314 Prof. W. H. Bragg on the Structure of 



(4) Two planes containing three oxygen atoms each and 



having phases 7r/4-fa and — 7r/4 — a respectively. 

 I£ « is determined the size of the tetrahedron is 

 known. 



(5) Two planes containing one oxygen atom each and 



having phases 7r/4 — 3a and — 7r/4 + 3« respectively. 



The combination o£ the whole gives the same effect as that 

 of a single plane having a weight 



nir / tc \ /it \ 



56 + 112 cos -j- + 168 cos nir + 32 cos n I — — 3a ) + 96 cos n I — + a y 



where n is the order of the spectrum. We here assume 

 what is no doubt an approximation only, that every atom 

 contributes to every order of reflexion in proportion to its 

 weight. In order to find a value for a let us first examine 

 the effects of the iron atoms alone. Putting n = 1, 2, 3 . . . > 

 the first three terms give us the following series of values: — 



-34, 224, -190, 112, -190, 224, -34, 336. 



We have to allow for the rapid decline in intensities as we 

 proceed to higher orders, which seems an invariable effect. 

 In the Bakerian lecture for 1915 it is ascribed to the fact 

 that the centres scattering the X-rays are distributed through 

 the volume of the atom and are not concentrated in one 

 point. In general, we find that the intensity falls off in- 

 versely as the square of the order, where the reflecting 

 planes are similar and similarly spaced. We may approxi- 

 mately allow for this fact by multiplying the experimental 

 results, each by the square of its order, and then comparing 

 them with the figures just found by calculation. 



The experimental figures (see fig. 1) are 



6 28-5 48 25 12*6 2-3 '3 6'6, 

 which then become 



6 114 432 400 315 84 14 424. 



There is a steady rise to the 3rd or 4th followed by a 

 steady fall and a large rise to the 8th. 



Comparing these with the calculated figures due to the 

 iron alone, we see that the latter are at fault in having 

 the 2nd and 6th too large and the 4th too small. We 

 shall want all the influence we can get from the oxygen 



