It should not be overlooked that the work of both Cauchy and Poisson was only rendered possible by Fourier’s analysis of an arbitrary function into simple-harmonic components. Not long afterwards Poisson took up the problem of the sound waves in an unlimited medium due to arbitrary initial conditions. The result is given in what Airy (I think) called the unsatisfactory form of a definite integral. The interpretation was not dwelt upon by Poisson, but here again had to wait for the penetrating genius of Stokes. It is then recognized that Poisson’s formula, far from being [Pg 15] unsatisfactory, gives precisely what one would wish to know, in the most convenient and appropriate form. From this period onwards the flow of production was so rapid, and embraced so many subjects, that it is rather difficult to review it in any orderly sequence. One very important matter is the growth of the theory of Elasticity. The interest in this subject had been revived by the experiments of Chladni on vibrating plates, which formed a feature of the lectures on Acoustics which he gave in various places, as they have of most courses on the subject ever since. A skilled experimenter, and endowed with a fine musical ear, he was able not only to evoke a vast number of figures of nodal lines, formed by sand strewn on the plates, but also to assign their relative pitch, and even to formulate approximate numerical relations. His lectures were very successful, and appear to have excited the interest of the fashionable world, much as a lecture on soap-bubbles might at the present day. His visit to Paris was the occasion, at Napoleon’s suggestion, that [Pg 16] the theory of the figures now known by his name was proposed by the Academy as the subject of a prize essay for the year 1811. Among the competitors was one of the slender array of women who have figured in the history of Mathematics, Mdlle Sophie Germain. This lady had found inspiration in the pages of Montucla, and had devoted herself with great enthusiasm to the study of Mathematics, to the grievous distress of her parents. Lagrange, strange to say, had warned her that the problem was hopeless, and indeed her attempts were not very successful, even though she gained the prize at a subsequent competition. Like other of the earlier writers on the question, she assumed, on the analogy of Euler’s problem of the bar, that the energy of deformation of a plate is a quadratic function of the principal curvatures. This is sufficiently correct, but the choice of the particular function was unfortunate. The further history of the problem is very interesting mathematically, but would lead us too far. The question could not [Pg 17] be satisfactorily treated until the general theory of Elasticity had been further developed, and the relations between stresses and strains established. An additional impulse to the subject came from the wave-theory of Light which was growing rapidly at the hands of Young and Fresnel.