The dynamic similarity hypothesis postulates that different mammals move in a dynamically similar fashion whenever they travel at speeds that give them equal values of a dimensionless parameter, the Froude number. Thus, given information about one species, it could be possible to predict for others relationships between size, speed and features of gait such as stride length, duty factor, the phase relationships of the feet and the patterns of force exerted on the ground. Data for a diverse sample of mammals have been used to test the hypothesis. It is found to be tenable in many cases when comparisons are confined to quadrupedal mammals of the type described by Jenkins (1971) as “cursorial”. Most mammals of mass greater than 5 kg are of this type. Although the hypothesis applies less successfully to comparisons between cursorial and non‐cursorial mammals it is shown to be a reasonable approximation even for such comparisons and for comparisons between quadrupedal mammals and bipedal mammals and birds.

Measurements have been made of the leg muscles of mammals ranging from shrews Sorex to an elephant Loxodonta. Allometric equations based on body mass have been calculated for muscle masses, fibre lengths and moment arms and the thickness of a tendon, in several groups of mammals. Departures from geometric similarity in mammals in general (excluding bipedal hoppers) are noted and discussed. Differences between primates; fissipedes, bovids and bipedal hoppers are also demonstrated.

Measurements have been made of the principal leg bones of 37 species representing almost the full range of sizes of terrestrial mammals. The lengths of corresponding bones tend to be proportional to (body mass)0·35 and the diameters to (body mass)0·36, except in the family Bovidae in which the exponents for length are much nearer the value of 0·25 predicted by McMahon's (1973) theory of elastic similarity. Comparisons are made between mammals of similar size belonging to different orders.

Records have been made of the forces exerted on the ground by dogs and a sheep, in walking, trotting, cantering and slow galloping. Film has been taken simultaneously. The difference between walking and trotting was much less marked for the sheep than for the dogs. Step length and stride length increase as speed increases. They are expressed as functions of the Froude number. The vertical component of the force exerted by a foot on the ground shows two main maxima in walking, except in the case of the fore feet of sheep. In this case and in other gaits there is only one main maximum. The vertical movements of the fore and hind quarters which occurred in examples of each gait have been calculated from the force records. The force exerted by a foot on the ground changes direction in the course of a step so as to remain more or less in line with a point fixed relative to the animal, but dorsal to its back. The force records show impact disturbances in the first 003 sec of contact of each foot with the ground. The point of application of the force on the sole of a foot tends to move posteriorly as the force increases. The results are discussed in relation to a theoretical account of the mechanics of locomotion on legs.

With 1 figure in the text) The principal bones, muscles and tendons of the legs have been measured in a selection of running birds, ranging in size from 0.1 kg quail to 40 kg ostrich. Maximum stride frequencies of the same species have been determined from films. Allometric equations have been derived. Most of the exponents agree well with McMahon's (1973, 1975a) theory of elastic similarity, which is discussed.