( 514 ) 



or at first approximation for the equation of that line in the vicinity 

 of the piaitpoint : 



4c,t^,.t; + (24c,.,-4(i,')r = (11) 



The equation of the binodal line in the vicinity of point is^): 



d,.v + 2e,f=.0 (12) 



We now write (10), (11) and (12^ in such a way that the coefficient 

 of .1' is the same for these three ; so we find : 



for the curve of contact : 2c^dyV -j- c/,^?/' = 0. . . . . (13) 



,, „ spinodal line: 2c,(IyV -\- 2 {Qc,e,-d,') y' = . (14) 



„ binodal line: 2c,(IyV -\- 4:C,e^l/ ^ .... (15) 



We shall now restrict ourselves, as only this is liable to realisation, 

 to a piaitpoint of the first kind ^), so that 



4c/3-^,'>0 (16) 



thus also c/^ > and 6c,e^ — (/,' > 0. 



From this ensues immediately that in the vicinity of the piaitpoint 

 the curve of contact, the spinodal line, and the binodal line are curved 

 in the same direction. 



Out of (IQ) we can deduce: 



2 (6c,. — fli,^) > 4v, > r/,* (17) 



If we call the radii of curvature of the spinodal line, the binodal 

 line, and the curve of contact Rg, Ri, and Rr, it follows from (13), 

 (14) and (15): 



R,- 'A ,i2, = ^i^ , i^,.^_^-i^|. (18) 



' ~ (12c,é'3— 2^3^) sin e ic.e, sin 6 d^' sin 6/ \ 



where <9 represents the angle between the line OP and the tangent 

 in the piaitpoint to the binodal line. 



In connection with (17) follows from this that the spinodal line 

 has the smallest radius of curvature and the curve of contact the 

 largest. 



From (18) we can furthermore deduce: 



2 8 1 



— = (I8«) 



R,. Rb Rs 



Out of this relation it is evident that R,. is also independent of 



the direction of the line OP; for Rb and Rs are quantities, which 



depend exclusively on the shape of the surface at point 0. 



1) D. J. KORTEWEG. I.e. 61 (1891). 



