604 G.P.Thomson. Gold. Plate. S.G. P D D'√P(1+Pe/100moc). mms. cms October 13 (1) …小… 75 24.600 2,50 398 Oetober 12 (4) 10 31,800 2·15 390 October 12 (5) 12.75 39,400 2-00 404 October 12 (6) 15·25 45,600 1·86 405 October 12 (7) 54,300 163 388 October 17 61,200 161 410 Mean 399 This close agreement is in itself strong evidence for the de Broglie theory, and justifies us in considering in detail the other consequences to be expected on this view. 7.Suppose that a beam of cathode rays is incident at an angle 0 on a plane of indices (k)of a small element of crystal.According to the Bragg formula it will be reflected provided that 2d sin 0=aA,where d is the spacing between parallel planes of the type ()If L is the distance of the plate,this will give rise to a mark on the plate at a distance D/2 from the central spot where D=4 0L=2n AL/d,assuming 0 is small. If a large number of small crystals are present arranged at random so that some are present at all angles we shall have a ring of diameter given by the above formula for every spacing d in the 02 crystal lattice and n=1,2,3,ete.This Primary Beam is,of course,the well-known Hull-Debye- F1G.2. Scherrer pattern for powdered crystals. If the crystals have definite orientations with respect to the film some of these rings will be absent.Thus consider a crystal with rectangular axes and suppose a (1,0,0)face is always (approximately)parallel to the film surface,we shall have reflections from (0,1,0)and (0,1,1)faces because the small angle 0 required can be provided by the slight divergence of the cathode ray beam,and by lack of flatness in the film.On the other hand the reflection from(1,1,1)will not appear because the rays would have to make a large angle with the plane of the film in order to be incident on (1,1,1)at the small angle required by the law 2 d sin 0=nA remembering that is of the order of 1/50 that of d.If,further,the crystals are so orientated that not merely is one axis perpendicular to the film,but the