BRIDGMAN. — THE ELECTROSTATIC FIELD. 



621 



us so to assign values that either </> or \p shall be continuous, and hence 

 a potential function. 



If cf> is the potential, we give it the same value at every point on one 

 of the ellipses. varies from on the straight line joining the foci to 

 infinity at infinity. The first derivatives are continuous everywhere 



Figure 4. 



except on the line, where the amount of discontinuity shows that there 

 is a surface charge of 



J_ 1 



counting the charge on both sides of the line. This gives a total charge 

 all along the line of \. The values of ip are now determined. Every- 

 where on the same branch of a hyperbola it has the same numerical 

 value, but suffers an abrupt change of sign on passing through the 

 vertex, being positive above and negative below the X axis. On the 

 two different branches of the same hyperbola \p has supplementary values. 



