( 254 ) 

 fdT\ /<r-T\ 



I — ) being negative, will also he negative if q^'^VJ . 



\dxj, \d.c y„ 



The meltingpoint curve will then turn its concave side to the .x'-axis 

 at A, and no point of inflection \vill occur. This is in perfect agree- 

 ment with what we found in our former paper. ^) 



/d^T\ /'dT\ 



As to I — - we see that this expression, iust as ( — : | will 



always be negatively large. For great «' the concaA^e side of the 

 curve T = /{x'), running almost vertically downward, is turned 

 towards the .I'-axis, but the curve T=f{a;') finally touching the 

 ordinate .v = asymptotically at T=0, a point of inflection must 

 at any rate be present beyond the maximimi of the curve 7^=3 ƒ (.?■') 

 (see fig. 1 : at L). 



This point of inflection L will occur inunediately after the maxi- 

 mum at VI for large values of «', and these two points gradually 

 approach the point A, where T =i 2\, x z=0. 



As to the maximum m, this is of course represented b}^ 



(1 — x)w^-\-xw^=^0 (see (6)) or ,7; = Now ii\=^(i^—a,c'=iq.^,im(\ 



n\ := <j^ — a {1 — ,1"')' = — a', when a' is large and ./•' very small; 

 liencc the maximum occurs at 



If therefore ,i' approaches to x, then ,/',„ (so also .r',,,) approaches to 0. 

 As to the point of inflection at L, the following remarks hold 

 good for it. 



From the exi)re^sion for -— (see [a]) follows, when a = and 



d.v 



a IS large : 



dr _dT ,c{l-x) «', _dT .r{l-.c) q, _(/7 ,/(l-,y) 1 



d.v' dx .v\\-iv')ii\-{-x{w.^-u\) d.v x' q^-xii dx x' l-/i'.'f 

 At small ,r' we get : 



(/>*) 



1 -llof,{l—.r) 



'h 

 hence : 



dT 2\R1\ 1 RTr- 1 



dx N' q, 1-./- q, (l-.'-)(l 4-2<^.r) 



as N' = {1—e log (1— -0 )^ = (i + 6.C -f . .f = (1 + 2 6,v). 



1) These proceedings, Febr. 25lli 1902, p. 427; June 2ith 1903, p. 29—30, 



