e to deal
with material systems containing a great number of parts, as in the
kinetic theory of gases. The diagram of configuration then appears as
a region of space swarming with points representing molecules, and the
only way in which we can investigate it is by considering the number
of such points in unit of volume in different parts of that region,
and calling this the _density_ of the gas.

In like manner the diagram of velocities appears as a region
containing points equal in number but distributed in a different
manner, and the number of points in any given portion of the region
expresses the number of molecules whose velocities lie within given
limits. We may speak of this as the velocity-density.

_Diagrams of Stress._--Graphical methods are peculiarly applicable to
statical questions, because the state of the system is constant, so
that we do not need to construct a series of diagrams corresponding to
the successive states of the system. The most useful of these
applications, collectively termed Graphic Statics, relates to the
equilibrium of plane framed structures familiarly represented in
bridges and roof-trusses. Two diagrams are used, one called the
diagram of the frame and the other called the diagram of stress. The
structure itself consists of a number of separable pieces or links
jointed together at their extremities. In practice these joints have
friction, or may be made purposely stiff, so that the force acting at
the extremity of a piece may not pass exactly through the axis of the
joint; but as it is unsafe to make the stability of the structure
depend in any degree upon the stiffness of joints, we assume in our
calculations that all the joints are perfectly smooth, and therefore
that the force acting on the end of any link passes through the axis
of the joint.

The axes of the joints of the structure are represented by points in
the diagram of the frame. The link which connects two joints in the
actual structure may be of any shape, but in the diagram of the frame
it is represented by a straight line joining the points representing
the two joints. If no force acts on the link except the two forces
acting through the centres of the joints, these two forces must be
equal and opposite, and their direction must coincide with the
straight line joining the centres of the joints. If the force acting
on either extremity of the li