Of the various curves exhibited which have been drawn by the machine,
the following are of special physical interest.

Given the inclined straight line y = cx, the machine draws the parabola
y = cx squared / 2. This is the path of a projectile, as the space fallen is as
the area of the triangle between the inclined line, the axis of x, and
the traveling ordinate.

Given the curve representing attraction y = 1 / x squared the machine draws the
hyperbola y = 1 / x the curve representing potential, as the work done
in bringing a unit from an infinite distance to a point is measured
by the area between the curve of attraction, the axis of x, and the
ordinate at that point.

Given the logarithmic curve y = e^x, the machine draws an identical
curve. The vertical distance between these two curves, therefore,
is constant; if, then, the head of the cart and the pointer, A, are
connected by a link, this is the only curve they can draw. This motion
is very interesting, for the cart pulls the pointer and the pointer
directs the cart, and between they calculate a table of Naperian
logarithms.

Given a wave-line, the machine draws another wave-line a quarter of
a wave-length behind the first in point of time. If the first line
represents the varying strengths of an induced electrical current,
the second shows the nature of the primary that would produce such a
current.

Given any closed curve, the machine will find its area. It thus answers