Isothermals of Tsopentane. 79 



7 n Bo b 3 , . , „ i 



6= 1 — £ -\ — ~ -\- higher powers or - » 



V V 2 IT or v 



A A 1 



a= —r-\ — $■-{• higher powers of - ; 

 v v 6 ° v 



Then 



T = 



A 2 + A,u- 1 + 



B- + B.tf-» + .. 



= tt H » ■» u -1 + higher powers of -. 



If b and a in any gas-formula can be expanded in powers 

 of u -1 as assumed, and if A 3 B 2 — A 2 B 3 is different from zero, 

 which will in general happen, the decrease of r from the 

 maximum value will be as v~ l ; so that the proposed formula 

 is inadmissible. 



Let us now return to the quantities a and b. The values 



of — g were plotted against o~^ by Prof. Young, and the 



resulting diagram is given in his paper (loc. cit. p. 653). The 

 curve determined by the points plotted would seem to be 

 of a somewhat complicated character, and I do not think it 

 possible to obtain any simple formula that will reproduce it 

 entirely. On the other hand, there seems to be considerable 

 evidence of discontinuity in the neighbourhood of vol. 3*4 ; 

 and even if there is not discontinuity in the true mathematical 

 sense of the word, there appears to be such a rapid alteration 

 of behaviour as to amount in practice to the same thing. The 

 easiest plan is to treat the curve as consisting of two parts, 

 the formula passing abruptly from one expression to another 

 somewhere in the neighbourhood of vol. 34. Whether this 

 accurately represents what takes place in nature is uncertain, 

 but there is no doubt that it immensely simplifies the problem. 

 We may therefore confine our attention to volumes above 

 3'4 ; and of the formula? already proposed I found the best 

 to be that suggested by Mr. W. Sutherland, who has given a 

 gas-formula equivalent to putting 



I 

 a ~v(v + ky 



where / and k are two constants characteristic of the gas 

 (Phil. Mag. xxxv. p. 215). I have taken the following values 

 of the constants 



^ = 5,420,800, £=3-636. 



