In investigations of lubricated sliding friction between two crossed cylinders it is found that for hard, smooth surfaces the friction force is a straight‐line function of the applied load, although this line does not generally pass through the origin. The slope of this line defines a friction coefficient, designated as the incremental frictionf&Dgr;, which is thought to have certain advantages in the study of non‐fluid lubricated friction. It is obviously independent of the load. It is found to be independent of viscous fluid effects and hence permits investigation of non‐fluid friction at reasonable speeds. In spite of being devoid of any viscous component, it is found in a great many cases to decrease with increasing speed,U, over at least part of the range, and this variation often appears to be a linear function of the logarithm of the speed. The curve off&Dgr;vs.lnUseems to be characteristic of the chemical structure of the lubricant and of the rubbing surfaces. It is not contended that viscous effects are absent under the conditions of these experiments but simply that the value off&Dgr;, which is not thetotalfriction coefficient, does not, because of its method of determination, include such effects.