resent correctly the concentric directions in which the
swinging weights commence their downward movements.

Now, since it has been shewn that bodies begin to run down equal
descents with equal velocities, it follows that the weight on the
short string and that on the long string must commence to move down
the concentric curves of their respective arcs at an equal rate. But
it has been also shewn that the one of these weights has a nine times
longer journey to perform than the other; it is clear, therefore, that
both cannot accomplish their respective distances in the same time.
The weight on the shortest string in reality makes three vibrations,
and the weight on the string that is next to this in length makes two
vibrations, while the weight on the longest string is occupied about
one; and the differences would be as 9, 4, and 1, instead of as 3, 2,
1, but that the weights moving in the longer arcs benefit most from
acceleration of velocity. Although all the vibrating bodies begin to
move at equal rates, they pass the central positions directly beneath
their points of suspension at unequal ones. Those that have been the
longest in getting down to these positions, have of necessity
increased their paces the most while upon their route.

Suspended weights, then, only vibrate in equal times when hung upon
equal strings; but they continue to make vibrations in equal times
notwithstanding the diminution of the arcs in which they swing. This
was the fact that caught the attention of Galileo; he observed that
the vibrations of the lamp slowly died away as the effect of the
disturbing force was destroyed bit by bit, but that, nevertheless, the
last faint vibration that caught his eye, took the same apparent time
for its performance as the fullest and longest one in the series.

The instrument that has been designated by the learned name of
pendulum, is simply a weight of this description placed on the end of
a metallic or wooden rod, and hung up in such a way that free sideways
motion is permitted. This freedom of motion is generally attained by
fixing the top of the rod to a piece of thin, highly elastic steel. A
pendulum fitted up after this fashion, will continue in motion, if
once started, for many hours. It only stops at last, because the air
opposes a slight resistance to its passage, and because the suspending
spring is imperfectly elastic. The effects of these two causes
combined arrest the vibration at last, but no