i 459 ) 

 The spinodal cin've. 



20. The equation of the spinodal eiirve is found by cliniiiiatioii 

 of m from (40) and (41). We must, however, take into account, 

 when writing these two equations, that v' along tlie spinodal curve 

 must be considered to be of the order \/j', so liiat liie terms wilii 

 v'^ must also be taken into consideration. 



We get then: 



Q 



— --(2y'-3x')3=0 ((JO) 



and 



3 , , 9 , 27 ,.. , 



- - (2y'-3x') m + - i' + ^ tr . +- (y'-x') .^v =: . (01) 



from which follows for the equation of the spinodal curve: 



V-yL(2y'-3xr-8(y'-x')].v + y«' = o . . (02) 



This is, however, its equation on the tf?' -surface. In order to 

 know it on the original tjvsurface, we must transform il widi llie 

 aid of (20) into 



(V - ^^^y - ^^' [{2y' - 3x')-^ - 8 (y' - x')\ .V + 12^^ t' = 0. . (03) 



For that of the circle: 



{v-^b^y + {,;-E—ffy- — R\ {Ö small) 



we may write with the same approximation : 



{v-5b,Y — 2Ilv 4- 2R(f=0, 



from wliicli wo may immediately derive the "expression (10) for llie 

 radius of curvature of the (r, .r) projectioji of the spinodal curve. 



'J'he' tivo first connodal rehit'ioiis. Eqiiatio/t of the connodal curve. 



21. We shall now take /^ (.''i, '''J and /^., (.''.,, r'.J, for wliicli 

 r'.,'^ v\, as denoting two corresponding connodes. 



We put then : 

 c\^v"-,i; v\ = v"Jrri; .r,=,r"-in; •'•,-.''' + §1^ ; . (04) 

 hence : 



where therefore (.<•", v") indicates a poiiil halfway between the two 

 connodes and 5 denotes the tangent of the angle which the |)rojection 

 on the (r', .r)-surface of the join of the connodes foiius wi(h (he 

 v'-axis. 



