606 Dr. IS. Bohr on the Decrease of 



give strong support to the expressions used for the moment am 

 and the energy of a high speed electron. Let us for a 

 moment suppose that the ordinary expressions for the 

 momentum and the energy oE slowly moving electrons could 

 be used without alteration. This should not alter the equa- 

 tions (26) and (27), but the values for V deduced from the 

 values for H/? would be (1 — -/3 2 ) ~* times greater. Introducing 

 this in the formula (27) we should have found a value for 

 A(H^) which for the swiftest rays would be about 30 times 

 smaller than that observed by Danysz, and the values in the 

 last column of the table on p. 601 would, instead of being 

 nearly constant, be more than 20 times smaller for the 

 slowest rays than for the swiftest. If, on the other hand, we 

 had supposed that the expressions for the momentum were 

 correct, but that the "longitudinal" mass of the electron 

 was equal to the " transversal " mass, we should have obtained 

 the same values for V as in the table, but the equations (26) 

 and (27) would have been altered by a factor (1 — /3 2 ) _1 . In 

 this case the value calculated for /\(Kp) for the swiftest 

 rays would have been about 15 times larger than that ob- 

 served, and the values in the last column, instead of being 

 nearly constant as observed, should have been expected to 

 be 10 times greater for the fastest than for the slowest rays. 

 It thus appears that measurements on the decrease of velocity 

 of /3 rays in passing through matter may afford a very 

 effective means of testing the formula for the momentum 

 and the energy of a high speed electron. 



§ 6. The ionization produced by a, and /3 rays. 



A theory of the ionization produced by a and /3 rays in a 

 gas has been given by Sir J. J. Thomson*. In this theory 

 it is assumed that the swiftly moving particles penetrate 

 through the atoms of the gas and suffer collisions with the 

 electrons contained in them. The number of pairs of ions 

 produced is supposed to be equal to the number of collisions 

 in which the energy transferred from the particle to the 

 electron is greater than a certain energy W necessary to 

 remove the latter from the atom. If we neglect the inter- 

 atomic forces this number can be simply deduced. By dif- 

 ferentiating (I) with regard to p and introducing for pdp in 

 (3) we get 



, A 2?n? 2 E 2 NnAtf dQ, 



dA = — m^— <r (30) 



* Phil. Mag. xxiii. p. 449 (19]2). 



