CHAMBERS'S INFORMATION FOR THE PEOPLE. 



will balance a weight of two pounds at W. And 

 if the arms are in any other proportion if, for 



example, AF were 

 FA jr made seven feet 

 long, while FB were 

 W D only two feet ; then 

 Fig. 2. two pounds at P 



would balance seven 



pounds at W. In general, the power and the 

 weight are to one another inversely as their dis- 

 tances from the fulcrum. From this it follows, 

 by the well-known property of proportion, that 

 the weight multiplied by its distance from the 

 fulcrum, is equal to the power multiplied by its 

 distance 



It looks at first sight like magic that a weight 

 of one pound should be made .equal in effect to 

 one of two pounds. It seems as if the lever gave 

 us the means of multiplying force to any amount ; 

 as if the strength of a boy might be put on a 

 footing with that of a man. It is necessary to get 

 over this false impression. There is no creation 

 or multiplication of force in the lever, or in any 

 other machine, as will appear from the following 

 considerations. If we suppose the power slightly 

 increased beyond what is necessary to balance the 

 weight, it will begin to descend ; but in descending 

 six inches, for example, it will raise W only three 

 inches, as represented in fig. i. What is thus 

 gained in one way, is lost in another ; if we make 

 a small force raise a great weight, the force must 

 be exerted through a proportionally great space. 

 One pound will lift ten pounds ; but to lift the 

 ten pounds through one foot it must descend ten 

 feet. The two weights, when thus in motion, have 

 equal momenta ; the power multiplied into its 

 velocity, is equal to the weight multiplied into its 

 velocity. Since the velocities are in proportion to 

 the distances from the centre of motion, this is the 

 same as to say, the power multiplied into the 

 length of its arm, is equal to the weight multiplied 

 by its arm. 



The comparative spaces through which P and 

 W would move in the first instant of time if their 

 equilibrium were disturbed, are called their virtttal 

 velocities ; and the principle that when P and W 

 balance each other, P multiplied by its virtual 

 velocity is equal to W multiplied by its virtual 

 velocity, is called the Golden Rule of Mechanics, 

 and is true net only of the lever, but of all the 

 other simple machines. This is otherwise, and 

 perhaps better, expressed by saying, that the rate 

 of doing work during the movement is the same 

 in the case of the two forces. 



The law stated above namely, that the weight 

 multiplied by its distance from the fulcrum is 

 -equal to the power multiplied by its distance, 

 furnishes an easy rule for finding what force is 

 necessary to move a given weight, with a given 

 length of lever ; or what weight a given force will 

 move. 



Example i. Suppose a log of wood, weighing 

 a ton, or 2240 pounds, has to be raised by a lever 

 whose arms are 20 feet and 3 feet respectively, 

 what force must act on the longer arm ? Here 

 the product on the one side is 2240 X 3 = 6720 ; 

 what number multiplied by 20 will produce the 

 same product? This is found by dividing 6720 

 by 20. The quotient 336 is the number of pounds 

 at the long arm, that will balance 2240 pounds at 

 the short one. 



Example 2. Two boys, the one 80 pounds and 

 the other 60 pounds weight, are playing at see- 

 saw with a beam 28 feet long ; what point of the 

 beam must rest on the support ? The beam must 

 evidently be divided by the fulcrum in proportion 

 to the weights, that is as 80 to 60, or as 8 to 6 ; 



which is done thus : 8 + 6 : 8 : : 28 : 



28 X 8 



16 



feet, the long arm. The short arm is therefore 

 28 - 1 6 = 12. The products on both sides will 

 be found equal ; 16 X 60 = 960, and 12 X 80 = 

 960. 



The power does not necessarily act at the long 

 arm of the lever. The larger weight W (fig. 2) 

 may be used to raise the less P, as well as P to 

 raise W. When the power acts at the short arm, 

 it requires, of course, to be greater in amount than 

 the resistance it has to overcome ; but a small 

 motion of the power in this case makes the weight 

 move over a great space ; what is lost in power is 

 gained in velocity. This is often as great an 

 object as an increase of power. 



As yet we have represented the prop or fulcrum 

 as situated between the power and the weight. 



Fig- 3- 



Fig. 4. 



This constitutes a lever of the first kind, as in fig. 

 3. But the power and weight may be both on the 

 same side of the fulcrum. In this case, when the 

 weight is between the power and fulcrum, as in 

 fig. 4, the lever is of the 

 second kind; and when 

 the power is between the 

 weight and fulcrum, as in 

 fig. 5, it is a lever of the 

 third kind. 



These different arrange- 

 ments make no alteration 

 in the principles already 

 laid down. The effect of 

 each of the forces, P and 

 W, is still measured by 

 its distance from the ful- 



Fig. 5- 



crum. This distance forms its leverage or advan- 

 tage ; and the greater the leverage of either force, 

 so much less does it require to be to balance the 

 other. 



The following are examples of implements which 

 act, more or less, on the principle of the lever, 

 beginning with the lever of the first kind. 



When the common spade is used in delving, 

 the blade is first forced into the soil by the foot, 

 the handle is then pressed back, the edge of the 

 undelved ground becomes a fulcrum, and the 

 lever-power of the long handle enables a moderate 

 pressure to dislodge the earth from its place. 

 Fig. 6 represents an equally familiar example 

 namely, a wood-sawyer or carpenter moving a log 

 of timber from its place, by means of a long pole 

 or beam of wood. Stone-masons use a lever of 



