POLARISATION OF LIGHT. 



29 



viewed in this way, but our limits prevent 

 us from enlarging on the subject* In 

 the first of these cases, even when the 

 rings are produced by common light, the 

 light is polarised by reflexion at d, and 

 the rings are formed by the action of the 

 part dC' of the crystal ; but in the second 

 case where polarised light is used, the 

 rings are formed by the action of the 

 thickness C d, and the reflexion at d per- 

 forms the function of an analysing plate. 

 These effects are owing to the property of 

 topaz, by which its angle of maximum 

 polarisation is almost the same as the 

 angle which each of its resultant axes 

 forms with a line P C perpendicular to 

 the plate. 



The system of coloured rings, produced 

 by the interrupting films of calcareous spar 

 which will be described in a subsequent 

 chapter, may be seen by a proper method 

 of observation, without any polarising or 

 analysing plate. Dr. Brewster found 

 certain crystals of nitre which exhibited 

 their rings in the same manner; and Mr. 

 Herschel subsequently found that the 

 same property was common in carbonate 

 of potass. This last author has given to 

 such crystals the name of idiocyclopha- 

 nous, which indicates that they show their 

 own rings. 



CHAPTER VIII. 



Connexion between the Polarisation and 

 the Double Refraction of Light Law 

 of Double Refraction in. Crystals with 

 two Axes Combination of Axes of 

 Double Refraction Intensity of the 

 Polarizing and Doubly Refracting 

 Forces in different Crystals. 

 BY comparing the phenomena of the 

 polarised rings with the intensity of the 

 doubly refracting force in the various 

 crystals which produced them, it was 

 obvious that, in crystals with one system 

 of rings, the polarising and the doubly re- 

 fracting force increased and diminished 

 together ; but long after the complicated 

 tints in mica were discovered, and for 

 several years after the publication of Dr. 

 Brewster' s paper on the double system of 

 rings in topaz, nitre, Sec., it \vas confi- 

 dently maintained by the French philo- 

 sophers that the crystals which gave two 

 systems of rings had only one axis of 

 double refraction, and it consequently 

 followed that there was no connexion be- 

 tween the two classes of phenomena. 



In order to decide this question by 

 direct experiment, Dr. Brewster prepared 



* See the Philosophical Transactions, 1814, p. 203 



prisms of topaz so as to allow the inci- 

 dent ray to be powerfully refracted along 

 the resultant axis, and also along the axis 

 supposed to be that of the crystal ; but 

 along this latter axis he found a distinct 

 double refraction, while along the two 

 resultant axes there was none at all ; thus 

 establishing, beyond a doubt, the intimate 

 and necessary connexion between the two 

 classes of phenomena. In order to make 

 this result more general, Dr. Brewster 

 prepared plates of carbonate of potash, 

 which has a great double refraction, and 

 he observed and measured the separation 

 of the images in different planes near the 

 resultant axes. He had thus the satis- 

 faction of seeing the two images overlap 

 each other along the two resultant axes, 

 and again separate ; such separation be- 

 ing always proportional to the numerical 

 value of 'the tint at the point of incidence. 



In this way he w r as enabled to deter- 

 mine the law r of extraordinary refraction, 

 and to confirm it by direct measures of 

 the separation of the images. This law 

 may be thus expressed : 



The increment of the square of the 

 velocity of the extraordinary ray pro- 

 duced by the action of TWO axes of dou- 

 ble refraction is equal to the diagonal of 

 a parallelogram, whose sides are the 

 increments of the square of the velocity 

 produced by each axis separately, and 

 calculated by the laic of Huygens, and 

 whose angle is double of the angle formed 

 by the two planes passing through the 

 ray and the respective axes. 



This law is now admitted as the uni- 

 versal law of refraction for the extraordi- 

 nary ray ; and M. Fresnel has shown that 

 it coincides rigorously with the results 

 deduced from the theory of waves *. 



This distinguished author, whom a 

 . premature death has recently cut down 

 in the middle of the most brilliant career, 

 has discovered that the ordinary ray in 

 crystals with two axes is not, as was sup- 

 posed, under the influence of the ordinary 

 refracting force, but is regulated by a law 

 analogous to that of the extraordinary ray. 



When the two axes are of equal inten- 

 sity, and are both negative or both posi- 

 tive, the law above described gives iden- 

 tically the same results, as the law of 

 Huygens does, for a single axis of double 



* " This consequence of the theory of waves," says 

 M. Fresnel, " translated into the language of emis- 

 sion, where the ratios of the velocities attribute.! to 

 the rays are inverse, is precisely the law of the dif- 

 ference of the squares of the velocities which Dr. 

 Brewster had del need from his experiments, and 

 which was afterwards confirmed by those of M. Biot, 

 to whom we owe the simple form of the product of the 

 two sines." Annales de Chim. et de Phys. 1825 



