States, the pioneers of advancing civilisation-and through Mexico -the most ill-conditioned country under the sun, as far as its people are concerned, yet in itself fair, rich, and fruitful, and worthy of being the home of an energetic and industrious race, instead of a paradise of thieves and cut-throats-we come to Central America, which deserves a passing mention here for the explorations of Captain, now Admiral, Bedford Pim and others, who are seeking to turn the stream of emigration setting steadily out from the southern parts of the United States into British Honduras, a country especially adapted for the production of cotton, sugar, and indigo; and the attempts that have been made to bring about the cutting of a ship canal across the narrow ship of land that separates Lake Nicaragua from the waters of the Pacific, to form with the lake itself and the river St. Juan a water-way through the isthmus for ships trading from Europe and the eastern coasts of America to India, China, Japan, and the shores and thousand islands of the vast Pacific. Southward yet a little further, and we come to South America, the Tapajos River, another vast tributary of that river, which drains the central and northern part of the province of Matto Grosso. Of the semi-organised republics of South America, which have scarcely recovered the effects of the revolution which separated them from Spain in the first quarter of the present century, and which (especially La Plata, or the States of the Argentine Confederation) have much to do in eradicating the sources of intestine discord before they can attain the condition of prosperous, peace-loving countries, there is little or nothing new to say; and turning eastward across the Atlantic we reach the last of the six great divisions of the world, the continent of Africa, in which it is necessary to trace the history of geographical discovery since 1820. After the travels of Sporrman, Shaw, Norden, Bruce, Le Vaillant, Mungo Park, and Horneman, which threw a flood of light upon the geography of Africa in the last century, we owe much to Adams, Tuckey, Bowditch, Mollien, Major Laing, a continent of whose central regions little more is known with any degree of certainty than has been yet learnt of the unexplored heart of Africa. But even here travellers have been busy in collecting facts to add to our limited knowledge of these parts of the world's surface, for Mr. Henry W. Bates, the present assistant secretary of the Royal Geographical Society, explored the countries on either bank of the mighty river Amazons between the years 1848 and 1859, giving us a series of vivid and animated descriptions of the habits of animals, sketches of Brazilian and Indian life, and aspects of nature under the equator, during eleven years of travel, in his work entitled "The Naturalist on the River Amazons." Mr. Bates's researches have been ably supplemented by Mr. W. Chandless, who received the Patron's Gold Medal in 1866 for his exploration of the river Purus, one of the southern affluents of the Amazons, which he ascended for a distance of 1,800 miles, making, by observations as he proceeded, an accurate map of the windings of the river. Previous to this journey of discovery Mr. Chandless had travelled through South America from the head-streams of the Paraguaya river which rises in the Brazilian province of Matto Grosso, and joins the Parana near the town of Corrientes, in the Argentine State of that name-to the mouth of the Amazons, down and Messrs. Ritchie and Lyon in the present century. The labours of Messrs. Denham and Clapperton, and Dr. Oudney, in exploring the interior of this continent in 1822, added considerably to our knowledge of North-Central Africa. When we look upon a modern map of Africa, all the geographical positions which are laid down in Bornou, round Lake Tchad, the lake itself, the direction of the course of rivers in this region, the rectification of the course of the Niger, and other topographical details, such as the position of mountains, etc., are due to the last-mentioned travellers. Clapperton closed his successful career by reaching Sockatoo from the Gulf of Benin, and died in 1826, leaving his labours unfinished, after having accomplished the remarkable journey from Tripoli to Benin, and enriched geography with a vast collection of new and accurate discoveries. Timbuctoo, that singular object of African travellers, was reached by Major Laing in the same year, but at a later period, when he also paid the debt of nature. In 1830, Richard and John Lander undertook to resolve the problem of the direction of the Niger from the point to which it had been traced by Park and Clapperton. They proposed to descend the river along its course from Boussa, where it had so far been traced, and to follow its course to the Atlantic Ocean, in order to ascertain its embouchure. After encountering many and great dangers, they reached the sea by the central or principal branch of the Niger, which is the river called Nun, and which disembogues itself into the Atlantic Ocean, between the Bight of Benin and the Bight of Biafra. The source of this river, as determined by Laing, is at the foot of Mount Loma, in the Kong Mountains. From this point to Timbuctoo its course was known; but the brothers Lander made it known from Boussa to the ocean, and so solved a part of the geographical problem which had so long existed without a satisfactory solution. LESSONS IN ARITHMETIC.-XXI. CONCRETE OR COMMERCIAL ARITHMETIC. 1. WE have hitherto been concerned with what are called abstract numbers-that is to say, numbers abstracted from their connection with any special thing, object, or magnitude; and we have established all the principles connected with them which are necessary to be known by the student of elementary arithmetic. We now proceed to apply these principles to concrete numbers-that is to say, to numbers which indicate some actual magnitude, object, or thing-as, for instance, time, money, length, etc. Theoretically, we are already in possession of principles which enable us to perform any calculation with reference to any concrete number. Take length, for instance. Suppose that we fix upon a certain length, and call it a mile. By means of this mile we could measure any other length whatever. For by fractions or decimals we could express any part or parts of a mile whatsoever; we could add, subtract, multiply, or divide any number of miles or parts of a mile, etc. etc. But it is manifest that, although this could be done, great inconvenience would arise from the cumbrous nature of the operations. In treating, for instance, of fractional parts of a mile, it would be often very difficult to realise the length indicated. What idea would most people have of of a mile? But if they were told that this length is very nearly indeed equal to a foot, they would form a very clear conception of the length. Hence, in measuring all magnitudes, the method of subdivision has been employed. Certain magnitudes have been fixed upon and named, and then these again divided and subdivided, and names given to the divisions, as convenience best suggested. Quantities expressed in this way by means of different subdivisions are called compound quantities. Thus, a sum of money, expressed in pounds, shillings, and pence, is a compound quantity. The names of the various subdivisions are generally called denominations. 2. Accurate Standard or Unit. On proceeding to measure any magnitude or quantity, it is evident that it is of the utmost importance to come to an exact definition of some one fixed magnitude of the same kind, with which we may compare all such magnitudes. Such a fixed magnitude is called a standard. When this has been done, then the standard can be subdivided, or multiples of it can be taken, as we please, and names given to the subdivisions or multiples. The subdivisions which are employed in England in the coinage and weights and measures are, as might be expected, not founded upon one carefully prepared and philosophical system, but have gradually grown up during long centuries, having often been suggested by special convenience or local usage. The subject has of late received much attention, and the possibility and advantage of establishing a uniform decimal system of coinage, weights, and measures, have been discussed with considerable warmth. On July 29th, 1864, an Act of Parliament was passed to render permissive the use of a decimal system of weights and measures called the "Metric System." Contracts and transactions, therefore, based on this system are now legal. We shall, however, return to this subject hereafter. We proceed now to treat of the subdivisions of various concrete quantities which are now generally in use. MEASURES OF TIME. 3. The time of the revolution of the earth in its orbit can be shown by the calculations of astronomical science to be an unvarying quantity, or, at any rate, to be subject to no appreci able variation for an immense number of centuries. Now, it is found that this time is 365-24224 (i.e., about 365-25, or 3654) mean solar days, a solar day being the interval which elapses between noon and noon-that is, between the times when the sun is successively highest in the heavens.* The year is made to consist of 365 days-i.e., about 1 of a day less than the time of the revolution of the earth in its orbit. To every fourth year (Bissextile or leap year, as it is called) one day is added, and thus at the end of every four years the earth is again very nearly in the same part of its orbit as it was at the beginning of them. We say very nearly, because the earth actually revolves round the sun in 365-24224 days, which is less than 365 days by 00776 of a day. This error in excess amounts to a day in about 128 years-i.e., to very nearly 3 days in 4 centuries. Hence, to make our reckoning still more accurate, we omit 3 days in 4 centuries; and this is done by making the year which completes every century not a leap year, except such centuries as are divisible by 4. Thus A.D. 1700, 1800, and 1900 are not leap years, but A.D. 2000-i.e., the year completing the twentieth century-is a leap year. The establishment of the leap year is due to Julius Cæsar; that of the omission of the leap year three times in 400 years to amounted to ten days, caused the ten days which followed Pope Gregory XIII., who, in the year A.D. 1582, when the error October 4th to be omitted in the reckoning. October 5th consequently was called October 15th. This latter system, the New Style, as it is called, was not adopted in England until A.D. 1752, when the difference between this and the old mode of reckoning amounted to about eleven days. The difference between the Old and New Style amounts Christmas Day and Lady Day, for instance-Old Style, would at present to about twelve days. Thus any fixed dayoccur twelve days later than our present Christmas and Lady Day. Russia is now the only country in Europe which retains the Old Style, Having, then, thus established a fixed invariable standard whereby to measure time, we are enabled to make any further subdivisions for convenience. 4. Having determined, as above explained, an exact measure of time, we are enabled, curious as it may appear, to deduce from it a fixed and invariable measure of length. We might, of course, take any object-a piece of metal, say-and, giving to its length a particular name, thus obtain a means of measuring all other magnitudes. But this object, whatever it might be, and however carefully preserved, would be liable to be lost, to alteration from decay, variation of temperature, etc. It is therefore very desirable to have some invariable and independent times in the year rather longer, and at others rather shorter, than its A solar day is not actually of unvarying duration, but is at some average length. It is this average length of the solar day which is called the mean solar day, and is divided into 24 hours. means to which we can always have recourse, to give us an exactly accurate standard of length with which to compare all other lengths. Now, the interval of time called a second being invariable, it is found that a pendulum which, in the latitude of Greenwich, under certain conditions, oscillates in one second, is of a certain length. It is further proved, from mechanical and mathematical principles, that this length must always be exactly the same whenever the experiment is tried under exactly the same conditions. This accurate and scientific method, however, as might be expected, was not the way in which a measure of length was first determined. A certain measure called a yard having been established, and this yard divided into 36 equal parts, called inches, it was found that the length of the pendulum oscillating in one second of time at Greenwich contained 39-1393 such inches. We thus see that we have a means of recovering and correcting, at any time, the measure of the yard. The actual standard yard was fixed, by Act of Parliament passed 1835, to be "the straight line or distance between the centre of the two points in the gold studs in the straight brass rod now in the custody of the Clerk of the House of Commons, whereon the words 'Standard Yard, 1760,' are engraved." The Act further states that in the latitude of London the pendulum vibrating seconds of mean time in vacuo at the level of the sea is 39-1393 inches. This standard, however, was, in fact, destroyed in 1834, at the fire of the House of Commons, before the Act passed. The Astronomical Society, however, had carefully prepared a standard yard, which is calculated to differ from the old one by not more thanth of an inch. We cannot here touch upon the ingenious and refined processes by which measurements are made when extreme accuracy is required, as, for instance, in determining a new standard length from the old one, or in finding to what amount of variation a given measured length is subject, from unavoidable external causes. The reader may consult the article Standard in the Penny Cyclopædia," which will give him a good general idea of the subject. SUBDIVISIONS OF LENGTH, OR LINEAR MEASURE. 5. The smallest measure is a barleycorn, or one-third of an inch; so called because, originally, the inch was obtained by placing together lengthwise three barleycorns taken from the centre of the ear. Little more, however, than the name of this subdivision remains, measurements being generally conducted in decimal or fractional parts of an inch. TABLE OF LINEAR MEASURE. 3 barley corns 12 inches 3 feet 5 yards 40 rods, or 220 yards 8 furlongs, or 320 rods 3 miles or} 60 geographical miles, or 69 common miles 360 degrees written 1 in. = 1 inch = 1 foot 1 ft. = 1 yard " 1 yd. Other measures of length are sometimes used, having reference to special descriptions of magnitudes. For instance, 12 lines make 1 inch; 4 inches make 1 hand; 9 inches 1 span; 18 inches 1 cubit; 6 feet 1 fathom. In measuring roads and land, a chain 22 yards or 4 rods long is used, called, from its inventor, Gunter's chain. It is divided into 100 links, each of which therefore contains of a rod, or 7·92 inches. CLOTH MEASURE. OUR HOLIDAY. CRICKET.-I. THE early days of spring bring with them the return of the cricketing season, and by many persons they are more gladly welcomed on that account, than for all the other charms which accompany them. Cricket is, undoubtedly, the national pastime of England. Every rural village has its players; towns and counties all over the kingdom are pitted against each other in rivalry for the palm of superiority in the game. Commencing in school-days, the pastime is often carried on as the chosen recreation of mature years; and with real benefit to him who practises it. For cricket is a vigorous and manly game, free from abuses that attend some other field sports, and well calculated to refresh and strengthen the physical powers, while it has sufficient science in its elements to give a not unprofitable exercise to the mental faculties also. Cricket, for so universal a pastime, is a very modern game. It owes its origin, in its present form, to a meeting in the year 1774, of some noblemen and gentlemen, who wished to improve the "bat and ball" of the period, and drew up a set of rules to fix the character of the implements employed, as well as the mode of play. These rules were subsequently amended and modified, and they gradually gained general acceptance. The first great cricket club was established at the close of the last century. It was called the White Conduit Club, from the circumstance of its play usually being held in the White Conduit Fields; and from this club the far-famed Marylebone Club of the present day took its rise. There are two forms of the game of cricket-one known as single, and the other as double wicket. For single wicket only a few players are required; but for double wicket, it is necessary, to play the proper game, that two sides should be formed, with eleven players on each side. Any large open field, that is tolerably level, will do for the practice of the game; but a good cricket ground, fit for the set play of club against club, should be at least that portion of it between the wicketsas level and as well kept as a good bowling-green, or, as is sometimes said with but little exaggeration, as a billiard-table." The implements used in the game are bats, balls, and wickets. In single wicket one bat and one wicket only are necessary; for the double game there must be at least two of each, an extra supply being always advisable in case of an accident during the game. The form of the cricket-bat is, no doubt, familiar to all our readers; its length should be suited to the height of the player, and such that he may wield it readily and with good effect; but, by the rules of the game, no bat must be more than thirty-eight inches long, or more than four-and-aquarter inches in the widest part. The ball is made of leather, and as it has to undergo very hard usage, it is best if made with what is known as the "treble seam." Its size is fixed at not less than nine inches nor more than nine-and-a-quarter inches in circumference. It must weigh not less than five-and-a-half ounces, nor more than five ounces and three-quarters. Both sides in the game play with the same ball; but at the commencement of each innings either party may call for a new one. The player is not restricted as to the precise bat he may use, provided it be a cricket-bat within the dimensions above specified. Each wicket consists of three stumps, usually made of strong and polished wood, and pointed at one end so as to be firmly fixed in the ground. The height at which they stand when set is fixed at twenty-seven inches out of the ground. There must be sufficient space between the stumps to prevent the ball from passing through. The top of each stump is grooved, and in In the measurement of cloth, linen, etc., the following lengths the grooves, when the stumps are set, two small pieces of wood called bails are laid from stump to stump. The length of the bails is fixed at eight inches. These are all the accessories that are actually required for the game. But padded gloves and leg-guards are frequently used by the principal players-the batsman and the wicketkeeper to prevent injury to the hands or legs when playing. The last three measures are now very seldom used in England. They are especially useful when the bowling is of the fast order A degree is in reality an angle; but, in measuring the earth's circumference, we give the name of degree to that portion of it which subtends an angle of one degree at the centre. See "Angular Measure," in Lesson 23. which has become so much in vogue in recent times. One set is sufficient for a small club, or for a school party, for the common use of its members; but young players can do very well without them, when they have only beginners like themselves to contend against. RETURN CREASE. BOWLER. All being now in readiness for the game, the bowler takes the ball, and, after calling "play" before starting, delivers the ball in the direction of the wicket farthest from him. His object is to strike it with the ball, and if he succeed in the attempt, the batsman stationed at that wicket is out. The object of the batsman obviously is to keep the ball off his wicket, and also, by striking it to a distance, to make one or more runs towards the game for his party. A run is scored when the batsman is able to pass from wicket to wicket without being put out before he comes fairly behind the popping crease, or places the end of his bat within it. If the batsman runs from one wicket to the other, and then returns to the wicket he started from, he counts two runs for his party, and so on. BOWLING CREASE ... WICKET. BATSMAN. ; We come now to the preparation and allotment of the cricket ground preparatory to play, confining our remarks at present to the usual game of double wicket. If only an ordinary field be available for the game, the most level portion of it, as near the centre as possible, is selected for the purpose of pitching the wickets. These must be directly opposite each other, and at a distance of twenty-two yards apart. A line six feet eight inches in length is drawn with chalk upon the ground at each wicket, so that the stumps stand in its centre. This is called the bowling crease. At each end of it another but short line is drawn at right angles behind the wicket, and this is named the return crease. The object of these lines is to mark out the space within which the bowler must be standing when he delivers the ball. In front of the wicket, four feet from it, and parallel with the bowling crease, another line, called the popping crease, is drawn. No precise length is defined for the popping crease, save that it must be at least as long as the bowling crease behind it. Within the space marked by these two creases is the batsman's proper ground, passing out of which he risks being put out of the game, by a touch of the wicket with the ball by one of the opposite side. The nature of the creases, and the ground marked out by them, will be made clear by diagram No. 1. POPPING CREASE. RETURN CREASE. DIAGRAM No. 1. THE BOWLING AND POPPING CREASES. 8 4 POINT. 3 When the ball is struck, the fielders, waiting in eager expectation, strive to catch it or otherwise stop it, and return it immediately to the wicket-keeper or bowler, that he may strike the wicket with it before the batsman reaches home. If this be done, or if the ball be caught in the first instance, the batsman is out, and another of his party succeeds him, until all the eleven have taken the bat in turn. The number of runs they have made between them is then counted up, and their opponents, now taking their innings, try to get a higher number if possible. Usually, in a game of double wicket, each side has two innings, and the party that can boast the highest total at the end of the play wins the game. LONG-STOP. 2 WICKET-KEEPER. 11 LONG-LEG. This is a brief explanation of the mode and the object of the play; but it may be as well to remark here that, besides the runs gained by the batsmen in the manner before mentioned, the side which has the innings are sometimes allowed to score runs through the negli gence of their opponents. Thus, if the ball, instead of being fairly bowled, is thrown or jerked towards the wicket, it is called a "no ball," and the batsman's party score one for it. Again, if it pass over the striker's head, or so wide of the wicket as to be out of his reach, it is a "wide ball," and the in side score one. Or, if either the no ... WICKET. facing each other; and they are then ready for the game. The opposite side select their bowler, and the captain of this eleven stations his men at the various points of the ground, according to his knowledge of their particular aptitude in fielding that is, in catching the ball, stopping it, etc. The positions in which the fielders as a body shall be placed are fixed by custom, which is founded on experience of where they are most likely to be effective. These positions are occasionally varied to suit the character of the bowling, whether fast or slow; but as a rule the men are stationed for medium bowling nearly in the positions indicated by diagram No. 2. LONG-OFF. DIAGRAM NO. 2. 10 SHORT-LEG. 66 ball" or "wide ball" be not stopped by the fielders, the batsmen may run from wicket to wicket, as if the ball had been struck in their play, and count as many runs as they can make. There are also. other ways of the batsman's being put out than those mentioned in the foregoing description; but these will be found fully detailed in the laws of the game, which will be given in another paper. In this we shall also give a little practical advice to the young player, with illustrations of the proper attitudes in batting, bowling, etc. LESSONS IN ARCHITECTURE-II. BUILDINGS IN UNHEWN STONE. WE will now proceed to trace briefly but distinctly the progress The simplicity of the first erections for religious purposes may be seen in the construction of the altars of early times. The first sacrifices, which the Bible and ancient tradition trace up to the creation, were made upon consecrated heaps of stones, which were collected upon high places. These first altars, called BETH-EL (the House of God), were erected in Chaldea, in Judea, and in Egypt. They were built, according to the Scriptures, of stones without cement, if the places where they were raised afforded proper materials. In other places they were constructed of turf and earth, where the plain country presented no solid materials. Such erections or mounds are found in Asia Minor and in India; at Heliopolis, celebrated for the worship of the DRUIDICAL REMAINS ON THE PLAIN OF CARNAC, IN THE DEPARTMENT OF MORBIHAN. FRANCE presents at first only simple rudiments, quite in accordance with primitive manners. From the earliest ages we find three great divisions established amongst all nations: first, private buildings; secondly, religious edifices; and thirdly, military constructions of a defensive character. The first care of a people, as we remarked before, would be to construct individual habitations; but being at first hunters and shepherds, they would be necessarily wanderers, and their dwellings would be tents constructed of the skins of animals, or cottages made of branches of trees. When they dwelt on the borders of rivers they would employ reeds; Asia and Egypt present us with examples of this kind. In some exceptional cases they dwelt in caverns, or in shallow excavations. The cottages were usually circular; piles of stones and earth, arranged in a circle, constituted their foundation. This form is found amongst all nations; that of the square, requiring more complicated combinations, was not adopted at first. VOL. L sun, and the great sidereal divinity of the Syrians. Lucian describes a throne or altar to the sun composed of four great stones arranged in the form of a table. At Ortosia, in Syria, there is an edifice of this kind raised in an open enclosure, and built of stones in a square form. Strabo relates that, travelling in Egypt, he saw his road covered with temples devoted to the god Mercury, which were composed of two unhewn stones, which supported a third, resembling the cromlechs which are to be seen in some parts of England. Artemidorus, quoted by Strabo, mentions that in Africa, near Carthage, the god Melkart (Moloch), or the Phoenician Hercules, was worshipped in a similar manner three or four stones being placed one upon another in the form of a rude altar or table. This simple manner of building applied to primitive altars, and to the sacred enclosures which surrounded them, after having been developed, as we have seen, in Asia and Africa, extended into Europe from the borders of the Black Sea and the Caucasus, 24 |