44, Mr Bragg, The Diffraction of 
whose cosines are a, , y, for incident radiation of wave-length 2, 
the following equations must be satisfied 
aa—h)r, “ap—hr, a(l—vy)— hee (1) 
where h, h, hs are integers. 
These equations express the condition that the secondary 
waves of wave-length »X from a molecule, considered for simplicity 
as being at the origin of coordinates, should be in phase with those 
from its neighbours along the three axes, and that therefore the 
secondary waves from all the molecules in the crystal must be in 
phase in the direction whose cosines are a 8 ¥. 
The distance of the crystal from the photographic plate in the 
experiment was 3°56 cm. The pencil of X-rays on striking the 
crystal had for cross-section a circle of diameter about a millimetre, 
and the dimensions of the spots are of the same order. The plate 
of crystal was only 5 millimetre thick. It is thus easy to calculate 
with considerable accuracy from the position of a spot on the 
photographic plate the direction cosines of the pencil to which it 
corresponds, since the pencils of rays may be all taken as coming from 
the centre of the crystal. Laue found, on doing this for each spot, 
that as a matter of fact the values for a 8 1—y so obtained were 
in the numerical ratio of three small integers h, h, h, as they 
should be by equations (1). 
For instance, a spot appears on the photographic plate whose 
coordinates referred to the x and y axes are 
x= 28cm, y=142 cm. 
The distance of the crystal from the photographic plate, 
3°56 cm., gives Zz. 
Thus since S/S BED BOP SB 
aoe B me 1 ae 1 
b) BOLT Us 8B a2 =v 
ars 98 142 27° 
or a 8 Alive ole 
Laue considers some thirteen of the most intense spots in the 
pattern. Owing to the high symmetry of the figure, the whole 
pattern is a repetition of that part of it contained in an octant. 
Thus these thirteen represent a very large proportion of all the 
spots in the figure. For these spots he obtains corresponding 
integers h, h, h; which are always small, the greatest being the 
number 10. But even if one confines oneself to integers less than 
10, there are a great many combinations of h, h, h; which might 
