, so that the transformed equation will be:
Taking into account the extended region of validity of this equation, one will be able to regard the
which arise from the accelerational transformation (vide [Note 25]) just as well, as due to the action of a gravitational field, which asserts its existence in effecting just these accelerations. Gravitational problems thus resolve into the general science of motion of a relativity-theory of all motions.
By thus accentuating the equivalence of gravitational and accelerational events, we raise the fundamental fact, that all bodies in the gravitational field of the earth fall with equal acceleration, to a fundamental assumption for a new theory of gravitational phenomena. This fact, in spite of its being reckoned amongst the most certain of those gathered from experience, has hitherto not been allotted any position whatsoever in the foundations of mechanics. On the contrary, the Galilean law of inertia makes an event which had never been actually observed (the uniform rectilinear motion of a body, which is not subject to external forces) function as the main-pillar amongst the fundamental laws of mechanics. This brought about the strange view that inertial and gravitational phenomena, which are probably not less intimately connected with one another than electric and magnetic phenomena, have nothing to do with one another. The phenomenon of inertia is placed at the base of classical mechanics as the fundamental property of matter, whereas gravitation is only, as it were, introduced by Newton's law as one of the many possible forces of nature. The remarkable fact of the equality of the inertial and gravitational mass of bodies only appears as an accidental coincidence.
Einstein's principle of equivalence assigns to this fact the rank to which it is entitled in the theory of motional phenomena. The new equation of motion (1) is intended to describe the relative motions of bodies with respect to one another under the influence of both inertia and gravity. The gravitational and inertial phenomena are amalgamated in the one principle that the motion take place in the geodetic line
. Since the element of arc
