I 



Feb. I2,"i874j 



; NATURE 



283 



If a ray of light pass through a plate of quartz which 

 has been cut perpendicularly to the axis, or line parallel 

 to the main planes bounding the crystal, it is as usual 

 divided into two ; but the vibrations m each ray, instead 

 of being rectihnear and at right angles to one another, are 

 circular and in opposite directions. That is to say, if the 

 motion of vibration in one ray is directed like the hands 

 of a clock, that in the other is directed in the opposite 

 sense ; and the light in each ray is then said to be circu- 

 larly polarised. The motion of a series of particles of 

 ether, which when at rest lie in a straight line, is cir- 

 cular, and, as in plane polarisation, successive ; and con- 

 sequently, at any instant during the motion such a series 

 of particles will be arranged in a helix or corkscrew curve. 

 The sweep of the helix will follow the same direction as 

 that of the circular motion ; and, on that account, a cir- 

 cularly polarised ray is spoken of as right-handed or left- 

 handed, according to the direction of motion. A right- 

 handed ray is one in which, to a person looking in the 

 direction in which the light is moving, the plane of vibra- 

 tion appears turned in the same sense as the hands of a 

 watch. Or, what is the same thing, to a person meeting 

 the ray, it appears turned in the opposite sense, viz., that 

 in which angles when measured geometrically are usually 

 reckoned as positive. 



The question, however, which mainly concerns us is the 

 condition of the vibrations after emerging from the plate 

 of quartz and before entering the analyser. In the 

 passage of the ray through the plate the ether is subjected 

 to a double circular motion, one right-handed, the other 

 left-handed ; but, as one of these motions is transmitted 

 with greater velocity than the other, it follows that at any 

 given point and at the same instant of time one of the 

 revolutions will, in general, be more nearly completed 

 than the other, or, to use an expression adopted in plane 

 polarisation, there will be a difference of phase. The 

 motions may be represented by two clock hands moving 

 at the same rate in opposite directions, and the difference 

 of phase by the angle between them when one of them is 

 in the position from which angles- are reckoned. As both 

 are supposed to move at the same rate, they will have met 

 in a position midway between their actual positions ; and 

 if we consider a particle of the ether (say) at the extremity 

 of the clock-hands, it will be solicited when the hands are 

 coincident by forces producing two opposite circular mo- 

 tions. Xow, whatever may have been the forces or struc- 

 tural character within the crystal whereby this double 

 circular motion is perpetuated, it is clear that when the 

 ray emerges into air the particle of ether immediately 

 contiguous to the surface of the crystal will be acted on 

 by two sets of forces, one whereby it would be caused to 

 follow the right-handed and the other the left-handed 

 rotation. Each of these may, as is well known, be repre- 

 sented by a pair of forces, one directed towards the centre 

 of the circle, the other in the direction of the motion and 

 at right angles to the first, or, to use geometrical language, 

 one along the radius and towards the centre, the other 

 along the tangent and in the direction of the motion. 

 The two forces acting along the tangent being in opposite 

 directions will neutralise one another, and the resultant 

 of the whole will, therefore, be a force in the direction of 

 the centre. The particle in question, and consequently 

 all those which following in succession serve to compose 

 the entire ray until it enters the analyser, will vibrate in 

 the direction of the diameter drawn through the point 

 under consideration ; or, to express it otherwise, the ray 

 will be plane-polarised, and the plane of vibration will be 

 inclined to the plane from which angles are measured by 

 an angle equal to half the difference of phase on emer- 

 gence due to the thickness of the crystal. The retarda- 

 tion being the same absolute quantity for all rays, will, as 

 in the case of plane polarisation, be a different fraction of 

 the wave-length for rays of different colours, and will be 

 greater for the shorter waves than for the longer. Hence 



the planes of vibration of the different coloured rays, after 

 emerging from the quaitz, will be differently inclined. 

 Each ray will therefore enter the analyser in a condition 

 of plane polarisation ; and if the analyser be turned round, 

 it will cross the vibrations of the various coloured ravs in 

 succession, and extinguish each of them in turn. Each 

 of the images will consequently exhibit a gradual change 

 of colour while the analyser is being turned ; and the 

 tints will be, as explained before, complementary to those 

 which are successively extinguished. For a given plate 

 of quartz the order of the tints will be reversed when the 

 direction of rotation of the analyser is reversed. But it 

 should be here explained that there are two kinds of 

 quartz, one called right-handed and the other left ; and 

 that, for a given direction of rotation of the analyser, 

 these cause the colours to follow one another in opposite 

 orders. A similar effect is produced by turning the 

 polariser round in the opposite direction. 



The angle of rotation of the plane of vibration for any 

 particular colour varies, as stated above, with the thick- 

 ness of the plate ; while for a given thickness it increases 

 nearly as the square (product of the quantity into itself) 

 of the wave-length decreases. In mathematical language 

 it varies approximately inversely as the square of the 

 wave-length. If this law were accurately true, the product 

 of the angles of rotation into the square of the corre- 

 sponding wave-lengths (X) would be the same for all rays. 

 The following are some measurements made by Brock, 

 with a quartz plate one millimetre thick, which show that 

 the law may be considered as true for a first approxima- 

 tion. 



If the colours exhibited by a plate of quartz when sub- 

 mitted to polarised light be examined by a spectroscope, 

 in the way described when we were speaking of selenite, 

 the spectrum will be found to be traversed by one or 

 more dark bands, whose position and number depend 

 upon the thickness of the plate. But there will be this 

 difference between plane and circular polarised light, that 

 if the analyser be turned round, the bands will never 

 disappear, but will be seen to move along the spectrum in 

 one direction or the other, according as the plate of quartz 

 be right-handed or left-handed, and according to the 

 direction in which the analyser is turned. This is, in fact, 

 identical with the statement made before, that the analyser 

 in its different positions successively crosses the plane of 

 vibration of each ray in turn, and extinguishes it. 



This being so, it is clear that a change of colour exhi- 

 bited by a quartz plate when submitted to plane-polarised 

 li:4ht and examined with an analyser, forms a test of a 

 change in the plane of original polarisation. And if the 

 plate be composed of two parts, one of right-handed, the 

 other of left-handed quartz, placed side by side, any 

 change in the plane of polarisation will affect the two 

 parts in opposite ways. In one part the colours will 

 change from red to violet, in the other froin violet to red. 

 At two positions of the polariser, or analyser, the colours 

 must be identical. With plates, as usually cut, one of 

 these identities will be in the yellow, the other at the 

 abrupt passage from violet to red, or i>icc versa. In this 

 I case the field appears of a neutral tint, tcinti: scns:blc or 

 I tcintc dc passage, as the French call it, and the slightest 

 i change in the plane of polarisation exhibits a marked 

 ] distinction of colour, one part verging rapidly to red, the 

 other to violet. This arrangement is called a biquartz, 

 and affords a very delicate test for determining the posi- 



Ition, or change of position, of the plane of polarisation, 

 especially in cases where feebleness of light or other 



