﻿Partition of Energy and Newtonian Mechanics. 393 



It is perhaps worth while here emphasizing again the 

 essential difference between Planck's formula and many 

 interpretations of it. Although it is quite obvious that the 

 only certain point about Planck's law is that the formula 



ce dX 



e**-l 



expresses the energy per unit volume to be associated with 

 the component of the radiation with wave-length between 

 X and \ + d\, many authors interpret the theory in a manner 

 that implies that the energy of a perfectly monochromatic 

 constituent must be finite. Such a statement can, however, 

 hardly be true, when we consider that ultimately an infinite 

 number of such constituents are to be associated with any 

 small range in the spectrum. 



Co7iclusions. — In any case the general conclusion must be 

 that Planck's law does not require or necessitate anything in 

 the form of definite multiples of a fixed unit of energy, nor 

 is it in this or in any other respect in contradiction with a 

 general interpretation of the ordinary laws of Newtonian 

 dvnamics. It is not sugo-ested that this formula does not 

 involve anything but what can be derived from ordinary 

 dynamical principles ; but it is insisted that any statistical 

 considerations regarding dynamical problems do, in fact, 

 involve an additional hypothesis over and above those 

 provided in our usual dynamical schemes, and that therefore 

 a modified form of this hypothesis cannot be said to be 

 inconsistent with dynamical principles, since it has in reality 

 nothing whatever to do with these principles. 



The modification thus introduced into the theory involves 

 merely a revision of the principles of the calculus of 

 probabilities as applied in such problems. After all it is the 

 method of application of this calculus which is most probably 

 the vulnerable point in any statistical theory, so that it is 

 hardly surprising that the new phenomena of radiation force 

 us into new paths in this direction. While it is possible 

 thus to shift the responsibility for the particular form of the 

 theory necessitated by experience from the definite dynamical 

 principles to the indefinite statistical ones, it would appear 

 that no conclusions regarding the general applicability or 

 otherwise of these principles can be drawn from the theory. 



The only impression left by the foregoing discussion i> 

 rather one of indefiniteness. There appear to be so many 

 indefinite constants in the theory, that it is difficult to draw 

 any definite conclusions respecting any of the quantities 



