5. As forces differ in magnitude, it becomes necessary to establish
some convenient means of expressing their measurements. The pressure
exerted by one pound weight at London is the standard with which we
shall compare other forces. The piece of iron or other substance which
is attracted to the earth with this force in London, is attracted to
the earth with a greater force at the pole and a less force at the
equator; hence, in order to define the standard force, we have to
mention the locality in which the pressure of the weight is exerted.
It is easy to conceive how the magnitude of a pushing or a pulling
force may be described as equivalent to so many pounds. The force which
the muscles of a man’s arm can exert is measured by the weight which
he can lift. If a weight be suspended from an india-rubber spring, it
is evident the spring will stretch so that the weight pulls the spring
and the spring pulls the weight; hence the number of pounds in the
weight is the measure of the force the spring is exerting. In every
case the magnitude of a force can be described by the number of pounds
expressing the weight to which it is equivalent. There is another but
much more difficult mode of measuring force occasionally used in the
higher branches of mechanics (Art. 497), but the simpler method is
preferable for our present purpose.
[Illustration: FIG. 1.]
6. The straight line in which a force tends to move the body to which
it is applied is called the direction of the force. Let us suppose,
for example, that a force of 3 lbs. is applied at the point A, Fig.
1, tending to make A move in the direction AB. A standard line C of
certain length is to be taken. It is supposed that a line of this
length represents a force of 1 lb. The line AB is to be measured,
equal to three times C in length, and an arrow-head is to be placed
upon it to show the direction in which the force acts. Hence, by means
of a line of certain length and direction, and having an arrow-head
attached, we are able completely to represent a force.