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LIY. On Poisson's imestigation of the Theory of Sound. 

 BijWJ. Macquorn Rankine, C.E., F.R.S.E., F.R.S.S.A. ^-c * 



PROFESSOR POTTERt conceives that he has found a defect 

 in the reasoning of Poisson's investigation of the velocity of 

 sound in air, in the follomug respect. 



Poisson supposes, that when the density of a gas is changed 

 in the ratio 



l+s, 



s being a very small fraction, the pressure is changed in the ratio 



l+s + a; 



and remarks, " A' cause de la petitesse de s, on pent supposer 

 cette quantite <t proportionelle h s, et faire 



/8 etarit un coefficient positif et indepeiidant de s." 



The proportionality of cr to s is considered by Professor Potter 

 to be a pure assumption. Poisson, however, gives a reason for 

 it, viz. " h cause de la petitesse de s ;" and this reason is a suffi- 

 cient one. 



For let Pq and p^ be the pressure and density in their undis- 

 turbed state, and 



p=spo + 8p, p=pQ + Bp 



those in the disturbed state, and let 



p = <l>p. 

 Then by Tayloi-'s theorem, 



Sp = 0'po ■^P+2' '^"Po • Sp^ + &c. ; 



or, in the notation adopted by Poisson, 



p p ^'^ 2 p ^ '^^ 



which, " a cause de la petitesse de s," is sensibly equal to 



and — (f>'po, which is equivalent to 1+/3 in Poisson's notation, 



is a coefficient independent of s, whatsoever may be the form oi^p. 

 With reference to the concluding remark of Professor Potter's 

 paper, I have to state, that my reason for considering any theoiy 

 of sound objectionable, according to which different portions of 

 the same wave travel with diffi:?rent velocities, isj, that sounds 



* Communicated by the Author, 

 t Page 318. 



