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Abstract 1.)The energy expenditure, the vertical lift work of the trunk per step, and the leg and foot lengths have boon measured for 11 young male subjects walking on a horizontal treadmill at 1-4 m.p.h. at natural step frequency and in some instances at controlled frequencies and up and down hill. Similar measurements have been made whilst box stepping. These data and others from the literature have been analysed. 2.)The vertical lift per stop (L) is a geometric function of the lengths of the leg, foot and pace (R, d and P respectively) such that, L = (P−d)2/8R. 3.)The energy expenditure of walking at natural step frequency on the horizontal troadmill is linearly related to the vertical lift work which is the product of lift per step, stop frequency and body weight. This relationship does not hold at arbitrary stop frequencies above and below those chosen spontaneously. Under those circumstances the energy expenditure of walking at a given speed increases : by contrast the lift and the lift work decrease progressively with increasing step frequency in accordance with the geometric configuration. However, a relationship has been developed which suggests that energy expenditure may again be a linear function of lift work when step frequency is taken into account. The energy expenditure of uphill but not of downhill walking at natural stop frequency can be described in similar terms when allowance is made for the additional vertical work. Analysis of the energy expenditure of stepping exercise suggests that, as compared with walking, a smaller proportion of the total energy is expended in vertical work. 4.)The energy expenditure of horizontal walking at natural stop frequency is linearly related to the square of the forward velocity (u 2). This relationship has been used to calculate the velocity of minimal energy expenditure per unit of horizontal distance moved. The velocities so obtained, including and excluding the resting energy expenditures, are respectively 3½ and 2¼, m.p.h. which agree with those experimentally determined. The linear extrapolation of the regression relationship gives a mean energy expenditure at zero velocity of 2·4 kcal/min which is in excess of the observed mean resting level. 5.)Prediction of walking energy expenditure (E O2 ) has been attempted using both the lift work and velocity squared relationships. Use of the first requires knowledge both of leg and foot lengths and of the pace which the subject will adopt at a given velocity; the latter has not so far proved amenable to prediction. The second in the form E O2 /W = 0·0386 × 4·25 × 10−6 v 2 kcal/kg/min can be used to predict the walking energy expenditure of our subjects to within 0·7 kcal in 95 per cent of cases. Greater precision can be achieved by individual calibration of the subjects.