138 REPORT ON PHYSICAL OPTICS. 



section a perpendicular be drawn to the refracting surface, meeting- 

 the two sheets of the surface of wave-slowness for the crystal, the 

 interval of retardation of the rays at emergence will be measured 

 by the thickness of the crystal multiplied by the difference of the 

 corresponding ordinates.* By the aid of an expressive notation 

 for the path of a ray, the author has extended his conclusions to 

 the case of a ray which has undergone any number of internal 

 reflexions. 



If the double-refracting energy of the crystal were the same 

 for the light of every colour, the colours of the rings should follow 

 exactly the Newtonian scale of tints, and their magnitudes should 

 observe the same laws as those of the rings formed between two 

 object-glasses. This is the case in carbonate of lime, beryl, and 

 some other crystals ; and in these, therefore, the colours are similar 

 to those of thin plates. But many remarkable deviations from 

 this law have been observed by Sir John Herschel and Sir David 

 Brewster. Thus, in the common uniaxal apophyllite, it waa 

 observed by the former writer, the diameters of the rings are very 

 nearly the same for all the colours of the spectrum ; so that the 

 rings of different colours are superposed, and form a succession 

 alternately black and white, which may be traced through a great 

 number of orders, f In this remarkable case, then, the double- 

 refracting energy of the crystal varies, very nearly, in the sub- 

 duplicate ratio of the lengths of the waves for the rays of different 

 colours. A very remarkable case of the inversion of the New- 

 tonian scale of tints was observed by Sir John Herschel in some 

 rare varieties of the same mineral. The diameters of the rings, 

 instead of contracting as the refrangibility increases, enlarge, and 

 actually become infinite for rays of mean refrangibility. Having 

 passed through infinity, they again acquire a finite value; and 

 diminish as the refrangibility increases up to the extremity of the 

 spectrum. Here, then, for rays of a certain mean refrangibility 

 the crystal is singly refractive ; and as the double refraction changes 

 its character in passing through zero, the crystal is positive for the 



If yi , y , y. represent the corresponding ordinates of the sphere, and of the two 

 sheets of the surface of wave-slowness for the medium, and the thickness of the 



stal, (y. - y,.), (y. _ y ,.) ^11 be the retardations of the two refracted waves at 

 emergence, and (y. - yj will be the interval between them.-" Geometrical Propo- 

 sitions applied to the Wave-theory of Light," Tram. Royal Irish Academy, vol. xviL 



t Phil. Tram., 1820. 



