may, mẫnd the life of the greatest navigator of modern times. Capitact Jurka who was second in command, took charge of shi egyed to and sailed to the north-east in search of the passion as the Atlantic; but the same obstacles compelled him 3 Khandra, the enterprise, and he died on the voyage home. Erazmumps to describe all the benefits which the discoveries of Captain Cook have conferred on the sciences of geography and 1phy, is more than can be done in this historical sketch at these memorable expeditions. The accuracy with which has strious navigator determined the geographical positions at the places which he discovered or visited, rectified numerous es in the maps and charts of the century in which he fristed, and accelerated the progress of the science to which these remarks form our introduction, in a degree hitherto unMathematical geography has, since this time, taken her place among the exact sciences.

In concluding this lesson, we may remark that Cook lifted the veil of darkness which hung over the extremities of the Pacific Ocean, and the junction of the continents of Asia and America. His last voyage, by disclosing the vast breadth of America at the latitude of Behring Strait, made the hopes of discovering the north-western passage darker than ever. That continent had, previous to the time of the English navigator, been considered as terminating to the north in a point or cape, after passing which, the navigator would find himself at once in the South Seas, and in full sail to China or Japan. But the discovery of Cook showed that there was found intervening a apace of land of nearly three thousand miles in breadth, a very large portion of the circumference of the globe. Hence, geographers viewing the coast running northward from Behring Strait, Hudson Bay, and Baffin Bay, all enclosed by land, received the impression, and constructed their maps accordingly, that an unbroken mass of land reached onwards to the pole, and that all these boundaries were for ever barred against the

enterprising navigator.

LESSONS IN ARITHMETIC.-XI.
FRACTIONS (continued).

10. To reduce fractions to equivalent fractions having the same denominator.

KULE. Find the least common multiple of all the denominaMultiply the numerator and denominator of each fraction by the quotient obtained from dividing the least common multipe by that denominator.

XAMPLE. Reduce,,,, to a common denominator. 120 is the least common multiple of 9, 7, 10, 12 (see page 134), and tum quotients of 1260 by these respectively are 140, 180, 128, 10%. Multiplying each numerator and each denominator by Spemes tuumbers respectively, we get H,, which men fractions equivalent to the given ones, and all of which have kod sand, Alenominator.

900 756

much as 3 x 6 x 5 x 9, the common multiple of 3, 6, 5, and 9, which we have taken, is not the least common multiple. 12. We are enabled by this means to find which of two fractions is the greater. For instance, if we wished to know which of the four fractions given in Art. 11 is the greatest, having reduced them to a common denominator, 810, we are able to say that the second fraction, §, is the greatest, because it contains the greatest number of the 810 parts into which the unit is divided, viz., 675; and in the same way we see that the order of magnitude of the four fractions is , LI EXERCISE 24.

Place in order of magnitude the following sets of fractions:1. 2. 4, 3, 4. 3. 1, 16, 14. 5., 11, 1, 4. 2. 4, 1, 1, 4. 4. 13, 186, 1. 6., 14, 1, 4.

= 18+ =

(Art. 8).

or, as it could be written, 1 We have here effected the addition, i.e., found a single fraction which is equal to the sum of the two given ones, by reducing the fractions to a common denominator, 15.

The same method will apply to any other two or more fractions. Hence we are able to enunciate the following Rule for the Addition of Fractions.

Reduce the fractions to a common denominator, add the new numerators so formed for a numerator, and take the common will be the sum of the given fractions. denominator for a denominator. The single fraction so formed

fraction, before commencing the operation, to its lowest terms, Obs. It will generally be most convenient to reduce each if it is not already in them, and then to take the least common

denominator.

Hence the following

Hence

Rule for the Subtraction of Fractions.

Roduce the two fractions to a common denominator, subtract the less numerator from the greater for a numerator, and take the common denominator for a denominator. The fraction so formed will be the difference of the given fractions.

The same observation with respect to the least common denominator, which was made with reference to the rule for Addition, evidently applies equally to that for Subtraction.

N.B. In all cases a whole number must be treated as a fraction having a denominator unity. For instance, to subtract from 2. 2 == }

1. Find the difference between

3 × 3 × 6 × 9,

7 × 3 × 6 × 5,

3 x 6 x 5 x 9

3 x 6 x 5 x 9

2. Simplify the following expressions :

12. 5 and 3.

4. 411053 − + 300 + 41} + 472) — 230}.

LESSONS IN ENGLISH.-VI. HAVING thus furnished you with some criteria or means of ascertaining what words have their origin in Saxon, or, as it is more correctly called, the Teutonic branch of our language, I must now request, that in all your studies you will constantly ask yourself, whether each word you meet with, is, or is not, of Saxon derivation? Among English writers, no one has a larger portion of Saxon in his compositions than Dean Swift; and no one writes the language more correctly. I shall therefore make use of his writings in this part of my task. William Cobbett's works may be advantageously studied for the Saxon treasures which they contain.

EXERCISES IN PARSING.

It is a miserable thing to live in suspense. To live in suspense, is to live the life of a spider. No wise man ever wished to be younger. An idle reason lessens the weight of good reasons. Complaint is the largest tribute paid to heaven. Complaint is the sincerest part of our devotion.

Praise is the daughter of present power. Every man desires to live long. No man is willing to be old. Kings are said to have long hands. Kings ought to have long ears. Vision is the art of seeing things invisible. Good manners is the art of making assocates easy. Flattery is the worst and falsest way of showing our esteem. A fine gentleman has both wit and learning. Come into the garden, Maud. He gave me half-a-crown for my trouble. The king's crown is made of solid gold.

The reader may exeroise his ingenuity, as well as his grammar, while he discovers the explanation of a riddle of the learned Dean, which is appropriate to my subject:—

ance.

"We are little airy creatures,

All of different voice and features;
One of us in glass is set,
One of us you'll find in jet;
T'other you may see in tin,

And a fourth a box within;

If the fifth you should pursue,

It can never fly from you."

An excellent practice in composition is letter-writing. I shall therefore give, in this lesson, some specimens of epistolary correspondence. And I advise my pupils to accustom themselves to express their thoughts in the form of letters. Let the letters be real; I mean, let them be written, not as exercises in composition, but on some business, and to some friend or acquaintYour chief want at first, as I have before intimated, is the want of matter. "I don't know what to say," is a complaint with young composers no less true than embarrassing. You will find something to say if you take your pen in hand, and sit down to address a few lines to an absent friend. Only do not attempt anything great or fine. Be simple. Consult your heart, if your head is silent. Just say what occurs to you, without being anxious whether it is very wise or very foolish ; whether it is trivial or important. Specially would I advise my pupils to correspond one with another. For instance, say that a young man in Exeter writes a letter to a former companion who has gone to reside at Bristol. B., living at Bristol, replies The two continue to interchange letters. If they have nothing else to write about, they may write about these lessons. Let them endeavour to give each other aid in their study of the English language. Let them freely and kindly criticise each other's letters. Let them ask and give explanations. Let A. correct B.'s exercises, and let B. do the same for A. Let them agree on some book which they will both read, with a view to make in writing and submit to each other remarks on the composition. For this purpose I would suggest to them the Spectator, in which they will find many papers by Addison and other eminent writers.

to his friend A. at Exeter.

In this counsel I have mentioned young men, by no means intending to exclude young women. Most desirous am I that young women should receive a good education. Most necessary to them, as being the future mothers of our land, is a good education. A far better education ought they to receive than the best which they do receive. But to be well-educated they must be self-educated. Let young women then consider themselves specially addressed in the lessons I supply, and the advice I give.

LETTER I.

FROM DEAN SWIFT TO THE REV. WILLIAM DRAPER.

To the Rev. Mr. William Draper,

Dean, near Basingstoke, Hampshire.

London, April 13, 1713. SIR,-I am ashamed to tell you how ill a philosopher I am, and that a very ill situation of my affairs for three weeks past made me utterly incapable of answering your obliging letter, and thanking you for your condemned again to live in Ireland; and all that the court and minismost agreeable copy of verses. The prints will tell you that I am try did for me, was to let me choose my situation in the country

where I am banished. I could not forbear showing both your letter and verses to our great men, as well as to the men of wit of my acquaintance; and they were highly approved of by all. I am altogether a stranger to your friend Oppian; and am a little angry when those who have a genius lay it out in translations. I question whether "Res angusta domi" (narrow means) be not one of your motives. Perhaps you want such a bridle as translation, for your genius is too fruitful, as appears by the frequency of your similes; and this employment may teach you to write like a modest man, as Shakespeare expresses it.

I have been minding my Lord Bolingbroke, Mr. Harcourt, and Sir William Windham, to give you a living; as a business which belongs to our society, who assume the title of awarders of merit. They are very well disposed, and I shall not fail to negotiate for you while I stay in England, which will not be above six weeks; but I hope to return in October, and if you are not then provided for, I will move heaven and earth that something may be done for you. Our society has not met of late, else I would have moved to have two of us sent in form to request a living for you from my lord chancellor; and if you have any way to employ my services, I desire you will let me know it; and believe me to be very sincerely,

Sir,

Your most faithful, humble servant, JONATHAN SWIFT.

LETTER II.

FROM CHARLES LAMB TO SAMUEL TAYLOR COLERIDGE.

[Giving a detailed account of the death of his mother, who was stabbed by his sister, in a fit of delirium.]

me.

October 3rd, 1796.

MY DEAREST FRIEND.-Your letter was an inestimable treasure to It will be a comfort to you, I know, to know that our prospects are somewhat brighter. My poor dear, dearest sister, the unhappy and unconscious instrument of the Almighty's judgments on our house, is restored to her senses; to a dreadful sense and recollection of what has passed, awful to her mind and impressive (as it must be to the end of life), but tempered with religious resignation, and the reasonings of a sound judgment, which, in this early stage, knows how to distinguish between a deed committed in a transient fit of I have seen her. frenzy, and the terrible guilt of a mother's murder.

I found her, this morning, calm and serene; far, very far from an indecent forgetful serenity; she has a most affectionate tender concern for what has happened. Indeed, from the beginning, frightful and hopeless as her disorder seemed, I had confidence enough in her strength of mind and religious principle, to look forward to a time when even she might recover tranquillity.

God be praised, Coleridge, wonderful as it is to tell, I have never once been otherwise than collected and calm; even on the dreadful day, and in the midst of the terrible scene, I preserved a tranquillity which bystanders may have construed into indifference-a tranquillity not of despair. Is it folly or sin in me to say that it was a religious principle that most supported me? I allow much to other favourable circumstances. I felt that I had something else to do than to regret. On the first evening (September 22nd), my aunt was lying insensible, to all appearances like one dying,-my father, with his poor forehead plaistered over, from a wound he had received from a daughter dearly loved by him, and who loved him no less dearly,-my mother, a dead and murdered corpse in the next room-yet I was wonderfully supported. I closed not my eyes in sleep that night, but lay without terrors and without despair. I have lost no sleep since. I had been long used not to rest in things of sense,-had endeavoured after a comprehension of mind, unsatisfied with the "ignorant present time," and this kept me up. I had the whole weight of the family thrown on ine; for my brother, little disposed (I speak not without tenderness for him) at any time to take care of old age and infirmities, had now, with his bad leg, an exemption from such duties, and I was now left

alone.

I mention these things because I hate concealment, and love to give a faithful journal of what passes within me. Our friends are very good. Sam Le Grice, who was then in town, was with me the first three or four days, and was as a brother to me. He gave up every hour of his time, to the very hurting of his health and spirits, in constant attendance and humouring my poor father; talked with him, read to him, played at cribbage with him (for so short is the old man's recollection, that he was playing at cards as though nothing had happened, while the coroner's inquest was sitting over the way)! Of all the people I ever saw in the world, my poor sister was most and thoroughly devoid of the least tincture of selfishness. I will enlarge upon her qualities, poor dear, dear soul, in a future letter, for my own comfort, for I understand her thoroughly; and, if I mistake not, in the most trying situation that a human being can be found in, she will be found (I speak not with sufficient humility, I fear, but humanly and foolishly speaking), she will be found, I trust, uniformly great and amiable. God keep her in her present mind, to whom be thanks and praise for all His dispensations to mankind! C. LAMB.

LETTER III.

FROM LADY MARY WORTLEY MONTAGU TO HER SISTER, THE COUNTESS OF MAR.

[Giving a brief description of her journey from Ratisbon to Vienna, and some account of the last-named city.]

Vienna, September 8th, 1716.

I am now, my dear sister, safely arrived at Vienna; and, I thank God, have not at all suffered in my health, nor (what is dearer to me) in that of my child, by all our fatigues.

We travelled by water from Ratisbon, a journey perfectly agreeable, down the Danube, in one of those little vessels, that they very properly call wooden houses, having in them almost all the conveniences of a palace-stoves in the chambers, kitchens, etc. They are rowed by twelve men each, and move with an incredible swiftness, that in the same day you have the pleasure of a vast variety of prospects; and, within a few hours' space of time, one has the different diversion of seeing a populous city adorned with magnificent palaces, and the most romantic solitudes, which appear distant from the commerce of mankind, the banks of the Danube being charmingly diversified with woods, rocks, mountains covered with vines, large cities, and ruins of ancient castles. I saw the great towns of Passau and Lintz, famous for the retreat of the Imperial Court when Vienna was besieged.

This town, which has the honour of being the Emperor's residence, did not at all answer my idea of it, being much less than I expected to find it; the streets are very close, and so narrow one cannot observe the fine fronts of the palaces, though many of them very well deserve observation, being truly magnificent, all built of fine white stone, and excessively high. The town being so much too little for the number of people that desire to live in it, the buildings seem to have been projected to repair that misfortune by clapping one town on the top of another, most of the houses being of five, and some of them of six storeys. You may easily imagine that the streets being so narrow, the lower rooms are extremely dark, and what is an inconvenience much more intolerable, in my opinion, there is no house that has so few as five or six families in it. The apartments of the greatest ladies, and even of the ministers of state, are divided but by a partition from that of a tailor or a shoemaker; and I know nobody that has above two floors in any house, one for their own use, and one higher for their servants. Those who have houses of their own, let out the rest of them to whoever will take them; thus the great stairs (which are all stone) are as common and as dirty as the street. 'Tis true, when you have once travelled through them, nothing can be more surprisingly magnificent than the apartments. They are commonly a suite of eight or ten large rooms, all inlaid, the doors and windows richly carved and gilt, and the furniture such as is seldom seen in the palaces of sovereign princes in other countries—the hangings the finest tapestry of Brussels, prodigious large looking-glasses in silver frames, fine Japan tables, beds, chairs, canopies, and window curtains of the richest Genoa damask or velvet, almost covered with gold lace or embroidery, the whole made gay by pictures and vast jars of Japan china, and almost in every room large lustres of rock crystal.

I have already had the honour of being invited to dinner by several of the first people of quality, and I must do them the justice to say the good taste and magnificence of their tables very well answers to that of their furniture. I have been more than once entertained with fifty dishes of meat, all served in silver, and well dressed, the dessert proportionable, served in the finest china. But the variety and richness of their wines is what appears the most surprising. The constant way is, to lay a list of their names upon the plates of their guests, along with the napkins; and I have counted several times to the number of eighteen different sorts, all exquisite in their kinds.

I was yesterday at Count Schönbrunn, the vice-chancellor's garden, where I was invited to dinner, and I must own that I never saw a place so perfectly delightful as the Fauxbourgs of Vienna. It is very large, and almost wholly composed of delicious palaces; and if the emperor found it proper to permit the gates of the town to be laid open, that the Fauxbourgs might be joined to it, he would have one of the largest and best-built cities of Europe. Count Schönbrunn's villa is one of the most magnificent; the furniture, all rich brocades, so well fancied and fitted up, nothing can look more gay or splendid; not to speak of a gallery, full of rarities of coral, mother-of-pearl, etc., and, throughout the whole house, a profusion of gilding, carving, fine paintings, the most beautiful porcelain, statues of alabaster and ivory, and vast orange and lemon trees in gilt pots. The dinner was per. fectly fine and well ordered, and made still more agreeable by the good

humour of the count.

I have not yet been to court, being forced to stay for my gown, without which there is no waiting on the empress; though I am not without a great impatience to see a beauty that has been the admira. tion of so many different nations. When I have had that honour, I will not fail to let you know my real thoughts, always taking a particular pleasure in communicating them to my dear sister.

EXERCISES IN COMPOSITION.

1. Form sentences, each having in it one of the following words: :

Debts; light; sing; come; health; water; sky; home; day; night; lark; rose; Victoria; Mary; Henry; mother; bread; England; wife; buttercup; linnet; daisy; stone.

2. Give brief descriptions of the following objects and places:

A chair; a wheel of a coach; a kite; a waterpot; an oak-tree; the room in which you write; and the place where you work.

3. Write historical themes on the following subjects:1. The patriarch Abraham's visit to Egypt.

2. The battle of Hastings.

3. The conversion of St. Paul.

4. The murder of Thomas à Becket.

4. Write letters on the following subjects :

1. A letter of condolence to an intimate friend on the death of a near relation.

2. A letter to a friend in town, inviting him to pay you a visit in the country, and describing the scenery of the neighbourhood in which you live.

3. A letter of thanks to a gentleman who has enabled you to obtain a situation in a house of business by his recommendation.

LESSONS IN PENMANSHIP.-XI.

DUE attention to the instructions that have been given in the preceding lessons in the art of Penmanship, and assiduous practice for about an hour a day, will have rendered any one, who is endeavouring to learn to write from our copy-slips, a tolerable proficient in making letters, composed of right or straight lines, or lines that are commenced, or finished, or commenced and finished, as in the case of the top-and-bottomturn, with a hook or turn.

A great number of copies, consisting of letters of this kind, have been supplied to give the learner a sufficient variety in the words or combinations of letters that he is copying, and to give him confidence in his power to make the four strokes which enter into the formation of by far the greater part of the letters of

present it will be sufficient to deal with those into whose formation it enters without any alteration or modification whatever. The letter o is purely a curved letter, for no portion of it consists of a perfectly straight stroke, as the other letters which have already been brought under the reader's notice. It may be commenced on the straight line c c, but it is better to begin and end the letter at the point, a little above the line, as it is from this point that a fine hair-line is carried to the right, when it is necessary to connect the letter o with any letter that may follow it, as the learner will see in Copy-slip No. 40. Commencing, then, at the point, the hair-line, of which the right side of the letter consists, is carried upwards to the line a a, and then turned to the left and brought downwards. By a gradual pressure on the pen the hair-line is now turned into a thick stroke, which attains its broadest part at the line c c, when the pressure

the writing alphabet, before he begins to make the remaining elementary strokes, which are of less frequent occurrence. The practice that he has now had, and the knowledge and amount of skill in writing that he has already acquired, will enable him to advance more rapidly, and we shall proceed as quickly as possible to the end of our elementary lessons in the formation of the small letters of the writing alphabet, as exhibited in large text, giving fewer copies than we have hitherto done, for the sake of affording practice in the formation of each particular letter in combination with others.

In Copy-slip No. 35 the learner's attention is directed to the letter o, which is a complete and perfect letter in itself, while, at the same time, it may be considered as a simple elementary form, since it enters into the composition of the letters a, d, and q. It also influences the formation of many other letters of the alphabet, as the learner will see hereafter; but for the

of the pen is relaxed, and the thick down-stroke is gradually narrowed again into a hair-line, which is turned upwards towards the right and joined to the hair-line with which the letter was commenced at the point 2. The learner will notice that the upper part of the letter o, which lies above the line c c, is the only portion of the letter that is really new to him, for the lower part of the letter is very nearly the same as that portion of the bottom-turn or top-and-bottom-turn which is below the line c c.

In Copy-slip No. 36 the letter O and the bottom-turn are given. These strokes, in combination from the letter a, as in Copy-slip 37, the bottom-turn being appended to the letter O in such a manner that the point where the hair-line forming the right side of the letter cuts the line c c lies in a line passing along the centre of the thick down-stroke of the bottom-turn. The letters d and q are formed by adding modifications of the bottom-turn to the letter O, as shown in Copy-slips 38 and 39.