ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 145 



ceding experiments is, that in wood in which the annual layers are 

 nearly cylindrical and concentric, the elasticity is sensibly uniform in all 

 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 phsenomena 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 a series 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 Jjy 

 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 phaenomena. 



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 A X B Z 

 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 phaenomena 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 



Vol. I — Part I. l 



