THE WEEK. supremacy of this able, patriotic, and popular minister. November 15.- The anniversary of the birth of William In October, 1760, George II, died, and the ascendency of Pitt, commonly distinguished as the Great Lord Chatham. new principles, which the new reign brought along with This illustrious statesman was born at London in the it, before long compelled Pitt to tender his resignation of year 1708, and was the son of Robert Pitt, Esq., of his services. His administration terminated, and that Boconnoc in Cornwall. He was educated first at Eton of Lord Bute commenced in October, 1761. Although and afterwards at Trinity College, Oxford, of which he Pitt, however, had found it necessary to retire from the was entered a gentleman commoner in 1726. On management of affairs, his sovereign was so sensible leaving the university he purchased a cornetcy in the of his great deserts, that a barony was bestowed upon Blues; but urged probably by the desire of obtaining a his lady, and a pension of three thousand a year granted more suitable field for the display of his abilities than a to him for their conjoint lives and for that of his eldest military life afforded, in 1735 he procured himself to be son. After this, he remained out of office till 1766, returned to parliament for the family borough of Old when, after the failure of the Rockingham administraSarum. Sir Robert Walpole was then at the head of tion, it was found necessary in the embarrassed state of affairs ; and Pitt immediately joined the opposition, public affairs, occasioned by the first troubles respecting which eventually compelled that minister to retire in the American Stamp Act, again to call for the assistance 1742. For the part which he thus took he was, the of the man who was generally believed best able to serve year after he entered parliament, deprived by Walpole the country; and in July that year he was intrusted of his commission, but was compensated by being made with the formation of a new cabinet. In the arrangeone of the Gentlemen of the Bedchamber to the Prince ment which he made upon this occasion he reserved of Wales. His eloquence, as soon as he began to to himself along with the premiership the office of Lord take a part in the debates, raised him to distinction Privy-Seal, as better suiting than one of more active duties, and importance; and imperfectly as the proceedings the enfeebled state of his health, now greatly broken of the House were then communicated to the public, down by attacks of the gout, to which he had long been his reputation as one of the most powerful speakers subject. He also went to the upper house with the title of the day seems to have rapidly spread itself over of Earl of Chatham. He now applied himself with his the nation. It was in 1740, in the course of this best endeavours to heal the differences with America ; contest with Walpole's administration, that, on a motion but the opposition of his colleagues rendered him unable relating to impressment, he made his famous reply to to carry into effect the measures which he would have Mr. Horatio Walpole, the brother of the minister, vindi- taken for this purpose; and, in December, 1768, he cating himself from the double charge of youth and again resigned. Lord Chatham lived for nearly ten theatrical elocution, which Johnson reported with so years after this; and, although his increasing infirmities much spirit in the 'Gentleman's Magazine.' Walpole's compelled hiin to spend much of his time in retireadministration was succeeded by that of Lord Carteret ment in the country, he frequently presented himself in (afterwards Earl of Granville); but this change did not his place in parliament, when important discussions were introduce Pitt to office. The celebrated Sarah Duchess to take place, and never distinguished himself more than of Marlborough, however, left him in 1744 a legacy of he did, on some of these occasions, by his eloquent £10,000, in reward, as it was expressed in the will, of and indignant appeals against the headlong course the noble disinterestedness with which he had main- of misgovernment in which ministers were proceeding, tained the authority of the laws, and prevented the ruin and his maintenance of the constitutional rights and of his country. The following year he resigned his post liberties of his countrymen. The conduct of the House in the household of the prince. In 1746, under the of Commons, in the case of the Middlesex election, premiership of the Duke of Newcastle, Mr. Pitt was for when, by the repeated rejection of Mr. Wilkes, after he the first time chosen to fill a place in the Government, had been returned by a majority of votes, they attempted being appointed to the office of Vice-Treasurer for Ireland, to establish the principle that an expulsion from the from which he was transferred the same year to that of House created a perpetual and indelible disqualification Paymaster-General of the Forces. In this situation, to serve as a representative, was earnestly and perwhich he held for nearly nine years, he displayed his severingly reprobated by Lord Chatham, who did not, characteristic activity, energy, and decision, and the however, live to witness the triumph of the doctrines most high-minded integrity and contempt for many of which he maintained in the rescinding of the obnoxious the customary profits of office. In 1755, however, on a resolutions by a subsequent House of Commons. This disagreement with the majority of his colleagues, he was the second violation of the constitution, in the perresigned : but, in little more than a year after, the force son of the same individual, which Lord Chatham had of public opinion compelled his recall; and on the 4th signalized himself in endeavouring to defeat; having, of December, 1756, he was appointed principal Secre- in 1764, taken a leading part in denouncing the attempt tary of State. In the April following, finding his views of the ministry of that day to revive against the authors still thwarted by the rest of the cabinet, he again retired; and printers of Wilkes's paper, the North Briton, the but within less than three months the King was obliged application of the old and already condemned system of to yield to the national voice, the ministry was driven general warrants,—that is of warrants which, mentioning from power, and a new one was formed under the no person by name, were directed against all who came, auspices of Pitt, who, reinstated in his former place of or were pretended to come, under a vague general Secretary of State, now exercised under that name the description. Principally for his exertions, in reference authority of Premier. For the next four years Pitt may to this matter, Sir William Pynsent, in the beginning of be regarded as having been the director of the energies the following year, left him his estates in Somersetshire. of England ; and they are four of the most glorious It was the contest with America, however, which called years in the history of the country. Victory crowned forth from Lord Chatham the most brilliant efforts of the British arms wherever they appeared, whether on his latter days, and perhaps of his life. He may be said sea or on land; the French were beaten at almost to have expired in resisting the infatuated measures every point both in the east and in the west ; the vast which, in provoking this war, led to the dismemberment territory of Canada was wrested from them, almost of the empire. On the 7th of April, 1778, when a before the Government at home was aware that it was in motion on this subject was to be discussed, he appeared danger; and they were eventually stripped of nearly all for the last time in the House of Lords, leaning on the their other colonies in every part of the world. Along arm of his son, with his majestic figure wrapped in with these successes abroad, tranquillity and content- flannels, and his face pale as death. After delivering his ment at home no less remarkably distinguished the sentiments with his accustomed fervour, he sat down. On rising again, however, a short time afterwards, to Far in the bosom of Helvellyn, reply to some observations which had been made upon Remote from public road or dwelling, his address, he fell back in the arms of the Duke of Pathway, or cultivated land; From trace of human foot or hand, Cumberland and Lord Temple, who sat beside him, There, sometimes does a leaping fish speechless, and, to all appearance, insensible. The late Send through the tarn a lonely cheer ; painter, Mr. Copley, father of the present Lord Lyndhurst, The crags repeat the raven's croak, has painted this scene. Lord Chatham recovered so far In symphony austere ; as to be removed to his country-house at Hayes, where Thither the rainbow comes, the cloud; he lingered till the 12th of May, when he expired, en And mists that spread the flying shroud And sun-beams; and the sounding blast tirely exhausted, in the seventieth year of his age. The That, if it could, would hurry past, characteristics of this celebrated minister were vigour, But that enormous barrier binds it fast. decision, a mind prophetic of consequences, and an elo Not knowing what to think, awhile quence so commanding that probably nothing quite The shepherd stood : then makes his way equal to it has distinguished any other speaker in modern Towards the dog, o'er rocks and stones, times. Judging rather by the effects which it is re As quickly as he may; Nor far had gone before he found corded to have produced, than by any pretended reports A human skeleton on the ground; of particular speeches, it must have contained an extra Sad sight! the shepherd with a sigh ordinary share of the vehemence and power by which Looks round, to learn the history. Demosthenes, in ancient Greece,“ wielded at will that From those abrupt and perilous rocks fierce democraty.” In feeling, Lord Chatham was an The man had fallen, that place of fear! Englishman to the heart's core; and had no stronger At length upon the shepherd's mind It breaks, and all is clear: passion than the love of his country. The unexampled He instantly recall’d the name, height of glory to which he raised that country, and the And who he was, and whence he came; noble stand he uniformly made for the rights of the Remember'd, too, the very day people and the best principles of the constitution, will On which the traveller pass'd this way. make his memory dear to England, so long as any reve But hear a wonder now, for sake rence for the great men of past times shall remain Of which this mournful tale I tell ! A lasting monument of words among us. This wonder merits well. On which the traveller thus had died Or by his master's side : Above all human cstimate. tation—he wandered from the track—and fell over the CHATHAM. rocks into one of those deep recesses where human fout 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; 'FIDELITY. but the sentiment of natural piety with which it conA BARKING sound the shepherd hears, cludes was on his lips : “God knows," he said, "how A cry as of a dog or fox ; the poor beast was supported so long." Among the scatter'd rocks : The Office of the Society for the Diffusion of Useful Knowledge is at 59, Lincoln's-Inn Fields. LONDON :-CHARLES KNIGHT, PALL-MALL EAST. Shopkeepers and Hawkers may be supplied Wholesale by the following The dog is not of mountain breed; Booksellers, of whom, also, any of the previous Numbers may be had:Its motions, too, are wild and shy ; London, GROOMBRIDGE, Panyer Alley. | Manchester, ROBINSON; and WEBB With something, as the shepherd thinks, Bath, Simms. and Simms. Unusual in its cry: Birmingham, DRAKE. Netocastle-upon-Tyne, CHARNLEY. Bristol, WESTLEY and Co. Norwich, JARROID and Son, Carlisle, THURNAM; and SCOTT, Nottingham, WRIGHT. Derby, WILKINS and Sox. O.xford, SLATTER. Doncaster, BROOKE and Co. Plymouth, NETTLETON. Portsea, HORSEY, Juu. Falmouth, PHILP. Sheffield, RIDGE. Hull, STEPHENSON, Staffordshire, Lane End, C. WATTS. Kendal, HUDSON and NICHOLSON. Worcester, DEIGHTON. Leeds, BAINES and NEWSOME. Dublin, WAREMAN. Lincoln, BROOKE and Sons. Edinburgh, ULIVER and Bord. A silent tarn * below! Liverpool, W11LMER and SMITH, Glasgow, ATKINSON and Co. * Tamn is a small mere or lake, mostly high up in the mountains. Printed by WILLIAM CLOWES, Stamford Street. (Bronze Statue of Peter the Great at St. Petersburgh.] 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 : Petersburgh, and two miles from the sea. At St. Petersburgh, in the square opposite the Isaac In a grooved railway, corresponding with an opposite bridge, at the western extremity of the Admiralty, the grooved space, fixed to the basis of the rock, were placed colossal equestrian statue of the founder of that magni- cannon balls; and as the stone was moved forwards, by ficent city, placed on a granite rock, seems to command means of ropes, pullies, and windlasses, drawn both by the individed attention of the stranger. The huge men and horses, the balls over which it had passed were block of granite which forms the pedestal, upwards of brought to the front. A drummer was stationed on the fifteen hundred tons in weight, was conveyed from a 1 rock to give i signal to the workmen. Its size, when Vol. J. 2 T brought to St. Petersburgh, was between forty and fifty i DECIMAL FRACTIONS. feet in length, upwards of twenty in breadth, and as In continuation of a former number, we now proceed much in height. to explain the species of fractions which are called deciOn approaching near to the rock, the simple inserip mal, a word derived from the Latin decem, ten. In lion fixed on it in bronze letters, “ Petro Primo, Catha- doing this it will be necessary to enter upon the derina Secunda, MDCCLXXXII," meets the eye. The same cimal system generally, and to point out the features inscription, in the Russian language, appears on the which distinguish our arithmetic from that of ancient opposite side. The area is enclosed within a handsome times. The Greeks and Romans reekoned as we do, by railing placed between granite pillars. The idea of Fal- tens ; that is to say, having given names to the first ten conet, the French architect, commissioned to erect an numbers, they made these names serve to reckon all equestrian statue to the extraordinary man at whose numbers as far as ten tens, or one hundred, for which a command a few scattered huts of fishermen were con- new name was introduced; with this they proceeded as verted into palaces, was to represent the hero as con- far as ten hundreds, or one thousand, where again a quering, by enterprise and personal courage, difficulties new name was adopted. In the symbols by which almost insurmountable. This the artist imagined might they represented numbers, they were not fortunate ; be properly represented by placing Peter on a fiery and the Roman method especially, which is often used steed, which he is supposed to have taught by skill, amongst us, is so clumsy as to make it no matter of management, and perseverance, to rush up a steep and wonder why that people never cultivated arithmetic precipitous rock to the very brink of a precipice, over with success. Our method came originally from India which the animal and the Imperial rider pause without through the Moors, who brought it into Spain. It enfear and in an attitude of triumph. The horse rears ables us to represent all numbers by means of ten symwith his fore-feet in the air, and seems to be impatient bols, one denoting nothing, and the rest standing for of restraint, while the sovereign surveys, with serene the first nine numbers. The value of a figure depends countenance, his capital rising out of the waters, over not only upon the number which it represents when it which he extends the hand of protection. The bold man- stands alone, but also upon the place or column in ner in which the group has been made to rest on the which it is found. Thus, in 2222 yards, the two on the hind-legs of the horse only, is not more surprising than right hand stands for two yards only; the next to it for the skill with which advantage has been tåken of the 2 tens of yards, or twice ten yards, or twenty yards; the allegorical figure of the serpent of envy spurned by the next for two tens of tens of yards, or two hundred horse, to assist in upholding so gigantic a mass. This yards; the next for two tens of hundreds of yards, or monument of bronze is said to have been cast at a single two thousand yards. It is necessary to recall this, jet. The head was modelled by Mademoiselle Calot, a which is well known to all our readers, and in which female artist of great merit, and is admitted to be a strong the superiority of the modern system consists, in order to resemblance of Peter. show how simply fractions may be represented by an The height of the figure of the Emperor is 11 feet ; extension of the same method. In the number 111ll, that of the horse, 17 feet. The bronze is in the thinnest if we proceed from left to right, each unit is the tenth part the fourth of an inch only, and one inch in the part of the one which preceded it. Thus the first I is thickest part: the general weight of metal in the group ten thousand, the second one thousand, the third one is equal to 36,636 English pounds. 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 it. 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- 1111l, 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 at 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 l 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 sudilenly, 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 fracstalue 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 sandths. The cipher is used in the same way as in the world so perfect a group, should have interfered with whole numbers, viz. to keep each number in its proper the rude form and outlines of the gigantic block of gra- place. Thus one-hundredth is distinguished from oneuite selected for its support. The paring, and hevelling, tenth by writing the first •01, and the second.1, since and scooping out, to which the original rock was sub- the second column on the right of the point is approjected, have greatly injured the grand and imposing priated to hundredths, and the first to tenths. Thus effect it would otherwise have had ; have diminished 308 is three tenths and eight thousandths; •0308 is the size of this unique pedestal to alınost incorrect 3 hundredths and 8 ten-thousandth parts. proportions ; and given it the appearance of an arti- These fractions may be represented in another way. ficial inclined plane, where a rude and broken rock, Thus, 123, which is one-tenth, 2 hundredths, and 3 with its natural and picturesque angles and fractures, thousandths, is also 123 thousandths, or one hundred was required: and twenty-three parts out of a thousand. For if we or U12 100 divide the unit into 1000 parts, one-tenth is 100 of these necessary, by adding ciphers to the left, and taking no ports, one hundredth is 10, and two hundredths are 20 account of the remainder, Thus 3 is within 1000000 of these parts, and 3 thousandths are three of these of 20 277777. parts Similarly •76 is either 7 tenths and 6 hun The rules for addition, subtraction, multiplication, and dredths, or 76 hundredths. The rule is :-To write a division, of deciinal fractions, are very similar to those in decinal fraction in the common way, let the numerator whole numbers. In addition and subtraction the decimal be the nunber which follows the point, throwing away points are to be placed under one another, which will ciphers from the beginning, if necessary ; let the deno-bring units under units, tens under tens, tenths under minator be unity followed by as many ciphers as there tenths, &c. The process is then precisely the same as in are places of figures after the point. By the same rule whole numbers, the decimal point in the result being a number and decimal fraction may be converted into placed under the other points. In multiplication we one common fraction, the numerator being formed by must proceed to multiply as if there were no decimal throwing away the decimal point. Thus 7.12 is 7100 points, and afterwards inake as many decimal places in the result as were in both the multiplier and multiplicand. The decimal point is always understood as coming For the product of • 238 and 112 or 238 and 112 1000 after the unit's place, even when there are no fractions. is, by the common rule, 2 6 6.36 : and as one decimal Thus 16 is 16. or 16.000. And any number of number is multiplied by another by forming a third ciphers may be placed after a decimal without altering decimal nuniber, which shall have as many ciphers as its value. Thus •4 and 40 are the same, the first both the former ones together, and since the number of being 4 parts out of ten, and the second also 4 parts out ciphers in the denominator of a decimal fraction; exof ten, or which is the same thing, 40 parts out of pressed in the common way, is the number of places 100. No fraction can be converted into a decimal of which it will have when the point is substituted for the exactly the same value, unless its denominator be either denominator, the reason of the rule is evident. The 5 or 2, or a product of some number of fives and twos, product obtained above is .026656 by the rule, one such as 250, which is the product of 5, 5, 5, and 2. cipher being necessary to make up six places. It is For the changing a common into a decimal fraction is moreover evident that 100056. is less than I or th: the the finding a second fraction, equal in value to the first, latter being 190000.. and whose denominator shall be one of the series of de 1000000" cimal numbers, 10, 100, 1000, &c. There is only one The rule for division of une 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 easily be found by experiment, and it is proved in books possible case. If there be no decimals, either in the diof algebra, that a decimal number, that is, à unit fol- vidend or divisor, the rule has been already explained lowed by ciphers, is not divisible by any number except 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. Hense duction of Y to a decimal fraction, since, as we showa 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 11. Again, we must observe ber; for if so, since the product is always divisible by that when two fractions have the same denominator, the multiplicand, there would be a decimal number their quotient is the same as the quotient of their numedivisible by 7, which is impossible. rators. Thus j is contained in y, just as 2 is conHence there is no decimal fraction exactly equal to which having the numerator and denominator both di tained in 17. By the rule, 1. divided by f gives 37, H, or ģ, or 15, and so on. tion can be found as near as we please to any fraction visible by 8, is the same as y. If then two fractions whatever; that is, if we take šs, and take any fraction rejected in division, and the one numerator divided by have the same denominator, the denominator may be as small as we please, for example, too boo or 00001, the other. Two decimal fractions may be reduced to we can find a decimal fraction which shall not differ from the same denominator, by annexing ciphers to the is by so much as .00001; and if we please, we can come right of that which has the fewest number of places, so still nearer than that small difference. Suppose it is required to find a decimal fraction which shall not differ as to make the same number of places in both. For we have shown that a decimal is not altered by annexing from it by so much as 1ooo or .001. Multiply the numerator and denominator by 1000, which gives 13.00: which have the same number of places have the same ciphers on the right, and we know that two decimals The numerator 2000, divided by 13, gives the quotient denominator, viz. unity followed by as many ciphers as 153 and the remainder 11; so that both 2000 diminished there are places. If then we have to divide 42• 1 by by 11, and 2000 increased by 2, are divisible by 13, that .0017 we begin by annexing three ciphers to 42•1 which is , 1989 and 2002 are divisible by 13, and give the quo gives 42-1000 and .0017, which having the same detients 153 and 154. Of the three fractions 14000 15000 nominator, we retain only, the numerators, which are and to, which have the same denominator, the first is 421000 and 17. It only remains to reduce 181000 to the least, the third is the greatest, and the second lies between the first and third. But the first and third (dividing a decimal fraction, to do which, we annex as many more both numerator and denominator by 13) are so and ciphers to the numerator as we want decimal places. or 153 and · 154, and the second is the same as pes. Thus, if we want 4 places we divide 421000,0000 by 17, The first and third differ from one another by todo or the quotient of which, taking no account of the remain·001; hence the second, which lies between them, does der, is the answer required. Again, to divide 4.03812 not differ by so much as To'oo from either. annex four ciphers to the latter, therefore, two decimal fractions •153 and · 154, the first a 17 we We have, by 1161:7 and reject the denominators, which gives 403812 and 40381 to a decimal little less, and the second a little greater, than 1s, each 116170000. We then reduce 116110000 within ooo of us. The rule derived from this process fraction, but in doing this, the rule may be somewhat is—To find a decimal fraction which shall not differ simplified, since the annexing a cipher to the numerator from a common fraction by so much as is the same thing as taking one away from the de1000 kc. nominator : thus 4038120_ is the same fraction as as many ciphers to the numerator as there are ciphers in 40381 1000 &c., divide by the denominator, and cut off by the 1161.000 If therefore we want five places of deci, decimal point from the quotient as many places as there mals, instead of annexing five ciphers to the numerator, were ciphers in 1000 &c., completing the nunber, if we take away the four from the denominator and annex % TZ annex 116170000 |