<~)26 Mr. J. P. Dalton on the Variation of Specific 



yjv-isothermals between the points o£ maximum and minimum 

 pressure have been omitted as of no practical importance.) 



Since (X does not vary with the volume { ^-" = T^—- = )> 



the same curves must also determine the variation of C p and 

 o£ C p /C v with the volume. From the diagram it appears 

 that C p is independent o£ the volume at large volumes and at 

 high temperatures ; as the temperature falls, G p increases ; at 

 temperatures above the critical it reaches a maximum at a 

 volume equal to the critical volume ; and at temperatures 

 below the critical it becomes infinite at two volumes, one o£ 

 which is greater, and the other less than the critical volume. 

 These points where Cp = ao correspond to the points o£ maxi- 

 mum and minimum pressures in the jpy-isothermals, i. e. where 



(~) = 0*. They may be determined from the relation t 



(3o>-1) 2 = 4g) 3 0. 



For the isothermals shown in the figure C p =x> when 



= 0-5 ftj^O-5 ft) 2 = 3-732 



= 0-75 &> 1 = 0-605 a) 2 = 2-137 



0=1-0 O) 1 = l'0 © 2 = 1'0 



van der Waals's equation is notoriously incorrect, but the 

 general features of fig. 1 may still be the same as for real 

 substances. The variations of C„ are known to be small and 

 to take place only between narrow limits ; that quantity, 

 therefore, cannot disturb the general features of the diagram. 



B. Experimental Evidence. 



Owing to the scantiness of data available only a partial 

 and incomplete comparison of the foregoing results with 

 direct experimental results is possible. 



(1) Ether. 



The author has calculated the variations of C^ — Cr and 

 'C p /C v in the case of ether, and, as w T ili be seen 5 the results 

 afford striking confirmation of the above deductions. 



Data were obtained from papers bv Ramsay and Young, 

 " On the Thermal Properties of Ethyl Oxide" J, and : 'On 

 the Continuous Transition from the Liquid to the Gaseous 

 State of Matter at all Temperatures " §, and by Per man and 

 Ramsay, " Ein Versuch, die adiabatischen Verhaltnisse des 

 Athyloxyds zu bestimmen " ||. 



* Cf. Cord . i. p. 133. t Cf. H. Hilton, Phil. Majr. [6] i. p. 584 (1901). 



J Ramsay & Young, Phil, trans, clxxviii. A, pp. 57-93 (1887). 



§ Ramsay & Young, Phil. Mag. [5] xxiii. pp. 435-458 (1887). 



j'l Perinan, Ramsay, & Rose-lnnes, Zeits. f. phys. Chemie, xxiii. 

 pp. 385 et seq. 



