Fig. 128. be used. Some have drawn their figures as low as seven heads, others as high as eight and a-half and nine, and occasionally, even more; the heroic cannot be less than eight. But certainly, whichever of these units of measurement we may choose, if the one employed represents the head large in proportion to the body, it is not a distinctive mark of beauty; this defect may be noticed amongst Laplanders, Tartars, and some other nations. Consequently, if we desire to give dignity and beauty to the figure, we must endeavour to avoid littleness of style, which unavoidably belongs to lowness of stature, unless, of course, the character of the subject demands it. The Apollo Belvedere, a celebrated ancient Greek statue, is eight heads and a half high. Rubens, a painter who flourished in the reign of Charles I., occasionally drew his figures eight heads high; but there is generally an appearance of heaviness in most, of his figures, which may be partly attributed to their being only seven heads high. Michael Angelo, the Florentine painter and sculptor, who was born in 1474, did not restrict himself to any fixed proportion, but would employ that which he deemed the best for his purpose. Eight heads might have been his lowest standard, but Professor Camper says, "C. Vander Mander has proved that in some of the figures of Michael Angelo, the size is equal to nine, ten, nay twelve heads, in order to communicate more grace to a stooping attitude." It is generally allowed that eight heads is the better proportion for a figure than one of a less number. Men above six feet high, for the most part, reach that standard, some a little more. The reason of lowness of stature in men is, in most cases, attributable to the shortness of their legs; and this leads us to another proportion proper to be observed, namely, that the distance from the top of the head to the pubis should be equal to that from the pubis to the feet; the face to be one-tenth, and the foot one-sixth of the figure. Therefore, adopting the above standards of proportion, the heights of the figures we draw are determined by the number of the repeated measurements of the head; two figures may be drawn, each on a separate piece of paper, and although the one may not occupy a larger space than the other, yet it is according to the size of the head that we decide which is the tall man, and which the short. The next consideration connected with this part of our subject relates to the head and face alone, and the proportions of their parts relative to each other; a knowledge of these is as important as those of the body, but there is a difference in the use and application which must not be overlooked. No part of the whole frame is subject to such a variety of change and expression as the face. We look into it for a reflex of the mind; it is stronger than the arm in its power of repelling or attract ing those who seek to approach us; and the whole state of the mind, whether as friend or foe, is revealed in the countenance. In short, so keen are our detective powers when reading the signs depicted in the human face, that dissimulation must be a practised art before it can be thoroughly successful. The smile of some men is repulsive because it is not genuine, and we see that it is not; there is a raising of the upper lip and exposure of the teeth along with it, which betrays envy or malice. The kind. hearted man can frown only with his brows, and in spite of himself the generous feelings of his heart will linger about the corners of the mouth, slightly raised by the swelling muscles of the cheeks. Thus, in either case, the cha racter of the indivi dual, which is one of the most difficult things to conceal, will show itself; the most trifling acci dental circumstance will serve to reveal it, and he will be esteemed or disliked accordingly. When we reflect that the same features are capable of expressing opposite pas sions, such as jor and sorrow, love and hatred, compassi and revenge, we have to make the esta blished rules of proportion subservient to the end sought for. There are occa sions when these received regulations must be set aside when some particu lar passion or emotion is to be expressed. According to the scale of depar ture from true proportion, in like man ner does the ratio of 1 deformity increase. fin Deformity in the countenance ought only to be employed to express deformity of mind; and therefore, in order to be able to represent the bad passions, the rules of proportion must be learnt, that we may know when and how to break them. !! * When animal expression is associated with the human face, it degenerates into caricature, and although there are brutal passions found amongst men, and they are deeply imprinted on their countenances, yet those countenances must be humanised; for, notwithstanding the similarity of character which exists between the most degraded of mankind and the brute creation, we cannot go so far as to transgress the laws which regulate the human face as a whole, so entirely as to divest it of the higher nature belonging to man, and substitute that of the animal. We select an example from Lavater's "Essays on Physiognomy" to illustrate our observations, "The head of Judas, after Hol bein" (Fig. 128). It is the personification of selfishness, deceit, and hypocrisy, combined with other latent and bad qualities that nurture them and contribute to their development. It of the nose; the third at the base of the nose; and the last ending with the chin: thus making the whole head four noses in length. The width of the head is equal to three-fourths of the length. Bisect the second division in E, and with the distance EA describe the circle A D F C, and draw CD through E at right angles to A B. On the third division, with F as centre and F B as radius, describe another circle; then, by drawing the curve upon which the ears are placed between 2 and 3, the oval will be made. Divide the line C D into five equal parts; the eyes will be placed under the second and the fourth divisions. Divide the lowest division from 3 to 4 into two equal parts; the 2 line G will mark the position of 3 E was necessary to employ these features to represent the man, for, however revolting they may be, the painter is justified in the extremity of the means by the intensity of the character to be portrayed. Lavater says of it: "Who can persuade himself that an apostle of Jesus Christ ever had an aspect like this, or that the Saviour could have called such a countenance to the apostleship? And whose feelings will be offended when we pronounce a visage like this base and wicked? Who could place confidence in such a man?" Mr. Charles Bell, in his "Essays on the Anatomy of Expression in Painting," says: "To brutify a human countenance, we have only to diminish the forehead, bring the eyes nearer, lengthen the jaws, shorten the nose, and depress the mouth. If this be done, no expression of individual features will give elevation to the character. A breadth and squareness in the lower part of the face is quite consistent in a vulgar head with a certain representation of strength and manliness; but if the eyes be diminished and the space between them contracted, the expanse of the human countenance is lost, and there can remain no dignity of expression." We have gone thus far into our subject to show that when the proportions of the figure and face are properly understood and practised, the draughtsman must not rest there; he has only acquired the means of proceeding; afterwards, we repeat, he has to employ them for purposes of a higher kind than those which belong to mere imitation: these refer to the mind, and how he can best express its intentions, knowing the influence it has in controlling the actions of the body. If we examine the practice of the ancient Greeks, we shall find that their proportions were generally arbitrary. They considered the oval to be the most perfect form of the human head; this proportion may be adopted in some cases where the ideal is intended, but it is not the rule in nature; such a standard would make the crown of the head too high, and they, in order to relieve this, reduced the length from the front to the back. We will give these proportions, although to employ them invariably would produce a mannerism that B Fig. 130. 3 the under lip. The distance from line G to the division of the mouth is one-third of the line from 3 to G; the width of the upper lip somewhat smaller; the ears equal to the length of the nose (between the divisions 2 and 3). These proportions may, no doubt, assist us in drawing the head; where nature deviates, we must make the necessary alteration, otherwise we shall fail in representing individual character. The most remarkable point of difference in the shape of the head amongst nations especially, and frequently between individuals of the same nation, is in the facial angle (the inclination of the face from the base-line of the skull, rejecting the lower jaw). In the profile of the negro (Fig. 130) we find this angle, Fig. 129. A B C, much more acute than that of the European (Fig. 131). In the former it is about 50°, and in the latter about 70°. We give but these two examples as representing the extremes of the human family, between which the various degrees of intellectual capacity exist. We have already remarked that where this would be extremely objectionable, and in portrait painting they would be altogether useless. (See Fig. 129.) Draw a perpendicular line, A B, of the required length of the whole head, and divide it into four equal parts. The first of the several divisions will be seen at the root of the hair; the second at the bridge а Fig. 132. angle becomes still more acute, we leave the hu man and take up the brute creation; on the other hand, where the angle increases, then we approach the ideal conceived and practised by the ancients (Fig. 132). It is very evident that they avoided everything that was deemed characteristic of the brute when they represented their gods or heroes; thus, by enlarging the mean angle common amongst men, they felt that they had increased those distinguishing attributes which marked the difference between the intellectual and the brutal; and then again, when the subject was a satyr or a faun, the sensual was indicated by a decreased angle. No one will question the truth of these prin ciples, since they are founded upon nature. 3. In the first conjugation, the subjunctive is in the singular, similar to the present of the indicative. Exception: allerje vais, que j'aille. 4. The first and second persons plural of the subjunctive, in the four conjugations, are the same as the corresponding persons of the imperfect of the indicative. The third person plural is like the corresponding person in the indicative present. Exceptions: avoir, subjunctive, nous ayons, vous ayez, ils aient; savoir, nous sackions, vous sachiez, ils sachent; être, nous soyons, nous soyez, ils soient; faire, nous fassions, vous fassiez, ils fassent; aller, ils aillent; vouloir, ils veuillent; valoir, ils Je veux que vous lui parliez, I wish you to speak to him. Je désire que vous arriviez à temps, I wish you to arrive in time. 9. When the first verb expresses fear or apprehension, the verb preceded by que must also be preceded by ne, which, however, has no negative sense [§ 127 (3), § 138 (4) (5) (6)]. Je crains qu'il ne tombe, I am afraid lest he fall. 10. After craindre, to fear; appréhender, to apprehend; avoir peur, to be afraid; trembler, to tremble, pas is used in connection with the ne, when we wish for the accomplishment of the action or occurrence expressed by the second verb [§ 138(7)]. Je tremble qu'il n'arrive pas à I tremble that he may not arrive in I require you to give him that. J'exige que vous lui donniez cela. Artisan, m., mechanic. | Empêch-er,1, to prevent. | Moulin-à-scie, saw-mill, ments. warehouse. EXERCISE 137. 1. Que voulez-vous que nous fassions? 2. Je désire vous fassiez attention vos études. 3. Ne craignez-vous pas que la pluie ne vous empêche de sortir? 4. Nous craignons fortement que la pluie ne nous empêche de remplir nos engage. 5. Doutez-vous qu'il soit chez lui maintenant? 6. Je doute qu'il y soit, il est déjà dix heures. 7. Exigez-vous qu'il parte de bonne heure? 8. Je m'étonne qu'il ne soit pas déjà parti. 9. Aimez-vous mieux que je vous rende ces brace lets? 10. J'aime mieux que vous me les payiez. 11. Votre voisin craint-il que son enfant ne sorte? 12. Il craint qua ne tombe dans la rue. 13. Ne désirez-vous pas que vos élèves vous obéissent? 14. Je souhaite qu'ils m'obéissent et qu'ils obéissent à leurs professeurs. 15. Ne craignez-vous pas que cet artisan ne tombe malade? 16. Je crains qu'il ne tombe malade, car son atelier est très-malsain. vous pas qu'il soit obligé de travailler? 18. Je regrette qu'il 19. Ne dé soit obligé de travailler au-dessus de ses forces. sirez-vous pas qu'on lui apprenne cette nouvelle ? 20. Je désire qu'on la lui apprenne le plus tôt possible. 21. Votre père ne veut-il pas que vous achetiez un magasin ? 22. П veut que j'achète un moulin-à-scie. 23. Désirez-vous que je vous quitte? 24. Je désire que vous restiez avec moi. 25. Je veux que vous partiez ce matin. EXERCISE 138. 17. Ne regrettez 1. Do you wish me to speak to the mechanic? 2. I wish you to tell him to (de) come here to-morrow morning. 3 What do you wish me to do? 4. I wish you to bring me a book. 5. Do you not wish me to read your letter? 6. I wish you to read it and (que) give it to my sisters. 7. Does not your sister fear lest the rain may prevent her going out? 8. She fears that the rain may prevent our going out. 9. Do 10. I doubt his you doubt that your father be at home now? being there. 11. Do you require me to do my work now? 12 I wish you to do your work before going out (avant de sortir). 13. Do you not regret your being obliged to work? 14. I do not regret my being obliged to work. 15. Are you not astonished that he knows that? 16. I am astonished that he knows all. 17. Do you require me to pay him to-day? 18. I wish you to pay him to-morrow. 19. What would you have me do (see No. 1 of the above exercise)? 20. I will have you pay him immediately. 21. Do you fear lest the master punish your son? 22. I fear that he may not punish him. 23. What 24. I would have you say the would you have me say? truth. 25. Does not your father wish you to buy a house? 26. He wishes me to buy a storehouse. 27. Do you wish us to leave you? 28. I wish you to go away to-morrow. 29. Da you wish me to stay with you? 30. I wish you to stay here. 31. Do you wish me to tell him that news? 32. I wish you to tell it to him. 33. Do you wish your children to obey ther teacher? 34. I wish them to obey him. SECTION LXXII.-USE OF THE SUBJUNCTIVE. 1. A verb preceded by the conjunction que and one of the unipersonal verbs, il faut, it is necessary; il importe, it matters, it is important; il convient, it is proper, becoming; il vaut time. mieux, it is better; il plait, it pleases, suits; il se peut, il peut RÉSUMÉ OF EXAMPLES. se faire, it may be; il est juste, it is just; il est bon, it is proper; Le médecin veut-il que je boive de Does the physician wish me to drink il est nécessaire, it is necessary; il est important, it is important temps, l'eau ? Je consens que vous alliez le voir. Nous doutons que vous arriviez à temps. water? I consent that you go to see him. il est temps, it is time; il est indispensable, it is indispensable: il est à propos, it is proper; il est fâcheux, it is sad, it is a pity: il est urgent, it is urgent, or by another verb or expression Je crains que votre maitre ne vous I fear lest your master may punish plying necessity, will, or propriety, must be put in the su punisse. you. junctive [§ 127 (4)]. Il faut que vous restiez ici, Il est juste que vous soyez ré- You must remain here. 2. The unipersonal verb il est governs the indicative present or the future, when it is used affirmatively, and followed by 4. After certain conjunctions, afin que, in order that; quoique, although, etc. [see full list, § 143 (2)], the subjunctive is always used. Quoique vous fassiez, quoique vous disiez, 26. ever you may do, you will not succeed (réussir). 21. Whatever your brother may say, nobody will believe him (croire, ir.). 22. Must I write to you? 23. You must write to me. 24. Do you wish me to be ill? 25. I do not wish you to be ill. Do you require me to tell you that? 27. It is necessary that you tell me all. 28. Do you wish me to go to your house? 29. I wish you to go there. 30. Must I get up? 31. You must rise immediately (à l'instant). 32. Must your brother retire? 33. He must go to bed immediately. 34. It is time for him to go to bed, it is twelve o'clock. KEY TO EXERCISES IN LESSONS IN FRENCH. EXERCISE 50 (Vol. I., page 252). 1. Voulez-vous nous envoyer cette lettre? 2. Je veux vous l'envoyer, Whatever you may do, whatever you si vous voulez la lire. 3. Je veux la lire si je puis. 4. Pouvez-vous may say. me prêter votre plume? 5. Je puis vous la prêter, si vous voulez en 5. Other important rules on the government of conjunctions avoir soin. 6. Puis-je parler à M. votre père? 7. Vous pouvez lui will be found in § 143. parler, il est ici. 8. Avez-vous peur de l'oublier? 9. Je n'ai pas peur de l'oublier. 10. Voulez-vous les lui envoyer? 11. J'ai l'intention de les lui envoyer si j'ai le temps. 12. Est-ce que vous lui parlez de votre voyage? 13. Je lui parle de mon voyage. 14. Je leur en parle. 15. Pouvez-vous le lui communiquer? 16. J'ai envie de le lui com RÉSUMÉ OF EXAMPLES. Que faut-il que votre sœur fasse ? Faut-il que je lui écrive? What must your sister do? Must I write to him? Il est nécessaire que vous lui It is necessary for you to write to muniquer. 17. Voyez-vous vos connaissances tous les lundis? 18. Je écriviez. Il est temps que vous lui donniez son argent. [si tard? N'est-il pas fâcheux qu'il soit arrivé Il est certain qu'il est arrivé. Il n'est point certain qu'il se soit blessé. Restez ici jusqu'à ce qu'il arrive. Pourvu que vous finissiez à temps. Affaire, f., affair. him. It is time that you should give him his money. Is it not a pity that he arrived so late? It is certain that he is arrived. It is not certain that he has hurt himself. Remain here until he comes. 1. Que faut-il que je dise? 2. Il faut que vous disiez ce que vous avez entendu. 3. Ne faut-il pas que je finisse cette histoire ? 4. Il n'est pas nécessaire que vous la finissiez. 5. N'est-il pas à propos que je satisfasse mes créanciers ? 6. Il est à propos que vous le fassiez. 7. N'est-il pas juste que je vous paie ce que je vous ai emprunté ? 8. Il est juste que vous me le payiez. 9. Se peut-il que votre frère ait oublié sa famille. 10. Il ne peut pas se faire qu'il l'ait oublié. 11. Est-il certain que votre frère se soit oublié à un tel point? 12. Il est certain qu'il s'est oublié. 13. Il est bien fâcheux qu'il se soit oublié ainsi. 14. Resterez-vous jusqu'à ce que j'aie mis ordre à mes affaires. 15. Je resterai jusqu'à ce que vous les ayez réglées. 16. Ne faudra-t-il pas que je fournisse des provisions à cette famille? 17. Il faudra que vous lui en fournissiez, pourvu que vous en ayez. 18. Ne vaudra-t-il pas mieux que vous lui prêtiez de l'argent. que de la laisser manquer du nécessaire ? 19. Il vaudra mieux que nous lui en prêtions. 20. Que faut-il que nous fassions? 21. Il faut que vous portiez ce linge chez moi. 22. N'est-il pas temps que je me couche? 23. Il est temps que vous vous couchiez. 24. Faut-il que je me lève? 25. Il faut que vous vous levicz. EXERCISE 140. 1. What must our friend do? 2. He must remain at our house until I come. 3. What must our neighbour do? 4. He must put his añairs in order. 5. Is it not right that you should pay your creditors? 6. It is right that I should pay them. 7. Is it time for your little boy to go to school? 8. It is time for him to go to school, it is ten o'clock. 9. Must I write to your correspondent to-day or to-morrow? 10. You must write to him to-morrow morning. 11. Is it not a pity that your brother has torn his cap (casquette)? 12. It is a pity that he has torn it. 13. Is it necessary for your mother to finish her letter? 14. It is not necessary that she finish it. 15. Is it certain that your son has forgotten his money? 16. It is certain that he has forgotten it. 17. It is by no means certain that he has forgotten it. 18. Must you furnish money to that mechanic? 19. I must furnish him some, he has none. 20. What les vois tous les lundis et tous les jeudis. 19. Où avez-vous l'intention de les voir? 20. J'ai l'intention de les voir chez M. votre frère et chez Mlle. votre sœur. 21. Pouvez-vous l'y envoyer tous les jours? 22. Je puis l'y envoyer tous les lundis, s'il le veut. 23. Pouvez-vous me les donner? 24. Je puis vous les donner. 25. Qui veut leur prêter des livres? 26. Personne ne veut leur en prêter. 27. Votre libraire veut leur vendre de bons livres et de bon papier. 28. Est-il à la maison ? 29. Il est chez son frère. 30. Avez-vous tort de payer vos dettes? 31. J'ai raison de les payer. 32. Voulez-vous nous l'envoyer? 33. Je veux vous l'envoyer si vous en avez besoin. 34. Voulez-vous nous les donner? 35. Nous voulons les donner à vos connaissances. EXERCISE 51 (Vol. I., page 271). 1. Do you like bread or meat? 2. I like bread, meat, and fruit. 3. Have we peaches in our garden ? 4. We have peaches, strawberries, raspberries, and cherries? 5. Does your brother like cherries? 6. He does not like cherries much, he prefers plums. 7. Have you vegetables? 8. I do not like vegetables. 9. We have neither vegetables nor fruit. 10. We like neither vegetables nor fruits. 11. Do you go every day to your brother's wood? 12. I do not go every day. 13. Does your bring flowers ? sister bring the flowers? 14. She brings them. 15. Does your mother 16. She brings some every Monday. 17. Do you see General Bertrand ? 18. I do not see him, I see Corporal Duchêne. 19. Are your sisters weary? 20. My sisters are weary of studying. EXERCISE 52 (Vol. I., page 271). honte ni 1. Votre sœur aime-t-elle les fleurs? 2. Ma sœur aime les fleurs et mon frère aime les livres. 3. A-t-il tort d'aimer les livres ? 4. Non, Monsieur, il a raison d'aimer les livres et les fleurs. 5. Avez-vous beaucoup de fleurs dans votre jardin ? 6. Nous y avons beaucoup de fleurs et beaucoup de fruits. 7. M. votre cousin aime-t-il les framboises ? 8. Mon cousin aime les framboises et les fraises. 9. M. le capitaine aime-t-il les louanges? 10. Il n'aime pas les louanges. 11. Le jardinier vous a-t-il apporté des légumes? 12. Il m'a apporté des légumes et du fruit. 13. A-t-il honte de vous apporter des legumes? 14. Il n'a ni fatiguée? 16. Ma mère n'est pas fatiguée. 17. M. votre frère est-il peur de vendre des légumes. 15. Madame votre mère est-elle chez le colonel D.? 18. 11 demeure chez M. le colonel D., mais il n'est pas à la maison à présent. 19. Combien de pêches avez-vous ? 20. Je n'ai guère de pêches, mais j'ai beaucoup de prunes. 21. M. le capitaine B. aime-t-il les pêches? 22. Il aime les pêches, les prunes, les framboises et les fraises. 23. Allez-vous dans le bois de M. votre frère ? 24. J'y vais tous les matins. 25. M. le général L. est-il ici! 26. Non, Monsieur, il n'est pas ici, il est chez votre cousin. EXERCISE 53 (Vol. I., page 276). 1. Do you know that gentleman? 2. Yes, Madam, I know him very well. 3. Do you know from what country he is? 4. He is a Hun6. He speaks German, Polish, garian. 5. Does he speak German? before the revolution he was a captain. 9. Have you a wish to learn Russian, Swedish, and Danish. 7. Is he not a physician? 8. No, Sir, Russian? 10. I have a wish to learn Russian and modern Greek. 11. Do you know the gentlemen who are speaking to your sister? 12. I do not know them. 13. Do you know where they live? 14. They live at the house of your brother's upholsterer. 15. Have you not the history of Louis the Fourteenth in your library? 16. I have neither that of Louis the Fourteenth, nor that of Henry the Fourth. you wrong to learn Chinese? 18. I am not wrong to learn Chinese. 19. Do your companions learn the ancient languages? 20. They know 22. I know English, and I speak it. several ancient and modern languages. 21. Do you speak English? 23. Do you know the Englishman whom we see? 24. I do not know him. 25. He does not know me, and I do not know him. 17. Are WYCHANICS.—XIX. AIR FORCE THE PENDULUM-CENTRE OF OSCILLATION. Jos särke one another, they touch first in some , and the motion of these is usually comde whole body. Thus, when a carpenter strikes - vid is hammer, it only touches part of the head, but and acquired by this part is shared by the whole. 1, descia the blow be not true, the head alone may receive and fly off by itself, leaving the rest unmoved. , especially if the body struck be soft or brittle, and she velocity of the other be great, there is no time for the to be thus shared, and then the shape of the mass is wd or the part struck flies off as a chip. A homely illuson of this is afforded by a simple experiment which all way try. Nalance a small piece of card on one of the fingers of the left band, and lay a shilling on the top of it. By a sudden blow with the finger and thumb of the other hand the card may be jerked away without moving the shilling. Care must, however, be taken to strike the card exactly in the direction of its surface, as if it be tilted up or down the shilling will, of course, be jerked off. After a few trials, however, you may be pretty certain of success. The explanation is, that the motion of the card is so rapid that it has moved quite away before it has had time to communicate its motion to the shilling. There are many other familiar examples of this, some of which verge on the marvellous. If a bullet be fired at a door set half open, it will pass through the panel without shutting the door or moving it on its hinges. We may even go further, and, instead of a bullet, put a tallow candle into the gun and fire it at the door, it will be found to pass through instead of being smashed against it, as we should naturally expect. The velocity of the particles of tallow is so great that they have passed through the door before they have time to alter their relative position. So, if we fire a ball at a window, it will pass through the pane without cracking it, merely making a clean round hole. If, however, the bullet be nearly spent, or its velocity be not sufficiently great, the glass will be shivered to pieces. This, too, explains why a good skater will glide swiftly over ice far too thin to sustain his weight. His motion is so rapid, that before the ice has time to yield he has passed on to another portion of it. We see, then, that a certain amount of time is required for any motion to be imparted from one body to another. CENTRIFUGAL FORCE. If a lump of metal or other heavy substance be fastened to a piece of string, and then swung round and round, we shall find that the string is stretched with a strain which varies in proportion to the speed with which the body revolves. This strain is called centrifugal force, and is merely one of the results of the first H B law of motion. right angles to the motion of the body, no velocity is destroyed, the only alteration being in its direction. We constantly meet with illustrations of the action of this force. A can filled with water may be swung round the head without a drop being spilt. When the can is at its highest point, and therefore mouth downwards, the water is attracted towards the earth; but this attraction is more than overcome by the centrifugal force, and hence it remains in the can as if it were a solid. So, too, when rapidly turning a corner or running round the inside of a ring, we lean inwards. The body has tendency to move onwards in its previous direction, the feet are, however, compelled to move in another, and thus the head and body are thrown outward; to obviate this we lean in the contrary way. For the same reason, in a curve on a railway the inner rails are lower than the outer, so that the carriage inclines inwards, and thus removes the danger of its upsetting or tearing up the rails. A carriage is not unfrequently upset in this way while rapidly turning a corner. If a glass of water be placed on a small whirling table so that it can be rapidly turned, the water will leave the centre and rise towards the edges; it may even be scattered over the sides if the rotation be rapid enough. The same effect is seen if we rapidly stir a cup of tea, the level at the sides being above that at the centre. A practical application of these principles is seen in the cylinder, the bottom of which is perforated by a number of centrifugal drying machine. This consists of a large hollow holes. The linen is put into this, and it is then made to rotate rapidly. In this way it is closely pressed against the sides, and the water is given off and runs away through the holes in the cylinder. Linen can thus be rendered almost dry in a very short space of time. Another useful application of this force is seen in the "governors" of a steam-engine. These consist of two heavy balls suspended by rods, and when the speed of the engine is increased beyond the proper degree they fly apart, and in collar below them, and so doing raise a loose by a series of levers steam. a e Fig. 105. In Fig. 105 a, a represent the balls suspended by rods, which are hinged at b to the vertical shaft g. Motion is imparted to this by means of a strap, which passes round the shaft of the fly-wheel, or some other convenient part of the engine, and then round the driving-pulley, d. When the engine is moving too rapidly the balls fly further apart, and Let B (Fig. 104) represent a body re-by so doing raise the runner, e. This, by means of the bent volving round a centre A, and confined lever, k, works the rods, f, and thus partly closes the valve. by the string AB; its tendency at every Were it not for some such arrangement as this, there would instant is to continue in the same line be great danger of the engine at times moving so rapidly, that in which it is travelling at that instant, the fly-wheel would from the momentum of its particles be that is, to fly off at a tangent, as shivered to pieces. These balls keep the speed nearly uni along B C. We can easily prove that form; for if it diminishes much they fall, and thus open the this is the case, for if, when whirling throttle-valve to a greater extent and allow more steam to pass. a sling, we suddenly cut the cord or leave the end free, the stone will fly off in a straight line. Suppose D to be the point which the stone has reached at the end of one second, then B D will represent the space passed over, and therefore the velocity of B. This we can resolve into two parts, BF acting along the tangent BC, and BG acting along the direction of the cord. The former represents the velocity the stone has acquired, the latter is the force exerted by the string to keep it moving in a circle; this, therefore, represents the centrifugal force. We can thus easily see that the greater the velocity with which B moves, the greater will be the strain on the cord. If, for example, the velocity be so much increased that at the end of one second B is at E instead Fig. 104. of D, the tension of the cord will be represented by BH instead of BG. As, however, this tension always acts in a direction at The laws of centrifugal force are important, because they help to explain the motions of the heavenly bodies. The planets, when first made, were started from the hand of their Creator with a certain velocity. This produces a constant tendency to fly off at a tangent from their orbits. They are, however, restrained by another force, and that is the universal attraction of all bodies for each other. Gravity is but one manifestation of this: the earth draws the small bodies to it merely on account of its superior weight, and for the same reason the sun attracts all the planets; or, to speak more accurately, all are attracted to the common centre of gravity of our own solar system, which is situated very near to the sun. This attraction, then, constantly deflects the planets from the line in which they would otherwise move, and as a result of these two forces they describe ellipses, in one focus of which |