The “gravitational” mass is differently defined. It is capable of two meanings. We may mean (1), the way a body responds in a situation where gravitation has a known intensity, for example, on the surface of the earth, or on the surface of the sun; or (2), the intensity of the gravitational force produced by the body, as, for example, the sun produces stronger gravitational forces than the earth does. Newton says that the force of gravitation between two bodies is proportional to the product of their masses. Now let us consider the attraction of different bodies to one and the same body, say the sun. Then different bodies are attracted by forces which are proportional to their masses, and which, therefore, produce exactly the same acceleration in all of them. Thus if we mean “gravitational mass” in sense (1), that is to say, the way a body responds to gravitation, we find that “the equality of inertial and gravitational mass,” which sounds formidable, reduces to this: that in a given gravitational situation, all bodies behave exactly alike. As regards the surface of the earth, this was one of the first discoveries of Galileo. Aristotle thought that heavy bodies fall faster than light ones; Galileo showed that this is not the case, when the resistance of the air is eliminated. In a vacuum, a feather falls as fast as a lump of lead. As regards the planets, it was Newton who established the corresponding facts. At a given distance from the sun, a comet, which has a very small mass, experiences exactly the same acceleration towards the sun as a planet experiences at the same distance. Thus the way in which gravitation affects a body depends only upon where the body is, and in no degree upon the nature of the body. This suggests that the gravitational effect is a characteristic of the locality, which is what Einstein makes it. As for the gravitational mass in sense (2), _i.e._, the intensity of the force produced by a body, this is no longer _exactly_ proportional to its inertial mass. The question involves some rather complicated mathematics, and I shall not go into it.[7] [7] See Eddington, _The Mathematical Theory of Relativity_, Cambridge University Press, 2d edition, p. 128.