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Careful measurements have been made of the wear of rubbing steel surfaces as a function of load, distance of travel, and hardness under controlled conditions which eliminated the effect of all factors except adhesion. At normal pressures averaged over the apparent contact area which are less than one third the hardness of the softer material the amount of wear was found to depend linearly on the distance of travel and on the load but was independent of the apparent area of contact. At average pressures greater than one third of the hardness, the depth of wear varied linearly with the distance of travel, was independent of the apparent area of contact for a given average normal stress, but increased many fold for small increases in stress. These findings rationalize the familiar observations on the running‐in of machine surfaces. The results are discussed in the light of the current adhesion theory of dry friction.