Mr Bevan, On the Joule-Thomson Effect. 129 



The term I — -^ — - dO is the term depending on the cooling 



effect and we notice as has been frequently pointed out that even 

 if the cooling effect vanishes, the substance does not necessarily 

 obey Boyle's law. 



If now we know the form of the cooling effect and can 

 evaluate the integral on "the right-hand side of equation (2), we 

 should be well advanced in determining by this method the 

 characteristic equation. Thomson and Joule first assumed that 



the cooling effect could be represented by the expression ^ where 



a is a constant. With this assumption we have 



whence z = ^— . 



3a 



and therefore 



aC p = 2 F(3ap-6 s ). 



Now if p be small we may assume that G p tends to a limiting 

 constant value G , we thus have 



aC o =6 2 F(-0% 



which determines the form of the function F. and we have 



aC p = aC 6 2 {e z -'3apf, 



and therefore 



v ~ f dd , . . 



or 



,-*(p) + ^(l-£!) 



We know however that the Thomson- Joule formula for the 

 cooling effect is inapplicable owing to the existence of the inver- 

 sion temperature — the temperature at which the sign of the 

 effect considered changes. It is therefore not worth while to 

 investigate the equation derived on this assumption any further. 



* For this special case see Planck's Thermodynamics. An equation for this case 

 is also deduced in Thomson and Joule's paper " On the Thermal Effects of Fluids in 

 Motion," but in this equation G p is regarded as constant all through. Joule's 

 Scientific Papers, Vol. ii., p. 359. 



VOL. XII. PT. II. 9 



