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# April 3d. 1754.

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 {12} common Center of gravity of the former 2 as a Body containing a quantity of matter equal to Both said Bodys.

1See description begins The Oxford English Dictionary, Oxford, 1933; 12 vols. and supplement. description ends under Peritrochium, quoting John Harris, Lexicon Technicum (1704): “The use of this Peritrochium is to make the Cylinder or Axis be turned the more easily by the means of Staves or Levers, which are fix’d in its Circumference.” See also Thomas Jefferson’s Notes of a Tour through Holland and the Rhine Valley in 1788:

“A machine for drawing light empty boats over a dam at Amsterdam. It is an Axis in peritrochio fixed on the dam. From the dam each way is a sloping stage. The boat is presented to this, the rope of the axis made fast to it, and it is drawn up. The water [on one] side of the dam is about 4.f. higher than on the other” ( description begins The Papers of Thomas Jefferson, ed. Julian P. Boyd and others, Princeton, 1950– . description ends , 13:9).

Evidently Winthrop dealt in more detail with this mechanical device in a later lecture; see entry of 6 April, below.