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Mr. M. It would be difficult for you to name any of the ordinary occupations of life without giving an instance of the utility of friction. It holds the nails and screws in our houses, enables us to walk, and even to hold knives, pencils, and books in our hands. It is increased by roughness, and it has been found that there is more friction between pieces of metal of the same kind, than between similar pieces of different metals.
5. Frank. I wonder if that was the reason why Juno's chariot wheels were of brass, and the axle of iron or steel. Homer, who is good authority on such matters, says,
"Hebe to the chariot roll'd
6. Mr. M. If I may add to Master Frank's classical allusions, I will mention that the gates of the infernal regions, according to Homer were of iron, and the threshold of brass; though, if I recollect correctly, Virgil says "they are open night and day."
7. John. I know that all machinists say that surfaces of brass and steel move upon each other easier than when both are alike.
Frank. That is just what the engineer of a steam-ship said when I was on board, and asked why he was using what he called anti-attrition metal, made from copper, antimony, and tin.
8. Ida. I see now why a jeweled watch is better than a common one. The friction is less.
Ella. When we apply oil to our sewing machines, I suppose it must be to diminish friction.
9. Mr. M. You have an excellent habit of observation, which saves me much time and trouble in giving illustrations and experiments. Useful as friction is, we sometimes try to avoid it, as in putting wheels under loads to be transported, and casters or rollers on tables and other articles of furniture.
10. John. I would like to ask a question. May not the pulley be regarded as a modification of the lever?
Mr. M. The wheel we call the pulley may be so considered, but, taken as a whole, the cord and wheel may be called the
pulley, though the term cord would be more proper. Now, as we are approaching the conclusion of the department of Philosophy called Mechanics, I would suggest that each one of you propose a question involving some of the principles which have formed the topics of our conversations.
11. Frank. I am really glad to have such an opportunity to get a solution' of my own difficulties and those of my classmates. I would like to ask if it is possible to construct a machine which, when put in motion, will never stop till it is worn out.
12. Mr. M. In other words, a perpetual motion. Thousands of dollars have been uselessly spent in vain attempts to accomplish it. I will reply to your very proper. question by reading a brief extract from Professor Loomis's Natural Philosophy. He says,
'By perpetual motion in mechanics we understand a machine which moves without ceasing, and requires no new application of force from without. A machine which renews itself (as, for example, a watch which runs for 24 hours, and then winds itself up, so as to be ready to run another 24 hours, without any assistance from beyond itself) would be such a perpetual motion as has been long sought for by visionary inventors. A machine of this kind is impossible, because no combination of machinery produces any positive increase of power."
13. A great many machines have been proposed for producing perpetual motion. Here is a drawing of one of them-a large wheel, carrying twelve equal arms, each movable on a hinge, and having at its extremity a heavy ball. But all machines for perpetual motion have failed, unless sustained by expansion and contraction from change of temperature, or electricals action in some way; and when the motion is thus sustained, it is no more perpetual motion than the paper-mill at Niagara Falls.
14. Frank. The reply satisfies me fully, and I shall report it to a good neighbor of ours who is constantly engaged in efforts to produce a perpetual motion.
John. I would like to understand what is meant by a horse-power and a unit of work.
15. Mr. M. What is called a unit of work is the labor expended in raising one pound of matter one foot in height, in opposition to gravity. The eminent engineer Watt estimated that a horse could perform 33,000 units of work in a minute; in other words, that a horse could raise 33,000 pounds to the height of one foot in a minute of time, or one pound to the height of 33,000 feet. To see if you understand my reply, I will propose a question. How many horses' power will be required to raise 500 pounds of coal per minute from a pit 330 feet deep?
16. John. The amount of work consists of the power multiplied by the distance; therefore 500 pounds raised 330 feet will be 165,000 units of work. A horse can perform 33,000 of these units in a minute; therefore I divide the whole number of units by 33,000, and get for an answer 5 horses' power. Mr. M. John has answered admirably. What question has George?
George. I wish to know if the large hind wheels of a carriage tend to push forward the small fore wheels.
17. Mr. M. They do not; hence the wheels of railroad cars are made of the same size. In carriages it is convenient to have the fore-wheels smaller, on account of turning the carriage more easily, and often for facility in getting into and out of them. Besides, the line of traction, or draft, should extend to a point lower than the horse's breast, otherwise the collar by which he draws will rise up and choke him, which would be very inconvenient for all concerned.
Ida. My question is one which I never could understand. Why can ships sail in opposite directions when driven by the same wind?
18. Mr. M. I will try to make the matter plain to you. On the opposite page is a drawing in which you will see the direction of several ships, and the position in which the wind strikes against the sails. The wind, which is here represented as blowing from the north, strikes directly against the ship at m, and she is scudding, or sailing before the wind, in the same direction the wind blows. In all the other ves
sels the sails receive the wind obliquely, or not at right angles with the keel.
19. The wind, blowing against the sail of the ship at f, the keel being kept w,N. in the same direction by the rudder, is resolved into two forces, one of which tends to drive the vessel ahead, and the other to push her sideways. If the vessel were in the form of a tub, she would move toward h, or in the diagonal of a square, provided the sail could be kept so as to receive the wind as shown at f.
20. Vessels are not round, but long; so it requires much more force to push them sideways than forward. By a proper management of the rudder, not shown in the figure, the ship can be made to sail almost against the wind. When sailing as nearly opposite or against the wind as possible, the ship is said to be close hauled, as those marked a and b.
21. Ida. The whole matter seems very plain to me now. Ella. I fear I shall not so easily understand the answer to my question, as it is perhaps beyond the capacity of a little girl; but no question is too hard to ask. Ever since I heard that philosophers had weighed the earth, I have been anxious to know how it was done.
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22. Mr. M. To understand the method pursued by those who have weighed the earth will require a fuller explanation than I have given of the action of gravity. Every particle of matter attracts every other particle, as you have learned; but the attraction is rapidly diminished as the distance increases. It is inversely 10 as the square of the distance that is, at twice the earth's radius11 from its centre gravity is one fourth what it is at the surface. In other words, a pound of matter, as weighed at the surface, would weigh only four ounces 4000 miles above the surface.
23. If a lead ball were to hang from the top of a tower, it
would be attracted a little toward the tower as well as a great deal toward the earth. Now if I can find how much the tower attracts the ball, also the weight of the tower and the position of its centre of gravity, as I know the distance of the earth's centre of gravity, I can find the weight of the earth.
Do you understand how?
Ella. I confess I am as much perplexed as ever.
24. Mr. M. I did not expect you to understand with so slight an explanation, and am glad to hear you frankly admit that you do not. That is the way to learn. If there were two globes of equal weight, as two earths, for instance, and a ball were suspended from some distant point so as to be only under the influence of the two spheres,12 toward which would it hang?
Ella. Toward neither, but half way between them.
25. Mr. M. You will soon see, then, how the earth is weighed. Let us suppose the spheres unequal; you must understand that the ball would hang nearer the heavier sphere, but still between them. If you knew the weight of one sphere, and the distance apart of the centres of both, and how much nearer the ball hung to one than to the other, could you find the weight of the other?
26. Ella. I think I see now how it could be done, and how the earth could be weighed by these principles; for, if we have the weight of one sphere, its distance from the little ball, and the power exerted by it on the ball, we know that the power exerted by the earth must bear a similar proportion to its weight and distance. It does not appear to me half so surprising as it did before that philosophers can weigh the earth; but it seems more and more wonderful that all things are governed by laws so fixed and uniform.
27. Mr. M. And the more you study Natural Philosophy, the more plain and simple will its principles seem to you, and the more enlarged will become your views of the works of the Creator. The mind that comprehends the wonderful laws, so sublimely simple and beautiful, that regulate the vast universe of worlds, must ever be deeply impressed with the conviction that there is a great and overruling mind which plan