132 SCIENCE PROGRESS 
weight of the particles at the corners of a cubic cell and upon 
the volume of the cell, and will vary directly as the former and 
inversely as the latter. The former is, of course, given by the 
molecular weight—the weight of the atoms of which the molecule 
consists. If, therefore, the two crystals are to have cells of the 
same volume, the molecular weight divided by the specific 
gravity (2.e. the molecular volume) must be the same for both. 
The same principle applies to any two similar structures—not 
necessarily cubic. The equality of molecular volume accounts, 
therefore, for the fact that sodium nitrate crystallises in parallel 
position on calcite alone. That they do possess similar structures 
is indicated by their similarity of angle, cleavage, and optical 
and other physical properties. 
If this be a true explanation, it must hold good for other 
groups. Now Mr. Barker has discovered that the alkaline 
perchlorates and permanganates have the same structure as 
the mineral sulphates of lead, strontium, and barium (anglesite, 
celestine, and barytes), as shown by their similarity of angle, 
cleavage, and constitution. 
Among the nine salts examined he found only two, namely, 
KCl1O, and KMnO,, which readily yielded parallel growths on 
barytes BaSO, and the other two minerals of the barytes group, 
and these are precisely the salts which possess nearly the same 
molecular volumes as the sulphates. 
A yet more extensive series has been studied by Mr. Barker, 
the alkaline haloids which crystallise in the cubic system. No 
less than seventeen of these were examined, and among the two 
hundred and seventy-two possible combinations realised, parallel 
growths were only obtained between those which possess most 
nearly the same molecular volumes. 
[Equality of molecular volume in a series of substances having 
the same crystalline structure may also be expressed as equality 
of topic axes, a conception which is rapidly becoming familiar 
since its introduction by Becke, Muthmann, Tutton, and others, 
and one which enables us to compare not only volumes, but 
corresponding magnitudes along parallel directions in such a 
series. | 
In all these groups it seems that when the molecular volumes 
are almost exactly equal, the parallel growth is so perfect and 
uniform that it takes place over the whole surface of the crystal, 
which then appears simply to increase in size by the addition 
