( 729 ) 



And as for x = also y — A must bo = 0, the curve =0 starts 



dx l 



(i 2 h 



from the same point from which all the (/-lines start. If should 



das 1 



not he equal to 0, wo have ground for putting this quantity positive 



(Cont. II, j). 21), and we arrive at the same result for the initial 



rf'ip 



point and the final point of the curve = 0. 



1 ' das 9 



d*y 



So the points of the curve — = 0, where tangents may he 



dx* 



drawn to it parallel to the ./--axis, 

 lie certainly at values of x smal- 

 ler than \, and accordingly the 

 two outer ones of the group of 

 the (/-lines with maximum and 

 minimum volume have their hori- 

 zontal tangents also in the left 

 side of the figure. The (/-line 

 with the highest value of q at 

 lower value of x than that with 

 the lowest value. This is repre- 

 sented in fig. 4. 



We notice at the same time 

 that the points in which a (/-line 



Fig- 4. touches the curve - = 0, are 



points of inflection for such a (/-line, just as this is the case with 



the /7-lines when a />-line touches the curve 



(Pip 



From 



follows 



and 



<Pty d 2 v 



+ 



dip 

 das 



d*Vp fdv\ <P» =0 



dxdv\dxj g </.r 7 



d 3 xp fdvy d*xp /dv\ </>/ 



dasdv das*q \dxdv*\dxjq das*dv\dasjq d,c* 



= 0. 



,/, 



d\p 



In the points mentioned I — (), because = 0, and at the 



1 dasjq dx' 



