318 Prof. Potter's Reply to the Observations of Mr. Rankine. 



then says, " Nous supposerons done qu'ou ait, en general, 



p =zgmh(l + s + cr) ; 



cr designant une quantite de meme signe que s, et qvii en est 

 une certaine fonction. A cause de la petitesse de s, on pent sup- 

 poser cettc quantite ct proportionelle ^ s, et faire 



o-=/35; ioolav ortJ Jfifl 



/9 etant un coeflSeient positii et mdependant de s." ,,,,.,!, i,,irio^ 

 Now the only condition which we have between <r and; s is, 

 that they must p^, of the same sign ; so that if we put 



■ '' '" " '^^M, ^ : • , 



'. -,r:J ti'iifl/v if.HJiigi.;!vi7..i 

 and expand /(s) in a series ascending by integral ppwe;:? pf ,s,,|«ve 

 must have the index of the first term an odd integer ; and also 

 sijjce s is small, we might neglect all terms but the first^ and put 



»l' cr=8s, or a=^s^, of (T=sl3^,^^cr<'iJmbiuso? \o 



! '^ ' , . , .AT ,1.:,.;, 



Now to take the first of these without any reason, more than the 

 need to procure a solution of the problem under investigation, is 

 a pure assumption ; and the whole process fails with any oth^r 

 power of s than the first. 



We are thus thrown back on the original popular view of 

 Laplace in seeking for an explanation. Sometimes it is so worded, 

 as if the acceleration of the vibrations of the particles of the me- 

 dium by the heat and cold developed, proved necessarily an ac- 

 celeration of the velocity of the propagation of the wave-motion ; 

 although at the same time it is one of the acknowledged facts of 

 sound, that the velocity of propagation is independent of the 

 velocity and frequency of the vibrations of the particles. 



The velocity of propagation, however, varies with the elasticity 

 of the medium for the same vibrating mass ; so that the only 

 way in which Laplace's view need be taken, is that stated in my 

 paper on Sound in the February Number, by considering the 

 heat or cold developed by the first pulse which is transmitted; 

 and this leads to consequences, as there shown, which »re cpri- 

 traiy to experience. . i 



Mr. Rankine is, however, in error when he supposes an objec- 

 tion would also hold, since, because " every wave must consist of 

 a compressed and a dilated part, the difi'crent parts of a wave 

 would travel with dift'erent velocities," for this would only make 

 the waves unsymmetrical in form. 



London, March 7, 1851. 



