and the Isothermals of Vapours. 445 



on the Equation of State, in which Dieterici's equation is 

 studied. In this paper MacDougall develops the same 

 equation as (1) above for vapour pressures. He reaches it 



by assuming that — I = — , where V\ and v* have the 



v l l 2 ? -3 



same meanings as in the present paper and r 3 is the volume 

 corresponding to the same pressure (the vapour pressure) on 

 the unstable (James Thomson) part of the isothermal. Thus 

 v 3 . 1 

 ■jz is equal to b, and the equation b = -? r of course follows 



immediately. The grounds for the assumption are given : — 

 (!) v } =v 2 = v i =2b at the critical temperature, and v varies 

 slowly as the temperature falls, so that it is plausible to 

 assume v = 2b for all temperatures. (2) The Cailletet- 

 Mathias relation becomes d^ = d (l — «I); a small and linear 

 temperature coefficient suggests a real significance for the 

 quantity c/ 3 . (3) The saturation pressure is the geometric 

 mean of the maximum and minimum pressures on the 

 isothermal, if i< = 26. 



MacDougall also notes and illustrates in tables the approxi- 

 mate constancy of the product Ah (see § 3 below), but draws 

 no further conclusion from this. He does not appear to have 

 noticed the remarkable relation (§ 1 above) that liquid and 

 saturated vapour are complementary as regards free and 

 occupied volumes per c.c. 



The thermodynamic relations of Dieterici's equation and 

 the calculation of the latent heat of vaporization are discussed 

 in detail, and the whole paper is of great interest. 



§ 3. The matter may usefully be examined from a slightly 

 different point of view. The work done in transferring 

 unit mass of a substance isothermally from liquid to 

 vapour is 



J*l J«, V-b *V x -b °<V 



the symbols having the same meanings as before. This work 

 may be equated to A T — A 2 , where A] is the work required 

 to overcome the cohesive forces of the liquid, per unit mass, 

 and A 2 is the similar quantity for the saturated vapour. 

 These quantities, A x and A 2 , as mentioned in § 1, are pro- 

 portional, at any assigned temperature, to the densities 

 d 1 and d 2 at that temperature. 



Hence we have , 



d i d\ {o £j 



2RTlog7 =A 1 ( 1- /) or A 1 = 2RT ( / 1 = , . 



a 2 \ "1/ a 1 — a 2 



