(31.) To determine which set of bands belongs to the ordinary and which to the extraordinary pencil, we may proceed as follows:- Placing a rhomb of calc-spar with a small aperture behind it, so as to give two images, in the same relative position as the plate (see fig. 6) when the section of the Nicol-prism has its short diagonal perpendicular to that of the rhomb (1.), E disappears; when parallel (2.) O disappears. In the spectrum, in the former case the finer bands disappear, in the latter the broader. The fine bands therefore belong to E, the broad to O. (1) Fig. 6. Or the same result might perhaps be deduced more directly from considering that as O is polarized parallel, and E perpendicular to the principal section, and that the short diagonal of the Nicol-prism is horizontal when light polarized by reflexion from an horizontal surface is transmitted, or that the short diagonal is perpendicular to the plane of polarization of the transmitted ray. Then since when the short diagonal is perpendicular to the principal section of the calc-spar, the fine bands are stopped and the broad transmitted, it follows that the broad bands are polarized parallel to the principal section, or belong to O. With the plate inclined in position 1, eight intervals of indistinctness (extending over four or five bands each) occur from H to about E; from E to D the bands altogether become very faint: perhaps two such intervals may be discerned from D to B no bands appear. On applying a Nicol-prism, the intervals of indistinctness disappear at each quarter of a revolution. Calculation. (33.) In all the following calculations for n by the formula (22.), the values employed for the reciprocals of the wave-lengths of primary rays are as follows: val of route in wave-lengths of the two interfering rays, and thus, when compared with observation, conveying an idea of the extent to which the regularity of the undulations is kept up. The indices here used are those contained in my "Report on Refractive Indices"*. For glass I have assumed the indices of FRAUNHOFER's crown glass, No. 9. * British Association Report, 1839. 2 G2 (35.) Glass and Oil of Cassia (Report, No. ii.), 7='015 inch. (37.) We may remark that the indices for oil of cummin are all open to some uncertainty*, and it is easily found that a change in the indices of D and E of 001 only would give no bands between B and E with either arrangement; for we should have on this supposition (40.) Calc-spar and Oil of Cassia, ordinary ray. RUDBERG's indices. (41.) For the extraordinary ray, in a plate bounded by the planes of cleavage, Mr. STOKES has calculated the results as follows: "The incidence is supposed to be perpendicular; that is, strictly, the rays B, D, &c. are supposed to be received in succession at a perpendicular incidence: but the results may be applied with very little error to the case in which rays of mean refrangibility are incident perpendicularly. "The dihedral angle of the rhombohedron of calc-spar is 105° 5' *. "If i be the inclination of the axis to the normal of the plate, we get by a spherical triangle, "The direction considered being about 45° from the axis, ought to be nearly equal to the mean of 'o 'E. Now the values of found above, fall short of the mean μ ομ of po and ' by the following quantities:— "The smallness and regularity of these numbers is a test of the correctness of the arithmetic." (43.) Quartz and Oil of Sassafras. The angle of the prism being 60° and the ray F at the minimum deviation, and , ' being the angles of incidence and refraction for the first surface, we have for either pencil, 'x=30°, sin FF sin 'F, which gives PF, and therefore for the other rays; also sin = gives p' for the other rays. sin If i be the angle of incidence on the plate then in position (1) (see figs. 2, 3) i=60°-p', and in position (2) i=p'. Then (as in AIRY's Tract, Art. 151) if i be the angle of refraction referring to the normal of the wave, we have |