Attraction of Mass, and some New Gas Equations. 79 

 of v, and the two points of the latter curve for which 

 -£=.0, j^ — 0- The curves described by (D) and (E) are 

 therefore identical with the " Border-curve. " Their vertices 

 are the critical points, and at these points ^- = 0, ^— = 0. 



We have already solved (D) and (E) for |^=0. We 



-dt BV 



get the same results for — =0. 



Differentiating equation (D) we find : 

 4 Co r273l' 4c» 278* 2 <^ + t O- t7 



As | = °> 



273 1 ^. </>,-+ ^ c 273. 

 + X >« d * £5- * T7 ^ *• 



2(<£ c +^) T c , , , .. 



= ~~ 273 273 ^ ' aS ^ c = * e ' 



1 JL J 273 \ 1 f 273 V 



which are the values obtained in equations (17) and (18). 



These values substituted in the original equation lead to 

 the expressions (19),- .(20), and (21). 



The critical point consequently is the point of intersection 

 of the Critical Isothermal, the Border-curve, and the Curve 

 2p c . v c = 1. For gases with critical temperatures below 273 

 the analogous curve of the latter is 2p c .cf) c =l. It is therefore 

 defined by three equations. ( Vide fig. 1.) 



Differentiating equation (E), we find (for T c <273) 



4 SfTo-) 2 4T C 1 2(v c +b c ) T c 

 —& 1 273 J B " + 273* • ^ ~ VF ■ 2T3 3 " 



T c 1 v c + h„ 1 



