( 447 ) 
ties"), we are in a position to calculate the quantities vand W (§ 1) 
with which we are principally concerned. If the value (20) is sub- 
stituted in (4) and (5), the term A e#” leads to an integral containing 
the factor §; this integral vanishes, if taken over the full extent of 
o2 
the diagram of velocities. In the remaining integrals the factor 8 
7 Ee ] 
occurs ; these are easily found, if we replace §* by at the element 
dà by 4277 dr, and if then we integrate from r=0O to r =o. 
Taking 7? = s as a new variable, we are led to the integrals 
ie} 
aoe ao) 
|: ehsds, fe eAsds and fs ehs ds, 
0 
0 0 
whose values are 
Finally, the “stream of electrons’ and the flux of heat are given by 
ee Mee lie (2 ae =) ae ae | 
3 h° da hs dx 
Aen E (2 hAX a) mie =| ey) 
3 1 Ge) Se hide 
These are the equations that will be used in all that follows. 
For the sake of generality, I shall suppose (though, of course, this 
is not strictly true) that, if only a proper value be assigned to /, 
the formulae may still be applied even if we make other assumptions 
concerning the metallic atoms and their action on the electrons. From 
this point of view, we may also admit the possibility of different 
kinds of electrons, if such there are, having unequal mean lengths 
of free paths, and of, for each kind, / varying with the temperature. 
‘Provisionally, we shall have to do with only one kind of electrons, 
reserving the discussion of the more general case for a future com- 
munication. 
§ 8 From the equation (21) we may in the first place deduce a 
formula for the electric conductivity 6 of the metal. 
Let a homogeneous bar, which is kept in all its parts at the same 
temperature, be acted on by an electric force # in the direction of 
its length. Then, the force on each electron being e 4, we have to put 
1) It may be observed that, as must be the case, the value (20) gives N for 
: 33 B 
the number of electrons per unit volume and B) for the mean square of velocity. 
aly 
