THE ELLIPSOID OF ELASTICITY. 



321 



In order to bring these properties into a definite connection 

 with the inner structure, it is well to recall to memory the 

 analogous properties of compressed or expanded glass. We know 

 that in a parallelepiped of glass, which is compressed by means of 

 ;a screw- vice, the molecules become condensed or approach each 

 other in the direction of the active force. A sphere, which we may 

 imagine within the glass before compression (Fig. 179 A), becomes 



J I 



FIG. 179. 



t t 



I 1 



B 



FIG. 180. 



flattened in consequence of the pressure in the direction indicated 

 in Fig. 179-5, and hence becomes an ellipsoid of revolution whose 

 principal axis is parallel to that direction. If the compression 

 takes place in two directions at right angles (Fig. 180 B com- 

 pared with A), only that diameter of the sphere which is perpen- 

 dicular to the plane of the paper retains its original form (strictly 

 speaking, it is somewhat lengthened by the lateral pressure), whilst 

 the two others are shortened by an equal or unequal fraction, 

 according as the active forces are equal or unequal. Hence, equal 

 forces transform the sphere into a lengthened ellipsoid of revolution ; 

 unequal ones into an ellipsoid with three unequal axes. 



The changes of form which the imaged sphere suffers in conse- 

 quence of compression may therefore be readily determined. For 



Y 



