1146 



will) the ci-yolijclric' curve inulei- its own viipourprcssiire. Iji tlie 

 point of intersection of this curve with the line F— ice is viz. mj—^lv, 

 therefore E—0. From (11) and (12) it follows therefore, that JP=0 

 and r/J'=0. In this point of intersection pressure and temperature 

 are, therefore, either maximum or minimum. In order to examine 

 more in detail whether a maximum or a minimum occurs, we assume 

 the conditions of equilibrium for the system F -\- ice -\- L -\- G. 

 These are: 



« ^ + ^ ^ _|_ 5' _ $ = and Z, - S' = 

 ox oy 



Now it follows from the first of these conditions: 



/ OF dF A 



XT f ys) dx + {xs -1- yt) <V + ( •^- ^ -f 2/ ^ ^ + ^' 1 ^P 



.-f. ^ +, - - // + V J ^IT V k [r + . ^ + .^ ] ^.- ^- ] (42) 



(41) 



From the second it follows: 



/ dF OF , \ 

 {uT + |?s) (^.f + («s + i^O ^.^ + ( «ö7 + '^a ^ '' ~'" j "^ 





/ dr Ös\ / OS Öi \ 1 



+ (% + "d^j'^^''^' + * ("fly + '*s; j'^' + ''' = '' ' 



Herein R and /?' contain terms with dFclx, clTdx etc., which we 

 may neglect as will appear later. From the third condition follows: 



{V^-v')dF — {H,—ii)dTz:^^ (44) 



wherein the terms of hioher order can also be neglected. As in the 

 point of intersection of the curve with the line F—lce ay = ^x, so 

 we may substitute in (43) « = ).x and p' = ly. 



When we subtract (42) from (43) after having mnitiplied (42) 

 by P., we find : 



\l{v-v') + y-v\ dP-\).{H-~n) + n-n\dTi ^^ 



— ^,).{rdx' + 2sdxdy + tdy') + /«*" ^ ■ ■ \ J 



Let us substitute the value of dy from (43) into (45) ; it is apparent 

 from (45) that it is sufficient tliat : 



{as 4- ^t)dy = — {ar -|- ^s)dx 

 and that we may neglect the terms with dP, dT etc. We may 



