(114.) The second method of producing a rotatory motion, which was subsequently continued for many years in practical operation, was that which was called the _Sun-and-planet Wheels_. A toothed wheel A (_fig._ 32.), called the sun wheel, was fixed on the axle of the fly-wheel, to which rotation was to be imparted. The wheel B, called the planet wheel, having an equal diameter, was fastened on the end I of the connecting rod H I, so as to be incapable of revolving. During the descent of the piston, the working end of the beam was drawn upwards, and the end I of the connecting rod travelled from C to D, through the dotted semicircle C I D. The wheel B not being capable of revolving on the centre I, would, during this motion, drive the sun wheel A. During the ascent of the steam piston, the working end of the beam would descend, and the centre I of [Pg188] the planet wheel B would be driven downwards from D to C, through the other dotted semicircle, and would consequently continue to drive the sun wheel round in the same direction. This contrivance, although in the main inferior to the more simple one of the crank, is not without some advantages; among others, it gives to the sun wheel double the velocity which would be communicated by the crank; for in the crank one revolution only on the axle is produced by one revolution of the crank, but in the sun-and-planet wheel, two revolutions of the sun wheel are produced by one of the planet wheel; thus a double velocity is obtained from the same motion of the beam. This will be evident from considering that when the planet wheel is in its highest position, its lowest tooth is engaged with the highest tooth of the sun wheel; as the planet wheel passes from the highest position, its teeth drive those of the sun wheel before them, and when it comes into the lowest position, the highest tooth of the planet wheel is engaged with the lowest of the sun wheel: but then half of the sun wheel has _rolled off_ the planet wheel, and, therefore, the tooth which was engaged with it in its highest position, must now be distant from it by half the circumference of the wheel, and must, therefore, be again in the highest position; so that while the planet wheel has been carried from the top to the bottom, the sun wheel has made a complete revolution. This advantage of giving an increased velocity may be obtained also by the crank, by placing toothed wheels on its axle. Independently of the greater expense attending the construction of the sun-and-planet wheel, its liability to go out of order, and the rapid wear of the teeth, and other objections, rendered it inferior to the crank, which has entirely superseded it.