312 



ELECTROSTATICS. 



[PT. II. CH. VII. 



and multiplying together, 



~~ (x a) 2 + 2/ 2 ' 



We will now make use of the results of the preceding example, 

 denoting, however, by our present u and v what were there denoted 

 by x and y. The cylinders 



(as + a) 2 + 



transform into 

 (7) 



V u, u/y -r y \a J - 



which on clearing of fractions, 



O 2 + 2/ 2 ) (1 - rf) 4- 2a# (1 + 



(8) 



+ a 2 (l-n 2 )=0, 

 + a 2 (l-r 2 2 )=0, 



are seen to be eccentric circular cylinders. Their trace on the new 

 XF-plane is shown in Fig. 65, which represents the transformation 

 of the right-hand part of Fig. 24 by means of the function 



a 



w 



log 



a 



If we denote for either cylinder the radius by R and the distance 

 of the center from the origin by d, since we may write (8) 



FIG. 65. 



