e,
1873. From A. B. Kempe, _How to Draw a Straight Line_ (London, 1877, p.
12).]

[Illustration: Figure 23.--Model of the Peaucellier "Compas Compose,"
deposited in Conservatoire National des Arts et Metiers, 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
mathematiques_ (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.

This letter stirred no pens in reply, and during the next 10 years the
problem merely led to the filling of a few academic pages by Peaucellier
and Amedee Mannheim (1831-1906), also a graduate of Ecole Polytechnique,
a professor of mathematics, and the designer of the Mannheim slide rule.
Finally, in 1873, Captain Peaucellier gave his solution to the readers
of the _Nouvelles Annales_. His reasoning, which has a distinct flavor
of discovery by hindsight, was that since a linkage generates a curve
that can be expressed algebraically, it must follow that any algebraic
curve can be generated by a suitable linkage--it was only necessary to
find the suitable linkage. He then gave a neat geometric proof,
suggested by Mannheim, for his straight-line "compound compass."[42]

[Footnote 42: Charles-Nicholas Peaucellier, "Note sur une question de
geometrie de compas," _Nouvelles Annales de mathematiques_, 1873, ser.
2, vol. 12, pp. 71-78. A sketch of Mannheim's work is in Florian Cajori,
_A History of the Logarithmic Slide Rule_, New York, about 1910,
reprinted in _String Figures and Other Monographs_, New York, Chelsea
Publishing Company, 1960.]

On a Friday evening in January 1874 Albemarle Street in London was
filled with carriages, each maneuvering to unload its charge of
gentlemen and their ladies at the door of the venerable hall of the
Royal Institution. Amidst