14 Preston — Radiating Phenomena in a Strong Magnetic Field. 



jiiiirs of lines, like the great D pair of sodium, and Dr. Stoney's object was to 

 explain these pairs of lines. In the fii-st place, he showed that if the disturbing 

 forces exist which cause the orbit to revolve in its own jjlane, that is produce an 

 apsidal motion, then each spectral line will become a pair of lines, and if N be 

 the frequency of the original line, that is the frequency of revolution of the ion in 

 its orbit, and n the frequency of the apsidal revolution, then the frequencies of the 

 new pairs will be i\^+ w and N — n. This is very easily deduced by Dr. Stoney 

 from the expressions for the coordinates of the moving ion at any time t. 

 Thus, if a particle describes an elliptic orbit under a central force (law of 

 direct distance) directed towards its centre, its coordinates at any instant may 

 be written in the form 



x = a cos Q.t, y = b sm W, 



in which fl is equal to ^ttN where N is the frequency of revolution. But if, in 

 addition, the orbit be forced to revolve round its own centre in its own plane 

 with angular velocity <u, then it is easily seen by projection that the coordinates 

 at any time are — 



X = a cos Q,t cos wt ~ b sin Qt sin tot, 



y = a cos Qjt sin wt + b sin Q,t cos mt ; 



and these are equivalent to 



a: = -J (a + S) cos (Q + w) < + 5 (« - i) cos (i2 - oj) /, 

 y -\(ci ^h) sm[Q. ^^ ij)t - \{a -h) sin (ii - o)) t, 



while these in turn are equivalent to the two opposite circular vibrations 



«, = 5 (ft + b) cos (ii + (u) / \ irj = I (rt - h) cos (Q - w) i 

 yi = 2 {n + i) sin (£2 + tu) ;; ' 11-'. = - \ (« - ^') sin (Q - o) t 



The resultant motion is consequently equivalent to two circular motions described 

 in opposite senses, and of frequencies N -\- n and N — n respectively. These 

 circular motions will be polarised when the perturbating forces remain fixed in 

 direction, and for this reason the doublets, &c., produced by the magnetic field 

 are polarised. On the other hand, the doublets, c^c, existing in natural spectra 

 are not polarised, and this is what we should expect when we consider the effects 

 of collisions. 



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

 of it. It is merely postulated tliat certain perturbations exist, and their effects 

 on the pure radiation frequencies are examined. If, however, we treat tlie 

 question 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 a 



