( 634 ) 



larger volume, and ( — ) is always positive. Therefore f — J and as 

 will presently appear, — are always positive in such a region. As 



v becomes greater the value of q approaches to MRTl -—— , and 



for very large value of v the (/-lines may be considered as lines 

 parallel to the v-axis, for which the distribution over the region 

 from x = to x = 1 is symmetrical. The lines for which q is 

 negative, extend therefore from x = to x—\ and for x = £ the 

 value of q = 0. It will only appear later on that yet in their course 

 probably two points of inflection always occur for small volumes, 

 a fact to which my attention was first drawn by a remark of Dr. 

 Kohnstamm, who had concluded to the presence of such points of 

 inflection in the (/-lines from perfectly different phenomena. 



But as soon as the line ( — J = is present (the case that also 



\da;J v 



d*\b 



— — may be = will be discussed later on), a new particularity 



dx % 



makes its appearance in the course of the (/-lines. A (/-line, viz., 

 which cuts this locus, has a tangent // v-axis in its point of inter- 

 section, and reverses its course in so far that further it does not 

 proceed to higher value of x, but runs back to smaller value — 



so that ( — ) , which is always positive in the beginning, is hence- 

 \dxj q 



forth negative. From that point where they intersect the line 



( — ) = and where ( — ) may be considered negatively infinite, 

 \dxjv \d.vjq 



this quantity becomes smaller negative. Still for v = x> , the (/-line 



must again run parallel v-axis. So there must again be a point of 



inflection in the course of the (/-line. In ng. 2 this course of the 



(/-lines has been represented, both in the former case when they do 



not intersect the curve ( — ) , and when they do so. In the latter 



\dicj v 



case they have already proceeded to a higher value of x in their 



course than that they end in. They end asymptotical toaline#=#c, 



and at much smaller volume they also pass through a point x — x c . 



The point at which with smaller volume they have the same value 



of x as that with which they end, lies on a locus which has a 



fdp\ 



shape presenting great resemblance with the line 1 — 1 = 0. The value 



