PHENOMENA IN DELATION TO THE ELLIPSOID OF ELASTICITY. 323 



We have preferred to pass over these conceptions, and to connect 

 our explanations with the ellipsoid of glass, without theorizing how 

 it arises from the sphere by pressure or tension. We accordingly 

 ascribe to the negative uniaxial crystals an ellipsoid of revolution 

 flattened at the poles, since they act in layers, which are cut 

 parallel to the optic axis, like a glass plate compressed in the 

 direction of that axis. On the other hand, the positive uniaxial 

 crystals act as an ellipsoid lengthened in the direction of the optic 

 axis, since they behave optically like a glass plate expanded in 

 a similar direction. The comparison of double-refracting media 

 with compressed or expanded glass will enable us, in general, to 

 determine accurately the form and position of the ellipsoid of 

 elasticity. 



We think we may conveniently retain the phrase " ellipsoid of 

 elasticity," although we by no means imply thereby an algebraically 

 formulated conception such as that where the motion of light is 

 determined through the radii of our ellipsoid. The connection, 

 which has significance for our purposes, does not require to be 

 expressed either numerically or through formulae ; it may just as 

 well be a reciprocal as a direct one ; but it is obviously everywhere 

 the same. 



2. THE PHENOMENA OF POLARISATION IN RELATION TO THE 

 ELLIPSOID OF ELASTICITY. 



We now proceed to the determination of the relations which 

 exist between the ellipsoid of elasticity and the phenomena of 

 double refraction and polarisation ; we must premise, however, 

 that we treat only of those cases which are of importance in 

 microscopical observation. Facts which can be of interest to the 

 physicist or mathematician alone are not discussed here. 



Let us assume that the ellipsoid of elasticity, which we will 

 regard as in the substance, has three unequal axes ; let a be the 

 major axis, b the mean, and c the minor. Then the sectional sur- 

 faces, which we assume to be in any direction through the centre, 

 are in general ellipses whose excentricity is greatest when they 

 lie in the plane of the major or the minor axis. In two cases, how- 

 ever as we learn from analytical geometry these ellipses become 

 circles, and these circular sections of the ellipsoid always pass 



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