166 BKIDGMAN. 



effect. It is usually considered that this effect is important only at 

 optical frequencies, but it is worth our while to consider it here. The 

 formula may be found on page 432 of Richardson's book on Electron 

 Theory of Matter, and is 



(To 



1 + F 



9 o 



Here o-p is the conductivity at the frequency in cjuestion, ao the con- 

 ductivity at zero frequency, j^ the angular velocity corresponding to 

 the frequency, m the mass of the electron, e the charge on the electron, 

 and N the number of electrons per cm^. The only quantity in this 

 formula which we do not know definitely is N. Let us assume for the 

 moment that N is equal to the number of atoms. If now we sub- 

 stitute numerical values for silver we find that cTp differs from co by 

 5.3 X 10~^^. (I have used for p = 27r X 10^, which is more than twice 

 the highest experimental value). But now according to my theory 

 of conduction, the number of electrons must be very considerably less 

 than the number of atoms, and this will increase the difference between 

 (Tp and ctq. If we assume as an extreme value that the number of 

 electrons is 10~^ as great as the number of atoms, we find that o-p still 

 differs from^o by 5.3 X lO-^" at 10,000 cycles. Evidently this effect 

 is not a factor under our conditions. 



Computation of the Departure from Ohm's Law. 



Referring again to Figure 2, we have defined the departure from 

 Ohm's law as (tan d — tan 0o)/tan ^o- What we have actually meas- 

 ured and plotted in Figures 10, 11, and 12 is (tan 6' — tan ^o)/tan do. 

 Given this as a function of current, we require to find the departure 

 from Ohm's law as a function of current. For convenience replace 

 E by y, and / by x. Let the required curve be represented by y = f{x). 

 Experimentally we determined 



(Jjl _ y 



dx X 



= ^(.r), 



