2 Prof. E. C. C. Baly on 



having a constant frequency difference. The observed 

 frequencies, however, are not exact, the difference between 

 the extreme values of any one frequency being equal to the 

 difference between two consecutive mean values. Then again 

 there is the formula given by Bjerrum * for the molecular 

 heat of hydrogen, Cw = 5R/2 + Rc^(2 , 0/x), which involves the 

 function of a definite wave-length supposed to be charac- 

 teristic of hydrogen. It is well known, however, that 

 hydrogen exerts no measurable absorption of energy of this 

 wave-length, and consequently it is difficult to understand 

 how the quantum theory is likely to gain more than discredit, 

 from such a case. 



On the other hand, the quantitative relations between the 

 various frequencies possessed by a given set of molecules 

 are exact within the highest limit of accuracy reached in 

 observation. Unless therefore the energy quantum theory 

 is capable of explaining the relationships with an equal 

 accuracy, it cannot claim to justify its application. 



The relationships which exist may be briefly stated as 

 follows : — 



1. Every elementary atom possesses one or more fre- 

 quencies which are characteristic of the element. 



2. When atoms of different elements enter into com- 

 bination the resulting molecule is endowed with a new 

 frequency which is the least common multiple of the 

 frequencies of the atoms it contains. This may be called 

 the true molecular frequency. 



3. The central features of all absorption-bands — that is, 

 those frequencies for which the absorptive power is greatest — 

 are molecular frequencies characteristic of the molecules, 

 since these alone persist when the substance is cooled to low 

 temperatures. 



4. The molecular frequencies in the visible and ultra-violet 

 regions are exact multiples of a molecular frequency in the 

 short-wave infra-red, which may be called the infra-red 

 fundamental frequency. 



5. The infra-red fundamental frequency is an exact 

 multiple of the true molecular frequency. 



6. The breadth of an absorption-band as observed at. 

 ordinary temperatures is due to the combination of the 

 molecular central frequency with subsidiary frequencies. 



7. Each observed absorption-band consists of a series of 

 sub-groups symmetrically arranged round a central sub- 

 group. If M be the central molecular frequency, the 

 frequencies of the central lines of the sub-groups will be 



* Zeitsch. Elektroehem. xvii. p. 731 (1911), xviii. p. 101 (1912). 



