432 Prof. Kowland on Spherical Waves of Light 

 9.11 f 3.4 2 gA/ I 



_ (2n-l)(2n + lH (n-2)(n-l) 



A "~ «(» + l) t Z (2n-5)(2n-l) A "- 2 

 ( w _4)(re_3) 1 , 



— To STTo 7\- tt -»-4 — Oii-n-2 (• 



(2n— 5)(2n— 7) J 



These all depend on A\, whose value can be found by deve- 

 loping sin 2 0, sin 4 0, &c, in harmonics. In the following 

 values one must add the second term with — i in place of +i 

 before substituting in the formula 



A'^ICxOy, 



91 

 A',= -jiC,(ry, 



A'-SUcw-H *<*)}<*. 



A'7 = &C. 



These reduce to Bessel's functions when we obtain the real 

 form. Thus 



Each term of the original series is now of the form A! n Q r n sin #. 

 But by the theorem of p. 428 we have only to multiply the 

 terms of this by C n (B), and it gives the value for any finite 

 distance outside a sphere around the origin which contains 

 the circle. Hence 



W = ^^ (R - V 'H A'A + A^Q / 8 8 (B) + A^C 8 (R) + &c.} . 



Dynamical Theory of Diffraction. 



When a ray of light strikes upon a screen in which there 

 is an opening, a disturbance takes place in that opening, whose 

 effect can be calculated by the preceding formulas. Maxwell 

 has shown that in a plane wave the energy is half magnetic 

 and half electrostatic, and that the magnetic and electric dis- 

 placements are at right angles to each other and in the same 

 phase. 



