For instance, suppose it to be required to find the value of 375 cwt. 3 qrs. 21 lbs. at £4 14s. 6d. per cwt. First find the value of 375 cwt. at £4 14s. 6d. per cwt. by the previous method. This will be done as follows: 375 cwt. would cost at £1 per cwt. and South America, which are connected with each other by the The relative position of the greater part of the places mentioned in this lesson may be ascertained from an inspection of the figures in the preceding page, or the Map of the World in page 144. Our readers will find it useful, when studying our Lessons in Geography, to make a map of the world on a large scale according to the directions given in the last lesson, and to mark in the position and name of each place, as soon as it occurs for the first time. LESSONS IN ARITHMETIC.-XXIX. PRACTICE. 8. Definition.-Any fraction of a quantity the numerator of which is unity, is called an aliquot part of that quantity. Thus 4s. and 6s. 8d. are each aliquot parts of a pound, being respectively and of it. In finding the value of any given compound quantity from the given value of any other given quantity of the same kind, a convenient form of multiplication, called Practice, is often employed. It depends, as will be seen, upon the principles of fractions and the judicious choice of aliquot parts. 9. EXAMPLE 1.-Find the value of 3589 cwts. at £1 11s. 6d. per cwt. This might be effected in various ways. We might, for instance, reduce the money to farthings, multiply by 3589, and then reduce the result to pounds, shillings, and pence; or we might reduce the money to the fraction of a pound, and then, multiplying by 3589, reduce the resulting fraction to pounds, shillings, and pence. But we may also evidently obtain a correct result if we divide the whole sum into portions, multiply each of these portions separately by 3589, and then add the results together. This we are able to do, simply by the aid of aliquot parts, as follows: Since 6d. is of 1s., 3589 cwts, at 6d. each will cost of 179 9 0 89 14 6 7 9 6 £4 10s. which is of £1 48. " 6d. of £1 2 7 3 Therefore 375 cwt. 3 qrs. 21 lbs. would cost . £1776 6 1 } The fraction being of a farthing. If, however, the fractional part of the farthing were put in terms of a fraction of a penny, the result would be written £1776 6s. 1d. 11. Sometimes, by inspection, we can see that one or both of the compound quantities which are expressed in different denominations can be simply expressed as a fraction of one of the denominations. This will much simplify the operation. EXAMPLE. Find the value of 24 cwt. 1 qr. 9 lbs. 5 oz, at £2 5s. 6d. per cwt. Here it is readily seen that 1 qr. 9 lbs. 5 oz. is of a cwt. 13. In employing the method of practice, a good deal must be left to the student's judgment as to dividing the compound quantity into separate portions, so that the aliquot parts sta be the most convenient. Tables of aliquot parts of £1, of a hundredweight, an acre, etc., are drawn up for the convenience of persons much engaged in calculations; but the learner had better trust to his memery 3 149 and knowledge of fractions in solving any question of the ki with which he may be concerned. Hence 3589 at £1 + 3589 at 10s. + 3589 at 1s. + 3589 EXERCISE 48.-EXAMPLES IN PRACTICE. Find the cost of S. d. 2 1 2 5 8881 per yard. 4 103 per yard. per yard. per yard. 0 18 6 8 88 6 3 11 1 8 11 4 per cut 14. 271 cwt. 1 qr. 14 lbs. at truest sense, we often see moral courage connected with material enrichment and outward honour. Moreover, let it be remembered that it requires far more moral courage rightly to use the gifts bestowed upon us, than to ignore them altogether. It is easier to deny ourselves all indulgences, and by stoical process of endurance to learn to do without them, than to regulate our life aright whilst we move amid its blessings, and moderately enjoy its outward good. Moral courage is, for the most part, no sudden attainment. To some natures it is doubtless far easier of practice than others. Where, for instance, there are strong passions and a weak will, it is manifest that the power of strong desire being co-existent with weak power of resistance, the battle of right and duty will be very severe and trying indeed. But in all cases an energetic sense of moral courage is the reward of persevering endeavour. Just as in the military campaign, courage grows by frequent encounters with the foe, and the standing firm amid the belching fires of iron hail. Thus the veteran is steady, where the young recruit is almost unnerved. The continuous conflict with those temptations which beset the higher nature, not only brings experience, but nerves the heart and renders victory easier in times to come. Moral courage may, indeed, become the habit of our life, and like all habits, good or bad, become a second nature. There can be but little doubt that there is a secret respect for moral courage in the heart of men, even where they differ with regard to the necessity for the course pursued by those who are perhaps defying public opinion and incurring odium and danger. The majority may not believe the course pursued to be either wise or necessary, but they admire the virtue which the circumstances develop, and they honour the man even when they disagree with his actions or opinions. On the other hand, a want of moral courage in the pursuit of the most commonly confessed good exposes the discovered coward to contumely and disrespect. EVERY noble and beautiful life will be found to have in it the power of a brave courage. So seductive are the temptations to an inglorious ease on the one hand, and so bitter the jealousies of a begrudging envy on the other, that every path of earnest life-pursuit of duty will be found a difficult one. In such a course Moral courage should, therefore, be practised with steadfastfear will faint and lose, courage will fight on and win-will battle ness, and any discovery of our own weakness should be punished heroically against the native love of ease in the heart, and over- as men punish refractory horses, by making them pass again the come the envies and jealousies of its fellows in the world. He objects which at first they shied. The feeling that we had not who is craven enough to fear criticism, or to dread detraction, moral courage enough to deny our own dominant desires, or to face need not expect to reach the goal of his ambition, for there is our opponents' ridicule, will, even when not made public, rankle nothing worth having which a faint heart ever won, or ever will in our own hearts, and we shall even, when we do not lose the win. respect of others, cease to respect ourselves. Cowardice is Courage is essential to all the noble and virtuous ambitions always contemptible, never, however, so much as when it is not of life, because in the pursuit of these mankind often have to the result of a sudden temptation, when indeed we have become deny themselves temporary pleasures and material profits. habitués in non-resistance to what seems expedient and pleasant. Nothing tests character, or tries endurance, more than a per- Want of moral courage lies at the base of sensuality, self-indulsistent course of conduct which pays allegiance to truth and gence, and many other forms of degradation. Had these inhonour, at the expense, perchance, of pleasure and repose. cipient desires been crushed by a brave hand, had the fibres never been permitted by permissive indulgence to thicken into the cord which holds and binds, but been snapped at once, then the higher nature would have triumphed over the lower. The heroes of moral courage are not far to find, neither are they few, and we should both brace the nerves of our own character, and also in turn inspire imitation, as well as admiration, in others, if we contemplated the career and character of those noble men and women who fill the roll of departed heroes and heroines. The world wants brave men in every department of duty, and all success worth the endeavour to attain, and likely to produce permanent satisfaction when it is attained, must be sought and won under the inspiration of a lofty moral courage. In thus treating of courage, it will at once be seen that moral courage is our theme. This, however, in no sense need be glorified, as it often is in moral theses, at the expense of physical courage; for this, too, is an enviable blessing, and may be weakened or strengthened by our own neglect or endeavour. It must not be depreciated, because courage in the moral nature is of a higher and nobler kind. Moral courage is connected with human life in every sphere of temptation. Sometimes the bristling guns of inimical forces, such as contempt, aversion, and derision, make us afraid; but the balls, though they may hurt, cannot destroy the brave, and they will in time reach their end amid the rewards of honour. But the time-serving and the timorous will turn back, and will in the end be despised by those who at first opposed and ridiculed them. They altogether lose both the honour of the race and the reward of the prize. Moral courage is not alone the prerogative and appanage of some leading and time-honoured men, it may be the possession of the humblest. A beautiful statue is just as beautiful in a coal-cellar as in a drawing-room; and a bravely heroic life is just as glorious in itself, whether it be in a mechanic's workroom, or in some field of wider fame. Moral courage consists in serving the right, and never succumbing to mere might. It consists in unflinching resistance to the temptations of the popular and the profitable, the easy or the expedient, if principle is to be sacrificed, or the shrine of truth to be desecrated. It will be seen at once that moral courage does not require the sacrifice of pleasant things when they can be fairly won and innocently enjoyed. Evil does not reside in material possessions themselves, or in human honours, but in the sacrifice of truth, which sometimes accompanies the attainment of them. In the LESSONS IN DRAWING.-XIX. WE now enter upon the study of the human figure, a subject of other subject in the whole range of art that so thoroughly depends upon the judgment, the eye, and the power of the hand. There are very few practical rules which can afford us any help, except the general rules of proportion, and some knowledge of anatomy, which is indispensable; beyond these there is very little besides the all-important principle of arrang ing the work: therefore, before we give the rules relating to the proportions of the human figure, or say anything upon its anatomical construction, we must again repeat some of our former observations respecting the necessity of arrangement. Our pupils will remember how earnestly in the early lessons we advised them first to decide where the lines are to be drawn, and not to attempt the finished drawing until the positions of the lines are satisfactorily determined: the success or failure of their efforts will depend upon how far they follow or neglect this fundamental course of proceeding. We trust this once more repeated appeal to their practical sense and judgment will suffice, being ourselves assured that if they are really in earnest in their desires and endeavours to draw the human figure well, they will show their appreciation of this advice by following it out to the letter; for both master and pupil must now remember they have entered upon a noble, and at the same time a difficult subject. It We have just observed that it is indispensably necessary to be acquainted with the various proportions of the human body, and to have some knowledge of anatomy. To these points we wish for a few moments to direct the attention of our pupils, and to place before them some powerful reasons why this course is so necessary. must be borne in mind that the human figure in its action is almost independent of any fixed laws; it is seen in every possible position, and under every form of expression; it is seen at rest, and in violent action; it is seen in its strength and in its weakness; it is seen in old age and childhood, in delicate womanly beauty and manly vigour. Then in addition to this there is the face, the index to the mind, subject to every variety of change resulting from inward emotions of joy or sorrow, revealing the best and the worst feelings of the heart-passion, despair, love, hatred, malice, revenge -and though last, not least, the various gradations of mental power, from the highest intellectuality to imbecility and madness. Surely here is a field for study which in its extent and grandeur has no rival. Now we wish our pupils thoroughly to understand that we are in earnest in what we are about to lay before them, and they must be in earnest also in their application. We are desirous to impart something more than a superficial knowledge of the human form; we wish to go thoroughly, as far as we can, into the subject, but at the same time it is not our intention to write a work upon anatomy in our drawing lessons; instead of this, we will recommend our pupils to study carefully the lessons upon this and kindred subjects which are to be found elsewhere in the pages of the POPULAR EDUCATOR. In these they will find quite sufficient information for all they may require. Our object is only to open out a path for them to pursue, to point out other sources of information, and direct them in the way of applying the knowledge thus gained: therefore any of our pupils who do not care to enter into the subject to the extent we propose may stop when they think fit; but as to those who desire to make their knowledge really useful for all practical purposes-and there are many engaged in the mechanical arts who will find it a great acquisition to be able to draw the figure well-we will en deavour not to disappoint them. When we consider how much this branch of art is required in decorating, stonemasonry, modelling, wood-engraving, and many other occupations, including all kinds of designing, we feel it incumbent on us not to allow so useful an addition to their education to be passed over lightly, and oblige them to lay our lessons aside, disappointed in not finding the instruction they require. We will first give the relative proportions of the whole form, as represented in Fig. 119. The skeleton may be properly considered the framework upon which the whole body is built, and by which it is strengthened and supported; the proportion and height, the efficiency and freedom of the whole structure, depend principally upon the right formation of the skele ton; this hard and solid framework may be considered the timbers and beams of the superstructure, and the muscles which cover it are the ropes and pulleys for moving it; thus the framework is for strength, the muscles for action, and these determine the visible and varying outline of the body. Taking the head as a standardthat is, from the crown to the chinthe whole length of the figure of a man may be considered as measuring seven and a-half or eight heads; of a child, the proportion will be according to its age; one of seven or eight years old may be allowed five and a-half heads; and an infant, nearly four. When the arms and hands are fully extended horizontally from the body, and if the distance between the tips of the fingers from the right hand across to the left be measured, it will be found equal in length to the whole body, so that a well-proportioned man can stand in a square frame and be able to touch the sides of the square respectively with his head, his feet, and the extremities of his fingers. The distance from the top of the shoulder-that is, from the head of the humerus, a (the upper bone of the arm)-to the elbow, b, is the same as from the elbow b to the first knuckle of the hand, c; the same distance occurs horizontally between the outer parts of the shoulders from a to d; from the top of the sternum (breastbone), e, to the navel f, the same; from the lower part of the breast-bone, g, to the pubis h (the bone across the lower part of the body), the same; thence to the top of the patella i (or small bone on the knee, generally called the knee-cap), the same; and from the lower part of the patella k to the instep m, the same. The knowledge of these uniform lengths, so repeatedly occurring, is a very material help in drawing the figure, preventing many doubts and difficulties. In the same way that the skeleton establishes the proportion and construction of the body, so in like manner does the skull, by its peculiarities of character and diversity of form, assist us to define and classify peoples, nations, and tribes, and also to decide upon their different intellectual capabilities. All must have noticed how very different the size of the human cranium or braincase is, when compared with the face, to that of the brute creation; and also that the head itself, comparatively speaking, undergoes very little change from growth: likewise that the brain almost reaches maturity at a very early period, and consequently the head of the infant is considerably larger in proportion to its body than when it has arrived at manhood; the cause of this is to be attributed the incompleteness of the lower part, which, as the teeth grow, expands from a greater extension of the jaw; when in old age the teeth have fallen out, and the face has contracted again, it resembles in many respects that of the child, excepting for the falling in of the lips and the wrinkling of the skin. Thus as the child grows the face becomes elongated, and the proportionate difference between the length of the face and the depth from the forehead to the back of the head is less striking. The characteristic difference in the human head between the Grecian standard, as usually seen in ancient sculpture, and that of the negro,exists in the facial line. (See Fig. 120.) Draw a line from the lower part of the ear to the closing of the teeth in front, and from thence draw another to touch the outer projection of the forehead; this last line is called the facial line, and the two together form the facial angle the angle at e. The more acute this angle is, the nearer it approaches that of the Fig. 121. lower animals; the most desirable angle, as characteristic of the | higher powers of intellect, judgment, capability, and we include beauty also, is that of about 80°. The Grecian sculptors, in representing their gods, reached 90°, the right angle, and in some instances they went even beyond this. We will not enter into any argument as to whether this modification of the facial angle indicated greater strength of mind and wisdom: it certainly has not been found to represent the standard of excel a lence in man. As the facial angle formed by these two lines decreases, so we approach the negro, and when it is farther diminished we descend to the projecting jaws and smaller brain of the brute creation. (See Fig. 121, the facial angle of the cow.) These remarks are merely hints for the pupil, showing him the course he is to pursue in studying the human head. To go into a classification of the skulls of various tribes and nations, and point out the remarkable differences between them, is not our immediate object; to show there are these varieties, and to establish a standard as a base of construction, is all that is necessary : we leave our pupils to discover these differences for themselves, and resume our more legitimate subject the method of drawing them. Now before we say anything about the proportions of the head and face, we wish to make a few observations upon the kind of drawing which belongs to the human figure more than any other subject, and which will become more evident as we proceed. In drawing the human form, the term outline must be used in a far wider sense than that in which it is generally considered when it relates to inanimate objects or ornaments. Within the boundary line of any portion of the human form, be it face or limb, there is as great an amount of character and form to be expressed as in the outward or marginal line itself, and we cannot consider any one to be proficient who has not the power fully to represent it. The foreshortenings and projections of the body, and the unequal surfaces upon every part, arising from muscular action, as they press forward towards the eye, require an amount of anatomical knowledge which any one who attempted to draw them, without possessing, would soon discover to be indispensable. To confine our practice to the mere outline of the human figure, would give but a small idea of what is meant by drawing it; children do no more than this. To represent an advancing limb, or an uneven surface when placed directly before us, is quite another affair to that of representing the surface or limb when it is turned a quarter round, and is seen in profile. To acquire this pretend to sleep, he sleeps really (réellement). 5. Will you take a walk this morning? 6. I would do so with pleasure, if I had time. 7. Have you become acquainted with the physician? 8. I have not yet become acquainted with him. 9. How many questions have you asked (a) the child? 10. I asked him many questions. 11. Have you asked him if he had studied his lesson ? 12. I did not ask him. 13. Will not that little girl do her best to learn her lesson ? 14. She will do her best to learn it. 15. Of what food do you make use when you are ill? 16. We make use of bread and rice. 17. Have you forgotten to bid farewell to your mother? 18. I had not forgotten it; I intended to go to her house this afternoon. 19. With whom have you become acquainted? 20. With the bookseller. 21. Do you not keep those ladies waiting? 22. I do not keep them waiting, they are not ready (prêtes). 23. Do I make you wait? 24. You do not make me wait. 25. done so (le). 27. Have you sent them out? Have you left your children in your room? 26. I have not 28. I have not sent them out, I have let them remain where Have you made purchases this morning? 30. I have made none, I have no money. 31. Has the servant made a fire in my room? 32. He has made one. 33. Will you do your best to come to-morrow ? 34. I will do my best to come early. 35. We travelled yesterday forty leagues in sixteen hours. they were. 29. SECTION LXIV.-IDIOMS: FAIRE USED REFLECTIVELY AND UNIPERSONALLY. 1. Faire is also used in the sense of playing the part of, or pretending to be. Il fait le grand seigneur, 2. Faire also means to matter, Cela ne fait rien, Cela ne vous fait rien, You travelled twenty miles in ten self. hours. We shall take a walk. I asked him several questions. That child pretends to be asleep. We will do our best to see him. [voir. Nous ferons notre possible pour le VOCABULARY. Aise, glad. Aliment, m., food. Crédit, m., credit. Demand-er, 1, to ask. Dorm-ir, 2, ir., to sleep. Etude, f., study. Se fâch-er, 1, ref., to be- Négociant, m., come angry. chant. mer Rarement, seldom. Réuss-ir, 2, to succeed. Riz, m., rice. Faire l'aumône, to give Quart, m., quarter. 1. Seriez-vous bien aise de faire connaissance avec ce monsicur? 2. J'en serais bien aise. 3. Ce cheval fait-il une lieue en un quart d'heure ? 4. Il a fait ce matin une lieue en douze minutes. 5. Leur avez-vous fait des questions? 6. Je leur en ai fait [Sect. XLI. 11; § 135 (7)]. 7. Quelles questions leur 8. Je leur ai demandé s'ils avaient fait des avez-vous faites ? emplettes. 9. Vos élèves font-ils des progrès dans leurs études? 10. Ils n'en font pas beaucoup ils viennent rarement à l'école. 11. Si vous étiez chez vous, feriez-vous semblant de dormir? 12. Je ne ferais certainement pas semblant de dormir. 13. Pourquoi ne faites-vous pas entrer ce mendiant ? 14. Ma mère vient de lui faire l'aumône. 15. Le négociant fait-il usage de son crédit? 16. Il en fait usage. 17. De quels aliments ce malade fait-il usage? 18. Il fait usage de riz et de bouillon. 19. Faites-vous votre possible pour réussir? 20. Je fais tout mon possible. 21. Avez-vous fait entrer ces enfants, ou les avez-vous fait sortir ? 22. Je les ai laissés où ils étaient. 23. Vous avons-nous fait attendre ? 24. Vous nous avez fait attendre plusieurs heures. 25. Si vous faisiez attendre dames, elles se fâcheraient. EXERCISE 122. ces 1. Does that child pretend to read? 2. He pretends to read. 3. Does not that gentleman pretend to sleep? 4. He does not 3. Se faire mal conjugated reflectively, means to hurt one's Se faire is used reflectively in the sense of the English verbs to become, to turn. It is also used with the significa tion of the words cause, have, get, etc. Se faire takes étre as its auxiliary [Sect. XLIV., § 46]. |
