Force in this form has a definite mechanical measure, in the amount of
work that it can perform. The simplest form of work is the raising of
a weight. A man walking up-hill, or up-stairs, with a pound weight in
his hand, to an elevation say of sixteen feet, performs a certain
amount of work, over and above the lifting of his own body. If he
carries the pound to a height of thirty-two feet, he does twice the
work; if to a height of forty-eight feet, he does three times the
work; if to sixty-four feet, he does four times the work, and so on.
If, moreover, he carries up two pounds instead of one, other things
being equal, he does twice the work; if three, four, or five pounds,
he does three, four, or five times the work. In fact, it is plain
that the work performed depends on two factors, the weight raised and
the height to which it is raised. It is expressed by the product of
these two factors.

But a body may be caused to reach a certain elevation in opposition to
the force of gravity, without being actually carried up. If a hodman,
for example, wished to land a brick at an elevation of sixteen feet
above the place where he stood, he would probably pitch it up to the
bricklayer. He would thus impart, by a sudden effort, a velocity to
the brick sufficient to raise it to the required height; the work
accomplished by that effort being precisely the same as if he had
slowly carried up the brick. The initial velocity to be imparted, in
this case, is well known. To reach a height of sixteen feet, the
brick must quit the man's hand with a velocity of thirty-two feet a
second. It is needless to say, that a body starting with any
velocity, would, if wholly unopposed or unaided, continue to move for
ever with the same velocity. But when, as in the case before us, the
body is thrown upwards, it moves in opposition to gravity, which
incessantly retards its motion, and finally brings it to rest at an
elevation of sixteen feet. If not here caught by the bricklayer, it
would return to the hodman with an accelerated motion, and reach his
hand with the precise velocity it possessed on quitting it.

An important relation between velocity and work is here to be pointed
out. Supposing the hodman competent to impart to the brick, at
starting, a velocity of sixty-four feet a second, or twice its former
velocity, would the amount of work performed be twice what it was in
the first instance? No; it would be four times that qua