demonstrate it to you), that whenever this rule (see page 126) is found to hold "the squares of the periodic times of several bodies moving round a central body are proportional to the cubes of the distances of the several bodies from that central body," then it will be found, by a process exactly similar to that which we have gone through, that the effects of the central body's attraction at the different distances are inversely as the squares of the distances. Now, this law (that the squares of the times are proportional to the cubes of the distances) was discovered by Kepler, long before the theory of gravitation was invented, to hold in regard to the times and distances of the planets in their revolutions round the sun. Moreover, in regard to the four satellites of Jupiter, the same law holds. For we are able without difficulty to observe their periodic times; we are able also (by observing the transits and the difference of Polar distances of Jupiter and each satellite, or by other methods) to ascertain their apparent angular distance from Jupiter; and from this, knowing the distance of Jupiter from the earth in miles, we can compute the distance of each satellite from Jupiter in miles; and we find that the squares of their times are proportional to the cubes of their distances; and therefore the attraction of Jupiter upon his several satellites is inversely proportional to the squares of their distances from him. In like manner, it is found that the attraction of Saturn upon his seven satellites is inversely proportional to the squares of their distance from him; and, as far as we can examine, the same law holds with regard to the attraction of Uranus on his satellites. Thus for every body which we know, around which other bodies revolve, the force of attraction of the central body on the different bodies that revolve
