Theory of X Rays and Photoelectric Rays. 547 



wholly in the x direction, but where u is only a fraction of v. 

 We shall in this way be led to a theory more in accordance 

 with the facts of the photoelectric effect. There are two 

 ways in which w T e may proceed. We may accept as a hypo- 

 thesis that the electron absorbs energy in Planck units, 

 either because the pulses themselves carry it in these units, 

 and are so narrow that they give up all their energy to the 

 electron when they pass it, or because the mechanism of the 

 atom is such that the energy becomes absorbed in units. 

 On the other hand, we may attempt to derive the result in a 

 manner which is perhaps more satisfying to the mind, that 

 is to say, by considering the actual effect of the wave on the 

 electron, in which case we are unfortunately obliged to make 

 some assumptions with regard to the relationship between 

 the restoring forces and the displacements. 



The first method leads to a result very quickly. If N is 

 the smallest number of whole Planck units necessary to free 

 the electron, the quantity represented by E on p. 544 becomes 



6*5tfN 

 equal to -r— — X 10 ~ 2 '. If co is the actual amount of energy 



6*5Nc 

 necessary — x 10 ~ 27 — co will be of the order of a single 



Planck unit, and we may take half this quantity as very 

 fairly representing \mv 2 . Thus we see that v 2 is proportional 

 to the frequency c/\, and is such that 



V 2 = 6^. x10 -h=4^, . . . . (17) 



so that if in (15) we pat 



. . 9 e Tr 6*5Nc v 1A 97 6 # 5Nc 

 i2/ 2 +-V= — — xl0" 27 = — — , 

 2J m uiX A, 



we rind • 6*5 N , u Ni? n Q , 



x=u= and - = — . . . (lo) 



A, v c 



Thus in the case of photoelectric effects where X= say 

 2xl0" 5 , we find u = 10 8 , which is of the correct order of 

 magnitude. In order to obtain a want of symmetry of the 



order ^expressed by - =1/15, which is about the correct 



value, it would be necessary to have N = 20. 



Adopting the second method of procedure, in which we 

 do not make use of the Planck unit, we must, following the 

 usual practise in such cases, imagine the electrons to be 

 constrained by forces proportional to the displacement; and 



2P2 



