Nov., 1922] SPONSLER STRUCTURE OF STARCH GRAIN 
479 
that from P2, but also by the waves from Piooo, and from any other plane 
the rays can reach. But if that distance is greater or less than X, by even 
one part in 2000, for example, then the wave from Piooo will neutralize that 
from Pii and the one from Piooi will neutralize that from P2, and so on. 
The neutralizing effect is not quite complete, because the incident rays 
reaching Piooo are weakened by passing through so many planes. So it 
happens that unless X is almost exactly equal to 2d sin 6, reflection will fail 
to occur. It is important to notice that this conclusion is based on the 
assumption that the reflecting body consists of a large number of planes. 
If, on the other hand, the number of planes from which reflection occurs is 
small, then the neutralizing effect becomes less complete and the reflected 
line becomes broad and blurred; and an unusually large range of angles 
will be effective in producing the reflected line. 
In discussing the structure of the crystal a few pages back, three prom- 
inent sets of planes were mentioned. Those parallel to the faces of the 
cube, which were called the 100 planes, were separated by a uniform distance 
d. If that crystal were placed so that a narrow beam of X-rays hit these 
faces making the glancing angle equal to ^1, then a reinforced train of waves 
would be reflected from them. If it were placed so that the angle were 
slightly greater than 261, another reinforced train of waves would be re- 
flected, and the equations would be 
These are reflections of the first order, second order, third order, respectively. 
The subscript figure is used to designate the larger angles and incidentally 
the order of reflection. The second-order lines are very weak, and those 
of the third order are still weaker. The latter are not considered in the 
present work. 
If the crystal were placed so that the beam made the proper glancing 
angle with the no set of planes, then again a reinforced reflection would 
occur. The distance between these planes is J V2 times the distance 
between the 100 planes, so that now d has a new value, and since X remains 
the same, sin 6 must be a new value in the equation, \ = 2d sin d. Another 
change in values takes place when the in planes are in position to reflect 
the beam, and again d and d would have new values. The equations would 
read for the first-order reflections : 
Reflection from Crystal Planes 
\ = 2d sin di, 
2X = 2d sin 02, 
3X = 2d sin ^3, etc. 
For 100 planes, X 
For no planes, X 
For III planes, X 
(2^^ X i) sin di'. 
{2d X .707) sin Bi''. 
{2d X .577) sin 6^"' 
