Page:Scientific Memoirs, Vol. 1 (1837).djvu/278

266 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 phænomenon, 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 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 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 frequently susceptible of a mechanical division according to the directions parallel to its diagonal planes; now, these planes cutting each other perpendicularly 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