SEC. XJ11.I OF NATURAL PHILOSOPHY. 233 O be proportional to this quantity ; and the curvilinear area BDI, which the ordinate FN, drawn through the length DB with a continued motion will describe, will be as the whole force with which the whole segment RBSD attracts the body P. Q.E.I. PROPOSITION LXXXIV. PROBLEM XLIII. To find the force with which a corpuscle, placed without the centre of a sphere iti the axis of any segment, is attracted by that segment. Let the body P placed in. the axis ADB of the segment KBK be attracted by that seg ment. About the centre P, with the interval PE, let the spherical superficies EFK be described; and let it divide the segment into two parts EBKFE and EFKDE. Find the force of the first of those parts by Prop. LXXXI, and the force of the latter part by Prop. LXXXIII, and the sum of the forces will be the force of the whole segment EBKDE. Q.E.I. SCHOLIUM. The attractions of sphaerical bodies being now explained, it comes next in order to treat of the laws of attraction in other bodies consisting in like manner of attractive particles ; but to treat of them particularly is not neces sary to my design. It will be sufficient to subjoin some general proposi tions relating to the forces of such bodies, and the motions thence arising, because the knowledge of these will be of some little use in philosophical inquiries. SECTION XIII. Of the attractive forces of bodies which are not of a sphcerical figure. PROPOSITION LXXXV. THEOREM XLIL If a body be attracted by another, and its attraction be vastly stronger when it is contiguous to the attracting body than when they are sepa rated from one another by a very small interval ; the forces of the particles of the attracting body decrease, in the recess of the body at tracted, in more than a duplicate ratio of the distance of the particles. For if the forces decrease in a duplicate ratio of the distances from the particles, the attraction towards a sphaerical body being (by Prop. LXXIV) reciprocally as the square of the distance of the attracted body from the centre of the sphere, will not be sensibly increased by the contact, and it