Discharge in Rarefied Gases, 241 



right angles to its axis. When the second layer had attained 

 a thickness of 6 centims., the opposite end of the tube phos- 

 phoresced brilliantly under the influence of negative rays 

 reaching so far. 



According to experiments of Mr. E. Hagen, Assistant in 

 the Physical Institute of Berlin, the smallest density attain- 

 able by the use of a mercury pump of the construction which 

 I employed is y^g- millim. of mercury. If we assume that 

 this smallest possible density was reached in my experiment, 

 then the corresponding mean free path, assuming the value 

 given by Maxwell for atmospheric pressure, would be only 

 0-00006x760x125 millims. = 5*7 millims. But the above 

 observation shows that the actual distance of the second layer 

 is more than ten times as great. 



Inasmuch as a surface almost 90 centims. distant from the 

 kathode phosphoresced brilliantly at this pressure, a consider- 

 able number of molecules must have passed through a distance 

 about 150 times as great as the mean free path. The proba- 

 bility of this for a single molecule would be e~ 150 or about 

 7 x 10" 68 . The discharge-tube has a capacity of about half a 

 litre. According to Thomson a cubic centimetre of air at 

 ordinary temperature and pressure contains about 3 x 10 20 

 molecules. In our tube at the given density there would be 

 about 2 x 10 17 . The probability that even a single one of the 

 molecules thrown off from the kathode should reach the end 

 of the tube without previous collision, is therefore a vanishing 

 quantity. The value of this probability is still less if we take 

 account not only of the density of the residual gas, but also 

 of the tension of the mercury- vapour present. 



Mr. Crookes has in various publications expressed the 

 opinion that the kathode-rays always radiate at right angles 

 to the surface from which they are emitted. As a proof of 

 this, he describes an experiment in which a small spherical 

 concave mirror is employed as kathode, and in which the 

 phosphorescent surface on the wall of the tube is reduced 

 to a point when the wall coincides with the centre of 

 curvature of the mirror. I was convinced from my own 

 experiments that this statement of Crookes's could not be 

 correct ; and from observations which I had previously 

 made with variously curved kathodes, I suspected that the 

 experiment cited as proof by Crookes had not been completely 

 described. 



In order to verify my suspicion I made experiments with 

 a concave spherical mirror as kathode, whose aperture was 

 21-J millims. and radius of curvature 12^ millims. The result 

 was, that when the mirror was placed in the position with 



