ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 259 



vertheless, the interval which is observed between the sounds of the two 

 systems being always very small, and not being constant in different cry- 

 stals, it appears more natural to attribute this difference of elasticity to 

 an irregularity of structure than to suppose that it depends on a deter- 

 minate and regular arrangement, the more so as in very large crystals, 

 like those I have employed, it is very rare not to meet with irregularities 

 of structure sufficiently obvious even to be recognised by the naked 

 eye. 



The plate No. 2, inclined 78° to the axis, begins to present a differ- 

 ence in the disposition of these two systems of nodal lines ; one of the 

 two transforms itself into two hyperbolic branches, which become more 

 straightened in the plate No. 3, inclined 75° to the axis, and which 

 aftenvards approach each other again, and become two straight lines, 

 which intersect each other at right angles in the plate No. 4, inclined 

 about 51° to the axis, and which consequently is nearly perpendicular 

 to the face a X b of the pyramid fig. 1 ; the inclination of the faces of 

 the pyramid to those of the hexahedron being 140° 40'. 



The numbers of vibrations which were nearly the same for No. 1, 

 from which only the sounds D and D -J- were obtained, differ more as 

 the plate approaches No. 4, when the gravest sound being C, the second 

 is the G of the same octave, although the two modes of division are 

 the same as those of No. I . It is this sound C, given by one of the 

 modes of division of the plate perpendicular to the face of the pyramid, 

 which I have taken as the term of comparison, and to which the sounds 

 of all the other plates are referred. Recommencing with the plate 

 No. 4, the variable system separates once more, but in the contrary 

 way ; the curves which form it continue to straighten, whilst their 

 summits recede from each other, and at the same time the two sounds 

 approximate until they are sensibly the same in No. 8, inclined about 

 12° to the axis. The hyperbolic system ceases to assume a determined 

 position, and it can, without the sound undergoing any change, trans- 

 form itself gradually into the rectangular system which form the axes, 

 so that this plate appears to be exactly in the same conditions as No. 5 

 of fig. 8, PL III. In a crj^stal of quartz there are three planes analogous 

 to the preceding, since the phasnomena which are presented by the 

 plates cut round the edge a b of the base of the prism, are, as I have 

 satisfied myself, precisely the same as those which are presented, for 

 the same degrees of inclination, by plates cut round the two other edges 

 c d, ef. 



Beyond No. 8. the sounds begin to differ from each other, and the 

 branches of the hyperbola continue to straighten until No. 11, parallel 

 to the second face of the pyramid. There the distance between their 

 summits is greater than for any other degree of inclination of the 

 l)lates, and the sound of the rectangular system is the same as that of 



