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so continual, that, notwithstanding their being polished and oiled, a considerable degree of friction is produced. It is a remarkable circumstance, that there is generally less friction between two bodies of different substances than of the same. It is on this account that the holes in which the spindles of watches work, are frequently made of jewels; and that when two cog-wheels work in one another, the cogs of the one are often made of wood, and the other of metal.
There are two modes of friction; the one occasioned by the sliding of the flat surface of a body, the other by the rolling of a circular body. The friction resulting from the first is much the more considerable ; for great force is required to enable the sliding body to overcome the resistance which the asperities of the surfaces in contact oppose to its motion, and it must be either lifted over, or break through them; whilst, in the other kind, the friction is transferred to a smaller surface, and the rough parts roll over each other with comparative facility. Hence it is, that wheels are often used for the sole purpose of diminishing the resistance of friction. When, in descending a steep hill in a carriage, we fasten one of the wheels, we decrease the velocity of the carriage, by increasing the friction, that is to say, by converting the rolling friction of one of the wheels into the dragging friction ; and when casters are put to the legs of a table, the dragging is converted into the rolling friction.
A fly-wheel, which is a large heavy wheel attached to the axis of one of the principal wheels of the machinery in steam-engines and other large machines, acts in the first instance as a heavy weight to impede their free and uncontrolled motion. However paradoxical this mode of improving machinery may appear, it is, nevertheless, of great advantage. The motion of a machine is always more or less variable. Whether the power consists in wind, water, steam, or the strength of animals, it cannot be made to act with perfect regularity, nor can the work which the machine has to perform be always uniform. Yet in manufactures, and most cases
in which machinery is employed, uniformity of action is essentially requisite, both in order to prevent injury to the machine, and imperfection in the work performed. The fly-wheel answers this purpose, by regulating the action of the machine ; by its weight it diminishes the effect of increased action, and by its inertia it carries on the machine with uniform velocity when the power transiently slackens; thus, by either checking or impelling the action of the machine, it regulates its motion so as to render it tolerably uniform.
There is another circumstance which diminishes the motion of bodies, and which greatly affects the power of machines ; this is the resistance of the medium in which a machine is worked.
All fluids, whether of the nature of air, or of water, are called mediums : and their resistance is generally proportioned to their density; for the more matter a body contains, the greater the resistance it will oppose to the motion of another body striking against it. It is, therefore, more difficult to work a machine under water than in the air. If a machine could be worked in vacuo, and without friction, it would be perfect; but this is unattainable. A considerable reduction of power must, therefore, be allowed for the resistance of the air.
THE EARTH'S ANNUAL MOTION.
In attempting to give some general notions on astronomy, we shall not begin by entering into an explanation of the system of the celestial bodies, but select that portion which is most interesting to us, the earth, and when we have formed a distinct idea of the part which it performs in the general system, we shall be able to form some conception of the grandeur and
immensity of the universe. Let us suppose the earth at its creation to have been projected forwards. We know, from the laws of motion, that if no obstacle impeded its course it would proceed interminably in the same direction, and with a uniform velocity. Let A represent the earth, and s the sun. We shall suppose the earth arrived at the point in which it is represented in the figure, having a velocity which would carry it on to B in the space of one month ; whilst the sun's attraction would bring it to c in the same space of time. Reasoning upon the laws of uniform motion we might hastily conclude that the earth would move in the diagonal A D of the parallelogram A B D C, as a ball struck by two forces will do. But the force of attraction is continually acting upon our terrestrial ball, and producing an incessant deviation from a course in a straight line, and thus converts it into a course in a curve line.
Let us detain the earth a moment at the point D, and consider how it will be affected by the combined action of the two forces in its new situation. It still retains its tendency to fly off in a straight line ; but a straight line would now carry it away to F, whilst the sun would attract it in the direction D s. In order to know exactly what course the earth will follow, another parallelogram must be drawn in the same manner as the first; the line D F describing the force of projection, and the line d s that of attraction; and it will be found that the earth will proceed in the curve line D G drawn in the parallelogram D F G E ; and if we go on throughout the whole of the circle, drawing a line from the earth to the sun, to represent the force of attraction, and another at a right angle to it, to describe that of
projection, we shall find that the earth will proceed in a curve line passing through similar parallelograms till it has completed the whole of the circle. The attraction of the sun is the centripetal force, which confines the earth to a centre; and the impulse of projection, or the force which impels the earth to quit the sun and fly off, is the centrifugal force.
We have described the earth as moving in a circle, merely to render the explanation more simple, for in reality the centripetal and centrifugal forces are not so proportioned as to produce circular motion ; and the earth's orbit or path round the sun, is not circular but elliptical or oval.
Let us suppose that when the earth is at A, its projectile force does not give it a velocity sufficient to counterbalance that of gravity, so as to enable these powers conjointly to carry it round the sun in a circle ; the earth instead of describing the line A c, as in the former figure, will approach nearer the sun in the line A B. Under these circumstances it will be asked, what is to prevent our approaching nearer and nearer the sun till we fall into it; for its attraction increases as
we advance towards it. There also seems to be another danger.
As the earth approaches the sun, the direction of its motion is no longer perpendicular to that of attraction, but inclines more nearly to it. When the earth reaches that part of its orbit at b, the force of projection would carry it to D, which brings it nearer the sun instead of bearing it away from it; so that being driven, by one power, and drawn by the other towa this' centre of destruction, it would seem impossible for us to escape. But with God nothing is impossible. The earth continues approaching the sun with an accelerated motion till it reaches the point E ;
when the projectile force impels it in the direction E F. Here then the two forces act perpendicularly to each other, and the earth is situated as in the preceding figure, yet it will not revolve round the sun in a circle for the following reasons. The centrifugal force increases with the velocity of the body; or, in other words, the quicker it moves the stronger is its tendency to fly off in a right line. When the earth arrives at E, its accelerated motion will have so far increased its velocity and consequently its centrifugal force, that the latter will prevail over the force of attraction, and drag the earth away from the sun till it reaches g. It is thus that we escape from the dangerous vicinity of the sun ; and as we recede from it, both the force of its attraction, and the velocity of the earth's motion diminish. From G, the direction of projection is towards y, that of attraction towards s, and the earth proceeds between them with a retarded motion, till it has completed its revolution. Thus the earth travels round the sun, not in a circle, but an ellipsis, of which the sun occupies one of the foci ; and in its course the earth alternately approaches and recedes from it, so that what at first appeared a dangerous irregularity, is the means by which the most perfect order and harmony are produced. The earth, then, travels on at a very unequal rate, its velocity being accelerated as it approaches the sun, and retarded as it recedes from it.
That part of the earth's orbit nearest the sun is called its perihelion, that part most distant from the sun its aphelion. The earth is about three millions of miles nearer the sun at its perihelion than at its aphelion. Some are surprised to learn that during the height of our summer, the earth is in that part of its orbit which is most distant from the sun, and that it is during the severity of winter that we are nearest to it. The difference, however; of the earth's distance from the sun in summer and winter, when compared with its total distance from the sun, is but inconsiderable, for three millions of miles sink into insignificance in comparison of 95 millions of miles, which is our mean distance from the sun. The change of temperature,