586 Mr. H. Hilton on van der Waals* Equation. 



The curves (/3) and (7) only meet in 2 finite points^ 



namely (1; 1) t\- -27). 



Their radii or curvature at the point whose abscissa is x 

 are respectively 



]x* + 36(l-x) 2 \i {^° + 4(6^ 2 -9^ + 2) 2 } 1 



6.z 7 (3#-4) ' an 4# 9 (3tf-5)(3^-l) ' 



If ACE is a straight line parallel to y = 0, such that for a 

 certain value of 6 the areas ABC, EDC are equal (see 

 rig. 3) ; then the ordinate of A (^or E) represents the pressure 



Fig. 3. 



at which the substance boils for that particular value of P. 

 The curve through all such points as A and E we will call 

 the "border"" curve. (Cf. Memoirs of Phys. Soc. London, 

 vol. i. part 3, p. 453.) Let a?„ qp 2 , x z be the abscissae of A, E, 

 and C respectively, and y their ordinate. Then 



[See Nernst's 'Theoretical Chemistry/] 



Now x u x 2 , x 3 are the roots of 3yx d — (j/ + 8#).r 2 -f 9jj — 3 = 0, 



X 1 ^ 2 .'i' 3 = 



and therefore x,x 2 4- x Xo -f a? 5 a?i = - 



V 



.*. eliminating x$, yx 2 x 2 + x x + #2 ~~ 3^!^ = 0, and therefore 

 _Sx l — 1-f \Z(3^ — l) 2 — 4^i 3 



# 2 , 



2yx x 2 



the positive sign being taken, for y is positive in the region 

 considered, and x 2 >x 3 . 



Substituting this value for x 2 and ^ Xl } " 1 



x L 



