LESSONS IN FRENCH.-XXXI. France ? 12. I long to be there. 13. Does not your mother tarry too long? 14. She is very long in coming. 15. Have SECTION LVII.-IDIOMATIC PHRASES. you changed the forty-franc piece ? 16. I have not changed it 1. CHANGER [1, see § 49 (1)], used in the sense of to change, to yet. 17. Why have you not changed it? 18. Because your leave one thing for another, is followed by the preposition de : father has no change. 19. Have you the change for a guinea ? changer d'habit, de chapeau, etc., to put on another coat, hat, 20. No, Sir, I have only twelve shillings. etc. ; changer d'avis, to change one's mind; changer de maison, to move, to change houses; changer de place, changer de pays, SECTION LVIII.-RULES FOR THE PLURAL OF COMPOUND NOUNS. changer de climat, to go to another place, country, climate ; changer de nom, to change one's name. The student will per 1. We have given, in Section IX., rules for forming the plural ceivo that the noun following changer is not preceded by a of nouns, but, in accordance with our plan of not presenting too possessive adjective, like the noun of the English sentence. many difficulties at once, we have deferred until the present section the rules for the formation of the plural of compound Voulez-vous changer d'habit? Will you change your coat ? Ce monsieur a changé de nom, nouns. That gentleman has changed his name. 2. When a noun is composed of two substantivea, or of a 2. Changer contro means to exchange for ; changer pour, to substantive and an adjective, both take the form of the plural : change for, to get change for. un chef-lieu, des chefs-lieux, a chief place, chief places; un Voulez-vous changer votre chapeau Will you exchange your hat for gentilhomme, des gentilshommes, a nobleman, noblemen [$ 9 contre le mien ? mine? (1) (3)]. Changez ce billet pour de l'argent, Change that note for silver, 3. When, however, two nouns are connected by a preposition, 3. Tarder means to tarry, to be long in coming. Tarder used the first only becomes plural: un chef-d'ouvre, des chefsunipersonally, and preceded by an indirect object, means to long, l'œuvre, a master-piece, master-pieces [S 9 (2)]. to wish for. 4. In words composed of a noun and a verb, preposition or Votre sceur tarde bien à venir, Your sister is very long coming. adverb, the noun only becomes plural: passe-port, passe-ports, I me tarde de la voir, I long to see her. passport, passports [$ 9 (6)]. 5. Words composed of two verbs, or of a verb, and adverb, RÉSUMÉ OF EXAMPLES. and a preposition, are invariable: un passe-partout, des passeN'avez-vous pas changé d'apparte. Have you not taken another apart. partout, master-key, master-keys (S 9 (8)]. ment? ment? 6. We have seen [Sect. III. 4] that the name of the material Nous avons changé de maisons. We have changed houses. always follows the name of the object, and that both are united Votre frère a changé de conduite. Your brother has changed his con. by the preposition de. The name of the profession or occupa. duct. Contre quoi avez-vous changé votre For what have you exchanged your tion also follows the noun representing the individual, and the cheval ? horse? samo preposition de connects the two : un maître d'armes, 4 J'ai besoin de monnaie, pouvez. I want change, can you change me fencing-master; un maître de dessin, a drawing-master ; un vous me changer cette pièce de this twenty-franc piece ? marchand de farino, a dealer in flour ($ 76 (12), § 81 (4)]. vingt francs ? 7. The name of a vehicle, boat, mill, etc., always precedes tho Ce garçon a beaucoup terdé. That boy tarried very much. noun describing the power by which it is impelled, or the purIl nous tardait d'arriver. We longed to arrive. pose to which it is adapted; the name of an apartment, that of Il leur tardait de revoir leurs amis. They longed to see their friends the use to which it is appropriated. The connocting preposition again. is d : un moulin à vapour, a steam mill; un bateau à vapeur, a Il mo tarde de revoir la France. I long to see France again, steamboat ; un moulin à eau, a water-inill; la salle à manger, VOCABULARY. the dining-room ($ 76 (13), § 81 (5)]. RÉSUMÉ OF EXAMPLES. Lille et Arras sont les chefs-lieux Lisle and Arras are the chief places Blanc, -che, white. Maitre, m., master. again. des départements du Nord et du of the departments of the North Pas-de-Calais. Chang-er, 1, to change, Manteau, m., cloak. Schelling, m., shilling. and of the Pas-de-Calais, to alter. Monnaie, f., change, Vie, f., life, conduct. Les chemins de fer et les bateaux Railroads and steamboals are very Combat, m., combat. Mouillé, -e, wet. Visage, m., counte à vapeur sont très-nombreux en numerous in America. Conduite, f., conduct. Parceque, because, Amérique. nance, face. Cette maison contient un salon, That house contains a drawing-room, EXERCISE 109. une salle à manger, une cuisine, a dining-room, a kitchen, and seve1. Cet homme n'a-t-il pas changé de vie ? 2. Il a changé Les moulins à vent sont plus com et plusieurs chambres à coucher. ral bedrooms. Windmills common in de conduite. 3. Cette grande maison n'a-t-elle pas changé de muns en France que les moulins Franco than water or steam-inills. maître ? 4. Elle a changé de maître, le Capitaine G. vient de à eau ou vapeur. l'acheter. 5. Vous êtes monillé, pourquoi ne changez-vous VOCABULARY. pas de manteau ? 6. Parceque je n'en ai pas d'autre. 7. Votre cousine ne change-t-elle pas souvent d'avis ? 8. Elle en change Armes, f. pl., fencing. Dessin, m., drawing. Ordinaire, usual. Båt-ir, 2, to build, Engag-er, 1, to engage. Rone, f., wheel. bien souvent. 9. Pendant le combat, ce jeune soldat n'a-t-il Bouteille, f., bottle. Faire bât-ir, 2, to have Vapeur,i.vapour, steam pas changé de visage? 10. Il n'a point changé de visage. 11. Cabriolet, m., gig. built. Voile, f., sail. Ce malade ne devrait-il pas changer d'air ? 12. Le médecin Chat-huant, m., owl. Se munir, 2 ref., to pro-Voiture, f., carriage. lui recommande de changer de pays. 13. Où est votre cheval Chauve-souris, f., bat. vide one's self with Voyag-er, 1, to travel. gris ? 14. Je ne l'ai plus, je l'ai changé contre un blanc. 15. EXERCISE 111. Avec qui l'avez-vous changó ? 16. Je l'ai changé avec le jeune homme qui demeurait ici le mois passé. 17. Le marchand 1. Faut-il avoir un passe-port pour voyager en Franco? 2. peut-il me changer cette pièce de quarante francs ? 18. Il ne Il faut en avoir un. 3. Les Anglais se munissent-ils de passesaurait (cannot) vons la changer, il n'a pas de monnaie. 19. ports pour voyager en Angleterre ? 4. On n'a pas besoin do Avez-vous la monnaie d'uno guinée (change for a guinea) ? passe-port en Angleterre. 5. Aimez-vous à voyager sur les chemins de fer ? 6. J'aime mieux voyager sur les chemins do EXERCISE 110. fer que sur les chemins ordinaires. 7. Avez-vous apporté ros 1. Why do you not change your cout? 2. For a very good passe-partout ? 8. Je n'ai point de passe-partout, je n'ai qne reason (raison, f.), because I have no other. 3. Has your father des clefs ordinaires. 9. Votre frère est-il venn dans un bateau changed houses? 4. No, Sir, but we intend to do so (de le faire) à vapeur ? 10. Il est venu dans un bateau à voiles. 11. Avezto-morrow. 5. Has that child altered his conduct? 6. He has vous une voituro à quatre chevaux ? 12. Non, Monsieur, nons altered his conduct, he is very good now (maintenant). 7. Was n'avons qu’un cabriolet à un choval. 13. Votre frère a-t-il bati not your brother afraid ; did not his countenance change? 8. un moulin à vapeur ? 14. Il a fait bâtir deux moulins, l'un à His countenance changed, but he was not afraid. 9. Have you vent et l'autre à eau ? 15. Votre compagnon a-t-il engagé un not changed rooms (chambre, f.)? 10. I have not changed maître d'armes ? 16. Non, Monsieur, il a déjà un maître de rooms, my room is very good. 11. Do you not long to be in dessin et un maître de dansé. 17. Combien de chambres à are more coucher avez-vous ? 18. Nous en avons deux. 19. Avez-vous 27. Cette belle petite fille n'a ni faim ni soif. 28. Qu'a-t-elle ? 29. une bouteille de vin ? 20. Non, Monsieur, mais j'ai une bouteillo Elle n'a ni parents ni amis. 30. Cette montre d'or est-elle bonne ? 32. L'avez-yous ? à vin (wine-bottle) ($ 81]. 21. Voyez-vous les chats-huants ? 31. Celle-ci est bonne, mais celle-là est meilleure. 22. Non, mais je vois les chauves-souris. 33. Je l'ai, mais je n'ai pas celle de votre sour. 34. Je n'ai ni la vôtre ni la mienne, j'ai celle de votre mère. EXERCISE 112. 1. Is your father in Engiand? 2. No, Sir, he is in France MECHANICS.—XIV. with my brother. 3. Have they taken passports ? 4. Yes, Sir, they ha taken two. 5. Is it necessary to have a passport to ILLUSTRATIONS OF PRECEDING PRINCIPLES-KITE, BOAT, ETC. travel in America ? 6. No, Sir, but it is necessary to have one -ELEMENTS OF MACHINERY. to travel in Italy. 7. Is there a steamboat from Calais to We have now to trace the practical application of the principles Dover (Douvres)? 8. There are several. 9. Is there a railroad already laid down, and the best way of doing this is to take from Paris to Brussels (Bruxelles) ? 10. There is one from some common instances and carefully examine them, and we Paris to Brussels, and one from Paris to Tours. 11. Has your shall see that the same rules will apply to other and more combrother bought a windmill ? 12. No, Sir, but he has built a plicated cases. steam-mill. 13. Are there many wind-mills in America ? 14. A heavy box is resting on a four-legged table. What are the No, Sir, but there are many water and steam-mills. 15. Does forces that act on it, and what on the table ? On the box there your cousin learn drawing ? 16. He does not learn it, he are only two-its own weight acting downwards, and the upward cannot find a drawing-master. 17. Is the fencing-master in the pressure of the table, exactly counterbalancing this weight. We . dining-room? 18. No, Sir, he is in the drawing-room. 19. Is turn, then, to the table, the forces acting on which are not quito your cousin in his bedroom 2 20. No, Sir, he is out (sorti). so easily determined. There are its own weight and the weight 21. How many rooms are there in your house ? 22. Five: а of the box acting through their respective centres of gravity. kitchen, a dining-room, a drawing-room, and two bedrooms. 23. These are parallel forces, and, as we have seen, have a resultant Are there owls here ? 24. Yes, Sir, and bats too. equal to their sum, and acting at a point in the line joining them, so taken that their distances from it are in the inverse proportion to their intensities. The other force which acts on KEY TO EXERCISES IN LESSONS IN FRENCH. the table is the resistance of the floor on which it rests, which EXERCISE 18 (Vol. I., page 78). resistance is transmitted upward through the four legs. If the 1. Avez-vous mes tables on les vôtres ? 2. Je n'ai ni les vôtres ni weight act at a point equally distant from these, each bears an les miennes, j'ai celles de l'aubergiste. 3. Les avez-vous ? 4. Non, equal share; but if not, it is divided between them in the inverse Monsieur, je ne les ai pas. 5. Votre sæur a-t-elle mes chevaux ? proportion to their distances. To make this more clear, we will 6. Oui, Monsieur, elle a vos deux chevaux et ceux de votro frère. suppose these distances to be 2, 6, 6, and 8 feet respectively. Find 7. Avez-vous raison ou tort ? 8. J'ai raison, je n'ai pas tort. 9. Le the least common multiple of these numbers, that is, the least ferblantier a-t-il mes chandeliers d'argent ou les vôtres ? 10. Il n'a number each will divide without any remainder. In this case ni ros chandeliers d'argent ni les miens. 11. Qu'a-t-il? 12. Il a les it is 24. This we divide successively by the distances, and obtain tables de bois de l'ébéniste. 13. A-t-il vos chaises d'acajou? 14. Non, the quotients 12, 4, 4, and 3; and these numbers represent the Monsieur, il a mes tables de marbre blanc. 15. Avez-vous ces tables. ci ou celles-là ? 16. Je n'ai ni celles-ci ni celles-là, j'ai celles de proportion in which the weight is divided between the legs. l'ébéniste. 17. Avez-vous de bons porte-crayons ? 18. Non, Monsieur, Now suppose the weight of the table and box to be 207 pounds. mais j'ai de bons crayons. 19. Le voyageur a-t-il des fusils de fer Since 12, 4, 4, and 3, added together make 23, the leg 2 feet of 20. Oui, Monsieur, il a les miens, les vôtres et les siens. 21. N'a-t-il pas supports 12 parts out of every 23, i.e., 1 of the weight, or 108 ceux de votre frère ? 22. Il n'a pas ceux de mon frère. 23. L'ouvrier pounds. Those 6 feet off supports, or 36 pounds each; and the 2-t-il mes marteaux de fer ? 21. Oui, Monsieur, il les a. 25. Mon other sustains only, or 27 pounds. A calculation of this sort is tri re a-t-il vos plumes ou celles de mon cousin ? 26. Il a les miennes et les vötres. 27. Avez-vous les habits des enfants ? 28. Oui, Madame, mine the relative strength the dif very frequently required to deter RN je les ai. 29. Avez-vous le chapeau de votre sour? 30. J'ai celui de ma cousine. 31. Votre frère a-t-il quelque chose ? 32. Il a froid et ferent parts of a building should faim. 33. Avez-vous des chevaux ? 34. Oui, Monsieur, j'ai deux have. chevaux. 35. J'ai deux matelas de crin et un matelas de laine. We will take another case. A FZ body, G (Fig. 86), rests on an inEXERCISE 19 (Vol. I, page 79). Vw clined plane, the angle of which, A. 1. Is that lady pleased ? 2. No, Sir, that lady is not pleased. 3. Is CA B, is 30°, and the co-efficient of your daughter quick ? 4. My son is very quick, and my daughter is friction is . What forces act on idle. 5. Is she not wrong? 6. She is not right. 7. IS your cousin G, what are their amount, and what happy? 8. Yes, Madam, she is good, beautiful, and happy. 9. Has other force must be applied to keep she friends? 10. Yes, Sir, she has relations and friends. ii. Has she it in its place? We will try and a new dress and old shoes ? 12. She has old shoes and an old dress, Fig. 86. 13. Has not your brother a handsome coat? solve these questions. As already 14. He has a handsome coat and a good cravat. 15. Have you good meat, Sir ? 16. I have seen, three forces act on its weight acting along Gw, the resistexcellent meat. 17. Is this meat better than that? 18. This is better ance of the plane acting along a E, and the force of friction, which than that. 19. Has your friend the beautiful china inkstand ? 20. His is * of the weight and acts along FG. We found, when considerinkstand is beautiful, but it is not china. 21. Is any one hungry? ing the inclined pļane, that the power necessary to sustain G 22. No one is hungry. 23. Are the generals here? 24. The generals must bear the same proportion to its weight that b c does to a C. and the blacksmiths are here. 25. I have your parasols and your This, then, is the first thing we must find out, and we must umbrellas, and your children's. have a slight acquaintance with mathematics for this; there is, EXERCISE 20 (Vol. I., page 79). however, no difficulty in the matter. Produce c B to D, 80 as to make B D the same length as B C, and join A D. The triangles 1. Votre petite soeur est-elle contente ? 2. Qui, Madame, elle est contente, 3. Cetto petite fille est-elle belle ? ABC and ABD are exactly equal. For as Bc is equal to BD, 4. Cette petite fille n'est pas belle, mais elle est bonno. 5. Avez-vous de bon drap et de and each is at right angles with a B, A B C would, if we were to bonne soie ? 6. Mon drap et ma soie sont ici. 7. Votre squr est- turn it over, exactly lie on A B D. AD is, then, equal to AC. Now elle heureuse ? 8. Ma sour est bonne et heureuse. 9. La seur de ce in any and every triangle the three interior angles are together médecin a-t-elle des amis ? 10. Non, Madame, elle n'a pas d'amis. equal to 180°, or two right angles, and in A B C we know that 11. Votre viande est-elle bonne ? 12. Ma viande est bonne, mais mon the angle CAB is 30°, and A B C, being a right angle, is 90°; fromage est meilleur. 13. L: libraire a-t-il un bel encrier de porce-therefore A C B must be 60°, and A D B is equal to it, and therelaine ? 14. Il a un bel encrier d'argent et une paire de souliers de cuir. fore is also 60°. The angle B A D is likewise equal to BaC, and 15. Avez-vous mes parasols de soie ? 16. J'ai vos parapluies de coton. as each is 30°, the angle CAD is 600. We see thus that each of 17. L'habit de votre frère est-il beau ? 18. Mon frère a un bel habit the angles of the triangle cad is 60°, and therefore they are et une vieille cravate de soie. 19. Avez-vous des parents et des amis ? 2). Je n'ai pas de parents, mais j'ai des amis. 21. Cette belle dame equal to one another; and, since the angles are equal, the sides a-t-elle tort? 22. Cette belle dame n'a pas tort. 23. Avez-vous de are also equal, for there is no reason why one should be greater belle porcelaine ? 24. Notre porcelaine est belle et bonne. 25. Ello than annther. The triangle is thus equilateral and equiangular. est meilleure que la vôtre. 26. Cette petite fille u'a-t-elle pas faim ? We have now found out what we wanted; for, if BC be repre B sented in length by 1, C D will be 2; and AC is equal to CD, Here is another case, involving the same principle. A bracket therefore it is also 2, and the proportion Bc bears to a c is 1 A B (Fig. 88), projects from a wall, to which it is fastened by a to 2, or. On an incline of 300, then, the power must be half screw. A strut, A C, supports the outer end, and a weight, w, the weight; but, in this case, friction sustains one-fourth, and rests on it. In what direction is the strain on the screw? The therefore a power must be applied, acting in the direction GP, three forces here are, gravity acting along w g, the thrust of and equal to one-fourth of the weight, in order to maintain the beam, A c, and the strain on the screw. The two former equilibrium. act through the point o, and the direcWe have now to solve the remainder of the question. We tion of the third is found by drawing a know how much gw, G F, and GP are; but we want to know line from this point to the screw. We what portion of the weight is borne by the plane, that is, what may take a line, o c, of such a length proportion A B, which represents the resistance of the plane, as to represent the weight, and resolve bears to AC. To find this, we need another very important it into o b and o a, one acting along geometrical proposition, which you will find fully proved in the strut, the other perpendicular to Lessons in Geometry, Problem XXX., Vol. I., page 337. the wall. These will represent two In every right-angled triangle the square described on the forces, which are together equivalent to side opposite the right angle is equal to the sum of the squares o c, and of these o b will be overcome on the sides containing it. If we represent the sides by numbers by the pressure of the strut, and the expressing their lengths, the role holds equally true. Suppose, other force, o a, tends to draw the for example, we measure off from one of the sides containing screw from the wall. A portion, how. the right angle a length of 4 inches, and from the other a length ever, of the pressure of the strat will of 3 inches, we shall find the line joining these two points is be borne by the screw, and these two equal to 5 inches. forces combining produce the resultant, The square of 4 (which means 4 multiplied by itself) is 16, which acts on the screw towards the Fig. 88. and the square of 3 is 9. These added together make 25, which point o. is the square of 5. The usual way of writing this is 4+32 = 52. It is frequently very important to be able thus to tell in In this way, if we know the length of any two sides of a right- what direction a strain will act, as the strength of our materials angled triangle, we can always calculate the third. Now in the must be proportionate to it. In this way the direction of the case we are examining, we know that the side A C is equal to 2 tie-beams and king and queen posts of a roof are determined. and the side b c to 1; but the square of Ac is equal to the sum We know, too, where to apply struts and braces to the of the squares a B and BC; the square of A B must, therefore, be framework of a building, so as to gain the greatest benefit from equal to the difference between those of Ac and B C. Now these them. are 4 and 1; the square of A B is, then, equal to 3, and the length Now there are one or two cases of the composition and resoloof A B must be represented by the quantity which, multiplied by tion of forces that are frequently given as illustrations, and if itself, will make 3. This is called the square root of 3, and is we clearly understand them we shall be able to master most written 73. By arithmetic we can easily find exactly what this others. The first is that of a kite, for there is science to be number is, but you can see that it is very nearly 13. The pro- learned even from this common plaything. Indeed, we shall portion, then, of A B to A c is 18 to 2, or 7 to 8, and the plane frequently find, among the very commonest things, good illustrasustains a pressure equal to about of the weight. We have tions of any subject wo may be studying. thus discovered the magnitude of all the forces as required. Let K (Fig. 89) represent a kite. The forces which act on it are, When, as in our last lesson, we have resolved all the forces the force of the wind, acting, we will suppose, in the direction of acting on a body along two lines at right angles, we can in this the arrow, the tension of the string, acting along it in the direcway find the magnitude of the resultant without the trouble tion K s, and the weight of the kite; and by the action of these and possible inaccuracy of actual measurement. Suppose we three forces it is kept at rest. We will consider them singly; have a remainder of 12 pounds acting along one of the lines, and first, we will take the force of the wind. Take a w, of such and one of 5 pounds along the other, the resultant will be equal a length as to represent this force. The kite is always so made to V12? + 5°; that is, to the square root of 144 + 25, or 169, as to present a large surface to the wind in proportion to its which is 13. In the same way we can solve many questions weight, and the string is fastened to the loop in such a way that frequently met with. Here is an example. Two forces act on it does not hang vertical, but inclined at an angle; the tai, a body; the resultant is 34 pounds, and one of the forces is 16 however, prevents its being so acted on by the wind as to come pounds; what is the other ? We first find the square of 34, which is 1,156 ; from this we take the square of 16, or 256, and we have left 900. The square root of this is 30, and this accordingly is the intensity of the other force. Now turn to another common thing. A ladder, A B (Fig. 87), leans against a wall. What are the forces acting on it ? Its own weight acts vertically downwards through G, and the other forces which keep it at rest are the reaction of the wall and the ground at A and B respectively. Now there is but little friction at a, and we may therefore consider the reaction to be in the direction A P perpendicular to the wall. Fig. 89. edgewise on the kite, is the resultant of two others—the resistance the other perpendicular to its surface. We draw the paralleloof the ground acting vertically upwards, and gram Kowa, and thus have the two forces, K 0 and K A, instead the force of friction which acts along the of Kw. K o has no effect, as it acts on the edge, and we need, ground and towards the base of the wall; and therefore, only consider the pa. K A. Fig. 87. we easily see that the more nearly vertical the Now we will introduce a second force, that of the string. ladder is, the greater is the former as com- Produce 8 k backward, draw A B perpendicular to B K, and compared with the latter, and therefore the less the amount of plete the parallelogram DK BA. We can again resolve K A friction which is required to keep it in its place. We have thus into K D and K B. The latter will be expended in stretching the the scientific reason for the well-known fact that the more a string, and have no tendency to move the kite, and thus we have ladder is inclined, the greater need there is for the foot to be KD left as the effective resultant of these two forces. We DOW held, so as to keep it from slipping. consider the third, which is the weight of the kite. Draw KG W R W B S of such a length as to represent this, and complete the parallelo- Sometimes toothed wheels are used instead of straps, espe. gram DCGK. We have then k c the resultant of K D and ko, cially when the distance through which the power has to be and therefore of all the forces which act on the kite, and this transmitted is small. The advantage is that they do not slip, is the direction in which the kite will move, but as it does so, as straps are liable to do; the friction with them is, however, the angle at which it is inclined varies till K D and k g become greater. If we want to transmit motion from a shaft to another opposite and equal, and then the kite will remain at rest as long placed at an angle with it (Fig. 91), we employ what are known as the force of the wind remains unaltered. as bevelled wheels. The action of these will be clear from the The other case we will consider is that of a ship, which will figure, without any explanation. sail within a few points of the wind. Let co (Fig. 90) represent Often it is required to change a rotating motion into a prothe direction and intensity of the wind, and s v the direction in gressive one, and we can accomplish this by means of a rack and which it is desired that the vessel pinion. A number of notches are in the direction A B, which is mid- of such a size and at such dis- that of the vessel. We must, as wheel exactly fit into them, and sail, has no effect in moving the slow and regular motion is re- vessel ; F 0, which acts perpendi- quired, as in the adjustment of Fig. 92. portion. We must now again resolve this force along two direc- stead of a rack a chain is sometions, one being that in which the boat moves, the other at right times used (Fig. 92 b), the links being made of a peculiar shape, angles to it. We make a o equal to F 0, and about it describe so that the teeth of the wheel may catch in them. the parallelogram H G 10, and thus have two forces, represented The crank (Fig. 93) is, perhaps, one of the most common of these by 0 H and 0 1, in the place of the original force, co. Now, of elements of machinery. The piston-rod of an engine is usually these, o I has no tendency to cause the vessel to advance; it jointed, and the end of the jointed part fixed to an arm proacts sideways on the vessel, usually inclining it, and causing a jecting from the axle to be turned, and called a crank. Someslight motion, but it is resisted by the pressure of the water times it is fixed to a pin in one of the spokes of the wheel, but against the side ; the other portion, o 1, represents the portion the action is just the same. The force, however, with which it of the force of the wind which is effective, and produces motion. | drives the wheel is continually varying. When the piston is In the same way you can calculate what portion of the force at the bottom of the cylinder the crank and piston-rod are in of the wind is effective in turning a windmill. The vanes are one straight line, and therefore all the power presses on the always set at an inclination with the plane in which they turn, bearing of the axle, and is lost. As the wheel turns the power and you must resolve the force along two directions, one per acts with a leverage which increases pendicular to the surface, and the other along it. The former till the wheel has made nearly oneyou again resolve, and thus find what part of it produces rota- fourth of a revolution; it is then at tion, and what part presses against the face of the mill. its maximum, and diminishes till the piston-rod reaches its highest point, ELEMENTS OF MACHINERY. Fig. 93. when it is all again lost. Now it is As it is our object to make these lessons as practical as pos- clear that unless we have some means of regulating the speed sible, it will be well to look at a few of the simpler modes of the machine will work very unevenly, and at times stop altering and transmitting power. Sometimes this is advanced altogether. To obviate this, a large and heavy wheel, called the to the rank of a separate science, and called kinematics, or the fly-wheel, is fixed on the axle of the crank. This, when once science of motion, but it should be referred to hero as a part of started, acquires an amount of momentum or moving force practical mechanics. which carries it over the dead points when the power is lost. We seldom have our power available for use in the exact way On account of the weight of the wheel, its motion is but we desire. Sometimes we have an alternate motion, like that of slightly accelerated when the piston acts at its greatest leverthe piston-rod of an engine, and we want to derive from it a rota- age, but the additional force is stored up in it, and thus ensures tory or progressive motion; or we want to transmit it along a a steady motion. The heavy wheel of a foot-lathe serves prodirection making some angle with its course, or to make many cisely the same purpose. The power is here applied during other alterations in its mode of action. rather less than one-half of the revolution, but the momentum In large factories there is frequently a long shaft running then acquired carries it through the remaining part. along the building, and driven by an engine. From this it is reqnired to drive all the machines in the place. This is accom EXAMPLES. plished by fixing wheels on the shaft, and letting endless straps 1. Forces of 9 and 12 act at right angles; what is their resultant? pass over these and then over the driving pulleys of the machines. 2. The resultant of two forces which act at right angles is 10 pounds. The motion may often be greatly altered in this way. The strap One of the forces is 6; find the other. itself merely transmits the power, and whether there is a gain or 3. Two mon, one on each side of a stream, tow a barge. The angle loss in speed or power depends on the comparative size of the the two ropes make is 60°, and each pulls with a force of 100 pounds. sheaves. Frequently there are several of these wheels of what is the total force exerted on the barge ? different sizes fixed on the axle and on the machine, and thus 4. The tension of a wire in a piano is 100 pounds, its length is 5 feet. the speed may be altered at pleasure. If the strap passes over What force is required to draw its middle point 2 inches out of its a large one on the shaft and a small one on position ? 5. A weight of 90 pounds rests on a plane inclined at an angle of the machine, there will be an increase of 30°. The co-efficient of friction is ļ. What force is required to keep speed, and if we reverse the condition there it at rest? will be a loss. A common illustration of a similar arrangement is seen in a watch. The spring when fully wound up exerts a ANSWERS TO EXAMPLES IN LESSON XIII. much greater power than it does when the 1. The forces acting at the longer end are the power of 10 pounds watch has run nearly down. Now this acting at a distance from the fulcrum of 6 feet, and the weight of the would make it go irregularly, and therefore lever, which is also 10 pounds, and acts through its middle point, or the fusee is introduced. When the force 21 feet from the fulcrum. The moments on this end are thus 10*67. of the spring is greatest the chain acts or 67), and 10x 27 or 27). These make 95 pounds. As w acts at a Fig. 91. on the smallest part of the fusee, and there- distance of 14 feet, it must be or 76 pounds. 13 fore has only a short leverage, but as it 2. Since is lost by friction, we may regard the weight as 12 pounds unwinds and loses its force the chain acts at a greater lever-only. Now of the weight of the first pulley is supported by the age, and a uniform rate of motion is thus maintained. power, of the next, and } and its of the other two; and since each H 95 |