the Glacial Epoch in the Northern Hemisphere. 173 



rise in the sea-level. The problem is, in fact, one of Attractions. 

 I have of late years given much attention to this subject in 

 attempting to estimate the influence of the vast superficial moun- 

 tain-mass north of India, and also of the deficiency of matter in 

 the extensive ocean south of India down to the south pole, upon 

 the plumbline used in the Trigonometrical Survey of Hindostan. 

 The present problem is one of precisely the same character, as it 

 is to ascertain the attracting force of the supposed Ice-Sheet 

 upon the waters of the ocean and its effect in drawing them up. 

 In the absence of all knowledge of the form and extent of the 

 ice-mass, which has now disappeared, I will adopt Mr. CrolFs 

 hypothesis, as a means of making a calculation from which a 

 general idea of the operation of the causes can be obtained. He 

 takes the Ice-Sheet to be a hemispherical meniscus of a certain 

 thickness at the pole, and gradually getting thinner towards 

 the equator, where it is supposed to be zero. The specific gra- 

 vity of ice is 0'92, and of superficial rock 2*75. Hence the 

 ratio of that of ice to that of rock = 1 to 3. 



2. Following the same course by which I have estimated the 

 attraction of the Himalayan mass and of the deficiency of mat- 

 ter in the ocean, I have calculated that the Horizontal Attrac- 

 tion of a Spherical Meniscus of rock (of thickness h miles at the 

 pole and radius a) at a place in the opposite hemisphere the polar 

 distance of which is 0, measured from the pole of the attracting 

 meniscus, 



= (0-1446 sin + 0-0958 sin 2(9 + 0-0244 sin 30) -g, . (1) 



where g is gravity*. 



From this formula it is not difficult to find the attraction of 

 the meniscus upon a place on its own surface. For the tan- 

 gential attraction of an oblate spheroid of small ellipticity e, at a 

 place on its surface of which the distance from the nearer pole 

 is (f>, =0*6 sin 2<£ . e .g, and acts from the nearer pole. From 

 this it is easily seen, by taking the difference of effects of two 

 oblate spheroids having the same equator and differing in their 

 compressions by h, that the combined attraction of the northern 

 and southern hemispherical meniscuses at the place in the north- 



* See my treatise ' On the Figure of the Earth/ 3rd edit. p. 58. I avail 

 myself of this opportunity to state that in two formulae, (2) p. 59, and (6) 

 p. 60, derived from the above formula, there is a misprint. It is not of much 

 importance, as no use is made of those two formulae. They should stand 

 as follows : — 



h 

 (0- 1446 sin + 0-5042 sin 20 + 0-0244 sin 30) # ... (2) 



h 



(2-0608 sin 0-2-4884 sin 20 + 0-7362 sin 30)-^ ... (6) 



