MECHANIC POWERS. 25 



or to raise great weights to small heights, in order 

 to get ropes under them, or other means of raising 

 them to still greater heights. 



ABC (Plate 1. fig. 6.) is this lever; in which B 

 is the fulcrum, A the end at which the power is 

 applied, and C the end where the weight acts. 



To find when an equilibrium will take place be- 

 tween the power and the weight, in this as in every 

 other species of lever, it is necessary to recur to 

 what has formerly been mentioned, that when the 

 momenta, or quantities of force, in two bodies were 

 equal, they would balance each other. Now, let us 

 consider when this will take place in the lever. Sup- 

 pose the lever A B (fig. 70 to be turned on its axis, 

 or fulcrum, so as to come into the situation D C ; 

 as the end D is farthest from the centre of motion, 

 and as it has moved through the arch A D in the 

 same time as the end B moved through the arch 

 B C, it is evident that the velocity of A B must 

 have been greater than that of B. But the mo- 

 menta being the products of the quantities of mat- 

 ter multiplied into the velocities, the greater the 

 velocity, the less the quantity of matter need be to 

 get the same product. Therefore, as the velocity 

 of A is the greatest, it will require less matter to 

 produce an equilibrium than B. 



Let us next see how much more weight B will re- 

 quire than A, to balance. As the radii of circles 

 are in proportion to their circumferences, they are 

 also proportionate to similar parts of them ; there- 

 fore, as the arches A D, C B, are similar, the ra- 

 dius, or arm, D E, bears the same proportion to 

 E C that the arch A D bears to C B. But the 

 arches A D and C B represent the velocities of the 

 ends of the lever, because they are the spaces 

 which they moved over in the same time; therefore 



