Interaction between Radiation and Electrons. 1069 



for the interchange of energy at collisions would diminish in 

 the same ratio, and, if so, the principles applicable to the 

 partition of energy would possibly be unaltered, provided 

 that the velocities attributed to the heavy particles were not 

 much smaller than the average velocity of the gas particles. 



There is, however, an important new condition introduced. 

 The probability laws governing the distribution of energy in 

 gases are arrived at by conceiving encounters to take place 

 between heavy and light particles successively. When we 

 have multiplied the light particles ad infinitum, however, by 

 the process of division above suggested, we have now to 

 conceive that instead of the mass M having successive 

 encounters, altering its velocity as stated, for instance, by 

 IDdgeworth, there would be simultaneous encounters on all 

 sides. In a direction at right angles to the motion of M 

 there would be no momentum given to M. When the 

 velocity of M is comparable with the velocities of the light 

 particles, however, there would be more particles in contact 

 with M in front than in the rear, and M would lose 

 momentum. 



In working towards something supposed to be analogous 

 to the aether, however, we may postulate very high velocities 

 for the ultimate particles — velocities, say, of the order of 

 magnitude of the velocity of light. In that case, a heavy 

 particle moving in such a medium, with velocity of a lower 

 order of magnitude, would have practically as many light 

 particles, at any moment, in contact in front as in contact 

 behind. The impacts would be transmitted through M, 

 which would have its velocity unaltered. M, then, once in 

 uniform motion, would move through such a gas as through 

 a perfect fluid, without loss of energy — or only extremely 

 slow loss. 



It may be objected that electrons also have very high 

 velocities, and that they are the " heavy particles " dealt with 

 by Jeans. The introduction of high velocities involves, 

 however, a further consideration which can be neglected in 

 dealing with ordinary gases. 



The length of the free path is made indefinitely small, 

 although, if we keep to the idea of a limitation of the amount 

 of mass (i. e. conceiving the masses to be diminished in 

 proportion to the increase of numbers), there is still the 

 possibility of motion of the individual particles. The time 

 occupied by free motion may be so reduced, however, that it 

 is no longer small compared with the time occupied by an 

 encounter, and may be less than such time. 



In that case, the heavy particle, being impinged upon by a 



