478 
AMERICAN JOURNAL OF BOTANY 
[Vol. 9. 
was made and is clearly explained by Bragg and Bragg (45). The relation 
which is fundamental in all work of this sort is expressed by the equation 
\ = 2d sin 6, 
where X is the wave-length, d is the distance between the planes of atoms 
and 6 is the angle between the planes and the beam of X-rays. From 
these relations it follows at once that where only one wave-length and only 
one set of planes is used, the crystal will produce "reflections" only when 
in very definite positions. 
These points become clearer perhaps with a little study of figure I. 
Fig. I. From "X-ray and crystal structure," by W. H. Bragg and W. L. Bragg. 
If Pl, P2, P3, P4 represent the planes of a crystal, planes perpendicular 
to the paper, and FGH a wave front moving towards these planes, a part 
of the wave front reflected from plane Pi follows the path AE and a part 
reflected from P2 will likewise fall into the path AE extended from D, and 
similarly from plane P3, etc. Now in order to have the wave from P2 
reinforce that from Pi, i.e., to have crest coincide with crest, the wave from 
D must be exactly i wave-length, X, behind that from A. In other words, 
the part of the wave from F must travel through a distance i wave-length 
less than the part from G, or 
FA -f AE must equal GD + DE — X. 
Without going into the details of the proof, it happens that CB is the 
difference between the distances traveled by F and G to reach E; and CB 
then, if the waves reinforce each other, must be equal to X. It can easily 
be shown that the angle opposite CB is equal to the angle 6 formed by the 
beam and the planes, and since AB = 2d, then, 
CB = AB sin d, 
or 
\ = 2d sin 6. 
If the difference between the distances traveled by F and G to reach E is 
exactly equal to X, then the wave from Pi will be reinforced not only by 
