Moving Electrified Particles jiassing through Matter. 21 



forces from the particle is small compared with the 

 dimensions of their undisturbed orbits, for such col- 

 lisions for which we have to take the forces from the 

 side of the atom into account ; or in other words, 

 that nothing of the same sort as ionization will occur 

 for such collisions. As, however, the forces between 

 the particles and the electrons for the same distance 

 are of the same order of magnitude as the forces 

 which act upon the electron from the central charge 

 and the other electrons, we see that condition (4) is 

 satisfied if condition (3) is. 



It seems very difficult to account accurately for the altera- 

 tions in the result, if the above assumptions are not satisfied ; 



but it is easy to see that if the ratios ^ and ~- are small 



quantities, then the corrections in the result will be propor- 

 tional to the squares of these ratios *. 



Comparison icith Experiments. 

 I. ci-rays. 



We shall at first consider the absorption of a-rays, as the 

 behaviour of these rays, on account of the small scattering, 

 is much more accurately known than the corresponding facts 

 for /3- or cathode-rays. 



Absolute measurements of the variation of the velocity of 

 a-rays with the thickness of matter traversed have lately 

 been made by Geiger t for air. This author found that the 

 relation 



V 3 = KR, (6) 



where V is the velocity of the a-rays and R the corresponding 

 range of the rays in air, was satisfied with great accuracy for 

 a very great part of the path of the rays. In determining 

 K, we have that the range in air of a-rays from radium C is 

 7*06 cm. (at 76 cm. and 20° C.) J, and that the initial velocity 

 of these rays is § 1*98 . 10 9 cm. /sec; this gives K=l*10 . 10 27 . 

 Elaborate measurements of the relative absorption- 

 coefficients of different elements for a-rays corresponding 

 to different ranges in air have been made by Taylor || . The 



* Compare Darwin, loc. cit. p. 902. 



t H. Geiger, Proc. Roy. Soc. A. lxxxiii. p. 505 (19L0) 



% Bragg and Kleeman, loc. cit. p. 318. 



§ E. Rutherford, Phil. Mag. xii. p. 358 (1906). (The above value 

 for V is Rutherford's value for V . M/E, multiplied by 4*87 . 10 3 , i. e. the 

 value of E/M for helium.) 



|| T. S. Taylor, Phil. Mag. xviii. p. 604 (1909). 



