The second lecture, which was wholly taken up in explaining the Propertys of the Centers of gravity and motion, which were applyed to the instruments, Cheifly in use in Common life, such as, the lever, pulley, Ballance axis in peritrocheo,1 &c. But the Ballance was principally insisted on. The reason of it was fully explained and the method of weighing, viz the distances of the Bodys from the Center of motion, must be precisely in a reciprocall proportion of their quantitys of matter or weights, always alowing for the weight of the Beam on which they are suspended, as well as friction, and the falsity of the supposition, that radii proceeding from the center of the earth are parrellel. Mr. Winthrop also demonstrated to us that all the advantages arising from any of the engines in use, resulted from the different possion position of them, with relation to force and velocity, thence he shew’d the famous problem of Archimedes viz, to move any weight however great by any force however small.—I had like to have forgot that he applied the doctrines of the center of gravity to the heavenly Bodys, shewing us the affections of the sun and planets with respect to their Centers of gravity, and instructed us in the manner of finding the Common Center of gravity of any 2 of ’em e.g. earth and moon, viz By this proportion as the quantitys of matter in Both added together is to the quantity of matter in the one separtely so is the distance of their centers to the distance of the Center of the other, from the Common Center sought. And to find the common Center of gravity of 3, 4 or 5 or any given number of Bodys, having found the common center of any 2, from that said Center draw a line to another of said Bodys and find the common Center of gravity of these two respecting the common Center of gravity of the former 2 as a Body containing a quantity of matter equal to Both said Bodys.

The theory of the Ballance, scales, steel-yard &c. and all and the 3 species of lever’s continued to which (viz) the lever he referred allmost all the instruments in life, and universally. To make a aequilibrium, the product of the quantity of matter in the weight multiplyed into its distance from the Center of motion, must be equal to the quantity of matter in the power, multiplyed into it’s distance from said Center.

The phaenomina of The nature of the Pulley, axis in peritrochaeo, and inclined Plane explained, which all depend on the laws before laid down (viz) that the quantity of matter in the weight bears the same proportion to the quantity of matter in the power, as the distance of the power from the Center of motion, to the distance of the weight from said Center.

The Theory of simple machines and in particular of the inclined plane, of the wedge and screw, and other machines compounded of these simple ones, finish’d.

Sir Isaac Newtons three laws of nature proved and illustrated, together with the application of them to the planets, which are kept in their orbits by two forces acting upon them, viz that of gravity and that which is call’d their Centrifugal force whereby it they strives to recede from the Center of their orbits, and fly off therefrom in tangents.

The theory of Centrifugal forces, continued; and aplyed to the Cases of the planets; and from this Centrifugal force, Mr. Winthrop confuted the hypothesis of vortices, from this also arises the spheroidal form of the earth.

Some thing’s observed concerning gravity, which encreases as you 64approach the Center of the earth in a reciprocal proportion of the squares of the distances, and under this head were introduced pendula and we saw that all pendula of equall length oscilated in equal time whether the arches they described were greater or less. We were also inform’d that bodys falling in Chords of a Circle will fall in equal times Caeteris paribus; and in the same time that the same Body would pass through the diameter, as