MECHANICS. 



[Lesson IV. 



this is kept in equilibrium by a movable 

 weight p, on the other arm of the lever. As 

 the weight j> can be slipped along the lever 

 to any required point, it follows that the 



Fig. 1. 



heavier the weight is, the further must the { 

 movable weight be placed from the ful- { 

 crum a, in order to balance the weight. 



The common scale-beam for weighing 

 is another example of this class, and is 

 generally prefered to the steelyard, because 

 the subdivision of weights is more precise. 



GENERAL QUESTIONS ON LESSON III. 



1. Why is one arm of a lever usuaJly 

 longer than the other ? 



2. When a lever is balanced in its centre, 

 and equal weights placed at either end, 

 what takes place? 



3. Give me a rule, to prove that power 

 increases and diminishes with distance. 



4. How can we calculate the proper 

 power we require to employ ? 



5. Explain what is meant by units of 

 weight and distance. 



6. "Why is a short lever generally better 

 than a long one ? 



7. Explain how a see-saw acts. 



8. Explain the principle of the steel- 

 yard. 



LESSON IV. 



SUPPOSE that aline passed round a pulley, to the end of which a weight p was attached, 

 and that some force was acting in the direction ab, equal to the weight p. By the 

 theory of the parallelogram of forces, we are enabled 

 to decompose the forces meeting at a, and acting in the 

 direction a b, into lateral forces ; one of which acts in 

 the direction of d from a, being a prolongation of the 

 direction of the radius g a, while the direction of the 

 other force a e is parallel with h p. If the pulley is 

 fixed, the action of the force a d will be counteracted by 

 the resistance, altogether, of the central point g; we 

 " may therefore take away the component force which 

 is acting in the direction a d without disturbing the 

 equilibrium ; and we may replace the active force a b, 

 by its component force acting in the direction a e. If 

 the line a c represent the force p acting in the direction 

 a b, then the line a e, will give the amount of the 

 f^o- 8 - " ^3J component force P, (Fig. 9) and without working out the 



relations of size between a c and a e, or p and P, we can easily see thatP is larger than p- 

 Therefore, without disturbing the equilibrium, we may replace the force p, acting in the 

 direction a b by another force P, acting at a in a vertical instead of a lateral direction. 

 Snppose that, instead of the force P being allowed to act directly at a, we make it act 

 in any part of the line a e, we shall find that the equilibrium will not be disturbed. 

 For example, let the force P act at the point /in the line a e, where it is intersected by 

 the line ft g, and we shall then find that we have two rectangular forces p and P in a 

 state of equilibrium, at the ends of the line fh revolving round g, as in Fig. 9. The 

 two forces are unequal, as their respective points of action at / and /* are at unequal 



