﻿Interrrupted Spectra of Gases, 293 



Moreover these vibrations will coexist in a state of mechanical 

 independence of one another, if the disturbance be not too violent 

 for the legitimate employment of the principle of the superposi- 

 tion of small motions. So long as the light traverses undisper- 

 sing space these constituent vibrations will strictly accompany 

 one another, since in open space waves of all periods travel at 

 the same velocity. The general resulting undulation will there- 

 fore here retain whatever complicated form it may have had at 

 first. But when the undulation enters such a medium as glass, 

 in which waves of different periods travel at different rates, the 

 constituent vibrations are no longer able to keep together, each 

 being forced to advance through the glass at a speed depending 

 on its periodic time. Thus there arises a physical resolution 

 within the glass of series (4) into its constituent terms*. And 

 if the glass be in the form of a prism, the pendulous undulations 

 corresponding to the successive terms of series (4) will emerge 

 in different directions, so that each will give rise to a separate 

 line in the spectrum of the gas. 



We thus find that one periodic motion in the molecules of the 

 incandescent gas may be the source of a whole series of lines in 

 the spectrum of the gas. The nth of these lines is represented 

 by the term 



C n sm(n$+a n ) 3 



in which C n is the amplitude of the vibration ; and consequently 

 Qn represents the brightness of the line. If some of the coeffi- 

 cients of series (4) vanish, the corresponding lines are absent 

 from the spectrum. This is analogous to the familiar case of the 

 suppression of some of the harmonics in music, and appears to 

 be what usually occurs in those spectra which are called by 

 Plucker spectra of the Second Order. 



* Other expansions similar to Fourier's series can be conceived, in 

 which the terms, instead of representing pendulous vibrations, would re- 

 present vibrations of any other prescribed form ; and hence a doubt may 

 arise whether the physical resolution effected by the prism is into the 

 terms of the simpler series. That it is so may, perhaps, not be sus- 

 ceptible of demonstration ; but the following considerations seem to 

 show it to be probable in so high a degree that it is the hypothesis which 

 we ought provisionally to accept. For, first, the form of the emerging 

 vibrations is independent of the material of the prism, since the lines cor- 

 respond to the same wave-lengths as seen in all prisms ; and, secondly, it is 

 independent of the amplitude of the vibration within very wide limits, since 

 the positions of the lines remain fixed through great ranges of temperature, 

 and, in many cases, when the temperature falls so low that the lines fade 

 out through excessive faintness. The first consideration shows the series 

 to be the same under varying circumstances ; and the second consideration 

 suggests, as in the theory of the superposition of small motions, that this 

 series is a series of pendulous vibrations. 



Phil. Mag. S. 4. Vol. 41. No. 273. April 1871. X 



