260 FELIX savart's researches on the 



the same mode of division in No. ■i, perpendicular to the face a X 6 of 

 the pyramid. Lastly, from No. 1 1 until the plate perpendicular to the 

 axis, the sounds approximate again, as well as the summits of the hy- 

 perbolic curves, and at the same time the two systems of nodal lines 

 again become rectangular ; the sounds thus become almost the same. 



Among the plates which we have just examined there are two which 

 merit particular attention; tiiese are Nos. 5 and 11, parallel to the 

 the faces eXc? and aX6 of the pyramid, and the elastic state of which 

 undoubtedly differs very much, since in one it is the hyperbolic system 

 w hich gives the gravest sound, whilst in the other it is the rectangular 

 system, and that, besides, there is a great difference between the sounds 

 which correspond to each of their nodal systems. The faces aXb and 

 and eXc? of the pyramid being opposite, one of the two ought to be 

 susceptible of cleavage, whilst the other ought not to be capable of 

 this mechanical division ; consequently if we knew which of the two 

 plates Nos. 5 and 1 1 possesses this property, we might, by examining 

 its acoustic figures, determine which are the faces of the pyramid pa- 

 rallel to the faces of the primitive rhorabohedron. Rock crystal not 

 yielding in the least to any attempt at dividing it into regular layers in 

 any direction, it was impossible for me to ascertain directly which of 

 the two faces aXb or cXrf were those of cleavage; but this question 

 can be resolved with ferriferous carbonate of lime, a substance which 

 is cleaved with almost the same facility as pure carbonate of lime, and 

 which appears to possess, in reference to sonorous vibrations, properties 

 in general analogous to those of rock crystal. Now, if we cut in such 

 a crystal two plates, — one taken parallel to a natural face of the rhom- 

 bohedron, the other corresponding with a plane inclined to the axis 

 by the same number of degrees as these faces, and which are besides 

 equally inclined to the two faces which form one of the obtuse solid 

 angles, — we find that the first possesses the same properties as No. 11, 

 whilst the second has a structure analogous to that of No.5; whence 

 it ought to be concluded, from analogy, that the face aXb of the 

 pyramid fig. 1. is that which is susceptible of cleavage. This once 

 established, it is not even requisite, in order to ascertain which of tJie 

 faces is susceptible of cleavage, to cut a plate parallel to one of these 

 faces ; it is obvious that a plate parallel to the axis and normal to two 

 parallel faces of the hexahedron should be sufficient to attain this end. 

 Thus, let fig. 5, a b c d ef, be the horizontal projection of the prism 

 represented fig. 1 ; according to what has been said, r s t v will be the 

 projection of the primitive rhombohedron ; again, let IV be the projec- 

 tion of a plate parallel to the axis and equally inclined to the two faces 

 of « and f of the hexahedron; according to what we have above said, 

 this plate will assume the mode of division of No. 3, fig.2,iw, and the line 

 op will be parallel to the plane r stu normal to the plate, that is to say, 



