and the Properties of Liquids. 583 



(Young and Thomas' law), and therefore 



H 2 



— =3-7 



The value of W e thus becomes (1 + 3'7K 4 ), and since 

 K 4 = 1'75 we obtain finally 





e** 



The above equation has already been put forward as an 

 empirical relation by Dieterici * who finds that 



fdp\ _2R 



\d?)r~^ Pc > 



which may be written 



(dp) = Pc 7 .± 

 \dT/ c T c ' 



and thus agrees well with the equation deduced theoretically. 



The value of -^ at the critical point may be obtained 



from the law of attraction between molecules. From equa- 

 tion (4) we have — 



dL _ (2 ^m x f (dAi 4;3 dA, 4/3 , AiW! dRl - A 2W 3 c1 P2 \ 

 dT " mi 3 I dT pl ^ r/T p2 + " 3 rfT 3 rfT j * 



Now A 1 = 3 ( fir , ^ c ) = </> 3 ( w 3, — ), 



A 2 = ^J *W» S ,A), 



and 



and therefore 

 and 



dA x _ dfa 1 _ ^03 p c dpi 



<iA 2 _ d(f> 3 1 __ c/</> 3 p c dp 2 

 dT dn z T c dn 2 p% 2 d T 

 From thermodynamics we have 



dpi _ dp 2 



dT~ dT~"°° 



at the critical point It will now be easily seen that at .the 



• : v ■■■■*■ ^ L 



critical point -j™ = c© . 



* .4w?. der Physik, vol. xii. 1903, p. 144. 



2Q2 



