A systematic description is given of the vascular system of a female foetal finback, 1430 mm. long. This is supplemented by histological accounts of many of the tissues. The heart and the retia mirabilia have been more fully described than the other parts. The retia are relatively much larger in the adult than they are in the foetus, and therefore a description of the retial system as observed in adult sperm and finback whales has been added. In the discussion the functional significance of the retia mirabilia, the multiple arterial stems and the thiek»walled aorta and pulmonary artery has been considered. In summing up the peculiarities of the vascular system in the Cetacea, it may be said, that they are not provisions for a possible shortage of oxygen, for a shortage does not occur, but that they are adaptations to the differences of pressure under which their habits compel them to live.