LESSONS IN FRENCH.-XXXI.

SECTION LVII.-IDIOMATIC PHRASES.

1. CHANGER [1, see § 49 (1)], used in the sense of to change, to leave one thing for another, is followed by the preposition de : changer d'habit, de chapeau, etc., to put on another coat, hat, etc.; changer d'avis, to change one's mind; changer de maison, to move, to change houses; changer de place, changer de pays, changer de climat, to go to another place, country, climate; changer de nom, to change one's name. The student will perceive that the noun following changer is not preceded by a possessive adjective, like the noun of the English sentence.

Voulez-vous changer d'habit?
Ce monsieur a changé de nom,

2. Changer contre means to change for, to get change for. Voulez-vous changer votre chapeau contre le mien ?

Will you change your coat? That gentleman has changed his name. exchange for; changer pour, to

France? 12. I long to be there. 13. Does not your mother tarry too long? 14. She is very long in coming. 15. Have you changed the forty-franc piece? 16. I have not changed it yet. 17. Why have you not changed it? 18. Because your father has no change. 19. Have you the change for a guinea? 20. No, Sir, I have only twelve shillings.

SECTION LVIII.-RULES FOR THE PLURAL OF COMPOUND NOUNS.

1. We have given, in Section IX., rules for forming the plural of nouns, but, in accordance with our plan of not presenting too many difficulties at once, we have deferred until the present section the rules for the formation of the plural of compound

nouns.

mine?

Change that note for silver.

Changez ce billet pour de l'argent, 3. Tarder means to tarry, to be long in coming. Tarder used unipersonally, and preceded by an indirect object, means to long, to wish for.

Votre sœur tarde bien à venir, Il me tarde de la voir,

Your sister is very long coming. I long to see her.

RÉSUMÉ OF EXAMPLES.

N'avez-vous pas changé d'apparte.

ment?

Nous avons changé de maisons. Votre frère a changé de conduite.

ment?

duct.

We have changed houses. Your brother has changed his conContre quoi avez-vous changé votre For what have you exchanged your cheval ? horse?

6. We have seen [Sect. III. 4] that the name of the material always follows the name of the object, and that both are united by the preposition de. The name of the profession or occupation also follows the noun representing the individual, and the same preposition de connects the two: un maître d'armes, a fencing-master; un maître de dessin, a drawing-master; un marchand de farine, a dealer in flour [§ 76 (12), § 81 (4)]. 7. The name of a vehicle, boat, mill, etc., always precedes the noun describing the power by which it is impelled, or the purpose to which it is adapted; the name of an apartment, that of

Il me tarde de revoir la France.

Air, m., air.

again.

I long to see France again.

VOCABULARY.

Gris, -e, grey.

Passé, -e, past, last. Pays, in., country. Rentr-er, 1, to come in again.

Schelling, m., shilling. Vie, f., life, conduct. Visage, m., countenance, face.

11.

1. Cet homme n'a-t-il pas changé de vie? 2. Il a changé de conduite. 3. Cette grande maison n'a-t-elle pas changé de maître? 4. Elle a changé de maître, le Capitaine G. vient de l'acheter. 5. Vous êtes mouillé, pourquoi ne changez-vous 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 bien souvent. 9. Pendant le combat, ce jeune soldat n'a-t-il pas changé de visage? 10. Il n'a point changé de visage. Ce malade ne devrait-il pas changer d'air? 12. Le médecin lui recommande de changer de pays. 13. Où est votre cheval gris ? 14. Je ne l'ai plus, je l'ai changé contre un blanc. Avec qui l'avez-vous changé ? 16. Je l'ai changé avec le jeune homme qui demeurait ici le mois passé. 17. Le marchand peut-il me changer cette pièce de quarante francs? 18. Il ne saurait (cannot) vous la changer, il n'a pas de monnaie. 19. Avez-vous la monnaie d'une guinée (change for a guinea)?

VOCABULARY. Dessin, m., drawing. Eugag-er, 1, to engage. Faire bat-ir, 2, to have buill.

Se munir, 2 ref., to provide one's self with. EXERCISE 111.

Ordinaire, usual, Roue, f., wheel. Vapeur,f.vapour, steam Voile, f., sail. Voiture, f., carriage, Voyag-er, 1, to truesi.

1. Faut-il avoir un passe-port pour voyager en France? 2 Il faut en avoir un. 3. Les Anglais se munissent-ils de passe ports pour voyager en Angleterre? 4. On n'a pas besoin de passe-port en Angleterre. 5. Aimez-vous à voyager sur les chemins de fer? 6. J'aime mieux voyager sur les chemins de fer que sur les chemins ordinaires. 7. Avez-vous apporté vos passe-partout? 8. Je n'ai point de passe-partout, je n'ai que des clefs ordinaires. 9. Votre frère est-il venu dans un bateau à vapeur? 10. Il est venu dans un bateau à voiles. 11. Aver vous une voiture à quatre chevaux? 12. Non, Monsieur, nous n'avons qu'un cabriolet à un cheval. 13. Votre frère a-t-il bati un moulin à vapeur? 14. Il a fait bâtir deux moulins, l'un à vent et l'autre à eau? 15. Votre compagnon a-t-il engage an maître d'armes? 16. Non, Monsieur, il a déjà un maître dessin et un maître de danse. 17. Combien de chambres à

22. Non, mais je vois les chauves-souris.

EXERCISE 112.

1. Is your father in England? 2. No, Sir, he is in France with my brother. 3. Have they taken passports ? 4. Yes, Sir, they have taken two. 5. Is it necessary to have a passport to travel in America ? 6. No, Sir, but it is necessary to have one to travel in Italy. 7. Is there a steamboat from Calais to Dover (Douvres) ? 8. There are several. 9. Is there a railroad from Paris to Brussels (Bruxelles) ? 10. There is one from Paris to Brussels, and one from Paris to Tours. 11. Has your brother bought a windmill ? 12. No, Sir, but he has built a steam-mill. 13. Are there many wind-mills in America? 14. No, Sir, but there are many water and steam-mills. 15. Does your cousin learn drawing? 16. He does not learn it, he cannot find a drawing-master. 17. Is the fencing-master in the aining-room? 18. No, Sir, he is in the drawing-room. 19. Is your cousin in his bedroom? 20. No, Sir, he is out (sorti). 21. How many rooms are there in your house? 22. Five: a kitchen, a dining-room, a drawing-room, and two bedrooms. 23. Are there owls here ? 24. Yes, Sir, and bats too.

KEY TO EXERCISES IN LESSONS IN FRENCH. EXERCISE 18 (Vol. I., page 78).

1. Avez-vous mes tables ou les vôtres ? 2. Je n'ai ni les vôtres ni les miennes, j'ai celles de l'aubergiste. 3. Les avez-vous ? 4. Non, Monsieur, je ne les ai pas. 5. Votre sœur a-t-elle mes chevaux ? 6. Oui, Monsieur, elle a vos deux chevaux et ceux de votre frère. 7. Avez-vous raison ou tort? 8. J'ai raison, je n'ai pas tort. 9. Le ferblantier a-t-il mes chandeliers d'argent ou les vôtres ? 10. Il n'a ni vos chandeliers d'argent ni les miens. 11. Qu'a-t-il? 12. Il a les tables de bois de l'ébéniste. 13. A-t-il vos chaises d'acajou? 14. Non, ci ou celles-là? 16. Je n'ai ni celles-ci ni celles-là, j'ai celles de l'ébéniste. 17. Avez-vous de bons porte-crayons ? 18. Non, Monsieur, mais j'ai de bons crayons. 19. Le voyageur a-t-il des fusils de fer? 20. Oui, Monsieur, il a les miens, les vôtres et les siens. 21. N'a-t-il pas ceux de votre frère ? 22. Il n'a pas ceux de mon frère. 23. L'ouvrier a-t-il mes marteaux de fer? 24. Oui, Monsieur, il les a. 25. Mon frère a-t-il vos plumes ou celles de mon cousin ? 26. Il a les miennes et les vôtres. 27. Avez-vous les habits des enfants? 28. Oui, Madame, je les ai. 29. Avez-vous le chapeau de votre sœur? ma cousine. 31. Votre frère a-t-il quelque chose? 32. Il a froid et faim. 33. Avez-vous des chevaux ? 31. Oui, Monsieur, j'ai deux chevaux. 35. J'ai deux matelas de crin et un matelas de laine.

Monsieur, il a mes tables de marbre blanc. 15. Avez-vous ces tables

EXERCISE 19 (Vol. I., page 79).

30. J'ai celui de

1. Is that lady pleased? 2. No, Sir, that lady is not pleased. 3. Is your daughter quick ? 4. My son is very quick, and my daughter is idle. 5. Is she not wrong? 6. She is not right. 7. Is your cousin happy? 8. Yes, Madam, she is good, beautiful, and happy. 9. Has she friends? 10. Yes, Sir, she has relations and friends. 11. Has she a new dress and old shoes? 12. She has old shoes and an old dress. 13. Has not your brother a handsome coat? 14. He has a handsome

coat and a good cravat. 15. Have you good meat, Sir? 16. I have excellent meat. 17. Is this meat better than that? 18. This is better than that. 19. Has your friend the beautiful china inkstand? 20. His inkstand is beautiful, but it is not china. 21. Is any one hungry? 22. No one is hungry. 23. Are the generals here? 24. The generals and the blacksmiths are here. 25. I have your parasols and your umbrellas, and your children's.

contente.

EXERCISE 20 (Vol. I., page 79).

1. Votre petite sœur est-elle contente? 2. Oui, Madame, elle est 3. Cette petite fille est-elle belle ? 4. Cette petite fille n'est pas belle, mais elle est bonne. 5. Avez-vous de bon drap et de 6. Mon drap et ma soie sont ici. 7. Votre sœur est

bonne soie?

elle heureuse ? 8. Ma sœur est bonne et heureuse. 9. La sœur de ce médecin a-t-elle des amis ? 10. Non, Madame, elle n'a pas d'amis. 11. Votre viande est-elle bonne ? 12. Ma viande est bonne, mais mon fromage est meilleur. 13. Le libraire a-t-il un bel encrier de porcelaine? 14. Il a un bel encrier d'argent et une paire de souliers de cuir. 15. Avez-vous mes parasols de soie ? 16. J'ai vos parapluies de coton. 17. L'habit de votre frère est-il beau ? 18. Mon frère a un bel habit et une vieille cravate de soie. 19. Avez-vous des parents et des amis ? 20. Je n'ai pas de parents, mais j'ai des amis. 21. Cette belle dame a-t-elle tort ? 22. Cette belle dame n'a pas tort. 23. Avez-vous de belle porcelaine? 24. Notre porcelaine est belle et bonne. 25. Elle est meilleure que la vôtre. 26. Cette petite fille n'a-t-elle pas faim ?

Elle n'a ni parents ni amis, 30. Cette montre d'or est-elle bonne ? 31. Celle-ci est bonne, mais celle-là est meilleure. 32. L'avez-vous ? 33. Je l'ai, mais je n'ai pas celle de votre sœur. 34. Je n'ai ni la vôtre ni la mienne, j'ai celle de votre mère.

MECHANICS.-XIV.

ILLUSTRATIONS OF PRECEDING PRINCIPLES-KITE, BOAT, ETC. -ELEMENTS OF MACHINERY.

WE have now to trace the practical application of the principles already laid down, and the best way of doing this is to take some common instances and carefully examine them, and we shall see that the same rules will apply to other and more complicated cases.

A heavy box is resting on a four-legged table. What are the forces that act on it, and what on the table? On the box there are only two-its own weight acting downwards, and the upward pressure of the table, exactly counterbalancing this weight. We turn, then, to the table, the forces acting on which are not quite so casily determined. There are its own weight and the weight of the box acting through their respective centres of gravity. These are parallel forces, and, as we have seen, have a resultant 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 the table is the resistance of the floor on which it rests, which resistance is transmitted upward through the four legs. If the weight act at a point equally distant from these, each bears an equal share; but if not, it is divided between them in the inverse proportion to their distances. To make this more clear, we will suppose these distances to be 2, 6, 6, and 8 feet respectively. Find the least common multiple of these numbers, that is, the least number each will divide without any remainder. In this case it is 24. This we divide successively by the distances, and obtain the quotients 12, 4, 4, and 3; and these numbers represent the proportion in which the weight is divided between the legs.

Now suppose the weight of the table and box to be 207 pounds. Since 12, 4, 4, and 3, added together make 23, the leg 2 feet off supports 12 parts out of every 23, i.e., of the weight, or 108 pounds. Those 6 feet off support, or 36 pounds each; and the other sustains only, or 27 pounds. A calculation of this sort is mine the relative strength the difvery frequently required to deterferent parts of a building should

have.

seen,

R

Vw

Fig. 86.

We will take another case. A body, a (Fig. 86), rests on an inclined plane, the angle of which, A. CA B, is 30°, and the co-efficient of friction is . What forces act on G, what are their amount, and what other force must be applied to keep it in its place? We will try and solve these questions. As already three forces act on a-its weight acting along G w, the resist ance of the plane acting along G R, and the force of friction, which is of the weight and acts along F G. We found, when considering the inclined plane, that the power necessary to sustain a must bear the same proportion to its weight that B C does to A c. This, then, is the first thing we must find out, and we must have a slight acquaintance with mathematics for this; there is, however, no difficulty in the matter. Produce C B to D, so as to make B D the same length as B C, and join A D. The triangles ABC and ABD are exactly equal. For as B C is equal to B D, and each is at right angles with AB, A B C would, if we were to turn it over, exactly lie on A B D. A D is, then, equal to A c. Now in any and every triangle the three interior angles are together equal to 180°, or two right angles, and in ABC we know that the angle CAB is 30°, and ABC, being a right angle, is 90°; therefore A C B must be 60°, and A D B is equal to it, and therefore is also 60°. The angle B A D is likewise equal to BA C, and as each is 30°, the angle CAD is 60°. We see thus that each of the angles of the triangle CAD is 60°, and therefore they are equal to one another; and, since the angles are equal, the sides are also equal, for there is no reason why one should be greater than another. The triangle is thus equilateral and equiangular. We have now found out what we wanted; for, if вo be repre

s

of such a length as to represent this, and complete the parallelogram D C G K. We have then K c the resultant of K D and K G, and therefore of all the forces which act on the kite, and this is the direction in which the kite will move, but as it does so, the angle at which it is inclined varies till K D and K G become opposite and equal, and then the kite will remain at rest as long as the force of the wind remains unaltered.

Fig. 90.

The other case we will consider is that of a ship, which will sail within a few points of the wind. Let co (Fig. 90) represent the direction and intensity of the wind, and s v the direction in which it is desired that the vessel should advance. The sail is placed in the direction A B, which is midB way between that of the wind and that of the vessel. We must, as before, resolve c o into two forces, E O and F O. The part E o, which acts along the direction of the sail, has no effect in moving the vessel; FO, which acts perpendicularly to the sail, is the effective portion. We must now again resolve this force along two directions, one being that in which the boat moves, the other at right angles to it. We make a o equal to F O, and about it describe the parallelogram H GIO, and thus have two forces, represented by o H and O I, in the place of the original force, co. Now, of these, o I has no tendency to cause the vessel to advance; it acts sideways on the vessel, usually inclining it, and causing a slight motion, but it is resisted by the pressure of the water against the side; the other portion, o H, represents the portion of the force of the wind which is effective, and produces motion. In the same way you can calculate what portion of the force of the wind is effective in turning a windmill. The vanes are always set at an inclination with the plane in which they turn, and you must resolve the force along two directions, one perpendicular to the surface, and the other along it. The former you again resolve, and thus find what part of it produces rotation, and what part presses against the face of the mill.

ELEMENTS OF MACHINERY.

As it is our object to make these lessons as practical as possible, it will be well to look at a few of the simpler modes of altering and transmitting power. Sometimes this is advanced to the rank of a separate science, and called kinematics, or the science of motion, but it should be referred to here as a part of practical mechanics.

We seldom have our power available for use in the exact way we desire. Sometimes we have an alternate motion, like that of the piston-rod of an engine, and we want to derive from it a rotatory or progressive motion; or we want to transmit it along a direction making some angle with its course, or to make many other alterations in its mode of action.

In large factories there is frequently a long shaft running along the building, and driven by an engine. From this it is required to drive all the machines in the place. This is accomplished by fixing wheels on the shaft, and letting endless straps pass over these and then over the driving pulleys of the machines. The motion may often be greatly altered in this way. The strap itself merely transmits the power, and whether there is a gain or loss in speed or power depends on the comparative size of the sheaves. Frequently there are several of these wheels of different sizes fixed on the axle and on the machine, and thus the speed may be altered at pleasure. If the strap passes over a large one on the shaft and a small one on the machine, there will be an increase of speed, and if we reverse the condition there will be a loss. A common illustration of a similar arrangement is seen in a watch. The spring when fully wound up exerts a much greater power than it does when the watch has run nearly down. Now this would make it go irregularly, and therefore the fusee is introduced. When the force of the spring is greatest the chain acts Fig. 91. on the smallest part of the fusee, and therefore has only a short leverage, but as it unwinds and loses its force the chain acts at a greater leverage, and a uniform rate of motion is thus maintained.

Sometimes toothed wheels are used instead of straps, especially when the distance through which the power has to be transmitted is small. The advantage is that they do not slip, as straps are liable to do; the friction with them is, however, greater. If we want to transmit motion from a shaft to another placed at an angle with it (Fig. 91), we employ what are known as bevelled wheels. The action of these will be clear from the figure, without any explanation.

Often it is required to change a rotating motion into a progressive one, and we can accomplish this by means of a rack and pinion. A number of notches are cut in a bar of metal (Fig. 92a), of such a size and at such distances that the teeth of the wheel exactly fit into them, and as the wheel is turned the rack is moved onwards. This is very frequently employed when slow and regular motion is required, as in the adjustment of the tube of a microscope. Instead of a rack a chain is sometimes used (Fig. 92 b), the links being made of a peculiar shape, so that the teeth of the wheel may catch in them.

Fig. 92.

The crank (Fig. 93) is, perhaps, one of the most common of these elements of machinery. The piston-rod of an engine is usually jointed, and the end of the jointed part fixed to an arm projecting from the axle to be turned, and called a crank. Sometimes it is fixed to a pin in one of the spokes of the wheel, but the action is just the same. The force, however, with which it drives the wheel is continually varying. When the piston is at the bottom of the cylinder the crank and piston-rod are in one straight line, and therefore all the power presses on the bearing of the axle, and is lost. As the wheel turns the power acts with a leverage which increases till the wheel has made nearly onefourth of a revolution; it is then at its maximum, and diminishes till the piston-rod reaches its highest point, when it is all again lost. Now it is clear that unless we have some means of regulating the speed the machine will work very unevenly, and at times stop altogether. To obviate this, a large and heavy wheel, called the fly-wheel, is fixed on the axle of the crank. This, when once started, acquires an amount of momentum or moving force which carries it over the dead points when the power is lost. On account of the weight of the wheel, its motion is but slightly accelerated when the piston acts at its greatest leverage, but the additional force is stored up in it, and thus ensures a steady motion. The heavy wheel of a foot-lathe serves precisely the same purpose. The power is here applied during rather less than one-half of the revolution, but the momentum then acquired carries it through the remaining part.

EXAMPLES.

Fig. 93.

1. Forces of 9 and 12 act at right angles; what is their resultant? 2. The resultant of two forces which act at right angles is 10 pounds. One of the forces is 6; find the other.

3. Two men, one on each side of a stream, tow a barge. The angle the two ropes make is 60°, and each pulls with a force of 100 pounds. What is the total force exerted on the barge?

4. The tension of a wire in a piano is 100 pounds, its length is 5 feet. What force is required to draw its middle point 2 inches out of its position? 30°. The co-efficient of friction is }. 5. A weight of 90 pounds rests on a plane inclined at an angle of What force is required to keep it at rest?

ANSWERS TO EXAMPLES IN LESSON XIII.

1. The forces acting at the longer end are the power of 10 pounds acting at a distance from the fulcrum of 6 feet, and the weight of the lever, which is also 10 pounds, and acts through its middle point, or The moments on this end are thus 10x6, 2 feet from the fulcrum. or 671, and 10× 21 or 27. These make 95 pounds. As w acts at a distance of 14 feet, it must be or 76 pounds. 11'

95

2. Since is lost by friction, we may regard the weight as 12 pounds only. Now of the weight of the first pulley is supported by the power, of the next, and and of the other two; and since each

weighs 2 pounds, these amounts are 1 pound, pound, pound, and pound, together 17. Take this from 12, and we have an effective power of 10 remaining; and as the gain is 16, the weight raised is 16 × 101, or 162 pounds.

3. Friction requires a strain of 9× 20, or 180 pounds, to overcome it, and of the weight has to be borne. The strain, therefore, is 180+ 448, or 628 pounds.

4. Friction is here of 27 cwt., which equals

cwt. The amount cwt. The

of the weight sustained by the horse is of 27 cwt., or total strain is thus 1 cwt., or 144 pounds.

5. The weight of the carriage is 25 × 80, or 2,000 pounds. 6. The co-efficient of friction is, or nearly.

Examples in finding a Fractional Part of a Compound Quantity, and in reducing One Quantity to the Fraction of another of the same kind.

Find the value, expressed in successive denominations, of— 1. of £1; of £1; of 1s.

of £1; of 1s.; of 3s. 2d.

of 1 lb. avoir.; of 1 oz. Troy; of 1 cwt. of 1 yard; of 1 rod.

Again, Again,

Thus, of £2

=

-S.

s.;

2.

3

3.

of a shilling is of 12 pence, or 2 x yd. = 8d. Therefore, of £2 = 10s. 8d.

4.

of 1 ton;

5.

6.

of 1 mile; of 1 gallon; of 1 peck.

of 1 hour; of 1 minute; of 1 degree.

7. 3 of of a mile; of of a week.

Therefore, of 3 days 4 hrs. 25 min. is 1 day 6 hrs. 34 min. 3. To reduce one Compound Quantity to a Fraction of any other.

Finding what fractional part of one compound quantity another given compound quantity is, is called reducing the latter quantity to the fraction of the first.

Thus, finding what fraction of one pound 6s. is, is reducing 68. to the fraction of a pound.

This is, in fact, only another name for performing the operation of dividing one compound quantity by another, or of finding the ratio of two compound quantities (see Art. 11, Lesson XXVII., page 101).

4. EXAMPLE.-What fraction of £1 7s. 6d. is 3s. 6d. ?

£1 78. 6d. 330 pence.

3s. 6d. == 42 pence.

Hence, if £1 7s. 6d. be divided into 330 equal parts, 3s. 6d.

contains 42 of them;

Therefore, 3s. 6d. is % of £1 7s. 6d. ; and

reduced to its lowest terms.

11. Find the sum of of 2s. 6d. + of £3 2s. 6d. +

of a quart to the fraction of a gallon. of 1 secon to the fraction of a week. 22. Reduce £3 17s. 11 d. to the fraction of £7 3s. 23. Reduce 3 pecks 2 gallons to the fraction of 2 bushels. 24. Reduce 15 cwt. 65 lbs. to the fraction of 2 tons 3 cwt. 25. Reduce 1° 15' 10" to the fraction of a right angle. 26. Reduce 1 acre to the fraction of 5 acres 2 r. 40 p. 27. Reduce at of £1 to the fraction of a penny. 28. Reduce

of a week to the fraction of a minute. 29. Reduce of of £2 8s. 9d. to the fraction of £1 1s. 8d. 30. Express as a fraction of £10 the difference betwen £81 and of £8. 31. Find the value of

32. Find the value of

= when

136 gals. 2 qts. 178 gals. 3 qts.

33. Find the value of

1 lb. 7 oz. 4 dwts. 2 lb. 7 oz. 10 dwts. 77 dys. 4 hrs. 30 min. 6 dys. 12 hrs. of 517 square feet 72 inches. £3 18s. 8d. £6 12s. 9d.

of 15 guineas.

of

1° 17 17' 15"

of

of 104 yards 9 inches.

XXVIL

13. 338 cubic feet 1722

cubic inches,

14. 25° 3′ 15′′.

15. 35° 8' 30".

9. 55 yards 2 grs. 3, 16. 54 yrs. 2 mo. 2 wks

nails.

10. 44 yds. 1 qr. 3 nls.

6 ds. 2 hrs. 45 min.

6 secs.

11. 85 acres 119 rods. 17. 2 years 88 days.

12. 234 acres 138 rods.

18. 1 year 164 days.