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

 in the surrounding aether, to the average amount A. When 

 a stationary state is reached we have R=W + K + A. 



By the results of §§16, 19-22, we have W = a5 + 6B2, 

 where a, b are of the order U 2 /C 2 , while R, R 2 are, to the 

 first order, independent of U/C ; since _each varies as the 

 square of the amplitude of vibration, R 2 /R and W/R are 

 independent of the amplitude and depend only on the struc- 

 ture of the system. 



A varies as the energy- density of the field around the 

 system and is of the form cR4-E ; cR denoting the part of 

 the energy-density due to radiation from neighbouring 

 systems, E that due to external sources. Hence we may write 

 A = c?(cR + E), where c, d depend on the nature of the systems 

 and their mean distance apart, but not on the amplitude of 

 vibration. 



With these values for W, A, we get 



- K + 4E 



l—a — bR 2 /B,-cd 



This equation shows that, because W is very nearly pro- 

 portional to R, R is determined by the external energy E, 

 and by the kinetic energy K transformed into energy of 

 vibration at collisions. Resonance between the several 

 systems and radiation pressure merely increase the value 

 of R. 



It is well to bear in mind that R does not directly measure 

 the radiation emitted by the group of systems constituting 

 the canal-ray bundle or radiating gas as a whole ; for on 

 account of resonance the greater part of R may be absorbed 

 by neighbouring systems. In § 24 we saw that resonance 

 will generally be diminished between systems moving with 

 different velocities, on account of Doppler effect due to 

 relative motion ; it is hardly possible that for systems moving 

 with the same velocity it can be appreciably greater than for 

 systems at rest ; for the structure of a system is only altered 

 by motion by quantities of the second order in U/C. Thus it is 

 unlikely that resonance can play a greater part in a bundle 

 of canal rays than it does in a radiating gas with atoms 

 moving with relatively small velocities. 



§26. Thus Stark's hypothesis cannot be reconciled with 

 an electron theory ; it is therefore of importance to enquire 

 how far his experimental results require that hypothesis. 

 The fundamental results are given in §§ 11-12, 14.-16 of his 



