A.—MATHEMATICS AND PHYSICS. 49 
or in graphite, where there are two kinds of bonding, and the plane of 
cleavage cuts across all the longer distances from centre to centre. In 
calcium fluoride the centres of calcium atoms are closer together than they 
are in the metal itself in spite of the interposition of the fluorine atoms ; 
and in calcium oxide they are still closer. The change in the type of the 
bonding has altered the value of the radius. 
There is also the very interesting but still more unsettled question of 
the mutual orientation of the bonds between an atom and its neighbours. 
It is, of course, the carbon atom which is the occasion of this problem in 
its most pressing form. In the diamond the exactly tetrahedral arrange- 
ment of bonds is associated with great rigidity, which implies great stiffness 
of orientation. The analysis of the structure of graphite has lately been 
carried by Bernal to a stage very near completion, but the only point 
_ in any doubt is unfortunately the very one as to which certainty would be 
welcome. Has the great weakening of one bond interfered with the relative 
orientation of the other three? Debye thought that the structure was 
trigonal, and that the atoms were arranged in layers which were like the 
layers of diamond, except that they were flattened out without a sideways 
extension of the network. This would involve a closer approach of carbon 
atom centres from 1.54 A.U. to 1.45 A.U. ; against which no obvious objec- 
tion can be offered, but it would be interesting to know how it happened. 
Hull believed the structure to be hexagonal, and that the layers remained 
as in the diamond. Bernal, having found some good graphite crystals 
to which the single crystal methods could be applied, finds that Hull is 
_ correct as to the hexagonal structure, but inclines to the belief that the 
_ layer is flattened. In the latter case, we must suppose that the carbon 
_atom has three very strong bonds almost coplanar with the carbon, and 
_ one weak bond at right angles to this plane. 
___ The question arises in another form in the investigations of the long 
_ carbon chains by Piper and others, and especially by Muller and Shearer. 
_ If the chains are formed by the linking of carbon atoms together in such a 
_ way that the junctions of one atom to its two carbonneighbours are inclined 
to one another at the tetrahedral angle of 109°28’, as in diamond, then there 
are three possible forms of chain. In one of them, each two carbon atoms 
imply an increase of 2.00 A.U. in the length of the chain, and, in a second, 
an increase of 2.44 A.U. In these two cases the carbon atoms of a chain 
canliein a plane. With one exception, all the cases examined show one or 
other of these two rates of increase. The third form of chain is a spiral, 
for which the growth of each single atom added is 1.12. In one case this 
tate of increase is found to hold: it is that in which the chain contains a 
benzene ring. This agreement between calculation and experiment shows 
with some force that the relative orientation of the bonds is maintained. 
ven when two or four hydrogens are stripped from the chain at various 
points, so as to leave a double or triple bond between consecutive carbon 
atoms, to adopt the ordinary chemical language and theory, no measurable 
change is found in the length of the chain. This does not mean that there 
is no change in the distance between neighbours : such a change would be 
mall and might escape detection. But it does mean that there is no great 
hange in the general straightness of the chain, such as might be expected 
om any large change in the mutual orientation of the bonds between the 
arbon atom and its neighbours. 
1924 E 
