an Arbitrary Electro-magnetic Disturbance. 429 



F= e ^li CqEoYo' + CxEiY/ + C 2 E 2 Y/ + &c \, 

 P ( 



e c(g-Vt) 



G = — { C E Y " + CxExY^ + C 2 E 2 Y 2 " + &c. \, 



P 



ec(o-Yt) 



H = { CqEoYo^ + C 1 E 1 Y 1 /// + C 2 E 2 Y/" + &c. } . 



P 



The best point for the origin will be somewhere near the 

 centre of gravity of the illuminated body. 



That the light is perfectly determined in this way for all 

 points outside a sphere around the origin which does not cut 

 the illuminated body is evident from the fact that we might 

 reverse the motions so as to make the light return along its 

 previous path. 



These expansions and this theorem entirely change the 

 ideas of those who have only been in the habit of regarding 

 light from the point of view of rays of light. For we here 

 see that light coming from any source may be replaced by 

 light from another source ; so that the true source might be 

 entirely invisible, and we " see " only the false source. This, 

 however, could only happen for a point outside a sphere 

 drawn around the false point and the real point, and we could 

 always detect the deception by making a complete spherical 

 journey around the real point and inside the false point. 



As an illustration, let us compute the effect of a circular 

 electric current which is caused to vibrate back and forth 

 according to a simple harmonic function, so as to make the 

 displacement C e~ cV *. In this case we must make 



0=X'=X? =Y"~Z"; Y'dv= -C r sin ada; 

 Z / = G Q r COS ada, 



where r is the radius of the circle. 



From the symmetry around the axis of x we have F r = 0, 

 and can write for the component of the electric displacement 

 around x at a distance K sin 8 from that axis, 



r tf e -cvt?** c 2C + C 2 . 3BrC 2 sin0 . ) , 



N' = 5 — \ < — 2 sin a \ cos 2 a V evd*. 



8tt Jo I p p 3 S 



p 2 =R 2 -2Rrsin0sina + r 2 . 



Integrating the first term by parts, taking sin ada for one 

 part, we have, since the first part disappears, 



I — e cs sin ada =1 — I — € cs ) cos ada. 



Jo P Jo da\ p / 



Phil Mag. S. 5. Vol. 17. No. 108. June 1884. 2 G 



