Nous sommes arrivés aujourd'hui.

Votre fière s'est blessé hier.

Aujourd'hui il fait beau temps; demain il peluvra. GIRAULT DUVIVIER.

§ 137.-OBSERVATIONS.

We came to-day Timber and Iron."-ETA DELTA: If a workman labours twelve or fourteen hours a-day, the best part of Physical Education for him is Bathing or Your brother hurt himself yester-Swimming, if it agrees with him. As to the best plan of learning Geometry day. and Euclid, see Cassell's "Self and Class Examiner in Euclid," price 3d. To-day, it is fine weather; to- J. CROSSLEY (Radcliffe): Not quite.-J. CHRISTIE (Montrose): Your morrow it will rain. plan is good in idea; but it would involve us in an amount of labour from which we shrink, seeing what we have already before us. Take our advice and study Orthography and Penmanship a little more.-JEAN (Devonport): Grolle means a rook; our dictionary does not tell us the rest.-SELF-TAUGHT, &c. (Warrington): Under consideration.-OLD SUBSCRIBER (Norwich): Solution of question 17, p. 105. Cassell's Arithmetic; it is stated that the

(1.) The adverbs of comparison, plus, moins, must be repeated hound runs & rods in the time that the fox runs 5 rods; call this time 1: before every adjective which they modify :

:

then, since the hound gains 3 rods every time called 1, we have 3 rods: 150 rods: 1 time: 50 times, the hound runs 8 x 50-400 rods.-IPSEDOCTUS (Southampton) should consult an optician.-TYRO JOHNSON (Penzance): He is less idle and obstinate than Telemaque, a popular French work, will soon be published at this office,

Il est moins paresseux et moins his brother.

obstiné que son frère.

ANSWERS TO CORRESPONDENTS.

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P. D. (Oxford-street): The standard of the French weights and measures is called the Metre, and it is reckoned to be the ten millionth part of the quadrant of the terrestrial meridian.-SUBSCRIBER (Cheadle): Envelope is a French word, and must be pronounced accordingly, see Cassell's French Dictionary. Seringapatám should be pronounced as accented.-J. OLIVER (Burslem): For a succinct History of England," take Cassell's in 4 vols., or 4 vols. in one, price 3s.; for a more extended one adapted to the young, take that published by the Religious Tract Society, in 4 vols. cloth, price 128.; for an extended political one, take Hume and Smollett's, with continuations to the present time, published at all manner of prices. For particular portions of English History, take Macaulay, Hallam, Turner,

See p. 28, vol iv., at the bottom. An edition of the Greek New Testament may also be expected.-PHILO (Nottingham): Thanks; we recommend Read all our articles on the University of London, in vols ii. and iti. of the Cassell's Spelling Book as the best for a little girl.-G. W. A. (Slough): P. E.-W. H. Mc ELLEN (Manchester): The wolf, tiger, and lion question is not correct.-CONSTANT SUBSCRIBER (Barnstaple): The translation of dealer in old books, from 6d. to 10s. according to the edition.-W. A. G. the Psalms into Latin verse is George Buchanan's, and it may be had of any (London): See our Literary Notices.-TLOH 32 (Eastborn): In the equa tion 12x-420-1200, the values of x are 31 86 and 3-14. We think that more will be necessary for Matriculation than what is likely to be printed of our Greek lessons, by the time he mentions. He must serve under articles to become a barrister. We cannot inspect and give opinions on MSS. without a regular fee.-J. B. ROSE (Coventry): We know of no cheap editions of the Italian poets.-J. MEDLEY (Hertford): Received,

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CASSELL'S LESSONS IN LATIN, price 2s. in stiff covers, or 2s. 6d. cloth. CASSELL'S KEY TO THE LATIN EXERCISES, now ready, price ls. The first volume of CASSELL'S CLASSICAL LIBRARY is now ready. WATSON: Read our articles on the University of London.-T. STOKES Ancient Geography; with a suitable Dictionary. subjects-Easy Fables, Mythology, Biography, The History of Rome, and (Exeter): Punctuation and Elocution will come in their turn: many which is publishing in weekly numbers, prices 2d. each, will consist of eminent persons speak highly in favour of Short-hand.-A. MUNRO (Pres-useful Latin Exercises, or English sentences, to be translated into Latin, ton): Music is at rest for a little.-D. W. (Leith): Finish one set of lessons with numerous references to Andrews and Stoddart's Latin Grammar, a before you begin another set; reading and conversation will supply you valuable treatise now in the press. with words.-JOHN CHADWICK: Certainly; all right.-RESOLU DE VAINORE (Staines): Zymotic comes from (vuow, to leaven, and this from Cuun, leaven; the latter again most probably comes from Čew, to boil.-W. V. YATES (Ormskirk): A Pupil Teacher's Association" might be formed with great advantage for the study of the principles of General and Com. parative Grammar, in relation to all languages but especially the English, which is now a compound of all languages, taking, as it does, new words daily from every tongue under the sun. This association might take Dr. Beard's Lessons in English in the P. E. as a foundation for its studies and inquiries. Every word in English should then be traced and silted till its origin and true meaning are discovered, as well as its various and curious applications. Thus English Philology would lead to Universal Philology; and the study of names or nouns would lead to the study of things, or to Natural Philosophy; and these again, to that of Mental Philosophy.

T. GUY (Broomside): The verb ovare comes from ovv, together, and OTEAA, I set, place, or bring, and therefore signifies I set together, I place together, or I bring together. In Acts v. 6, it is applied to the act of winding up a dead body, or bringing its limbs together in a winding-sheet or cloak. In 1 Cor. vii. 29, it is applied to the bringing together, or shortening, of periods of time, as the periods of life and death, so beautifully expressed in the Church Burial Service, "in the midst of life we are in death."

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Acts of the Apostles in the original Greek, according to the text of Augustus
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ON PHYSICS OR NATURAL PHILOSOPHY.

No. IV.

ON GRAVITY AND MOLECULAR ATTRACTION.
GENERAL EFFECTS OF GRAVITY,

Universal Attraction and its Laws.-Universal attraction is
that force by which all the material particles of bodies are con-
tinually attracted or drawn towards each other. This force is
considered as a general property inherent in matter. It acts
apon all bodies, whether at rest or in motion. Its action is always
mutual between bodies; and it operates at all distances, as well
as through all substances.

radius of the earth, or straight line drawn from its centre to its length. But when two points on the earth's surface are considerably distant from each other, the angle between the vertical lines must not be neglected. Thus, in the English measurement of an arc of the meridian, the angle between the vertical lines at Dunnose, in the Isle of Wight, and at Clifton near Doncaster, was found to be 2° 50′ 23′′ 38; and in the French measurement of an arc of the meridian, the angle between the vertical lines at Paris and at Dunkirk was found to be 2° 12' nearly. These measurements were both made at the close of the last century, at the expense of the respective governments.

A horizontal line may now be defined as a straight line perpendicular 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 at 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-Line.-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 a cord, having a small (300 B.C.), maintained the opinion, that matter was attracted to ball of lead attached 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 sun, 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 attrac-body which has only one point of support can only be in equition. To Newton (1665 A.D.) 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 terms: All bodies in the material universe gravitate towards each other with a force which is directly proportional to their quantities of matter, or masses, and inversely proportional to the 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, which is called the Balance of Cavendish, the inventor not only rendered sensible to the eye the attraction of a large ball 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 times that of water. The apparatus of Cavendish may, therefore, be considered as a scale in which the earth, sun, moon, and planets have been weighed.

Gravity-The force which causes all bodies when left to themselves to fall towards the centre of the earth, is called gravity. This force, which is only a particular case of the law of universal attraction, exemplifies the mutual attraction which takes place between the mass of the earth and the mass of the falling body. The law of gravity is like that of universal gravitation, and bodies fall to the earth with a force directly proportional to their mass, and inversely proportional to the square of their distance from its centre. Gravity acts on all bodies, and in every variety of condition; and if some bodies, such as the clouds, smoke, &c., seem to be freed from its action by their rising in the atmosphere, we shall soon see that the cause of this phenomenon must be referred to gravity itself.

The following cut exhibits a drawing of the common mason's level, in which a plumb-line A c must fall on a certain point B, in the fiducial line of the instrument, if its two feet are correctly placed on two points of the level:

The plumb-line does not indicate whether or not the direction of gravity in a given place is constant. Thus, if a plumb-line which is found to be parallel to the wall of a building at a given period, should be found afterwards to have deviated from this position, it cannot be inferred, without further observation, whether gravity has changed its direction, or whether the wall has departed from the vertical position. In treating of the properties of liquids, we shall see that their surface can only remain in the horizontal position, that is, remain level, when that surface is perpendicular to the direction of gravity. But if this direction were to change, so would the level of the sea; the stability of this level, therefore, is a proof that the direction of gravity is constant, or invariable. In the vicinity of a large mass of matter, however, such as a mountain, the plumb-line has been found to deviate from the true vertical by a sensible quantity, as has been demonstrated by the experiments of several observers.

ON DENSITY, WEIGHT, CENTRE OF GRAVITY, &c. Direction of Gravity; Vertical and Horizontal.-When the par- Absolute and Relative 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 ture. Hence, when the density of zinc, for instance, is said to poles, the difference in density between the masses of matter of be 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 occasion slight deviations in the direction of gravity, but sc slight as to be sensible only by a very small quantity.

The direction of the force of gravity is called vertical; that is, 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 vertical lines sensibly converge towards the centre-that is, their directions are not parallel; but for points which are at a little distance from each other, such as the particles of the same body, or of bodies lying near each other, the vertical lines are considered as strictly parallel. It is obvious that no error can arise from this consideration in ordinary cases, when we remember that the mean

VOL. IV.

If v represents the volume or bulk of a body, M its absolute mass, and D its quantity of matter under the unit of volume, that is, its absolute density, it is evident that the quantity of maiter contained in the volume V, is V times D; whence, MVD. From this equation, we have D= that is, the absolute density of a V ; body is the ratio of its mass to its volume.

M

Weight. In every body, weight is considered under three aspects, viz., the absolute, the relative, and the specific weight. The absolute weight of a body is the pressure which it exerts on any obstacle which prevents it from falling. This pressure is the

resultant of the forces by which gravity acts on each of the par ticles of a body, and it increases with the quantity of matter in the body; this principle is expressed by saying that the weight of a body is proportional to, or increases with, its mass.

The relative weight of a body is that which is found by means of a balance; it is the ratio of the absolute weight of a body to that of another body selected as unity. In our system of weights, the smallest unit is the grain, which is the seren-thousandth part of a larger unit called the pound Avoirdupois, or the Imperial pound. In France, the smallest unit is the gramme, which is the weight of a cubic centimetre of distilled water at its maximum density. Hence, a body which weighs one gramme, weighs also 15434 grains, and these are the relative weights of this body in France and England; but if other units of weight were adopted in these countries, the relative weights of the body would be altered, but the absolute weights of the body would remain the

The weight of bodies of equal volume being proportional to their mass, 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 masces, or relative densities. For this reason, the expression relative density and specific gravity are generally considered as synonymous, or, at least, equivalent to each other. If, however, 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 communicate to these matses the same velocity in the same time.

P

In many instances, the centre of gravity may be found by trial. This is done by suspending the body by a string successively in two different positions, and when it is at rest, drawing a straight line in the body in the direction of the string; we thus obtain two straight lines which intersect each other in the same point: this point is the centre of gravity required. For, in each position, the equilibrium of the body can only take place when its centre of gravity is below the point of suspension, and in the direction of the string produced; it follows, therefore, that the centre of gravity must be at the same time on the two different directions of the string produced, and must consequently be at their point of intersection. In bodies whose form and homogeneity are invariable, the position of the centre of gravity is constant; but where these are variable, the position of the centre of gravity changes with them. The latter is the case in animated beings, their centres of gravity varying with their attitudes, or postures. Thus, the pedestrian this position when he goes down the hill; that is, he endeavours who walks up a hill leans his body forwards; but he reverses in both cases to preserve the vertical which passes through his centre of gravity, within the space between his feet, which are his points of support, as shown in the following cut. The centre of gravity of a well-proportioned man, when standing firm and erect, is a point within the body just about the height of the

navel.

Equilibrium of Heavy Bodies.-As gravity is a single force whose direction is vertically downwards, and whose action is applied The weight of a body being proportional to its mass M, 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 My may be taken as the measure of this weight, that is Pg. 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 = a formula for finding the mass when Points of support. In the first case, the centre of gracity must either coincide with the point of support, or be situated on the the weight is known. If in this equation we substitute ID for Vertical which passes through this point. In the second case, the M, according to the preceding formula relating to density, we base, that is, within the polygon formed by successively joining vertical drawn though the centre of gravity must 18s within the have P=VDg, a second expression for the weight of a boly. In all the points of support. In the towers of Fisa and Bologna, the case of a body whose weight, density, and volume are repre-which are 8, inclin d to the horizon as to seem just ready to fail sented by P', D', and V, we have, in like manner, P=VDg. Comparing this result with the former, we have P: P:: ID: upon the passengers in the street, their equilibrium is still mainV'D. When DD', we have P: P :: F: I'; and when tained, b. cause their centres of gravity are situated on the verti PP, we have VDVD'; whence we have :: D: D. cals which pass through the interior of their bases. A man stands From these proportions we infer 1st, that when the densities of more firmly in proportion as he extends his feet and widens his 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 centre of gravity is situated without this base. If he stands on inversely as their densities. We shall soon show the method of one foot only, his base is diminished and consequently his firmdetermining the specific gravities of solids and liquids; but as theness; 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 up gravity beyond the base, and destroy his equilibrium. after we have treated of the subject of heat.

Centre of Gravity; Determined by Experiment.-The centre of gravity of a body is a point through which the resultant of the 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 vertex to the middle of the base, at the distance of two-thirds

of that line from the vertex. In homogeneous pyramids and cones, the centre of gravity is in the straight line joining the vertex to the centre of gravity of the base, at the distance of three-fourths of that line from the vertex.

A man who carries a load on his shoulders is compelled to lean centre of gravity when loaded and standing erect is without the forwards, lest he should be drawn backwards by the load; for his base; these different positions may be seen in the following cut.

For a similar reason, any one who carries a load in front, as a nurse with a child in her arms, is obliged to lean backwards. Se bakers and pastrycooks, who carry their loads upon their heads, require to be as upright as possible.

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.
that of unstable equilibrium; and 3rd. that of indifferent equili.
brium.
Stable equilibrium is that state of a body in which, after it has
been drawn out of its position of equilibrium, it returns to that
position instantly, provided there be no obstacle to prevent it. This
state of equilibrium always takes place when the centre of gravity
of a body is placed lower than it could be in any other position.
If the body is then displaced from that position, its centre of
gravity cannot be raised higher, and as gravity tends continually
to lower it, the body returns, after a series of oscillations, to its
original position, and the equilibrium is restored. Examples of
this may be seen in the motions of the pendulum of a clock, or in
the motions of an egg on a plane or level table when its greater
axis is parallel to this plane.

As examples of stable equilibrium, small ivory figures are made, fig. 8, so as to stand on tiptoe, by loading them with leaden balls placed so low, that in all positions the centre of gravity is situated below the point of support.

Fig. 8.

resting with its sharp edge upon a polished agate plane, in order to diminish friction. A long needle fixed at its upper extremity to the beam, and traversing at its lower extremity a graduated circular arc placed near the bottom of the supporting pillar, determines whether the beam is horizontal, according to its position. In order to relieve the knife-edge from pressure when the balance is not in use, the beam is supported by means of a moveable piece of mechanism called a fork. This mechanism rests on a fixed piece A A, having two vertical rods at its extremities. Two pieces D D, fitted to the beam, are intended to receive the pressure of the fork. The fork consists of a bar, a a, to which are fixed two horizontal cross-pieces E E, which rise with the fork, and support the two pieces DD, and with them the beam. The fork is guided in its motion by the rods at A A, which work nearly free of friction at its extremities. The motion of the fork is obtained by means of a button-handle at o, which transmits the turning motion made by the fingers to a screw placed in the interior of the pillar. The turning of this screw raises the fork and with it the two pieces E E, which in their turn raise the beam B B.

Fig. 10.

Unstable equilibrium is the state of a body in which, after it has 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 attempt to balance a rod when standing on the tip of the finger, or to make an egg stand on a horizontal plane or level table, so that its greater axis may be vertical.

Lastly, indifferent equilibrium is that state of a body in which it assumes any position which may be given to it. This kind of 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 carriage resting on its axle-tree, or a sphere resting on a horizontal plane. Fig. 9 shows three cones A, B, and c, placed in the positions of stable, unstable, and indifferent equilibrium respectively.

Fig. 9.

C

B

The Balance. A balance is an apparatus for measuring the relative weights of bodies. Balances are made of various constructions. The following is a description of a very delicate balance, fig. 10. It is constructed of a horizontal lever, BB, of the first kind, called the beam, at the extremities of which the scales or pans are suspended. The beam is furnished with a steel

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 exact 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 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 known weights of any kind until the equilibrium is again established. The amount of known weights thus obtained is the exact weight of the body; for in the operation, the body and the weights act on the same arm of the beam, in order to produce an equilibrium with the same resistance.