( 163 ) 



Graduall}^ .v' and //' assume practically measurable Aalues. 

 We find from (9) for the maximum J): 



.r = .v' z=z 0,571; T — 223°. 

 We tiiid for E, .v' = 0,423 ; for F, ,v' = 0,633 (sec (10) and (K)'"'*)). 



YI. We now proceed to tlie description of the further de\elop- 

 ment of the parts of the meltingpoint-curve lyinj»; below (.'. 



According as [3' decreases, the curve A' JDB mounts higher and 

 higher and finalij ir will touch the line ^^', e.g. in y^((k)mp. fig. 6). 

 But the values of .v and T of both curves T=/{,v) coinciding in 

 P, the values of x' also will necessarily coincide — or iii other 

 words the curves BA' and EDF will meet at the same lime, namely 



in the point Q. In this point however - must vanish, as J^nuiv be 



regarded as a citq) in the continuous curve ^4.1' X)Pi>\ If therefore we 



trace in the figure the curve--^=0, — i.e. 7=«' x' (1 —.i-') = q^ ,i',r' (1 — x'}, 



which will be a parabolic curve, whose axis of symmetry is the 

 ordinate x = ^/^, and whose summit lies lower according as ^i' 

 decreases — then the curves BA' and EDF meet tliis curxe at 

 the same time in Q. 



The direction of the tw^o curves BA' and EDF will there not be 

 horizontal, as appears immediately from the direction of the curve 



- — = in the |)oint Q. Therefore not only the iiumerators iu the 



dT 

 expressions for — , of those two curves must vanish in consequence 



d^ 



ot the factor - — , butalso the denominators (l-.^')«',+'^•^f'8. In other words: 



the two curves will meet each other at the place of their )na,vinia 



for ,v' and 1 — .v' , exactly at a point where both curves had a vertical 



dT 

 tangent a moment before. So the expressions for — - are undetermined 



d,v 



in Q and the real direction of the pieces BQ and.l'Q, />^^and F(^ 



nmst be determined in another way. 



Fig. 7 represents the i)Osition of the different lines a moment 



later. ^' is here somewhat smaller than in fig. 6. It may be clearly 



seen that the lower branches B'F'B' and A'Q'F have got detached; 



henceforth they are isolated and disappear more and more downwards 



according as ^' decreases. They may be regarded as rudiments of the 



original meltingpoint-curve. The upper parts form henceforth the j)roper 



