ACp-\-Av-TA^ 



66 BRIDGMAN. 



is necessary to compute these three quantities. But at a horizontal 

 or vertical tangent, the relations simplify in such a way as to determine 

 uniquely two of these three quantities without the necessity for a 

 third relation. We shall assume for the deduction that we know 

 AV and AH along the transition line. These date are, as a matter 

 of fact, determined in the following work. We are at liberty there- 

 fore to use the following relations: 



dAv dT .- . 

 -r- = —A^-Aa 

 dp dp 



dAH ^ dr 



dp dp' 



dr 

 Now at a horizontal tangent, "i- = 0. We immediately see that at 



such a point the equations give us the means of determining both Aa 

 and Aj8 from the transition data alone. These values are; 



dp 



^ T dp 



We cannot find ACp from the equations; the only method is direct 



experimental determination. These relations are of application to 



Hgl2. The equations furthermore show that for those substances 



which we may call normal [Aa>0, A/3>0], the maximum of the AH 



curve must come before the maximum of the transition curve. 



dj) 

 At a vertical tangent, 3" ~ 0, and we get 



These relations are of application to water or benzol. We cannot 

 determine Aa at a vertical tangent from the transition data alone. 



Two of the relations may be written in a simpler form, involving 

 the curvature of the transition line. These relations are ; 



Aa = X curvature, at a horizontal tangent [~r — ^ j> 



fdr 

 ACp = — r Ai) X curvature, at a vertical tangent ( ;/" = °° 



and 



