Stoney — Cause of Double Lines in Spectra. 



575 



circular motions of P in that plane. These will give rise to three lines in the 

 spectrum, of which the positions on a map of oscillation-frequencies will be 



and 



m + n + k, position of (ti a) 

 m + 11 — k^ . . . . (6 ^)[-, 

 m + n , . . . • (5 c) 



(7-) 



with intensities proportional to 



25'' cos* ^, intensity of (6 a) 



2s'' sin* TT, 



2' 



a 



2' 



4s^ sin^ ^, cos^ ^ 



(5.) 



■ 



(8) 



If a is small, i. e. if the plane of the elliptic motion is nearly coincident with the 

 invariable plane, as it probably is in the molecules of the monad elements H, Li, 

 Na, Rb, Cs. then the line (6 a) is strong, (5 c) is faint, and (6 5) is excessively 

 faint. 



The foregoing investigation traces what becomes of the circular motion (4 a) 

 when affected by precession. A similar treatment of (4 h) is made by substituting 

 d for s and — D for S. We thus obtain the following : — 



X, 



\ = -\-d cos^ ^ cos {D — o))t\ 



Yi = —d cos^ ^ sin [D — (o)t 



2 



(9 a) 



a 



X2 = -\-d sin^ ^ cos (Z) + w) ^ 



a . 



and 



F2 = + rfsin^ jr sin {D-\-o))t 



z = — 2d sin- cos -x sin Dt, 



(9 3) 



(10) 



producing three lines in the spectrum in the positions 



m — 11 — k, position of (9 a)^ 

 m — n + k, . . . . (9 i) 

 m — n , . . . . (10), 



(11) 



