the results:

These experiments establish the curious fact of the total destruction of the magnetic virtue by a white heat; and also the no less important one, that every kind of iron or steel has a greater capacity for developing its magnetism when softened by fire than when cold.

SECT. II.—On the Anomalous Attraction observed in Cast and Malleable Iron during the Bright Red and Red Heats.

In pursuing the preceding researches, Mr Barlow was Anomaled to observe a remarkable anomaly in the action of the magnetism of iron at the red heat. When iron brought to a white heat has wholly lost its power, it again acquires, as it passes at a red heat, into the bright red and red, a magnetic power; but, what is truly strange, its power is attractive for the south end of the needle; that is, if the north pole of the needle was attracted when the iron was cold, the south end will be attracted when the iron is at a bright red heat.

In order to investigate this subject thoroughly, Mr Barlow made a very extensive series of experiments with four different bars, each twenty-five inches long and an inch and a quarter square, two of them being of cast and two of malleable iron. He used also other two bars, one of cast and one of malleable iron, of the same dimensions, which were kept as standards to determine the quantity of cold attraction. The time employed in each experiment was a quarter of an hour: the white heat generally continued about three minutes when the negative attraction commenced. This attraction lasted about two minutes more, when the usual attraction began. This sometimes reached its maximum with great rapidity, but at other times it increased very gradually. The following table contains the results of Mr Barlow's experiments. The letters CB denote the cast-iron bar, and MB the malleable-iron bar; and the sign + indicates when the ordinary attraction of the iron takes place; and — the anomalous or negative attraction.

Influence of Heat on Magnetism. One of the most remarkable results of these experiments is, that the anomalous action of the bar between a bright-red and blood-red heat increases as we raise the bar above the needle, and becomes a maximum at the centre of the bar; whereas at low temperatures the action of a bar of iron under the very same circumstances goes on diminishing as the bar is raised, and becomes a minimum at the centre. When the needle is placed at the height of the centre of the bar, when heated to produce the anomalous effect, the smallest displacement is sufficient to change the sign and the quantity of the deviation.

Anomalous action of red-hot iron. Mr Barlow made some experiments with a twenty-four pound ball of iron, but the heat was too intense to allow any very accurate observations to be made. The results, however, were as follow:

No effect whatever was produced on the needle by heated bars of copper.

In order to explain the singularly anomalous action above described, Mr Barlow supposes, that during the cooling of the bars, the extremities where this cooling is most rapid become magnetic before the rest of the metal, and that there results from this a complex action. He allows, however, that this supposition does not sufficiently explain all the observed phenomena. The explanation given by Professor Kupffer is more satisfactory. In weakly magnetised bars the points of indifference are very near the extremities; but in Mr Barlow's experiment the magnetism communicated to soft iron by the earth being nothing at a bright-red, and reaching its maximum at a blood-red heat, there is probably formed a point of indifference at each extremity of the bar. If this is the case, the raising of the bar places the needle in front of points which are beyond the point of indifference, and which possess a magnetism opposite to that of the extremity itself. At the first epoch of cooling, this opposite magnetism should even increase to a certain point, and the more as we approach the middle of the bar; but in proportion as the magnetism of the bar increases, the point of indifference will approach its middle, and the phenomena of ordinary attraction re-appear.

SECT. III.—On the Effects of Heat on the Distribution of Magnetism in Magnets.

M. Coulomb was the first philosopher who investigated the important subject of the influence of heat on the distribution of magnetism, in needles and magnets.¹ He took a bar of steel 162 millimetres long, fourteen wide, and weighing eighty-two grammes. This bar was brought to a cherry-red heat, about 900°, and cooled slowly in the air, so as to have no temper. It was then magnetised to saturation at the temperature of about 12° Reaumur. In this state the time of making ten oscillations was observed. Its temperature was again raised successively so many degrees, and, after being cooled, the time of performing ten oscillations was again measured. The following were the results:

Hence it is obvious that the magnetic intensity of the bar diminishes rapidly as its temperature is raised.

From another set of experiments Coulomb concludes that the tempering of a bar previous to its being magnetised has no influence until the heat at which it is tempered becomes about 750°. When the tempering is at 900°, the bar will take double the magnetic force that it did at 12°; the ratio of the time of ten oscillations being 63" and 93", the squares of which, to which the magnetic forces are proportional, are nearly as one to two.

After the magnet had received the hardest temper at 950°, it was magnetised to saturation. When it was brought back, by annealing, to lower temperatures, and again magnetised, the effects were as follow:

Hence we see that the progressive rise of temperature alters the magnetism of the bar much more when it had been first tempered towards 900° and cooled slowly, than when it had been first put into the annealed state.

When in the annealed state the bar is exposed only to temperatures below 500°, it receives its original force by being again magnetised; but in the state of temper it is not so. Each rise of temperature diminishes perceptibly the magnetic force which the bar can receive from being again magnetised. This is shown in the following table:

The bar, therefore, attained its maximum energy when tempered at 900°. It then performed ten oscillations in 63". Setting out from this term, the directive force diminished in proportion as the annealing temperature increased. At 900° the bar, magnetised anew to saturation, employed 93" to make ten oscillations, as in the first experiments, which ought to have been the case, as it was brought back to the same state of perfect annealing from which it was at first taken.

The bars used by Coulomb were about thirty times as long as they were thick, and with such bars similar results were always obtained. But this was not the case with larger bars. Having taken a steel wire 326 millimetres long and four in diameter, he tempered it at 820°, magnetised it to saturation, and determined its directive force. He repeated the same operation after having annealed it at different temperatures, and the following were the results:

¹ Biot, Traité de Physique, tom. iii. p. 106.

Here the hard temper gives the weakest directive force, as we have already seen in the preceding experiments. The maximum effect takes place when the wire is annealed at about 450°, and this result is a general one for all wires and plates whose length is very great relative to their width.

This result seems to be connected with a particular mode of distribution of free magnetism. In bars whose length does not exceed thirty times their diameter, there is never more than one magnetic centre, which is in the middle of the bar. But when the ratio of the length to the breadth is greater than this, magnetising it produces always three centres, one in the middle of the bar, and the other two at equal distances from its extremities. This effect is shown in fig. 30, and in fig. 31. The effect of

placing such a magnet in iron filings is shown in fig. 31; and in fig. 30 the curve of the intensities is seen to cross the

axis between the centre C and the poles A, B, the two new centres being at C' and C''.

M. Coulomb found that the distance C'A, C'B of the two new centres from the extremities of the magnet varies with the temper; and the annealing heat is shown by the following results obtained with a wire-magnet 326 millimetres long:—

In proportion as the annealing heat increases, the two centres C, C' approach each other, and are re-united with the centre C at a cherry-red heat. This last result is very important in the construction of compass-needles. Coulomb regards the dark red as the best annealing heat for needles or bars whose length exceeds thirty times their thickness, and the state of hard temper for those where the ratio between the length and the thickness is less.

It is extremely probable, as M. Biot supposes, that when magnets are larger in proportion to their thickness than those used in the preceding experiments, a greater number of centres will be produced, were it from no other cause than the re-action of the plate upon itself.

In examining the influence of temperature on magnets, Professor Kupffer began by examining the effect of heat in altering the distribution of magnetism. For this purpose he took a parallelopiped of tempered steel, 503 millimetres long, 15½ wide, and 5 thick, and having magnetised it to saturation, he heated it, and allowing it to cool slowly, he submitted it to examination. The magnet was placed vertically, as at a'b', and a needle suspended by a silk fibre was made to oscillate before any point ab, in order to determine the intensity of magnetism at that point. In this way he obtained the following results:—

Hence it appears that the bar heated to 80° had not only lost much of its magnetic virtue, but that this loss was not uniform along the whole length of the bar, being greater towards the extremities a', b' than towards the middle. This may be easily seen by dividing the forces in columns 2 and 3 by one another, when it will appear that the quotients are greater for points nearest a' and b'.

M. Kupffer next studied the changes which take place in the forces of a magnetic needle when its temperature is increasing, the heat being kept constant during the time of each experiment. He used a cylindrical needle of fused steel, 0.57 millimetre long, and 2.395 grammes in weight. The temperature increased from 8½° to 18°, and the deviation of 300 oscillations varied from 777½ to 781, which shows, as Coulomb had previously observed, that the magnetic force diminished as the temperature increased. By another series of experiments, M. Kupffer has shown, that the diurnal variations of the needle did not at all affect these results.

In order to determine the law of the decrease of the magnetic forces at temperatures above 30°, he made a needle oscillate above a newly magnetised bar 0.5 millimetre long, the opposite poles looking to each other, and he raised the temperature of the bar from 13° to 80°, by means of hot water. At 13°, the needle, when by itself, performed 300 oscillations in 762", and in presence of the magnet it lost only 429". When brought to the temperatures in the table, and then cooled, the oscillations of the needle were observed.

Hence it appears that the magnetic force diminishes with heat, and that a magnet at the temperature of 13°, when heated to 80°, and then cooled to 13°, does not resume its first magnetic state, which is diminished. The cause of this is, that in cooling slowly the bar loses a part of its temper, and consequently a part of its free magnetism.

From these observations M. Kupffer deduces the following formulae, which represent with great accuracy the influence of temperature, viz.

where c is the force exerted by the earth on the oscillating needle.

x, the number of seconds in which n oscillations are made.

F, the force exerted by the bar at the same temperature.

x', the number of seconds which the same needle employs at the temperature t.

$p$, the intensity of the magnetic force of the bar at $13^\{\backslash circ\}$; and

$q$, the intensity of the same force at $80^\{\backslash circ\}$.

M. Kupffer proceeded to examine the effects which the heating of only one pole of a magnet produced upon the distribution of its magnetism. With this view he placed a magnet parallel to a needle suspended horizontally, the dissimilar poles being placed opposite to each other. The needle will not remain in the magnetic meridian unless its neutral point and that of the bar are in the same line perpendicular to the needle. This position may be found by a few trials. When by shifting the magnet its neutral point approaches one of the poles of the needle, and always in the same direction, this pole will be repelled, because the opposite pole of the needle is more strongly attracted by the corresponding pole of the magnet, which is brought near it, while the other is removed from it.

Let us now heat the north pole of the magnet; the south pole of the needle opposite to it will be soon attracted. Hence it is clear that the point of indifference, or neutral point, has receded from the heated pole, or from the pole whose magnetic intensity is diminished, which agrees with the law of Coulomb. The following results were obtained with a magnet 0.5 millimetre long, the needle being placed in the magnetic meridian:—

When the magnet had cooled slowly, the needle returned gradually to its first position; but it never recovered it entirely. By the earth's action only, the needle performed 50 oscillations in 207".

When a bar of soft iron was substituted for the magnet, and placed in the magnetic meridian, it was magnetised by the action of the earth. When one of its extremities was heated, the pole of the needle next it was attracted instead of repelled, the neutral point having approached to the heated extremity, in place of receding from it as formerly. Hence the magnetic force of the iron was increased by heat.

In examining the diurnal deviations of the needle when under the influence of magnets, Mr Christie conceived that the deviations might be partly the effect of changes in the temperature of the magnets; and he therefore undertook a series of experiments to determine the precise effects of changes of temperature on magnets. By a peculiar apparatus and a method of observation which our limits will not allow us to introduce, he obtained the following results:—

By discussing these results, Mr Christie concludes that 0.1226 is the mean variation of the intensity of the

magnets, from a change in their temperature of $1^\{\backslash circ\}$ between the temperatures of $59^\{\backslash circ\}.05$ and $77^\{\backslash circ\}.65$. Taking the case where the intensity at $60^\{\backslash circ\}$ was 218, the change for $1^\{\backslash circ\}$ was 0.123; and supposing the intensity to be 1, each degree will produce a diminution of 0.000564.

From a number of experiments made with a balance of torsion, the needle being suspended by a brass wire $\backslash frac\{1\}\{100\}$th of an inch in diameter, Mr Christie ascertained the following facts:

1. Beginning with $-3^\{\backslash circ\}$ of Fahrenheit, up to $127^\{\backslash circ\}$, the intensity of magnets decreased as their temperature increased.

2. With a certain increment of temperature the decrement of intensity is not constant at all temperatures, but increases as the temperature increases.

3. From a temperature of about $80^\{\backslash circ\}$, the intensity decreases very rapidly as the temperature increases; so that if, up to this temperature, the differences of the decrements are nearly constant, the differences in the decrements also increase.

4. Beyond the temperature of $100^\{\backslash circ\}$ a portion of the power of the magnet is permanently destroyed.

5. On a change of temperature, the most considerable portion of the effect on the intensity of the magnet is produced instantaneously, showing that the magnetic power resides on or very near the surface.

6. The effects produced on soft iron by changes of temperature are directly the reverse of those produced on a magnet; an increase of temperature causing an increase in the magnetic power of the iron. This was observed between the temperatures $50^\{\backslash circ\}$ and $100^\{\backslash circ\}$ Fahr. Mr Christie regards this fact as a strong argument against the hypothesis, that the action of iron upon the needle arises from the polarity which it receives from the earth.¹

CHAP. VI.—ON THE ACTION OF SIMPLE IRON BODIES ON THE MAGNETIC NEEDLE.

Mr Barlow undertook the interesting experiments which we are about to describe, with the view of discovering some method of correcting the local attraction of a ship's guns and other iron on the compass-needle.

His attention was first directed to the action of solid spheres and spherical shells of iron; but he afterwards applied the principles to which he was led, to the action of bars and plates of simple iron, and to irregular masses. We shall therefore lay before our readers, in three separate sections, the results of his experiments and theoretical investigations respecting these two forms of unmagnetised iron.

SECT. I.—On the Action of Spheres and Spherical Shells of Iron on the Magnetic Needle.

The earliest experiments of Mr Barlow, by which he was led to some of the properties of iron spheres, were made in an imperfect manner; but the phenomena were such as to induce him to construct an apparatus capable of affording him the most accurate measures of the deviation of the needle.

The apparatus which he finally employed is shown in Plate CCCXXV. fig. 6. It consists of a large and steady round table TT, having its surface horizontal. The points of the compass are laid down on its upper face. In its centre is a hole $18\backslash frac\{1\}\{2\}$ inches wide, for receiving an eighteen-inch or smaller iron shell or ball B, which is suspended above it by pulleys pp, which allow the observer to raise

¹ See Philosophical Transactions, 1825, p. 1-65.

lower it at pleasure. When a diameter of this table is brought into the magnetic meridian, Mr Barlow found, that in whatever part of the table a compass-needle was placed, except in the meridian, the south end of the needle was drawn to the ball when the latter was wholly above the table, as in the figure. The attraction increases as the ball descends, till at a certain point it is a maximum, and then decreases again towards zero as the ball descends farther. Hence it is clear, that there is all round the ball a position where the attraction is zero; and it was easily observed that these points lay in a plane inclined to the horizon. In this way Mr Barlow established his fundamental principle, that

In every ball or shell of plain unmagnetised iron there exists a plane of no attraction, or a plane in which the iron produces no disturbance on the needle, and which plane inclines from north to south (magnetic), forming with the horizon an angle equal to the complement of the dip.

This line on the surface of the ball may be called the magnetic equator; and, taking the meridian which passes through the east and west points as the first, Mr Barlow was able to designate every part of his iron sphere by the magnetic longitude and latitude of that point.

Mr Barlow therefore proceeded to determine whether the quantity and deviation at any point could be expressed by any function of the latitude and longitude of that point, when the mass of the ball and the distance of the needle from it were constant. From these experiments, which it is unnecessary to detail, he found,

That the tangent of the deviation of the needle is proportional to the rectangle of the sine and cosine of the latitude, and to the sine of the double latitude.

By observing the deviations throughout a great circle in which the longitude was constant, and also in a circle in which the latitude and longitude were variable, he found the following law,—

That the tangent of the deviation of the needle is nearly proportional to the sine of the double latitude multiplied by the cosine of the longitude.

By comparing the constant numbers obtained on the preceding principles at different distances from the centre of the sphere, Mr Barlow found,

That the tangent of the deviation is inversely proportional to the cube of the distance.

The remaining object of Mr Barlow's inquiry was a very interesting one, namely, to determine the law of the deviation as dependent on the mass of the iron ball by the action of which it was produced. The result was equally new and unexpected. He found,

That the tangent of the deviation was directly proportional to the cube of the diameter of the ball or shell; but that it is all wholly independent of the mass, being the same in quantity whatever be the thickness of the metal, provided only that it exceed one twentieth of an inch.

Hence it follows, that the entire magnetic power of an iron sphere resides on the surface, and is independent of the solidity.

Mr Barlow was so much surprised at this result, that he constructed a ten-inch shell of tin plate and another of iron plate, the former weighing forty-three ounces and the latter forty-five ounces, and he found that the power of neither was so great as that of the solid ball of the same diameter, but approached to it in the ratio of two to three. As the thickness of the iron in these shells was at an average about one thirtieth of an inch, Mr Barlow concluded that the magnetic fluid requires a certain thickness of metal, exceeding one thirtieth of an inch, in order effectually to develope itself, and act with its maximum energy.

This important result was some time afterwards verified by Captain Kater, with three cylinders, one of soft iron, and one tenth of an inch thick; another of what is

called chest-plate, 0.185 of an inch thick; and the third solid. The deviations produced by these three cylinders, when reduced to the same extent of surface, were 141, 184, and 187, thus proving that the cylinder whose thickness was only 0.185, or between one fifth and one sixth of an inch thick, had the same magnetic power as a solid cylinder of iron. The distribution of magnetism on the surface of magnetic bodies presents us with another interesting analogy between the magnetic and electric fluids; and it deserves our particular notice, that in the results obtained by Mr Barlow, the action of the sphere is related to the centre of its mass, and not to the poles of its magnetic equator.

Mr Barlow next proceeds to the investigation of analytical formulae which shall exhibit the action of iron spheres upon a magnetic needle. In this inquiry he sets out with the established experimental fact already mentioned, that the entire magnetic power of an iron sphere resides on the surface, and is independent of the solidity; and he proceeds on the following hypothesis.

1. Magnetic phenomena are due to the existence of two fluids in a greater or less degree of combination, and such that the particles of the same fluid repel, and those of an opposite nature attract, each other.

2. These fluids in iron bodies exist naturally in a state of combination and equilibrium till, that state is disturbed by some exciting cause.

3. But if a body already magnetic, i. e. one in which the fluids are held in a state of separation, be brought within the vicinity of a mass of iron, such as is supposed above, the concentrated action of each fluid in the magnetised body will act upon the latent fluids in the quiescent body, by repelling those of the same, and attracting those of the contrary kind, and thus impress upon the latter a temporary state of magnetic action, which will remain only while the two bodies maintain their respective situations.

4. The quantity of action impressed upon the iron body will depend, 1st, upon the intensity of the exciting magnet; 2dly, upon the capacity of the quiescent body for magnetism, or the quantity of those fluids contained in it; and, 3dly, upon the cohesive power of the iron; which latter quality determines the depth to which the exciting magnet is able to disengage the two fluids.

The above embraces every case, namely, of any magnet, natural or artificial, developing the magnetism in any given iron body; but the displacement occasioned by the magnetic action of the earth, or spheres of iron, is more limited in its results, and more susceptible of correct mathematical investigation.

5. In this case, for instance, we may suppose the action to take place on every particle of the mass in lines parallel to each other, and corresponding in direction with the dipping needle; also, that every particle is at the same distance from the centre of the disturbing force, and consequently that the displacement in each particle is equal also.

6. For the sake of illustration, let ABED represent a sphere of iron in its non-magnetic or quiescent state, and let CM be the line on which the terrestrial magnetism is exerted from a centre of action M, which is at such a distance that the diameter of the sphere is inconsiderable in comparison with it; then every particle on its surface, and to a certain distance within it, will be acted upon by equal powers, and in directions parallel to each other, whereby the fluids

The diagram, labeled Fig. 33, depicts a sphere with its center marked as C. A line segment CM is drawn from the center C to a point M outside the sphere, representing the center of action for terrestrial magnetism. The sphere's surface is represented by a circle with points A, B, E, and D marked around its circumference. A line segment AB is drawn through the center C, representing a diameter. The diagram illustrates the geometry used to analyze the magnetic action on the sphere.

Action of Simple Iron Bodies on the Magnetic Needle.

in the quiescent body, before in a state of combination, will be separated in each particle; and the two fluids may now therefore be conceived to form two spherical shells $AeBd$, $Ae\text{'}Bd\text{'}$, whose centres of action will be $e$, $e\text{'}$, their distances from each other being greater or less, according to the circumstances stated in No. 4.

Professor Barlow on the action of iron spheres.

7. Therefore, in computing the action of such a mass of iron, in its temporary state of magnetism, upon a distant particle of magnetic fluid, Mr Barlow refers it to these centres, and assumes that the law of action in this, as in other cases of emanating forces, is inversely as the squares of the distance.

By means of this hypothesis Mr Barlow arrives at the following formula for the deviation $\backslash Delta$ of a horizontal needle.

where $r$ = radius of the iron spheres;

$d$ = the distance of the needle from the centre of the spheres;

$\backslash lambda$ = the complement of the magnetic latitude;

$l$ = the complement of the magnetic longitude;

$\backslash delta$ = the dip of the needle; and

$\backslash frac\{C\}\{M\}\; =\; 1.0539$ a constant quantity for cast-iron balls

and shells, of every diameter, and for all distances and positions.

From this formula it necessarily follows,—

1. That though the development of the magnetism of the spheres takes place by the hypothesis only at the surface, yet the effect, as shown by the tangent of the deviation, is proportional to the cube of the diameter.

2. That the tangent of deviation is inversely as the cube of the distance.

3. That the tangent of the deviation is proportional to the sine of the double latitude and cosine of the longitude, the latter being extended from the east and west points.

These are the very laws which Mr Barlow had deduced from experiment, and he has established the correctness of his formula by comparing it with a great body of experiments made by himself and Mr Christie, and also with observations on the dipping needle.

SECT. II.—On the Action of Simple Iron Bars and Plates on the Magnetic Needle.

As spherical bodies possess the peculiar property of having their centre of attraction in the centre of the mass, the former becomes a fixed point, whatever be the distance of the magnetic needle. As this is not the case, however, with bodies of other forms, such as bars and plates, Mr Barlow was desirous of ascertaining whether, in these cases also, the magnetic attraction of the body could be referred to the action of two centres indefinitely near to each other in the general centre of attraction of the surface of the body, viz. that point into which, if all the matter of the surface were collected, its action on the centre of the needle would be the same as the action of the whole body in its natural form.

In pursuance of this plan, he supposes AB to be a bar of iron, and C the place of the needle, and, letting CD fall perpendicular on AB, he joins AC, mC, BC. He then finds the following expression for

the deviation, $\backslash text\{tan.\; \}\; \backslash Delta\; =\; A\; \backslash frac\{mn\; \backslash cos.\; l\}\{(m^2\; +\; n^2)^\{\backslash frac\{1\}\{2\}\}\}$, A

being a constant quantity, $l$ the longitude, $m$ the force in the direction DC, and $n$ the force in DA. In the experiments with which Mr Barlow proposed to compare this formula, the needle was placed due east and west of the bar, the longitude of its position was zero, and

hence $\backslash cos.\; l\; =\; 1$. The formula, therefore, becomes

ever may be the distance of the needle or its position, provided its longitude be zero. The following experiments were made by Mr Charles Bonnycastle, with a bar twenty-four inches long and an inch and a quarter square, inclined in the direction of the dipping needle. The magnetic needle was placed to the east and west of the bar, first opposite to its centre $m$, and then at every three inches from the centre to the extremities, at the distance of twelve and sixteen inches from the axis of the bar. The following were the results.

Fig. 34.

These results Mr Barlow justly regards as a further proof of the accuracy of the principles upon which his hypothesis is founded, and of his general deduction that the action of plain unmagnetised iron on a compass needle may be referred to two poles indefinitely near to each other in the common centre of attraction of the surface of the body.

Mr Bonnycastle performed another series of experiments with a plate of malleable iron twelve inches square and half an inch thick, and he obtained results almost equally accordant with Mr Barlow's hypothesis.

SECT. III.—On the Action of Irregular Masses of Iron on the Magnetic Needle.

Mr Barlow was next desirous of ascertaining if the same law which applied to spheres, bars, and plates, was true in irregular masses of iron, such as a 24-pounder gun; an experiment peculiarly applicable to the object he had in view. He found that the plane of no attraction existed in the most irregular masses of iron, and the agreement between the observed deviations produced by the gun, and those calculated by his formula, was such as to satisfy him that

the same laws applied to irregular as to regular masses of iron; and he was thus furnished with the means of computing the local attraction of a ship's guns upon the compass under all circumstances, and in all parts of the world.

These views have been strikingly confirmed by several ingenious observations, made, without knowing of Mr Barlow's labours, by Mr Lecount of the navy, with bars, handspikes, mast rings, and various other iron bodies, from which he concluded "that a plane or circle held east and west (magnetic), and at right angles to the direction of the dipping needle, divides the north from the south magnetic effluvia, each lying on that side to which the dipping needle points; and by referring the position of all iron bodies to this plane, the plane of section shall divide it into two into north and south polarity, provided it be of uniform thickness, or, if not, the section must be drawn through its centre of (gravity) attraction."

MAP. VII.—ON THE INFLUENCE OF MAGNETISM ON CHEMICAL ACTION.

An opinion had long prevailed among philosophers that the phenomena of magnetism and electricity had a similar origin; and hence various observers had been led, previous to the discovery of electro-magnetism by Oersted, to inquire if any actions of a chemical nature could be produced by magnetism.

The German philosopher Ritter was the earliest and the most active of these inquirers. He maintained that a magnetic wire, combined with another wire not magnetised, produced contractions in a frog, the south pole of the wire-magnet producing stronger contractions than the unmagnetised wire; and as he had constantly observed that the metals most susceptible of excitation excited the strongest contractions, he concluded that the south pole of a magnet has a greater affinity for oxygen than simple iron, and the north pole a less affinity. Hence he was led to confirm these views by means of several chemical reagents. He placed a magnetised wire upon pieces of glass in an earthenware dish containing weak nitric acid, when he found that the south pole was more corroded by the acid than the other, and was soon encircled with a deposition of oxygen greater than that at the other pole. In another experiment he took two flasks filled with tincture of turnsol, in one of which he placed the two south poles of two wire-magnets, and in the other the north poles of two similar magnets. In the last flask the oxidation of the wires was much greater than in the first.

The difference in the oxidation of the south pole was exhibited by Ritter in another way. He took three small and equal bottles filled either with pure or slightly acidulated water, and having placed in one the south pole of a wire-magnet, in another the north pole, and in the third the extremity of an unmagnetised wire of the same length, he observed that the south pole first began to deposit oxide, the unmagnetised wire next, and the north pole last. In order to exclude the access of air, the surface of the water should be covered with very fresh oil of almonds; and as light accelerates oxidation, none of the bottles should be more exposed to the sun than the rest. In support of this last observation, Ritter exposed two iron wires to the sun when placed in water, and having covered one of the bottles with black paper, he found that the wire in the uncovered bottle was oxidated more rapidly than the other.

Ritter repeated the preceding experiment with the three bottles containing an infusion of litmus in place of acidulated water. The south pole reddened the infusion most,

the unmagnetic wire less, and the north pole least of all. A week is required to produce a distinct effect; and in order even to effect this, Ritter found it necessary to add as much acetic acid as would incline the infusion to red without completely changing its colour.

The following experiment of Ritter, if correctly repeated, establishes the same result. We shall give it nearly in his own words: "Sixteen magnetic wires, of equal size and power, were placed in six vessels, all equally full of a mixture of one part nitric acid and thirty-six parts water, in the following manner: In the first glass were placed two wires, one with the north pole immersed in the fluid, the other with the south, and not more than half a line asunder; in the second, the same, but the wires an inch and three fourths apart; in the third and fourth were each three wires, with the south poles of all immersed, but their distances in the two glasses different, as in the first and second; in the fifth and sixth were wires similarly arranged, but with the north poles immersed. Different quantities of oxide were gradually deposited, and, to express the whole in a few words, we will call the south pole S, the north pole N, their greater distance $g$, and their less $p$, and we will express the order of oxidations as follows: $SNg\; >\; SNp\; >\; 3Sp\; >\; 3Sg\; >\; 3Np\; >\; 3Ng$. On the nineteenth day it was observed that the loss of fluid by evaporation had not been equal in all the vessels, but took place in the inverse order of the oxidations. All the magnetic wires were weakened in power; $NSg$ least, $NSp$ more; of the wires $3Sp$, two had lost less power than the third; and in like manner $3Sg$, $3Np$, $3Ng$, had each two left more powerful than the third; the strongest were equal to $NSg$."

The next experiments on this subject were made by M. Muschman, professor of chemistry in the university of Christiania, who endeavoured to ascertain the effect of the earth's magnetism on the precipitation of silver. In his chemical course in 1817, when he was desirous of explaining the chemical theory of the tree of Diana, he took a tube like a syphon, and poured mercury into it, which accordingly occupied the lower part of the two branches: above the mercury he poured a strong solution of nitrate of silver. He then placed the two branches of the syphon so that the plane passing through them was in the magnetic meridian, and after standing a few seconds, the silver began to precipitate itself with its natural lustre; but it accumulated itself particularly in the northern branch of the syphon, while that which was less copiously precipitated in the other branch had a less brilliant lustre, and was mixed with the mercurial salt deposited from the solution. M. Muschman and Professor Hansteen repeated this experiment in an improved form with the very same result. On this occasion they used simultaneously two syphons prepared in the same manner, the one being placed in the direction of north and south, and the other in that of east and west. The silver began to precipitate itself in the direction of north and south, and it particularly raised itself in the north branch with a lustre more brilliant than in the south one; whereas in the syphon whose plane lay east and west, no change had taken place even at the end of twelve hours. Hence the two Norwegian philosophers concluded, with some reason, that the magnetism of the earth had an influence on the precipitation of silver from a solution of its nitrate; and M. Muschman inferred, from the experiment, the identity of galvanism and magnetism. He regarded every dissolution as the result of a galvanic effect, the precipitated metal carrying off the electricity set at liberty, and carrying itself, in order to be disengaged, to the place where it could find the opposite electricity, which was the north pole. M. Muschman considered this hypothesis confirmed by

Laws of Magnetic Forces, &c. the geological fact, that at Königsberg silver was found in the metallic form, stretching from north to south; and the presence of the silver is always indicated by a certain quantity of pyrites and blendes. Hence he conceived that the silver had been insensibly united to sulphur, and that by the effect of the earth's magnetism alone it had been carried towards the copper and the zinc.

Experiments of Fresnel; M. Fresnel made a series of experiments with the view of decomposing water by the magnet. He proposed to produce an electric current in an electro-magnetic helix enclosing a bar-magnet covered with silk. The two ends of the wire were plunged in slightly acidulated water, and he observed very decided effects; but there were so many anomalies in the result, which he could not explain, that he abandoned the inquiry. He was particularly struck with the fact, that the wire which should be the positive one was strongly oxidated, whilst the other extremity preserved its metallic lustre during a whole week. The negative extremity was covered with a saline deposit, which he conjectured to be sulphate of lime, and which he supposed had protected the wire from oxidation.

of Erdman. M. Erdman, after a very elaborate inquiry into the effects of magnets as chemical agents, came to the conclusion that the observed phenomena were due to the influence of other causes, which had not been sufficiently guarded against.

A curious fact, connected perhaps with the class of phenomena under our observation, was noticed by M. Lebaillif. He observed that the poles of a magnetic needle delicately suspended were repelled by pieces of antimony or bismuth that were brought near them.

CHAP. VIII.—ON THE LAWS OF THE MAGNETIC FORCES, THE MUTUAL ACTION OF MAGNETS, AND MAGNETIC CURVES.

SECT. I.—On the Law of the Magnetic Force.

Law of the magnetic force. In our history of magnetism we have given very full details of the various attempts which were made by philosophers to determine the law according to which the intensity of the attractive and repulsive power of magnets varied with the distance at which these forces were exerted. Like all other laws, an approach to the discovery of it had been made by various philosophers; but the merit of its perfect establishment undoubtedly belongs to Dr Robison and Coulomb, the last of whom placed it beyond the reach of doubt. The difficulties which were to be overcome in this inquiry arose from the invariable co-existence of two opposite polarities in each of the two bodies whose mutual action was under examination; and this difficulty was increased from these polarities not being concentrated in particular points, but diffused in an unequal degree over each half of the magnet and the needle.

Researches of Coulomb. In this delicate inquiry Coulomb employed two methods. In the first he suspended a magnetic needle by a silk fibre, and when it was in the magnetic meridian, he presented to it at different distances another magnetic needle, and determined by observation and calculation the force with which they acted upon each other at these distances. A needle an inch long, weighing seventy grains, and magnetised to saturation, was suspended by a fibre of silk three lines long, and a steel wire magnet twenty-five inches long was placed vertically in the magnetic meridian at different distances, so that its south pole was always ten lines below the northern extremity of the suspended needle. The needle was now made to oscillate when the magnet was at different distances from it, and the following were the number of oscillations in 60°, the number being fifteen when the magnet was removed, and the needle influenced only by the magnetism of the earth.

By means of the formula for the pendulum, in which the forces are in the direct ratio of the square of the number of oscillations performed in the same time, Coulomb has computed their intensity. As all the forces concerned are in the plane of the magnetic meridian, the force which produces the horizontal oscillations depends on the parts of these forces which are decomposed in a horizontal direction. Now Coulomb had demonstrated that the magnetic fluid might be considered as concentrated at a point ten lines from the extremity of the wire-magnet; but as the suspended needle was one inch long, its north pole was attracted at the distance of three and a half inches, and its south pole at the distance of four and a half inches, so that four inches was the mean distance at which, in the first experiment, the lower pole of the wire-magnet exerted its action on the two poles of the needle. In the second experiment the mean distance was eight inches. But as the horizontal force which produces the oscillations is the square of the number performed in 60°, the magnetic force of the earth will be $15^2$, and the combined forces of the earth and the wire-magnet will, in the first, second, and third experiments, be $41^2$, $24^2$, and $17^2$, so that the forces which emanate from the wire-magnet will be $41^2\; -\; 15^2$, $24^2\; -\; 15^2$, $17^2\; -\; 15^2$, whence we deduce the following results:

The distances in the first and second experiments being as one to two, the variation of the force would have been exactly as the squares of these numbers had the force in the second experiment been 364 instead of 351; and the same would have been the case had the force in the second and third experiments been 332 and 83, instead of 351 and 64. This difference, therefore, requires to be investigated. Coulomb has accounted for it, and calculated the correction for these numbers in the following manner. In the experiments the action of the superior pole of the wire-magnet was neglected. The distance of its inferior pole from the centre of the needle was sixteen inches, and the distance of the superior pole from the centre of the needle is nearly $\backslash sqrt\{(16^2\; +\; 23^2)\}$, so that the force of the former is to that of the latter nearly as 100 to 19. Hence, as the oscillations of the needle are produced by the action of these two poles, which exert their force in opposite directions, the square of the number of oscillations which the single action of the inferior pole of the magnet would produce should be diminished $\backslash frac\{19\}\{100\}$ths by the opposite action of the superior pole; so that 64 is only the excess of the real amount of the single action of the lower part of the magnet over $\backslash frac\{19\}\{100\}$ths of the number which represents it. The true value will therefore be 79. The true intensities of the forces will, at the distances 4, 8, and 16 inches, be 1456, 351, and 79, or nearly in the inverse ratio of the squares of the distances.

M. Coulomb has in like manner demonstrated, that the repulsive force of similar poles follows the same law of the distance.

The second method employed by Coulomb requires the Coulomb use of the magnetic balance, which is represented in Plate CCCXXV. figs. 1 and 5, which is a modification of the torsion balance already described in our article on ELECTRICITY. The suspending wire, ab fig. 1, carries at its lower extremity a pair of pincers c, which holds a stirrup

1, 2, 3, formed of a plate of very light copper. In this stirrup is placed a small piece of card covered with a coat of Spanish wax, on which is impressed the mark of the wire or bar of steel SN to be used, in order that it may always be put in the same position. Under the middle of the stirrup is fixed a vertical plane PP, wholly immersed in a vessel VV of water, the resistance of which may quickly stop the oscillations of the needle or magnet SN in the stirrup. When fitted up for the experiments under our consideration, the apparatus shown in fig. 1 is placed in a square box AB (see fig. 5), three feet wide and eighteen inches high. At the height of nine inches above the bottom is placed a horizontal circle of wood or copper, two feet ten inches in diameter, and divided into degrees. On this box is placed a cross piece CD, which supports at its middle point a tube EF, thirty inches long, and terminating in a torsion micrometer at M. The pincer of this micrometer holds the upper end of a brass wire, to the other extremity of which is adapted a ring of copper intended to carry a steel needle.

Before the commencement of the experiment, the box AB is placed so that the direction of the magnetic meridian passes through the divisions zero and 18° of the horizontal circle. The next step is to place in the stirrup a well-magnetised steel needle NS, of a rectangular form, and to adjust the torsion micrometer M, so that the torsion of the wire is nothing when the needle NS is in the magnetic meridian, or that the magnetic meridian passes through the zero on the scale of the torsion micrometer. In the direction of the magnetic meridian, a vertical ruler of wood or copper, one or two lines thick, is fixed, so that the end of the needle may come against it when it is in the magnetic meridian.

Coulomb now took two wire-magnets, twenty-four inches long and one and a half inch in diameter, and he placed one of them in the stirrup, as at NS, and he determined the force with which the magnetism of the earth drew it back into the magnetic meridian. For this purpose he twisted the suspending wire ab through two circles or circumferences minus 20°, till the needle stopped 20° from the magnetic meridian, so that, considering the forces as nearly proportional to the arcs (when the angle is about 20°), about 35° of torsion were necessary to keep the magnetic needle one degree out of the magnetic meridian. The two circles of torsion minus 20° are equal to $2\; \backslash times\; 360^\backslash circ\; -\; 20^\backslash circ\; =\; 700^\backslash circ$; the degrees of torsion required to keep the needle 20° out of the magnetic meridian, or 700° of torsion, are a measure of the directive force of the needle when 20° out of the magnetic meridian. For any other number of degrees, $\backslash delta$, the degree of torsion necessary to balance the directive force

will be $700\; \backslash frac\{\backslash sin.\; \backslash delta\}\{\backslash sin.\; 20^\backslash circ\}$, because the directive forces are proportional to the sines of the angles. But at 20° the angles

may be substituted for the forces, and we shall have $\backslash frac\{700\; \backslash delta\}\{20\}$

= 35$\backslash delta$, that is, as we stated above, 35° of torsion will balance the directive force of the needle when one degree out of the magnetic meridian. Coulomb now placed the other similarly magnetised wire vertically in the magnetic meridian, so that if the two wires had been prolonged, they would have met at the distance of ten lines from their extremities, the point where the magnetism of each acts as if it were concentrated there. He placed the similar poles of each opposite to each other, and consequently the horizontal needle or wire was repelled out of the magnetic meridian; and it took a position at which the force of repulsion of the vertical needle or wire was balanced by the united forces of torsion and the earth's magnetism, which tended to bring the horizontal wire to rest. The following results were obtained after different trials:

Circles of Torsion given to the Suspending Wire by the Torsion Micrometer.

Observed Angles of Repulsion.

Now, in the first experiment, the angle through which the horizontal wire was repelled was 24°, reckoning from the zero of torsion; and when it rested in this position, it was driven towards the zero by a force of torsion of 24° plus the directive force of the earth's magnetism, which being 35° for every 1°, amounts to $24\; \backslash times\; 35^\backslash circ\; =\; 840^\backslash circ$. The total repulsive force was therefore $840^\backslash circ\; +\; 24^\backslash circ\; =\; 864^\backslash circ$.

In the second experiment the torsion micrometer was turned round three circles in a direction opposite to the 24° first produced; but notwithstanding this great torsion, the horizontal wire-magnet, repelled by the vertical one, returned only to 17° from the magnetic meridian. The force of torsion was therefore 3 circles + 17° = 1097°; but the directive force for 17° is $17^\backslash circ\; \backslash times\; 35^\backslash circ\; =\; 595^\backslash circ$, hence we have for the total repulsive force $1097^\backslash circ\; +\; 595^\backslash circ\; =\; 1692^\backslash circ$.

In the third experiment the torsion micrometer was turned round eight circles, and the wire-magnet stopped at 12° from the magnetic meridian. The force of torsion was therefore 8 circles + 12° = 2892°; but the directive force for 12° is $12^\backslash circ\; \backslash times\; 35^\backslash circ\; =\; 420^\backslash circ$, hence we have for the total repulsive force $2892^\backslash circ\; +\; 420^\backslash circ\; =\; 3312^\backslash circ$.

As the arcs of repulsion are in these experiments so small, we may safely reckon them equal to their chords, and we obtain the following results:

Assuming 3312° as correct, the other numbers ought to have been 1650 and 828 instead of 1692 and 864, if the force varies inversely as the square of the distance. The differences 42° and 36° correspond nearly with a degree of error in the observed position of the moveable steel wire, since the directive force is 35° for every degree of deviation from the magnetic meridian. Such an error is certainly a very small one in experiments of this kind, and we therefore conclude that the attractive and repulsive forces of magnets decrease as the squares of their distances increase.

Had the experiments been made upon magnetic points, such an error would not have existed; but they were made with forces diffused over portions of the wire-magnet of some extent. In the last experiment (M. Biot remarks) "when the two wires were nearest each other, the influence of the points lying near the intersection was more weakened by obliquity than in the other experiment; or, in other words, there were at equal obliquities more points which acted in the greater distances (24 and 17) than in the smaller one (12). But as we did not take this augmentation into account, we ought to find that the repulsive force observed at the smaller distance, being reduced in the ratio of the square of the distance, gives for larger distances repulsive forces a little more feeble than those which were actually observed."

In the first method of observation, Coulomb was obliged to calculate the effect of the distant pole; but in the present method this was unnecessary, as the wire-magnets were two feet long, and the greatest arc of repulsion, viz. 24°, corresponded to a distance of five inches between the repelling poles. The other poles were therefore at least four times more distant than those whose repulsive action was calculated; their direct action was therefore sixteen times weaker, besides being greatly weakened by the extreme obliquity with which it acted. Had the wire-mag-

Laws of Magnetic Forces, &c. nets been shorter, the action of all the poles might have been taken into consideration.

SECT. II.—On the Mutual Action of Magnets.

We have already seen, from Professor Barlow's experiments on spheres and bars of soft iron, that they act upon needles, whether temporarily or permanently magnetised, as if their magnetism emanated from the centre of their surface, or from two points indefinitely near to each other. This, however, is not the case with permanent magnets, in which the magnetic force is concentrated in poles considerably distant from each other.

CASE 1. When the needle or a small magnet is placed in the line joining the poles of the other magnet.—In considering the mutual action of magnets, we shall suppose the larger one NS to be fixed, and the smaller one $ns$ to have the form of a needle, moveable in a horizontal plane round the pivot in its centre A, B, or C. Let the needle then be placed at A, with its centre A in the line SN prolonged, and let us suppose that the magnetic forces emanate from points N, S; $n$, $s$, being the analogous poles of the needle. The north pole N of the magnet attracts the south pole $s$ of the needle with a force inversely proportional to the square of $Ns$, and repels the north pole $n$ with a force inversely proportional to the square of $Nn$. The effect of both of these forces is to bring $s$ as near as possible to N, and to remove $n$ as far as possible, that is, to place the needle in the same straight line as N, S, as shown in fig. 35.

Fig. 35.

CASE 2. Let the needle, $ns$, be now placed at B, so that its centre B is anywhere in the direction of a right line, MB, perpendicular to the middle M of the magnet. When the centre of the needle is placed above M, it is quite clear that it will stand with its north pole $n$ towards the south pole S of the magnet, and its south pole $s$ towards the north pole N. When the needle is removed to B, the same thing will happen; S will attract $n$ with a force equal to $nb$, while N repels $n$ with a force $nc$, a little less than $nb$, on account of the increase of distance. The result of these will be the force $na$, in the diagonal of the parallelogram $ncab$. In the same manner, the pole N will attract $s$ with a force $es$, and the pole S will repel $s$ with a less force $fs$, the resultant of which is $sg$; but as the poles S, N, are equally strong, and act at equal distances upon the needle, the resulting force $as$ must be equal to $gs$, and the needle will remain in that position, which is parallel to the axis SN of the magnet.

Fig. 36.

CASE 3. When the centre of the needle is placed in an intermediate position, as at C, fig. 36, neither in the axis NS, nor in the perpendicular MB, it will take an intermediate position, which may be thus found. Its north pole $n$ is shown in the figure as directed to the centre M of the magnet; but it cannot remain in this position; N repels $n$ with a force equal to $nc$, and S attracts it with a force $nb$ smaller than $nc$, from the greater distance. The resultant

of these is $na$, which is very different from $ns$. For the same reason, the south pole $s$, repelled by S with a force $sf$, and attracted by N with a force $se$, will have a tendency to move in the direction $sg$, nearly equal and opposite to each other; it will therefore take a position $ns$, fig. 36, nearly at right angles to its former position. It will rest therefore in its new position, with its north pole towards N, and its south pole towards S.

If we project upon paper the magnet and the needle placed in different positions, and make the forces of each pole of the magnet on each pole of the needle inversely proportional to the squares of the distances, it will be easy to find the position in which the needle will rest at any distance from the magnet, and at any position of its centre, with regard to the axis of the magnet.

When a needle is exposed to the combined action of two magnets, as shown in the annexed figure, the phenomena, though capable of calculation by the principles already explained, are extremely perplexing and complicated when studied experimentally. Dr Robison, who first discovered and explained these phenomena, has given such an interesting account of them, that we shall make use of his description of the phenomena, leaving the explanation of them to the next section on magnetic curves.

Fig. 37.

"Two large and strong magnets A and B 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 a considerable verticity, turning its north pole to-

Law of Magnetic Forces, &c.
wards the magnet B; and it required to be taken farther out towards 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 showing great verticity. This naturally surprised the beholders; and he 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 vivacity 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."

In the preceding observations, the action of the one magnet tended only to change the direction of the other, and this change is clearly produced by the sum of the actions of the two poles of the magnet; for while the one pole tends to draw the one half of the needle into its position of equilibrium, the other pole repels the other half into the same position. The force, therefore, which thus acts upon a needle, is called the directive force of a magnet.

The attractive force of a magnet is, on the other hand, equal to the difference of the two forces exerted by its poles on the needle; and when the two forces happen to be equal, the attractive force will be nothing, and the needle will have no tendency to approach the magnet, though the directive power of the latter may be very great. This will be understood from fig. 36, when the needle $ns$ is at right angles to the axis of the magnet. The attraction of the pole N for $s$ is equal to its repulsion of $n$, and these two forces will neutralise each other, so as to prevent any tendency to approach N, even if the needle $ns$ were free to do it. On the other hand, in fig. 35, where the needle at C has its south pole $s$ more attracted by N than its north pole $n$ is repelled by it, the predominance of the attraction would carry the needle towards N if it were at liberty. These views explain the well-known fact, that a needle floated on a piece of cork quickly places itself in the magnetic meridian; but it never will approach the north side of the vessel. In order to explain this fact, Dr Gilbert asserted, that the directive power of a magnet extended much farther than its attractive power; a mistake which arose from his not having observed the effects of the simultaneous action of the four poles of the magnets which acted upon each other.

SECT. III.—On Magnetic Curves.

Law of Magnetic Forces, &c.
The name of magnetic curves has been given to those curves into which an infinite number of very minute needles would arrange themselves when placed round a magnet, and at liberty to move round an axis. A rude idea of these curves is given by the appearance of iron filings when scattered upon a sheet of paper, and agitated immediately above a magnet.

The action of a magnet upon a needle is greatly simplified when the needle is so small that its two poles may be considered as coincident; in which case the difference between the action of any one pole of a magnet upon them

will be infinitely small. When this is the case, the directive force of the magnet upon the small needle must be very considerable, while the attractive force, measured by the difference of the action on the two poles, is nothing. Hence it is that alone which is concerned in the arrangement of minute needles or particles subjected to the action of a magnet.

An investigation of the force of the magnetic curves was made by Professor Playfair, at the request of Professor Robison. Professor Leslie afterwards undertook the same investigation; and Dr Roget² has more recently given a more simple demonstration of the two fundamental propositions respecting them, and has described an instrument which he has invented for the mechanical description of these curves. Mr Playfair's investigation, which is sufficiently simple, is as follows; the only change which we have made upon it being the substitution of the second power of the distance for the $n$th power as used by him.

PROP. Two magnetical poles being given in position, the force of each of which is inversely as the square of the distance from it, it is required to find a curve, in any point of which a needle (infinitely short) being placed, its direction, when at rest, may be a tangent to the curve.

"1. Let A and B 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 $\backslash frac\{1\}\{AC^2\}\; :\; \backslash frac\{1\}\{BC^2\}\; =\; AC\; :\; AD$; join CD, then CDF will touch the curve in C.

"2. Hence an expression for AF may be obtained; for, by the construction, $AD\; =\; \backslash frac\{AC^3\}\{BC^2\}$; and since $BC\; :\; AD\; =\; BF\; :\; FA$, and $BC\; -\; AD\; :\; AD\; =\; AB\; :\; AF$, we have $AF\; =\; \backslash frac\{AB\; \backslash times\; AC^3\}\{BC^3\; -\; AC^3\}$.

"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 BG and AM at right angles to FH. Let the angles CAB = $\backslash phi$ and CBA = $\backslash psi$, then CAH = $\backslash phi$ and CBH = $-\backslash psi$; also CL = $AC\; \backslash times\; \backslash dot\{\backslash phi\}$, and CK = $-BC\; \backslash times\; \backslash dot\{\backslash psi\}$. Now HC : CL = AC : AM = $\backslash frac\{AC^2\; \backslash times\; \backslash dot\{\backslash phi\}\}\{HC\}$; and for the same reason

BG = $-\backslash frac\{BC^2\; \backslash times\; \backslash dot\{\backslash psi\}\}\{HC\}$. Therefore, since AF : FB = AM : BG, we have $AF\; :\; FB\; =\; \backslash frac\{AC^2\; \backslash times\; \backslash dot\{\backslash phi\}\}\{HC\}\; :\; -\backslash frac\{BC^2\; \backslash times\; \backslash dot\{\backslash psi\}\}\{HC\}$, and $AF\; :\; AB\; =\; \backslash sin.\; \backslash dot\{\backslash psi\}\; \backslash dot\{\backslash phi\}\; :\; -\backslash sin.\; \backslash dot\{\backslash psi\}\; \backslash dot\{\backslash phi\}\; -\; \backslash sin.\; \backslash phi\; \backslash dot\{\backslash psi\}$; wherefore, if AB = $a$, $AF\; =\; \backslash frac\{-a\; \backslash dot\{\backslash phi\}\; \backslash sin.\; \backslash dot\{\backslash psi\}\}\{\backslash dot\{\backslash psi\}\; \backslash sin.\; \backslash phi\; +\; \backslash dot\{\backslash phi\}\; \backslash sin.\; \backslash psi\}$.

"4. If this value of AF be put equal to that already found, a fluxionary equation will be obtained, by the inte-

¹ Geometrical Analysis.

² Journal of the Royal Institution of Great Britain, vol. I. p. 311. Feb. 1831.

Laws of Magnetic Forces, &c. gration of which the curve may be constructed. Because $AF\; =\; \backslash frac\{AB\; \backslash times\; AC^2\}\{BC^3\; -\; AC^3\}$; and since $AC\; =\; \backslash frac\{a\; \backslash sin.\; \backslash psi\}\{\backslash sin.\; (\backslash phi\; +\; \backslash psi)\}$, and

“5. Hence, if, beside the points A and B, any other point be given in the curve, the whole may be described. For instance, let the point E be given in the curve, and in the line DE which bisects AB at right angles. Describe from the centre A a circle through E, viz. QER, then AD being the cosine of DAE to the radius AE, the sum of the cosines of $\backslash phi\; \backslash times\; \backslash psi$ will be everywhere (to the same radius) $=\; 2AD\; =\; AB$. Therefore, to

find E', the point in which any other line AN, making a given angle with AB, meets the curve, draw from N the point in which it meets the circumference of the circle QER, NO perpendicular to AB, so that AO may be the cosine of NAO, and from O toward A take OP = AB, then AP will be the cosine of the angle ABE'; so, to find BE', draw PQ perpendicular to AP, meeting the circle in Q; join AQ and draw BE' parallel to AQ, meeting AE' in E'; the point E' is in the curve. In this way the other points of the curve may be found.

“The curve will pass through B, and will cut AB at an angle of which the cosine = RB. If then E be such, that AE = AB, the curve will cut AB at right angles. If E' be more remote from A, the curve will make with AB an obtuse angle toward D; in other cases it will make with it an acute angle.

“A construction somewhat more expeditious may be had by describing the semicircle AFB, cutting AE in F, and AE' in N, and describing a circle round A with the distance AL = 2AF, cutting AE' in b. If BG be ap-

plied in the semicircle AFB = Nb, BG must cut AN in a point E' of the curve, because AN + BG = 2AF, and AN and GB are cosines of the angles at A and B.

“As the lines AN and BG may be applied either above or below AB, there is another situation of their intersection E'. Thus An being applied above, and Bg below, the intersection is in e'. The curve has a branch extending below A; and if De be made = DE, and Be be drawn, it will be an asymptote to this branch. There is a similar branch below B. But these portions of the curve evidently suppose an opposite direction of one of the two magnetic forces, and therefore have no connection with the position of the needle.”

The general form of the magnetic curves is shown in fig. 40, where they are seen converging to the two poles N, S of the magnet NS, and changing their form with their distance from the magnet.

We have already stated that iron filings, arranged by the action of a powerful magnet, afford the finest experimental illustration of the magnetic curves. The best way to do this is to stretch a sheet of paper tightly over a wooden frame, and place it horizontally immediately above a powerful bar magnet lying on the table. Fine iron filings are now to be shaken through a gauze bag upon the surface of the paper. When the filings are thrown into a state of agitation by gently tapping upon the paper frame, they will dispose themselves into regular lines, stretching from one pole of the magnet to the other, and following the course of the magnetic curves, and exhibiting them beautifully to the eye. This effect is shown in the annexed figure, where N, S are the poles of the magnet NS, mn being the mean line where no filings adhere. The same arrangement is also produced when the magnet is held above the paper containing the filings.

In the case of induced magnetism, the steel filings arrange themselves in curves round the iron on which the magnetism is induced, as shown in fig. 42, where the small bar of iron is in contact with the north pole N of a magnet, mn being the mean line which separates the two opposite actions of the little iron bar. When the little bar of iron is placed at a distance from the magnet N, as in fig. 43, the filings arrange themselves as in that figure, mn being the mean line as before.

Dr Roget has given the following interesting account of the phenomena which take place by continuing to agitate the filings when they are arranged as in fig. 44.

“By continuing to tap upon the paper,” says he,

"the filings arrange themselves still more visibly into separate lines; but here a curious and perhaps unlooked-for phenomenon presents itself. The lines gradually move and recede from the magnet, appearing as if they were repelled instead of attracted, as theory would lead us to expect. This arises from the circumstance that each particle of iron, or cluster of particles, is thrown up into the air by the shaking of the paper, and, while unsupported, immediately turns on its centre, and acquires a position more or less oblique to the plane of the paper. This is shown in fig. 44, in which M

represents a section of the magnet, PP a section of the paper, and f f the position of the filaments of iron thrown up into the air. The end of each filament nearest to the magnet is thus turned a little downwards, and the filament falls upon the paper at a point a little more distant than that which it before occupied; and thus, step by step, it moves farther and farther from the magnet, till it reaches the edge of the paper, and falls off.

"When the magnet, instead of being beneath the paper, is held above it, the effect is just the reverse. In this latter case, the lower ends of the filaments having a tendency to turn towards the magnet, the filings gradually collect under it, when made to dance by the vibrations of the paper, instead of falling outwards as they did before. This will be seen from fig. 45, where the letters have the same indications as in the preceding figure."

A different set of magnetic curves is produced when two similar poles, for example, two north poles, as shown in the annexed figure, are placed near each other. These curves are called divergent curves, and may be exhibited by iron filings like the convergent ones.

Dr Roget has given the following expeditious method of delineating a great number of magnetic curves, related to the same distance between two magnetic poles. He describes from each pole N, S, as centres, the equal of circles or semicircles AA, BB, with as large a radius as the paper will allow; and dividing the axis produced till it meets both circles, he marks off, on the circumferences of both circles, the points where they are cut by perpendiculars from these points of division; then drawing radii from the centre of each circle to the divisions of its respective circumferences, the mutual intersections of these radii will give different sets of points indicating the form of the magnetic curves which pass through them. These curves are, in the present case, composed of a succession of diagonals of the lozenge-shaped interstices formed by the intersecting radii, as shown from convergent curves in the upper half of the figure. In the case of divergent curves in fig. 46, we must

take the other diagonals of the lozenge-shaped intervals between the intersecting radii; that is, the diagonals which cross those constituting the convergent curves. This is shown in the lower half of the figure.

The curves which are formed when the north and south poles of two magnets are placed near each other, as in fig. 37, enable us to explain the phenomena discovered by Dr Robison, and described in the preceding section. The following is the explanation given by that eminent philosopher. (See fig. 37.)

"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 verticity, 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 in 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,

Terrestrial Magnetism. Terrestrial 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. 37. These may be called compound or secondary magnetic curves. Moreover, these 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 sub-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 said, 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 means 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 front 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."

CHAP. IX.—ON TERRESTRIAL MAGNETISM.

Terrestrial magnetism. We have already seen, in preceding chapters, that a magnetic bar or needle, when either suspended by a thread, or at liberty to move freely upon a pivot, will, when all other magnetic bodies are entirely removed from it, settle in a fixed position, which, in this country, is about 25° to the west of north: this deviation of the needle from the north is called its variation. The very same thing will take place if a magnet or magnetised needle is placed on a piece of cork, and made to float on any fluid surface. The magnetic force by which the magnetic needle is thus made to take a fixed direction, and to return to it

when it is pushed aside from that direction, has been naturally supposed to reside in the earth, and hence it has been called terrestrial magnetism. Terrestrial Magnetism.

But not only is a magnetised body directed in this manner by some unseen power; an unmagnetised body, such as a piece of iron, may be rendered permanently magnetic by the same power. This phenomenon is said to have been first observed in the vertical rod of the weather-cock of the church of the Augustines at Mantua, though others have ascribed the discovery of the fact to Gassendi. This rod had become magnetised by the continued action of the invisible power of which we speak. In later times it has been observed, that a bar of soft iron is, by the influence of the same power, converted into a temporary magnet, with a north and south pole, when it is placed in the direction which a magnetic needle assumes, and is inclined to the horizon.

If, in place of suspending the needle, or making it move horizontally on a pivot, we take an unmagnetised needle, and balance it upon a horizontal axis, then it will of course lie horizontally; but if we magnetise the needle, we shall find that it no longer remains horizontal, but takes an inclined position, or dips, as it is called; the dip, or the inclination downwards from a horizontal line, being about 70° in this country.

If we now take a magnetic needle, and suspend it by a silk fibre, we shall find, that when it is pushed out of its position of rest, it will perform a certain number of oscillations in a given time before it again takes a fixed position. When this observation is made in different latitudes, it is found that the needle is brought to rest sooner in some places than in others; which proves that the intensity or strength of the magnetic force which directs the needle to the north varies in different latitudes. Hence we have to consider three important classes of phenomena in reference to terrestrial magnetism.

1. 1. The variation or declination of the needle, and its laws;
2. 2. The dip or inclination of the needle;
3. 3. The intensity of terrestrial magnetism;

of which we shall treat as perspicuously and fully as the nature of the subject and our confined limits will permit.

SECT. I.—On the Variation of the Needle.

A general account of the phenomena of the variation of the needle has been given in the order of their discovery in the historical part of this article. We shall now proceed to give a more minute account of them.

Measures of the variation of the needle have been taken by navigators and travellers in every part of the globe. Setting aside the inaccuracies common to them all, arising from the imperfect instruments which were in many cases employed, the observations made on ship-board were particularly liable to error, owing to the action which the iron on board exercised upon the compass.

The first person who attempted to collect and generalize the immense number of observations which had been made on the variation of the needle was Dr. Halley, who published them in a sea-chart in 1700, in which he traced lines through all the parts of the globe where the variation was 0°, 5°, 10°, &c. These lines, which have since been called the Halleyan lines or curves, excited great interest, and had the advantage of giving, at one glance, an ocular picture of the phenomena in every part of the world. As this Variation Chart, however, soon became old, from the rapid changes in the variation, as well as from confused methods of observation, Messrs. Mountain and Dodson collected, from the records of the admiralty, and from the papers of various naval officers, about 50,000, which they laid down in variation charts for 1745 and 1756.

The next step in the generalization of the phenomena

general of variation was made by Mr Churchman, who published, in 1794, a programme of a Magnetic Atlas. He refers his variation lines to two poles, one of which he places, for the year 1800, in latitude 58° north, and longitude 134° west of Greenwich, very near Cape Fairweather; while the other pole is in latitude 58° south, and longitude 165° east of Greenwich. He supposes the northern pole to revolve in 1096 years, and the southern one in 2289 years.

It is to Professor Hansteen, however, that we are indebted for the most satisfactory collection of observations on the variation of the needle, and for the most philosophical generalization of them. In the Magnetic Atlas which accompanies his work on the magnetism of the earth, he has published a variation chart for 1787, in which the irregularities and inflexions of the curves, and their total want of symmetry, prove how irregular are the causes on which terrestrial magnetism depends. In this chart, the western line of no variation, or that which passes through all the places on the globe where the needle points to the true north, begins in latitude 60°, to the west of Hudson's Bay, proceeds in a south-east direction through the North American lakes, passes the Antilles and Cape St Roque, till it reaches the South Atlantic Ocean, where it cuts the meridian of Greenwich in about 65° of south latitude. This line of no variation is extremely regular, being almost straight till it bends round the eastern part of South America a little south of the equator. The eastern line of no variation is exceedingly irregular, being full of loops and inflexions of the most extraordinary kind, indicating the action of local magnetic forces. It begins in latitude 60° south, below New Holland, crosses that island through its centre, extends through the Indian archipelago with a double sinuosity, so as to cross the equator three times, first passing north of it, to the east of Borneo, then returning to it and passing south between Sumatra and Borneo, and then crossing it again beneath Ceylon, from which it passes to the east through the Yellow Sea. It then stretches along the coast of China, making a semicircular sweep to the west till it reaches the latitude of 71°, where it descends again to the south, and returns northwards with a great semicircular bend, which terminates in the White Sea. These lines of no variation are accom-

panied through all their windings by other lines where the terrestrial variation is 5°, 10°, 15°, &c. these last lines becoming more irregular as they recede from those of no variation. In the South Pacific Ocean, and the equatorial part of the North Pacific, they are so little dependent on the lines of no variation, that they form returning curves of an elongated oval form, the curves of 2°, 3°, 4°, 5°, 6°, and 7°, crossing the equator and the tropic of Capricorn twice, so that, in the centre or axis of the ovals which these lines form, there should be a fragment of a line of no variation.

The great changes which had taken place in the variation since 1787, and the number of new observations which had been made in every part of the world, induced Professor Barlow, in 1833, to construct a new variation chart, which forms a very interesting and valuable record of the present state of our knowledge on this subject.¹ With the kind permission of Professor Barlow, we have given a reduced copy of this chart in Plate CCCXXVII, and have included in it his separate polar projection of the variation lines within the arctic zone. When compared with the account given above of the two lines of no variation in Hansteen's chart, the motion of these lines, and of the whole system, will be distinctly seen.

In the charts both of Hansteen and Barlow the variation lines exhibit a convergence at their extremities;² and Hansteen considers it proved that there are four points of convergence, two in each hemisphere, a weaker and a stronger, on opposite sides of the poles of revolution. These four points he considers as the four magnetic poles of the globe; and, by comparing observations which have been made at different times, he concludes that they have a regular motion round the globe, the two northern ones from west to east, in an oblique direction, and the two southern ones from east to west, also obliquely. The following are the periods of their revolution, as calculated from the best observations previous to 1817, when his work was published:

The strongest NORTH pole in 1740 years.

The strongest SOUTH pole in 4609 years.

The weakest NORTH pole in 860 years.

The weakest SOUTH pole in 1304 years.

Upon these data he computed the following table, showing the position of these poles from 1800 to 1850:

Hansteen remarks, that the four periods above mentioned, viz. 860, 1304, 1740, and 4609, become, by a slight alteration, 864, 1246, 1728, and 4820; and he adds, rather fancifully for a matter of science, that these numbers are equal to $2\; \backslash times\; 432$, $3\; \backslash times\; 432$, $4\; \backslash times\; 432$, and $10\; \backslash times\; 432$, and that the number 432 is one of the most important among the sacred numbers of the Indians, Babylonians, Greeks, and Egyptians, which are said to depend on certain combinations of natural events. According to the mythology

of the Brahmins, the duration of the world is divided into four periods; the first of which is 432,000 years; the second, $2\; \backslash times\; 432,000$; the third, and so in all $(1\; +\; 2\; +\; 3\; +\; 4)\; =\; 10\; \backslash times\; 432,000$. Hansteen also considers it worthy of remark, that the sun's mean distance from the earth is 216 (the half of 432) radii of the sun, the moon's mean distance 216 radii of the moon, and, what he says is still more striking, $60\; \backslash times\; 432\; =\; 25920$, the smallest number divisible at once by all the four periods; and hence, he

¹ See Philosophical Transactions, 1833, p. 667-675, and plates xvii. and xviii.

² Professor Barlow has inserted the magnetic observations of Commander Ross; and he remarks, that the very spot where this officer found the needle perpendicular, "that is, the pole itself, is precisely that point in my globe and chart in which, by supposing all the lines to meet, the several curves would best preserve their unity of character, both separately and conjointly, as a system." The exact place of the pole is laid down in the accompanying chart, Plate CCCXXVII.

Terrestrial adds, the shortest line in which all the four poles can accomplish a cycle, and return to the same state as at present, coincides exactly with the period in which the precession of the equinoxes will amount to a complete circle, reckoning the precession at a degree in seventy-two years.

Hansteen considers the four poles as originating in two magnetic axes, the two strongest being the termination of one axis, and the two weakest, of the other; and he conceives that they may have been produced either along with the earth itself, or at a later epoch. According to the first supposition, it is not easy to account for their change of position; but according to the last, they must have originated either from the earth alone, or from some external cause. If they originated in the earth, their change of position is still unsusceptible of explanation; and hence Hansteen conceives that they have their origin from the action of the sun heating and illuminating the earth, and producing a magnetic tension, as it produces electrical phenomena.

Since the publication of Professor Hansteen's work, the valuable observations made during the British voyages of discovery in the arctic regions have been given to the world; and, by availing himself of these, and obtaining access to others unpublished in the marine chart office at the Admiralty, the Norwegian philosopher has obtained more accurate determinations both of the positions and periods of revolution of the magnetic pole. The following is a brief abstract of his calculations.

1. Strongest north pole. In 1818 the observations made on board his majesty's ship Brazen, in Hudson's Bay, give $67^\{\backslash circ\}\; 10\text{'}$ for the latitude of the strongest north magnetic pole, and $92^\{\backslash circ\}\; 24\text{'}$ for its west longitude. Hence, by comparing this with previous determinations, we have

From these data we obtain the motion of the pole to the east.

From which we obtain
Mean annual motion of the pole.....$11^\{\backslash circ\}\; 42\backslash frac\{1\}\{2\}\text{'}$
Period of complete revolution.....1890 years.

In August 1819, Captain Parry was to the north of this pole, and found the dip to be $88^\{\backslash circ\}\; 37\text{'}$, and on the 11th September he was three degrees west of the pole. Hence, as his latitude was then $74^\{\backslash circ\}\; 27\text{'}$, the latitude of the pole must have been about $71^\{\backslash circ\}\; 27\text{'}$.

According to the more recent observations of Commander Ross, this pole, upon which he erected a flag, is situated in north latitude $70^\{\backslash circ\}\; 5\text{'}\; 17\text{'}\text{'}$, and west longitude $96^\{\backslash circ\}\; 45\text{'}\; 48\text{'}\text{'}$, which coincides strikingly with Hansteen's result.

2. Strongest south pole. By combining the observations of Cook in 1773 and 1777, with those of Furneaux in 1773, and comparing these with Tasman's observations in 1642, Hansteen has found the following position of it.

Hence the real motion of this pole in 131 years is $10^\{\backslash circ\}\; 14\text{'}$, or $4^\{\backslash circ\}\; 67\text{'}$ annually, and its period of complete revolution will be 4605 years.

3. Weakest north pole. By comparing observations made in 1770 and 1805, at Tobolsk, Tara, and Udinsk, in Siberia, Professor Hansteen found—

Hence this pole completes its revolution from east to west in 860 years.

4. Weakest south pole. By comparing observations made by Cook and Furneaux in 1774, with those recorded by Halley as made in 1670, Hansteen obtained the following results:

Hence this pole completes its revolution from east to west in 1303 years.

Professor Barlow has endeavoured to deduce the position of the magnetic pole, upon the supposition that the magnetic phenomena of the earth are analogous to those exhibited by a simple iron ball. The tangent of the dip being equal to double the tangent of the magnetic latitude, Mr Barlow supposes $\backslash pi$ to be the magnetic pole, N, S the terrestrial poles, and L a known place where the dip and variation have been well ascertained. Then by the dip we obtain the magnetic latitude $\backslash pi\; L$; NL being the terrestrial latitude, and $NL\backslash pi$ the variation. Hence, in the spherical triangle $NL\backslash pi$, we have two sides and the contained angle to find the side $N\backslash pi$ the terrestrial latitude of the magnetic poles, and $\backslash pi\; NL$ the longitude of the same pole, in reference to the meridian NL.

In making this computation, Mr Barlow selected a certain number of the best observations on the dip and variation of the needle, made in different parts of the world, and he obtained the following results:

Among these results there is a discrepancy of no less than $55^\{\backslash circ\}$ in longitude, and $10^\{\backslash circ\}$ in latitude; and hence Mr Barlow concludes that every place has its particular polarising axis, which probably in all cases falls within the frigid zones, varying within these limits through all possible degrees of latitude and longitude.

These aberrations Mr Barlow ascribes to local inequalities in the distribution of the ferruginous parts of the terrestrial sphere.

The following tables contain the best measures of the variation of the needle. Table XI, containing the observations collected by Hansteen since the publication of his work, was communicated to the writer of this article by that eminent philosopher.