Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/359

 Rh differences) will attract the whole phere GH (compoed of any concentric pheres or their differences) in the ame ratio. Let the number of the concentric pheres be increaed in infinitum, o that the denity of the matter together with the attractive force may, in the progres from the circumference to the centre, increae or decreae according to any given law; and by the addition of matter not attractive let the deficient denity be upplied that o the pheres may acquire any form deired; and the force with which one of thee attracts the other, will be till, by the former reaoning, in the ame ratio of the quare of the ditance inverely. Q. E. D.

Hence if many pheres of this kind, imilar in all repects, attract each other mutually; the accelerative attractions of each to each, at any equal ditances of the centres, will be as the attracting pheres.

And at any unequal ditances, as the attracting pheres applied to the quares of the ditances between the centres.

The motive attractions, or the weights of the pheres towards one another will be at equal ditances of the centres as the attracting and attracted pheres conjunctly; that is, as the products ariing from multiplying the pheres into each other.

And at unequal ditances, as thoe products directly and the quares of the ditances between the centres inverely.

Thee proportions take place alo, when the attraction aries from the attractive virtue of both pheres mutually exerted upon each other. For the attraction is only doubled by the on