BOOK XII.
MECHANICO-CHEMICAL SCIENCES.
(CONTINUED.)
HISTORY OF MAGNETISM.
Effice, ut interea fera munera militiaï
Per maria ac terras omneis sopita quiescant.
Nam tu sola potes tranquilla pace juvare
Mortales; quoniam belli fera munera Mavors
Armipotens regit, in gremium qui sæpe tuum se
Rejicit, æterno devictus vulnere amoris;
Atque ita suspiciens tereti cervice reposta,
Pascit amore avidos inhians in te, Dea, visus,
Eque tuo pendet resupini spiritus ore.
Hunc tu, Diva, tuo recubantem corpore sancto
Circumfusa super, suaves ex ore loquelas
Funde, petens placidam Romanis, incluta, pacem.
Lucret. i. 31.
O charming Goddess, whose mysterious sway
The unseen hosts of earth and sky obey;
To whom, though cold and hard to all besides,
The Iron God by strong affection glides.
Flings himself eager to thy close embrace,
And bends his head to gaze upon thy face;
Do thou, what time thy fondling arms are thrown
Around his form, and he is all thy own,
Do thou, thy Rome to save, thy power to prove,
Beg him to grant a boon for thy dear love;
Beg him no more in battle-fields to deal.
Or crush the nations with his mailed heel.
But, touched and softened by a worthy flame,
Quit sword and spear, and seek a better fame.
Bid him to make all war and slaughter cease,
And ply his genuine task in arts of peace;
And by thee guided o’er the trackless surge,
Bear wealth and joy to ocean’s farthest verge.
CHAPTER I.
Discovery of Laws of Magnetic Phenomena.
THE history of Magnetism is in a great degree similar to that of Electricity, and many of the same persons were employed in the two trains of research. The general fact, that the magnet attracts iron, was nearly all that was known to the ancients, and is frequently mentioned and referred to; for instance, by Pliny, who wonders and declaims concerning it, in his usual exaggerated style.[1] The writers of the Stationary Period, in this subject as in others, employed themselves in collecting and adorning a number of extravagant tales, which the slightest reference to experiment would have disproved; as, for example, that a magnet, when it has lost its virtue, has it restored by goat’s blood. Gilbert, whose work De Magnete we have [already] mentioned, speaks with becoming indignation and pity of this bookish folly, and repeatedly asserts the paramount value of experiments. He himself, no doubt, acted up to his own precepts; for his work contains all the fundamental facts of the science, so fully examined indeed, that even at this day we have little to add to them. Thus, in his first Book, the subjects of the third, fourth, and fifth Chapters are,—that the magnet has poles,—that we may call these poles the north and the south pole,—that in two magnets the north pole of each attracts the south pole and repels the north pole of the other. This is, indeed, the cardinal fact on which our generalizations rest; and the reader will perceive at once its resemblance to the leading phenomena of statical electricity.
[1] Hist. Nat. lib. xxxvi. c. 25.
But the doctrines of magnetism, like those of heat, have an additional claim on our notice from the manner in which they are exemplified in the globe of the earth. The subject of terrestrial magnetism forms a very important addition to the general facts of magnetic attraction and repulsion. The property of the magnet by which it directs its poles exactly or nearly north and south, when once discovered, was of immense importance to the mariner. It does not [218] appear easy to trace with certainty the period of this discovery. Passing over certain legends of the Chinese, as at any rate not bearing upon the progress of European science,[2] the earliest notice of this property appears to be contained in the Poem of Guyot de Provence, who describes the needle as being magnetized, and then placed in or on a straw, (floating on water, as I presume:)
Puis se torne la pointe toute
Contre l’estoile sans doute;
that is, it turns towards the pole-star. This account would make the knowledge of this property in Europe anterior to 1200. It was afterwards found[3] that the needle does not point exactly towards the north. Gilbert was aware of this deviation, which he calls the variation, and also, that it is different in different places.[4] He maintained on theoretical principles also,[5] that at the same place the variation is constant; probably in his time there were not any recorded observations by which the truth of this assertion could be tested; it was afterwards found to be false. The alteration of the variation in proceeding from one place to another was, it will be recollected, one of the circumstances which most alarmed the companions of Columbus in 1492. Gilbert says,[6] “Other learned men have, in long navigations, observed the differences of magnetic variations, as Thomas Hariot, Robert Hues, Edward Wright, Abraham Kendall, all Englishmen: others have invented magnetic instruments and convenient modes of observation, such as are requisite for those who take long voyages, as William Borough in his Book concerning the variation of the compass, William Barlo in his supplement, William Norman in his New Attractive. This is that Robert Norman (a good seaman and an ingenious artificer,) who first discovered the dip of magnetic iron.” This important discovery was made[7] in 1576. From the time when the difference of the variation of the compass in different places became known, it was important to mariners to register the variation in all parts of the world. Halley was appointed to the command of a ship in the Royal Navy by the Government of William and Mary, with orders “to seek by observation the discovery of the rule for the variation of the compass.” He published Magnetic Charts, which [219] have been since corrected and improved by various persons. The most recent are those of Mr. Yates in 1817, and of M. Hansteen. The dip, as well as the variation, was found to be different in different places. M. Humboldt, in the course of his travels, collected many such observations. And both the observations of variation and of dip seemed to indicate that the earth, as to its effect on the magnetic needle, may, approximately at least, be considered as a magnet, the poles of which are not far removed from the earth’s poles of rotation. Thus we have a magnetic equator, in which the needle has no dip, and which does not deviate far from the earth’s equator; although, from the best observations, it appears to be by no means a regular circle. And the phenomena, both of the dip and of the variation, in high northern latitudes, appear to indicate the existence of a pole below the surface of the earth to the north of Hudson’s Bay. In his second remarkable expedition into those regions, Captain Ross is supposed to have reached the place of this pole; the dipping-needle there pointing vertically downwards, and the variation-compass turning towards this point in the adjacent regions. We shall [hereafter] have to consider the more complete and connected views which have been taken of terrestrial magnetism.
[2] Enc. Met. art. Magnetism, p. 736.
[3] Before 1269. Enc. Met. p. 737.
[4] De Magnete, lib. iv. c. 1.
[5] c. 3.
[6] Lib. i. c. 1.
[7] Enc. Met. p. 738.
In 1633, Gellibrand discovered that the variation is not constant, as Gilbert imagined, but that at London it had diminished from eleven degrees east in 1580, to four degrees in 1633. Since that time the variation has become more and more westerly; it is now about twenty-five degrees west, and the needle is supposed to have begun to travel eastward again.
The next important fact which appeared with respect to terrestrial magnetism was, that the position of the needle is subject to a small diurnal variation: this was discovered in 1722, by Graham, a philosophical instrument-maker, of London. The daily variation was established by one thousand observations of Graham, and confirmed by four thousand more made by Canton, and is now considered to be out of dispute. It appeared also, by Canton’s researches, that the diurnal variation undergoes an annual inequality, being nearly a quarter of a degree in June and July, and only half that quantity in December and January.
Having thus noticed the principal facts which belong to terrestrial magnetism, we must return to the consideration of those phenomena which gradually led to a consistent magnetic theory. Gilbert observed that both smelted iron and hammered iron have the magnetic virtue, [220] though in a weaker degree than the magnet itself,[8] and he asserted distinctly that the magnet is merely an ore of iron, (lib. i. c. 16, Quod magnes et vena ferri idem sunt.) He also noted the increased energy which magnets acquire by being armed; that is, fitted with a cap of polished iron at each pole.[9] But we do not find till a later period any notice of the distinction which exists between the magnetical properties of soft iron and of hard steel;—the latter being susceptible of being formed into artificial magnets, with permanent poles; while soft iron is only passively magnetic, receiving a temporary polarity from the action of a magnet near it, but losing this property when the magnet is removed. About the middle of the last century, various methods were devised of making artificial magnets, which exceeded in power all magnetic bodies previously known.
[8] Lib. i. c. 9–13.
[9] Lib. ii. c. 17.
The remaining experimental researches had so close an historical connexion with the theory, that they will be best considered along with it, and to that, therefore, we now proceed.
CHAPTER II.
Progress of Magnetic Theory.
Theory of Magnetic Action.—The assumption of a fluid, as a mode of explaining the phenomena, was far less obvious in magnetic than in electric cases, yet it was soon arrived at. After the usual philosophy of the middle ages, the “forms” of Aquinas, the “efflux” of Cusanus, the “vapors” of Costæus, and the like, which are recorded by Gilbert,[10] we have his own theory, which he also expresses by ascribing the effects to a “formal efficiency;”—a “form of primary globes; the proper entity and existence of their homogeneous parts, which we may call a primary and radical and astral form;”—of which forms there is one in the sun, one in the moon, one in the earth, the latter being the magnetic virtue.
[10] Gilb. lib. ii. c. 3, 4
Without attempting to analyse the precise import of these expressions, we may proceed to Descartes’s explanation of magnetic phenomena. The mode in which he presents this subject[11] is, perhaps, the [221] most persuasive of his physical attempts. If a magnet be placed among iron filings, these arrange themselves in curved lines, which proceed from one pole of the magnet to the other. It was not difficult to conceive these to be the traces of currents of ethereal matter which circulate through the magnet, and which are thus rendered sensible even to the eye. When phenomena could not be explained by means of one vortex, several were introduced. Three Memoirs on Magnetism, written on such principles, had the prize adjudged[12] by the French Academy of Sciences in 1746.
[11] Prin. Phil. pars c. iv. 146.
[12] Coulomb, 1789, p. 482.
But the Cartesian philosophy gradually declined; and it was not difficult to show that the magnetic curves, as well as other phenomena, would, in fact, result from the attraction and repulsion of two poles. The analogy of magnetism with electricity was so strong and clear, that similar theories were naturally proposed for the two sets of facts; the distinction of bodies into conductors and electrics in the one case, corresponding to the distinction of soft and hard steel, in their relations to magnetism. Æpinus published a theory of magnetism and electricity at the same time (1759); and the former theory, like the latter, explained the phenomena of the opposite poles as results of the excess and defect of a magnetic “fluid,” which was dislodged and accumulated in the ends of the body, by the repulsion of its own particles, and by the attraction of iron or steel, as in the case of induced electricity. The Æpinian theory of magnetism, as of electricity, was recast by Coulomb, and presented in a new shape, with two fluids instead of one. But before this theory was reduced to calculation, it was obviously desirable, in the first place, to determine the law of force.
In magnetic, as in electric action, the determination of the law of attraction of the particles was attended at first with some difficulty, because the action which a finite magnet exerts is a compound result of the attractions and repulsions of many points. Newton had imagined the attractive force of magnetism to be inversely as the cube of the distance; but Mayer in 1760, and Lambert a few years later, asserted the law to be, in this as in other forces, the inverse square. Coulomb has the merit of having first clearly confirmed this law, by the use of his torsion-balance.[13] He established, at the same time, other very important facts, for instance, “that the directive magnetic force, which the earth exerts upon a needle, is a constant quantity, parallel [222] to the magnetic meridian, and passing through the same point of the needle whatever be its position.” This was the more important, because it was necessary, in the first place, to allow for the effect of the terrestrial force, before the mutual action of the magnets could be extricated from the phenomena.[14] Coulomb then proceeded to correct the theory of magnetism.
[13] Mem. A. P. 1784, 2d Mem. p. 593.
[14] p. 603.
Coulomb’s reform of the Æpinian theory, in the case of magnetism, as in that of electricity, substituted two fluids (an austral and a boreal fluid,) for the single fluid; and in this way removed the necessity under which Æpinus found himself, of supposing all the particles of iron and steel and other magnetic bodies to have a peculiar repulsion for each other, exactly equal to their attraction for the magnetic fluid. But in the case of magnetism, another modification was necessary. It was impossible to suppose here, as in the electrical phenomena, that one of the fluids was accumulated on one extremity of a body, and the other fluid on the other extremity; for though this might appear, at first sight, to be the case in a magnetic needle, it was found that when the needle was cut into two halves, the half in which the austral fluid had seemed to predominate, acquired immediately a boreal pole opposite to its austral pole, and a similar effect followed in the other half. The same is true, into however many parts the magnetic body be cut. The way in which Coulomb modified the theory so as to reconcile it with such facts, is simple and satisfactory. He supposes[15] the magnetic body to be made up of “molecules or integral parts,” or, as they were afterwards called by M. Poisson, “magnetic elements.” In each of these elements, (which are extremely minute,) the fluids can be separated, so that each element has an austral and a boreal pole; but the austral pole of an element which is adjacent to the boreal pole of the next, neutralizes, or nearly neutralizes, its effect; so that the sensible magnetism appears only towards the extremities of the body, as it would do if the fluids could permeate the body freely. We shall have exactly the same result, as to sensible magnetic force, on the one supposition and on the other, as Coulomb showed.[16]
[15] Mem. A. P. 1789, p. 488.
[16] Mem. A. P. p. 492.
The theory, thus freed from manifest incongruities, was to be reduced to calculation, and compared with experiment; this was done in Coulomb’s Seventh Memoir.[17] The difficulties of calculation in this, as in the electric problem, could not be entirely surmounted by the analysis of Coulomb; but by various artifices, he obtained theoretically the [223] relative amount of magnetism at several points of a needle,[18] and the proposition that the directive force of the earth on similar needles saturated with magnetism, was as the cube of their dimensions; conclusions which agreed with experiment.
[17] A. P. 1789.
[18] p. 485.
The agreement thus obtained was sufficient to give a great probability to the theory; but an improvement of the methods of calculation and a repetition of experiments, was, in this as in other cases, desirable, as a confirmation of the labors of the original theorist. These requisites, in the course of time, were supplied. The researches of Laplace and Legendre on the figure of the earth had (as we have already [stated],) introduced some very peculiar analytical artifices, applicable to the attractions of spheroids; and these methods were employed by M. Biot in 1811, to show that on an elliptical spheroid, the thickness of the fluid in the direction of the radius would be as the distance from the centre.[19] But the subject was taken up in a more complete manner in 1824 by M. Poisson, who obtained general expressions for the attractions or repulsions of a body of any form whatever, magnetized by influence, upon a given point; and in the case of spherical bodies was able completely to solve the equations which determine these forces.[20]
[19] Bull. des Sc. No. li.
[20] A. P. for 1821 and 2, published 1826.
Previously to these theoretical investigations, Mr. Barlow had made a series of experiments on the effect of an iron sphere upon a compass needle; and had obtained empirical formulæ for the amount of the deviation of the needle, according to its dependence upon the position and magnitude of the sphere. He afterwards deduced the same formulæ from a theory which was, in fact, identical with that of Coulomb, but which he considered as different, in that it supposed the magnetic fluids to be entirely collected at the surface of the sphere. He had indeed found, by experiment, that the surface was the only part in which there was any sensible magnetism; and that a thin shell of iron would produce the same effect as a solid ball of the same diameter.
But this was, in fact, a most complete verification of Coulomb’s theory. For though that theory did not suppose the magnetism to be collected solely at the surface, as Mr. Barlow found it, it followed from the theory, that the sensible magnetic intensity assumed the same distribution (namely, a surface distribution,) as if the fluids could permeate the whole body, instead of the “magnetic elements” only. Coulomb, indeed, had not expressly noticed the result, that the sensible [224] magnetism would be confined to the surface of bodies; but he had found that, in a long needle, the magnetic fluid might be supposed to be concentrated very near the extremities, just as it is in a long electric body. The theoretical confirmation of this rule among the other consequences of the theory,—that the sensible magnetism would be collected at the surface,—was one of the results of Poisson’s analysis. For it appeared that if the sum of the electric elements of the body was equal to the whole body, there would be no difference between the action of a solid sphere and very thin shell.
We may, then, consider the Coulombian theory to be fully established and verified, as a representation of the laws of magnetical phenomena. We may add, as a remarkable and valuable example of an ulterior step in the course of sciences, the application of the laws of the distribution of magnetism to the purposes of navigation. It had been found that the mass of iron which exists in a ship produces a deviation in the direction of the compass-needle, which was termed “local attraction,” and which rendered the compass an erroneous guide. Mr. Barlow proposed to correct this by a plate of iron placed near the compass; the plate being of comparatively small mass, but, in consequence of its expanded form, and its proximity to the needle, of equivalent effect to the disturbing cause.
[2nd Ed.] [This proposed arrangement was not successful, because as the ship turns into different positions, it may be considered as revolving round a vertical axis; and as this does not coincide with the magnetic axis, the relative magnetic position of the disturbing parts of the ship, and of the correcting plate, will be altered, so that they will not continue to counteract each other. In high magnetic latitudes the correcting plate was used with success.
But when iron ships became common, a correction of the effect of the iron upon the ship’s compass in the general case became necessary. Mr. Airy devised the means of making this correction. By placing a magnet and a mass of iron in certain positions relative to the compass, the effect of the rest of the iron in the ship is completely counteracted in all positions.[21]] ~Additional material in the [3rd edition].~
[21] See Phil. Trans. 1836.
But we have still to trace the progress of the theory of terrestrial magnetism.
Theory of Terrestrial Magnetism.—Gilbert had begun a plausible course of speculation on this point. “We must reject,” he says,[22] “in [225] the first place, that vulgar opinion of recent writers concerning magnetic mountains, or a certain magnetic rock, or an imaginary pole at a certain distance from the pole of the earth.” For, he adds, “we learn by experience, that there is no such fixed pole or term in the earth for the variation.” Gilbert describes the whole earth as a magnetic globe, and attributes the variation to the irregular form of its protuberances, the solid parts only being magnetic. It was not easy to confirm or refute this opinion, but other hypotheses were tried by various writers; for instance, Halley had imagined, from the forms of the lines of equal variation, that there must be four magnetic poles; but Euler[23] showed that the “Halleian lines” would, for the most part, result from the supposition of two magnetic poles, and assigned their position so as to represent pretty well the known state of the variation all over the world in 1744. But the variation was not the only phenomenon which required to be taken into account; the dip at different places, and also the intensity of the force, were to be considered. We have [already] mentioned M. de Humboldt’s collection of observations of the dip. These were examined by M. Biot, with the view of reducing them to the action of two poles in the supposed terrestrial magnetic axis. Having, at first, made the distance of these poles from the centre of the earth indefinite, he found that his formulæ agreed more and more nearly with the observations, as the poles were brought nearer; and that fact and theory coincided tolerably well when both poles were at the centre. In 1809,[24] Krafft simplified this result, by showing that, on this supposition, the tangent of the dip was twice the tangent of the latitude of the place as measured from the magnetic equator. But M. Hansteen, who has devoted to the subject of terrestrial magnetism a great amount of labor and skill, has shown that, taking together all the observations which we possess, we are compelled to suppose four magnetic poles; two near the north pole, and two near the south pole, of the terrestrial globe; and that these poles, no two of which are exactly opposite each other, are all in motion, with different velocities, some moving to the east and some to the west. This curious collection of facts awaits the hand of future theorists, when the ripeness of time shall invite them to the task.
[22] Lib. iv. c. 1. De Variatione.
[23] Ac. Berlin, 1757.
[24] Enc. Met. p. 742.
[2nd Ed.] [I had thus written in the first edition. The theorist who was needed to reduce this accumulation of facts to their laws, [226] had already laid his powerful hand upon them; namely, M. Gauss, a mathematician not inferior to any of the great men who completed the theory of gravitation. And institutions had been established for extending the collection of the facts pertaining to it, on a scale which elevates Magnetism into a companionship with Astronomy. M. Hansteen’s Magnetismus der Erde was published in 1819. His conclusions respecting the position of the four magnetic “poles” excited so much interest in his own country, that the Norwegian Storthing, or parliament, by a unanimous vote, provided funds for a magnetic expedition which he was to conduct along the north of Europe and Asia; and this they did at the very time when they refused to make a grant to the king for building a palace at Christiania. The expedition was made in 1828–30, and verified Hansteen’s anticipations as to the existence of a region of magnetic convergence in Siberia, which he considered as indicating a “pole” to the north of that country. M. Erman also travelled round the earth at the same time, making magnetic observations.
About the same time another magnetical phenomenon attracted attention. Besides the general motion of the magnetic poles, and the diurnal movements of the needle, it was found that small and irregular disturbances take place in its position, which M. de Humboldt termed magnetic storms. And that which excited a strong interest on this subject was the discovery that these magnetic storms, seen only by philosophers who watch the needle with microscopic exactness, rage simultaneously over large tracts of the surface of our globe. This was detected about 1825 by a comparison of the observations of M. Arago at Paris with simultaneous observations of M. Kupffer at Kasan in Russia, distant more than 47 degrees of longitude.
At the instance of M. de Humboldt, the Imperial Academy of Russia adopted with zeal the prosecution of this inquiry, and formed a chain of magnetic stations across the whole of the Russian empire. Magnetic observations were established at Petersburg and at Kasan, and corresponding observations were made at Moscow, at Nicolaieff in the Crimea, and Barnaoul and Nertchinsk in Siberia, at Sitka in Russian America, and even at Pekin. To these magnetic stations the Russian government afterwards added, Catharineburg in Russia Proper, Helsingfors in Finland, Teflis in Georgia. A comparison of the results obtained at four of these stations made by MM. de Humboldt and Dove, in the year 1830, showed that the magnetic disturbances were simultaneous, and were for the most parallel in their progress. [227]
Important steps in the prosecution of this subject were soon after made by M. Gauss, the great mathematician of Göttingen. He contrived instruments and modes of observation far more perfect than any before employed, and organized a system of comparative observations throughout Europe. In 1835, stations for this purpose were established at Altona, Augsburg, Berlin, Breda, Breslau, Copenhagen, Dublin, Freiberg, Göttingen, Greenwich, Hanover, Leipsic, Marburg, Milan, Munich, Petersburg, Stockholm, and Upsala. At these places, six times in the year, observations were taken simultaneously, at intervals of five minutes for 24 hours. The Results of the Magnetic Association (Resultaten des Magnetischen Vereins) were published by MM. Gauss and Weber, beginning in 1836.
British physicists did not at first take any leading part in these plans. But in 1836, Baron Humboldt, who by his long labors and important discoveries in this subject might be considered as peculiarly entitled to urge its claims, addressed a letter to the Duke of Sussex, then President of the Royal Society, asking for the co-operation of this country in so large and hopeful a scheme for the promotion of science. The Royal Society willingly entertained this appeal; and the progress of the cause was still further promoted when it was zealously taken up by the British Association for the Advancement of Science, assembled at Newcastle in 1838. The Association there expressed its strong interest in the German system of magnetic observations; and at the instigation of this body, and of the Royal Society, four complete magnetical observatories were established by the British government, at Toronto, St. Helena, the Cape of Good Hope, and Van Diemen’s Land. The munificence of the Directors of the East India Company founded and furnished an equal number at Simla (in the Himalayah), Madras, Bombay, and Sincapore. Sir Thomas Brisbane added another at his own expense at Kelso, in Scotland. Besides this, the government sent out a naval expedition to make discoveries (magnetic among others), in the Antarctic regions, under the command of Sir James Ross. Other states lent their assistance also, and founded or reorganized their magnetic observatories. Besides those already mentioned, one was established by the French government at Algiers; one by the Belgian, at Brussels; two by Austria, at Prague and Milan; one by Prussia, at Breslau; one by Bavaria, at Munich; one by Spain, at Cadiz; there are two in the United States, at Philadelphia and Cambridge; one at Cairo, founded by the Pasha of Egypt; and in India, one at Trevandrum, established by the Rajah of Travancore; and one by [228] the King of Oude, at Lucknow. At all these distant stations the same plan was followed out, by observations strictly simultaneous, made according to the same methods, with the same instrumental means. Such a scheme, combining world-wide extent with the singleness of action of an individual mind, is hitherto without parallel.
At first, the British stations were established for three years only; but it was thought advisable to extend this period three years longer, to end in 1845. And when the termination of that period arrived, a discussion was held among the magneticians themselves, whether it was better to continue the observations still, or to examine and compare the vast mass of observations already collected, so as to see to what results and improvements of methods they pointed. This question was argued at the meeting of the British Association at Cambridge in that year; and the conference ended in the magneticians requesting to have the observations continued, at some of the observatories for an indefinite period, at others, till the year 1848. In the mean time the Antarctic expedition had brought back a rich store of observations, fitted to disclose the magnetic condition of those regions which it had explored. These were discussed, and their results exhibited, in the Philosophical Transactions for 1843, by Col. Sabine, who had himself at various periods, made magnetic observations in the Arctic regions, and in several remote parts of the globe, and had always been a zealous laborer in this fruitful field. The general mass of the observations was placed under the management of Professor Lloyd, of Dublin, who has enriched the science of magnetism with several valuable instruments and methods, and who, along with Col. Sabine, made a magnetic survey of the British Isles in 1835 and 1836.
I do not dwell upon magnetic surveys of various countries made by many excellent observers; as MM. Quetelet, Forbes, Fox, Bache and others.
The facts observed at each station were, the intensity of the magnetic force; the declination of the needle from the meridian, sometimes called the variation; and its inclination to the horizon, the dip;—or at least, some elements equivalent to these. The values of these elements at any given time, if known, can be expressed by charts of the earth’s surface, on which are drawn the isodynamic, isogonal, and isoclinal curves. The second of these kinds of charts contain the “Halleian lines” spoken of in a previous [page]. Moreover the magnetic elements at each place are to be observed in such a [229] manner as to determine both their periodical variations (the changes which occur in the period of a day, and of a year), the secular changes, as the gradual increase or diminution of the declination at the same place for many years; and the irregular fluctuations which, as we have said, are simultaneous over a large part, or the whole, of the earth’s surface.
When these Facts have been ascertained over the whole extent of the earth’s surface, we shall still have to inquire what is the Cause of the changes in the forces which these phenomena disclose. But as a basis for all speculation on that subject, we must know the law of the phenomena, and of the forces which immediately produce them. I have already [said] that Euler tried to account for the Halleian lines by means of two magnetic “poles,” but that M. Hansteen conceived it necessary to assume four. But an entirely new light has been thrown upon this subject by the beautiful investigations of Gauss, in his Theory of Terrestrial Magnetism, published in 1839. He remarks that the term “poles,” as used by his predecessors, involves an assumption arbitrary, and, as it is now found, false; namely, that certain definite points, two, four, or more, acting according to the laws of ordinary magnetical poles, will explain the phenomena. He starts from a more comprehensive assumption, that magnetism is distributed throughout the mass of the earth in an unknown manner. On this assumption he obtains a function V, by the differentials of which the elements of the magnetic force at any point will be expressed. This function V is well known in physical astronomy, and is obtained by summing all the elements of magnetic force in each particle, each multiplied by the reciprocal of its distance; or as we may express it, by taking the sum of each element and its proximity jointly. Hence it has been proposed[25] to term this function the “integral proximity” of the attracting mass.[26] By using the most refined [230] mathematical artifices for deducing the values of V and its differentials in converging series, he is able to derive the coefficients of these series from the observed magnetic elements at certain places, and hence, to calculate them for all places. The comparison of the calculation with the observed results is, of course, the test of the truth of the theory.
[25] Quart. Rev. No. 131, p. 283.
[26] The function V is of constant occurrence in investigations respecting attractions. It is introduced by Laplace in his investigations respecting the attractions of spheroids, Méc. Cél. Livr. iii. Art. 4. Mr. Green and Professor Mac Cullagh have proposed to term this function the Potential of the system; but this term (though suggested, I suppose, by analogy with the substantive Exponential), does not appear convenient in its form. On the other hand, the term Integral Proximity does not indicate that which gives the function its peculiar claim to distinction; namely, that its differentials express the power or attraction of the system. Perhaps Integral Potentiality, or Integral Attractivity, would be a term combining the recommendations of both the others.
The degree of convergence of the series depends upon the unknown distribution of magnetism within the earth. “If we could venture to assume,” says M. Gauss, “that the members have a sensible influence only as far as the fourth order, complete observations from eight points would be sufficient, theoretically considered, for the determination of the coefficients.” And under certain limitations, making this assumption, as the best we can do at present, M. Gauss obtains from eight places, 24 coefficients (each supplying three elements), and hence calculates the magnetic elements (intensity, variation and dip) at 91 places in all parts of the earth. He finds his calculations approach the observed values with a degree of exactness which appears to be quite convincing as to the general truth of his results; especially taking into account how entirely unlimited is his original hypothesis.
It is one of the most curious results of this investigation that according to the most simple meaning which we can give to the term “pole” the earth has only two magnetic poles; that is, two points where the direction of the magnetic force is vertical. And thus the isogonal curves may be looked upon as deformations of the curves deduced by Euler from the supposition of two poles, the deformation arising from this, that the earth does not contain a single definite magnet, but irregularly diffused magnetical elements, which still have collectively a distinct resemblance to a single magnet. And instead of Hansteen’s Siberian pole, we have a Siberian region in which the needles converge; but if the apparent convergence be pursued it nowhere comes to a point; and the like is the case in the Antarctic region. When the 24 Gaussian elements at any time are known the magnetic condition of the globe is known, just as the mechanical condition of the solar system is known, when we know the elements of the orbits of the satellites and planets and the mass of each. And the comparison of this magnetic condition of the globe at distant periods of time cannot fail to supply materials for future researches and speculations with regard to the agencies by which the condition of the earth is determined. The condition of which we here speak must necessarily be its mechanico-chemical condition, being expressed, as it will be, in terms of the mechanico-chemical sciences. The [231] investigations I have been describing belong to the mechanical side of the subject: but when philosophers have to consider the causes of the secular changes which are found to occur in this mechanical condition, they cannot fail to be driven to electrical, that is, chemical agencies and laws.
I can only allude to Gauss’s investigations respecting the Absolute Measure of the Earth’s Magnetic Force. To determine the ratio of the magnetic force of the earth to that of a known magnet, Poisson proposed to observe the time of vibration of a second magnet. The method of Gauss, now universally adopted, consists in observing the position of equilibrium of the second magnet when deflected by the first.
The manner in which the business of magnetic observation has been taken up by the governments of our time makes this by far the greatest scientific undertaking which the world has ever seen. The result will be that we shall obtain in a few years a knowledge of the magnetic constitution of the earth which otherwise it might have required centuries to accumulate. The secular magnetic changes must still require a long time to reduce to their laws of phenomena, except observation be anticipated or assisted by some happy discovery as to the cause of these changes. But besides the special gain to magnetic science by this great plan of joint action among the nations of the earth, there is thereby a beginning made in the recognition and execution of the duty of forwarding science in general by national exertions. For at most of the magnetic observatories, meteorological observations are also carried on; and such observations, being far more extensive, systematic, and permanent than those which have usually been made, can hardly fail to produce important additions to science. But at any rate they do for science that which nations can do, and individuals cannot; and they seek for scientific truths in a manner suitable to the respect now professed for science and to the progress which its methods have made. Nor are we to overlook the effect of such observations as means of training men in the pursuit of science. “There is amongst us,” says one of the magnetic observers, “a growing recognition of the importance, both for science and for practical life, of forming exact observers of nature. Hitherto astronomy alone has afforded a very partial opportunity for the formation of fine observers, of which few could avail themselves. Experience has shown that magnetic observations may serve as excellent training schools in this respect.”[27]]
[27] Letter of W. Weber. Brit. Assoc. Rep. 1845, p. 17.
[232] The various other circumstances which terrestrial magnetism exhibits,—the diurnal and annual changes of the position of the compass-needle;—the larger secular change which affects it in the course of years;—the difference of intensity at different places, and other facts, have naturally occupied philosophers with the attempt to determine, both the laws of the phenomena and their causes. But these attempts necessarily depend, not upon laws of statical magnetism, such as they have been explained above; but upon the laws by which the production and intensity of magnetism in different cases are regulated;—laws which belong to a different province, and are related to a different set of principles. Thus, for example, we have not attempted to explain the discovery of the laws by which heat influences magnetism; and therefore we cannot now give an account of those theories of the facts relating to terrestrial magnetism, which depend upon the influence of temperature. The conditions of excitation of magnetism are best studied by comparing this force with other cases where the same effects are produced by very different apparent agencies; such as galvanic and thermo-electricity. To the history of these we shall presently proceed.
Conclusion.—The hypothesis of magnetic fluids, as physical realities, was never widely or strongly embraced, as that of electric fluids was. For though the hypothesis accounted, to a remarkable degree of exactness, for large classes of the phenomena, the presence of a material fluid was not indicated by facts of a different kind, such as the spark, the discharge from points, the shock, and its mechanical effects. Thus the belief of a peculiar magnetic fluid or fluids was not forced upon men’s minds; and the doctrine above stated was probably entertained by most of its adherents, chiefly as a means of expressing the laws of phenomena in their elementary form.
One other observation occurs here. We have seen that the supposition of a fluid moveable from one part of bodies to another, and capable of accumulation in different parts of the surface, appeared at first to be as distinctly authorized by magnetic as by electric phenomena; and yet that it afterwards appeared, by calculation, that this must be considered as a derivative result; no real transfer of fluid taking place except within the limits of the insensible particles of the body. Without attempting to found a formula of philosophizing on this circumstance, we may observe, that this occurrence, like the disproof of heat as a material fluid, shows the possibility of an hypothesis which shall very exactly satisfy many phenomena, and yet be incomplete: it [233] shows, too, the necessity of bringing facts of all kinds to bear on the hypothesis; thus, in this case it was requisite to take into account the facts of junction and separation of magnetic bodies, as well as their attractions and repulsions.
If we have seen reason to doubt the doctrine of electric fluids as physical realities, we cannot help pronouncing upon the magnetic fluids as having still more insecure claims to a material existence, even on the grounds just stated. But we may add considerations still more decisive; for at a further stage of discovery, as we shall see, magnetic and electric action were found to be connected in the closest manner, so as to lead to the persuasion of their being different effects of one common cause. After those discoveries, no philosopher would dream of assuming electric fluids and magnetic fluids as two distinct material agents. Yet even now the nature of the dependence of magnetism upon any other cause is extremely difficult to conceive. But till we have noticed some of the discoveries to which we have alluded, we cannot even speculate about that dependence. We now, therefore, proceed to sketch the history of these discoveries. ~Additional material in the [3rd edition].~