723 



We call those three equations 1 1". As, however, in accordance with (5) 



0^. 



K 



— = -~ etc., it follows from (II) and ( 11") also r— = r^-^ etc. 

 o>r dd\ dm 0171^ 



For a ternary system with llie composants F^ F, and F, we 



have, when we choose F, as fundamental component: 



F =^m F^ + nF, + {l-m — n) F, .... (15) 



When we represent the compositions of the components by « and 

 (i with the corresponding index, then the equations (9) pass into: 



m («,-«,) — n («, — «,) =: .« — «, 



We now shall deduce those equations also in another waj, by 

 which at the same time the meaning of m and 11 in the graphical 

 representation becomes clear. 



We take a system of coordinates with the axes C^A^ and UY 

 (Fig. I) in which we represent the composition of the phases, 



(16) 







U^ 



Fig. 1. 



expressed in the components. We imagine the three composants 

 F, F^ and F^ and the arbitrary phase F to be represented b}' the 

 points F, F, F, and F. Consequently in the figure is F^v = <(„, 

 F,u = (i, etc. Now we take F„F, as new A'-axis and F^F, as new 

 y-axis; then the new coordinates of the point F are Fq and Fr , 

 we put Fq = x' and Fr=iy'. When we call the angles, which the 

 new axes F^F^ and F,F, are making with the original X-axis <p^ 

 and </', then it follows from the figure; 



