Given the inclined straight line y = cx, the machine draws the parabola y = cx² / 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 / x² 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 = ex, 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 the same purpose as Ainslee's polar planimeter, and though not so handy, is free from the defect due to the sliding of the integrating wheel on the paper.
The rules connected with maxima and minima and points of inflexion are illustrated by the machine, for the cart cannot be made to describe a maximum or a minimum unless the pointer, A, crosses the axis of x, or a point of inflexion unless A passes a maximum or minimum.
UPON A MODIFICATION OF WHEATSTONE'S MICROPHONE AND ITS APPLICABILITY TO RADIOPHONIC RESEARCHES.
[Footnote: A paper read before the Philosophical Society of Washington. D. C., June 11, 1881.]