SECTIONAL ADDRESSES. 
SECTION A.—_MATHEMATICAL AND PHYSICAL SCIENCE. 
THE ANALYSIS OF CRYSTAL 
STRUCTURE BY X-RAYS. 
ADDRESS BY 
Proressor Sir W. H. BRAGG, K.B.E., D.Sc., F.R.S., 
PRESIDENT OF THE SECTION. 
In this address I propose to consider the new methods of analysing the 
structure of materials by means of X-rays, considering especially the 
stages by which they move towards their objective. It is convenient to 
recognise three such stages, of which the first comprises the simplest and 
most direct measurements and the last the most indirect and complex. 
The fundamental measurement of the method is the angle at which 
rays of a given wave-length are reflected by a set of planes within the 
crystal. The planes of a‘ set ’ are all exactly like one another: an imagi- 
nary observer within the crystal could not tell by any change in his sur- 
roundings that he had been moved from one plane to another. Sometimes 
there is no reflection of the first order from a set so defined, because the 
planes may be interleaved by other planes so spaced and of such strength 
as to annul the true reflection; but this can always be allowed for. 
When the wave-length of the X-rays is known, the angular measurement 
can be used to find the spacing of the set of planes, and in this way a 
linear dimension of the crystal is measured. The spacing is the distance 
between any plane and its nearest like neighbour on either side. If the 
spacings of three different sets of planes are found, the volume of the 
unit cell isfound. The crystal unit cell is bounded by six faces, each set 
of planes furnishing a pair. The pair consists of two neighbouring planes 
of the set. The cell may have a great variety of forms, but has always the 
same volume. The specific gravity of the substance being known, it is 
possible to find the number of atoms of various kinds which the cell con- 
tains: the proportion of the various kinds is necessarily the same as in 
the molecule of the substance. The cell is in practice found always to 
contain a small integral number of molecules, one, two, three, or four, rarely 
more. This assemblage of molecules is fully representative of the crystal ; 
by the mere repetition of the cell, without the addition of any new 
features, the crystal with all its properties is produced. 
There are, therefore, three types of assemblage. The simplest is that 
of the single atom, as in helium in the gaseous state, in which the behaviour 
of every atom is on the whole the same as the behaviour of any other. 
The next is that of the molecule, the smallest portion of a liquid or gas 
which has all the properties of the whole: and lastly, the crystal unit, 
the smallest portion of a crystal (really the simplest form of a solid 
