522 ) 



and ( - 1 =1 GO. The nicl(iiiu[H)int-(.Mirves approach to the type C 



vh/'Jo 



(fig--2). 



fdT\ li7\- fdT\ 

 If, however, q„=zcc, then ^ ^ = , — - =z — co , and 



dT\ fdT\ fdT\ 



— and — , approach both to 0. No\\^ — approaches to a 



limit, as e~ '^ converges to 0. This gives rise to the limiting- type 

 D (fig.2). 



We sliall see ))i'csently, that according to q^ l)eing greater or 

 smaller, tlie tinal course for 7' =/'(,/;') in tiic case 6', and the initial 

 course for T=^/U} in the case D may vary as to their curvature. 



All the otiier cases lie between these extremes, but we shall see 

 that there can yet be a great difference in course as to concavity 

 and convexity. In order to form an 0[)inion on tiiis, however, we 

 must w^rite down the second differential-quotients. 



III. We found for them in our ^t^cwzt/ communication ^) for T=1^, 

 when « and «' = : 



d-'l' 

 dx' 



1 fdT\ 





'J I Vf^'^Vo_ 



(</: - 4 TO 





(9. + 4Ï\) 



(?:-'i^\)-2(7-'7,) 



(7, + 47\)-2(9,~^,) 



,(7) 



in which ( - j is (^ ' according to (2) and (6). For the corresponding 



X /o 



expressions for 7, we find by tlie same changes as for 



dT 

 dx 



(see above) : 

 fd'T\_ 1 rdT 



\^y'J,~~ 9, \dyJo 



'd'T\_ 1 rdT 



W'JrV.Kdy' 

 y 



('7,-47;) 



\{<h-^T,)-^2{q-q,) 



, (7a) 



(?,+47',)-(^) l(^, + 4T,) + 2(^,-^,) 



in which ( — ) = e ^ according to (2) and (6a). 

 \y J, 



That tliese equations can give rise to a point of iiijlection in the 

 meltingpoint-curve, so even at «' = 0, 1 have already proved in my 

 second communication (loc. cit. p. 256 — 257). 



1) These Proc. VI, Oct. 31, 1903, p. 256. 



