years after the final solution of the
problem, Professor Chebyshev,[36] a noted mathematician of the
University of St. Petersburg, was interested in the matter. Judging by
his published works and his reputation abroad, Chebyshev's interest
amounted to an obsession.

[Footnote 36: This is the Library of Congress spelling]

Pafnuti[)i] L'vovich Chebyshev was born in 1821, near Moscow, and
entered the University of Moscow in 1837. In 1853, after visiting France
and England and observing carefully the progress of applied mechanics in
those countries, he read his first paper on approximate straight-line
linkages, and over the next 30 years he attacked the problem with new
vigor at least a dozen times. He found that the two principal
straight-line linkages then in use were Watt's and Evans'. Chebyshev
noted the departure of these linkages from a straight line and
calculated the deviation as of the fifth degree, or about 0.0008 inch
per inch of beam length. He proposed a modification of the Watt linkage
to refine its accuracy but found that he would have to more than double
the length of the working beam. Chebyshev concluded ruefully that his
modification would "present great practical difficulties."[37]

[Footnote 37: _Oeuvres de P. L. Tchebychef_, 2 vols., St. Petersburg,
1899-1907, vol. 1, p. 538; vol. 2, pp. 57, 85.]

At length an idea occurred to Chebyshev that would enable him to
approach if not quite attain a true straight line. If one mechanism was
good, he reasoned, two would be better, _et cetera, ad infinitum_. The
idea was simply to combine, or compound, four-link approximate linkages,
arranging them in such a way that the errors would be successively
reduced. Contemplating first a combination of the Watt and Evans
linkages (fig. 19), Chebyshev recognized that if point D of the Watt
linkage followed nearly a straight line, point A of the Evans linkage
would depart even less from a straight line. He calculated the deviation
in this case as of the 11th degree. He then replaced Watt's linkage by
one that is usually called the Chebyshev straight-line mechanism (fig.
20), with the result that precision was increased to the 13th
degree.[38] The steam engine that he displayed at the Vienna Exhibition
in 1873 employed this linkage--the Chebyshev mechanism compounded with
the Evans, or approximate isosceles, linkage. An English visitor to the
exhibition commented that "the motion is of little or no practical use,
for w