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LXVIII. Further investigation of the Nature of Aerial Vibra- 

 tions, By the Rev. J. Challis, M.A., F.R.S., F.R.A.S., 

 Plumian Professor of Astronomy and Experimental Philo- 

 sophy in the University of Cambridge* . 



13EFORE I proceed with the inquiry carried on in several 

 AJ preceding Numbers of this Journal, I wish briefly to no- 

 tice the views put forth by Mr. Stokes in the November 

 Number, respecting a supposed remarkable difficulty in the 

 Theory of Sound which he says that I have pointed out. 

 What he alludes to I have not myself called a difficulty, nor 

 do I so regard it. By an investigation contained in the Phi- 

 losophical Magazine for last April, I found that the general 

 character of aerial vibrations is non-divergence, and that the 

 theoretical velocity of sound is different from that usually 

 adopted. Mr. Airy urged against these conclusions, that my 

 equations represent a particular case of the propagation of 

 # plane-waves : in answer to which I proved, by a reductio ad 

 absurdum, that plane-waves are physically impossible. This 

 proof, which forms the subject of Mr. Stokes's remarks, is 

 given in the Philosophical Magazine, S. 3, vol. xxxii., from 

 line 16 of page 496 to line 12 of page 497. The absurdity to 

 which the hypothesis of plane-waves conducts is, that the 

 points of maximum velocity and of no velocity in the same 

 wave may be at the same, point of space at the same time. 

 Mr. Airy did not reply. Mr. Stokes, however, undertakes to 

 maintain plane-waves by the following considerations. He 

 first finds that a point of maximum velocity of a wave travels 

 at a rate different from that of a point of no velocity, and con- 

 sequently that there is at least great danger of one overtaking 

 the other. When this absurdity is on the point of being 

 consummated, the wave, as he conceives (for there is nothing 

 in the analysis to indicate such a result), is converted into a 

 breaker. What the subsequent motion is Mr. Stokes thinks 

 it would not be worth while to inquire, but proceeds to sup- 

 port by considerations, which it is not necessary to particula- 

 rize, the possibility of the physical existence of a surface of 

 discontinuity at the position where the abrupt alteration of the 

 character of the wave takes place. How then stands the 

 question ? According to my reasoning plane-waves are phy- 

 sically impossible ; according to Mr. Stokes's, plane-waves are 

 'wholly incompatible with the transmission of articulate and 

 musical sounds. The only conclusion from either result is, 

 that the hypothesis of plane-waves is inadmissible. 



It may, however, be urged that spherical waves are physi- 



* Communicated by the Author. 



