334 Mr H. Meikle on the Specific Heat 



adopting the fraction J, Mr Ivory obtains the following equa- 

 tion, 



1 4- ar 



= ^' ; or. 





Where t is the initial temperature, a a constant, and i the change 

 of temperature, produced by changing the density from unit to 

 g. That this is the true value of i, considered as proportional 

 to the change in the quantity of heat, Mr Ivory thinks pretty 

 certain ; because he supposes a consequence of it to be, " that, 

 when air contracts or enlarges its dimensions, the heat disen- 

 gaged or absorbed follows the proportion in which the linear 

 distance of the particles is lessened or augmented," — an opinion 

 which he thinks so probable, that it should not be rejected till 

 the contrary be placed beyond all doubt. 



Now, although my experiments are favourable to Mr Ivory's 

 conjecture regarding the value of this ratio, yet I cannot ac- 

 quiesce in the reason which that able mathematician has given 

 for fixing on that quantity. I shall not enlarge on its incompati- 

 bility with the law of temperature which I formerly laid down ; 

 but that it may not be urged as an argument against that law, 

 I shall, with every deference to Mr Ivory, shew that his view 

 of this part of the subject is otherwise untenable ; because it in- 

 volves a mistake, in that he has inadvertently taken the linear 

 distance of the particles of a mass of air as proportional to the 

 cube root of the density, in place of the cube root of the volume. 

 For it is obvious, that 5^ is not proportional to the linear dis- 

 tance of the particles, but to its reciprocal ; and whilst t is the 

 same, i varies as g^ — l^ that is, as the difference of the re- 

 ciprocals of the linear distances at the beginning and end of 

 the change of density ; so that neither the heat of combination 

 nor the quantity i follows the variation of the linear distance of 

 the particles. For, as we formerly saw, the first follows the va- 

 riation of the logarithm of the volume or cube of the linear dis- 

 tance. 



The following is a different mode of estimating the ratio of 

 the specific heats, by using great changes of density. 



Let the density of the external air = e, and suppose the air 

 in a close vessel to be rarified till its mass or density = r ; and 

 that when it has acquired the common temperature, a communi- 



