The purity of the note emitted by a sound has been often invoked as a proof of the perfect isochronism of the oscillation, and, consequently, as a demonstration a posteriori of the correctness of the early law of Hoocke governing elastic deformations.  This law has, however, during some years been frequently disputed.  Certain mechanicians or physicists freely admit it to be incorrect, especially as regards extremely weak deformations.  According to a theory in some favour, especially in Germany, i.e. the theory of Bach, the law which connects the elastic deformations with the efforts would be an exponential one.  Recent experiments by Professors Kohlrausch and Gruncisen, executed under varied and precise conditions on brass, cast iron, slate, and wrought iron, do not appear to confirm Bach’s law.  Nothing, in point of fact, authorises the rejection of the law of Hoocke, which presents itself as the most natural and most simple approximation to reality.

The phenomena of permanent deformation are very complex, and it certainly seems that they cannot be explained by the older theories which insisted that the molecules only acted along the straight line which joined their centres.  It becomes necessary, then, to construct more complete hypotheses, as the MM.  Cosserat have done in some excellent memoirs, and we may then succeed in grouping together the facts resulting from new experiments.  Among the experiments of which every theory must take account may be mentioned those by which Colonel Hartmann has placed in evidence the importance of the lines which are produced on the surface of metals when the limit of elasticity is exceeded.

It is to questions of the same order that the minute and patient researches of M. Bouasse have been directed.  This physicist, as ingenious as he is profound, has pursued for several years experiments on the most delicate points relating to the theory of elasticity, and he has succeeded in defining with a precision not always attained even in the best esteemed works, the deformations to which a body must be subjected in order to obtain comparable experiments.  With regard to the slight oscillations of torsion which he has specially studied, M. Bouasse arrives at the conclusion, in an acute discussion, that we hardly know anything more than was proclaimed a hundred years ago by Coulomb.  We see, by this example, that admirable as is the progress accomplished in certain regions of physics, there still exist many over-neglected regions which remain in painful darkness.  The skill shown by M. Bouasse authorises us to hope that, thanks to his researches, a strong light will some day illumine these unknown corners.

A particularly interesting chapter on elasticity is that relating to the study of crystals; and in the last few years it has been the object of remarkable researches on the part of M. Voigt.  These researches have permitted a few controversial questions between theorists and experimenters to be solved:  in particular, M. Voigt has verified the consequences of the calculations, taking care not to make, like Cauchy and Poisson, the hypothesis of central forces a mere function of distance, and has recognized a potential which depends on the relative orientation of the molecules.  These considerations also apply to quasi-isotropic bodies which are, in fact, networks of crystals.