An introduction to mathematics, by A. N. Whitehead.

DYNAMICS 53
the compass bearing of the course which he is
to keep. Again the rate of change of velocity,
that is velocity added per unit time, is also a
vector quantity: it is called the acceleration.
Similarly a force in the dynamical sense is
another vector quantity. Indeed, the vector
nature of forces follows at once according to
dynamical principles from that of velocities
and accelerations; but this is a point which
we need not go into. It is sufficient here to
say that a force acts on a body with a certain
magnitude in a certain direction.
Now all vectors can be graphically represented by straight lines. All that has to be
done is to arrange: (i) a scale according to
which units of length correspond to units of
magnitude of the vector-for example, one
inch to a velocity of 10 miles per hour in the
case of velocities, and one inch to a force of
10 tons weight in the case of forces-and (ii)
a direction of the line on the diagram corresponding to the direction of the vector. Then
a line drawn with the proper number of inches
of length in the proper direction represents the
required vector on the arbitrarily assigned
scale of magnitude. This diagrammatic representation of vectors is of the first importance. By its aid we can enunciate the famous
"parallelogram law" for the addition of
vectors of the same kind but in different
directions.