( 161 ) 



AA' and B'B. EDF is the c()rrey|)Oiiding curve T^f{x), which 

 touches A DB in the common mininuim B, where x = x'. 

 Tiie j)oint D is therefore determined by the equations 



T:z=7;(l-iiV).= T.,(l-^ii'(l-..r) (9) 



or willi our values: 



T = 1200 (1 — 5.7,-^) = 500 (1_G(1— .r)^), 



wliich gives X = x' = 0,494, T = ~ 2(54°. 



The [)oint I'j indicates another value of ,/', corres[)()nding to the 

 point A of the curve T = f{x), where x = l, but now 7'— — 0°. 

 This point is obviously deterinined b)' the ecjuation (coin|). (6)) 



1 _ 1' ^i' (1 _..^.')2 — (therefore iv^ = 0), . . . (10) 



which yields ,/;' = 0,592 . 



The point F indicates a value of x' corresponding to the point 

 F/ of the curve 7'=/{x), where x = 0, T= — 0\ Now we have : 

 1-/?V^ = (therefore 7^^ == 0), . . . {lOfns) 

 from which follows: ,?' ^ 0,447. 



The curve 7^ = ƒ(,?') has tlierefore obtained a continuous course 

 through the points A and B', the curve 7^:= ƒ(,!■') however changes 

 abruptly at B' from B' to E, and at A' from A to F; further its 

 course is continuous from E through D to F. 



The question might be put: in what case does the point E come 

 in A and the point F in B' and has the discontinuity in the curve 

 T ^ f {x) therefore reached its highest possible value? Obviously 

 this is the case for /5' = go. For then w.^ = can vanish for .// = 1 

 and ii\ for x' = 0. In this case die lines AD and ED coincide 

 over their whole length with the axis x = l, and the lines B' D 

 and FD with the axis x = 0. 



At all temperatures above the absolute zero the values of -/;' and 

 ?/' vanish in this case continuously; this represents therefore the 

 case, that the solid phase coiitains oidy one component. 



The lines ADB and EDF lie, as we have seen, wholly in the 

 region of negative al)solute temperatures; besides this they lie with 

 their wdiole coui'se in the region of the luisUihle phases, as is 

 showm by a closer examination of the relations 



0^5 _ RT d^?' _ RT ^ , 



d^ ~ x{l—x) ' 0^ ~~ x\l—x) ~ "" ' 



V. The value of /?', for which the point D, Avhere x = x\ is 

 found exactly at T = 0, may be calculated by solving the equations 



