86 The consequences of the

the least is impelled against the next greatest,the quantity of motion will be increased ineach of them to the last. Now if there bea hundred bodies in the series, and if thequantity of matter in each be double that inthe former, the smallest in the series beingimpelled against the next greatest, the quan-tity of motion, or force, in the last, will betwo million of million, three hundred thirtyeight thousand four hundred and eighty sixmillion, eight hundred and seven thousandsix hundred and fifty six times greater thanit was in the first: or the force in the lastwill be to that in the first, as the number2,338486,807656.13 to 1. (d), This num-ber

(d) Let the bodies be A, B, C, D, &c. and as r, 2,8, csV. if the distance betwixt A and B is called 1,the distance of the center of gravity from B will be j.The velocity of this center before the lhock is as ' , andas f after it ; and the distance of B from it as V at thesame time. The whole velocity of B is f, and the mat-ter of it as 2; so its moment is as i. Just so, the ve-locity of the center of gravity betwixt B and C, is \of 4 (B’s celerity) or §■; and C’s celerity double that,or ±; its matter as 4; its moment therefore as SoD’s celerity is f of (C’s celerity) f, or , 8 V ; its matter8; and its moment 44, (s’c. Thus the several momentsin the last 99 bodies are the several powers of j ; and

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