172 Mr. W. Sutherland on the 



at 0° greater by about 2 metres out of 30 than the mean 

 of Regnault's determinations at nearly the same tem- 

 perature. 



If we desire to carry the application of our equation to much 

 lower temperatures, we are met by the difficulty that solid 

 C0 2 melts according to Faraday at a temperature of —57° 

 under a pressure of 5*33 atmospheres; and according to Reg- 

 nault, at a temperature of — 78°*2 solid C0 2 evaporates freely 

 into the air under a pressure of 760 millim. Now at these 

 temperatures and pressures a kilogramme of C0 2 can exist 

 entirely in the solid, entirely in the liquid, and entirely in the 

 gaseous state; so that its true and complete characteristic 

 equation has three real roots for v corresponding to these 

 three states, and it must also have two real roots corresponding 

 to physically impossible homogeneous passage from the 

 gaseous to the liquid and from the liquid to the solid states. 

 Thus at these temperatures and pressures our equation ought 

 to give five real roots for v, which it does not do, nor does any 

 equation yet proposed. But it is enough for the present if 

 we bridge the discontinuity between the gaseous and liquid 

 states ; much experimental work remains to be done before we 

 can do so for the solid and liquid states by means of a single 

 continuous equation. However, to get an idea as to how far 

 the equation, when applied by means of Maxwell's principle, 

 assumed still to hold, would succeed in giving the pressure of 

 saturation at these temperatures, I made the necessary calcu- 

 lations, and found for the pressure of saturation at —57° 

 5 metres of mercury, instead of 5 "33 atmospheres as Faraday 

 determined it, and at —78° 1*5 metres or 2 atmospheres, 

 instead of 1 atmosphere as Regnault found it or 1*14 atmo- 

 sphere as Faraday. 



When we pass on to test the equation by its power to give 

 the volume of liquid C0 2 at different temperatures and pres- 

 sures, we are met by remarkable discord amongst the experi- 

 mental results. The subjoined table contains the volume in 

 litres of a kilogramme of liquid C0 2 under pressures of 100, 

 200, and 300 atmospheres, as determined in capillary tubes 

 by Cailletet and Hautefeuille (Comptes Rendus, xcii.) at the 

 temperatures 0° and —23° C., as determined in capillary 

 tubes by Amagat for 18° C. (Ann. de Chim. et de Phys. 5 ser. 

 xxii.), and as furnished by the equation for the same tem- 

 peratures. 



