E from PS as a centre. Now this horizontal plane through the eye, E, is turned up upon the perpendicular or picture-plane; mark the course of the dotted arc from E to E2, therefore PS E2 is equal to PS E. Thus, it will be seen, two planes are reduced to one. The result is shown also in Fig. 22. Now we must turn the ground-plane upon the picture-plane. First, let us repeat a remark or two made in Lesson II., Fig. 5 (page 225). The line from E to ▲ (Fig. 21) is a visual ray cutting the pictureplane in B; B then is the picture of the point A. The line from A to s P, on the ground-plane, is the ground plan of this visual ray; therefore a perpendicular line from c (where A SP cuts the base of the picture) drawn to the line E A, determines B, the picture of A, the object. The pupil will now perceive there is a plane perpendicular to the ground, and also to the picture-plane, upon which the distinctive points E, PS, B, C, A, and SP are placed; but first make C A equal to C A, as shown in the arc from A to A; this brings the ground-plane upon the pictureplane (in the same way as we turned E to E2). Compare Fig. 22 with Fig. 21; A2 will be seen in both figures. From c, in Fig. 22, draw the arc A2 A3. This will be recognised in Fig. 21; with the picture-plane. From H and I draw perpendiculars to the picture-plane, and proceed with each extremity as was done with the line A B; hi will be the perspective of the given line HI. The following remarks upon the line K I will refer to all the lines similarly drawn-that is, perpendicularly to PP; because the line KI is perpendicular to PP, therefore the perspective representation of that line is drawn to the point of sight, viz., K i PS, and somewhere upon that line is the position of I in i found first by drawing from the centre K the arc I L, and joining L with DE1; this last line cutting K PS in i, fixes the perspective view of I; the same may be repeated for h; ih being joined gives the perspective view of H I. PROBLEM IX. (Fig. 24).-Draw the perspective view of a pavement composed of square slabs, the edges of which shall measure 15 feet; height of eye and distance as before. Let A B be the total width of all the slabs, and A1, 12, 23, 34, 4 B, each equal to 1.5 feet. Draw lines from each of these divisions to the point of sight: upon the horizontal line set off from PS to DE 10 feet. From each of the divisions on AB, viz., A, 1, 2, etc., draw lines to DE; where these lines intersect those 1 and the line A3 to DE1 will also be seen in both figures; therefore the line E B A in Fig. 21 is turned round upon the pictureplane, and represented by A3 B DE', shown also in Fig. 22. Thus the perspective projection в of the point a on the ground is determined. We have remarked (see Lesson II.) that points are the extremities of lines; and if we can determine the positions of points in the picture, we can represent straight lines by uniting these points. Our pupils will also recollect that we have said, "all lines which are perpendicular to the picture-plane have the point of sight for their vanishingpoint." Let these observations be borne in mind as we proceed. PROBLEM VIII. (Fig. 23).—A straight line, A B, 5 feet long, is perpendicular to the picture-plane lying on the ground, and 1 foot from it; height of eye, 5 feet, and distance from the picture-plane, 10 feet. Scale, 4 feet to the inch. Draw the line C A B perpendicularly to PP, make c A 1 foot, and AB 5 feet. Draw HL parallel with PP, and 5 feet from it. Draw PS E perpendicularly to H L, and 10 feet long. From Ps, with distance PS E, describe the semicircle DE1 E DE'. From c, and with the distance cA, draw the arc A D. From 2, again draw the arc B F, join F and D with DE2, also draw the line C PS. Between the intersections of c PS with the lines from F and D to DE2 will be the perspective of A B, viz., a b. Let the line H 1 be 5 feet long, and at an angle of 50° drawn from the given divisions A, 1, 2, etc., will be found the angles from which are drawn the opposite sides of the squares, viz., 5, 6, 7, 8, 9. We must here observe, as will be seen in Fig. 24, that all lines which retire at an angle of 45o with the P P have the distance-point for their point of sight. For if one side of a square is parallel with the PP, the other side will be at right angles with the P P; therefore the diagonal of the square will be 45° with PP. PROBLEM X. (Fig. 25).—Draw the perspective view of a square, the sides of which are 3 feet in length, 2 feet from the PP, and one side at an angle of 50° with the PP. Draw a b at the given angle. Find the point c according to Figs. 13 and 14, Lesson III., and Fig. 20. Construct the square c def, and from each angle draw perpendicular lines to the PP, and from thence vanishing lines to the PS. In these several vanishing lines find the projected angles of the square as in Problem VIII., Fig. 23; between these points respectively draw straight lines which will produce the perspective representation of the square. In the next problem we only give the proposition and the diagram, trusting the pupil will be able to work it, as the explanation would be a repetition of Problems VIII. and X. PROBLEM XI. (Fig. 26).-Draw the perspective view of a parallelogram 5 feet long, 3 feet broad, one edge at an angle of 40° with the PP, and the nearest angle 1 foot within, or from the PP. As £93 : £100 :: 3s. : prime cost per pound. = shillings 100 shillings. Now if I am to gain 10 per cent., we have the proportionAs 100 : 110 :: s. : selling price required. Therefore the selling price required = 110 3s. 61fd. Loss, ETC. Thus, at 27 per cent. £28 is the per centage on £400. Again, if we have to find how much per cent. one given number is of or on another, it is the same thing as dividing the first number into as many equal parts as there are hundreds in the second number. One of these equal parts in the first will then correspond to EXERCISE 53.-EXAMPLES OF PER CENTAGE, PROFIT AND each hundred of the second number, which is the same thing as saying that the first number is so much per cent. on the other. Thus, if we want to find how much per cent. 27 is of 900, we must divide 27 into 9 parts, which gives 3, and hence we see that for every 100 of the 900 there corresponds 3 in the 27. Hence 27 is 3 per cent. on 900. 1. How much is 4 per cent. upon £375 ? 2. How much is 3 per cent. upon 373, to 4 places of decimals? 3. How much is 31 per cent. upon 27?? 4. The population of London in 1861 being 2,803,034, and that of the whole of England 29,307,276, how many per cent. of the population lived in London ? 5. If the population of a town in a certain time increases by 8 per cent., and the actual population at the beginning of the time was 20,000, what was it at the end of the time? 6. If at the same rate of increase, it is found at the end of the time to be 20,000, what was it at the beginning? 7. How much per cent. on 353 is 29 to 2 places of decimals? 8. How much per cent. on 534 is 27 to 2 places of decimals? 9. If standard silver can be bought for 5s. an ounce, what profit does the Mint make per cent. by coining a pound Troy into 66 shillings? 10. A mixture professing to be coffee contains 24 per cent. chicory. How much chicory would there be in one pound of coffee? 11. In the last question, if the cost price of pure coffee be 1s. a pound, and of chicory 4d. a pound, what does the grocer gain per cent. by selling the mixture at 1s. 4d. a pound? 12. The population of a town increases in 10 years from 26,485 to 28,351. What is the rate of increase per cent.? 13. A grocer mixes 9 lbs. of coffee at 2s. 3d. a pound with 6 pounds of chicory at 74d. a pound. At what price must he sell the mixture to gain 25 per cent.? 14. If 3 per cent. is lost by selling steel pens at 3s. 6d. a gross, how much would be gained or lost per cent. by selling them at 2s. 6d. a hundred ? 15. At what rate must sherry be sold which costs 40s. a doz., if on every £100 of outlay the selling price of 5 doz. is gained? What is the gain per cent.? 16. What sum must A bequeath to B, so that B may receive £1,000 after a legacy-duty of 10 per cent. has been paid? 17. What must be the gross rental of an estate, so that after deducting 7d. in the pound for income-tax, and 4 per cent. upon the remainder for expenses of collection, there may be left a nett rental of £1,000 P 18. By the sale of goods which cost me £3 19s. 2d., I lost a sum equal to 5 per cent. of the proceeds; and by the sale of another quantity which cost me £5, I gained a sum equal to 31 of the proWhat did I gain per cent. on the whole outlay? ceeds. 19. A man bought a house which cost him 4 per cent. upon the outlay to put into repair; it then stood empty for a year, during which time he reckoned he was losing 5 per cent. upon his total outlay. He then sold it for £1,192, by which means he gained 10 per cent, upon the original purchase-money. What did he give for the house? LESSONS IN CHEMISTRY.-XII. THERE are many compounds of carbon and hydrogen. They bining weight, 16; density, 8).-When the mud at the bottom of stagnant pools is stirred, bubbles of this gas rise to the surface; and when mixed with the spontaneously inflammable gas, phosphoretted hydrogen, the bubbles ignite, giving rise to the ignis fatuus, or the "Will-o'-the-Wisp." In collieries it exudes from the coal-beds, and often in such quantities as to come with a hissing noise from the seams, called by the miners "blowers." Here, when mixed with a certain quantity of air, it becomes the dangerous "fire-damp." In many parts of the world it issues from the ground, and is utilised by the inhabitants as a source of light and heat. Preparation. The gas may be artificially procured by heating, in a flask of German glass, sodium acetate mixed with caustic soda. Considerably under red-heat the gas comes off, and may be secured in the usual way. The reaction may be thus expressedNa,CO,+CH.; NaOC,H,OHNaO On reference to the numerals, it will be seen that for the complete combustion of marsh gas a double quantity of oxygen is required, or ten volumes of air. It will also be noticed that one-half the volume of oxygen makes the carbonic acid gas, whilst the other half becomes water with the hydrogen. This fact enables us to analyse marsh gas by means of the eudiometer. Seeing the explosion is very violent, it is better not to use pure oxygen, but air, adding to the quantity of gas in the instrument at least ten times its volume of air. After the spark has passed, the diminution will indicate the quantity of gas which has become water; and as this water possesses all the hydrogen of the gas, its composition is discovered. Marsh gas may be decomposed by a series of electric sparks being passed through it, or if the gas be sent through a tube heated to whiteness. The carbon is deposited, and a volume of hydrogen, double that of the gas, is received. This will be indicated by the numerals Coal Gas.-Coal gas, so generally used for illuminating purposes, is procured by the destructive distillation of coal, a process which is effected by exposing the coal to a high heat in cast-iron tubes called retorts. Coke remains in the retort, and various volatile products, together with a mixture of some dozen gases, pass into the condensers and purifiers. Many of these retorts are heated in the same furnace, and a pipe from each dips into the main, which is a tube of great diameter, half-filled with water, beneath the surface of which the pipes from the retorts dip. As the products of the distillation pass through this water, the tar, an ammoniacal liquid called gas liquor, and water, condense, whilst the gas bubbles through and is carried away by the main to the purifiers, and thence to the gasometer. The tar has proved productive of many useful substances, such as the aniline colours, mauve, magenta, etc. From the ammoniacal liquid we derive our chief supply of ammonia. The gas in the main is a mixture of Of these the sulphide of hydrogen, the bisulphide of carbon, and carbonic acid gas are not only useless, but injurious. To remove them the gas is exposed to a surface of slaked lime; this retains the sulphide of hydrogen and carbonic acid. The bisulphide of carbon may be removed by passing the gas through a tube filled with slaked lime, maintained at a temperature of 250 Cent. Under these circumstances the bisulphide is decomposed. The presence of this compound is so minute that its separation is seldom attempted; yet it is chiefly due to it that plants cannot live in rooms lit with gas. Purified gas, therefore, consists of marsh gas, olefiant gas, oil gas, and other hydro-carbons; carbonic oxide, hydrogen, and nitrogen. An idea of the relative quantities of these gases may be had from an analysis, made by Bunsen, of a Manchester gas: What causes the luminosity of flame?-The presence in the flame of a solid. If sulphur be ignited, it burns with a blue non-luminous flame; because the product of the combustion is not a solid, but a gas (SO). Phosphorus, on the other hand, has a luminous flame, because the result of the action is a solid, phosphoric acid, the particles of which being heated in the chemical action, become white hot, and emit light. A striking instance of this truth is offered in the oxy-hydrogen light. The flame of the gas is scarcely visible, but when it plays upon a piece of lime (a solid), it raises it to a white heat, and a brilliant light mis the result. Therefore, those gases are the illumi nators of "coal gas," which contains carbon, the only solid in the list except the trace of sulphur. The gas will not give light unless this carbon be in a free state, and while in this state heated to a white heat. In considering the structure of flame, the conditions which secure this result will become evident. Flame.-The flame of a candle is supported by Fig. 39. the decomposition of the tallow, etc., of which it is composed, into the vapours of hydro-carbons. This decomposition is furthered by the melted fat being spread over the wick by capillary action. In the non-luminous cone, m (Fig. 39), the vapours are rising from the wick; in the other two cones, i and e, these vapours mix with air, and chemical action ensues. Only a certain limited quantity of air can mix with the Fig. 40. A flame cannot exist if too much heat be taken from it. Thus, when we blow a candle too violently, it "goes out," because we have caused such a quantity of cold air to take away its heat as to render it unable to exist. vapours as they rise from the wick. The hydrogen, having a the carbon, a portion of which comes away unburnt in the shape much greater affinity for the oxygen than the carbon has, at of smoke. If a fire can be fed with hot air, or supplied with once appropriates it all, forming water; but, as we have before a limited quantity, all the carbon will be burnt, and there will noticed, the combination of oxygen and hydrogen produces be no smoke. One or other of these means is resorted to in great heat. This raises the atom of carbon, just liberated from all "engine" fires. Perhaps the most satisfactory method is its combination with the hydrogen, to a white heat. This to bend an iron pipe, about four inches in diameter, in the form of process goes on in the light-giving cone of the flame, i. These a U: place it beneath the grate, and turn one end into the mouth heated particles of carbon pass to the outside of the flame, where of the furnace, which is closed by tightly-fitting doors. The they combine air passes through the tube, which is red-hot, and then enters with the oxy- the furnace, which is now enabled to burn without smoke. gen of the air, first forming carbonic oxide, which again, taking another atom of oxygen, burns into carbonic acid with a blue flame, e, which forms the third cone of the flame. Thus it is seen that the luminosity of a flame entirely depends upon the quantity of air which can find an entrance into the body of the vapour undergoing combustion. If there be present too little oxygen, some of the hydrogen will pass to the outside of the flame unburnt, and thus much of its heating power will be wasted. On the other hand, if too much oxygen mix with the flame, then not only is the hydrogen burnt, but also some of the carbon at once becomes carbonic oxide, and the illuminating power of the flame will be diminished. This is illustrated in "Bunsen's burner." Here the air is mixed with the gas before it escapes at the top of the tube. When ignited, there is not only sufficient oxygen to satisfy the demands of the hydrogen, but also enough for the combustion of the carbon, which is never "free," burning at once into carbonic oxide. If the holes be covered with the fingers, the flame becomes luminous, the supply of air being limited to that which can mix with the gas as it escapes from the tube. A flame may be deprived of its luminosity by simply blowing it, for then, by mechanical means, sufficient oxygen has been introduced to burn the carbon, and the flame becomes blue. It will be evident, then, in all flames, that the maximum illuminating power will entirely depend on the right quantity of air; as may often be noticed by moving the chimney of a moderator lamp higher or lower. If a cold surface be depressed into the flame of a Bunsen's burner or a spirit-lamp, it will be found that a film of moisture is deposited upon it, which is, of course, driven off as soon as the body is heated, for the products of such a flame are water and carbonic acid, and the latter being a gas cannot be deposited; but if the same experiment be tried in a luminous flame, besides the moisture, carbonsoot-will be found on the cold surface; the reason being, that carbon will only combine with oxygen at certain temperatures. Coals will remain in a cellar for any length of time, but when once heated to a certain temperature their combination with oxygen commences, and we say they burn. In a flame, the combustion of the hydrogen just produces a sufficient heat to raise the carbon to this required temperature; but if any of this heat be detractedby the cold surface, for instance, above alluded to-the carbon is deprived of the power of combustion, and is therefore deposited in its elementary condition. Fig. 41. This accounts for the smoking of fires. Cold air passes through them, and its temperature is raised at the expense of the heat given out by the combustion of the hydrogen, thus taking away the heat necessary for the complete combustion of If a piece of wire gauze be held in the flame of a spirit-lamp (Fig. 40), the flame will not pass through the gauze, although the unburnt vapour will, which may be ignited on the upper side. The fact is admirably shown in Fig. 41, where the gas from a Bunsen's burner is lit above the gauze, but is unable to ignite the gas below it, because at the place where the flame touches the gauze it is extinguished. The iron, which is a good conductor of heat, robs the flame of so much, that it cannot exist, and is therefore extinguished. The Davy lamp owes its value to this fact. Fig. 42a shows that the common oillamp, b, is supported by a frame of iron wire, while the flame is entirely enclosed in a cylinder of iron wire gauze, d. Fig. 42. The "fire-damp" passes through the gauze, and is ignited by the flame. An explosion occurs in the lamp, which extinguishes the light; but the cooling power of the gauze prohibits the flame from passing out to ignite the mine. Thus the miner is warned of his danger. Even if the flame of the lamp be allowed to come in contact with the cylinder, it cannot do more than make it red-hot, and as fire-damp cannot be ignited unless by a white heat, there is no danger. The cylinder is fastened down to the body of the lamp by a lock, the key of which is kept by the clerk of the mine. The miner trims his wick by the wire c, which passes through the oil in a tube, as the section shows. The gauze cylinder greatly darkens the light, and the miner is much tempted to work with a naked flame; and to this recklessness may be traced almost all colliery explosions. The results of the combustion of fire-damp are water, which condenses on the sides of the mine, and carbonic acid-chokedamp. LESSONS IN FRENCH.-XXXIX. SECTION LXXXVII.-IDIOMS RELATING TO PRONOUNS, ETC. |