We have seen, that when the annual, bar of the tellu rian and lunarmm united is converted into Jupiter's radius vector, the diminution of velocity is effected by means of the pinions I I and 40 driving their wheels 47 and 111 ; therefore the same train, if the wheels be made to drive the pinions, will increase the velocity of the earth's arm that carries the lamp, in the same proportion; or will convert the period of Jupiter back again to the period of the earth, without any further computation ; which we find to be the case in the machine we are now describing. Three small columns ascend from Jupiter's radius vector, at equal distances from the circumference of a circle de scribed round the central contrate wheel 62 under the sun, and form the fixed supports of the wheel 111, which wheel therefore turns round the sun once in Jupiter's pe riod; then a horizontal arm is clamped to the sun's'stem, and bears at its extreme end a pillion 22 under it, in con nexion with the wheel t ; and the wheel 94, attached to pinion 22 by a short piece of revolving arbor without pi vots, drives the tubed pinion 40, and with it the earth's (or lamp's) arm in a solar year. Thus a lamp, carried by the small annual bar round the sun, projects the shadows of Jupiter and of his four satellites on the paper skreen, attached to the opposite side of the box ; and when the geocentric places of the satellites are viewed by day-light without the lamp, the eye viewing them must be situate in the place of the lamp. The distances of the satellites from the body of Jupiter are given in diameters of Jupi ter's little ball, so as to correspond with the configura tions given in the Nautical Almanac ; but as the distance of the earth from Jupiter cannot be made in a machine in the same proportion, a small hole is drilled and tapped in the earth's arm at a short distance from the sun, into which the lamp's stem is made to screw, and from which the projections on the skreen will fall more correctly, for exhibiting the places where the immersions and emersions take place to the right and left of Jupiter's body, or small circle on the screen, agreeably to his relative position with respect to the time of his opposition. The synodic period of Jupiter will, however, be affected very sensibly by the grand equation of the centre, and may accelerate or retard the day of opposition by several weeks; on which account, the inventor of this machine applied a new wheel of 269, adapted for the eccentricity of Jupiter's orbit, in stead of the one adapted for the earth's eccentricity. The teeth of this fixed wheel for Jupiter are so distributed, by the eccentric cutting in the engine, that 143 are contained in one semicircle, and only 126 in the other ; so that the radius vector has what is called the equated motion of Ju. piter thus mechanically produced, without affecting the motions and periods of the satellites. The earth's arm, however, which is destined to carry the lamp, derives its motion from Jupiter's radius vector, and would also be an equated motion, constantly varying its velocity, if no pro vision were made to prevent such improper effect ; but the wheel 111 is also cut into teeth, gradually varying in size throughout each of its two semicircles, from an ec centric point duly proportioned to counteract the inequa lity of motion given to Jupiter's radius vector. The mo tion of the earth's arm is rendered equable, by reversing the position of the two wheels 269 and III, so that the smallest teeth of wheel 111 shall be acting with the pinion 22, when the largest teeth of wheel 269 are in action with its pinion 10, and -vice versa. The pinions are so propor tioned, as to work well enough with both the largest and smallest teeth, which individually differ almost insensibly from each other ; but contiguous teeth, taken by a num ber together, occupy larger and smaller arcs in the cir cumference of the respective wheels, and produce the de sired • fleet in the motions. The small bearing piece over wheel 111, which carries the pinion 22. may be clumped to the sun's stem in any position, to bring the said pinion into action with the large or small teeth of 111, as the ad justment may require.
In adjusting the positions of the four satellites, the mean places may be computed from the Tables, and the arms placed accordingly ; or the monthly, weekly, and hourly hands being adjusted for the immersion or emer sion of the first satellite, its shadow may be moved to the proper edge of Jupiter's shadow by a manual adjustment of the arm, according to the time given in the Nautical Almanac ; and then as many turns and parts of the han dle. as sill bring the othersatellites in succession to their
respective times of immersion or emersion, must be suc cessively made before the other arms are in like manner adjusted to the proper edge of Jupiter's shadow ; and when all the adjustments are finished, any number of turns given to the handle will cause the corresponding motions of Jupiter and of his satellites, as well as of the earth, from whence they are viewed ; and all the variety of the Jovian phenomena will be represented in the most natural and pleasing manner, as well as with the utmost precision as to time, for ages past and to come.
The Orrery.
The difference between a PLANETARIUM and an OR RERY is now understood to consist in this, that a planeta rium exhibits by wheelwork the periodic or tropical re volutions of the primary planets round the sun, without any reference to their rotations, whereas the orrery gives, besides the revolutions of the primary planets, the revo lutions of some or all of the secondaries, and the rotation of the earth, together with the moon's anomalistic revo lution, and her revolution with respect to the period of the retrograde motion of the nodes. Hence the orrery, when constructed on its comprehensive plan, may be said to comprise within itself the planetarium, the tellurian, the lunarium, and the machine for Jupiter's satellites. As we have given descriptions of these different machines in their detached states, we shall now be able, we trust, to render intelligible our account of a machine, that unites in itself the properties of all the others, and that is adapted for explaining the various phenomena of the solar system, as far as can be done by mechanical repre sentation.
The orrery which we propose to describe, is at the same time the most comprehensive, the most correct, and yet the most simple, considering the numerous motions pro duced, of any that has yet been contrived. It was con structed in the year 1813, by the same artist, and under the same superintendent, as the machines that immedi ately precede it, and includes the proper motions of the two small planets last discovered, Juno and Vesta. In this machine, for the sake of simplicity, all the motions are equable, except those of the moon and Mercury, the latter of which was at first carried round by an equable motion in the plane of the ecliptic, but was afterwards made to move in an eccentric orbit, and in its own plane, as a specimen of planetary motion, by means of which equal areas are passed over in equal times. \Ve shall first give a synoptic table of the wheelwork contained in this machine, with the periods produced by them, and their errors, and then proceed to explain, by reference to en gravings, the positions of the different pairs and trains of wheels that are employed in the different parts of the ma chine. The construction is founded on the principle of concentric tubes carrying the respective planetary arms, or radii vectores, and in this respect resembles the plane tarium for equable motions; but the planets that move much faster and much slower than the earth have trains, while those between the earth and Jupiter inclusive have only pairs of wheels, instead of trains, in consequence of their velocity admitting of simple fractions of a year. Some of these pairs of wheels are the same which we have recommended to be adopted in the planetarium, and the mode of applying them is also the same ; so that the description of certain parts of the present machine will illustrate the construction of the planetarium also, which is our reason for not having given an engraved drawing of the planetarium in a separate plate. Indeed, the pre sent orrery is so contrived, that its planetarium portion may be used either with or without the tellurian, luna rium, and Jovian portions, by a temporary disengagement of their respective trains, without dismounting them ; and on many occasions it may be desirable to confine the attention of an audience to certain parts of the system, in succession, before a display of all the motions is made at once ; which otherwise would be liable to confound the mind, not yet prepared to comprehend the separate effects produced by the distinct parts of the machine. The first orrery of this construction, was made in the short space of two months; and the price put upon it by the maker, without profit for the sale, was eighty-five guineas.