Page:Scientific Memoirs, Vol. 1 (1837).djvu/161

Rh 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 approach by a very small quantity, in proportion as the plates more nearly approach containing the intermediate axis in their plane.

Plates cut round the diagonal $A D$, and perpendicular to the plane $B C Y Z$; figs. 13 and 14.

These plates present much more complicated phænomena 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 correspond 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.

— Plates cut round the diagonal $A E$, and 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 three 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