108 Mr. E. F. J. Love on the 



from the equation 



(j>+£)(t>-ft)r=RTj 



dividing throughout by v—b, and differentiating with respect 

 to T, on the assumption p = const., we obtain 



v 3 \-df) p ~ v-b {v-b) 2 ' IbtV 



R 



e. e. 



\'dTJ~ 



v — b 





RT 



(v-b)" 



2a 



^h-^-^kh 



Multiplying out on the right-hand side and neglecting 

 powers and products of a and b (since both are very small) 

 we obtain 



whence 



T (%\- V ~ h *m> • • • • (q-pO 



m /"dv \ 2a , 



i. e 



-J.K p . l ^ = 4^-b. 



dT _ 2a 

 dp~RT 



Following Joule and Kelvin, let us write 



_dT = e_ 

 dp~U } 



whence we obtain 



j.kArt > 



— m H) 



where a and /3 are constants. This is exactly the formula 

 proposed by Rose-Innes, from an examination of the results 

 of the experiments of Joule and Lord Kelvin ; it is not 

 without interest to find that this formula is directly deducible 

 from van der AVaals's equation. 



