( 523 ) 



Between the radii of curvature Ri,, II' i aiui Rs exists of course 

 also the rehition 



2 _ 3 1 



7^ I Ml) R.s 



in which R^ represents the radius of curvature of the binodal line to 

 which the plaitpoint belongs and R'l, the radius of curvature of the 

 accidental branch of die binodal line passing through (he plaitpoint. 

 We now substitute in (28)' and (29)': 



The equation (33) represents at approximation the curve c 0^ c' 

 (tig. 13) ; its tangent in point is determined by 



2 c\ i, + c\ !/, = . (34) 



The line determined by (34) is the diameter conjugated to the 

 X-axis of the indicatrix in 0.^ ; so we find that the tangent in O^ 

 and the conjugated line in 0^ O^ are conjugated diameters of the 

 indicatrix in (A,. This property however has been known already 

 for a long time ^). 



We now take that tangent in 0., as new I^-axis, whilst we 

 keep the line 0^ 0^ as the A-axis. 



Equation (33) now changes into: 



(;.A' -\- iivy = vX' 



where /, ft and v have definite values. From this ensues as a first 

 approximation of the binodal line in the vicinity of point 0.^ : 



or 



Y' = KX' (35) 



If we calculate the radius of curvature in point 0^ we then find 



D. J. KORTEWEG. 1. c. p. 299. 



