362 Mr. A. Stephenson on 
and duration; in the case of the system these qualities depend 
on the natural frequency of the coordinate directly acted on 
by the incident disturbance. If the frequency of this co- 
ordinate is equal to that of the emission, it is evident that 
maximum intensity in emission is obtained. 
8. The simple vapours that give line spectra in fluorescence 
show no trace of phosphorescence, and it would appear that 
the band spectrum of phosphorescence is, perhaps, an essential 
property of the phenomenon. The difference between the 
system and the phosphorescent substance may thus be funda- 
mental, but the agreement in other respects is of such a 
nature as to indicate the possibility that in essence there is 
mechanical identity between the two ; that the incident light 
forces a vibration in a coordinate, which in turn communi- 
cates kinetic energy in intensifying vibration in another 
coordinate until the saturation limit is reached ; the reverse 
process being set up on the removal of the exciting light, 
with the emission of energy in a frequency double that of 
the storing coordinate. 
The analogue affords marked economy of thought in con- 
necting a number of the chief facts of phosphorescence. It 
may also be of service in suggesting new directions of 
experimental examination. We shall conclude with a 
reference to two of these. 
9. If the spring of a simple oscillation is subject to periodic 
variation, the amplitude is magnified not only in the case of 
double frequency, but more generally when the ratio of the 
natural frequency to that of the disturbance lies anywhere 
within a range in the vicinity of ^r, where r is any integer*. 
As r becomes greater the magnifying influence diminishes 
very rapidly, but when r = 2 it is easily observable, although 
not nearly so pronounced as in the case of double frequency, 
r = l. Thus if our system is subject to a radial disturbance 
of frequency nearly equal to that of the pendulum motion, 
energy will be absorbed, and at once emitted again during 
the action of the disturbance in approximately double 
frequency. 
It would be of interest to inquire whether phosphorescent 
substances exhibit a similar phenomenon. As the effect is 
of the second order, it would be necessary to have the exciting 
light of great intensity in order to give the matter a fair 
trial. Experiments to determine the various effects of the 
infra-red rays have been carried out by Nichols and Merritt 
* See the paper already referred to in § 2.. 
