MECHANICS. 





Thus the mechanical efficacy of this 

 machine increases as the distance of the 

 power from the prop is increased, and 

 as the distance of the weight from the 

 prop is diminished. 



(16.) It is evident on inspection, that 

 in a lever of the second kind, the power 

 must necessarily be less than the weight, 

 since it must be farther from the ful- 

 crum ; and in a lever of the third kind it 

 must be greater than the weight because 

 it is nearer to the fulcrum. 



It appears also, that in a lever of the 

 first kind the power and weight act in 

 the same direction, both acting down- 

 wards ; while in those of the second 

 and third kinds they act in opposite 

 directions. 



In the lever of the third kind there is 

 a mechanical disadvantage, the power 

 being greater than the weight, and 

 therefore, this species of lever is never 

 used except in cases in which velocity, 

 and not power, is wanted ; for it will be 

 remembered that the velocities of the 

 power and weight are as their distances 

 from the prop (7). 



(17.) If the centre of gravity of the 

 bar itself be not over the prop, the 

 weight of the bar must be taken into 

 account. Let this be G, and let the 

 distance of the centre of gravity from 

 the prop be g. The moment of this is 

 G x g. If this force tend to turn the 

 lever in the same direction with the 

 power, the condition of equilibrium is 

 P x p + G x g = W x w. 



But if it conspire with the force of the 

 weight, the condition is 



Pxp = \Vxw+Gxg. 



If the lever be of uniform thickness, 

 its centre of gravity will be at its middle 

 point. In a lever of the first kind, the 

 whole length is equal to p + w : and 

 therefore, if H (fig. 4.) be the centre of 

 gravity, C H is equal to \ p + i w ; but 

 H G org is equal to C G H C = p ^p 

 % w = i p ic. Hence, g = k 

 (p~-w.) "That is, the distance of the 

 centre of grav ity from the prop is equal 

 to half the difference of the arms. 



In levers of the second and third 

 kinds, when they are of uniform thick- 

 ness, the distance of the centre of gra- 

 vity from the prop is half the length of 

 the arm, the lever being supposed.) 

 extend only on one side of the prop. If 

 it extend on both sides, the distance is 

 the same as in the last case. 



(18.) If the arms of the lever be not 

 straight but curved, as in//^. 7, the 

 distances p and w are the perpendicu- 



lars GB, G C, drawn from the prop 

 upon the directions of the power and 

 weight. But still the condition of equi- 

 librium remains the same, P x p - W 

 x w. (7.) 



(19.) Also, if the power and weight 

 be not parallel, as in fig. 8, the dis- 



f 



Fig. 8. 



tances p and w are the perpendiculars 

 drawn from the prop upon the direc- 

 tions of the strings which act upon the 

 lever, and which are drawn by the power 

 and weight. 



(20.) If several weights act upon dif- 

 ferent sides of the prop, as in Jig, 9, 



J5 B' 



C" 



ffi ^vQ 



or in different directions on the same 

 side, the condition of equilibrium is im- 

 mediately derived from (10.) ; viz. the 



;,i> <p' |f W ^ 



AV" AA'" 



sum of the moments of those which 

 tend to turn the machine round in one 

 direction is equal to the sum of mo- 



