368 Dr. H. C. Pocklington on Rotatory 



final result by ck. In this case the forces causing the rota- 

 tional phenomena are the same for all directions of propa- 

 gation of the wave, but they only produce a visible effect 

 (unless c is much larger than one could expect) on waves 

 propagated nearly in the directions of the axes. The two axes 

 will possess similar properties. If we replace r by a linear 

 vector function of \7, we must replace 7 by a linear vector 

 function of \, say 6\, in the final result. The axes will 

 now in general have different properties. If Sa0a and S/30/3 

 have opposite signs, the rotations of plane-polarized beams 

 proceeding along the axes will be in opposite senses. 



8. We may expect to find phenomena of the kind discussed 

 in this paper in biaxial crystals of substances that possess 

 rotatory power when in a state of solution. I have examined 

 plates of cane-sugar cut perpendicular to an axis and from *4 

 to '8 cm. thick. The plates were held between two nicols, 

 one of which was provided with a graduated circle and index, 

 and examined by sodium light without using a converging 

 system of lenses (a better arrangement would be — polarizer, 

 plate, object-glass of telescope, eyepiece, and analyser, since 

 with the thicker plates used the rings are inconveniently 

 small when viewed with the naked eye). The brush was 

 not black where it passed the axis ; but this part of the brush 

 could be made black by turning the analyser in one direction, 

 while turning it in the opposite direction made this part of 

 the brush fainter. The angle of rotation necessary to make 

 the brush black at the centre was read off the circle, and the 

 rotation per centimetre calculated. The results are, for that 

 axis which is approximately perpendicular to the cleavage- 

 plane 22° ±2° to the left, and for the other axis 64° -6° to 

 the right. The same coefficient has values 217° for quartz, 

 31° for sodium chlorate, and 10°'2tothe right for amorphous 

 sugar (by extrapolation from concentrated solutions) ; so that 

 the rotation observed for crystallized sugar is more of the 

 order of magnitude of that found in crystals than that found 

 in amorphous solids or in liquids. In the former case the 

 rotation can only be attributed to some spiral arrangement of 

 the molecules in the crystal (cf. Reusch's artificial quartz com- 

 posed of films of mica arranged spirally). In the case of the 

 sugar crystal this arrangement is unlikely, from the nature of 

 the symmetry of the monoclinic system of crystals. A possible 

 explanation both of the greater rotatory power of the crystal 

 and of the difference of sign in the case of the two axes, is 

 that the sugar molecule acts differently on polarized light 

 which falls on it in different directions. These differences 

 could be seen when the molecules are arranged in an orderly 



