eye, but considerest not the bevin || that is in thine own VII.-RIGHT EMPHASIS. Emphasis distinguishes the most significant or expressive 9. “ As it is the part of justice I never to do violence. so it is words of a sentence.

the part of modesty || never to commit offence." It properly includes several functions of voice, in addition 10. “A friend | cannot be linoun 11 in prosperity, and an enemy to the element of force. An einphatic word is not unfrequently I cannot be hidden || in adversity." distinguished by the peculiar time,' 'pitch,' 'stress,' and inflection of its accented sound. But all these properties cmphatic) are sometimes pronounced on a lower, sometimes

NOTE. Emphatic clauses (those in which every word is are partially merged, to the ear, in the great comparative force on a higher key, but always with an intense force. of the sound. Hence it is customary to regard emphasis as merely special force. This view of the subject would not be

Examples. practically incorrect, if it were understood as conveying the

1. “Heaven and earth will witness,
idea of a special force superadded to all the other character-
istics of tone and emotion, in the word to which it applies.

Ir! ROME MUST FALI,—that we || are innocent."
Emphasis is either absolute' or relative.' The former

2. “This state had then not one ship,-NO, NOT' ONE' occurs in the utterance of a single thought or feeling, of great

WALL !" energy; the latter, in the correspondence or contrast of two 3. “But youth, it seems, is not my only crime: I hare

been accused of acting a ThEATRICAL part.". or more ideas. Absolute'empliasis is either 'impassioned' or 'distinctive.'

4. “ As to the present ministry, I cannot give them my conThe former expresses strong emotion.- Example. " False wizard, fidence., Pardon me, gentlemen : Confidence is a plant

of slow AVAUNT !"'*-'The latter designates objects to the attention, or growth.distinguishes them to the understanding. Ex. “The fall of General Remark. Young readers are commonly deficient in man is the main subject of Milton's great poem."

emphasis, and, hence, feeble and unimpressive, in their style • Relatire' emphasis occurs in words which express compari- of reading. Students should exert much vigilance on this 80n, correspondence, or contrast. - Examplc. * Cowards die point. At the same time, an overdone emphasis is one of the inany times; the brave but once."

surest indications of defective judgment and bad taste.

Faults which result from study are always the most offensive.
Rules on Emphasis.

Rule 1. Exclamations and interjections usually require
'empassioned' emphasis, or the strongest force of ulierance. The true Christian must show that he is in earnest about
Examples. " Woe! to the traitor, WOE!"-"UP! comrades religion. In the management of his worldly affairs, he must
UP!"" AWAKE! ARISE! or be for EVER FALLEN !" let it clearly be seen, that he is not influenced by a worldly
" Ye icefalls !

mind; :bat his heart is not upon earth; that he pursues his Motionless torrents! silent cataracts !

worldly calling from a principle of duty, not from a sordid love Who made you glorious as the gates of heaven,

of gain ; and that, in truth, his treasures are in heaven. He Beneath the keen full moon:

must, therefore, not only “provide things honcsi in the sight God! GOD! the torrents, like a shout of nations,

or all men ;", not only avoid every thing which is fraudulent Uurcr: the ice.plain bursts, and answers, God!

and unjust in his dealings with others; not only openly protest The silent snow mass, loosening, thunders, GOD!"

against those iniquitous practices which the custom of trade too

frequently countenances and approves ;- but, also, he must "let Role II. Every new incident in a narration, every new object his moderation be known unto all men. He must not push in a description, and every new subject in a didactic passage, his gains with seeming eagerness, even to the utmost LAWFUL requires distinctive' emphasis, or a sorce of utterance suffi-extent. He must exercise forbearance. He must be content cient to render it striking or prominent.

with moderate profits. He must sometimes even forego advanExamples. “Their frail bark was, in a moment, overset, and tages, which, in themselves, he might innocently take, lest he a watery grave seemed to be the inevitable doom of the whole should seem to give any ground for suspecting that his heart is party."

;">The eye rested with delight on the long, low range secretly set upon these things. of beautifully tinted clouds, which skirted the horizon."

Thus, also, with respect to worldly pleasures ; he must -"The power of faith was the subject of the preacher's endeavour to convince men that the pleasures which ReLIGION discourse.

furnishes, are far greater than those which the world can yield. RULE III. Al correspondent, and all antithetic, or con. While, therefore, he conscientiously keeps from joining in trasted words, require a force sufficient to distinguish them those irifling, and, too often, profane amusements, in which from all the other words in a sentence, and to make them stand ungodly men profess to seek their happiness, he must yet labour out prominently. When the comparison or contrast is of to show, that, in keeping from those things, he is, in respect equal force, in iis constituent parts, the emphasis is exactly to real happiness, no loser, but even a GAINER by religion, He balanced, in the words to which it is applied : when one of must avoid every thing which may look like moroseness and the objects compared or oontrasted is meant to preponderate gloon. Ile must cultivare a cheerfulness of spirit. He must over the other, the emphasis is stronger on the word by which endeavour to show, in his whole deportment, the contentment the preponderance is expressed.

and tranquillity which naturally flow from heavenly affections, Examples. "The gospel is preached equally to the rich and from a mind at peace with God, and from a lope full of IMMORto the poor."-"Custom is the plague of wise men, and the idol of fools," "The man is more Knave than fool."

The spirit which Christianity enjoins and produces, is so

widely different from the spirit of the world, and so immensely Exercises in 'Relative' Emphasis.

superior to it, that, as it cannot fail of being noticed, so it cannot 1. "Virtue || is better than riches."

fail of being admired, even by those who are strangers to its 3: Study | not so much to show knowledge, as to acquire it.” power. Do you ask in what particulars this spirit shows itsell? They went out from us, but they were not of us."..

I answer, in the exercises of humility, of meekness, of gentleness ; 4. "lle | that cannot bear a jest, should not make one."

in a patient bearing of injuries; in a readiness to forgive offences ; 6. "It is not so easy to hide one's faults, as to mend them."

in a uniform endeavour to orercome evil with good ; in self denial 6. "If that denied thee gold, will give my heart...

and disinterestedness ; in universal kindness and courtesy; in 7. “You have done that you should be sorry for."

slowness to wrath; in an unwillingness to hear or to speak evil 8. “Why beholdest thou the mote | that is in thy brother's of others ; in a forwardness to defend, to advise, and to assist

them ; in loving our enemics ; in blessing them that ourse us; in

doing good to them that hate us. These are genuine fruits of Three degrees of emphasis are usuilly thus denoted in type: the first, true Christianity. by Italic Sellers; the second, by small capitals; and the third, by large fatale. Thus, you shall bie, Dase pool and that before you cloud charging in a faithful, a diligent, and a consistent manner, the per

The Christian must " let his light shine before men,” by disa has passed over the sun!"~Sometimes a fourth, by Italic capitals,-thus, Isonal and particular duties of his station. "NEVER, NEVER, NEVER!"

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As a member of society, he must be distinguished by a blame- elle ;' alors elle recueillite ce qui lui restait de forcesd et less and an inoffersire conduct; by a simplicity and an ingenuous voulut s'enfuir. Mais, hélas ! comment une enfant si faible, ness of character, free froin every degree of guile; by uprightness et dont tous les membres sont presque engourdis, pourra®-tand fidlity in all his engagements.

elle échappper à ce danger ? Déjà l'our est sur le point As a neighbour, he must be kind, friendly, and accomodating. de l'atteindre, Fædora pousse un cri, appelant au secours. His discourse must be mild and instructive. He must labour in Par une faveur inespérée de la providence, au moment où prevent quarrels, to reconcile those who differ, to comfort the la bête féroce se précipite sur elle, un coup de feu' part, aflicted.“ In short, he must be "ready for every good work ;" et l'ours tombe. Bientôt un étranger arrive à la place où and all his dealings with others must show the HEAVENLY Fædora s'était arrêtée, à peine revenue de son effroi.? Il PRINCIPLE which dwells and works in his HEART,

regarde avec bonté et d'un ail de compassion cette enfants Exerc136.

dont le ciel venait de lui confier le salut. The real glory and prosperity of a nation does not consist in C'était un gentilhomme polonais appelé Polowski," il tira the hereditary rank or titled privileges of a very small class in the de sa gibecière de la viande froide , du pain, du vin, et en community; in the great wealth of the few, and the great poverty offrit à Fædora, ce qui la ranima bientôt. Puis il prit l'enof the many; in the splendid palices of nobles, and the wretched fant par la main et l'emmena' dans son château, i éloigné huts of a numerous and half-famished peasantry. No! such a d'environ deux lieues. state of things may give pleasure to proud, ambitious, and selfish minds, but there is nothing here on which the eye of a patriot noble Polonais,12 ne tarda pas à se rétablir de 13 toutes ses

Là, Fedora accueillieavec bienveillance par la femme du can rest with unmingled satisfaction. In his deliberate souffrances. Elle put alors leur raconter tout ce qu'elle sajudgment, ]Il fares the land, to hastening ills a prey,

vait de son histoire.ló Emus jusqu'aux larmes par le récit Where wealth accumulates, and men decay,

de l'enfant, Polowski et sa femme la comblèrent des plus Princes and lords may flourish or may fade ;

touchantes caresses, 15 et Fædora n'eut bientôt plus que le

souvenir de scs maux.
A BREATH can make them, as a breath has made
But a BOLD PEASANTRY, their country's pride,

Plusieurs années s'écoulèrent 16 ainsi sans qu'on apprit
When once DESTROYED, can never be supplied.

rien des parents de Fædora. Cependant, elle avait grandi It is an intelligent, virtuous, free, and extensive population, able, en sagesse et en beauté ; rien n'avait été négligé 1 pour by their talents and industry, to obtain a competent support, former au bien son cæur et son esprit. Elle avait alors which constituies the strength and prosperity of a nation. quinze ans. Chaque année, le jour de sa délivrance était

It is not the least advantage of a popular government, that un jour de fête.!! Durant l'une de ces réunions, tandis que
it brings into operation a greater amount of talent than any Fædora racontait de nouveau les accidents de son enfance 20
other. It is acknowledged by every one, that the occurrence of si agitée, et passait en revue tous les bienfaits dont la com-
great erents awakens the dormant energies of the human mind, blaient tous les jours ses parents d'adoption, on entendit
and calls forth the most splendid and powerful abilities. It was l'explosion d'un coup de fou? parti à quelque distance du
the momentous question, whether your country should be free chateau.
and independent, and the declaration that it was so, which gave
to you orators, statesmen, and generals, whose names all future flocons et obscurcissait le ciel de manière à ce qu'on ne pût

Le vent souffait avec violence, 22 la neige tombait à gros a9c3 will delight to honour.

The characters of men are generally moulded by the circum- rien voir à trois pas devant soi. stances in which they are placed. They seldom put forth their -C'est quelque voyageur égaré qui demande du secours strength, without some powerfully exciting motives. But what ou qui est attaqué par les bêtes féroces,23 car il est impossimolives can they have to qualify themselves for stations, from ble de se livrer au plaisir de la chasse par un temps semblawhich they are for ever excluded on account of PLEBEIAN ble, s'écria Polowski, et il donna l'ordre à ses gens d'aller å EXTRACTION ? How can they be expected to prepare themselves sa recherche. Lui-même se mit' à la tête du cortège, 24 qui for the service of their country, when they know that their se dirigea vers la forêt. Quelque temps après, il reparut. services would be reJXCTED, because, unfortunately, they Les domestiques portaient sur un brancard le corps d'un dissent from the established religion, and have the honesty to Russe ensanglanté.25 Fædora se précipite au devant son

But in a country like ours, where the most obscure indivi- compatriote ; elle-même veut panser sa blessure. Bientôt duals in society may, by their talents, virtues, and public services, celui-ci put témoigner sa reconnaissance aux hôtes du château rise to the most honourable distinctions, and attain to the highest et leur raconter son histoire. offices which the people can give, the most effectual inducements are presented. It is indeed true, that only a few who run in

COLLOQUIAL EXERCISE. the race for political honour, can obtain the prize. But, 1. Où Fædora fut-elle con.

14. Que raconta-t-elle à ses although many come short, yet the exertions and the progress

duite ?

bienfaiteurs ? which they make, are not lost either on themselves or society, 2. Qu'étaient derenus 8CS 15. Comment Polowski et så The suitableness of their talerts and characters for some other

compagnons ?

femme traitèrent-ils notre hé. important station may have been perceited; at least the cultiva

3. Où se trouva la petite Mos. roïne? tion of their minds, and the effort to acquire an honourable covite?

16. Apprit-on bientôt des nou. reputation, may render them active and useful members of the

4. Que vit-elle soudainement velles de ses parents ? community. These are some of the benefits peculiar to a POPULAR

au milieu de la forêt ?

17. Prit-on soin de son éducigorcinment; benefits which we have long enjoyed.

5. Que fit Fædora à l'approche tion?
de l'ours ?

18. Quel ige avait-elle ?

6. Comment échappa-t-ello à 19. Que faisait-on chaque aile FRENCH READINGS.No. XI.

un si grand danger?


7. Que vit alors Fædora ? FEDOR A.

20. Que faisait Fædora dans 8. De quelle manière l'étranger

une de ces réunions ? SECTION II.

regarda-t-il l'orpheline ?

21. Qu'entendit-on alors ? Cependant Fadora parvint jusqu'en Pologne avec un dé: 10. Que fit alors le gi ntilhomme

9. Qui était l'étranger?

22. Quel temps faisait-il dans

ce moment ? tachement de troupes ;', plusieurs de ses compagnons

23. Que dit Polowaki en enterre voyage avaient succombé, moissonnés par le froid ou par la 11. Que fit pour l'enfant ? dant le coup de fou? fuim, et les autres se disperserent? tout à coup, de sorte!

12. Par qui Fedora fut-elle ac

21. Quo fit-il alors ? que la petite Moscovite se trouva seule, abandonnée au

cucillie ? milieu d'une forêt." Mourante de froid, ayant de la neige 13. Fut-elle long-temps à se ré

25. Que portaicut les domca

tiques ? jusqu'aux genous, elle vit soudain un ours se diriger vers tablir?

AYOW it!

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NOTES AND REFERENCES.-a. parvint, reached; froin parvenir; | if necessary, keep a good dictionary, beside you, and when you are L. part ii., p. 98.—b. de sorte que, so that.—c. from recueillir; at a loss, look for the required word in the dictionary, and there L. part ii., p. 102.-d. ce qui lui restait de forces, her remaining you will see the true order of spelling. After a little practice in strength. - from pouvoir ; L. part ii., p. 100.--f. coup de feu, forming the letters into words, proceed to put the words into a shot.-9. L. S. 25, R. 2.—h. L. S. 81, R. 1.-i. L. S. 43, R. 6. at a time) from a book; and never forget to make use of good

sentence; this is best done by copying some short sentences (one --j. from accueillir; L. part ii, p. 76.– k. from apprendre; L. authors for imitation in this respect. part ii., p. 78.—from mettre ; L. part ii., p. 96.-m. L. S. 84, You may next write whole sentences, following each other so as R. 5.

to form a subject. Learn a ve: 89 of the Scriptures, or a passage from some author of good erudition and well-meaning principles, and having committed it to memory so as to retain an idea of the

true drift and real meaning thereof, close the book, and write the CORRESPONDENCE.

sentence, verse, or passage entirely from recollection; having done

so, open the book, and if on comparison you find your copy doth HINTS ON SELF-EDUCATION.

not in word and sense agree therewith, I would advise you to corADDRESSED CHIEFLY TO THE YOUNG.

rect it, by making proper alterations on what you have wrongly

written; nevertheless, though one word or more may be different WHERBAS I find that a former paper, the production of my pen, from the original, if the meaning be not materially affected, and it 00, " Self-Education briefly considered," inserted in the P. E., be written so that the real sense of both is the same, it need not be volume iii., page 59, was well pleasing to some of its readers, altered. By proceeding in this manner, you will acquire a capacity and I hope conveyed a lesson of encouragement to others, for useful thinking; and you will be able to form a composition I hereby aim at another endeavour to advise those who, in their for yourself, by drawing conclusions from your own stock of desire to obtain knowledge, may be left comparatively to them. mental ideas. selves, and who perhaps have not the leisure, the opportunity, or To understand the method of casting accounts, or, as we may the fortitude to apply at any time to a tutor. Besides, my advice say, making calculations in the science of numbers, called arithmay meet the eye of such as prefer a course of instruction by them. metic or cyphering, get a book on arithmetic, and therein you will selves, and it may encourage them to make progressive advances find rules for casting up sums and working the diverse rules of both in literature and science.

arithmetic, together with useful directions for performing the said Ny ardent wish is to convince my young friends, as well as my operations, and necessary tables for assistance; but arithmetic, as more adult sellow-students, that the alphabet once learned, or at well as many other valuable departments of knowledge, is most most with a few short words besides the letters, a person is in a fully explained in Cassell's P. E. fair way of attaining sell-education. To the truth of this I am The first four rules of arithmetic are addition, subtraction, mul. able to testify, as it was the case with myself; and that, too, under tiplication, and division, called the four fundamental rules; these a grierous weight of affliction and conscquent discouragement, must be first mastered, for by them all the other rules are perbeing at the age of six years so debilitated in my limbs, the weak formed. It is best to get the tables by heart, that while doing a Dees extending from the spine down wards, that I have never since sum, any required part of the necessary table may occur to the walked or even stood on my feet; and of course I am quite unable retentive memory. to earn a livelihood; but the main incentive to my studies was an You may succeed in the study of any foreign language without a ardent thirst for knowledge and innate desire for usefulness. master, if you first make yourself well acquainted with your native

Being thus circumstanced, dwelling in a lone habitation, and tongue, as explained in books of English grammar and of English being deprived of those opportunities possessed by others of seeing literature. You may likewise make self-progress in geometry, the world, I was for some few years not conscious of the existence navigation, and other useful accomplishments, by obtaining the of any publications, except such tooks as from time to time I proper books written on these subjects, and, by attentive perusal, found to be in the rooms of my residence; consequently, I was making yourself master of their contents a little at a time ; and quite a stranger to orthography. Accordingly, I learned to commit above all, do not attempt to acquire too many kinds of information the words I read to memory, without knowing the true pronuncia- at one and the same period of life. In every difficulty do not lose tion of many of them; but afterwards, alighting on some spelling sight of my now repeated recommendation, to solicit the kind books, wherein I observed the rules of accentuation explained and assistance of some well-meaning, candid proficient in scholarship. the exercises marked, I got over my first difficulty, and soon un.

Do not relax from your studies; let your application to the attainlearned the sounds which I had already so imperfectly acquired. ment of knowledge be earnest, diligent, persevering, and constant, Now, I would advise any one who may be destitute of a teacher to and you will be sure to improve and succeed in your learning. take the like course of self-instruction, without being discouraged Children stand most in need of a teacher; their mental capacities by the want of a teacher, or intimidated by difficulties, for they are have (so to speak) only begun to develop themselves; ihus some not insurmountable; and if a dificulty occurs which he finds too verbal director is the more required for them, in order to teach

the perplexing for the mental efforts of self-cultivation, recourse should young idea how to shoot. I have known some people strangely be had in that case to some educated person of good judgment and blame young boys for not making quicker progress; yet those sound understanding, who (whether it relate to reading, writing, same persons will tell me that they themselves have no time for

: the sciences) may be able to point out the true method, and application to lessons of instruction; but many hours which are was remove, or at least, by verbal explanation, lessen the 'diffi

. sometimes extravagantly wasted, would go a very considerable culty. After a long period, I perused Johnson's Dictionary (small way towards their own improvement, and their usefulness in dition), and for a short time only; and in subsequent years, by forming the minds of their children, the loan of the works of various lexicographers, and other kinds of My young friends, I anxiously advise you to guard against disliterary and scientific works, I obtained a greater insight into lan: sipation, drunkenness, and riot. By living soberly and tempeguage, and some skill in the pronunciation, the accentuation, and rately your minds will retain a greater clearness of ideas, and will the meaning of words.

be better adapted for engaging in mental exercises, Let it be your Thus may you, my young thinkers, lay the foundation, and aim to steer through the voyage of life by the rules of the Sacred there on build the superstructure of your own accomplishments; Scriptures, and in conclusion I bid you God speed. remembering, as I said before, that so to do you need to have

West Road, near Bridport,

HENRY HALLETT. learned only the alphabet, or at any rate a few little words, which April 5th, 1854. will enable you to make self-progress. Begin writing by first learning to form all the letters of the

ECLECTIC INSTITUTE, 132, BROAD STREET. alphabet, copying the characters from well-shaped letters fairly written, and if your model be the production of a masterly hand, it SIR, -I have read your POPULAR EDUCATOR, and induced a will greatly facilitate your attainments in the first use of the pen. number of my friends to do the same; the result has been the Observe that at first you need a copy of the letters only, and this formation of classes for the study of Music, French, Mathematics, may be had from well-printed letters in the written character. &c. We have also lectures, discussions, &c., and a library. I While writing, endeavour to impress on your mind the image of a you think well of this, and refer your' readers in town to our good letter, and you will soon be enabled to make

a good imitation Institute, we shall be glad to see them; and I doubt not they will of the same; it is necessary, however, to hold your pen in the derive from association advantages the same as, or similar to, right position, and to keep it firm in the fingers.

those which we have ourselves obtained. Many young men When you can well form the characters, you will find it quite cannot study conveniently at home, and some cannot afford to easy to join several letters together to form a word. Be sure pay the expense of teachers; to such we give our invitation. If alsó to spell every word right; and in order to assist your spelling, you will notice this in your Educator, you will oblige yours

faithfully in the cause of enlightenment,

CHARLES C. CATTELI, Secretary. • See Vol. il. P.E.

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First Two


order that it may not be hindered in its motion, it rests on two

glass rollers. ON PHYSICS, OR NATURAL PHILOSOPHY. The bar k h having been carefully measured at 0° Centi.

grade, and placed as shown in the cut, that is, in contact with No. XXXIII.

the two rules, and the telescope being horizontal, we observe

to what division it corresponds on a vertical scale A B placed at (Continued from page 81.)

a great distance. We then replace the bar k by a second

bar longer by a given quantity, say one-tenth of an inch. The EXPANSION OF SOLIDS.

rule D being thus displaced and made to assume the position

GC, imparts to the axis of the telescope a motion of rotation, Kinds and Co-efficients of Expansion. Two kinds of expansion and makes it take the oblique direction G B. By looking then in 80!ids were mentioned in a former lesson, viz., Linear Expan- through the telescope, we read off from the scale of deviation sion, or that which takes place in the direction of one dimen- the quantity A B, which we shall suppose contains 180 divi. sion only; and Cubic Expansion, or that which takes place in sions; this result being obtained, we remove the second bar the volume or bulk. The co-efficient of linear expansion is the and restore the first to its place; we then heat the furnace, elongation or increase which a unit of the length of a body having filled the trough with oil, a liquid which can be cartakes, when its temperature is raised by 1o Centigrade from ried to a much higher temperature than water. In proporthe freezing point; or, it is the increase in its length for every tion as the heat increases the bar is lengthened, and the teledegree between the freezing and the boiling points of water. scope is again made to take an oblique direction. The number The co-efficient of cubic expansion is the increase which a unit of divisions which it indicates on the scale are then measured, of the rolume of a body takes under the same circumstances. say 120, and at the same time the temperature of the

bath, by These co-efficients vary in different bodies; but for the same means of the thermometer, a temperature which we shall supbody there exists a simple relation between the two co-effi. pose to be 80o Centigrade. From these data, it is easy to cients

, viz., that the co-efficient of cubic expansion is three deduce the elongation uc of the har. For, since 180 divisions times the co-efficient of linear expansion, for all ordinary of the scale, from A to B, correspond to an elongation of the purposes. Thus by multiplying or dividing by the number 3, bar by one-tenth of an inch, a deviation of a single division is we can always find one of these co-efficients when the other equivalent to an elongation of Tobo of an inch ; consequently, is known.

a deviation of 120 divisions is equivalent to an elongation of To demonstrate that the preceding rule is correct for gradual 120 times nabo of an inch, that is 100% or is of an inch; or, as expansions, suppose that a cube whose side is unity, or 1, is at 180: 120 :: 4:15. 00 Centigrade." "If we represent the increase which the length The length x o being thus determined, we obtain the coof a side of the cube receives in rising from 0° to 1° Centigrade efficient of linear expansion—that is, the elongation which corby 1, its length at the latter point will be 1+l, and the volume responds to a single degree and to a single unit of length—by of the cube, which was 1 at the former point, will now be dividing the elongation thus obtained, by the temperature of (1 +73 or 1+31 +382 +38. Now, the increase in length in the bath, and by the length of the bar at 0° Centigrade-or, is always a very small fraction, as will be seen in a subsequent by the product of these quantities. If in the experiment just table ; therefore, its square 1 and its cube B, are in general mentioned we had taken, for example, a bar of lead of 29% fractions so very small, that they have no effect on the final inches, we should obtain the co-efficient of the linear expandecimal of the numbers which represent the cubic expansion. sion of lead, by dividing is of an inch by the product of 29% These quanties are consequently neglected in practice, and the and 80; thus,


= 0.000028571 ; and this would volume of the body at 1o becomes approximately 1 + 31.

'15 x 29 x 80

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linear expansion.

The increase of the volume is therefore 31, that is, triple the then be the linear expansion required. If this experiment be

made on different metals, and repeated with various temperaDetermination of the Co-efficients.-MM. Lavoisier and Laplace tures between 0 and 100° Centigrade, it will be found that determined the co-efficients of the linear expansion of the the co-efficient of the linear expansion of the metal between metals by means of an apparatus represented in fig. 174. these limits is sensibly constant; that is, for the same number It is composed of a copper trough placed on a stove or fur- of degrees,

the length increases constantly by the same fraction nace between four blocks of stone. The two which are on the of the length which it had at 0° Centigrade. But, according to right of the cut support a horizontal axis, at the extremity of the researches of MM. Dulong and Perit

, the co-efficient which there is a telescope ; and in the middle of this axis is becomes greater between 1000 and 200° Centigrade, and fixed a glass rule, which turns with it as well as the telescope. increases between 2009 and 300° Centigrade, and so on, to the In the other two blocks are fixed two iron cross-pieces which point of fusion. Tempered steel is an exception; its co-efficisupport a second glass rule. Lastly, in the trough, there is a ent decreases when its temperature passes a certain

limit. The water or oil bath, where the bar is placed, whose co-efficient of following is a table of the expansions of the most useful metals, expansion is to be measured.

when heated from 0° to 100° Centigrade, or from 32° to 2120 Fig

. 175, is the representation of a section of the apparatus. Fahrenheit ; that is, of the co-efficients of their linear expane is the telescope, k'u the bar, of which the two

ends rest on sion for the distance between the freezing and the boiling points the two glass rules p and D. The rule p being fixed, the bar of water, according to MM. Dulong and Petit, Lavoisier, and can only be lengthened in the direction from * to h; and in others.

111 :


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