448 Mr. R. Moon's Reply to Prof. ChalhVs further Remarks 



p — 1-</>( v+ - )> 



P \ P' 



p + J <*>'(*>) -2« -TH d J 



A result more rigorously deduced or more analytically complete 

 is not to be found in the whole range of mathematical physics; 

 and my main objection to the received theory of hydrodynamics 

 is that its upholders must arbitrarily set aside the above rela- 

 tions, being such as have been described, substituting in their 

 room the equation p = a?p with such emasculated results as have 

 been or may be* derived from it — an equation, be it remembered, 

 which is unsupported by a single fact, which is opposed to every 

 sound principle, and as to which all that can be said in its 

 favour is that, in the infancy of the theory, the founders of the 

 theory seized upon it in desperation, amidst the overwhelming 

 difficulties by which they were beset, as the only law of pressure 

 prevailing under any circumstances that up to that time had 

 ever been so much as suggested. 



But although I do not rest my main objection to the received 

 principles of hydrodynamics upon the two points to which Pro- 

 fessor Challis refers, I regard the views I have put forth in rela- 

 tion to those cases as of importance as showing in a popular 

 manner, conclusively and at a glance as it were, the wholly un- 

 tenable character of the existing theory of fluid pressure. 



As to the first of these cases, Professor Challis writes : — " Mr. 

 Moon founds an argument on the immediate juxtaposition of 

 two densities one of which is double of the other; in other 



terms, he admits that - -/- may have an infinite value." 



p ax J 



I do not know on what ground Professor Challis attributes to 

 me this admission ; for, although on entirely different princi- 

 ples f, I am as satisfied as he can be as to the impossibility of 



* It is well known that the only solution of the equation of motion 

 under these circumstances which has ever been demonstrated is that de- 

 rived by Poisson, containing a single arbitrary function, and involving a 

 relation between the velocity and density which it is quite impossible can 

 always or even generally subsist. In a recent Number of the Philosophical 

 Magazine I have shown, as I believe irrefragably, that this solution of 

 Poisson's is the most general which, consistently with the relation p = a?p, 

 the equation of motion admits of. 



'T Professor Challis regards equality of pressure in all directions as a law 

 upon which " the whole of analytical hydrodynamics depends." It is true 

 that the founders of the theory of fluid motion in three dimensions, in their 



