A concrete illustration of the difference between inertial and gravitational mass is given by the following example: Consider a billiard ball at rest on a table. We should discover that the more massive the ball, the greater would be the effort necessary to set it in motion, as also to arrest its motion once started. The type of mass with which we should here be concerned would be inertial mass; and we may say that it is inertial mass which opposes a departure from rectilinear uniform motion or rest, hence which opposes acceleration. If, now, we were to lift the ball from the table and hold it at arm’s length, the effort we should have to exert to prevent our arm and ball from falling would again vary with the mass of the ball. This time, however, the mass whose effects we were seeking to resist would be the gravitational mass, i.e., the mass which is responsible for weight. It is this same gravitational mass which enters into the expression of Newton’s law of attraction. There is no a priori reason why any connection should exist between these two different types of masses. Thus, if a billiard ball is found to weigh twice as much as another, there is no logical necessity to anticipate that its inertial mass will also be twice that of the other. Yet it so happens that the most refined physical experiments have invariably proved the strictest proportionality between these two types of masses; so that by choosing our units [Pg 252] suitably it was always possible to represent both the inertial and the gravitational mass of a given body by the same number. Classical science had accepted the equality of the two types of masses as an empirical fact, but had found itself incapable of suggesting any theoretical justification for it. It appeared to be due to some miraculous coincidence. [Pg 253]