Oldalképek
PDF

LESSONS IN FRENCH.-XXX.

1 your books have you mislaid ? 10. I had mislaid five, but my SECTION LIV.-THE PAST ANTERIOR AND THE PLUPER. | brother has found them. 11. Where had you left them? 12 FECT TENSES ($ 122, § 123].

I had left them in the garden. 13. Was your brother's watch 1. The past anterior is formed from the past definite of the

stopped ? 14. It was stopped. 15. Why was it stopped? 16. auxiliary and the past participle of the verb. J'eus parlé, I

He had forgotten to wind it up. 17. Had he not lost his key had spoken; je fus venu, I had come.

(clef, f.)? 18. He had not lost it. 19. Was the dyer gone 2. The past anterior expresses generally a momentary action,

20. He was not yet gone, he intended to leave at five. 21. Had which took place before another action. The latter immediately

you spoken to him when I came yesterday? 22. I had spoken follows the former, and often depends upon it. The action

- to him. 23. Had you told him that my sister is here ? 24. I expressed by this tense is not a customapy one. The past

had told him. 25. Is he still here ? 26. No, Sir, he is gone ; anterior is often preceded by à peine, scarcely; dès que, aussitôt

| he went this morning at six. que, as soon as ; quand, lorsque, when [$ 122, § 123 (3)].

SECTION LV.-IDIOMATIC CONSTRUCTIONS IN Dès que j'eus fini ma tâche je m'en As soon as I had finished my task I

REGIMEN, ETC. allai, went away.

1. We have given [Sect. IV. 4, and 9 76 (4)] a rule for the 3. This tense partakes of the nature of the past definite place of the noun, subject or nominative of an interrogative

4. The plaperfect is composed of the imperfect of the anxi. sentence. To avoid confusing the student, we have hitherto liary, and the past participle of the verb. J'avais parlé, I had refrained from introducing another construction which is often spoken ; j'étais venu, I had come.

used by the French instead of that given in the rule. When a 5. To this tense might be applied nearly all the rules on the sentence commences with où, where; que, what ; quel, which; use of the imperfect. The action which it expresses, or the

combien, how much, how many; and quand, when, the noun may situation which it depicts, is frequently a customary one, or one be place

be placed immediately after the verb. This construction is often repeated.

similar to that of the English interrogative sentence when the Dès que j'avais fini ma tâche je As soon as my task was finished I

verb has no auxiliary [S 76 (5)]. m'en allais,

used to go away.

Où sont nos amis et nos parents? Where are our friends and relations? RÉSUMÉ OF EXAMPLES.

Qu'écrit votre correspondant ? What does your correspondent write! Aviez-vous eu soin de vos effets ? Had you taken care of your things ?

2. When there are in a French sentence two regimens of equal J'en avais eu soin. I had taken care of them.

length, the direct should precede the indirect (S 76 (7)]. N'aviez-vous pas eu besoin de moi? Had you not wanted me!

Avez-vous donné les jouets à l'en. Have you given the child the playJ'avais eu besoin de vous et de I had wanted you and your brother. fant ?

things! votre frère.

Avez-vous donné cette lettre à Have you given the man that letter! N'aviez-vous pas eu l'intention de Had you not intended to speak to me?

l'homme ? me parler ? Dès que vous eûtes fini votre lettre, As soon as you had finished your

3. The régime indirect precedes the direct, when the latter is ne la portátes-vous pas à la letter, did you not carry it to the

followed by a relative pronoun, or by other words qualifying it, poste ?

post-office ?

and rendering it much longer than the indirect ($ 76 (8)]. The Dès que vous aviez fini vos lettres, As soon as your letters were finished, indirect regimen should also precede the direct, when the sen. ne les portiez-vous pas à la poste? did you not take them to the post- tence would otherwise be equivocal ($ 76 (9)].

office?

Avez-vous donné à l'enfant les Have you given the child the play, Dès que vous fûtes arrivé, ne com. As soon as you had arrived, did you

jouets que vous lui aviez promis? things which you had promised mençâtes-vous pas à écrire ? not commence writing ?

him ? Dès que vous étiez arrivé, ne com- As soon as you used to arrive, did menciez-vous pas à écrire ?

RÉSUMÉ OF EXAMPLES. you not commence writing ?

Quel âge a cette demoiselle ? How old is that young lady? VOCABULARY.

| Que veulent dire ces messieurs ? What do those gentlemen mean? Arrêt-er, 1, to stop. | Egar-er, 1, to mislay. | Perd-re, 1, to lose. Où sont allés messieurs vos frères ? Where are your brothers gone! Bal, m., ball.

Invit-er, 1, to invite. Remont-er, 1, to wind | Combien d'enfants a co monsieur? How many children has that gentilda Bourse, f., purse. Se lev-er, ref., to rise. up.

man ? Se coucher, 1, ref., to Malade, sick.

Retrouv-er, 1, to find Avez-vous payé cet argent au mar. Have you paid the merchant that go to bed. Musicien, m., musi again.

chand ?

money ? Dangereusement, dan cian.

Sort-ir, 2, ir., to go J'ai payé mon habit au tailleur, I paid the tailor for my coat. gerously. Oublier, 1, to forget, out.

N'aviez-vous pas demandé cela à Had you not asked the child for Diner, m., dinner. Part-ir, 2, to set out. Spectacle, m., play. l'enfant ?

that! EXERCISE 103.

VOCABULARY. 1. Ne saviez-vous pas où le musicien était allé ? ù le musicien était allé ? 2. Je savais | Accompagn-er, 1, to ac- | Bouteille, f., bottle. 2. Je savais

Commis, m., clerk qu'il était allé à Paris. 3. Ne vous avait-on pas dit que votre

company.

Chaine, f., chain. Dernier, -e, last. frère est mort ? 4. On m'avait dit qu'il était dangereusement

Ainé, -e, eldest.

Chapeau, m., hat, bon Près, near, nearly. malade. 5. Ne vous couchiez-vous pas ordinairement, dès que

Associé, m., partner. net.

Rend-re, 4, to mu

Serrurier,m., bocksmith, vous aviez fini vos leçons ?

Aubergiste, m., inn- Cinquante, f., fifty.
6. Dès que je les avais finies, j'allais

keeper.
| Clef, f., key.

Serviette, f., raphis au spectacle. 7. Dès que vous eûtes fini vos leçons, que fitesvous hier au soir ? 8. Aussitôt que je les eus finies, j'allai au bal.

EXERCISE 105. 9. Cette petite fille n'avait-elle pas envie de dormir ? 10. Elle 1. Où étaient vos parents l'année dernière ? 2. Ils étaient avait plus envie de dormir que d'étudier. 11. Qu'aviez-vous fait en Angleterre. 3. Où sont restés les messieurs qui vous : de (with) votre livre quand je vous le demandai. 12. Je l'avais compagnaient ce matin P 4 . Ils sont restés chez leurs assoCIAS égaré. 13. Je l'avais oublié dans le jardin. 14. Pourquoi votre 5. Que lisaient vos amies lorsque vous les avez quittees! montre était-elle arrêtée ? 15. Parce que j'avais oublié de la Elles lisaient les nouvelles qu'elles venaient de recevoir. remonter. 16. L'horloger ne l'avait-il pas remontée ? 17. 11 Que dit monsieur votre père P 8. Il ne dit rien. 9. Quel de avait oublié de le faire. 18. N'aviez-vous pas perdu votre a ce monsieur P 10. Il a près de cinquante ans. 11. Quel so bourse? 19. Je l'avais perdue, mais je l'ai retrouvée. 20. ont vos enfants ? 12. L'aîné a dix ans, et le plus jeunes Votre cousin était-il parta P 21. I n'était pas encore parti. ang. 13. Avez-vous demandé votre chaîne d'or à ce monde 22. Était-il sorti? 23. Il était sorti avec ma mère. 24. Od 14. Je la lui ai demandée. 15. Avez-vous rendu au como était-il allé ? 25. Il était allé chez mon frère, qui l'avait invité l'argent qu'il vous avait prêté ? 16. Je le lui ai rendu.. à diner.

Aviez-vous envie d'envoyer vos clefs au serrurier? 18. J'ai EXERCISE 104.

envie de les lui envoyer, car elles sont cassées ? 19. Valalt 1. Hop

ed to speak to my brother? 2. I had | la peine d'envoyer ces bouteilles à l'aubergiste ? 20. Il Tuar inten

ut he was gone. 3. Did your sister la peine de les lui envoyer, car il n'en avait pas. 21. AUS
on as she had read (lu) her book P vous demandé des serviettes à votre père ? 22. Je n'a pas

as she had read it. 5. Were you voulu lui en demander.
P 6. I was told that she had been

EXERCISE 106.
you know what you had done with 1. What was the locksmith saying to you? 2. He was saya
at I had mislaid it. 9. How many of ing that he had brought my key. 3. How many letters

[graphic]

you taken to the post-office? 4. I have taken seven, three | 13. Savez-vous combien il y a de Paris à Vienne ? 14. Il y a for you and fonr for my father. 5. Where is the gentleman trois cent six lieues de Paris à Vienne et deux cents lieues de who has brought that letter ? 6. He lives at my father's; do Vienne à Copenhague. 15. Y a-t-il longtemps que la compagnie you wish to speak to him? 7. I wished to sond him a letter est venue ? 16. Il y a plus de deux heures qu'elle est ioi. 17. Which I brought from England. 8. Have you returned to that Y a-t-il longtemps que vous avez lu cette affiche ? 18. Il y a man the money which he had lent you? 9. I have returned plus de trois heures que je l'ai lue. 19. N'y a-t-il pas plus it to him. 10. Did you wish to send your brother the key d'une demi-heure que votre scur lit ? 20. Il y a si longtemps of your room? 11. I wished to send it to him. 12. Was it qu'elle lit, qu'elle en est fatiguée. 21. Y a-t-il longtemps que worth the while to give your brother that book ? 13. It was vous attendez ce morceau de musique ? 22. Il y a plus d'un an worth the while to give it to him, for (car) he wanted it. 14. que je l'attends. Was it worth the while to send those bottles to the druggist

EXERCISE 108. (apothicaire)? 15. It was worth the while to send them to him. 1. Do you not know where my father lives? 2. I know 16. Where is the innkeeper ? 17. He is in England. 18. How where he lives, but I have no time to go to his house to-day? many children has the locksmith ? 19. He has ten. 20. How 3. How long has the physician lived in Paris ? 4. He has lived many books has the physician ? 21. He has five hundred there ten years. 5. How long did he live in England ? 6. He volumes. 22. Have you given the gentleman that letter? 23. lived in England six years and a half. 7. Can you tell me where I have forgotten to give it to him.

the locksmith lives? 8. He lives at my brother's. 9. Have SECTION LVI.-IDIOMATIC USES OF TENSES OF VERBS. you been waiting long for this book? 10. I have been waiting

1. The French avoid placing the verb at the end of such for it more than a year. 11. How long has your son been learnsentences as the following, when the nominative is a noun.

ing Greek ? 12. He has been learning it these two yoars. 13.

How long has your brother had this orchard ? 14. He has had Dites-moi où demeure M. H., Tell me whers Mr. H. lives.

it more than six months. 15. How far is it from Paris to Je ne sais où est mon père, I do not know where my fathor is.

Lyons ? 16. It is one hundred and sixteen leagues from Paris Savez-vous où est George ? Do you lenow where George is ?

to Lyons. 17. Is it farther (plus loin) from Lyons to Geneva 2. In speaking of a state, condition, or action, commenced in

than from Lyons to Turin ? 18. It is farther from Lyons to the past but still continuing, the French use the present of the Trin than from Luong to Genera19 Hour 7

Turin than from Lyons to Geneva. 19. How long did your indicative. The past is commonly used in English in similar father live in Germany? 20. He lived in Germany two years,

and in England six months. 21. How long did you live in Combien de temps y a-t-il qu'il est How long has he been here?

Rome? 22. We lived there more than a year. 23. Have you ici?

been learning German more than one year? 24. I have been Il y a deux heures qu'il écrit, He has been writing these two hours.

| learning it more than four years. Il y a un mois qu'il demeure à He has lived in Paris one month.

Paris,
Il y a deux ans qu'il est mort, He has been dead these two years.

KEY TO EXERCISES IN LESSONS IN FRENCH, 3. When, however, the state no longer continues, the past

EXERCISE 16 (Vol. I., page 60). may be used in French, in the same manner as it is used in 1. Avez-vous les chevaux de mon frère ? 2. Je n'ai pas les chevaux English.

de votre frère, j'ai les chapeaux de votre cousin. 3. Les maréchaux Combien de temps avez-vous de- How long did you live in L. ?

ont-ils de bon fer? 4. Le maréchal a deux morceaux de fer. 5. Avez. meuré à L. ?

vous deux paires de bas ? 6. J'ai une paire de bas, et deux paires Combien de mois avez-vous appris How many months did you learn

de gants. 7. Votre soeur a-t-elle les bijoux d'or ? 8. Ma scur a les l'allemand ? Gorman?

bijoux d'or et les joujoux de papier. 9. Avez-vous les choux dans Il y un mois que je ne l'ai va, I have not seen him this month. votre jardin ? 10. Nous avons deux choux dans notre jardin. 11. Avez.

vous les chapeaux de soie? 12. Les généraux ont les chapeaux de soie. 4. Combien y a-t-il.... Combien de milles y a-t-il .... 13. Avez-vous du café ou du sucre ? 14. Nous n'avons ni café ni sucre. Quelle distance y a-t-il ? answer to the English expressions, 15. Vos frères ont-ils honte ? 16. Mes frères n'ont ni honte ni peur. How far .... How many miles is it.... What is the distance ? 17. Qui a deux barils de farine ? 18. Le meunier a deux barils de Combien y a-t-il de Paris à Lon. How far is it from Paris to London?

farine. 19. Les oiseaux ont-ils du pain? 20. Les oiseaux n'ont pas dres?

de pain. 21. Le marchand a-t-il du thé, du chocolat, du sucre, et du RÉSUMÉ OF EXAMPLES.

poivre ? 22. Il a du sucre et du poivre, mais il n'a ni thé ni chocolat.

23. Votre sour qu'a-t-elle ! 24. Elle n'a rien. 25. Votre frère qu'a-t-il ? Combien de temps y a-t-il que vous How long have you had that house ?

26. Il n'a rien, 27. N'a-t-il pas froid? 28. Il n'a pas froid, il a chaud. arez cette maison ? Il y a deux ans que nous l'avons. We have had it these two years.

EXERCISE 17 (Vol. I., page 78). Combien de temps avez-vous eu How long did you have that house ? | 1. Have you the blacksmiths' hammers ? 2. Yes, Sir, I have cette maison ?

them. 3. Have you them not? 4. No, Sir, we have them not. 5. The Nous l'avions dix ans. We had it ten years.

workman has them. 6. Has the innkeeper your horses ? 7. The innCombien de temps y a-t-il que How long has your brother boen keeper has neither my horses nor yours, he has his. 8. Has the votre frère apprend le grec ? learning Greek ?

physician books? 9. Yes, Sir, he has good books. 10. Have you not Il y a six ans qu'il l'apprend. He has been learning it six years.

my best pens? 11. Yes, Sir, I have your best pens, mine, and those Qnelle distance y a-t-il de Calais à How far is it from Calais to Bou- of your cousin. 12. Has the traveller good guns Boulogne ?

logne ?

good guns, he has iron guns. 14. Has not the sailor my horse-bair Dy a huit lieues de Calais à Bou- It is right leagues from Calais to

mattresses ? 15. He has them not. 16. What has he? 17. He has logne,

Boulogne.

the cabinet-maker's woollen mattresses. 18. Has the cabinet-maker VOCABULARY.

mahogany tables ? 19. Yes, Madam, he has mahogany tables and Affiche, 1., bill. Copenhague, Copon- Maintenant, now.

white marble tables. 20. Have you my chairs or yours? 21. I have An, m., année, f., year. hagen.

Mois, m., month.

neither yours vor mine, I have the cabinet-maker's. 22. Are you not Attend-re, 4, to expect, | Demi, -e, half. Morceau, m., piece.

sleepy ? 23. No, Sir, I am neither sleepy nor hungry. 24. Has the to wait for.

Fatigué, -e, tired. Ne from. naitre to tinman your iron candlesticks? 25. No, Sir, he has the blacksmith's. Compagnie, i., com- Imprimeur, m., prin. be born. pany.

ter.

Verger, m., orchard.
| Liene, f., league. (Vienne, Vienna.

MECHANICS.--XIII.
EXERCISE 107.

STATICAL FORCES.-FRICTION. 1. Combien de temps y a-t-il que M. L. demeure à Paris? We have now mastered the elementary principles of the simple 2. Il y a dix ans qu'il y demeure. 3. N'a-t-il pas demeuré à machines, and are in a position to resolve a compound machine Lyon ? 4. Il y a demeuré autrefois. 5. Pouvez-vous me dire into the elementary ones of which it is made up, and thus to ou est le fils du capitaine ? 6. Il y a un an qu'il est en Angle- find the benefit derived from its use. Our inquiry now is, what terre. 7. Savez-vous où demeure M. B.? 8. Il demeurait are the forces which most generally act on a body or a system autrefois à Rouen ; je ne sais pas où il demeure maintenant. of bodies when in a state of equilibrium? We shall consider 9. Y a-t-il longtemps que vous êtes ici P 10. Il y a plus de further on the main “prime movers" or forces which produce deux mois que nous sommes ici. 11. Combien de temps y motion. &-t-il que vous avez ce verger? 12. Il y a un an que nous l'avons. There are, then, four kinds of forces with which statics deals.

Tas are: 1. Gravity. 2. Resistance of surface. 3. Tension. we obtain, it is very important for us to become familiar with 4. Friction.

its effects. Gravity is the most universal of these, as it acts constantly If we attempt to cause one body to slide or move over and on every substance. Hence we ought always to take it another, we find a certain amount of resistance to our efforts. into account, though, for the sake of simplicity, we have hitherto , This resistance or opposition to attempted motion is friction. All neglected it. Most that is requisite was, however, said about it, surfaces have a degree of roughness or unevenness of texture, in our lessons on the centre of gravity.

and the inequalities of two such surfaces fit into one another, All bodies attract each other with a force proportionate to the projections of the one catching those of the other. We find their bulk. If a heavy weight be suspended by a cord over the this friction more or less in all cases of attempted motion. If edge of an almost vertical precipice, and looked at from a short | two surfaces were absolutely smooth, there would be none; distance by a telescope, we shall find that the cord does not this, however, we cannot obtain, but the nearer we approach to hang perfectly vertical, but is inclined slightly inwards by the it, the less friction we have. attraction of the rock for the weight.

If a block of wood lies on the ground, I may be unable to This principle of universal attraction, which was discovered push it along. Move it now to a surface of elear ice, the by the great Sir Isaac Newton, is applicable to all bodies what- resistance will be less; and if we place it on narrow smooth ever. It holds the smallest stone to the ground, and at the runners, like those of a sledge, we still further reduce friction. same time keeps the planets in their orbits, and thus lies at the In all cases, however, it exists; and as we see, it is only called basis of the science of astronomy. When a body is raised from into play when motion is attempted; and since it prevents the the earth and then left free, this attraction causes it to fall. body from moving (unless the force applied be powerful enough The reason why it falls towards the earth, instead of the earth to overcome it), its line of action must be contrary to that of rising to it, is the immensely superior bulk of the latter. the attempted motion, as otherwise it could not neutralise the Strictly speaking, they do move towards each other in the exact force applied. proportion of their bulk. If a body of equal size with the Now it will easily be seen that it is of great importance to be earth were allowed to fall towards it, they would meet just half able to ascertain the amount of friction between surfaces. On way. This force always acts towards the centre of the earth, and a railway we want to know what force is required to overcome its amount is easily ascertained, being simply the weight of the the friction of a train along a level part of the line. We can body. When we say that a body weighs eight pounds, we merely easily, by the principles of the inclined plane, find the additional mean that that is the force with which the attraction of the force required to draw it up an incline. Many practical ques. earth draws it. This attraction diminishes as we remove tions of this sort are constantly met with, and there are two farther from the earth's centre; hence, as the diameter is common ways of solving them. greater at the equator than at the poles, a substance weighs less The most usual method is by the apparatus represented in there than it does as we travel northward or southward. Of course Fig. 82. A slab of the substance over which the other is to this must be ascertained by a spring balance; in any other kind, slide, is laid the weight would be altered as much as the substance weighed. horizontally

We see, then, that gravity acts in a line perpendicular to the on a table. A earth's surface, is equal to the weight of the body on which it block, A, of acts, and, as before shown, may be considered to act through the second its centre of gravity. It is now easy to calculate what allow. substance is ance is to be made for the weight of the simple machines, and taken, a cord

Fig. 82. whether this weight tells in their favour or against them. In is fastened to an a lever of the first kind, for instance, as the power acts at the it and passed longer arm, the centre of gravity will, if the lever be uniform, over a pulley at the edge of the table, so as to be parallel to its be in that arm, and therefore gravity is here a third force, surface; at the other end of this cord a scale-pan is fastened. which helps the power to sustain a greater weight than it other. Weights are now placed in this, or, better still, sand is poured wise could.

into it, until A just begins to move. The weight of the sand in In the first system of pulleys, on the other hand, their weight the pan divided by that of a, gives the fraction which expresses acts against the power, one-half of the weight of the pulley | the proportion that the friction bears to the weight to be moved. next the power being supported by it, one-fourth of the next, Thus, if the substance weigh 2 pounds or 32 ounces, and a weight and so on. Hence the weight that can be raised is less than of 5 ounces is required to move it, the fraction is . This is theoretically it should be.

called the Co-efficient of Friction. We now pass to the second kind of force-resistance of The other way of ascertaining this quantity is sometimes surfaces. We shall better understand this by assuming a case. easier. A block, A (Fig. 83), of one substance is laid on a plane, A ball rests on a horizontal table; the force of gravity presses BC, made of the other, and the end o is then lifted till A it vertically downwards with a force equal to its weight, and just on the point of sliding down the plane. The full amount yet the ball does not fall. Evidently there must be some force of friction is now at work, and we may consider this as a case counteracting that of gravity. This force is the resistance of of a body kept at rest on an inclined plane. The forces which the table, which presses it upwards with a force exactly equal to act on A are its own weight in the direction A w, the resistance its weight; for, if it were not equal, motion would ensue. This of the plane in the direction AR perpendicular to its surface, and resistance acts, too, in a line perpendicular to the surface, for it

the force of friction must be exactly opposite to the line in which gravity acts, or else

which acts up the the two forces would have a resultant, in whose direction the ball

F plane along A F. Now, would move. We learn, then, the following general principle :

since there is equiAction and re-action are always equal, and act in exactly

librium, this last force opposite directions.

is equal and opposite When two surfaces press on one another, the line of action of

to the resultant of AB the resistance must pass through the point of contact. If the

and Aw, that is, to AE. surfaces be smooth and one be a plane, it will also be perpen.

The three forces, then, dicular to that plane.

may be represented The third kind of force is the tension of strings or fine rods. When an omnibus is drawn by horses, the forces which act

by the three sides of w

the triangle w A E, but directly on it are the tensions of the traces, and by these ten

Fig. 83.

this triangle is similar cions it is moved. About this kind of force there is little

to the triangle BCD; difficulty, as it acts along the direction of the cord by which it therefore we may take BC as representing the weight, and o is communicated to the body moved, and its intensity is measured by the number of pounds it will support. We

| the friction, and is the co-efficient of friction. We have, ассор

pass on to consider the nature and effects of the then, the following rule-Incline the plane till the body
hely, friction. This has been frequently referred the point of motion; the elevation of the end of the past

interferes with the accuracy of the results divided by its length gives the required fraction,

4 is

[graphic]

E

[ocr errors]

This suggests the way of making a useful calculation, like the When a body is kept at rest by the action of any number of following :-On how steep an incline will a cart stand safely if forces upon it, if we resolve these forces along any two directions the co-efficient of friction be ? We see that the incline must at right angles to one another, their resolved parts in each direcbe somewhat less than 1 foot in 30, as, if it be greater, the cart | tion must neutralise each other. If they did not, some motion will run down from its own weight. By these and similar means must ensue. In a similar way we can often find whether any thousands of experiments have been tried, a few of which are here number of forces will produce equilibrium, and if not, what their given as illustrations. You can easily try others yourself. Along resultant will be. This mode of solving the question is somea railway friction is reckoned to be from 8 to 10 pounds per ton; times more convenient than the polygon of forces. on a good road about th of the load; this amount, however, Suppose three forces, represented by A B, AC, and A D (Fig. 84), varies very greatly with the character of the road. The co act on A. Fix on any two lines E F and G i at right angles to efficient of friction for steel on ice is only so, while that of oak one another, and both passing through A. From B, C, and D on oak or elm is over 4.

drop perpendiculars on E F and G H. This may be done with a There are, however, certain general rules, discovered by expe- square. Now A B is the diagonal of the parallelogram KAN B, riment, which are more important to remember.

and thus is the resultant of two forces which are represented by 1. Friction is proportional to the pressure. If we place A N and a K. We may therefore resolve it into those two, and, weights on A (Fig. 82) so as to double the pressure, we shall find it requisite, also, to double the weights in the pan, and so for any other alteration of the pressure of A.

2. The amount of friction does not vary with the extent of the surfaces in contact. This at first seems strange, but, if we consider it, we see the reason. Suppose a block of deal two inches thick move over another surface of deal. If the block weigh 10 pounds, the force required to overcome friction will be about 3pounds. Now saw the block into two, of half the thickness, and lay them side by side. Each has half the weight of the original block and the same surface, and so the friction of each will be one-half of 31 pounds; the two together will therefore move with the same friction as the one did, though the extent of surface is doubled. 3. The amount of friction varies with the nature of the bodies

HP and the smoothness or otherwise of their surfaces.

Various ways of diminishing friction are adopted in practice. Those parts of any machine which work together are made as

Fig. 84. smooth as possible, and oil or grease applied to them. The bearings, too, or boxes in which the axles of wheels turn, are instead of a B acting on A, we shall have the two forces AN made of a different kind of metal from the axles themselves, and

acting along E F, and A K acting along 1 g. many other expedients are resorted to. Still there is a loss of

In the same way resolve A c and A d into A L and A M, and power from this cause, which often amounts to or even

A O and A P respectively. There are two kinds of friction-sliding and rolling. Sliding

We have thus resolved all our forces into others acting in friction is that of which we have spoken; but if a body be made

the directions we fixed upon. Three of these, AN, AM, and round, and allowed to roll over and over instead of sliding, a LA o. act along EF: and if an equals the sum of the other two. different kind of friction comes into action. The rudest appli- 14h

these will cancel one another, and so of the forces along G H. cation of this is when a man, instead of pushing a stone along | If there are any residues in either case we mark off distances the ground, pats rollers under it, and thus moves it with far

from A to represent them, and complete the parallelogram, the more ease, fresh rollers being put under in front when needed.

diagonal of which will be the resultant. Wheels are a further advance upon this, as they not only save The other proposition is as follows: If a body be kept at the trouble of constantly replacing the rollers, but, as they only

rest by the action of three forces, their lines of action must, touch the ground at the sides of the body, and not along the

unless the forces be parallel, pass through one point. For if not, whole width as rollers do, they avoid much of the friction.

since two of them pass through the point in which they meet Sometimes when a large axle has to turn in bearings, frictionwheels are introduced.

(and they must meet, not being parallel), the body will turn till These are small wheels, on the edge of this point comes into the line of action of the third. If in Fig. which the axle turns, and they transfer the friction to their own

| 85 two of the forces act through B, and the third through a in small axles. Many such appliances to avoid friction are con- the direction A c. the body will evidently turn till B. A. and c are stantly met with. Castors on chairs and tables, and narrow

in one straight line. The cases when the forces are parallel irons on skates, are familiar examples.

have all been considered except the one when equal and parallel We must not, however, imagine from all this that friction is

forces act in opposite directions, and we have what is termed a always a hindrance. Far from it. If we try and walk along a

couple. Let ac and BD represent two such forces. In any very glassy surface of ice, we are soon painfully reminded of the

the other case, if forces act on a body, a single resultant can be absence of the customary friction between our boots and the found, but here no one force that can be applied will produce surface on which we are walking, and hence in frosty weather

equilibrium. The motion, however, which these forces tend to gravel or ashes are scattered on the paths. All the driving force

produce, is not one of progression a railway engine has is from the friction of its wheels with the

through space, but merely one of rails. It was at first proposed that the driving-wheels should

c rotation round a point midway be toothed, and notches cut into the rails into which these teeth

between A and B. This tendency might catch; but the friction was soon found to be sufficient.

to rotation increases with the On damp days, however, we frequently see the porters at a

distance A B, and is clearly station putting gravel on the rails, in order that there may be more friction at starting.

equal to the sum of the forces

Fig. 85.
The brake, also, which is applied to

multiplied by half that distance. stop a train or machine, acts by pressing a block against the

ist the The only way to overcome these forces is to introduce another wheel, and thus causing an amount of friction which is soon suffi-|

couple having an equal tendency to turn the body in the concient to overcome the momentum acquired. So, when a nail is

trary direction. The application of these principles we shall driven into a piece of wood, it is held in its place merely by friction,

see in the next lesson. and the same cause enables the fibres of cotton or hemp to cling

EXAMPLES together so as to be woven into a cord or rope. We see, then, that friction is one of the most important forces we have to consider.

1. A lever of the first kind, 8 feet long, weighs 10 pounds. What We must now look at two propositions which are often very | weight will a power of 10 pounds raise, the fulcrum being 15 inches useful, and we shall then be able to trace the application of from the end ? what has been said to a few common cases.

2. In the first system of pulleys there are four blocks, each weighing 2 pounds. If one-fifth of the power be lost by friction, what weight again, resemble nouns in ing, in having (for the most part) an will 15 pounds support?

active signification ; but the ending ion differs from the ter3. If friction be reckoned at 9 pounds per ton, what power will be

mination ing, inasmuch as the former can be affixed only to required to draw a train weighing 20 tons up an incline of 1 in 100 ?

nouns of Latin parentage: thus, we say the communication, or 4. What strain must a horse pull with, to draw a load of 27 cwt.

the communicating ; but WE CANNOT SAY the runion (running), up an incline of 1 foot in 70, the co-efficient of friction being 16?

nor the rision (rising). 5. If the co-offlcient of friction bet, and the strain on a rope

Nouns in ion are not so purely active as which jast moves a carriage be 80 pounds, what is the weight of the

are nouns ending in ing. For instance, communication may carriage ?

signify either the act of communicating, or the thing communi6. A horse has to exert a strain of 116 pounds to pull a wagon cated, the result of the act of communicating. So devotion may weighing 1} tons. What is the co-efficient of friction ?

denote the act of devoting, or the object devoted.

Ique, from the Latin iquus, another form of icus; as in

antiquus, antique. Antiquus means ancient ; but antique does ANSWERS TO EXAMPLES IN MECHANICS, XII.

not mean ancient merely or generally, so much as ancient in 1. A power of 201 pounds.

relation to the immediate past, the age of the Reformation, the 2. He must pull with a strain of t of a ton, or 89% pounds. Middle Ages. Not seldom has antique the subordinate notion of 3. It would support a resistance of 616 pounds,

curious, singular, or odd connected with it; probably becanse 4. A force of nearly 10 pounds must be applied, the gain being 2x 37 Lantionies are rare. feet divided by inch, which equals 3014. 5. The prossure will be 8,3044 pounds.

“ Name not these living death-heads unto me, 6. The difference between the threads is to of a foot. The gain is

For these not ancient but antique be."-Donne. therefore 14 x 2 x 34 x 110, or 1,210.

“ And sooner may a gulling weather-spy, 7. 135 pounds. The gain is - or 270.

By drawing forth heaven's scheme, tell certainly

What fashion'd hats or ruffs, or suits next year, In the foregoing, friction was not taken into consideration.

Our giddy-headed antique South will wear.”—Donne.

The word antic, from antique (formerly spelt antick), takes its LESSONS IN ENGLISH.-XVII.

force from this associated notion of singularity.

“ We cannot feast your eyes with masks and revels, SUFFIXES (continued).

Or courtly anticks."

Shakespeare, LANGUAGE has many a tale to tell respecting national character

“ Within the hollow crown

That rounds the mortal temples of a king and manners. The fact that the English names of animals,

Keeps Death his court; and there the antick sits when alive, are of Saxon origin-for example, bull, sheep, calf

Scoffing his state."

Shakespeare. and that the English names of animals, when dead, are of

“ A work of rich entail and curious mold, French origin-as beef, mutton, veal-in showing that at one

Woven with anticks and wild imagery."-Spenser. period of our history the Saxon population fed the animals, and the French population ate them, shows also that the former

Ise, formerly ize, of Greek origin, introduced through the New were in hard servitude to the latter; in other words, that our

Testament; as in the word baptise, from the Greek Battica, Saxon ancestors were serfs, and the forefathers of the present!

pronounced bap-ti'-zo, I dip frequently. From the same Greek French were masters on this soil of England.

ending we have dogmatise, methodise, criticise. This terminaSuch a relation was not likely to be durable. A proof of the

tion gives rise to others; as from baptizo come baptist, baptisma, assertion is found in the words etiquette and coquette, to which baptistry, baptismal. reference was made in the last lesson (page 71). Etiquette “He (the pope) solicited the favour of England by sending Henry a and coquette are both of French origin. Essentially French sacred rose, perfumed with musk, and anointed with chrism."—Hume. are the things the words stand for. Among the French -anointed; that is, with a consecrated unguent or holy oil. those things had their birth, and on the soil of France they The suffix ise or ize, added to nouns, gives them the force of flourished. Hence you learn that lightness, weakness, and verbs, thus : to christianise, is to make Christian; to evangelio, vanity are essential features in the character of Frenchmen. I is to bring men to the evangel. that is the Gospel. In the use Superficial, if pleasing, a true type of the French character may outshine, or for a moment overcome, an Englishman, but The termination ism is employed to describe religious or social he is utterly unable to hold our countryman in permanent diversities; it is found in Atheism, Deism, Swedenborgianisti,

Calvinism, Arminianism, Owenism, etc. Equally illustrative of national character is the fact that Pan. While ism denotes the sect, ist denotes the sectary; as, taloon and Punch come to us from Italy. Pantaloon is from Atheist, Deist, Methodist, etc. the Italian Pantalone, which when written in full is Piantaleone, The adherents to particular modes of faith are also designated a word signifying lion-planter. Pianteleone was a surname or by arian; as, Trinitarian, Unitarian; or ian, as Episcopalian. name of honour, given in the Middle Ages to a very powerful Sometimes the word man holds a similar post, as in Churchmak, Venetian, who planted the banner bearing the winged lion of used in contrast with Dissenter. Ist, too, performs the same St. Mark, the symbol of the Venetian Republic, on many islands office; as in Nonconformist. Another form is found in ite; as of the Mediterranean. His renown caused Piantaleone to be Iryingite, Mormonite, eto. Analogy is a dangerous gude... brought on the stage. Hence Pantaloon, the lion-hearted, who English, for, while we say Irvingite, We DO NOT say Southcotite originally bore a nearer resemblance to his prototype than is but Southcotian-probably for the sake of euphony. This found in the impudence and hardihood of the modern degenerated comes, we are disposed to think, not from the raro Latin ending specimen. And hence the peculiar dress of Pantaloon (also itus (as auritus, with pricked-up ears), but the scriptural ste ; & trousers called pantaloons), which, making due abatement for in Jebusite. exaggerations, was the attire of distinguished Italians in former Ish, probably from the Saxon ic and the German isch (28 days.

mürrisch, peevish), denotes, as in peevish, quality, and so foros Our Punch owes his birth and his name to Italy. Punoh is adjectives. Ish has sometimes a diminutive foroe; as this derived from the Italian Pulcinella ; and Puloinella seems to be thickish. When forming part of verbs, as in punish, pablo made up of Puccio d' Aniello; that is, Puccio, an ill made, witty has a different origin, and may be a softened form of the Great clown of the town Aniello, who gained a livelihood by his antics termination ise or ize. in the market-places and public highways. The character being Ite, a patronymio, or father-name—the name that is expressive transferred to the stage, Panch oame to be the recognised symbol of a race, like the Greek ides is very common in the Old Te of fun and frolic.

ment, from the language of which it may have come into the Ion, from the Latin termination io; as actio, action ; quæstio, English ; thus, Israelite is a descendant of Israel; 50 weba question; motio. motion; visio, vision. Nouns in ion, like Hittites, Hivites, etc. Donne ir

be called verbal, seeing they are derived Ire, of Latin origin, from ivius, as seen in captixus, a captits. imme

28; as actio, from the Latin verb ago also in fugitive (Latin, fagio, I flee); nativus (Latin, na! D), I do; motio, from the Latin verb born), a native ; votivus (Latin, votum, a vow), votive. This

motus), I move, etc. Nouns in ion, ) in French becomes if, whence we have plaintif (French, plaidu

of this term

subjection.

[graphic]
[ocr errors]
« ElőzőTovább »