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 phse- 

 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 Ave have been able to 

 study — we shall pass to the much more comjjlicated phaenomena which 

 regularly crystallized bodies, such as rock ciystal 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 pEissing 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 B C D E, and according to the different directions 

 1 , 2, 3, i, 5, &c. round n n', ought to present different phaenomena, since 

 they all will contain the axis of least elasticity n n' 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 

 «ase ; 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 r s contained in the plane B C D E, than in the direction n n! 

 normal to this plane, this circumstance ought to determine the nodal 

 lines to place themselves according to these two directions. However, 

 ajs this difference is veiy 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 tlie 

 right or left of the position which it assumes in preference; but the 

 hyperbolic system, the sununits a. and b of whicli recede more from 

 each other tlian in fig. 2, will present the remarkable peculiarity of 



