890 Prof. J. S. Townsend and Mr. V. A. Bailey on 



an electromagnetic wave only in definite quantities which 

 are proportional to the frequency n of the radiation. Thus 

 if the molecules of a gas have a free period of vibration of 

 frequency n } they can only absorb energy in amounts 

 which are exact multiples of the quantity Jin, Ji being Planck's 

 constant. 



It is convenient to express this quantity in volts, that is, 

 the energy acquired by an electron moving under the action 

 of an electric force between two points differing in potential 

 by a certain number of volts. If n be the frequency of the 

 yellow sodium line, the quantity of energy Jin corresponds to 

 a fall of potential of about 2 volts. 



When electrons moving with high velocities collide w r ith 

 molecules the frequency of the radiation which is excited 

 depends on the velocity, and if the quantum theory be 

 extended to cases where energy is supplied to molecules by 

 the impacts of electrons, the highest f requency which could be 

 excited by an electron moving with a velocity u is obtained 

 from the relation Jin—(mu 2 )/2. Also in a gas containing 

 molecules which have no free periods of vibration less than 

 that of the light in the visible spectrum, they would absorb 

 no energy from electrons moving with velocities smaller 

 than that corresponding to potentials of about 2 volts. 



The mean velocity of agitation of electrons corresponding 

 to the various values of the ratio Z/p may easily be obtained 

 in volts from the values which have been found for the 

 quantity k. In a gas at 15° C. the energy of agitation of 

 the molecules corresponds to a fall of potential of l/27th 

 of a volt, so that Jc/27 is the energy of the electrons ex- 

 pressed in volts. Thus in nitrogen at a millimetre pressure 

 the value of k is 54 for electrons moving under a force of 

 15*2 volts per centimetre, so that the mean velocity of 

 agitation corresponds to a potential fall of 2 volts. In this 

 case the total number of collisions made by an electron with 

 molecules (it)Wl) is about 470 in moving through a distance 

 of one centimetre in the direction of the force and the 

 average loss of energy in each collision is approximately 

 -^q volt. 



In order to explain the loss of energy of electrons due to 

 collisions with molecules on this theory, it is necessary to 

 suppose that in a small proportion of the total number of 

 collisions there is a comparatively large loss of energy 

 and in most of the collisions there is no loss (excepting the 

 extremely small loss corresponding to the momentum trans- 

 ferred from the electron to the molecule, and the loss by 

 radiation due to acceleration of the electron, both of which 

 may be neglected in comparison with the observed effect). 



