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163. There are no titles, no orders of nobility, nor privileged orders of any kind in the United States. Merit alone it is considered ought to distinguish men. Nor is there any established religion here: every man is allowed to worship Almighty God according to the dictates of his own conscience. Well may the exclaimation of the Mantuan poet be applied to these people: “O fortunatos nimium, sua si bona norint."
IX. Of the Mechanical Powers. 164. Without the aid of art, man could not raise massy stones to the tops of churches and palaces; he could not apply immense beams of timber to his purposes ; in short, he would still have been a builder of huts and cottages. He however, soon discovered the use of a lever; and the principle of that power he soon applied, in various shapes.
Obs.-A lever is the foundation of all the mechanical powers. It is nothing more than a straight stick or bar of wood or iron; and any common lever may be applied in an instant to any object by way of experiment:poker, a fire-shovel, or strong walking-stick, for the purpose of illustration, is as good a lever, as any that could be made. Lay a shovel across a fender, and put a large eoal into it, then balance the coal with the hand at the other end of the shovel; in this situation, the shovel is a lever, the fender is the fulcrum, the coal is the weight or resistance, and the hand is the power to raise and overcome it.
165. The force with which any body moves is called its momentum. If a boy walk at the rate
of two miles an hour, and go against a wall, he will strike it with a sensible
force or momentum ; if he walk at the rate of four miles an hour, and go against it, he will strike it with double the force; or if he run at the rate of six miles an hour, he will strike it with three times the momentum.
Obs.--Every child that throws a ball, or shoots a marble, is sensible that its force or momentum is in proportion to its velocity; the same marble will hit twice as hard, he will tell you, if it move twice as fast, or ten times as hard, if it move ten times as fast. Let him substitute the word momentum for hard, and velocity for fast, and he will at once understand the principle of the mechanical powers.
166. If á man, twice the weight of the boy, go with the same degree of swiftness, or with the same velocity as the boy; he will go against the wall with twice the momentum of the boy in every instance. Hence, it is a general rule, which must not be forgotten, that the momemtum is always in proportion to the combined or united size and velocity of the forces employed.
Obs.-A marble, twice the size of another, thrown with equal velocity, will strike with twice the force, and this is all that need be understood. Any one who has learnt the multiplication-table, may easily calculate forces or momenta: a ball of two pounds weight, moving with a velocity of six miles an hour, will strike with a momentum which may be represented by two multiplied by six, producing twelve; and a 'ball weighing six pounds, and moving at the rate of eight miles an hour, will have a momentum equal to six multiplied by eight, producing 48: hence, those two balls move with separate momenta equal to 12 and to 48; or, in simpler terms, one moves with four times the force of the other.
167. If a stone weighing 500 pounds, is to be raised one foot by a man, who can lift only 100
pounds, he cannot raise it, unless he can contrive to make his arm move five feet, while the stone moves only one foot; because 100 multiplied by five, is equal to 500 multiplied by one.
168. This increase of motion in the arm is effected by the lever; because the motion of one end is in the same proportion to the motion of the other, as the distance of the two ends are from the fulcrum.
If a lever, six yards in length, be laid on a fulcrum, at one yard from one end, and the above. named stone be fixed to that end; the hand which pulls at the long, or five yards' end, moves over five times the space that the other end does; consequently, though pulling but 100 pounds, it will be equal to 500 pounds at the short end of the le
169. The grand principle then of mechanics is this,—that we gain in power, what we lose in motion ; and hence, the strength of one man could move the earth, if he could bring his strength to act upon it with such a velocity, as there is difference betwixt his power and the weight of the earth.
Obs. The property of the simple lever is exemplified in the steelyard used by butchers for weighing meat; and in the iron crow.
170. Single pulleys merely improve the pur chase ; but compound pulleys enable the hands of those who pull them, to move over twice the space according to the number of pulleys; hence, two acting pulleys increase the power four times, and three
increase it six times. 171. A force applied to the circumference of a Yarge wheel, as water, wind, and the feet, or
strength of men and horses, gains power in the proportion of the diameter of the wheel to the axle.
If a water-wheel be 12 feet in diameter, and turn an axle of one foot, the powers acting at the circumference of the large wheel, movės over twelve times the space which the circumference of the axle movės ; hence 12 cwt. may be raised with the
of one cwt. Obs.-All windlasses, cranes, mills, windmills, and watermills, are formed on this principle. The power, whatever it be, is applied to the circumference of a large wheel, whose circumference moves in consequence, perhaps, ten miles an hour, while its axle, one tenth of the diameter, moves but one mile an hour; consequently, the strength of one man at the circumference, will be equal to that of ten men at the axle.
€172. Inclined planes, or sides of hills, wedges, screws, jacks, &c., are all used in mechanics on the same principle: their power depends on the proportion between the height actually attained, and the length of the plane moved over.
A screw is an inclined plane; and if a lever be added to it as in presses, the power gained is so great, that a man can multiply his own strength many thouand times.
Obs. If I wish to roll a cask weighing six hundred weight, on an elevation equal to ten feet, and my own force is but two hundred weight, it is obvious, on the above principle, that an inclined plane must be three times ten feet, or 30 feet long. If a mail-coach weighs two tons, and is drawn on level ground, by a force equal to eight hundred weight, and is to be drawn to the top of a hill which rises twenty yards in a hundred, the horses will have to pull with an additional force equal to one-fifth of the weight of the carriage, i.e. one fifth of 40 cwt., or double that with which they could draw on level. ground.
173. A body put in motion, would move for ever, if it were not for the friction of the parts, and the resistance of the air, which alone stop it. A fourth of all power is lost in machinery, from Friction and Resistance: hence, the use of oil to soften the parts.; the necessity of smooth roads for wheel-carriages; and hence, various contri. vances called friction-wheels for diminishing friction.
Obs. 1.-The principle of bodies continuing in motion after being put into it, is felt by those who are in a car. riage which suddenly stops. They are thrown forwards, owing to their not parting with the motion they have acquired. From this cause, when a ship in full sail strikes on a rock, every one on board is thrown down, and generally the masts snap in two; so when an open chaise stops from a horse falling, those in it are thrown forward; not from the position of the chaise, but owing to the motion which has been communicated to their bodies
2.-Hence also,' rollers are very useful assistants in moving heavy stones or bodies, from the little friction they create.
174. The principle of all the mechanical powers, however they are combined, is the same s that is to say, to create all the difference possible between the velocity of the power, and the velocity of that body which is to be acted upon, so as to increase the momentum of the power.
One of the most common combinations is effected by cogged-wheels; which, when turned by some power, move greater or smaller wheels, or give new directions to the force.
175. A small wheel, with eight cogs or teeth, moving another which has forty cogs, diminishes the motion of the axle of the larger wheel a fifth, and increases the power five times, and this is the common windlass.