\A 



( 4?. ) 



l. 



= ?.. 



the simple relation 



> 3-4-2 \/x ' 



(<0 



follows from (a) and (h) after some reduction, in which the sign ^> 



refers to the existence of a minimum in the neighbourhood of C a . 



The condition (c) found by us is quite identical with that, which 



1 fdT x \ 



we derived before from the formula tor — I found by us 



J t \dx J 



(Aug. 17, 1905, p. 150 and .Ian. 25, 1906, p. 580). This condition was: 



^(3^.t— iy 



l fdT x \ 



With this difference, however, that we then considered ~\ 



J , \dx J 



at Ci, whereas we have now examined the branch of the plaitpoinl 



line which starts from C t , so that we have to calculate — [ - — |, 



and to derive the condition of the minimum from this. But it is 



immediately seen that it is obtained by substituting - for 6 and - 



for Jt in the above condition. 

 So we find : 



4 

 1 .Tl/jr 



6^-' 



fè- 1 )" 



°> Ï < c ) 



And it appears immediately that (c) is identical with (c'), when 



6* , 6 



we substitute — for x ! and — tor ^ in (c). 



This furnishes a good test, both of the accuracy of the above 

 derived formula (c), and of the condition (c') } derived by us before. 



Let us now examine what values of )■ and x correspond according 

 to the condition (c), so that the minimum still appears exactly in C 2 . 

 The corresponding values of z required for the calculation of T , 

 may be found from (a), giving: 



_ 1 l/x— 3 



~3 ï/wï* 



