The earth is placed over a long steel rod screwed fast into the annual bar, which, in being turned in the lathe, is left a small trifle thicker at the two ends, in order that a long tube revolving round it may have its friction reduced to the ends only. This tube, which is nearly six inches long, carries at its lower end a pinion, 18, acting with the edge of wheel 94,which is cut into teeth that are so round ed as to act both on the points and edges ; and its motion, therefore, is precisely the same as that of the handle : it carries, moreover, at the upper end, a small wheel, 40, which drives another 40, attached to the earth's axis by the intervention of another similar or third wheel 40, that only changes the direction of the motion. These three si milar wheels are all bevelled a little, for the purpose of allowing the earth's axis to have its proper inclination ; and, so far as their connexion with the handle is concerned, it is obvious that the earth's axis must have a revolution every time that the handle is turned round, provided that no cause interfere to alter this effect : but, as the earth's inclined axis must necessarily continue to point, as in na ture, to the north pole of the heavens, in order to produce the requisite change in the seasons, while the rotations ef fect the succession of clay and night, a contrivance becomes • indispensable for preserving the parallelism of that axis on every part of the earth's course round the sun. For this purpose the contrate wheel 62 is fixed at the centre of the table with its teeth pointing downwards, to catch the pinion 8, which has a long arbor passing under a bridge, and ex tending above and parallel to the annual bar, till its similar pinion 8 takes hold of another connate wheel, 62, with its teeth pointing upwards, in order that its motion may be in a retrograde direction just once in every year. As it is of no importance what the number of teeth of these two wheels and of these two pinions may be, provided that they be respectively alike, we have left them out of the table of trains, and consider them only as an appendage, that do not affect the trains otherwise than by giving the earth an additional rotation, as we shall now explain. The long bridge standing lengthwise over the pinion 18, of which two or three teeth only can be seen, has a tube fixed in it, which ascends towards the earth ; and the tube of the lat ter 62 moves round it, and, at its upper end, supports the small ecliptic ring, to which the bar is screwed fast that carries the three similar wheels of 40 teeth each above de scribed ; this bar, therefore, in common with the small ecliptic ring, has a retrograde motion, which amounts to a revolution in each year, by virtue of its connexion with the revolving tube of wheel 62; but the first small wheel 40 is fast to the diurnal tube, round which the second and third similar wheels arc carried backwards once every year ; the second wheel, therefore, receives a revolution in conse quence of its circuit round the first, and, in the same di rection as its revolutions from the train are performed, and the joint effect of these two causes of motion is the per formance of 366.24222 turns, in 365.24222 revolutions of the handle, consequently, the third wheel, immediately im pelled by the second, gives the earth 366.24222 rotations in a solar year ; which, with respect to a star, or other fix ed point in the heavens, is exactly according to nature. But, though the absolute rotations of the earth are 366 24222, the relative rotations, as they regard the sun, are only 365.24222 in so many solar days ; for the apparatus that preserves the parallelism, by giving one retrograde revo lution to the bar that supports the earth, deducts one ro tation in each year, by turning the earth backwards as it proceeds in its annual course, thereby affecting the differ ence between solar and sidereal time ; and when a dial of 24 hours is borne by the upper end of the diurnal tube, an index, made fast to the fixed rod of steel, shows solar time, while another index, placed on the retrograde bar, shows sidereal time on the same graduated circle; and, on any day, the difference between the two times, thus indicated, is equal to the sun's mean right ascension, provided that the two hands are adjusted to indicate the same time at the mo ment of the vernal equinox. This combination of the me chanism produces, in a beautiful manner, and with perfect accuracy, all the changes of summer and winter, clay and night, both as to solar and sidereal time.
The lunation, or synodic period of the moon, as she has reference to the earth, comes next to be considered. The
value of the lunar train may be ascertained by taking it as the compound fraction of either a clay or a year, accordingly as we reckon from the handle or from the great wheel. For the sake of diminishing the number of wheels, and of rendering all the motions dependent, as much as possible, on the same wheels, a part of the diurnal and annual train is made common to the moon's wheclwork. If we count from the great wheel, -- 10 is the common part, but if front269 the handle, X is the common portion ; in either 18 10 case 4 X are all the additional wheels and pinions re quircd for completing the lunar train for its lunations. When motion has been communicated from the handle, so as to cause the long concealed arbor to revolve with the contrate wheel 26, a pinion, 13, fixed on the same arbor, revolves in the same time, and compels a contrate wheel, 43, and also the wheel 73, fixed on its vertical arbor, to turn together ; while the latter drives the last wheel of the lunar train, 48, round in a month, this last wheel, 48, rests on a cross bridge, having a tube fixed to it that ascends above the monthly bar, and a tube fixed to the wheel 48 revolves round the said fixed tube, and carries the monthly bar round in each lunation. if the moon's stem had been screwed into the remote end of the monthly bar, as is usual in common machines, there would have been no variation of either latitude, velocity, or distance, from the earth in her motion; and, to effect these purposes, two additional trains arc introduced, which respectively derive their mo tions from the lunation. The train for exhibiting the moon's variable velocity and distance has reference to the period of the progressive motion of the moon's apogee, and is thus arranged. The wheel 64 is made fast on the upper end of the cross bridge's tube, round which the monthly bar revolves, while the wheel 67 is connected with it ; the latter, therefore, being carried by the monthly bar, revolves in of a lunation. On the arbor of 67 is 67 made fast a smaller wheel, 46, which ought to reach the 41, so as to impel it ; but, in that case, either the wheels must have been inconveniently large and heavy, or the dis tance of the moon would not have allowed a nine inch globe to represent the earth ; the motion is, therefore, conveyed from 46 to 41, by two similar pinions on the same horizon tal arbor, which take the motion from 46, and give it un altered to 41, the last wheel of the apogeal train. Above the last wheel, which has, as its arbor, a piece of brass tube, squared within, is a light dial, borne by the small cock of wheel 41; and a hand inserted on the revolving tube,or short arbor, indicates thereon the moon's equation of the centre, and the place of the apogee and perigee, in each month. The stem of the moon is squared, so as to fit nicely into the squared bore of the short tube, forming the arbor of wheel 41, and the moon's weight makes the squared stem descend till it rests on a small edge bar of steel, connected with the train of the moon's nodes, to be noticed again presently. The crank-piece, which bears the upper part of the moon's stem, fits the lower squared part, and performs a revolution every time that the wheel 41 turns round ; that is, once during the period of an ano malistic revolution. The length of the horizontal part of the crank-piece of the moon's stem is equal to twice the eccentri ity of her orbit, to radius eight inches, the length of the monthly arm from the earth ; and the motion thereof being retrograde, as it regards the direct motion of the moon round the earth, is continually increasing or dimi nishing the mean motion of the moon, by carrying her al ternately forward or back, round the squared portion of the stem. The equation thus arising will keep the moon con tinually retarding or accelerating her velocity in her orbit, as the greatest equation is subtended by a line equal to twice her eccentricity. The distance also is as constantly varying, and would vary very nearly in conformity to her true orbit, if the upper part of the stem were screwed into a small hole, made at the distance of once the eccentricity denoted by the head of a pin; hut as the true distances and sizes of in heavenly bodies cannot be represented mecha nically n due proportion, this part of the stem may keep its situation for giving the equation of the centre without detriment to the distance; a change in which will thus be rendered still more perceptible to the eve.