of Electrons, and the Spectrum of Canal Rays, 667 



It is probable that a group of electrons in periodic motion 

 in any closed curve whatever can be permanent by itself, 

 provided its electrons pass in succession through every point 

 of the curve at regular and equal intervals ; but it by no 

 means follows that a system built up of such groups is 

 permanent. Any two groups, on account of their permanent 

 motion, disturb each other and emit waves, whose energy is a 

 drain on the energy of the groups ; hence the system is not 

 permanent. But the drain of energy, and consequent change 

 in structure, can proceed extremely slowly, provided all the 

 most powerful waves due to perturbations are destroyed by 

 interference between the several electrons of each group. 

 This occurs for circles of equidistant electrons, provided they 

 have a common axis of rotation and are not too close together, 

 certain combinations of circles being excluded ; but it does 

 not occur for groups other than circles. 



Therefore we make the following assumption (A) : — The 

 system (2) when at rest consists of a number of circular rings 

 of equidistant electrons in rotation about a common axis, in a 

 controlling field of such a kind as to make the system stable. 

 The number of electrons, the angular velocity and radius of 

 each ring, and the mutual distances of all pairs of rings, are 

 such that the system is quasipermanent. 



§ 12. At a great distance from the quasipermanent system 

 at rest the electromagnetic forces T', P' are the sums of terms 



of the type — C . |p(^-p) —m<j> I , where p, m are con- 

 stants depending on the type of vibration producing the 

 forces. The polar axis can be chosen so that the amplitude 

 A is a function of 6 alone and at most changes sign when we 

 put 7T — in place of 0. 



We shall make a second assumption (B) : — 



The system of reference (2') has the property just 

 mentioned. 



In order to explain the negative Michelson result Lorentz, 

 as is well known, makes the assumption that the system (2') 

 is identical with the system (2) when at rest. In this case 

 assumption (B) at once follows. 



AVe can now average the expressions (8}..., (1) for the 

 time, (2) for the coordinate <f>. 



(1) Let us average for an interval of time containing a 

 large number of periods. 



During this interval (2) moves, and the relative coordinates 

 of a fixed point change by amounts of order UX/GV. On 

 account of the smallness of X/r' these changes may be 



