the Magnetic Influence on Spectra. 505 



considered, radiation of this kind will usually be practically 

 nonexistent. Thus each spectral line of the vibrator will be 

 split up inio two with righthanded and lefthanded circular 

 polarizations when seen along the axis, and plane-polarized 

 with phase difference of half a wave-length when seen at 

 right angles to it, and with differences of frequency the same 

 for all lines in the spectrum, as in the special case above. 

 This simple statement applies to all systems in which the 

 electric charge of each mobile ion in the vibrator is pro- 

 portional to its effective mass, which implies that the charges 

 of the mobile ions are all of the same sign. 



3. The characters of the three principal oscillations in § I 

 may be determined in the usual manner by substituting in 

 the equations of motion (x, y, z) = (x , y , Zo)e tpt and deter- 

 mining (xq, y , z ) from the resulting system of linear 

 equations. But algebraic reductions will be avoided by 

 taking the magnetic field to be along the axis of z, so that 

 {I, in, n) = (0, 0, 1), as might in fact have been done from the 

 beginning. The equations of motion are then 



x = — a?x -f- Ky , y=— a~y — kx } 'z=— o?z. 



They show at once that the unmodified principal vibration is 

 a linear oscillation parallel to the c-axis. As regards the 

 others, writing (x, if) — (x , yo)e^ we have 



(a 2 — p 2 ) x = tfcpy, (a 2 —p 2 )y = iicpx ; 



thus ^ 2 + «p — a 2 = 0, or very approximately p = a + h K as 

 before ; and separating the real parts of this solution 



A M A . 



X = —5 5 cos pt, %j = — sin pt, 



ar—jr * icp 1 



which to our order of approximation represents motion round 

 a circle in the plane of (x, y) righthanded or lefthanded 

 according to the value of p that is taken*. The character of 

 the radiation ' from such a vibrator is thus precisely indepen- 

 dent of the orientation of its orbit with respect to the magnetic 

 field. With a large number of such vibrators, orientated 

 indifferently, every spectral line seen in a direction at right 

 angles to the magnetic field would be split up into three lines, 

 each of the same breadth as the original, the middle one plane- 

 polarized at right angles to the magnetic field, the outer ones 

 in the direction of the field : as the aggregate light must be 



* This is no doubt the analysis recently indicated, by Prof. FitzGerald 

 in ' Nature/ Sept. 1897. 



