334 Prof.W. L. Bragg and Messrs. James and Bosanquet : 



definite conclusions as to the arrangement of the electrons 

 in the atom, the results so far obtained indicate that : — 



(a) The formula for the amplitude of the wave scattered 

 by each electron holds good, at any rate for small glancing- 

 angles. The values for F when sin0 = O'l are of the order 

 to be expected if the curves for chlorine and sodium have 

 maxima at about 18 and 10 respectively. 



(b) A uniform distribution of the diffracting points 

 throughout a sphere cannot explain the form of the curve, 

 for the theoretical form of the F function for such a model, 

 which would coincide with the actual curve at small glancing- 

 angles, meets and crosses the horizontal axis, whereas the 

 observed curve falls away far more gradually with in- 

 creasing 6. 



(c) The general form of the curve makes it probable that 

 as increases, the outer electrons for some reason become 

 less and less effective in diffracting the X-rays. The result of 

 assuming them to be in vibration is that the corresponding 

 theoretical curve for F falls rapidly at first, and then very 

 slowly, with increasing 6. It would seem necessary to 

 make some such assumption, in order to obtain a theoretical 

 curve approximating in form to that actually observed. 



The electrons have been taken to be in radial vibration in 

 the model, but this has only been done in order to obtain a 

 theoretical expression in which the effect of the outer 

 electrons falls away with increasing 6. It may be due to 

 the electrons having a form such as that of the ring-electron 

 assumed by Coster * in discussing diffraction by rings of 

 connecting electrons in diamond. 



Unless we suppose that the outer electrons become less 

 effective with increasing 0, we must conclude, in order to 

 explain the very gradual falling away of both curves, that 

 the electrons are within a sphere of diameter smaller than is 

 probable. By analogous reasoning, Debye (Phys. Zeitschr. 

 loc. cit. p. 10) comes to the conclusion that in diamond the 

 electrons are within a sphere of 0"43xl0~ 8 cm. radius. 

 This must not be excluded as impossible, or even very im- 

 probable ; but if this is assumed, the difficulty remains of 

 explaining why the curve for sodium approaches the hori- 

 zontal axis more rapidly than that for chlorine, as if the 

 former atom were the larger. 



A uniform distribution of electrons throughout the volume 

 of the atom will not account for the observed curves. A 



* D. Coster, Proc. Roy. Acad. Sci. Amsterdam, xxi. No. 6, Oct. 1919. 



