3 86 SCIENCE PROGRESS 



dextro- and laevo-rotatory quartz are superposed in various 

 ways are discussed mathematically by T. Liebisch {Sits, preuss. 

 Akad. Berlin, 15, 821, 191 8). In a paper on " The Perpen- 

 dicular Passage of Linearly Polarised Plane Waves through 

 Plane Parallel Plates of Transparent Inactive Crystals " (Ann. 

 Phys., 58, 165, 1 9 19 ; Set. Abs., 20A, 219, 19 19) M. Berek calls 

 attention to the fact that ordinary optical theory ignores the 

 wave-absorption in the crystal, as well as certain boundary 

 effects. The former is negligible in the case of completely 

 transparent media, but the effect on the amplitudes of the 

 reflections at the boundary surfaces is appreciable since the 

 reflecting power varies with the refractive index. The dis- 

 crepancy between the theoretical (geometrical) and observed 

 results should become appreciable in crystals having high 

 double refraction. Adopting the conventional method of 

 representing the component amplitudes by two sides of a 

 parallelogram, it is found that, for perpendicularly incident 

 light, the resultant diagonals, obtained from the electro- 

 magnetic and geometrical theories respectively, do not coin- 

 cide. An expression connecting the tangent of the angle 

 between the diagonals and the refractive indices is given, and 

 according to this relation the former increases with the double 

 refraction. The phenomena seem to be of an order of magni- 

 tude sufficiently great for experimental determination. The 

 reflection of infra-red rays by various crystals has been investi- 

 gated by T. Liebisch and H. Rubens (Site, preuss. Akad. Berlin, 

 16, 198, 1919). The minerals examined include quartz, apa- 

 tite, rhombohedral and orthorhombic carbonates and the 

 orthorhombic sulphates, the variation of reflecting power with 

 the wave-length being indicated by means of curves. A 

 theoretical paper by M. Born (Phys. Zeit., 19, 539, 191 8), deals 

 with the derivation of the frequency of infra-red oscillations 

 in diatomic crystals by means of the space lattice, while a 

 mathematical discussion of dispersion is given in another 

 paper by the same author (Verh. deutsch. phys. Ges., 19, 243, 

 1917). K. Brieger (Ann. Phys., 57, 287, 191 8) has investigated 

 the optical behaviour of water of crystallisation by deter- 

 mining the displacement of the position of proper oscillation, 

 compared with that of free water, in several types of sulphates, 

 such as the alums, some orthorhombic monoclinic sulphates 

 and selenates, and in analcite. The curve of the reflection 

 intensities for water shows certain maxima, which, however, 

 are double in the case of most of the salts examined. Further, 

 the displacement in the case of sulphates is generally appre- 

 ciable and towards the longer wave-lengths, but in analcite, on 

 the other hand, it is in the opposite direction. The results 

 are held to be in agreement with the work of Schaefer and 



