Cathode, Lenard, and Rontgen Rays. 275 



electrons to formulate a priori what ought to be the law of 

 the resistance of bodies to the passage of a stream of electrons 

 through them ; but fortunately we have the comprehensive 

 investigations of Lenard on the subject and can give a 

 reasonable explanation of his results. He found (Wied. Ann. 

 lvi.) that for a great variety of substances of densities varying 

 from that of hydrogen at 3 mm. of mercury pressure ('0 6 368) 

 to that of gold (19*3), the resistance to the passage of Lenard 

 rays depended almost solely on density, the coefficient of 

 absorption being proportional to the density. Now we should 

 expect our electron being so small compared to atoms, and 

 moving with high velocities, to deform locally any atom 

 which it strikes, and to rebound before the deformation had 

 travelled far into the substance of the atom, so that after the 

 electron had departed the atom would be left with an increase 

 of vibrational energy, but no direct appreciable increase of 

 translatory energy ; then, if the velocity of propagation of a 

 disturbance in all atoms is the same, and also the time of an 

 encounter between atom and electron constant, the energy 

 given up by an electron in an encounter with an atom will 

 be proportional to the density of the substance of the atom. 

 Now in the case of a solid, as an electron threads its way 

 through the molecular interspaces, the number of its encounters 

 will be proportional to the length of path, and therefore to 

 the thickness of the solid, and therefore the coefficient of 

 absorption, which will relate to unit thickness of all substances, 

 will be proportional to the density of the substance of the 

 atom, which is nearly the same as the density of the sub- 

 stance ; thus for solids we interpret Lenard's law of the 

 absorption of cathode rays. 



In the case of gases an interesting difference presents 

 itself. The electron is not now threading its way through 

 narrow passages, but has far more clear space than obstacle 

 ahead of it. As the electron is very small itself, we may say 

 that in passing through a gas the number of times it en- 

 counters a molecule is proportional to the mean sectional area, 

 and therefore to the square of the radius R of the molecule 

 regarded as a sphere, and also to the number of molecules 

 per unit volume (n) ; and if m is the mass of the molecule the 

 density of its substance is proportional to ?n/R 3 , and thus the 

 coefficient of absorption for a gas is proportional to nWrn/W 

 or rnn/R; but nm is the density p, so that the coefficient of 

 absorption of a gas is proportional to the density, but also 

 inversely proportional to the molecular radius. Now this 

 theoretical conclusion corresponds partly with one of Lenard's 

 experimental results, namely, that although the coefficient of 



