Mass, Energy, and Radiation. 689 



when the temperature is less than this only a fraction of 

 the molecules will acquire any additional energy from the 

 rise in temperature. When a large number of molecules 

 have acquired no additional energy at all, it would seem 

 improbable that any large number should hare acquired the 

 extra energy corresponding to additional degrees of freedom, 

 for example, for a diatomic molecule to have acquired the 

 energy due to its rotation round the centre of mass as well 

 as that corresponding to energy of translation, but unless it 

 did this the specific heats of diatomic gases at temperatures 

 less than 1*8 x 10 6 x w x 273 absolute, would approximate to 

 those of monatomic gases ; this consideration shows that co 

 must be less than 10~ 8 . Again, we know from Michelson's 

 experiments on the green line of mercury that the source of 

 this line can give out more than 400,000 vibrations without 

 abrupt change of phase ; from Planck's rule, the energy in 

 this radiation is that due to the fall of the atomic charge 

 through a potential difference of 2*5 volts, i. e. is about 

 1/(2*4 x 10 4 ) of the energy of an electron. If there is only 

 one mass particle per wave-length of the radiation, there 

 will be more than 4xl0 :> mass particles in this amount of 

 energv, so that the energy of one of these particles will be 

 less than 1 /(2'4 x 10 4 x 4x 10 5 ) of that of any electron. 

 Since the ratio of the masses is the same as that of: tho 

 energies we conclude that at least 10 10 and probably many 

 more mass particles are required to supply the mass of an 

 electron. 



If energy is indivisible beyond 'a certain limit, then the 

 inverse square law of electrical attraction cannot hold at 

 all distances. For when this law holds, the energy outside 

 a sphere of radius r with its centre at an electron, bears to the 

 energy of the electron the ratio a/r, where a is the radius of 

 the electron; hence if a/r is less than w the energv outside 

 the sphere will be less than the energy possessed by one 

 mass particle. Thus since the particles are indivisible there 

 would be no particles and no force when r is greater 

 than a/co, so that the law of electric force cannot be 

 the inverse square . law over more than a certain finite^ 

 distance. 



