( 816 ) 



(?) z=- ƒ [O . ()] d S 

 shows thtat 



C% = -^ I (by l): - b, \)y} d S 



Therefore, by (6), since ()' = () 



kHUvC Ida- r , 



©, = -— j (b;-^ + b:'-^) ./ 6' = —J (b,/^ + b,-^) (/ S. . (22) 



§ 7. Our stroiul s[)eeial ease is lluit of a [)artiele liaviiig- an elee- 

 trie iiionient, i. e. a small space N, with a total ciiarge I (> (/ aS' = 0, 



but witii such a distribution of density, that the integrals I (> .v d S, 



iQi/dS, iQzdS liave values differing from 0. 



Let X, y, z l>e the coordinates, taken relatively to a fixed point A 

 of the particle, which may be called its centre, and let the electric 

 moment be defined as a \ector p whose components are 



P:r = I QXd S, p,/ = i QY d N, V\~ = I (i Z d S. . . (23) 



Then 



Of course, if X, y, z are treated as infinitely small, u.,^ u^, u~ must 

 be so likewise. We shall neglect squares and pioducts of these six 

 quantities. 



We shall now aj)i»ly the equation (17) to the determination of 



the scalar potential cp' for an exterior point /^ (./',//, c), at finite distance 



from the polarized j)article, and for the instant at which the local 



time of this point has some definite value t'. In doing so, we shall 



give the symbol [(>], which, in (17), relates to the instant at which 



r' 



the local time in d >S is t' , a slightly different meaniug. Distinguishing 



c 



by r'„ the value of r' for the centre ^1, we shall understand by ^q] 



the value of tlie density existing in the element (/ .S' at the point 



(X, y, Z), at the instant /„ at which the local time of ^1 is t' . 



It may be seen from (5) that this instant i)recedes that for which 

 we have to take the numerator in (17; by 



