44. Reasons for believing that Terrestrial Magnetism does not reside, in any important degree, in the earth's surface. The first class of reasons are those general ones which are founded on ordinary observation, of the materials of which the earth's surface is composed, and of their non-magnetic property: and upon the general absence of any perceptible change in magnetism depending on the change of soil. The materials of a clay-field are not sensibly magnetic, nor are those of a sand-field, nor is there any change of the general terrestrial magnetism in going from one to the other; nor are the granite rocks in one district, or the limestone rocks in another, sensibly magnetic. In some places there are ferruginous rocks, specimens of which when brought near to a delicate compass are found to produce sensible disturbance: but the great masses of those rocks on the earth's surface, when examined (by examination of the declination, dip, and horizontal intensity) at corresponding distances in their neighbourhood, produce no sensible disturbance. The second class of reasons consists of those founded on measures of the magnetic elements at different elevations above the earth's surface. One series includes the observations taken on mountain-heights of these the most valuable are those of Professor James Forbes (Edinburgh Transactions, vol. xiv.), from which it appears that, for a height of 100 feet, horizontal magnetic force is diminished, in Europe, by ʊʊ part, and dip is increased by 5". Both these would correspond to the supposition that the magnetic power is sensibly below the earth's surface. As the observer was not actually separated from the earth, the validity of inference from these may be disputed. Another series is that of observations in balloons, which are free from every objection of that kind, but which are not quite so accurate; and which are necessarily almost limited to observations of horizontal intensity, as found by vibrations (Article 25). The following are the results of these observations : Gay Lussac, 1803, at the height 4000 metres found no sensible diminution of magnetic force (Annales de Chimie, vol. 52). Gay Lussac, 1804, at the height 6900 metres found an apparent very small increase: but this was probably caused by the low temperature of the needle, for which no correction was applied. The dip, imperfectly observed, was not sensibly altered. (A. de C. vol. 52.) Glaisher, 1862, found at the height 20200 feet a diminution of power: but in other observations at 5300, 11000, and 3800 feet, found the same as on the earth (Report of British Association 1862). Glaisher, 1864, found a diminution of about part at the height 14000 feet. (R. of B. A. 1864.) Glaisher and Evans, 1864, found an even larger diminution at height 3600 to 5000 feet. B. A. 1865.) (R. of It would appear generally from these observations, that there is a sensible diminution of magnetic hori zontal force at a great elevation. But the last set of observations casts much doubt on this conclusion. It is to be remarked that all the balloon-observations at great height were compared with observations on the earth. It might have been safer to compare them with balloon-observations at small elevations. Now the last set of observations seems to shew that an apparent large diminution arises simply from the effect of localization in the balloon-car; and, if this be accepted, there is scarcely any sensible effect to be ascribed to the great elevations. Now, remarking how rapidly magnetic power diminishes with increase of proportion of distance from the magnetic poles, it follows from the observations above that the height of three or four miles must bear a small proportion to the distance of the magnet which produces the magnetic power observed at the earth's surface, and therefore the source of magnetism must be deep. 45. Attempt to explain Terrestrial Magnetism by the action of a magnet of small dimensions but of very great power, near the center of the earth. About the middle of the last century it was suggested by Mayer, and in the present century the same idea was independently adopted by Humboldt and Biot (Biot, Traité de Physique, 1816, vol. iii. page 139), that the principal phænomena of Terrestrial Magnetism could be explained by the action of a powerful magnet, of limited dimensions, near the center of the earth. Its theory is as follows. In Figure 38, let the magnetic Fig. 38. B b Z pole be defined by prolonging the axis of the magnet till it cuts the earth's surface; 0 will be the complement of magnetic latitude. The action of the northern or blue pole upon the red end of a needle at P will be represented by B (a+b2-2ab cos 01: its resolved part in the horizontal plane at P, towards the pole, will be Bb. sin 0 . (a2 + b2 — 2ab cos 0); the action of the red pole in the same direction will be Bb. sin 0 . (a2 + b2 +2ab cos 0) ̄* : the total horizontal force will be the sum of these two quantities: which, retaining only the first term in the expression when b is considered a small quantity, is 2Bb. sin 0. a2. A similar expression with opposite sign gives the action on the blue pole (the needle being considered to be small); and the algebraical difference or numerical sum of these gives the whole horizontal directive force = 4 Bb. a. sin 0. The resolved part of the action of the blue pole upon the red end of the needle, in the direction of the vertical at P, is B. (a-b cos 0) . (a2 + b2 − 2 ab cos 0) ̄ : which, expanded to the first power of b, gives B. a. (a + 2b cos 0). The action of the red pole upon the same red end of the needle is -B. a. (a-2b cos 0). The sum of these gives for the total vertical force downwards upon the red end, 4 Bb. a. cos 0. As above, there is an opposite force, numerically additive, upon the blue end: and the whole vertical directive force is |