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LXIV. On the Fluid Theory of the Earth. 

 By Archdeacon Pratt. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



IN the third edition of my ' Treatise on the Figure of the 

 Earth ' I have introduced the following proposition (see 

 page 80, Art. 84) :— 



"Prop. To prove that if the form of the earth's surface be a 

 spheroid of equilibrium, the earth's mass must necessarily be ar- 

 ranged according to the fluid law, whether the mass is or has been 

 fluid or not , in part or in whole." 



Exception has been taken by a friendly reviewer of the book 

 in your Number for February last, to my demonstration of this 

 proposition ; and I am free to admit that his criticism has some 

 truth in it in the abstract. I think, however, as he has left the 

 matter, it stands in a wrong light ; and I feel no doubt that you 

 will not grudge some of your space being taken up in discussing 

 a point which is of very great importance. 



The step in my reasoning which he objects to is this : — " Sup- 

 pose some change were made in the arrangement of the earth's 

 mass without altering its external form. It is evident that, 

 although the resultant attraction of the whole mass on the sur- 

 face might possibly be unaltered by this change at particular 

 points of the surface, it could not remain the same as before at 

 every point of the surface." From the well-known property of 

 a spherical shell — that it attracts an external point precisely as 

 if the mass of the shell were concentrated into its centre — he 

 shows that if equal portions of the mass at the same distance on 

 all sides around any point in its interior were moved to equal 

 distances towards or from that point, so as still in themselves to 

 form a complete spherical shell, the attraction of the whole on 

 any external point would remain unaffected by the change. This 

 exception had occurred to me before the proofsheets left me. 

 But it seemed to imply an arrangement of the mass so incon- 

 gruous that I dismissed the thought — a thought which was 

 neither suggested nor supported by any physical considerations, 

 but is solely a creation of the integral calculus. I see that I 

 dismissed it too hastily ; for in what I have written there are a 

 few expressions which are stronger than I should have used, e.g. 

 " must necessarily " and " could not " in the above quotations ; 

 and "the only possible law" at the end of the article. When 

 the book issued from the press, I regretted that I had not men- 

 tioned this exception, for the purpose of replying to it, as I do 

 below. It is a singular coincidence that I began a letter to you 



