106 BELL SYSTEM TECHNICAL JOURNAL 



frequency n; e and m have their usual meanings. The index of re- 

 fraction is less than unity, the X-rays travel faster in glass or in 

 lacquer than in air or in vacuo, and are totally reflected from a glass 

 surface if incident at a sufficiently small angle with the surface. The 

 agreement between experiment and theory is, quantitatively as well 

 as qualitatively, very good. It is equally good for silver, allowance 

 being made for the fact that the frequency of the X-rays used lay 

 between the two absorption-bands of silver. It seems conceivable 

 that this might be refined into a method for determining the numbers 

 of electrons in different orbits of the atom. 



The atoms of the inert or "rare" gases argon, krypton, and xenon 

 are almost completely transparent to slow electrons — electrons moving 

 with a speed of one or two equivalent volts. In more exact language, 

 the radius of the effective cross-section of one of these atoms relatively 

 to slow electrons is much smaller than its radius relatively to faster 

 electrons or to other atoms. This almost incredible statement, having 

 been tested by several different experimenters and by at least two 

 entirely distinct methods, now appears to stand beyond doubt. This 

 radius of the effective cross-section of the atom, relatively to an 

 electron, is (by definition) the least distance at which the electron can 

 pass by the centre of the atom without being intercepted or deflected ; 

 the radius of the atom relatively to another of the same kind is, 

 naturally, half the least distance at which the centres of the two 

 atoms can pass each other without affecting one another's paths. 

 The concept is not perfectly exact, depending as it does on what we 

 choose to take as the least perceptible alteration of the path of a par- 

 ticle; nevertheless, it is practicable and useful. Years ago the radius 

 relative to other atoms was determined (from the viscosity of the 

 gas). There is no binding reason why it should be identical with 

 the radius relative to electrons, but the first measurements of this 

 latter quantity on such gases as hydrogen, nitrogen, and helium 

 yielded fairly good agreements between the two. Recent measure- 

 ments on argon disclosed a surprising difference. 



The method consists essentially in measuring the fraction of a 

 beam of electrons, projected against a layer of gas, which pass through 

 the layer undeflected. (Another and entirely different method used 

 by Townsend resulted in a valuable confirmation of the result.) If 

 there are N atoms under unit area of the surface of the layer (looking 

 through it in the direction from which the electrons come) and N is 

 not so large that many of the atoms are partly shielded, in the per- 

 spective, by others, the fraction of the electrons which go through 

 undeviated is (1 — N^r 2 ); r being the radius just defined. The most 



