PHYSICAL AND .MATHEMATICAL SCIENCES. 3 ()~

objections, yet the point cannot be said to have beencompletely cleared up till D'Alembert showed the realapplication of the principle of limits in its simplest sense;and, finally, Lagrange, in his “Theorie des Fonctions,”discarding all idea both of infinitesimals, and even oflimits, reduced the whole into an elementary, thoughsomewhat prolix, algebraical investigation, by the de-velopement of functions in serieses : while the valuableessay of Carnot on the metaphysical principles of theinfinitesimal calculus, tends more to clear the method oflimits from objections than, perhaps, any thing that hasappeared on the subject; and the researches of professorWoodhouse have placed the general principles of themethods of analysis on a secure basis of demonstration.To his writings we owe the first introduction of the in-ventions of the continental analysts into this country.

Of the vast improvements effected in every branch ofanalytical mathematics by the foreign mathematicians,it would here be a vain attempt to convey an idea. Wehave mentioned the names of the earlier of that illus-trious school, who reared so large a portion of the super-structure of the science; and, in more modern times, theyhave not been wanting in successors truly worthy ofthem. The names of Legendre and Lacroix, of Abro-gast and Poinsot, of Gamier and Cauchy , are a few onlyamong a multitude of those most highly distinguishedin the different branches of pure analytics ; while manyof those whom we have mentioned in other departmentswere likewise no less eminent in this. Our own countryhas hitherto had to boast but a very small list of namesin the higher branches of mathematics; but, since wehave had the wisdom to give up a few of our absurdexclusive prejudices, and to cultivate the methods inwhich our continental neighbours have achieved suchdistinguished renown, we have begun to exhibit an arrayof analytical talent to which we may look forward withconfidence for the happiest results.

It was not, however, till at a comparatively veryrecent period that there appeared any marked changein the state of mathematical learning in England. It it