Partition of Energy between Matter and Radiation. 25 

 (34) and (35) can now be written 



i(fc+ ;i\F ra )-£(Tu„ a F„-V»)=0. (35)' 



Suppose p ;i is derived from a Lagrangian function L for 

 the purely material energy. Then the whole system of 

 equations (34)' and (35)' has the Lagrangian function L. 



.... (36) 

 remembering that F^, is a function only of q„. 

 The corresponding Hamiltonian function is 



The "gyrostatic terms " linear in u n and « r disappear. 

 The need for a function L appears at once if we are to 

 transform (34)' and (35) ' to Hamilton's form. 



If L is zero the momentum -jr- does not contain the 



velocities at all. The 3N material momenta are functions of 

 the coordinates a r and q[„ only. Therefore the velocities u n 

 cannot be expressed as functions involving the corresponding 

 momenta. By (35/ we can derive relations between the 

 various velocities so that these are not independent. The 

 statistical method cannot be applied. If, on the other hand, 

 L is not zero we may apply Maxwell's method in the 

 ordinary way. By the first part of this paper the equi- 

 partition of kinetic energy is expressed by the equation 



2^ r d Vr ~2^ s d^ 

 the bars denoting average values. 



Or 1_ dX_± dL 



2 Ur du -2 Us du/ 



where w>'and Us denote different velocities. 



