Physical Significance of the Least Common Multiple. 715- 



becomes infinite. With this critical intensity the reaction 

 passes as an explosion wave through the mixed gases. 



Reference may also be made to Slade and Higson's results * 

 with a photographic plate, which show that the amount of 

 silver obtained with a given exposure is not proportional to 

 the intensity of the light but increases at a greater rate than 

 the intensity. 



All the phenomena foretold from my theory have therefore 

 been experimentally proved. 1 lay great stress on the fact 

 that this re-absorption by the reactant molecules of the 

 energy radiated by the resultant molecules is only possible it* 

 the quanta characteristic of the former are exact integral 

 multiples of those characteristic of the latter. Moreover, 

 these observations lie outside the purview of Dr. Campbell's 

 criticism and the question of coincidence does not arise. 



These results would seem to have considerable importance 

 apart from the present discussion, for they clearly establish 

 the possibility of a new type of photocatalysis. A reaction, 

 for instance, which requires light of extremely short wave- 

 length (Schumann region) should be induced by light of a 

 longer wave-length in the presence of a suitable catalyst. 

 The criterion of this catalyst will be that it contains the 

 same atoms as the reactant molecules. This substance when 

 absorbing light rays of its own characteristic irequency will 

 radiate this energy in the infra-red at frequencies which are 

 exactly equal to those of the reactant molecules with the 

 result that, provided the radiation density is sufficient, these 

 molecules will become reactivated and will react. Experi- 

 ments on these lines, were commenced some time ago in these 

 laboratories and are still in progress. 



During the writing of this note an interesting paper has 

 been published by Daniels and Johnston f in which is de- 

 scribed a typical instance of this very phenomenon. These 

 authors have proved that light of wave-length 400-460 /^a 

 has no action on pure nitrogen pentoxide, but that this sub- 

 stance is decomposed by light of this wave-length in the 

 presence of nitrogen dioxide which is known to absorb these 

 rays. They put forward the same explanation as given 

 above, but state that the energy radiated by the dioxide can 

 be absorbed by the pentoxide if the absorption bands of the 

 two substances in the infra-red overlap. This process is im- 

 possible on the quantum theory unless the infra-red quanta 

 characteristic of the two are exactly equal, that is to say are 

 integral multiples of a fundamental unit. 



* Proc. Roy. Soc. xcviii. p. 154 (1920). 

 t J. Amer. Chem. Soc. xliii. p. 73 (1921), 



