298 Mr. C. K. Akin on the Compressibility of Gases, 

 since H p a 



Employing now again two different values of a, to be denoted by 

 ct and a v and discriminating properly, moreover, between the 

 various p's and <£'s, we obtain the equation 



from which follows 



p = 4>WK) i-«-*'wl" 



To simplify this formula, it may be observed, in the first place, 

 that, according to their signification, the ratios iM and ?-S£0 



cannot but be each extremely near in value to 1 ; and being 

 both at the same time either >■ 1 or < 1, the fraction of which 

 one of these ratios is the numerator and the other appears as the 

 denominator, which occurs in the above formula, may be safely 

 replaced by 1. Similarly <pl , and <$ ., which, like all the <f>'s, 

 are but little different from unity each, and appear multiplied in 



the above exponentials by the very small quantity r— , may be ex- 

 changed for two other values cf> l and <£ , to be considered as 

 similar in meaning to the simple cf) a of former formulae; from 

 which definition it is easy to conclude that <f>\ ) and xf) v and cj>° { . 

 and <f> are of necessity very nearly identical in numerical value. 

 In this manner we find at last 



from which, after developing and on retaining but first powers of 

 — , which will be sufficient, we deduce 



H 



&-£T = 1+ !H<**>-* lfl '> 5 • •■- (a) 

 Pi V\ a \ * M 



while for — , which is the ratio of pressures corresponding to the 

 p. 



ratio of densities — , will be got the simpler expression 



By means of formula (a) it is now possible to employ the ex- 



