8 LECTURE I. 



which we pass over, as supposed to be previously understood, or as suffi- 

 ciently explained in the mathematical elements, and go on to their imme- 

 diate application to mechanics and hydrodynamics, or to such cases 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 mathematical 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 na- 

 I ture and of art, and to lay down such laws, as, to an uninformed person, 

 I it would appear to be beyond the powers of reason to determine without the 

 /^assistance of experiment. The affections of falling bodies and of projectiles, 

 the phenomena of bodies revolving round a centre, the motions of pendu- 

 lums, the properties of the centre of gravity, the equilibrium of forces in 

 machines of different kinds, the laws of preponderance, and the effects of 

 collision ; all these are wholly referable to axiomatical evidence, and are 

 frequently applicable to important uses in practice. Upon these founda- 

 tions we shall proceed ta the general principles of machinery, and the 

 application of forces of different kinds : we shall inquire what are the 

 principal sources of motion that we can subject to our command, and what 

 advantages are peculiar to each of them : and then, according to the 

 purposes for which they are employed, we shall separately examine the 

 principal machines and manufactures in which those forces are applied to 

 the service of mankind. 



Such instruments and machines as are more or less immediately subser- 

 vient to mathematical purposes will be the first in order, including all the 

 mechanism of literature, the arts of writing, engraving and printing, in 

 their various branches, and the comparison of measures with each other 

 and with different standards ; the principles of perspective will also form a 

 useful appendage to the description of geometrical instruments. The deter- 

 mination of weights, and of the magnitude of moving forces of various 

 kinds, constituting the science of statics, will be the next subject, and will 

 be followed by the consideration of the retarding force of friction, and of 

 the passive strength of the various materials that are employed in building 

 and in machinery. 



All these subjects are in part preparatory to the immediate examination 

 of the mechanical arts and manufactures, which are so numerous and com- 

 plicated as not to admit of regular arrangement without some difficulty : 

 they may howeve^ be divided into such as are principally employed for 

 resisting, for modifying, or for counteracting, any motion or force ; thus 

 architecture and carpentry are chiefly intended to resist the force of gravi- 

 tation : these comprehend the employments of the mason, the bricklayer, 

 the joiner, the cabinet maker, and the locksmith. In these departments it 

 is often of the utmost importance to the mechanic to recur, especially in 

 ! works of magnitude, to philosophical principles ; and in many other cases, 

 fo where there is no need of much calculation, we may still be of service, by 

 collecting such inventions of ingenious artists as are convenient and elegant, 

 and which, although simple in their principles, are not obvious in their 



