On the Thickness of the Crust of the Earth. 259 



body struck, the distance I V being proportional to the square 



root of the ratio — . 

 m 



When ?n = Mj IV becomes simply A/K^ + rf^, in other words, 

 equal to the arm of inertia of the body with respect to the fixed 

 point. 



If m becomes infinite, and thus itself represents a fixed point, 

 I V becomes zero ; the fixed point I or centre of rotation then 

 becomes the centre oi maximum percussion, — a result which agrees 

 perfectly with one previously established (art. 14). 



If m were very small in comparison with ]\I, the distance I V 

 would become very great. 



XXXVIII. On the Thickness of the Crust of the Earth. By the 

 Venerable John Henry Pratt, 31. A., Archdeacon of Calcutta. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



IN your Number for June last, Professor Haughton has replied 

 to my remarks in your May Number on his investigations 

 regarding the internal constitution of the earth's mass. I shall 

 feel obliged by your publishing the following rejoinder. 



1. Professor Haughton states, (p. 397) : — " The fallacy in rea- 

 soning of which I am accused, is deliberate, and consists in assu- 

 ming the same law of ellipticity and density to hold both for the 

 crust and for the nucleus." 



These words at once show me that Professor Haughton has 

 misapprehended my meaning. The fallacy I referred to was 

 this — that in the same course of reasoning he virtually assumed 

 two principles or conditions, and those o/?/wsef? to each other : 

 viz. (1) that the same law of ellipticity and density holds for the 

 solid and fluid parts of the earth ; and (2) that the same law 

 does not hold. 



The first of these is tacitly asssumed in obtaining his equation 

 (13) from his equation (12), or my equation (2) from my equa- 

 tion (1), as shown in my paper in your May Number. The 

 second is to be found a little more than a page further on, in 

 page 2GG of Professor llaughtou's original paper in the Royal 

 Irish Transactions, vol. xxii., where he states that two hypo- 

 theses are necessary regarding the density of the solid and fluid 

 parts. 



2. Professor Ilaughton's investigation, moreover (as I stated 

 in my former communication), is one regarding densities only, 

 and in no respect touches the question of solidity and fluidity. 

 After he has got his equation to a stratum, he introduces no 



S3 



