204 Mr. G. G. Stokes om the Theory of Sound. 



" Hence by the principle of tlie constancy of mass employed 

 in investigating one of the hydrodynamical equations, those 

 two quantities must be equal to each other." I deny that the 

 equality follows in any manner from the principle in question. 

 As the onus ■probandi evidently rests with Professor Challis, 

 I might here stop; but to render everything as definite as 

 possible, I will give a precise enunciation of the principle of 

 the constancy of mass, at least as I myself regard it, and I 

 have no reason to suppose that Professor Challis differs from 

 me in this respect. 



Let S be any closed surface, finite or infinitesimal, drawn 

 in the fluid at the time /, r any finite or infinitesimal interval 

 of time ; and at the time ^ + t let the surface S' be the locus 

 of the particles which at the time t were situated in the sur- 

 face S : then the mass contained within the surface S' at the 

 time ^ + T is equal to the mass contained within the surface S 

 at the time /. 



The principle of the constancy of mass might have been 

 enunciated somewhat differently, as follows ; and it will be 

 easily seen that the two enunciations come to the same thing. 



Let S be any closed surface, finite or infinitesimal, drawn 

 within the fluid and remaining fixed in space; and let M be 

 the whole mass of fluid which flows across the surface S during 

 the time t, those portions being reckoned positive which flow 

 from without to within S, and those negative which flow from 

 within to without: then the mass contained within the surface 

 S at the time t-{-r exceeds the mass contained within the same 

 surface at the time t by the quantity M. 



I will not at present say anything about the paragraph 

 Vi^hich follows (5.) ; because if Professor Challis and 1 can 

 agree about (5.), we shall probably have little difficulty in 

 agreeing about the paragraph in question. 



Neither will I pursue the discussion further in the present 

 communication ; because, in addition to the motives which I 

 have already mentioned for declining to do so, it seems to me 

 that too great discursiveness is an evil in controversy, espe- 

 cially in mathematics, where one false step may invalidate all 

 that follows. I think it best to discuss only one fundamental 

 point at a time. 



Pembroke College, 

 Feb. 3, 1849. 



