172 Dr. T. Preston on Radiation Phenomena 



that time the influence of the magnetic field was not known 

 to exist. The character of certain spectra indicated that the 

 lines resolved themselves naturally into groups, or series. For 

 example, in the monad elements Na, K, &c. the spectrum 

 resolves itself into three series of doublets like the D doublet 

 in sodium, and Dr. Stoney's object was to explain the exist- 

 ence of these pairs of lines. For this purpose he considered 

 what the effect would be on the period of the radiations from 

 a moving electron if subject to disturbing forces. In the 

 first place he determined that if the disturbing forces cause 

 the orbit to revolve in its own plane, that is, cause an apsidal 

 motion, then each spectral line will become a doublet. The 

 frequencies of the new lines will be N + ft and N — n, where N 

 is the frequency of the original line and n the frequency of 

 the apsidal revolution. This is very easily deduced by 

 Dr. Stoney from the expressions for the coordinates of the 

 moving point at any time t. Thus if a particle describes an 

 ellipse under a force directed towards its centre (law of direct 

 distance), its coordinates at any instant are 



x = a cos fit, y — b sinl2£, 



in which fl is equal to 27rISr, where N is the frequency of 

 revolution. But if, in addition, the ellipse revolves around 

 its centre in its own plane with an angular velocity co, it is 

 easily seen by projection that the coordinates at any time 

 are 



x = a cos fit cos cot — b sin fit sin cot, 



y = a cos H t sin cot + b sin fit cos cot , 



and these are equivalent to 



# = i(a + h) cos (fl + co)t + i(a — b) cos (12 — a>)t, 



y — ^{a-[-b) sin (fl + co)t — i(a — 6) sin (fl — co)t, 



and these in turn are equivalent to the two opposite circular 

 vibrations 



x x = J(a + b) cos (12 + ©)£ "1 x 2 = i(a — b) cos (12 - »)n 



j/i = i(a + &) sin (fl + co)t J y 2 = — J(a— 6) sin (12 — co)t J ' 



The resultant motion is consequently equivalent to two 

 circular motions in opposite senses of frequencies N + n and 

 N — n. 



This is an analysis of the motion without any regard to the 

 dynamical origin of it ; but if we treat it from a dynamical 

 point of view, the equations of motion will exhibit the forces 

 which are necessary to bring about the supposed motion. 

 Thus, if the orbit rotates with angular velocity o> in its own 



