Finite Volume of Molecules and Equation of State. 199 



The position in respect to P, Q, or </>, is that for r very 

 great, outside an angle /3 on each side of a critical line, a 

 single asymptotic value exists. For the series we have 

 different asymptotic values in the different ranges. Thus the 

 series (17 a) has asymptotic values : — 



in A, ±co3k(Yl+y) — iGosk{Yt—y)', 



in C, icosk(Yt+y) + iG05k(Yt~y) ; 



and in B, — | cos Je( Yt +y) + \ cos k(Yt -y) . 

 These values hold in A from <9 = to 6= ~ — /3, 



IT 



3tt 



3tt 



in C from^- -f {3 to -~ /3, and in B from— + ft to 27r. 



The modifications needed for (17 b) and (18 a, 6) are of 

 an obvious character. It will be noted that the range of 

 validity of the asymptotic forms is wider than we were 

 justified in demanding at the outset as a condition of 

 solution. The simplicity of the changes needed to pass to 

 the 3-dimensional plane wave is also noteworthy. 



XV. On the Influence of the Finite Volume of Molecules on 

 the Equation of State. By Megh Nad Shaha, M.Sc.,and 

 Satyendea Nath Basit, M.Sc, Lecturers on Mathematical 

 Physics, Calcutta University *. 



IT is well known that the departure of the actual behaviour 

 of gases from the ideal state, defined by the equation 



p= is due to two causes : — (1) the finiteness of the 



v 



volume of the molecules, (2) the influence of the forces of 



cohesion, i. <?., the attractive forces amongst the molecules. 



van der Waals was the first to deduce an equation of state 



in which all these factors are taken into account : according 



to van der Waals, we have 



NK6> 



v — b 



u> 



where 6 = 8 x volume of the molecules, a defines the forces 

 of cohesion. 



In all subsequent modifications of this equation (Clausius, 

 Dieterici, or D. Berthelot), the changes which have been 



* Communicated by the Authors. 



