232 REPORTS ON THE STATE OF SCIENCE. — 1920. 



The first fact to be dealt with is that when two or more atoms unite together 

 the resulting molecule becomes endowed with a new frequency which is the 

 least common multiple of the frequencies characteristic of the atoms. Leaving 

 on one side the cause of the chemical combination, the energy lost in the process 

 may be considered. The simplest possible assumption to make is that in the 

 synthesis of any one molecule each of the component atoms contributes an equal 

 amount of the total energy lost. An elementary atom ez hypothesi can only 

 gain or lose energy in elementary quanta, and, further, can only enter into 

 chemical combination if it already contains energy that can be evolved. Let 

 the case be considered of two elementai-y atoms, the characteristic frequencie.s 

 of which are 9 X lO^" and r5 X 10", or in wave numbers (1/ ^) 3 and 5. 

 The smallest equal amounts of energy that the two atoms can lose are five ele- 

 mentary quanta at the frequency 9 X lO'" in the one case, and three elementary 

 quanta at the frequency I'S x 10" in the other. These two amounts are each 

 equal to one quantum measured at the frequency 4-5 x 10", which is the least 

 common multiple of the two atomic frequencies. In this is doubtless to be found 

 the key to the first problem— namely, that the true molecular frequency is the 

 least common multiple of the frequencies of the atoms in the molecule. 



Further, the gain or loss of energy by a molecule as a whole must be equally 

 shared in by the component atoms. When a molecule absorbs or loses energy 

 as a whole, it must do so by means of the elementary quanta characteristic of 

 its atoms. In the case of the molecule specified above, the smallest amount 

 of energy it can gain or lose as a whole is the sum of five quanta at the frequency 

 9 X lO'" and three quanta at the frequency 15 x 10". This minimum amount 

 of molecular energy is two quanta at the true molecular frequency, and in this 

 again is to be found an explanation of the fact that the true molecular frequency 

 is the least common multiple of the atomic frequencies. 



It is evident, therefore, that starting from the conception of the elementary 

 energy quantum required to shift one electron and making the simple assumption 

 that the combining atoms share equally in the energy loss on combination and 

 in the future energy changes of the resulting molecule, we arrive at the con- 

 ception of molecular quanta, and hence molecular frequency, the latter being 

 the least common multiple of the atomic frequencies. 



It can be shown that, when molecules under normal conditions are dealt with, 

 one of the most important frequencies they possess is the infra-red fundamental 

 frequency, which is an exact multiple of the true molecular frequency. In the 

 case of sulphur dioxide the infra-red fundamental is fourteen times the true 

 molecular frequency, and in the case of water it is eight times the true molecular 

 frequency. It was stated above that the smallest possible equal amounts of 

 energy which two or more atoms can evolve when combining together are equal 

 to one quantum measured at the frequency which is the least common multiple 

 of their atomic frequencies. It does not follow, of course, that the reacting 

 atoms only evolve this smallest possible amount of energy. They may evolve 

 an amount of energy which is 2, 3, 4, &c., times this smallest quantity, with 

 the result that the smallest frequency truly characteristic of the molecule may 

 be a multiple of the true molecular frequency. Indeed, it would seem that the 

 infra-red fundamental is the frequency which is truly characteristic of the 

 fresJily synthesised molecule. 



At the commencement the simplest possible case was considered of the com- 

 bination of two atoms, each characterised by a single elementary quantum. 

 There is no necessity to restrict the conditions in this way, and it is to be 

 expected that, at any rate in the atoms of some elements, there will exist more 

 than one possibility of shift of the electrons, and that there will be elementary 

 quanta of different sizes associated with such atoms. It has already been found 

 that two different elementary quanta are associated with the atom of oxygen 

 in the water molecule and with the atom of sulphur in the molecule of sulphur 

 dioxide. 



Whilst the establishment of molecular quanta, and hence of molecular 

 frequency, is a simple deduction from the conception of elementary atomic 

 quanta, it cannot be denied that the molecule may also exhibit those frequencies 

 which are characteristic of its component atoms. Although these atoms have 

 united together to form the molecule, there is no reason to expect that they have 



