76 Transactions of the Royal Society of South Africa. 
have supposed them to be by placing atoms merely at the corners of the 
rhomb. If we take a face-centred lattice — 
then d m = '6071a as before (8) 
but d m = -4,99a (9) 
and d UQ = - 367<x (10) 
hence from (5) and (8) a = 612 x 10— 8 cm. 
(6) „ (9) a = 6-18 x 10- 8 „ 
(7) „ (10) a = 6-12 x 10- 8 „ 
mean value of a = 6' 14 x 10~ 8 ,, 
Taking the density of antimony as 6' 70 grms./cm. 3 the mass of the 
rhomb is equal to — 
670 x 614 3 x 0 9973 2 x 10-24 
= 1545 x 10-24 grm. 
Since the atomic weight of antimony = 120*2, and the mass of the 
hydrogen atom = 164 x 10~ 24 grin., then n x 1202 x 1*64 x 10 — 24 = 
1545 x 10 _2i grm., where n is the number of atoms per unit rhomb. This 
gives n = 7'85. 
It is clear, then, that there are 8 atoms per unit rhomb. 
Let us take 8 atoms per unit rhomb, find the mass of the rhomb, hence 
its volume and then find a. We find a = 6 20 x 10~ 8 cm. 
Assuming a face-centred lattice we find then — 
d 100 = 3-09 x 10- 8 cm. 
d ni = 376 x 10- 8 „ 
d uo = 2-24 x 10- 8 „ 
^ 110 = 2-13 x 10- 8 „ 
We can now calculate the glancing angles for the spectra from the 
different faces. 
Planes. 
(Too) (111) (110) 
Observed angle . 5°-30'' . 4° 30' . 7 a 30' 
Calculated . . 5°-25' . 4°-27' . 7°-32'. 
Arrangement and Spacings of the Atoms, 
(a) (111) planes : 
We conclude that the underlying structure is the face-centred lattice, 
but a face-centred lattice gives only 4 atoms per unit rhomb. To determine 
the positions of the other 4 atoms we must investigate the relative intensi- 
ties of the spectra from different faces. The observed intensities of the 
spectra of five orders from the (I'll) planes were — 30 : 100 : 33 : 4 : 12. 
The first order being weaker than the second shows that there is a plane 
of atoms dividing the distance (3*76 x 10 -8 cm.) between the (111 ) planes. 
Let /J be the phase difference between the two sets of planes, and taking the 
