PHENOMENA IN RELATION TO THE ELLIPSOID OF ELASTICITY. 327 



Accordingly, the light incident from below undergoes ordinary 

 refraction only, and polarisation does not take place. Hence the 

 normals upon the circular sections correspond to the directions in 

 which the light moves as in a single-refracting medium ; these are 

 the optic axes. The line which bisects their acute angle is termed 

 the middle line ; according as the latter coincides with the major 

 or with the minor axis of our ellipsoid, the bodies are usually 

 called optically positive or optically negative. 



Let us now return to our starting-point (Fig. 185 A), and from 

 thence trace the rotation round the axis. We will suppose that 

 the ellipsoid is rolled upon the surface of the paper, so that the 

 axis of revolution, after a quarter of a turn, coincides with a a in 

 Fig. 185 D. In this position b b will evidently be perpendicular 

 to the surface of the paper, and the minor axis c c will become 

 optically effective. The axes of the ellipse of elasticity are there- 

 fore a a and c c. In our figure the optic axes are also represented 

 (o o and o o), since they lie in the plane of the drawing. On 

 continued rotation the minor axis of the ellipse would, of course, 

 again increase till after half a revolution it had a second time 

 reached its maximum value b b. 



If, finally, we turn the ellipsoid round the third axis c c, then c c 

 obviously forms the one axis of the effective ellipses of elasticity, 

 which represent the different positions, while the other axis 

 gradually assumes all values between a a 

 and b b. In our figure the ellipse which 

 comes into play with a rotation of 90 is 

 shown (Fig. 185 E). 



We have still to trace the rotation round 

 a line which does not coincide with either of 

 the three axes. We will suppose that the 

 ellipse has first been turned round the axis 

 b b till it has attained the inclination shown 

 in Fig. 183 or any other inclination, and 

 then begin the rotation round the line m n 

 from this position. After a rotation of 90, 

 we obtain an ellipse of elasticity whose 

 major axis is a a, and whose minor axis is 

 cc (Fig. 186). This ellipse is, however, 

 differently explained, according to the direction of the rotation ; 

 it is inclined to the right (A), if the upper vertex in Fig. 183 



FIG. 186. 



