 In this equation the sums are to be taken over all massive bodies in the universe. Since the top sum is weighted by distance, distant masses count much more than near ones. In a world with a (reasonably) static distribution of heavy distant bodies, such as we appear to live in, the equation entails that the velocity of a free body will be constant (to an extremely good approximation) in precisely those frames that we already consider to be ‘inertial’ frames. The upshot of this equation is that the frame of the fixed stars plays the role of absolute space in the statement of the 1st law. This proposal does not, by itself, offer an alternative to Newtonian mechanics, and as Mach himself pointed out, the law is not well-behaved in an infinite universe filled with stars; but the same can perhaps be said of Newton’s law of gravitation (see Malament 1995, and Norton 1993). But Mach did not offer this equation as a proposed law valid in any circumstances; he avers, “it is impossible to say whether the new expression would still represent the true condition of things if the stars were to perform rapid movements among one another.” (p. 289)