[ [16] Watt to De Luc, April 26, 1783, quoted in Muirhead, op. cit. (footnote 3), vol. 2, p. 174.
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]
[ [17] Watt's was a four-bar linkage. All four-bar straight-line linkages that have no sliding pairs trace only an approximately straight line. The exact straight-line linkage in a single plane was not known until 1864 (see p. 204). In 1853 Pierre-Frédéric Sarrus (1798-1861), a French professor of mathematics at Strasbourg, devised an accordion-like spatial linkage that traced a true straight line. Described but not illustrated (Académie des Sciences, Paris, Comptes rendus, 1853, vol. 36, pp. 1036-1038, 1125), the mechanism was forgotten and twice reinvented; finally, the original invention was rediscovered by an English writer in 1905. For chronology, see Florian Cajori, A History of Mathematics, ed. 2, New York, 1919, p. 301.
[ [18] Muirhead, op. cit. (footnote 3), vol. 2, pp. 191-192.
Watt's marvelously simple straight-line linkage was incorporated into a large beam engine almost immediately, and the usually pessimistic and reserved inventor was close to a state of elation when he told Boulton that the "new central perpendicular motion answers beyond expectation, and does not make the shadow of a noise."[19] This linkage, which was included in an extensive patent of 1784, and two alternative devices are illustrated here (fig. 9). One of the alternatives is a guided crosshead (fig. 9, top right).
[ [19] Ibid., p. 202.
Figure 9.—Watt's mechanisms for guiding the upper end of the piston rod of a double-acting engine (British Patent 1432, April 28, 1784). Top left, straight-line linkage; top right, crosshead and guide arrangement; lower left, piston rod A is guided by sectors D and E, suspended by flexible cords. From James P. Muirhead, The Origin and Progress of the Mechanical Inventions of James Watt (London, 1854, vol. 3, pls. 21, 22).