Figure 26. — Sylvester-Kempe trans- 

 lating linkage, 1877. The upper and 

 lower plates remain parallel and 

 equidistant. From A. B. Kempe, 

 How to Draw a Straight Line (London, 

 i877> P- 37)- 



he had already devised square-root and cube-root 

 extractors, an angle trisector, and a quadratic- 

 binomial root extractor, and he could see no limits 

 to the computing abilities of linkages as yet un- 

 discovered.^" 



Sylvester recalled fondly, in a footnote to his lecture, 

 his experience with a little mechanical m.odel of the 

 Peaucellier linkage at an earlier dinner meeting of 

 the Philosophical Club of the Royal Society. The 

 Peaucellier model had been greeted by the members 

 with lively expressions of admiration "when it was 

 brought in with the dessert, to be seen by them after 

 dinner, as is the laudable custom among members of 

 that eminent body in making known to each other the 

 latest scientific novelties." And Sylvester would 

 never forget the reaction of his brilliant friend Sir 

 William Thomson (later Lord Kelvin) upon being 

 handed the same model in the Athenaeum Club. 

 After Sir William had operated it for a time, Sylvester 

 reached for the model, but he was rebuffed by the 

 exclamation "No ! I have not had nearly enough of 

 it — it is the most beautiful thing I have ever seen in 

 my life." =' 



The aftermath of Professor Sylvester's performance 

 at the Royal Institution was considerable excitement 

 amongst a limited company of interested mathemati- 

 cians. Many alternatives to the Peaucellier straight- 



Figure 27. — Gaspard Monge (1746-1818), 

 professor of mathematics at the Ecole Poly- 

 technique from 1794 and founder of the 

 academic discipline of machine kinematics, 

 From Livre du Centenaire, iyg4-i8g4, Ecole 

 Polytechnique (Paris, 1 895, vol. i , frontispece) . 



line linkage were suggested by several writers of 

 papers for learned journals.'^ 



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 provocati\e title "How to Draw a Straight 

 Line." =3 



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 diffi- 

 cult if not impossible until Captain Peaucellier came 



*° Sylvester, op. cit. (footnote 41), p. 191. 

 51 Ibid., p. 183. 



*- For a summary of developments and references, see 

 Kempe, op. cit. (footnote 21), pp. 49-51. Two of Hart's six-link 

 exact straight-line linkages referred to by Kempe are illus- 

 trated in Henry M. Cundy and A. P. RoUett, Mathematical 

 Models, Oxford, Oxford University Press, 1952, pp. 204-205. 

 Peaucellier's linkage was of eight links. 



'^ Kempe, op. cit. (footnote 21), p. 26. 



PAPER 27: KINEMATICS FROM THE TIME OF WATT 



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