494 The Rev. J. Challis's Reply to the 



distinguished philosophers as Wollaston, Young, and Sir 

 WiUiam and Sir John- Herschel, I feel assured that my Ana- 

 lysis of the Spectrum will be confirmed by future observers 

 who may repeat my experiments with the same care with which 

 they were made, and without any prejudice in favour of their 

 own speculations. 



St. Leonai'il's College, St. Andrews, 



May 8, 1848. 



LXV. On the Velocity of Sound, in Reply to the Remarla> of 

 the Astronomer Royal. By the Rev. J. Challis, M.A., 

 F.R.A.S., Pliimian Professor of Ast7-onomy in the University 

 of Cambridge^. 



THE mathematical investigation of the velocity of sound 

 which I gave in the Philosophical Magazine for last 

 April, has elicited Remarks from the Astronomer Royal, on 

 whicli I must make a few observations, before I proceed to 

 defend the principles of my investigation against the arguments 

 which the Astronomer Royal has brought forward. 



The not giving a reason for attaching a negative sign to i% 

 was an omission on my part, which Mr. Airy has supplied 

 exactly according to my views. 



After allowing that the constant b^ is admissible and may 

 be introduced for trial, Mr. Airy adds, " It is accordingly 

 introduced and tried, and we immediately perceive that if it 

 has a value different from zero, the result of non-divergence 

 of vibrations cannot be obtained. Most reasoners would con- 

 clude, either that such a result is not legitimately to be ex- 

 pected, or that a last trial should be made by supposing 

 i^ = 0." The result of non-divergence of vibrations is obtained 

 by that part of my reasoning which terminates at line 8 of 

 page 280, in which Mr. Airy "sees no ground for questioning 

 any important step." I am not, therefore, chargeable with 

 acting differently from "most reasoners" in not coming to the 

 conclusion that such a result is not to be expected. Respect- 

 ing the case in which b^ = 0, which' is that of plane-waves, I 

 propose to speak shortly. 



In the next sentence Mr. Airy goes on to say, " Instead of 

 this, Professor Challis has recourse to aiiother equation ex- 

 tracted from another memoir, and not demonstrated here, 

 which he considers more accurate than his equation (4.), and 

 he then uses this new equation in conjunction with equation (3.), 

 and thus obtains the startling results to which I have alluded." 



• Communicated by the Author. 



