134, 135] LAPLACE'S EQUATION IN SPHERICAL COORDINATES. 383 



Accordingly the components of <D = curl P along the coordinate 

 directions are, inserting trie values of _R 1; jR 2 , E s . 



If these vanish, the vector P is lamellar, and the above equa- 

 tions give the conditions that 



so that 



P =h 3V 

 s dq s 



as in the previous section. 



135. Laplace's Equation in Spherical and Cylindrical 

 Coordinates. Applying equation 33) to spherical coordinates 



h r =l, *,-i, hy-j^v 



_, . , P ^, _ 



r ar "V r 2 a^- 2 ^ r 2 a-9- "*" r 2 sin 2 



We may apply this equation to determine the attraction of a 

 sphere. For external points A V = 0, and since by symmetry V is 

 independent of # and qp 7 



45) + _0 or - 



dr 2 ~ r 6?r dr 



But since 



lim (VF) = M, 



r^oo 



lim [ c + cV] = 



r = oo 



we must have c' = 0^ c = M. 



