722 



Above we have seen that for an equilibrium F -\- L a,9 well 

 equation (3) as (4) is valid ; we are able also to prove this by 

 converting equation (3) into (4) with the aid of the above relations. 

 We write (3) in the form : 



g-mi-_«^-p^ = ?, -(„-«J_"-(/._^J^-(c-y,)^- . (13) 

 Om On 



The composition of the phase in components is represented bj 

 (I, b and c ; tt p and y represent liie composition of this same phase 

 in composants. In accordance with (9) the following relations are 

 valid : 



« (",—",) + !*(«,— «<) + 7 («,— «J = a~(t, 



« (y, —74) + ^ (y,— y«) f- y (y, — yJ — «— y. 



When we add those three equations to one another, atter having 



d: a: 



multiplied the first one with , the second one with - and the 



Ox Oy 



K 

 third one with — , then we find, with the aid of (11) 

 oz 



" ^ +/?T^ + y,- = («-'OT^ ^ (fc -/?,)/ + ('-yJs- 



dm d n dp Ox oy oz 



Witli the aid of this (13) now passes into: 



, dS dg d§ ^ d? 05 dg 



5—»»^ — "s — Pa^=^>~"a — i^A — "yï" 



dm On Op Om On op 



which is in accordance with (4). 



We may also write the four equations (5) in the form (6). For 

 the first one of the equations (5) we may viz. write: 



dg dg dg i 



g— («—«,)- (y-^t)^ —{^—v,)'r' 

 ax oy Oz 



= ?.—(«,— «4)^ (yy-'^*)\ (^,— y,)^- 



d.r, dy, dz, 



(U) 



With the aid of (12j (14) passes into the first one of the equations (6). 



The three equations (11) excepted, which are valid for the phase 

 without index, we have still also three similar equations, which we 

 obtain from (11) by giving to all variables and to s also, the index 1. 



