differences) will attract the whole ſphere GH (compoſed of any concentric ſpheres or their differences) in the ſame ratio. Let the number of the concentric ſpheres be increaſed in infinitum, ſo that the denſity of the matter together with the attractive force may, in the progreſs from the circumference to the centre, increaſe or decreaſe according to any given law; and by the addition of matter not attractive let the deficient denſity be ſupplied that ſo the ſpheres may acquire any form deſired; and the force with which one of theſe attracts the other, will be ſtill, by the former reaſoning, in the ſame ratio of the ſquare of the diſtance inverſely. Q. E. D.
Cor. 1. Hence if many ſpheres of this kind, ſimilar in all reſpects, attract each other mutually; the accelerative attractions of each to each, at any equal diſtances of the centres, will be as the attracting ſpheres.
Cor. 2. And at any unequal diſtances, as the attracting ſpheres applied to the ſquares of the diſtances between the centres.
Cor. 3. The motive attractions, or the weights of the ſpheres towards one another will be at equal diſtances of the centres as the attracting and attracted ſpheres conjunctly; that is, as the products ariſing from multiplying the ſpheres into each other.
Cor. 4. And at unequal diſtances, as thoſe products directly and the ſquares of the diſtances between the centres inverſely.
Cor. 5. Theſe proportions take place alſo, when the attraction ariſes from the attractive virtue of both ſpheres mutually exerted upon each other. For the attraction is only doubled by the conjuncti-
