BODIES.

This is a subject with which every one who expects to be concerned with
machinery, either as designer or constructor, ought to be familiar. The
principles which underlie it are very simple, but in order to be of use,
these need to be thoroughly understood. If they have once been mastered,
made familiar, incorporated into your intellectual being, so as to be
readily and naturally applied to every case as it arises, then you
occupy a high vantage ground. In this particular, at least, you will not
go about your work uncertainly, trying first this method and then that
one, or leaving errors to be disclosed when too late to remedy them. On
the contrary, you will make, first your calculations and then your
plans, with the certainty that the result will be precisely what you
intend.

Moreover, when you read discussions on any branch of this subject, you
will not receive these into unprepared minds, just as apt to admit error
as truth, and possessing no test by which to distinguish the one from
the other; but you will be able to form intelligent judgments with
respect to them. You will discover at once whether or not the writers
are anchored to the sure holding ground of sound principles.

It is to be observed that I do not speak of balancing bodies, but of
balancing forces. Forces are the realities with which, as mechanical
engineers, you will have directly to deal, all through your lives. The
present discussion is limited also to those forces which are developed
in moving bodies, or by the motion of bodies. This limitation excludes
the force of gravity, which acts on all bodies alike, whether at rest or
in motion. It is, indeed, often desirable to neutralize the effect of
gravity on machinery. The methods of doing this are, however, obvious,