U4 PROF. H. M. MACDONALD ON THE DIFFRACTION OF 



The general solution of this equation is 

 7P = r'>> S (A,J. + v, (r) 



where J n+v . (r) is BESSEL'S function of order n + ^, and P B is the zonal harmonic of 

 order n. 



If y! is the magnetic force at the point P due to the oscillator, y, is the real part of 



C - =: - , where V is the velocity of radiation and R is the distance OjP ; this 

 dp B 



has to be expressed in the form given above for the solution of equation ( 1 ). Writing 



where 



it follows that 



U 2 = 



= p ~ r- 1 -rrV/*" (2n + 1) e r -"'K, + ,, (^r,) J n+lj (*r) P n> 



up (I 



where r,>r, and 



^=p - r -VrV> i (2/i+l) e 1 2 ""'K,, +lj (,-) J. +v> ( K r,) P., 

 ()p n 



when /> /[, where 



Now 



a a 



v / r~ v ^ ' \"> i A / \ > 



< P. c/ji a/A 



/.; p _ 9P n + i _ ?P-i 



a/A a/A 



therefore, rj>r, 



,-- 1 /.J ll _, , ( K r)-(n - 1) r" -J,.,,. (K 



-^ fl "K. + *(i^){r |^V^ 



that is 



^ 1 = -/crrVV^i{eV.<-K H _ Vi ( l crO+e I/ '<" +1 >"K, + .J l ^ 



or 



= -rrV/' 2 (2n + 1) eV.<-*vj ? K, (^.^ J)>+ (lcr) (1 _^) ^, . . 



