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 the 

 analytical mode, on the contrary, which is absolutely necessary for the first 

 investigation of truth, we are obliged to begin by collecting a number of in- 

 sulated circumstances, which lead us back by degrees to the knowledge of 

 original principles, but which, until we arrive at those principles, are merely 

 a burden to the memory. For the phenomena of nature resemble the scatter- 

 ed leaves of the Sibylline prophecies; a Avord only, or a single syllable, is 

 written 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 at 

 once to speak a perspicuous and a hai-monious language. 



Proceeding therefore in the synthetical order, we set out from the abstract 

 doctrines of mathematics, relating to quantity, space, and number, which we 

 pass over, as supposed to be previously understood, or as sufficiently explained 

 in the mathematical elements, and go on to their immediate application to 

 mechanics and hydrodynamics, or to such eases of the motions of solids and 

 fluids as are dependent on arbitrary assumptions, that is, where we do not 

 confine our inquiries to any particular cases of existing phenomena. By 

 means 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 us 

 very important information respecting the operations of nature and of art, and 

 to 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 phenomen*^ of bodies 

 revolving round a centre, the motions of pendulums, the properties of the centre 

 of gravity, the equilibrium of forces in machines of diflferent kinds, the laws 

 of preponderance, and the efi'ects of collision ; all these are wholly referable to 

 axiomatical evidence, and are frequently applicable to important uses in prac- 

 tice. Upon these foundations, we shall proceed to the general principles of 

 machinery, and the application of forces of different kinds : we shall inquire 

 what 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 



