VECTOR ANALYSIS. 

 186. If we have 



where F is complete, the integral equation will be of the form 

 For this gives , 



O /V s\ 



dt 2 ~ ' 



and a and /3 may be determined so as to satisfy the equations 



187. The differential equation 



will be satisfied by 

 whence , 



.a 4- 



If F is complete, the constants a and /3 may be determined to satisfy 

 the equations 



188. If 

 where F 2 A 2 is a complete dyadic, and 



we may set 



which gives 



+ {iF.e< r +|F.e- tr + A.cos{*A}}./3, 

 d*o 



= {F 2 -A 2 }.p. 



