Lastly, an arbor for the handle, to give motion to the different pairs of wheels at the same time, has a double screw cut upon it, so as to act with Venus's wheel of 104 teeth, not much rounded ; and as this wheel revolves in a year, it will require 52 turns of the handle to produce an entire revolution of it, and consequently of the annual ar bor to which it is made fast ; hence a turn of the handle will give very nearly seven days motion to the whole planetary system ; and all the eleven primary planets and the moon will preserve their respective velocities with considerable precision from year to year, with as many pairs of wheels only as there are planetary bodies.
According to this table of dimensions, the earth's stem must stand at three inches exactly from the sun, or cen tral fixed stem which supports the sun ; and the dial with 235 teeth will be 5.55 inches in diameter, and will admit of an ecliptic circle to be divided into twelve signs,,and each sign into 30°. The arms of Mercury, Venus, and Mars, may be in their due proportions ; but the other su perior planets must have their arms in fractional parts of their due distances. In the second column, the nume rators of the fractions are those which are attached to the revolving tubes, and the denominators are those made fast on the annual arbor, which communicate the motion to their numerators respectively, with the exception of Herschel's. The usual apparatus for showing the direct and retrograde comparative motions, and stationary places, when viewed from any one planet, as it regards any other, may be applied to this machine with great advantage, as its structure is firm, and its parts all sufficiently compact. The mechanism and external appearance of this new ma chine resembles the planetarian portion of the orrery, which we have yet to describe, so much so that the draw ings of the one which wellave to give will suffice to ex plain the construction of the other, when the parts not be longing to the planetarium are omitted, and when the numbers designating the teeth are taken, as we have here given them, in their most simple form.
?1 short ?iCCOUIll of Planetaria with equated Motions.
To give a minute detail of all the constituent parts of the various planetary machines that have been invented, and to illustrate the principles of their construction by reference to engravings, would occupy a large volume : we have consequently been ohliged to abridge our article into such compass, as will render it admissible into a work that embraces all the various departments of science. We were unwilling to pass over in silence the more complex machinery that has been contrived to represent the equa• tions of the mean planetary motions ; but we have to re gret, that our plan will not allow us to extend our plates and descriptions beyond what our readers in general may be disposed to approve.
Soon after the Royal Institution of London was founded, the managers had occasion to procure a planetarium among other apparatus for the lectures, when Dr. Garnett
ceased to he the lecturer ; and a plan was suggested about the year 1801, by one of its original proprietors, (to whom we are indebted for this short account,) for exhi biting the equated motions of all the planets at that time discovered. This suggestion, being soon after the two planets Ceres and Pallas had been discovered, was adopt ed ; and Kenneth M'Culloch, an aged workman brought up under James Ferguson, was employed in the con struction of the machine in the workshops of the institu tion. The inventor was aware, that, if a small arm carrying a planet was by any means made to revolve backwards at the remote end of a radius vector, while the radius vector itself revolved forwards in the same period, the planet would have an eccentric orbit, in which the variable dis tances would be preserved, and also one half of the grand equation would be produced, provided that the small arm bore the same proportion to the radius vector that the planet's eccentricity does to its mean distance from the sun. The plane of the planetary orbits was therefore made vertical in this machine, in order that small weights, suspended on the small revolving arms, under certain limitations, should keep them always parallel ; that is, always pointing in one direction, by the simple el fact of gravity. In this way, the variations of distance, and one hall' of the alternate increase and decrease of ve locity were occasioned, and the remainder of the equa tion depended on the eccentric cutting of the planetary wheels into teeth of unequal sizes. A train of four wheels, or wheels and pinions, was employed for each planet ex cept for Ceres and Pallas, whose periods are very nearly the same, and therefore required only one train. The an nual arbor, which we will call A, without reference to any figure, had all the first driving wheels made fast on it ; and the second and third wheels, pinned together, re volved in as many pairs on a fixed stem B ; while the fourth or planetary wheels, revolving with unequal teeth in the proper periods of the different planets, were fixed on the lower extremities of as many concentric tubes, re volving round C, the sun's stem, and carrying as many radii vectores attached to their superior or projecting ends. In this construction, the common plane of the or bits was presented to the audience in the lecture-room, and the person who turned the handle stood behind a ver tical wooden frame, which supported the small brass frame of the wheelwork. But though the natural position of the machine was vertical, whenever the small arms re presenting the eccentricity were removed, the radii vec tores might be put into the usual horizontal position by simply discharging a bolt, and fixing it again in the hori zontal position. The mechanist, who may wish for in formation respecting the farther particulars of the con struction, will obtain it from the contents of the subjoined Table.