MONOCLINIC DOUBLE SELENATES OF THE NICKEL GROUP. 
233 
magnesium and zinc groups of double selenates, and for the eight groups of double 
sulphates, the investigation of which was completed by the publication of the author’s 
last memoir (of June, 1915). # The two main results are that the progression of all 
the morphological and optical properties of the crystals, with the atomic weight of the 
alkali metal (K = 38'85, Rb = 84'9, Cs = 131'9, and Rb — K = 46, Cs —Rb = 47), is 
beautifully shown once more in this nickel group of double selenates ; and that the 
true isomorphism, but not eutropism, of the ammonium salt with the potassium, 
rubidium and caesium salts is clearly indicated by the principal determinative constants 
(such as interfacial angles, size of the unit cell of the space-lattice, refractive indices 
and molecular refraction) of the ammonium salt never falling outside the limits of 
these constants for the two extreme, potassium and caesium, salts of the group. 
The former of these two main results is admirably illustrated by the fact that both 
the average and the maximum amounts of interfacial angular change, brought about 
by replacing one alkali metal by another, are directly proportional to the change in 
atomic weight. The differences of atomic weight between potassium and rubidium 
and between the latter and csesium are practically the same (46 and 47), and the 
changes in angle, whether the mean of all the changes of the 36 angles measured or 
the greatest change of angle observed, are also equal ; or to express it differently, the 
replacement of K by Cs is accompanied by twice as much angular change as that of 
K by Rb (average changes K by Rb, 23', and K by Cs, 47', maxima 57' and 119'), 
just as the change of atomic weight Cs —K (= 93) is double that for Rb —K (= 46). 
The amounts are so large as to be entirely removed from any possibility of error, 
which, on a generous estimate, cannot exceed 3'. 
The second main fact is illustrated by the closeness of the structural dimensions 
(those of the unit cell of the space-lattice) of the ammonium and rubidium salts, the 
rubidium salt being the intermediate metallic salt. So very close are the total 
volumes of the cells (the molecular volumes, for the Rb salt 216'96 and for the NH 4 
salt 216‘53)and their edge-lengths (the topic axial ratios), that the crystals of the 
two salts are practically iso-structural, that is, their space-lattices are congruent, 
practically identical, capable of being represented by the same model on any scale 
within reason. 
The author has the more confidence in putting forward this important result inas¬ 
much as the similar result found with regard to the simple rhombic alkali sulphates 
has just been verified in the laboratory of Prof. Bragg, by Prof. Ogg and 
Mr. F. Lloyd Hopwood,! who have succeeded in measuring the actual dimensions of 
the space-lattice cells (the distances separating analogous atoms of contiguous 
structural units in space) by means of the X-rays, these absolute lengths being in 
remarkable concordance with the author’s published topic axial ratios. For this 
result, as to congruency of the ammonium and rubidium salts, has been general for 
* ‘Phil. Trans.,’ A, vol. 216, p. 1 (1916). 
t ‘Phil. Mag.,’ November, 1916, vol. 32, p. 518. 
2 k 2 
