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standing up would elevate the centre of gravity, and that it would be much safer for all persons in the boat to keep as near the bottom of the boat as possible.
28. Mr. M. The principle that you would adopt to secure your own safety in a small boat is the same that is followed in the arrangement of the ballast and cargo of a ship. Ballast is some heavy material placed low down in the hold13 of a vessel to give it steadiness in the water.
29. George. Boys who walk on stilts, or attempt to stand on skates, can understand the importance of keeping the line of direction within the base; but I can not understand why it is so much easier to keep one's balance when moving swiftly, than when standing still.
30. Frank. I have noticed Mr. D. walks much faster after he has visited two or three grog-shops, than at other times; and I heard a person say that probably he could walk straighter by walking faster.
Ida. I know that a hoop will roll for a long time leaning much to one side, while it would fall at once if it were not in motion. 31. Ella. I think my father's gyroscope11 is the most wonderful instance of a moving body supporting itself against gravity. Here it is, now. See me spin the heavy wheel rapidly around inside of the ring. The ring, wheel, and axle remain in a horizontal position; and not only that, but they revolve around the stem on which they rest. I would Fig. 12. The Gyroscope. like to understand that.
32. John. Motion seems to play strange pranks with the centre of gravity. I know that by giving a quoit a whirling motion, I can make it strike much truer. I recollect reading of a crooked stick, called a bommerang, which the natives of Australia throw in a curved path, and even make it come around to them again.
33. Mr. M. Although you are wandering somewhat from the topic for to-day, I have listened with pleasure to the instances you have given of the curiosities of motion, and I shall not have a better opportunity than this to explain the mysteries of momentum, and show how
"The skater, motion-poised, may proudly swim
You have seen that when two forces act on a body at the same time, their united effect is represented by a single force called a resultant.15
34. John. Yes, sir, we understood that, as it was explained under the head of composition of forces.
Mr. M. Are you aware that whenever the particles of a body are moving in any direction, it requires force to change the direction of the motion?
35. John. I think this is the reason why a quoit can be thrown more accurately when it has a whirling motion. When the slaters were repairing our roof, I noticed that when they threw any of the slates to the ground, they gave them a whirling motion, and that they would strike on the edge without being broken.
36. Mr. M. The rolling of the inclined hoop illustrates my point. Gravity can not overcome the tendency of the particles to continue on in the direction which has been given to them. There is a composition of motions as well as of forces; and do you not see that the particles in the wheel of the gyroscope are revolving in a vertical plane', or direction', by the impulse given in spinning the wheel', while at the same instant the weight of the wheel tends to make it fall' ?
37. As, when two forces act on a body, it will not move in the direction of either, but in a diagonal between them, so when a body in motion is under the influence of two forces, one to retain it in the direction of its motion, and the other to change that direction, it will obey neither, but go between them, and nearer one than the other, in proportion as one force is greater than the other. As one end of the axis16 of the wheel is supported, while the other tends to fall, the force of gravity is expended in giving to the instrument itself a rotary motion in a direction opposite that of the rim of the wheel.
38. I am aware that the explanation I have attempted requires more knowledge of philosophy than I could expect from you now, and I do not suppose you to understand so
difficult a matter clearly at present, but have thought best to point out the way that will lead you to an understanding of it in future.
39. John. I think the spinning of a top in a leaning position so long a time is explained on the same principle.
Mr. M. Yes; and not only the spinning of a top, but a grand astronomical motion, which requires about 25,000 years to accomplish one revolution. Do not forget this lesson when we come to the Precession of the Equinoxes, in Astronomy.
40. But, George, when you introduced the stilts and skates into this conversation, we all walked off from the immediate subject, to which it is time to return. We were speaking of the support of the centre of gravity. Can you give any instances of stability" when the line of direction seems to fall without the base?
41. Ella. Those toys made of pith, and fashioned in the shape of soldiers, which rise up as often as we knock them down, have the centre of gravity very low down. I once had the curiosity to pick one to pieces, and found it well ballasted18 with lead.
John. Just so the "old ship righted" when the wind had blown her on her "beam ends."
Mr. M. So, you see, there is philosophy every where.
42. Ida. I always like to see the graceful motions of those prancing toy horses, which are kept from falling by a weight attached to a stiff wire, and so placed as to fall nearly under the hind feet.
Mr. M. In this case, does the horse support the weight, or the weight support the horse?
43. Frank. I think the horse supports the weight, and the centre of gravity of the whole compound figure is within the leaden ball. (Fig. 13.)
John. Then the centre of gravity is not over the base.
Frank. It is under it, and the line of direction comes in the right place. In this case the motion is a swinging one, like a clock pendulum.
44. Mr. M. The reference to the clock pendulum reminds me that our hour has elapsed, and I shall expect you to come next week with what you can prepare on the subject of MECHANICAL POWERS.
12 A'-ER-O-NAUT, one who sails or floats in the air; a balloonist.
13 HOLD, the whole interior cavity of a ship below the lower deck.
14 GY'-RO-SCOPE, an instrument for illustrating the phenomena of rotation and the composition of rotations.
15 RE-SULT-ANT, that which results from the combination of two or more.
16 Ax'-Is, that which passes through the centre of the wheel, and on which it revolves.
17 STA-BIL'-I-TY, strength to stand without being overthrown.
18 BAL'-LAST-ED, kept steady by ballast.
1. Mr. M. The topic for this lesson will certainly be an interesting one to the young ladies who wish to know about scissors and sewing machines, as well as to the lad who knows all about mills, and the one who understands the mechanical1 arrangements used in farm work; but as for Frank, who has spent his life thus far in his father's office and the Latin school, I can hardly expect that our mechanical lesson will be so pleasing to him.
2. Frank. But, Mr. Maynard, while I was reading Cæsar and Virgil, I found it necessary to know something about the mechanical powers, in order to understand the machines which the Romans used to batter down walls, and to discharge arrows, darts, and stones. I have constructed a model of Cæsar's bridge,2 from his description of it; and also models of the catapulta, ballista, and scorpio;3 and I think no one can feel more desirous to understand the mechanical than I do.
3. Mr. M. Very well; I am glad to see that you appreciate the importance of such knowledge to a correct under
The Mechanical Powers are certain instruments or simple machines employed to facilitate the moving of weights, or the overcoming of resistance.
standing of what you read. What is a simple machine, Frank?
Frank. An instrument by which weights can be raised, resistance of heavy bodies overcome, and motion communicated to masses of matter.
4. Mr. M. A very good definition. How many primary* mechanical powers are there?
John. Three; the lever, pulley, and inclined plane.
Mr. M. That is the division I prefer, as the wheel and axle, the wedge, and screw, are modifications of the first three. What is a lever?
George. A lever is an inflexible bar, supported on a point called a fulcrum," about which it moves freely.
5. Mr. M. I like to have you give the definitions so clearly. In the cut which I here show you, you see a man trying to move a heavy stone. Here L is the lever, F the fulcrum, W the weight. By pressing down at the end L, the other end of the lever raises W, the weight. The centre of motion is at F, the fulcrum. In other words, the power or force resting on the prop or fulcrum overcomes the weight or resistance. Thus, if the lever be under the centre of gravity of the weight, and the length of the lever from the fulcrum be twice as long as the other part, a man can raise the weight one inch for every two inches he presses down the end of the lever.
6. I wish you to notice that there are four things to be considered, viz., the power applied, and its distance from the fulcrum; also the weight or resistance, and its distance from the fulcrum. Now if the stone weighs 500 pounds, and is two feet from the fulcrum, how much power must the man apply, at a distance of five feet from the fulcrum, in order to move the stone?
7. John. I have learned that in all such cases the product of the weight by its distance is equal to the product of the power by its distance; therefore I find the required power to be 200 pounds.