344 Archdeacon Pratt on the Thickness of 



69. The inference which I have already drawn* respecting 

 the sextic in ^ or t supports this conclusion. For, since every 

 root of a rational equation is a rational function of its own square, 

 the square of a rational function of a root is a rational function 

 of the square of the root. Indeed, if a, b, c, d and a', b', c', d' 

 be two sets of Eulerian constituents, to which d, 6 and S', 6' 

 respectively correspond, a!, V , c', and «f' are each linear functions 

 of a, h, c, and d, each of which is a rational function of •&. 



White Cottage, Felixstow, near Ipswich, 

 Suffolk, September 24, 1859. 



LIV. Js the Thickness of the Earth's Crust a small or a large 

 fraction of the Earth's Radius ? By the Venerable John 

 Henky Pratt, M.A., Archdeacon of Calcutta. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



THE extreme values which have been assigned to the thick- 

 ness of the solid crust of the earth by those who have 

 made any calculations on the subject, may be stated to be about 

 ^^_th and |th part of the radius of the earth. In your Num- 

 ber for May last, I made some remarks in support of Mr. Hop- 

 kins's view of this question, and added what I conceived to be, 

 as far as it went, a confirmation of his general result. It was 

 drawn from a consideration of the peculiar geographical circum- 

 stances of Hindostan, bounded on the north by a vast mountain 

 region, and on the south by a vast ocean. In your Number for 

 July, which has just reached this country. Professor Hennessy 

 makes the following observations on my reasoning: — " Here I 

 may be allowed to refer to Archdeacon Pratt's attempt at con- 

 firming Mr. Hopkins's conclusion relative to the supposed very 

 great thickness of the earth's crust. [1] He proposes to ascer- 

 tain the conditions of equilibrium of that portion of the crust 

 occupied by the great peninsula of India stretching from beyond 

 the Himalayan Mountains to Cape Comorin. The meridional 

 section thus studied comprises an arc of about 24°, and the cur- 

 vature of this segment of the shell is a very important element 

 in the consideration of its stability ; yet it has been totally ne- 

 glected. [2] Moreover, the Himalayan Mountains and plateau 

 of Central India are assumed to be masses superimposed upon 



* Mr. Harley has pointed out to me, that in arts. 65 to 58, by an over- 

 sight which does not affect the argument, I have made i''©i instead of ©j 

 the basis of the formulae. The investigations to which I alluded in art. 41 

 will be found in the Manchester Memoirs, vol. xv. (" On the Method of 

 Symmetric Products," &c., by the Rev. Robert Harley, F.R.A.S.) 



