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]

[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-Frederic 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 (Academie 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
illustra