e can scarcely imagine circumstances under which it would be more
advantageous to use such a complicated system of levers, with so many
joints to be lubricated and so many pins to wear, than a solid guide of
some kind; but at the same time the arrangement is very ingenious and in
this respect reflects great credit on its designer."[39]

[Footnote 38: _Ibid._, vol. 2, pp. 93, 94.]

[Footnote 39: _Engineering_, October 3, 1873, vol. 16, p. 284.]

[Illustration: Figure 19.--Pafnuti[)i] L'vovich Chebyshev (1821-1894),
Russian mathematician active in analysis and synthesis of straight-line
mechanisms. From _Ouvres de P. L. Tchebychef_ (St. Petersburg, 1907,
vol. 2, frontispiece).]

[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 Encyclopedie_[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 Encyclopedie_, 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 linkag