70 Mr. J. Katn on Molecular Attraction and 



i.e., at the critical state the density of an actual gas is | of 

 the density of a perfect gas at the same temperature and 

 pressure li c . 



The experiment, however, gives us the volume of an actual 

 gas reduced to v — 1, 0° C. and 760 mm. If c is the constant 

 of attraction at v Q = l, we can express equation (6) in two 

 forms, (B) and (C), in a cubic and in a quadratic form, viz. 



2c R.T ™ 



v+Y> = v—(? < B > 



*J* + b m ±T 



x IT V V 



Treating equation (B) in the same manner as equation (A), 

 we have for the critical state, 



dv u ' v* (v c -#r • • • • w 



dv 2 ~ v ' tV " (tv-yS) 35 • • • • W 

 whence % _ g^ ( 12 ) 



in accordance with equations (7) and (11). 



The curve of equation (C) is a quadratic curve. For 

 every value of p there are two values of v satisfying the 

 equation, which coincide with the two extreme values of v 

 on the curve of equation (B). At the critical point these 

 two values coincide in the vertex of the curve for which 



^=0. We find 

 dv 



dp = 4c^ 2R.T c Q c + 6) R.T C ^ 



dv ' v c 6 v c 3 v c 2 ' 



(v. eq. 10) c = ±R . %{v c + 2b) = JR . T c . v e , . . (13) 



and the critical state can only be attained if this equation (13) 

 is realized. 



On substituting this value of c in the original equation, we 

 find at once 



p c = -r — — ? or 2p c . v c = R . T c , 2p c (f> c - 1, if <£ c is 



^ V c 



expressed in <£ = 1, at T, and II = 1. . . . (14) 



c 1 R.T, 

 P. = J* = ,3 = J.- ~^- 



3 E T 



e = 3p c =3p lc = 



9 



W« 



