and tlw Partition of Energy in Continuous Media. 251 



the system neither gains nor loses energy, and is free from 

 all external disturbance for an unlimited time. In the 

 observed state there is both a loss and a gain of energy (the- 

 two being of course equal in amount), and the oscillations 

 are " forced/'' Any dynamical system subject to a loss of 

 energy will, after a sufficient time, reach a state from which 

 all traces of the initial conditions have disappeared ; its state 

 will depend solely on the forces which act upon it from 

 outside. There exists a final state of this kind, to which every 

 system necessarily tends when acted on by definite external 

 agencies, and this final state may be something entirely dif- 

 ferent from the " normal state " : it is such a final state that 

 Planck's formula represents. We may speak of this state 

 as the " steady state " : it is the state reached as soon as 

 the influence of the initial conditions has been dissipated 

 away. 



27. The " normal state " can depend only on the rather, 

 but the " steady state " will depend in addition on the 

 materia] agencies which force the vibrations in the rather. 

 Consequently, Planck's formula (4) contains more constants 

 than the formula (3) of the " normal state. " 



There is no a priori reason why there should not be 

 different " steady state " formulae corresponding to different 

 kinds of matter: the vibrations forced in the rather might 

 reasonably be expected to depend on the nature of the forcing 

 agency. In point of fact it is found that the specification of 

 the "steady state " involves only the temperature, and not 

 the nature or structure, of the matter by which the ratherial 

 vibrations are forced. This is easily seen to be a necessary 

 consequence of Kirchhoff's law*. Once the truth of this 

 law is accepted it is readily seen that there can be only one 

 "steady state" corresponding to a given temperature, so 

 that this steady state must be the same for all kinds of 

 matter. Thus the constants which enter into the steady-state 

 formula must be quantities which are common to all kinds 

 of matter. 



In Planck's formula there are two constants, c and k. 

 Of these k is either identical with the ffas- constant R or is 



* If the views of the present paper are sound, the structure commonly 

 called "The Thermodynamics of Radiation " requires modification, and the 

 usual theoretical proof of Kirchhotf's law with it. We then have to fall 

 back on experimental investigation as to the truth of the law. The law 

 seems undoubtedly to be true, whether the usual theoretical proof of it 

 is valid or not. 



Lorentz, on the basis of the electrical structure of matter, has verified 

 the truth of Kirchhoff's law for radiation of long wave-length (Konink. 

 A/cud. van Wetenschappen, Amsterdam, 1903, p. 678). 



