PRINCIPLES OF CRYSTALLOGRAPHY. 257 



is only dependent on the color of the beam of light, and on a factor 

 which is constant for the entire uiedinm, and not from the direction in. 

 which it moves. 



If, therefore, a beam of light, under any condition of vibration, enters 

 such an isotrope medium, it can very easily, taking into consideration 

 its angle of incidence, change the direction, and, taking into considera- 

 tion its color and molecular constants, the velocity of its propagation ; 

 the condition of vibration, however, remains constant. The condition of 

 vibration of the beam of light is said to be con)pleteIy polarized, partially 

 polarized, or unpolarized, according as the whole of the light or only 

 part of it vibrates in a constant path, or this course takes in an infinitely 

 short space every possible transversal position. In the first case, where 

 the whole light has a constant path of vibration, we say again that the 

 light is polarized in a straight line, circularly, or elliptically, according 

 as the path of oscillation is a straight line, perpendicular to the direc- 

 tion of propagation, a circle, or an ellipse. The movement of the light 

 in an isotrope medium is, therefore, dependent on that of the incident 

 light, the angle of incidence, and a molecular constant. 



In a crystallized medium, in which the density can be supposed vari- 

 able with the direction, only two beams of light of a determined velocity 

 of propagation for each color, and determined direction of vibration, 

 can, in general, be propagated in any determined direction ; on the con- 

 trary, a beam of light entering a crystalline medium will not only be 

 deviated from its direction, but separated into two divergent beams, 

 each one of which, according to its direction in the crystal, will have 

 variable velocities of propagation and direction of vibration. 



Just as the intensity of the light is weakened by its passage through 

 an isotrope medium, and has different strengths for different colors, so 

 is it the case Avith crystalline media, only here the unequal absorption for 

 different colors depends on the direction in the crystal; the same is here 

 true as of the manner of vibration and the velocity of propagation. 

 The same direction in a crystal corresponds thus to two determined 

 beams with determined velocities of propagation, direction of vibration, 

 and absorption ; and a ray of light entering a crystal is divided into two 

 beams of determined but different directions of proj^agation, velocities, 

 directions of vibration, and absorption. 



§ 2. — The Ellipsoid of Polarization. 



The law according to which the whole inovemeut of light in a crystal 

 is determined can, so far as is necessary for our present pur^iose, be 

 enunciated as follows : 



In every crystal an ellipsoid with three axes can be constructed in 

 such a way that the velocity of propagation and the direction of vibra- 

 tion of the two rays of light, which can move in a fixed direction in a 

 crystal, may be determined by the major and minor axes of the ellipse, 

 which are formed when, from the center of the ellipsoid, a plane is passed 

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