260 Dr. J. W, Nicholson on a General 



Or (!c r 2 sin 0, y r sin 0, zr) = V 2 curl (a, br, cr sin 0), (2) 



the differentiations in the operation " curl " being 



~dr' 3#* 3o)" 



In a similar manner, since the electromotive force in the 

 circuit is the rate of decrease of the total magnetic induction 

 across it, 



(a r 2 sin 0, br sin 0, cr) = — curl (a?, ?/T, sr sin 0) . (3) ; 



We have further, as necessary for the existence of these 

 relations, the solenoid al conditions 



div (xr 2 sin 0, yr sin 0, zr) = . . . (4) 



div (ar 2 sin 3 br sin 0, cr) = 0, . . . (5): 



the differentiations in "div" bein«' =i-, ^^, <— • 



8 3>' 3# 3^ 



Thus 



— r sin ^— = ^— (a r 2 sin 0) + ?'^-, (b sin 0) 

 0<w 0>' 00 



or 



Be 



-{^w+^p^ 81 ^)}- • • w 



Now by certain relations embodied in the circuital 

 formulae, 



d> 2 sin0 I' 3 ••>. • /ix IB /• \ 



-yi- = - y, §g ("■ *" «) | y^ (H 



3 • a S -3 '77 \ 3« I 



= -B5-.f ,ntf A^. (Jr) 7S»/ 



0<t) sin0 loo) o> J 



TO = ~* S < 7 > : 



But 



if 27T//c is the wave-length. 

 Thus with the help of (6), 



72 9 • /) 3 • /i3C^'') 3 • /i 3^ 1 3^ 



00 0'' 3# 3# S1H0O®'" 



K~ . r sin (9«< - (r-a + tr^^S .(» sm 0) U 

 3^ l'r 0>' sm #00 J 



