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17. Frank. As the pushing and pulling would be equal, no motion would be produced.
Mr. M. If this string which I take from the table can sustain just seventy-five pounds before parting, and Ida and Ella can each pull seventy pounds, can they two break the string while pulling in opposite directions?
18. Ida. Yes, sir, we should break the string with our united force of 140 pounds.
Ella. No, sir; the string will only be pulled with a force of seventy pounds, just the same as if the other end were attached to a hook in the wall, instead of being held by Ida's hand.
19. Mr. M. Most certainly you could not break the string, for the two forces act in opposite directions, and one may be called action, and the other reaction. When Ella pulls with a force of seventy pounds, Ida merely sustains that force, the same as though her end of the string were fastened to the wall. If I pull a string fastened to the wall, the wall pulls as much as I do. I must ask you to recollect these laws of motion, which seem so plain to you now, as we shall frequently have to refer to them hereafter. The picture I now show
you will illustrate the principles of the three laws, and give you some idea of momentum.
20. George. Will you have the kindness, Mr. Maynard, to give us such familiar examples as occur to you to illustrate the laws of motion?
Mr. M. With the greatest pleasure. I will relate to you some from Dr. Arnott's interesting book on Physics:
21. If a man in one boat pull at a rope attached to another, the two boats will approach. If they be of equal size and load, they will both move at the same rate, in whichever of the boats the man may be; and if there be a difference in the sizes and resistances, there will be a corresponding difference in the velocities, the smaller boat moving the faster.
22. A magnet and a piece of iron attract each other equally, whatever disproportion there may be between the masses. If the two were hanging near each other as pendulums, they would approach and meet; but the little one would perform more than half of the journey.
23. A man in a boat pulling a rope attached to a large ship seems only to move the boat; but he really moves the ship a little; for, supposing the resistance of the ship to be just a thousand times greater than that of the boat, a thousand men in a thousand boats, pulling simultaneously 12 in the same manner, would make the ship meet them half way.
24. A pound of lead and the earth attract each other with equal force, but that force makes the lead approach sixteen feet in a second toward the earth, while the contrary motion of the earth is, of course, as much less than this as the earth is weightier than one pound, and is therefore unnoticed. Speaking strictly, it is true that even a feather falling lifts the earth toward it, and that a man jumping kicks the earth away.
25. He was a foolish man who thought he had found the means of commanding always a fair wind for his pleasureboat by erecting an immense bellows in the stern. The bellows and sails acted against each other, and there was no motion. Indeed, in a perfect calm, there would be a little backward motion, because the sail would not catch all the wind from the bellows. If he had turned the bellows around, and blown astern,13 he might have moved his boat a little.
26. A ship in chase, by firing her bow guns, retards her motion; by firing from her stern she quickens it.
A ship, firing a broadside, heels or inclines to the opposite side.
A man pushing against the ground with a stick is pushed up as much as he pushes down.
27. When a child cries, on knocking his head against a table or pane of glass, it is common to tell him, and it is true, that he has given as hard a blow as he has received, although his philosophy probably, looking chiefly to results, blames the table for his head hurt, and his head for the glass broken.
28. When one billiard ball strikes directly another ball of
equal size, it stops, and the second ball proceeds with the whole velocity which the first had, the action which imparts the new motion being equal to the reaction which destroys the old.
29. But these examples are quite sufficient for our purpose. It only remains in this conversation to explain the laws of reflected motion, and what is called the composition of forces, or compound motion.
30. If a ball be dropped perpendicularly on a smooth pavement, it will rebound to a certain point in the same straight line in which it descended; but if it be thrown in some other direction against the pavement, it will not rise in a perpendicular line, but in a line having the same degree of obliquity14 as that in which it struck the pavement.
31. Thus, if the ball were dropped from a to the pavement at b, its upward course would be in the same line, ba; but if it be thrown in the line c b, it will rebound in the line bd. In this case the angle formed by the B line c b, with the line a b, is called the "angle of inFig. 3. cidence," and that formed by the line d b, with the line a b, "the angle of reflection;" and it is to be observed that these angles will always be precisely equal.
32. There are many interesting things about the composition of forces, some of which may be illustrated by the two diagrams which I show you. If two forces of equal intensity, but in opposite directions, act upon a given point, that point will remain motionless. But if the two forces act at an angle to each other, a motion is produced that is called the resultant of the two forces. Perhaps, John, you can explain the principle from these two diagrams.
33. John. I think I can. If I understand the composition of forces, a ball at a acted on by forces moving in the direc
tion of the arrows, will in each case be driven to d. In Fig. 4, however, the forces are unequal in intensity, 15 one being represented by the line a c, and the other by the line a b. But in Fig. 5 the forces appear to be equal.*
On the same principles we can determine the common resultant of many forces act
d Fig. 5.
34. Mr. M. I believe you correctly understand the theory. The operations of every-day life afford numerous examples of the motion resulting from a composition of forces. If we attempt to row a boat directly across a rapid river, the action of the oars and the action of the current will result in a diagonal motion down the stream. In the science of projectiles, or of gunnery, it is necessary to take into consideration not only the force exerted by the powder, but of gravity, or the earth's attraction, also; for the cannon ball must take the direction of what is called the resultant of these two forces. This, however, brings us to the consideration of our next subject, which is GRAVITY AND FALLING BODIES; and on that you may prepare yourselves for our next conversation.
35. Here Master John remarked that Natural Philosophy was a most delightful study, because it led the mind to think about almost every thing.
"And to think with some satisfaction, too," said George, "because it puts one in the way of learning real truths about things; and I think nothing is so satisfactory as truth."
“I would like,” said Ella, "to learn the truth about every thing in nature."
“That is a very large wish,” said Frank, "for it seems to me to be a wish to know every thing."
"And that," said John, "is what Deity alone can know." 36. This was leading to quite a long discussion upon the nature of truth, when Mr. Maynard suggested that it might be well to postpone16 the consideration of that subject until they came to the departments of Mental and Moral Philoso phy, which they would find treated in their Sixth Reader. The class then separated, and the several members proceeded to make preparations for their afternoon's rambles, which
ing on a point. Two of the forces are first taken, and their resultant found. This resultant is combined with the third force, and a second resultant found. This again is combined with the fourth force, and so on, until the forces are exhausted. The final resultant represents the conjoint action of all.
Thus, let there be three forces applied to the point a, represented in intensity and direction by the lines a b, b a c, a d, respectively. If a b and a c be combined, they give as their resultant a e; and if this resultant, a e, be combined with the third force, a d, the resultant will be af, which, therefore, represents the common action of all three forces.
were so planned by their teacher as to have in view the acquisition of new truths in some of the departments of Natural History.
1 IN-TER'-RO-GA-TORS, those who ask ques-
2 A¤-CEL-ER-A-TED, quickened in motion.
9 FRIC'-TION, the act of rubbing the surface of one body against that of another.
10 GRAV'-I-TY, weight; the tendency of a
14 OB-LIQ'-UI-TY, deviation from a perpen-
15 IN-TENS'-I-TY, degree of violence, energy, or power.
16 POST-PONE', put off; defer.
GRAVITY AND FALLING BODIES.
1. WHILE the class were on their way to the library, Miss Ida remarked that it was so pleasant out of doors that morning she wished Mr. Maynard would give them their lesson under the old oak-tree on the lawn. This suggestion was very favorably received by the class, and on arriving at the library, and making known their wishes to Mr. Maynard that he would give them an out-door lesson, he very cheerfully complied with their request. So they all proceeded to the oak-tree, where Mr. Maynard took his seat in a chair which Frank had brought for him, and the others on the rustic benches which were placed there.
2. Mr. M. On the ground you observe acorns which have fallen from the tree above us. Will you tell me why they very appropriately suggest the consideration of the subject of gravity?
Ella. Because in falling from the tree to the earth they have illustrated the great law of falling bodies; and if there had been no such law as gravity, they would have been just as likely to go upward as downward.
3. Frank. I have another reason to give. I have seen it stated that while Newton was sitting alone in his garden, the falling of an apple from a tree suggested the inquiry, "Why did the apple fall?" and that this trifling circumstance led