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of four poles and no more, thus adopting without any calculation, that the total mag. so far the Halleian hypothesis. But he is netic action of the earth on a needle at a obliged to complicate it with additional cy. given place is equivalent to that of one cles, by declaring each pole to have a sep: infinitely small magnet of infinite power plac. arate and independent movement and period ed at a point not very remote from the cen. -a modification which goes a great way to-tre. But it by no means follows (except in wards divesting them of any attribute of phy- the single case of an equal and parallel sepasical reality. But on the other hand, Mr. ration of the opposite magnetisms in each Barlow, who, so recently as 1833, has pub- molecule of a homogeneous sphere), but lished a variation chart, perhaps the most quite the reverse, that one and the same such elaborate which has yet been produced, de- magnet, or any finite combination of such, clares quite as strongly against them. I can should possess this property for every point see (says he, speaking of the variation lines in the surface. We cannot help concluding, in the Pacific Ocean) no possible position of therefore, that it is lost labour to make further four poles which can lead to such a configu- attempts to reconcile the phenomena with ration. And again, in discussing their any hypotheses of this nature. course in the Indian seas, he considers it In considering the distribution of the equally inconsistent with the notion that all earth's magnetic action over its surface, the these phenomena are due to the action of variation lines have hitherto received by far four or more magnetic poles. For this hy- the greater, and, theoretically speaking, an pothesis he accordingly substitutes one more undue share of attention, by reason of their general, “That there is no determinate pole nautical importance. They have the disadto which all needles point, but that each place vantage (as a graphical representation of has its own particular pole and polar revo. phenomena) of offering nothing distinct to lution, governed probably by some one gene- the imagination except their own unaccount. ral but unknown cause.' On this we have able flexures—and rather tend to complicate only to remark that it amounts to giving up than to aid conception of the play of forces altogether the hypothesis of poles,' and in which they originate. It has been pro
magnetic axes,'since there is no conceivable posed to substitute for them a system of lines law of change in the magnetic lines to which perpendicular at every point to the direction a proposition so general will not apply. It of the needle. This would be a great imdeclares, in effect, that the true law of these provement, were it practicable to construct changes is still to seek—a position in which such lines from direct observation, which it we fully agree. It is clear that the possi- unfortunately is not, by reason of a difficulty bility or impossibility of representing the purely mathematical-our inability to inte. magnetic action of the globe on every point grate differential equations, whose variable of its surface by that of two or more fixed co.efficients are only given by observation. points within it, must depend on the geome. It is otherwise wit! what are called the trical resultant of the sum of its molecular at- isoclinal and isodynamic lines. Their course, tractions and repulsions passing or not passing graphically projected, speaks not only to the through an invariable attractive and another eye but immediately to the mind. It is only, invariable repulsive point, or being equiva- however, within a comparatively short perilent to several others so passing, a condition od that charts of their course have been conin the abstract generally incapable of fulfil structed. The work of Mr. Hansteen exhib. ment, and in the highest degree improbable its the specimens of such charts, or fragin any particular case. In effect, we may ments of them, for 1600, 1700, and 1780, conceive the magnetic force of the earth on which, so far as they can be depended on, a boreal molecule at its surface, as being the (and he considers them entitled to considerdifference of two forces whereof the austral, able confidence,) confirm the general westor attractive, is the total attraction of a solid ward tendency of the magnetic system, of unknown form and density, but approach. though in a manner less striking than in ing to a sphere whose particles attract with a the case of the variation or isogonal lines, by force identical in law with gravity; and the reason of their gentler flexures and more boreal, or repulsive is the total repulsion of general parallelism to the equator of the a solid exactly similar and equal, whose globe. molecules repel with equal forces, but of The direction taken by the magnetic ncewhich each particle is removed from the dle is determined by the two elements, its corresponding particle of the attractive solid horizontal position, or declination from the by an infinitesimal quantity, according to an meridian, and the dip or inclination. Comunknown law of displacement. From this plete charts of the dip and declination, thereview of the matter (which strikes us as new fore, did such exist, would afford complete and as offering some advantages), it follows' knowledge of this direction over the globe. But another important element remains, viz. the polarised rays-somewhat wanting in the intensity of the total magnetic force, or symmetry, it is true, but, especially as reof the power with which, when withdrawn gards the two northern systems of isody. from its position of equilibrium, it tends to namic ovals, very definitely marked out; revert to it. The discovery that this power while in the south, unequivocal traces, shais not equal in all parts of the globe, as a dowing out the existence of two similar ovals, matter of observed fact, (for, theoretically, point to a distribution of magnetism in that it may be said to have been always under- hemisphere analogous to what obtains in the stood,) is of comparatively recent date. Ma. northern Observations are yet wanting to jor Sabine, to whom we are indebted for a determine whether this system of lines be in report on this subject, (Seventh Report of a similar state of secular progress westward the British Association,) remarks, that this over ihe globe, with those of the dip and important fact remained, at the commence- variation, (though that such is the case can ment of this century, unattested by a single hardly be doubted,) and whether and what published observation,' while, such has been changes of form and mutual relation they ihe diligence with which they have been undergo in its course. since accumulated, that the charts with The direction taken by a needle freely which that report is accompanied, represent- suspended, and the force by wbich it tends ing the course of the isodynamic lines (lines to settle in that position, being koown on of equal intensity) over both hemispheres, every accessible point of the earth's surface rest on no less than 753 distinct determina- to a certain degree of approximation, the tions at 670 stations, collected, arranged, next step in the inductive process of discoand discussed, with a care, precision, and very is to embody this knowledge in a law luminous order which it is difficult to esti. mathematically stated, and either derived mate too highly. We consider this report, from some rational theory of magnetic action, indeed, as one of the most finished things of or at least shown to be not inconsistent with the kind that have ever been produced, and such a theory. In the remarkable work as having accomplished, in the completest which we have selected as part of the subject manner, the objects proposed by that asso. matter of these pages, (Allgemeine Theorie, ciation in calling for such reports, by so &c.*) M. Gauss has succeeded in obtaining comprehending in ore view the results of our snch a formula by a mixed process of thcoknowledge and the amount of our ignorance, retical investigation in general, and empirical as to afford the greatest possible stimulus to adaptation in particular, which represents, in further inquiry. It is, indeed, impossible to a most striking and unexpected manner ininspect these charts without perceiving that deed, the whole mass of these complicated a new branch of magnetic science has been phenomena, so far as they have been yet created, and here for the first time embodied. developed. Setting out with the most geneThe observations on which they are ground. ral suppositions as to the distribution of mag. ed are, for the most part, those of Humboldt netism over the surface and through the in his travels and voyages in Equinoctial substance of the earth, and assuming only America—of Hansteen and Due, in their that the magnetic force follows the same journey through Siberia, in which they tra- law of decrease with that of gravity, he apversed the whole north of Europe and Asia, plies the Laplacian method of representing and carried their researches to the polar the attraction of a spherical or spheroidal circle; and of Erman, who, with the same solid to the expression of the resultant mag. object, encircled the globe by a mixed land netic force considered as resolved into three and sea voyage, setting out from Petersburg, components, one perpendicular to the hori. embarking in Kamtschatka, and returning zon at any point producing the dip, the other by the Cape. Major Sabine's personal con- two in the horizontal plane. The whole tributions to the same stock, also, are both investigation, after the examples of Laplace numerous and important, the scenes of his and Poisson, is made to turn upon the prolabours having the unique interest of having perties and development of that peculiar been chosen in the most inaccessible, the function which represents the sum of the most desolate, and the most unhealthy re- active molecules, whether attractive or re. gions upon earth — such as Spitzbergen, pulsive, each divided by its distance from Melville Island, St. Thomas's, &c. The the point attracted or repelled--a function general result is, that the isodynamic lines which much wants a name, and for which appear to be arranged on the globe in forms we would venture to propose that of the which strongly remind us of the lemniscate integral proximity' of the attracting mass. curves exhibited by crystals exposed to rolarised light, when referred to a sphere tra. * This work will be found extremely well trans versed in all directions through its centre by Ilated in Taylor's Scientific Memoirs.'
The differential co-efficients of this function which analysis, assisted by the theory of express the resolved components of the total probabilities, supplies in such cases, eliciting magnetic action; and the art of the analyst the numerical values of those co-efficients is shown in the elegant and masterly manner which suit the observations best. This in which he succeeds in obtaining laws and method is familiar to geometers by the exrelations susceptible of practical verification, tensive applination which has been made of without compromising the generality of this it in the lunar theory, in which the forms of auxiliary function, and involving himself in the equations, or, as they are termed, their the difficulties which would aitend its ex. arguments, being assigned by theory, the pression in terms of any presumed law of comparison of their series (with unknown distribution of magnetic power, such as, for co-esficients,) with an extensive series of instance, its concentration in poles, axes, &c. observations, has been resorted to as a Some of these relations are propositions of means of determining the values of those coconsiderable interest; as, for example, M. efficients, otherwise too complicated to be Gauss demonstrates that-whatever be the directly investigated. Such is the process law of magnetic distribution—if there be any followed in this case by M. Gauss, assisted, series of stations forming a polygon of incon- however, and stripped of the worst part of siderable dimensions compared with the its otherwise almost insuperable labour and area of the globe, the dip, horizontal direc. difficulty, by a choice of data in the highest tion, and intensity at each of these stations, degree ingenious and artificial—which is must satisfy a certain very simple equation rendered possible by the possession of the of condition, by which, if all but one of them charts above alluded to—and to which, as a be given, that one may be calculated and fine example of the kind of power placed in taking the case of a triangle formed by the hands of geometers by the method of Paris, Göttingen, and Milan, he finds the graphical representation in general, we are condition to be, in fact, exactly satisfied by desirous to draw especial attention. It conthe actual elements furnished by observation sists in comparing the series expressing the for those stations. Another of these propo- elements in question, noi with their values, sitions may be instanced as still more gen- as actually assigned by observation at real eral and remarkable, viz., that the knowledge stations, but with values.graphically interof the value of that particular component of polated by the aid of the charts,' 10 corresthe horizontal magnetic force on!y which pond to a set of imaginary stations, so disacts in the direction of the meridian, suppos- tributed over the globe as to afford the great. ing that knowledge complete, and to extend est possible facility to the calculations, and to every point of the earth's surface, would to break up the mass of unknown quantities, enable us to assign the nature of the function which in the general case would be hope. expressing the integral proximity,' and lessly entangled one with another, into thence to deduce every other particular of groups of easy management. Thus, in the terrestrial magnetism.
case before us, M. Gauss distributes his staThe development of this function, and tions over seven parallels of latitude, so as thence of the three magnetic components to divide each parallel into twelve equal depending on that function in terms of the parts. latitude and longitude of the point acted on, It has been usual to consider such charts without any compromise of its generality, is and graphical representations as mere helps performed by the aid of those co-efficients to the imagination, or as rough registers, introduced by Laplace in the analysis of the giving by inspection approximate values for attraction of spheroids and the figure of the ready practical use ; but this we consider earth, which have been found to facilitate in to be quite an under-estimate of their im. so high a degree these difficult investiga-portance. We regard such projections, tions. The form of these developments as when carefully executed, not only in this, functions of the sines and co-sines of arcs, but in every other science in a similar stage arranged into successive orders by their of progress, as necessary instruments and powers and products, is thus generally as. adjuncts to the highest applications of theosigned, but the special values of the co-effi- ry—as the only means we possess, or ever cients remain to be discovered ; and this can can possess, of purifying great masses of obonly be done in two ways, viz., à priori, by servational data from the effects of local a knowledge of the actual law of the distri- influence and personal casual error. bution of magnetism in the earth, and the They furnish, in short, and will, hencefor. performance of the requisite integrations; ward, as this their important office becomes or à posteriori, by comparing the develop betier understood, every day more and more ments of each component force with actual furnish that intermediate step between ob. observation ; and thus, by the usual aids servation and theory which has long been
wanting to the perfection of both. They |tion lines, in the Pacific and Indian seas, enable the theorist in particular to choose noticed by Mr. Barlow as so characteristic his ground above all individual place and cir- and unaccountable, are made perfectly intelcumstance, and 10 select his Jaia, not where ligible as parts of a connected system which casualty or convenience shall have led the would be incomplete without them. The observer to collect them, but in pure accord- northern magnetic pole too, or point of per. ance with the requirements of his geometry, pendicular dip given by M. Gauss's formula, and the simplification of his calculus. In coincides, within little more than 200 miles, consonance with this view of the subject, we with its place actually observed, or at least anticipate the time when no computist will closely approached, by Ross in 1832; while ever take the trouble to compare formulæ the European, African, and Atlantic lines with single observations in their crude state, exhibit a correspondence approaching to for the purpose of determining elements, identity. Some small, but not unimportant, such comparison being reserved for finally systematic deviations have been pointed out testing the validity of theories.
by M. Erman, which a resumption of the The charts used by M. Gauss for this calculations with more dependable data will, purpose were, that of the dip published by no doubt, cause to disappear. Horner (Physicalisches Wörterbuch, b. 6), A feature we cannot help noticing in this and those of the variation and intensity, by work of M. Gauss is the uniform predomiBarlow and Sabine already mentioned. Wenance of the philosopher over the mere gemay be proud as Englishmen to have fur- ometer. From his well known eminence in nished two out of the three digested masses of the latter line, we might have expecteil undata for this vast undertaking, especially as due prominence to be given to methods and it is to the appearance of the last of these artifices, and have looked for displays of forcharts that M. Gauss expressly ascribes his mulæ ostentatiously spreading into luxurihaving been induced to enter upon the for- ance; but, on the contrary, the analysis is midable calculations it involves.
everywhere kept subordinate to the physical The success of this remarkable attempt inquiry, and, though handled throughout we consider as signally encouraging. M. with the skill and power of a consummate Gauss has himself compared his resulting master, is nowhere suffered to appear as a formula with actual observation, at ninety. primary object. one of the best stations in every variety of One incidental result of these investiga. latitude and longitude, and in all the particu. tions will appear very striking—astounding lars of dip, variation and intensity. In one indeed to those whom habit has not familiar. instance only does the error in dip exceed ised with the enormous numbers which oc. 40; in only two does that of the variation cur when the operations of nature are meaamount to 5°; while the intensity is repre. sured by man's diminutive units. It is the sented throughout within an extremely mi. estimate of the total magnetic power or nute fraction of the whole, with exception of moment of magnetism' of the Earth, as two stations, Port Fanzine and Santa Cruz, compared with that of a saturated steel bar where there is no doubt some error of ob. one pound in weight. This proportion M. servation.
Gauss calculates to be as 8,454,000,000,000,This comparison becomes more interest- 000,000,000 to 1, which, supposing the ing, and assumes almost the character of magnetic force uniformly distributed, will be ocular evidence, when as is done in the report found to amount to about six such bars to made by the Committee of the Royal Soci- every cubic yard. ety now before us, charts construcied from Besides the secular changes in the magthe formulæ alone are placed side by side netic forces which gradually carry the needle with those derived from observation. This far from a fixed direction, according to laws comparison with his own variation chart at present unknown, but which at all events constructed from observations made between act with steadiness and regularity, observa. 1827 and 1830 has been made by M. Er- tion has recognised two subordinate systems man, and accompanies a most interesting let- of fluctuation to which it is subject, the one ter from him appended to the report in ques. periodical, the other, so far as we can see tion; and a similar comparison with Major at present, quite capricious and irregularSabine's chart of the total intensiiy is also in consequence of which the name of mag. annexed; and the resemblance in both cases netic perturbations has been assigned to them, between the type and the antitype is so close as if the needle were disturbed by some as to justify a conviction of our having at external influence of a transitory nature. length made a real approach to a geome The periodical oscillations of the magnet. trical expression of the phenomena. In ic needle were first observed by Graham in particular, the singular courses of the varia. 1722, and have since been studied with
much diligence and perseverance by sever-bations, which have of late and deservedly al assiduous and careful observers, among attracted great attention by reason of some whom our countryman Mr. Gilpin de- very extraordinary facts brought to light serves especially to be noticed as having by their comparison at different and remote made these observations his consant occu- stations. pation during the whole period from 1787 to The illustrious Humboldt, to whom every 1806, and having for upwards of sixteen department of science owes so much, and months kept an hourly register extending to whom the rare glory belongs of being to twelve hours of every twenty-four, a pro- the first to push onward in so many differcess by which alorie the true laws of such ent lines, gave the forward impulse in this. oscillations can be deduced. By these and During the course of those his most memora. similar observations by Canton, Wargentin, ble voyages and travels in the equinoctial and Cassini, the existence of periodical regions of America, in which, all eye, all movements, both diurnal and annual, has ear, all thought, he seemed to have received been established. The deficiency of nightly on the expansive retina of his mind the pic. observations has since been supplied by ture of universal nature, and to have treasurBaron Von Humboldt, who, by investigat- ed up its images in the stores of a memory ing the particulars of the nocturnal progress and an intellect worthy of such a prospect of the oscillation, has completed the outline -the observation of the magnetic phenomewhich Gilpin and others had begun, and na in all their particulars occupied a large enabled us to state with some degree of pre- portion of his attention. On his return to cision the nature and extent of these periodi- Europe, as he informs us in his letter to the cal changes. The horizontally suspended Duke of Sussex, he conceived the project of needle is found to make, each twenty-four examining the hourly changes of the yaria. hours, two eastward and two westward de- lion, and the perturbations with which af. viations from its mean position, those which progress of those changes appeared to be the occur in the day time being greater than fected, on a scale and in a mode not before those taking place in the night. It is curi- attempted, and with instruments of superior ous to remark that this irregularity seems to accuracy. Established in a large garden extend to all similar cases of diurnal Auctua. at Berlin, he observed at the solstices and tion. In that of the barometer it is a mark. equinoxes of 1806 and 1807 the changes in ed and striking feature ; and in the case of the direction of the horizontal needle every the tides, a phenomenon holding a strong half hour during four, five, or six days, and analogy to this, called the diurnal inequality, the intervening nights. The immediate constitutes one of their most singular, and object of this undertaking was the establishat present, mysterious characters. It is al ment of the nocturnal poriion of the daily so observed that the extent of excursion dif- oscillation already mentioned. But the fers in summer and winter, as does also the delicacy of his instrumental means allowing difference between the daily and nightly os him to appreciate the smallest changes, his cillations. Finally, when the mean places attention was excited by the singular and of the needle for each day of a whole year apparently capricious march of the instru. are eleared of the regularly progressive el- ment, which appeared agitated by frequent fect of the secular movement, a Auctuation and occasionally sudden and rapid movehaving an annual period is disclosed. Simi. ments, attributable to no accidental or lar periodic changes have of late been traced mechanical cause. To these, regarding in the position of the dipping-needle, and there them as indications of a reaction propagated can be no doubt ihat the total intensity is al. from the interior of the globe to its surface, 60 subject to periodical increase and diminu- he gave the name of magnetic storms, in tion.
analogy to the sudden changes of electric The periodical oscillations of the needle, tension which take place in thunder. then, form a regular and compact system, storms. In consequence of this discovery of which there can be little doubt that the M. Von Humboldt conceived the project of cause is to be sought in superficial changes procuring magnetic observations to be estabof temperature developing electric currents lished 10 the east and west of Berlin with a either in the crust of the earth or in the view of tracing the limits and correspon. atmosphere. Be this as it may, their gen-dence (if any) of these perturbations. Po. eral nature and laws may be considered as litical events, however, frustrated this protolerably well sketched out, though they ject; nor did the subject receive further elustill require much study in detail. It is cidations till the year 1818, when it was asotherwise with those irregular and some certained by a comparison of simultaneous times almost convulsive movements of the hourly observations by M. Arago at Paris, needle which constitute the magnetic perlur. and M. Kupffer at Kasan, that on making VOL. LXVI.