hts vibrate, is perfect so long as both the unequal arcs
of motion are short ones, when compared with the length of the
suspending strings; but even when one of the arcs is five times longer
than the other, ten thousand vibrations will be completed before one
weight is an entire stride in advance of the other; and even this
small amount of difference is destroyed when the arc in which the
weights swing is a little flattened from the circular curve.

But there is yet another surprise to be encountered. Hang a weight of
a pound upon one of the strings, and a weight of two pounds upon the
other, and set them vibrating in arcs of unequal length as before, and
still their motions will be found to be isochronous. Unequal weights,
as well as equal ones, when hung on equal strings, will swing through
arcs of unequal length in equal periods of time. This seeming
inconsistency also admits of a satisfactory explanation. It has been
stated, that the motion of swinging bodies is caused by the earth's
attraction. But what are the facts that are more particularly implied
in this statement? What discoveries does the philosophic inquirer make
when he looks more narrowly into it? For the sake of familiar
illustration, let it be imagined that a man stands at the top of the
Monument of London, with two leaden bullets in his hand, each weighing
an ounce, and that he drops these together. They go to the earth,
because the earth's mass draws them thither; and since the two bodies
exactly resemble each other, and start at the same instant upon their
descent, they must of course both strike the pavement beneath
simultaneously. There can be no reason why one should get down before
the other, for the same influence causes the fall of each. The entire
mass of the huge earth attracts each bullet alike, and the bullets,
therefore, yield like obedience to the influence, and fall together to
the ground.

But now, suppose that the two bullets were to be all at once fused
into one, and that this combined mass were then dropped from the top
of the Monument as a single bullet, would there then be any reason why
the two ounces of lead should make a more rapid descent than they
would have made while in separate halves? Clearly not. There is but
the same earth to attract, and the same number of particles to be
drawn in each case, and therefore the same result must ensue. Each
particle still renders its own individual obedience, and makes its own
independen