X- Rays from Imperfect Crystals. 813 



off rather rapidly to zero. Inside the crystal the trans- 

 mitted beam was found to be extinguished at a rate 

 depending on the exact angle, the greatest factor being 

 e -2qz/ a a ^. fa e cen t r al point. Now if we take the numerical 

 value which q would have in JBragg's experiments, using 

 rhodium K ff rays and the (1, 0, 0) planes of rock-salt, we 

 find that ^ = 2xl0" 4 and 2g/a = UO00. The ordinary ab- 

 sorption, measured by depth, is yitcosec 0=100 ; so it is quite 

 clear that extinction will be of far greater importance. 

 Moreover, if we suppose the crystal only a thousand layers 

 thick we have 2qzja — 2q x 1000=- 0*4, so in even quite a 

 thin layer the extinction may be expected to become con- 

 siderable, and its influence must be examined. We shall see 

 that it cannot be neglected, but that there is a considerable 

 modification in the formulae. 



In D. ii. the phenomenon was studied for an infinitely broad 

 and infinitely deep crystal. The latter condition is to be 

 altered, but to give up the infinite breadth would lead to great 

 difficulty and we shall therefore retain this condition. It 

 requires, however, an alteration in the type of observation, for 

 an infinite plane will always reflect the rays from some point of 

 its surface and so there will be no definite reflecting position. 

 We therefore take a fixed crystal and find the total power 

 reflected for a point source. 



Take a crystal composed of m planes, and first consider 

 its effect on plane waves. The equations of D. ii. p. 678 are 

 applicable. They deal with the multiple reflexions in the 

 successive planes of the crystal, allowing, of course, for their 

 phase relations. The difference equations connecting T r) the 

 amplitude of the transmitted wave at the rth plane, with S,., 

 that of the reflected, take the form * 



S r = -iqT r +(-) n (l-h-ika cos 6 .u)S r+ i "| 

 T r +i = ( — ) n (l—h — ika cos# . u)T r —iq S r+ i J 



where h = ^/jLa cose c is the absorption factor for amplitude. 

 The form of the solution will differ from that in D.ii., as the 



* It lias not been possible to retain completely the same notation as 

 D. ii. The following are the chief differences : — 



D. ii 9 <f> v 



Here 9 4- u 9 ka cos 9 . u. 



I am afraid that in D. ii. e was used in two senses ; on p. 679 it has the 

 same meaning as here, but on p. 681 it is the same as u here. 



