5o8 



NA rURE 



[April 2P, 1874 



placed that the line joining the centres of the two systems 

 of rings is vertical, and the crystal is first turned so as to 

 bring one centre into the centre of the field of view 

 (usually marked by cross wires) ; the index is then read, 

 and the crystal turned so as to bring the centre of the 

 second system of rings to the centre of the field. The 

 index is again read, and the difference of the two read- 

 ings noted. This, however, gives not the true angle of 

 the optic axes, but the apparent angle in air, that is, the 

 angle between the rays as affected by refraction on emerg- 

 ing from the crystal. (See Fig. 27.) 



In some crystals the optic axes have different angles of 

 inclination for the different rays of the spectrum. Of this 

 titanite or sphene is an example. All rays have a common 

 middle line, and lie in the same plane, but the optic axes for 

 the red rays are more widely separated than those for the 

 blue, and consequently the part of the field which would 

 exhibit a dark brush if red light were used is deprived of 

 the red rays but not of the blue. The brushes, therefore, 

 appear broader than whh ordinary crystals, and are tinged 

 with blue on the edges farthest from the middle point, 

 and with red on the edges nearest to it. It is said that 

 a similar distribution of the optic axes, or its opposite 

 in which the red rays are least separated and the blue 

 most, is found in all crystals belonging to the rhombic 

 system. 



In other crystals, the axes all lie in one plane, but all 

 have not the same middle line, so that the two ring sys- 

 tems are unsymmetrical. This is the case with borax. 

 In others the optic axes for different colours lie in diffe- 

 rent planes, all of which pass through the middle line. 



Lastly, we may mention the crystals brookite and tar- 

 trate of ammonia soda and potash, in which the optic 

 axes for the two extremities of the spectrum lie in planes 

 at right angles to one another, both passing through the 

 same middle line. If the systems of rings be examined 

 with light which has been so widely dispersed that the 

 portion illuminating the field in any given position is prac- 

 tically monochromatic, and the position ot the instrument 

 shifted through the different parts of the spectrum (or 

 what is more convenient, if the different parts of the 

 spectrum be successively thrown on the polariscope by 

 means of a totally reflecting prism), the optic axes will 

 be seen to draw gradually together until the figure closely 

 resembles that of a uni-axal crystal ; after which the axes 

 open out in a direction at right angles to the former, until 

 they have attained their greatest expansion. This experi- 

 ment requires a strong light, but|it is instructive, as show- 

 ing the exact distribution of the optic axes for different 

 rays. 



In some bi-axal crystals, notably in gypsum, the distri- 

 bution of the optic axes varies with the temperature. 

 When the crystal is heated the angle between the optic 

 axes diminishes until the crystal appears uni-axal ; with a 

 further increase of temperature the axes again open out, 

 but in a direction at right angles to the former. When 

 the crystal is cooled the axes generally resume their 

 original directions. Sometimes, however, when the heat- 

 ing has been carried to a great degree, or has been con- 

 tinued for a long time, the axes never completely return to 

 their normal condition ; and in such a case the crystal 

 may appear permanently uni-axal. Such an appearance, 

 when permanent, has been considered a test of former 

 heating ; and this phenomenon, when presented by crys- 

 tals found in a state of nature, may be taken as evidence 

 that the rocks in which they have been formed have been 

 subject to high temperatures. 



In the production and examination of the rings 

 hitherto described, we have used light which has been 

 plane-polarised and plane-analysed ; but there is nothing 

 to prevent our polarising the hght or analysing it circu- 

 larly, or indeed doing both. 



If a quarter-undulation plate be placed between the 

 polariser and the crystal to be examined, with its axis in- 



clined at 45' to the plane of original vibration, the light 

 will fall upon the plate in a state of circular polarisation ; 

 and as the polarisation will then have no reference to any 

 particular plane of vibration, the black cross v/ill dis- 

 appear. A system of rings will be produced, but they 

 will be discontinuous. At each quadrant, depending 

 upon the position of the analyser, the rings will be 

 broken, the portions in opposite quadrants being con- 

 tracted or expanded, so that in passing from one quadrant 

 to the next the colours pass into their complementaries. 

 If either the direction of the axis of the quarter-undu- 

 lation plate be changed from 45° on one side to 45° on the 

 other side of the plane of vibration of the polariser ; or 

 if the crystal be changed for another of an opposite 

 character {i.e. negative for positive, or vice versa), the 

 quadrants which were first contracted will be expanded, 

 and those which were first expanded will be contracted. 

 Hence for a given position of the quarter-undulation 

 plate the appearance of the rings will furnish a means 

 of determining the character of the crystal under exami- 

 nation. 



Similar effects are produced if the quarter-undulation 

 plate be placed between the crystal and the analyser ; that 

 is, if the light be analysed circularly. 



In the case of bi-axal crystals under the action of light 

 polarised or analysed circularly, the black brushes are 

 wan'ing, but they are replaced by lines of the same form 

 marking where the segments of the lemniscatas pass from 

 given colours into their complementaries. 



If the light be both polarised and analysed circularly, 

 all trace of du'ection will have disappeared. In uni-axal 

 crystals the rings will take the form of perfect circles 

 without break of any kind ; and in bi-axal they will exhi- 

 bit complete lemniscatas. 



To pursue this matter one step farther. Suppose that, 

 the arrangements remaining otherwise as before (viz., 

 first, the polariser ; secondly, a quarter-undulation plate 

 with its axis at 45° to the principal plane of the polariser ; 

 thirdly, a uni-axal cr)Stal; fourthly, a quarter-undulation 

 plate with its axis parallel or perpendicular to the first ; 

 and, lastly, the analyser), the analyser be turned round ; 

 then in any position intermediate to 0° and 90" the rings 

 will be contracted and extended in opposite quadrants 

 until at 45° they are divided by two diagonals, on each 

 side of which the colours are complementary. Beyond 

 45° the rings begin to coalesce, until at 90° the four 

 quadrants coincide again. During this movement the 

 centre has changed from bright to dark. If the motion of 

 the analyser be reversed the quadrants which before con- 

 tracted now expand, and vice verier. Again, if the crystal 

 be replaced by another of an opposite character, say posi- 

 tive for negative, the effect on the quadrants of the rings 

 will be reversed. This method of examination, therefore, 

 affords a test of the character of a crystal. 



A similar process applies to bi-axal crystals ; but in 

 this case the diagonals interrupting the rings are replaced 

 by a pair of rectangular hyperbolas, on eitlier side of 

 which the rings expand or contract, and the effect is re- 

 versed by reversing the motion of the analyser, or by re- 

 placing a positive by a negative crjstal. The test experi- 

 ment may then be made by turning the analyser slightly 

 to the right or left, and observing whether the rings 

 appear to advance to, or recede from, one another in the 

 centre of the field. In particular if, the polariser and 

 analyser being parallel, the first plate have its axis in a 

 N.E. direction to a person looking through the analyser, 

 the second plate with its axis at right angles to the 

 former, and the crystal be so placed that the line joining 

 the optic axes by N.S., then on turning the analyser to the 

 right, the rings will advance towards one another if the 

 crystal be negative, and recede if it be positive. 



W. Spottiswjodf. 

 (/■f 6e continued.) 



