[ 156 ] 



XXII. The Quantum of Action. By William Wilson, 

 Ph.D., Lecturer in Physics, University of London, King's 

 College *. 



IN a recent paper on the Quantum Theory f, Jun Ishiwara 

 starts out from an assumption which closely resembles 

 an hypothesis published by me about the same date |. The 

 aim of Ishiwara's theory also appears to be the same as that 

 of mine — namely, to furnish a common basis on which the 

 theory of complete (black body) radiation, spectral series, 

 and other phenomena can be established. It is therefore 

 desirable that the two hypotheses should be compared and 

 the differences between them clearly pointed out. 

 Ishiwara's assumption may be stated as follows : — 



" Let q x q 2 . .. . qj and p x p 2 Pj be the positional and 



impulse coordinates of an elementary material system in 

 a state of steady periodic motion, or of a system consisting 

 of a very large number of elementary systems in statistical 

 equilibrium, and let each pair, q { , p { , be represented by 

 rectangular coordinates in a plane ; then the motion of the 

 system is such that we may divide each plane into regions 

 of ' equal probability,' whose mean value, for any state of 

 the system, 



-. X £pidgi=h 



is a universal constant " §. 



The hypotheses which I have proposed as a foundation for 

 the Quantum Theory are stated at some length in the paper 

 mentioned above ||, and may be put rather more shortly in 

 the following form : — 



(1) Each dynamical system behaves as a conservative one 

 during certain intervals, and between these intervals are 

 relatively very short ones during which definite amounts 

 of energy may be emitted or absorbed. 



(2) The motion of a system in the intervals between such 

 discontinuous energy exchanges is determined by Hamil- 

 toninn dynamics as applied to conservative systems. We 

 may speak of a system, during such an interval, as being in 

 one of its steady states. 



* Communicated by Prof. J. W. Nicholson. 



t J. Ishiwara, Tokyo Sngaki-Buturigakkwai Kizi, 2nd ser. vol viii 

 No. 4, p. 106. 



% W. Wilson, Phil. Mag. xxix. p. 795 (1915). 



§ This is a free translation from the original, which is in German. 



|| W. Wilson, loc. eit. 



