et us suppose that
we know an induced current, and that we can represent it by a curve
y=f(x). The question is to find the inductive current, that is to say,
the curve represented by the equation

_
/
|
y = | f(x)dx + C.
|
_/

[TEX: y = \int f(x) dx + C.]

The apparatus called an integraph, constructed by Messrs. Napoli and
Abdank-Abakanowicz, is designed for solving this problem mechanically,
by tracing the curve sought. Let us take another example from the domain
of electricity, in order to better show the utility of the apparatus;
let us suppose that we have a curve representing the discharge of a pile
or of an accumulator. The abscisses represent the times, and the
ordinates the amperes. The question is to know at every moment the
quantity of coulombs produced by the pile. The apparatus traces a curve
whose ordinates give the number of coulombs sought. We might find a
large number of analogous applications.

[Illustration: THE INTEGRAPH.]

The apparatus is represented in the accompanying figure. An iron ruler,
I, parallel with the axis of the X's, is fixed upon a drawing-board, and
is provided with a longitudinal groove in its upper surface. In this
groove move two rollers, which, in the center of the piece that connects
them, carry two brass T-squares that are parallel with each other and at
right angles with the first, or parallel with the axis of the Y's.
Between these two rulers move two carriages, the first of which (nearest
the axis of the X's) carries a point, A, designed to follow the contour
of the curve to be integrated, while the second, which is placed further
away, is provided at the center with a drawing-pen, A', whose point is
guided by two equidistant wheels, R, R', that roll over the paper in
such a way as to have their plane parallel with a given straight line,
and that have always a direction such that the tangent of the point's
angle with the axes of the X's is constantly proportional to the
ordinate of the primitive curve.

The carriages are rendered very movable by substituting rolling for a
sliding friction of the axes. To this effect, the extremities of the
axes of the wheels that support and guide them are made thin, and roll
over the plane surface of recesses formed for the purpose in the lateral
steel surfaces of the carriages, while the circumference of the wheels
rolls in grooves along the two T-squares.

These latter are, on the one hand, carried by