in the Magnetic Field. 175 



and remark that this will represent two superposed vibrations 

 of different periods, if we regard A as a periodic function of 

 the time instead of a constant. That is, if we take A to be 

 of the form a sin nt, we shall have 



z = a sin nt sin Clt = -p[GOS (ft — n)t — cos {Q, + n)t] } 



which represents two vibrations of equal amplitude and of 

 frequencies (ft — ?i)/2tt and (ft + w)/27r as required to produce 

 the quartet. The magnitude of n determines whether the 

 separation of the constituents of the central line A (fig. 2) 

 shall be less than, or greater than, the separation of the side 

 lines B and C, and if the former is sensible while the latter is 

 insensible we are presented with the case depicted in fig. 6 — 

 although, as I have said before, my observations do not 

 confirm the existence of this case. 



The supposition made above to account for the doubling of 

 the middle line, viz. that the amplitude of the z component of 

 the vibration varies periodically, is one which appears to be 

 justified when we consider the nature of the moving system and 

 the forces which control it. For the revolving ion is part of 

 some more or less complex system which must set in some 

 definite way under the action of the magnetic field — say with 

 its axis along the direction of the magnetic force — and, in 

 coming into this position, the inertia of the system will cause it 

 to vibrate with small oscillations about that position of equi- 

 librium, and this vibration superposed on the precessional 

 motion of the ionic orbit gives the motion postulated above 

 to explain the quartet. 



This, indeed, comes to the same thing as a suggestion made 

 by Professor Gr. F. FitzGrerald about a year ago — shortly 

 after I discovered the existence of the quartet form (Oct. 1897). 

 In Professor Fitz Gerald's view, the ion revolving in its orbit is 

 equivalent to an electric current round the orbit, and therefore 

 the revolving ion and the matter with which it is associated 

 behave as a little magnet having its axis perpendicular to the 

 plane of the orbit. The action of the magnetic field will be to 

 set the axis of this magnet along the lines of force, and in 

 taking up this set the ionic orbit will vibrate about its position 

 of equilibrium just as an ordinary magnet vibrates about its 

 position of rest under the earth's magnetic force. 



In a similar way a periodic change in the eliipticity of the 

 orbit produces a doubling of the lines, while a periodic 

 oscillation in the apsidal motion renders the line nebulous or 

 diffuse; and by treating these cases in the foregoing manner 

 ■the corresponding forces may be discovered. It is clear, 



