338 
MR. C. GODFREY ON THE APPLICATION OF FOURIER’S 
analysis of constant light depends solely upon the instrument and the distribution of 
energy among the elements of the Fourier integral. 
§ 16. A dispersive medium, apart from its possible selective absorption of the 
different wave-lengths, will always alter the relative phases of the different elements, 
the transmitted light will thus be altered. But the preceding work has shown that 
these phase-changes will not affect the sensible properties of the light. 
§ 17. We have arrived at the conclusion that the different simple components of 
constant light are not only superposed, hut also independent as regards all energy 
properties. 
Radiations composed of a random Aggregate of Pulses. 
§ 18. A constantly-recurring problem in optics is that of the composition of an 
irregular sequence of pulses of a given tyjie. 
The question occurs in dealing with the radiation of an incandescent gas. The 
pulse here consists of the train of waves given off by the molecule during its free path ; 
after an encounter the trai ij will he entirely changed, and practically independent of 
the former train. 
Again, what is the total effect on radiation of the damping to which the vibrations 
of the molecules are subject ? The question was raised by LommelA This author 
was content to analyse e~ kt sin ( pt -f i|i) as a Fourier integral, and assume that the 
different elements are independent. This, of course, will not be true for the simple 
pulse which Lommel considered. It is true that the motion e~ ,d sin (pt + xjj) can he 
reconstructed by means of an infinite series of vibrators whose amplitudes follow 
the law of the Fourier expansion. But the phases of these vibrators will not he inde¬ 
pendent ; they must be carefully adjusted to give the requisite effect. 
§ 19. We shall find that, when we deal with an infinite and irregular succession of 
such pulses, the energy properties do completely specify the motion. The disturbing 
influence of phase will disappear; in the Fourier integral representing the complete 
motion, the phase will he a rapidly-fluctuating function of the wave-length, and all 
distinctive phase-properties will average out. 
The omission to deal with a sequence of pulses has exposed Lommel’s analysis to 
adverse criticism. It will he seen that a more complete treatment confirms the 
results which he obtained as regards the widening of spectrum lines through 
damping. 
§ 20. Another case in point is that of Rontgen rays. These are satisfactorily 
covered by Professor J. J. Thomson’s theory of electric pulses. The pulses are of 
given type ; each one may be analysed by Fourier’s theorem. We find a certain 
energy-wave-length curve ; in dealing with an infinite succession of pulses the phase- 
* Lommel, ‘ Wied. Ann.,’ 3, 251, 1878. 
