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plan is gooil in idea; but it would involve us in an amount of labour from GIRAULT DUVIVIER.
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GENERAL EFFECTS OF GRAVITY.
ON PHYSICS OR NATURAL PHILOSOPHY. radius of the earth, or straight line drawn from its centre to its
length. But when two points on the earth's surface are consiNo. IV.
derably distant from each other, the angle between the vertical ON GRAVITY AND MOLECULAR ATTRACTION. lincs must not be neglected. Thus, in the English measurement
of an arc of the meridian, the angle between the vertical lines at
Dunnose, the Isle of Wight, and at Clifton near Doncaster, Universal Attraction and its Lau's.-Universal attraction is was found to be 2° 50' 23" 38; and in the French measurement that force by which all the material particles of bodies are con- of an arc of the meridian, the angle between the vertical lines at
These tinually attracted or drawn towards each other. This force is Paris and at Dunkirk was found to be 2° 12' neerly. considered as a general property inherent in matter. It acts measurements were both made at the close of the last century, at "pon all bodies, whether at rest or in motion. Its action is always the expense of the respective governments. mutual between bodies; and it operates at all distances, as well
A horizontal line may now be defined as a straight line peras through all substances.
pendicular to a vertical line; it received its name, however, from Universal attraction is called Gravitation, when it operates the consideration that it was a straight line which joined any two among the heavenly bodies ; it is called Gravity, when the attrac- diametrically opposite points of the horizon; or that it was a tion of the earth causes bodies to fall; and it is called Molecular tangent a: any point on the earth's surface, and therefore coinAttraction, when applied to the force which unites the particles ciding with the horizon at that point. of bodies to each other.
Plumb-Linc.-The vertical line of any place is determined by The ancient philosophers, Democritus (360 B c.) and Epicurus the plumb-line. This name is given to & cord, having a small (300 B.C.), maintained the opinion, that matter was attracted to ball of lead aitached to one of its extremities, and having its other common centres in the earth and the heavenly bodies. Kepler extremity fixed or supported; when the cord and ball are per(1600 A.D) asserted the principle of mutual attraction between mitted to hang freely, the former naturally takes the direction of
the earth, and the other planets. Bacon, Galileo, and the vertical line, in consequence of the action of gravity; for a Hook, also recognised the fact of the existence of universal attrae- body which has only one point of support can only be in equi. tion. To Newton (1665 4.v.) was reserved the glory of mathe- librium when its centre of gravity and the point of support are matically demonstrating the laws of Kepler concerning the mo- situated in the same vertical line, as we shall see when treating tion of the planets, and of proving that gravitation is a general of the centre of gravity. law of nature. This law is generally expressed in the following
The following cut exhibits a drawing of the common mason's All budies in the material universe gravitate towards level, in which a plumb-line Ac must fall on a certain point B, each other with a force which is directly proportional to their in the fiducial line of the instrument, if its two feet are correctly quantities of matter, or masses, and inversely proportional to the placed on two points of the level :squares of their distances.
Since Newton's time, the attraction of matter by matter has been experimentally demonstrated by Cavendish (1798 A.D.), a celebrated chemist and natural philosopher. By means of an apparatus, wbich is called the Balance of Cavendish, the inventor not only rendered sensible to the eye the attraction of a large ball
00? of lead on a small copper bullet, but he ascertained by this experiment the density of the earth, and found it to be about 5.1
The plumb-line does not indicate whether or not the direction times that of water. The apparatus of Cavendish may, therefore, of gravity in a given place is constant. Thus, if a plumb-line be considered as a scale in which the earth, sun, moon, and planets wbich is found to be parallel to the wall of a building at a given have been weighed.
period, should be found afterwards to have deviated from this Gravity. The force which causes all bodies when left to position, it cannot be inferred, without further observation, themselves to fall towards the centre of the earth, is called gravity. Whether gravity has changed its direction, or whether the wall This force, which is only a particular case of the law of univcrsal has departed from the vertical position. In treating of the attraction, exemplifies the mutual attraction which takes place properties of liquids, we shall see that their surface can only between the mass of the earth and the mass of the falling body. remain in the horizontal position, that is, remain level, when that The law of gravity is like that of universal gravitation, and surface is perpendicular to the direction of gravity. But if this bodies fall to the earth with a force directly proportional to their direction were to change, so would the level of the sea ; the stamass, and inversely proportional to the square of their distance bility of this level, therefore, is a proof that the direction of from its centre. Gravity acts on all bodies, and in every variety gravity is constant, or invariable. In the vicinity of a large mass of condition;, and if some bodies, such as the clouds, smoke, &c., of matter, however, such as a mountain, the plumb-line has been seem to be trecd from its action by their riving in the atmosphere, found to deviate from the true vertical by a sensible quantity, as we shall soon see that the cause of this phenomenon must be has been demonstrated by the experiments of several observers. referred to gravity itself.
ON DENSITY, WEIGHT, CENTRE OF GRAVITY, &c. Direction of Gravity; Vertical and Horizontal.- When the par- Absolute and Relatire Density. The mass of a body contained ticles of a material sphere act, according to the law of attraction, in a certain unit of volume or bulk is called its density. The in the inverse ratio of the square of the distance, upon a particle absolute density of a body cannot be determined ; that is, we canof matter situated without that sphere ; it is demonstrated in not tell the real quantity of matter which it contains; but we can treatises on Rational Mechanics, that the resultant of the attrac-ascertain its relative density, or the quantity of matter which it tive force of all the particles of the sphere, is the same as if they contains, under the same volume, in relation to another body were all collected at its centre. It follows from this, that at every taken as the unit or standard of comparison. This standard body point on the surface of the globe the attraction of the earth is for solids and liquids is distilled water taken at a given temperadirected towards its centre. The depression of the earth at the tura. Hence, when the density of zinc, for instance, is said to poles, the difference in density between the masses of matter of ba 7, this means that under the same volume or bulk this metal which it is composed, and the inequalities of its surface as to contains 7 times the quantity of matter that water contains. mountains, valleys, and plains, are all so many causes which occa- If v represents the volume or bulk of a body, M its absolute sion slight deviations in the direction of gravity, but so slight as mass, and D its quantity of matter under the unit of volume, that to be sensible only by a very small quantity:
is, its absolute density, it is evident that the quantity of maiter conThe direction of he force of gravity is called vertical; that is, tained in the volume 7, is V times D; whence, M=VD. From the straight line in which a body falls to the ground is called a vertical line. At all points on the surface of the globe, the verti- this equation, we have D = ; that is, the absolute density of a cal lines sensibly converge towards the centre--that is, their
v directions are not parallel ; but for points which are at a little body is the ratio of its mass to its volume. distance from each other, such as the particles of the same body, or IVeight.--In every body, weight is considered under three of bodies lying near each other, the vertical lines are considered as aspects, viz., the absolute, the relative, and the specific weight. strictly parallel. It is obvious that no error can arise from this The absolute weight of a body is the pressure which it exerts on consideration in ordinary, cases, when we remember that the mean any obstacle which prevents it from falling. This pressure is the TOL. IT.
resultant of the forces by which gravity acts on each of the par In many instances, the centre of gravity may be found by trial. ticles of a body, and it increases with the quantity of matter in the This is done by suspending the body by a string successively in hody; this principle is expressed by saying that the weight of a two different positions, and when it is at rest, drawing a straight body is proportional to, or increases with its mass.
line in the body in the direction of the string; we thus obtain The relative weight of a body is that which is found by means two straight lines which intersect each other in the same point: of a balance ; it is the ratio of the absolute weight of a body to this point is the centre of gravity required. For, in each position, that of another body selected as unity. In our system of weights, the equilibrium of the body can only take place when its centre the smallest unit is the grain, which is the seven-thousandth part of gravity is below the point of suspension, and in the direction of of a larger unit called the pound Avoirdupois, of the Imperial the string produced ; it follows, therefore, that the centre of pound. In France, the smallest unit is the gramme, which is the gravity must be at the same time on the two different directions weight of a cubic centimetré of distilled water at its maximum of the string produced, and must consequently be at their point of density. Hence, a body which weighs one gramme, weighs also intersection. 16:434 grains, and these are the relative weights of this body in
In bodies whose form and homogeneity are invariable, the France and England; but if other units of weight were adopted position of the centre of gravity is constant; but where these are in these countries, the relative weights of the body would be variable, the position of the centre of gravity changes with them. altered, but the absolute weights of the body would remain the The latter is the case in animated beings, their centres of gravity
Varying with their attitudes, or postures. Thus, the pedestrian Lastly, the specific weight, or, as it is often called, the specific this position when he goes down the hill; that is, he endeavours
who walks up a hill leans his body forwards; but he reverses grarity, of a body is the ratio of its relative weight, under a cer- in both cases to preserve the vertical which passes through his tain volume to that of an equal volume of distilled water at the centre of gravity, within the spåce between his feet
, which are maximum density. Hence, if we say that the spécific weight of his points of support, as shown in the following cut. The centre specific gravity of zinc is 7, the meaning is, that under an equal of gravity of a well-proportioned man, when standing firm and volume or bulk, zinc weighs 7 times heavier than distilled erect, is å point within the body iust about tħe height of the
The weight of bodies of equal volume being proportional to their mess, it follows that if a body contains two or three times the quantity of matter that water does, its weight must be two or three times the weight of water; consequently the ratio between their weights, or specific gravities, must be the same as the ratio between their masses, or relative densities. For this reason, the 'spression relative density and specific gravity are generally considered as synonymous, or, at least, equivalent to each other. If, 20wever, the action of gravity were removed, there would be neither absolute nor relative weight in bodies, yet their densities would remain to be considered. These could not be determined by the balance; but we have seen that the ratio of the masses of bodies is the same as the ratio of the forces which would com- Equilibrium of Heavy Bodies.--As gravity is a single force municate to these masses the same velocity in the same time.
whose direction is vertically downwards, and whose action is applied The weight P of a body being proportional to its mass jí, and to at the centre of gravity of all bodies, equilibrium will always be the intensity of gravity which may be represented by g, the product produced if this force be counteracted by the resistance of a fixed Afg may be taken as the measure of this weight, that is P=0.g. point through which its direction passes. There are two cases of
equilibrium, according as the heavy body rests on one or several Whence we have M
either coincide wise the first case, the centre of gravity must
either coincide with the point of support, or be situated on the the weight is known. If in this equation we substitute ?D for vertical drawn though the centre of gravity must pass within the
vertical which passes through this point. In the second case, the II, according to the preceding formula relating to density, we base, that is, within the polygon formed by successively joining have P=VD9, a second expression for
the weight of a body. In all the points of support. In the towers of Pisa and Bologna, the case of a body whose weighi, density, and volume are repre- which are so inclined to the horizon as to seem just ready to fall sented by P', D', and V, we have, in like manner, PSV'D'g. Comparing this result with the former, we have P: P::VD: upon the passengers in the street, their equilibrium is stiil mainV"D': When D=D', we have P:P :: V : 17; and when tained, because their centres of gravity are situated on the vertiP-P', we have VD=VID'; whence we have Tiv::D:D. cals which pass through the interior of their bases. A man stands From these proportions we infer Ist, that when the densities of more firmly in proportion as he extends his feet and widens his From these proportions we infer Istio that when the wil centre of gravity is situated without this base. If he stands on bodies are equal, their weights are proportional to their volumes; base; he can thus give to his motions more amplitude, unless his and 2nd, that when their weights are equal, their volumes are inversely as their densities. We shall soon show the méthod of one foot only, his base is diminished and consequently his firmdetermining the specific gravities of solids and liquids ; but as the ness; these are diminished still more, if he stands on tiptoe. In specific gravities of gases are determined with relation to the this position, a very slight oscillation will throw his centre of atmospheric air as unity, their determination must be taken un gravity beyond the base, and destroy his equilibrium. after we have treated of the subject of heat.
A man who carries a load on his shoulders is compelled to lean
forfards, lest he shoulų be drawn backwards by the load; for his Centre of Gravity; Determined by Experiment.-The centre of centre of gravity when loaded and standing erect is without the gravity of a body is a point through which the resultant of the base; these different positions may be sien in the following cut. actions of gravity on all its particles always passes, whatever position it may assume.
It is demonstrated in Statics, that every body has a centre of gravity.
The full investigation of the centre of gravity of any body belongs to Geometry; but in many ordinary cases it can be determined at once. Thus, in a homogeneous straight line, the centre of gravity is in the middle point ; in a homogeneous circle or sphere, it is in the centre; in homogeneous cylinders, it is in the middle of the axis. In Statics, it is shown that the centre of gravity of a homogeneous triangle is in the straight line joining the vertes to the middle of the base, at the distance of two-thirds For a similar reason, any one who carries a load in front, as a of that line from the vertex. In homogeneous pyramids and purse with a child in her arms, iš obliged to lean backwards. So cones, the centre of gravity is in the straight line joining the bakers and pastrycooks, who carry their loads upon their heads, vertex to the centre of gravity of the base, at the distance of require to be as upright as possible. three, fourths of that line fona the pertex,
Different States of Equilibrium. ---According to the position of
gravity with regard to the point of support, there are three diffe- prism K, called a knife, placed perpendicularly to its length, and rent states of equilibrium; 1st: that of stable equilibrium ; 2nd. resting with its sharp edge upon a polished agate plane, in order to that of unstable equilibrium; and 3rd. that of indifferent equili. diminish friction. Ä long Deedle fixed at its upper extremity to the brium.
beam, and traversing at its lower extremity a graduated circular arc Stable equilibrium is that state of a body in which, after it has placed near the bottom of the supporting pillar, determines whether been drawn out of its position of equilibrium, it returns to that the beam is horizontal, according to its position. In order to relieve position instantly, provided there be no obstacle to prevent it. This the knife-edge from pressure when the balance is not in use, state of equilibrium always takes place when the centre of gravity the beam is supported by means of a moveable piece of mechanism of a body is placed lower than it could be in any other position. called a fork. This mechanism rests on a fixed piece A a, having If the body is then displaced from that position, its centre of two vertical rods at its extremities. Two pieces D D, fitted to gravity cannot be raised higher, and as gravity tends continually the beam, are intended to receive the pressure of the fork. The to lower it, the body returns, after a series of oscillations, to its fork consists of a bar, a a, 80 which are fixed two horizontal original position, and the equilibrium is restored. Examples of cross-pieces E E, which rise with the fork, and support the two this may be seen in the motions of the pendulum of a clock, or in pieces" Dd, and with them the beam. The fork is guided in its the motions. of an egg on a plane or level table when its greater motion by the rods at A A, which work nearly free of friction at axis is parallel to this plane.
its extremities. The motion of the fork is obtained by means of 4s examples of stable equilibrium, small ivory figures are made, a button-handle at 0, which transmits the turning motion made fig. 8, so as to stand on tiptoe, by loading them with leaden balls by the fingers to a screw placed in the interior of the pillar. The placed so low, that in all positions the centre of gravity is turning of this screw raises the fork and with it the two pieces E situated below the point of support.
E, which in their turn raise the beam B B.
Instuble equilibrium is the state of a body in whicli, after it bas been drawn out of its position of equilibrium, it tends to depart still more from that position. This is always the case when a body is in such a position that its centre of gravity is the highest possible ; for by any displacement of the body whatever this point is lowered, and gravity only tends to lower it still more. Examples of this may be seen in the atrempt to balance a rod when standing on the tip of the finger, or to make an egg stand The following cut is a more common form of the balance; in on a horizontal plane or leyel table, so that its greater axis may which co' is the beam; o the point of suspension ; A B the suppuoti be vertical,
ing pillar; and FG, the scales. In this construction the index Lastly, indifferent equilibrium is that state of a body in which needle points upwards to a graduated arc, as more convenient for it assumes any position which may be given to it. This kind of ordinary use: equilibrium is manifested when, in the different positions of a body, the centre of gravity is neither elevated nor depressed, such as the wheel of a carriaye resting on its axle-tree, or a sphere resting on a horizontal plane. Fig. 9 shows three cones A, B,
c' and c, placed in the positions of stable, unstable, and indifferent equilibrium respectively.
The Balance. --- balance is an apparatus for nueasuring the relative weights of bodire. Balances are made of various constructions.
The fllowing is a description of a Firy delicate balance, tig, 10. It is constructed of a hurizontal lever, BB, of thie first kind, called the beam, at the extremities of which the scales or pans aie suspended. The beam is furnished with a steel
Conditions Requisite for a Good Balance. In order that a balance should be perfectly exact, the following conditions must Now mark the difference between these two verbs, go and be fulfilled :
pull; the first, you know, is intransitive, the second is transitive. 1st. The two arms of the beam, that is, the distances from the The first has an object, but not without the aid of a preposition, knife-edge at K to the points of suspension of the scales, must and the business of the preposition is to define the relation of the be perfectly equal ; for it is proved in Mechanics, that two equal verb go to the objects city and country. The second or transitive forces can only be in equilibrium by means of a lever when the verb has one object in immediate dependence on itself, and another two arms are equal. Yet there is a method by which the exact object connected with itself by means of a preposition ; and the weight of a body can be obtained from a balance although its business of the preposition is to define the relation of the verb to arms are unequal.
the second object, that is, to the shore. It cannot be inferred that the two arms of a balance are equal, Hence you learn that transitive verbs in the active voice have two by the single circumstance that when the scales are empty the objects, the immediate and the mediate (or the near and the remote), beam is horizontal ; for it is enough to hang from the longer arm the former dependent on themselres exclusively, the latter dependent a lighter scale in order to make it so. To determine whether the on themselres through the link of a preposition. arms are equal, place weights in the two scales so that the beam
The verb and preposition may indeed be regarded as one word may take the horizontal position. Make these weights change thus, to come-from, to go-to-when by means of the several places from one basin to another; the beam will still be horizontal suffixes a modification of meaning is in each instance caused. if the arms are equal; if not, it will incline to the side of the These intransitive verbs thus supplemented become transitive, that longer arm.
is, have an immediate object, for we can say, 2nd. The length of the arms of the beam must remain perfectly invariable during the oscillations of the balance. For this purpose,
I come from Bath ; I go-to Bath, &c. the beam and the scale-hooks must be furnished with very sharp The preposition is thus seen to stand between the verb and its points of support.
object in order to assist the former in the expression of the latter. 3rd. When the beam is horizontal, its centre of gravity must As, however, the object stands in immediate dependence on the be in the vertical passing through the knife-edge and a little preposition, and only in remote dependence on the verb, so we below this edge; unless this be so, the beam will not assume the may frame the rule thus :position of stable equilibrium.
A noun as an object may be dependent on a preposition; 4th. The balance must be very sensible, that is, it must oscillate or thus:with a very small difference of weight in the scales; and this A preposition may govern a noun as its object; e. g., requires that the beam should be very easily put in motion. For
Ah! who can tell the triumphs of the mind, this purpose, it is made to rest on two supports in agate, or in
By truth illumin'd, and by taste refin'd ?"-Rogers. well-tempered and polished steel; this greatly diminisbes the friction. In general, the sensibility of a balance is greater in
The use of the participle refined here brings this example into proportion to the length of the arms of the beam; the lightness of and water.” By comparing the two together, we see that past
, a beverage made of wine the beam and scales; the proximity of the centre of gravity of the participles take after them a preposition governing an object, and beam and the knife-edge, or point of support ; and the length of that the preposition varies with the sense ; it is, indeed, dictated by the needle which marks the Oscillations of the balance. In order to increase at pleasure the sensibility of a balance, a preposition should follow participles, adjectives, and verbs, much
the usages of the language. In the usages which determine what button-screw or nut is placed on the beam at c, fig. 10. When of the idiom of our English tongue is involved. Equally does a this screw is raised, the centre of gravity of the beam approaches regard to a propriety of speech require attention to the exact mean
-the axis of suspension, its effect in opposing the oscillations of the ing, and the right application of the several prepositions, that is, to beam is diminished. If the centre of gravity reaches the knife the syntax of the prepositions. edge, the balance is in a state of indifferent equilibrium; if it
We have already seen that an infinitive mood may be the object passes this point, the equilibrium is unstable, and the balance is of a verb in the finite mood; as, then useless.
I love to wander ; Method of Double Weighing.– This method, due to M. Borda where wander is an infinitive governed by I love. Now, instead of of Paris, of ascertaining the exect weight of a body by means of to wander you may supply a noun and say, a balance whose arms are unequal, is the following :-Place the body to be weighed in one of the scales, and make an equilibrium
I lore wandering ; or, in the other scale with lead drops or sand; then, remove from the former scale the body to be weighed, and in its place put kuow. The preposition to you thus see, connects its object with a weights of any kind until the equilibriuin is again established. transitive verb, when that object is a verb. The preposition in The amount of known weights thus obtained is the exact weight such cases is a connecting word, but a connecting word which is of the body; for in the operation, the body and the weights act on essential to the inport. That it is essential you may learn by the same arm of the beam, in order to produce an equilibrium removing it ; thus, I love, wander. Here, too, the object wander with the same resistance.
is in immediate dependence on to, and only in remote dependence on I love; consequently, we inay say that
The latter of two verbs connected together by the preposition to as LESSONS IN ENGLISH. No. LXX. dependent on, or governed by, that preposition. By JOHN R. BEARD, D.D.
We may also lay it down as a fact that
The preposition to stands before a verb when it is used in its most SYNTAX. PREPOSITIONS.
general application, or in the infinitive mnood. The preposition is intimately connected with two other parts of Now a verb so used is in meaning very near to the noun. speech, the verb and the noun. The relation of the verb to its indeed, a verbal noun; e. g., object, or of the doer and the doing to the thing done, is often
To learn to die is the great business of life. expressed but imperfectly by the verb. Thus, when I say I go, I make a merely general statement; if I wish to give specific informa- Usage allows the preposition to, thus employed, to be in one kind tion, I say,
of sentence strengthened by another preposition, namely, for, I go from the city into the country.
which, however, has its own object; e. g., It is not every object, however, which requires a preposition.
“For us to learn to die is the great business of life.' When I say,
The preposition for thus set at the beginning, followed by an I pull the boat,
infinitive, forms a clause or member which is the subject of the boat stands in immediate dependence on pull, and neither has nor finite verb. needs any preposition; hut if I add a second object with that
As prepositions govern nouns, so may they govern whatever object: I for the most par!) employ a preposition; e. go, stands às, or is used with, the force of a noun, and consequently I pull the boat from the shore.
propositions may govern,
I lovca stroll.