258 



PRINCIPLES OF CRYSTALLOGRAPHY. 



perpendicular to the given direction of propagation of both of the beams, 

 and this prolonged to its section with the ellipse. 



Let o A, B, o C, (Fig. 27,) be the principal axes of the ellip- 



F.-^S7. 



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^ 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, 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 = 



