48 SECTIONAL ADDRESSES. 
probably the carboxy] end, there is an excess per unit length; at the other, 
the methyl end, a deficiency. Thus we may say that the effect on an odd 
order of the spectrum due to a single layer, the thickness of a layer being 
twice the length of a molecule, contains a factor :— 
A sin(@t—a)—B sin(wt—a—2n-+ 1m) = (A+B) sin(@t—a«). 
The factor for an even order is :— 
(A—B) sin(wt—«). 
If at both ends there had been an excess of scattering centres, we should 
have found the even orders stronger than the odd: the effect we find, for 
example, in the (111) planes of rock-salt. In the case of the simpler inorganic 
crystals like rock-salt, diamond, and so on, intensity observations are con- 
clusive as to the structure: in the case of iron pyrites or calcite they are 
very nearly so. But in the case of quartz, where the cell contains nine 
atoms, still more in the case of an organic compound, they do not carry 
us very far. We hope that greater experience will give us in the future 
the power of using them to better advantage. 
In what other direction then shall we look for additional means of 
approaching more nearly to the final solution of the problem of structure ? 
The answer to this question will take account of all the store of physical 
and chemical knowledge which we already possess. Having solved, 
wholly or in great part, the structure of some of the simpler crystals, and 
being able to proceed in all cases, even of the most complicated crystals, 
to the determination of the number of molecules in the cell, and of their 
mode of arrangement, we must try to correlate what we have found with 
the properties of the crystal. By that means we shall become gradually 
more certain of the general connection between the structure and its 
physical and chemical properties ; we shall become able to settle further 
structural details in various cases, and so, by alternate and mutually 
supporting advances, we may hope to reach our goal. 
Let us consider what is being done in this direction. First of all there 
is the question of the distribution of the atoms in space. Given so many 
atoms, to be packed into a cell of known dimensions, what information 
have we as to the space that each must occupy ? The answer to the ques- 
tion cannot be simple, because we may not expect that the atoms are 
always to be treated as spheres, still less as spheres of constant radius. 
It is as generally difficult to state the distance between one atom and 
another as to state the distance between a table andachair. Nevertheless, 
the atom-radius is a useful conception, especially when its dependence 
on the nature of combination is taken into account. The question has 
been considered by W. L. Bragg, Wyckoff, Davey, and others, and it 
appears that an atom does make a definite contribution to the distance 
between its centre—when it can be assumed to have a centre—and the 
centre of a neighbour, so long as the nature of the bond remains the same. 
This is a valuable contribution to the study of structure. It is proved by 
the examination of simple structures like those of the alkaline halides, 
and we may assume its reliability in our attempt on more complicated 
problems. And, of course, it is interesting from the point of view of atomic 
structure itself, and atomic linkages. 
The radius seems to depend on the tightness of the bond as in bismuth 
