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THE WEEK. NOVEMBER 15.-The anniversary of the birth of William Pitt, commonly distinguished as the Great Lord Chatham. This illustrious statesman was born at London in the year 1708, and was the son of Robert Pitt, Esq., of Boconnoc in Cornwall. He was educated first at Eton and afterwards at Trinity College, Oxford, of which he was entered a gentleman commoner in 1726. On leaving the university he purchased a cornetcy in the Blues; but urged probably by the desire of obtaining a more suitable field for the display of his abilities than a military life afforded, in 1735 he procured himself to be returned to parliament for the family borough of Old Sarum. Sir Robert Walpole was then at the head of affairs; and Pitt immediately joined the opposition, which eventually compelled that minister to retire in 1742. For the part which he thus took he was, the year after he entered parliament, deprived by Walpole of his commission, but was compensated by being made one of the Gentlemen of the Bedchamber to the Prince of Wales. His eloquence, as soon as he began to take a part in the debates, raised him to distinction and importance; and imperfectly as the proceedings of the House were then communicated to the public, his reputation as one of the most powerful speakers of the day seems to have rapidly spread itself over the nation. It was in 1740, in the course of this contest with Walpole's administration, that, on a motion relating to impressment, he made his famous reply to Mr. Horatio Walpole, the brother of the minister, vindicating himself from the double charge of youth and theatrical elocution, which Johnson reported with so much spirit in the Gentleman's Magazine.' Walpole's administration was succeeded by that of Lord Carteret (afterwards Earl of Granville); but this change did not introduce Pitt to office. The celebrated Sarah Duchess of Marlborough, however, left him in 1744 a legacy of £10,000, in reward, as it was expressed in the will, of the noble disinterestedness with which he had maintained the authority of the laws, and prevented the ruin of his country. The following year he resigned his post in the household of the prince. In 1746, under the premiership of the Duke of Newcastle, Mr. Pitt was for the first time chosen to fill a place in the Government, being appointed to the office of Vice-Treasurer for Ireland, from which he was transferred the same year to that of Paymaster-General of the Forces. In this situation, which he held for nearly nine years, he displayed his characteristic activity, energy, and decision, and the most high-minded integrity and contempt for many of the customary profits of office. In 1755, however, on a disagreement with the majority of his colleagues, he resigned but, in little more than a year after, the force of public opinion compelled his recall; and on the 4th of December, 1756, he was appointed principal Secretary of State. In the April following, finding his views still thwarted by the rest of the cabinet, he again retired; but within less than three months the King was obliged to yield to the national voice, the ministry was driven from power, and a new one was formed under the auspices of Pitt, who, reinstated in his former place of Secretary of State, now exercised under that name the authority of Premier. For the next four years Pitt may be regarded as having been the director of the energies of England; and they are four of the most glorious years in the history of the country. Victory crowned the British arms wherever they appeared, whether on sea or on land; the French were beaten at almost every point both in the east and in the west; the vast territory of Canada was wrested from them, almost before the Government at home was aware that it was in danger; and they were eventually stripped of nearly all their other colonies in every part of the world. Along with these successes abroad, tranquillity and contentment at home no less remarkably distinguished the

supremacy of this able, patriotic, and popular minister. In October, 1760, George II. died, and the ascendency of new principles, which the new reign brought along with it, before long compelled Pitt to tender his resignation of his services. His administration terminated, and that of Lord Bute commenced in October, 1761. Although Pitt, however, had found it necessary to retire from the management of affairs, his sovereign was so sensible of his great deserts, that a barony was bestowed upon his lady, and a pension of three thousand a year granted to him for their conjoint lives and for that of his eldest son. After this, he remained out of office till 1766, when, after the failure of the Rockingham administration, it was found necessary in the embarrassed state of public affairs, occasioned by the first troubles respecting the American Stamp Act, again to call for the assistance of the man who was generally believed best able to serve the country; and in July that year he was intrusted with the formation of a new cabinet. In the arrangement which he made upon this occasion he reserved to himself along with the premiership the office of Lord Privy-Seal, as better suiting than one of more active duties, the enfeebled state of his health, now greatly broken down by attacks of the gout, to which he had long been subject. He also went to the upper house with the title of Earl of Chatham. He now applied himself with his best endeavours to heal the differences with America; but the opposition of his colleagues rendered him unable to carry into effect the measures which he would have taken for this purpose; and, in December, 1768, he again resigned. Lord Chatham lived for nearly ten years after this; and, although his increasing infirmities compelled him to spend much of his time in retirement in the country, he frequently presented himself in his place in parliament, when important discussions were to take place, and never distinguished himself more than he did, on some of these occasions, by his eloquent and indignant appeals against the headlong course of misgovernment in which ministers were proceeding, and his maintenance of the constitutional rights and liberties of his countrymen. The conduct of the House of Commons, in the case of the Middlesex election, when, by the repeated rejection of Mr. Wilkes, after he had been returned by a majority of votes, they attempted to establish the principle that an expulsion from the House created a perpetual and indelible disqualification to serve as a representative, was earnestly and perseveringly reprobated by Lord Chatham, who did not, however, live to witness the triumph of the doctrines which he maintained in the rescinding of the obnoxious resolutions by a subsequent House of Commons. This was the second violation of the constitution, in the person of the same individual, which Lord Chatham had signalized himself in endeavouring to defeat; having, in 1764, taken a leading part in denouncing the attempt of the ministry of that day to revive against the authors and printers of Wilkes's paper, the North Briton, the application of the old and already condemned system of general warrants,—that is of warrants which, mentioning no person by name, were directed against all who came, or were pretended to come, under a vague general description. Principally for his exertions, in reference to this matter, Sir William Pynsent, in the beginning of the following year, left him his estates in Somersetshire. It was the contest with America, however, which called forth from Lord Chatham the most brilliant efforts of his latter days, and perhaps of his life. He may be said to have expired in resisting the infatuated measures which, in provoking this war, led to the dismemberment of the empire. On the 7th of April, 1778, when a motion on this subject was to be discussed, he appeared for the last time in the House of Lords, leaning on the arm of his son, with his majestic figure wrapped in flannels, and his face pale as death. After delivering his sentiments with his accustomed fervour, he sat down.

On rising again, however, a short time afterwards, to reply to some observations which had been made upon his address, he fell back in the arms of the Duke of Cumberland and Lord Temple, who sat beside him, speechless, and, to all appearance, insensible. The late painter, Mr. Copley, father of the present Lord Lyndhurst, has painted this scene. Lord Chatham recovered so far as to be removed to his country-house at Hayes, where he lingered till the 12th of May, when he expired, entirely exhausted, in the seventieth year of his age. The characteristics of this celebrated minister were vigour, decision, a mind prophetic of consequences, and an eloquence so commanding that probably nothing quite equal to it has distinguished any other speaker in modern times. Judging rather by the effects which it is recorded to have produced, than by any pretended reports of particular speeches, it must have contained an extraordinary share of the vehemence and power by which Demosthenes, in ancient Greece, " wielded at will that fierce democraty." In feeling, Lord Chatham was an Englishman to the heart's core; and had no stronger passion than the love of his country. The unexampled height of glory to which he raised that country, and the noble stand he uniformly made for the rights of the people and the best principles of the constitution, will make his memory dear to England, so long as any reverence for the great men of past times shall remain among us.

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Far in the bosom of Helvellyn,
Remote from public road or dwelling,
Pathway, or cultivated land;
From trace of human foot or hand.
There, sometimes does a leaping fish

Send through the tarn a lonely cheer;
The crags repeat the raven's croak,
In symphony austere ;
Thither the rainbow comes, the cloud;
And mists that spread the flying shroud
And sun-beams; and the sounding blast
That, if it could, would hurry past,
But that enormous barrier binds it fast.
Not knowing what to think, awhile
The shepherd stood: then makes his way
Towards the dog, o'er rocks and stones,
As quickly as he may;
Nor far had gone before he found
A human skeleton on the ground;
Sad sight! the shepherd with a sigh
Looks round, to learn the history.
From those abrupt and perilous rocks
The man had fallen, that place of fear!
At length upon the shepherd's mind

It breaks, and all is clear:
He instantly recall'd the name,
And who he was, and whence he came;
Remember'd, too, the very day

On which the traveller pass'd this way.
But hear a wonder now, for sake

Of which this mournful tale I tell!
A lasting monument of words
This wonder merits well.

The dog, which still was hovering nigh,
Repeating the same timid cry,

This dog had been through three months' space

A dweller in that savage place.

Yes, proof was plain that since the day

On which the traveller thus had died

The dog had watch'd about the spot,

Or by his master's side:

How nourished here through such long time
He knows, who gave that love sublime,

And gave that strength of feeling, great

Above all human cstimate.

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It is about twenty-seven years ago, that the fata. accident happened which furnished a subject for the above beautiful poem by Mr. Wordsworth. The circumstances were recently detailed to us by one of the guides who conducts the tourist to the summits of Skiddaw and Helvellyn. The unfortunate man who perished amidst these solitudes was a resident at Manchester, who was periodically in the habit of visiting the Lakes, and who, confiding in his knowledge of the country, had ventured to cross one of the passes of Helvellyn, late in a summer afternoon, in company only with his faithful dog. Darkness, it is supposed, came on before his expectation-he wandered from the track-and fell over the rocks into one of those deep recesses where human foot never treads. The dog was found by the side of his master's body, after many weeks' fruitless search. The man who told us the story had never heard of the poem ; but the sentiment of natural piety with which it concludes was on his lips: "God knows," he said, "how the poor beast was supported so long."

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THE following account is abridged, with a few trifling | marsh at a distance of four English miles from St. alterations, from Dr. Granville's Travels :

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At St. Petersburgh, in the square opposite the Isaacbridge, at the western extremity of the Admiralty, the colossal equestrian statue of the founder of that magnificent city, placed on a granite rock, seems to command the undivided attention of the stranger. The huge block of granite which forms the pedestal, upwards of fifteen hundred tons in weight, was conveyed from a VOL. I.

Petersburgh, and two miles from the sea.

In a grooved railway, corresponding with an opposite grooved space, fixed to the basis of the rock, were placed cannon balls; and as the stone was moved forwards, by means of ropes, pullies, and windlasses, drawn both by men and horses, the balls over which it had passed were brought to the front. A drummer was stationed on the rock to give a signal to the workmen. Its size, when 2 T

brought to St. Petersburgh, was between forty and fifty p feet in length, upwards of twenty in breadth, and as much in height.

On approaching near to the rock, the simple inscription fixed on it in bronze letters, " Petro Primo, Catharina Secunda, M,DCCLXXXII," meets the eye. The same inscription, in the Russian language, appears on the opposite side. The area is enclosed within a handsome railing placed between granite pillars. The idea of Falconet, the French architect, commissioned to erect an equestrian statue to the extraordinary man at whose command a few scattered huts of fishermen were converted into palaces, was to represent the hero as conquering, by enterprise and personal courage, difficulties almost insurmountable. This the artist imagined might be properly represented by placing Peter on a fiery steed, which he is supposed to have taught by skill, management, and perseverance, to rush up a steep and precipitous rock to the very brink of a precipice, over which the animal and the Imperial rider pause without fear and in an attitude of triumph. The horse rears with his fore-feet in the air, and seems to be impatient of restraint, while the sovereign surveys, with serene countenance, his capital rising out of the waters, over which he extends the hand of protection. The bold manner in which the group has been made to rest on the hind-legs of the horse only, is not more surprising than the skill with which advantage has been taken of the allegorical figure of the serpent of envy spurned by the horse, to assist in upholding so gigantic a mass. This monument of bronze is said to have been cast at a single jet. The head was modelled by Mademoiselle Calot, a female artist of great merit, and is admitted to be a strong resemblance of Peter.

The height of the figure of the Emperor is 11 feet; that of the horse, 17 feet. The bronze is in the thinnest part the fourth of an inch only, and one inch in the thickest part: the general weight of metal in the group is equal to 36,636 English pounds.

DECIMAL FRACTIONS. IN continuation of a former number, we now proceed to explain the species of fractions which are called decimal, a word derived from the Latin decem, ten. In doing this it will be necessary to enter upon the decimal system generally, and to point out the features which distinguish our arithmetic from that of ancient times. The Greeks and Romans reckoned as we do, by tens; that is to say, having given names to the first ten numbers, they made these names serve to reckon all numbers as far as ten tens, or one hundred, for which a new name was introduced; with this they proceeded as far as ten hundreds, or one thousand, where again a new name was adopted. In the symbols by which they represented numbers, they were not fortunate; and the Roman method especially, which is often used amongst us, is so clumsy as to make it no matter of wonder why that people never cultivated arithmetic with success. Our method came originally from India through the Moors, who brought it into Spain. It enables us to represent all numbers by means of ten symbols, one denoting nothing, and the rest standing for the first nine numbers. The value of a figure depends not only upon the number which it represents when it stands alone, but also upon the place or column in which it is found. Thus, in 2222 yards, the two on the right hand stands for two yards only; the next to it for 2 tens of yards, or twice ten yards, or twenty yards; the next for two tens of tens of yards, or two hundred yards; the next for two tens of hundreds of yards, or two thousand yards. It is necessary to recall this, which is well known to all our readers, and in which the superiority of the modern system consists, in order to show how simply fractions may be represented by an extension of the same method. In the number 11111, if we proceed from left to right, each unit is the tenth part of the one which preceded it. Thus the first 1 is ten thousand, the second one thousand, the third one hundred, and so on. The last 1 is simply a unit, which A venerable Russian nobleman, who was living at may, introducing fractions, be divided into ten parts, St. Petersburgh when this monument was in progress, each of which will be one-tenth of the unit, and will be informed Dr. Granville, that as soon as the artist represented in the common way by . If we would had formed his conception of the design, he commu- carry on the notation just explained, in the case of nicated it to the Empress, together with the impossi-11111, we may place one more unit on the right, and bility of naturally representing so striking a position of agree that it shall stand for of the unit. This would man and animal, without having before his eyes a horse give 11111 1, in which the separation is made to avoid and rider in the attitude he had devised. General Me- confounding this, which is eleven thousand one hundred lissino, an officer having the reputation of being the and eleven yards and one-tenth of a yard, with 111111, most expert as well as the boldest rider of the day, to which is one hundred and eleven thousand one hundred whom the difficulties of the architect were made known, and eleven yards. In the same way in 11111 1111, offered to ride daily one of Count Alexis Orloff's best the first 1 after the unit's place, or the first which is seArabians to the summit of a steep artificial mound parated from the rest, stands for one-tenth of a yard, the formed for the purpose; accustoming the horse to gallop second for one-tenth of a tenth, or one-hundredth of a up to it and to halt suddenly, with his fore-legs raised, yard, the third for a tenth of a hundred of a yard or pawing the air over the brink of a precipice. This dan- one-thousandth of a yard, and the fourth for one-tenth gerous experiment was carried into effect by the General of a thousandth, or one-ten-thousandth part of a yard. for some days, in the presence of several spectators, and Instead of a separation, it is usual to mark a point after of Falconet, who sketched the various movements and the unit's place, and all figures which come before the parts of the group from day to day, and was thus enabled point are whole yards, pounds, acres, &c., as the case to produce perhaps the finest, certainly the most correct, may be, while all which come after the point are fracstatue of the kind in Europe. tions of the same. Thus 12.34 yards stands for 12 It will be always a matter of regret to the admirers yards, 3 tenths of a yard, and 4 hundredths of a yard; of the sublime in the fine arts that the chisel of Falconet,758 stands for 7 tenths, 6 hundredths, and 8 thouwhich had been so successfully employed in giving to the world so perfect a group, should have interfered with the rude form and outlines of the gigantic block of granite selected for its support. The paring, and bevelling, and scooping out, to which the original rock was subjected, have greatly injured the grand and imposing effect it would otherwise have had; have diminished the size of this unique pedestal to almost incorrect proportions; and given it the appearance of an artificial inclined plane, where a rude and broken rock, with its natural and picturesque angles and fractures, was required.

sandths. The cipher is used in the same way as in whole numbers, viz. to keep each number in its proper place. Thus one-hundredth is distinguished from onetenth by writing the first 01, and the second 1, since the second column on the right of the point is appropriated to hundredths, and the first to tenths. Thus 308 is three tenths and eight thousandths; 0308 is 3 hundredths and 8 ten-thousandth parts.

These fractions may be represented in another way. Thus, 123, which is one-tenth, 2 hundredths, and 3 thousandths, is also 123 thousandths, or one hundred and twenty-three parts out of a thousand. For if we

ivide the unit into 1000 parts, one-tenth is 100 of these parts, one hundredth is 10, and two hundredths are 20 of these parts, and 3 thousandths are three of these parts Similarly 76 is either 7 tenths and 6 hundredths, or 76 hundredths. The rule is :-To write a decimal fraction in the common way, let the numerator be the number which follows the point, throwing away ciphers from the beginning, if necessary; let the denominator be unity followed by as many ciphers as there are places of figures after the point. By the same rule a number and decimal fraction may be converted into one common fraction, the numerator being formed by throwing away the decimal point. Thus 7.12 is 710

or 112. гоо

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12

The decimal point is always understood as coming after the unit's place, even when there are no fractions. Thus 16 is 16 or 16.000. And any number of ciphers may be placed after a decimal without altering its value. Thus 4 and 40 are the same, the first being 4 parts out of ten, and the second also 4 parts out of ten, or which is the same thing, 40 parts out of 100. No fraction can be converted into a decimal of exactly the same value, unless its denominator be either 5 or 2, or a product of some number of fives and twos, such as 250, which is the product of 5, 5, 5, and 2. For the changing a common into a decimal fraction is the finding a second fraction, equal in value to the first,

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necessary, by adding ciphers to the left, and taking no
account of the remainder. Thus 365 is within
of 20·277777.

1000

1000000

1000

The rules for addition, subtraction, multiplication, and division, of decimal fractions, are very similar to those in whole numbers. In addition and subtraction the decimal points are to be placed under one another, which will bring units under units, tens under tens, tenths under tenths, &c. The process is then precisely the same as in whole numbers, the decimal point in the result being placed under the other points. In multiplication we must proceed to multiply as if there were no decimal points, and afterwards make as many decimal places in the result as were in both the multiplier and multiplicand. For the product of 238 and 112 or 238 and 112 is, by the common rule, 26656 : and as one decimal number is multiplied by another by forming a third decimal number, which shall have as many ciphers as both the former ones together, and since the number of ciphers in the denominator of a decimal fraction, expressed in the common way, is the number of places which it will have when the point is substituted for the denominator, the reason of the rale is evident. The product obtained above is 026656 by the rule, one cipher being necessary to make up six places. It is moreover evident that 26656 is less than 1 or the latter being

100000 1000000

1000000

1000000

and whose denominator shall be one of the series of decimal numbers, 10, 100, 1000, &c. There is only one The rule for division of one decimal by another, as way of altering the terms of a fraction without altering given in many books of arithmetic, is likely to mislead its value, viz. by multiplying or dividing both nume the student in various cases. From the following prinrator and denominator by the same number. It will ciples a rule may be drawn which will apply to every If there be no decimals, either in the dieasily be found by experiment, and it is proved in books possible case. of algebra, that a decimal number, that is, a unit fol- vidend or divisor, the rule has been already explained lowed by ciphers, is not divisible by any number except duction of to a decimal fraction, since, as we showed Thus the division of 17 by 6 is the same thing as the reit be either 2, 5, or a product of twos and fives. Hence it is impossible that a multiplier can be found for 7, for in our former paper, the sixth part of unity repeated 17 example, which shall make the product a decimal num-times is the sixth part of 17. Again, we must observe ber; for if so, since the product is always divisible by the multiplicand, there would be a decimal number divisible by 7, which is impossible.

Hence there is no decimal fraction exactly equal to , or, or, and so on. Nevertheless, a decimal fraction can be found as near as we please to any fraction whatever; that is, if we take, and take any fraction as small as we please, for example, Tooooo or 00001, we can find a decimal fraction which shall not differ from by so much as '00001; and if we please, we can come still nearer than that small difference. Suppose it is required to find a decimal fraction which shall not differ from by so much as 100 or 001. Multiply the numerator and denominator by 1000, which gives 3000 The numerator 2000, divided by 13, gives the quotient 153 and the remainder 11; so that both 2000 diminished

2000

989 2000

15

by 11, and 2000 increased by 2, are divisible by 13, that is, 1989 and 2002 are divisible by 13, and give the quotients 153 and 154. Of the three fractions 13000 13000 and, which have the same denominator, the first is the least, the third is the greatest, and the second lies between the first and third. But the first and third (dividing both numerator and denominator by 13) are and 15 or 153 and 154, and the second is the same as. The first and third differ from one another by or ⚫001; hence the second, which lies between them, does not differ by so much as 1ooo from either. We have, therefore, two decimal fractions 153 and 154, the first a little less, and the second a little greater, than, each within 10 of 13. The rule derived from this process is-To find a decimal fraction which shall not differ from a common fraction by so much as annex as many ciphers to the numerator as there are ciphers in 1000 &c., divide by the denominator, and cut off by the decimal point from the quotient as many places as there were ciphers in 1000 &c., completing the number, if

1000

that when two fractions have the same denominator, their quotient is the same as the quotient of their numerators. Thus is contained in 7, just as 2 is conwhich having the numerator and denominator both ditained in 17. By the rule, divided by gives, visible by 8, is the same as . If then two fractions

have the same denominator, the denominator may be the other. Two decimal fractions may be reduced to rejected in division, and the one numerator divided by the same denominator, by annexing ciphers to the right of that which has the fewest number of places, so as to make the same number of places in both. For we have shown that a decimal is not altered by annexing which have the same number of places have the same ciphers on the right, and we know that two decimals denominator, viz. unity followed by as many ciphers as there are places.

17

0017 we begin by annexing three ciphers to 42.1 which
If then we have to divide 42 1 by
gives 42 1000 and 0017, which having the same de-
nominator, we retain only the numerators, which are
421000 and 17. It only remains to reduce 11000 to
a decimal fraction, to do which, we annex as many more
ciphers to the numerator as we want decimal places.
Thus, if we want 4 places we divide 421000,0000 by 17,
the quotient of which, taking no account of the remain-
der, is the answer required. Again, to divide 4.03812
we
by 1161 7
annex four ciphers to the latter,
and reject the denominators, which gives 403812 and
403812 to a decimal

116170000. We then reduce 116170000
fraction; but in doing this, the rule may be somewhat
simplified, since the annexing a cipher to the numerator
is the same thing as taking one away from the de-
4038120 is the same fraction as
nominator: thus 116170000
1101-000* It therefore we want five places of deci
mals, instead of annexing five ciphers to the numerator,
we take away the four from the denominator and annex

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