square inch, what will be its pressure on the area of a circle 20 inches in diameter ? Ans. 4586.73 pounds. T75. COMPOSITION AND PROPERTIES OF WATER. Water is composed of two gases, oxygen and hydrogen; there being 2 parts of hydrogen to 1 of oxygen by volume, and 8 parts of oxygen to 1 of hydrogen by weight. Hydrogen gas is the lightest of all known ponderable substances, it being 16 times lighter than oxygen, and nearly 14 times lighter than common air. One cubic foot of hydrogen gas will buoy up, or sustain in the atmosphere, a body weighing 1.16313 oz. avoirdupois; and 1,000 cubic feet would sustain in the atmosphere 72.6 pounds. It is the material used for filling balloons. It burns slowly in the atmosphere; but when burned in connection with oxygen gas, it emits a most intense heat, far exceeding that of a furnace. Water, which communicates with other water by means of a channel or pipe, will settle at the same height in all places; and its pressure at any depth is as the depth of the fluid; and it is the same in all directions: and the amount of pressure on a given surface, its depth being given, will be as the surface; that is, the pressure against the base of any vessel, in all cases, will be the same as that of a column of water in the form of a cylinder of an equal base and height. If, therefore, the base be 1 square foot, and the height or depth 1 foot, the pressure on the base will be 1,000 oz., or 62 lbs.; and at twice this depth, whatever be the form of the vessel, the pressure will be twice 1,000 oz., or 125 lbs., and so on. Thus, at the depth of 100 feet the pressure on a square foot would be 6,250 pounds, or 43.403 lbs. on a square inch. If a vessel be filled with water, and a hole or an orifice be made in the bottom or side, the water at the same depth will spout out with the same velocity, whether it be upwards, or sidewise, or downwards: and if it be upwards, it would ascend very nearly to the height of the water above the orifice, were it not for the resistance of the atmosphere. In practice, it is found that water under a pressure of 43.403 lbs. to the square inch, will spout upwards about 80 feet. A jet 5 feet high requires the pressure of a column 5 feet 1 inch; and a jet of 100 feet high requires a column of 133 feet. The resistance which any body meets with in moving through a fluid is as the square of the velocity. For example, if a body moving at the rate of 10 feet per second meets with a resistance equal to 4 pounds, if its velocity be doubled the resistance will be 4 times as great, or 16 lbs.; and if its velocity be trebled, or 30 feet per second, the resistance will be 9 times as great, or 36 lbs.; and if its velocity be increased to 40 feet per second, the resistance will be 16 times 4 pounds, and so on. Water in freezing expands with a force equal to 35,000 lbs. to the square inch, and enlarges its volume about one-seventeenth. EXAMPLES. 1. A spherical balloon filled with hydrogen gas is 30 feet in diameter; how many pounds will it sustain in the atmosphere near the earth's surface? Ans. 1,016.36 lbs. 2. A cylindric vessel 30 feet deep and 10 feet in diameter is filled with water; required the pressure on its bottom. Ans. 147,262.5 lbs. 76. ELASTICITY, OR FORCE OF STEAM. Water is converted into steam at the temperature of 212 degrees, when it enlarges its volume 1,700 times; that is, a cubic inch of water will occupy 1,700 cubic inches when converted into steam under the pressure of the atmosphere, or a pressure of 14.6 lbs. to the square inch; and its force or power of resisting pressure increases in proportion to the degree of heat communicated to the steam. The following table exhibits the force or elasticity of steam at various temperatures, one atmosphere being equivalent to 14.6 pounds to the square inch, and two atmospheres to 29.2 pounds, and so on. The pendulum is a heavy body suspended from a fixed point by an inflexible rod. If the pendulum be drawn aside from a vertical position and let fall, it will descend in the arc of a circle, of which the point of suspension is the centre. On reaching the vertical position, it will have acquired a velocity equal to that which it would have acquired by falling vertically through the versed sine of the arc it has described; and if no other than the moving force of gravity acted on the pendulum, it would ascend to a height equal to that from which it fell, and continue to vibrate in the same arc forever. Its passage from the greatest distance on one side to the greatest distance on the other is called the oscillation. CM represents the pendulum rod, and AMB the arc described by the mass or ball of the pendulum. If the ball, M, be drawn aside from its point of rest to A, and let fall, the velocity acquired by the mass at M will be equal to that which it would acquire in falling through the versed sine of the arc, AMB, or from D to M. The pendulum performs the double office of measuring time, and of determining the relative force of gravity; the lengths of pendulums, vibrating (in different parts of the earth) in the same time, being directly as the forces of gravity; and the forces of gravity, in different places, are as their respective distances from the earth's centre, due allowance being made for the diminution of the force of gravity caused by the earth's rotation on its axis, which at the equator of the force of gravity. = At the equator a pendulum 39.016 inches in length performs one oscillation in one second; and in latitude 20 degrees north or south of the equator the length of the second's pendulum is 39.0468 inches; in latitude 39 degrees it is 39.1 inches; in New York city (lat. 40° 43') it is 39.1012 inches; in latitude 44 degrees, 39.11; in latitude 50 degrees, 39.13; in latitude 60 degrees, 39.17; in latitude 80 degrees, 39.22; and at the pole, 39.281 inches. Let 2 L represent twice the length of a pendulum in feet, and d 16, the distance described by a falling body in one second, and 1.570796326, the ratio of the semi-circumference of a circle to the diameter; then will the formula 1.570796326 2 L oscillation of the pendulum, whatever its length. Or, when the length of the pendulum is given, to find how many oscillations it shall make in a given time : Say-As the pendulum's length in inches is to the length of the second's pendulum for that latitude, (viz. 39.109 inches in New England,) so is the square of the given time to the square of the required number of vibrations; the square root of which will be the number of oscillations sought. EXAMPLE. Suppose the number of vibrations in a minute is required, the length of the pendulum being 56.34 inches, and the latitude 50 degrees. Ans. 50 oscillations. To find the length of a pendulum that shall perform any number of oscillations in a given time: Say-As the square of the given number of vibrations is to the square of the time in seconds, so is the length of the second's pendulum for that latitude to the length of the pendulum sought. EXAMPLE. Suppose a pendulum makes 50 vibrations in a minute, in latitude 44 degrees; required its length. Ans. 56.318 inches. 78. LAWS OF MOTION. A body acted on by a single force will describe a straight line; and its velocity will be proportionate to the amount of force applied; that is, if any force applied to a body generates any quantity of motion, double that force will produce double that motion, and treble the force treble the motion, and so on. The time of describing any space by a body moving with uniform velocity, equals the space divided by the velocity; and the velocity equals the quotient of the space divided by the time. It is assumed, that every body in motion has the power of communicating motion to another body. The degree of this |