170 Mr. W. Sutherland on the 



power to give the pressures of saturated vapour of C0 2 as 

 determined bv Thilorier (Ann. de Chirn. et de Phys. 2 ser. lx. 

 1835), Mitchell (Journ. Franklin Inst. xxvi. 1838), Faraday 

 (Phil. Trans. 1845), Regnault (Mem. de VAcad. des Sciences, 

 xxvi.), and Andrews (Proc. Roy. Soc. xxiii. 1874-75). 



To Maxwell (Journ. Chein. Soc. 1875) we owe the method 

 of obtaining the pressure of saturation of a fluid at any tem- 

 perature from its characteristic equation. Accepting James 

 Thomson's suggestion that the isothermal for a fluid below its 

 critical temperature, when traced by means of the charac- 

 teristic equation for the fluid, ought to be a continuous curve 

 lying partly above and partly below the isopiestic of satu- 

 ration, he showed from thermodynamical considerations that 

 the area enclosed by the part above the isopiestic should be 

 equal to that enclosed by the part below. Expressed in 

 symbols, this is 



-P(v 3 -v 1 )=\ 'pdv, 



where P is the pressure of saturation at temperature T, v s is 

 the volume of the saturated vapour at T°, and v l the volume 

 of the liquid at T° and pressure P; so that v z and v Y are the 

 greatest and least of the three real roots for v of the charac- 

 teristic equation, when the temperature has the value T and 

 the pressure the value P. Applying this condition to the 

 equation for C0 2 , we obtain the following equation for the 

 pressure of saturation at T° as a function of T: — 



where v 3 and v x are the greatest and least real roots of the 

 equation 



-4= rT — l 



Pv=aT^+£±_4, 



v 



The only part of the integral which is not integratable is that 

 involving the exponential factor, which, however, can be 

 expressed as the difference of two exponential integrals which 

 are now regarded as primary, since the tabulation of values 

 for them by Soldner, Bretschneider, and more elaborately by 

 J. W. L. Glaisher (Phil. Trans. 1870). However, as the 

 values of v 3 and v x are indeterminable functions of P and T, 

 we are unable to use the tables in the present application of 

 the integral, and must content ourselves with determining P 

 graphically — that is, by tracing the isothermal for certain 



