aken from its mass. But now we enter upon
altogether new relations with our little neophyte, and find that we
have reached the limits of its patience.

Take three pieces of string of unequal lengths--one being one foot
long; the second, four feet; and the third, nine feet. Hang them up by
one extremity, and attach to each of the other ends a weight. Then
start the three weights all off together vibrating, and observe what
happens. The several bodies do not now all vibrate in the same times
as in the previous experiments. By making the lengths of the strings
unequal, we have introduced elements of discord into the company. The
weight on the shortest string makes three journeys, and the weight on
the next longest string makes two journeys, while the other is
loitering through one.

This discrepancy, again, is only what the behaviour of the vibrating
masses in the previous experiments should have taught the observer to
anticipate. Each of the weights in this new arrangement of the
strings, has to swing in the portion of a circle, which, if completed,
would have a different dimension from the circles in which the other
weights swing. The one on the shortest string swings in the segment of
a circle that would be two feet across; the one on the longest string
swings in the segment of a circle that would be eighteen feet across.
Now, if these two weights be made to vibrate in arcs that shall
measure exactly the twelfth part of the entire circumference of their
respective circles, then one will go backwards and forwards in a
curved line only half a foot long, while the other will move in a line
four feet and a half long.

But both these weights, the one going upon the short journey, and the
other upon the long, will start down exactly the same inclination or
declivity. The reader will see that this must be the case if he will
draw two circles on paper round a common centre, the one at the
distance of one inch, and the other at the distance of nine inches.
Having done this, let him cut a notch out of the paper, extending
through both the circles to the centre, and including a twelfth part,
or thirty degrees, of each between its converging sides. He will then
observe, that the two arcs cut out by the notch are everywhere
concentric with each other; therefore, their beginnings and endings
are concentric or inclined in exactly the same degree to a
perpendicular crossing their centres. These concentric beginnings and
endings rep