Velocity of Swiftly Moving Electrified Particles. 611 



but an estimate indicates that it would be less than a fifth of 

 the observed value. While the formulae (31) and (33) give 

 values which vary simply as the inverse square of the 

 velocity, the formula (36) gives a variation of I with V 

 which is similar to the variation of AT given by the formula 



(5). Usino- the same value for -2 log v as above, we thus 

 ' c n 



get for a rays in air, that the ratio between the values for I, 



given by (36), for V = 1'8 . 10 9 and for V=T2 . 10 9 is equal 



to 1"65. The corresponding ratio for AT given by (5) is 



1'54. This is in agreement with Geiger's* measurements, 



which gave that the ionization produced by an a particle in 



air, at any point of the path, was nearly proportional to the 



loss of energy suffered by the particle; both quantities being 



approximately proportional to the inverse first power of the 



velocity. 



The number of ions produced by cathode rays in air has 

 been measured by W. Kosself and J. L. Glassonlf. For a 

 velocity of 1*88 . 10 9 Kossel found 3*28 pairs of ions per cm. 

 at 1 mm. pressure. Under the same conditions Glasson 

 found 2-01 and 099 pairs of ions for the velocities 4'08 . 10 9 

 and 6'12.10 9 respectively. At atmospheric pressure this 

 gives for the same three velocities 2*49 . 10 3 , 1*53 . 10 3 , and 

 0*75. 10 3 pairs of ions respectively; or 9"0, 14'7, and 30*0 

 times smaller than Geiger's value for a rays from radium C. 

 The values calculated from (36) for cathode rays of tlie three 

 velocities in question are 7*1, 17*4, and 31*2 times smaller 

 than the value calculated for a. rays from radium C. 



The calculations in this section cannot be immediately 

 compared with measurements of the ionization produced by 

 high speed ft rays, since we have made use of the formula (1) 

 which is valid only if V is small compared with the velocity 

 of light. In a manner analogous to the considerations in 

 section 3, it can, however, be simply shown that the cor- 

 rection to be introduced in the formula (36) is very small 

 and will only affect the logarithmic term. For high speed 

 ft rays, the variation of this term with the velocity V will 

 further — as in the calculations in section 5 — be very small 

 compared with the variation of the first factor. From (36) 

 we shall therefore expect that the ionization produced by 

 these rays will be approximately proportional to the inverse 

 square of the velocity. This is in agreement with W. Wilson's§ 

 measurements. 



* Proc. Roy. Soc. A. lxxxiii. p. 505 (1010). • 

 t Loc. cit. * 1 Phil. Mag. xxii. p. 647 (1911). 



§ Proc. Roy. Soc. A. lxxxv. p. '240 (1911). 

 2 K 2 



