Physical Significance of the Least Common Multiple. 1Y6 



Dr. Campbell says that all the numerical agreements I 

 have obtained must be coincidences if the fundamental unit 

 does not exist, but after all the multiplication of coincidences 

 must sooner or later engender a belief in their reality. The 

 " coincidences^' I have obtained are very numerous indeed. 

 The calculation of all the 600 individual lines in the absorp- 

 tion band of sulphur dioxide from the infra-red absorption 

 spectrum of hydrogen sulphide, the calculation of the lines of 

 water from sulphur dioxide are only two isolated cases. I laid 

 more stress upon these because of their very great accuracy. 

 There are many others equally striking *, and I do not think I 

 am unduly biassed in saying that it surely is easier to believe 

 in the existence of a fundamental unit of energy associated 

 with matter than to disbelieve in the reality of these results. 



There have also been obtained in these laboratories some 

 results which very strongly support the L.C.M. principle 

 and hence the existence of the fundamental unit of energy. 

 In my paper on molecular phases f I suggested that the 

 observed deviations from Einstein's law of the photo- 

 chemical equivalent are due to the re-absorption by the 

 surrounding reactant molecules of the energy radiated 

 during the reaction. This will clearly result in more than 

 one molecule reacting for every quantum of energy absorbed. 

 In any photochemical reaction it is obvious that the energy 

 evolved must be radiated by the products of the reaction 

 and at frequencies characteristic of them, since if the 

 reactant molecules radiate the energy they have absorbed 

 they will no longer be in a reactive condition. It must 

 be emphasised that, if the energy radiated by the products 

 is absorbed by the reactant molecules, the quanta charac- 

 teristic of the former must be exact multiples of the latter, 

 which is the fundamental basis of my theory and indeed 

 is the point at issue between Dr. Campbell and myself. 

 If, therefore, it can be proved that in any reaction the energy 

 radiated by the resultant molecules is absorbed by the re- 

 nctant molecules, I venture to think that the integral relations 

 between the quanta characteristic of the two will be very 

 strongly supported, if not absolutely proved. 



In the paper referred to it was pointed out that the 

 re-absorption by the reactant molecules of the energy radiated 

 by the resultant molecules will obviously depend upon two 

 factors. In the case of a photochemical reaction it will 

 depend firstly on the concentration of the reactant molecules, 



* Astrophvs. Joiirn. xlii. p. -1 (HUT)). 

 t Phil. Mag. xl. p. 15 (1920). 



