ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 143 
a small diameter, cut at a little distance from the surface, we may sup- 
pose without any very notable error, at least for the whole of the phe- 
nomena, that the experiments have been made on a body the elasticity 
of which is not the same, according to three directions rectangular to 
each other, since, as is well known, this property does not exist in the 
same degree according to the direction of the fibres, according to that 
of the radius of the tree, and according to a direction perpendicular to 
the fibres and tangential to the ligneous layers. 
After these two cases—the most simple that we have been able to 
study—we shall pass to the much more complicated phenomena which 
regularly crystallized bodies, such as rock crystal and carbonate of lime, 
present. 
§ II. Analysis of Wood by means of Sonorous Vibrations. 
Let us suppose that fig. 1 (Plate III.) represents a cylinder of wood the 
annual layers of which are concentric to the circumference; let B C D E, 
fig. 2, be any plane passing through the axis A Y of the cylinder, and let 
n n' be a line normal to this plane: it is obvious that the plates taken 
perpendicularly to BC DE, and according to the different directions 
1, 2, 3, 4, 5, &c. round nx’, ought to present different phenomena, since 
they all will contain the axis of least elasticity 2 m! in their plane, and 
the resistance to flexure, according to the lines 1, 2, 3, 4, 5, will go on 
increasing in proportion as the plates shall more nearly approach being 
parallel to the axis of greatest elasticity A Y. 
For the plate No. 1, fig. 3, perpendicular to this axis, all being sym- 
metrical around the centre, the mode of division consisting of two 
lines which intersect each other at right angles, ought to be able to 
place itself in all kinds of directions, according as ‘the place of excitation 
shall occupy different points of the circumference: this is really the 
‘ease; but it is no longer so, for the plate No. 2 inclined 22° 5! to the 
preceding. ‘In the latter, the elasticity becoming a little greater in the 
direction 7 s contained in the plane B C D E, than in the direction x »! 
normal to this plane, this circumstance ought to determine the nodal 
lines to place themselves according to these two directions. However, 
as this difference is very slight, the system of these two lines may still 
be displaced, when the place of excitation is made to vary ; but it will 
change its form a little, and it will assume the appearance of two hyper- 
bolic branches when it has arrived at 45° from its first position. In the 
plate No. 3, inclined 45° to the axis A Y, the difference of the two 
extreme elasticities being greater, the system of crossed lines becomes 
entirely fixed, or rather it can only move through a few degrees to the 
right or left of the position which it assumes in preference; but the 
hyperbolic system, the summits a@ and 6 of which recede more from 
each other than in fig. 2, will present the remarkable peculiarity of 
