648 CHEMISTRY: BURDICK AND ELLIS 
planes of the iron and copper atoms; and that there is a plane of sul- 
fur atoms in the (HI) plane displaced one-fourth of the interplanar dis- 
tance between the composite planes of iron and copper atoms. Cor- 
respondingly, the (110) and (101) planes show the normal ratios of 
intensities of the reflections for the first, second, and third orders; 
and the (111) plane shows the required decrease of the second-order 
reflection, and the expected normal ratio of the first-order and third- 
order reflections. 
The relative intensities of the different orders can be calculated from 
the principle that the intensity of reflection from a plane of atoms is 
proportional to the square of the mass per unit-area.^ Thus, the in- 
tensity of reflection from the (111) sulfur-atom plane would be to that 
from the (111) composite iron-copper atom plane as (2 X 32)^: (56 -f 
63.6) ,2 since there are two atoms of sulfur in an area equal to that in 
which there is one atom of iron and one atom of copper. The intensity 
of the resultant reflection will evidently be dependent both on the mag- 
nitudes of these two component reflections, and on the difference in 
phase in which they emerge. Algebraic expressions for the relative 
resultant intensities of the reflections of the different orders can be 
readily formulated. With the aid of these expressions the 'calculated' 
ratios of intensities given in the above table were obtained. It will 
be seen that there is a striking parallelism between the calculated and 
observed intensities. 
Finally, we may further test the correctness of the deduced atomic 
structure by calculating the density of the substance and comparing 
it with the known density. Referring to the figure, it is seen that the 
space which it represents has associated with it two iron atoms, two 
copper atoms, and four sulfur atoms, or 2 of the atom-groups CuFeS2. 
Since the mass of the hydrogen atom is 1.64 X 10"^* grams, that of 
these two CuFeS2 groups is 2 X times as great, or 5.972 X 10"^^ 
1.008 
grams. The volume of the space in question is, however, equal to 
^ X 0.985, where d represents the distance between the (100) planes 
of copper-iron atoms (that between the (001) planes being 0.985 d). 
This distance d may be obtained from the law of reflection \ = 2 d 
sin B by substituting for d the observed angle of reflection (6°25') for 
the (100) plane, and by substituting for X its value 0.584 X 10~^ cm. as 
determined by W. L. Bragg^ for a palladium target. The value of d 
is thus found to be 2.614 X 10~^ cm., and that of the volume in ques- 
tion 1.407 X 10-22 cm. The calculated density is therefore 5.972/1.407, 
or 4.24. The density of the mineral chalcopyrite, according to the 
