ill be the same by this construction as
by the former construction, only we must observe that in this second
construction we use only vectors such as AB, A'B', which represent the
relative position of points both of which exist simultaneously,
instead of vectors such as AA', BB', which express the position of a
point at one instant relative to its position at a former instant, and
which therefore cannot be determined by observation, because the two
ends of the vector do not exist simultaneously.

It appears therefore that the diagram of displacements, when drawn by
the first construction, includes an origin o, which indicates that we
have assumed a knowledge of absolute displacements. But no such point
occurs in the second construction, because we use such vectors only as
we can actually observe. Hence the diagram of displacements _without
an origin_ represents neither more nor less than all we can ever know
about the displacement of the material system.

_Diagram of Velocity._--If the relative velocities of the points of
the system are constant, then the diagram of displacement
corresponding to an interval of a unit of time between the initial and
the final configuration is called a diagram of relative velocity. If
the relative velocities are not constant, we suppose another system in
which the velocities are equal to the velocities of the given system
at the given instant and continue constant for a unit of time. The
diagram of displacements for this imaginary system is the required
diagram of relative velocities of the actual system at the given
instant. It is easy to see that the diagram gives the velocity of any
one point relative to any other, but cannot give the absolute velocity
of any of them.

_Diagram of Acceleration._--By the same process by which we formed the
diagram of displacements from the two diagrams of initial and final
configuration, we may form a diagram of changes of relative velocity
from the two diagrams of initial and final velocities. This diagram
may be called that of total accelerations in a finite interval of
time. And by the same process by which we deduced the diagram of
velocities from that of displacements we may deduce the diagram of
rates of acceleration from that of total acceleration.

We have mentioned this system of diagrams in elementary kinematics
because they are found to be of use especially when we hav