Art. XVI.—On a simple Method of illustrating the Motions of the Earth.

Transactions and Proceedings of the Royal Society of New Zealand, Volume 13, 1880, Page 164

Art. XVI.—On a simple Method of illustrating the Motions of the Earth. By Professor A. W. Bickerton. [Read before the Philosophical Institute of Canterbury, 2nd September, 1880.] Plate IIB. This model is one of the extempore pieces of apparatus that I designed for the purpose of illustrating a course of experimental lectures, which were delivered with the special object of showing that many of the most important of physical phenomena might be illustrated by apparatus at a cost not exceeding a few pounds. The model itself cost less than a shilling, and I made it in about half-an-hour. Since it was made I have found it useful to illustrate so large a number of cosmical phenomena that I thought it of sufficient importance to bring before the Institute. A much larger number of phenomena may be illustrated by its means than by the expensive models usually sold for the purpose. Among these are day and

Sketch representing the orbit of a double Star at origin. Model to illustrate the Motions of the Earth

night, seasons, the solstices, and equinoxes and the precession of equinoxes, eccentricity of orbits, the lines of the globe, etc. It has also the advantage over the ordinary model of possessing nearly all the dynamical peculiarities of the heavenly bodies themselves. It is, as it were, a double pendulum, and so it may easily be made to illustrate the laws of motion, resultant motion, the properties of the pendulum, Foucault's pendulum, and a large number of facts of both the kinetics and kinematics of dynamics. The accompanying diagram Plate IIB. represents it on a large scale, and shows it in use. The angle is shown exaggerated. The model consists of a ball of wood or other material with a thick knitting-needle through it: this represents the earth and its polar axis; the ends of the needle are sprung into two centre punch dents in a light brass ring, the ball thus rotates on the needle as on an axis. This brass ring is hung in a vertical plane in such a manner that the needle makes an angle of 23° to the vertical. There are also other points of suspension for exaggerating the inclination, to render the phenomena more evident. The two cords are attached to the ceiling so as to hang parallel. On swinging the apparatus as a conical pendulum, the direction of the axis remains all the time parallel to itself. If a lamp be placed in the centre of this cone, and the ball be made to spin, the phenomena of day and night and summer and winter are at once illustrated. The solstices and equinoxes are of course shown with the greatest readiness; the equator, tropics, and polar circle also show themselves, and the peculiarities of polar seasons can, of course, readily be shown. By making the swing of the pendulum an ellipse instead of a circle, and placing the lamp at a focus, the long winter and short summer of great eccentricity are explained. This illustration of the rate of motion during eccentric orbits is, of course, not mathematically accurate. With the apparatus moving in an ellipse it becomes easy to explain the reason why, in the northern hemisphere, the sun is nearer in winter than in summer. By merely spinning the whole model on its two cords, and so twisting them up, the precession of the equinoxes is readily understood. By these two experiments it is easy to render Croll's theory of glaciation intelligible, by taking a card to represent the moon's orbit to the plane of the ecliptic the causes of the lunar and solar eclipses and their cycles are rendered intelligible. The whole of the motions being due to inertia, and the centrifugal point being the centre of the circle, we have a true central force acting on the body. Thus planetary dynamics is almost exactly represented. By taking off the ring and hanging two similar balls the exact isocranism of equal length pendulums may be shown, and this may be amplified

by having the oscillations of one small and the other large. By hanging two balls of equal volume and different mass, the oscillations of the lighter will be destroyed much quicker than those of the heavier one; thus illustrating the greater power to do work possessed by the heavy body, as the resistance of the air is the same in both cases. A large number of experiments of resultant motion may be proved by first showing the isocranism of all lengths of vibrations, and then striking the moving pendulum when at its several points of motion. These form a most instructive series of experiments. The conversion of circular into straight, and straight into circular, elliptical, and diagonal motion, is of course very easily illustrated. As is well known, the peculiarities of kinetic and potential energy are better shown to a class by a pendulum, than probably by any other method.