my 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 curriculum (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.]

Lanz and Betancourt, scholars from Spain at the Ecole Polytechnique,
plugged some of the gaps in Hachette's system by adding continuous and
alternating 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.[64]

[Footnote 64: 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 Betancourt work. This copy
probably represents the first textbook of kinematics. Betancourt was
born in 1760 in Teneriffe, attended 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 Farey, _op. cit._, p. 655). He entered
Russian service in 1808 and died in St. Petersburg in 1826 J. C.
Poggendorff, _Biographisches-literarisches Handwoerterbuch fuer Mathematik
..._, Leipzig, 1863, vol. 1.]

[Illustration: Figure 29.--Robert Willis (1800-1875), Jacksonian
Professor, Cambridge University, and author of _Principles of
Mechanism_, one of the landmark books in the development of kinematics
of mechanisms. Photo courtesy Gonville and Caius College, Cambridge
University.]

Giuseppe Antonio Borgnis, an Italian "engineer and member 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 subdivid