While searching for papers by Amontons, several volumes of the Memoirs of the Paris Academy for the first years of the eighteenth century, fell into my hands. It is difficult to portray the delight which one experiences in running over the leaves of these volumes. One sees as an actual spectator almost the rise of the most important discoveries and witnesses the progress of many fields of knowledge from almost total ignorance to relatively perfect clearness. I propose to discuss here the fundamental researches of Sauveur in Acoustics. It is astonishing how extraordinarily near Sauveur was to the view which Helmholtz was the first to adopt in its full extent a hundred and fifty years later. The _Histoire de l'Académie_ for 1700, p. 131, tells us that Sauveur had succeeded in making music an object of scientific research, and that he had invested the new science with the name of "acoustics." On five successive pages a number of discoveries are recorded which are more fully discussed in the volume for the year following. Sauveur regards the _simplicity_ of the ratios obtaining between the rates of vibration of consonances as something universally known.[135] He is in hope, by further research, of determining the chief rules of musical composition and of fathoming the "metaphysics of the agreeable," the main law of which he asserts to be the union of "simplicity with multiplicity." Precisely as Euler[136] did a number of years later, he regards a consonance as more perfect according as the ratio of its vibrational rates is expressed in smaller whole numbers, because the smaller these whole numbers are the oftener the vibrations of the two tones coincide, and hence the more readily they are apprehended. As the limit of consonance, he takes the ratio 5:6, although he does not conceal the fact that practice, sharpened attention, habit, taste, and even prejudice play collateral rôles in the matter, and that consequently the question is not a purely scientific one.