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
(\text{Force}) = (\text{gravitational mass}) \ × (\text{intensity of the gravitational field}), \index{Gravitational mass}
where the "gravitational mass" is likewise a characteristic constant for the body. From these two relations follows:
(\text{acceleration}) = \frac{(\text{gravitational mass})}{(\text{inertial mass})} \ × (\text{intensity of the gravitational field}).
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 given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable choice of units we can thus make this ratio equal to unity. We then have the following law: The gravitational mass of a body is equal to its inertial mass.
It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as "inertia" or as "weight" (lit. "heaviness"). In the
following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.