588 



Stoney — Cause of Double Lines in Spectra. 



undulation either advances into a dispersing medium, or suffers diffraction. In 

 the open ^ther the pendulous elliptic components travel at the same rate and keep 

 together, but on entering a dispersing medium they advance with different speeds 

 and become separated, or, if they encounter a diffraction grating they are by it 

 sent in different directions. It is one or other of these separations that the 

 spectroscope makes manifest to us. 



But the motions of the electrons, the electric charges in the molecules of the 

 gases, which are what excite this sethereal undulation, may be motions that are not 

 confined to one plane. Accordingly, to study them, we must investigate — 



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

 takes place along a line of double curvature ? 



Such a motion is in general represented by — 



x = F, (t); 



y^F, {t), . 

 z = F, {t). 



These when expanded by 



- 



When referred to the rectangular axes Ox, Oy, Oz. 

 Fourier's theorem become — 



X = Aa + Ai cos 6it + A2 cos Oit + . 



+ A\ sin d^t + A' 2 sin O^t + . 



1/ = Bo + Bi cos dit + Bi cos 6it + . 



+ B\ sin e^t + B'i sin O^t + . 



^ = Co + C, cos dit + C2 cos Bit + . 



+ C\ sin dit + C'a sin d^t + . 



Let us take any vertical column from these, e. g. 



Xk — Ai, cos 6J+ A\ sin 6 J, 

 yu = B^ cos 6ut + B\ sin d^t, 

 Zu = Cu COS 6J,-\- C\ sin Q^t.^ 

 or, leaving the suffixes to be understood, 



X = A (to's, 6t -V A! sin dt, 

 y = BGO&et + B' sin Ot, 

 z^ Ccoset+ C sin dt, 

 of which (by Problem A) the first two are equivalent to the elliptic motion, 



x' — u cos {6t + c), 

 y' — V sin {6t + e), 



(«2) 



(^0 



[h) 



