( 736 ) 



part contracts, and disappears as isolated point. This takes place 

 before q lias descended to negative infinite, so that (/-lines of very 

 low degree have entirely resumed the simple course which such 



fdp\ 



lines have when only the curve (-—1 = exists. 



Also in this general case for the course of the (/-lines we can 

 form an opinion about the locus of the points of inflection of these 



curves, so of the points in which — — J = 0. We already mentioned 



fdp\ 



above that when the line — = exists at a certain distance from 



\dxjv 



it there must be points of inflection on the (/-lines at larger volume. 



fdp\ 

 If also the asymptote of ( — = should exist, also this series ot 



points of inflection of' the (/-lines lias evidently the same asymptote. 

 In fig. 6 this asymptote lies outside the figure, and so it is not 

 represented ■ — but the remaining part is represented, modified, however, 

 in its shape by the existence of the double point. The said series 

 of points of inflection is now sooner to be considered as consisting 

 of two series which meet in the double point, and which have, therefore, 



got into the immediate neighbourhood of the line (— ) =0 there. 



\d»J B 



So there comes a series from the left, which as it approaches the 



double point, draws nearer to ( — J = 0, and from the double point 



there goes a series to the right, which first remains within the space 



in which — — = is found, and which passes through the lowest 

 ax 



point of this curve, but then moves further to the side of the second 



component at larger volume than that of the curve ( — 1 = 0. The 



\daj v 



double point of the (/-loop-line is, therefore, also double point for the 



locus of the points of inflection of the (/-lines, and the continuation 



of the two branches which we mentioned above, must be found 



fdp\ 

 above the curve 1 — 1 = 0. Accordingly, we have there a right branch, 



which runs within — -=0, and passes through the highest point of 



this curve, and a left branch which from the double point runs to 

 the left of the loop-(/-line, and probably merges into the preceding 



