4 Prof. E. 0. C. Baly on 



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, 

 ex hypotliesi can only gain or lose energy in elementary 

 quanta, and, further, can only enter into chemical com- 

 bination if it already contains energy that can be evolved. 

 Let the case be considered of two elementary atoms, the 

 characteristic frequencies of which are 9 x 10 10 and 1*5 X 10 11 ,. 

 or in wave numbers (1/X.) 3 and 5. The smallest equal 

 amounts of energy that the two atoms can lose is five 

 elementary quanta at the frequency 9 X 10 10 , and three 

 elementary quanta at the frequency 1*5 x 10 11 . These two 

 amounts are equal to one quantum measured at the 

 frequency 4*5 X 10 11 , 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 10 10 and three 

 quanta at the frequency 1*5 X 10 11 . 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 ihe 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 com- 

 bining atoms share equally in the energy loss on combination 

 and in the future energy changes of the resulting molecule, 

 we arrive at the conception 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 con- 

 ditions are dealt with, one of the most important frequencies 



