4 
' then two other values for the distances apart of the planes will also give an 
arrangement of the points according to the cubic system, and that these values are 
respectively one half and one quarter of the values first employed. 
He then pointed out the effects of interlacing th> systems thus obtained in 
reproducing similar systems differing only in scale. 
. He then passed to the principal topic of his paper—some additional evidence 
in favour of the theory which he had previously put forward, that it is the diffe- 
rent kinds of atoms of the elements rather than the molecules or units of chemical 
compounds which are symmetrically arranged in crystals. 
Symmetrical systems of atom-arrangement were shown in the model as pro- 
bably those of Iceland spar and Tetrahedrite, the numerical proportions of the beads 
of different colours, and the symmetry of grouping being respectively, in both 
cases, in harmony with the atom-composition and the crystal forms of these 
substances. 
With regard to the former, he pointed out that the theory given by Huyghens, 
that the rhombohedric form of Iceland spar is derived by shrinkage of the tetra- 
hedric form of grouping along a perpendicular to one of the faces of the pile, and 
the theory of Sir William Thomson that it is derived from shrinkage of a cubic 
grouping, have their parallel in the case of the symmetrical arrangement suggested, 
the grouping exhibited being derived by shrinkage of a cubic grouping. This 
cubic grouping was then exhibited by shifting the planes of the model further 
apart. 
The author remarked that the view that the symmetrical grouping in Iceland 
spar is the result of the shrinkage of a cubic arrangement derives great support 
from Baumhauer’s beautiful discovery that crystals of this substance can be twinned 
artificially by means of a Imife. For corresponding to each! pair of alternative 
positions for the atoms revealed by the phenomenon there must evidently be an 
intermediate position similarly related to both, and, for the arrangement of the 
atoms in the intermediate position to be similarly symmetrical with respect to the 
two extreme positions zn all the three cases, it must be derived from the cubic form. 
He then suggested the probability that all crystals which do not belong to the 
cubic system are produced by the shrinkage of assemblages originally belonging to 
this system. 
With regard to the atom-grouping exhibited, as probably that of Tetrahedrite, 
the author pointed out how completely the arrangement was in harmony with the 
form of the crystal—regular twin tetrahedra. He explained the method of build- 
ing up the group, and pointed out its opposite polarity along perpendiculars to the 
faces, which corresponds with the hemihedral form which the crystal displays. 
And he also remarked on the fact that the disposition of the layers of different. 
atoms resembled that of the arrangement of the elements in a thermo-electric pile, 
and would account for the pyro-electric properties of the substance if the atoms of 
different kinds exercise the same electric functions individually which they exercise 
when present in large masses not chemically combined, and therefore unintermixed 
with other atoms. 
He noted that the absence of one of the two atoms of antimony would deprive 
the assemblage of its opposite polarity. 
TRANSACTIONS OF SECTION A. 755 
2. On an Episode in the life of J. (Hertz’s Solution of Maxwell’s Equations). 
By Professor G. F. Firzapratp, F.R.8. 
If in Maxwell’s equation of the electromagnetic field it is assumed that 
dF dG dH dv. - dP dQ dR 
44 = = 1) 2 — ens 
mat ae ne and that instead of A?’¥=0 we take zt a a 0, 
which is the real condition for no electrification at a point in a non-conductor, we get 
Ay = g. If we take F.G, H, the proper form to satisfy Maxwell’s equations for 
dt 
1 There are three directions in which the knife can be held. 
