274 PEOF. W. H. BRAGG ON X-EAYS AND CRYSTAL STEUCTURE. 



that the intensity of any spectrum is proportional to l/sin 2 0, where 6 is the glancing 

 angle, no matter whether the spectra belong to one or to several spacings of the planes. 

 This involves both the facts just stated. 



We chose such a form of the density curve for the single atom that we could 

 account for the first fact. The important point is that without further hypothesis 

 we explain the second. The formula we have obtained shows that when a 2 c 2 is small 

 compared to nV the intensity varies inversely as n 2 when a is constant, and as a 2 when 

 n is constant. 



Thus our hypothesis is self consistent. It does not seem unreasonable. If it turns 

 out to be true, though there is much to be done before its truth can be considered 

 proved, it seems to offer an excellent means of determining the distribution of 

 electrons in the atom. 



One or two subsidiary points may be considered very briefly. 



I have considered the case of a crystal in which the atoms are all alike and the 

 planes are spaced regularly. It is easy to make the proper changes when more 

 complex cases are considered. 



When a\r is not small compared to V 2 which would be most likely to happen 

 when n = 1, and a or c, or both a and c are large, that is to say for reflections at small 

 angles when there is little overlapping of atoms, then the intensity should be smaller, 

 in comparison with other intensities, than is indicated by the inverse square law. It 

 may be a misleading coincidence, but certainly this effect sometimes appears, for 



example, in the first (ill) of calcite : perhaps, too, in the first (100) of zinc blende. 



An atom for which c is large a " condensed " atom should on that account give 

 relatively stronger reflections in the higher orders. The high order intensities can be 

 measured with considerable accuracy, and their comparison should be interesting. 



