158 Dr. W. Wilson on the 



out of place here. Regions of "equal probability" consti- 

 tute a feature of Planck's later theory and that of Ishiwara. 

 The essentials of Planck's theory, which appears to me to be 

 included as a special case in that of Ishiwara, can be very 

 shortly stated. He deals with a very simple type of system, 

 the equation of motion of which is 



d?q 



^ + Kq=0 



when it is in a steady state, i. e. neither emitting nor 

 absorbing energy. We easily deduce the following relation 

 between p and q : — 



{2irmvKY A 2- ' 



where j2 = m -7^, A is the amplitude of the motion, and v the 



frequency. This is the equation of an ellipse. For different 

 amplitudes we have a number of similar and similarly 

 situated ellipses, and it can be shown in a very simple way 

 that the energy of the system, or oscillator, is equal to 



Hz/, 



where H is the area of the corresponding ellipse. This 

 result is obtained by the use of the principles of ordinary 

 dynamics. If, now, we suppose the oscillators to be capable 

 of interchanging energy with one another, and proceed to 

 investigate, by the same principles, the law of their distribu- 

 tion throughout the q, p plane, under statistical equilibrium, 

 we assume the distribution to be uniform in an infinitesimal 

 region 



dpdq = dH, 

 and write 



dl$ = T$fdpdq, 



where N is the number of oscillators and d'N the number in 

 the region dp dq. We readily find 



where H is the area of the ellipse on which the element 

 dpdq is situated and k is the "gas constant" reckoned for 

 one molecule. This result may be called the Maxwell law 

 of distribution. It leads to the conclusions, (a) that the 



* We are assuming, as Planck does, that the directions of vibration 

 are perpendicular to a fixed plane, and that the oscillators are fixed. 



