580 



Stoney — Cause of Double Lines in Spectra. 



Let the system which is equivalent to the coexistence of motion in these two 

 orbits undergo an apsidal shift, the frequency of which is n. Then, proceeding 

 as in Prop. II., we find that each of the two orbits gives rise to a double line. 

 We thus get four lines at the positions and with the intensities. 



Positions. 

 VI + e + n 

 m — e + n 

 m + e — n 

 m — e — 11 



Intensities. 

 {a + 5)78 

 (« + 5)78 

 (a - 5)78 



equal. 



{a - bf/8 



equal. 



Hence when the perturbation is accompanied by apsidal motion there will be four 

 lines, which will appear in the spectrum, as in («) or (5) of fig. 11, if e is greater 

 than n ; and as in (a) or (5) of fig. 12, if e is less than n. 



ct 



(a) 



(b. 



ih) 



Fig. 11. 



Fio. 12. 



It remains to consider what appearance in the spectrum would present itself if 

 there be a periodic oscillation in any of these perturbations, such as nutation 

 produces on the precessional motion of the earth. Let us — to take one instance — 

 suppose that the apsidal motion is affected in this way. Then — 



Pjioblem VII. — If there be a periodic oscillation in the apsidal motion, what 

 effect will this have on the spectrum ? 



To represent such an oscillation we must write 



{li^t + a sin If) instead of ^t 



in the equations of Problem II., where 



i/> = 27rw/y and t, — ^Trqlj. 



