( 527 ) 



perature at which the intersection of these curves takes place in 



such a way thai al one of the points of intersection a tangent may 



dhp do 



be drawn to -^— = 0. for which — ■ = 0. 

 ox 2 da 



To determine these circumstances we have the three equations 



dhp d a ip d 8 tf> 



^— = 0, — — = u and — ■ = and this problem proves to be the 



do; 2 oxdo da* 



d 8 ip d\p 



analogue of that mentioned above, for which - — = 0, = o ;l nd 



dv* Oadv 



b'\p do da do 



- T — = 0. If tliere — was ;= go, now — = oo or — = 0. 

 do dx do dx 



d 2 ip d\p o\p 



So if the 3 equations ^— = 0, — -- = and - — = admit of a 



Ox 2 OxO o ö,/; :i 



solution, the circumstances may be realised in which at the plaitpoinf 

 a tangent may be drawn /' .y-axis. Neglecting the variability of h 

 with v we find for the three equations: 



d> MRT \dxj dx" 



— _ z= J - - — o m 



dx 2 x(l-x ' (v-b) 2 V ' ' ' ' { ' 



(diï 

 MRT — 

 o\\) MRT(l-2a) \da 



dx s a\l-af 1 (o — bf yj 



db da 



MRT — 



ohp dx dx 



zr-Z- = =0 (3) 



dxdv {v — b) 2 v* y } 



If we put a = A-\- 2Bx -f- GV and b = 6, + xp = b t -f * (h, — h x ) 

 we get the equation : 



4(£ + Cx)(Cb l - l jB) 



2.c 2 C [ 



= \ — — 1 ± |/ 



1—3* -f 2a* 2 i? + Cx ) 



1 + 



C\vi3(l—x) 



If B=a li — a x should be small in comparison with a. -\-a % — 2a li )x=Cx, 

 we get x equal to l / t by approximation, at least if — is aiso small. 



Then real values are found both for x and for T and v; only 

 this value of T can lie below the melting point in many cases, and 

 consequently it cannot be observed. 



However, I shall not enter into a further discussion. I will only 



point out, that for suitable values of T the curve - — = represents 



OA' 2 



a closed curve, which contracts with increasing value of 7' and 

 may contract into a point. 



