The results of our investigations may be summarized as follows: (1) In the heart of the Decapod Crustacea three systems of nervous elements can be distinguished, viz. (a) a local system of neurons which are distributed in the heart itself; (b) a system of fibres connecting the heart with the central nervous system; and (c) a system of nerves which supply the valves of the arteries arising from the heart as well as the muscles of the pericardium. (2) The local nervous system consists of a nervous trunk situated in the dorsal wall of the heart near to its inner surface from which branches to the muscle-fibres of the heart are distributed. The main trunk is generally called the ganglionic trunk from the presence of nerve-cells in it. The cells are of two kinds: large and small. Their number was found to be constant, and comprises in Cancer pagurus, Maia squinado, and Homarus vulgaris--the species which could be best investigated as to this point--nine elements., viz. five large and four small cells. It seems that in other species of marine Decapods the number of cells in the hearts, if not the same, does not at any rate vary much. Potamobius, however, has not less than sixteen elements (eight large, and eight, maybe, nine or ten, small ones). The cells are multipolar in shape. Their long processes--the axons--after sending out shorter ramifications run in regular courses, giving off long branches to all the muscles of the heart including those of the ostia, but excluding the muscle-fibres of the arterial valves. The short processes, which I regard as dendrites, spring from the cell-bodies and from the proximal parts of the axons. The endings of the dendrites which ramify in the muscle-bundles differ in appearance from the terminations of the long branches springing from the axons. The small cells possess similar processes, i.e. dendrites and axons. The latter could not be traced well. In the main or ganglionic trunk which in different species has different shapes, the following elements are present: (a) large and small cells, the arrangement of which varies in different species, but in all cases the small cells are situated in the posterior part of the trunk; (b) the axons of the large and small cells and a part of their branches; (c) the fibres of the dorsal nerves; (d) the neuropile-like networks of fibrils where the synapses between the efferent fibres and the neurons of the local system take place. These neuropiles form several more compact masses in Brachyura whilst in Macrura they are more diffusely scattered in the ganglionic trunk. (3) The fibres connecting the heart with the central nervous system take their origin in the infra-oesophageal ganglion and travel in the nerves running on the thoracic muscles. As separate bundles, one on each side, they turn towards the dorsal surface of the heart; hence the term nervi cardiaci dorsales is proposed; the other term--regulator nerves--indicates their physiological character. In their further course these nerves pierce the heart-wall and reach the local nervous system. The fibres of the dorsal nerves are of various diameters. The thicker, which in the description have been called System I, run throughout the ganglionic trunk and break up therein in many richly arborizing branches which at many places resemble in appearance the neuropile-like networks of fibrils. They are the fields of conjunction of all the fibres of System I with each other, as well as with the neurons of the local system. From the latter the following parts are in close relation with the fibrils of System I: (a) the collaterals of the axons entering the neuropile; (b) the dendrites; (c) the cell-bodies surrounded by a network of fibrils of the dorsal nerves; these basketworks, however, could not be seen in all the species investigated, and occur on the large cells only. Some branches of System I were found leaving the ganglionic trunk, but their destination is uncertain. The remaining fibres of the dorsal nerves which, it may be assumed, do not belong to the System I are of smaller but not equal diameter. Some take their course to the muscles without entering the ganglionic trunk, others travel in the latter, but their distribution could not be made out. (4) The third system of nerves, which enter into relationship with the heart by innervating the valves situated at the origin of the main arterial trunks, contains the following elements: (a) Nervi segmentales cord is, which number, as was found in Astacus, four on each side, branch from the thoracic nerves and pass on the ventral side of the pericardium towards the middle line. Here they join into--according to the species--one or two bundles, which take a longitudinal course. From these bundles branches are given off to the valves of five arteries, viz. arteriae antennales, arteriae hepaticae, and aorta posterior, and to the muscles of the ventral pericardial plate. The latter receive also branches springing directly from the segmental nerves. The system of the segmental nerves of the heart is connected with the nerves of the dorsal abdominal artery which in its turn receives segmental nerves originating in the abdominal ganglia and ending in the valves of the arteries arising from the vessel named. (b) The nervus cardiacus anterior arises from the stomatogastric nerve and runs alongside the median anterior artery. The territory of the terminal branches of this nerve, known as ‘nerf cardiaque’ of Lemoine, has been found to be confined entirely to the valve of the median anterior vessel (aorta anterior s. arteria ophthalmica). No connexion with the nerves of other valves could be ascertained. (5) Besides the three nervous systems enumerated which are in relation with the heart itself, several nerve branches running from the thoracic nerves penetrate the pericardial cavity. They break up here in...