( 510 ) 



R x = R 1 (l- l v) -f R t .v (3a) 



if R x — R/M l , R, = RjM^ , R representing the molecular gas-constant, 

 M 1 and J/ 2 representing the molecular weights; we put for this first 

 investigation o la = ka u a„, so that 



a x = \{/ ail . (l-.v) + |/a„ . ,f (36) 



and when we put for the molecular volumes 2b \%m = &iuf + &22i/i 

 the relation for 6* given by van der Waals Contin. 11 p. 27, reduces to: 



6 X = 6 U (1— «) + b, % x (3cj 



We get then (van dek Waals Contin. II p- 28): 



t| , — _ R v T h {v—b x ) — - + T \R X (1 — #) to ( 1 — .-•) -f Z2, « In as] . (4) 



§ 4. Taking equations (3) into consideration, and putting 



— — = u, a = — — (o) 



l' — - 



we get by the conditions (1) : 



l-\-z[ 2 ) 1— ci 2 J c—b da 



R 9 . — u H + 7t\ u = — — .... (tia) 



2 J ^ 1-J-«| ^ * 2 j 1 — z\ TV das 



l+zl 2 )- l—zi 2 1" 1 d\i 



R . _L u H + #. ' ri = — , .... (66) 



2 | 1-fc ' -l [ \ — z\ Tv dx* 



l+~l 2 ) J i 1 ] 1— z\ 2 Pi 1 J 



7»' . — « -I w 4- 22. u u -| =0 (6c) 



* 2 j l+*( j l + c( l 2 j 1— z\ \ l—z\ V ; 



These equations are sufficient to calculate the data for a barotropic 

 plaitpoint Xb p u l 'b,,i, l\ P i for a definite pair of substances. Eliminating 

 T from (6<i) and (6b), we get, taking (6c) into consideration and 

 putting: 



I ( V _6) L + y^J I" - YZTA ( ^ z) + l ' \ u + rr^J = °' (8) 



while elimination of v from this equation and (5), putting : 



(ft„+6»)/(ft..-&ii) = » (7&) 



yields : 



èU + ^JU-™|(^)-h j" + J^iJ |i(»+*)«+l}.= 0. (9) 



From this equation with (6e) : Zf,pi may be found for given RjR lt 

 fi and i', after which x^pi , r^/ and T/, /; / , as well as ^^/ follow easily. 



§ 5. That a barotropic plaitpoint exists on the liquid-gas-plait 

 Avith the assumed suppositions (2), (36), (3c) and with suitable 



