302 TRANSACTIONS OF SECTION B. 
system of sodium nitrate into a simple set of rectangular axes similar to those 
used for rubidium nitrate, the value, a: c=1:0°8276, becomes 
a:b: c=1:7320: 1: 0°7151. 
These values approximate very closely to those obtained by direct measure- 
ment of the orthorhombic rubidium salt. It seems difficult to avoid the con- 
clusion that the two dissimilar crystalline structures are built up by the arrange- 
ment of layers or blocks of the same relative dimensions in two different ways, 
the molecule of sodium nitrate, NaNO,, possessing practically the same relative 
dimensions as that of rubidium nitrate, RbNO,; this, of course, is in disaccord 
with the classic conception of atomic volume, but agrees entirely with the valency 
volume law. 
Another remarkable body of evidence is found in the interpretation of many 
morphotropic relationships between organic and inorganic substances which have 
been long recognised but have hitherto eluded interpretation. The description 
of one or two cases will make the bearing of the law of valency volumes clear in 
this connection. 
d-Camphoric anhydride, C,,H,,0,, and d-camphoric acid crystallised with 
acetone, C,,H,,0,, 1/2 (CH,),CO, both crystallise in the orthorhombic system 
and exhibit the axial ratios stated in the following Table II. :— 
TABLE II. 
W a 2b: c x y £ 
CoH.O, - - . « 60 1:0011:1:1°7270  3-2654: 32618; 5°6331 
CoH ,0,, 1/2 (CH,),CO . 74 1:2386:1:1°7172 40435 : 3:2646 : 56060 
The ratio c/b is approximately the same in the two cases and general 
similarity exists between the two crystalline substances. It will be observed 
that the values of a/b are very nearly in the ratio of the sums of the valencies, 
W, making up the two molecular complexes, namely, 60:74=100: 123. This 
and similar cases may be more conveniently discussed with the aid of the so- 
called equivalence parameters; these are the edge lengths, x, y, and z, of a 
parallelepipedon of which the volume is W, the sum of the valencies in the 
molecule, and of which the linear and angular dimensions express the crystal- 
lographic axial ratios. Thus, for orthorhombic substance, xyz—W, and 
x:y:2=a:6:c; the equivalence parameters of the two substances under dis- 
cussion are given in the table, and it will be seen that whilst y and z are almost 
identical for the two, the z values differ considerably. This correspondence 
indicates clearly that in passing from camphoric anhydride to the acetone com- 
pound of the acid the mass added to the molecular complex, H,O+1/2 (CH,),CO, 
occupies a volume proportional to the number of valency units which it 
contributes to the structure. 
A very remarkable relation has been long recognised between the crystalline 
forms of the three minerals chondrodite, Mg,(SiO,),, 2Mg(F,OH), humite, 
Mg,(Si0,),, 2Mg(F,OH), and clinohumite, Mg,(Si0,),, 2Mg(F,OH) ; the crystal- 
line forms are referable to three rectangular directions, a, 6, and c, and the 
ratio a: 6 is practically the same for all three minerals. The relationship is at 
once elucidated by the law of valency volumes in a simple manner. In the 
molecules of the three substances the sums of the valencies of the constituent 
atoms are respectively 34, 48, and 62; it follows from the law that these numbers 
are proportional to the relative volumes of the several molecules. The ratios, 
a: b: ¢, being known, the dimensions can be calculated of solid rectangular 
blocks having these volumes and having edge lengths proportional to the axial 
ratios, @:b:c. The equivalence parameters, x, y, and z, thus calculated are 
given in Table III.; the first observation of importance to be made is that the 
equivalence parameters, # and y, remain practically constant throughout the 
series of three minerals. 
It will be seen that chondrodite and humite, and humite and clinohumite, 
differ in molecular composition by the quantity, Mg,(Si0,); they form a series 
in which the increment of composition is Mg,(SiO,). Subtracting this incre- 
ment from the composition of chondrodite, the residue, Mg,(SiO,), 2Mg(l’,OH), 
