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PROCEEDINGS OF THE AMERICAN ACADEMY. 



them as the equipotential lines, and those of the other as the lines of 

 force of a distribution determined by the equations above. In general, 

 the distribution will depend upon which function is taken as the potential 

 function. 



It is a familiar fact that conjugate functions are additive; that is, 

 if fa fa and fa fa are two sets of conjugates, then fa + fa is conjugate 

 to \px + fa. But the potential function is also additive. Hence if we 

 know the potential and the force functions of two distributions sepa- 

 rately, we may find the potential and force functions of the combination 



Figure 1. 



by adding the functions of the distributions separately. This addition 

 may be performed very simply by a graphical method described by 

 Maxwell, provided that we know the shape of the curves of constant 

 fa and fa separately. "We draw the set of curves fa = C! for a set of 

 values of Cj differing by some constant, and the corresponding set 

 fa=C v for successive values of C 2 differing by the same constant. 

 We have thus divided the plane into a number of small curvilinear 

 parallelograms, at every vertex of which we know the new potential 

 fa + 4>2- An equipotential line of (/>! + fa is obtained by drawing a 



