UNIVERSITY OF COLORADO STUDIES 

 .2* 



252 



But w 1 = w.z~$ , and w=w I .z$ ; hence 



7f=— 2^^ — z~3+. . . . 

 3 



This series represents the function w in the neighborhood of 2=00 

 and clearly exhibits the permutability of its three determinations when 

 2 describes a path around this point. 



Fig. 6 



5. Example IV. Riemann Surface for the Function 



3 \z-a 



This example is explained in Durege's treatise, loc. cit, p. 50. 

 After one, two, three turns of 2 around a (not including b) w l ,w a , w 3 

 are changed into 



1. w 2 , w 3 , w x ; 



2. w 3 , w x , w 3 ; 



3. w t , w 2 , w 3 . 



