In the midline of the body are two triangular _dorsal fins_, each attached to the body for about half its length. The basal portion of each is thick and muscular, and contains supporting cartilages embedded in the muscles. The remainder of the fin is flexible and semi-transparent, horny fin-rays being faintly visible between the layers of skin. In front of each fin is a strong spine which seems to serve both as a cutwater and a weapon of defense. (Eugaleus has no spines.) The broad, paired, _pectoral fins_, having the general characteristics of the dorsals, spring from the ventral edges of the body just back of the head. A hard bar of cartilage connecting the bases of the pectoral fins can be felt through the skin of the ventral surface of the body. This is the ventral part of the _pectoral girdle_. Farther back, and also on the ventral surface, are the paired _pelvic fins_. The pelvic girdle can be felt through the skin between the bases of these fins. If the specimen is a male, it will have a fingerlike process projecting backward from the base and along the inner side of each pelvic fin. These organs, which attain a considerable size in adults, are modified portions of the pelvic fin used as copulatory organs. They are named variously _claspers_, myxopterygia, or pterygopodia. A groove runs along the dorsal side of the clasper from the tip to near the base, where it opens into a long sac (_glandula pterygopodia_) extending some distance in front of the pelvic fins just within the skin of the ventral surface. By feeling a cartilaginous axis of the clasper can be discovered, which extends to the tip of the organ. On the dorsal surface and near the end of the clasper is a sharp grooved spine on the outer side, and a strongly recurved hook on the inner side, both almost hidden by a flap projecting from the inner edge of the groove. This flap is stiffened by a series of small cartilages similar to the radial cartilages in the bases of the fins. The _caudal fin_ is asymmetrical, extending along the dorsal and ventral edges of the posterior end of the body. Observe the upward bend of the vertebral column which occurs in the tail; it is this character which marks the heterocercal type of tail. Eugaleus has a median ventral, or _anal_, fin a short distance anterior to the caudal fin.