MECHANICS. 



of these suppositions, however, really 

 obtain in the practical application and 

 use of machinery ; the various sur- 

 faces which move in contact are never 

 perfectly smooth : axles are of sensible 

 thickness, and move in sockets never 

 perfectly polished ; ropes, so far from 

 being perfectly flexible, have consider- 

 able rigidity, and this rigidity is ge- 

 nerally great in proportion to their 

 strength. Art may do, and has done, 

 much to diminish the effects of these re- 

 sistances ; surfaces have been produced 

 of high polish, and various means have 

 been adopted to give them additional 

 smoothness, but still they continue to 

 be studded with small asperities, which, 

 coming constantly in opposition during 

 then 1 motion one upon another, obstruct 

 that motion, offer a considerable resist- 

 ance to the action of the prime mover, 

 and robbing that power of a great part 

 of its efficacy, send it with proportionally 

 diminished intensity to the working 

 point. It is clear, therefore, that if we 

 would estimate the real practical efficacy 

 of a machine, we should possess the 

 means of calculating the amount of 

 these resistances, and when so found, 

 we should subduct it from the effect 

 computed on the theoretical principles 

 laid down in our second treatise, where 

 no regard was had to these resisting 

 forces. The overplus of force after this 

 deduction is the only part of the effect 

 of the first mover, which can be con- 

 sidered as practically available in any 

 application of the machine. 



(3). Passive or resisting forces pro- 

 duces very different effects in Statics 

 and Dynamics, that is, in machines in a 

 state of equilibrium, and in a state of 

 motion. If the machine be in a state of 

 equilibrium, the resisting forces are said 

 to assist the power. The meaning of 

 this is, that in a real machine having 

 those resistances, a less power will be 

 sufficient to support a given weight than 

 would be necessary to support it were 

 those resistances removed. As an ex- 

 ample, suppose that a weight of two 

 pounds were placed upon an inclined 

 plane, of which the length is twice the 

 height. If there were no friction be- 

 tween the surfaces of the weight and the 

 plane, a power of one pound acting pa- 

 rallel to the plane would be necessary 

 to sustain the weight in equilibrium. 

 But if we suppose, what ah\ ays really 

 obtains, that Hie surfaces of the weight 

 and plane are subject to friction, this 

 friction conspires with the power in re- 



sisting the descent of the weight, and 

 consequently the power requisite to sus- 

 tain the weight will be less than before 

 by the amount of the friction. 



Again, suppose a weight suspended 

 from a single moveable pulley, the 

 " amount of the weight and pulley toge- 

 ther being two pounds. If the rope had 

 no rigidity, and passed without friction 

 over the wheels, the wheels themselves 

 also moving without friction, either with 

 the blocks or on their axles, the power 

 necessary to sustain the weight would be 

 one pound. But if on the other hand, the 

 rope have a stiffness which requires a 

 certain force to bend it over the wheels ; 

 if also, in passing over the wheels, the 

 roughness of its surface, and that of 

 the wheel produce a resistance from 

 friction ; and lastly, if the wheel rubs 

 against the block, the surfaces not being 

 perfectly smooth, and also is subject to 

 friction in its motion on its axis ; then 

 all these resistances require a consider- 

 able portion of the weight to overcome 

 them, and, consequently, they conspire 

 with the power in supporting the weight, 

 so that the power which will accomplish 

 this, will be less than in the former case, 

 by the total effect of the several re- 

 sistances. 



In cases of equilibrium, therefore, 

 and in the sense we have explained, the 

 power is said to be assisted by the re- 

 sisting forces. The very opposite effect 

 obtains in dynamics, or when the power 

 is used not merely to sustain the weight, 

 but to move it. Here the resisting forces 

 obviously oppose the power, and deprive 

 it of a part of its efficacy. 



Let us take the same examples. Sup- 

 pose a weight of two pounds placed 

 upon an inclined plane, whose length is 

 twice its height. If there be no friction, 

 any power exceeding one pound will be 

 sufficient to draw the weight up the 

 plane. But this will not be true, if 

 there be, as there always is, friction. 

 For a power of one pound being only 

 sufficient to sustain the body on the 

 plane without moving it when there is 

 no friction, if a small quantity be added 

 to this, that quantity may not exert suf- 

 ficient force to overcome the friction, 

 and to put the weight in motion. In fact, 

 the weight will not commence to move 

 up the plane, until such a quantity be 

 added to the power of one pound, as is 

 commensurate to the friction. When 

 this quantity precisely has been added, 

 the weight will still be at rest, but will 

 be with respect to its motion up the 



