( 164 ) 



meltingpoijit-curve, namely AA' D PB, constituting the line T=^f{.v), 

 and AB'EDQB, constituting the corresponding line T=/\i''). Tlie 

 curves T^=/{x') now run liorizontally in Q and Q\ inconsequence 



of the rehition r — , for the denominator {l—.i^n\ ■\- xu\ no longer 



vanishes for both curves at the same time. The places in the two 

 curves where this occurred before (we may imagine them to lie 

 !)etween Q and Q') have henceforth disappeared. These points Q 

 and Q' of the curves T=f{.v') correspoiid to the two cusps P and 

 P' of the curves T=f{x). 



The process of detaching, described above, took place on the side of 

 B — i. e. on the side of the highest temperature — but we shall 

 see that the same process is rejjeated on the side of A, when /?' still 

 further decreases, which is represented in the iigiires 8 and 9. 



The second detaching takes place at R and S and gives rise to 

 two new rudimentaiy parts of the original meltingpoint curve on the 

 lower side. The proper meltingpoint-cnrve is now ARJJPB for 

 T = f{.v), and ASDQB for T = f{,v'). The two points S and S' , 

 where the curves 7' = f{.v') run horizontally in consequence of tlie 



relation := correspond witii the new cusps R and It' in Ihe 



lines T = /[a'). 



It is of course important to knoAv at what values of ,i' I he t\\() 

 processes of detaching described above, take place. 



In the point Q (fig. 6) we have in the first place — ^ = or 



T=:q^ ^i'.v' {l—,i'); biit wc liavc tlierc also {l—.v)it\-\-.inv^=iO, from 

 which follows : 



.v = -^^^— ; 1-.. = ^ (12) 



In connection with the equations (6) and taking into account the 

 equations (3) for ii\ and n\_, we may deduce from these relations 

 a set of transcendental equations from which tlie quantities T, x' and ,?' 

 may be solved by successive approximations. So we find for the 

 first detaching with the \alues assumed by us for 1\ etc.: 



;r = 1^45_ , .// = 0,9108(Q) , .6- = 0,2555(P) , T = 301.2 . 



For the second we find as second solution : 



^S'= 1,1020, ■/'= :0,1149(>$) , X = 0,9705(7?) , T = 26£^. 



The case of fig. 9, i. e. just after the second det<ichin<j, has been 

 calculated by me point for point throughout its course,' putting /?' 



