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EXERCISE 163.

J'ai laissé votre lettre à son domes. I left your letter with his servant.

tique. 1. La plapart de vos parents ne sont-ils pas venus vous voir ? Mon père m'a laissé cinquante My fathor left me fifty thousand 3. Beaucoup sont venus. 3. Que sont devenus les autres ?

mille francs.

francs. 4. Je ne saurais vous dire ce qu'ils sont devenus. 5. Que Les avez-vous laissés tranquilles? Have you left them alone ? deviendra ce jeune homme s'il ne s'applique pas à l'étude ? Je leur ai laissé le champ libre. I have left them a free choice (free 6. Je ne sais pas ce qu'il deviendra. 7. Je sais qu'il ne devi.

room). endra jamais savant. *8. Combien de francs avez-vons de reste ? Ce malade a quitté le lit. That sick man lias left his bed. 9. Il ne me reste qu'un franc. 10. Combien vous restera-t-il Votre frère a quitté le barreau. Your brother has left the bar. quand vous aurez fait vos emplettes ? 11. Il ne me restera Je vous laisserai ce chapeau à ce I will let you have that hat at that

prix.

price. qu'une bagatelle. 12. Cet apprenti est-il devenu habile dans con état? 13. Il y est devenu habile. 14. Ce monsieur est-il

VOCABULARY. aveagle de naissance, ou l'est-il devenu ? 15. Il l'est devenu. À bon compte, cheap. Mauvais, -e, bad. | Pension, f., boarding16. Savez-vous ce que sont devenus ces jeunes gens ? 17. Ils Carte, f., card. Moins, less.

school. sont devenns médecins. 18. Ne savez-vous pas ce que sont Epée, f., sword, army Noyau, m., fruit-stone. Portier, m., porter. devenus mes livres ? 19. Il sont égarés. 20. Ne deviendrez

(figuratively). Pourquoi, why.

Prix, m., price.

Pavie, m., clingstone Robe, f., gown. vons pas boiteux si vous marchez tant ? 21. Je deviendrai Habitude, f., habit.

Juge, m., judge.

peach, boiteux et maigre. 22. La foule ne s'est-elle pas égarée dans

Service,m.,service,army ce bois? 23. La foule s'y est égarée, et n'a pu retrouver son

EXERCISE 165. chemin. 24. Une nuée de barbares désolèrent le pays. (ACAD.) 1. Vos oncles, vos cousins et vos neveux ont-ils quitté le 25. Une foule de citoyens ruinés, remplissaient les rues de commerce ? 2. Ils ont quitté le commerce, et sont devenus Stockholm. (VOLTAIRE.)

médecins. 3. Le capitaine G. n'a-t-il pas quitté le service ? EXERCISE 164.

4. Il a quitté la France, mais il n'a pas quitté le service. 5. Où 1. Have not most of your friends become rich ? 2. Most of avez-vous laissé votre fils ? 6. Je l'ai laissé dans une pension. them have become poor. 3. Has not that young lady become ... Est-il trop jeune pour quitter ses études ? 8. Il est trop jeune ; learned? 4. I think that she will never become learned. 5. il n'a que douze ans. 9. À qui avez-vous laissé votre carte de Is not the American army (armée) very small ? 6. The Ameri- visite ? 10. Je l'ai laissée chez le portier. 11. Pourquoi ne le can army is small, but most of the American soldiers are very

laissez-vous pas parler ? 12. Parce qu'il est temps que nous brave (braves). 7. Can you tell me what has become of that

vous quittions. 13. Me permettez-vous de lui communiquer gentleman ? 8. I cannot tell you what has become of him. cela ? 14. Je vous laisse le champ libre à cet égard. 15. Ce 9. Is your brother blind by birth (was your brother born blind) ? jeune homme n'a-t-il pas quitté ses mauvaises habitades? 16. 10. No, Sir, he has become so. 11. Were you born lame?

Il les a quittées. 17. M. L. n'a-t-il pas quitté la robe pour 12. No, Sir, I became so three years ago (il y a). 13. Are not l'épée ? 18. Oui, Monsieur ; il n'est plus juge; il est capitaine. most of your hours devoted to play (jeu, m.)? 14. No, Sir, 19. Ces pêches quittent-elles facilement le noyau ? 20. Non, they are devoted to study. 15. How much of your money Monsieur ; ce sont des pavies. 21. Je vous laisse cet habit have you left? 16. I have only twenty-five francs left. 17. pour cinquante francs. 22. À quel prix me le laisserez-vous ? Do you know how much I have left? 18. You have only a à bon compte ; je ne saurais vous le laisser à moins.

23. Je vous le laisserai pour dix francs. 24. Je vous le laisse trifle left. 19. How much shall you have left to-morrow? 20. I shall only have six francs left. 21. I shall only have

EXERCISE 166. two francs left when I have made my purchase. 22. What has 1. The son, daughter, and cousin have left Paris. 2. My become of your grammar? 23. I have mislaid it. 24. Do you father, mother, and sister have left me here. 3. Do you like know what has become of my hat? 25. You have left (laissé) to leave your country ? 4. I do not like to leave my friends it upon the table. 26. Will not that gentleman become blind ? | and country. 5. My parents do not like to leave me here ; I 27. He will not become blind, but lame. 28. Has your son am too young. 6. Why does not your brother let his son speak become skilful in his trade ? 29. He has not become skilful in [Sect. XCVI. 4]? 7. Because he has nothing to say. 8. Have it. 30. What has become of him? 31. He has lost his way you let him alone ? 9. I have let him alone. 10. Why do you not in the wood. 32. Did the crowd lose its way? 33. Most of let me alone? 11. I will let them alone. 12. Has your friend the soldiers lost their way. 34. A cloud of locusts desolated left his bed? 13. He has not yet left his bed; he is yet very ill. our country.

14. Has Captain G. left the army? 15. He has not left the SECTION LXXXV.--IDIOMS RELATING TO THE ARTICLE, army. 16. Has not that gentleman left the army for the bar ? ADJECTIVE, ETC.

17. He has left the army for the bar. 18. My friend has left the 1. The article, the demonstrative and the possessive adjec. bar. 19. At what price will you let me have this silk? 20. I tives, must be repeated, as before said, before every noun or

will let you have it at two francs a yard. 21. Can you not let adjective used substantively, which they determine [$ 80, 93, you let me have that book for twenty francs ? 24. I will let

me have it for less ? 22. I let you have it cheap. 23. Will 21.) 2. The prepositions d, de, and en, are repeated before every less. 26. With whom (a qui) have you left my book? 27. I

you have it for twenty-two. 25. I could not let you have it for word which they govern [$ 141].

3. The verb quitter, to leave (to quit), is said of persons and left it with your sister. 28. Why did you not leave it with my places, and also of things in the sense of to abandon, to give like to leave your friends P 31. I do not like to leave them.

servant ? 29. Because he had left your house. 30. Do you wp.

32. Where have you left your book? 33. I left it at my Vous avez quitté vos parents et You have left your relations and

father's. 34. Has that merchant given up commerce ? 35. vos amis,

friends. Nous avons quitté nos études, We havo discontinued our studies.

He has not given it up. 36. Those peaches do not part easily

from the stone; they are clingstone peaches, 4. Laisser, to leave, to let, is generally said of things. It is, however, said of persons in the sense of to suffer to remain.

KEY TO EXERCISES IN LESSONS IN FRENCH. Vous avez laissé votre livre sur la You left your book upon the table. table,

EXERCISE 103 (Vol. II., page 106). The examples below will illustrate the use of those two verbs. 1. Did you not know where the musician was gone? 2. I knew RÉSUMÉ OF EXAMPLES.

that he was gone to Paris. 3. Had you not been told that your

brother is dend ? 4. I had been told that he was dangerously ill. N'avez-vous pas quitté votre mai. Have you not left your house ? 5. Did you not generally go to bed as soon as you had finished your son?

lessons ? 6. As soon as I had finished them, I used to go to the play. J'ai quitté mon pays et mes parents. I have left my country and relations. 7. As soon as you had finished your lessons, what did you do last J'ai laissé ma bibliothèque en I left my library in Europe.

evening ? 8. As soon as I had finished them, I went to the ball. 9. Europe ?

Did not that little girl want to sleep? 10. She wished more to sleep Ne voulez-vous pas laisser votre Will you not leave your son here? than to study. 11. What had you done with your book when I fils ici ?

asked you for it? 12. I had mislaid it. 13. I had forgotten it in Je n'aime pas à le quitter, I do not like to quit lim.

the garden. 14. Why was your watch stopped ? 15. Because I had

forgotten to wind it up. 16. Had not the watchmaker wound it up ? gold. Calculate the value of the money which can be coined 17. He had forgotten to do it. 18. Had you not lost your purse ? out of 1 oz. of fine gold. 19. I had lost it, but have found it again. 20. Had your cousin left? 21. He had not left yet. 22. Was he out? 23. He was out

148 x 12 = weight of one sovereign in ounces. with my mother. 24. Whither was he gone? 25. He was gone to This contains 4 * & * 12 ounces of fine gold, which (neglecting my brother's, who had invited him to dinner,

the value of the alloy) are worth £1.

11 x 40 EXERCISE 104 (Vol. II., page 106).

Therefore, as oz. : £1 :: 1 oz. : value of 1 oz.

1869 1. N'aviez-vous pas eu l'intention de parler à mon frère ? 2. J'avais

440) 1869 (£4 4s. 11 . - Answer. en l'intention de lui parler, mais il était parti. 3. Mlle. votre seur

1760 se coucha-t-elle, hier au soir, aussitôt qu'elle eut lu son livre ? 4. Elle se coucha aussitôt qu'elle l'eut lu. 5. Vous avait-on dit que

109 votre scur était malade ? 6. On m'avait dit qu'elle avait été dangereuse

29 ment malade. 7. Saviez-vous ce que vous aviez fait de votre plume ? 8. Je savais que je l'avais égarée. 9. Combien de vos livres avez-vous

2180 égarés ? 10. J'en avais égaré cinq, mais mon frère les a trouvés. 11.

1760 Où les aviez-vous laissés ? 12. Je les avais laissés dans le jardin. 13, La montre de votre frère était-elle arrêtée ? 14. Elle était arrêtée.

420 15. Pourquoi était-elle arrêtée ? 16. Il avait oublié de la remonter.

12 17. N'avait-il pas perdu sa clef? 18. Il ne l'avait pas perdue. 19. Le teinturier était-il parti ? 20. Il n'était pas encore parti, il avait

5040 l'intention de partir à cinq heures. 21. Lui aviez-vous parlé, quand

4840 j'arrivai hier? 22. Je lui avais parlé. 23. Lui aviez-vous dit que ma seur est ici? 24. Je le lui avais dit. 25. Est-il encore ici? 26. Non,

200 Monsieur, il est parti, il est parti ce matin à six heures.

5. A convenient way of arranging the operation in questions of

this kind is called the Chain Rule. It is especially useful in all LESSONS IN ARITHMETIC.-XLI.

questions connected with Exchange, and is the method generally

used by merchants. EXCHANGE

Write down the quantity of which the equivalent is required 1. The value of a fixed sum of the money of one country expressed quantity is generally called the Term of Demand.

at the head of a column, as in the working given below. This in that of another, when this value is calculated by a comparison of the weight and fineness of the coins of the two countries, is which write down in a second column a quantity of the same

Draw a sloping line from it to the left, at the extremity of called the Par of Exchange. When for this fixed sum the kind as the first. Opposite to this place in the first column its correct equivalent in money of the other country, calculated on equivalent in value of another quantity, and so on. this supposition, can be obtained, the exchange is said to be at par. The exchange, however, between any two countries fluc

1 oz. fine gold tuates from various causes.

The Course of Exchange is the variable sum of the money of one country which happens at a particular time to be equivalent

11

12 oz. standard gold to a fixed sum of the money of another country. Thus, for £1 sterling at one time, 25.15 francs, at another 25.20 francs, may be obtained, according to the course of exchange between England

1 pound Troy and France. 2. If A owes a correspondent in Berlin, for instance, £500,

40 he might pay his debt by transmitting the value in coin or

1869 sovereigns bullion. But this would be both cumbersome and expensive.

11 x 12 x 40 12 x 1869. If, then, he can find a person, B, who has money owing to him

12 x 1869 in Berlin, B can draw a bill upon his debtor in Berlin, and sell

The answer is
11 x 12 x 40

L1 = £4 4g. 111d. it to A, who then transmits it to his own correspondent in Berlin. Such bills of exchange are the means by which money the term of demand. 11 oz. fine gold are equivalent to 12.03

;

Thus, in the example already given, 1 oz. of fine gold is transactions between different countries are conducted. price of such bills will fluctuate according to the demand there standard gold, 12 oz. standard gold are equivalent to 1 pound may be for them at the time. The excess of their price over the Troy standard gold, and 40 pounds Troy standard gold are sum they represent can clearly never exceed the amount of the equivalent to 1869 sovereigns; the last term in the right hand cost of carriage and money value of the risk incurred in for column being arranged to be sovereigns, because the answer is warding the same sum in specie or bullion.

required in sovereigns. 3. The Arbitration of Exchange is the process of fixing the rate

Multiply together all the numbers in the longer column, and or course of exchange between two places, by means of a com- divide by the product of the numbers in the other column. This parison of the exchange between them and one or more inter will give the equivalent of the term of demand in terms of the vening places. Thus a debt in Paris may be paid by means of quantity standing lowest in the longer column (in the above a bill on Berlin, which is to be again replaced by one on Ham- example, sovereigns); burg, and that, finally, by one from thence upon Faris. The

N.B. The sloping lines connect quantities of the same kind; arbitration is said to be simple when there is only one inter- the horizontal lines, quantities of equivalent value. mediate place, compound when there are more.

6. The reason of the truth of this rule may be gathered from The subject of exchange, however, is too complicated for us to observing that in reality we multiply the term of demand by a go into more than very superficially.

succession of fractions which respectively express the value of For information we refer our readers to Kelly's “ Universal one unit of a quantity in terms of the succeeding quantity

: Cambist."

Thus we multiply the term of demand, which is 1 oz. fine gold, A large number of questions in exchange can be worked out by by Hi, the number of ounces of standard gold equivalent to 1 oz. the aid of the principles already laid down. Before proceeding of fine gold. This gives us the amount of standard gold equi

. to treat of them, we shall explain a method called the Chain valent to 1 oz. of fine gold. We next multiply by which Rule.

expresses the same quantity in pounds Troy, and next by, THE CHAIN RULE.

which is the equivalent of 1 pound Troy of standard gold in

sovereigns. 4. If the equivalent of any amount of one quantity is given For a more detailed explanation of the rule we refer our in terms of another, that in terms of a third, and so on, it is readers to Peacock's " Algebra, Vol. I., Arts. 346—353. required to find the equivalent of a certain amount of the first We give some additional examples worked out. The reader quantity in terms of the last.

should carefully in each case examine the reason for the process EXAMPLE 1.-40 lbs. Troy of standard gold are coined into in the way indicated above. 1869 sovereigns, and standard gold contains 11 parts in 12 fine EXAMPLE 2.-If 7 lbs. of rice be worth 2 lbs. of currants,

12 oz.

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3 lbs. of carrants 1 lb. of hops, 5 lbs. of hops 2 lbs. of tobacco This being determined, we need only multiply it by the ratio at 4s. per lb, what is the value of 1 lb. of rice ?

of the two variable quantities, to determine the course of ex1 lb. rice.

change in any given case.

This invariable ratio is called the Fixed Number, and is of

important practical use in the regulation of exchanges.
7
2 lbs. currants.

KEY TO EXERCISES IN ARITHMETIC.-XL,

EXERCISE 61. 1 lb, hops.

1. 5.

7. 3 lbs. of the first 10, (1) 1 gall, of each 2. 15%

two to 4 of the of the spirits to 3 3. 25

last.

galls. of water, 2 lbs, tobacco.

4. 11; shillings. 8. Equal quantities (2) 6 galls, of the 5. 416 per cent.

of each,

last to 1 gall, of 6. 2680, 9:27. 9. 21s. 23d.

cach of the others 48.

and of the water,

NW

1

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24

NiN

20

24 lbs.

24 x 20

4000 x 5 x 24a. = 10000. = £4 3s. 4d.

24 x 20

105
16

SKETCHING FROM NATURE.-II. 1 shillings = $1d. = 13%d.-Answer.

RETIRING LINES-POINT OF SIGHT, ETC. EXAMPLE 3.-A certain book is to contain 5 sheets of paper, If our pupils will carefully follow the advice we gave them in and 4000 copies are to be printed. to weigh 24 lbs., what would be the saving upon the expense of the last lesson, and at first strictly confine their attention to publishing the work, owing to a reduction of the price of the very simple subjects, they will soon find themselves in a position paper là. per pound?

to attempt with confidence something more advanced, which

will include much that will make a demand upon their know4000 copies.

ledge and experience in perspective. When we consider the infinite variety of the positions of lines, and the relations they

bear to each other, so many difficulties arise, that we must 5 sheets.

naturally look about us for assistance altogether independent of mere manual practice, of which no amount of experience, how

ever large it may be, can satisfactorily help us, and therefore 1 quire.

we must haverecourse to perspective. In our very first attempts the one great difficulty presents itself, viz., how to draw the lines

which retire; here is the starting point from which every rule 1 ream,

proceeds, and this difficulty every one will discover immediately he sits down to draw from nature. Objects parallel with our position, or with the picture plane, like the posts in Fig. 1, have no retiring lines—the lines which represent them are either horizontal or perpendicular; if horizontal, they are drawn across

the picture, and those which are perpendicular in the object are 1d. reduction.

drawn so. Therefore, with propor attention to the positions and

proportions of these lines, exercises of this kind will be found 4000 x 5 x 24

very easy ; but when we come to lines in other positions with Answer.

regard to the picture plane, those which retire-that is, go away

from us, like the lines of a railway when viewed from the top of EXAMPLE 4.-Find the course of exchange between London a bridge other considerations present themselves; lines of this and Paris—i.e., the number of francs equivalent to £1—from class may retire either horizontally, or at an inclination. Those the following data :

of our pupils who are accompanying us through the course of The market price of standard gold in London is 78s. per oz.,

“Geometrical Perspective” given in these pages, will not have and the premium on gold in Paris is 8 francs per thousand. to be told that there are established rules to aid us in drawing

The Mint price of a kilogramme (32.154 oz.) of pure gold in these lines according to the position in which they may be Paris is 3434-44 francs.

placed; they will be satisfied upon this point, and they will have discovered that by working out these problems their practice in drawing them is rendered easier, and they will have found the

result to be satisfactory. We have said before, there is no 20s.'

necessity, even if it were possible, to go through all the geometrical rules that can be applied to the subject when

drawing from nature; but we do assert that it is necessary 78 1 oz. standard gold.,

to know them, because, from having practised them upon subjects under given conditions, we can satisfactorily account for the position of every line we draw, let them be placed as they may.

There are many who take great delight in drawing from nature, 11 oz, fine gold.

£1

12

who affirm that perspective is a science not at all necessary to them, although they allow that it is essentially so for architects.

This is a mistake, which may be coupled with another, into which 32.154 3434-44 francs, mint price.

they frequently fall, viz., that "it is too difficult to learn." They contend that “if the eye is properly educated, nothing

more is required." This vague expression is one we have heard 1000 1008 francs (with premium).

very often, and, of course, many who use it have no definite Therefore the Answer is 1008 x 3434:44 x 11 x 20

idea of what they mean by it. We ask such, what they wish

= 25-30 nearly. 1000 x 32.154 x 12 x 78

us to understand by the "education of the eye?” The eye is

not an instrument like the hand, which must have some conObs. Fixed Number.—In the above operation, the only siderable and practical experience in order to carry out the variable quantities are the 78s. expressing the price of gold in i intentions; the eye has no practical duty to perform, it is simply London at the time, and the 1008 francs indicating the amount the medium through which is conveyed to the mind the form, of premium upon gold in Paris at the time.

positions, and proportions of the objects to be represented; and If we omit these two terms, we get an invariable ratio

since positions and proportions are not arbitrary, it follows that 3434-44 x 11 x 20

some kind of education is necessary to guide our judgment and practice in dealing with them : in other words, the mind must

francs

1000 x 32-154 x 12 or 1-95822.

be prepared by some process to receive the full impression of it comes to our rescue when doubts arise, all of which can be everything connected with the object as it stands, or under any satisfactorily disposed of by a knowledge of perspective. Withcondition in which it may be placed, and to recognise details out this knowledge, how very discouraging it is when we atand peculiarities which, without a previous preparation, we tempt to draw some large buildings, or a number of them should inevitably pass over, totally ignorant of their existence.' together, to find that we have no principles to guido us, hoping

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We maintain that a little scientific education reveals facts which the drawing may be right in the end, but labouring all i would otherwise be lost upon us. Consequently, we assert that while in the greatest uncertainty, and dreading, at the sa the surest and shortest way to "educate the eye” is to educate time, that should our work come under the inspection of the understanding, and one of the most effectual means for educated artist, he may detect many faults that might ea: accomplishing this is the study of geometrical perspective. have been avoided if we had previously studied the grammai Experience in this branch of science strengthens our judgment the art. We do not say this to discourage, quite the rever with regard to the true positions of lines, and, more than that, we wish to prove the necessity of the course of study we rect

PS

e

mend; it is short and easy, and we may remark, for the encou on the line of sight. In general practice we must so place ournagement of the timid, there is no need to carry it to the extent selves, when we are looking down a street, that the parallel required by architects. As we proceed with our lessons, our sides of the street shall be parallel to the imaginary line called pupils will easily find out for themselves how much is requisite, the direction of sight, which goes from the eye to the Ps—in becanse, according to the class of subject we are drawing, other words, the sides of the street must retire at right angles occasions will present themselves which will make it necessary with our position. Fig. 3 is a plan representing our position, for us to refer to those rules which are applicable to the case, or station point at a; b the point of sight opposite the eye; do and most of which will be found already given in the previous the sides of the street which, when parallel with each other, and pages of the POPULAR EDUCATOR.

also when they retire directly, or at a right angle from us, have We will now direct the attention of our pupils to Fig. 2, the Ps (point of sight) for their vanishing point; the sides which is nothing more than an arrangement of straight lines in e and fare parallel with our position, and consequently are various directions, each of which, whatever the direction may drawn across the picture. In our view (Fig. 2) ps is the point be, is subject to some especial rule for its treatment. The view of sight, and all the lines of the buildings on the right vanish at we have selected (and we call it a

it-viz., the eaves of the roof, the view, becanse we wish to talk about

tops and bottoms of the windows, it to our pupils as though we were

the tops of the doors, the foundation setually out of doors in front of

line, and the courses of the bricks, it) is as practical and simple as we

b

all these lines being parallel with could select : it is taken from a

each other, and at right angles with small street in one of our Yorkshire

our position. The lines of the buildtowns. We have just said, “it is

ing on the left vanish at vpl, bean arrangement of straight lines in

cause they do not retire in the same various directions." Now lines in

direction, the two sides of the street the positions of those which com

in this case not being parallel. pose our subject are so common,

It is not a difficult matter to dethat there will scarcely be found an

termine precisely where the point of out-door scene which does not con

sight is to be found. If the pupil tain them; therefore the observa

will do as we recommended in the tions we are about to make will be

last lesson—that is, hold his pencil found not only applicable to thou

between his eye and one of the sands of a similar description, but

upper retiring lines, say the eaves, to numerous others of a much more

so that the line of the eaves shall ambitious character. If we were

f

coincide with, or be made apparently drawing the interior of a cathedral,

to lie upon the length of the pencil, we should have to repeat all that we

and when thus placed, carry his eye have to say here, with as much

downwards along the pencil until it more as might be rendered neces.

comes to the line of sight-he will sary by the different positions of

find the pencil directed to the point other lines found in the cathedral.

opposite the eye. This can be proved Our pupils must now refer back to

by placing the pencil upon another Lesson III. (Vol.I., page 71), and read

line which is parallel to the eaves, again the fixed principles relating to

d

say the foundation line of the wall; retiring lines and planes, as we are

the pencil thus placed will point in about to show how they may assist

the same direction, and it would do as to understand and draw the lines

the same if it be made to coincide of the houses before us. The in

with the tops of the doors, or with structions we speak of referred more

any other lines that may be parallel immediately to drawing from copies;

with them. There is another way we will now make them applicable

of proving that the point of sight to drawing from nature; and if they

is the vanishing point for lines going Irave been clearly understood in the

off at a right angle with our position: former case, we have an easy task

Fig. 3.

if we hold out our arm horizontally, before us. Let us suppose that we

and place it in a parallel position are seated opposite the end of the

with the retiring side of the street, street, at about twenty or thirty

we shall find we are pointing to the yards from the nearest building,

point of sight. Let the pupil try and that we have looked it over

this, which he can do in a room, if before we begin, and ascertained

he places himself in such a position, which lines retire from, and which

that on looking before him the are parallel with our position, and

direction of sight shall be parallel have particularly observed the

to the sides of the room on the general arrangement and the cha

right hand and the left (see Fig. racter of the details. We must first determine the line of 3). We shall have to refer to this again when we place sight, or as it is sometimes called, the horizontal line, HL; by ourselves before a subject in which there is a building having holding the pencil horizontally before the eye, and noting the an angle towards us, and not a side; we especially request places where it cuts the lines of the subject, it will be seen in our pupils to read again Lessons in Drawing, III. and IV., our view to cross the door on the right hand at about one-third Vol. I., pages 72, 103. The first line that the pupil must from the top. This is a very necessary step to take at the com- mark in (we do not adviso him to draw any lines until he has mencement, and must not be omitted, when we know that all first determined the places of all the principal ones) will be the horizontal retiring lines have their vanishing points on the line of one nearest the Ps. Let this be the course of procedure in all sight. Our next consideration will be, if we find that half of cases, that is, when arranging the positions of the lines he must the subject upwards is above the eye (that is, the HL), and the begin from the point of sight, and as he passes on, if to the right, other half below it, then the hĽ will be drawn across the mark the place for each line which crosses the line of sight as middle of the paper; if the al is placed as in the view be- he comes to it, then take up those lines on the left, commencing fore nis, at about two-thirds from the top of the subject, then from the ps, and treat them in the same way; then he must the line must be drawn at two-thirds of the distance from the determine the heights of the perpendicular lines drawn through top to the bottom of the paper. Afterwards we must determine these points of position. He must exercise his judgment in this the position of the point of sight : this is always opposite the eye matter by the comparison of widths and heights in the original.

The direction of sight.

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