( 750 ) 



For values of c between and 1 it is easy to solve ?/„ out of 

 the equation 



7v 



r dw 



J sn^ V 







bj means of the tables of Lkokndhk. If n' ^ is an approximate value 

 of the critical argument, the calculation of Nkwton furnishes 



as following approximation. In this way the critical argument is 

 calculated in the following table for some values of Ir = c 



and moreover are indicated in it the coordinates c^, C^ of the point 

 P, in which the curve OA belonging to each value of I: touches 

 the envelope of that system of curves. 

 \^y the equations 



bo = ^<^ en ^'0 ^ {''0) 1 ^0= ^'^ '^'0 '''^ "0 

 we now lind in connection with the condition 



Q («„) = 

 that èu and ^^ are given as functions of c only. We can deduce 

 out of it 



dS, 1 



T — ~ :77T ^^^' "0 ^' ("0) [^^' "0 ^^" "u + «0 ^" «"' >'oh 

 dc 2yc 



dc 



I 



2[/< 



dn Ug B (?ij [en ti^ dn ?<„ -\- u^ c sn^ ti^\, 



d'èo k ' 



From this appears that for increasing k or i'^c the coordinate So 

 decreases regularly and the coordinate So increases regularly. In 

 connection with the numbers inserted in the table it follows that the 



