( 186 ) 



d*Tdx 



dp dx 7 dp 

 dx _ d*T 



d*T d*T d*T 



'dv\*_daï fdv\'_df ( dp\* _dië i ~ 



jLx) ~~ dFf ' [dp) ~~ d*T and \dx) ~ ¥f ' 



dv* dv 2 dp 3 



We may verify these properties by writing for the immediate 

 neighbourhood of the minimum or maximum plaitpoint temperature: 

 T =l\±a (0 - xrf = l\±p(v- v,y = T 1 ±y (p - Pl )\ 



in which the sign -f- holds for minimum value of T, and reversely 

 the sign — for maximum value. 

 From this follows : 



« (*— *i) 5 = P (v— l \Y = y {p— Pi)', 

 or 



± (0—0,) l/« = ± (»—«,) |/0 = ± (p-/>,) l/y, 

 and 



da 



* = ±|/^ , *=±|X£. and ^=±1/1 



i.i' v $ dv V y dp y a 



dv dp dx 



As — X~r Xt = + 1» we have to take all the signs positive, or 

 dx dv dp 



one positive and two negative. Thus in the case that there is mini- 

 mum or maximum plaitpoint temperature, and we choose the direction 



db dv dp dp 



of x such that — is positive, — ]> and — <C , and so also — 



dx dx dx dv 



dp 

 negative. It is, however, not always the case that — is negative. 



dv 



(dp \ 



Thus for a plaitpoint line with maximum value of p, I — = J 



dp dp 



also — = and — = 0. So in such a case reversal of the sign of 

 dx dv 



dp 



— must lake place. 



dv 



If we examine the criteria for an heterogeneous double point, we 



dT dT dT 



have in the first place — = and — = 0. Then — is not equal 

 dx dv dp 



to 0. Bui iu its stead there are two other differential quotients which 



