[Illustration: (d) "Eccentric wheel" with internal driving wheel hung from working beam. Wheel _B_ is pivoted at center of shaft _A_.] [Illustration: (e) Sun-and-planet gearing. This is the idea actually employed in Boulton and Watt engines. As the optional link _JK_ held the gearwheel centers always equidistant, the annular guide _G_ was not used.] The sun-and-planet arrangement, with gears of equal size, was adopted by Watt for nearly all the rotative engines that he built during the term of the "crank patents." This arrangement had the advantage of turning the flywheel through two revolutions during a single cycle of operation of the piston, thus requiring a flywheel only one-fourth the size of the flywheel needed if a simple crank were used. The optional link (JK of fig. 7e) was used in the engines as built. From the first, the rotative engines were made double-acting--that is, work was done by steam alternately in each end of the cylinder. The double-acting engine, unlike the single-acting pumping engine, required a piston rod that would push as well as pull. It was in the solution of this problem that Watt's originality and sure judgment were most clearly demonstrated. A rack and sector arrangement (fig. 8) was used on some engines. The first one, according to Watt, "has broke out several teeth of the rack, but works steady."[15] A little later he told a correspondent that his double-acting engine "acts so powerfully that it has broken all its tackling repeatedly. We have now tamed it, however."[16] [Footnote 15: James Watt, March 31, 1783, quoted in Dickinson and Jenkins, _op. cit._ (footnote 5), p. 140.] [Footnote 16: Watt to De Luc, April 26, 1783, quoted in Muirhead, _op. cit._ (footnote 3), vol. 2, p. 174.] [Illustration: Figure 8.--Watt engine of 1782 (British Patent 1321, March 12, 1782) showing the rack and sector used to guide the upper end of the piston rod and to transmit force from piston to working beam. This engine, with a 30-inch cylinder and an 8-foot stroke, was arranged for pumping. Pump rod _SS_ is hung from sector of the working beam. From James P. Muirhead, _The Origin and Progress of the Mechanical Inventions of James Watt_ (London, 1854, vol. 3, pl. 15).] It was about a year later that the straight-line linkage[17] was thought out. "I have started a new hare," Watt wrote to his partner. "I have got a glimpse of a method of causing the piston-rod to move up and down perpendicularly, by only fixing it to a piece of iron upon the beam, without chains, or perpendicular guides, or untowardly frictions, arch-heads, or other pieces of clumsiness.... I have only tried it in a slight model yet, so cannot build upon it, though I think it a very probable thing to succeed, and one of the most ingenious simple pieces of mechanism I have contrived...."[18]