mptions of
Ampere.]--Diamagnetism and Magne-crystallic Action, p. 136-7.

********************

XVI. ON FORCE.

[Footnote: A discourse delivered in the Royal Institution, June 6,
1862.]

A SPHERE of lead was suspended at a height of 16 feet above the
theatre floor of the Royal Institution. It was liberated, and fell by
gravity. That weight required a second to fall to the floor from that
elevation; and the instant before it touched the floor, it had a
velocity of 32 feet a second. That is to say, if at that instant the
earth were annihilated, and its attraction annulled, the weight would
proceed through space at the uniform velocity of 32 feet a second.

If instead of being pulled downward by gravity, the weight be cast
upward in opposition to gravity, then, to reach a height of 16 feet it
must start with a velocity of 32 feet a second. This velocity
imparted to the weight by the human hand, or by any other mechanical
means, would carry it to the precise height from which we saw it fall.

Now the lifting of the weight may be regarded as so much mechanical
work performed. By means of a ladder placed against the wall, the
weight might be carried up to a height of 16 feet; or it might be
drawn up to this height by means of a string and pulley, or it might
be suddenly jerked up to a height of 16 feet. The amount of work done
in all these cases, as far as the raising of the weight is concerned,
would be absolutely the same. The work done at one and the same
place, and neglecting the small change of gravity with the height,
depends solely upon two things; on the quantity of matter lifted, and
on the height to which it is lifted. If we call the quantity or mass
of matter m, and the height through which it is lifted h, then the
product of m into h, or mh, expresses, or is proportional to, the
amount of work done.

Supposing, instead of imparting a velocity of 32 feet a second we
impart at starting twice this velocity. To what height will the
weight rise? You might be disposed to answer, 'To twice the height;'
but this would be quite incorrect. Instead of twice 16, or 32 feet,
it would reach a height of four times 16, or 64 feet. So also, if we
treble the starting velocity, the weight would reach nine times the
height; if we quadruple the speed at starting, we attain sixteen times
the height. Thus, with a four-fold velocity of 128 feet a second at
starting, the weight would attain an elevation of 256 feet.