Light Absorption and Fluorescence. 9 



there is no reason to assume that only one electron can 

 be so shifted. There may be many such electrons which 

 can be shifted, the amount of energy being the same for 

 each ; and consequently it will be possible for one atom 

 to absorb 1, 2, 3, etc. elementary quanta in the same unit 

 of time. The atom will therefore exhibit frequencies which 

 are 1, 2, 3, etc. times its fundamental frequency. The two 

 atoms specified above will in the free state exhibit fre- 

 quencies of n x 9 X 10 10 and n x 1*5 X 10 11 respectively, where 

 « = 1, 2, 3, etc. The molecule formed by the combination 

 of these two atoms will also exhibit these frequencies, but 

 now the upper limit of n will be fixed by the critical 

 quantity previously defined. Since the least common 

 multiple of the two atomic frequencies is 4*5 xlO 11 , the 

 upper limits of n for the two atomic frequency series shown 

 by the molecule will be 4 and 2 respectively, since when 

 n = o and 3, the two atomic frequency series will converge in 

 the true molecular frequency. Perhaps, therefore, the true 

 molecular frequency will be better understood as the con- 

 vergence frequenev of the atomic frequency series than as 

 the least common multiple of the atomic frequencies. 



We may now consider one of the true molecular fre- 

 quencies. Since the molecule can absorb as a whole 

 one quantum at that frequency, and since also each atom 

 within the molecule can absorb one or more elementary 

 quanta, there is no reason why the two processes should 

 not be simultaneous. The molecule will then absorb in 

 one unit of time an amount of energy equal to the sum 

 of one true molecular quantum and one or more elementary 

 quanta. This will result in the establishment of the sub- 

 sidiary frequencies M + ?iA, where M is the true molecular 

 frequency, A is the atomic frequency, and n = l, 2, 3, etc., 

 the upper limit of n being fixed by the critical value as 

 already explained. The essential point is that, although 

 one quantum is absorbed at a subsidiary frequency, the 

 molecule itself as a whole only receives one molecular 

 quantum. The amount of energy in excess of this is 

 taken up by the atoms, and if this leads to the energy 

 content of the atoms being greater than that associated 

 with them when the molecule is in radiant equilibrium with 

 its surroundings, the excess amount will be radiated as 

 elementary quanta. 



Similarly, there will be established the subsidiary fre- 

 quencies M — ;iA, for the following reason. Let the 

 molecule which is in radiant equilibrium with its sur- 

 roundings absorb a quantum of energy at one of its atomic 



