Puslapio vaizdai

CHARLES. Will you now, Papa, explain the Mechanical


Father. I will: and you must bear in mind four things: 1st, that the power acting may be either the effort of men or animals, springs, weight, steam, &c.; 2. The resistance to be overcome by the power, is the weight or object to be moved; 3. The point about which all the parts of the body move is the prop or fulcrum; 4. Observe the respective velocities of the power, and of the resisting body. But first, I hope you have not forgotten what the Momentum of a body is.

Ch. No, Papa: It is that force of a moving body which is estimated by the weight, multiplied into its velocity.

Fa. May a small body, therefore, have an equal momentum with one much larger?

Ch. Yes, provided the smaller body move much swifter than the larger one, as the weight of the latter is greater than that of the former.

Fa. What do you mean when you say that one body moves swifter, or has a greater velocity than another?

Ch. I mean that it passes over a greater space in the same time. Your watch will explain my meaning. The minutehand travels round the dial-plate in an hour; but the hourhand takes twelve hours to perform its course; consequently the velocity of the minute-hand is twelve times greater than that of the hour-hand; because, in the same time, (viz. twelve hours) it travels over twelve times the space that is gone through by the hour-hand.

Fa. But this can be true only on the supposition that the two circles are equal. In my watch, the minute-hand is longer than the other, and consequently the circle described by it is larger than that described by the hour-hand.

Ch. I see at once that my reasoning holds good only in the case where the hands are equal.

Fa. There is, however, a particular point of the longer hand, of which it may be said, with the strictest truth, that it has exactly twelve times the velocity of the extreme point of the shorter hand.

Ch. That is the point at which, if the remainder were cut off, the two hands would be equal. And, in fact, every dif ferent point of the hand describes different spaces in the same time.

Fa. The little pivot on which the two hands seem to move

(for they are really moved by different pivots, one within another) may be called the centre of motion, which is a fixed point; and the longer the hand is, the greater is the space described.

Ch. The extremities of the vanes of a windmill, when they are going very fast, are scarcely distinguishable, though the separate parts, nearer the mill, are easily discerned. This is owing to the velocity of the extremities being so much greater than that of the other parts.

Em. Does not the swiftness of the round-abouts which we see at fairs depend on the same principle; viz. the length of the poles upon which the seats are fixed?

Fa. Yes; the greater the distance at which these seats are placed from the centre of motion, the greater is the space which the boys and girls travel for their halfpenny.

Em. Those in the second row then, had a shorter ride for their money than those at the end of the poles.

Fa. Yes; shorter as to space, but the same as to time. In the same way, when you and Charles go round the gravel walk for half an hour's exercise, if he run, while you walk, he will, perhaps, have gone six or eight times round in the same time that you have been but three or four times. Now, as to time, your exercise has been equal; but he may have passed over double the space in the same time.

Ch. How does this apply to the explanation of the mechanical powers?

Fa. You will find the application very easy. Without clear ideas of what is meant by time and space, it cannot be expected that you could readily comprehend the principles of Mechanics; but let us proceed :

There are six Mechanical powers: the Lever; the Wheel and Axle; the Pulley; the Inclined-plane; the Wedge; and the Screw; and one or more of them will be found employed in every machine; in fact, the great body of mechanism to be seen in our largest manufactories may be resolved into some one or more of these six powers.

Em. Why are they called Mechanical Powers?

Fa. Because by their means we are enabled mechanically to raise weights, move heavy bodies, and overcome resistances, which, without their assistance, could not be done.

Ch. But is there no limit to the assistance gained by

these powers? I remember reading of Archimedes,' who said that with a place for his fulcrum, he would move the earth itself.

Fa. Human power, with all the wonderful assistance which art can give, is yet very limited, and upon this principle, that “what we gain in power we lose in time." For example: if by your own unassisted strength you are able to raise fifty pounds to a certain distance in one minute, and if by the help of machinery, you wish to raise 500 pounds to the same height, you will require ten minutes to perform it: thus you increase your power ten-fold, but it is at the expense of time; or, in other words, you are enabled to do, with one effort, in ten minutes, that which you could have done in ten separate efforts in the same time.

Em. The importance of mechanics, then, is not so great as we might imagine it to be at first sight; as there is no real gain of force acquired by the mechanical powers.

Fa. You must consider that, although there be not any actual increase of force gained by these powers; the advan. tages which men derive from them are inestimable. Suppose, for example, that several small weights, manageable by human strength, are to be raised to a certain height, it may be fully as convenient to elevate them one by one as to take the advantage of the mechanical powers, in raising them all at once; because, as we have shown, the same time will be necessary in both cases: but suppose you have a large block of stone, of a ton weight, to carry away, or a weight still greater, what would you do?

Em. I did not give that a thought.

Fa. Bodies of this kind cannot be separated into parts proportionate to human strength without immense labour, nor, perhaps, without rendering them unfit for those purposes to which they are to be applied. Hence, then, you perceive the great importance of the mechanical powers; by the use of which a man is enabled to manage with ease a weight many times greater than himself.

Ch. I have, in fact, seen a few men, by means of pulleys, and seemingly with no very great exertion, raise an enormous oak into a timber-carriage, in order to convey it to its destination.

1 Archimedes, the most celebrated of the Greek Geometers, was born in Sicily, 287 R.C. He was killed when Syracuse was taken by the Romans, under Marcellus, B.C. 212, aged 75.

Fa. A very excellent instance, Charles: for if the tree had been cut into such pieces as could have been managed by the natural strength of these men, it would not have been worth carrying away for any purpose which required an extended length.

Em. I now perceive it clearly. What is a fulcrum, Papa? Fa. It is the fixed point, or prop, round which the other parts of a machine move. It is a Latin word, meaning a prop. Ch. The pivot, upon which the hands of your watch move, is a fulcrum, is it not, Papa?

Fa. Certainly it is: and you remember we called it also the centre of motion. The rivet of these scissors is also a fulcrum.

Em. Is that a fixed point, or prop?

Fa. Undoubtedly, as it regards the two parts of the scissors; for that always remains in the same position, while the other parts move about it. Again; take the poker, and stir the fire, now that part of the bar on which the poker rests is a fulcrum; for the poker moves upon it as a centre.

It must be borne in mind, that a greater force, the weight, can under no circumstances be supported by a less, the power; the fact is, that by the contrivance of the lever, a portion of the resistance is made to be borne by the fulcrum, the whole of it being divided between that point and the point of application of the power.

Are you now, my children, satisfied with the foregoing explanation of the Laws of Motion?

Ch. Yes, Papa; and besides what you have there set forth, experience teaches us that it requires the same force to destroy motion as to produce it: therefore, all bodies are inactive, so that they cannot move unless impelled, or stop unless by some force impressed on them.

Fa. Is motion perpetual?.

Ch. Yes; as regards itself; but no motion contrived by art can be perpetual, on account of the resistance of the medium.

Fa. Are the centripetal and centrifugal forces always equal?

Ch. Yes, for as they act in contrary directions, they destroy each other's effect; so that neither body is suffered to fly off nor fall in, but is continued on its own proper and acquired orbit.

Fa. Then you account for the continued motions of the heavenly bodies in this way?

Ch. Such, I find, is the opinion established by Science. The moon revolves about the earth from the same causes that the earth and other planets revolve about the sun; that is, by means of a projectile force, and a centripetal force tending to the centre of the earth.

Fa. Does this apply to all other kinds of motion?

Ch. The same principles certainly apply to all kinds of motion.

Fa. In our Ninth Conversation you were informed of the effect produced by motion on a person riding on horseback. Have you ever heard of any other example of this operation of the laws of motion?

Ch. I recollect a circumstance in point, related to me some time ago by a friend, who was present when it happened. But I never reflected till now how much it illustrates the present subject. It is this:-A troop of yeomanry cavalry had been raised in a northern district during the late war, consisting of farmers, butchers, &c., as is usual, and had become tolerably expert in their exercise; but their horses had not been sufficiently trained to execute any manœuvres with honour to themselves. Notice having been given that the reviewing officer of the district would pay them a visit on a certain day, for the purpose of inspection, the volunteers solicited the Colonel of a cavalry regiment, stationed in a neighbouring barracks, to lend them, for the important day, as many regularly trained horses as would mount them all for the review. The Colonel, smiling, complied. The yeomen were mounted. Manoeuvres began, and went on tolerably well till a charge was sounded. The gallant troop rushed on with great rapidity, sword in hand, elate with pride in their own dexterity, when, lo! the bugle suddenly sounded a halt. The dead stop of the horses at this signal, so different from anything their riders had been before accustomed to, threw most of them several feet over their heads, to the no small humiliation of the yeomanry. Fortunately, they received but little personal injury. These poor fellows had therefore such a lesson on the Laws of Motion as, I suppose, they will never forget.

Fa. I am glad to find your memory so excellent; but we will now revert to our present Lecture: you have in this be

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