( 652 ) 



as critical pointe). Here it consists, in the neighbourhood of that 

 same point, in a double system of curves of hyperbolical shape, 

 as may be seen in the annexed figure, separated by two curves, 

 of which the equation is obtained by putting p = pTk- To the first 

 approximation the system of isobars is represented by the equation 



^02 (■^— '^T/b)" + in^^ {'V—XTk) {v — VTk) = p—pTk , . • (8) 

 Avhich represents hyperbolae, of which the one asymptote is : 



X — A' J/- = (r — VTk) 



while the second, x — xxk = 0, ina,v be written to the second 

 approximation 



(9) 



^^3 



XTh = i^'—fTlcY 



The connodal line. In order to find the projection of the connodal 

 line on the x, y-surface we eliminate p — pxk between the equation 

 of the isobar and that of the border curve; we then find to the 

 first approximation 



{x—XTk)^ '-{v—VTkY (1Ö) 



The critical point of contact, the apex of this hyperbola, coin- 

 cides, like the plaitpoint, to the first approximation with the point 



XTk,VTk,pTk- 



The border curve for a mixture x. If in the equation (8) we con- 

 sider X as constant and T, hence xjk and vjk as variable, and if 

 finally we make use of the equation of state of the mixture 

 (equation (13) I.e. p. 325) to express T in p and v, we obtain the 



1) The systems of isobars may then be written in the form: 



X z= n„ -\- Wj {v—VTk) + ^2 {v — t'TkY + 



where the «'s are still functions of p, for instance : 



^ = ^00 + ^01 (p—PTk) + n,^ (p—pTkY + 



If the ns are expressed in the m's, we find: 



= 



^\. 



m„ 



, etc. 



