32 On Machines in General. 



r — s m7id (V cosine y) ■= o ; therefore by decomposing p 

 into three other forces parallel to the three axes, if these 

 component forces are designated by p', p", p"', the preceding 

 equations will become, ihe Urst, smW p' dt + s mW' p" dl 

 + s m V"'.p" dt = smW dV + smWdV" + s m V" 

 d V'"; and the second, smu'p' d I + s m u" p" d t + 

 s m u"' p'" d t =■ s imi' dy + s m u' d V" + sm u'" d V" : 

 finally, in the case of equilibrium, the first will vanish, 

 and the second will be reduced to 5 m W p' + s m u" p" + 

 s m u"' p'" = 0. 



Second Remark. 



XXVIII. Hitherto I have regarded wires, rods, levers, &c, 

 as bodies making of themselves part of the system. And 

 this hypothesis entirely conforms to nature ; but one thing 

 indispensably necessary to observe is, that, strictly speaking, 

 there is probably no absolutely fixed point in the universe, 

 no obstacle absolutely innuovcable ; the fulcrum of a lever 

 is not so, because it is supported upon the earth, which 

 is not fixed itself; but the mass of which is almost infinitely 

 great in comparison of those the action and reaction of 

 which upon each other we generally consider in machines : 

 in order to move the hyponiochlion of a lever, we must 

 also put in motion the globe of the earth ; and it is so in 

 fact, however feeble be the powers which act upon the ma- 

 chine * : the quantity of movement which they produce upon 

 it, is equal to the resistance of the hypomochlion ; but this 

 finite quantity of movement distributing itself into a mass 

 almost infinitely great, tliere results to this mass a velocity 

 almost infinitely small, and this is the reason why this move- 

 ment is not sensible, and may be neglected in practice. 



Hence it follows, that what we call immoveable obstacles 

 in mechanics, are nothing else than bodies the mass of 

 which is so considerable, and consequently the vtlocilv so 

 small, that their movement cannot be observed. We shall 

 therefore approach nearer nature, by consideringtheobstacles,. 



* M. Carrot does not cvl.ibit here liis usual accuracy. If the power ap- 

 plied to the lever belonged to any other systcni than tJiat of the earth, the 

 earth would be moved; but in the case of the fact here assumed, it is not 

 moved, even in an ir.fmitely small degree. — Edit^ 



or 



