Adhesion is the frictional resistance that prevents a locomotive's driving wheels from slipping on the rail. Available adhesion depends on the conditions of both the rail and the wheel.  With a clean dry wheel running on a clean dry rail the "frictional coefficient" between them may be as high as 0.35 or 35%.  The presence of oil and other contaminents may reduce it to near zero.

Adhesive Weight is that part of a locomotive's weight that is supported by its driving wheels. In the case of modern Bo-Bo and Co-Co diesels and electrics, 100% of their weight is supported by their driving (or driven) wheels which allows them to deliver a very large starting Tractive Effort.  The same applies to 0-6-0T steam engine, however with 0-6-0 tender engines, perhaps no more than 70% of its total weight may be supported by its drivers.  The greater the number of carrying wheels, the less weight is available for adhesion, and in the case of a typical Pacific locomotive less than 50% of total weight may be available for adhesion.  This has serious consequences in terms of limiting the locomotive's wheel-rim tractive effort and its drawbar power.

Coefficient of Friction is defined as the frictional resistance between two bodies and the "normal" force applied between them.  In the case of a locomotive, the Frictional Coefficient = available frictional resistance ÷ adhesive weight on the driving wheels. 

Adhesion Factor is the inverse of Friction Coefficient, i.e. Adhesion Factor = adhesive weight on the driving wheels ÷ available frictional resistance.

Frictional Coefficient between Wheels and Rail: A clean dry wheel on a clean dry rail may have a coefficient of friction as high as 0.35 or 35% at zero speed. This can drop to 0.25 in wet conditions, and very much lower if the rail is contaminated with lubricating substances such as ice, oil and leaves.

However the frictional coefficient between wheel and rail is not constant: due to "elastic slip" it falls as speed rises which is why wheel slip can (and does) occur at speed.  Curves showing the relationship between speed and friction coefficient are shown below (taken from Koffman's equations):

Estimating a locomotive's adhesion limit is further complicated by the fact that its wheel-rim tractive effort varies considerably over each wheel revolution, even at high speed.  As a result, momentary slipping can occur where the tractive force peaks and this can, in unfavourable circumstances, initiate full-scale slip at low and high speeds.