678 Mr. G. A. Schott on Radiation from Moving Systems 

 on the right-hand side of the equations, these become 



.(x + J»-S«)-J^^±s! + g-*x) 



__ 



^ /U dm u 



JAfidfiG 



d /U (i?n zi 2 \ 



d(mv) 

 dt 



d(mw) 



( T+ c L 7; N ) = (rW-oTi*c*)t (44) 



On the left-hand side the coordinates, velocities, and forces 

 have their actual values, including disturbances of all kinds. 

 The effect of the translation is represented by the disturbing 

 force on the right-hand side, which causes the system to 

 deviate from the configuration it would have had in the 

 absence of translation. A knowledge of the equations of 

 motion of the system thus enables us to calculate the deviation 

 due to translation. To this we now proceed. 



§ 19. In accordance with assumptions (A), (B) of §§ 11, 12, 

 we shall suppose the system to consist of a number of circles 

 of equidistant electrons, each revolving with its own uniform 

 velocity about the common axis, and so adjusted as to be 

 stable and quasipermanent. Perturbations of a ring due to 

 its neighbours are neglected, so that only their steady field 

 need be taken into account. The forces on any one electron 

 due to the rest of its ring are obviously constant ; thus by, 

 what has been said, the total forces, due to the whole system, 

 are also constant. 



Consider an}' one ring of n electrons, of radius p and 



angular velocity co, so that /3= ^ ; let 



be its centre, P an electron. For 

 initial line 01 take the projection on 

 the plane of the ring of the velocity 

 of translation U. For the 2th electron 

 we write 



n 1 

 where 8 is a constant. 



Take moving axes Pf , P77, Pf along the tangent, towards 

 the centre, and parallel to the axis. The projections of U in 

 these directions are — U sin a sin </>, — U sin a. cos <£>, U cos a, 

 where a is as before the angle between U and the axis. 



