366 SECTIONAL TRANSACTIONS.—A. 
this difference manifests itself as surface tension. With increase of tempera- 
ture, the cohesion and the surface tension in general diminish, but not neces- 
sarily at the same rate. At high temperatures, the surface tension may be 
sufficient to cause rounding of the sharp angles of a crystal. This is shown by 
experiments with gold. Beads of gold, slowly cooled from the liquid state, have 
a skin which has properties like those of a film of gelatin, the normal structure 
being exposed when the film is removed by etching. The sharp octahedral 
“etch-figures’ on large crystals of gold, or the angles of minute crystals prepared 
by precipitation, become rounded at temperatures several hundred degrees below 
melting-point. Other effects of surface tension in solid metals are given. 
(c) Dr. G. Suearer.—The Chemical and Physical Significance 
of X-ray Measurements of Compounds containing Long Chains 
of Carbon Atoms. 
Such measurements appear to give reliable values for the lengths of these 
molecules ; they show that the basis of the structure is actually a chain of carbon 
atoms which may have one or other of a limited number of forms. The observed 
rates of increase of the lengths of the molecules with the number of carbon 
atoms they contain are in accordance with the assumption that successive pairs 
of carbons are linked together at the tetrahedral angle; this would imply a 
marked directive property of the valency bond in carbon. The method of 
investigation would appear capable of throwing light on many problems of 
stereochemistry—geometrical isomerism, the nature of double and triple bonds, 
&c. The existence of spacings often as great as 60 A.U. makes it possible to 
observe a large number of successive orders of reflection, and a study of the 
intensity distribution among these different orders is of interest. 
(d) Prof. W. L. Brace, F.R.S., and Prof. §. Cuapman, F.R.S.— 
A Theoretical Calculation of the Rhombohedral Angle of Calcite. 
The paper describes an attempt to calculate theoretically the rhombohedral 
angle, or axial ratio, of crystals of the calcite type. A number of carbonates 
form rhombohedral crystals similar to calcite, which can be referred to three 
equal axes. The angle between the axes is in the neighbourhood of 102° for the 
whole series. 
There must be some fundamental reason for the occurrence of this angle 
throughout the series. The crystals consist of ions R*+ and CO,--, where R 
may be Mg, Ca, Mn, Fe, Co, Ni, Zn, Cd. One can picture the rhombohedral 
crystal symmetrically extended or compressed along a trigonal axis, keeping 
constant the distance between neighbouring oxygen and metal centres, and 
neighbouring carbon and oxygen centres. The electrostatic potential energy per 
gram-molecule has been calculated for a series of such positions, and it has been 
found that it has a minimum value in the neighbourhood of 106°. Taking into 
account the approximate nature of the assumptions on which the calculation 1s 
based, this may be regarded as in satisfactory agreement with the observed 
value of 102°. Further, it is possible to calculate the effect on the rhombohedral 
angle of substituting other metal ions for calcium, and it has been found that 
the slight variation in angle, which is 101° 55’ in CaCO, and 103° 2’ in 
MgCoO,, is accurately explained. 
(e) Mr. W. T. Astsury.—The Determination of Molecular Sym- 
metry in Crystals and its Possibilities as a Method of Deriving 
Structural Formule. 
Given the class of any crystal, we can, with two exceptions, decide definitely 
the space-group, and thence, from the number of molecules per cell, derive the 
only symmetry elements possible to the molecules as they are built into the 
crystal. Then, by a critical examination of the dimensions of the cell and the 
relative positions of the molecules within it as given by the space-group, it is 
often possible to make a clear choice between two or more suggested structural 
formule. even though the molecule be faizly complex. But, in general, it is 
essential to know from chemistry the various possibilities. The molecular 
symmetry in the crystal is in general less than what would be expected of a 
