INTRODUCTION TO MECHANICS. xxi 



Fig. 20. Fig. 21. Fig. 22. 



another point which then becomes the fulcrum. In this case the equilibrium 

 is destroyed ; the longest arm of the lever is heaviest and descends. The 

 centre of gravity is not supported because it is no longer immediately below 

 the point of suspension ; but if we can bring the centre of gravity imme- 

 diately below that point, as it is now situated, the scales will again balance 

 each other. Now if a heavy weight be placed in the scale suspended to the 

 shortest arm of the lever, and a lighter one into that suspended to the longest 

 arm, the equilibrium will be restored. It is not, therefore, impracticable to 

 make a heavy body balance a light one ; and by this means an imposition 

 in the weight of goods might be effected, as a weight often or twelve 

 ounces might thus be made to balance a pound of goods. An ingenious 

 balance called a steelyard has been invented on the principle that a 

 weight increases in effect in proportion to its distance from the fulcrum. 

 In this machine a single pound weight, for instance, answers the purpose 

 of weighing any quantity of goods, simply by moving it along the lever ; 

 for, in proportion as it recedes from the fulcrum, it will balance five, ten, 

 twenty, or- perhaps even lOOlbs. weight. The hook by which the instru- 

 ment is suspended, forms the fulcrum ; it is, for instance, two inches distant 

 from the basin which is to contain the articles to be weighed, while the 

 opposite arm of the lever extends two feet ; a small weight is suspended 

 to it, and the graduations on the lever indicate the different powers of 

 this weight according- to the situation which it occupies on the long arm 

 of the lever ; when pushed to the extremity, a weight of 51bs. is equiva- 

 lent to 60 Ibs. placed in the basin. The same steelyard, when suspended 

 by a second hook, which divides the lever with less inequality, and corre- 

 sponds with another scale of graduation, is used for weighing smaller 

 quantities of goods, and the same weight, when hung at the extremity, 

 may be equal only to 20 Ibs. placed in the basin. 



Let us now return to the balance (Jig- 22), and divesting it of the 

 basins, consider the lever simply. In this state the fulcrum is no longer 

 in the line of direction of the centre of gravity, but it is and must ever be 

 the centre of motion, as it is the only point which remains at rest while 

 the other parts move about it. When a lever is put in motion the longest 

 arm, or acting part of the lever must move with greater velocity than the 

 shortest arm, or resisting part of the lever, because it is furthest from the 

 centre of motion. When two boys ride on a plank drawn over a log of 

 wood, the plank becomes a lever, the log which supports it the fulcrum, 

 and the two boys the power and the resistance at each end of the lever. 

 When the boys are of equal weight the plank must be supported in the 

 middle to make the two arms equal ; if they differ in weight, the plank 

 must be drawn over the prop so as to make the arms unequal, and the 

 lightest boy be placed at the extremity of the longest arm, in order that 

 the greater velocity of his motion may compensate for the superior gravity 

 of his companion, so as to render their momentums equal. But we know 

 that the action of the power must be greater than the resistance in 



