MECHANICS. 



ments of those which tend to turn it 

 round in the other. 



Thus, if the several weights which 

 tend to turn the lever round in one way 

 be P, P', P", and their distances from 

 the prop be p, p', p" ; and those which 

 tend to turn it in the opposite way be 

 W, W', W", W", and their distances 

 from the prop be w, w', w", w'" ; the 

 condition of equilibrium is 

 Px p + P' x p" + P"xp" =Wxw + 

 W x w' + W" x w"+ W'" x w"'. 



If the centre of gravity be not over 

 the prop, the moment G x g must be 

 added to whichever of these the weight 

 of the machine conspires with. 



(21.) Of levers of the first kind there 

 are numerous instances. Scissars, pin- 

 cers, snuffers, and all similar instru- 

 ments, consist of two levers, of which 

 the rivet by which they are united is the 

 common fulcrum. A crow-bar used to 

 raise stones and for other purposes, is a 

 lever of the first kind. A poker used for 

 raising the coals in the grate is an in- 

 stanee of this, the bar of the grate being 

 the finlcrum. 



Levers of the second kind are not so 

 frequent, yet several instances of them 

 occur. The oar of a boat is an instance. 

 In this case, the water against which 

 the blade presses is the fulcrum, the 

 boat is the weight, and the hand of the 

 rower is the power. The rudder is 

 another instance of the same kind. A 

 door turning on its hinges, or the lid 

 of a desk, are also examples ; the hinges 

 being the fulcrum ; the door, acting at 

 the centre of gravity, is the weight. A 

 chipping-knife is also an example. This 

 instrument is fixed at one end, the ful- 

 crum ; the substance to be cut is placed 

 under it, and the power is applied at 

 the other extremity. 



Levers of the third kind, having a 

 mechanical disadvantage, as we have 

 already proved, are the least common. 

 They are used only in cases where de- 

 spatch is more an object than the exer- 

 tion of great force. The most striking 

 instance of the use of levers of this kind 

 is in the structure of the limbs of 

 animals, in which the bones are so con- 

 nected at the joints as to form levers of 

 this kind. In this case their use is 

 peculiarly well adapted to the conve- 

 nience of the animal, for in almost 

 every case facility and despatch is rather 

 an object than the exertion of intense 

 force. Tongs are also an instance of 

 this species of lever; and shears for 

 shearing sheep, 



In elevating a ladder, it is first a lever 

 of the second and afterwards of the 

 third kind. While the centre of gravity 

 is between the hands that raise it and 

 the end on which it rests, it is a lever of 

 the second kind, and when the hands 

 pass the centre of gravity it becomes a 

 lever of the third kind. 



(22.) A bar supporting a weight by 

 two props acts on the principles of a 

 lever. Suppose the _prop E removed 



IW 



^ijjpv 



and replaced by a power P, as repre- 

 sented in the figure ; that power will 

 evidently represent the pressure of the 

 w r eight W on the prop B. Now, by 

 the principles already established are 



P x A B = W x A C, 

 and therefore, 



and in exactly the same manner, if P' 

 represent the pressure on the prop A, 

 we find 



p, _ w x BC 

 - w x AB- 



The pressure on each prop is therefore 

 a certain fractional part of the weight, 

 viz. that fraction whose numerator is 

 the distance of the weight from the other 

 prop, and whose denominator is the 

 distance between the props. 



It follows from. this that the sum of 

 the pressures is equal to the weight, 

 and that the weight is distributed be- 

 tween the props in the inverse propor- 

 tion of its distances from them. 



(23.) It easily follows from this, that 

 the pressure upon the fulcrum of a lever 

 of the second or third kind is equal to 

 the difference between the power and 

 weight. For if A be considered as the 

 fulcrum, W the weight, and P the 

 power ; the lever will be of the second 

 kind, and P' will be the pressure on the 

 fulcrum ; and by what we have already 

 proved, P' is the difference between W 

 and P. If P be considered as the 

 weight, and W as the power, it is a lever 

 of the third kind, and the same observa- 

 tion applies. 



If at C a fulcrum be placed presented 

 downwards, and the weight W be re- 

 moved, and in place of the props A and 



