360 
MR. C. GODFREY ON THE APPLICATION OF FOURIER’S 
not arouse the natural vibrations of the molecule. He held that the motion of the 
molecule would be mainly in the mean period of the incident light. This conclusion 
we take to be erroneous. 
§65. Sellmeier does not adopt the Fourier method; he builds up the incident 
light by means of a great number of finite superimposed trains of simple waves, all 
having the same phase and period, but of amplitudes, durations, and positions so 
adjusted as to give the actual fluctuation of amplitude which is present in the 
resultant motion. In passing, it may be noticed that this arrangement will give no 
irregularity of 'phase in the light motion; whereas we have shown that such 
irregularity will generally be present. The defect may be remedied by removing 
the condition that the component trains shall be of the same phase; but this con¬ 
sideration will not alter Sellmeier’s reasoning in any essential.* 
Sellmeier supposes the motion of the vibrator to be free from all damping. We 
will show that in this case his conclusion ought to be that the natural periods of 
the vibrator become continually more and more prominent without limit. 
§ 66. His reasoning is as follows. Each new train of waves, as it strikes the 
vibrator, arouses :— 
i. a vibration in the period of the incident light (forced), 
ii. a vibration in the period proper to the vibrator (natural). 
The forced vibration (i) will be of the same phase as the exciting train, and of 
amplitude proportional to that of the said train. The natural vibration will 
generally have an amplitude of the same order; its phase will, however, be 
different. 
§ 67. The motion of the vibrator at any time results from the superposition of all 
the vibrations previously started. It will be partly forced and partly “ natural.’’ 
The forced vibrations at any instant will clearly differ from the incident motion at 
that instant by a numerical factor only. 
The natural vibration, on the other hand, is compounded of members, whose phases 
are practically fortuitous. This is easily seen as follows. The phase of natural 
vibration aroused by the beginning of a new train depends upon the point of time 
at which this event takes place. The difference of a fraction of a period in the 
position of this point of time produces a finite change in the phase of the natural 
vibration aroused. But, in building up the slowly varying vibration by means of 
simple trains, the instant at which each start is, to a few periods, immaterial. 
§ 68. Sellmeier concludes from this that the natural vibration will be insignifi¬ 
cant compared with the forced vibration. This mistake arises from the fact that 
* It will be convenient to get rid of the endings of these trains. This we may do by supposing that a 
train, once started, is unending ; and by introducing a train of equal amplitude and opposite phase, whose 
beginning is so fixed as to extinguish the former train at the right moment. By this arrangement we shall 
only have to deal with beginnings. 
