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



§ 13. The equations (14) . . . (22) give the solution of the 

 problems relating to the radiation from a single system 

 moving with uniform velocity U, on the assumptions (A) and 

 (B), the values of T /2 , P' 2 being those of the system of 

 reference (S') for the corresponding type of vibration. 

 Since the process of averaging for t gets rid of products of 

 forces due to different types of vibration, the total radiation 

 from the system is simply the sum of a series of terms such 

 as those considered, and each of these may be treated 

 separately. 



When the external field, in which the system- is moving, 

 contains no terms of the period of the vibration considered, 

 the forces T x , P' are those due to the system alone. But 

 when terms of the same period are present resonance effects 

 are produced ; in this case the values of X . . . in (6) of § 7 

 must be supplemented by the addition of terms X . . . due to 

 the external field ; in addition T', P' include terms produced 

 from X . . . by resonance, as well as terms independent of the 

 external field. The values of P, Q, B given by (7) must be 

 correspondingly supplemented. 



When we wish to represent the action of a quantity of 

 radiating gas, or of a bundle of canal rays, by means of a 

 group of systems of electrons such as the one considered 

 above, resonance effects necessarily arise in consequence of 

 the interaction of the several systems. These effects are 

 particularly large when two systems happen to approach very 

 near to one another, that is, at collisionSo Since we have 

 supposed our system to be moving with uniform velocity, 

 our analysis can only apply to the interval between successive 

 collisions of the system, during which its distance from other 

 systems is so large that resonance effects are comparatively 

 unimportant. In extending our results to the case of a 

 group of svstems we shall therefore make a third assumption 



In the groups of systems to be considered, the density, i. e. 

 the number of systems per unit volume, is so small, and the 

 mean free path of a system so large, that the interval between 

 successive collisions is a large multiple of the duration of a 

 collision. 



This is equivalent to assuming that at any one instant the 

 number of systems in collision is a small fraction of the wdiole 

 number. 



It must be remembered that for ions the radius of 

 appreciable action is very much larger than for a neutral 

 system, such as an atom, and therefore the duration of a 

 collision must be reckoned as longer in proportion. On the 



