MONOCLINIC DOUBLE SULPHATES CONTAINING AMMONIUM. 
59 
ellipsoid, on replacing potassium successively by rubidium and caesium, the positions 
following the order of the atomic weights of the alkali metals. The a axis of the 
ellipsoid is nearest to the vertical axis c of the crystal, and the approximation is 
closest, among the alkali-metal salts, for the potassium salt. It is even closer, except 
in the copper group, for the ammonium salt, the potassium salt coming next, then 
the rubidium salt and the caesium salt at such angles as accord with the order of the 
atomic weights, but with a higher function than mere direct proportion to atomic 
weight. In the copper group the ammonium and potassium salts exhibit optical 
ellipsoids almost identically situated, with the a axis inclined 18f° from the vertical 
axis c, the positions of the-ellipsoids of the rubidium and caesium salts still following 
the rule of progression. 
Refractive Indices. —In all the eight groups the refractive indices, including the 
mean index, of the ammonium salt are very close to those of the rubidium salt (which 
are always intermediate between those for the K and Cs salts), and usually very slightly 
higher. The double refraction of the ammonium salt also lies intermediate between 
the values for the corresponding rubidium and caesium salts, the situation varying in 
the different groups on either side of the half-way position ; on the average it lies 
nearer to the value for the rubidium salt. As regards the axial ratios (the directional 
dimensions) of the optical ellipsoid, the values for the ammonium salt of any group 
are intermediate between the values for the rubidium and caesium salts of the same 
group, and much nearer to the rubidium salt values. 
Molecular Optical Constants. —In specific refraction and dispersion the ammonium 
salt of every group is distinguished by values much higher than those for the alkali- 
metal salts of the same group. As regards the important property of molecular 
refraction, in every group of the series the value for the ammonium salt, whether 
calculated by the Lorenz or the Gladstone and Dale formula, is very close to and 
just slightly higher than the value for the rubidium salt, which itself is inter¬ 
mediate between the values for the potassium and caesium salts, in accordance with 
the law of progression with the atomic weight of the alkali metal. The molecular 
dispersion of the ammonium salt is nearest to the value for the corresponding caesium 
salt, in four groups being just lower than the latter, and in the other four groups 
just higher; for high dispersion is a characteristic property in which the ammonium 
salts exhibit the constitutional difference of the NIT 4 radicle from the alkali metals 
which form the other R-bases in the isomorphous salts of the series. 
Optic Axial Angle. —No definite rule can be traced from a comparison of the optic 
axial angles of the ammonium salts with those of the salts containing the alkali 
metals ; these latter salts show a progressive change in optic axial angle with change 
of atomic weight of the alkali metal. 
Final Conclusion. —The work now described on the remaining five double sulphates 
containing ammonium confirms and emphasises the two main conclusions derived 
from the study of the three ammonium salts already described, which may be 
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