of Refraction, Reflexion, and Extinction. 271 



field E (a) , H (2) initiated by the vibrator is known to be 

 pressible in the form 



X?A 



E»)=curl s ^ 5 (2) 



H ( ? ) = ocnrIOS?/a*>, (3) 



where ac = l. To utilize this principle we have only to adopt 

 for "SP a suitable form of expression. Let \{l x , l y , l z ) be a 

 direction unit vector belonging to a given vibrator. We 

 will suppose that the direction of 1 remains invariable ; and 

 we will call it, for shortness, the axis of the vibrator. If r 

 denotes the distance between M and V, we will assume 



¥ x =Z x ¥(r,0etc (4) 



where Mfy-, t) represents the magnitude of M* apart from 

 direction. 



Let r be a unit vector pointing in the direction of r, from 

 V to M. Substituting from (4) we get 



div^= s (rl) — ^- — > ...... (5) 



s( ) being the symbol of the scalar product. Let us now 

 write 



= cWM) _ l B^0%j) 



d>' 2 



(6) 



B= a,-* 4 r ~^r~' • • • ( 7 ) 



•and let (5) be substituted in (2) ; then this equation becomes 

 E (2 >=-lB + r s (rl)A (8) 



The projections of E (2) on 1 and r are 



Ei 2) =-B + ( s (rl;) 2 A, ' . (9) 



E< a) = B (rl)(A-B) (10) 



We now proceed to obtain the expression of H (2) . Com- 

 bining (3) with (4) we easily find 



H< 2 > = y (rl)C, (11) 



where the vector product is denoted by the symbol y( ) and 



C=aW(r,tydrtt (12) 



It appears from (S) and (11) that E (2) is always in the 

 plane through r and 1, and that H (2) is perpendicular to the 



