MENSURATION. To find the area of a triangle. (1) What is the area of a triangle whose base is 7 ft. 9 in. and perpendicular height 3 ft. 6 in. ? (2) How many acres are there in a triangular field whose base is 13 chains and perpendicular 10.25 chains? (3) If a rectangular field contains 12 acres, what is its breadth, its length being 25 chains? (4) How many square yards are there in a triangular field whose base is 13.5 chains and perpendicular 7.68 chains? (5) What would be the cost of mowing a rectangular field of grass at 58. per acre, its length being 24.5 chains and breadth 21.32 chains? ATTRACTION. (From the Laboratory of Chemical Wonders,' by G. W. Septimus Piesse.) co-he'-sive, having the power of sticking cap'-il-la-ry, like a hair, small co-in'-ci-dence, an event happening at If there be any one phenomenon more than another which has puzzled philosophers to explain, it is that which is called attraction. Any attempt to explain it by words involves the necessity of stating that several kinds of powers of attraction are recognised. First may be noticed the attraction of the earth towards all bodies above its surface. That which causes matter to 'tumble' or 'fall down' is called gravitation, or the earth's attraction. Secondly, there is what is termed cohesive attraction, which regulates the form of bodies, whether they be solid, as a rock, or granular, like sand. Another sort of attraction is named affinity, or chemical attraction, which produces all sorts of compounds; such as water, salt, sugar, &c., which are made up of substances of a totally opposite nature, held together by affinity. Were it not for this peculiar attraction of one substance to another, the whole world would be resolved into its elements; nothing would exist but a few metals, three or four gases, some sulphur, and charcoal; but by the force of affinity these different things unite, and produce all the beauties of nature. Thirdly, there is a magnetic attraction, or magnetisman effect observed in only a very few substances, such as iron, nickel, and cobalt. Lastly, we have capillary attraction. By this force the sap rises in trees: a drop of water at the root finds its way to the summit of the loftiest poplar. Although we have made these divisions of the various powers which attraction exhibits, yet we are no nearer to the comprehension of the cause which produces the effect. Could we but ascertain the reason why a stone falls towards the earth when released from the hands, it is probable that we should soon discover the cause of the motion of all the heavenly bodies. Could we but suspend and resume the power of gravitation at will, we could travel round the earth in twenty-four hours; we could then rise a little above the earth's surface, and remain like a gossamer in the air; the world would continue to revolve as it now does, upon its axis, at the rate of a thousand miles an hour. This would rapidly bring Africa and Australia under us, and by resuming gravitation we could descend where we pleased. Wonderful as this idea may be to the uninitiated, it is nevertheless not beyond the hope of realisation by many philosophers. This desire is buoyed up by analogy. The law of nature can be overcome and subverted in many ways. For instance, Davy produced the metal potassium from pearlash by counteracting affinity with a stream of electricity. AFFINITY ILLUSTRATED. Affinity, or power of uniting of one substance with another, is so great, that were it not for living plants and animals each element of the world would soon seek out its fondest ally, and, these being united, there would quickly be an end to any further chemical change of matter on the face of the earth. The vital power, however, of living plants and animals is constantly undoing what the inorganic or non-vital materials are ever consummating; the very few native or natural elements that are found by man show how this power has already done its work. Man never finds iron, phosphorus, potassium, carbon, and a host of other materials, in their primitive state, but always combined with some other of the elements: and it is his ingenuity and chemical knowledge which break them up and separate them, giving us iron for the ploughshare, phosphorus for the match, and many other necessaries of civilised life. The laws of affinity are best illustrated by many of the events of everyday life, such as the burning of a candle, the decay of wood, the change of lime into chalk, and the rusting of iron. Tallow at the ordinary temperature has but little affinity for the oxygen in the air; it has however sufficient affinity for it, and gradually changes, or becomes, as we say, rancid. The higher the temperature, the greater is this affinity. If tallow be thrown on to hot iron, as in a frying-pan, then a further change is noticed in the powerful odorous bodies produced. At a burning heat, however, the affinity of the oxygen of the air and the components of the tallow is so great, that the whole disappears in invisible gases. Wood shows a similar action, according to the temperature it is exposed to. If air, wood, and water be exposed together, their mutual affinities are sufficient to sap 'the heart of oak' in a few years; and if heated to the combustion point, this change takes place in a few minutes. If we make a paste of lime and water, and spread it on a tile, and then expose it to the air, in less than a month the carbonic acid which is in the air will unite with the lime and produce chalk. Now, if vinegar be poured on to this chalk, an effervescence is produced by the escape of the carbonic acid; the vinegar (acetic acid) having a greater affinity for the lime than the carbonic acid, throws out the latter. Iron-stone as it is dug from the mine is little else but rust (or oxide) of iron-that is, oxygen from the air united with the metal. The smelter's business is to make the oxygen in the metallic rust unite with the coal, which it readily does at a furnace heat; and thus he shows us how he can break up that affinity which has hidden the bright metal from mortal gaze since the world began. The want of the knowledge of the laws of affinity betokens savage life; on the contrary, a thorough comprehension of affinity indicates a high state of civilisation. MAGNETISM. At no great distance from Constantinople is the ancient town of Magnesia, once a city, and the residence of the great Ottoman rulers of the East, and the centre of oriental splendour. A pleasant ride from this old Magnesia brings us to the vicinity of the most remarkable iron mines in the world; remarkable not for the quantity of metal produced, but for the peculiar properties of the ore. The mineral here obtained has the specific name of leadstone, or (as now corrupted) loadstone. If a strip of this stone be balanced on a point, it will turn on that point till it takes a direction which is opposite to the motion of the earth; and as the globe revolves from west to east, so therefore does the loadstone stand in a direction north and south. According both to history and tradition, round and about Magnesia dwelt, at a very remote period, a civilised race. Men of thought and science naturally had their attention directed to the astonishing and almost life-like property of this stone. Nearly all of us have read, or intend to read, the story of Sinbad the Sailor, in the Arabian Nights' Entertainments.' How long ago it is since that tale was written it is difficult to say, but it is certain that it was as popular before the Christian era as now. The loadstone of the tale is the Mountain of Adamant, which drew the nails out of the wonderful navigator's ship. We read in the legend, that 'About noon we had come so near that we found what the pilot had foretold to be true, for we saw all the nails and iron in the ship fly towards the mountain by the violence of their attraction, with a horrible noise; so the ship split, and sank into the sea.' Since the Crimean war navigation has been very much extended in the Black Sea, and here is a confirmation of the Arabian fable by a recent traveller. 'Ships have lately run ashore on the coasts of the Black Sea, near Sinope; and the captain of one that narrowly escaped wreck, suspected that the compass had been deflected by magnetic influence. This suspicion led to an investigation, which has issued in the discovery of a valuable mine of iron ore or leadstone on those coasts, the danger of which is calamitous.' Now, if this, or the mines near Magnesia (and both are not far apart), be not the identical Mountain of Adamant referred to by Sinbad, it is certainly a very remarkable coincidence. The power which we call magnetism derives its name from Magnesia, because of this loadstone, and as the subject is an old one, we ought perhaps to know all about it; but nevertheless, it still mystifies the most profound philosophers, and what we do know has been discovered by men of our own age. As we have before said, if a piece of this adamant, or loadstone, be balanced, it will turn till its direction is north and south, and then remain stationary; but this is not all, for the loadstone has the power to impart the same quality to a piece of steel, which it does by mere friction, losing by the operation not the slightest power itself, yet giving to the steel no less an amount of power than itself possesses; and steel thus treated is said to be magnetised. But this power of placing itself at right angles to the motion of the earth is not the only quality that a magnet possesses. The attractive influence it exercises over iron and steel is no less wonderful, and indeed so much so, that considerable force is necessary to remove the object attracted when once brought in contact with it. A number of mechanicians are now engaged in solving the problem-how to make this power useful for locomotion, and there is great probability that they may eventually succeed. Although we are not able to explain the cause of magnetism, yet we have ascertained that it is intimately connected with electricity, for we can produce the one from the other. The mariner's compass consists of a piece of steel, shaped like an arrow, that has been rubbed with either a loadstone or magnet. When thus treated, it is called a magnetic needle; it is then fixed to a card, on which are marked all the points of the horizon. In this way it becomes useful to the traveller by land and by sea, as he can direct his course to any point he pleases, knowing well thatThe obedient steel with living instinct moves, And veers for ever to the pole it loves.' Hence the old name of leadstone* is correct. Another remarkable property inherent in the magnet is that of having a power which we call the repulsive or repelling power, which is no less active than its attracting power. If two magnets, with the same lettered points, be placed near together, they instantly move away from each other with considerable force. In this way the chemists have given to the mechanics two horses, one that pulls, and one that pushes; and it is for them to solve the means of harnessing them to the vehicle-a feat probably beyond the horse-taming powers of Mr. Rarey himself. A great number of beautiful magnetic experiments can be made, and, for the purpose of illustration, Mr. Myers, toy merchant, of Leadenhall Street, has constructed a box of magnetic toys. This is accompanied by a little book of explanation, in which the author says, and very wisely, 'There is no reason why a young lady should not study all that is known about this or any other branch of science.' The laws of nature exert their influence on women as well as men, and all alike may suffer from neglecting them; for there is nothing peculiar in a woman's mind which prevents it from acquiring a deeper insight into natural laws, and there is nothing peculiar in a man's mind that he should appropriate this knowledge to himself. MENSURATION.-PARALLELOGRAMS AND TRIANGLES. (1) What is the length in yards of the hedge surrounding a square field whose area is 14 a. 29 p. 63 yds.? (2) If the length of a rectangular court-yard be 100 ft. and its area 538 yds. 8 ft., what is its width? (3) What length of carpet 3 qrs. wide will be required to cover the floor of a drawing-room which measures 45 ft. by 25 ft. 6 in.? (4) If the area of a triangular field be 12 acres and its base 12 chains, what is the length of its perpendicular? (5) A field is cut up into a square whose side is 57 yards, a rectangle 320 yards by 57, and a triangle with base 57 yards and perpendicular 36 yards: find the area of the field. *Guidance stone. |