Mr. G. G. Stokes on the Theory of Sound. 501 



ternal diameter, and of 63 millimetres internal diameter, the 

 insertion of an iron nucleus of 9 millimetres in thickness di- 

 minished the rotation of the substances placed in the interior. 

 In my experiments I have never made use of coils enclosing 

 such thin iron cylinders ; the thickness of these cylinders was 

 not less than 25 millimetres ; their length was moreover always 

 equal to that of the external helix. 



LXXII. On the Theory of Sound. By G. G. Stokes, M.A., 

 Fellow of Pembroke College^ Cambridge. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 A S I see no advantage likely to result from further discus- 

 ■^^ sion of the question of the possibility of the existence of 

 spherical waves of sound, it is not my intention to continue 

 the controversy. I have, as 1 conceive, shown that the " con- 

 tradiction " arrived at by Professor Challis has no real exist- 

 ence ; and I am quite content to leave the question as it now 

 stands to the judgement of mathematicians. 



I feel it, however, to be but justice to myself to notice one 

 sentence in Professor Challis's last paper; for if your readers 

 take their views of the controversy from this sentence, they 

 must think I have strange notions of reasoning. 



Professor Challis, in speaking of my last three papers, ob- 

 serves, " In the first attempt he produced an argument which 

 took for granted the very point in dispute ; in the next he 

 denied, without giving any reason, what was altogether unde- 

 niable; in the third attempt he admits what he before denied, 

 and denies, again without assigning a reason, what in the 

 second attempt he admitted." In the first of these papers it 

 was not until I had, as I conceived, overthrown Professor 

 Challis's a priori demonstration of the impossibility of sphe- 

 rical waves by pointing out that it rested on a tacit assumption 

 (Phil. Mag., vol. xxxiv. p. 54), that I proceeded to inquire 

 whether there was any foundation for this assumption in the 

 received equations of motion. Properly speaking, the mere 

 pointing out of the omission in Professor Challis's train of 

 reasoning was my answer to his ai'gument. As to my second 

 paper, what Professor Challis regards as unde?iiable I regard 

 as untrue. In this paper 1 admitted the possibility (as a par- 

 ticular case of possible motion) of a solitary wave of conden- 

 sation, and I continue to admit it; in my next I denied that 

 in this instance of motion the velocity of the fluid can be con- 

 fined to the wave of condensation, except when a special con- 



