Theory of X Rays and Photoelectric Rays. 543 



energy in thin filaments is introduced not so much to explain 

 the want of symmetry and the magnitude of the velocities 

 produced as to account for the fact that only one electron 

 here and there appears to be affected as the rays pass through 

 the metal, and the further equally curious fact that the 

 velocity of the ejected electrons is independent of the distance 

 from the source of the X rays. 



Some of the main difficulties associated with the theory 

 which attempts to explain the production of the j3 rays from 

 the free electrons between the molecules are, in addition to 

 those already mentioned : — 



(a) The theory, though accounting for the necessary want 

 of symmetry in the case of the ft rays ejected by X rays, 

 gives far too small a want of symmetry for photoelectric 

 electrons, which travel with much smaller velocities (velocities 

 of the order 5 x 10 7 cm./sec.) . 



(fr) The theory gives no explanation of the variation for 

 different metals in the want of symmetry in the {3 rays 

 produced by X rays. 



(c) It does not readily lead to an explanation of the law 

 relating the velocity of photoelectric electrons and the fre- 

 quency of the light, though there are one or two ways in 

 which it may be made to do so — e. </., the view suggested on 

 p. 539. 



A much more powerful theory evolves when we consider 

 the ejected electrons to come, not from the free electrons, 

 but from the electrons inside the atoms. 



(2) Action of a wave-train on the electrons in the atoms. — 

 We shall consider the case where a train of electromagnetic 

 waves passes over an atom. JSome of the electrons in the 

 atom will have a natural period equal to that of the waves, 

 and these will absorb energy rapidly from the waves. When 

 the electron has got a sufficiently large amount of energy it 

 will be able to get away, and we shall find that when it 

 escapes the ratio of x, the velocity in the direction in which 

 the wave is moving, to y, the velocity transA r erse to the 

 direction of propagation of the wave, is no longer dependent 

 only on y, and other facts with regard to the relationship 

 between the velocity of ejection, frequency, want of symmetry, 

 &c. will evolve. 



Let Ye be the potential energy of the electron. The 

 equations of motion are : — 



m dry dV v , . / 



tJ + w ** ] ' (1) 



md 2 x BV dy Y dy .. , _,^ N 



