Experiments on Diffraction of Cathode Rays. 605 axes in the film are not arranged at random,then the rings which do appear will not be of uniform intensity,each direction of the axes giving rise,in the case of cubic symmetry,to four spots on the circumference of the ring. 8.Aluminiwm.-Let us examine the results obtained with aluminium from this point of view.The films used were the thinnest foil etched down by floating in caustic potash till they were transparent.It is difficult to estimate the thickness actually used as the films so formed are not uniform,but probably to give good results they must not be more than 10-5 cm.Looking at figs.1 and 2(Plate 19),we see that the rings are non-uniform so that presumably the crystals have become orientated in the process of rolling the film.Besides the inner ring Di,two others,D2 and Ds:can be distinguished outside it,and traces of a fourth between D2 and Da. The ratios of D./D,Da/D,are shown below. Plate. 0ct.12 0ct.11 0ct.7 0ct.7 0ct.7 0ct.7 0ct.7 Mean. (3). (1). (6). (5). (2) (2). (1). D./D 141 1.39 142 137 1.38 142 141 140 D:/D 2-15 2-02 2-08 In some of the cases in which no value of Da/D,is given the ring was outside the field on view,in some it was too faint to measure.It will be seen that the ratios correspond closely to√2：land2:l. Now aluminium is found from X-ray experiments to have a fore-centred cubic lattice.For such a lattice the distances "d"of the planes are given by d=a√+2+2 where五，k,I are the indices of the plane and“a”the side of the unit cube.If some of the quantities(亿，，)are odd and some even,. counting zero even,all are to be doubled. Now,if one axis is perpendicular to the film,the possible planes are those for which one index is zero,and the smallest values of k,l are (1,0,0),(1,1,0), (1,2,0),etc.Now D=2nLVa,hence doubling the indices when required we have in succession Da/xL=n4,n412,n4V5,etc.If we put n=1,2in the first and n=2 in the second,we get Da/L=4,4V2,8 or in the ratio 1:V2:2 as found for D1:Da:Da and it is easy to see that any other ring will be outside these.The faint ring between Da and Ds is, I think,probably due to a few of them not being orientated in the way assumed.As far as can be measured its diameter is to D,as V3:1 and thus would correspond to the second order reflection from a(1,1,1)plane. In the examples reproduced there are too many crystals,as shown by the *Da is not visible in the reproductions. VOL.CXVII.一A. 2T