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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,i‘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 to the elevation. If a hodman, for example,
wished to land a brick at an elevation of sixteen feet above
the place where he stands, 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 pre-
cisely the same as if he had slowly carried up the brick.
The initial velocity which must be imparted in the case here
assumed, 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 forever with the same velocity.
But when, in the case before us, the body is thrown upward,
it moves in oppositiOn to gravity, which incessantly retards
its metion, 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 this handwith the precise velocity it possessed on
quitting it.

Supposing the man competent to impart to the brick, at
starting, a speed of sixty-four feet a second, or twice its
former speed, would the amount of work performed in this
effort be only twice What it was in the first instance ? N o;
it would be four times that quantity. A body starting with
twice the velocity of another, will rise to four times the

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