The object proposed by the author of this paper, was to present, in a complete form, the results of investigations into the phenomena of Waves, in which he had been engaged for several years. A part of the experiments referred to in the paper, had been carried on by Sir John Robison, conjointly with the author of this paper, as a Committee of the British Association. The others were new, and had been carried on by himself, for the purpose of completing and giving that systematic form to our knowledge of the subject, which was attempted in this paper.