Short Electromagnetic Waves by a Crystal. 49 
Consider the atoms as arranged in vertical rows parallel to 
the z axis in the figure. A plane for which p=1 and r=1 passes 
through one atom in every one of these vertical rows (see fig. 3). 
Therefore the next plane to it passes through a set of atoms all 
2a above the corresponding atoms in the first plane. Thus for 
this set of planes, J=2a and the wave-length \=4an2. The 
effective density of atoms on such a set of planes is the greatest 
possible. 
If p=1, r=2, each plane now passes through atoms in one 
half of the vertical rows. For instance, the plane through the 
origin contains no atoms in those vertical rows for which r 1s odd. 
| 2 
The successive planes must cut the z axis at intervals >: since 
the effective density of atoms in each is half as great as before and 
the whole number of atoms in unit volume of the crystal remains 
constant. Similarly if p=1, r=3 jae and so forth. 
3 
2a 
In the general case / = TERmNonpiandy 
In the tables given below planes with the same effective 
density of atoms on them, and therefore the same values of /, are 
grouped together. 
__ The position of the spot reflected by each system of planes 
considered has been calculated, also the wave-length of the 
| 
: : a 
reflected train expressed for convenience in the form 7 and when 
‘in the photograph a spot is visible in the position calculated, its 
‘intensity is denoted by star according to an arbitrary scale. 
vv Vv y 
ae * * + e 
| When no spot appears in the calculated position, I have put 
‘invisible’ opposite that plane. 
_ There is no need to go any further than the set for which 
| p=" , to obtain all the spots in the photograph. Indeed only 
one spot is given by this last set. 
Only one spot on the plate is to be assigned to planes of this 
class. It is curious that the value of corresponding to this spot 
should be as great as 11°2. It is noticeable in the photograph 
that all spots at any distance from the centre of the pattern tend 
‘to become very faint, and the values of p, g, 7, s which do give a 
spot in Table IV are the only ones to be found giving a spot 
at all near the centre. In the first three tables the parameters 
VOL. XVII. PT. 1. 4 
