MECHANICS. 



11 



braic notation to follow the preceding 

 very simple proof, may easily be satisfied 

 of the truth of the result by actual ex- 

 periment. 



Let us suppose that the arms p,p',p", 

 are 4, 6 and 8 inches respectively, and 

 that u\ w', w' r are I, 2 and 3 inches; 

 it will be found that a power of two 

 ounces at B will sustain a weight of 64 

 ounces at C". In this case we have the 



Fig. 17. 

 C/ C' 



product 2x4x6x8 equal to 384, and 

 the product 64 x 1 x 2 x 3 also equal 

 to 334 ; and the same would be found 

 to be true of any power and weight 

 which would balance each other. 



The demonstration which we have 

 given above of the condition of equili- 

 brium will be found to apply equally to 

 any system of compound levers. Fig. 17 

 is a system of levers of the second kind. 



r* c 



Cr" C" 



The alternate arms, beginning from the system of mixed levers, some of the first, 

 power, and those beginning from the and some of the second, kind. The 

 weight, are marked by the same letter same condition establishes the equi- 



as in fig. 16. 

 In Jig. IS, we have represented a 



librium. 



(27.) A rectangular lever is a form 



c" c" 



:\V 



Fig. 18. 



not unfrequently used, and is governed 

 by the same condition of equilibrium as 

 other levers. Such a lever is repre- 

 sented in fig. 19. The weight W is 



Fig. 19. 



suspended from the shorter arm G C or 

 w, and the power P from the longer G B, 

 or p: the condition of equilibrium is 

 evidently 



When a hammer is used for drawing a 

 nail it is a lever of this kind, G C being 

 the claw and G B the handle. In this 

 and all the other cases which we have 

 now noticed, we consider the axis, or 

 fulcrum, to pass through the centre of 

 gravity of the lever, and therefore we 

 have not attended to the effect of the 

 weight of the bar itself. 



The condition of equilibrium in the 

 rectangular lever may be verified by ex- 

 periment in a manner similar to the 

 other cases, by suspending such weights 

 as will produce equilibrium, and mul- 

 tiplying them by the lengths of the arms 

 by "which they respectively act, and 

 snowing that Pp=Vf w. 



(28.) The rectangular lever may form 

 part of a compound system, as in fig. 20 

 but the general condition of equilibrium 

 established in (7.) will still be ap- 

 plicable. 



