"It is surprising that so great a mathematician as Dr. Smith could have entertained for a moment, an idea that the vibrations constituting different sounds should be able to cross each other in all directions, without affecting the same individual particles of air by their joint forces: undoubtedly they cross, without disturbing each other's progress; but this can be no otherwise effected than by each particle's partaking of both motions. If this assertion stood in need of any proof, it might be amply furnished by the phenomena of beats, and of the grave harmonics observed..."

“A permanent alteration of form limits the strength of materials with regard to practical purposes, almost as much as fracture; since, in general, the force which is capable of producing this effect is sufficient, with a small addition, to increase it till fracture takes place.”

“With respect to the cohesion and of liquids, I have had the good fortune to anticipate Mr. Laplace in his late researches, and I have endeavoured to show, that my assumptions are more universally applicable to the facts, than those which that justly celebrated mathematician has employed.”

“The fundamental doctrines of motion have ... been more immediately referred to axioms simply mathematical than has hitherto been usual; and the application of these doctrines to practical purposes has ... been facilitated.”

“In the hydraulic and optical part, may be enumerated an over flowing lamp; a simplification of the rules for finding the velocity of running water; remarks on the application of force to hydraulic machines; a mode of letting out air from water pipes; an analysis of the human voice; and some arrangements for solars, and for other optical instruments of a similar nature.”

“The theory of waves has been much simplified, and somewhat extended, and their motions have been illustrated by experiments... A similar method of reasoning has been applied to the circulation of the blood, to the propagation of sound, either in fluids or in solids, and to the vibrations of musical chords; the general principle of a velocity, corresponding to half the height of a certain modulus, being shown to be applicable to all these cases: and a connexion has been established between the sound to be obtained from a given solid, and its strength in resisting a flexure of any kind; or, in the case of ice and water, between the sound in a solid and the compressibility in a fluid state. The doctrine of sound and of sounding bodies in general has also received some new illustrations, and the theory of music and of musical intervals has been particularly discussed.”

“I have... attempted to throw some new light on the general properties of matter in other forms: and on the doctrine of heat, which is materially concerned in them; and to deduce some useful conclusions from a comparison of various experiments on the elasticity of, on evaporation, and on the indications ofs.”