260 ‘ FELIX SAVART’S RESEARCHES ON THE 
the same mode of division in No. 4, perpendicular to the face a Xb of 
the pyramid. Lastly, from No. 11 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; these are Nos. 5 and 11, parallel to the 
the faces eXd and aXb of the pyramid, and the elastic state of which 
undoubtedly differs very much, since in one it is the hyperbolic system 
which 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 aX6 and 
and e Xd 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 11 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 rhombohedron. 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 eXd 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 a X 6 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 the 
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, ab ede f, be the horizontal projection of the prism 
represented fig. 1 ; according to what has been said, 7 s ¢ v will be the’ 
projection of the primitive rhombohedron ; again, let //' be the projec- 
tion of a plate parallel to the axis and equally inclined to the two faces 
of a 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, bts, and the line 
op will be parallel to the plane 7 s¢w normal to the plate, that is tosay,. 
