230 REPORTS ON THE STATE OF SCIENCE. — 1920. 



frequencies or is a multiple of that least oommon multiple, and indeed this rela- 

 tionsliip gives the key to the whole of the system of fi-equencies exhibited by a 

 molecule. Again, the whole of the principal frequencies in the infra-red are 

 derived from certain constants, and these constants are characteristic of the 

 elementary atoms of which the absorbing molecules are composed. These con- 

 stants or elementary atomic frequencies lie in the very long wave infra-red 

 region, and the corresponding wave-lengths are of the order of 1000//. 



The whole of the principal frequencies shown by a molecule are determined 

 as follows : The fundamental infra-red frequency either is the least common 

 multiple of all the elementary atomic frequencies which are active in the mole- 

 cule or is an exact multiple of that least common multiple. The principal 

 frequencies of all the visible or ultra-violet absorption bands shown by that 

 molecule under various conditions are exact multiples of that fundamental infra- 

 red frequency, and therefore are characteristic of that molecule. In addition 

 to all these frequencies which are true molecular frequencies, there also exist 

 frequencies which are the least common multiples of some (not all) of the 

 elementary atomic frequencies, and these are due to specific groups of atoms in 

 the molecule, and are called intra-molecular frequencies. 



The question might be asked as to how these relationships have been proved 

 within a very high degree of accuracy in view of the fact that measurements 

 of absorption in the infra-red have not reached a high level of accuracy. It 

 has been found that if a molecule exhibit a principal frequency F in the infra- 

 red, visible, or ultra-violet, there will be associated with that frequency sub- 

 sidiary frequencies F + A, where A stands for either the intra-molecular fre- 

 quencies or the elementary atomic frequencies. Indeed, it is to this cause that 

 the breadth of the absorption bands is due. As the result of this it is possible 

 to arrive at highly accurate determinations of the intra-molecular and ele- 

 mentary atomic frequencies by analysis of the absorption bands, especially 

 those ill the ultra-violet where the accuracy of measurement is very high. 



The most usual arrangement of the subsidiary frequencies within an absorp- 

 tion band is as follows : The band consists of a series of sub-groups symmetrically 

 arranged with respect to the principal sub-group with the greatest absorptive 

 power. These sub-groups each possess a principal line for which the absorptive 

 power is a maximum, and ail these principal lines form a series of constant 

 frequency difference. This frequency difference is an intra-molecular frequency 

 and is characteristic of a specitic group of atoms within the molecule. 



Then, again, each sub-group is exactly similar in structure and consists of 

 two or more series of lines, each with constant frequency difference and 

 symmetrically arranged with respect to the principal line. These constant 

 frequency differences are the elementary atomic frequencies characteristic of 

 the atoms composing the specific group within the molecule, and the least common 

 multiple of these is the intra-molecular frequency characteristic of that group 

 of atoms. 



Two instances may be given which exemplify very fully these relationships. 

 The complete absorption system of sulphur dioxide has been found to be based 

 on three elementary atomic frequencies. ^^ Of these, two, 8-19 x 10" and 

 1"296 X 10'^, are characteristic of the sulphur atom because they also form 

 the basis of the infra-red frequencies of hydrogen sulphide, and the third, 

 2'4531 X 10'^, is characteristic of the oxygen atom. From direct measurement 

 the two possible intra-molecular frequencies of the water molecule have been 

 found lo be 7-5 X 10' i and r7301 X 10'-. Obviously if 2-4531 X 10^ is 

 characteristic of the oxygen atom it should form one of the fundamental constants 

 of the water molecule. From these three values alone it has been found 

 possible '' to calculate the whole of the structure of the infra-red bands of 

 water, and the values obtained agree absolutely with those observed." 



Again, in one of the ultra-violet bands of naphthalene there exists a constant 

 frequency difference of 1-4136 x 10" between the sub-groups, which is therefore 

 an intra-molecular frequency, and thus must be characteristic of a definite 

 group of atoms within the naphthalene molecule. The two most obvious groups 

 of atoms are the phenyl group and the olefine group, and therefore the frequency 

 1"4136 X 10" should be the true molecular frequency of either benzene or one 

 of the olefines, the olefines being very similar in their characteristic frequencies. 



