Theory of X-Ray Reflexion. 331 



at 4°, we have X = o # 92 x 10" 9 cm. We then get a curve of 

 intensity given in the following table : — 



■\/\ 1 a a 7 i ii ii il ii 9 9i 



A / A o 2 8" 4 8 - 1 ^8 ± 4 - L 2 ± 4 - -4 



E A ; 3 10 32 68 100 101 99 79 48 22 11 



By a rough quadrature it appears that about 7 per cent, of 

 the radiation is contributed by the characteristic platinum 

 radiations ; and it happens that f Ea^X is very nearly equal to 

 E A , where E refers to the value at X G . In deducing this 

 result it is assumed that the ionization is proportional to the 

 energy. This assumption is rather doubtful, as we should 

 expect that the secondnry electrons from the softer rays would 

 be so appreciably absorbed by the gas that they produce less 

 than their due share of ionization. 



Using this quadrature and the experimental value 0'0035 

 for the efficiency of reflexion at 4°, we can estimate the value 



of v + 2 2)2 cos (Ps~-$>t)- It is 26. But there is strong- 

 reason to believe that the efficiency was overestimated. 

 We have seen that, assuming the independence of scattering 

 from separate atoms, the whole reflexion really only takes 

 place within a breadth of about 5 ;/ . If we assume that the 

 radiation in this breadth is completely reflected, we arrive at 



E„§S<9 



an efficiency — tt— , where 80 is 5". Using the quadra- 



ture, this is cot 686 or 0*0004. It is possible that when the 

 reflexion becomes strong it is spread over a broader angle, so 

 that we cannot conclude that the overestimate of efficiency 

 is as great as suggested by this figure. It may be observed 

 that the disagreement cannot be due to the less ionization 

 by the softer rays, since the efficiency is measured by com- 

 pari son with the ionization of the whole beam. It seems 

 possible that in comparing two effects one of which is 300 

 times the other, there should be incomplete saturation in the 

 larger. 



Unfortunately the fact that the reflexion must be regarded 

 as nearly perfect vitiates the formulae for reflexion. It does 

 not even appear why the second order should be so much 

 weaker than the first. It is hoped to discuss this aspect of 

 the matter in a future paper. 



