90 



dlK I \ 1 I 



= — f, — f„^ (9 + U\ (21) 



The expression between braces represents the thermal value of 



the reaction. For in the free space the potential energy is e^ and 



3 

 the mean kinetic energy - 6. In associated condition the potential 



energy would be s^, if the particles where always in the centres of 

 the regions v. For the average potential energy of the deviation 

 from that position of equilibrium in tiie direction v^ we have found 

 I U and for the two components of the deviation normal to f» each 

 {0. For the kinetic energy we assumed in the same way ^ U-\-&. 

 So we get for the thermal value of the reaction : 



8, + 2<9+ U-(e, + ^(9] = 8,-8,i-~a+ U. 



It is by no means snpcrtiuous to investigate whether this law is 

 satisfied. If e.g. we had assumed Maxwell's law for the distribution 



of I' and if in connectioJi with this we had written Ce ^ dr„ 

 for the probability of a deviation Vü in the dii-ection i> then we 

 should have found a formula for A' which in general would not 

 satisfy the hiw of the equilibrium change. Artificial additional sup- 

 positions would be required if we wished this law to be satisfied. 



^ 11. The didrllnitlon in conjiguratloii in arbitrary fields of force. 



The above considerations only refer to j)articles subjected to forces, 

 under the intluence of which they can execute tautochronic harmonic 

 vibrations. About the question what the formula for the distribution 

 of particles in arbitrary fields of forces will look like, I should not 

 venture to express so much as a supposition, except of course in 

 those cases in which Boltzmann's original formula is a sufficient 

 approximation. I will only express the following surmise. 



For quasi-elastic forces the energy of the particles is governed by 

 the quantity r, which in its turn is again determined by the quantity/. 

 The conclusion now naturally suggests itself that for an arbitrary 



clF 

 tield of forces the quantity — {F =^ the force that acts on a particle) 



dx 



will be decisive for the energy of the particles. This supposition 

 comes to this, that we assume that the particles, when they get into 

 a very inhomogeneous field of forces, in consequence of this are 

 subjected to changes in properties (shape, mass etc.), which changes 

 are not governed by the laws of classical mechanics, and give rise 

 to th3 deviations from the equipartition law. 



