10

LECTURE I.

referable to certain fundamental laws. For these laws being- once established,each fact, as soon as it is known, assumes its place in the system, and is re-tained in the memory by its relation to the rest as a connecting link. In theanalytical mode, on the contrary, which is absolutely necessary for the histinvestigation of truth, we are obliged to begin by collecting a number of in-sulated circumstances, which lead us back by degrees to the knowledge oforiginal principles, but which, until we arrive at those principles, are merelya burden to the memory. For the phenomena of nature resemble the scatter-ed leaves of the Sibyiline prophecies; a word only, or a single syllable, iswritten on each leaf, which, when separately considered, conveys no in-struction to the mind; but when, by the labour of patient investigation,every fragment is replaced in its appropriate connexion, the whole begins atonce to speak a perspicuous and a harmonious language.

Proceeding therefore in the synthetical order, we set out from the abstractdoctrines of mathematics, relating to quantity, space, and number, which wepass over, as supposed to be previously understood, or as sufficiently explainedin the mathematical elements, and go on to their immediate application tomechanics and hydrodynamics, or to such cases of the motions of solids andfluids as are dependent on arbitrary assumptions, that is, where we do notconfine our inquiries to any particular cases of existing phenomena, liymeans of principles which are deducible in a satisfactory manner from mathe-matical axioms, with the assistance only of the general logic of induction,we shall be able to draw such conclusions, as are capable of giving usvery important information respecting the operations of nature and of art, andto lay down such laws, as, to an uninformed person, it would appear to be be-yond the powers of reason to determine, without the assistance of experiment.The affections of falling bodies, and of projectiles, the phenomena of bodiesrevolving round a centre, the motions of pendulums, the properties of the centreof gravity, the equilibrium of forces in machines of different kinds, the lawsof preponderance, and the effects of collision; all these arc wholly referable toaxiomatical evidence, and are frequently applicable to important uses in prac-tice. Upon these foundations, we shall proceed to the general principles ofmachinery, and the application of forces of different kinds: we shall inquirewhat are the principle sources of motion that we can subject to our command,and what advantages are peculiar to each of them: and then, according to