CONTEMPORARY ADVANCES IN PHYSICS 601 



This expression is strictly valid only when the gas does not interfere 

 at all with the motion of the electrons; otherwise the frequency is 

 reduced, in the same way as the natural frequency of a pendulum or a 

 circuit is lowered by damping. The equation of motion of the electrons 

 in a high-frequency field is as follows: 



m(d^x/dt'') + gidx/dt) + fx = eE sin nt; f = ^irNeK (25) 



The solution has already been indicated (equations 10). 



Attempts to discover this natural frequency have been made in 

 two ways: by examining curves of tr or e or other correlated quantities 

 plotted against frequency or against degree of ionization, and by 

 searching for electromagnetic waves due to oscillations arising of 

 themselves in highly-ionized gases. 



The most thorough experiments by the former way are due to 

 Tonks. He placed a tube containing a mercury arc between condenser- 

 plates attached to long parallel wires, these being crossed by a movable 

 bridge including a thermocouple, and coupled to an oscillating circuit. 

 After establishing fixed values of the frequency and the current- 

 strength in the latter circuit, he shifted the bridge until the thermo- 

 couple reported a maximum of current, and measured this maximum 

 value; it and the shift of the bridge (the zero from which this latter is 

 measured is unimportant) were plotted as functions of the current- 

 strength in the mercury arc, which controls the number of free electrons 

 per cc. A natural frequency is indicated by a minimum in the former 

 of the curves, and in the latter curve a peculiar crinkle, similar to that 

 which appears in a dispersion-curve in the neighborhood of an ab- 

 sorption-frequency, and in the curve with black dots in Fig. 9. 



Embarrassingly it turned out that there were two, and indeed 

 sometimes three, minima in the one curve and crinkles in the other. 

 To these the corresponding values of N were correlated, being obtained 

 by the Langmuir probe-method. The comparison with theory may 

 then be made in either of two ways: by putting the value of the 

 applied high frequency into equation (24), computing N, and com- 

 paring it with the observed values of TV at the minima; or alternatively, 

 by putting the observed values of N into equation (24), computing fi, 

 and comparing its values with that of the applied frequency v. As an 

 example of the result of the first procedure: in one experiment, the 

 applied frequency was 1.59- 10^ this should coincide with the plasma- 

 electron frequency, resonance should occur, when A^= 0.63-10^ 

 electrons per cc; the values of A" at the two minima which were 

 observed were 0.27 and 0.86 times 10^ The latter is illustrated by a 

 graph in Tonks' article; it turns out that when the comparison is 



