PHYSICS: A. ST. JOHN 
195 
a and a height c. An elementary triangular cell of such a structure will 
have a volume V = \/3a?c/4:. If the density is p, the mass of a molecule m 
and the number of molecules per cell n, the mass of the cell is nm = 3a 2 cp/4:. 
For ice 2 c/a = 1.4026, p = .91 gm/cml, w = 29.73 X 10~ 24 gm. The mole- 
cular weight is taken, as the arrangement of diffracting centers is funda- 
mentally that of the molecule, each pair of hydrogen atoms being presuma- 
bly near an oxygen atom. These values gave 
a = (54.35»)* X 10~ 8 cm. 
For triangular lattices the following values of n occur: simple lattice, n = 
J; two interpenetrating lattices, n = 1; three interpenetrating lattices, n = 
f or f ; four interpenetrating lattices, n — 2. 
Values of a, a/2, (the spacing of the 1210 planes), ay/3/2 (the spacing of 
the 1010 planes and ca (the height of a cell) have been computed and are 
given in columns 2, 3, 4 and 5 of table 1. When h is the distance of the plate 
TABLE 1 
- 
4 
5 
6 
• 
10 
ii 
n 
x io- 
■s cm. 
h 
= 19.00 cm. 
h 
= 14.75 cm. 
a 
a/2 
ai 
ca 
ZlOTO 
zoooi 
31130 
^10 10 
^00 0 I 
l 
2 
3.01 
1.50 
2.60 
4.22 
2.67 
1.54 
0.95 
2.07 
1.20 
0.74 
3 
4 
3.44 
1.72 
2.98 
4.83 
2.33 
2.35 
0.83 
1.81 
1.04 
0.65 
1 
3.79 
1.89 
3.38 
5.32 
2.11 
1.18 
0.76 
1.65 
0.92 
0.59 
I 
4.33 
2.16 
3.75 
6.08 
1.85 
1.07 
0.66 
1.44 
0.83 
0.51 
from the axis of rotation, x the distance of a given line from the undeviated 
central image, d the distance between planes in the crystal, X the wave-length 
of the radiation and N the order of the spectrum x/h = N\/d, giving the 
relations d = NXh/x and x = N\h/d. The wave-length used was the K 
line of tungsten X = .211 X 10~ 8 cm. In certain cases h was 19.00 cm., in 
others 14.75 cm. Values of x corresponding to these values have been cal- 
culated for the three fundamental spacings of each of the forms having values 
of n already givin. They are shown in columns 6 to 11 of table 1. The val- 
ues of x determined from the four plates used in the calculations and the 
corresponding values of a are given in tables 2 to 5. The average value 
of a is 4.74 X 10~ 8 cm. indicating four interpenetrating lattices. From 
talb 4 it appears that the 0001 spacing is c/2, i.e., the four sets of basal planes 
occur in pairs. A number of plausible models having such arrangement 
exist. They may be differentiated by the spacings of the pyramidal planes. 
It may be shown that in mterpenetrating triangular lattices pyramids hav- 
ing indices of the form (nO~p) have spacings according to the relation 
a r- 
^nOnp = K 2 VS sin - ^nOnp, 
