longer time, it is well to look for a moment at the early 

 work that was done there. If one is interested in ori- 

 gins, it might be profitable for him to investigate the 

 military school in the ancient town of Mezieres, about 

 150 miles northeast of Paris. It was here that Lazare 

 Carnot, one of the principal founders of the Ecole 

 Poly technique, in 1783 published his essay on ma- 

 chines,^" which was concerned, among other things, 

 with showing the impossibility of "perpetual motion" ; 

 and it was from Mezieres that Gaspard Monge and 

 Jean Hachette *' came to Paris to work out the system 

 of mechanism classification that has come to be asso- 

 ciated with the names of Lanz and Betancourt. 



Gaspard Monge (1746-1818), who while a drafts- 

 man at Mezieres originated the methods of descriptive 

 geometry, came to the Ecole Polytechnique as pro- 

 fessor of mathematics upon its founding in 1794, the 

 second year of the French Republic. According to 

 Jean Nicolas Pien-e Hachette (1769-1834), who was 

 junior to Monge in the department of descriptive ge- 

 ometry, Monge planned to give a two-months' course 

 devoted to the elements of machines. Having barely 

 gotten his department under way, however, Monge 

 became involved in Napoleon's ambitious scientific 

 mission to Egypt and, taking leave of his family and his 

 students, embarked for the distant shores. 



"Being left in charge," wrote Hachette, "I prepared 

 the course of which Monge had given only the first 

 idea, and I pursued the study of machines in order to 

 analyze and classify them, and to relate geometrical 

 and mechanical principles to their construction." 

 Changes of curriculum delayed introduction of the 

 course until 1806, and not until 1811 was his textbook 

 ready, but the outline of his ideas was presented to his 

 classes in chart form (fig. 28). This chart was the 

 first of the widely popular synoptical tables of me- 

 chanical movements. ^^ 



Hachette classified all mechanisms by considering 

 the conversion of one motion into another. His ele- 

 mentary motions were continuous circular, alternating 

 circular, continuous rectilinear, and alternating rec- 

 tilinear. Combining one motion with another — for 



*" Lazare N. M. Carnot, Essai sur les machines en general, 

 Mezieres, 1783 (later published as Principes fondamentaux de 

 Vequilibre et du mouvement, Paris, 1803). 



'1 Biographical notices of Monge and Hachette appear in 

 Encyclopaedia Britannica, ed. 11. See also V Ecole Polytechnique, 

 Livie du Centenaire, Paris, 1895, vol. 1, p. llff. 



"^ Jean N. P. Hachette, Traite elementaire des machines, Paris, 

 1811, p. V. 



example, a treadle and crank converted alternating 

 circular to continuous circular motion — he devised a 

 system that supplied a frame of reference for the study 

 of mechanisms. In the U.S. Military Academy at 

 West Point, Hachette's treatise, in the original French, 

 was used as a textbook in 1824, and perhaps earlier.*' 



Lanz and Betancourt, scholars from Spain at the 

 Ecole Polytechnique, plugged some of the gaps in 

 Hachette's system by adding continuous and alter- 

 nating curvilinear motion, which doubled the number 

 of combinations to be treated, but the advance of 

 their work over that of Hachette was one of degree 

 rather than of kind.** 



Giuseppe Antonio Borgnis, an Italian "engineer 

 and mem.ber of many academies" and professor of 

 mechanics at the University of Pavia in Italy, in his 

 monumental, nine-volume Traite complet de mechanique 

 appliquee aux arts, caused a bifurcation of the structure 

 built upon Hachette's foundation of classification 

 when he introduced six orders of machine elements 

 and subdivided these into classes and species. His 

 six orders were recepteurs (receivers of motion from the 

 prime mover), communicateurs, modificateurs (modifiers 

 of velocity), supports (e.g., bearings), regulateurs (e.g., 



^' This work was among the books sent back by Sylvanus 

 Thayer when he visited France in 1 81 6 to observe the education 

 of the French army cadets. Thayer's visit resulted in his 

 adopting the philosophy of the Ecole Polytechnique in his 

 reorganization of the U.S. Military Academy and, incidentally, 

 in his inclusion of Hachette's course in the Academy's curric- 

 ulum (U.S. Congress, American State Papers, Washington, 

 1832-1861, Class v, Military Affairs, vol. 2, p. 661: Sidney 

 Forman, West Point, New York, 1950, pp. 36-60). There is 

 a collection of miscellaneous papers (indexed under Sylvanus 

 Thayer and William McRee, U.S. National Archives, RG 

 77, Office, Chief of Engineers, Boxes 1 and 6) pertaining to 

 the U.S. Military Academy of this period, but I found no 

 mention of kinematics in this collection. 



*■' Phillipe Louis Lanz and Augustin de Betancourt, Essai sur 

 la composition des machines, Paris, 1808. Hachette's chart and 

 an outline of his elementary course on machines is bound with 

 the Princeton University Library copy of the Lanz and Betan- 

 court work. This copy probably represents the first textbook of 

 kinematics. Betancourt was born in 1760 in Teneriffe, at- 

 tended the military school in Madrid, and became inspector- 

 general of Spanish roads and canals. He was in England 

 before 1789, learning how to build Watt engines, and he 

 introduced the engines to Paris in 1790 (see Farcy, op. cit., p. 

 655). He entered Russian service in 1808 and died in St. 

 Petersburg in 1826 {J. C. PoggendorfF, Biographisches-litera- 

 risches Handworterbuch Jiir Mathematik . . . , Leipzig, 1863, 

 vol. 1. 



210 



BULLETIN 228: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY 



