478 Prof. 0. W. Richardson on the Theory of 



atoms which are returned to each unit area of the substance 

 in unit time is 



N 1 = 7i^TI=AT^J ET2 , (4) 



where ft is a constant readily calculated from the kinetic 

 theory of gases and A is thus still independent of T and 

 characteristic for the substance. 



Let eF(v) be the number of atoms emitted from unit area 

 of the substance in unit time in the presence of unit energy 

 density of frequency between v and v + dv, and assume that 

 the number of atoms emitted in the presence of the whole 

 spectrum characteristic of T is, using Planck's formula, 



H,-5£f>,)-£-*. ••• (5) 



J"o 6 ET — 1 



This equation contains the important assumption, which does 

 not yet seem to have tested experimentally, that the number 

 of atoms emitted by a given amount of light is the same 

 whether the light is undecomposed or is broken up, without 

 loss of energy, into its spectral constituents. In other words, 

 it assumes that the photochemical substance acts as its own 

 grating. This may be justified as being the simplest as- 

 sumption which is consistent with the conclusions drawn 

 from experiments on photoelectric action, that the number 

 of emitted electrons is simply proportional to the intensity of 

 light of definite spectral composition but varies greatly when 

 equal energies of light of different frequencies are compared. 



In (5) we have taken the lower limit of the integral to be 

 finite and equal to v . This is to cover the possibility, which 

 appears to be demanded by the results of photoelectric 

 experiments, that eF(v) is a function which takes the value 

 zero when v = v and does not exist for values of v between 

 and v . If eF(i>) is a function which extends over the 

 wdiole spectrum the case can be provided for by simply 

 putting v = 0. 



Now consider the kinetic energy which is carried away 

 from the substance by the atoms liberated under the in- 

 fluence of the radiation. If eF(v) has the properties we have 

 attributed to it, this amount of kinetic energy is, by virtue 

 of (2) and (5), 



c J*o <■ L J e™ -1 



2tt^ 



(6) 



\ °° <f>(v)e¥(v) -J^—dv-K 2 (w- |bt) . (7) 



* *V RT 



