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HISTORICAL VIEW OF THE

their researches in proportion to the facilities suppliedto their hands by the increasing powers of the newcalculus. The discussion which arose in 1724 respect-ing the true measure of force, and which, in the end,was clearly seen to be a mere dispute about terms, hadthe effect of calling forth many valuable researches;though, when the English philosophers, Maclaurin ,Stirling, Clarke, and others, took a share in it, and op-posed Bernoulli, Herman, S’Gravesande, and Muschen-broek, the discussion assumed too much of the angrytone of the fluxional controversy, the bitterness of whichhad not worked itself out till a later period. The con-troversy may be considered to have ended with thepublication of D'Alembert’s “ Dynamique,” in 1743.

The general character of the improvements effectedin mechanical and liydrostatical science, about this pe-riod, was marked chiefly by the increasing developementof the analytical formuke. To this has been owing thegreat advances in the investigation of principles andlaws, which, perhaps, may be dated from Bernoulli andD’Alembert , and which have been so advantageouslypursued by a long train of their illustrious successors,and perfected in the “ Mecanique Analytique ” of LaGrange. These, however, are precisely those of whichit is the least in our power, within our limits, to giveany adequate notion, and of which an enumeration,without such illustration, could answer no useful pur-pose.

Of Lagrange, however, we must add, that the dis-tinctive mark of his genius consists in the unity andgrandeur of his views. He attached himself wholly toa simple, though just and highly elevated thought. Hisprincipal work, just mentioned, refers all the laws ofequilibrium and motion to a single principle: and, whatis not less admirable, it submits them to a single methodof calculation, of which he himself was the inventor.All his mathematical compositions are remarkable fortheir singular elegance, for that symmetry of form and