PHYSICAL AND MATHEMATICAL SCIENCES. 2f)3

conception, but which yet (as far as the most essentialpoint of the result is concerned), has been confirmed asan inherent peculiarity in the nature of light, by thewhole extent of modern researoh. The “Optics ” is pre-faced by a declaration, that its design is to explain theproperties of light by means of experiment alone, with-out any admixture of hypothesis. In this respect aloneit was quite a novelty in the age when it appeared: andwhen we compare the true philosophic spirit thus ex-hibited, with the extent, importance, and precision ofthe actual results, we shall be constrained to assign it aplace in the first rank of experimental investigations,and to say that in that rank it stands alone.

Newtons Mathematical Discoveries.

In tracing the progress of those inventions whichwere directed to the object of overcoming the difficultieswhich elementary methods were incompetent to sur-mount, we have noticed the improvements successivelymade by some of the greatest mathematicians, whichwere chiefly called forth in the attempts to solve theproblem of the quadrature of curvilinear areas, or thedetermination of an area equal to that of the curve ex-pressed by some algebraical value in simple terms, de-rived from its equation. We have noticed the severalprinciples which were suggested, but which receivedvery limited applications; and the ingenious idea oiWallis, of interpolating in the series of known areasthose which ought to hold an intermediate place.

Invention of the Methods of Series and Fluxions.

Newton, on taking up the subject, which, we havereason to believe, he did as early as 1665, soon extendedthe method of Wallis by the invention of general seriesesfor this purpose ; and, at the same time, connected theprocess of such serieses with a highly refined method,which was, in like manner, an improvement uponv 3