X-Rays from Imperfect Crystals. 809 



The averaging process will introduce the temperature 

 factor ^-Bsinsa and, if desired, the meaning of this may 

 be modified so as to include the relative motions of the 

 atoms in the molecule. There will also be the usual polari- 

 zation factor i(l + cos2 2#). If these are put in explicitly 



Q = N 2 / 2 *. 8 cosec 2de- BtA ** e i(l + cos 2 26). . (4'9) 



Here /will represent the mean scattering in the equatorial 

 plane of the emergent spherical wave from a molecule ; it is 

 the right quantity for determining the distribution of the 

 electrons. In this paper we shall only be concerned in 

 the deduction of the value of Q and nothing further will be 

 said about the other half of the problem. 



The result of this section has been proved without allow- 

 ance for the fact that the incident waves are really spherical 

 and that the Fresnel zones are exceedingly small in X-ray 

 work. It is easy to carry out the whole process, retaining 

 the squares of #, y, z ; but the formulae are much more 

 cumbrous. As they lead to precisely the same result, it is 

 not necessary to give them. 



5. Reflexion from a Conglomerate. 



The next problem to be considered is the reflexion from a 

 small imperfect crystal. It is supposed to be made up of 

 a number of perfect crystals differing slightly in their orien- 

 tations, and the whole is to be so thin that extinction and 

 absorption are negligible. We shall describe it as a con- 

 glomerate and the component perfect crystals as blocks. 

 Suppose that such a conglomerate is put through the same 

 experiment as in § 4. At every point of the observing 

 instrument the intensity will be the sum of the intensities 

 from the separate blocks. Hence the integrated energy 

 will be given by (4*8) , where now V is the volume of the 

 whole conglomerate. But this is not enough; it is also 

 necessary to find the actual reflexion when the crystal is 

 fixed at any angle of incidence — a much more difficult 

 matter. However, Bragg's experiments showed that there 

 was reflexion for settings of the crystal differing by as much 

 as a degree, which is very much larger than the breadth of 

 the diffraction pattern of a single block, and this fact makes 

 it possible to approximate. "We defer the discussion of the 

 size of blocks required for the approximation to be valid. 



Consider a block of volume W which has normal /, m, —1 

 (it is convenient to take it in the negative direction), where 



