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you like this bread 22. I find it very good. 23. Did your two friends arrive in time at the appointed place?. 24. Neither was there in (d) time. 25. Do you find fault with that (cela)? 26. I do not find fault with it (y). 27. Will you both expose yourselves to this danger?, 28. We will not expose ourselves to it. 29. Do you find fault with my secretary's conduct 30. I do not find fault with it. 31. Do you find fault with his writing? 32. I find fault with it; for it is very bad. 33. Will you not watch over my interests? 34. My brother and I will watch over them. 35. We will not cease to watch over

your interests. Section LXXXIV.

1. A verb having, as its subject, a general collective noun {{ 3 (6)] preceded by the article, agrees with the noun [$ 115 1)]:—

La foule des pauvres est grande. The crowd of the poor is great. 2. A verb preceded by a partitive collective [$ 3 (6)] takes the number of the noun following the collective, unless attention be particularly directed to the collective itself [$115 (2)]:— Une foule de pauvres reçoivent des A crowd of poor people receive assistsecours. ance. 3. The words, la plupart, most; un nombre, a number, &c., and the adverbs of quantity, peu, assez, beaucoup, plus, moins, trop, tant, combien, belong to this class. 4. Rester is often used unipersonally in the sense of to have left. The adverbial expression de reste is often used in the same manner as the English word left:Il mereste deux francs. I have two francs left—or literally, There remain to me two francs. We have fifty crowns left.

5. Devenir (2, ir.) to become, with étre as an auxiliary, corresponds in signification to the English to become, followed by of. It is also Englished by to become, or simply to turn :

Qu'est devenu votre frère? What has become of your brother? Il est en France, et est devenu He is in France, and has turned lawavocat. yer.

Nous avons cinquante écus de reste.

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1. La plupart devosparents ne sont-ils pas venus vous voir; 2. Beaucoup sont venus. 3. Que sont devenus les autres? 4. Je ne saurais vous dire ce qu'ils sont devenus. 5. Que deviendra ce jeune homme s'il ne s'applique pas à l'étude? 6. Je ne sais pas ce qu'il deviendra. 7. Je sais qu'il ne deviendrajamaissavant. 8. Combien de francs avez-vous dereste? 9. Il ne me reste qu'un franc. 10. Combien vous restera-t-il quand vous aurez fait vos emplettes ? 11. Il ne me restera qu'une bagatelle. 12. Cet apprenti est-il devenu habile dans son État?, 13. Il y est devenu habile, 14. Ce monsieur est-il aveugle de naissance, ou l'est-il devenu? 15. Il l'est devenu. 16. Savez-vous ce que sont devenus ces jeunes gens? 17. Ils sont devenus médecins. 18. Ne savez-vous pas ce que sont devenus mes livres? 19. Ils sont égarés. 20. Ne deviendrezvous pas boiteux si vous marchez tant? 21. Je deviendrai boiteux et maigre. 22. Lafoule ne s'est-elle pas €garée dans ce bois* 23. Lafoule s'y est égarée, et n'a pu retrouver son chemin. 24. Une nuée de barbares désolerent le pays. (AcAD.) 25. Une foule de citoyens ruinés, remplissaient ses rues de Stockholm. (Vourauns.)

ExERcise 168.

1. Have not most of your friends become rich; 2. Most of them have become poor. 3. Has not that young lady become learned 4. I think that she will never become learned. 5. Is not the American army (armée) very small 6. The American army is small, but most of the American soldiers are very brave (braves). 7. Can you tell me what has become of that gentleman * 8. I cannot tell you what has become of him. 9. Is your brother blind by birth (was your brother born blind)? 10. No, Sir, he has become so. 11. Were you born lame? 12. No, Sir, I became so three years ago (il ya). 13, Are not most of your hours devoted to play (jeu, m.) : 14. No, Sir, they are devoted to study, 15. How much of your money have you left? 16. I have only twenty-five francs left. 17. Do you know how much I have left? 18. You have only a trifle left. 19. How much shall you have left to-morrow? 20. I shall only have six francs left. 21. I shall only have two francs left when I have made my purchase. 22. What has become of your grammar; 23. Ihave mislaid it. 24. Do you know what has become of my hat? 25. You have left (laisse) it upon the table. 26. Will not that gentleman become blind? 27. He will not become blind, but lame. 28. Has your son become skilful in his trade? 29. He has not become skilful in it. 30. What has become of him # 31. He has lost his way in the wood. 32. Did the crowd lose its way 33. Most of the soldiers lost their way. 34. A cloud of locusts (sauterelles) desolated our country.

SECTION LXXXV.

1. The article, the demonstrative and the possessive adjectives, must be repeated, as before said, before every noun or adjective used substantively, which they determine [$80, 93, 21

2. The prepositions à, de, and en, are repeated before every word which they govern [$141]. 3. The verb quitter, to leave (to quit), is said of persons and places, and also of things in the sense of to abandon, to give up :— Wous avez quittévos parents et vos You have left your relations and amis. friends. Nous avons quitté nos études, We have discontinued our studies. 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 :Wous avez laissé votre livre sur la You lost your book upon the table. table.

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4. Il a quitté la France, mais il n'apas quittéle service. 5. Oil avez vous laissé votre fils? 6. Je l'ai laissé dans une pension. 7. Est-i: tropjeune pour quitterses études? 8. Ilest tropjeune; il n'a que douze ans. , 9. A qui avez-vous laissé votre carte de visite? 10. Je l'ai laissée chez le portier. 11. Pourquoine le laissez-vous pas parlero 12. Parce qu'il est temps que nous vous quittions. 13. Me permettez-vous de lui communiquer cela 14. Je vous laisse le champ libre a cet égard. 15. Ce jeune homme n'a-t-il pas quitté ses mauvaises habitudes? 16. 1 les a quittées. 17. M. L. n'a-t-il pas quitté la robe pour l'épée? is. Oui, Monsieur; il n'est plus juge; il est capitaine. 19. Ces pêches quittent-elles facilement le noyau ? 20. Non, Ysonsieur; ce sont des pavies. 21. Je vous laisse cet habit pour cinquante francs. 22. A quel prix me le laisserez-vous? 23. Je vous le laisserai pour dix francs. 24. Je vous le laisse abon compte; je ne saurais vous le laisser a moins. ExERcis E 170. 1. The son, daughter, and cousin, have left Paris. 2. My father, mother, and sister, have left me here. 3. Do you like to leave your country? 4. I do not like to leave my friends and country. 5. My parents do not like to leave me here; I am too young. 6. Why does not your brother let his son speak [Sect. 96,4]? 7. Because he has nothing to say. 8. Have you jet him alone? 9. I have let him alone. 10. Why do you not let me alone? 11. I will let them alone. 12. Has your friend left his bed : 13. He has not yet left his bed; he is yet very sick. 14. Has Captain G. left the army?, 15. He has not left the army. 16. Has not that gentleman left the army for the bar? 17. He has left the army for the bar. 18. Myfriend has left the bar. 19. At what price will you let me, have this silk 20.. I will let you have it at two francs a yard. 21. Can you not let me have it for less 22. I let you have it cheap. 23. Will you let me have that book for twenty francs. 24. I will let you have it for twenty-two. 25. I could not let you have it for less. 26. With whom (a que) have you left my book? 27. I left it with your sister. 28. Why did you not leave it with my servant; 29. Because he had left your house. 30. Do you like to leave your friends? 31. I do not like to leave them. 32. Where have you left your book? 33. I left it at my father's. 34. Has that merchant given up commerce? 35. He has not given it up. 36. Those peaches do not part easily from the stone; they are clingstone peaches.

ANSWERS TO CORRESPONDENTS.

Music.—The following extracts from a letter written by an intelligent selfteacher we insert in the hope that they will stimulate and encourage many:“Sir, I cannot retrain from bearing my feeble testimony to the excellence and soundness of your method for imparting a thorough and substantial knowledge of music. I am, myself, but an humble amateur; yet, like the immortal Martin Luther, "I would not for a great deal give up my poor knowledge of music." It is now some years since I entered upon the study of the “divine art," and I may mention, for the encouragement of the million pupils of the Educator, and as an incentive to their increased perseverance and application, that it was not long ere I was able to read music with facility at sight. I have since, also, studied HARMony to advantage, and have farther attained some proficiency on the pianoforte—and all this I have accomplished without the aid of a single lesson from a teacher, aye, and from books much less explicit and distinct than the lessons in the Educator. I now consider myselfvery fortunate in having acquired my knowledge of music under the old Guidonian sol-fa system inculcated by Mr. Curwen, as I am convinced of the utter worthlessness of the French method, where the syllable Doh is never changed from c.. I had not long begun to study music, when the latter system became highly popular under the auspices of the late Dr. Mainzer. ... I was at first all but łł away by the rapid progress of his pupils to adopt the same system myself, but being satisfied with the advance I was then making, and reflecting that, if there was no “royal road' to the knowledge of the other sciences, there could be none to music, I resisted the temptation, and applied myself with renewed assiduity to my studies under the old system. Events have proved that my determination was right, for while the Mainzerian system seems now to be falling into merited oblivion, I have acquired, under the old method, a more lasting and thorough knowledge than I could ever have attained under the former. I can hardly imagine that a man of such talent as Dr. Mainzer could ibly be himself deceived, or that he truly supposed the system which he taught capable of imparting an effectual knowledge of music. His E. certainly reached some degree of proficiency in the scale of c, but

eyond this they could not advance one iota, for the moment the key was changed they were completely at sea. In his programme (now before me) announcing the performance of Handel's oratorio," Judas Maccabeus,' by two hundred and fifty of his adranced pupils (which took place in Edin. * in June, .547), he treats the mere fact of the performance of such a work as evidence of the great musical knowledge of his pupils, and as leading to the inference that, after such performance, they were capable of reading any music however difficult, while, so far from such an inference

being correct, the truth is, that the children had been previously so well drilled that they had learned the oratorio entirely by rote, a fact of which he must have been perfectly aware. This result was certainly an instance of the doctor's great patience and perseverance (and I have myself seen him labouring for an hour in getting the children to master a few bars of the more difficult passages), but it was by no means an impossible task, for we are all familiar with the aptitude of children for learning music by heart, and the practice of many masters in so teaching them, without the smallest pretension being made to their ability to read music. I may add, that I have never in my experience met with a single reader of music who had learned under the Mainzerian system; and it is a singular fact that, on the occasion of the performance I have alluded to, not one of the doctor’s adult pupils were qualified for the tenor and bass parts—these being taken by the professional choristers of the town In short, it were easy to prove to demonstration the impracticability of . the defects inseparable from this system, but this has already been ably illustrated in the lessons in the Educator. I am afraid I have trespassed too much on your time, but I have been induced to trouble you with the above remarks in the hope of their being useful in encouraging the pupils of the Educaton to redouble their erertions, and resolve to profit by its invaluable lessons. With earnest wishes for the continued prosperity of your truly national work, I am, Sir, yours most respectfully, JAs. H.” D. M. J. (Newport): A good pair of 12 inch globes, to stand on a table, may be had for £3 or £1, at the following makers: Cary, Bardin, Newton, and Addison, London. We have not seen those he mentions.-Philo (Burslem): The man who told you that man had been an actual observer for 44 millions of years was greatly mistaken; dou’t believe him.—Joshua: Thanks for his good letter; Drawing has begun; try the glass harmonicon. -XENorikon : The jubilee is mentioned by Josephus, Ant. iii. 12, who is a profane author.—A. R. J. (Belfast): 1. The solution is correct. 2. Cassell's Arithmetic is published, and may be had of the agent of the P.E. by order. 3. The binding of vol.I. in cloth is ls, common edition; 1s. 6d., fine edition. 4. The penmanship is very fair, but not for a first-rate clerk.-A STUDENT (Belfast) is too hasty; it was at the request of many who intended to use the Arithmetic that the answers were purposely omitted. This want will be supplied to all who wish it; see Literary Notices.-W. Booth: Under consideration.-W. T.: The lessons he wants are in preparation.—AngloSaxon (Limerick): See page 104, vol. II., col. 1, line? from bottom. Goethe is, pronounced geuté.-Piil (West Ham, London): French first. Cassell's History of England is published at 3s.6d. complete, 3 vols. in one.

LITE R A R Y NOTICE S.

Mns. HARRIET BEEcHER Stowe, AUTHoness of “Uncle Toxt's CABIN.” &c.—A magnificent PontRA1T of this celebrated and talented lady will be given in the Illustrated Exhibitor AND MAgazine of ART, for the week ending December 23. John Cassell fels highly honoured by the kindness of Mrs. H. Beecher Stowe in furnishing him with her portrait, and thus enabling him to present to the British public a striking likeness, engraved in the first style of art, in a cheap and popular form. The Illustrated Exiiibitor AND MAgazine of ART is published in Weekly Numbers, price Twopence each. A new and improved series, under the title of the IllusThated MAGAZINE of ART, will be commenced on January 1, price 3d. in a meat cover; when, in addition to numerous Engravings in the text, each Number will contain a flue Engraving worked on Plate Paper; and with No. 1 will be presented, gratis, a splendid View of the Interior of St. Paul's Cathedral, during the Interment of the late Duke of Wellington; printed upon fine Plate Paper, measuring eighteen inches by thirteen. This Engraving will be worth four times the cost of the Number of the MAGAxixe of Altt. THE ALTAR of The Household; or, Domesric Woosnip. Part J. will be published on the 1st of January, 1853, pricels. This work will contain a Series of Services for the Family, adapted for every morning and evening throughout the year, viz., portions of Scripture, Prayers and Thanksgivings, suitably adapted to each other, to which will be added short practical comments to explain the subjects read, or enforce the duties enjoined. This work will be edited by the Rev. Dr. Harris, Principal of New College, assisted by a band of eminent divines in London and the country. The SELF AND CLAss ExAMINER IN Euclid, containing the Enunciations of all the Propositions and Corollaries in Cassell's Edition, for the use of Colleges, Schools, and Private Students, is now ready, price 3d. CAssell's ELEMENTs of ARITH MET1c (uniform with Cassell's Euclid), is now ready, pricels. in stiff covers, or 1s. 6d. neat cloth. The Answers to ALL THE Questions in Cassell's ARITHMRT19. for the use of Private Students, and of Teachers and Professors who use this work in their classes, is preparing for publication.

Pricels., beautifully printed, super-royal 8vo., THEAUNCLE TOM'S CABIN ALMANACK : or, The Abolitionist MEMENTo Fon 1853.-The most complete work on the question of slavery that has hitherto been published. Everybody who has read “Uncle Tom's Cabin" should possess themselves of a copy of this book, which more than verifies all the statements in Mrs. Stowe's thrilling narrative. This work is splendidly Illustrated by George Cruikshank, Esq.; J. Gilbert, Esq.; W. Harvey, Esq.; H. K. Browne, Esq. (“Phiz"); and other eminent artists; and contains upwards of 70 pages super-royal 8vo., replete with the most stirring incidents—Lives of Escaped Negroes; the Workings of the Fugitive slave Law; Anecdotes, Narratives, and Historical and Descriptive Accounts of American Slavery. The sale already is very large, 30,000 copies having been disposed of within three weeks. The Illustrated Exhibiton ALMANAck, for 1853, containing upwards of Thirty beautiful Engravings, price 6d. Porulan Educaton ALMANAck, Notices and Essays on Education, od. TEMPERANCE ALMANAck, Tale by the Authoress of Uncle Tom, &c., od. Paorestant Dissenteks' ALMANAck, with new Historical Notices, &c. 6d.

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In learning to draw it is of great importance to have distinct and clear ideas on the subject of the directions of the lines that are to be drawn. For example, if you were told to draw a line inclining either to the left or to the right of a vertical (up and down) line, or in other words leaning either to the left or to the right upon a horizontal (sea level) line, you would naturally and properly ask how much to the left or how much to the right must I draw it? In this case, you see, precision and accuracy of expression are necessary to enable you to draw the line required; and where words fail to convey exact notions on the subject of the directions of lines, we must employ apparatus or geometrical construction. The word angle is generally employed in speaking of the directions of lines, and by making angles of various kinds we are enabled to give clear and definite explanations of these directions. The word angle originally meant a corner. For instance, a block of wood having six square faces (which is properly called a cube by geometers) has evidently eight corners (see fig. 13). These corners are called solid angles, and are only seen in perspective in fig. 13, but with such solid angles we have nothing to do at present; we must first call your attention chiefly to plane angles, that is, angles which can only be properly represented or drawn on a flat surface. Now each face of the cube has four corners, which are called the plane angles of a square; the ordinary definition of a plane angle being this: “When two lines drawn on a plane or flat surface in different directions meet in a point, they are said to make an angle at that point.” For drawing purposes it is necessary to include in this definition curve lines, as well as straight lines; hence, the figures represented in fig. 14 are all considered as plane angles. A plane angle is simply such a one as you can correctly draw upon paper.

Fig. 13.

Fig. 14.

The terms horizontal and vertical have been already so far * plained, but it will be advisable to fix them in the mind by a more enlarged explanation. The horizon (pronounced hori zon) is the extreme boundary line or limit of vision on the earth's surface. To understand this clearly, suppose that you were out at se”.”” vessel, entirely out of sight of land, then the extreme boundary of the water as far as you can see, and whichever way you may look, where the sky and sea appear to meet, is called the horizon, from the Greek horos, a limit or boundary. The horizon, then, accord. ing to this explanation, is the circumference of a circle of which every point appears equally distant from the eye of the observer. Any straight line drawn from one point of the circumference of this circle to the opposite point, say from north to south, or from east to west, is called a diameter of the horizon; and any line parallel to a diameterofthehorizonor to a plane of the horizon, that is, to the circle itself, is called a horizontal line. This is the direction which the surface of stagnant water always assumes; it is the direction which the surface of water in any vessel, such as a tumbler, always takes and preserves inevery position of the vesselsolongas it remains in the vessel.

wroL. II.

The term vertical must now be explained, and this may be done at once by saying that it is the direction which the plumb-line or string of the plummetalways assumes when allowed to hang freely. Lest any reader should be unacquainted with this instrument, we shall explain it farther. Fasten any weight to the end of a string sufficiently strong to bear it, then fasten the other end of the string to a stout nailin a wall, or, what is better, in a cross beam in a roof or in a ceiling, then allow the weight to hang freely, and the direction which the string takes when it is completely at rest is the vertical. This is frequently called the perpendicular direction as well as the vertical direction, but the former term alone is not strictly correct, according to the definition given by geometers; if, however, we say perpendicular to the horizon, it is then complete, and as accurate as the term vertical. The directions of straight lines that are either vertical or horizontal, will now be easily understood and recognised; but between these two directions there are an infinite variety of others, which may all be exhibited to the eye by taking the weight in the hand and gradually drawing the string out of the vertical position, by keeping it stretched until it reaches the horizontal position. Now there is some method by which any position between the horizontal and the vertical may be determined and remembered for future use. This method consists in the measurement of angles. To understand this it will be necessary to observe that when two lines form an angle, the magnitude of the angle does not depend upon the lengths of the legs or lines which form the angle, but upon the degree of divergence (bending back) or separation between them. Thus, in fig. 15, the angle B A c is the same as the angle D A E : that is, the angle is the same whether the legs A c, A B, be used, or the legs A E, A D. Let it be remembered also that when an angle is spoken of by three letters, the letter at

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the point where the legs meet is always put in the middle between the two letters placed at a distance on the legs, or at their extremity. Thus the letter A is put in the middle between the letters c and B, or the letters E and D, in saying the angle B A c or d ar. An angle may be made up of other angles, or may be a part of another angle. Thus in fig. 16, the angle A B c is made up of the two angles A B D and D B c, and the angle D B c or the angle A B D is a part of the angle A B c. All plane angles formed of straight lines are divided into three kinds, right angles, acute angles, and obtuse angles. When a vertical line meets a horizonta! line, the one line is said to be perpendicular to the other, or at right angles to it. The vertical line may meet the horizontal line at one extremity only, as in fig. 17; in this case, they form only one right

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from the Lat. acutus, having a sharp edge, as in fig. 21. An angle which is greater than a right angle is called obtuse, from the Lat.

obtusus, blunt, as in fig. 22. When one straight line meets ano-
ther at any point between its extremities, it always makes either two
two right angles, as in fig. 23, one being acute, and the other obtuse.
When two straight lines cross each other, they always make either
equal to four right angles, as in fig. 24, two being acute and equal
to each other, and two being obtuse and equal to each Fig. 21.
and obtuse, are all that are spoken of in distinguish-
ing plane angles from each other. It may also be
about a point on one side of any straight line; and four right angles
all the space about a point on both sides of it. Hence all the space
together equal to four right angles.

Fig. 22. Fig. 23. Fig. 21.

A circle is well defined to be a figure such that its boundary, called its circumference (from the Lat. circumferens, carrying distant from a fixed point within the figure, which is called the Centre (from the Greek kentron, a point), see fig. 25. The straigh *adius of the circle (from the Lat. radius, a rod, or spoke of a wheel), see fig. 25. The straight line drawn through the centre,

right angles, as in fig. 18, or two angles which are together equal to
four right angles, as in fig. 19, or four angles which are together
other. Thus, the three kinds of angles, right, acute, s
observed, that two right angles occupy all the space
made by any number of straight lines meeting in a point, are
G
\ S. *>=
- D
ound) or outline, is a line everywhere, that is, at all points, equally
line drawn from the centre to the circumference is called the
Fig. 25. Fig. 26. Fig. 27.

and terminated both ways in the circumference is called the dia-
meter of the circle (from the Greek diametros, that which is
measured out, or across), see fig. 26. The diameteris, of course,
double the radius of a circle. Any straight line drawn through two
points in the circumference, and not passing through the centre, is
called a chord (from the Greek chordé, and Lat. chorda, a string of
a lyre), see fig. 26. The half of a circle bounded by the diameter,
is called a semicircle (from Lat. semi, half, and circle), see fig. 27.
The half of the circumference is called a semicircumference, see
fig. 28. The half of a semicircle is called a quadrant (from the
Lat. quadrans, antis, a fourth part). Sometimes this term is
applied to the half of the semicircumference.
The method employed by practical geometers to express clearly
the magnitude of any angle, and consequently the direction of any
line, is the following: they divide the whole circumference of a
circle into three hundred and sixty equal parts called degrees,
marked thus, 360°. Now, the magnitude of any angle is expressed
in words by stating the number of degrees which this angle takesin,
by supposing that the angular point is the centre of a circle, and
that the legs of the angle intercept a certain number of degrees on
the circumference of the circle; see the following instrument, fig.
29, used for this purpose, explained at page 50, col. 1, vol.I.

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ference bounding each of these parts, contains 90°, or the fourth
part of 360°. Whence, a right angle takes in, or contains 90°;
and a right angle is commonly described as an angle of 90°, that
is, “an angle of ninety,” or, “an angle of Fig. 30.
ninety degrees.” The half of a right angle, is
therefore an angle of 45°; and the third part of
a right angle is an angle of 30°. An angle
composed of a right angle and a half, is an angle
of 135°; and so on. You will see, therefore,
that the size of the circle, and the lengths of the
legs of the angle, cannot affect these numerical
statements of the angles; for a right angle, if its
legs be extended. will take in as fully and
completely one-fourth part of the circumference of a circle of
forty feet radius, as it will take in one-fourth part do one of only
jour inches radius. An acute angle is, from what we have seen in
the previous definitions, an angle of less than 90°; and an obtuse
angle, one of more than 90°. Two right angles make an angle of
180°; but in this case, the angle becomes a straight line, and the
angular point the middle of that straight line, when the legs are
equal. Such, then, is the method of measuring the slope or inclina-
tion of one line to another, or of two lines making an angle; and
such is the method of measuring the inclination of a rail-road, or
of a hilly-road of uniform slope, to the horizon or the level ground
above which it is raised. The parts of a degree are expressed in
minutes; that is, every degree is divided into sirty equal parts
called minutes; whence, half a degree is called 30 minutes, and is
marked 30'; a quarter of a degree, 15'; and so on. Again, every
minute is subdivided into 60 equal parts called seconds; whence
half a minute is called 30 seconds, and is marked 30”; a quarter
of a minute, 15"; and so on... Small account, however, is taken of
these minute subdivisions in drawing.

The lessons on practical geometry in vol. I. of this work will be very useful to you in the art of drawing, and you are recommended to study them attentively, after reading this lesson. More instructions, however, will be given as occasion arises, when treating of perspective, architecture, and ornament, but the lessons on practical geometry will explain to you some points of greater length than it will be necessary to repeatin our lessons on drawing. The following definitions of geometrical figures are those of which the knowledge is absolutely requisite for your future studies.

Lines are said to be oblique to one another when they are drawn in any . not ...: f / ; I right angles with each other.

*...* the breadth be- / _tween two or more lines remains always the same, the lines are called parallel lines, whether they becurved

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When a triangle has its three sides all unequal it is called a scalene triangle. Scalene means unequal-legged. A triangle is also said to be right

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angled when it has one right angle ; it cannot have more than one right angle. - An obtuse-angled triangle is that which |\ has one obtuse angle; it cannot have more than one | \ obtuse angle. - - ‘SV An acute-angled triangle is that which \ has three acute angles; it cannot have less than these, otherwise it would become one or other of the preceding two triangles. A square has four sides and four angles, all its sides being equal, and all its angles right angles. An oblong has all its angles right angles, and has four sides, but the sides are unequal. It is sometimes called a long square, but this is an absurd name. No side of a square can be longer than another. A rhombus, or lozenge, sometimes called a diamond, or diamondshaped figure, has all its sides equal, but its angles are oblique, i.e., not right angles. A rhomboid has its sides equalin pairs, opposite to one another; but

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the one pair is not equal to the other pair, and its angles are oblique. These four figures are all parallelograms (pa-ra-lel’.o-gram), the first two being right-angled parallelograms—the square having this distinction, that all its sides are equal. All other four-sided figures are called trapeziums, or trapezoids, the trapezoid having one pair of its opposite sides parallel, and the trapezium none of its sides equal nor parallel. Trape'zium means a table or slab. A five-sided figure is called a pentagon; and a sixsided figure, a hexagon. A seven-sided figure is a heptagon; a figure with eight sides is an octagon; one with nine sides is an enneagon; and one with ten sides is a decagon. . Accent the first syllable in all these names, thus: pen'-ta-gon, deko-a-gon. When the sides are all equal, and the angles also all equal, the figures are said to be regular; as a regular pentagon, a regular hexagon, &c. When the sides are not all equal, or the angles not all equal, the figure is called irregular; as, an irregular heptagon, decagon, &c. A many-sided figure is sometimes called a multilat'eral figure, and a triangle, a trilat'eral figure, and four-sided figures are very commonly called quadrilate'rals. By fixing these definitions in your memory, you will get distinctly-shaped images in your mind, which will last you through your whole life, and become clearer the oftener you refer to

-oIt is scarcely possible to overrate the importance of geometrical

information to the ornamental and architectural draughtsman; and it is of nearly equal utility in all landscape drawing which comprises buildings, the buildings being actually constructed by strict geometrical rules. The architect, indeed, cannot work without them. Should we not, then, in our representations or drawings bear this in mind 2 We cannot fail to do so, if the principles be well understood, and it is only then that we can be said to draw with unimpeachable accuracy.

True, it is not absolutely necessary that you should study Euclid along with these lessons; but if you have any inclination for the study of geometry at greater length than can be given in these lessons, we cannot too strongly advise you to follow that inclination. For, if well followed up, you will thus make an acquisition of which the importance cannot be conceived until it be attained. The proportions of form and of quantity regulate all the works of nature. The old Greeks assigned to the Graces and to the Muses the origin and the patronage of the arts. There is, indeed, a verbal connexion between the Graces and gratitude; and it may be truly said that all the arts are grateful as well as graceful. They return to the student, in the amplest manner, every attention he bestows upon them; and from them, at last, he receives his crown of laurel, Endeavour to commit the greater part of this lesson to memory, as we shall have to refer to it from time to time throughout this course. Give it your early and best attention; and read, also, the lessons in practical geometry already mentioned. If you make yourself well acquainted with geometry, you will find in drawing natural objects that you know the leading characteristics of an immense nun.ber of forms at a glance, while in the most complex forms and outlines you will be able to dissect them, and to separate one component part from another with comparative ease. Read, again, what is said of outline in the first lesson, and you will see that, as outline is necessarily composed of lines, geometry must so far govern outline,—not, indeed, rigidly in all cases, as nature possesses a free hand; but you will still find yourself compelled to go to geometry for the forms and principles which nature handles with such freedom. In our next lesson we shall treat of the drawing of curved and mixed outline. In the meantime, we recommend you to read both these lessons over again, and to practise them with the utmost care until you acquire a readiness in them which will be a prelude to future success.

L ES SON S IN LAT IN.—No. XXXVII. By John R. BEARD, D.D.

DEVIATIONS IN THE THIRD CONJUGATION. 7. Perfect with Reduplication,

THE reduplication in the verbs, the first vowel of whose stem is i, o, or u, consists in the repetition of the first consonant of the stem, together with that vowel; in the rest, however, it consists in the repetition of the first consonant of the stem, together with e. The compounds have, in the perfect, no reduplication; except those from curro, 1 run; disco, I learn; and posco, I demand. i. Cado, cadere, cecidi, casum, to fall, happen. Compounds are in cido, cidere, cidi, cisum, thus: occido, I go down, die; incido, I fall on (E. R. incident); recido, I fall back : the rest want the supine; as, concido, concidere, concidir to fall together, ii. Caedo, caedere, cecidi, caesum, to cut, to kill. Compounds are in cido, cidere, cidi, cisum; as, occido, I put to death. iii. Cano, canere, cecini, cantum, to sing. Compounds in cino, cinere, cinui; so concino, to sing together; and occino, to sing inauspiciously; the rest are without perfect and supine. iv. Curro, currere, cucurri, cursum, to run. Most of the compounds in the perfect have, but oftener have not, the reduplication. v. Disco, discere, didici (no supine, but disciturus), to learn; so the compounds, as perdisco, perdiscere, perdidici, to learn thoroughly. vi. Fallo, fallere, fefelli, falsum, to deceive; fallit me, it. escapes one, I am not aware, I am unconscious. The participle falsus, false, is mostly employed as an adjective; compound, refello, refellere, .# (no supine), to refute,

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