Stoney — Cause of Double Lines in Spectra. 585 



to molecules acting on tlie sether, the setlier reacts on tliem ; and thus each molecule 

 is indirectly influenced through the sether by all its neighbours, whereby the 

 direction and phase of its oscillations will inevitably fall into a sufficient accord- 

 ance with theirs. 



We may therefore freely use the whole of the investigation in the last chapter 

 to represent what takes place under the electro-magnetic theory of light ; merely 

 remembering that 6t is now a quadrant in advance of where it was under the 

 dynamical hypothesis, so that to represent the position of the point P we must sub- 

 stitute {6t — v/2) for 6t in all the equations of Chapter II. This, in no respect, 

 affects any of the conclusions. 



CHAPTER IV. 



ANALYSIS BY FOUEIEr's THEOREM. 



We have hitherto treated in detail only those cases (if any such occur) in which 

 the original motion of the electron, set up by the encounter, is a pendulous elliptic 

 motion. But this degree of simplicity is not met with in any known spectrum. 

 The line spectrum of hydrogen is the least complex with which we are acquainted, 

 and the next in simplicity are the spectra of the other light monad elements, 

 lithium, sodium, potassium, rubidium, and csesium. In the spectrum of hydrogen 

 there is at all events one great series of lines (probably double lines), and in the 

 spectrum of each of the others three such series are known. It becomes therefore 

 of importance to inquire whether the entire of one of these series of lines emanates 

 from the motion of one of the electric charges in the molecules of the gas. The 

 following propositions, in conjunction with what has been done in the preceding 

 chapters, lay much of the foundation for following up this inquiry. 



However complex the motion of a point may be, provided it takes place in a 

 straight line, Fourier's theorem resolves it into pendulous elements. This is enough 

 for the purposes of acoustics, inasmuch as the motions to be dealt with in that 

 science are sensibly rectilinear. But it is not sufficient when dealing with the 

 transmission of electro-magnetic stresses through the sether, since the alternations 

 of such stresses are propagated under the laws of an undulation in which the motion 

 of each point is restricted, not to a line but to a plane. Hence arises — 



Problem A. — What theorem corresponds to Fourier's theorem when the motion 

 takes place along any plane curve ? 



