[Illustration: Figure 20.--Chebyshev's combination (about 1867) of Watt's and Evans' linkages to reduce errors inherent in each. Points _C_, _C'_, and _C"_ are fixed; _A_ is the tracing point. From _Oeuvres de P. L. Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 93).] [Illustration: Figure 21.--_Top_: Chebyshev straight-line linkage, 1867; from A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p. 11). _Bottom_: Chebyshev-Evans combination, 1867; from _Oeuvres de P. L. Tchebychef_ (St. Petersburg, 1907, vol. 2, p. 94). Points _C_, _C'_, and _C"_ are fixed. _A_ is the tracing point.] There is a persistent rumor that Professor Chebyshev sought to demonstrate the impossibility of constructing any linkage, regardless of the number of links, that would generate a straight line; but I have found only a dubious statement in the _Grande Encyclopédie_[40] of the late 19th century and a report of a conversation with the Russian by an Englishman, James Sylvester, to the effect that Chebyshev had "succeeded in proving the nonexistence of a five-bar link-work capable of producing a perfect parallel motion...."[41] Regardless of what tradition may have to say about what Chebyshev said, it is of course well known that Captain Peaucellier was the man who finally synthesized the exact straight-line mechanism that bears his name. [Footnote 40: _La Grande Encyclopédie_, Paris, 1886 ("Peaucellier").] [Footnote 41: James Sylvester, "Recent Discoveries in Mechanical Conversion of Motion," _Notices of the Proceedings of the Royal Institution of Great Britain_, 1873-1875, vol. 7, p. 181. The fixed link was not counted by Sylvester; in modern parlance this would be a six-link mechanism.] [Illustration: Figure 22.--Peaucellier exact straight-line linkage, 1873. From A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p. 12).] [Illustration: Figure 23.--Model of the Peaucellier "Compas Composé," deposited in Conservatoire National des Arts et Métiers, Paris, 1875. Photo courtesy of the Conservatoire.] [Illustration: Figure 24.--James Joseph Sylvester (1814-1897), mathematician and lecturer on straight-line linkages. From _Proceedings of the Royal Society of London_ (1898, vol. 63, opposite p. 161).] Charles-Nicolas Peaucellier, a graduate of the Ecole Polytechnique and a captain in the French corps of engineers, was 32 years old in 1864 when he wrote a short letter to the editor of _Nouvelles Annales de mathématiques_ (ser. 2, vol. 3, pp. 414-415) in Paris. He called attention to what he termed "compound compasses," a class of linkages that included Watt's parallel motion, the pantograph, and the polar planimeter. He proposed to design linkages to describe a straight line, a circle of any radius no matter how large, and conic sections, and he indicated in his letter that he had arrived at a solution.