for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a different form in the light of the following consideration.
According to Newton’s law of motion, we have
,
where the “inertial mass” is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have
,
where the “gravitational mass” is likewise a characteristic constant for the body. From these two relations follows:
.
If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a
