658 Mr. Gr. A. Schott on Radiation from Moving Systems 



maximum of intensity, which increases with the velocity, and 

 that more rapidly for high-frequency lines. Mainly because 

 of the dark space, he considers that the energy radiated in 

 the displaced line is transformed from kinetic energy. of 

 translation, not by the agency of collisions, but by the direct 

 action of radiation pressure. The energy radiated in the 

 undisplaced line is attributable directly to collisions. He 

 formulates the following question : — 



" Given a system of electrons in orbital motion, so arranged 

 that their radiation into the external medium is mutually 

 compensated'''' (presumably by interference); u does the 

 compensation subsist when the system is given a motion 

 of translation through the aether? " 



§ 3. The following theoretical investigation of §§ 4-24 

 supplies the answer to this question. For a uniform trans- 

 lation it is in the affirmative, in so far as no periodic waves 

 are emitted in consequence of the motion ; for non-uniform 

 motions periodic waves are emitted when the changes in 

 velocity and orientation of the system are rapid enough. It 

 is further shown that the radiant energy cannot be due to 

 radiation pressure, since the work done by that pressure is 

 but a very small fraction of the energy radiated. 



The rest of the paper is devoted to a brief discussion of 

 Stark's experimental results in the light oE the theoretical 

 conclusions arrived at in the first portion of the paper. 

 [vide Note I.] 



§ 4, Lorentz* has given a general method of deducing 

 the electromagnetic field due to a system of electric charges, 

 in motion relative to a set of axes, which are themselves 

 moving with a uniform velocity less than that o£ light, from 

 the field due to a second sytem in motion relative to a fixed 

 set of axes. 



Let E be the vector which represents the electric force, 

 (X, Y, Z) its rectangular components in the actual system 

 (2), H, (L, M, N) the magnetic force, V, (u, v, w) the relative 

 velocity, p the electric volume density. 



Let accented letters denote the same quantities in the 

 system o£ reference (2')- 



Let U be the velocity of the moving axes, C the velocity 

 of light, k — y/l — V 2 /C 2 ; and let Ox be taken in the direction 

 ofU. 



The relations between the coordinates, time and velocities 

 of the two systems are as follows : — 



(x, y, z) are coordinates of a point relative to axes fixed in 

 the aether, supposed at rest in LoremVs theory. 



* Abrahauiet Langevin, Ions, Electrons, Corpuscules, vol. i. p. 477. 



