266 FELIX savaut's researches on the 



greatest elasticity and the intermediate axis are contained in the plane 

 which foi'ins 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 hoAvever so great a 

 complication in the particulars of the phsenomenon, especially in the 

 progression of the sounds, that the elastic state of this substance 

 can 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 be a great difference between the greatest and the least degree 

 of elasticity in rock crystal, since, among the various plates of beech- 

 wood, a substance in which these two extremes aie 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 ferriferoiis carbonate of lime appear to possess elastic 

 properties which are, for the most part, analogous to those of rock 

 crystal ; 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 

 crystal, 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, if a 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 



