450 PROFESSOR CHALLIS, ON ATMOSPHERIC TEMPERATURE 



consequently be considered to be entirely owing to difference of den- 

 sity. We have therefore (p a function of p, and 



d . p(j> d , p(p dp 

 dx dp ' dx 



Hence the value of b may be put under the form. 



«^5T^.{**r^-^}' 



The known facts of the transmission of articulate and musical 

 sounds prove that diflferent parts of the same aerial wave and waves 

 of different magnitudes are propagated through air of given tem- 

 perature with exactly the same velocity. It follows from this that 



f^ is constant for a given value of d,. Suppose 

 dp 



^_^ = * (1 + ae), (C). 



up a 



Then, 



b = a V'l + a0, \/l + k ; 



the numerical value of 1 + A can therefore be obtained by an experi- 

 mental determination of the velocity of sound. The mean value found 

 by this method is 1,4152.* 



The equation (c) gives, 



1 +a6/ dp 



Hence, 



, , ;■ ■ {l+aO,)dp + ad.p<p 



(1 + aO,) dp 



d.a'p\l +a{9, + (j))\ 

 ~ d . (i'p (1 + a0,) 



The expression under the latter form shews that 1 + * is the ratio of 

 the increment of pressure due to an increase of density produced sud- 

 denly and consequently accompanied by an increase of temperature, to 



* From the experiments of Professor Moll. See Phil. Trans, of the Royal Socielt/, 

 1824. p. 424, and 1830. p. 213. 



