100 



SCIENTIFIC THOUGHT. 



of a force by the product of the force (itself measured by 

 the velocity of a moving mass) and the velocity or space 

 per unit of time through which it pushes or pulls a 

 moving body, and Leibniz ^ had suggested the term vis 

 viva to distinguish it from the vis mortua, the force 

 or pressure itself. But the first clear and consistent 

 fixing of the terminology which has since been universally 

 adopted is to be found — not in the ' Mecanique analy- 

 tique ' of Lagrange (that classical work on theoretical 

 mechanics), but in the ' Mecanique industrielle ' of 

 Poncelet (1829).^ He introduced the term "mechanical 



•" Leibniz's occupation with dyn- 

 amics began with his publication of 

 two theses in 1672, which he dedi- 

 cated respectively to the Academy 

 of Sciences in Paris and to the 

 Royal Society. In distinction from 

 the writings of Huygens and 

 Newton, where precise definitions 

 take the place of metaphysical 

 discussions, Leibniz's tracts — ex- 

 cept in the comparatively rare cases 

 where he confines himself to mathe- 

 matical formulae — are vitiated, like 

 those of Descartes, by philosophical 

 speculations. Thus, though emi- 

 nently suggestive, they contributed 

 little to the clearing up of ideas. 

 Influenced by Huygens and by 

 Newton, he opposed in 1686 the 

 ideas of Descartes on the measure 

 of force, and has the merit of 

 having introduced the term vis 

 viva in 1695, and of having started 

 the celebrated discussion on the 

 measure of force which was- carried 

 on during fifty -seven years on the 

 Continent, and onlj- settled by 

 D'Alembert in his ' Traits de Dyn- 

 amique' (1743) by stricter defini- 

 tions. An excellent account of the 

 questions involved, and of the 

 gradual clearing up of ideas, will 

 be found in Prof. Mach's historical 

 treatise on dynamics referred to 



above. See the English translation 

 by M'Cormack, p. 272, &c. It is 

 there shown that one of the great 

 defects of Descartes' and Leibniz's 

 dynamical writings was the want 

 of a clear definition of mass or 

 inertia ; also that this conception 

 follows more simply from Newton's 

 definition of force than from Huy- 

 gens' conception of work (ibid., 

 p. ^251). 



- By the side of, and sometimes 

 in opposition to the purely analytical 

 school headed by Lagrange, Laplace, 

 and later by Cauchy, there grew 

 up in Paris the school of practical 

 mathematicians which taught the 

 application of theory to practice, 

 to problems of artillery, engineer- 

 ing, and architecture. They created 

 modern geometrj", and to a great 

 extent modern mechanics. Monge, 

 Coulomb, the elder Carnot, Pon- 

 celet, Coriolis, were their leaders : 

 Navier, Lame, Charles, de Saint 

 Venant, followed, and combined 

 their more synthetic methods with 

 the analytical methods of the 

 former school. Through Monge, 

 Carnot, Navier, and Poncelet, 

 geometry and dynamics were led 

 into those channels which have 

 since been so successfully followed 

 in all applied work. To them 



