216 Dr. J. W. Nicholson on the ^Number of 



an agreement which is satisfactory within the limits of ex- 

 perimental error, when its results are compared with the 

 experiments hitherto made. Certain conclusions can be 

 drawn as to the exact number of free electrons pertaining to an 

 atom of a metal. This special portion of the paper is specu- 

 lative, and of a strictly tentative character, but it may be 

 stated at ouce that the results therein suggested are supported 

 in detail by other experiments which have been made by 

 Drude, and which are not treated in the present paper, but 

 which are to form the subject of a later communication. 



The simplest investigation of the number of effective free 

 electrons, proceeding from a minimum of assumptions, was 

 made by Schuster *, whose conclusion was that the number 

 of free electrons in a metal at ordinary temperatures is equal 

 to the number of atoms, or exceeds that number not more 

 than three times. The formula on which this conclusion 

 was based is equivalent to that of Drude, and makes use of a 

 mean velocity of all the electrons in the element of volume. 

 Jeans f obtained the Same formula in another manner. 



The general agreement of Drude's theory with the experi- 

 mental details of the electrical and thermal properties of metals 

 was to some extent negatived by a later investigation of 

 Lorentz J, in which the velocities of the electrons were treated 

 a> subject to Maxwell's exponential law, as in the kinetic theory 

 of gases. The most recent investigation of the matter is that 

 of Prof. H. A. Wilson §, whose mode of treatment is very 

 direct. Wilson also uses the Maxwellian law of velocity 

 distribution, but his formula for the conductivity of the 

 metal under a steady electric force differs from that of Lorentz 

 by a factor 2/3. He' also worts out the case of frequencies 

 of the applied electric force which can fail within the visible 

 spectrum, neglecting, as in the previous theories to which we 

 have referred, the sympathetic vibrations which may be set 

 up within the molecules of the metal. 



It seems to the writer that Wilson's treatment is the most 

 satisfactory yet published, for the problem in which sympa- 

 thetic vibrations are not set up, and that, from a theoretical 

 point of view, it is complete. The results of the investigation 

 are left in the form of integrals, which, as he states, may be 

 evaluated by graphical methods. But it will appear that 

 such methods are not necessary, for the integrals may be 

 quickly reduced to others of known type, for which ex- 

 haustive tables have been constructed. Moreover, the values 



* Phil. Mag. February 1904. 



f Phil. Mag. June 1902 ; July 1909. 



% Vide ' Theory of Electrons.' 



§ Phil. Mag, November 1910. 



