Short Electromagnetic Waves by a Crystal. 55 
corresponds to a deviation of the reflected beam through 6°. This 
alone is, I think, strong evidence that the wave-length X is elastic, 
and not confined to a few definite values, and that equations (1) 
are satisfied rigorously and not merely approximately. 
Besides the distortion of the figure due to the tilting of the 
erystal, a very marked alteration in the intensity of the spots is 
to be noticed. This is especially marked for those spots which 
are near the centre of the pattern, but not on or near the axis 
about which the crystal is tilted. This is probably due to the 
fact that for these spots a considerable change in wave-length has 
taken place. 
When the angle of incidence @ of the primary beam on a set 
of reflecting planes varies, the value of 2d cos @ is altered and the 
alteration for the same 80 is greater the greater @ is. 
One spot in particular changes from being hardly visible in the 
symmetrical pattern to being by far the most intense when the 
erystal is tilted. It is the spot reflected in a plane passing through 
the origin and 
SOOO Oat. O. 
Planes parallel to this have for d, the shortest distance between 
successive planes, the value ati . It can easily be calculated from 
the position of the spot that the value of cos @ changes from ‘19 
to 12 when the crystal is tilted. This corresponds to a change 
in the value of = from 43 to 6°5, and it was found before for the 
square pattern that spots corresponding to the former wave-lengths 
were weak, those corresponding to the latter intense. 
A curious feature of the photographs may be explained by 
regarding the spots as formed by reflection. As the distance of 
the photographic plate from the crystal is altered, the shape of 
each individual spot varies. At first round, they become more 
and more elliptical as the plate is moved further away. A reason 
for this is found in the following. If the incident beam is not 
perfectly parallel, but slightly conical, rays will strike the crystal 
at slightly different angles. Regard the crystal as a set of 
reflecting planes perpendicular to the plane of the paper (fig. 2). 
The rays striking the reflecting planes on the upper part of the 
erystal on the whole meet them at a less angle of incidence than 
those striking the planes at the bottom; the latter are deflected 
more, and the rays tend on reflection to come to a focus in a hori- 
zontal line. On the other hand, rays deviating from the axial 
direction in a horizontal plane diverge still more after reflection. 
Thus as the plate is removed from the crystal, the spots up to a 
certain distance become more and more elliptical. 
