[ 449 ] 



LXVI. On Spherical Waves in an Elastic Fluids in reply to 

 Mr. Stokes. By the Rev. J. Challis, M.A.^ F.R.S., 

 F.R. A.S., Plumian Professor of Astronomy and Experimental 

 Philosophy in the University of Cambridge* . 



THE question which has been discussed by Mr. Stokes and 

 myself in several recent Numbers of this Magazine, is of 

 the following nature. On supposing the waves in a compress- 

 ible fluid to be spherical, I deduced from that supposition, 

 by reasoning given at length in the Philosophical Magazine 

 for last February, a result inconsistent with one of the funda- 

 mental principles of hydrodynamics, viz. that of constancy of 

 mass. Hence I concluded that the supposition of spherical 

 waves is inadmissible. Mr. Stokes undertook to dispute this 

 inference. Now although by an acknowledged rule of logic, 

 the inference could not be set aside except by showing some 

 fallacy in the reasoning which conducted to the absurdity, 

 Mr. Stokes, in three attempts to set it aside, has not once 

 alluded to any step in the reasoning. 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 undeniable; in the third attempt (Phil. 

 Mag. for May) he admits what he before denied, and denies, 

 again without assigning a reason, what in the second attempt 

 he admitted. The denial in this instance refers to the possi- 

 bility of the propagation of a solitary wave of arbitrary' con- 

 densation and constant type. I infer the possibility from the 

 principle of discontinuity. Mr. Stokes calls this inference a 

 gratuitous assumption, without making the slightest allusion 

 to the principle on which it rests ; and yet he has drawn a like 

 inference from the same principle in the same way. ( Phil. 

 Mag., vol. xxxiv. p. 54. 1.27-31.) 



With respect to my having deduced only a part of the re- 

 sults to which the supposition of spherical waves leads, I am 

 able to give a very good reason for not proceeding further. 

 I obtained, as already stated, from that supposition, by rea- 

 soning of which Mr. Stokes has not shown, and I am unable 

 to perceive, the fallacy, a result inconsistent with one of the 

 fundamental principles of hydrodynamics. The supposition 

 I consider to be thereby condemned. If I allowed myself to 

 qualify this course of reasoning by another from the same 

 supposition, I should proceed in direct opposition to an in- 

 controvertible rule of logic, and neutralize a highly important 

 and significant result. 



Mr. Stokes appeals with great confidence to the results he 

 * Communicated by the Author. 



Phil, Mag. S. 3. Vol. 34. No. 231. June 1849. 2 G 



