( 827 ) 



the value assumed already before as an approximate equation of 

 this line: 



/db\' d'a 



d*tb I 1 \dx J j dx 2 



</.r 2 {a^-x) (v-b) 2 \ v 



will prove adapted to give an insight into the different possible 



<Pib d*ib 



positions of this line with respect to = and = (). 



dv 2 dadv 



m d 2 \b 



The curve - = 0. 

 dx 2 



The differential equation of this curve: 



d*ty d\b d\p 



-4- da H dv -\ — dT — 



da 9 dx*dv da*dT 



may also be written in the following forms: 



d 3 ty ^d*q d*Tn dT 



dx -\ dv — = 



dx 3 dx 2 dv dx 2 v T T 



or 



or 



or 



rf> </hp d 2 (e—ip)dT 



dx -| dv = 



da' dx'*dv dx* v T T 



d 3 ty dhp d 2 s dT 



dx -1 dv = 



dx 3 dx*dv da* v T T 



d 3 xb d*ti> 1 d'adT 



— - dx -| — dv -\ = 0. 



dx 3 dx 2 dv v da* T 



d*ip 

 The curve = can only be found for positive value of T 



r/,/' 3 



d*a 



when — is positive. So we derive from the latter form that 



dx 2 



(dx \ d*ip 



I — I is positive for the points for which is negative, and the 



\d I J „ dx 3 



other way about. 



dr\ 



the same way, that I 



is negative and vice versa. The transition of the points for 

 dvda* 



In the same way, that I — I is positive for the points for which 



\dTJr 



