Theory of X Rays and Photoelectric Rays. 557 



place that the second term would become of the same order 

 as the first. The first term is always positive, and while it 

 is all important x must always be positive. The second 

 term is oscillatory in sign, however, and when it becomes so 

 great as to mask the first term, oc may be positive or nega- 

 tive. We see, however, that there is time for plenty of 

 oscillations before it becomes important. 



In order that the theory in the form in which we have 

 developed it on pp. 547 to 549 should strictly speaking 

 apply, it is necessary for /jl to be so small compared with n 



that — 2 2 j is sensibly unity, in which case of course (38) 



reverts to the form given on p. 549. 



To take an illustration, suppose that iryut must not be more 



77" 



than - . We must have iit<\, and since p = nt approxi- 



1 

 mately, this means that we must have - < -r~ , i. e. in the 



. n n ±p' 



problem considered on p. 550 - > 320. 



Expressing the results of the theory in the form here 

 developed, we have from (39), since nt—p approximately, 



1 / Y e V 7l 2 . 7TLL . . , , . rt . 



^rAw^ 2 ^ ,approx 7 ' • (4 °) 



subject to the restriction that 



£fc 2 TT 



~2<^ 



n 2 2p 

 so that from (28) and (29), which still apply when ^ is not 



zero, 



irp*c ' fM m it mp v y 



Thus 



U 1 (7l 2 \ V . 2 TT/J^p 



- = — ) -j— sin 2 -££- (42) 



v 2 \urj nr l cp n v ' 



Physical Laboratory, 



The University of Sheffield, 



January 1, 1913. 



