wien: eecent theories of heat and radiation 279 



surface. The expression which represents the fluctuations con- 

 tains two terms, one having the form which would result if the 

 elements of energy were concentrated in points of space, the other 

 expressing the fluctuations caused by interference alone. ^ But 

 the second term of the formula also contains the constant h and 

 one can combine the two terms into one, in consequence of which 

 it is not quite certain whether the separation into two terms is 

 due to the phj^sical phenomena. Certain it is that at low tem- 

 peratures the calculated fluctuations are larger than those caused 

 by interference alone. Inasmuch as this case applies only to 

 radiation which exists free in space it has no relation to observa- 

 tion. 



Another case, which was also treated by Einstein, is therefore 

 of great interest here. It concerns the irregular motion of a mirror 

 accelerated by pressure of radiation in free space. In the calcula- 

 tion of this pressure the effect of small velocities vanishes because 

 the pressure is the same on the front and on the back of the mirror. 

 It is therefore necessary to calculate the second term which is 

 proportional to the velocity. The expression for the mean energy 

 of the irregular motion of the mirror is also made up of two terms 

 and is quite analogous to the expression for radiant energy. 



If the mirror be suspended in a space filled with radiation 



from a black body an energy equilibrium is established and it 



may be expected that the irregularities in the pressure of radiation 



will reach the magnitude given by the law of equipartition of 



energy. Therefore the mean energy of the mirror moving in one 



direction would be ^ kTJ But if we calculate the irregular motions 



caused by interference alone w^e shall find them smaller, the mean 



energy being proportional to kT and independent of h. It is 



unlikely that the mean energy of the real motions would be differ-" 



kT 

 ent from the value -^, for the irregularities caused by the pres- 



sure of radiation must be in equilibrium with the irregularities 

 caused by other thermal phenomena. It seems therefore neces- 



' From this expression Einstein was led to suggest the assumption that quanta 

 also exist in space. 



^ Where k is the constant of the theory of gases and T the absolute temperature. 

 This quantity of energy is equal to the mean energy of a gas-molecule. 



