ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 145 
ceding experiments is, that in wood in which the annual layers are 
. hearly cylindrical and concentric, the elasticity is sensibly uniform in alt 
i 
> 
the diameters of any section perpendicular to the axis of the branch. 
We shall see further on, that plates of carbonate of lime or rock crystal, 
cut perpendicularly to the axis, very seldom present this uniformity of 
structure for all their diameters, although the modifications which such 
plates impress on polarized light appear symmetrical round this same 
axis. 
In the case which we have just examined, two of the three axes of 
elasticity being equal, the pheenomena are, as we have just seen, exempt 
from any great complication. It is not so when the three axes possess 
each a different elasticity: it would then be indispensable to cut, first a 
series of plates round each of the axes, then a fourth series round a line 
equally inclined with respect to the three axes, and lastly, it would be ne- 
cessary again to take aseries round each of the lines which divide equally 
into two the angle contained between any two of the axes; and not- 
withstanding the great number of results which would be obtained by 
this process, the end would. be far from attained, since these different 
series would want connexion with each other, and consequently this 
process cannot give a clear idea of the whole of the transformations of 
the nodal lines. Nevertheless, I shall content myself to follow this 
route, which appears to me less complicated than any other, and is 
sufficient to render fully evident all the principal peculiarities of this 
kind of phenomena. 
In order that the relative positions of the lines round which I have 
cut the different series of plates of which I have spoken, and the rela- 
tions they have to the planes of the ligneous layers, as well as to the 
direction of their fibres, may be more easily represented, I shall refer 
them all to the edges of a cube A E fig. 5, the face of which AX BZ 
I shall suppose is parallel to the ligneous layers, and the edge A X to 
the direction of the fibres, which will allow the three edges A X, A Y, 
A Z to be considered as being themselves the axes of elasticity. After- 
wards I shall indicate the different degrees of inclination of the plates 
of each series, on a plane normal to the line round which they are to be 
cut; the position and outline of this plane being at the same time re- 
ferred to the natural faces of the cube. 
But before commencing to describe the phenomena which each of 
these series presents, it is indispensable to endeavour to determine the 
ratio of the resistance to flexion, in wood, in the direction of each of the 
three axes of elasticity: this may be easily done by means of vibrations, 
by cutting three small square prismatic rods, of the same dimensions, 
according to the three directions just indicated ; for, the degree of their 
elasticity can be ascertained by comparing the numbers of the vibrations 
which they perform, for the same mode of division, knowing besides 
Vou, I.—Panrt I. L 
