ON NATURAL MOTIONS caused by Gravity

Chapter 2. On the moments The measure of the tendency of a weight to cause movement or rotation around a point or axis. of heavy bodies floating in a fluid.

PROPOSITION IV.

In a channel or siphon A U-shaped tube used to move liquids. having two straight arms, and elevated perpendicularly to the horizon, the center of gravity of the fluid descending in it moves along a curved path in a parabolic line.

IN the siphon TFGV let there be two channels TF and GV parallel to each other. They are raised perpendicularly to the base FG, and to the horizon. Let each of them be of equal thickness. The capacity of the portion of the cylinder TF above the horizontal line drawn through V (which is TA in the first case, and TC in the second) is equal to the capacity of GV. This capacity is divided into any number of equal parts measured by fours at X, Y, Z, I, L, 2. The points A, B, C, D, E are the centers of gravity of the cylinders TF, XF, YF, ZF, and AF, or CF. Likewise, H, I, K, L are the centers of gravity of the cylinders GI, GL, G2, GV. Because the centers of gravity A and B bisect the cylinders TF and XF, therefore TF is to XF as AF is to BF. By the conversion of the ratio, and by alternating the terms, TF has the same ratio to AF as TX has to AB. Therefore, AB is half of TX itself, just as HG is half

A geometric diagram shows a U-shaped siphon labeled TFGV. The left vertical arm TF and the right vertical arm VG are joined by a horizontal base FG. Points T, A, B, C, D, and E are marked on the left arm. Points V, 2, L, K, I, and H are marked on the right arm. Several diagonal lines connect specific points between the two arms. A curved line representing a parabola is drawn through the center of the vessel, passing through a point marked M. Vertical dashed lines are dropped from this curve to a horizontal line labeled with points N, O, and P.