.. Opera Omnia ..._, Lausanne, 1742, vol. 4, p. 265ff.).]

[Illustration: Figure 30.--Franz Reuleaux (1829-1905). His _Theoretische
Kinematik_, published in 1875, provided the basis for modern kinematic
analysis. Photo courtesy Deutsches Museum, Munich.]

Acting upon Ampere's clear exposition of the province of kinematics and
excluding, as Ampere had done, the consideration of forces, an
Englishman, Robert Willis, made the next giant stride forward in the
analysis of mechanisms. Willis was 37 years old in 1837 when he was
appointed professor of natural and experimental philosophy at Cambridge.
In the same year Professor Willis--a man of prodigious energy and
industry and an authority on archeology and architectural history as
well as mechanisms--read his important paper "On the Teeth of Wheels"
before the Institution of Civil Engineers[70] and commenced at Cambridge
his lectures on kinematics of mechanisms that culminated in his 1841
book _Principles of Mechanism_.[71]

[Footnote 70: Robert Willis, "On the Teeth of Wheels," _Transactions of
the Institution of Civil Engineers of London_, 1838, vol. 2, pp.
89-112.]

[Footnote 71: Willis, _op. cit._ (footnote 21). Through the kindness of
its owner (Mr. Warren G. Ogden of North Andover, Massachusetts), I have
had access to Willis' own copy of his 1841 edition of _Principles of
Mechanism_. The book is interleaved, and it contains notes made by
Willis from time to time until at least 1870, when the second edition
was issued. Corrections, emendations, notations of some of his sources
(for example, the De Voglie linkage mentioned in footnote 35 above),
notes to himself to "examine the general case" and "examine the modern
forms" of straight-line devices are interspersed with references to
authors that had borrowed from his work without acknowledgment. Of one
author Willis writes an indignant "He ignores my work."]

It seemed clear to Willis that the problem of devising a mechanism for a
given purpose ought to be attacked systematically, perhaps
mathematically, in order to determine "all the forms and arrangements
that are applicable to the desired purpose," from which the designer
might select the simplest or most suitable combination. "At present," he
wrote, "questions of this kind can only be solved by that species of
intuition which long familiarity with a subject usually confers upon
experienced persons, but which they are totally unable to communicate to
others."

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