RF.PORT ON PHYSICAL OPTICS. 403 



exact accordance witli the observed facts ; and all the circum- 

 stances of the coloured rings in uniaxal and biaxal crystals are 

 completely explained. 



The/orm of the rings, or isochromatic curves, depends upon 

 the interval of retardation alone ; and the value of this interval 

 had been deduced but approximately. Mr. M'CuUagh has re- 

 cently given a general and exact method for its calculation, and 

 for the determination of the forms of the rings for any plate of 

 a double-refracting crystal bounded by pai-allel planes. This 

 method is made to depend upon the properties of the surface of 

 rvave-slowness, of which I have spoken in another place ; and 

 it is found that if the incident ray be produced to meet the 

 sphere, (vehich is the surface of wave-slowness for air,) and 

 through the point of intersection a perpendicular drawn to the 

 refracting surface, meeting the two sheets of the surface of 

 wave-slowness for the crystal, the intervals of retardation of the 

 rays at emergence will be measured by the thickness of the cry- 

 stal 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 devi- 

 ations from this law have been observed by Sir John Herschel 

 and Sir David Brewster. Thus, in the common uniaxal apo- 

 phyllite, it was 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 remark- 

 able case, then, the double-refracting energy of the crystal 

 varies very nearly in the subduplicate ratio of the lengths of the 

 waves for the rays of different colours. A very remarkable case 



* liy.y y represent the corresponding ordinates of the sphere, and of the 

 two sheets of the surface of wave-slowness for the medium, and 6 the thickness 

 of the crystal, 6 (y — y.)> 6 {y — y) will be the retardations of the two refracted 

 waves at emergence, and 6 (y —y ) will be the interval between them. — 



" Geometrical Propositions applied to the Wave-theory of Light," Trans. R. I. 

 Academy, vol. xvii. 

 t Phil. Trans, 1820. 



2 d2 



