Law of Molecular Force, 133 



a quadrate equation for the square root of the critical tempe- 

 rature, of which the physically permissible root is 



-a(l +/)*/ +\/[a(l +/VP+ W • t 

 VT = -• 



Substituting the numerical values of all the constants, we 

 find 



T = 3l5°-8, and *=42°-8 C. 



Thus the critical temperature given by the equation is 42 0, 8, 

 instead of 31° as found by Andrews in his experiments with 

 capillary tubes. The equation gives the critical volume of a 

 kilogramme of C0 2 as '002536 cubic metres, or '005026 of 

 that volume occupied by the gas at 0° C. and 760 millim., 

 and the critical pressure as 849700 kilogrammes weight per 

 square metre, or 82*23 atmospheres, or 62'5 metres of mer- 

 cury. Andrews found the critical pressure in his tubes to be 

 something about 75 or 77 atmospheres. 



As 1 deemed it indispensable that the characteristic equa- 

 tion should give with great accuracy the numerics of the 

 critical state before any sound conclusions could be drawn from 

 its form as to the internal virial, these discrepancies caused 

 me to abandon the above equation for many months, during 

 which I tried, by variations in the values of the constants, and 

 by variations in the whole form, to get a reasonably simple 

 equation that would represent Amagat's experimental results, 

 and at the same time give the critical temperature as 31° C. ; 

 but with many forms, involving a larger number of constants, 

 I always found that if Amagat's numbers for 100° and 70° were 

 represented accurately in their whole range, a critical tem- 

 perature markedly above 31° was obtained. At length, in the 

 hope of getting a further clue to the proper form of equation, 

 I looked up Regnault's data for the saturation-pressures of 

 C0 2 at different temperatures*, and found that he declares 

 explicitly that at 42° C. he had liquid C0 2 . His words are: — 

 " Enfin par la quantite d'acide carbonique que Ton fait sortir 

 de l'appareil a la fin des experiences on a reconnu que meme 

 a la temperature de 42° il devait res-ter encore beancoup 

 d'acide carbonique liquide." The pressure of saturation 

 which he gives for 42°'5 C. is 61967 millim-- of mercury ; a 

 number in good agreement with the critical pressure of 62*5 

 metres of mercury determined above by the equation as cor- 

 responding to a critical temperature of 42°*8 0. 



* "Forces elastiques des vapeurs/' Memoires de VAcademie, xxvi 

 p. 618. 



