324? Mr. Ivory's Answer to an Article by Mr. Henry Meikle 



as far as experiments have been extended, the ratios — and 



— are found to remain constant, as the theory requires. 



But in applying the foregoing doctrine to the velocity of 

 sound, I made use of algebraic formulas, which are things held in 

 abhorrence by a certain class, although it appears that others 

 know very well how to turn them to their own purposes. 

 Taking a mass of air at a given temperature, suppose zero of 

 the centigrade scale, let a denote the dilatation under a con- 

 stant pressure for 1° of temperature, and /3 the dilatation re- 

 quisite for the absorption of 1° of latent heat; then it is ob- 

 vious that shall we have, 



I now take one of the formulas marked (C) at p. 252 of this 

 Journal for April 1827, viz. 



e l +«j 



whence I get, i = — • (1 -f a 0) (- l\ 



It will perhaps contribute in some degree to perspicuity, if, 

 instead of the proportion of the densities — , we substitute the 



inverse proportion of the volumes, viz. -—7- ; then 



*•«- s-(i+««)(-f-i). 



The formula will be still more simplified if we make the initial 

 temperature equal to zero, in which case V will be the vo- 

 lume of the air at the beginning of the thermometrical scale ; 

 then ! v . 



And, if t be the variation of temperature, we obtain, by the 

 theory of the thermometer, 



--K-v-r-0- 



These formulas show clearly the relation that subsists be- 

 tween the temperature and the latent heat, and in what man- 

 ner both these quantities are derived from the volume. Both 

 the expressions are significant, and represent what actually 

 takes place in nature, so long as the postulate on which they 

 are founded holds good ; or so long as the capacity of the air 

 for heat remains constant, and the absolute heat which changes 

 the bulk of a mass of air is proportional to the variation of 

 temperature. Beyond this limit on either side, the formulas 

 become insignificant; they are mere abstract expressions 



which 



