A FEW EXAMPLES IN THE THEORY OF FUNCTIONS 253 



Similarly, turning around b, w x , w 2 , w 3 are changed into 



1. w 3 , w 1} w 2 ; 



2. w 2 , w 3 , w z ; 



3. w 1} w a , w 3 . 



According to this the Riemann surface for this function may be 

 represented by Fig. 6. 



If z describes a closed contour around both branch-points once, 

 then each determination arrives at the starting-point with the same 

 value. Consequently, z=oo is not a branch-point. In the figure 

 the paths around the branch-points on which the three determinations 

 are permuted are shown in solid lines. The complete path around both 

 branch-points is represented by a dash-line. 



