( 453 ) 



continues lo exist. They even hecouio zfro when (he plail point 

 coincides with the critical i)uint K, so (hal holh ciii-ves have (hen a cusp. 



12. The knowle(l2:e of the radius of curvature /?<,,««. is of importance 

 specially because it may be used in connectioji with the tornnda: 

 Fig. d. I 



^,,;i = ft = ^-(2y'-3;c>^ (12) 



through which we know the small angle which 

 the tangent of the plaitpoint forms with the ?;-axis, 

 to calculate in a Aery simple way the differences 

 in density and volume between the phases of the 

 plaitpoint F and the critical point of contact R 

 at first approximation ^). 



According to fig. (/ we have, within the indicated 

 limit of accuracy : 



v^-Vj^ = PQ^PR =r ,iA^,„„ - ^(2y'-3x') [(2y'-3,cr-8(y'-x')l..^,.. (13) 

 ^>-'^Ve=^^= 2 ^'^ "^'^ =^(2y'-3xr[(2y'-3;cr-8(y'-x')>'^,. (14) 



13. We proceed now to give the formulae relating to the ])lait- 

 points phase at a tempcraiurc T, which docs not differ much from 

 the critical temperature Tk of the principal component. 



They are : 



^'P (2y'-3xr-8(y'->c')' 1\ ^ ^^ 



^,.-3/>.= |M(2y'-3>cr-4(4y'-3x')(2y'-3x') + 16y' j..^ • (16) 



8 

 Pk 



|(2y'_3xr-4y' + 2x'|.r^, .... (17) 



\\\ means of (15) we may transform (13) and (14), so lha( ihey 

 become : 



9/>, T—Ti, 



and 



. . (19) 



^) A similar molliod is given l)y 1vkf.:o.\i at tlic concliisiKii «iflhc bofoi'o-im'nlioiK'd 

 paper of Verschaffelt. 



