POLARISATION OF LIGHT. 



41 



axes of the icosatetrahedron. This re- 

 markable structure produces a distinct 

 separation of the ordinary and extraor- 

 dinary images of a minute luminous ob- 

 ject when the incident ray passes through 

 any pair of the four planes which are ad- 

 jacent to any of the three axes of the 

 solid. The least refracted image is the 

 extraordinary one, and consequently the 

 doubly refracting force is negative in 

 relation to the axis to which the doubly 

 refracted ray is perpendicular. 



The phenomena of the tints exhibited 

 in any individual sector, COB, Jig. 45, 



Fig. 45. 



have no relation to the axis of the icosa- 

 tetrahedron passing through O, consi- 

 dered as an axis of double refraction. 

 The direction of polarisation of every 

 portion in each sector as COB, is, on 

 the contrary, perpendicular to the line 

 C B, or parallel to one of the rectangu- 

 lar axes of the icosatetrahedron which 

 is perpendicular to the axis passing 

 through O. The tint at any point, p for 

 example, does not depend upon its dis- 

 tance p O, from any point O, but upon 

 its distance p q, from the nearest plane 

 of no polarisation taken in a direction 

 perpendicular to C B. Calling T the 

 tint as determined by experiment at any 

 point p whose distance P r, taken in the 

 manner now mentioned, is D, we shall 

 have the tint t at any other point p whose 

 distance p q is d, by the following for- 



mula, t = ~Y ' tt* thickness of the crys- 



tal being supposed equal at both these 

 points. One of the most important 

 results of these experiments is the sin- 

 gular distribution of the doubly refract- 

 ing force. In all other crystals" in which 

 the laws of double refraction have been 

 studied, the axis to which the doubly 

 refracting force is related, has no fixed 

 locality in the mineral. It is a line pa- 

 rallel to a given line in the primitive 



form,' and every fragment of a crystal, 

 however minute, possesses this axis, and 

 all the optical properties of the original 

 crystal, however large. The property of 

 double refraction, in short, in regularly 

 crystallised substances, resides in the 

 ultimate particles of the bod}*, and does 

 not depend upon the mode in which they 

 are aggregated to form an individual 

 crystal. In analcime, on the 'contrary, 

 we have planes of no double refraction, 

 having a definite and invariable position, 

 and we may even extract a portion of 

 each separate pentahedron which has no 

 axis at all*. 



CHAPTER XII. 



Circular Polarisation in Quartz 

 Right and Left handed Quartz Ma- 

 giedrol Crystals Both these struc- 

 tures united in Amethyst Circular 

 Double Refraction Circular Polar- 

 isation in Fluids. 



IN the year 1811, M. Arago observed 

 along the axis of quartz, when exposed 

 to polarised light, certain colours, which 

 descended in the scale when the doubly 

 refracting prism by which the emergent 

 light was analysed, was made to revolve 

 round its axis/ He observed also that the 

 two images displayed the complementary 

 colours. In this state of the subject, 

 M. Biot directed to it his particular at- 

 tention, and was enabled to analyse the 

 phenomena with his usual sagacity. 



We have already seen that in crystals 

 with one axis the system of rings is tra- 

 versed by a black cross at the intersec- 

 tion of whose rectangular branches there 

 is neither double refraction nor polarisa- 

 tion, as shown mjig- 25, p. 21. In rock 

 crystal, however, the black cross is ob- 

 literated by colours which fill up the first 

 ring, and encroach upon the rest, as shown 

 m fig. 46. These colours vary with the 

 thickness of the plate of quartz*; but they 

 Fig. 46. 



* SP* Edinburgh Transactions, vol. x. part i. pp. 

 187194, where Dr. Brewster first described the 

 phenomena contained in this chapter. 



