20 

 THE FORCE F. 



We define 



-J 



F,riJ = - p[r X fcj • n)q - (r X w • q)n + (I)(n x ta)]da 

 S, 



Then 



^iZ/3^^^- 



r^ x4«? -wCr^ • w) + r (w a) 



^ at ^ ^ 



P^ 



[40] 



[41] 



We can write 



I 



(r X <a • n)q - (r x w • q)n 





da = \ p(r xii»)x(qxn)(iCT 



and bv substitution [33] 



p (r . X w) X (q X n) + (R x 0)) x (q x n) c(ct 



i(r. X f^) X q X n c^a — p(R x (i> • q)nfi?<T 



Jr. Jo 



[421 



since R x n = on S-. We evaluate these integrals separately, again taking advantage of the 

 fact that they are independent of ^. It is easily seen from Equations [23], [25], and [28] 

 that only the term with the coefficient a° can contribute to 



q x n da 



Rut this term represents a source, and for a source, q x n must vanish on S-. So 



(\ X nda = 



[431 



The integral 



/.,■ 



(R X a» • q)nc?a 



can similarly be seen to involve only terms with coefficients a° , o^, and b^, namely the vec- 

 tor doublet strength A of the singularity. From Equation [35] 



