April lo, 1874] 



NA TURE 



507 



POLARISATION OF LIGHT* 

 VIII. 

 A QUARTZ plate cut parallel to the axis, when exa- 

 -'*- mined with convergent light, gives curves in the form 

 of hyperbolas. These curves are wider in proportion to the 

 thinness of the plate, but if the plate be thick enough to 

 render the curves moderately fine, the colour becomes 

 very faint. They may, however, be rendered distinct by 

 using homogeneous light. The dark and light parts ex- 

 change positions when the analyser is turned through 90". 

 Two such plates with their axes at right angles to one 

 another give coloured hyperbolas perfectly visible with 

 the white light. Plates of Iceland spar exhibit similar 

 phenomena, but the lines and curves are far more closely 

 packed. 



If the plate be cut in a direction inclined at 45° (or at 

 any angle differing considerably from 0° or 90°) to the 

 axis, the curves are approximately straight lines perpen- 

 dicular to the principal section of the plate. Two such 

 plates placed with their principal planes at right angles 

 to one another give straight lines bisecting the angle 

 between the principal planes. On this principle Savart 

 constructed the polariscope which bears his name. It 

 consists of two such plates and an analyser, and forms a 

 very delicate test of the presence of polarisation. The 

 lines are, of course, always in the direction described 



of vibration of the two rays will be those of the bisectors 

 of the angles made by the two lines. If, therefore, the 

 crystal be so placed that the line joining the extremities 

 of the two axes coincides with the plane of vibration of 

 either polariser or analyser, it is not difficult to see that 

 there will be a black cross passing through the centre of 

 the field, with one pair of arms in the line joining the ex- 

 tremities of the axes and the other pair at right angles 

 to it. But if the plate be turned in its own plane round 

 the central point, the points, for which the vibrations are 

 parallel or perpendicular to those of the polariser or 

 analyser, will no longer lie in straight lines passing 

 through the centre, but will forni two branches of a 

 hyperbolic curve, passing respectively through the extremi- 

 ties of the optic axes. 



If the analyser be turned round, the dark hyperbolic 

 brushes, or the black cross, will undergo the changes 

 analogous to those shown in the cross in the case of uni- 

 axal crystals ; but the most interesting effects are those 

 seen when the polariser and analyser are crossed, and the 

 crystal is turned in its own plane. 



The angle between the optic axes in different kinds of 

 crystals varies very much ; in those where the angle is 

 small it is easy to exhibit both at once in the field of view, 

 but in others where the angle is large it is necessary to 

 tilt the crystal so as to bring the two successively into 

 view. In the latter case the crystal is sometimes cut in a 

 direction perpendicular to one of the axes. The rings are 

 then nearly circular, especially towards the centre, and in 

 that respect they resemble those of a uni-axal crystal ; 



above, and the delicacy of the test increases in proportion 

 as their direction becomes more and more nearly perpen- 

 dicular to the original plane of vibration. 



Bi-axal crystals exhibit a more complicated system of 

 rings and crosses, or brushes as they may in this case be 

 better termed. If such a crystal be cut in a direction 

 perpendicular to the line which bisects the angle between 

 the two optic axes (or the middle line, as it is called), the 

 extremity of each of the axes will be surrounded with 

 rings similar to those described in the case of the uni-axal 

 crystals. The larger rings, however, are not strictly 

 circles, but are distorted and drawn out towards one 

 another ; those which arc larger still meet at a point mid- 

 way between the centres, and form a figure of S, or lem- 

 niscata ; beyond this they form curves less and less com- 

 pressed towards the crossing point, and approximate more 

 ani more nearly to an oval (sec Fig. 26). 



The vibrations of the two rays emerging from any 

 point of a bi-axal cr>'stal are as follows : — Of the two rays 

 produced by the double refraction of a bi-axal crystal 

 neither follows the ordinary law of refraction ; but one 

 •does so more nearly than the other, and is on that 

 account called for convenience the ordinary ray. And if 

 through any point of the field of view we draw two lines 

 to the points where the optic axes emerge, the directions 

 * Contir.aed from p. 466. 



but the character of the specimen can never bemistaken 

 because the rings are intersected by a black bar, or two 

 arms in the same straight line, instead of by four arms at 

 right angles to one another, as would have been the case 

 if the crystal had been uni-axal. The following are the 

 angles made by the optic waves in a few crystals : — 



Carbonate of lead . . . . 5 '5 



•Saltpetre 5 20 



Talc 7 24 



Titanite 30 o 



Bora.x . . . . . . . 28 43 



Mica 30 to 37 o 



Carbonate of Ammonii . . . 43 24 

 Topaz of Brazil . . . . 49 to 50 o 



Sugar 50 o 



Gypsum 57 3° 



Felspar 64 o 



Topaz of Aberdeen . . . . 65 o 



Oxyde of Lead 7° 25 



Cyanite 81 48 



Chrysolite 87 56 



These angles are determined by placing the crystal 

 for an examination into an apparatus adapted to show the 

 rings, and attaching it to an arm whereby the plate can 

 be turned about an axis in its own plane. The axis is 

 furnished with a circle divided into degrees and seconds, 

 and an index. If this axis be horizontal, the plate is so 



