398 Prof. R. Clausius on the Behaviour of Carbonic Acid 



bodies in other states of aggregation, is 



(p + r)(v~f) = -RT (3) 



Herein yfr denotes "la somme de volumes des atonies," and 

 r " la somme des actions internes ;" the latter quantity he also 

 names " la pression interne," In his further treatment of this 

 equation, by which he seeks to determine the quantities ty 

 and r, he makes inferences which seem to me not to be jus- 

 tified, and the result of which therefore, in my opinion, does 

 not correspond with the reality. 



Recknagel, in a memoir* which appeared in 1871, and 

 which he supplemented in 1872, formed instead of (1) an 

 equation agreeing externally with that set up by Rankine. It 

 has the form 



= RT ( 1 -?)' (4 > 



in which R is a constant, and B ; a function of the tempera- 

 ture, which latter Recknagel determines differently from Ran- 

 kine, since according to him it is directly proportional to the 

 absolute temperature, and inversely proportional to the corre- 

 sponding pressure of the saturated vapour of the given sub- 

 stance. 



J. D. van der Waals, in a very interesting workf published 

 since Andrews's above-cited experiments, has substituted for 

 (1) an equation in which, as in Hirn's, the two circumstances, 

 the space filled by the molecules and the reciprocal attraction 

 of the molecules, are taken into account : it has the form 



(p+ £)(»-&) =BT, (5) 



pv 



or, resolved with respect to p 



P=*^r b -I>> ( 5a ) 



where R, a, and b are constants. The values of these constants 

 for carbonic acid Yan der Waals determined J as follows, 

 taking as unit of pressure one atmosphere, and as unit of 

 volume that which the carbonic acid occupies under the pres- 

 sure of one atmosphere at the freezing-point ; the quantity 

 T standing as denominator in the value of the first constant 

 represents the absolute temperature corresponding to the freez- 

 ing-point, consequently approximately the number 273 : — 



* Pogg. Ann. ErgM. v. p. 563, & cxlv. p. 469. 



t Over de Continuiteit van den Gas- en Vloeistoftoestand (Leiden, 1873), 

 p. 56. % Op. cit. p. 76. 



