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We wish to find a potential function c^ , defined 

 outside a given sphere, with a given distribution of sources 

 outside the sphere and vanishing normal derivative, -^- = 0, 

 on the boundaryo A standard method for constructing ^ is 

 to place a suitable arrangement of sources inside the sphere, 

 called the image of the original distribution. 



The image of a point souJ?ce and a radial dipole are 

 well known, and will be found in Mi Ine -Thorns on , pp. 420,421. 

 Here we consider the image of a line source. 



Theorem 1 . Consider a sphere with center and radius 

 a. The image of a uniform line source of strength lx, per unit 

 length stretching from Q-j^ t o Qg is the following: a uniform 



OQ2 

 line source of strength M— g— pei' unit length, stretching 



between the points Q]_,Q2 inverse to Q^, Qg, and a uniform 



line sink of strength u. \^ 



to Q,. 



per unit length extending from 



