CHEMISTRY: BURDICK AND ELLIS 
647 
tion of the atoms in the lattice, taking as a basis the observed angle 
for the (100) plane. 
We may now proceed to determine the location of the sulfur atoms, 
which can be done with the aid of the intensity measurements. It is 
known that, when the reflection takes place from only one kind of 
plane, the reflections of the first, second, and third orders have inten- 
sities which stand to one another approximately in the ratios 
100 : 20: 7, commonly called the normal intensity-ratios. It is evident, if 
there be secondary planes of lighter atoms intermediate between the 
primary planes of heavier atoms giving rise to a given reflection, that 
the reflection will be diminished or increased in intensity in correspond- 
ence with the difference in phase of the two trains of emerging rays 
waves. In case the secondary planes of atoms lie midway between the 
primary planes, there would be a phase-difference of half a wave-length 
for the first order, one wave-length for the second order, and If wave- 
lengths for the third order; hence there would result a weakening of the 
intensity of the first-order and third-order reflections (equal for the 
two orders) and a strengthening of that of the second order. In case 
the secondary planes are displaced one-fourth of the distance between 
the primary planes, the phase difference will be \, J, and f of a wave- 
length for the first, second, and third orders, and hence there will 
be an increase in the intensities of the first order and third orders (equal 
in the two cases) and a relatively large decrease in the second order. 
Let us consider now the relative intensities of the different orders for 
the different planes. We see that for the (100) plane the ratio of the 
observed intensities of the first and second orders has the value 
100 : 164 in place of the normal one 100 : 20. This large relative weakening 
of the first order and strengthening of the second order shows that 
planes of sulfur atoms are located not far from midway between the 
(100) planes of iron and copper atoms. The reflections from the (001) 
plane show a similar reversal of the normal ratio; and lead to the cor- 
responding conclusion that planes of sulfur atoms are located also not 
far from midway between the (001) planes of iron and copper atoms. 
The form and location of the lattice of sulfur atoms becomes thereby 
fixed, if we consider the additional fact that the number of sulfur 
atoms is equal to the number of iron and copper atoms. In the figure 
given above a sulfur atom would be located at the center of each 
alternate cube (that is, in four of the eight cubes there represented). 
This conclusion is confirmed by the observations of the reflections 
from the other planes. The geometrical relations show that this loca- 
tion of the sulfur atoms involves that they lie in the (110) and (101) 
