510 Mr. J. Larmor on the Theory of 



in H vanishes because dM/dt is null at the beginning and 

 end of the operation. The aggregate amount of magnetic 

 force thus propagated in the spherical sheet is the same 

 as the steady magnetic force due to a permanent steady 

 current-element of intensity equal to M/St, or ev : it is clear, 

 in fact, that this must be so, if we consider a sudden creation 

 .of this current-element and remember that its magnetic 

 field establishes itself by spreading out ready formed with 

 the velocity of radiation. 



The magnetic force at a point at distance r due to a moving 

 ion thus depends on the state of the ion at a time r/c previously; 

 for near points it is in the plane perpendicular to r. at right 

 angles to the projection v of the velocity of the ion on that plane, 

 and equal to evr~ 2 . For vibrations whose wave-length in free 

 aether is very great compared with the dimensions of the 

 molecular orbit, if we interpret magnetic force as velocity 

 of the aether, the vibration-path of a point attached to the 

 aether, and close to the vibrator, will be in the plane transverse 

 to r, and similar to the projection of the orbit of the electron 

 on that plane when turned round through a right angle *. 

 If the condition of wave-length very large compared with 

 molecular magnitude were not satisfied, phase-differences 

 would sensibly disturb this result, and in effect each spectral 

 line would be accompanied, more or lets, by its system of 

 harmonics. 



As the vibration of a near point in the aether is thus similar 

 to the projection on the wave-front of the vibration of the 

 electrons in the molecule, it is verified that the free periods 

 of the radiation are those of the system of ions. 



10. It might appear also at first sight that every steady 

 orbital motion must rapidly lose its energy by radiation just 

 as vibrations on the conductor in § 7 would do if the ions on 

 it formed a continuous charge. On the other hand it might 

 be argued that what we have really been calculating is the 

 amount added on to the previous motion in the medium 

 by the successive displacements of the electrons ; and in 

 the cases of steady motion it is just this amount that is 

 needed to maintain the permanency of the motion in the 

 aether, which of itself has a tendency to be carried away. 

 Thus in the parallel case of the movement of a very long- 

 stretched cord when an end of it has a steady circular motion 

 imparted to it, an analysis in the ordinary way leads to a 

 train of circular waves running along the cord ; but there 



* For a different treatment of similar topics cf. H. A. Lorentz, " La 

 Theorie Electromasnetique de Maxwell," §§ 112-119, Archives Neer- 

 landaises, 1892; u Versuch . . . ," 1895; quoted by Zeeman, Phil. Mug. 

 March, 1897. 



