Short Electromagnetic Waves by a Crystal. 53 
locus of the reflected spot as it turns is again an ellipse, which 
now touches the # axis. The intersections of the two ellipses 
will give the position of a spot reflected by a plane passing 
through all three points, the origin, the point a, 0, a, and the 
point 0, a, 3a. 
The ellipses are drawn in the figure, and the plane corresponding 
to any spot can be found by noting the ellipses at the intersection 
of which the spot lies. Only those ellipses have been drawn which 
give the points in Table I. It will be seen that a very large 
proportion of the spots in the photograph lie at the intersection 
of these. 
The analysis involved in this way of regarding the interference 
phenomena must be fundamentally the same as that employed by 
Laue. In fig. 1, suppose the phase difference between vibrations 
from successive atoms along the three axes, when waves of wave- 
length » fall on the crystal, to be 27rh,, 27rh,, 27h;. Then in order 
that the vibrations from those atoms, which are arranged in the 
figure at the centres of the cube faces, should also be in phase, 
one must have 
fo = an integer, = Ra an integer. 
This condition is simply expressed by saying that h,, h., hz 
must all be even or all odd integers. When hy, hy, hs are given, 
the value of X follows from 
Ie 2h, 
2a VAP the the 
since here 2a has been taken as the distance between neighbouring 
molecules along the three axes. 
If the three simplest values of h,, h., hs for a spot on the plate 
are not all odd, or all even, then these numbers must be doubled 
to make them even and the wave-length accordingly halved. 
When this is done, it can be seen that for each value of h, there 
is a series of values of h, and h,. These numbers all give spots in 
the photograph if the corresponding value of - lies within a certain 
range. The smaller the number /,, the larger is the range of = for 
which spots are visible. Spots whose - lies near the extremity of 
the range are very faint, those whose - is in the middle of the 
range are intense. In the tables the values of h,, hz, hz corre- 
sponding to each spot are set down. 
