. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. sold, at right angles to each other; S o, the direction, l^assing through the center, in which the two beams of light should move. Let us pass through O a plane per- ; pendicular to o S, which cuts the ellipsoid in the points M J^ 0 M', which points be- long to an ellipse whose ma- jor ai;.d minor half-axes are o X and o Y; of these two beams, propagated in the di- rection S o, the one has the direction of vibration o X and the velocity of
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. sold, at right angles to each other; S o, the direction, l^assing through the center, in which the two beams of light should move. Let us pass through O a plane per- ; pendicular to o S, which cuts the ellipsoid in the points M J^ 0 M', which points be- long to an ellipse whose ma- jor ai;.d minor half-axes are o X and o Y; of these two beams, propagated in the di- rection S o, the one has the direction of vibration o X and the velocity of propagation -, and the other O Y and -. The situation and the length of the principal axiaof this ellipsoid are, in general, dift'ereut for every color. The absorption of the light in any direction can also be determined from the principal axis. With the co- efScient of absorption of the principal axis we can again construct an ellipsoid whose axes correspond to those of the ellipsoid of polarization. The co-efficient of absorption for the two rays of light corresponding to a direction will be determined sometimes by the ellipse-section and sometimes by the absorption-ellipsoid; the major and minor axes of this ellipse, it is true, do not coincide exactly, but they do approximatively with those of the direction of vibration. In the most general case, which we shall first discuss, the three axes jr/^o^ /\ of the ellipsoid are of unequal lengths; they will be called axes of polarization or of elas- ticity; by the last is also spe- cially understood their recip- rocal lengths, as— oA' ^H' ^~ olJ in which « > & > c is chosen; hence the distances o A, o B, 0 0, are themselves propor- tional to the priscipal quotient of refraction. A plane of the axes containing two axes of elasticity is called the principal section, and is jjerpendicular to the third axis. A plane parallel to one axis, as o C, (Fig. 28,) cuts the ellipsoid in an. a =. Please note that these images are e
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