and not an integrator.

[Illustration: A NEW INTEGRATOR]

Before I turn to its claims to be considered new, I must first remind
you of the importance of an instrument of this kind to the
draughtsman. I put aside its purely mechanical applications, where it
has been, or can be, attached to the indicators of steam engines, to
dynamometers, dynamos, and a variety of other instruments where
mechanical integration is of value. These lie entirely outside my
field, and I propose only to refer to a few of the possible services
of the integrator when used by hand, and not attached to a machine.

The simple finding of areas we may omit, as the planimeter will do
that equally well. But of purely graphical processes which the
integraph will undertake for us, I may mention the discovery of
centroids, of moments of inertia (or second moments), of a scale of
logarithms, of the real roots of cubic equations, and of equations of
higher order (with, however, increasing labor). Further, the
calculation of the cost of cutting and embanking for railways by the
method of Bruckner & Culmann, the solution of a very considerable
number of rather complex differential equations, various problems in
the storage of water, and a great variety of statistical questions may
all be completely dealt with, or very much simplified by aid of the
integraph.

In graphical statics proper the integraph draws successively the
curves of shear, bending moment slope, and deflection for simple
beams; it does the like service for continuous beams, after certain
analytical or graphical calculations have first been made; it can