XXIX. On the deflection of the plumb-line in India, caused by the attraction of the Himmalaya mountains and of the elevated regions beyond; and its modification by the compensating effect of a deficiency of matter below the mountain mass

Abstract

1. Two notices which appeared last year in the Journal of the Astronomical Society on my Paper on Himmalayan Attraction, written at the Cape of Good Hope in 1854, and published by the Royal Society the year following, have called my attention again to this subject. Those who read that paper will remember, that it consisted of two parts; the first a calculation of the amount of deflection of the plumb-line, caused by the Mountain Mass in India, at the principal stations of the northern part of the Great Indian Arc; and the second, the effect which the application of these deflections, as corrections to the astronomical amplitudes, would have upon the calculated ellipticity of the Indian Arc. The results I arrived at are much greater than were anticipated. The author of the communications to the Astronomical Society proposes to test the truth of my results, by comparing the curvature thus deduced with the curvature of other arc on the continent of India. But this proceeds upon the gratuitous hypothesis, and one which for geological reasons is most likely not true, that the earth is at present an exact spheroid of revolution; i. e . that all meridians are ellipses, and indeed the same ellipses, and that every arc of longitude is circular. There are only two ways of avoiding the conclusion regarding the curvature of the Indian Arc to which I came in my paper of 1855; either by showing that my data and reasoning are wrong, or by pointing out that some other cause is in operation, which either in whole or in part counteracts the effect of the Himmalayan Mass. My calculation has been before the public three years and, though some small numerical errors have been detected, they are not of sufficient importance to affect the result; and the data I have every reason for believing to be correctly taken, as the Surveyor-General—who first called my attention to the subject in 1852, as an unsolved difficulty in the operations of the Great Trigonometrical Survey of India—has been requested to forward to me any corrections which may appear to him to be advisable, and none have been sent. There remains, then, only the resource of looking for some counteracting cause to compensate for the large disturbance produced by the Himmalayas and the regions beyond. 2. The Astronomer Royal, in a paper published in the Transactions for 1855, suggested that immediately beneath the mountain-mass there was most probably a deficiency of matter, which would produce, as it were, a negative attraction, and so counteract the effect on the plumb-line. This hypothesis appears, however, to be untenable for three reasons:—(1) It supposes the thickness of the earth’s solid crust to be considerably smaller than that assigned by the only satisfactory physical calculations made on the subject—those by Mr. Hopkins of Cambridge. He considers the thickness to be about 800 or 1000 miles at least. (2) It assumes that this thin crust is lighter than the fluid on which it is supposed to rest. But we should expect that in becoming solid from the fluid state, it would contract by loss of heat and become heavier. (3) The same reasoning by which Mr. Airy makes it appear that every protuberance outside this thin crust must be accompanied by a protuberance inside, down into the fluid mass, would equally prove that wherever there was a hollow, as in deep seas, in the outward surface, there must be one also in the inner surface of the crust corresponding to it; thus leading to a law of varying thickness which no process of cooling could have produced.