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XIII. On the Constitution of the Solid Crust of the Earth. 
By Archdeacon Pratt, M.A., F.B.S. 
Received September 19, — Read December 22, 1870. 
Contents. 
Introduction , 335 
§ 1. Data regarding Pendulum Observations in India 339 
§ 2. Data regarding the contour of the continent of India 339 
§ 3. Formulae for the Vertical Attraction of a spherical cap of matter on the earth’s surface on the 
mid points of its upper and lower surfaces, and of its divisions into a central portion and zones . . 340 
§ 4. Formulae for the “ Resultant Vertical Attraction” of the central portion of the cap, and of the zones 344 
§ 5. Numerical application of the formulae to find the “ Resultant Vertical Attraction” of the Hima- 
layas upon stations of the Indian Arc of Meridian through Cape Comorin 348 
§ 6. Calculation of the “Resultant Vertical Attraction” of the Sea at stations on a continent, on a 
coast, or on an island 353 
§ 7. Application of these results to test the truth of the author’s hypothesis regarding the Constitution 
of the Earth’s Crust 355 
Introduction. 
A pew years ago I proposed the following hypothesis regarding the Constitution of the 
Earth’s Solid Crust, viz. : — that the variety we see in the elevation and depression of the 
earth’s surface, in mountains and plains and ocean-beds, has arisen from the mass having 
contracted unequally in becoming solid from a fluid or semifluid condition * : and that 
* I first proposed this hypothesis in a paper printed in the Proceedings of the Royal Society, No. 64, 1864; 
see pp. 270-276 of that paper ; and afterwards in the third edition of my ‘ Figure of the Earth,’ pp. 134—137. 
Mr. Airy was the first to suggest, in Phil. Trans. 1855, p. 101, a deficiency of matter below mountain- 
regions ; and he there pointed out that such a deficiency would counteract in great measure the effect of the 
Himalayas themselves on the plumb-line, the attraction of which, I had shown in a previous paper in the same 
volume, by direct calculation, would be considerable and would introduce new anomalies. The reasoning, how- 
ever, by which he proceeded to show that this deficiency must exist involved conditions which appeared to me 
inadmissible — viz. (1) that the solid crust is comparatively thin, and (2) that the density of the solid crust is 
less than that of the lava on which it was supposed to float. See my remarks on Mr. Aiby’s paper at pp. 51, 52, 
Phil. Trans. 1856 ; in which also I give reasons for not admitting, what his data require, that the present form 
of the surface has arisen solely or mainly from hydrostatic principles. This hypothesis of deficiency of matter, 
as there advanced, does not appear to rest on any true physical basis. 
In the Phil. Trans. 1858, p. 745, following up Mr. Airy’s suggestion of deficiency of matter — but not as he 
conceived it to exist, in a thin crust, immediately below the mountain-mass, and by buoyancy supporting the 
crust by the principle of floatation— I proposed the hypothesis of the mountain-mass having been formed by 
upheaval, by a slight expansion of the solid crust, and a corresponding attenuation of its density, from a great 
depth below (par. 4, p. 747) ; and I showed by calculation, in that paper, that the resulting effect of such 
attenuation on the plumb-line would be considerable, and quite comparable with the effect which calculation 
showed would be produced by the mountains themselves. 
Immediately after this another source of disturbance of the plumb-line suggested itself to me, viz. deficiency 
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