an Arbitrary Electro-magnetic Disturbance, 427 



where I have written 



S'=X'a + Y'y + 2?z, 



For a general expression the term e -^(p-vo mus t be replaced 

 by any function of p — Yt or p + Yt, as before. 



Before integration, one must of course substitute (# — a/), 

 (y—y f ), and {z — z') for the w, y, and £ of the formula. It 

 is evident that the components of the electric displacement 

 can be replaced by the true convection-displacement of elec- 

 tricity as carried along by the actual motion of ihe medium, 

 and the disturbance due to a moving magnet can be calculated 

 in a similar manner. 



To obtain an idea of the relative magnitude of the quantities 

 which enter into these expressions, I may remark that the value 



27T 



of b in wave-lengths is — . Hence, for any ordinary calcu- 

 lations with respect to light, the distance need be only a few 

 inches, or, indeed, one inch, to cause the values of Cx, C 2 , &c. 

 to become constant and equal to C . But if we are treating 

 of longer waves, we must retain such terms. 



I have already given the proper expansion into series of 

 the quantities here involved ; but it will be better to put them 

 in a reduced form, 



c=.—ib\ p=p\/l + 2s; cps = q. 



n / \ n |i nn + 1 n(n 2 — l)n + 2 

 yr/ L 2 cp 2.4 c 2 p 2 



n(n 2 -l)(n 2 -2) n + 3 - \ 



^=f{c 1 M + fc, W+1 4c.oo + 4o.} 1 



^=f{c s (p) + fC,(p) + I t ClW+ 4c.}, 

 2 ^- ) -=f{i( 2 C„ + C ! (rt) +S o. 



+ (2n + 8)l!!2,3,.,n K* 1 + 2 >°'<P> + °*M ] + & °' ) ' 



Thus one has 



p 2 =W-2(xx'+yy' + zz') +r 2 , 



