58 
I)R. A. E. H. TUTTON ON THE 
Molecular Volumes Compared. 
M 
metal. 
Molecular 
volume 
of 
K salt. 
Difference 
between 
K and Rb 
salts. 
Molecular 
volume 
of 
Rb salt. 
Difference 
between 
K and NH 4 
salts. 
Molecular 
volume 
of 
NH 4 salt. 
Difference 
between 
Rb and Cs 
salts. 
Molecular 
volume 
of 
Cs salt. 
Difference 
between 
K and Cs 
salts. 
Ni 
193-99 
9-44 
203-43 
9-92 
203-91 
12-47 
215-90 
21-91 
Co 
195-68 
9-35 
205-03 
10-72 
206-40 
13-08 
218-11 
22-43 
Mn 
— 
— 
212-26 
— 
212-13 
12-69 
224-95 
— 
Cu 
196-49 
9-75 
206-24 
9-59 
206-08 
12-40 
218-64 
22-15 
Cd 
— 
— 
214-98 
— 
216-12 
12-74 
227-72 
— 
Mg 
196-58 
9-60 
206-18 
11-20 
207-78 
12-78 
218-96 
22-38 
Zn 
196-16 
9-42 
205-58 
10-22 
206•38 
12-39 
217-97 
21-81 
Fe 
198-05 
9-76 
207-81 
10-81 
208-86 
12-96 
220-77 
22-72 
Mean . . . 
9 • 55 
Mean . . . 
10-41 
Mean . . . 
12-69 
Mean . . . 
22-23 
Molecular Distance Ratios (topic axial ratios ).—When considered comparatively 
for the different salts these represent directionally in the crystal the same changes 
as are represented in total alteration of volume by the comparison of the molecular 
volumes. The ratios may be regarded as expressing the relative dimensions in space of 
the unit cells of the space-lattice of the crystal structure, the volume of the cell being 
expressed by the molecular volume. In the zinc and cadmium groups all three ratios 
of the ammonium salt are slightly greater than those of the rubidium salt ; in the 
magnesium, iron, manganese, nickel and cobalt groups x and V are slightly greater 
and m slightly less, and in the copper group y and f are slightly less and « slightly 
greater. Thus, on the average, just as for the molecular volume, the spatial axial 
ratios of the ammonium salt are slightly greater than for the intermediate rubidium 
salt. It will be observed that these results include, and are in agreement with, those 
previously published for the magnesium, zinc, and iron groups. 
It may now, therefore, be stated definitely for the whole series of double sulphates, 
without exception, that the replacement of potassium by ammonium (K 2 by 2NH 4 ) is 
accompanied by scarcely more change of volume, or change in the directional 
dimensions of the unit cell of the space-lattice, than when potassium is replaced by 
rubidium (K 2 by Rb 2 ), and by only half the change of volume which ensues on the 
replacement of potassium by csesium (K 2 by Cs 2 ). Regarded in another light, the 
replacement of the two atoms of rubidium by the ten atoms of the two ammonium 
NH 4 radicle-groups is accompanied by scarcely any appreciable change in the structural 
dimensions, either molecular volume or topic axial ratios (volume or directional 
extension). 
Orientation of the Optical Ellipsoid .—Throughout the series the optical ellipsoid 
rotates about the symmetry axis h, which is in all cases the intermediate 8 axis of the 
