( 629 ) 



fdp\ 

 the curve — = O on the left of this point, funis its concave side 

 \dxj v 



to the .t'-axis, but when it passes for the second time through the 

 said curve on the right of' the point, its convex side. Hence an isobar 

 where these two intersections have coincided, has its point of inflec- 

 tion in the point itself'. If we wish to divide all the ^-diagram into 



( d * v \ 



regions where I is either positive or negative, it must be 



borne in mind that also the two branches of line { — — ) = thein- 



\dvy x 



selves form the boundaries for these regions, because on that line 



dv 



d*a 



In all this - — is supposed to be positive. For on the contrary 



dx 



fdp\ 

 the course of the line I — 1 =0, to which we could now assign 



an existence on the right of the asymptote which is given, by 



db da 

 MRT — =-r-, would be directed to the left of this asymptote 

 dx dx 



d*a 

 when — should be negative, so if 2a 12 could be > a, -f a 2 . For as 



da • • 



f v Y dx i i c " i da 

 = , the value of — decreases only, when — - increases. 



"-*' MRT* ' dX 



. dx 



_ da 



If we put a = A + 2 Bx + Cx\ and so — = 2(i?-f Cx), it appears 



ax 



s> • da 



that with G negative a: must decrease in order to make — increase. 



dx 



For the points of this linep would then possess a minimum forgiven 



d*p 

 value of v, and so — - would be positi^'e. From this follows then that 

 dx\ 



the two points of intersection of this line with the curve ( — J z= 



have interchanged roles. The point of intersection with the smallest 



volume represents then a real minimum of p, and will have the 



same significance for the course of the p-lines as the second point 



d'a 

 of intersection has, when — — - is positive. And the point of intersection 



dx 



