626 Mr. K. D. Kleeman on the Secondary Cathode 



give approximately the secondary cathode radiation from 

 suhstances exposed only to /5 rays. 



The curves which he obtains by plotting the secondary 

 radiation against the atomic weight, and joining the elements 

 of the same period by a smooth curve, differ in shape from 

 those obtained by the writer with 7 rays ; but still there are 

 points of resemblance. Both of his curves, representing the 

 first and second long periods of the elements, are concave 

 towards the atomic weight axis, at the extremities of the 

 curves corresponding to higher atomic weight, a result 

 obtained also by the writer in the case of 7 rays. But his 

 curves show that, on the whole, the change of secondary 

 radiation with atomic weight decreases with increase of 

 atomic weight; the opposite, we have seen, is the case with 

 7 rays. Moreover, his curves approximate to a series of 

 straight lines. 



Also, he obtained with the /3 rays no such comparatively 

 large difference in the radiating powers of lead and bismuth 

 as the writer obtained with 7 rays. 



A stream of /3 rays falling on a plate diminishes very 

 rapidly in intensity as it penetrates into the plate, and the 

 amount of secondary radiation must therefore depend to a 

 certain extent on the rate of absorption of the rays. In the 

 case of 7 rays the decrease in the intensity of the rays is 

 small when they are passed through a thickness of matter 

 producing the maximum amount of secondary cathode radia- 

 tion. Therefore the difference in the rate of absorption of 

 the /3 and 7 rays by a substance, is one of the factors which 

 tend to make the relative radiating powers of the various 

 substances different with ft and y rays. We will now ex- 

 press the secondary radiation from a thick layer of a substance 

 in terms of other quantities. 



Let us suppose that the 7 rays are not diminished in 

 intensity when passing through a layer of a substance of the 

 thickness necessary to produce the maximum amount of 

 radiation, and let K denote the number of electrons ejected 

 in each c.c. of the substance due to the action of the 7 rays. 

 The moving electrons in the substance may be resolved into 

 two streams parallel to one another, but moving in opposite 

 directions and at right angles to the parallel surfaces of the 

 layer. Let r denote the intensity of the stream at a distance 

 x from one of the radiating surfaces, moving away from the 

 surface, and R the intensity of the stream approaching the 

 surface. Let jn denote the coefficient of absorption of the 

 electrons if there were no secondary radiation, and k the 

 ratio of the secondary to the absorbed radiation. Then we 



