BRIDGMAN. — THE ELECTROSTATIC FIELD. 



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smooth curve through vertices at which fa + fa has the same value. 

 This line will have the general direction of one of the diagonals in each 

 parallelogram. The line of constant fa — fa is obtained from the same 

 figure by following along the other diagonal. By an exactly similar 

 method we find the lines of force fa + fa of the new combination. This 

 is the method by which the curves of this paper were drawn. The 

 diagrams represent the field surrounding two elements, the field of each 

 of which singly is known. 



Figure 2. 



The simple functions that were combined are 



x = cosh <£ cos \f/ 

 y = sinh <£ sin \p 



x and y are conjugate functions of <f> and fa and hence conversely <f> and 

 \p are conjugate functions of x and y. Therefore both </> and \j/ satisfy 

 Laplace's equation, and if they are continuous, may be taken as poten- 



