278 wien: recent theories of heat and radiation 



It is possible to develop a theory of electric conductivity if 

 one considers the motion of electrons in metals to be independent 

 of temperature. In this case the conductivity of metals could 

 change only thru variation of the free path of the electrons. The 

 free path of electrons will depend only upon the vibrati ons of the 

 atoms, and must be inversely proportional to the numberof vibrat- 

 ing atoms. It would be more difficult to find the relation between 

 the free path and the amplitude of the vibrations. A statistical 

 consideration shows that the free path must be independent of the 

 partition of the quanta only in case the free path be inversely pro- 

 portional to the square of the amplitude. The vibrations are sup- 

 posed to be identical with the elastic vibrations of the solid. In 

 this way, one arrives at a formula for the conductivity, using the 

 values obtained by the theory of elasticity, which agrees with the 

 observations of Kammerlingh-Onnes except at very low tempera- 

 tures. It also yields the high value for the temperature coeffi- 

 cient for iron and nickel. The derivation of the formula for elec- 

 tric conductivity suggests that the electrons are in irregular motion 

 but the energy of this motion will not depend, as assumed in 

 Drude's theory, on the temperature, for the motion considered 

 remains unchanged even at the lowest temperatures. It is 

 possible to identify this energy of the electrons with the energy 



^ of the theory of radiation. 



Some considerations have been offered by Einstein, which 

 have considerable importance for the theory of quanta. They 

 relate to fluctuations in the radiant energy caused by the irregu- 

 larity of the emission. The theory of the Brownian movements 

 founded on the theory of errors has shown such a surprising agree- 

 ment with observation that it is necessarj^ to take account of 

 this theory in its application to radiation. Using Boltzmann's 

 theorem of the relation between entropy and probability, this 

 can be calculated from the known formula of the entropy of radia- 

 tion. Applying the law of errors we can calculate the fluctuations 

 of the radiant energy about its mean value. The calculation gives 

 an expression which cannot be interpreted from the mean values 

 for interfering rays, meeting in a point distant from the radiating 



