476 Prof. Potter on the Solution of the Problem of Sound. 



I have discovered these correct methods is open to discussion. 

 I believe that my solution of the interesting case of diverging 

 streams of air has no competitor which can approximate to an 

 explanation of the facts. In regard to the numerical velocity of 

 sound it is othei-wise ; and I have to acknowledge a very great 

 oversight in the computations on which the close agi-eement with 

 the true velocity, stated at the end of my first paper on sound, 

 was based. The error is this ; using Poisson's numbers in cal- 

 culation, I omitted to see that the ratio of the density of mer- 

 cury to the density of the air there given was for the temperature 

 of freezing, and of course the velocity of sound calculated there-* 

 from should have been compared with the experimental velocity 

 at the freezing-point. My theoretical velocity with these data 

 comes out thii-ty-two feet per second more than the experimental 

 result. 



Mr. Rankine, in his paper in the last Number, appears still to 

 misunderstand the bearing of the method on which Poisson's 

 solution of the problem of sound is obtained. 



We have cr an unknown function of s, and of the same sign 

 with it, s being small ; these are their only known relations. 

 What is in reality a physical law, is attempted to be determined 

 by mathematical reasoning from these imperfect data. 



Supposing the unknown function a-=f{s) to be expanded in 

 a series ascending by integral powers of s, we have the form 



where a=0; but to say "k cause de la petitesse de s," that yS 

 is a finite quantity is a non sequitur, since the conditions will be 

 satisfied if either S, ^, or other coefficient of an odd power, be 

 the first coefficient which does not vanish. 



Mr. Rankine takes the form p = (^p, or the pressure in the 

 general disturbed state an unknown function of the density, and 

 uses in Taylor's theorem the first derived function </)'/Jo, which is 

 of course also imknowTi. His expansion, s being small, gives 

 for (T this value. 



<r=|^°fpo-l|. + &c. 



Now it is a pm'e assumption to take the coefficient 



Pa 

 a finite quantity ; physical laws being something beyond alge- 

 braic expansions. 



As to his reference to a former argument, he should have told 

 us what observed facts are inconsistent with unsymmetncal 

 waves ; he did not mean perhaps the sounds arising from the 

 super-imposed vibrations in musical strings. 



London, May 10, 1851. 



