Statistical Theory of Heat Radiation. 121 



47 sums wanted can be found by simple addition of the 

 numbers in the 47 columns (omitting the third to the ninth 

 columns, — whose sums are not wanted, and which may be 

 written on a sheet by themselves ; as these seven numbers 

 have to be combined by addition and subtraction, it may be 

 most convenient to arrange them in columns corresponding 

 to the several observations, to effect their combinations in 

 these columns, and to transfer the values of /, and l 2 thus 

 found to the main sheets). 



Worcester, Mass., U.S.A., 

 January 1, 1909. 



IX. On the Statistical Theory of Heat Radiation, By 

 Prof. Harold A. Wilson, F.R.S., McGill University, 

 Montreal * 



THE theory of the distribution of the energy in the 

 spectrum of full radiation which we owe to Planck 

 has recently been presented in a new and more general form 

 by Sir J. Larmor f . In Planck's theory the energy is taken 

 to be emitted by u resonators " contained in the body which 

 are supposed to only gain and lose energy by certain finite 

 increments the magnitude of which is proportional to the 

 frequency of vibration. On this view it is not absolutely 

 necessary to regard the radiation itself as made up of finite 

 elements ; but Einstein and others have shown that Planck's 

 theory can be so interpreted. Larmor considers the radiation 

 itself as made up of "elements of disturbance" which are 

 regarded as definite entities possessing energy, but the energy 

 in an element can vary continuously. 



Larmor states that on his view " it would be the limiting 

 differential ratio of energy element to extent of cell that is 

 somehow predetermined, but now without any implication 

 that energy is itself constituted on an atomic basis." I find 

 that Larmor's theory seems to require the radiation to be 

 made up of finite elements of the same magnitude as those 

 contemplated by Planck and Einstein. This does not mean 

 that energy itself has an atomic constitution, but it does 

 appear to require some such sort of constitution for the 

 radiation. -^ 



Larmor obtains the equation ed — log/l-f — ), where e 



denotes the energy per element of disturbance of a particular 

 wave-length, n the number of such elements, and N the 



* Communicated by the Author. 



t Proc. Roy. Soc. A., vol. lxxxiii., 1909. 



