Experiments were carried out to test the applicability of the ‘diffusion equilibrium’ technique to the estimation of the rate of umbilical blood flow in unstressed ewes and does (female goats) in the last third of gestation. Antipyrine was infused into the maternal circulation for 5–7 min. whilst the concentration difference across the umbilical circuit was followed for 30 min. during which it rose and then fell to insignificance. A comparison of the concentrations of antipyrine in umbilical blood and fetal tissue at the 30th min. indicated such a degree of agreement that blood concentration can be substituted for tissue concentration as the numerator in the equation expressing the Fick principle. Results of the application of the method in both acute and chronic experiments are presented, together with data on the v‐a oxygen difference across the umbilical circuit and the oxygen consumption of the fetus in utero.