When this machine is placed on its small tripod, and fixed by means of a slit tuhe and clamping piece, made fast to the under face of the box, the lamp, which repre sents the sun, must stand at the same height on a table that the satellites and screen are, and must occasionally be moved to the right or left ; so that the geocentric place, or shadow of Jupiter's body, may fall to the right or left of a small circle described on the centre of the screen as the heliocentric place, accordingly as the Nautical Almanack gives immersions or emersions at the time for which the machine is rectified.
When the box is dismounted from its small tripod, and made an appendage to the table of 21 feet diameter, which carries the united mechanism of the tellurian an lunarium, the motions of Jupiter and the-earth are then superadded to the trains of the satellites, which we have described above ; and a small lamp, carried round the sun by the earth's revolving arm, while Jupiter himself has also his proper motion, throws the shadow of Jupiter at all times on its proper geocentric place on the screen, for exhibit ing transits and occultations as they occur naturally in the heavens, and thus supersedes the necessity of manual rectification of the lamp. We shall now proceed to ex plain what additional wheelwork is required to give the machine the advantage we have here stated, together with other advantages, which will presently be manifest. The velocity of Jupiter in his orbit is to that of the earth as 440:5217, as may be seen in our " list of planetary continuous fractions," and the fraction —5217 is reducible 440 1into the train 4 — x 1 0 • if therefore the yelocity of the 11 4 annual index, or earth's bar, in the tellurian and lunarium be diminished in this ratio, it will become the radius vec tor of Jupiter, and the ecliptic circle will serve to point out Jupiter's heliocentric place instead of the earth's; but the spiral and circle of the sun's declination will be come useless. The train for 365.24222 days, which was explained in its place, will become a part of the train of 47 11 Jupiter, if we add thereto the other portion x to diminish its velocity in the due proportion. Thus the two trains taken as one, will be 4330d 14" 39'n 17.6'. In this case, the handle which re volved in a solar day, when inserted on the arbor of 18, the first pinion of the earth's train, will still revolve in the same time as it regards Jupiter's period, when imme diately connected with the arbor of 11, Jupiter's first pi nion. Accordingly, when the handle is applied to the side of the small box, containing the trains of Jupiter's satellites, the arbor which it turns has a pinion of 11 teeth driving the contrate wheel 47, which we before passed over in silence; and the driving wheel 40, fixed to its ver tical arbor, drives another wheel 1 1 1, which completes the additional portion of Jupiter's long train. The wheels
40 and 111 are seen under the box in both the Figures 1 and 3. The connexion with the earth's, or now the se cond portion of Jupiter's train, is thus effected : The wheel 111 is clamped fast to the upper end of the tellu rian's diurnal tube, that has the pinion 18 at its lower end, driving the wheel 94; and while its pinion 10 actuates the contrate wheel 26, the second pinion 10, as was before explained, takes hold of the large wheel 269, which by its resistance occasions the annual bar, now the radius vector of Jupiter, to revolve with its due velocity in the period above specified. In the mean time, the trains, which carry Jupiter's satellites in their proper synodic periods, continue in action, and thus all the motions com mence with the first turn of the handle, and all the revo lutions are performed with reference to the diurnal handle in their exact relative times, and without any perceptible error in the indication arising from the length of the trains, and the play that is necessary to prevent friction. In Fig. 3. the lunar wheels connected with the earth's train are not dismounted, viz. wheels 13, 43, and 73, because they do not interfere with the new arrangement ; but the other parts of the lunar apparatus, (which are fixed only by clamping pieces of slit tube with screws,) are necessarily removed, and leave the tube of parallelism and its little ecliptic circle in their places, together with the two con trate wheels 62 and 62, and their respective pinions before described. As this small ecliptic circle is always kept parallel to the first position given it, namely, in such a way that its divisions continually accord with the same divi sions on the large fixed ecliptic, it becomes very useful in the geocentric place of Jupiter at any time, by the help of a silk thread stretched from the earth's stem to the stem of Jupiter, standing over the centre of the box, while the heliocentric place of the planet is pointed out on the large ecliptic by the cranked index. Also the angular distauce of each satellite from Jupiter may be seen, by its arm to the circle surrounding the box beneath if.