94 Mr. J. H. Jeans on the Partition of 



§ 3. As a result o£ the assumed absence of interaction 

 between matter and aether, the condition o£ " continuity of 

 path" is not yet satisfied: the fluid moves as though the 

 space were divided into water-tight compartments. The 

 equations of the divisions between these compartments are 

 simply the integrals of the equations of motion (3) and (4), 

 such, e. g., as the family of surfaces 



Xj 2 + Y x 2 + « 2 2 + A 2 = constant. 



If the material system is divided into separate masses of 

 gas, we have as further integrals 



E x = const. E 2 = const. &c, 



where Ei, E 2 . . . are the material energies of these systems 

 separately. 



§ 4. If we now admit a very small interaction between 

 matter and aether, the conditions are changed. The equations 

 of motion are changed by the introduction of cross-terms 

 which link up the material system with the aether, and we may 

 assume that no integrals are left except the energy equation. 

 Thus the whole system of water-tight compartments is broken 

 down except for the family of surfaces E = constant where E 

 is the total energy. The new coordinates of position and 

 momentum differ from the old by terms which depend on the 

 interaction just introduced, and so may be regarded as 

 approximately unaltered when this interaction is small. The 

 whole system, regarded now as a single electromagnetic 

 system, will still have equations of motion of the Hamiltonian 

 type, so that the equation DpjDt = remains true accurately. 

 The conditions for the theorem of equipartition are now 

 satisfied, so that the expectation of the energy of each of the 

 decrees of freedom is the same, namely 



E 



3N-hwi 



$ 5. When we have a finite amount of matter in infinite 

 aether, 1ST is finite while m is infinite, so that the ratio of energy 

 of mciatter to that of aether, namely 31ST/m, is infinitesimal. 



Definite though this result may seem, the partition of 

 energy is not yet completely known. If we attempt to find 

 the! law of distribution of energy in the radiation-spectrum, 

 the equipartition theorem directs us to assign equal amounts of 

 energy to each coordinate, and therefore to each value of k, 

 but gives no information as to the " density " of coordinates 

 wijthin the different range of values of k. This circumstance 



