This equality in the numerical values of the two types of masses will entail important consequences. For suppose, indeed, that the equality did not hold. This would imply that two billiard balls might present exactly the same gravitational mass, yet differ in the value of their respective inertial masses. If, then, the two balls were to be released simultaneously and allowed to fall from the same height towards the earth, their gravitational masses being equal, both balls would be subjected to exactly the same pull by the earth. But their inertial masses being assumed unequal, the ball whose inertial mass was greater would oppose the acceleration of the fall more strenuously than would be the case with the ball of lesser inertial mass. As a result, the balls would not reach the earth’s surface simultaneously. On the other hand, if the two types of masses are identical, we may be assured that any two objects released from the same point will reach the earth’s surface at the same instant (provided we operate in vacuo so that the resistance of the air does not interfere with their fall). It was precisely because experiment had demonstrated the existence of the same rate of fall for all bodies released from the same height, that Galileo was led to recognise the equality of the two masses. It may be mentioned, however, that ultra-precise experiments (notably with Eötvös’ torsion balance) have since verified these results with extreme accuracy.[80] We see, therefore, that the equality of the two types of masses allows us to anticipate that an observer situated in a falling elevator would have no weight. He might be standing on a weighing machine, but the needle would always register zero. The fact is that both observer and weighing balance would be falling with the same motion towards the earth; hence the observer’s feet would never press against the balance. These anticipations may appear to be self-evident; but it is important to note that they are in no wise self-evident until we have recognised the perfect equality of the two types of masses. If such an equality did not exist, the observer in the elevator might still press against the scales of the weighing machine or might hit the ceiling of the elevator, and it would no longer be correct to anticipate that elevator, scales and observer would all fall with exactly the same velocity and acceleration. [Pg 254]