From the centre wheel hole on the fore frame plate, to wards the left hand, and a little upwards, take, with a pair of compasses, a distance of 3.8 inches, and sweep an arch ; and then from the centre of the hole, in which the arbor runs, which carries the annual plate wheel, take in the com passes an extent of 4.6 inches, and sweep another arch so as to intersect the first, the place of intersection will be that of an arbor having pivots, one of which runs into a cock, screwed on the back of the pillar plate ; the other runs into a cock screwed on the front of the fore frame plate ; a notch is made on the edge of each frame plate to admit the arbor to come into its place. On the end of this arbor, which is just behind the pillar plate, is fixed a rack or segment of a circle 5 inches radius, having 32 teeth cut on it, and cut from a number on the engine plate of 318 ; the rack-teeth pitches into the small wheel of 32, which lies behind the pillar plate, and whose centre coincides with that of the minute pinion arbor, as mentioned before. On the other end of this arbor, and beyond the fore frame plate a very little, is fixed an arm of 4.5 inches long, having at the end of it a smooth hard steel pin, which bears on the edge of the annual elliptic equation plate, being made to do so by means of a coil or two of watch main spring, not very strong, attached to the arbor, near to the inside of the fore frame plate, the outer end being fixed to one of the pillars, or to a stud fixed for that purpose on the inside of the fore plate. The elliptic equation plate is a very irregular sort of a figure, as may be conceived in some degree by the de scription of its shape ; its greatest length over all is 6.5 inches ; the centre is 3.8 inches from the broadest end, and 2.7 inches from the narrowest ; the nearest edge across the centre is about one inch, and the edge opposite is 1.8 inch; the greatest breadth of the broad end is near to 4 inches, that of the narrowest end is 2.8 inches. During the course of its annual revolution, the edge of the elliptic plate makes the arm which has the steel pin in it rise to various heights, and fall as variously to different depths. By this rising and falling, the rack which is at the opposite end of the arbor, is made to have a motion sometimes backward, and at other times forward, which it communicates to the small wheel of 32, behind the pillar plate, and of course to the bevelled wheel of 38, on the same arbor with it. This continually causes a small change of place to the bevelled wheel of 38, consequently a change of place to that which turns on the stud, and hence to the wheel carrying the sun hand ; this change is what gives the equa tion shewn by the difference of time between the minute and sun hands. When the pin in the arm falls, the equa tion or sun hand goes forward, and when rising it goes backward. The greatest negative equation for 1815, on the 3d day of November, is 16 minutes, 14.9 seconds, which, added to the greatest positive equation for the same year on the llth of February, is 14 minutes, 36.5 seconds, making in all 30 minutes, 51.4 seconds ; so that one tooth of the wheel of 32 may be nearly equivalent to one minute of equation. To trace properly a true figure to the equa tion plate must be a very tedious and nice operation ; for this purpose the rack, and all the wheels immediately con nected with the equation, must be put into their places, as also all those which give motion to the annual plate, and to have a spring tight arm, having a sharp point to it, bearing on the face of the brass plate which is to be the elliptic one : the sharp point must lie so as to coincide with the side of the steel pin, when bearing on the edge of the elliptic plate. The sun and minute hands being on, and the annual plate set to the 1st of January, the equation hand set to the equa tion for that day, then by setting forward the minute hand until 12 or 24 hours have elapsed, the equation hand may lrchanged to what it ought to be, in the same time ; so by going on step by step in this way, the figure of the equation plate may be truly done. The rack must be artificially made to assist in this ; and when the revolution is com pletely at the end, before taking out the rack and the equa tion wheels, marks must be made to one of those teeth, which must be mat ked by its corresponding space in the other wheels, so that when they are again put into their places, they shall give such equation as was done when tracing for the elliptic plate.
Besides the days of the month, which are shewn on the annual plate, there is a common month ring, having 31 fi gures engraved on it, placed as usual at the back of the dial. One of these figures is shifted every clay through the whole ring when the month consists of 31 days; and two figures at the last are shifted at once when the month consists of 30 days, to bring the ring to the first day of the succeeding month ; and at the 28th of Februtry four figures are shifted, so as to bring the ring to the 1st of March : by this means the day of the month ring requires no shift ing or correcting at these periods, as those in the common way do. To produce this motion, five short steel pins are plac ed in a circle, on the under side of the elliptic plate, whose radius may be about half an inch, and set at such a distance from one another as to correspond with the number of days between February and April, between April and June, be tween June and September, between September and No vember, and between November and February. This may
be done by applying the elliptic plate on a cutting or divid ing engine, having the number 365 on the dividing plate. When fixed on the engine, and set to the first point of the number, make a point for February on the elliptic plate; then count off 61 from the dividing plate, which will give the place for the pin on the 30th of April; another 61 will bring it to June 30th ; 92 will give the 30th of September; 61 the 30th of November ; and 90 more will bring it. to the 28th of February, the point which was set out from. When the pins are put in the elliptic plate, that for February will require to be longer than the others, for a reason which will be explained when we come to spew the use of these pins. The month-wheel of 84 teeth, and whose diameter is 2.75 inches, has its centre on the left hand side, distant from the central perpendicular line 1.4 inch, and from the centre hole in the fore frame plate 2 inches. The month wheel, as usual, is turned about by the month nut. A long piece of brass forming two arms, each four inches in length, has a small arbor through the middle of the whole length of eight inches. The pivots of this arbor run into small cocks, attached to the front of the fore plate, keeping the long piece of brass very near to the plate ; indeed a great part, particularly the end of the upper arm, and towards it, is sunk partly into the fore plate. This long piece of brass is placed so that one of the arms shall come to the socket of the month wheel, and the other, with its end nearly below the circle in which are the five pins, in the annual elliptic plate described as before. A spring is placed below this upper arm to keep it up, unless when any of the pins get on the end of the arm and press it down. The end of the arm is chamfered, or made so that any pin, when approach ing it, gets easily on, and presses it down gradually, by means of ascending the chamfered part as it were ; and when past this, it meets with a flat and very narrow place, where it cannot remain longer than some time short of 24 hours, say 16 or 18 hours, or perhaps not so long. After having passed the flat part, it meets with a chamfered side oppo site to that of the first. Besides that of fleeing the pin, this is made for the purpose of more easily setting back or for •ard the annual plate.
The month wheel has its socket equally long on both sides, and quite straight ; the length of each may be .6 or .7 of an inch. Two small brass pillars are rivetted on the up per side, and opposite one another, each at a distance from the centre of the wheel about .7 of an inch, (see Plate CCCIV. Figs. 8, 9.) the height of the pillars from the wheel to the shoulder about half an inch ; and from the shoulder of each pillar a sort of straight pivot is pro longed, about one half inch more ; the diameter of these pivots about one-tenth of an inch; that of the pillar .2 of an inch. There is another socket which goes easily on the lower or under socket of the month wheel, which is rivetted in a rectangular piece of brass, about an inch long, and half an inch broad, or nearly so, say .4 of an inch. In this piece of brass, on the side opposite that of the socket, are also rivetted two small and straight brass pillars, about an inch in length, and the diameter about one-tenth of an inch. There are holes in the month wheel, to allow these pillars to go easily back and forward in them; their places will be equally between the month wheel socket, and the pillars which are rivetted in the month wheel. The other ends of the small straight pillars are made fast, by two small steel screws, to a piece of brass, which is formed to correspond with two broad crosses of the month wheel. Only one of them is made to have at the end a segment of a circle, whose radius is nearly equal to that of the month wheel. On this segment three teeth are cut, equal in their spaces and form to those of the month ring. In the arms or crosses of the segment are three holes, one of which goes easily over or on the up per socket of the month wheel ; the other two holes go easily on the small straight pivots which have been al ready mentioned. This segment cannot be put on the ends of the small pillars, till the socket of the rectangu lar piece of brass is put on the lower socket of the month wheel, having previously made the pillars connected with it to pass through their holes in the month wheel. It will be easy to perceive, that when the segment is put on to its pillars, and a sufficient space left behind the month wheel and the rectangular piece of brass, its socket may be made to pump up and down on that of the month wheel, and at the same time carrying the segment back and forward with it; a pin in the month wheel stud keeps the month wheel socket always to its proper end shake, notwithstand ing any motion of the segment backwards and forwards. Below the rectangular piece on its socket, a small groove is turned out of it, for the purpose of a forked piece get ting in on it ; this forked piece is formed on that end of the arm which lies along the fore plate, and on to the socket or centre of the mouth wheel.