ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 141 



the transverse axis of the hyperbola is always in the direction of the 

 least resistance to flexure. 



Let us now suppose that, the plate remaining perfectly circular and 

 of equal thickness, it possesses in its plane a degree of elasticity which 

 is not the same in two directions perpendicular to each other ; the sym- 

 metrical disposition round the centre being then found to be destroyed, 

 although in another manner than in the two examples we have just ad- 

 duced, an analogous result ought still to be obtained. 



Thus, if we take a plate of this description, a plate of wood, for in- 

 stance, cut parallel to the fibres, and fixing it lightly by its centre, en- 

 deavour to make it produce the mode of division consisting of two lines 

 crossed rectangularly, we shall find that when it thus divides itself, the lines 

 of rest always place themselves according to the directions of the greatest 

 and least resistance to flexure, and that putting it afterwards in motion 

 at the extremity of the preceding lines, it may be made to produce a 

 second mode of division, which presents itself under the aspect of a hy- 

 perbola the branches of which are much straightened, and which would 

 have for its conjugate axis that line of the cross which corresponds to the 

 direction of the greatest resistance to flexure. In short, when the sym- 

 metrical disposition round the centre is destroyed, no matter in what 

 way, the mode of division formed by two nodal lines which intersect 

 each other rectangularly can place itself only in two determinate posi- 

 tions, for one of which it presents frequently the appearance of two hy- 

 perbolic branches more or less straightened ; and, as we shall soon see, 

 it may even happen that, for certain distributions of elasticity, this mode 

 of division presents itself under the form of two hyperbolic curves in 

 the two positions in which it becomes possible. Lastly, if a similar 

 plate be caused to produce some of the high modes of division, but yet 

 consisting of diametrical lines, experiment shows that they can likewise 

 place themselves in two invariable positions, and pass through certain 

 modifications analogous to those which the system of two lines crossed 

 at right angles undergoes. Thus the immoveability of the nodal figures, 

 and the double position which they can assume, are distinctive cha- 

 racters of circular plates all the diameters of which do not possess a uni- 

 form elasticity or cohesion. 



It follows therefore from the preceding, that by forming with different 

 substances circular plates of very equal thickness, we may, by the fixed 

 or indeterminate position of an acoustic figure consisting of diametrical 

 nodal lines, ascertain whether the properties of the substance in ques- 

 tion are the same in all directions. By applying this mode of examina- 

 tion to a great number of plates formed of different substances regularly 

 or confusedly crystallized, as the metals, glass, sulphur, rock-crystal, carbo- 

 nate of lime, sulphate of lime, gypsum, &c., it is constantly found that the 

 acoustic figure, formed of two lines crossed rectangularly, can only place 



