Spectra and Planck's Law. 437 



considering, possessing vibrators able to respond to any vibra- 

 tions within a wide range of frequency. Thus, if light of any 

 frequency between these limits were to fall on the metal it 

 would find some electrons whose frequency under the magnetic 

 force at the place where the} 7 were situated was the same as its 

 own ; these would acquire a high velocity. If an electron is 

 to get free, it must get to a place where the magnetic force 

 vanishes, because, as we can easily prove, the effect of the 

 magnetic field on an electron displaced from a position of 

 equilibrium, is the same as if there were an attraction on the 

 electron to the point equal to B e/m times the displacement 

 of the electron. Suppose that P is a place where the magnetic 

 induction vanishes, and where consequently an electron can 

 get free. Suppose that Q is the place from which the electron 

 to be liberated at P starts. To enable it to get from Q to P 

 it must acquire an amount of energy equal to iv, where w is 

 the work required to move an electron against the electric 

 field from Q to P. If it is to acquire this by radiation, it 

 must be by resonance, so that the radiant energy from which 

 it gets it must have the frequency of the free vibrations of 

 the electron at Q. Since the magnetic force vanishes at P 

 this frequency is, by equation (2), equal to ic/Ji. Thus the 

 electron at Q, by absorbing energy of frequenc}' n, can be 

 liberated at P with an amount of Potential Energy equal 

 to 7m. 



This would produce the well-known photoelectric effects. 

 If Q were to absorb a smaller amount than w of energy from 

 the radiation, it would not get liberated. After the radiation 

 had passed over it this energy would be again radiated by the 

 electron at Q vibrating under the magnetic force at Q with 

 the frequency n. Thus the absorbed radiation would be again 

 radiated as radiation of the same frequency, and there would 

 not be any transformation of energy. For the energy to be 

 transformed, energy equal to w must be given to Q ; and 

 since iv = 1m, we get the result given by the quantum theory 

 that the transference from radiant to potential or kinetic 

 energy takes place by definite quanta each equal to hn. 



The explanation of the photoelectric effect assumes the 

 possibility of finding in the metal an electron with a natural 

 frequency n, where n may be any assigned number within a 

 wide range of values. In a complex system like a metal this 

 seems probable ; and it is noteworthy that the photoelectric 

 effects are on quite a different scale in metals from what 

 they are in gases ; thus Hughes found no trace of ionization 

 when ultra-violet light was totally absorbed by the vapour of 

 zinc ethyl, though when the same light fell on a zinc plate 



