The sidereal rotation of the earth is converted into a solar day, without any regard to the wheel work, in this way : the retrograde contrate wheel 62 carries a small ecliptic circle 00, to which the bearing piece P already referred to is fixed, and the earth, carried backwards by this small ecliptic while its parallelism is preserved, ex poses every meridian line on it in succession to the sun, as it proceeds in its annual orbit, while a vertical solar ray travels once round the globe in the course of the year; and if the earth had no rotation on its axis, the effect of the parallelism of the earth's axis, as it regards a star, or other fixed point in the heavens, would be an annual solar day given to the inhabitants of the earth, but in such a way, that the sun would appear to rise in the west, and to set in the east six months afterwards. This effect takes place gradually ; and if we conceive it to exist, while the earth is making her regular rotations in a contrary direc tion, we shall perceive that66.;423 part of a day, or 3m. 56.5" will be deducted from the time of each rotation ; hence the earth makes 366.2423 rotations in 365.2423 so lar days, the sidereal day being an absolute, and the solar day a synodic or relative period. This mode of producing the proper number of sidereal rotations of the earth in a solar year, renders the machine perfect, so far as the earth's position at any given time has reference to the lu nar and planetary phenomena to he viewed from her sur face. The solar time at which any of the phenomena will occur is indicated by a hand on the pivot of the diurnal arbor, pointing to a fixed rim, or dial on the lid of the box ; and sidereal time is pointed out by the same hand on a dial, consisting of a small circular plate that revolves backwards once in a year, and meets the hand sooner every day by a space equal to 4m• 56.5'• This annual re trograde motion of the sidereal dial is produced by a very simple contrivance, thus : the revolution of Jupiter is pro . 166 duced by the wheel and pinion as we have already seen ; hence, reversing the position thus, ,and making 166 the driver, in Jupiter's period, will give just a year's motion to the pinion 14; therefore Jupiter's wheel 166 has a pinion 14 acting with it, when fixed to a tube that revolves round the diurnal arbor as a stud, and the under end of this annual tube carries this sidereal dial in its pro per direction and due period, without farther contrivance, and in the most correct manner.
We come next to describe the Lunarium portion of the Orrery. The moon's lunation is derived from the re volving wheel of parallelism 62, which, we have said, moves once backwards in a year. This part of the me chanism will best be explained by reference to Fig. 4, which gives the trains for the lunation, and the period of of the nodes, in a detached state, so that all the wheels may be seen. Wheel 107 revolves in a year, by being fast to the retrograde wheel of parallelism 62, and drives the pinion 12, through the medium of a pinion 15, to change the direction of motion ; and the tubed arbor of pinion 12 takes wheel 86 at its upper end, which wheel drives the lunar wheel 62 round in the lunation, and to gether with it the moon's arm fixed on the upper end of its tubed arbor. In like manner, the period of the moon's node is derived from the annual wheel of parallelism 62; thus, the contrate wheel 62 has its teeth rounded also on the edge, and carries the small wheel 24, together with 31, on the same revolving arbor, which 3 impels the last wheel of the train 76 in the period of the nodes. The
wheel 76 is made fast to a short tube, which revolves round the lunation tube, and which supports the node's plate that has the moon's latitude engraved on it, and is inclined in an angle equal to the angle that the lunar orbit makes, on an average, with the ecliptic ; then the cranked stem of the moon, being squared, descends through' the moon's arm, and rests on the inclined plane, so as to be at liberty to rise or fall as the moon is carried forwards, accordingly as the inclined plane directs. The anoma listic revolution of the moon, on which the change of dis tance and velocity depends. is effected by the train carried by the moon's arm ; the wheel 64 is attached to a fixed plate Q, on which the moon's age is indicated, which plate is borne by a long tube ascending from a cock under the moon's arm, a part of which is seen dotted : then, as wheel 67 is carried round the 64, thus fixed, in every lunation, the 41 pinned to it drives the 46, in the period of an ano malistic revolution. The revolving arbor of the last wheel 46 is perforated with a square hole, so as just to admit the moon's squared stem to pass without friction ; and from this combination the moon performs her luna tion in the proper period, but undergoes all her variations of latitude in the period of the nodes, and her variations of velocity and distance, as occasioned by the revolving crank of the stet", in the proper anomalistic period. Above the small cock at the remote end of the moon's arm, which supports the upper pivot of the perforated ar bor of wheel 46, is a small circular dial R fixed, to which an index borne by the said arbor points, to show the apo geal and perigeal points of the moon's orbit, and also her grand equation at any specified time of her lunation.
We proceed, lastly. to describe the ?/wah portion of the machine now under consideration. Fig. 2 exhibits the weekly arbor GG, which we have before had occa sion to mention, as an arbor revolving in seven days. On the middle of this arbor a wheel 70 is seen, which drives another wheel 55, having a tube revolving next to and within Jupiter's tube, in 51 days, or 70 of a week : to the upper end of this tube a contrate wheel 60 is clamped fast, with its teeth pointing downwards, to take the pinion 8 on a long arbor that lies within the horizontal tube, which constitutes Jupiter's radius vector, and another similar pinion 8 at the remote end of the concealed arbor drives another contrate wheel 60, with its teeth pointing upwards, in order to have the proper direction when moving ; a piece is cut away at each end of the tube, or radius vector, to allow the pinions to be engaged. Now, as the first contrate wheel of 60 teeth revolves in 51 days, the second wheel having 60 teeth and a similar pinion would also re volve in the same period, if Jupiter's radius vector had no motion ; but as Jupiter makes a revolution in his proper period, the first pinion 8 makes 71 revolutions du 3 ring this time by means of its circuit round the central wheel 60, while their teeth are engaged, and these 71 re volutions are given by the remote similar pinion 8 to the._ wheel 60 at the remote end of the radius vector, which therefore has its motion accelerated so as to gain an addi tional revolution in Jupiter's period, or in 4330.72916 days, which is the period produced by of a solar year.