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One hundred and forty-six prisoners, including one woman, were thrust into a dungeon, "the Black Hole," a place eighteen feet by fourteen, and having but two small windows, without water, and so densely packed that the doors had to be pressed on the last to enter, and were shut by main force. Only twenty-three survived the horrors of that night, and they were driven from their factory, in which a garrison was placed, while the Nabob marched back to Moorshedabad, his capital, flushed with his victory, and pleased with the plunder he had won.

As soon as the news reached Madras, Clive started, with 900 Europeans and 1,500 Sepoys,* to re-capture Fort William, and to avenge the raid on it. The garrison fled at the mere sight of him; the English flag was hoisted once more on the walls of the fort and the factory; and Surajah Dowlah, who with 40,000 men came down to give him battle, ended by granting the English full right to do as they liked at Calcutta, and entered into an offensive and defensive alliance with them.

It were long to tell how Clive, finding Surajah Dowlah incompatible with the British rule, contrived his overthrow; how he defeated him with an incredibly small force of about 3,000 Europeans and natives at the battle of Plassy (fought June 23, 1757); how Meer Jaffier, the Nabob's general, was placed on the throne; and how the Nabob was taken and slain by his own people. Nor will space permit us to trace out the course of Indian politics, to show how-sometimes by fair means, often by foul -the English managed to acquire territorial rights far beyond the wildest dreams of the first settlers; but it should be mentioned that the French power in India was crushed for ever on the 22nd of January, 1760, when at the battle of Wandewash, Count Lally Tollendal, the French commander who had been sent out on the renewal of war between England and France, was totally beaten by Colonel Eyre Coote, and driven to take refuge in Pondicherry, which subsequently surrendered at discretion, and Lally and 2,000 European troops became prisoners of war to the English.

Through the instrumentality of Clive and his brave assistants, the British power in India was made dominant over that of all other European powers, and in Bengal at least, where their tool, Meer Jaffier, was enthroned, they also had the dominion. But troubles came thick and fast, through the mismanagement of the rulers who succeeded Clive, through the reckless cupidity of individual merchants, and through the restless enmity of the more active native princes.

Clive was at home when the disorganised state into which affairs had got in India necessitated his re-employment. In spite of many enemies, his election was carried to the post of Governor of Bengal and Commander-in-Chief of the Forces, and in May, 1765, he landed at Calcutta, with full power to root out the injurers of the government and to restore order. Promptly, thoroughly he did so, and while he stayed the rapacity of the Company's servants on the one hand, he disarmed the ill-will of the Bengali princes, and obtained on terms for the English the right of sole administration throughout the provinces of Bengal, Orissa, and Bahar, the independent rights of the Great Mogul having been bought off; and he placed the administration of the native affairs of the provinces on a firm and substantial basis. Then he applied himself to remedy evils which had grown up in the civil and military services; stopped, for a time at least, the practice of receiving presents from native princes; and deprived the army of certain pecuniary profits which it was deemed scandalous they should enjoy. He quelled quickly and firmly a mutiny among the officers which this latter step engendered, and in the course of a few months he had restored order and strength in the governmental affairs of Bengal; but work, anxiety, and climate told upon him, and in January, 1767, he returned home to recruit his shattered health. He never went back, but died by his own hand in 1774.

After him came Warren Hastings, the first Governor-General of India, whose administration was marked by a great accession of power to the British, and by the overthrow of many native princes. The manner in which he ruled, and the unhesitating use he made of his power, led to his impeachment before the House of Lords in 1788. The trial lasted for seven years and three months, but ended in his acquittal. Under him the three presidencies of Madras, Bombay, and Bengal were united under one general government, of which the seat was at Calcutta, and

⚫ Sepoy is a corruption of sipahi, the Indian word for soldier.

the plan originated by Mr. Pitt, of making the government of the East India Company controllable by the home government, was carried into effect. Hyder Ali, the adventurer, who had risen by sheer force of will and unscrupulousness to the throne of Mysore, and who, nourishing a secret hatred towards the English, had nearly succeeded in expelling them from Madras, was compelled to make apparent submission, though he bequeathed his hatred and his power to his son Tippoo, commonly called Tippoo Saib, or Tippoo Sultan, whose restless hostility brought on the war against him, and ended in his death at Seringapatam, his capital, which was stormed by the British forces under General Harris and Colonel Wellesley, afterwards Duke of Wellington. Lord Cornwallis, who, in the short time he was GovernorGeneral, added to the British dominions 24,000 square miles, was succeeded by Sir John Shore (created Lord Teignmouth), whose policy was to play off one native prince against another, and not to interfere in any of their quarrels-a policy which was dictated by the East India Company at home, and was backed by the Imperial Government. It was not, however, the policy which suited the British interests in the East: in order to maintain the Anglo-Saxon power, it behoved the Anglo-Saxon to take the lead: to do otherwise was to cause that power to retrograde.

The policy, then, pursued by successive governors-general, from the time that Clive changed the holding of the British from a precarious into a territorial holding, has been a policy of annexation. Up to this policy the British have acted as rapidly as their digestion has allowed, and the pursuance of it has added to the lustre of their military glory many a battle-gem. Not only in Mysore, but in Scinde, Oude, and the Punjab, have they found "foemen worthy of their steel;" on Indian battle-fields some of their best warriors have been trained, and in Indian administration has been found an outlet for the energy and talents of some of their wisest sons.

Not unchequered, however, has the course of their rule been. Secure from any real danger from foreign enemies since the final extinction of the French power, the British power has had to face and countervail the exertions of the dispossessed princes to regain their thrones, and in 1857 to stand a shock which made it vibrate to its very roots. The great mutiny which sprang from national and religious causes was, perhaps, the greatest and most terrible blow that ever fell upon English shoulders; the horrors of the outbreak and repression will still remain in the memory for many a long day. But the mutiny ended with the British power more thoroughly riveted on India than ever it had been before; it revealed the sources of weakness both of the natives and their rulers, and showed what was faulty and wrong in the principles of the administration. Since the mutiny was quelled, sincere efforts have been made to remedy many undoubted wrongs which previously existed, and exertions are yet being made which it is hoped and intended will have the effect of improving and raising the condition of the people. For, morally speaking, there is no other reason for the existence of the British power in India than the reason that under it the native population is better off materially and morally than they would be under their own princes. Judging from these princes not only by what we found them, but also by what we know of the Asiatic mind and character, we cannot escape the conclusion that a selfish despotism, by which all general interests are made subservient to those of the sovereign, and which would never trouble itself about the real progress and advantage of the country, is all that could be hoped for from them.

At one time it must be confessed that this description would have applied equally to our own government in India, at the time when men sought only how they might grow rich quickly, omitting, while doing so, the weightier matters of the law, jus tice and mercy. Now, however, when the system of government by a trading company, directly interested in gain, has been abolished, when the premiums on extortion and peculation in high places have been taken away, when the fountains of justice are purer and more accessible, and the character of the govern ment has become paternal instead of commercial, we may not unreasonably claim to hold the rule in India, governing it as we should any other trust committed to us by the Most High.

The Queen's Government in India (the government was transferred from the Company to the Crown in 1858) extends over about 160,000,000 of people, and over an approximate area of 1,500,000 square miles of territory.

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SWIMMING may be ranked both as a pastime and as a purely gymnastic exercise, but it has a still higher claim to be included in these papers. It is one of the most essential features in physical education; and it should never be left to the choice of youth to acquire the art, but its practice should be inculcated as an absolute duty. It is strange that this branch of bodily training should have been hitherto so much neglected in this country, even among the classes whose lives are passed chiefly on the waters. Lamentable accidents are frequently reported as the consequence of this neglect, such as that which occurred in 1865 at Erith, in which several boys belonging to the training ship Worcester, unable to swim, were drowned by the upsetting of a boat. But a change is in progress, and at some of our public schools the rule has been very properly adopted, that no youth shall be allowed to practise rowing until he has been certificated as a swimmer.

We would have all our readers cultivate this most useful art, not only for the benefit it may possibly be in delivering them at some time from danger, but also as at all times one of the most healthy and invigorating physical pursuits. We shall give a few plain instructions, calculated to assist any youth in learning to swim; but we must advise him to have recourse at the outset, if he can, to the practical aid of some friend who has acquired the art. His example and occasional help may inspire the learner at once with confidence in the water, which is the first thing to be acquired in swimming, and will make the rest

come easy.

There is little difficulty, either in town or country, in obtaining access to the water. We believe all our large towns are now supplied with swimming baths, in which it is preferable that the beginner should practise, rather than that he should seek an open stream for the purpose. The baths are usually attended by experienced persons, from whom lessons may be obtained if desired, or whose help may be useful in an emergency; and at such places the learner may also gain kindly hints and assistance from others who have recently experienced, and are ready to sympathise with, his difficulties. But if the beginner is the denizen of a rural locality which is destitute of such an advantage, he should exercise care in the selection of a spot in which to practise. Let him, in the first place, choose a stream the bottom of which slopes gradually from the bank, and ascertain its precise depth at various distances. Let him be very careful to select a place which is free from weeds, either attached to the bottom and scarcely seen from the bank, or floating freely on the surface. A clear stream, with a gravelly or sandy bottom, is by far the best. One with a muddy or rough and stony bottom should be avoided; and especially keep clear of water the bed of which is full of deep and sudden holes. Bathing on the sea-shore can only be practised with safety when the beach is shelving, and its general features, as to freedom from rocks, etc., are well known. The novice should select still weather only for the purpose, or the sudden coming in of a wave may take him off his legs, and carry him helplessly out to sea. A terrible calamity occurred very recently in this way, seven youths out of eight who were bathing on the Hampshire coast being swept away and drowned.

The best time for practising is in the morning, an hour or two after sunrise; but bathing or swimming on an empty stomach is not advisable. A crust of bread, with the addition of a cup of coffee if practicable, is all, however, that will be necessary. Bathing either shortly before or shortly after a full meal is injurious, but the latter especially so. Take a brisk walk before you enter the water, that the body may be in a glow when you step in; then strip as quickly as possible, and take your plunge while the blood is still coursing freely through the veins. When you have learnt to swim, you will be able to enter by diving; but until you have, you must walk into the water, and in this latter case you should dip the upper part of the body in and out again, otherwise the blood will be driven too much to the head. We must say a word as to the mechanical aids to Swimming, as the youth desirous of learning the art may, in the absence of all other help, think it necessary to have recourse to such assistance. Hardly any contrivance, however, yet devised is free from some objection; and we must not be understood as recommending the resort to either, if it can be avoided.

Among the most venerable and at the same time the most objectionable of these appliances, are the cork-floats or buoys, which may be seen in the shop of almost any cork-cutter. They usually consist of several circular pieces of cork, of various sizes, fastened together by a strap or thong of leather, the larger pieces in the centre, and the rest tapering off at top and bottom. Two of these floats are used by each person, and are fastened under the armpits, so that the chest rests upon them in swimming, and the head and shoulders are thus buoyed up in the water. But the contrivance is an awkward and cumbersome one: it hampers the free movement of the arms, and, even if it should lead to nothing worse, it causes the learner to contract a very clumsy and defective style of swimming. The floats, however, are liable also to slip from their position, and in this case they become worse than useless. The novice in this case feels his legs thrown upward instead of his head, and, the proper movement of his arms being checked, his supposed means of safety become a source of positive danger. Some fatal accidents have happened in this manner. The use of floats is, therefore, gradually being discarded, as their evils become more widely known.

Better by far, and perhaps best of all such aids, is a modern contrivance made of the same material, and known as the cork jacket. Stout strips of cork are attached together in such a fashion that they encircle the body completely round, and, being fastened by strings at top and bottom, leave the limbs comparatively free, while the necessary buoyancy is obtained from the light armour in which the chest and back are thus encased. This jacket was invented more particularly for the purpose of saving life at sea, but its obvious utility has commended it to the use of persons learning to swim, and it is likely to meet with wider favour as its merits become more generally known. It was first brought before the public by that excellent society, the Royal National Lifeboat Institution, through whose agency, we believe, it may be obtained, at the cost of a few shillings.

An ordinary life-belt, fastened round the waist, is sometimes used for the same purpose, and is far less objectionable than the cork floats; but it must be obvious to our readers that even such appliances as the jacket and the life-preserver leave less freedom of action to the body than is the case when they are dispensed with, and consequently that the learner who desires to swim with grace and ease is placed at a disadvantage by their use. Moreover, when such help has been habitually relied upon, it becomes a source of embarrassment to part with it suddenly; something has to be unlearned, and something more to be learned-namely, the power of the body to float by its own natural buoyancy while the limbs maintain a proper position.

In some swimming baths, where a teacher is present, use is made of a leather belt fastened round the waist, and suspended by a rope from a projecting arm of wood or iron. The belt is adjusted by the swimming master, who, when his pupil has entered the water, holds it by the hands while he guides and regulates the movements of his pupil. If proper care were exercised in the adjustment of such a rope, the learner who cannot command the aid of a teacher might adapt the contrivance to his own use, with a beneficial result. He might select a spot in some stream overhung by the strong branches of a tree, to which his suspending cord might be attached; and then, taking care to adjust the belt securely round his waist at the proper balance for the body, he might enter the water without fear, and draw himself out of it at any moment, by grasping the rope above his head. But we need hardly point out that every precaution should be taken by the solitary learner in availing himself of this method, as he is placed in a position of danger if any part of the apparatus should slip from its proper position, and especially if, through the strain produced by the movement of the body, the belt should suddenly give way.

Confidence, founded on a right apprehension of the principles involved in swimming, and self-command, or presence of mind in the water, are the first essentials in learning the art. If the learner could trust to theory only, confidence should come at once, for he has only to be told that the specific gravity of the body is less than that of water, and consequently that the body, if left to itself, with the limbs in a proper position, will float of its own accord. Benjamin Franklin's method of demonstrating this, by entering shallow water, and trying at once to dive in the direction of the shore, requires more nerve and

coolness on the part of the novice than many are in possession of. All who can satisfy themselves of the buoyancy of the water without such a practical test, may be content to attempt the simple motions of swimming, and leave diving of every kind until they have become somewhat used to the water. Supposing, then, that the learner is about to make

FIG. 1.-BEFORE THE STROKE.

his first effort, without either personal or mechanical assistance, he must carry out into practice what we have already remarked as to the selection of a spot characterised by a shelving bottom, and having done this, walking into it until he is nearly breast high, turn round towards the shore, and try to reach it by swimming. The head must be held up and thrown backward, the chin being kept well clear of the surface of the water; the chest must lean, as it were, upon the water, being well inflated with air before the stroke is taken; and, while the chest is thrown well forward, the back should be hollowed, so that all the muscular power of the body may be exercised in the forward motion. These movements, the work of a second in execution, are preliminary to the stroke itself, which is performed in the following manner :-Bring the hands together a few inches below the surface, and a little in advance of the chin, the elbows being bent below the stomach; the fingers should be quite close together, and the palms slightly concave. Now extend the hands forward as far as possible, and, when the full distance is reached, separate them with the palms downward, and sweep the water backwards in a half circle. The elbows thus come back to the body, and the hands are brought quickly together as before, the edges only being presented to the water until the hands meet.

While these movements are being performed by the arms, the legs have their part to play as follows:-At the moment when the learner's arms are first thrown forward, as described, he will find his legs rising towards the surface; the knees should then be bent forwards, so that the legs may presently be thrown well out behind; the feet should be kept apart, and the toes turned out. When the hands have made their sweep, the legs are thrown downwards and sideways by a vigorous effort, the stroke of the legs thus alternating with that of the arms, and the movement of both arms and legs being so timed that the legs are fully extended out behind at the moment when the arn.s are stretched straight forward. The movement of the legs is performed with more celerity than that of the arms, and you must time their action accordingly, remembering that, in pre

FIG. 2.-AFTER THE STROKE. •

paring for each stroke, the legs and the arms are both drawn back towards the body at the same instant.

The illustrations given with the present paper will enable the learner to comprehend these instructions clearly. Fig. 1 shows the position of the swimmer in the water just before the stroke made, and Fig. 2 the attitude when the limbs are fully exd, the arms being just about to make their sweep. The the stroke itself is shown as far as possible in the

accompanying diagram (Fig. 3). The arms, gathered up at a, with the hands together, are then thrust forward to b, and swept round to c, when the elbows are bent inwards and the hands come back together as before described. The movement of the legs cannot be properly shown in the diagram, but will be at once understood by a comparison of their position in Fig. 1 before the stroke, and that after they are fully thrown out, in Fig. 3.

In the stroke of the legs, you should press against the water with the soles of the feet, not with the toes only; and in that of the hands, you should not only thrust or sweep the water aside, but press it downward also. By these combined movements, the resistance afforded by the water is turned to account both in propelling the body and keeping it on the surface. You rise with a rebound from the downward motion, and you are made to shoot forward by the backward impulse of the limbs.

The various movements thus described may be practised before the learner attempts to enter the water. He may take a stool or form, and, lying across it on his stomach, may go through the successive evolutions, so as to become familiar, to a certain extent, with the nature of the stroke, and to learn to time the action of his hands and legs. A little practice of this

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FIG. 3.-THE ACTION OF THE LIMBS.

self

kind will be useful, by helping to give him the necessary possession when he first trusts himself to the open stream. We shall follow this preliminary paper by a description of the methods of floating, and of the principal modes of "fancy" swimming; and meanwhile append, for the reader's attentive consideration, Dr. Arnott's reasons why people drown:-"1. From their believing that their constant exertions are necessary to prevent the body from sinking, and their hence assuming the positions of a swimmer with the face downwards, in which the whole head must be kept out of the water in order to enable him to breathe; whereas, when lying on the back (i.e., in "floating "), the face only need be above the water. 2. From the groundless fear that water entering in at the ears may drown as if it entered the mouth or nose, and their employing exertions to prevent this. 3. The keeping of the hands above water. 4. Neglecting to take the opportunity of the intervals of the waves passing over the head, to renew the air in the chest by an inspiration. 5. Their not knowing the importance of keeping the chest as full of air as possible, which has nearly the same effect as tying a bladder filled with air round their necks would have." To these we may add, that vague and unreasoning fear of the water which leads people to suppose that the body, in relation to it, is something like a lump of lead, and must infallibly go down; whereas the contrary is the case.

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GEOMETRICAL PERSPECTIVE.-I.

INTRODUCTION-DEFINITIONS-PROPORTIONAL SCALES.

THERE are several very important remarks to be made before we enter upon the subject of Geometrical Perspective. In the first place, we must say a few words respecting the instruments and materials required for this branch of drawing. 1. A T square; 2. A parallel ruler, or set square and flat ruler; 3. A drawing-board; 4. A sector; 5. A pair of compasses, with a movable pencil-leg, and pen; 6. A ruling-pen; 7. A protractor, for making and measuring angles; 8. A plane scale-all fully explained in Lessons in Geometry, III. and IV., pages 95 and 113, Vol. I. It will also be indispensable that the student should be well acquainted with the theory and practice of Plane Geometry: it is the language of the science upon which depends the practical working of all the problems that we shall have to propose in the course of these lessons. In previous parts of the POPULAR EDUCATOR will be found all that is necessary for this purpose. Trusting, therefore, that these lessons have been carefully and diligently studied, we take it for granted that it will not be

distances between objects, or parts of the same object; no heights or depths are expressed on plans. Thus, when a house is being built, before the walls are raised, and the foundations only are laid, we then recognise the plan of the house. A map is a plan, say of a county; we can understand by it the relative positions of the towns and villages, their distances from one another, the courses of the rivers, and the directions of the roads. If a card be laid horizontally on a sheet of paper, and a pencil is drawn about it close to the margin, we shall have a plan of the whole extent of the card. If the card is placed perpendicularly to the sheet of paper, the plan would be only a line, because perpendicular lines projected from every portion of the upright card would only produce a line. This will, perhaps, make it evident that all plans are merely the tracings of perpendicular lines from every part of the object upon a horizontal plane. 2. The Picture Plane is the surface of the picture upon which the object is represented. In Fig. 1 it is shown by the letters f g i h; in this case it is shown in position between the eye at E, and the object, a b c d. Fig. 1 will be further explained presently. When practically working out a problem, the lower

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necessary for us to do more than refer the pupil to any particular problem in plane geometry which may be required in connection with our subject as we proceed. It is our intention, as far as possible, to make a practical application of all that we shall advance, knowing the valuable assistance Geometrical Perspective affords to those who are engaged in any constructive art, as well as to draughtsmen in general. We hope, also, to create an interest in this useful science amongst those who have a loving sympathy with art for its own sake, and who take a pleasure in all scientific inquiries, especially those which claim to have a mathematical foundation. In a pictorial sense, there is no other branch of drawing more capable of satisfying the mind with regard to the appearances of nature than perspective; it is an art which enables us to draw upon a plane surface things far and near as they appear to the eye, the effect of which can be as clearly and as truthfully presented to us by the help of geometry as if the objects themselves had been traced upon a piece of glass placed between them and the eye. We will now request the pupil to make himself familiar with the following terms and definitions:

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1. The Plan of an object. A plan is the representation of all horizontal lengths and breadths, showing only the horizontal

VOL. II.

line, hi, is the only line drawn to represent the picture plane, because this hi is the plan of the picture plane, the picture plane being always considered in a perpendicular position.

3. The Horizontal Line, or Line of Sight, represents the height of the eye in the picture, and is marked in Fig. 1 and figures in future lessons, H L.

4. The Point of Sight is the point opposite the eye in the picture, and consequently upon the line of sight. It is marked P S. 5. The Station Point, marked s P, is the place where the spectator is supposed to stand when viewing the object represented. 6. The Distance Point, marked D P, represents the distance between the eye and the picture plane. Sometimes the distance point and station point represent the same thing. It will be found in the course of our lessons to vary according to circumstances; in some instances it refers to the distance of any vanishing point in the picture from the eye. All these variations will be explained in their proper places.

7. Vanishing Point. If a line be drawn from the eye parallel to any original straight line of the object, the point marked V P, where that line cuts the picture plane, marked PP, is the vanishing point of that original line.

8. Visual Rays are lines proceeding from every part of the 37

object to the eye. Fig. 1 will assist to explain this. Let a b c d be a slab or board lying upon the ground, let s P be the station point where we are supposed to stand, and E the eye; f g ih is the plane of glass, or picture plane, through which we see the slab. Lines from each angle of the object passing through the picture plane towards the eye are termed visual rays, and where they pass through the picture plane determine upon the plane the points of the original object; these points united by straight lines produce the perspective representation required. It must be understood that these visual rays are not limited to proceed from the angles only; they come from every part at the same time; but when representing the object we use only those lines which proceed from angles and terminations of lines, and thus determine the proportion of the object in sight upon the picture plane. It will be seen when we come to work the problems that these visual rays are drawn from the various angles and characteristic points of the plan of the object towards the station point, 8 P. It will be noticed, also, that it is not necessary to draw these lines beyond the picture plane, P P, but invariably in the direction of the station point.

9. The Point of Contact is that point found by continuing in the same direction any original line of the ground plan, until it meets the picture plane; if the original line touches the picture plane, it then produces its own point of contact.

10. Line of Contact is a term given to that line which is drawn perpendicularly from the point of contact; it is sometimes called a measuring line, from its being used to point, or mark off, all heights in working a perspective drawing. Of course in this case the same scale is used as that for laying out the ground plan.

11. All retiring lines have vanishing points.

12. All horizontal retiring lines have their vanishing points upon the line of sight.

13. All parallel retiring lines have the same vanishing point. 14. All horizontal lines which are parallel with the picture plane are drawn parallel with each other and with the line of sight.

15. All horizontal retiring lines forming right angles with the picture plane have the point of sight for their vanishing point. 16. All lines inclined with the horizon and with the picture plane have their vanishing points above or below the horizontal line, or line of sight, according to the angle they form with the horizon, their vanishing points being always on a line perpendicular to the vanishing point upon the line of sight to which they would have retired had they been horizontal. Observe, all heights are set off on the lines of contact; all horizontal lengths and breadths are arranged on the ground plan.

As it is our intention to apply these lessons practically-that is, to make the drawings according to some given scale-it will be necessary to step aside a little from our course, and explain what is meant by a scale, and the method of constructing it, so that any one who wishes to make a perspective drawing of a building or any other object, according to some stated dimensions, may have no difficulty in this respect in carrying it out. A scale is a means by which a proportional measurement of an object is represented; or, by having a plan of that object, it is a means by which we may obtain an exact idea of all its parts in proportion to one another and to the original object. For instance, suppose a room to be 20 feet long and 15 broad, represented by a plan in the proportion of 1 inch to a foot, the drawing or plan will be then 20 inches long and 15 broad; and if we require single inches in the scale for the plan, the first inch of the scale must be divided into 12 parts. The scale being thus completed, we can measure spaces not limited to feet. Suppose the distance from one corner of the room to the side of a window should measure 6 feet 8 inches, the scale divided as above in the first division will enable us to show that distance on the plan.

To construct a scale of half an inch to a foot, draw a line of any length, and upon it mark off any required number of half. inches. (See Fig. 2.) Divide the first division into twelve parts, to represent inches, or into four parts to represent spaces of 3 inches, and number the divisions as shown in the figure. To measure 9 feet 9 inches, we must place one leg of the compasses on nine of the main divisions, and the other on nine of the minor divisions, marked in Fig. 2 from a to b.

Sometimes scales are much smaller than the above, when the sult is extensive and the drawing small. It is advisable to · . scales generally about 6 inches long-they may be

either a little more or less; the length is not important, so that there be a sufficient number of parts on the scale to make it useful, but the average length of about 6 inches is the most convenient for general purposes.

To obtain the average length, we raise or lower both terms, as the case may require, by multiplying or dividing each by the same figure, so that the proportion remains the same: for example, 1 inch to 7 feet, 1x6 = 6, 7 x6 = 42. Therefore 1 to 7 is the same proportion as 6 to 42. Again, 14 inches to 100 feet; this must be lowered, because a scale 14 inches long would be of unnecessary length, therefore 1427, 100 ÷ 2 = 50; so that we can make a more manageable scale of 7 inches long to repre sent 50 feet, which will be the same as 14 to 100. It will be rendered clearer if we propose to make a scale of 1 inch to 38 feet. The pupil will see the difficulty of dividing an inch into 38 parts and then constructing a lengthened scale from it. To avoid this, we first raise the terms by multiplying both by 6, which will be 6 to 228, and then state the question in the form of a Rule of Three sum. But as we do not wish to go through the trouble of dividing 6 inches into 228 parts, we must find the length of line necessary to include the nearest whole number to 228, which is 200, and say as 38: 1 :: 200 : 5:26.

It will be seen by this that 5:26 inches to 200 feet is the same proportion as 1 inch to 38 feet, and this simplifies the work in making the scale. To do this we draw a line 5.26 inches long (to measure this distance, see Lessons in Geometry, page 113, Vol. I.), and divide it into two equal parts to represent hundreds, and the first division into ten equal parts to represent tens. (See Fig. 3.) The distance, 170 feet, measured from this scale will be from a to b. To divide a line into any given number of equal parts, see Lessons in Geometry, Problem XII., page 192, Vol. I.

We will give two other examples, and leave the pupil to practise this method of constructing scales of any given proportion. Construct a scale of 1 inch to 13 feet. 13×6=78. In this case 80 is the nearest whole number to 78, to be stated thus: as 13: 1 :: 80: 615; therefore draw a line 6:15 inches long, and divide it into eight equal parts to represent tens, and the first division into ten equal parts to represent units. Suppose it were 2 inches to 13 feet, then we should have to raise the number 13 by 3. 13 x 3 = 39; 40 would be the nearest whole number in this case; then as 13: 2 :: 40: 6:15. Therefore a line 6:15 inches long is to be divided into four parts to represent tens, and the first division into ten parts to represent units.

We will now explain how a' b' e' d', on the picture plane f gi of Fig. 1, is the perspective representation of the square a bed, the plan of the square. E is the eye of the spectator when he is standing at s P, the station point; PS is the point of sight, and HL the horizontal line; the lines from a b c d to E are the visual rays; the lines from a b c d to S P are the plans of the visual rays; from the points where these last lines (the plans of the rays) cut the base of the picture plane, hi, draw perpend cular lines to cut the corresponding visual rays in a' b'e d', join these points respectively, and then will be produced on the picture plane, f g ih, the perspective representation required. This figure is intended only to show how the plan, the eye, and the picture plane are supposed to be arranged with regard to each other, and that the point of sight, P S, is opposite the eye and on the horizontal line, H L, which is on a level with the eye.

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