Intelligence and Miscellaneous Articles. 307 



The eminent physicist has verified, with the aid of Andrews's 

 experiments, that this relation represents exactly the transforma- 

 tions of gaseous or liquid carbonic acid ; and he thinks that the 

 same formula, with suitable values of the constants E, K, a, (3, 

 must be correct for all gases. 



Among the consequences resulting from this formula must be 

 noticed those concerning the critical point. Indeed it follows, from 

 the interpretation given by M. Clausius of the results of his for- 

 mula, that when the critical point is reached the function p satis- 

 fies the two conditions ^=0, -4r = 0. By combining these con- 

 dv dv 



ditions with the relation (1) we get three equations, from which we 

 deduce the following values of v. T, p corresponding to the critical 

 point : — 



v e =3*+2P; T c =(§) f (§)V+/3)-*; A=6-f(KE)Ha+/3)-K2) 



2. I proposed to myself to verify M. Clausius's relation for other 

 gases than carbonic acid, making use of the extensive experiments 

 of M. Amagat, in which the temperature varied from 15° to 100°, 

 and the pressure from 25 to 320 metres of mercury. 



The numerical determination of the coefficients being not without 

 difficulties, it is not needless to indicate the course which I have 

 uniformly pursued to accomplish it. Let p andj./ be the pressures 

 corresponding to one and the same value v at two different tempe- 

 ratures T, T'; we have the two relations 



ET K , ET' K 



1 J== 7—7. ~ ^7m2> P 



Putting 



T(v + (3f 1 v-a T'(v+(3f 

 T' 2 -T 2 / T' 2 -T 2 



p'T'-pT' * V TT'(yT-pT') 



we deduce from the above two equations, by successively eliminating 

 K and R, 



V—OL V + P 



n ■ y K » (3) 



Therefore knowing two corresponding values of v and x suffices 

 for obtaining E and a, and two corresponding values of v and y for 

 obtaining K and /3 ; but if we take a superabundaut number of 

 simultaneous values (v, as) and (v, y), we can verify the exactness 

 of the relations (3) and make all the equations contribute to the 

 calculation of the coefficients. M. Amagat's experiments do not 

 give directly the pressures which at different temperatures corre- 

 spond to the same volume; I obtained them by interpolation. The 

 mode of calculation adopted employs for the values of the coeffi- 

 cients the units employed by M. Amagat. The pressures are ex- 

 pressed in metres of mercury, or, dividing by 0-760, in atmospheres. 

 The unit of volume is not specified ; but without knowing this we 

 can determine the values possessed by the constants by taking for 

 unit the volume of the gas under the atmospheric pressure and at 

 zero. In fact, in consequence of the change of unit, v must be re- 



