The theory of waves has formed the subject of two profound memoirs by MM. Poisson and Cauchy, in which some of the highest resources of analysis are employed, and the results deduced from expressions of great complexity. This circumstance might naturally lead to the notion that the subject of waves was unapproachable by one who was either unable or unwilling to grapple with mathematical difficulties of a high order. The complexity, however, of the memoirs alluded to arises from the nature of the problem which the authors have thought fit to attack, which is the determination of the motion of a mass of liquid of great depth when a small portion of the surface has been slightly oisturbed in a given arbitrary manner. But after all it is not such problems that possess the greatest interest. It is seldom possible to. realize in experiment the conditions assumed in theory respecting the initial disturbance. Waves are usually produced either by some sudden disturbing cause, which acts at a particular part of the fluid in a manner too complicated for calculation, or by the wind exciting the surface in a manner which cannot be strictly investigated. What chiefly strikes our attention is the propagation of waves already produced, no matter how : what we feel most desire to investigate is the mechanism and the laws of such propagation.