[Footnote 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.] [Footnote 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). [Footnote 19: _Ibid._, p. 202.] [Illustration: 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).] Brilliant as was the conception of this linkage, it was followed up by a synthesis that is very little short of incredible. In order to make the linkage attached to the beam of his engines more compact, Watt had plumbed his experience for ideas; his experience had yielded up the work done much earlier on a drafting machine that made use of a pantograph.[20] Watt combined his straight-line linkage with a pantograph, one link becoming a member of the pantograph. [Footnote 20: "It has only one fault," he had told a friend on December 24, 1773, after describing the drafting machine to him, "which is, that it will not do, because it describes conic sections instead of straight lines." _Ibid._, p. 71.]