T , = 27M/m/ eR 



on the Nature of the Light emitted by a Substance. 233 

 or T _ livs/m ,^ 



If H is not 0, it follows from (3) approximately that 



_ . k /" eR \ 



\/m\ 2k Vm/' 



Putting T f for the period in this case, we have 



k V- 2kVm) ® 



Hence the ratio of the change of period to the original 

 period becomes 



_eH_ = e_ HT 



%ks/m m ' 4:7r ' ." " . 



A particular solution of (1) is that representing the motion 

 of the ions in circles. If revolving in the positive direction 

 (viz., in the direction of the hands of a watch for an observer 

 standing at the side towards which the lines of force are 

 running) the period is somewhat less than if revolving in the 

 negative direction. The period in the first case is determined 

 by the value of (5) with the minus sign, in the second with 

 the plus. 



The general solution of (1) shows that the ions describe, 

 besides circles, also slowly rotating elliptical orbits. In the 

 general case, the original motion of the ion having an arbitrary 

 position in space, it is perfectly clear that the projection of 

 the motion in the plane of (x,y) has the same character. The 

 motion resolved in the direction of the axis of z is a simple 

 harmonic motion, independent of and not disturbing the 

 one in the plane of (^,y), and hence one not influenced by the 

 magnetic forces. Of course, the consideration of the motion 

 of an ion now given is only to be regarded as the very first 

 sketch of the theory of luminiferous motions. 



19. Imagine an observer looking at a flame placed in a 

 magnetic field in a direction such that the lines of force run 

 towards or from him. 



Let us suppose that the said observer could see the very 

 ions of § 18 as they are revolving; then the following will be 

 remarked : — There are some ions moving in circles and hence 

 emitting circularly polarized light; if the motion is round in 

 the positive direction the period will, for instance, be longer 

 than with no magnetic field ; if in the negative direction, 

 shorter. There will also be ions seemingly stationary and 

 really moving parallel to the lines of force with unaltered 



Phil. Mag. S. 5. Vol. 43. No. 262. March 1897. T 



