[Illustration: FIG. 9.]
24. As the last lecture was principally concerned with discussing how
one force could replace two forces, so in the present we shall examine
the converse question, How may two forces replace one force? Since
the diagonal of a parallelogram represents a single force equivalent
to those represented by the sides, it is obvious that one force may
be resolved into two others, provided it be the diagonal of the
parallelogram formed by them.
25. We shall frequently employ in the present lecture, and in some of
those that follow, the spring balance, which is represented in Fig. 9:
the weight is attached to the hook, and when the balance is suspended
by the ring, a pointer indicates the number of pounds on a scale. This
balance is very convenient for showing the strain along a cord; for
this purpose the balance is held by the ring while the cord is attached
to the hook. It will be noticed that the balance has two rings and two
corresponding hooks. The hook and ring at the top and bottom will weigh
up to 300 lbs., corresponding to the scale which is seen. The hook and
ring at the side correspond to another scale on the other face of the
plate: this second scale weighs up to about 50 lbs., consequently for a
weight under 50 lbs. the side hook and ring are employed, as they give
a more accurate result than would be obtained by the top and bottom
hook and ring, which are intended for larger weights. These ingenious
and useful balances are sufficiently accurate, and can easily be tested
by raising known weights. Besides the instrument thus described, we
shall sometimes use one of a smaller size, and we shall be able with
this aid to trace the existence and magnitude of forces in a most
convenient manner.