266 ? FELIX SAVART’S RESEARCHES ON THE 
greatest elasticity and the intermediate axis are contained in the plane 
which forms the face of the rhombohedron, and they are perpendicular 
to each other; secondly, the intermediate axis and the axis of least 
elasticity are contained in the diagonal plane, and they are in like 
manner perpendicular to each other. 
Such are the consequences to which the analogy observed between 
the successive transformations of the nodal lines in plates of wood and 
of rock crystal seems to lead. The co-existence of three systems of 
axes of elasticity in the latter body, introduces however so great a 
complication in the particulars of the phenomenon, especially in the 
progression of the sounds, that the elastic state of this substance 
ean only be definitively determined by a method analogous to that 
which I have above employed for wood, that is to say, by comparing 
together the numbers of vibrations of a series of small rods of the same 
dimensions, and cut according to the different directions in which 
the preceding experiments appear to indicate that the elasticity differs 
the most. Without in the least prejudging the results to which these 
new researches might lead us, we may even now foresee that there 
ought to bea great difference between the greatest and the least degree 
of elasticity in rock erystal, since, among the various plates of beech- 
wood, a substance in which these two extremes are as one to sixteen, 
there is none the sounds of which have a greater interval than that of 
a major third between them, whilst, among the plates of crystal, there 
are some, the two sounds of which are a fifth from each other. 
As we have already remarked above, the transparent carbonate of 
lime and the ferriferous carbonate of lime appear to possess elastic 
properties which are, for the most part, analogous to those of rock 
erystal; three systems of principal lines of elasticity, which appear 
exactly similar to each other, are likewise recognised in them; but the 
extreme facility with which carbonate of lime may be cleaved, enables 
us to discover in it a peculiarity which cannot be perceived in rock 
erystal, and which may explain why it is that the plates cut round one 
of the edges of the base of the hexahedron, all present a nodal system 
composed of two lines crossed rectangularly. 
It is well known that the rhombohedron of carbonate of lime is fre- 
quently susceptible of a mechanical division according to the directions 
parallel to its diagonal planes; now, these planes cutting each other per- 
pendicularly two and two, the intersection of each of these pairs with 
the lozenge faces of the crystal, forms the great and small diagonal of 
each of them, so that, ifa plane be imagined which turns round the great 
diagonal, it ought always to remain normal to the supernumerary joint 
which passes through the small diagonal. It hence results that, if a 
series of plates be cut round the same line, their structure, considered 
in the different directions of their plane, will differ according to two 
