1. An account is given of the functional morphology of the coxal articulations in the cockroach. The greater range of movements executed by the prothoracic legs is made possible by the mobility of the trochantinal condyle relative to the episternal condyle.
2. The movements of the individual legs were studied by means of films taken at speeds of 16-32 frames/sec. These show that more than three legs are in contact with the ground throughout the cycle of movements at normal speeds. Suggestions are also made concerning the mechanics of walking, but these require experimental verification.
3. The rhythm of walking movements in Periplaneta, Blatta, Dytiscus, Hydropkilus, Carabus, Blaps and Chrysomela obeys two rules: (i) no foreleg or middle leg is protracted until the leg behind has taken up its supporting position; (ii) each leg alternates with the contralateral one of the same segment. Other pterygote insects appeared not to differ from the species studied in any essential feature.
4. An increase in speed is accompanied by a decrease in the times of both protraction (p) and retraction (r), a shortening of the stride length, and an increase in the distance between the successive points d'appui. The range of speeds is continuous and no distinction could be recognized between walking and running.
5. Several gaits have been observed, the most common order of protraction being R1, L2, R3, L1 , R2, L3, R1, etc., but these grade into one another if the ratio p/r is altered and the two rules obeyed. A system of rigidly alternating tripods would result if the ratio p/r was unity, but this is never quite realized as there is always a delay, sometimes extremely short, between the protraction of the three legs of a triangle. At very slow speeds the rhythm R3, R2, R1, L3, L2, L1 , R3, etc., may be present.
6. It is concluded that insects are the end-product of a process of limb reduction among terrestrial Arthropoda in which p/r may be increased to nearly one and yet the animal retains static stability throughout the whole cycle. This is impossible with fewer than six legs.