LESSONS IN DRAWING. No. IV. LINEAR DRAWING—{ Car Tard,, CURVE lines, very different in appearance, may be produced by various combinations of arcs of circles. The three following illustrations (fig. 50) are examples of the outlines of architectural mouldings. The first, consisting of a waving line, in a moulding called an ogee. It is also called the cima recta, when it is concave or hollow in the upper half of the curve; and cima reversa when the upper half is convex. According as you imagine the white part or the shaded part to be the moulding, you may see each of these in the figure. Undulations (from Lac. undulatus, in the form of waces) are the characteristic of grace, whether in motion or in form; and it may be justly said that wherever the waving line is seen, there is elegance and beauty. Arrangements of straight lines are capable of much elegance; but the waving line, by itself, is beautiful. There are two extremes to be avoided in drawing outline, viz., frigid precision and fantastical looseness; the latter is especially to be avoided; the former is of the nature of Geometry. When the pupil allows his hand to wander,-drawing lines and figures at random, he may, as it were, by accident, cause his lines, here and there, to assume a graceful appearance; but nothing like true art will ever flow from his pencil. On the other hand, if he be accustomed to draw his lines too precise, too severe and rigidly correct, they will never correspond to the lines we see in nature. And it should be deeply impressed on the pupil's mind, that "to represent nature is, and ought to be, the aim of all art. Drawings executed in the precise style may be compared to language clothed in formal phraseology. Grammatical correctness may be there, but elegance and feeling are absent. At the same time it is of the utmost importance to have a perfectly clear and distinct idea of what you are about to do. This consideration, indeed, led us to choose artificial rather than natural forms for the pupil's early practice. These he should construct, and endeavour to know all about them; and when he can do them well, he will be prepared to engage in the more difficult task of correctly representing the outlines of natural objects, with all their elevations and depressions, without reference to rule. In drawing the following figures, no instruments are to be used. This we cannot too often repeat to those who wish to acquire freedom of hand. If you have the black board, with the notches cut as directed in the last lesson, they will sufficiently indicate the directions of a horizontal and a perpendicular line; so that even a ruler should be considered as inadmissible in drawing these figures. A sheet of paper carefully folded to a straight edge, and then doubled over on itself, will give you a right-angle which will occasionally be useful as a test. In fig. 51, which is as simple as can well be imagined, you have the outline of a shallow basin. In drawing it, mark a few points: first, one at the middle point of the edge, and then another at the Fig. 51. Architectural Mouldings. The last of these three figures is a variety of the hollow moulding called a scotia. In practical works on architecture, and in Robertson's "Treatise of such Mathematical Instruments as are usually put in a Portable Case," the geometrical methods of producing these curves are shown at length.* The centres of the component circles are marked with a small cross in the figures above given. Similar combinations might be made of ellipses and of the other conic sections; but to enter into any detail on these methods would be beyond our present purpose. It is sufficient to observe that curves composed of portions of the circle, may be multiplied to any extent, by arranging them so that every two adjoining arcs of the circle shall have a common tangent at their point of junction. The waving line which is placed first, was called by the great painter Hogarth the line of beauty. The construction of these curves will be shown in the Lessons on Architectural Drawing. VOL. II. lowest point of the curve; next mark the terminal points of the edge, and a few in the curve. Drawing the lines thus indicated, and adding the lower portion of the figure, it is completed. Fig. 52. In fig. 52, which is the outline of a cup or vase, you will be 44 258 enabled easily to draw the form by following the same method as Fig. 53. In fig. 53, which represents a vase or jar, an ellipse is employed as the basis of its form; the lines which sweep into the main curve are also elliptical. In this example you should begin by indicating the central perpendicular line by points, and having determined the length of the ellipse, point off the breadth, and draw the curve. In pointing the curves required to complete the figure, mark the extremities of each, and take care that the points which you place in the curves are opposite to each other; for placing them truly in this position will assist you greatly in drawing the curves. The round moulding at the bottom of this figure is called a torus (from Lat. torus, a soft heap or protuberance). The square tablet which supports the torus is called a plinth, (from Gr. plinthos, a brick or tile.) In fig. 54, which is another outline of a vase, you will observe the points, the centres of the circles which combine in forming the principal curve, are marked; but, observe, these are placed in the figure only for your information, and, of course, they are not to be drawn by you in making a copy. You should copy all the preceding figures on a large scale, and endeavour to attain both steadiness and freedom of hand in drawing them, without pedantic stiffness or geometrical rigidity. Fig. 55. copy than any of the preceding. First mark out a square by points; then mark the points bisecting the sides of the square, as truly as you can; next draw the four lines which are dotted in the figure, joining the angles, and dividing the square into four parts; marking then the central points of the square, the other points may be considered as on the circumferences of three circles described from this centre. The whole figure is now readily seen to be entirely composed of circular lines. It is the outline of what is called a quatre-foil, or quatre-feuille (from Fr. quatre, four, and feuille, a leaf), and is very commonly employed as an ornament in Gothic architecture. In copying the figures in this lesson, you will do well to make the copies of a larger size. Of course, unless the larger copy be drawn in porportion, it must be deemed a failure. By drawing in proportion, we mean that each part of your copy should have the same relation to any other part, that the corresponding parts of the original have to each other. The word proportion is often used in such a manner as to show that the speaker has but a vague apprehension of its meaning; an explanation of its real signification will, therefore, not be out of place in this lesson. Proportion is the equality of ratios between two pairs of objects, or the lines which represent them. The ratio of each pair is ascertained by comparison, and the comparison must be made between two things at a time. Where you have three or more things to compare together, the comparison must still be made two by two; and we must compare them in those qualities or parts in which they correspond; that is, by some property which they have in common; for until we have done this we can know nothing about their ratio to each other. As a familiar example, compare a rod of wood with a bar of iron. In comparing their respective weights we take a quality, gravity, or their tendency to press downwards, which is common to both. In comparing their bulk, we take the product of the length, breadth, and thickness of the one, and compare it with that of the length, breadth, and thickness of the other; we thus compare that which constitutes the bulk of the one, with that which constitutes the bulk of the other. In comparing their lengths, we find the number of feet or inches in each, and compare these numbers, which gives the ratio of their lengths; and so on with respect to any other qualities or properties which they have in common. Now, in all these comparisons, the ratio of any two things of, like kind is ascertained by means of numbers. The numbers expressing the weights enable us to judge of the rod and bar with respect to weight; the numbers expressing the feet and inches in each, enable us to determine the ratio of their lengths; and the numbers expressing their respective bulks, enable us to determine the ratio of their sizes. Now, if two lines in one figure have to each other the same ratio which two lines have to each other in another figure, these four lines are said to be proportional. Hence proportion in the art of drawing is, as in everything else, a comparison betweer ratios, which may be expressed arithmetically, or by numbers. When we say that a living or statuary figure of a man is not well-proportioned in form, we mean that his limbs have not the same ratio to each other, or to the whole body, which those of the average of men have. Perhaps his arms are too long, or his legs are too short. Now, we come to this conclusion by making a ready comparison in our own minds between the ratio of the length of his arms to that of his body, and the ratio of the length of the arms to that of the body in some standard or model figure existing in the mind's eye. For instance, the ratio of the number of feet and inches in the length of the arms of the supposed figure to those in its whole length, is greater than the ratio of the number of inches in the length of the arms of the ideal or model standard figure to those in its whole length; and the instantaneous mental comparison of these ratios in the two figures, has rendered the disagreement in the proportion self-evident. In the supposed perfect ideal figure, the length of the arms measures a certain number of inches, and the whole height of the figure measures another certain number of inches; and because the length of the arms of the other figure has not the same ratio to its whole height, it is reasonably considered as not well-proportioned. A comparison of numbers, measured by the eye, has settled the question in this instance. It is, in fact, decided arithmetically, and, whether consciously or unconsciously, it must be so decided by every one who forms a judgment in such a case. Actual measurement, or the use of instrumental methods of ascertaining proportions, is forbidden to the student of drawing. Fig. 55 is an example which you will find it more difficult to He may measure in comparing what he has done with his model; but in what he is going to do, his eye and his hand are the only assistants which he must call to his aid; and the eye may be so trained, and become so accustomed to judge of proportions, that the use of an instrument would be far more embarrassing to the drawer than the want of it; for a just appreciation of proportion is not at all dependent on the hand. This power manifests itself in a ready perception of the mind. The eye is the instrument through which the mind operates; and a skilful hand expresses proportion in a manner which one unskilled cannot reach. Nevertheless, artists skilful in many essential points, sometimes show a great deficiency in their judgment of proportions; especially if they are debarred the use of those instrumental means by which they have been accustomed to determine them. A just appreciation of proportion seems to be in some a natural faculty; in others, it is the growth of experience. Like the rest of our faculties, either natural or acquired, if it be judiciously developed and cultivated, it is sure to operate with readiness and accuracy. The following exercises are proposed to the pupil, in order that he may see, as has been said, how proportions are ascertained and expressed by numbers. Draw a straight line in any direction, horizontal, perpendicular, or at any angle, and divide it into two equal parts by a mark at the middle point, see fig. 56. Divide each of these halves again into Fig. 56. two equal parts by marks at their middle points. When you are satisfied in your own mind that you have divided these by the eye as accurately as possible, then test them by a pair of com passes or dividers: a pair of spring dividers is best adapted for marking off distances. In this instrument, the spring causes one of its legs to press strongly outwards against a small head which turns on a screw passing through one leg and fixed on the other, as seen in fig. 57. The same figure shows, also, another form of the Fig. 57. АА dividers, where a screw fastens one leg to a circular arc which passes through it; but the latter form does not admit of such nice adjustment as the former, which contains the spring. You may test the four divisions of the straight line without a pair of compasses, by folding a piece of paper exactly the length of the line first into two, and then again into two, when the three division-marks will be at the folds. As another exercise, make four marks at equal distances, on a straight line, beginning at one end, and ending at the other; and test them by the dividers. Then, divide a straight line into three, five, seven, and nine equal parts, beginning at one end, and ending at the other. When you can do these exercises, so as to stand the test of measurement, then proceed to divide an angle into a similar number of equal parts; as an example, see fig. 58. Fig. 58. the angular point, and turn an arc with the other; if your divisions To test the divisions of an angle, set one leg of the compasses at The Apollo Belvedere. The sum of what we have said amounts to this: as proportion depends on lengths and breadths, convexities and concavities (heights and hollows), so, in order to preserve proportion in your drawings, you must observe how many times one length or breadth is contained in another; what multiple or submultiple one angle is This is a representation of a celebrated statue discovered at Porto-Ancio, under the reign of Nero, which takes its designation from the Belvédère (Fine-view) of the Vatican at Rome, where it was placed, and where it now remains. of another; and in curves, what ratio the radius of curvature in one mihi nunquam persuaderi potuit, animos dum in corporibus essent curve, has to the radius of enrvature in another. mortalibus, vivere, quum exissent ex iis, emori; quicquid transiit temporis, periit; quum rure rediero, statim te adibo; Pompeius multique alii clari viri foede perierunt; i quo te fata vocant: abüt ad deos Hercules; nunquam abisset, nisi quum inter homincs esset, eam sibi viam munivisset; muros turresque urbis praealtum mare ambiebat. ENGLISH-LATIN. They came to me unseasonably; I will not go to my uncle unseasonably; I have passed over the book placed before my eyes; good men die, but not perish; good men will never perish; who not to pass thy life in silence; you must go against (oppose) base doubts that great men may come forth from cottages? take care ness; they have gone to the town; when they return (will have returned), they will come to your house; Romulus is said to have gone to the gods; dost thou think that Romulus went to the gods? the children will go to meet their parents; the general takes care not to be surrounded; I fear the city will be surrounded by the multitude of soldiers; they might go; they might have gone; I will go; wilt thou go? he was going home when his father was returning; I might have gone; I must go home; my father must go to meet the citizens; I am about to go to bed; dost thou not know that I am about to go to bed? they have gone to bed. 6. Queo, quire, quivi, quitum, to be able;' nequeo, nequire, nequívi, nequitum, to be unable. Nequeo is merely queo and ne or non. These two verbs follow eo, ire, ivi, itum. Many parts of these verbs appear but seldom, and not at all in good prose; these parts are omitted in the following table : SUBJUNCTIVE. IMPERATIVE. SUPINE. GERUND. In the same way the compounds, as, exeo, I go out; abeo, I go from; re-d-eo, I go back; so also ven-čo, ven-ii, ven-itum, ven-ere, to be sold (imperative, participle, and gerund wanting); ambire, to go round, surround, canvass, is an exception, as it strictly follows the fourth conjugation, thus: ambio, ambiam, ambiebam, ambirem, ambiens; ambivi, ambitum, ambitus (the substantive has the i short, ambitus, us), ambiendum. The compounds in the perfect throw out the v, and when s follows, vi; as, abii, for abivi; abisti, for abivisti; so abiit, abierim, abisse, abissem; venii, venieram, veniero, &c. The IMP. 2. FUT. quivero INFINITIVE. nequívĕram quivissem nequivissem nequívěro PERF. quivisse, nequivísse PARTICIPLE. other parts are wanting, or rarely occur. 7. Fio, fieri, factus sum, to be made, to become. This verb stands as the passive of facio, I make. INDICATIVE. Of the simple verb, the passive is used only in the third person singular; as, itur, literally, it is gone, that is, one goes, they go; ibatur, they were going; itum est, they went. By the passive infinitive, iri, in union with the supine, is formed the infinitive future passive, as amatum iri. But the compounds with a transitive force, like other transitives, have a complete PR. passive, e. g., praeterire, to go by; praetereor, I am gone by; praetereor, praeteriris, praeteritur, praeterimur, praeterimini, praetereuntur, praeteribar, and so forth. Ambior (ambiuntur, 1. FUT. fiam, &c. ambiebar) in the passive, also, follows the model of the fourth conjugation. VOCABULARY. Adire, to go to; circumire, to go round; interire, to go between, perish; obire, to die; perire, to perish; transire, to pass over; emoti 3, to die; casa, ae, f. a cottage, hut; angustiae, arum, f. a narrow pass; excessus, ûs, m. a going out, beyond (E. R. excess); praealtus, a, um, very high; aliquando, some time; foede, foully, shamefully; intempestive, unseasonably, out of time; obviam (ob and via), in the way of, against; ire ob, to go to meet; sero, late, too late; priscus, a, um, old; prisci, the ancients; turpitudo, inis, f. baseness; cubitus, ûs, a bed; ire cubitum, to go to bed. EXERCISES.-LATIN-ENGLISH. Qui ad nos intempestive adeunt, molesti saepe sunt; pleraque ante oculos posita, transimus; abeunt hirundines hibernis mensibus; corpus mortale aliquo tempore interire necesse est; pereunt aliquando innocentes; quis neget? nocentes tamen saepius pereunt; omnes homines summâ ope niti decet ne vitam silentio transeant; quis dubitet quin ex casâ vir magnus exire possit? potius sero quam nunquam, obviam eundum est audaciae temeritatique ; omnes cives militibus, qui e bello domum redibant, laeti obviam ibant; si ita naturâ paratum esset, ut ea dormientes agerent quae somniarent, alligandi omnes essent, qui cubitum irent; illud erat insitum priscis esse in morte sensum, neque excessu vitae sic deleri hominem ut funditus interiret; angustias Themistocles quaerebat ne multitudine hostium circumiretur;' Romulus ad deos transisse creditus est; Augustus obiit septuagesimo et sexto actatis anno; SUBJUNCTIVE. fiam, fias, fiat, PARTICIPLE. factus, a, um, FUT. PASS. faciendus, a, um FUT. ACT. futurus, a, um The other parts are wanting, or only of infrequent occurrence. The compounds of facio formed from verbs, retain facio in the active voice, and in the passive follow fio; e. g., calefacio, calefacere, calefeci, calefactum, to make warm; calefio, calefieri, calefactus sum, to be made or become warm. The compounds with prepositions, however, have in the active ficio, ficere, feci, fectum; and in the passive, ficior, fici, fectus sum; as, perficio, perficere, perfeci, perfectum; in the passive, per ficior, perfici, perfectus sum. Only a few compounds with prepositions, together with the regular forms, have, in the pas sive, forms from fio; e. g., confit for conficitur, confieri; defit, defiat. VOCABULARY. Exulcerare, to make sore, or ulcerous; generare 1, to beget, generate; retinére 2, to hold back, retain; eloqui 3, to speak out, utter; cogitato, with thought, advisedly; crebro, frequently; fataliter, according to fate; interdum, sometimes; civiliter, like a citizen, politely, elegantly adversus, a, um, turned towards, opposite; rho, the Greek letter ti definitus esse fataliter, to be fore-ordained by fate. 1 EXERCISES.-LATIN-ENGLISH. Nach Abzug aller Kosten blieb ihm nichts übrig, als einige Groschen. After deduction of all costs, there remained for him nothing but a few groats. Man wird das Geld schneller los, One gets rid of money faster Intueri solem adversum nequimus; decóri vis ea est ut ab honesto non queat separari; risus interdum ita repente erumpit ut eum cupientes tenere nequeamus; dic utrum queas an nequeas mecum ire; quum hostes exercitum nostrum fundere nequirent, in castra munita se receperunt; quum dux precibus retinere militem nequiret, vim adhibendam censuit; saepe imperiti medicí ea quae sanare nequeunt, 1. Der Arzt hat mir gerathen, so wenig wie möglich auszugehen. 2. exulcerant; quum Demosthenes rho dicere nequiret, exercitatione Emilie arbeitet so wenig wie möglich, um die Feinheit ihrer Hänte zu fecit ut planissime diceret; ex inimico cogita posse fieri amicum; erhalten. 3. Die Kinder sollten jeder Zeit so wenig wie möglich unbe. nemo fit casu bonus; si fato omnia fiunt, nihil nos admonere potest ut cautiores fiamus; nemo ignaviâ immortalis factus est; permultum interest utrum perturbatione aliquâ animi, quae plerumque brevis est, an consulto et cogitato fiat injuria; homo quod crebro videt, non miratur, etiamsí cur fiat nesciat; non ita gene rati a naturâ sumus ut ad ludum et focum facti esse videamur, sed ad severitatem potius et ad quaedam studia graviora atque majora; prudentior fis, accedente senectute; nego esse fortunam, et omnia quae fiunt, quaeque futura sunt, ex omni aeternitate definita dico esse fataliter; quâ de causâ dicebas omnia quae fierent futurane essent, fato contineri? fieri potest ut recte quis sentiat, et id quod sentit, polite eloqui nequet. ENGLISH-LATIN. schäftigt sein. 4. Er spricht so wenig, um keine Aufmerksamkeit zu erregen 5. Ferdinand ist jezt ganz wenig zu Hause. 6. Auf der lehten Reise hatte ich ganz wenig Gepäck bei mir. 7. Wollen Sie etwas Fleisch haben ? 8. Ja, aber nur ganz wenig. 9. Es bleibt ihm nichts übrig, als zu betteln, oder zu arbeiten. 10. Es bleibt nicht Anteres übrig, Sie müssen jest handeln. 11. Von all seiner Habe blieb ihm nichts übrig, als ein Stück Land. 12. Diese Rose blich allein von allen Blumen übrig. 13. Er blieb allein vor dem ganzen Regimente übrig. 14. Ich kann diese traurigen Getanken nicht los werden. 15. Um seine falschen Freunde los zu werden, muß man ihnen Geld bergen. 16. Gewähren Sie ihm seine Men cannot look at the sun turned towards them (adversus sol); | Bitte, damit Sie ihn los werken. 17. Jcht ging der Spaß von Neuem the virtues are so (ita) bound together (inter se), that (ut) they cannot be separated; often we cannot restrain laughter, however 18. Der Kalk von der Mauer geht los. 19. Als der Krieg wieder (quamvis with sub.) we wish it (would); say whether you can or losging, jeg er mit einem großen Heere in das Feld. 20. Das Gewehr cannot go with us; there are many diseases which cannot be healed; ging los, als er es ergreifen wollte. can Demosthenes pronouncer? I cannot pronounce r; by exercise, I hope to be able to pronounce r; if thou wishest to become learned, learn diligently; an enemy is often made out of a friend; men do not become good or bad by chance; if all things took place (were done) by chance, foresight would be useless; dost thou think that any one through sluggishness becomes immortal? by old age, men become wiser; some philosophers were uncertain whether all things (omnia ne) took place by fate; I am convinced that nothing takes place by fate. We have now gone through what are generally called "The Irregular Verbs," and find them to be in number seven, namely, 1. Possum; 2. Edo; 3. Fero; 4. Volo; 5. Eo; 6. Queo; 7, Fio. If we add the compounds of volo (nolo, malo) and of queo (nequeo), we make the number ten. LESSONS IN GERMAN.-No. XXXIII. Los (loose apart, &c.) when combined with verbs, has a variety of significations. Its exact force in any given place, is best determined by the context, as, lesbinden, to unbind; lesgehen, to break out; losreißen, to tear asunder. Ein Gewehr losbrennen; to fire (off) a gun. Das Gewehr ist losgegangen; the gun (went off) discharged (accidentally). Der Streit geht wieter les; the contest is beginning again. EXERCISE 69. Aufmerksamkeit, f. at- Heer, n. host, army; tention; Borgen, to lend; raise; Kalf, m. lime; Ocpact', n. baggage, er Zufriedene braucht nur ganz wenig, um glücklich zu sein. The desire to be free and inde- mains to free-minded men The contented (man) needs but los. 4. 1. The physician advised my sister to stay at home as much as possible. 2 A teacher should always keep his scholars unemployed as little as possible. 3. The orator spoke with great enthusiasm, in order to raise the attention of his auditors. Most travellers take with them as little luggage as possible. 5. Will you have some apples? 6. Thank you, Sir, I have quite enough. 7. Augustus is now very much at home, hence we may go to him. 8. There is nothing left for him but submission to his destiny. 9. I had no other resource left me than to fly from the enemy. 10. Of all his property, nothing was left but a garden. 11. I cannot get rid of my cold. 12. Grant the request of this false friend, then you will get rid of him. 13. Who broke the foot of the table? 14. The servant broke it off, when she cleaned the room. 15. Frederic the Great marched at the head of his army to the war. 16. The gun went off accidentally, or he could have shot the hare. ! SECTION LXVII. Weije way, manner; as, auf diese Weise, in this way (on this wise). It is often compounded with adjectives and nouns, and used adverbially. Scherzweise, jestingly. Glüdlicher Weise, fortunately; in a fortunate manner. ($ 105.) I. Unter vier Augen, literally, under four eyes; i. e. secretly, in confidence; between two persons. Man hat es mir unter vier Augen gesagt; it has been told to me in confidence. Amts'geschäft, n. offi- ness; about; EXERCISE 70. Persian Gewalt'sam, violently, Perser, m. Persian ; to (adj.); draw away, to take |