[ 186 ] 



XXIII. On a new Theoretical Determination of the Velocity of 

 Sound. By the Rev. S. Earnshaw, M.A., Sheffield. 



[Continued from p. 41. J 

 The Triplicity of Sound. 



THAT the actual velocity of violent sounds should be greater 

 than that of ordinary sounds, and that the velocity of 

 ordinary sounds should be greater than was found by Newton, 

 are results which theoretically depend only on the hypothesis of 

 finite intervals as distinguished from that of continuity; but 

 that the numerical value of the velocity of ordinary sounds should 

 be exactly what it is, is a circumstance which depends also on 

 the particular law of force according to which the molecules of 

 the atmosphere act on each other. As far as I know, this law 

 has not hitherto been experimentally determined; it was open 

 to me, therefore, to assume any law to which there should be 

 no a priori objection. It is of course essential that the assumed 

 law must give a result agreeing with experiment ; and it might 

 have happened that no simple law of force could have been found 

 which would give a result agreeing with the experimental velo- 

 city of sound. But not only did a simple law present itself 

 capable of doing this, but the law which it was found necessary 

 to assume is seen to be the lowest power of the inverse distance 

 which the mathematical expressions themselves would permit us 

 to try. I take this to be a strong presumptive evidence in sup- 

 port of the theory advanced; and I shall not hesitate to employ 

 the modified forms of the preceding equations which this assumed 

 law of molecular action will enable us to introduce, — merely ob- 

 serving, in doing so, that the physical results obtained do not 

 really depend, as to their character, on the assumption of this 

 particular law, but follow from the more general equations also ; 

 only, the mathematical expressions are by this means rendered 

 shorter and more manageable, and consequently the results more 

 obvious to the general reader. 



Q 



14. Assuming, therefore, f'(z) — -4, the last equation of art. 6 



gives 



,- 7T* /Cn\ 



and by treating equation (7) in the same way we find 



