( 461 ) 



y M- -g V' - y (2y'-:)x') $- -|- 9 (y'-x) .."=:0, . . (72) 



from vvliifh follows in connection with (60) -. 



V-|{2y'-3xr-8(y'-x')].r" + 4«' = 0. . . . (Tü) 



2.3. Tills foi-iniila yields at oncc tlio radius of ciirvaliiic of llio 

 {v, .?0-pi"OJection of tlic coiinodal curve. We need only ohserve that 

 according to definition : 



v'conn.— v"±n'^ •^roun. = -'>'" ± ^n; .... (74) 



so at first approximation : 



tVojij). ~"~ Of), 

 7^ =z =t Vconti. = i: — ; .v" = .?;,,„,„. . . . . (75) 



Substitution of these last relations in (73) now yields immediately the 

 equation of the coimodal curve and in exactly the same way as for 

 the spinodal curve we find from it the value of the i-adius of cur- 

 vature Rcoun given in formula (11). A further exj)lanation of the way 

 in which the knowledge of this value leads to the formulae (13) and 

 and (14) need not be given here, nor need we ex{)laiii the derivation 

 of the formulae (18) and (19), (2J) and (22). 



But the derivation of formula (20) will detain us for a moment ; 

 we require, namely, for it a more accurate expression for p than 

 that given in formula (23). If we therefore develop (31) as far as 

 needful for the purpose, we find ') : 



8/339 3 \ 



P = - yP, ( - y - y ^' + ^ t' r' - ~ (2y'-3x') ..+ ^ (y'-x>.'.J, (76) 



or: 



= 4 «' — 6 «' i/ + 2 (2y'— 3x') .v — 12 (y— x') vx , . (77) 



Pk 

 thence : 



Pk 



- « t' {v'^ - r'^J f 2 (2y'-3x') {.v^ - .r^^ ) - 12 (y'-x') (r'^ - r'^p..^„(78) 



for, with regard to the last term, the ditference of .r^, ami ,r^^ is 

 slight compared to that between v' p and /''^ . 



9 

 ^) II might appear as if jVj v'^ ought also to be inserted in the following ex- 

 pression, but it is easy to see that this term leads to a small (|Mantity of higher 

 order than those that will occur in the final result. 



