Laws of Molecular Force. 239 



tically discovered the generalization, and expressed it in its 

 most striking aspects by means of several diagrams for a 

 number of bodies ; but tbe verbal expression of his results was 

 so unsystematic, and withal so crabbed, that his work has been 

 overlooked. 



There is one typical application of the generalization which 

 is of special importance — to the relation between pressure and 

 temperature of saturation. If with the aid of our equations 

 we trace the complete isothermals for temperatures below the 

 critical, we shall get curves with the James Thomson double- 

 bend as shown in Ramsay and Young's isothermals for ether 

 (Phil. Mag. May 1887)/ 



According to Maxwell's thermodynamical deduction, the 

 pressure of saturation at a given temperature is that cor- 

 responding to the line of constant pressure which cuts off 

 equal areas in the two bends, a result which Ramsay and 

 Young verified by actual measurement on their curves. 



Let v s and v± be the volumes of saturated vapour and liquid 



at pressure P and temperature T ; then Maxwell's principle 



gives us that the pressure of saturation is defined by the three 



equations : — 



r* v 



P(0b—»i)= pdv, 



p -- BT Kifi)-,-sj. 



v s is given in terms of P and T by a quadratic, and can 

 therefore be eliminated from the integral when evaluated ; 

 Vi is given by a cubic, but as T p v 1 can for practical purposes 

 be put 0, a very close approximation to v x can be obtained also 

 from a quadratic. The resulting relation between P and T, 

 which is the law of saturation, involves the constants R, k, I, 

 B, and "$. 



The actual evaluation of the integral would of course 

 proceed in three stages, corresponding to the supra-, circa-, 

 and infracritical equations. The law of the integral in the 

 first stage from v 3 to 7k/6, with critical values of the variables 

 as units, would be the same for all compounds ; and we have 



tseen that the integral in the other two stages will follow 

 approximately the same law in all cases. Hence if saturation 

 pressures and temperatures are expressed in terms of the 

 critical values, the law of their relation will be approximately 

 bhe same for all regular compounds. 

 " — ■ 



