Maximum Effect of Agents. 273 



effect ; and the principles which we have now laid down, will 

 serve to conduct us in such inquiries. 



Of the Maximum Effect of Agents and Machines. 



391 . When any power is made to act upon a given resistance, 

 by the intervention either of a simple or a compound machine, an 

 equilibrium will take place when the velocity of the power is to 

 the velocity of the resistance as the weight is to the power. In 

 this state of things, however, the machine must be actually at 227. 

 rest, and therefore incapable of performing any work. If we 

 can increase the power, the machine will move with more and 

 more velocity, and will have its motion gradually accelerated 

 as long as the power exceeds the resistance. But if from any 

 cause the power should begin to diminish, or if the resistance 

 should increase, or if both these changes in the state of the ma- 

 chine should take place at the same time, the acceleration of the 

 machine will diminish, and it will at last arrive at a state of uni- 

 form motion. Now this increase of resistance may arise in 

 many cases from an increase of friction, which often (though not 

 always) accompanies an augmentation of velocity ; or it may 

 arise from the resistance of the air, which must necessarily in- 

 crease with the velocity ; and therefore all machines are found 

 soon to attain a state of uniform motion. When an undershot 

 wheel is driven by the impulse of water, the uniformity of motion 

 to which it arrives, arises principally from the diminution of the 

 power which in this case accompanies an increase of velocity. 

 When the mass of fluid strikes one of the float-boards at rest, the 

 impulse is then a maximum. When the float-board is in motion 

 it withdraws itself, as it were, from the action of the power, and 

 therefore its mechanical effect will diminish as the velocity in- 

 creases, and if it were possible that the velocity of the wheel 

 should become equal to that of the fluid, the float-board would 

 not be struck at all by the moving water. Hence it follows, that 

 the power itself diminishes by an increase of velocity, and there- 

 fore that from this cause alone machines in general would soon 

 acquire a motion sensibly uniform. This effect will be more 

 easily understood, if we suppose an axle to be put in motion by 

 Mech. 35 



