Mr. C. K. Akin on the Compressibility of Gases, 297 

 start from the general relation 



which is similar to that expressed by the Boylean law, except 

 that it involves an additional magnitude <f>, by which that law 

 may be corrected to any degree, on considering (£> as a function, 

 be it of p or the corresponding pressure p, to be determined, as 

 to form, ultimately by the aid of experimental or other data. 

 Differentiating the last expression will furnish 



dp dd> , , IX , 

 p T H 



after some simplification, and on introducing again D and H in 

 the sense of the preceding article. Integrating again between 

 the same limits as before, we shall find 



but since the above integral may be written 



C a C x C a 



— (^1 dec instead of I dx or — I <j> dx : 



%J x *) a %j x 



to warrant which it is only necessary to give cp^ a proper value 

 in accordance with the inequalities below, 



(pa > </V > £r : 



we get at last 



9« 



and, on substituting this value of p in the expression for the 

 mass, 



M= pdx=^\ Ae*^*-" 



Jo fajo 



) dx. 



To perform the integration above only indicated, it is necessary 

 to introduce two new <^s, similar in meaning to the original (/>,,, 

 but now in accordance with the following inequalities, 



by which means M may be written 



Mss .«W H £ n_ r * w f?i. 



90*) D 9« ' 3 



or also 



M== &■*.& u_. c -^ H «> 

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