; IG6 Mr, Herschel on the Action of [Maeg^i, 



will lead to some very remarkable consequences, requires us to 

 know the form of the function 4/ and the values of /c, k\ We 

 will begin with the former, and in this investigation the first 

 step is to determine the general equation of the isochromatic 

 lines. In order to this, we must separate in all cases the law of 

 the tint from that of its intensity. The latter depends entirely 

 on the greater or less facility which the emergent ray finds m 

 penetrating the prism of Iceland spar employed for its analysis, 

 , and will not enter into the present investigation. When we 

 examine a crystallized plate in a convenient graduated apparatus 

 between tourmaline plates crossed at right angles, turning it 

 slowly round between them in its own plane, the form of the 

 coloured bands, if illuminated with homogeneous light, will 

 remain perfectly unchanged during the rotation, but the two 

 , black hyperbolic branches passing through the poles will oblite- 

 rate in succession every part of their periphery ; and the space 

 over which the darkness extends, as well as the degree of •illu- 

 mination of what remains visible, varying at every instant, 

 give rise to so great a variety of appearances, that some little 

 attention is required to recognize this perfect identity of figure. 

 W^hen the tourmaline next the eye is made to revolve, the crys- 

 •taUized plate remaining fixed, the complicated changes which 

 take place, are perfectly reconcilable with the superposition of 

 the primaiy on its complementary set of rings, the relative inten- 

 sities of the two sets at any point being regulated by laws, we 

 have no occasion to consider at present, but the figure of the 

 isochromatic lines, where visible, remains absolutely unchanged 

 by any rotation in this part of the apparatus. 



To form a first hypothesis on the nature of the function which 

 'determines the equation of any one of these curves, we must 

 select a crystal, where the proximity of the axes and intensity of 

 the polarising forces are such as to bring the whole system of 

 rings within a very small angular compass ; as by this means we 

 avoid almost entirely the disturbing efi'ect of the variation in 

 thickness, arising from obliquity of incidence. Dr. Brewster, in 

 his paper of 1818, has chosen nitre, as affording the best gene- 

 ral view of the phenomena, and it is admirably adapted for this 

 purpose ; the whole system of rings being comprised at a very 

 moderate thickness within a space of 10°, allowing us to regard 

 their projection on a plane perpendicular to the optic axis as a 

 true representation of their figure, undistorted by refraction at 

 the surface, &.c. If we examine the rings in this crystal (illumi- 

 nated with homogeneous light, or by the intervention of a red 

 ^lass in common day-light), it will be evident that the general 

 form of any one of them is a re-entering symmetrical oval^ 

 which no straight line can cut in more than four points, and 

 which, by a variation of some constant parameter, is m one state 

 wholly concave, as 1, fig. 4, then becomes flattened, as 2; then 

 acquires a minimum ordinate and points of contrary flexure, as 3 ; 



