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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 B.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
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
come acquainted with the simple mechanical powers, and learned their names. What have you to remark thereon?
Ch. I perceive, plainly, that they are calculated to perform what the strength of any animal could not effect without them; but I must confess I have not understood much of the principles on which they act; besides, nothing has been said in respect of the motion of weight.
Fa. What have you gathered from the authors you have read on that point.
Ch. I understand that the body which is moved, or hindered from moving, is the weight. That which moves or sustains the weight is called the power. By the action of the weight we are not to understand the motion of its centre of gravity in a horizontal line, nor the circular motion of the parts about the centre of gravity: for, in both these cases the gravitation of the body is no impediment to its motion. The motion of the weight is merely the ascent or descent of its centre of gravity.
But are there not, Papa, distinct centres to be considered in connexion with Mechanics in general?
Fa. Yes; there are three centres. First, the centre of magnitude of a body, which is a point taken as nearly as possible at an equal distance from all the outward parts. ondly, the centre of motion of a body, which is any point whereon the body may rest, or about which it may move. Thirdly, the centre of gravity of a body, which is a point whereon all the parts of the body balance each other; so that if this point be made the centre of motion, the body may be placed and continued at rest in any situation.
Ch. Can any body stand or retain its position upon either a horizontal or inclined plane suspended, unless a perpendicular proceeding from the centre of gravity fall within the base?
Fa. No. In all suspended bodies at rest upon any centre of motion, the centre of gravity is either directly over or directly under the centre of motion.
1. What do you mean by the momentum of a body?
2. Can you make a small body have a momentum equal to a large one?
3. What is meant by one body having a greater velocity than another?
4. Illustrate this by the motion of the hands of a watch.
Joyce's Scientific Dialogues.
5. How much slower does the hourhand travel than the minute-hand?
6. Does every part of the minute-hand travel twelve times faster than the hourhand?
7. What mean you by the centre of motion of a watch?
8. What parts of the vanes of a windmill move the fastest?
9. Whether does the boy in the outer seat of the round-abouts or the one in the inner seat get the longest ride?
10. Name the six Mechanical powers. 11. What limits the assistance gained by these powers?
12. Explain by an example what you mean by the phrase "what we gain in power we lose in time."
13. What is meant by a fulcrum ? 14. What is the fulcrum of a watch? 15. Why is the pivot on which scissors move, called a fulcrum ?
16. When you stir the fire with a poker, what forms the fulerum?
17. By means of what forces do the heav. enly bodies move round their centres ?
18. What made the Colonel of the cavalry regiment smile on lending his regularlytrained horses to the yeomanry?
19. When the bugle suddenly sounded a halt, what happened to these gallant soldiers?
20. What mean you by the centre of magnitude cf a body? what, by the centre of motion of a body? what, by the centre of gravity of a body?
VI. THE HAND OF GOD IN HISTORY.
THE Scriptures are full of illustrations of the truth, that God overrules, for the advancement of Christ's kingdom and glory, all the affairs of men, and, perhaps, it might be a profitable exercise for you, my dear scholars, to search the Bible at home, for instances of this cheering truth, in the history of the individuals there spoken of, and also of the nations. You will find the history of Joseph, recorded in Genesis; of Moses, in Exodus; of David, in I. Samuel. I will just inform you here, that Law. rence Koster, a man of Haarlem, a town in Holland, four centuries ago, (1430) discovered the art of printing, while amusing himself with cutting letters in the bark of a tree, and making impressions of them on paper. Claudius Ptolemy, spoken of in the lesson, was a celebrated astronomer and geographer of Egypt, who lived about 160. B.C. He was the author of that solar system which considered the Earth as the central point of the heavens. His work on Geography was used as a manual for centuries.
It cannot but interest the pious mind, and confirm the wavering, doubting soul, and quell the rising fears of unbelief, and give confidence in God's purposes and promises, and foster a delightful anticipation of the certain triumph of Christ's kingdom on earth, to see how, out of small beginnings, God is wont often to bring the most stupendous results; setting at naught the wisdom of man; ordering strength out of weakness, and making the most wonderful effects follow the most unlikely and insignificant causes. The following instances will further illustrate the mode of providential agency in carrying out the great work of human salvation:
It was a small matter that Joseph should dream a dream; or that the daughter of Pharaoh should discover, while bathing in the Nile, an ark of rushes, floating on the river; or that the same casualty should befall Daniel which fell to the lot of many a noble youth of that day, to be transported from his native hills of Palestine to an unwelcome captivity in Babylon. Each of these seemingly unimportant incidents was the first link in a chain of stupendous events. Great and noble purposes were answered by the captivity of Joseph in Egypt, and of Daniel in Babylon; and, perhaps, to no mere man that ever lived, has the Church and the world been so