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people, under the guidance of Henry, Jefferson, Adams, Franklin, and Lee, made good, as against all the world, the declaration of independence which they made on July 4, 1776. The British troops fought bravely enough, but were badly handled; the American troops fought equally well, and were admirably handled, and had the satisfaction to receive, as the reward of their valour, the surrender of almost all the British forces with their generals in succession. Finally, the British king was obliged to acknowledge the independence of his former colonies, to treat with them on the basis of an independent nation, and to accept a representative from them for all international

purposes.

Ninety-two years have now gone by since Independence Day first dawned. In the course of that time either side has found out that there is room enough for both in the world, and that there is no à priori reason why they should not exist with peace and good-will towards each other. There have been times when the silver bowl was threatened with destruction, when the cord which bound the two nations together strained at the tension which would rupture it; but with one exception (1812-14), when for a short time there was war, peace has been maintained; the interests and the better parts of the people on both sides are averse to violence and bloodshed, and the efforts of statesmen are happily encouraged to attempt peaceful solutions of all difficulties that may arise. Old jealousies, old suspicions have worn away; new principles, new bonds of union have taken their place; so that as an American of to-day still takes pleasure in England as the home of his race and his family, so an Englishman of to-day finds not any difficulty in sympathising with him when he talks about American independence, and tells with pride and satisfaction the story of how in the old time the States came to earn their motto-E pluribus unum!

LESSONS IN GERMAN.-XXX. SECTION LIX. PECULIAR IDIOMS (continued). Wie befinden Sie sich? (literally, how do you find yourself?) answers to our phrase "how do you do?"

Sich befinden is also applied to inanimate objects, and is then well rendered by "to be," as :-Das Buch befintet sich in meinem Zimmer, the book is in my room.

The adjective befintlich is frequently best translated by a relative clause, as :-Das Haus und die darin befindlichen Leute, the house and the people who are in it (literally, the house and the therein being people).

1. Statt finden is equivalent to "to take place," as:-Wann fand die Revolution in Baten Statt? when did the revolution in Baden take (find) place?

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Von nun an floß die übrige Zeit From this time forth the refeines Lebens ruhig tahin., maining time (portion) of his life passed tranquilly away. Thence it comes, that so many Germans and Hungarians emigrate to America. It is the boy's fault, therefore he suffers the punishment. Till the messenger arrived, an hour elapsed.

Daher kommt es, daß so vicle
Deutsche und Ungarn nach Ame
rika auswandern.

Der Knabe ist Schuld daran', tep'.
wegen erbul'tet er die Strafe.
Bis ter Bote ankam, versleß eine
Stunte.

Bis auf ein kleines habe ich ten
Brief beendigt.

Gs thut mir wirklich in der Seele
weh.

Morgen also reisen wir ab.
Das Band gehört' um den Hut.
Darum ist er auch so traurig.

Wie befin'ten Sie sich?

I have, within a little (all but), finished the letter. It really pains me to the soul.

To-morrow then we depart The ribbon belongs around (to) the hat.

Therefore he is likewise so sorrowful. How do you do? Ich danke Ihnen, ich befinde mich wohl. I am very well, I thank you. EXERCISE 112.

1. Das in der Zeitung angekündigte Concert wird heute Abend nicht tatt finden. 2. Wollen Sie meine Bitte gewähren? 3. Ich werte se gewähren wenn Sie von nun an versichtiger sind. 4. Demuth zeigt sich in wahrer Liebe zum Nächsten. 5. Von nun an wart tie Gegend iminer reizenter. 6. Wir wollen von nun an zufrieden sein. 7. Daher kam et, 8. Er ergriff daher die taß so viele Unternehmungen mißlangen. 9. Ihr seid selbst Schult taran, Gelegenheit, ihm Vorstellungen zu machen. könnt euch taber nicht beklagen. 10. Karl lernt stets fleißig, deßwegen leben ihn seine Lehrer. 11. Sie brauchen teßwegen (Sect. XLIII. 5) nicht bise zu sein, weil ich Ihre Feter gebraucht habe. 12. Der fleißige Schüle überwintet tie Schwierigkeiten, welche eine jete fremte Sprache bat. 13. Joseph II. war ein aufgeklärter Fürst und der Vater seines Velkes, refwegen srricht man noch stets mit vieler Achtung von ihm. 14. Er stieg bis auf (Sect. LVII.) tie Spiße des Verges. 15. Wellen Sie nicht warten, bis Sie eine Antwort haben? 16. Nein, ich kann nicht länger warten. 17. Da er nicht tableiben wollte, bis ich meinen Brief geschrieben hatte, se mufte ich also glauben, daß er mir diesen Gefallen nicht thun welle. 18. Aleranter besiegte bei seinem Regierungsantritt viele Völker und begann also feine Laufbahn mit kriegerischen Thaten. 19. Nach dieser Nachricht kann er also Heffnung haben, seinen Vater noch einmal zu sehen. 20. Ich werte Shren Alles pünktlich besorgen; haben Sie tarum feine Sorgen. 21. Er m nicht zu Hause, reßhalb konnte ich den Brief nicht selbst an ihn abgeben. 22. Nachdem der Oberst die Fahne aufgerflanzt hatte, schaarten sich die Soltaten darum. 23. Befindet sich Herr N. wohl ? 24. Ja, er befindet sich ausgezeichnet wohl.

EXERCISE 113.

1. Is there also a monument to Guttenberg, the inventor of the art of printing? 2. Yes, there are two; one is in Mainz, the other in Strasburg. 3. Are there naughty children in your school? 4. Oh, yes, there are many. 5. These hoops belong to those casks. 6. The interment of the Duke of Wellington took place the 18th of November, 1852. 7. In the assembly which took place yesterday, some public speakers spoke with great enthusiasm. 8. From that time forth he strove for greater fame. 9. He seized the first occasion to convince his brother of the truth of his assertions. 10. Till to-day I had not received any answer from him. 11. The rain has wetted us through to the skin; for that reason we shall postpone our voyage till this evening. 12. In former times more wonders and signs took place than in the present time.

KEY TO EXERCISES IN LESSONS IN GERMAN.
EXERCISE 27 (Vol. I., page 164).

1. Which table have you? 2. I have that of my friend, the joiner. 3. Which paper have you? 4. I have that of my friend, the teacher. 5. Which of these boys has my blue ink?

6. None of them has your 7. ink, but one of these boys has your beautiful pink-coloured paper. Which of them has it? 8. Adolphus has it, and Henry, your litt cousin, has your wooden pencil. 9. Which of my books is in your room? 10. Your Gellert's Fables are there. 11. Which of these two

little boys is your nephew? 12. They are both my cousins. 13. Are they brothers? 14. Yes, they are twins. 15. Which of your American friends are at the council-house? 16. Mr. C. and Mr. L. 17. Whose book have you? 18. I have that of your cousin. 19. When did Mr. Zimmermann have my letter? 20. He had it the day before

yesterday, and his friend, the painter, had it yesterday, and I have it to-day. 21. Has the teacher praised the baker's son, or that of the tailor? 22. He has praised neither that of the baker nor that of the tailor, but that of the mason. 23. Have you the merchant's pens, or those of the book-keeper? 24. I have neither those of the merchant nor those of the book-keeper, but I have those of the toll-gatherer. 25. Who praises the old captain? 26. The captain praises him. He praises the whole nation. 23. The Frenchman's wagon is large, and that of the Englishman beautiful.

EXERCISE 28 (Vol. I., page 164).

27.

1. Welchen Regenschirm haben Sie? 2. Ich habe ten meines Bruters, 4. Ich des Bildhauers. 3. Wann kauften Sie dieses rosenfarbene Kleid? kaufte es gestern von meinem Vetter, dem Tuchhändler. 5. Wollen Sie dieses Buch diesem oder jenem Manne geben? 6. Ich will es keinem geben.

EXERCISE 29 (Vol. I., page 179).

1. Has the captain his own or the general's sword? 2. He has his OWD. 3. Have you my scissors ? 4. No, I have my own. 5. Who has my stick? 6. Mr. S. has it. 7. Has my sister your umbrella ? 8. No, she has her own. 9. Has the locksmith my key? 10. No, he has his own. 11. Has the washerwoman my brother's and my friends' shirts? 12. She has his as well as theirs. 13. All people have their errors and peculiarities; I have mine, you have yours; and he has his. 14. God is almighty; man's destinies are in his hand, also mine and thine. 15. The ocean is between me and my family. 16. Has Mr. A. your paper or mine? 17. He has his own. 18. My brother has my book, and I have his. 19. Has he your wafers and stamps, or his own? 3. He has mine. 21. Whose wagon has your good friend Mr. G. ? 2. He has that of his uncle. 23. And whose horses has he? 21. He

has mine. 25. Whose coachman has he? 26. He has his own. 27. Whose sheep are those in the meadow? 28. They are ours. 29. Have these Germans their horses and their wagons, or ours? 30. They have

Gurs. 31. Whose books have these scholars? 32. They have their own. 33. Do you always take your property? 34. Yes, everybody takes his own. 35. When did you see your family? 33. I saw them the day before yesterday. 37. Did you see me and my family yesterday evening at the concert ? 38. Yes, I saw you and your family. 39. The commander praised his soldiers.

EXERCISE 30 (Vol. I., page 180).

1. Der Kutscher des Grafen B. hat meine Brille, und nicht die Ihrige. 2. Die Tochter des kranken Generals sind stolzer, als die meinigen. 3. Ich babe meinen Brichstempel verloren, aber hier ist der Ihrige und der seinige. 4. Wem gehören diese schönen Wiesen, sind sie die Ihrigen? 5. Nein, sie fine nicht tie meinigen; sie sind das Eigenthum meines Freuntes, des Kutschers. 6. Haben Sie seinen Schlüssel, oder den meinigen? 7. Ich habe weter ten seinigen, noch den meinigen, sondern denjenigen meiner Frau. 8. Sie entreckten den Dieb an dem Hemte, welches er trug, und welches nicht das seinige war. 9. Wann sahen Sie Ihre Freunte? 10. Ich habe sie seit jüngstem Sommer nicht gesehen. 11. Er licht zu sehr tas Seinige. 12. Haben Sie mich und tie Meinigen, Heinrich und tie Seinigen gestern Abend zwischen sieben und acht Uhr in der Allee gesehen? EXERCISE 31 (Vol. I., page 180). 1. Which child does the uncle love? 2. He loves that which he praises. 3. Whose child loves the uncle? 4. The one that he loves, loves him. 5. Which hat have you? 6. I have that which your brother has had. 7. Which boy does the father love? 8. He loves the one that the mother praises. 9. Which boy loves the mother? 10. The one that the father praises. 11. Which horse has your brother bought? 12. He has bought that which you had yesterday. 13. Which man do you praise? 14. I praise that man whose son you love. 15. Which books have you bought? 16. I have bought those which my brother has had in his hands. 17. Whose books have you? 18. I have the books of those boys whose hats you have. 19. Those who are vicious have no tranquillity of soul. 20. The one who has the Ecar on the forehead is the old magistrate. 21. That is good which is useful. 22. These men are the same whose barns, stables, and dwellings you saw yesterday. 23. The labourers in the vineyard of him who gives the least reward are few. 24. The hermit of youder chapel is a friend of those who are helpless and forsaken. 25. He is wise who is virtuous.

EXERCISE 32 (Vol. I., page 181).

1. Der Freund, welchen ich habe, ist treu. 2. Wessen Schlüssel haben Sie? 3. Ich habe den der Frau, deren Tochter Sie kennen. 4. Ich werte tieses Buch demjenigen geben, welcher zuerst hier sein wird. 5. Haben Sie mein Buch gesehen? 6. Nein, ich habe nicht dasjenige gesehen, welches Sie erwähnen. 7. Die Freute, die ich haben werte. 8. Ich kam, weil ich es ihm versprochen hatte. 9. Wo wohnen Sie? 10. Ich wohne in demselben Gause, in welchem ich wohnte, als Sie mich besuchten. 11. Welche dieser Damen ist Ihre Frau? 12. Diejenige, welche mit dem alten Herrn spricht. 13. Der Freund, welchen ich verloren habe, war mir sehr theuer. 14. Ich Babe ten Rock gekauft, welchen Sie in dem Fenster meines Schneiders fahen. 15. Empfehlen Sie mich dem Herrn, welcher so sehr höflich ist.

EXERCISE 33 (Vol. I., page 197).

1. Is this young man ill? 2. No, but he was ill yesterday. 3. Who has been in your father's garden? 4. Nobody has been in the garden, but somebody has been in his house. 5. How long does the old peasant still remain in the town? 6. I am not acquainted with the old peasant, and don't know how long he remains. 7. Is your old friend, the merchant, gone to Vienna ? 8. I believe he is gone to Berlin to his brother. 9. From whom have you heard this news to-day? 10. I have spoken to one of my friends, who has come from Dresden, and has brought a letter to me from my father. 11. I reside with my uncle, and go with him to the little village. 12. My beautiful bird has flown out of the cage, and my little horse has run to the forest. What has your father written to you? 14. He has written (to) me a long letter. 15. When were you at the market? 16. I was there the day before yesterday in the evening, and bought some beef. 17. We have had beautiful weather this afternoon. 18. These scholars have been lazy, and those diligent. 19. The snow was very deep the day before yesterday. 20. I have never been ill. 21. Frederick the Great was (a) King of Prussia.

OUR HOLIDAY.

SWIMMING.-II.

13.

WE will suppose our readers now to have become familiar with the practice as well as the principles of plain swimming, and will pass on to the necessary instructions in other departments of this useful art, a knowledge of which is essential to every one, but more especially necessary to those who are fond of yachting and rowing, to say nothing of sailors by profession, who have far more need of being able to swim well than landsmen.

In the first place, as to the manner of entering the water. When the learner has become somewhat familiar with the element and its buoyant power, and has learnt the proper use of his limbs in it according to the instructions previously given, he will look with some degree of contempt upon walking into the water. He will not be satisfied until he is able to dive; and in learning to do so he must practise with as much care as he displayed in his first lessons. He must use equal judgment in the selection of a suitable spot for his first attempts, for the water should not be too deep, even although he may have learnt the rudiments of swimming; and it is of more importance still that it should not be too shallow. Taking a header" in water only a few feet in depth is a dangerous thing. It has sometimes been attempted, even by experienced swimmers, with fatal results. If the head comes first in contact with the water, the liquid has sufficient resisting power to render the concussion certainly injurious, and to peril the safety of the inexperienced diver to a very great degree. The hands must be placed together as when they are pushed forward in swimming prior to the stroke; and, when thus placed, they must be extended in front of the head, to cleave a passage for it before it reaches the water.

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Supposing the water to be moderately deep-say ten feet or more-the position in which the diver should leave the bank is shown in our first illustration (Fig. 4). With the body thus bent, the diver enters the water with a plunge and a spring from the toes. After the spring he straightens his legs, and at the moment of total immersion he swoops, as it were, in an upward direction, when the buoyancy of the water assists the body in regaining the surface immediately. In completing the dive in deep water, the body assumes the position shown in the second figure (Fig. 5).

When diving in shallow water, the relative position of the limbs is as shown in Fig. 4, but the body is not nearly so much bent, the whole plunge being taken, in fact, in a slanting direc tion, and the body itself being but little curved. The head dips but little below the surface, the back is but just covered, and the whole figure slants upwards again immediately.

Floating is a most useful branch of the swimmer's art, and its practice must be made one of his earliest studies. It is attended with no difficulty beyond the knack of getting readily into the proper position, and this is easily acquired. It is of utility as a relief from the active exertions required in swimming, enabling the swimmer to take a rest without leaving the water; and it may be of the greatest service in a time of danger, whether arising from cramp, from over-fatigue, or from sudden immersion. All that it is necessary to do in order to float, is fo lean back in the water, throwing the face well upward extending the arms as far as they will reach behind th

The legs then come to the surface, and you may afterwards
bring the arms round to the side, and float in the position
shown in Fig. 6. But in floating you must remember to let the
chest play its proper part, as a bladder inflated to the fullest
possible extent; and in order to this you must inhale as much
air as you can into the lungs, and when
you expel the air in respiration, you must
draw a deep breath again immediately.

Having assumed the position shown in Fig. 6, you are ready for swimming on the back, which is usually performed in the following manner:-Placing the hands on the hips, you draw up the knees, but at the same time depress the toes, so as to raise the knees out of the water. You then strike out the legs, as in ordinary swimming, and you find yourself progressing with the head foremost. But it is possible to swim on the back without using the legs, and in the case of fatigue or cramp it may become necessary to do so. You then bring the hands towards the chest, and press back the water in the direction of the feet with a sweeping motion. By reversing this movement of the hands, and sweeping the water gently towards the chest instead

think it necessary to notice here. We believe the instructionnow given will be found sufficient for all purposes of general utility, and that practice in the modes described will suffice to make not only a good but a dexterous swimmer. Variations upon them will come easy when the groundwork has been well laid, and there is perfect familiarity with the water.

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Fig. 4. THE DIVE.

We must say a few words respecting cramp, and on this point we cannot do better than repeat Walker's instructions on the subject:-"Those chiefly are liable to it who plunge into the water when they are heated, who remain in it till they are benumbed with cold, or who exhaust themselves with violent exercise. Persons subject to this af fection must be careful with regard to the selection of the place where they bathe, if they are not sufficiently skilful in swimming to vary their atti tudes, and dispense instantly with the use of the limb attacked by cramp. Even when this does occur, the skil ful swimmer knows how to reach the shore by the aid of the limbs which are unaffected, while the uninstructed one is liable to be drowned.

of away from it, you are enabled to progress in the opposite | If attacked in this way in the leg, the swimmer must strike direction-i.e., feet foremost. The elbows in these movements should be kept near to the sides, only the fore-arm being used to give the hands their necessary action. Swimming on the side is sometimes practised as a change from the ordinary mode of progression. Turning on either side, you throw out the undermost arm along the water, and, with the palm of your hand hollowed out for the purpose, you scoop or drag the water towards you. The action of the legs is much the same as in ordinary swimming, and the uppermost hand is used at the same time as the legs in pressing back the water. The stroke of the legs must exactly alternate with that of the foremost arm.

The hand-over-hand style of swimming consists in swinging the hands, one after the other, forward out of the water to as great a reach as possible, then dragging the water backward to the hips, each leg striking out alternately, as soon as the arm on the same side has completed its movement. The whole movement of the arm describes an oval figure, of which the lower part is in and the other out of Fig. 5.-THE HEADER. the water, while the shoulder forms the centre. After being thrown forward, the hand, as it reaches the surface of the water, is turned edgewise, so that it encounters little resistance on entering the water, but it is immediately afterwards turned with the knuckles upward and the palm hollowed out, as in side-swimming.

Treading the water is accomplished by allowing the feet to fall from the floating or swimming position, and performing with the legs the same motion that is made in going up a flight of stairs. The feat is more easily achieved when the arms are employed to assist the legs by pressing the water with a downward motion, as shown in the illustration (Fig. 7).

out the limb with all his strength, thrusting the heel downward,
and drawing the toes upward, notwithstanding the momentary
pain it may occasion; or he may immediately turn flat on his
back, and jerk out the affected limb
in the air, taking care not to elevate
it so high as greatly to disturb the
balance of the body. If this does not
succeed, he must paddle ashore with
his hands, or keep himself afloat by
their aid until assistance reach him.
Should he even be unable to float on
his back, he must put himself in the
upright position, and keep his head
above the surface by merely striking
the water downward with his hands at
the hips, without any assistance from
the legs." But besides this, it must
be remarked that, although cramp is a
dangerous thing, it is not so dangerous
as the fear by which it is occasionally
accompanied, and which sometimes
leads to entire loss of self-possession,
with the worst results. If attacked
by cramp, therefore, act with calmness,
recall to mind the foregoing instruc-
tions, and, by adopting that method
which is best suited to the nature of
the seizure, you may maintain yourself
safely in the water until the pain has gone, or assistance can
reach you.

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Fig. 7.-TREADING THE
WATER.

One more word of advice, as to attempting to save a drowning person. Never approach him from the front, but take him from behind by the hair; and never allow him to grasp any

part of your body if you can possibly prevent it. But if you should find yourself so seized, sink at once to the bottom, when the hold upon you will probably be relaxed, and you will be released from your perilous position. It is only a good swimmer who should make such an attempt in deep water, as for a novice to try to rescue a drowning man by his own unaided efforts, is greatly to imperil a second life without reasonable chance of saving the first. Better hasten to secure a rope or pole, which, thrown quickly to the person in danger, may assist him in regaining shallow water or the shore. Young swimmers should never go out bathing together without having such a means of assistance at hand in case of emergency.

Fig. 6.-FLOATING.

Much the same position as this is maintained when standing in the water -or, as it is termed by some, perpendicular floating-only that the head is thrown back, with the nostrils elevated in the air, while the arms are either folded across the chest, which is arched well forward, or kept down close by the hips.

There are other styles of fancy swimming, such as the "dogstyle," swimming under the water, etc., which we do not

GEOMETRICAL PERSPECTIVE.—II.

In this course upon Geometrical Perspective we propose to place before our pupils several methods of construction, and show where they are applicable to special cases. The groundplan method is the most simple and general. The lineal method, although it is equally useful, involves the necessity, in some instances, of a greater number of lines; but as this system dispenses with the use of a ground-plan, it may to some extent curtail the amount of labour. Some of the problems will be worked by both systems; and with regard to the ground-plan

P

is perpendicularly over the plan e a. It will be observed that e a cuts the base of the picture, pl p1, in c, from which a perpendicular is drawn to meet the line EA in B, therefore B is the perspective projection on the picture-plane of the point or object, A. We give a similar representation of two points (Fig. 6), which are the extremities of the line A B. A is on the ground, B is above the ground; consequently the line A B is inclined to the horizon. We need not enter into an explanation of this after that of Fig. 5, as it will be seen by the working lines that CD is the perspective representation of A B.

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method, we shall introduce some modifications which we hope! will enable our pupils to understand it thoroughly.

We shall have to consider objects under various positions. Case 1. When they are parallel with the picture-plane, and also with the ground.

Case 2. When they are perpendicular to the picture-plane, and parallel with the ground.

Case 3. When they are perpendicular to the ground, and parallel with the picture-plane.

Case 4. When they form an angle with the picture-plane, and parallel with the ground.

Case 5. When they form an angle with the ground, and parallel with the picture-plane. Case 6. When they form an angle

PP

PIC

VP

HL

ΥΡΙ

Fig. 7.

both with the pictureplane and the ground.

To illustrate the first position, place a rectangular table before you, so that both ends may be equally distant from the eye: the front edge of the table will be parallel with the picture-plane, and the top will be parallel with the ground; and at the same time the retiring edges of the ends will be perpendicular to the picture-plane and parallel with the ground. This answers to the second case. The front of the table, from the top to

The station-point is sometimes determined by placing it at a given distance from the picture-plane, sometimes from the object represented by its ground-plan, the picture-plane intervening. In either case we must bear in mind that the visual rays from the two extremities of the object must not form an angle greater than 60°, meaning that the whole of the object must be included in that angle, because the full extent of vision each way, right and left, without moving the head, is not greater than 60°. But even if we include the object within 60° only, we should be too near it to make a satisfactory and effective drawing; therefore an angle of about 25° or 30° at the outside is sufficiently large, as in Fig. 4, where the eye at E embraces the line AB within an angle of 60°, while at F the same line is included within an angle of 25°. The latter point, F, is a better distance for viewing the object, A B. An explanation of the practical operations of perspective and their results may be limited to that which relates to a point, or in the same way to a series of points; for as points are the extremities of straight lines, no matter the ground, will explain the third case, because it is perpendicular their positions, it must be evident that if we can determine the to the ground, and parallel with the picture-plane. Now push position of one point upon the plane of projection, which we call one end of the table away from you, so as to cause the distance the picture-plane, we can do so of more, and thus determine between the two ends from the eye to be different, then the the extremities of lines. Let A (Fig. 5) be a point in space-front edge will be at an angle with the picture-plane, but the top that is, somewhere in the air above the ground, and away from will remain parallel with the ground. This illustrates the the picture-plane, PP, pl p1. The horizontal projection of this fourth case. Bring the table back to its first position, and let point-in other words, its plan-will be a. Let E be the posi- one end be raised, then the top will form an angle with the tion of the eye, e will be the horizontal projection of the eye-ground, and the front edge will be parallel with the picture-plane. that is, over where the eye is placed, otherwise called the This answers to the fifth case. The sixth case will be explained station-point, s P. Now if e and a are joined by a straight line, if you push the raised end of the table away from you, as was the line ea will be the horizontal projection or plan of the done in Case 4, then the front edge will be at an angle with visual ray from the object, A, to the eye, E; because A a and picture-plane, and the top will be at an angle with the Ee are perpendicular lines, therefore every part of the line E A These positions might have been illustrated by a line o

VOL. II.

BP

PC1

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SP

BASE OF PICTURE, OR PLANE of picture, BROUGHT DOWN.

41

probably they will be better understood from the table, as the positions of the several parts will be easily recognised. We recommend our pupils to go through this experiment with a table, it will help them better to understand the positions of objects in the problems that will be given in the course of these lessons.

In ground-plan perspective the rule for finding the vanishingpoint is :

Draw a line from the station-point, SP, parallel with the ground-plan, as far as the plane of the picture, PP, from which draw a perpendicular line to the horizontal line, HL; this will give the vanishing point, VP.

In order to assist the pupil in comprehending this, we request him to turn to Fig. 7 in the preceding page, and he will notice first the ground-plan, of a line only, A B, at an angle with the PP. It must be remembered that this line, PP, is the plan or projection of the whole surface of the picture, supposed to be in an upright position, and as we cannot draw upon a piece of paper so placed, it is necessary to rabat it-that is, turn it down and lay it flat upon the table. This is done by bringing down the picture-plane, and all the points of intersection of visual rays and points of contact (anywhere, so that there may be sufficient space to make the drawing), towards the station-point, SPwe have marked it BP, "base of picture, or plane of picture, brought down." From this line we arrange the height of the eye, or horizontal line. Now to find the vanishing point for the line represented by its ground-plan :-Draw a line from Sp to VP, parallel to A B, and draw a perpendicular line from VP to VP1. VP will be the vanishing point for the given line represented by the plan A B. This must be learnt at once, as it will be wanted in almost every case of ground-plan perspective. It does not signify whether the given line is inclined or parallel to the horizon; it is the plan only of the line we use for finding the VP, as will be seen when we come to problems relating to inclined lines and planes.

We advise the pupil to work the problems that we shall bring under his notice in the course of these lessons to a scale of half an inch to the foot-that is, if we say he is to draw a line five feet long, he will make it five half inches; and, to save a great deal of repetition, we will settle at once that the height of the eye, HL, from the ground is five feet, and ten feet from the picture-plane. This scale may be employed until we propose another, when we come to other problems.

PROBLEM I. (Fig. 7).-Draw the perspective view of a given line, A B, five feet long, lying on the ground, forming an angle with the picture-plane of 35°, and touching the picture-plane; the eye to be opposite the centre of the given line.

Draw a line, PP, to represent the picture-plane; from any point, A, draw a line, A B, at an angle of 35° with PP (see Lessons in Geometry, Problem XX., Vol. I., page 256), and make it, according to the given scale, five feet long; find the centre of A B in c, and from c draw a line perpendicularly to the pictureplane to any length; mark the point d on PP. Anywhere below, draw the base of the picture, BP, parallel to PP, and draw the line HL parallel to BP or PP. From d make d SP equal to ten feet. Now find the vanishing-point, vp1, as we have already explained. Because the end of the given line A B touches the PP at A, therefore A is the point of contact of the line A B; mark it PC. Bring it down perpendicularly to the line BP to PC1. Draw a line from PC to vr', and somewhere upon this line will be the perspective view of the given line, A B, to be found thus:-As the line A B touches or is in contact with the PP, therefore the perspective view will commence at PC1; the other end B, away from PP, is found by drawing a visual ray, V R, from B towards the SP, stopping at the picture-plane, from which it is taken perpendicularly until it cuts the line PC and VP in b; ab is then the perspective representation of the given line A B. Make the space between a and b somewhat darker than the rest of the line.

We advise the pupil to repeat this problem until he knows the method of working by heart, then to turn the line or plan th. way; and, again, increase or diminish the angle of the picture-plane. Also change the height izontal line, and the distance of the eye from ; these various positions of the object will

sist the pupil in understanding the method of lem.

LESSONS IN ENGLISH.-XXI. WORDS THAT ARE BOTH PREFIXES AND SUFFIXES. SOME of the words which we treated of in the last Lesson as uncombined suffixes, may also be regarded as uncombined prefixes. The same word stands before and after its stem. You may take, as an instance, to cast-down, and down-cast. In this instance the meaning varies, but does not greatly vary; to cast-down is used physically, and down-cast signifies dejected, sorrowful. Besides this difference, there is a difference also as to the function of the two words, for the former is a verb, the latter is an adjective. Rarely, perhaps, does the import remain the same, if the position of the adverb is altered. Make a prefix a postfix (or suffix), and in general you produce a greater or less modification of meaning. Indeed, some of the most delicate shades and hues of thought expressed in the English language are connected with, if not dependent on, the varied use of these movable particles. It may, therefore, be proper to go into some little detail on the point.

It is not all the prefixes and suffixes that usage permits to take their stand before or after their principal word. Out enjoys the privilege, and makes free use thereof. examples :

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An out-cast is one who undergoes the result and consequences of being cast-out. Corresponding with out-cast, is out-law. But though we may say to out-law, we cannot say to law-out. Outpost is again different from out-cast, for out-post does not make the idea of action so prominent as does out-cast. In this respect out-cast is not unlike out-lay. Out-lay may be reversed; thus, lay-out. But while the verb is lay-out, the noun is out-lay. To bid-out, is to bid with a clear, loud voice; but to out-bid, is to bid more than another. To grow-out is very different from to out-grow. A young brother, by becoming taller, out-grows an elder brother; and the elder brother, who is thus surpassed, may be grown-out at the shoulders so as to be hump-backed. To do a person out of anything, is to cheat him; but to out-do a competitor is to excel him. If my children live-out the century, they will out-live me. By crying-out lustily, boys make a great out-cry. That shameless man, by laughing-out so loud and so long, out-laughed all the company. If you look-out at the window, you will have a pleasant out-look. "We have taken all the out-lying parts of the Spanish monarchy."Temple.

"But for public dormitories, how many a poor creature would have been obliged to lie-out of doors in the nights of the last severe winter!" Anon. "Oh, my lord,

You said that idle weeds are fast in growth;

The prince, my brother, hath out-grown me far."-Shakespeare. "Albert has grown-out of his clothes."-Anon.

"But breathe his faults so quaintly That they may seem the taints of liberty; The flash and out-break of a fiery mind."-Shakespeare. "A fire breaking-out in the cellar, consumed the whole house."Anon.

"Nor they which use

To out-drink the sea."-Donne. "You have drunk-out the cask. Children cannot well drink out of goblets."-Anon.

"He looked and saw what numbers numberless The city gates out-poured."-Milton. "Pour-out a glass of wine for the famished woman."-Anon. "The workmen, in standing-out for the wages, have out-stood the appointed time."-Anon.

"Sense and appetite out-rote reason."-South. "A large majority of the constituency voted the old member out.""Better at home lie bed-rid, idle,

Anon.

Inglorious, unemployed, with age out-worn."-Milton. "This reverent leecher, quite worn out

With rheumatisms, and crippled with his gout."-Dryden. "By Shakespeare's, Johnson's, Fletcher's lines, Our stage's lustre Rome's out-shines."-Denham.

"Out of Zion, the perfection of beauty, God hath shined.”—Psalm 1. 2.

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