Attraction of Mass, and some Neiv Gas Equations. 81 



whence 



273 



c T = i . v c . -ftr = i<j> c 



c ± c 



in respect of = 1, T c and 11 = 1 ; 



/ T. V _T, 



c ° ~ Ct c\273 J ~ %V ° ' 273 



or i f T c ) 2 



* = *•?{ 373* 



in respect of Vo = l, 0° and 11 = 1, 



which are the values of equations 22 a, b, c. 



For substances with T c v273 it is clear that equations (17) 

 to (21) afford an opportunity to calculate T c if the volume 

 0c is given, i.e. the critical volume in respect of = 1, 11 = 1, 

 and at the temperature T c . 



For we have m 



and thus 97 o 



Tc = 



2 . p e . ( 



The argument leading up to the equations (D) and (E) 

 can be also expressed more shortly as follows : — 



The " theoretical co-volume " b is inversely proportional 

 to the absolute temperature T, i. e. 



b = T/273 bt, if b is given. 



Compressed at 0° from the- volume v = l, II = 1, to the 

 volume v the pressure is 



-, _ v + b 1 _ n-j-1 1 



. v v n ' n . b - 



To attain the same pressure II at the temperature T, the 

 compression must be different ; and 



n 



v + b T x _ T/273 n + 1 x 

 v ' v ~ T/273 n ' n.b Q 

 _ T/273 n + 1 



T/273?i ' T/273. n . &$' 

 Equating the two expressions for II, 



_ T/273(n + l) 

 X ~ T/273 Ti + 1* 

 Phil. Mag. S. 6. Vol. 37. No. 217. Jan. 1919. G 



