Page:Scientific Memoirs, Vol. 1 (1837).djvu/275

 

beyond which they approach each other until they coalesce in $K$, after which they again diverge until the plate $N$, which is parallel to the axis.

The nodal system indicated by the dotted lines follows another course; the summits of the two curves which compose it at first recede from each other, but they soon reapproach each other, and these curves transform themselves into two straight lines in the plate $E$, where the curves of the other mode of division attain their maximum of recession: beyond this limit they separate, but in a perpendicular direction to that in which they approached, and they attain their maximum of recession towards the plate $H$, for which the two systems of curves are nearly similar: they afterwards approach each other, and like those of the other system, they transform themselves, in $K$, into two straight lines, which intersect each other at right angles. Lastly, starting from this point, they diverge again, until the plate $N$, for which the two systems again become equal, assuming, with respect to the axis of the crystal, a direction different from that which they had taken at $I$ and at $H$. I must observe that my supply of rock crystal having failed at the end of my experiments, I have not been able to cut the plate $K$; but the transformations of the nodal lines so clearly indicate that there ought to be a plate which presents these modes of division, that I have not hesitated to admit its existence.

The course which the two sounds follow, in this series of plates, is much more simple than that of the nodal figures: at first those of the dotted system become lower, commencing with the plate $A$, and proceeding as far as the plate $E$, inclined 51° to the axis, and which gives the sound $C$ like the plate No. 4, inclined the same number of degrees to the axis; aftem^ards the sound of this system gradually ascends until the plate $N$ parallel to the axis, where it attains its maximum of elevation. As to the sounds of the other series of modes of division, it is observed that they gradually ascend from the plate perpendicular to the axis unto $K$, in which the nodal systems both consist of lines crossed rectangularly, and that they afterwards descend again until the plate $N$ parallel to the axis. It is obvious that it is not necessary to examine such plates as $A^{\prime }$, $B^{\prime }$, $C^{\prime }$, $D^{\prime }$, fig. 4, since they ought to present the same phænomena as the corresponding plates $A$, $B$, $C$, $D$: only, that which was inclined to the right of the axis in the plates $B$, $C$, $D$ is found inclined to the left in the plates $B^{\prime }$, $C^{\prime }$, $D^{\prime }$.

There is none of the modes of division of this series which is not analogous to some one of those which have been presented to us by bodies in which there are evidently three rectangular axes of elasticity; nevertheless, considered all together, the transformations we have just described present peculiarities which do not exist in the fourth series of plates of wood, fig. 14, Pl. III. The most striking consists in this, that in the transformations of this last series, none of the systems, except