Tite 
Physics. — “On the law of the partition of energy.’ By 
J. D. vaN DER Waats Jr. (Communicated by Prof. J. D. van 
DER WAALS). 
(Communicated in the meeting of January 25, 1913). 
§ 1. Zntroductvon. 
The law of equipartition of energy must hold for the kinetic 
energy of all systems whose equations of motion ') can be represented 
in the form of the equations of Hamtrrton. This is shown in statistical 
mechanics. 
Experiment shows that this law is not fulfilled. This has first 
clearly appeared from the fact, that the kinetic energy of monatomic 
and diatomic gases, as it may be derived from the value of c‚, 
accounts for only 3 and 5 degrees of freedom respectively, whereas 
the molecules of these gases have undoubtedly more degrees of 
freedom, which appears ia. from the light which they can emit. 
Later the observations of Nernst and his disciples have shown, 
that the c, of solids decreases indefinitely when we approach to the 
temperature 7’=0 (absolute) which is also in contradiction with 
the equipartition law. . 3 
Finally we usually deduce from the equipartition law that the 
partition of the energy over the different wavelengths in the 
normal spectrum must be as it is indicated by the spectral formula 
of Rayrrren. In this case also experiment shows that the conse- 
quences of the equipartition law are not fulfilled in nature. 
It appears from the above considerations that we .are obliged to 
assume, that the equations of motion of the real systems cannot have 
the form of the equations of Hamiuron. The following conside- 
rations are to be considered as an attempt to find a way, which 
may lead to the dedvetion of the form of the equations of motion 
of the real systems occurring in nature. In this attempt I will 
assume that the partition of energy in the normal spectrum is accu- 
rately represented by the spectral equation of Pranck; so I will try 
to indicate a way which may lead to the drawing up of equations 
of motion from which the equation of PLANcK can be derived. In 
consequence of the mathematical difficulties, however, I have not 
succeeded in finding those equations of motion themselves. 
1) With “equations of motion” [ mean the equations which are required to 
reduce the time derivatives of the independent variables by which the condition of 
a system is determined from the values which these variables have at a given 
ime, independent whether or no these changes refer to motions in the strict sense. 
