? by Mr. Cuming, the celebrated conchologist, who was at Valparaiso at the time; but it has been verified by the German travellers, Dr. Meyen M. Freyer, and by our own Darwin. Fig. 27. of the upraised portion was brought up to view. It is remarkable, that along the whole line of shift, the divided walls were found to adhere as firmly to each other, and to fit as closely as if they had been thus constructed and cemented from the very first. The only signs of their having been divided were, that the top of one part was much higher than the other, and the courses of the stone on each side of the rent did not correspond. This is represented in fig. 27. In North America, just above the falls of the Columbia River, there is a district twenty miles in length, and one mile in breadth, where a remarkable subsidence took place towards the close of the last century. In 1807, American travellers found here a forest of pines standing erect, under water, in the body of the river, some twenty The shift in the Round Tower of Terra Nova in Calabria, occasioned by the Earthquake of 1783. feet deep. Another traveller, in 1835, found the trees still standing in their natural position, but the tops of the trees, between high and low water-mark, had decayed away. The through the clear. water, spreading as they had grown in their native forest. This phenomenon occurs in a region of extinct volcanoes; for the river passes amid and through hills of basaltic rocks. The most extensive elevation of land by carthquake is that which took place on the coast of CHILI, South America, in 1822. The shock was felt along the coast for 2,000 Les. For More than one hundred miles the whole coast was elevated three or four feet high, and an area of about 100,000 square miles, nearly half the size of all France, was thus raised above the level of the sea. Some geologists suppose that the whole country, from the foot of the Andes to a great distance under the sea, was thus elevated; for the greatest rise was at the distance of two miles inland from the shore. On the coast, the rise was two or In 1819 a great subsidence of land took place in Hindostan, at the mouth of the river Indus, where the bed of the river sank eighteen feet, and the fort of Sindree became submerged. To the southeist of the eastern branch of the Indus, is an island district called Cutch. From the delta of the Indus to Cutch was an inlet of the sea, about a foot deep when the tide was out, and never more than six feet at flood-tide. After an earthquake in 1918, this inlet was deepened to more than eighteen feet at low water. In consequence of this sinking of the district, many parts of the inland navigation that had been closed for centuries be came again practicable. The fort of Sindree, on the eastern branch of the Indus, was completely submerged; and yet the masonry of the houses was not disturbed, either by the vioFig. 28. Present state of the Temple of Serapis at Puzzuoli, Italy. lence of the earth- When this region was examined in 1826-1827, it was found that, after the earthquake, the sea rushed into the mouth of the Indus, and then, in a few hours, converted a tract of land, about 2,000 square miles in area, into an inland sea. After the subsidence, one of the towers of Fort Sindree continued to stand above the water, and the inhabitants betook themselves in boats to this elevation for safety. While they were on this tower, they could see at the distance of full five miles to the north-west of them, an elevated land, where, before the earthquake, all had been level plains. This new-raised district turned out to be more than fifty miles in length from east to west. Its breadth from north to south was about sixteen miles. Its uniform Irise above the level four feet; but a mile inland, it was six or seven feet. This | of the delta was ten feet. Its direction ran parallel to the elevation has been disputed by several naturalists, especially district that had sunk, so that as one region subsided. the other rose. The most remarkable instance of the repeated processes of elevation and subsidence in the same district, is found in the Bay of Baiæ, to the north of Naples. In that bay is situated the town of Puzzuoli, formerly called Puteoli. It is the place where Paul landed after his voyage on his visit to Rome. And after one day the south-wind blew, and we came the next day to Puteoli, where we found brethren, and were desired to tarry with them seven days." (Acts xxviii. 13, 14.) Were he to land there now, he would not know the district; for, in the north of the bay, an entire mountain, called Monte Novo, has been raised up, which was not there at the time of his visit. At Puzzuoli, close by the sea-shore, are the remains of a magnificent building-whether of a bath or a temple has not been decided, but it is known all over the world as the Temple of Serápis. The building was quadrangular, 70 feet in diameter. The roof was supported by 46 pillars, 24 of granite, and 22 of marble, each consisting of a single block. Of these 22 marble columns, three remain standing, the tallest of them being 42 feet high. The surface of these columns is smooth and uninjured up to about twelve feet from the pedestal. Then begins a series of perforations and holes in the marble. These holes and perforations continue upward in a regular band round the column to the height of nine feet, and then cease; and the surface continues smooth all the way to the summit. The upper edge of the perforated band is now 23 feet above the level of the sea. How came these perforations into the columns? All the holes are deep, and in the shape of a pear,-i. e., very narrow at the entrance, but become larger as it enters the marble. It is evidently the work of a species of mussels called modiola lithophaga-marine shell-fish which eat into stones. A large number of these holes contain to this day the shells of the fish which perforated them, though many have been emptied by ravellers. How did the mussels come to attack these columns? and ow did they come to limit their operations just to a band nine eet in width? There can be no doubt that the temple to which they belonged, and the ground on which they are placed, were submerged under the water of the sea. When they were in this sunken state, the basement was protected from the boring mussels by masses of rubbish, tufa, and silt which the sea-water washed around them, and the upper part of the columns was beyond the reach of the sea. The perforations in this column prove-1, that this coast has, since the temple was built, sunk beneath the level of the sea; 2, that the same coast has been again elevated; 3, that the movement downward and again upward was more than twenty feet; and 4, that the elevation and subsidence was so gradual as to permit these columns to maintain their erect position. much studied by scientific geologists, and it is now ascertained that, for the last thirty or forty years, a gradual sinking of the coast is again going on, and that the floor of the temple becomes frequently covered again by water from the sea. LESSONS IN ARITHMETIC.-No. XVI. CONTRACTIONS IN DIVISION. THE operations in division, as well as those in multiplication, may often be shortened by a careful attention to the application of the preceding principles. CASE I. When the divisor is a composite number. EXAMPLE 1.-A man divided 837 crowns equally among 27 persons, who belonged to 3 families, each family containing 9 persons: how many crowns did each person receive? Analysis. Since 27 persons received 837 crowns, each one must have received as many crowns as the number of times that 27 is contained in 837. But as 27 (the number of persons), is a comporite number whose factors are 3 (the number of families), and 9 (the number of persons in each family), it is obvious we may first find how many crowns each family received, and then how many each person received. Operation. 3)837 Dividend. 9)279 Share of each family. Divisor 27 { Ans. 31 Share of each person. Explanation. If 3 families received 837 crowns, 1 family must have received as many crowns as 3 is contained times in 837; but 3 is in 837, 279 times. That is, each family received 279 crowns. Again, if 9 persons (the number in each family) received 279 crowns, 1 person must have received as many crowns as 9 is contained times in 279; and 9 is in 279, 31 times. Therefore 31 crowns is the share of each person. To divide by a composite number. Rule: Divide the dividend by one of the factors of the divisor, then divide the quotient thus obtained by another factor; and so on till all the factors are employed. The last quotient will be the answer required. To find the full remainder. Rule: If the divisor is resolved into but two factors, multiply the last remainder by the first divisor, and to the product add the first remainder, if any; the sum will be the compound remainder. mainder by all the preceding divisors, and to the sum of their When more than two factors are employed, multiply each reproducts add the first remainder; the sum will be the fo... e mainder. This contraction is exactly the reverse of that in multiplication, The quotient will evidently be the same, in whatever order the factors are taken. EXAMPLE 1.-A man bought a quantity of clover seed amounting to 507 pints, which he wished to divide into parcels containing 64 pints each: how many parcels can he make? Since 64-2X8X4, we divide by the factors respectively. 64 Quotient Now, all these changes of this temple have transpired since the time that Paul landed at Puteoli. Among the ruins, inscriptions have been discovered, which record that certain embellishments of marble were conferred on the building by Divisor Septimius Severus and Marcus Aurelius, The Emperor Severus died A. D. 211. This proves that this temple was in its original position at the commencement of the third century of our era. In A. D. 1198, in consequence of an eruption of Solfatara, in that neighbourhood, a subsidence of the coast took place, and the temple sank with it, and the columns came within the reach of the boring mussels. They continued for some time to sink lower and lower, and as they sank the mussels carried on their perforations higher and higher. They must have continued in this submerged state till near the middle of the sixteenth century, for in 1530 it is well known that the whole of that coast was covered by the sea. In 1538 an earthquake, connected with Vesuvius, agitated this district, threw up in one night on this shore a mountain 450 feet high, raised the coast on which the temple is built to the height of 20 feet, and formed a new tract of coast six hundred feet in breadth. It was then that these columns were raised beyond the reach of the mussels of the sea. These columns have been latterly Operation. 2)507 Dividend. 4)31-5 rem. Full remainder 59 pts. 7-3 rem. and 3X8X2 Quotient. 7 parcels, and 59 pints over. Dividing 507, the number of pints, by 2, gives 253 for the quotient, or distributes the seed into 253 equal parcels, leaving 1 pint over. Now the units of this quotient are evidently of a different vain, from those of the given dividend; for since there are but half as many parcels as at first, it is plain that each parce must contain 2 pints, or 1 quart; that is, every unit of the first quotient contains two of the units of the given dividend; consequently, every unit of it, as 5, that remains will contain the same; therefore this remainder must be multiplied by 2, in order to find the units of the given dividend which it contains. Dividing the quotient 253 parcels, by 8, will distribute them into 31 other equal parcels, each of which will evidently contain 8 times the quantity of the preceding, viz: 8 times 1 quart 8 quarts, or 1 eck; that is, every unit of the second quotient contains 8 of the units in the first quotient, or 8 times 2 of the units in the given dividend; therefore what remains of it, as 3, must be multiplied by 8×2, or 16, to find the units of the given dividend which it contains. In like manner, it may be shown, generally, that the division by each successive factor reduces each quotient to a class of units of a higher value than the preceding; that every unit which remains of any quotient, is of the same value as that quotient, and must therefore be multiplied by all the preceding divisors, in order to find the units of the given dividend which it contains. Finally, the several remainders being reduced to the same units as those of the given dividend according to the rule, their sum must evidently be the compound remainder. EXERCISES. 1. How many acres of land, at 35 crowns an acre, can you buy for 4650 crowns? 2. Divide 16128 by 24. 3. Divide 17220 by 84. 4. Divide 25760 by 56. 5. Divide 91080 by 72. 6. Divide 142857 by 112. 7. Divide 123456 by 168. CASE II.-When the divisor is 1 with ciphers annexed to it. It has been shown that annexing a cipher to a number increases its value ten times, or multiplies it by 10. Reversing this process-that is, removing a cipher from the right hand of a numberwill evidently diminish its value ten times, or divide it by 10; for, each figure in the number is thus restored to its original place, and consequently to its original value. Thus, annexing a cipher to 15, it becomes 150, which is the same as 15X10. On the other hand, removing the cipher from 150, it becomes 15, which is the same as 150-10. In the same manner it may be shown, that removing two ciphers from the right of a number, divides it by 100; removing three, divides it by 1000; removing four, divides it by 10000, &c. Hence, To divide by the numbers 10, 100, 1000, &c. Rule: Cut of as many figures from the right hand of the dividend as there are ciphers in the divisor. The remaining figures of the dividend will be the quotient, and those cut off will be the remainder. EXERCISES. 1. In one pound there are 10 florins; how many pounds are there in 200 florins? In 340 florins? In 560 florins? 2. In one metre there are 100 centimetres; how many metres are there in 65000 centimetres? In 765000 centimetres? In 4320000 centimetres ? 3. Divide 26750000 by 100000. 4. Divide 144360791 by 1000000. 5. Divide 582367180309 by 100000000. CASE III.-When the divisor has ciphers on the right hand. EXAMPLE.-How many hogsheads of molasses, at 30 crowns apiece, can you buy for 9643 crowns? The divisor 30 is a composite number, the factors of which are 3 and 10. We may, therefore, divide first by one factor and the quotient thence arising by the other. Now cutting off the righthand figure of the dividend divides it by ten, consequently dividing the remaining figures of the dividend by 3, the other factor of the divisor, will give the quotient. Operation. Divisor 30)964|3 Dividend Quotient 3218 Explanation. We first cut off the cipher on the right of the divisor, and also cut off the right-hand figure of the dividend; then dividing 964 by 3, we have 1 remainder. Now, as the 3 cut off is part of the remainder, we therefore annex it to the 1. Ans. 321 hogsheads. When there are ciphers on the right hand of the divisor. Rule: Cut off the ciphers, also cut off as many figures from the right of the dividend. Then divide the other figures of the dividend by the remaining figures of the divisor, and annex the figures cut off from the dividend to the remainder." EXERCISES. 1. How many vehicles at 70 pounds apiece, can you buy for 7350 pounds? 2. How many barrels will it take to pack 36800 pounds of pork, allowing 200 pounds to a barrel? 3. Divide 3360000 by 17000. When the divisor is the number 5. Rule: Multiply the dividend by 2, and divide the product by 10. When the figure cut off is a significant figure, it must be divided by 2 for the true remainder. This contraction depends upon the principle that any given divisor is contained in any given dividend, just as many times as twice that divisor is contained in twice that dividend, three times that divisor in three times that dividend, &c. 1. Divide 6035 by 5. 3. Divide 8450 by 5. 2. Divide 32561 by 5. CASE V. 4. Divide 43270 by 5. When the divisor terminates in 5. This method is simply doubling both the divisor and dividend, We must therefore divide the remainder, if any, by 2, for the true remainder. by 4. 3. Divide 2876 by 175. 4. Divide 8250 by 275. 1. Divide 1125 by 75. 2. Divide 3825 by 225. The preceding are among the most frequent and useful modes of contracting operations in division. Various other methods might be added, but they will naturally suggest themselves to the inventive student, as opportunities occur for their application. EXERCISES. 1. How long would it take a vessel sailing 100 miles per day to circumnavigate the earth, whose circumference is 25000 miles? 2. The distance of the Earth from the Sun is 95,000,000 of miles: how long would it take a balloon, going at the rate of 100,000 miles a year to reach the sun? 3. Divide 667000000000 by 25000000000. 10. 16753672÷35. 11. 325638555. 12. 4567240025. 13. 6245634-45. 14. 8245623125 23. 876240275. 25, 92004578100000. GENERAL PRINCIPLES IN DIVISION. From the nature of division, it is evident, that the value of the quotient depends both on the divisor and the dividend. I. If a given divisor is contained in a given dividend a certain number of times, the same divisor will obviously be contained, in double that dividend, twice as many times; in three times that dividend, tre as many times, &c. Hence, If the divisor remains the same, to multiply the dividend by any number, is in effect multiplying the quotient by that number. Thus, 6 is contained in 12, 2 times; in 2 times 12 or 24, 6 is contained 4 times i. e. twice 2 times); in 3 times 12 or 36, 6 is contained 6 times (i. e. thrice 2 times); &c. II. Again, if a given divisor is contained in a given dividend a certain number of times, the same divisor is contained in half that dividend, half as many times; in a third of that dividend, a third Hence, as many times, &c. If the divisor remains the same, dividing the dividend by any member, is in effect dividing the quotient by that number. Thus, 8 is contained in 48, 6 times; in 48-2 or 24 (half of 48), 8 is contained 3 times (i. e. half of 6 times); in 48-3 or 16 (a third of 48), 8 is contained 2 times (i. e. a third of 6 times); &c. III. If a given divisor is contained in a given dividend a certain number of times, then, in the same dividend, twice that divisor is contained only half as many times; three times that divisor, a third as many times, &c. Hence, plied into the divisor, will produce the dividend. If, therefore, the dividend is resolved into two such factors that one of them is the divisor, the other factor will, of course, be the quotient. Suppose, for example, 42 is to be divided by 6. Now the factors of 42 are 6 and 7, the first of which being the divisor, the other must be the quotient. Therefore, cancelling a factor of any number di vides the number by that factor. CASE 1.-When the dividend is the product of two factors, one of which is the same as the divisor. Rule: Cancel the factor common to the dividend and divisor; the other factor of the dividend will be the answer. NOTE. The term cancel signifies to erase or reject. Common Method. Divisor 34)952(28 Quotient 68 tient, as by the common method. By Case I. 34×28 28 Quotient Cancelling the factor 34, which common both to the divisor and dividend, we have 28 for the quo of examples and problenis, which involve both multiplication and division, that is, which require the product of two or more num- 84X5X9 =84X5=420. Proof. 3780 =420. If the dividend remains the same, multiplying the divisor by any 7. Divide 810 or the product of 45X18 by 90 or 18×5. number, is in effect dividing the quotient by that number. Thus, 4 is contained in 24, 6 times; 2 times 4 or 8 is contained in 24, 3 times (i. e. half of 6 times); 3 times 4 or 12 is contained in 24, 2 times (i. e. a third of 6 times); &c. IV. If a given divisor is contained in a given dividend a certain number of times, then, in the same dividend, half that divisor is contained twice as many times; a third of that divisor, three times as many times, &c. Hence, If the dividend remains the same, dividing the divisor by any number, is in effect multiplying the quotient by that number. Thus, 6 is contained in 36, 6 times; 6-2 or 3 (half of 6), is contained in 36, 12 times (i. e. twice 6 times); 6-3 or 2 (a third of 6), is contained in 36, 18 times (i. e. thrice 6 times); &c. V. From the preceding articles, it is evident that any given divisor is contained in any given dividend, just as many times as twice that divisor is contained in twice that dividend; three times that divisor in three times that dividend, &c. Conversely, any given divisor is contained in any given dividend just as many times, as half that divisor is contained in half that dividend; a third of that divisor, in a third of that dividend, &c. Hence, If the divisor and dividend are both multiplied, or both divided by the same number, the quotient will not be altered. Thus, 6 is contained in 12, 2 times; 2 times 6 is contained in 2 times 12, 2 times; 3 times 6 is contained in 3 times 12, 2 times, &c. Again, 12 is contained in 48, 4 times; 12-2 is contained in 48 2,4 times; 12÷3 is contained in 48-3, times, &c. VI. If the sum of two or more numbers is divided by any number the quotient will be equal to the sum of the quotients which will arise from dividing the given numbers separately. Thus, the sum of 12+18=30; and 30÷6—5. Now, 12-6-2; and 18÷÷6-3; but the sum of 2+3=5. Again, the sum of 32+24+40-96; and 96-8-12. Now, 32-8=4; 24-83; and 40÷8-5; but 4+3+5=12. CANCELLING FACTORS. DEFINITION. The method of contracting arithmetical operauns, by rejecting equal factors, is called CANCELLING FACTORS. We have seen that division is finding a quotient, which, multi Operation. 45X18 45 18x5 9. We cancel the factors 18 in the dividend and 18 in the divisor for cancelling the same or equal factors in the divisor and dividend, is dividing them both by the same number, and therefore does not affect the quotient. CASE II.-When the divisor and dividend have common factors. Rule: those remaining in the dividend by the product of those remaining 8. Divide 15X7X12 by 5×3×7X2. 10. Divide 75X15X24 by 25×3×6×4×5. The four preceding rules,-viz., Addition, Subtraction, Multiplication, and Division are usually called the FOUR FUNDAMENTAL RULES of Arithmetic, because they are the foundation or basis of all arithmetical calculations. LESSONS IN NATURAL HISTORY.-No. IX THE BEAR. [Order CARNIVORA, genus URSUS.] THE bear belongs to a section of the animal kingdom to which has been given the name of Plantigrades, from their applying the en tire sole of the foot to the ground, so as to have the free power of raising themselves on their hinder limbs, and maintaining with ease an upright position; their motions are slow and heavy; their habits are generally nocturnal; and in the northern regions, they usually pass the winter in a lethargic state, concealed in holes in the ground. Some of the species are able to use their fore-feet in conveying food to their mouths, or in seizing hold of objects. Their claws are strong, blunt, and well adapted to digging and climbing. In consequence of their adaptation to the latter purpose, bears are able to ascend trees in search of prey, and also to escape the pursuit of their enemies. Dancing bears used to be a common sight in the streets of Lon |