MECHANICS. 



THIRD TREATISE. 

 Ox FRICTION AND THE RIGIDITY OF CORDAGE. 



CHAPTER I. Of resisting Forces in 

 general. 



(I). WHATEVER is capable of putting a 

 quiescent body in motion, of increasing, 

 or diminishing, the quantity of motion 

 in a moving body, or finally, of destroy- 

 ing the motion of a moving body, and 

 reducing it to a state of rest, is deno- 

 minated a force. There are two kinds 

 of forces, distinguished one from the 

 other by the effects they are capable of 

 producing. The first species are those 

 which are capable of communicating 

 motion to a body which is quiescent. 

 Such forces will manifestly be also ca- 

 pable of producing, under different cir- 

 cumstances, all the other effects enume- 

 rated in the above definition of the word 

 force. Thus it is quite evident, that the 

 same force which would give motion to 

 a body at rest, would, if applied in the 

 proper direction to a body in motion, 

 increase the quantity of motion, and if 

 applied in the opposite direction would 

 diminish it. Also, it is clear that if such 

 a force, first applied to a body at rest 

 give it motion in a certain direction, and 

 be afterwards applied to the same body 

 in the opposite direction, it will destroy 

 the motion which it had communicated, 

 and will again reduce the body to a 

 state of rest. This species of force may 

 be denominated active force, and ail 

 those forces, the properties of which we 

 investigated in our first treatise, and 

 which are prime movers, come under 

 this class. 



The second species of forces are those 

 which are capable of diminishing the 

 quantity of motion in a moving body, 

 or of totally destroying it, and reducing 

 the body to a state of rest ; but which 

 are entirely incapable either of produc- 

 ing motion in a quiescent body, or of 

 increasing the motion of a moving body. 

 Such forces may be denominated pas- 

 sive or resisting forces. Examples of 

 such forces are numerous, and indeed 



it may be truly asserted, that no motion 

 ever takes place on the surface of the 

 earth without the manifestation of the 

 effect of resisting forces. The resist- 

 ance which fluids, both elastic and in- 

 elastic, oppose to the motion of bodies 

 through them, are, perhaps, the most 

 common and striking examples of the 

 effects of these forces. The resistance 

 which a projectile suffers in its pa's- 

 sage through the air, and a solid body 

 in descending through water, are familiar 

 examples. As, however, the resistance 

 of fluids properly belongs to another 

 branch of the science, we shall not 

 notice it particularly here, but shall 

 confine ourselves to those resisting 

 forces which arise from friction, and the 

 rigidity of cordage. 



(2). It requires but little considera- 

 tion to perceive of how great import- 

 ance the knowledge of the effects of these 

 resistances is in mechanical science. In 

 our first treatise, we explained the na- 

 ture and laws of the active forces, or 

 those mechanical agents which are com- 

 monly employed in giving motion to 

 machinery. In our second treatise, we 

 explained the nature, construction, and 

 properties of the machinery, which was 

 destined to receive motion from these 

 active forces just mentioned. But in 

 this investigation, in order to disembar- 

 rass the subject of its complexity, and 

 present it to the student in the most sim- 

 ple and intelligible form, \ve considered 

 that the machines by which the active 

 forces were transmitted to the working 

 points were absolutely free from all 

 resistances ; that the surfaces which 

 moved in contact were perfectly polished, 

 and acted without friction ; that axles 

 and pivots were mathematical lines 

 and points ; that ropes were perfectly 

 flexible ; and in a word, that the effect 

 of the prime mover was absolutely 

 undiminished by any resistance what- 

 ever in its transmission through the 

 machine to the working point. None 



B 



