On Machines in General. 827 



the figure of a machine, in order to know what effect any 

 power applied to it can produce, when we are acquainted 

 with that which it would produce without the machine : let 

 us suppose, for example, that a man is capahle of exercising - 

 a contuiual effort of 23", hy moving his own body conti- 

 nually with a velocity of three feet in the second : ibis beitig 

 granted, when we apply it to a machine, the niohientum of 

 activity F\ t, which this man wiil exercise, will be (XXXII) 

 23" 3 p' (3 feet) /, i. e. we shall have FV = 25" 3 p' t, 

 t expressing the numb^ of seconds : therefore, on account 

 of F V = q, we shall have q = 23" 3 p' /, whatever be the 

 machine : therefore the effect q is aLs'iUitely independent of 

 the fiaure of this machme, and can never surpass that which 

 the power is in a state to produce naturally, and without a 

 machine. 



Thus, for example, if this man with his effort of 23", and 

 his velocity of three feet in the second, is in a state with a 

 given machine, or without a machine, to raise, in a given 

 time, a weight p to a height H, we cannot invent any ma- 

 chine by which it is possible, with the same labour, [i.e. the 

 same force, and the same velocity as ni the first case,) to 

 raise, in the given time, the same weight to a greater height, 

 or a greater weight to the same height, or, finally, the same 

 weight to the same height, in a shorter time : this is evi- 

 dent : since then q bting (XXXII) equal to P H, we have, 

 by the preceding article, P 11 = 25" 3 p' /. 



LIV. The advantages resulting from machines do not 

 therefore consist in producing great effects from small causes, 

 but in affording the means of choosing, among different me- 

 thods which may be called equal, that which is most con- 

 venient in the existing circumstances. In order to for^^e a 

 weight P to ascend to any height proposed, a.spriiitrig dose 

 together in a given quantity, a body to assume any given 

 movement by insensible degrees, or, finally, any other Jiiveri 

 agent to produce any given momentum of activitv, the 

 moving forces employed must of themselves consume a 

 momentuni of activity equal to the first : no machine can 

 dispense with it: but as this momentum results from several 

 terms or factors, we may vary them at pleasure, by dimi- 



P 2 mshinrr 



