594 BELL SYSTEM TECHNICAL JOURNAL 



F standing for the fieldstrength. Despite the aspect of the equation, 

 u is not proportional to F\ the coefficient g must be regarded as a 

 function of F (over wide ranges of fieldstrength it is proportional 

 to the square root thereof). Though this is a fact of experience, 

 it will be helpful to develop the theory to some extent. 



Picture the drifting of electrons through a gas in the customary 

 (though far too primitive) way. Imagine the gas as a congregation 

 of elastic spheres, with which the electrons make elastic impacts. 

 When these latter enter the region where the constant and uniform 

 field is applied, they are speeded up in the direction of the field; 

 but owing to the deflections and the losses of energy which they 

 suffer at their impacts, their velocities become and remain almost 

 isotropic, and their average energy approaches but does not surpass a 

 certain limiting value determined by the fieldstrength. After they 

 have progressed sufficiently far, they form an "electron-gas" mingled 

 with the atoms of the material gas; this electron-gas drifts slowly 

 along towards the positive electrode, but its individual corpuscles 

 have (as a rule) random velocities tremendously in excess of that 

 comparatively modest drift-speed, just as the molecules of the air 

 have random velocities many times greater than the speed of the 

 wind. Let me denote the drift-speed by u, the mean speed of the 

 random motions of the electrons by co. Now it may easily be shown ^ 

 that if the simple picture of the molecules as big elastic spheres and 

 the electrons as little ones is acceptable, m and co and the mean-free- 

 path of the electrons / are related by the equation : 



u = deEl/nio}, (13) 



6 here standing for a numerical factor not very different from unity, 

 the exact value of which depends on the underlying assumptions made 

 in the statistical analysis of the motions of molecules and electrons. 

 The value 0.8 for 6 is probably as good as any, but it would be pointless 

 to spend time deciding between different values, since the molecules 

 cannot be represented exactly as elastic spheres, and the degree of 

 their deviation from this simple model would affect the quantity 6. 

 Now comparing the last two equations, we find : 



g = mco/dl 

 = m/dr = mZ/d, (14) 



T and Z here representing respectively the mean duration of the 

 free flight of an electron between consecutive impacts, and the number 

 of impacts made by an electron in unit time. (I introduce these 

 * "Electrical Phenomena in Gases," pp. 174-175. 



