A body descending in a curve suffers no loss of velocity.

122. By circular motion of bodies there are two effects produced; what are they?

Centrifugal force and centripetal force.

123. But what are they? What do the terms imply?

Centrifugal force implies a tendency that all bodies acquire by accumulated velocity of circular motion to fly off in a tangential line from the centre of revolution, the amount of tendency being as the square of increased velocity of the body in motion; hence the

RULE.-Multiply the square of the number of revolutions per minute by the radius of the circle in feet, by the weight of the body in any given unit of weight, and by .000331; the product is the centrifugal force in terms of the body's weight.

Ex. Suppose a body weighing 100 pounds, and describing a circle of ten feet radius, and at 300 revolutions per minute, required the centrifugal force

3002 x 10 x 100 x .000331 29.790 lbs.

Centripetal force, on the contrary, is the tendency, by reduced circular motion, to impel the weight toward the centre of rotation; as the balls of the governor of a steam-engine indicate by diminished velocity. When a body in circular motion is retained by means of centripetal force tending toward its centre of rotation, the velocity at every point of revolution is equal to that which it would acquire by falling perpendicularly through half the radius of its orbit. Consequently, if a body revolves uniformly in the circumference of a circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued uniformly.

124. What is meant by centre of gyration?

By centre of gyration is understood a certain point in a revolving body, into which the whole momentum of the mass is concentrated, and at which, or from which point, the greatest amount of power or effective force is transmitted; the distance between the centres of suspension and

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gyration is a geometrical mean between the centres of gravity and oscillation from the same point; hence, having found the distances of these centres in any proposed case, the square root of their product equal the distance of the centre of gyration. To find the centre of gyration or circle of greatest transmitting effect in a water-wheel.

RULE.-Multiply by the square of the radius twice the weight of shrouding and buckets, twothirds the weight of the arms, and the weight of the water; add the whole into one sum, and divide by twice the weight of shrouding and arms, added to the weight of water; the square root of the quotient is the distance of the centre of gyration from the centre of suspension.

Ex. Required the distance of the centre of gyration from the centre of suspension in a waterwheel 22.feet diameter, shrouding and buckets 18 tons, arms 12 tons, and water 10 tons.

22 ÷ 2 =

11 and 112 = 121

Then 18 x 2 = 36 × 121 = 4356

And 18+ 12 x 2 = 60+10=70; hence,

6534

9.6 feet from the centre of suspension.

70

125. What are logarithms?

Logarithms are artificial numbers which stand for natural numbers, and are so contrived that if the logarithm of one number be added to the logarithm of another, the sum will be the logarithm of the product of these numbers; and if the logarithm of one number be taken from the logarithm of another, the remainder is the logarithm of the latter divided by the former; and also if the logarithm of a number be multiplied by 2, 3, 4, 5, &c., we shall have the logarithm of the square, cube, &c., of that number; and, on the other hand, if divided by 2, 3, 4, 5, &c., we have the logarithm of the square root, cube root, fourth root, &c., of the proposed number; so that with the aid of logarithms, multiplication and division are performed by addition and subtraction, and the raising of powers and extracting of roots are effected by multiplying or dividing by the indices of the powers and roots.

126. What is meant by mechanic powers?

By mechanic, or mechanical powers, is commonly understood the application of certain simple machines, by which weight or resistance is overcome at a less expense of power, when time or space is disregarded. Thus a bar or lever resting upon a point or fulcrum at three-fourths distant from one end; it is obvious that the effect is as one to three, or one unit of power will equipoise three of resistance; but if the resistance is to be overcome by the power in any given time, the velocity or space passed through by the power will be three times that to which the resistance has been removed.

127. How are the mechanic powers usually distinguished.

They are almost invariably distinguished and arranged for simplicity in the following order, viz. the lever, pulley, inclined plane, wheel and axle, wedge and screw; the three first being considered primary, and the three last secondary, because partaking of the properties of the first by combi

nation.