RECENT PROGRESS IN CRYSTALLOGRAPHY 113 



and is generally not found to have either of its other two rectan- 

 gular axes coincident with either the inclined axis or the vertical 

 axis. The first optical result has been to show that this pos- 

 sible rotation of the optical ellipsoid does actually occur in the 

 double salt series, to an extent which varies for the different salts 

 from 4 to 33 , the actual amount being dependent on the atomic 

 weight of the alkali metal present, so that the position of the 

 ellipsoid in any rubidium salt is intermediate between the posi- 

 tions for the corresponding potassium and caesium salts. Further, 

 in both the rhombic and the monoclinic series the ellipsoid 

 expands in every direction when potassium is replaced by 

 rubidium, caesium, or ammonium, which is a graphic expression of 

 the fact that the refractive index increases for every direction 

 within the crystal. This inflation is likewise according to the 

 order of the atomic weights of the alkali metals, and in the case of 

 ammonium the amount of extension is almost exactly the same as 

 for rubidium — a result similar to that for the topic parameters, 

 the bearing of which on interatomic spaces has just been 

 discussed. Moreover, the molecular refractions, obtained by 

 combining the molecular volume with the refractive indices in 

 accordance with the formula either of Lorenz or of Gladstone, 

 obey a similar law of dependence on the atomic weight of the 

 alkali metal, and the molecular refraction of any ammonium salt 

 is also almost identical with that of the corresponding rubidium 

 salt. 



The double refraction, which is measured by the difference 

 between the maximum and minimum of the three refractive indices 

 of the crystals of any one salt for the same wave-length of light, 

 has been likewise shown to be a function of the atomic weight, 

 and obedience to this law has resulted in some of the most 

 beautiful and interesting optical phenomena in convergent 

 polarised light which have ever been observed. It is respon- 

 sible for no less than five cases of the rare phenomenon of 

 crossed-axial-plane dispersion of the optic axes. So compli- 

 cated are the interference figures, particularly with rise of 

 temperature and change of wave-length, that without the law 

 they would be quite unintelligible, but by it they are reduced to 

 perfect order and simplicity. 



It only remains now to mention briefly the results of the 

 determinations of thermal expansion. Owing to the presence 

 of water of crystallisation, and its ready efflorescence at only 



8 



