36 SECTIONAL ADDRESSES, 
measure the distance between each of the three pairs of parallel faces that 
contain it. The cell may be placed so that each corner of it is associated 
in the same way with a molecule of sodium, let us say: and, of course, the 
knowledge of the dimensions of the cell is equivalent to a knowledge of the 
distance between any two sodium atoms in the crystal, which atoms are 
all alike in every respect. But we have no direct measurement by the 
X-ray methods of the distance between a sodium and a chlorine atom. 
We infer that the chlorine atom lies at the centre of the sodium cell, or vice 
versd, from considerations of symmetry. Crystallographic observations of 
the exterior form of the cell assign to the crystal the fullest symmetry that 
a crystal can possess. If the cell that has been described is to contain the 
elements of such full symmetry, the chlorine atom must lie at the centre of 
it. It cannot lie anywhere else, for every cell would contain a chlorine 
atom similarly placed. There would then be unique directions in the 
crystal; that is to say, polarities. Moreover, both thesodiumand the chlorine 
atoms must themselves contain every symmetry of the highest class : 
the full tale of planes of symmetry, axes of rotation, and so on. They both 
have centres, and we can state the distance between a chlorine atom and a 
sodium atom because we can state it as between centre and centre, and put 
it equal to half the distance between two sodium atoms on either side 
of the chlorine. The structure of sodium chloride is then determined 
completely. 
It may possibly be a difficulty that the cell so described does not at 
first appear to have all the symmetries of the rock-salt cube, but it is to 
be remembered that we are to expect the full display of symmetries only 
when the cell has been repeated indefinitely in all directions. We may take 
a simple case as follows: 
——-8—_O-—_@—_O-—__8—__0__®—- 
Fia. 1 
Suppose sodium and chlorine atoms were to be arranged in a line as in 
the figure, just as they are in any of the three principal directions in the 
crystal. A plane of symmetry perpendicular to the line of atoms indefi- 
nitely prolonged may be drawn through the centre of any atom. The unit 
cell is one molecule: one chlorine and one sodium. The unit by itself 
has not this symmetry, but the repetition of the same molecule in either 
direction on either side provides the symmetry. Moreover, each sodium 
and each chlorine must itself have a plane of symmetry, and the planes 
are equally spaced. We can state the distance between a sodium and a 
chlorine atom as half the distance between two sodiums. 
Let us take one more instance, the diamond. The crystal unit cell 
contains two atoms of carbon: as in the case of rock-salt, it may be so chosen 
that, of its eight corners, six are the middle point of the faces of a 
certain cube and two are the ends of any diagonal of the cube. Thesides 
of this cell are determined by the X-rays, and are all equal to 2.52 A.U. 
This is the distance between any carbon atom and the nearest carbon atom 
which is exactly like itself. The distance between the two carbon atoms 
in the same cell is not measured directly, but can be inferred after it has 
