Figure 24. — James Joseph Sylvester 

 (1814-1897), mathematician and lec- 

 turer on straight-line linkages. From 

 Proceedings of the Royal Society of London 

 (i8g8, 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 link- 

 age — it was only necessary to find the suitable linkage. 

 He then gave a neat geometric proof, suggested by 

 Mannheim, for his straight-line "compound com- 

 pass. 



On a Friday evening in January 1874 Albemarle 

 Street in London was filled with carriages, each 



*2 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 0] the Logarithmic Slide Rule, New York, 

 about 1910, reprinted in String Figures and Other Monographs, 

 New York, Chelsea Publishing Company, 1960. 



Figure 25. — Mr. Prim's blowing engine used for ventilating the House of 

 Commons, 1877. The crosshead of the reciprocating air pump is guided by a 

 Peaucillier linkage shown at the center. The slate-lined air cylinders had 

 rubber-flap inlet and exhaust valves and a piston whose periphery was formed 

 by two rows of brush bristles. Prim's machine was driven by a steam engine. 

 Photograph by Science Museum, London. 



PAPER 27: KINEMATICS FROM THE TIME OF WATT 



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