674 BELL SYSTEM TECHNICAL JOURNAL 



as a mere point (as we are regularly doing) ; if it is to hit a molecule M, 

 the direction of the motion of its centre, which is itself, must be pointed 

 towards M. But if instead of an electron it is another molecule M' 

 which is to hit M, the sufficient condition is that the direction of mo- 

 tion of the centre of M' should be pointed towards a sphere of twice 

 the radius, four times the cross-section of M or M' . Merely on this 

 account, the mean free path of a molecule among similar molecules 

 should be only one-fourth as great as it would be, if the moving particle 

 were shrunk to a point. Another allowance must be made for the fact 

 that all the molecules of a gas are in motion, although their motions 

 are so slow that relatively to a free electron they may be viewed as 

 stationary. I shall not derive the formula for this latter allowance; 

 but the net result of both may be expressed in this way: the ratio of 

 the mean-free-paths of an electron and a molecule, in a given gas, 

 should be 4V2 if the ratio cro/cr of the gas-kinetic cross-section to the 

 cross-section for electron-impact were equal to unity. This result how- 

 ever is based on so very specific and in part fallacious assumptions, that 

 I should not have treated it at such length, but for the fact that it is 

 more or less the custom to divide the mean-free-path for interception 

 of electrons by 4a/2, and compare the result with the mean free path 

 of molecules as the kinetic theory of gases supplies it from the viscosity 

 of the gas. This amounts in practice to using still another measure of 

 the "likelihood of interception": to wit, the ratio 4V2o-o/a-. 



Doubtless it seems that I have spent excessive time in talking of these 

 measures of the likelihood of interception. There is however, an unim- 

 peachable reason for dwelling on the topic: the likelihood is the only 

 thing which can be measured. There are no critical "intercepting po- 

 tentials" like ionizing or resonance potentials; there are no specific 

 energy- values of the impinging electrons at which interception abruptly 

 starts; there is nothing in the nature of sudden "onset" to be detected. 

 The probability of the effect is the physical reality, it is the effect; and 

 its relation to the speed of the electrons is the only quality available for 

 study. Unless we know precisely how we are defining it, we know 

 nothing. Also we shall soon be looking at experiments which yield 

 values for quantities much like the c of interception, and yet not quite 

 the same; it will be necessary to discriminate with great care. But let 

 us first consider the direct experiments of the type which I have been 

 presuming. 



The experiments would certainly be simplest, if the electrons were 

 dashing along with enormous forward speeds, corresponding to vis 

 viva of the order of thousands of equivalent volts; for then their trans- 

 verse speeds would probably be negligible, the beam would have little 



