454 



to whicli we add 



14. We shall conclude with giving some formulae relating to 

 coexisting phases, where the index o?ie refers to the liquid-, the index 

 two to the gas phase. Where the index fails, we may arbitrarily 

 take the value for the one or for the other coexisting phase; either 

 because it is indifferent at the degree of approximation used, or 

 because the formula will equally hold for either state. 



,_3/._3/>,[/-4^^+[(2/-3>cr-8(y'-x')J.. . (21) 



r-3^ + 3^|/^-4-'^+[(2y'-3xr-8(/->c')>- • (22) 



>^Z^ = 4 ^JZj!1 4_ 2 (2y'-3H') x .... (23) 

 Pk ^'t 



.x-.v,=^{2y'-Sx'){i'-v,),v (24) 



1 (,,,4-.J -3/,. = - ^ ^ ^^^ + 3^ ! I [2y'-3xy-8(y -x')J4- 

 -}- i [(2/-3>cr-24(y'-x')(2y'-3x') + lG(3/-2K')j{.. . . .(25) 

 in wliicli foriiuihi (23j holds also for non-coexisting [)hases. 



SECOND DEMONSTRATING I'AKT. 



TmnsfoniKitioii of flw xp-surface and pirliutiiiary dei^cIop)ii('itt 



into series. 



15. We begin with a transformation of tlie if'-surfaco hy intro- 

 ducing the following variables: 



which means that we henceforth measure the volume v' from the 

 critical volume and with that volume as unit, the temperature in 



the same way with regard to the critical hmipcratiire '^'"^^i^J]^ 



and the free energy rp' with MBTk as unit. 



