( ^^^ ) 



A liigli value i\)v n (or /3) ineaii^ therefore a liigh value of the 

 latent heat of inixiuu', aiul when we shall presently see that a hip:h value 

 of /?' leads to very small values of x' or of 1 — ,c' , this cireunistance 

 may be interpreted as follows : 



If a large amount of energy is rccpiired in order to make one 

 of the solid components enter into the solid solution (or the mixed 

 crystal) then this solid solution will contain only a slight trace of 

 one of these two components. 



III. We now proceed to the discussion of the fundamental equa- 

 tions (2). 



dT dT 



Let us in the tirst place determine the quantities — and — by 

 ^ ^ dx dJ ^ 



totally differentiating the conditions of equilibrium — ft'^ -[- Mi = ^ '"i"cl 



— ft'a ^" f2 = ^ according to T. After several transformations we get : 



dT ^ 'bx^ dT ^ ^ dx'' 



— — — T ~ ; — — — T . . (4) 



dx (1 — x)ii\-\-x'iv^ dx' (1 — x)w^-\-xiö^ 



These well known equations have been deduced several times ^), 



i. a. by Prof, van dek Waals for the analogous equilibrium of liquid 



and gaseous phases. 



fdT\ , . . ^ ,. 



From (4) we may deduce the quantitv — ) , i.e. the initial clirec- 



tloji of the meltingpoint-curve. 



0/^, RT 



As ^- = — - — - + 2 ax, we have 

 Ox 1 — X 



ö^__ 1 dfi,_ ET ^^ 



dx^~ X dx ~ x{l—x) 



therefore, for ,/■ = 0, T = T, 



we have: . -x o 1 



if we write ,<•„ for ,r = 0. For .(' = \vc have also .r' = 0. The 



denominator of — appears therefore to be e(pial to {i(\)g = q^, hence 

 dx 



/^«^ \ _ _ rj, ^ _ _ J^^ I ( I — y 



\dxj, ~~ ' q, q, \ •>', 



1) See i. a. my Leliiljiich der nialh. ClieiDie, p. IIS and 123-121. (Leipzig, 

 J. A. Barth, 1901). 



