The rapid advances made of late in the diagnosis of cardiac and other diseases affecting the organs of circulation, render the present inquiry into the normal or healthy condition of the valves of the vascular system, not more important anatomically, than medically. As the nature and composition of the parts in which valves are found in some instances materially influence their action, I have deemed it necessary to advert briefly to the properties and structure of the veins and arteries, when describing the venous and arterial or semilunar valves; and to the arrangement of the muscular fibres in the ventricles, when pointing out the peculiarities of the auriculo-ventricular ones. As, moreover, much information is to be obtained by comparing analogous structures, I have, in the present instance, not confined my observations to any particular form of valve, but have examined in succession the entire valvular arrangements of the fish, the reptile, the bird, and the mammal; my object being to arrive, if possible, at a correct knowledge of the more elaborate varieties as they exist in man, and in the higher mammalia.