If the electricity carried by the electron is supposed to be distributed uniformly over a sphere of radius _a_, for speeds slow compared with the velocity of light, the apparent mass 2 _e²_ _m₀_ = --- ---- 3 _a_ Therefore 2 _e_ _a_ = --- ---- . _e_ 3 _m₀_ Taking the value of _e_ as 1·13 × 10⁻²⁰, _a_ is 1·4 × 10⁻¹³ cms. Thus the diameter of an electron is minute compared with the diameter of an atom. =83. Distribution of velocity amongst the β particles=. Some interesting experiments have been recently made by Paschen[132] to determine the relative number of β particles which are expelled from radium at the different speeds. The experimental arrangement is shown in Fig. 29. [Illustration: Fig. 29.] A small thin silvered glass tube _b_, containing 15 mgrs. of radium bromide, was placed in the axis of a number of lead vanes arranged round a cylinder of diameter 2 cms. and length 2·2 cms. When no magnetic field was acting, the β particles from the radium passed through the openings and were absorbed in an outer concentric cylinder _aa_ of lead of inner diameter 3·7 cms. and of thickness 5·5 mms. This outer cylinder was rigidly connected to the inner cylinder _cc_ by quartz rods _ii_, which also served to insulate it. The cylinder _c_ and the radium were connected with earth. A gold-leaf electroscope _E_ was attached to _a_, and the whole apparatus was enclosed in a glass vessel which was exhausted to a low vacuum by means of a mercury pump. The glass vessel was placed in the uniform field of a large electromagnet, so that the axis of the lead cylinder was parallel to the lines of force. The outer cylinder gains a negative charge on account of the particles which are absorbed in it. This negative charge, which is indicated by the movement of the gold-leaf, tends to be dissipated by the small ionization produced in the residual gas by the passage of the β rays. This action of the gas can be eliminated by observing the rate of movement of the gold leaf when charged alternately to an initial positive and negative potential. The mean of the two rates is proportional to the number of β particles which give up their charge to the lead cylinder. This is evidently the case, since, when the charge is positive, the ionization of the gas assists the rate of movement of the gold-leaf, and, when negative, diminishes it to an equal extent.