434 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



Consequently the lamellar part of R is determined by its divergence. 

 Secondly finding the curl of R, say o>, with components f, 77, f, 



a^_8F = a_/a^ < _ 



^~9# cte "cty \9fc 30 



Since Q is as yet undetermined except by the partial differential 

 equations (i) we may impose on it the condition of being sole- 

 noidal, 



dx dy dz 

 Hence 



r^glf 



9y 3^ 

 and in like manner 



3-ST 8^ 



" == aJ-te 



? - 9F ^- ATT 

 ? ~te~^- 



But since -B is continuous, curl R must be finite, and therefore as 

 before 



(?) 



The vector Q, whose components are l/4?r times the potentials of 

 the scalar functions , 77, , the components of G>, is derived from 

 o)/47T by the operation Pot, considering o> as a vector, so that we 

 may write 



(8) Q = ~ 



and call ^irQ the Fecfor Potential of o). Since the solenoidal part 

 of R is the curl of Q, we shall also say that Q is the vector 

 potential belonging to R. We accordingly see that the solenoidal 

 part of R is determined by curl R, and accordingly the vector 



