and medals, and rooms filled with the ancient relics of Herculaneum and Pompeii. The collection of vases, which have nearly all been discovered and dug up in the kingdom, is the richest in existence; but it is more especially the collection of the objects rescued from the two interred cities, that gives the Museum of Naples its superiority to others. [Remains of the Parthenon.] We shall proceed with our description of the Athenian antiquities in the British Museum, as soon as the collection is numbered according to its present arrangement. We understand from the Officers of the Institution that this essential assistance to the visitor will be immediately given; for the old order of the several pieces of sculpture being considerably altered, a reference to the former numbers only would prove embarrassing. In the mean time we give that view of the Parthenon, for which the representation of the temple of Apollo Epicurius, near Phigalia, was substituted by mistake. NAPLES. In a preceding number we endeavoured to give our readers a notion of the situation and main features of Naples. We shall now devote a page to a few of the interesting objects contained within that city. The first in importance is the Studj or Museo Borbonico, or, what we may better call, the National Museum. In many respects this magnificent establishment is unrivalled in the world. Besides a rich statue gallery which boasts the Farnesian Hercules, the all-perfect Aristides, the Farnesian Toro, a Venus perhaps superior in loveliness to the Medicean, and other masterpieces of ancient Greek art, the Museum contains a gallery of pictures with two of Raphael's best works, and splendid specimens of Titian, Correggio, Claude, Salvator Rosa, and other great masters: and, moreover, a library, a collection of Etruscan vases, a cabinet of ancient coins In this collection are found some of the most perfect works of ancient art in bronze, domestic implements of nearly every sort, mechanical tools, surgical and mathematical instruments, rings, necklaces, and other specimens of jewellery, and even the entire apparatus of a woman's toilet. The attentive visitor, by studying these objects, may in a few hours obtain a better insight into the domestic manners of the ancients, than whole years devoted to books can give him. One of the most interesting departments of this unique collection, is that of the papyri, or manuscripts, discovered in the excavations of Herculaneum. The ancients did not bind their books (which, of course, were all manuscripts) like us, but rolled them up in scrolls. When these of Herculaneum were discovered, they presented, as they still do, the appearance of burnt sticks, or cylindrical pieces of charcoal, which they had acquired from the action of the heat contained in the lava that buried the whole city. They seem quite solid both to the eye and touch, yet an ingenious monk discovered a process of detaching leaf from leaf and unrolling them, by which they could be read without much difficulty. When these manuscripts were first exposed to the air a considerable number of them crumbled to dust. Our countryman, I truth, must be acknowledged as the most spacious and the late Sir Humphry Davy, destroyed the integrity most splendid theatre in Europe. of a few by making unsuccessful experiments, which he fancied might produce a result that would supersede the slow and laborious process now adopted; but about eighteen hundred still remain. Four of them have been unrolled, and fac-similes of them, with translations, published by the Neapolitan government. To pass to a very different object. One of the singularities of Naples is its Campo Santo, or cemetery for the poor. This is situated on the skirts of the town, looking towards Mount Vesuvius. A wall of inconsiderable elevation encloses a quadrangular space, whose surface is cut into three hundred and sixty-five holes, like the mouths of wells or cisterns. One of these holes is opened every day; the dead bodies of the poor of that day-without coffins-without so much as a rag about them are thrown one upon another, as they arrive, through the mouth into a deep cave below cut in the tufa rock, and at night a stone is laid over the horrid sepulchre and secured by cement. The next day the cave next in order of date is opened, and so on, through the year. At the end of the year, the first cave is again opened, by which time its contents, the decomposition of which is assisted by quick-lime, are reduced to little more than bones. The catacombs of Naples, whose entrance is under the hill of Capo-di-Monte, and the grotto of Posilippo, at the extremity of the western suburb of the city, are also remarkable objects. The first are of great extent, and contain many curious specimens of painting and subterranean architecture by the early Christians, and an appalling mass of human skulls and bones, the relics of the victims of a plague that depopulated Naples some two centuries back. The second is a subterranean passage cut through the hill of Posilippo in remote antiquity, but enlarged and improved as a road in modern times. It is considerably more than half a mile long by twenty-four feet broad; its height is unequal, varying from twenty-five to sixty feet: it is well paved with large flags of lava. By night it is now tolerably well illuminated by lamps suspended from its rugged roof, but by day the "darkness visible" that reigns through the passage renders it always solemn and sometimes embarrassing. Being the only frequented road to and from the town of Pozzuoli, Baia, Cuma, and other places, there is seldom a lack of passengers; and their voices, as they cry to each other in the dark, and the noise of their horses' tread and of the wheels of their waggons, carriages, and gigs, echoing through the grotto and the deep vaults which in many places branch off from it laterally, produce to the ear of the stranger an effect that is almost terrific. Immediately above the entrance to the grotto, coming from the city, stands on a romantic cliff, which has been in part cut away to widen the approach to the subterranean road, an ancient Roman tomb in almost perfect preservation. This tomb is supposed to have been that of the great poet Virgil, and is visited as such by every traveller. Its claim has been questioned in vain; mankind are attached to such pleasant illusions, (if this be one, which we by no means decide,) and continue from age to age to crowd to the spot. A laurel once flourished by the side of the venerable sepulchre and covered its roof; but the successive thousands and thousands of visitors, each anxious for a memorial gathered in such a spot, have not left leaf, branch, stem, or root of the sacred tree. In the old part of the city, among some Roman ruins called the "Anticaglia," are supposed to exist part of the walls of the theatre where the Emperor Nero sang and played on the lyre like a common actor. The Neapolitans care little about this; but their great boast, that which they fancy renders them the envy of the world, is their Opera-house of San Carlo, which, in [The Grotto of Posilippo and Tomb of Virgil.] FRACTIONS. Ir is not our intention to write a treatise on the part of arithmetic which stands at the head of this article, or to enter into the reasons why so many persons, who can solve a simple question in which there are nothing but whole numbers, are puzzled by anything which contains fractions. Our object is, to give some slight notions on this part of the subject to those who are already able to work the four rules in whole numbers. When we add any two numbers together, it is understood that both of them have the same unit, or that both are some number of times the same thing. Thus, that two and three make five, means that two yards and three yards make five yards, or that two pounds and three pounds make five pounds, and so on. We do not in that case say anything of two yards and three feet, or of two pounds and three shillings. The following questions might arise :-If we have a distance which is neither six yards nor seven yards, but something between the two, how are we to represent this in numbers, and form rules for adding and subtracting this length to or from others of the same kind, without introducing a new measure, or talking of any other length except a yard? The answer to this will bring us, as we shall see, to the common meaning of the word fraction, and the way of representing a fraction. As we cannot measure anything exactly, we must first decide what degree of accuracy is necessary. This will vary in different operations, but we will suppose, for example's sake, that a line may be rejected as insignificant, of which it would take more than a hundred to make a yard. If then we divide a yard into one hundred equal parts, and first remove the six whole yards which the abovementioned distance contains, we have a remainder which does not contain all the hundred parts just men tioned, since it is less than one yard. Suppose that, on | sixth part of five, or as the sixth part of unity repeated 5 measuring the remainder, we find it to contain more times. It may sometimes be necessary to take a fraction than 53 and less than 54 of the hundred parts : if then of a fraction, such as f of f, or having found g of 1, to we call it 53 parts out of a hundred of a yard, the error | divide it into five parts, and take two of them. We ask, committed will be less than one part out of a hundred; what fraction of the unit would the result of this double that is, by what was supposed above, it will be sufficient operation give? The answer is, multiply the two numeto say that the length of the whole is 6 yards and 53 rators together, and also the two denominators, which of the hundred equal parts which would compose gives 1, or two-fifths of seven-eighths of a yard is fouranother yard, or 53 hundredths of a yard. If we were teen parts out of forty. To see the reason, let us first inventing a system of arithmetic, we might choose among take the more simple case of. It is plain that if we many different ways of representing this. For exam- divide one yard into eight equal parts, and afterwards ple, 6 yards 53100 of a yard; 6 yards and 53:100 | divide each of these parts into 5 equal parts, we have of a yard; and so on. The common method is the fol- | divided the whole yard into 8 times 5, or 40 equal parts. lowing, 65 yards, it being always understood that Consequently the fifth part of an eighth part is one fortieth of the whole, or of is. But one fifth of seven eighths will be 7 times as much as f of one eighth, and will therefore be ; again, two fifths of will be twice as much as one fifth of, and will therefore be 11, or of is 14, according to the rule. In the same way of is 3. This rule corresponds to the multiplication of whole numbers, and is therefore called multiplication of fractions. The connexion is not obvious at first, owing to a little difference in our manner of speaking about whole numbers and fractions. But if we were in the when we write two numbers under one another with a line between, the unit of which we speak, be it a yard, pound, acre, or any other, is cut into as many equal parts as are shown by the lower number, and as many of them are taken as is shown by the higher number. Thus, of a mile is the length obtained by cutting a mile into 8 equal parts, and taking 7 of them, being of course less than the whole mile by one of these parts. Such a fraction as we have described is less than the unit of which it is a part; but a whole number of units and a fraction may be represented together by the same habit of saying that 2 multiplied by 6 is six of 2, in the method. If, in the preceding example, we had divided same way as we say "six of them,' "six of his men," it each of the six yards into 100 parts, there would have would appear natural to call those rules which tell us been 600 such parts, which, with the 53 parts furnished | how many units there are in six of two, and what fracby the fraction, would have made 653, not of yards, but | tion of a unit there is in g of f, by the same name. By of the hundredth parts of yards. This we should re-this rule all questions of fractions are solved, which present by 453, denoting that each of a succession of would have required multiplication if they had been in yards has been divided into 100 parts, out of which col- | whole numbers. For example, if 1 pound cost 2 shillection of parts 653 have been taken. The term frac-lings, 6 pounds will cost 6 times 2 shillings; similarly, tion is applied equally to all cases; and with this ex- if 1 pound costs of a shilling, of a pound will cost tension of meaning, the unit itself may be represented as of of a shilling. a fraction, for one yard is g yards, or f yards, or 4 yards, and so on. The most important proposition relating to fractions, being the one on which the rules most materially depend, The lower line of a fraction is called the denominator, is the following: If the numerator and denominator be and the upper the numerator: these are Latin words, either both multiplied or both divided by the same numwhich may be literally translated by the namer and the ber, the value of the fraction is not altered. For exnumberer; the first tells what sort of parts is taken, ample, take and multiply its numerator and denomiand the second how many of them are taken. The fol- | nator by 4, which gives g. In the second fraction we lowing propositions will serve for consideration, and cut the unit into four times as many parts as in the first, also to familiarize the reader with the use of these terms. consequently each part of the unit signified in the When the numerator is less than the denominator, the second fraction is the fourth of that signified in the first. fraction is less than a unit. When the numerator is But in the second fraction, four times as many parts are greater than the denominator, the fraction is greater taken as in the first, by which the balance is restored. than the unit. Of two fractions which have the same Let us suppose that two yards of cloth are to be meadenominator, that is the greater which has the greater sured by a foot measure. The foot being of the unit, numerator. Of two fractions which have the same and 6 of these being necessary, will be the fraction in numerator, that is the greater which has the less de-yards, representing not only the number of yards meanominator. It is usual to distinguish fractions which are less than the unit from those which are greater by calling the former proper, and the latter improper, fractions. sured, but in what parts of yards they were measured. No one would object to an inch measure, which is of a foot, provided 12 times as many inches were given as there were feet in the first case. But one inch is of As yet we have only considered fractions of the unit; a yard, and 12 times 6 is 72; and in this way of meaand it is always understood that a simple fraction, such suring would represent the number of yards given, as, is a fraction of the unit, or it is one yard or one which is derived from by multiplying the numerator pound which is divided into 8 parts. Fractions of other and denominator by 12. Similarly, one shilling, the numbers are written by placing the number to be di-unit being a pound, is; and 12 pence, the unit being vided after the fraction of it which is to be taken, thus also a pound, is; and and only differ in that of 7, which means that 7 is to be divided into 4 parts, the numerator and denominator of the first must be of which parts, 3 are taken. We now ask, what fraction | multiplied by 12 in order to make the second. of the unit is of 7, or into how many parts must one yard be cut, and how many times must one of those parts be repeated, so as to give the same length which arises from cutting seven yards into 4 parts, and taking 3 of them? It is obvious that 3 of 7 yards is 7 times as much as of 1 yard, or simply f; and 3 quarters of a yard | repeated 7 times is 21 quarters or . Similarly of 8 is of 1, or 6. Hence it follows that of 3 is, of 13 is, and so on. If therefore we take the eighth part of nine, we get the same as if we had repeated the eighth part of the unit nine times. We may therefore consider a fraction, such as , in two ways, either as the Hence it is allowable to multiply the numerator and denominator of a fraction by any number which is convenient, and which is called multiplicand, since that operation does not alter its value. Thus,,,, TE &c. are all of the same value, when the unit is the same in all : in common language, we should say, that two out of three is the same as four out of six, six out of nine, and so on. We are now able to remove two fractions which have different denominators, and substitute others of the same value with the same denominator. Take the fractions and . If we ask which is the greater, dino answer can at first be given, for though the second is 4 We now come to the reverse of multiplication. We have shown how to find the value of one fraction of another, such as of; we now ask, what fraction of must be taken, to give of 1 or simply ? Into how many parts must we cut, and how many times must we repeat one of those parts, in order that the result may be the same as if we had cut unity into 3 parts, and taken 2 of them? Reduce the fractions and to other equivalent fractions having the same denominator, which are and. If we cut 1, which is, into twenty-one equal parts, each of these parts is 4; if we repeat sixteen times, the result is, which is hence, if be cut into 21 equal parts and 16 of these parts be taken, the resulting fraction is, or if we ask, what fraction of is? the answer is, of . By our former rule ofis, which does not appear at first sight to be the same as, but if we examine its terms, we shall find that on dividing the numerator and denominator by 56 (which does not alter its value) it is reduced to . This rule being the reverse of multiplication is called division; the fraction which is to be cut into parts is called the divisor, that which is to be produced from it the dividend, and the fraction of the first, which it is necessary to take, in order to produce the second, is called the quotient. Thus, is the quotient of divided by . The rule deduced from this reasoning is: Reverse the divisor, that is, for write, and proceed as in multiplication with the reversed divisor and the dividend. Thus, of is. This rule is used in every question where division would have been used, if whole numbers only had been given. Thus, if 4 pounds cost 20 shillings, the price of one pound is found by dividing 20 by 4, and is 5 shillings. If of a pound cost of a shilling, the price of one pound is found by dividing by and is of a shilling. This might be established by independent reasoning as follows: As of a pound costs of a shilling, and 7 pounds cost 8 times as much as of a pound, 7 pounds will cost 16 of a shilling. But as the price of one pound is one-seventh of that of 7 pounds, for every third of a shilling which 7 pounds cost, one pound will cost the twenty-first part of a shilling. Hence the price of one pound is 1f as before. and the first 2, yet the second is four of the fifth parts only | Master of the Mercury, one of the ships belonging to an of unity, while the first is 2 of the third parts. But if we expedition sent against Quebec. Thus by far the most multiply the numerator and denominator of each frac- formidable of the difficulties were overcome which he tion by the denominator of the other, the results will be had to encounter in emerging from obscurity; he was and, which have the same value as and, and now on the direct road to preferment, and in a position also have the same denominator as each other. Hence in which his good conduct and perseverance were sure we see that, being greater than 1, is greater to meet with their reward. While stationed in this than. The sum of the two is the fifteenth part of command on the coast of North America, he greatly disunity repeated 22 times or; the difference is two tinguished himself both by his skill and intrepidity as a parts out of fifteen or. Hence follow the common seaman; and he also made use of his leisure to rectify rules for addition and subtraction of fractions. the defects of his original education by studying mathematics and astronomy. He eventually made himself in this way one of the most scientific naval officers of that time. His reputation rose accordingly; and, in 1768, when Government resolved to send out the Endeavour to the South Sea to obtain an observation of the approaching transit of Venus, Cook was selected to command the ship. He conducted this expedition with admirable ability, and so entirely to the public satisfaction, that, having returned home in 1771, he was the following year appointed to proceed again to the same regions with two ships, the Resolution and the Adventure, with the object of endeavouring to settle the longdisputed question as to the existence of a southern polar continent. On this voyage, in which he circumnavigated the world, he was absent nearly three years; and notwithstanding all the vicissitudes of climate and weather, and the other dangers which he had encountered, he brought home, with the exception of one, every man of the crew he had taken out with him. He communicated to the Royal Society an account of the methods he had adopted on this occasion for preserving the health of his men; and that body in return elected him into their number, and voted him the Copley gold medal as a testimony of their sense of his merits. To crown his achievement, Captain Cook wrote the history of this expedition himself, and wrote it admirably. In little more than a year after his return, he sailed on his third and last voyage of discovery; the principal object of which was to ascertain the practicability of a passage between the Atlantic and Pacific Oceans along the northern coast of America. After having been out on this expedition nearly three years, and having explored a vast extent of sea and coast, the great circumnavigator put in at the island of Owhyhee on his return home; and he was there killed in a sudden and accidental rencontre with some of the natives on the 14th of February, 1779. The late Admiral Burney, who was present on this occasion, mentions, in a note to his History of Discoveries in the South Sea, an anecdote which deserves to be remembered. Of the party of marines, by whom Captain Cook was accompanied when he met his death, four were killed along with him; "and in the hasty retreat made," says Burney, "after the boats had put off, one man still remained on shore, who could not swim. His officer, Lieutenant (now Colonel) Molesworth Phillips, of the Marines, though himself wounded at the time, seeing his situation, jumped out of the boat, swam back to the shore, and brought him off safe." The author proceeds to compare this conduct of Lieutenant Phillips with a similar act performed in 1624 by a Dutch captain, Cornelys de Witte, who, when a boat's crew which he commanded was surprised in a port on the coast of America by an ambuscade of Spaniards, and driven to sea after four of them had been killed, seeing one of his men left behind on the beach, boldly returned to the shore in the face of the enemy, and took him into his boat. "This was an act of generosity," observes the French translator of the account of the Dutch voyage, "worth a wound which he received in his side, and of which he was afterwards cured." The news of the death of Cook was received by his countrymen, and it may be said by the world, with the feeling that one of the great men of the age was lost; and both in his own and in foreign nations public honours We shall proceed in a future number to the explana tion of Decimal Fractions. THE WEEK. OCTOBER 27.-The birth-day of Captain Cook. James Cook was born in 1728 at the village of Marton in the North Riding of Yorkshire. His parents were of the class of labourers. All the education he received amounted only to English reading, writing, and the elements of arithmetic. He was then, at the age of thirteen, bound apprentice to a small shopkeeper in the neighbouring town of Snaith, which is on the sea-coast. Here he became so smitten with the love of a sea-life that he could not rest till his wish was gratified; and his master was at last induced to let him off, when he entered himself as one of the crew of a vessel engaged in the coal trade. In this humble and laborious line of life he continued till the breaking out of the war of 1755. He then entered the navy, as a common seaman, of course. But now the native superiority of the man began to assert itself; and in four years he rose to be were liberally paid to his memory. In the half century of busy and enterprising exertion in every field of activity which has elapsed since his death, no newer name in the same department has yet eclipsed the lustre of his; and with reference to the peculiar character of his fame, as contrasted with that of our other renowned seamen, it has been well and justly remarked that, "while numberless have been our naval heroes who have sought and gained reputation at the cannon's mouth, and amidst the din of war, it has been the lot of Cook to derive celebrity from less imposing, but not less important exploits, as they tended to promote the intercourse of distant nations, and increase the stock of useful science*." [Portrait of Captain Cook.] DOMESTIC PEACE. Ants in Brazil.-So numerous were the ants, and so great was the mischief which they committed, that the Portugueze called this insect the King of Brazil; but it is said by Piso, that an active husbandman easily drove them away, either by means of fire or of water; and the evil which they did was more than counterbalanced by the incessant war which they waged against all other vermin. In some parts of South America they march periodically in armies, such myriads together, that the sound of their coming over the fallen leaves may be heard at some distance. The inhabitants, knowing the season, are on the watch, and quit their houses, which these tremendous, but welcome visitors clear of centipedes, forty-legs, scorpion, snake, every living thing; and having done their work, proceed upon their way.-Southey's Brazil. Singular Customs.-There is a custom, proper to Sicily, which I must not forget to mention. This is a right of purchase of a singular kind. If any man buy an estate, be it house, land, or vineyard, the neighbour of the purchaser, for the space of an entire year afterward, may eject him by an advance of price. In vain would the first purchaser give *Gorton's Biographical Dictionary. more to the original owner. This singular law is generally evaded by a falsehood. The purchase-money is stated, in the articles of agreement, at a higher sum than has been agreed upon in the presence of four witnesses. There is another no less singular law in Sicily, according to which any man can oblige his neighbour to sell his house, if he will pay him three times its value. The intention of this law was, the improvement of the towns. It was to encourage the possessors of large houses to purchase the humble abodes of the poor.-Count Stolberg's Travels. Volcano in Iceland.-The Oræfa mountain is not only the loftiest in Iceland, but has been rendered remarkable by the great devastation made by its eruption about a century ago. Nothing can be more striking than the account of this calamity given by Jon Thorlakson, the aged minister of a neighbouring parish. He was in the midst of his service on the Sabbath, when the agitation of the earth gave warning that some alarming event was to follow. Rushing from the church, he saw a peak of the neighbouring mountain alternately heaved up and sinking; the next day, this portion of the mountain ran down into the plain, like melted metal from a crucible, filling it to such a height, that, as he says, no more of a mountain which formerly towered above it could be seen, than about the size of a bird; volumes of water being in the mean time thrown forth in a deluge from the crater, sweeping away whatever they encountered in their course. The Öræfa itself then broke forth, hurling large masses of ice to a great distance; fire burst out in every direction from its sides; the sky was darkened by the smoke and ashes, so that the day could hardly be distinguished from the night. This scene of horror continued for more than three days, during which the whole region was converted into utter desolation.-North American Review for July, 1832. Farming in Iceland.-The most important branch of rural labour in Iceland, is the hay-making. About the middle of July, the peasant begins to cut down the grass of the tûn (the green around his house), which is immediately gathered to a convenient place, in order to dry, and, after having been turned once or twice, is conveyed home on horseback to the yard, where it is made up into stacks. At the poorer farms, both men and women handle the scythe; but in general, the women only assist in making the hay after it is cut. In many parts of the island, where there is much hay, the peasants hire men from the fishing plains, who are paid for their labour at the rate of thirty pounds of butter a week. They cut by measurement; the daily task being about thirty square fathoms. Hay-harvest being over, the sheep and cattle that had been out all summer on the mountains are collected; the houses are put into a state of repair for the winter; the wood needed for domestic purposes is brought home to each farm; the turf is also taken in. During the winter, the care of the cattle and the sheep devolves entirely on the men; and consists chiefly in feeding and watering the former, which are kept in the house, while the latter are turned out in the daytime to seek their food through the snow. When the snow happens to be so deep that they cannot scrape it away themselves, the boys do it for them; and as the sustenance thus procured is exceedingly scanty, they generally get a little of the meadow hay about this time. The farm hay is given to the cows alone. All the horses, excepting perhaps a favourite riding horse, are left to shift for themselves the whole winter, during which season they never lie down, but rest themselves by standing in some place of shelter.Henderson's Iceland. |