240 Theory of the Scattering of Rontgen Radiation. 



examination it may be seen that some variations of the sort 

 specified above will suffice. 



The fifth statement, about the changes of b y is equivalent 

 to a statement that as the primary beam becomes harder, the 

 excess radiation will be confined more and more to the smaller 

 angles. This is obviously equally true of the calculated value, 

 as an increase of hardness, and consequent decrease of T, 

 makes V begin to decrease sooner with increase of 0, and 

 confines the re-enforced radiations to smaller angles. 



While it seems probable from these considerations that no 

 further assumptions than the existence of electrons and the 

 truth of the electromagnetic equations as applied to theni 

 are necessary to explain most of the effects observed by 

 Mr. Crowther, it is by no means certain that the secondary 

 cathode particles of which he speaks in his second paper do 

 not have an important effect upon the phenomena. But as 

 his hypothesis is based partly on the assumption that a 

 cathode particle radiates only when being stopped, and then 

 only in the direction of its motion just before stoppage, the 

 accuracy of his conclusions mnst depend partly on the 

 accuracy of this assumption. On this the equations of the 

 electromagnetic field lead to some interesting suggestions. 



For if an electron already in rapid motion is accelerated 

 in any direction, and the retarded potentials due to it are 

 computed for any point in the radiated pulse, they will both 

 contain the factor (1 — /3 r )~\ where /3 r is the component of 

 the velocity of the electron in the direction of the point con- 

 sidered, the time units being the same as above. Therefore, 

 as a brief calculation would show, the radiated vectors would 

 differ from the values for the case of an electron momentarily 

 at rest by the same factor, and the radiated energy per unit 

 volume of the pulse by the square of this factor. But the 

 thickness of the pulse varies directly as (1— /3 r )> Hence the 

 radiation per unit area of the pulse will be stronger in the 

 ratio 



Ki> < 10) 



in this direction than in the opposite. To the extent indi- 

 cated by this ratio, and only to this extent, may we therefore 

 say that the Rontgen pulse follows the direction of the cathode- 

 ray from which it is produced. 



The results of the experiments by Mr. Kaye *, quoted by 

 Mr. Crowther as a confirmation of his hypothesis, are easily 

 explained by expression (10). For in these experiments it 

 * G. W. C. Kaye, Proc. Camb. Phil. Soc. xv. p. 269 (1909). 



G 



