DOUBLE INTEGRALS TO OPTICAL PROBLEMS. 
337 
theorem, we find that the terms connecting different periods drop out (a familiar 
property of ordinary harmonic analysis), and the rate of absorption is dependent on 
f 2ku~H 2 clic 
J 0 (P 3 - 
The phase i fj has again disappeared. 
Heating effects are directly dependent upon absorption. So again with physiolo¬ 
gical effects. 
§ 14. In the case of chemical and electrical effects produced by light we probably 
have some kind of dissociation. This is perhaps true of luminescence also. It may 
be that we do not yet understand the mechanism of dissociation. But, if the disso¬ 
ciation arises from separation of ions as their light-excited vibrations become large, 
the vibrator analogy will apply here as well. Doubtless some molecules will split 
up sooner and others later; for the individual molecule the precise timing of its own 
vibrations with the phase of the incident light will be all-important. But on the 
average of a large number of molecules, the amount of dissociation will perhaps depend 
on the rate of absorption of energy by a vibrator typifying the average structure. 
It is necessary to repeat that our assumption of a linear equation for the vibration 
of a molecule cannot be regarded as more than a first stej3 towards a solution of a 
difficult problem. In the words of Sir George Stokes, “ Linearity applies to the 
small disturbance of the single elastic medium—the ether—but it does not follow 
that linearity applies to all the effects produced in a complex system of molecules.” 
§ 15. Let us consider the application of the present treatment to the spectroscopic 
analysis of light. 
The light emergent from the instrument in a given direction is compounded of 
different wave-lengths. The element 
B cos (pit + \jj)du 
of the integral will contribute a component 
R <f)(u) cos {ut xfj)du. 
In this expression (fit) depends upon the structure of the instrument, and the 
direction chosen, as well as upon u. The change of phase xjj~-6 depends upon the same 
causes. We must note, however, that neither <p{u) nor xp — 0 depends upon xp. 
The emergent light will be 
o o 
co 
R 4>{u) cos {ut -f 6)du. 
■*0 
Now we have seen that the phase only enters as determining the constancy of the 
light. If the light which comes into the instrument is constant, so also is the 
emergent beam. The phase has no further part to play; hence, the spectroscopic 
vol. cxcv. — a. 2 x 
