320 



ELECTROSTATICS. 



[PT. II. CH. VII. 



the 7-axis outside the focal points and as y increases the hyper- 

 bolas become continually less sharp, until when y = Tr/2 the hyper- 

 bola reduces to the F-axis. As y goes on increasing we obtain the 

 same hyperbolas in inverse order. Accordingly the whole of the 

 Z7F-plane is represented by the portion of the XY- plane lying to 

 the right of the F-axis and between the lines y = and y 2ir. 

 Other regions of the JTF-plane of similar dimensions correspond 

 repeatedly to the 7F-plane. The point x 0, y = corresponds 

 to the two focal points. We may get a good idea of the corre- 

 spondence of the two planes by describing any path composed of 

 portions of horizontal and vertical lines in the JTF-plane, and 

 noticing that when we turn to the right or left through a right 

 angle in the XF-plane we turn in the same direction in the UV- 

 plane. Such a path is represented in Figs. 66 a and b, where 

 the correspondence of the various regions is indicated by the 

 shading. 



FIG. 66 a. AT-plane. 



The whole of the space between two ellipses corresponds to a 

 rectangle of altitude 2-7T in the right-hand upper quadrant of the 

 ZF-plane. 



