further lighten greatly the graphical work in the treatment of masonry
arches and of metal ribs. In graphical hydrostatics it finds centers
of pressure and gives a complete solution for the shear and bending
moment, curves in ships, besides curves for their stability. In
graphical dynamics the applications of the integraph seem still more
numerous. It enables us to pass from curves of acceleration to curves
of speed, and from curves of speed to curves of position. Applied to
the curve of energy of either a particle or the index point of a rigid
body, it enables us by the aid of easy auxiliary processes to
ascertain speeds and curves of action. In a slightly altered form,
that of "inverse summation," we can pass from curves of action to
curves of position, and deal with a great range of resisted motions,
the analysis of which still puzzles the pure mathematician; the
variations of motion in flywheels, connecting rods, and innumerable
other parts of mechanism, may all be calculated with much greater ease
by the aid of an integraph. Shortly, it is the fundamental instrument
of graphic dynamics.

It would be needless to further multiply the instances of its
application; the questions we have rather to ask are: Can a practical
instrument be made which will serve all these purposes? Has such an
instrument been already put upon the market? If I have to answer these
questions in the negative, it is rather a doubtful negative, for the
instrument I have to show you to-night goes so far, and suggests so
many modifications and possibilities, which would take it so much
further, that it is very close to bringing the practical solution to
the problem.

Let me here lay down the conditions which seem essential to a
practical integraph. These are, I think, the following: