ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 149 



systems consists of two lines crossed rectangularly, one of which, a x, 

 places itself always on the axis of greatest elasticity, and this line serves 

 as the second axis to the hyperbolic curves which compose the nodal 

 system. Doubtlessly these curves are not entirely similar in the different 

 plates; but I have not been able to perceive any very remarkable difference 

 between them, unless that it appears that their summits gradually ap- 

 proach by a verj' small quantity, in proportion as the plates more nearly 

 approach containing the intermediate axis in their plane. 



Fourth Series Plates cut round the diagonal A D, and perpendi- 

 cular to the plane B C Y Z ; figs. 13 and 14. 



These plates present much more complicated phaenomena than those 

 we have hitherto observed. Except for the first and the last, neither 

 of the two nodal systems consists of lines crossed rectangularly, which 

 shows that this kind of acoustic figure can only occur on plates which 

 contain at least one of the axes of elasticity in their plane, since Nos. 

 2, 3, 4, 5, which are inclined to the three axes, present only hyperbolic 

 lines, whilst No. 1, which contains two of the axes of elasticity, and 

 No. 6, which contains only one, are susceptible of assuming this kind 

 of division. 



In this series, neither of the modes of division remains constantly the 

 same for the different degrees of inclination of the plates: setting out 

 from the plate No. 1, one of the systems gradually passes from two 

 crossed lines to two hyperbolic branches, which are nearly transformed 

 into parallel straight lines in No. 6 ; on the contrary, the other system 

 appears in No. 1 under the form of two hyperbolic curves, the summits 

 of which approach nearer and nearer until they coalesce in No. 6, where 

 they assume the form of two straight lines which cut each other at 

 right angles and this contrary course in the modifications of the two 

 systems is such, that there is a certain inclination (No. 3) for which the 

 two modes of division are the same, although the sounds which cor- 

 respond to them are very different. 



As in the preceding series, and for the same reasons, the sound of 

 each nodal system goes on always ascending in proportion as the plate 

 more nearly approaches containing the axis of greatest elasticity in its 

 plane. 



Fifth Series. — Plates cut round the diagonal K^, (tnd perpendicular 

 to the plane r s t; figs. 5- 



Among all the plates which may be cut round the diagonal A E of 

 the cube fig. 5, there are tliree each of which contains one of the axes 

 of elasticity, and which consequently we have already had occasion to 

 observe; thus the plate No. 3, fig. 8, which passes through the diagonal 

 A B, and through the edge A Y, contains the diagonal A E in its 



