Asymmetric Emission of Secondary Hays. 147 



that under the supposed conditions the average energy of 

 the electrons instantaneously present in the slab remains 

 invariable. It is important to observe that the energy liv 

 which we have to consider here, is that which the disrupted 

 electrons possess before, not after, they leave the slab. 



But the incident beam is depleted of momentum as well 

 as energy. Without committing ourselves for the moment 

 as to the nature of this momentum, let us suppose that when 

 the incident beam loses an amount E of energy it loses an 

 amount \E of momentum. On the electromagnetic theory 



a, is constant and equal to — , where c is the velocity of light 



c 



in vacuo. According to the hypotheses which we have 

 adopted, the whole of this momentum is conveyed in the 

 first instance to the undisrupted electrons. Now consider 

 the increase of momentum of the slab and contained electrons 

 in any small interval of time. It arises from : — (1) the 

 momentum of electrons which come into the slab, [2) the 

 momentum, reckoned negatively, of the disrupted electrons, 

 and (3) the momentum accumulated during the interval by 

 the electrons present in the slab. Since the average state of 

 the electrons instantaneously present does not change with 

 time, it follows that the difference of (1) and (2) is equal to 

 (3). When (1) is zero, (3) is the momentum derived from 

 the radiation, if the principle of the conservation of 

 momentum is held to apply to the whole system of radiation 

 and matter. It follows that the momentum which is 

 acquired by all the absorbing electrons from the radiation, 

 is exactly equal to the sum of the momenta, measured at the 

 moment of disruption, of all the electrons disrupted during 

 the same interval. But since the energy absorbed is N/iv 

 the value of the former amount of momentum is \NJiv. If 

 u is the average component of velocity of the disrupted 

 electrons, in the direction of incidence of the radiation, an 

 alternative expression for the momentum of the N electrons 

 is Nmtt. Thus : — 



u= =«« (1) 



if v 2 is the average value of the square of their velocity at 

 the instant of disruption. If we take the expression for the 

 momentum of the radiation given by the electromagnetic 

 theory, 



cm Ac 



L2 



