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ago; yet no particular attention was paid to the changes it underwent in passing from one place to another, till nearly the close of the last century: and though it was suspected that the intensity like the dip increased from the equator towards the poles, yet till the return of Humboldt from his South American expedition, and the discussions of the observations which he had recorded by Biot, no certain evidence that such was the
Biot appears to have been the first who attempted to apply the laws of the variation of magnetic force to the actual determination of the magnetic poles, which he did in a mémoire read before the National Institute, at the end of 1804*. Laplace also gave the formula which connects the intensity in two different planes with the actual intensity of the force, and actual dip of the needle: and as Humboldt had observed all these, they operated as mutual checks upon one another, and verifications of the general fidelity of the recorded observations. This is the more satisfactory, as Biot has remarked, inasmuch as Humboldt could not be warped in his judgment by any hypothesis of his own, since he could not possibly foresee that Laplace would submit the observations to so severe a test.
Biot, however, in his investigations, was obliged, as his predecessors had been, to confine his attention to a representation of one of these essentially-connected phenomena, that is of the intensity, dip, and variation, and it was the dip which he selected for the purpose.
“ In regard to the declination and intensity," he says, we freely confess that we are entirely unacquainted with their laws, or their causes; and if any philosopher is so fortunate as to bring them to one principle, which explains at the same time, the variation of the inclination, it will no doubt be one of the greatest discoveries ever made." He does not even consider his “hypothesis as anything real, but only as a mathematical abstraction useful to connect the results, and proper to ascertain in future whether any changes take place." Still he does not view his formulæ as an “empirical construction of the observations.” Probably, he intends by empirical formulæ, formulæ which are fortuitously taken, and so modified by means of the constants, as to agree in their results with observation : yet still, if his physical hypothesis is not to be considered "anything real, but merely as a mathematical abstraction useful to connect the results,” there does not appear to us to be any essential difference between it and an empirical formula, since it is confessed to be only the algebraical expression of an empirical law-of a law which lays no pretension to physical accuracy. Yet it is upon the evidence of an investigation, thus characterized by its author, that the position of the poles, as concentrated in a molecule at the centre of the earth, has been generally adopted, and upon which the opinion maintains its ground to the present day, there being no new evidence nor new argument produced in favour of it.
Biot's hypothesis is that the magnetic forces are situated in two points (or, at all events, that the resultant of all the forces of each separate
This memoir has been translated in the 22nd volume of the Philosophical Magazine, and considerable extracts from it (all the essential parts) have been inserted in the article “Magnetism,” in the later editions of the Encyclopædia Britannica. It was originally published in the Journal de Physique, for the year 13 (1804-5).
kind, is a single force situated in a fixed point)—that these forces are equal in intensity but contrary in their quality—that these forces vary inversely as the square of the distance of the magnet acted upon—that these centres of force are situated in the same diameter of the earth-and, lastly, that they are equally distant from that centre.
Upon the first * of these hypotheses, considerable diversity of opinion has prevailed, and under every aspect the decision of the question is clogged with difficulties, both experimental and mathematical; but if this were admitted, it would seem almost inevitable to admit the second of the hypotheses. The third is now undoubted by all philosophers; but the fourth and fifth are not only unnecessary restrictions,—they are also incompatible with other phenomena, which must be accounted for by the true theory, whatever it may prove to be. The magnetic equator, for instance, must be a great circle-which it is not; the parallels of magnetic latitude ought to be actually parallel and circular—which they are not: the variation of the horizontal needle ought to be constantly of the same name (E. or W.), through the whole extent of any given meridianwhich it is not; the magnetic intensity ought to be altogether free from sensible change—which it is not. The hypothesis, even when the poles are at unequal distances from the centre of the earth, and at finite distances, is still liable to nearly all these objections, the form of statement of one or two of them being slightly modified. For instance, the magnetic equator would cease to be a great circle, but it would still be a circle which is contrary to experience: the lines of equal dip would still be parallel, though at different distances in the two hemispheres—which is contrary to experience; the magnetic intensity would now become (probably) sensibly different, but the lines of equal intensity would, like the lines of equal dip, be parallel to the magnetic equator—which is contrary to experience; and, finally, the objection unmodified, arising out of the necessary magnetic variation, still retains its fatal power against the hypothesis under this view also. Nor are these all the difficulties of the hypothesis; but as any one of them is sufficient to overturn it, we need not here enumerate more than are already set down.
In this dissertation, however, Biot not only pointed out the true mode of investigation, but derived also the formulæ for the dip in terms of the magnetic latitude, as well as determined the approximate position of the magnetic equator itself (viewed as a great circle), which are admitted (with slight modifications of the formulæ, and slight changes of position in the equator,) to the present time. The modified formula was furnished from original and independent investigation by Krafft of
* In his discussion of the state of the magnetic forces in a saturated bar, (in his Traité de Physique, vol. III., p. 77,) Biot has adopted a different hypothesis; viz. that at any point, the quantity of feromagnetism, is expressed by here? where y is a constant, depending on the state of the magnetised body generally, 2 l is the length of the bar, and, x the distance from the extremity of the bar, which contains one specified kind of magnetism.
Would not Biot's formula be improved, by referring the origin of x to the middle of the bar ? The result would be ulti-*!-x). This would be more elegant in a geometrical point of view at least ; but the writer of this paper will have occasion, shortly, to show, in another place, the fallacy of the whole reasoning; and hence it is unnecessary to dwell upon it here with any greater detail.
Petersburgh, and the determination of the change in the position of the equator, arising out of its positions at two different epochs, was effected by M. Morlet*. The method of Morlet consisted in the determination of certain points, in or very near the equator, from actual observation, and then from other points more remote, interpolating by means of Krafft's formulæ--the latitude being estimated on great circles, passing through the axis of the magnetic molecule, and the place of observation. We shall see hereafter the degree of inaccuracy that must result from this process; or rather, we should say, from the theory on which this process is formed. We have noticed above some fatal objections to the theory itself.
* Mém. des Savans Etrang., tom. iv.
[To be continued.]
THE VILLAGE OF LEADHILLS, LANARKSHIRE.
(From a Correspondent.) The village of Leadhills is situated in the parish of Crawford, and county of Lanark, Scotland, at the altitude of 1280 feet above the level of the
The prevailing rock in the neighbourhood is Greywacké, but at no great distance clay-state and greenstone are found, and coal within ten miles at Sanquhar and Douglas. The altitude of the Lowthers, the highest hill in the neighbourhood, as taken geometrically by Sir John Leslie, is 2396 feet; but, according to my measurement, made with a theodolite, under very favourable circumstances, its height is 2409,-or 13 feet higher a difference scarcely appreciable upon such an altitude.
According to common report, the lead-mines were discovered by a German of the name of Bulmer, when searching for gold in the banks of the adjoining rivulets. This account is extremely probable, for the numerous hillocks on the banks of the streams which discharge themselves into the Clyde and Nith, bear evident indications of having been thoroughly searched for that precious metal: even so much so, that those miners, who at present amuse themselves, during their leisure hours, in searching for gold, cannot find a spot that has not previously been explored.
The method of searching for gold is, I believe, the same in every country; however, the one adopted at Leadhills is as follows:The surface of the rock is laid bare; the earth, sand, &c., in its crevices are collected, riddled, and washed. The water carries away the earthy particles, and leaves those materials which are of greater specific gravity than itself, as flint, quartz, and what gold there may be. The proceeds from one puddle, as it is called, are generally, at the most, not more than a few particles, not larger than the point of a pin; but a man, in six hours, at an average, may collect about 4d. worth of gold. Some pieces, however, have been found as large as a pea, or small bean; and in 1827, one of the overseers at Wanlockhead had a piece so large imbedded on quartz.
These gold mines, however, were once productive, for history inforno us that in the reign of James the Fifth of Scotland, 300 men were employed in them; and when that monarch, in a hunting-excursion in the adjacent moors, dined in Crawford Castle: each of his retainers, for dessert after dinner, were presented, on a wooden platter, with a few bonnets crowns, as the produce of the soil. These pieces were coined from gold, obtained in the mines of Glengonar, the rivulet upon which Leadhills is now built.
Lead, however, for centuries has formed the mineral riches of these mines. The vein has more than once expanded to the enormous width of 14 feet, but, I myself never saw it more than 41 feet, and this was considered by the miners as a very good lead. At present the crip or annual number of bars (of 114lbs. each) amounts to 10,000 in Leadhills, and to about 8,000 in Wanlockhead, whereas at one period 35,000 were made at the former, and 15,000 at the latter.
It is not, however, to facts such as I have mentioned, that I particularly wish to call your attention, but to the mental superiority of these miners, over miners in other parts of the world, and to show, that even among a class of workmen, who might be supposed incapable of profiting by good example; one man of intelligence, may produce beneficial effects, that for ages will be felt and duly appreciated. The individual to whom I refer, was Mr. James Stirling, who, in the middle of the last century, was overseer at Leadhills. Mr. Stirling is known to the mathematical world, for two elegant propositions which he communicated to the Royal Society of London in 1735, for determining the form of a homogeneous spheroid turning round its axis; and which when applied to the earth, perfectly coincided with Newton's determination, that the revolving body was not an accurate elliptical spheroid, but approached infinitely near to that figure. When at Leadhills, he instituted a library among the miners, and strongly advised them to subscribe ; and with such success, that there is not a workman about the yillage who is not a member of the library. The number of volumes, embracing the standard works on every branch of science, in 1830, amounted to two thousand, whilst the miners at Wanlockhead, another mining village within two miles - of Leądhills, but in the county of Dumfries, possess another library, almost equally extensive. The effects of such institutions have been felt, not only in civilizing the inhabitants generally, but the small village of Leadhills, containing 1200 inhabitants, has the honour of producing two men whose names bid fair for immortality, Allan Ramsay, the poet, and William Symington, the engineer. Captain Basil Hall, in his North America, states that Symington was the first to apply steam to the propulsion of ships, at least in America. It is true, that Symington was one of the claimants, but the invention of steam-navigation, is one of those points of dispute, which probably will never be settled. We are, however, certain that Ramsay was the father of modern Scottish poetry, the precursor of Ferguson, of Burns, and of Scott.
Whilst in other mining districts, crimes are of frequent oocurrence ; none excepting petty offences were ever committed here, and whilst the children of colliers and miners are generally entirely illiterate, there is neither a boy nor a girl in these villages who cannot read, and most of them can write. In 1832, I visited these villages, with some friends of mine from Edinburgh. Keen phrenologists, who of course attributed the mental superiority of these miners to cranial developement, but to whatever cause it may be attributed, and I think it is due to the taste for reading that has been produced among them, the apparent comfort of the people—the neatness of dress of the children, and the intelligence of the men cannot be denied. For not only to miners in others parts of the world, are they superior, but to the working classes even in Scotland, which is admitted to possess the most intelligent peasantry on earth.
Seeing, then, that such beneficial effects have been produced by such apparently small causes, might not the overseers of other mining districts, instigated by the example of Leadhills, try to institute Reading Societies among their workmen? for it will always be found, that correctness of moral conduct follows the cultivation and enlightenment of the mind. It is true that the Leadhills and Wanlockhead miners possess two special advantages, they only work 6 hours in the 24, and have the perquisite of obtaining as much land from their landlords, the Earl of Hopetoun at Leadhills, and the Duke of Buccleuch at Wanlockhead, as they can cultivate with the spade. The last might be considered as of hardly any advantage in a pecuniary point of view, as the uncultivated land in the neighbourhood rents at 2s. per acre, but it is still unknown what spade labour can effect, even in the most unpromising circumstances, as will be proved from an account which I have received of the enormous crops that have been produced at Leadhills, and which I communicate as being important, not only in an economical, but also in a geological, point of view.
The altitude of Leadhills above the level of the sea, is, as I have already mentioned, 1280 feet, and to show the mean temperature of Leadhills, and the quantity of rain that fell there during the summer of 1828, I make the following extract from a paper of mine, which appeared in Jameson's Edinburgh Nen Philosophical Journal.
The temperature was taken at 7 A.M., and 8} P.M. The daily mean was then taken, and again the monthly.
The height of the gauge above the sea was 134°, and it was placed near to the highest inhabited house in this island.
54° Rain which fell 34 inches.
35 inches total; an enormous quantity. The account to which I refer appeared in the Scotsman, and is also copied into Colburn's New Monthly Magazine for March. It is as follows:“Mr. John Hunter, Leadhills, planted, in 1835, 16 Scotch falls (being the tenth part of a Scotch acre) with potatoes, which produced the extraordinary quantity of 335 imperial stones, being at the rate of 21 tons to the Scotch acre" (or 17} to the English). And from a square mile of surface, around the village, it is calculated that 25,000 stones of hay