e hand the
material system and on the other a set of points, each point
corresponding to a particle of the system, and the whole representing
the configuration of the system at a given instant.

This is called a diagram of configuration.

_Diagram of Displacement._--Let us next consider two diagrams of
configuration of the same system, corresponding to two different
instants. We call the first the initial configuration and the second
the final configuration, and the passage from the one configuration to
the other we call the displacement of the system. We do not at present
consider the length of time during which the displacement was
effected, nor the intermediate stages through which it passed, but
only the final result--a change of configuration. To study this change
we construct a diagram of displacement.

Let A, B, C be the points in the initial diagram of configuration, and
A', B', C' be the corresponding points in the final diagram of
configuration. From o, the origin of the diagram of displacement, draw
a vector oa equal and parallel to AA', ob equal and parallel to BB',
oc to CC', and so on. The points a, b, c, &c., will be such that the
vector ab indicates the displacement of B relative to A, and so on.
The diagram containing the points a, b, c, &c., is therefore called
the diagram of displacement.

In constructing the diagram of displacement we have hitherto assumed
that we know the absolute displacements of the points of the system.
For we are required to draw a line equal and parallel to AA', which we
cannot do unless we know the absolute final position of A, with
respect to its initial position. In this diagram of displacement there
is therefore, besides the points a, b, c, &c., an _origin_, o, which
represents a point absolutely fixed in space. This is necessary
because the two configurations do not exist at the same time; and
therefore to express their relative position we require to know a
point which remains the same at the beginning and end of the time.

But we may construct the diagram in another way which does not assume
a knowledge of absolute displacement or of a point fixed in space.
Assuming any point and calling it a, draw ak parallel and equal to BA
in the initial configuration, and from k draw kb parallel and equal to
A'B' in the final configuration. It is easy to see that the position
of the point b relative to a w