Velocities of a Particles from Radioactive Substances. 565 



Correction for the heterogeneity of the a radiation. 



The use of an a-ray tube as a source is not free from dis- 

 advantages, as will become obvious from a consideration of 

 the heterogeneity of the issuing a rays. The practical uni- 

 formity of the tube itself was ensured by careful selection 

 and examination, but we have also to take into consideration 

 the presence of rays which pass through the wall of the tube 

 with varying degrees of obliquity, and some of which go to 

 make up the trace obtained on the photographic plate. It 

 is obvious that the simple theory which applies to the case 

 of a line source of homogeneous radiation is no longer appli- 

 cable. It is not, however, difficult to obtain an approximate 

 formula from which a correction can be deduced for reducing 

 the observed deflexion to the corresponding deflexion in the 

 ideal case of a source of homogeneous rays. 



In the latter case the trace of the a rays on the photo- 

 graphic plate after deflexion is the geometrical image of the 

 rays passing through the slit. The distance betw r een the 

 centres of the bands obtained by reversal is a definite measure 

 of the deflexion of the central ray. Let us now consider the 

 effect of the rays issuing from the a-ray tube. 



Fig. .3. 



U ^- 





> 





In the diagram, fig. ?>, represents the a-ray tube on an 

 exaggerated scale, S is the slit, and P the photographic plate. 

 "We will concern ourselves only with those rays which make 

 the deflexion smaller than the normal. In the case of the 

 rays shown forming the upper trace A on the photographic 

 plate, we need consider only the upper half of the a-ray 

 tube. Take a point such as B in this half of the tube, and 

 let the radius through B make an angle 6 with OSP. Then 

 if the issuing ray makes an angle c£ with OSP, it makes an 

 angle (6-j-(f>) with the normal to the tube at B. Then, if 

 D cm. represents the loss of range in air, say, of an a ray in 

 passing normally through the tube, the loss of range of the 

 ray proceeding from B is approximately D sec (6 + <f>). It 

 must be remembered that the thickness of the wall of the 

 a-ray tube is small compared with the radius, e.g. in a typical 

 case the thickness of the glass would be about 1/20 of the 



