1.4889

1.4933

1.5100

1.4838

1.4889

1.5057

1.4834

1.4878

1.5032

1.4820

1.4972

An increase in the atomic weight of the contained alkali metal is accompanied by an increase in the refractive power of the crystal, and the increase in refraction becomes relatively greater, as the atomic weight becomes higher, than in mere numerical proportion to the increase of atomic weight. When the indices are considered, whose corresponding direction of vibration is constant throughout the series, being the invariable symmetry axis b, the amounts of increase due respectively to the replacement of potassium by rubidium, and of rubidium by casium, vary slightly in the different sets, according to the nature of the second metal present, from 1: 3 to 1: 4.

The difference between the indices for the potassium and cæsium salts of any group is not so large as was observed between those of the simple sulphates of potassium and caesium. In the latter case the difference of the ẞ indices for sodium light amounted to 0.0697 whereas the largest difference in the series under consideration is 0.0229.

No relation can be traced between the atomic weight of the second metal present and the refractive indices. For instance, although there is a rise in refraction when magnesium is replaced by zinc, yet there is a fall again when the latter is replaced by cadmium.

Ratio of Axes of Optical Velocity Ellipsoid.-The difference of refraction along the three axes of the optical ellipsoid in any one salt, the modification of that difference on replacement of the alkali metal by another, and the actual change of refraction along any one direction brought about by the same cause, are perhaps most clearly rendered evident by a consideration of the axial ratios of the optical ellipsoid, which are relative measures of the velocity of light vibration along the three rectangular axes a, b, c, of the ellipsoid. The ratios given in the description of each salt are calculated with reference to the value along the b axis as unity. Such ratios, therefore, only express the relative facility for light vibration along the three axial directions of the particular salt in question. It was shown in the memoir concerning the simple normal sulphates (loc. cit., 699) that by taking the value along the intermediate axis of the ellipsoid of the potassium salt as unity, and expressing all the other values for the set of three salts proportionately, the actual changes of velocity along all three axes on passing from a potassium to a rubidium salt, and from a rubidium to a cæsium salt, are exhibited. In the ratios thus obtained for any set of three salts, those for the potassium salt are, of course, identical with those given in the descriptions, and those for the rubidium and cæsium salts are obtained in each case by dividing the refractive index for sodium light, corresponding to the axis in question in that particular salt, into the ẞ, index of the potassium salt.

The two series of ratios are given side by side in the accompanying table.

Ratios of the Axes of the Optical Velocity Ellipsoids of the Series.

a.

b.

Salt.
KMg..... 10015 : 1

3

RbMg.... 1.0012 : 1

11

CsMg.... 10001

KZn..... 1.0039 : 1

5

RbZn.... 1.0031 : 1

17

CsZn..... 1.0017 : 1

:

0.9970

0.9966
109
0.9857

:

0.9905

77

: 0.9828

In discussing the results afforded by the comparison of these ratios, it will be convenient to consider first the total change represented by the second series of ratios, and subsequently to revert to the effect of this change in modifying the mutual relations of the three axes of the optical ellipsoid of each salt, as exhibited by the first series of ratios.