Models_, Oxford, Oxford
University Press, 1952, pp. 204-205. Peaucellier's linkage was of eight
links.]

In the summer of 1876, after Sylvester had departed from England to take
up his post as professor of mathematics in the new Johns Hopkins
University in Baltimore, Alfred Bray Kempe, a young barrister who
pursued mathematics as a hobby, delivered at London's South Kensington
Museum a lecture with the provocative title "How to Draw a Straight
Line."[53]

[Footnote 53: Kempe, _op. cit._ (footnote 21), p. 26.]

In order to justify the Peaucellier linkage, Kempe belabored the point
that a perfect circle could be generated by means of a pivoted bar and a
pencil, while the generation of a straight line was most difficult if
not impossible until Captain Peaucellier came along. A straight line
could be drawn along a straight edge; but how was one to determine
whether the straight edge was straight? He did not weaken his argument
by suggesting the obvious possibility of using a piece of string. Kempe
had collaborated with Sylvester in pursuing the latter's first thoughts
on the subject, and one result, that to my mind exemplifies the general
direction of their thinking, was the Sylvester-Kempe "parallel motion"
(fig. 26).

[Illustration: Figure 26.--Sylvester-Kempe translating linkage, 1877.
The upper and lower plates remain parallel and equidistant. From A. B.
Kempe, _How to Draw a Straight Line_ (London, 1877, p. 37).]

[Illustration: Figure 27.--Gaspard Monge (1746-1818), professor of
mathematics at the Ecole Polytechnique from 1794 and founder of the
academic discipline of machine kinematics, From _Livre du Centenaire,
1794-1894, Ecole Polytechnique_ (Paris, 1895, vol. 1, frontispiece).]

Enthusiastic as Kempe was, however, he injected an apologetic note in
his lecture. "That these results are valuable cannot I think be
doubted," he said, "though it may well be that their great beauty has
led some to attribute to them an importance which they do not really
possess...." He went on to say that 50 years earlier, before the great
improvements in the production of true plane surfaces, the straight-line
mechanisms would have been more important than in 1876, but he added
that "linkages have not at present, I think, been sufficiently put
before the mechanician to enable us to say what value should really be
set upon them."[54]

[Footnote 54: _Ibid._, pp. 6-7. I have not pursued the matter of cognate
linkages (the Watt an