12 



THE POPULAR EDUCATOR. 



finir votre lettre. 6. Je me depeche de la finir. 7. Le jardinier se 

 fache-t-il centre son frere ? 8. II se fache centre lui, quaud il ne se 

 depeche pas. 9. Depechez-vous, mon ami, il est dix lieures. 10. 

 Pourquoi ne vous de'pechez-vous pas ? 11. Je me plais a jouer, mais 

 je ne me plais pas a e^tudier. 12. Vous plaisez-vous chez moi ? 13. Je 

 m'y plais. 14. Vous rejouissez-vous de 1'arrivee de votre mere ? 15. 

 Je m'en rejouis. 16. Votre frere n'a-t-il pas tort de s'en aller si tot ? 

 17. II a raison de s'en aller, il a beaucoup a faire a la niaison. 18. 

 Vous rejouissez-vous des malheurs d'autrui ? 19. Je ne m'en rejouis 

 pas. 20. Je me rejouis de votre succes. 21. M. votre frere ne 

 s'approche-t-il pas du feu ? 22. II s'eloigne du feu, il a trop chaud. 

 23. Cette demoiselle se fache- t-elle centre vous? 24. Elle se fache d'un 

 rien (or de rien). 25. Vous plaisez-vous a Paris? 26. Je m'y plais. 

 27. Pouvez-vous vous passer de moi aujourd'hui? 28. Nous ne 

 pouvons nous passer de vous, de'pechez-vous de flnir votre ouvrage. 



MECHANICS. I. 



FOECE : ITS DIRECTION, MAGNITUDE, AND APPLICATION. 



THE aim of these Lessons is to make evident to ordinary 

 intelligent persons, who will take a little trouble, the prin- 

 ciples of Mechanics to treat that subject in a popular 

 way, yet so that the reader may form accurate notions about 

 it, and be enabled to apply it to practice in solving common 

 problems by calculation. We have much to do, but all 

 depends on the way of doing it. Study simultaneously with 



move towards the magnet, and stick to it, in the very same way 

 that the stone moves to, and sticks to, the earth until some 

 person pulls it away by a stronger force. And so likewise does 

 the electrified ball draw towards itself the small pieces of cork 

 or feather we place near it. In all these cases, you see, there is, 

 first, a body, the ball, or bolt, or stone, or iron-filing, or cork ; 

 secondly, a force applied to it ; and, thirdly, motion produced. 



But take now the lamp which hangs from the ceiling. It is 

 at rest; but the earth, by its attraction, is trying to pull it 

 down, and down it would come were we to cut the chain or rod 

 by which it is suspended. Here, then, is force again, but it 

 produces only tendency to motion. But observe further, that 

 although the lamp does not move, the chain that holds it is 

 strained by its weight. And not only is the chain strained, but 

 so is the ceiling joist to which it is attached; and, as this joist 

 rests its ends on the walls, this strain is transmitted to the walls 

 in the form of pressures on them. There is thus tendency to 

 motion, strain, and pressure produced as the effect of the force 

 applied by the earth to the lamp, but no motion. And, if any of 

 you feel a difficulty in believing in those strains, let him suppose, 

 instead of the lamp, a ton weight of iron suspended from the 

 ceiling : what will follow ? The chain will snap, or the joist, 

 or even ceiling, will give way, and down all will come on the 

 floor. They snap or give way because they are strained, beyond 

 their strength. So, in like manner, when a train stands at rest 

 on one of those great iron girder bridges that span our rivers, 



these lessons those upon Arithmetic ; for, as we proceed, a i there is tendency to motion, with strains and pressures ; the 

 knowledge of the four Common Rules of Arithmetic and of j great Earth below pulls at the train to bring it into the water ; 

 Proportion will be found essential. Any other mathematics you ' but the bridge resists, bears the pressure of the weight on it, 



and is strained throughout 

 its length besides. A more 

 familiar instance is the 

 struggle of two wrestlers. 

 No one will doubt that in 

 the contest great force is put 

 forth by each. For a mo- 

 ment they are motionless, 

 like statues ; the forces are 

 balanced, but the strain on 

 their muscles is terrific. 

 There is in each tendency 

 to motion, caused by the 

 force put forth by the other, 

 but as yet no motion. At 

 last one of the combatants 



may require, I shall teach 

 you as we go along, but the 

 amount will be small. Ob- 

 serve : accurate mechanical 

 conceptions, and the power 

 of solving mechanical pro- 

 blems by construction by 

 rule and compass or calcula- 

 tion, are the obj ects we aim at. 

 First, then, let us ascertain 

 what our science treats of. 

 ] believe it may accurately 

 be described as follows : 



MECHANICS is the science 

 of force applied to a material 

 body or bodies. 



DIAGRAM ILLUSTRATING THE APPLICATION OF FORCE. 



This let me fully explain. Mechanics is concerned about force [ prevails ; his force ends in producing motion, and his adversary 



that is its great subject. But it considers it only in the con- I falls to the ground. 



sequences which follow ita application to a body or bodies which j These examples will, I trust, be sufficient to make clear to 



must be material. A force may push through an empty point . you the account I have given you of force, namely that it is the 



of space ; but, as it can make no impression on that point, ; agency by which motion is produced in a material body, or a 



Mechanics does not consider it under such circumstances. The ! tendency to motion with pressures or strains. You will now under- 



body to which it is applied may be of any size, even an atom of j stand the reason why Mechanics is divided into two branches, 



matter, sometimes termed "a material point;" and Mechanics 

 does inquire what effect forces have on such atoms. But, in 

 the more common problems, it is concerned about bodies of 

 visible and tangible magnitude, such as a block of stone, a 

 beam of timber, a girder of iron, a cannon ball, the earth itself, 

 the moon, or the sun. 



This being clearly understood and agreed on, our next 

 question is, What is force ? I answer 



FORCE is the power, or agent, whatever be its nature, by which 

 motion is produced in a body, or a tendency to motion accom- 

 panied by strains or pressures in its parts. 



For instance, a blow is given by the bat to the cricket ball, 

 or a bolt is fired from a cannon : the blow in the one case, and 

 the exploding gunpowder in the other, furnish forces, the effect 

 of which is the motion of the ball or bolt. Steam enters the 

 cylinder of an engine, and away to work goes the machinery 

 connected with it, moving and printing this POPULAR 

 EDUCATOR. Here again is force, the elasticity of the steam, 

 and its effect is motion. A stone is let loose at the top of a 

 tower, or from a balloon, and it falls to the ground : what 

 makes it fall ? The great Earth does, which, by its attraction, 

 pulls the stone towards itself. This attraction is the force 

 producing the stone's motion. And if any of you doubt, or feel 

 any difficulty about this, let him take a magnet and put one of 

 its ends near a few loose iron-filings, scattered over a piece of 



Statics and Dynamics. Statics is the branch which treats of 

 forces which balance each other, and produce only tendencies 

 to motion with pressures and strains, and is so called from the 

 Latin word sto, which means "to stand," or "be at rest." 

 Forces which thus balance one another are said to be in equili- 

 bria, a Latin expression which denotes the balancing of equal 

 weights; and it is important that you should keep the expression 

 in memory, as we shall have frequent occasion to use it. The 

 ether branch, Dynamics, treats of force or forces which do not 

 balance.one another, but produce motion, and was so named from 

 the Greek word Swapis (du'-na-mis), power, under the mistaken 

 notion that there was more power in force when its effect is 

 motion, than when it produces strain. This, we have seen, ia 

 not the case; but the term "Dynamics" may, notwithstanding, 

 continue to be used without leading to error. The two branches 

 we may therefore define or describe as follows : 



STATICS is the branch of Mechanics in which forces are 

 considered which equilibrate, or balance one another, producing 

 tendencies to motion, with strains and pressures. 



DYNAMICS is the branch of Mechanics in which forces are 

 considered which produce motion. 



Now it so happens that, of these branches, Statics is tht 1 

 simpler and easier, and more natural for the student to 

 commence with. Questions about forces which balance each 

 other are not so complicated as those which involve motion. 



paper, and he will see how this is possible. The filings will ' The reason is, that time enters into all problems of motion, but 



