348 Mr. G. G. Stokes on the Theory of Sound, 



0=/(« + S) = X' + Y'/3 (1.) 



0=/(a-/3) = X'-Y'/3 (2.) 



where X' and Y' contain only even powers of + /3 and rational 

 functions of « ; and these powers and functions are the same 

 in (1.) and (2.). 



When /3 is different from zero, we get, by addition and sub- 

 traction of (1, 2), 



X'=0, and Y'=0, 



precisely as in Lagrange's method, where /3 -/ — 1 is put for |3. 



The separation into two subordinate equations is therefore 

 as legitimate in the general case as in Lagrange's restricted 

 one. 



When ^3 = 0, then Y' is indeterminate: but this does not 

 seem to be of much consequence, since the original equation 

 is then reduced, as it should be, to 



/(«) = 0,and/,M=o, 



indicative of a common measure .r— a between the equation 

 and its derivee. This we already know to be the consequence 

 of the given equation having equal roots. 



I shall shortly send you for insertion some extracts from 

 Mr. Horner's rough notes on the effect of the transformation 

 of/(<z') = by means of the quadratic divisor 



employing his synthetic method of transformation. 



Royal Military Academy, Woolwich, 

 April 6, 1849. 



L. On the Theory of Sound, in reply to Professor Challis. 

 By G. G. Stokes, M.A., Fellotx) of Pembroke College, 

 Cambridge^. 



IN my last communication I contented myself with a simple 

 denial in the case of the fifth head of Prof. Challis's de- 

 monstration, having nothing, as I conceived, to meet but a 

 simple assertion. I am unable to perceive the slightest con- 

 nexion between the conclusion that 47rrj^5ia = 47rr2%aand the 

 principle of the constancy of mass, irrespective of some tacitly 

 assumed step of reasoning. Without noticing this connexion 

 explicitly, Prof. Challis has certainly rendered his reasoning 

 more definite by the introduction of the supposition of rigid 

 envelopes. 



* Communicated by the Author. 



