XIILj OF NATURAL PHILOSOPHY". 241 n H m G ties, will decrease in the ratio of a power whose side is the distance oj the corpuscle from the plane, and its index less by 3 than the index oj the power of the distances. CASE 1. Let LG/be the plane by which the solid is terminated. Let the solid lie on that hand of the plane that is to wards I, and let it be resolved into in- _. numerable planes mHM, //IN, oKO, (fee., parallel to GL. And first let the attracted body C be placed without the solid. Let there be drawn CGHI per pendicular to those innumerable planes, and let the attractive forces of the points of the solid decrease in the ratio of a power of the distances whose index is the number n not less than 3. Therefore (by Cor. 3, Prop. XC) the force with which any plane mHM attracts the point C is reciprocally as CHn— 2. In the plane mHM take the length HM reciprocally proportional to CH1— 2, and that force will be as HM. In like manner in the several planes /GL, //,TN, oKO, (fee., take the lengths GL, IN, KO, (fee., reciprocally proportional to CGn— 2, CI1— 2, CKn — 2, (fee., and the forces of those planes will bs as the lengths so taken, and therefore the sum of the forces as the sum of the lengths, that is, the force of the Avhole solid as the area GLOK produced infinitely towards OK. But that area (by the known methods of quadratures) is reciprocally as CGn— 3, and therefore the force of the whole solid is reciprocally as CG"-3. Q.E.D. CASE 2. Let ttecorpuscleC be now placed on that hand of the plane /GL that is within the solid, and take the distance CK equal to the distance CG. And the part of the solid LG/oKO termi nated by the parallel planes /GL, oKO, will at tract the corpuscle C, situate in the middle, neither one way nor another, the contrary actions of the opposite points destroying one another by reason of their equality. Therefore the corpuscle C is attracted by the force only of the solid situate beyond the plane OK. But this force (by Case 1) is reciprocally as CKn—3, that is, (because CG, CK are equal) reciprocally as CG"— 3. Q,.E.D. COR. 1. Hence if the solid LGIN be terminated on each sitfe by two in finite parallel places LG, IN, its attractive force is known, subducting from the attractive force of the whole infinite solid LGKO the attractive force of the more distant part NIKO infinitely produced towards KO. COR. 2. If the more distant part of this solid be rejected, because its at traction compared with the attraction of the nearer part is inconsiderable, 16 0 N K 1 0 C