234 REPORTS ON THE STATE OF SCIENCE. — 1920. 



violet legion of the spectrum. The factors governing these various alternatives 

 are determined by the conditions under vrhich the molecules exist. It will be 

 seen from this that a molecule can acquire one or more molecular quanta at the 

 infra-red fundamental in three different ways : by exposure to radiation equal 

 to its atomic frequencies, by exposure to radiation of frequency equal to the 

 infra-red fundamental, or by exposure to radiation of a frequency which is an 

 exact multiple of the infra-red fundamental. 



The next point to be considered is the structure of the absorption bands, that 

 is to say, the system of subsidiary frequencies which are always found asso- 

 ciated with the true molecular frequency when the absorbing or radiating power 

 of molecules is examined at ordinary temperatures. These subsidiary frequencie.s 

 have been attributed by Bjerrum -" to the rotation of the molecules and by 

 Kriiger^^' to their precessional motions. Without discussion in detail it may 

 be pointed out that both these theories break down. In the first place neither 

 theory takes account of the fact that the subsidiary frequencies are due to the 

 atomic frequencies, and in the second place it is necessary for the purpose of 

 these theories to postulate impossibly large variations in the values of the 

 molecular rotation or molecular precession. 



On the other hand, the conception now put forward of elementai'y atomic 

 quanta of energy, whereby definite atomic frequencies are established, would 

 seem capable of affording a very simple and straightforward explanation. More- 

 over, this conception leads to the establishment of exact frequencies without 

 any possibility of variation. The case may again be considered of the molecule 

 formed by the combination of the two elementary atoms for which the elementary 

 quanta are 9 x 6-56 x 10"" and 1-5 x 6-56 x IQ-ie erg, and which therefore exhibit 

 the characteristic frequencies 9 X 10^° and 1-5 X 10" respectively. Ex hypothesi 

 the elementary quantum is associated with the shift of one electron from one 

 stationary orbit to another, and, of course, there is no reason to assume that 

 only one electron can be so shifted. There may be many such electrons which 

 can be so shifted, the amount of energy being the same for each; and conse- 

 quently it will be possible for one atom to absorb 1, 2, 3, &c., elementary quanta 

 in the same unit of time. The atom will therefore exhibit frequencies which 

 are 1, 2, 3, &c., times its fundamental frequency. The two atoms specified 

 above will in the free state exhibit frequencies of « X 9 X 10'° and « X 1"5 X 10" 

 respectively, where 7i = 1, 2, 3, &c. The molecule foi-med by the combination 

 of these two atoms can also exhibit these frequencies, but now the upper limit 

 of 71 will be fixed by the critical quantity previously defined. Since the least 

 common multiple of the two atomic frequencies is 4"5 x 10", the upper limits 

 of n for the two atomic frequency series shown by the molecule will be 4 and 2 

 respectively, since when n = 5 and 3, the two atomic frequency series will con- 

 verge in the true molecular frequency. Perhaps, therefore, the true molecular 

 frequency will be better understood as the convergence frequency of the atomic 

 frequency series than as the least common multiple of the atomic frequencies. 



We may now consider one of the true molecular frequencies. 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 imit 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 subsidiary frequencies M + nA, where 

 M is the true molecular frequency, A is the atomic frequency, and n = 1, 2, 3, &c., 

 the upper limit of n being fixed by the critical value as already explained. 



Similarly there will be established the subsidiary frequencies M — nA, for 

 the following reason. Let the molecule which is in radiant equilibrium with 

 its surroundings absorb one quantum of energy at one of its atomic frequencies. 

 In order for it to gain a molecular quantum at one of its true molecular 

 frequencies it will now only be necessary for it to absorb the molecular quantum, 

 less the atomic quantum already absorbed. It has already been shown how on 

 the present conception summation of atomic quanta can take place to form 

 molecular quanta ; so it would follow that, after the absorption of a given number 

 of elementary quanta beyond that associated with the radiant equilibrium, the 

 molecule will be able to absorb the balance necessary' to form one molecular 



