figure 93.
On account of the number of teeth required for the wheel which moves Uranus, it is frequently omitted in Planetariums, or the planet is placed upon the arbor which supports Saturn. If we now suppose a spindle or arbor with six wheels fixed upon it in an horizontal position, having the number of teeth in each corresponding to the numbers in the third column, namely the wheel AM (fig. 93.) of 83 teeth, BL of 52, CK of 50, for the earth, DI of 40, EH of 7, and FG of 5; and another set of wheels moving freely about an arbor having the number of teeth in the fourth column, namely AN of 20, BO of 32, CP of 50—for the earth; DQ of 75, ER of 83, and FS of 148. Then, if these two arbors of fixed and moveable wheels be made of the size, and fixed at the distance here represented, the teeth of the former will take hold of those of the latter, and turn them freely when the machine is in motion. These arbors, with their wheels, are to be placed in a box of a proper size, in a perpendicular position; the arbor of fixed wheels to move in pivots at the top and bottom of the box, and the arbor of the moveable wheels to go through the top of the box, and having on the top a wire fixed, and bent at a proper distance into a right angle upwards, bearing on the top a small round ball, representing its proper planet. If then, on the lower part of the arbor of fixed wheels, be placed a pinion of screw-teeth, a winch turning a spindle with an endless screw, playing in the teeth of the arbor, will turn it with all its wheels, and these wheels will turn the others about with their planets, in their proper and respective periods of time. For, while the fixed wheel CK moves its equal CP once round, the wheel AM will move AN a little more than four times round, and will consequently exhibit the motion of Mercury; the wheel EH will turn the wheel ER about 1/12 round, representing the proportional motion of Jupiter; and the wheel FG will turn the wheel FS, about 1/29.5 round, and represent the motion of Saturn, and so of all the rest.
figure 94.
The following figure (fig. 94.) represents the appearance of the instrument when completed. Upon the upper part of the circular box is pasted a Zodiac circle divided into 12 signs, and each sign into 30 degrees, with the corresponding days of the month. The wheel-work is understood to be within the box, which may either be supported by a tripod, or with four feet, as here represented. The moon, and the satellites of Jupiter, Saturn and Uranus, are moveable only by the hand. When the winch W is turned, then all the primary planets are made to move in their respective velocities. The ball in the centre represents the Sun, which is either made of brass or of wood gilded with gold.
By this Planetarium, simple as its construction may appear, a variety of interesting exhibitions may be made and problems performed, which may be conducive to the instruction of young students of astronomy. I shall mention only a few of those as specimens.
1. When the planets are placed in their respective positions by means of an Ephemeris or the Nautical Almanack, the relative positions of those bodies in respect to each other, the quarters of the heavens where they may be observed, and whether they are to be seen in the morning before sun-rise or in the evening after sun-set, may be at once determined. For example, on the 19th of December, 1844, the heliocentric places of the planets are as follows:—Uranus 2° Aries; Saturn 8° 27´ of Aquarius; Jupiter 7° 4´ Aries; Mars 12° 45´ Libra; the Earth 27° 46´ Gemini; Venus 29° 48´ Virgo; Mercury 7° 53´ Pisces. When the planets are placed on the planetarium in these positions, and the eye placed in a line with the balls representing the Earth and the Sun, all those situated to the left of the sun are to the east of him, and are to be seen in the evening, and those on the right, in the morning. In the present case, Uranus, Saturn, Jupiter, and Mercury are evening stars, and Mars and Venus can only be seen in the morning. Jupiter is in an aspect nearly quartile, or 3 signs distant from the sun, and Uranus is nearly in the same aspect. Saturn is much nearer the sun, and Mercury is not far from the period of its greatest eastern elongation. Mars is not far from being in a quartile aspect, west of the sun, and Venus is near the same point of the heavens, approaching to the period of its greatest western elongation, and consequently will be seen before sun-rise as a beautiful morning star. Jupiter and Uranus, to the east of the sun, appear nearly directly opposite to Venus and Mars, which are to the west of the sun. The phase[47] of Venus is nearly that of a half-moon, and Mercury is somewhat gibbous, approaching to a half-moon phase. If, now, we turn the machine by the winch till the Index of the earth point at the 8th of August, 1845, we shall find the planets in the following positions:—Mars and Saturn are nearly in opposition to the sun; Venus and Mercury are evening stars at no great distance from each other, and Jupiter is a morning star. In like manner if we turn the machine till the Index point to any future months, or even succeeding years, the various aspects and positions of the planets may be plainly perceived. When the planets are moved by the winch, in this machine, we see them all at once in motion around the sun, with the same respective velocities and periods of revolution which they have in the heavens. As the planets are represented in the preceding positions, Mercury, Jupiter and Mars, are evening stars, and Venus, Saturn, and Uranus, morning stars, if we suppose the earth placed in a line with our eye and the sun.
2. By this instrument, the truth of the Copernican or Solar system is clearly represented. When the planets are in motion, we perceive the planets Venus and Mercury to pass both before and behind the sun, and to have two conjunctions. We observe Mercury to be never more than a certain angular distance from the sun, as viewed from the earth, namely 27°; and Venus 47°. We perceive that the superior planets, particularly Mars, will be sometimes much nearer to the earth than at others, and therefore must appear larger at one time than at another, as they actually appear in the heavens. We see that the planets cannot appear from the earth to move with uniform velocity; for when nearest they appear to move faster, and slower when most remote. We likewise observe that the planets appear from the earth to move sometimes direct, or from west to east, then become retrograde, or from east to west, and between both to be stationary. All which particulars exactly correspond with celestial observations. For illustrating these particulars there is a simple apparatus represented by fig. 95, which consists of a hollow wire with a slit at top which is placed over the arm of Mercury or Venus at E. The arm DG represents a ray of light coming from the planet at D to the earth at F. The planets being then in motion, the planet D, as seen in the heavens from the earth at F, will undergo the several changes of position, which we have described above, sometimes appearing to go backwards and at other times forwards. The wire prop, now supposed to be placed over Mercury at E, may likewise be placed over any of the other planets, particularly Mars, and similar phenomena will be exhibited.
figure 95.