In the present study, a proportional relationship is derived between the specific rate of grinding, called the selection function, and the net mill power for tumbling ball mills and vibration ball mills. The proportionality constant is a function of material properties and some mill operating parameters. Also, the net mill power is expressed in terms of mill size and operating parameters. A convex trend of the net mill power in relation to the ball filling, J with a peak at about J = 0.4 is obtained for tumbling mills. Vibration mills have a so called double action showing an increase in mill power with increasing J even at J greater-than-or-equal-to 0.5. These results are confirmed to be in reasonable agreement with reported experiments.