GRAVITY.
Gravity is downward pressure, or weight, being the natural tendency of all bodies towards the centre of the earth. (Vide Gravity, Motion, Forces. [Page 320].)
Absolute gravity denotes the whole force with which a body tends downwards, as when the body is in empty space.
Specific gravity denotes the relative or comparative gravity of any body, in respect to that of another body of equal bulk, or magnitude.
Centre of gravity is that point in a body, or system of bodies, on which, if rested, or suspended, the whole would remain in a state of equilibrium about that point.
The centre of gravity of a circle, regular polygon, prism, cylinder, or sphere, is in its centre.
The centre of gravity of a triangle is found by bisecting any two of its sides, and drawing lines from the points of bisection to the opposite angles; the intersection of these lines will be the centre of gravity.
Force of gravity, or gravitation, is an accelerated velocity, which bodies acquire in falling freely from a state of rest.
1. The space through which a body will fall in feet, in any given time equals the product of the square of the time multiplied by 16·0833.
Example.—Required the space a falling body will pass through in five seconds?
16·0833 × 25 = 412·0825 feet.
2. The velocity in feet, which a body in descending freely will acquire in a given time, equals the product of the time in seconds multiplied by 32·1666.
Example.—What is the velocity acquired at the end of seven seconds?
32·1666 × 7 = 225·1662 feet.
3. The velocity in feet per second that a body will acquire, in falling through a given space, equals the square root of the product of the time multiplied by 64·3333.
Example.—The space through which a body has fallen is 201 feet; required its velocity at the end of the fall?
√64·3333 × 201 = √12931 = 1137 feet.
SPECIFIC GRAVITIES OF SEVERAL SOLID, AND FLUID BODIES.
| Air,[54] in a mean state | 1·232 | Pitch | 1150 |
| Brass, cast | 8000 | Sand[54] | 1520 |
| Brick | 2000 | Silver, standard | 10535 |
| Coal[54] | 1250 | Steel | 7850 |
| Copper | 9000 | Stone, common | 2520 |
| Cork | 240 | Tin | 7320 |
| Clay | 2160 | Water,[54] rain | 1000 |
| Earth, common | 1984 | sea | 1030 |
| Flint | 2570 | Wood—alder | 800 |
| Gold, standard | 18888 | ash, the trunk | 845 |
| Gun metal | 8784 | beech | 852 |
| Gunpowder—solid | 1745 | elm, and larch | 540 |
| ” loose | 868 | fir, Riga, & maple | 750 |
| Granite | 3000 | pine, pitch & red | 660 |
| Iron, cast | 7425 | oak | 950 |
| Lead | 11325 | walnut | 671 |
These numbers represent the weight of a cubic foot (or 1728 cubic inches) of each of the bodies in ounces (avoirdupois).
To find the magnitude of any body from its weight.
As the tabular specific gravity of the body
is to its weight in avoirdupois ounces;
so is one cubic foot (or 1728 cubic inches)
to its content in feet, or inches, respectively.
To find the weight of a body, from its magnitude.
As one cubic foot (1728 cubic inches)
is to the content of the body;
so is its tabular specific gravity
to the weight of the body.
To find the specific gravity of a body.
1.—When the body is heavier than water.
Weigh it both in water, and out of water, and take the difference:
Then,—As the weight lost in water
is to the whole or absolute weight;
so is the specific gravity of water
to the specific gravity of the body.
2.—When the body is lighter than water, so that it will not sink, annex to it another body heavier than water, so that the mass compounded of the two may sink together. Weigh the denser body, and the compound mass separately, both in water, and out of it; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater.
Then,—As the last remainder
is to the weight of the light body in air;
so is the specific gravity of water
to the specific gravity of the body.
3.—For a fluid of any sort.
Take a piece of a body of known specific gravity, weigh it both in, and out of the fluid, finding the loss of weight by taking the difference of the two:
Then,—As the whole or absolute weight
is to the loss of weight;
so is the specific gravity of the solid
to the specific gravity of the fluid.
To find the quantities of two ingredients in a given compound.
Take the three differences of every pair of the three specific gravities, namely, the specific gravities of the compound, and each ingredient, and multiply each specific gravity by the difference of the other two:
Then,—As the greatest product
is to the whole weight of the compound;
so is each of the other two products
to the weights of the two ingredients.
To find the diameter of any small sphere, or globule, whose specific gravity is given (or can be found in the Table) and weight known.
Divide its weight in grains by the number expressing its specific gravity; extract the cube root of this quotient, and multiply it by 1·9612 for the diameter.
WEIGHT OF A CUBIC FOOT OF THE FOLLOWING MATERIALS,
in pounds.
| Ash | 49 | Gravel | 120 |
| Beech | 43 | Granite | 166 |
| Birch | 49 | Brick, common | 98 |
| Box | 60 | Chalk | 145 |
| Cork | 15 | Coal, Newcastle | 78 |
| Elm | 36 | Antimony | 418 |
| Fir | 30 | Brass, cast | 525 |
| Mahogany, Spanish | 50 | Copper | 538 |
| Pine, red | 41 | Gold, pure | 1203 |
| Teak | 41 | Iron, cast, variable | 444 |
| Walnut | 41 | Lead | 717 |
| Coke | 46 | Silver, standard | 644 |
| Clay | 125 | Tin | 455 |
| Earth, loose | 95 |
By means of the foregoing table, the weight of any quantity of the materials specified (in cubic feet) may readily be found.
MOTION, FORCES, &c.
Body is the mass or quantity of matter in any material substance, and it is always proportional to its weight, or gravity, whatever its figure may be.
Density is the proportional weight, or quantity of matter in any body.
Velocity, or celerity, is an affection of motion by which a body passes over a certain space in a certain time.
Momentum, or quantity of motion, is the power, or force, in moving bodies.
Force is a power exerted on a body to move it, or to stop it. If the force act constantly, it is a permanent force, like pressure, or the force or gravity; but if it act instantaneously, or for an imperceptibly short time, it is called impulse, or percussion, like the smart blow of a hammer.
A motive, or moving force, is the power of an agent to produce motion.
Accelerative, or retardative force, is that which affects the velocity only, or it is that by which the velocity is accelerated, or retarded.
The change, or alteration of motion by any external force, is always proportional to that force, and in the direction of the right line in which it acts.
If a body be projected in free space, either parallel to the horizon, or in an oblique direction, by the force of gunpowder, or any other impulse: it will, by this motion, in conjunction with the action of gravity, describe the curve line of a parabola.
A parabola is the section formed by cutting a cone, with a plane, parallel to the side of the cone.
Gravity (vide [page 316]) is a force of such a nature that all bodies, whether light or heavy, fall perpendicularly through equal spaces in the same time, abstracting the resistance of the air; as lead, and a feather, which, in an exhausted receiver, fall from the top to the bottom in the same time. The velocities acquired by descending, are in the exact proportion of the times of descent, and the spaces descended are proportional to the squares of the times, and, therefore, to the squares of the velocities. Hence, then, it follows that the weights, or gravities of bodies near the surface of the earth are proportional to the quantities of matter contained in them; and that the spaces, times, and velocities generated by gravity, have the relations contained in the three general proportions before laid down.
A body in the latitude of London falls nearly 16-1/12 feet in the first second of time, and consequently, at the end of that time, it has acquired a velocity double, or of 32⅙ feet.
The times being as the velocities, and the spaces as the squares of either; therefore,
| if the times be as the Nos. | ||||||||||
| 1, | 2, | 3, | 4, | 5, | 6, | 7, | 8, | 9, | 10; | |
| the velocities will also be as | ||||||||||
| 1, | 2, | 3, | 4, | 5, | 6, | 7, | 8, | 9, | 10; | |
| and the spaces as their squares | ||||||||||
| 1, | 4, | 9, | 16, | 25, | 36, | 49, | 64, | 81, | 100; | |
| and the spaces for each time, | ||||||||||
| 1, | 3, | 5, | 7, | 9, | 11, | 13, | 15, | 17, | 19. | |
Namely, as the series of the odd numbers, which are the differences of the squares denoting the whole spaces. So that if the first series of natural numbers be seconds of time,
| namely: the times in seconds | 1 | 2 | 3 | 4 | &c. |
| the velocities in feet will be | 32⅙ | 64⅓ | 96½ | 128⅔, | &c. |
| the spaces in the whole times | 16 1 12 | 64⅓ | 144¾ | 257⅓, | &c. |
| and the space for each second | 16 1 12 | 48¼ | 80 5 12 | 112 7 12 , | &c. |
of which spaces the common difference is 32⅙ feet, the natural and obvious measure of the force of gravity.
Thus, a body falling from a state of rest acquires a velocity to pass through 9 spaces in the fifth second of time; 7 in the fourth; 5 in the third; 3 in the second; and 1 in the first. Thus it is 9 + 7 + 5 + 3 + 1 = 25, which shows that the whole spaces passed through in 5 seconds equal the square of 5.
The momentum, or force, of a body falling through the atmosphere is the mass or weight, multiplied by the square root of the height it has fallen through, multiplied by 8·021.
Suppose a weight of 10 tons to be raised 9 feet, and to drop thence suddenly on a bridge; the momentum is 10 × (3 × 8·021) = 240·63 tons. That is, a weight of 10 tons, so falling, would exert as great a strain to break down the bridge, as the pressure of 240·63 tons of dead weight.
Thus, a one-ounce ball falling from a height of 400 feet, would strike the earth with a momentum of
| oz. feet. | oz. | lb. |
| 1 × (20 × 8·021) | = 160·42 | = 10·026. |
By experiments to ascertain the effect of Carnot’s vertical fire, it was found that 4-oz. balls only penetrated 1 20 of an inch into deal board, and from 2 to 3 inches into meadow ground.
Amplitude signifies the range of a projectile, or the right line upon the ground, subtending the curvilinear path in which it moves.
The time of flight of different shot, and shells is equal to the time a heavy body takes to descend freely from the highest point described by the curve of the projectile.
To find the time of descent:
Divide the given height, or altitude, by 16 1 12 , and the square root of the quotient will be the time required. Thus, if the altitude is 1200 feet, and the time of descent is required,
1200 ÷ 16 1 12 = 74·61, the square root of which is 8·637, the time required.
When a body is projected vertically downwards with a given velocity, the space described is equal to the time multiplied by the velocity, together with the product of 16-1/12 by the square of the time; but, if the body is projected upwards, the latter product must be subtracted from the former.