466 



NATURE 



[April 1 6, 1874 



brushes undergo from the same cause. It has been ex- 

 plained that a ray of plane-polarised light in traversing a 

 crystal of quartz in the direction of its axis is divided 

 into two, the vibrations of which are circular, one right- 

 handed, the other left. If the ray traverses the crystal in 

 a direction perpendicular to the axis, and if the original 

 vibrations arc neither parallel nor perpendicular to the 

 axis it is also divided into two, whereof the vibrations are 

 not circular but rectilinear. It was suggested, first by 

 Sir G. Airy, that these circular and rectihnear vibrations 

 are limiting cases of elliptical ; and both theory and 

 experiment tend to confirm the suggestion, by showing 

 that if the ray be incident on the crystal in any direction 



a</ 



oblique to the axis, it is divided into tao, the vibrations of 

 which are similar ellipses having the longer diameter of 

 the disc coincident with the shorter of the other, and the 

 motion in the two oppositely directed. The longer 

 diameters of the ellipses coincide with the directions of 

 vibration of the ordmary and extraordinary rays in the 

 case of an ordinary positives crystal ; and are conse- 

 quently directed, the one toward the centre of the figure, 

 the other in a direction at right angles to the first. 



The exact, or even appproximate determination of the 

 figures produced is a complicated question, and requires 

 mathematical analysis for its solution, but a general idea 

 of their nature may nevertheless be easily formed. 



When the polariser and analyser are either parallel or 

 crossed, circular rings are formed, and towards the outer 

 parts of the field traces of the black cross are seen, which 

 grow stronger as we proceed outwards from the centre, 

 that is, towards the parts where the rays are more oblique, 

 and where the polarisation more nearly approaches to 

 rectilinear. But in the centre, and near to it, where the 

 polarisation is circular, or nearly so, the effects will re- 

 semble those produced by parallel rays, viz. the rays of 

 different colours will emerge plane-polarised in different 

 planes, and will be variously affected by the angle between 

 polariser and analyser. In no position can they all be 

 extinguished, and consequently in the centre all traces of 

 the black cross will disappear. 



When the planes of vibration of the polariser and the 

 analyser are inclined at any other angle than o' or 90°, the 

 arms of the cross are less strongly marked, and the 

 curvature of the rings becomes less uniform, increasing 

 in the four points where they are crossed by the arms, and 

 diminishing in the intermediate quadrants. When the 

 angle between the planes of vibration is 45°, the rings 

 assume a nearly square form, the corners of the square 

 lying upon the lines which bisect internally and externally 

 the angles between the planes. I f the figures are produced 



Fig. 25. 



wiih the analyser at 45° by two quartz plates of equal 

 thicknesses, one right-handed, the other left, it will be 

 foiiiid that the diagonals of the squares are at right angles 

 to one another, the remains of the black cross occupying 

 the same position in the field in both cases. 



If two plates of the same thickness, the one right- 

 handed and the other left, are placed one over the other, 

 a beautiful effect, called from their discoverer Airy's 

 spirals, is produced. In the centre of the field the rota- 

 tory powers of the plates neutralise one another, and a 

 black cross commences. As we proceed outwards, the 

 arms of the cross cease to be black, and become tinged 

 with red on one side, and with blue on the other. At the 

 same time they are bent round in a spiral form, in the 

 direction of the hands of a watch if the first plate be 

 right-handed, and in the opposite direction if the first 

 plate be kfc-handed. These spir.-\ls intersect at intervals 

 the circular rings ; the points of intersection lie in four 

 I'ectangular directions, which terminate towards the outer 

 margin of the field in four arms of a shadowy cross. The 

 colours of the rings and spirals are more brilliant and 

 better defined than in most other phenomena of chro- 

 matic polarisation. 



W. Spottiswoode 



{To be con I in tied.) 



