Stage 3

30 360 This stage of the astronomical section is arguably the most ingenious. As well as transmitting the sidereal drive to the star plate (one turn per sidereal day), it produces a drive at solar speed (one revolution per true solar day) which rotates the sun’s symbol and is also used in driving the moon and the dragon. Wheel 360 is fixed to a vertical tube which leads to the star plate at the top of the device. It is driven by pinion 30 in stage 2 so that it rotates 366^1/4 times per year. Wheel 331 is a contrate ring of teeth fixed to the face of wheel 360.
			The star plate tube runs inside another (yellow) tube which drives the sun’s symbol and so must rotate 365^1/4 times per year. The sun’s tube is attached to a bracket carrying a transported gear train.
		Pinion 8 meshes with the contrate teeth of wheel 331. When the latter rotates, pinion 8 cannot turn because it connects to gearwheel 16 which is meshed with the worm. Consequently pinion 8 and the bracket all revolve with wheel 331. At the same time wheel 32 is carried round wheel 29 (fixed to frame) and is consequently forced to rotate. This turns the worm which drives wheel 16 and hence pinion 8. The result is that while the bracket is being dragged round by pinion 8, the latter is very slowly rotating to make the bracket creep backwards.
When wheel 331 has made 366^1/4 turns, pinion 8 and the bracket have been retarded by one complete turn, so have only completed 365^1/4 turns.
For each revolution of the bracket, wheel 32 makes 29/32 of a turn. The worm (which has the equivalent of 2 teeth) does the same, so wheel 16 makes 29/32 x 2/16 turns. Pinion 8 does the same, so the bracket is cranked backwards by 29/32 x 2/16 x 8/331 turns = 0.002737915 turns. Thus after wheel 331 has made one turn, the sun’s tube has made 1 - 0.002737915 turns. This is 0.997262 turn. Hence, after the starplate tube has rotated 366^1/4 times, the sun’s tube has rotated 366¼ x 0.997262 = 365^1/4 times.
At first sight, it might seem pointless to convert from solar time to sidereal time and then back to solar time again. However, whereas the output from the timepiece is mean solar time, the drive to the sun’s tube is true solar time, which is achieved as follows.
	Consider two drives using contrate gearwheels of different diameters. Assuming that the input shafts rotate at the same rate, and that the driven pinions have equal numbers of teeth, the output from A will be faster than that from B. Now imagine a contrate gearwheel which is not circular. As it rotates, the speed of the driven pinion will vary. Of course, the pinion will need to be specially elongated so that it remains meshed with the gearwheel.
Wheel 331 is just such a non-circular contrate gearwheel. It is elliptical. This is known as a variable speed drive and the objective is to vary the speed of the sun’s tube in accordance with the Equation of Time. Remember that pinion 8 takes one year to crawl once around wheel 331 and the special shape of the latter ensures that the sun’s speed varies such that it is always in its true position. Richard’s original design showed a more complicated shape, comprising segments of four different circles. Because of the difficulty of constructing this shape - and the fact that not all of the necessary information was stated, our replica actually uses an elliptical gearwheel.