PHENOMENA IN RELATION TO THE ELLIPSOID OF ELASTICITY. 325 



field of view. In other words, a very thin section cut in any 

 shape from the substance and laid upon the object-slide always 

 acts as a section made in the same direc- 

 tion through the ellipsoid of elasticity. 

 Such a section, therefore, to a certain 

 extent replaces the ellipsoid ; it gives a 

 perfect image of the elasticities effective 

 under the given relations, and hence 

 may be denoted as an effective ellipse of 

 elasticity. 



The connection in point is thus re- 

 duced from space (three dimensional) to 

 the plane, and may be readily demon- 

 strated. If p q r s (Fig. 184) is the effec- 

 tive ellipse of elasticity, and p q the major, 

 r s the minor axis, the incident rays of 

 light (perpendicular to the plane of the 

 paper) are divided into two systems of 

 waves which are polarised in the planes 

 of the two axes. The vibrations of the 

 one system therefore take place parallel 

 to p q, those of the other parallel to r s. 

 The relative magnitude of the axes condi- 

 tions at the same time the velocities with which the two systems 

 traverse the object ; the greater p q is in relation to r s, the 

 greater is the difference between the two 

 velocities of propagation, as also the dif- 

 ference of phase thereby conditioned with 

 a given thickness of the object. 



On turning the object round, the ratio 

 between p q and r s is, of course, altered, 

 and it is important to examine the pro- 

 cess of these changes. We will first 

 suppose that the axis of rotation coin- 

 cides with the mean axis of the ellipsoid, and that the rotation 

 itself takes place in our side view (Fig. 183) in the plane of the 

 paper ; a a is then the major, c c the minor axis of the ellipsoid ; 

 the me- 1 axis I b appears perspectively shortened. If we now 

 consider the position in which a a coincides with the plane of the 

 field of view, the effective ellipse of elasticity passes through the 



t 



FIG. 183. 



FIG. 184. 



