Compendium of Natural and Experimental Philosophy 4

PLYMPTON’S PARKER’S PHILOSOPHY: A SCHOOL COMPENDIUM of NATURAL AND EXPERIMENTAL PHILOSOPHY, BY RICHARD GREEN PARKER
Index

PREFACE TO THE REVISED AND ENLARGED EDITION 1871
INTRODUCTION
DIVISIONS OF THE SUBJECT
OF MATTER AND ITS PROPERTIES
OF GRAVITY
MECHANICS, on THE LAWS OF MOTION
THE MECHANICAL POWERS
REGULATORS OF MOTION
HYDROSTATICS
HYDRAULICS
PNEUMATICS
ACOUSTICS
PYRONOMICS
THE STEAM-ENGINE
OPTICS
ELECTRICITY
GALVANISM, OR VOLTAIC ELECTRICITY
MAGNETISM
ELECTRO MAGNETISM
THE ELECTROMAGNETIC TELEGRAPH
THE ELECTROTYPE PROCESS
MAGNETO-ELECTRICITY
THERMO-ELECTRICITY
ASTRONOMY

OF GRAVITY

  1. GRAVITY. It has already been stated that matter in all its forms, whether solid, fluid or gaseous, possesses the property of attraction. This property, with its laws, is now to be particularly considered, under the name of Gravity.

What is gravity?

  1. Gravity is the reciprocal attraction of separate portions of matter.

With what force do all bodies attract each other?

A11 bodies attract each other with a force proportionate to their size, density and distance from each other [See No. 59.]

  1. This law explains the reason why a body which is not supported falls to the earth. Two bodies existing in any portion of space mutually attract each other, and would rush together were they not prevented by some superior force. Let us suppose, for instance, that two balls made of the same materials, but one weighing 11 pounds and the other weighing only one pound, were ten feet apart, but both were a hundred feet above the surface of the earth. According to this law, the two balls would rush together, the lighter ball passing over nine feet of the distance, and the heavier ball over one foot, and this they would do, were they not both prevented by a superior force. That superior force is the earth, which, being a much larger body, attracts them both with a superior force. This superior force they will both obey, and both will therefore fall to the earth. As the attraction of the earth and of the balls is mutual, the earth will also move towards the balls while the balls are falling to the earth, but the size of the earth is so much greater than that of the balls, that the distance that the earth would move towards the balls would be too small to be appreciated. **

** The earth is one quatrillion, that is, one thousand million millions times larger than the largest body which has ever been known to fall through our atmosphere. Supposing, then, that such a body should fall through a distance of one thousand feet, the earth would rise no more than the hundred billionth part of an inch, a distance altogether imperceptible to our senses.

The principle of mutual attraction is not confined to the earth. It extends to the sun, the planets, comets and stars. The earth attracts each of them, and each of them attracts the earth, and these mutual attractions are so nicely balanced by the power of God. as to cause the regular motions of all the heavenly bodies, the diversity of the seasons, the succession of day and night, summer and winter, and all the grand operations which are described in astronomy.

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  1. The attraction of the earth is the cause of what we call weight. When we say that a body weighs an ounce, a pound, or a ton, we express by these terms the degree of attraction by which it is drawn towards the earth. Therefore,

What is Weight?

  1. Weight is the measure of the earth’s attraction.*

* When we say that a body weighs an ounce, a pound, or a hundred pounds, we express, by these terms, the degree of attraction by which it is drawn towards the earth.

  1. As this attraction depends upon the quantity of matter which a body contains, it follows that

What bodies have the greatest weight?

Those bodies will have the greatest weight, which contain the greatest quantity of matter.**

** The weight of a body is not dependent solely on its size or bulk; its density must also be considered. If we take an equal quantity, by measure, of two substances,- lead and cork, for instance,- we shall find that, although both are of the same size, the lead will weigh much more than the cork. The cork is more porous than the lead, and, consequently, the particles of which it is composed must be further apart, and therefore there must be fewer of them within a given bulk; while, in the lead, the pores are much smaller, and the particles will, therefore, be crowded into a much smaller space

  1. TERRESTRIAL GRAVITY. – It has already been stated [see No. 97] that the attraction which one mass of matter has for another is in proportion to the quantity and the distance; and that, the larger the quantity of matter and the less its distance, the stronger will be the attraction. The law of this attraction may be stated as follows:

What is the law of attraction?

  1. Every portion of matter attracts every other portion of matter with a force proportioned directly to the quantity, and inversely as the square of the distance.

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  1. Let us now apply this law to terrestrial gravity – that is, to the earth’s attraction; and, for that purpose, let us suppose four balls, of the same size and density, to be placed respectively as follows, namely:
  • The first at the centre of the earth.
  • The second on the surface of the earth.
  • The third above the earth’s surface, at twice the distance of the surface from the centre (that distance being four thousand miles).
  • The fourth to be half way between the surface and the centre.

To ascertain the attractive force of the earth on each of these balls, we reason thus:

The first ball (at the centre) will be surrounded on all sides by an equal quantity of matter, and it will remain at rest.

The second ball will be attracted downwards to the centre by the whole mass below it. The third ball, being at twice the distance from the surface (gravity decreasing as the square of the distance increases), will be attracted by a force equal to only one-fourth of that at the surface.

The fourth ball, being attracted downwards by that portion of the earth which is below it, and upwards by that portion which is above it, will be influenced only by the difference between these two opposite attractions; and, as the downward attraction is twice as great as the upward, the downward attraction will prevail with half its original force, the other half being balanced by the upward attraction.

  1. As weight is the measure of the earth’s attraction, we may represent this principle by the weight of the balls, as follows (supposing the weight of each ball, at the surface of the earth, to be one pound):
  • The first ball will weigh nothing.
  • The second will weigh one pound.
  • The third will weigh one-quarter of a pound.
  • The fourth will weigh one-half of a pound.

The law of terrestrial gravity, then, may be stated as follows:

What is the law of Terrestrial Gravity?

  1. The force of gravity is greatest at the surface of the earth, and it decreases upwards as the square of the distance from the centre increases, and downwards simply as the distance from the centre decreases.

According to the principles just stated, a body which at the surface of the earth weighs a pound at the centre of the earth will weigh nothing.

1000 miles from the centre it will weigh      ¼ of a pound.

2000    ”           ”       ”        ”       ”              ”             ½ of a pound.

3000    ”           ”       ”        ”       ”              ”             3/4 of a pound.

4000    ”           ”       ”        ”       ”              ”             1 pound.

 

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8000 miles from the centre it will weigh   1/4 of a pound.

12000                             ”                                       1/9

16000                             ”                                       1/16

20000                             ”                                       1/25

24000                             ”                                       1/36

28000                             ”                                       1/49

32000                             ”                                       1/64

If the principles that have now been stated have been understood, the solution of the following questions will not be difficult.

  1. Questions for Solution.

[N. B. We use the term weight in these questions in its philosophical sense, as ” the measure of the earth’s attraction at the surface.”]

(1.) Suppose that a body weighing 800 pounds could be sunk 500 miles deep into the earth, what would it weigh?

Solution. 500 miles is 1/8 of 4000 miles; and, as the distance from the centre is decreased by 1/8, its weight would also be decreased in the same proportion, and the body would weigh 700 pounds.

(2.) Suppose a body weighing 2 tons were sunk one mile below the surface of the earth, what would it weigh? Ans. 1.99951 T.

(3.) If a load of coal weighs six tons at the surface of the earth, what would it weigh in the mine from which it was taken, supposing the mine were at a perpendicular distance of half a mile from the surface? Ans. 5.99925T.

(4.) If the fossil bones of an animal dug from a depth of 5228 feet from the surface, weigh four tons, what would be their weight at the depth where they were exhumed? Ans. 3 T. 19cwt. 98 lb. +

(5.) If a cubic yard of lead weigh 12 tons at the- surface of the earth, what would it weigh at the distance of 1000 miles from the centre? Ans. 3 T.

(6.) If a body on the surface of the earth weigh 4 tons, what would be its weight if it were elevated a thousand miles above the surface?

Solution. Square the two distances 4000 and 5000, &c.

Answer. 2 Tons. 11 qrs. 0 cwt. 20 lbs.

(7.) Which will weigh the most, a body of 3000 tons at the distance of 4 millions of miles from the earth, or a body of 4000 tons at

the distance of 3 millions of miles Ans..003 T. and. 0071 T. +

(8.) How far above the surface of the earth must a pound weight be carried to make it weigh one ounce avoirdupois? Ans. 12000 mi.

(9.) If a body weigh 2 tons when at the distance of a thousand miles above the surface of the earth, what would it weigh at the surface? Ans. 3 T. 2cwot. 501b.

(10.) Suppose two balls ten thousand miles apart were to approach each other under the influence of mutual attraction, the weight of one being represented by 15, that of the other by 30. How far would each move? Ans. 66662 mi. and 3333 mi.

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(11.) Which would have the stronger attraction on the earth, a body at the distance of 95 millions of miles from the earth, with a weight represented by 1000, or a body at the distance represented by 95, and a weight represented by one? Ans. As 1/9’025’000’000’000- to 1/9025.

(12.) Supposing the weight of a body to be represented by 4 and its distance at 6, and the weight of another body to be 6 and its distance at 4, which would exert the stronger power of attraction? Ans. The second, as 3/8 to 1/9.

 

  1. THE CENTRE OF GRAVITY. As every part of a body possesses the general property of attraction, it is evident that the attractive force of the mass of a body must be concentrated in some point; and this point is called the centre of gravity of the body.

What is the Centre of Gravity of a body?

 

  1. The Centre of Gravity of a body is the point about which, all the parts balance each other.
  2. This point in all spherical bodies of uniform density will be the centre of sphericity.
  3. As the earth is a spherical body, its centre of gravity is at the centre of its sphericity.
  4. When bodies- approach each other under the effect of mutual attraction, they tend mutually to approach the centre of gravity of each other.
  5. For this reason, when any body falls towards the earth its motion will be in a straight line towards the centre of the earth. No two bodies from different points can approach the centre of a sphere in a parallel direction, and no two bodies suspended from different points can hang parallel to one another.
  6. fig 3 compendium parkerEven a pair of scales hanging perpendicularly to the earth, as represented in Fig. 3, cannot
    be exactly parallel, because they both point to the same spot, namely, the centre of the earth. But their convergency is too small to be perceptible.

What is a Vertical Line?

  1. The direction in which a falling body approaches the surface of the earth is called a Vertical Line.

No two vertical lines can be parallel.

  1. A weight suspended from any point will always assume a vertical position.*

* Carpenters, masons and other artisans, make use of a weight of lead suspended at rest by a string, for the purpose of ascertaining whether their work stands in a vertical position. To this implement they give the name of plumb-line, from the Latin word plumbum, lead.

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  1. All bodies under the influence of terrestrial gravity will fall to the surface of the earth in the same space of time, when at an equal distance from the earth, if nothing impede them. But the air presents by its inertia a resistance to be overcome. This resistance can be more easily overcome by dense bodies, and therefore the rapidity of the fall of a body will be in proportion to its density.

To what is the resistance of the air to a falling body proportioned?

  1. The resistance of the air to the fall of a body is in direct proportion to the extent of its surface.
  2. Heavy bodies can be made to float in the air, instead of falling immediately to the ground, by making the extent of their surface counterbalance their weight. Thus gold, which is one of the heaviest of all substances, when spread out into thin leaf is not attracted by gravity with sufficient force to overcome the resistance of the air; it therefore floats in the air, or falls slowly. A sheet of paper also, for the same reason, will fall very slowly if spread open, but, if folded into a small compass, so as to present but a small surface to the air, it will fall much more rapidly.
  3. This principle will explain the reason why a person can with impunity leap from a greater height with an expanded umbrella in his hand. The resistance of the air to the broad surface of the umbrella checks the rapidity of the fall.
  4. In the same manner the aeronaut safely descends from a balloon at a great height by means of a parachute. But, if by any accident the parachute is not expanded as he falls, the rapidity of the fall will not be checked. [See Fig. 4.]
  5. EFFECT OF GRAVITY ON TIIE DENSITY OF THE AIR – The air extends to a very considerable distance above the surface of the earth.*

* We have no means of ascertaining the exact height to which the air extends. Sir John Herschel says: “Laying out of consideration all nice questions as to the probable existence of a definite limit to the atmosphere, beyond which there is, absolutely and rigorously speaking, no air, it is clear that, for all practical purposes, we may speak of those regions which are more distant above the earth’s surface than the hundredth part of its diameter as void of air, and, of course, of clouds (which are nothing but visible vapors, diffused and floating in the air, sustained by it, and rendering it turbid, as mud does water). It seems probable, from many indications, that the greatest height at which visible clouds ever exist does not exceed ten miles, at which height the density of the air is about an eighth part of what it is at the level of the sea.” Although the exact height to which the atmosphere extends has never been ascertained, it ceases to reflect the sun’s rays at a greater height than forty-five miles.

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That portion which lies near the surface of the earth has to sustain the weight of the portions above; and the pressure of the upper parts of the atmosphere on those beneath renders the air near the surface of the earth much more dense than that in the upper regions.

fig 4 parkers compendium

What effect has Gravity upon the air?

  1. The air or atmosphere exists in a state of compression, caused by Gravity, which increases its density near the surface of the earth.
  2. Gravity causes bodies in a fluid or gaseous form to move in a direction seemingly at variance with its own laws. Thus smoke and steam ascend, and oil poured into a vessel containing a heavier fluid will first sink and then rise to the surface. This seemingly anomalous circumstance, when rightly understood, will be found to be in perfect obedience to the laws of gravitation. Smoke and steam are both substances less dense than air, and are therefore less forcibly attracted by gravitation.

The air being more strongly attracted than steam or smoke, on account of its superior density, falls into the space occupied by the steam, and forces it upwards. The same reasoning applies in the case of oil; it is forced upwards by the heavier fluid, and both phenomena are thus seen to be the necessary consequences of gravity.

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The rising of a cork or other similar light substances from the bottom of a vessel of water is explained in the same way. This circumstance leads to the consideration of what is called specific gravity.

What is meant by Specific Gravity?

  1. SPECIFIC GRAVITY. Specific Gravity is a term used to express the relative weight of equal bulks of different bodies.*

* The quantity of matter in a body is estimated, not by its apparent size, but by its weight. Some bodies, as cork, feathers, &c., are termed light; others, as lead, gold, mercury, &c., are called heavy. The reason of this is, that the particles which compose the former are not closely packed together, and therefore they occupy considerable space; while in the latter they are joined more closely together, and occupy but little room. A pound of cork and a pound of lead, therefore, will differ very much in apparent size, while they are both equally attracted by the earth, that is, they weigh the same.

  1. If we take equal bulks of lead, wood, cork and air, we find the lead to be the heaviest, then the wood, then the cork, and lastly the air. Hence we say that the specific gravity of cork is greater than that of air, the specific gravity of wood is greater than that of cork, and the specific gravity of lead greater than that of wood, &c.
  2. From what has now been said with respect to the attraction of gravitation and the specific gravity of bodies, it appears that, although the earth attracts all substances, yet this very attraction causes some bodies to rise and others to fall.
  3. fig 5 parkers compendiumThose bodies or substances the specific gravity of which is greater than that of air will fall, and those whose specific gravity is less than that of air will rise; or, rather, the air, being more strongly attracted, will get beneath them, and, thus displacing them, will cause them to rise. For the same reason, cork and other light substances will not sink in water, because, the specific gravity of water being greater, the water is more strongly attracted, and will be drawn down beneath them. [For a table of the specific gravity of bodies, see Hydrostatics.]

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  1. The principle which causes balloons to rise is the same which occasions the ascent of smoke, steam, &c. The materials of which a balloon is made, are heavier than air, but their extension is

greatly increased, and they are filled with an elastic fluid of a different nature, specifically lighter than air, so that, on the whole, the balloon when thus filled is much lighter than a portion of air of the same dimensions, and it will rise.

  1. Gravity, therefore, causes bodies which are lighter than air to ascend, those which are of equal weight with air to remain stationary, and those which are heavier than air to descend. But the rapidity of their descent is affected by the resistance of the air, which resistance is proportioned to the extent of surface in the falling body.

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