Mr Bevan, On the Joule- Thomson Effect. 131 



since z is a function of 6 and therefore alone occurs in the 

 quantity under the integral sign. 



We may write equation (3) in the form 



p = + (j-hV)), 



where fa (0) is the term depending on the Joule-Thomson effect 

 and is small in the range to which our equations are applicable, 

 that is over a range where the rate of change of the coefficient of 

 expansion at constant pressure with the temperature is small 

 compared with the coefficient of expansion itself. 



If now we assume that Boyle's Law is obeyed as a limit when 

 p is very small and is not very small, this equation must reduce 



to p= — , when fa (0) is negligible. We have therefore for an 



infinite range of v and 



and therefore the form of yjr is determined and our equation 

 reduces to 



p=r^~ ■•••<*>• 



e -f(«) 



or if we neglect squares of fa (0), 



Re /_ e . /a \ 



pv = R6(l+P&p) (5). 



So far we have derived the equation for a gas from the cooling 

 effect with the aid of some justifiable approximations. We shall 

 now make use of results of experiments made to directly determine 

 relations between p, v, and 0. Ramsay and Young* found for 

 certain liquids and gases the relation 



p = b0 — a 

 for constant volume; a and b being constants. Amagatf has 



discovered an equivalent result £) = constant. These two rela- 



ouJv 

 tions we may express in the form 



V = Vr(v)-Mv) (6). 



* Phil. Mag., 23, 1887. 



t Bapports, Congres de Physique (Paris, 1900). 



