Iv] NATURE OF THE RADIATIONS 139 
particles. The experiments of Townsend! and Durack* point to the 
conclusion that the amount of ionization per unit distance passes 
through a maximum and then decreases as the velocity of the 
particle increases. For example, Townsend found that the number 
of ions produced by an electron moving in an electric field was 
small at first for weak fields, but increased with the strength of 
the electric field to a maximum corresponding to the production 
of 21 ions per cm. in air at a pressure of 1 mm. of mercury; 
while for a much higher velocity of about 5 x 10° cms. per second 
Durack found that the electrons only produce ‘4 ions per cm. at 
1 mm. pressure. In a later paper, Durack® showed that for the 
electrons from radium, which are projected with a velocity of 
about half the velocity of light, the corresponding number of ions 
per cm. of path is ‘19 or only about 1/100 of the maximum number 
observed by Townsend. 
It has been shown by Des Coudres that the velocity of the 
cathode rays diminishes when the rays pass through thin metal 
foil. This is probably also true of the a and 8 particles produced 
by the active substances. 
If the decrease of the ionization according to an exponential 
law with the distance were due only to a gradual retardation of 
the speed of the projected particles, it follows that the ionization 
per unit distance for both the a and 8 particles must vary as the 
square of the velocity of the particle. For suppose that im passing 
through a distance dw a particle of mass m decreases in speed from 
v to v—dv. The loss of energy of the particle is mvdv, and 
this should be proportional to the number of ions gda produced, 
where g is the rate of production of ions per unit length of the 
path. Since the ionization is assumed to fall off in an exponential 
law with the distance w, we get ¢= qe” where q, is the value of q 
when « =0. 
Then mody = kqe™ da, 
where k is a constant and 
kq ke 
iL gine 9 —AX q es q 
mv? = — at A= — EA =, 
z, r a r 
1 Phil. Mag. Feb. 1901. 2 Phil. Mag. July, 1902. 
° Phil. Mag. May, 1903. 
