April 1 6, 1874J 



NATURE 



465 



direction of the optic axis and of the central ray, O n, O n' 

 those of any two other rays. The ray O P will not be 

 divided ; but O n will be separated by the double refrac- 

 tion of the plate into two, n s, n r, the one ordinary, the 

 other extraordinary ; and these will emerge parallel to 

 one another, and may be represented by the lines s t, r v. 

 Similarly the effect of double refraction on O n' may be 

 represented by n' s', n' r', s' t', r'v'. Suppose now that 

 the process were reversed, and that two monochromatic 

 rays, one ordinary, the other extraordinary, reach the plate 

 at s and r in the directions t s, v r, respectively ; these 

 would meet at n and travel together to O. Suppose, fur- 

 ther, that the difference in length of s n and rn is equal 

 to one wave-length, then, since one of them is an ordinaiy 

 and the other an extraordinary ray, their vibrations will 

 be perpendicular to one another, and if the polariser and 

 analyser be crossed, the point n viewed from O will appear 

 dark. Similarly, if two rays arrive in the directions t' s', 

 v' r', at the points s' r' respectively, they will meet at n' 

 and proceed together to O ; and if the difference of the 

 paths s' n', r' n' be two wave-lengths, the point n' will also 

 appear dark. A pair of rays reaching the crystal at 

 points between the pairs before-mentioned, will emerge at 

 a point n" between n and n', and will present a difference 

 of phase equal to a half wave-length. On principles ex- 

 plained in an earlier part of these lectures, such a point n" 

 will appear bright. On either side of n", that is towards 

 n and n', the light will gradually fade. The same alter- 

 nations of light and darkness will recur at intervals as we 

 proceed along any straight line drawn outwards from the 

 central ray. And inasmuch as the obliquity of the ray is 

 the same for every point equidistant from the centre O, 

 it follows that the phenomena of light and darkness will 

 be the same throughout each circle drawn about the 

 centre O. In other words, the centre will be surrounded 

 by rings alternately bright and dark. The diameters of 

 the ring depend, as was seen above, on the wave-length of 

 the particular light used, and will consequently be different 

 for different coloured rays. If, therefore, white light be 

 used, the different coloured rings would not coincide, but 

 would be disposed in recurring series as we proceed out- 

 wards from the centre. 



Another effect would, however, also be produced. 

 Suppose the polariser and analyser to be so placed that, 

 the field being regarded as a map, the vibrations in the 

 one being K. and \V., those in the other N. and S. ; then 

 of the two rays emerging at the most northern or the 

 most southern point of any ring the vibrations of one 

 would be towards the axis, or N. and S. ; those of the 

 other would be across it, or E. and W. And of these 

 one would be extinguished by the polariser, the other by 

 the analyser ; and the same will be the case for every 

 ring. Hence, throughout a N. and S. line crossing the 

 entire field the light will be extinguished ; and a similar 

 effect will obviously occur along an E and a W. line. 

 Hence, when the polariser and analyser are crossed, the 

 entire system of rings will be intersected by a black 

 cross, two of whose arms are parallel to the plane of 

 vibration of the polariser and two to that of the analyser, 

 and the rings in the c[uadrants on each side of an arm 

 are of complementary tints. When the analyser is turned 

 round through a right angle from its former position, only 

 one set of vibrations (say those executed in a direction 

 E. and W.) will be extinguished, and consequently along 

 one pair of arms of the cross the ordinary rays will pass 

 undisturbed, along the other the extraordinary ; that is to 

 say, the cross will be white. When the polariser and 

 analyser occupy any other position than those noticed 

 above, there are two crosses inclined at an angle equal to 

 that between the planes of vibration, each arm of which 

 separates complementary rings. 



Various forms of polarise jpes have been devised for 

 showing the crystal rings. The simplest of these is the 

 tourmalin forceps, which consists of two plates of tour- 



inalin fixed in cork discs ; the latter are encircled in wire 

 in such a way that they may be turned round in their own 

 planes. The wire after encirchng one disc is bent round 

 so as to form a handle ; it then encircles the other ; and 

 the elasticity of the wire allows the pair of discs to be 

 opened and shut like a pair of pincers. If a crystal plate 

 be inserted between the two, and the whole held close to 

 the eye, the rays from parts of the field at different 

 distances from the centre will reach the eye, having 

 traversed the crystal with different degrees of obliquity ; 

 and a system of rings and brushes will be formed. 



Another method consists in applying to Norremberg's 

 polariscope a pair of lenses, one below the crystal with 

 the crystal in the focus, the other above it. The first en- 

 sures that the rays shall traverse the crystal with different 

 degrees of obhquity ; the second brings within the range 

 of vision rays which would otherwise fail to reach the 

 eye, and at the same time converging them into a cone 

 with a smaller vertical range, renders the ring smaller 

 than when seen with the simple tourmalins. An ad- 

 ditional lens of greater focal length, i.e. of less power, is 



often added in order to adjust the whole to individual 

 eyesight. 



Fig. 22 gives the general appearance of the addition to 

 the apparatus of Norremberg described above, and Fig. 

 23 the course of a system of rays brought to a focus on 

 the lens a b, and again converged by a second lens c d. 



But by far the most successful arrangement for enlarg- 

 ing the field of view so as to comprise the complete 

 system of rings even with bi-axal crystals having widely 

 inclined optic axes, is the system of lenses due in the 

 first instance to Norremberg. The disposition of the 

 parts is shown in Fig. 24 ; and the general appearance 

 of the instrument as constructed by Hofmann of Paris, 

 and called by him the " Polarimicroscope," is also given, 

 Fig. 25. In this instrument the lenses which converge 

 the rays upon the crystal plate can be taken out, and 

 replaced by others giving parallel light ; it can then be 

 used as an ordinary polariscope. 



Mention has been made above of the effect of the 

 circular polarisation of quartz in the colours produced by 

 a beam of parallel rays of polarised light. It remains for 

 us to examine the modification which the rings and 



