1821.] Crt/stallized Bodies on Homogeneous Light. 131,- 



It is, therefore, in the form of the function 4' (^> ^0 that we must 

 look for the cause of the phenomena ; and since, we have d' = 

 fl + 2 «, 2 a being the angle between the axes (because the 

 observations are made in the principal section) we see that 

 4^ {&, & + 2 a) must involve c, and consequently, Q being arbi- 

 trary and independent, a must be a function of c. In order thea 

 to render the theory of alternations apphcable, we must admit 

 the angle between the axes of double refraction to differ in the 

 same crystal for the differently coloured rays. We must now 

 show that this supposition is sufficient to represent the pheno* 

 mena correctly. 



The symmetry of the rings and total evanescence of colour ia , 

 the principal section at an azimuth zero, requires that the axes 

 of all the different colours shall be symmetrically arranged, ou 

 either side of a fixed fine (which may be called the optic axis) 

 in this plane, or in one perpendicular to it. At present we need 

 only consider the former case. Let a represent the angular dis- . 

 tance of the axis for any one standard species of ray C (the: 

 extreme red, for instance) from this hne, a + S «, the same 

 distance for any other ray. Then the distance of the transmitted 

 ray C, from the axes of rays of that colour being fi, 9\ the corre-, 

 sponding distances from, their respective axes for rays of any. 

 other colour C emerging in the same direction will be d ~ S a>. 

 -\- ^ <p and 6' + S« + rf(p, §(p being the difference (= <p' — (p)_ 

 of the angles of refraction, corresponding to the same incidence,.' 

 for the colours C, C^ The positive values of 6 here reckon^ 

 outwards from the pole ; 5' a is negative for crystals of the second,, 

 class, and 5 <p is negative or positive according as C or C is the. 

 less refrangible colour. 



Let us for a moment consider rays of only these two colours*, 

 The portion of the extraordinary pencil due to them will be 



€. sin.2 (— 4^ (d, 9') , tt) + C\ sin.2 (~ 4. (Q - d a + d f. 



'f- i' + 8a + S(p) . tt). 



The rays of these colours of the same order in their respective: 

 series of rings, will, therefore, coincide, and that in the proper 

 degree of proportional intensity for the production of a white 

 image, provided we suppose 



* 4^ (d, O = -^ . ^ (5 - ^« + s^, ^ + s « + ^^); m 



which, since k, k% a, I a, are constant elements, (p, (tf determi- 

 nate functions of 5, and d' = 6 + 2 «, suffices to determine d. 



If we suppose C and C to represent the extreme red and 

 violet rays, it is evident that the coincidence of the extraordi- 



conspiring with the causes which produce the deviation of tints. In the tables, Nos. V, 

 VI, VII, where the virtual poles were observed almost at a perpendicular incidence, the 

 influence of the dispersive power is quite insensible. 



i2 



