Mr. C. K. Akin on the Compressibility of Gases. 293 



in a certain number of cases in which they had been experimen- 

 tally determined, allowed of the construction of a continuous 

 curve having the initial pressure p for general abscissa, and ft 

 for ordinate ; which curve might hence be considered as a gra- 

 phical representation of the function /3 of p Q in the instance of 



— =2, according to the general meaning of ft, and the parti- 

 al 



cular values of a and a } adopted by M. Regnault. By the aid 

 of these curves (to each gas belonging, of course, a distinct one) 

 four values of ft were determined for each gas, as indicated below 

 — where, for brevity's sake, (« + l) has been made = m; viz. 



Mo = m i Mol = m n l J±Pol = m m ail d Mdl = m w (A ) 

 V \P\ v iPi v iPi V *P" 



corresponding to the following values of the abscissae p Q , 



Po '=F =(rE ff ), rf=ri, p m =p l ",^ip^-p 1 m . (B) 



Forming now the products* 



n r =jn'j n'^m'm", n , " = m'?n"m'" ) and n iy =m'm ! 'm'"m iv j 



V P 



we obtain four special values of the general function v p 



MM 



analogous to -^-9, but supposing at present P (instead of — ) to 

 v l p ] i\ 



V 



be constant, and ^ (instead of p ) to be variable. In the case 



1 Un- 



specified, P was made =1 metre mercury, and ~ successively 



' i 



l i i J ' 



2> 4J 8) 1"S"^ 



y p 



so that the above ^^'s,oy?i's, gave the values of the ratio ofpres- 



MM 



sures when the compression or ratio of mean densities (for which, 

 however, the proper bottom-densities should be substituted) 

 varies from 1 to 2, 4, 8, 16. Any two or more such values n 

 might hence be used to determine the two or more constants of 

 any such empirical formula, showing the pressure in the form of 

 function of the density, or conversely, which has before been 

 designated as the end of all these various operations; which last 

 calculations M. Regnault of course actually-accomplished. 



It is evident, however, that for the n's to have really the mean- 

 ing assigned to them above, it is necessary that the equa- 

 tions (B) be strictly attended to. iNow it was found by M. 

 Regnault in the first instance, and is mentioned by him as the 

 primary result of his researches in question, that the law of 

 Boyle is not accurate. This, applied to the case in hand, means 



* It is easy and instructive to translate the meaning of this arrthmetica 

 operation into the language of experiment. 



