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 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.] By ALEXANDER GRAHAM BELL. In August, 1880, I directed attention to the fact that thin disks or diaphragms of various materials become sonorous when exposed to the action of an intermittent beam of sunlight, and I stated my belief that the sounds were due to molecular disturbances produced in the substance composing the diaphragm.[1] Shortly afterwards Lord Raleigh undertook a mathematical investigation of the subject and came to the conclusion that the audible effects were caused by the bending of the plates under unequal heating.[2] This explanation has recently been called in question by Mr. Preece,[3] who has expressed the opinion that although vibrations may be produced in the disks by the action of the intermittent beam, such vibrations are not the cause of the sonorous effects observed. According to him the aerial disturbances that produce the sound arise spontaneously in the air itself by sudden expansion due to heat communicated from the diaphragm--every increase of heat giving rise to a fresh pulse of air. Mr. Preece was led to discard the theoretical explanation of Lord Raleigh on account of the failure of experiments undertaken to test the theory. [Footnote 1: Amer. Asso. for Advancement of Science, August 27, 1880.] [Footnote 2: _Nature_, vol. xxiii., p. 274.] [Footnote 3: Roy. Soc., Mar. 10, 1881.] [Illustration: Fig. 1. A B, Carbon Supports. C, Diaphragm.]