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; tomorrow it will rain.

Nous sommes arrivés aujourd'hui.

Votre frère s'est blessé hier.

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

GIRAULT DUVIVIER.

§ 137.-OBSERVATIONS.

J. CROSSLEY (Radcliffe): Not quite.-J. CHRISTIE (Montrose): Your 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 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, his brother.

(1.) The adverbs of comparison, plus, moins, must be repeated hound runs 8 rods in the time that the fox runs 5 rods; call this time 1: before every adjective which they modify

Il est moins paresseux et moins obstiné que son frère.

ANSWERS TO CORRESPONDENTS.

J. HEYWOOD, jun. (Lower Crumpsall): Of course we consider Cassell's "French and English Dictionary," and Cassell's "Lessons in French, l'art II.,” which is a French Grammar, as the best.-GEORGE B. (Woolwich): His writing is very good, but might be greatly improved, for a countinghouse.-J. H. (De Beauvoir Town): In using a dictionary of any language, take first the primary or natural meaning of any word, and try how it will answer in the passage to be translated: if this fails to make sense of the passage, then try the extended and metaphorical meanings. Any French book that is well written may be read by a student, provided there be no immorality or false doctrine contained in it: but we cannot afford either time or space to give an opinion on every book that may be proposed to us; our subscribers will kindly keep this in view. As to the questions relating to the form, size, price, &c., of the "Historical Educator," the "History of Hungary," and other works published by Mr. Cassell, we really wish that our subscribers would more carefully read our Literary Notices and Advertisements,

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. Scríngapalúm 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 12s.; 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, &c.-D. C. (Gravesend): Consult our Literary Notices and Advertise

ments.

WATSON: Read our articles on the University of London.-T. STOKES (Exeter): Punctuation and Elocution will come in their turn: many eminent persons speak highly in favour of Short-hand.-A. MUNRO (Preston): Music is at rest for a little.-D. W. (Leith): Finish one set of lessons before you begin another set; reading and conversation will supply you with words.-JOHN CHADWICK: Certainly; all right.-RESOLU VAINCRE (Staines): Zymotic comes from (vuow, to leaven, and this from Zvun, leaven; the latter again most probably comes from Cew, 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 Comparative 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 F. E. as a foundation for its studies and inquiries. Every word in English should then be traced and sifted 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 avoTeλλ comes from ovv, together, and TEλλw, 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 upadead 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."

E. CROSSLEY (Littleborough): Consult Barlow on the "Strength of

See p. 28, vol iv., at the bottom. An edition of the Greek New Testament may also be expected.-PHILO (Nottingham): Thanks; we recommend Cassell's Spelling Book as the best for a little girl.-G. W. A. (Slough): Read all our articles on the University of London, in vols ii, and iii. of the P. E.-W. H. Mc ELLEN (Manchester): The wolf, tiger, and lion question the Psalms into Latin verse is George Buchanan's, and it may be had of any is not correct.-CONSTANT SUBSCRIBER (Barnstaple): The translation of dealer in old books, from 6d. to 10s. according to the edition.-W. A. G. (London): See our Literary Notices.-TLOH 32 (Eastborn): In the equation 12x2-420x=-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.

LITERARY NOTICES

FRENCH.

Now ready, price 4s. in stiff Wrapper, or 5s. strongly bound in cloth, the First Part complete, consisting of the French and English, of CASSELL'S FRENCH DICTIONARY: the entire work will be completed in Twenty-six Threepenny Numbers, and will form one handsome Volume of eight hundred and thirty-two pages. Price 8s. 6d. bound in cloth, or the Two Divisions may be had separate.

A COMPLETE MANUAL OF THE FRENCH LANGUAGE, by Professor De Lolme, just published, price 3s. neatly bound. This forms one of the most simple, practical, and complete Guides to a thorough knowledge of the French Language which has hitherto been published. The plan upon which it is conducted is admirably calculated to accomplish the proposed object. In the first place, the Grammatical Principles of the Language are clearly laid down, and, secondly, these Principles are copiously illustrated by suitable Exercises of English to be turned into French.

CASSELL'S LESSONS IN FRENCH, in a neat volume, price 2s. in stiff covers, or 2s. 6d. neatly bound in cloth.

A KEY TO CASSELL'S LESSONS IN FRENCH, containing Translations of all the Exercises, with numerous references to the Grammatical Rules, price 1s. paper covers, or 1s. 6d. cloth.

GERMAN.

CASSELL'S GERMAN DICTIONARY is now issuing in Numbers, at 3d. each, Monthly Parts, 1s. each.

CASSELL'S LESSONS IN GERMAN, price 2s. in stiff covers, or 2s. 6d. cloth.

LATIN.

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. price 1s. 6d., containing Latin extracts for translation on the following subjects-Easy Fables, Mythology, Biography, The History of Rome, and Ancient Geography; with a suitable Dictionary. The second volume, which is publishing in weekly numbers, prices 2d. each, will coneist of useful Latin Exercises, or English sentences, to be translated into Latin, with numerous references to Andrews and Stoddart's Latin Grammar, a valuable treatise now in the press.

GREEK.

The Third Volume of CASSELL'S CLASSICAL LIBRARY will contain the Acts of the Apostles in the original Greek, according to the text of Augustus Hahn; with grammatical, historical, and expository Notes; followed by a Lexicon, explaining the meaning of every word-the whole carefully revised and corrected. This work is well adapted for the use of Schools, Colleges, and Theological Seminaries, and will supply our Greek students with excellent materials for practice in translation.

MISCELLANEOUS EDUCATIONAL WORKS.
CASSELL'S EUCLID.-THE ELEMENTS OF GEOMETRY. Containing the
First Six, and the Eleventh and Twelfth, Books of Euclid. Edited by Professor
Wallace, A.M., price 1s. in stiff covers, or 1s. 6d, neat cloth.
CASSELL'S ELEMENTS OF ARITHMETIC (uniform with Cassell's EUCLID)
is now ready, price Is. in stiff covers, or is. 6d. neat cloth.

THE SELF AND CLASS EXAMINER IN EUCLID, containing the enunciations of all the Propositions and Corollaries in Cassell's Edition, for the use of Colleges, Schools, and Private Students, is now ready, price 3d.

THE ANSWERS TO ALL THE QUESTIONS IN CASSELL'S ARITHMETIC, for the use of Private Students, and of Teachers and Professors who use this work in their classes, is just issued, price 3d.

Direction of Gravity; Vertical and Horizontal.-When the particles of a material sphere act, according to the law of attraction, in the inverse ratio of the square of the distance, upon a particle of matter situated without that sphere; it is demonstrated in 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 were all collected at its centre. It follows from this, that at every point on the surface of the globe the attraction of the earth is directed towards its centre. The depression of the earth at the poles, the difference in density between the masses of matter of which it is composed, and the inequalities of its surface as to mountains, valleys, and plains, are all so many causes which occasion slight deviations in the direction of gravity, but so slight as to be sensible only by a very small quantity.

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 seven-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 15:431 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

same.

Lastly, the specific weight, or, as it is often called, the specific gravity, of a body is the ratio of its relative weight, under a certain volume to that of an equal volume of distilled water at the maximum density. Hence, if we say that the specific weight or specific gravity of zinc is 7, the meaning is, that under an equal volume or bulk, zinc weighs 7 times heavier than distilled

water.

P

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 masses, or relative densities. For this reason, the rxpression relative density and specific gravity are generally considered as synonymous, or, at least, equivalent to each other. If, 10wever, 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 masses the same velocity in the same time. The weight P of a body being proportional to its mass, and to the intensity of gravity which may be represented by g, the product Mfg may be taken as the measure of this weight, that is Pg. Whence we have M, a formula for finding the mass when the weight is known. If in this equation we substitute I'D for M, according to the preceding formula relating to density, we have PVDg, a second expression for the weight of a body.' In the case of a body whose weight, density, and volume are represented by P', D', and V, we have, in like manner, PV'D'g. Comparing this result with the former, we have P: P:: VD: PVD V'D'. When DD', we have P: P' :: V: 17; and when P-P', we have VDV'D'; whence we have : V:: D: D. From these proportions we infer 1st, that when the densities of bodies are equal, their weights are proportional to their volumes; and 2nd, that when their weights are equal, their volumes are inversely as their densities. We shall soon show the method of determining the specific gravities of solids and liquids; but as the specific gravities of gases are determined with relation to the atmospheric air as unity, their determination must be taken up 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. 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,

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 who walks up a hill leans his body forwards; but he reverses this position when he goes down the hill; that is, he endeavours 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 at the centre of gravity of all bodies, equilibrium will always be produced if this force be counteracted by the resistance of a fixed equilibrium, according as the heavy body rests on one or several point through which its direction passes. There are two cases of points of support. In the first case, the centre of gravity must either coincide with the point of support, or be situated on the vertical which passes through this point. In the second case, the vertical drawn though the centre of gravity must pass within the base, that is, within the polygon formed by successively joining all the points of support. In the towers of Pisa and Bologna, which are so inclined to the horizon as to seem just ready to fall upon the passengers in the street, their equilibrium is still maintained, because their centres of gravity are situated on the verticals which pass through the interior of their bases. A man stands more firmly in proportion as he extends his feet and widens his base; he can thus give to his motions more amplitude, unless his centre of gravity is situated without this base. If he stands on one foot only, his base is diminished and consequently his firmness; these are diminished still more, if he stands on tiptoe. In this position, a very slight oscillation will throw his centre of gravity beyond the base, and destroy his equilibrium. A man who carries a load on his shoulders is compelled to lean forwards, lest he should be drawn backwards by the load; for his centre of gravity when loaded and standing erect is without the base; these different positions may be seen in the following cut.

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.

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. A long needle fixed at its upper extremity to the brium. beam, and traversing at its lower extremity a graduated circular are 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 eross-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.

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.

Enstable 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.

Conditions Requisite for a Good Balance.--In order that

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.