340 Dr. R. D. Kleeman on Relations let ween the 



At the critical point, when a=l, /3=1, <£ = 1, let the 

 numerical limiting values of D and E be denoted by D c and 



E c , so that ■ — tx=E c . Eliminating v c , 0, and p c . we have 



D E P eVc 



yr- = = , an equation which contains the quantities a, /?, and 

 ^c E c 



only. This proves the law of corresponding states in 



general. 



Meslin has shown (C. R. 116, 135, 1893) that if the 



equation of state contains as many constants as there are 



variables (i. e. three — volume, temperature, pressure), it can 



be reduced to an equation involving a, cf), and ft only, or the 



law of corresponding states applies in that case to substances. 



Since we have established the law in a different way, we 



deduce that the equation of state must contain three 



constants. 



CD C 



The equation ■ — —^ = E c 



Ice 



on substituting for p c , T c , and C, from the equations 



. , (S V^i) 2 

 p = <f>p e , v = otv c , and c = K ~^- , 



may be written 



P 



=m« (£)"<* •.»>), 



where M 2 is the same for all substances at corresponding 

 states. This equation we have previously obtained for a 

 liquid in contact with its saturated vapour. We now see 

 that it applies in general. 

 The equation 



where H 2 has the same value for all substances at corre- 

 sponding states, was also previously shown to apply to a 

 liquid in contact with its saturated vapour*. Now if we 

 substitute for the quantities T 1? p 3 , from the equations 

 pi^ap, Ti=fcT, where T and p refer to any given state of 

 matter, we obtain the equation 



T^&rw-o 2 , 



* The equation was deduced with the help of thermodynamics from 

 the general law of attraction quoted at the beginning of the' paper. 



