CONTEMPORARY ADVANCES IN PHYSICS 113 



to the A-axis; call it i'„. For Km, the maximum kinetic energy of the 

 electron, we then have (repeating equation 4): 



A„, = - m 7-0 H + Vn~ 



1 |_\ wv m / 



(28) 



and one sees that it is idle to assign an exact maximum value to the 

 energy of the free electrons roaming in a vacuum subjected to a 

 high-frequency field, since we cannot possibly know the initial velocity- 

 components T'o and Vn of all these corpuscles at the instant / = 0. 



If we do the easiest thing, and simply put I'o = 0, we get for K^ 

 the expression : 



K,n=^m(-^ — ] ' (29) 



Here, of course, energy and fieldstrength are expressed in electrostatic 

 units. Putting them in electron-volts and volts-per-cm. respectively, 

 and denoting them by K^v and £„ respectively to symbolize this 

 choice of units, we obtain: 



if,.,.= lO^/^'V (30) 



2m TT-c \ V 



8.95-10" f^ ) . (31) 



I recall from Part I that this choice of value for I'o, like every other 

 except one, leads to the result that the electron oscillates not about 

 a fixed but about a drifting centre. The solitary choice which results 

 in the electron vibrating about a stationary centre, — to wit, 



I'o = - eEjlTwrn (32) 



— produces for the maximum kinetic energy a value one-fourth as 

 great as that given by equation (31).2i 



On inserting into equation (31) the various frequencies at which 

 experiments have been made, and the amplitudes of the fieldstrength 

 corresponding to the minimum maintaining potentials at these fre- 

 quencies, one sometimes gets values of the order of magnitude of 

 ionizing or resonance potentials, sometimes values much lower. Thus, 

 Rohde's observations on helium give, at the frequency 10^, a minimum 

 maintaining-potential of 11 volts between electrodes 19 mm. apart, 

 therefore an oscillating fieldstrength of amplitude 5.8 (if there is no 



*i If Va is negative and algebraically less than — eE/lwvm, the energy of the 

 electron is always less than, or at most equal to i/2m{vo- + Vn^): the initial vis viva 

 is also the greatest. 



