396 Prof. W. H. Bragg on the Consequences of 



range of which can be found with precision. We may think 

 of the ft particle as possessing an average range in a given 

 material, best expressed perhaps as a weight of material 

 crossed. For purposes of definition we may suppose the 

 track to be the axis of a cylinder of a small cross- section s ; 

 then if ds is the weight of the cylinder, d is the range. 

 I hope to be able to show presently that it is possible to find 

 the relative values of d for given ft rays in various substances. 



We have already sufficient information to give us some 

 idea of the lengths of the short portions which make up the 

 total range. The work of Madsen * shows that such ft par- 

 ticles as have been turned aside from a main stream passing 

 normally through an aluminium sheet "004 cm. thick are not 

 likely to experience a second deflexion in the same plate. 

 Thus ft particles of a speed approximating to that of light 

 must often go through a tenth of a millimetre of aluminium 

 without deflexion, or through the equivalent 20 cm. of air. 

 Similar conclusions may be drawn from an earlier paper by 

 Crowther f. Crowther does indeed state that the scattering 

 of a pencil of ft rays is complete when it has passed through 

 '015 cm. of aluminium ; but he uses the term in a special 

 sense relating to the details of his experiment. It does not 

 mean that after going through such a plate the stream of 

 ft rays has lost ail sense of direction, and the various rays 

 are heading everyway; for his figures show that 30 per cent, 

 of the rays which emerge from the plate and were originally 

 directed normally upon it retain so much of their original 

 direction as to be grouped about the emergent normal in a 

 cone of a semi-vertical angle between 4° and 5°. The solid 

 angle of such a cone is about 250 of that of a hemisphere. 



I have now considered one by one several possible causes 

 of complexity; and I would conclude that on the whole they 

 can be put aside as having at present no obvious existence. 

 In this way we arrive at a comparatively simple idea of the 

 history of the radiant entity whatever its kind, a, ft, 7, X, or 

 cathode ray. In each case there is an initial store of energy 

 communicated to the entity : the subsequent motion is recti- 

 linear, varied by encounters which change the direction of 

 the motion but not its energy: ionization, if it takes place 

 at all, takes place along the track ; and it is in this way that 

 the energy is drawn upon. The form of the entity may 

 change, 7 into ft, X into cathode ray, and so on ; but there 

 is so little change in anything but form that practically we 

 may assume a continuity of existence. 



Phil. Mag. Dec. 1909. 



f Proc. Roy. Soc. March 1908, lxxx. p. 186. 



