When at the beginning of the year I was invited by the Council of the Society to give a Paper on oil cooling I had had little more than average contact with the subject, but nevertheless I was startled when I discovered the extent of my ignorance. Inquiry showed that this lack of knowledge was fairly general, and that apart from highly technical articles by specialists, there was remarkably little up-to-date published data.

This analytical treatment gives general considerations concerning “ true rolling ” of a rolling body in a circular path : firstly, for constant speed of its centre of gravity, and, secondly, for acceleration of its centre of gravity. From these are derived the relations of the dimensions, as function of the conditions, and the corresponding constructions for both taper roller bearings and ball bearings, which are essential to produce “ true rolling” at constant and variable shaft speeds.