LESSONS IN FRENCH.-XXX. SECTION LIV.-THE PAST ANTERIOR AND THE PLUPERFECT TENSES [§ 122, § 123]. 1. THE past anterior is formed from the past definite of the auxiliary and the past participle of the verb. J'eus parlé, I had spoken; je fus venu, I had come. 2. The past anterior expresses generally a momentary action, which took place before another action. The latter immediately follows the former, and often depends upon it. The action expressed by this tense is not a customary one. The past anterior is often preceded by à peine, scarcely; dès que, aussitôt que, as soon as ; quand, lorsque, when [§ 122, § 123 (3)]. Dès que j'eus fini ma tâche je m'en As soon as I had finished my task I allai, went away. 3. This tense partakes of the nature of the past definite. 4. The pluperfect is composed of the imperfect of the auxiliary, and the past participle of the verb. J'avais parlé, I had spoken; j'étais venu, I had come. 5. To this tense might be applied nearly all the rules on the use of the imperfect. The action which it expresses, or the situation which it depicts, is frequently a customary one, or one often repeated. Dès que j'avais fini ma tâche je As soon as my task was finished I m'en allais, RÉSUMÉ OF Aviez-vous eu soin de vos effets ? used to go away. EXAMPLES. N'aviez-vous pas eu l'intention de Had you not intended to speak to me? me parler? Dès que vous eûtes fini votre lettre, As soon as you had finished four ne la portâtes-vous pas à la poste ? Dès que vous aviez fini vos lettres, ne les portiez-vous pas à la poste? Dès que vous fûtes arrivé, ne commençâtes-vous pas à écrire ? Dès que vous étiez arrivé, ne commençiez-vous pas à écrire ? Arrêt-er, 1, to stop. Bal, m., ball. Bourse, f., purse. letter, did you not carry it to the post-office? your books have you mislaid? 10. I had mislaid five, but my 11. Where had you left them? 12. brother has found them. I had left them in the garden. 13. Was your brother's watch stopped? 14. It was stopped. 15. Why was it stopped? 16. He had forgotten to wind it up. 17. Had he not lost his key (clef, f.)? 18. He had not lost it. 19. Was the dyer gone? 20. He was not yet gone, he intended to leave at five. 21. Had you spoken to him when I came yesterday? 22. I had spoken to him. 23. Had you told him that my sister is here? 24. I had told him. 25. Is he still here? 26. No, Sir, he is gone; he went this morning at six. SECTION LV.-IDIOMATIC CONSTRUCTIONS IN 1. We have given [Sect. IV. 4, and § 76 (4)] a rule for the place of the noun, subject or nominative of an interrogative sentence. To avoid confusing the student, we have hitherto refrained from introducing another construction which is often used by the French instead of that given in the rule. When a sentence commences with où, where; que, what; quel, which; combien, how much, how many; and quand, when, the noun may be placed immediately after the verb. This construction is similar to that of the English interrogative sentence when the verb has no auxiliary [§ 76 (5)]. Où sont nos amis et nos parents ? 2. When there are in a French length, the direct should precede Avez-vous donné les jouets à l'enfant ? Avez-vous donné cette lettre à l'homme ? Where are our friends and relations? What does your correspondent writs! sentence two regimens of equal the indirect [§ 76 (7)]. Have you given the child the playthings? Have you given the man that letter? followed by a relative pronoun, or by other words qualifying it, and rendering it much longer than the indirect [§ 76 (8)]. The As soon as your letters were finished, indirect regimen should also precede the direct, when the sen did you not take them to the post-tence would otherwise be equivocal [§ 76 (9)]. office? Avez-vous donné à l'enfant les jouets que vous lui aviez promis? 3. The régime indirect precedes the direct, when the latter is As soon as you had arrived, did you not commence writing? As soon as you used to arrive, did you not commence writing? VOCABULARY. Egar-er, 1, to mislay. Invit-er, 1, to invite. Se lev-er, ref., to rise. Se coucher, 1, ref., to Malade, sick. go to bed. Dangereusement, dangerously. Diner, m., dinner. Musicien, m., musi cian. Oubli-er, 1, to forget. Perd-re, 1, to lose. Remont-er, 1, to wind up. Retrouv-er, 1, to find again. Sort-ir, 2, ir., to go out. Spectacle, m., play. 1. Ne saviez-vous pas où le musicien était allé? 2. Je savais qu'il était allé à Paris. 3. Ne vous avait-on pas dit que votre frère est mort? 4. On m'avait dit qu'il était dangereusement malade. 5. Ne vous couchiez-vous pas ordinairement, dès que vous aviez fini vos leçons? 6. Dès que je les avais finies, j'allais 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. 9. Cette petite fille n'avait-elle pas envie de dormir? 10. Elle avait plus envie de dormir que d'étudier. 11. Qu'aviez-vous fait de (with) votre livre quand je vous le demandai. 12. Je l'avais égaré. 13. Je l'avais oublié dans le jardin. 14. Pourquoi votre montre était-elle arrêtée ? 15. Parce que j'avais oublié de la remonter. 16. L'horloger ne l'avait-il pas remontée ? 17. I avait oublié de le faire. 18. N'aviez-vous pas perdu votre bourse? 19. Je l'avais perdue, mais je l'ai retrouvée. 20. Votre cousin était-il part? 21. Il n'était pas encore parti. 22. Était-il sorti? 23. Il était sorti avec ma mère. 24. Où était-il allé ? 25. Il était allé chez mon frère, qui l'avait invité à dîner. EXERCISE 104. to speak to my brother? 2. I had he was gone. 3. Did your sister as she had read (lu) her book? as she had read it. 5. Were you 6. I was told that she had been 1. Où étaient vos parents l'année dernière? 2. Ils étaient en Angleterre. 3. Où sont restés les messieurs qui vous a compagnaient ce matin? 4. Ils sont restés chez leurs associés. 5. Que lisaient vos amies lorsque vous les avez quittées? 6. Elles lisaient les nouvelles qu'elles venaient de recevoir. 7. Que dit monsieur votre père ? 8. Il ne dit rien. 9. Quel Age a ce monsieur? 10. Il a près de cinquante ans. 11. Quel Age ont vos enfants? 12. L'aîné a dix ans, et le plus jeune a six ans. 13. Avez-vous demandé votre chaîne d'or à ce monsieur? 14. Je la lui ai demandée. 15. Avez-vous rendu au commis l'argent qu'il vous avait prêté ? 16. Je le lui ai rendu. 17. Aviez-vous envie d'envoyer vos clefs au serrurier? 18. J'avais envie de les lui envoyer, car elles sont cassées? 19. Valait-il la peine d'envoyer ces bouteilles à l'aubergiste? 20. Il valait la peine de les lui envoyer, car il n'en avait pas. 21. Avezvous demandé des serviettes à votre père? 22. Je n'ai paš voulu lui en demander. EXERCISE 106. ou know what you had done with 1. What was the locksmith saying to you? 2. He was say t I had mislaid it. 9. How many of ing that he had brought my key. 3. How many letters have you taken to the post-office ? 4. I have taken seven, three for you and four for my father. 5. Where is the gentleman who has brought that letter? 6. He lives at my father's; do you wish to speak to him? 7. I wished to send him a letter which I brought from England. 8. Have you returned to that man the money which he had lent you? 9. I have returned it to him. 10. Did you wish to send your brother the key of your room? 11. I wished to send it to him. 12. Was it worth the while to give your brother that book? 13. It was worth the while to give it to him, for (car) he wanted it. 14. Was it worth the while to send those bottles to the druggist (apothicaire)? 15. It was worth the while to send them to him. 16. Where is the innkeeper? 17. He is in England. 18. How many children has the locksmith? 19. He has ten. 20. How many books has the physician? 21. He has five hundred volumes. 22. Have you given the gentleman that letter? 23. I have forgotten to give it to him. SECTION LVI.-IDIOMATIC USES OF TENSES OF VERBS. 1. The French avoid placing the verb at the end of such sentences as the following, when the nominative is a noun. He has been writing these two hours. 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. 3. When, however, the state no longer continues, the past may be used in French, in the same manner as it is used in English. Combien de temps avez-vous de- How long did you live in L.? Combien de mois avez-vous appris How many months did you learn Il y un mois que je ne l'ai vu, I have not seen him this month. Nous l'avions dix ans. Il y a huit lieues de Calais à Bou- Affiche, f., bill. We have had it these two years. We had it ten years. He has been learning it six years. 13. Savez-vous combien il y a de Paris à Vienne? 14. Il y a trois cent six lieues de Paris à Vienne et deux cents lieues de Vienne à Copenhague. 15. Y a-t-il longtemps que la compagnie est venue? 16. Il y a plus de deux heures qu'elle est ioi. 17. Y a-t-il longtemps que vous avez lu cette affiche? 18. Il y a plus de trois heures que je l'ai lue. 19. N'y a-t-il pas plus d'une demi-heure que votre sœur lit? 20. Il y a si longtemps qu'elle lit, qu'elle en est fatiguée. 21. Y a-t-il longtemps que vous attendez ce morceau de musique ? 22. Il y a plus d'un an que je l'attends. EXERCISE 108. 1. Do you not know where my father lives? 2. I know where he lives, but I have no time to go to his house to-day? 3. How long has the physician lived in Paris? 4. He has lived there ten years. 5. How long did he live in England? 6. He lived in England six years and a half. 7. Can you tell me where the locksmith lives? 8. He lives at my brother's. 9. Have you been waiting long for this book? 10. I have been waiting for it more than a year. 11. How long has your son been learning Greek? 12. He has been learning it these two years. 13. How long has your brother had this orchard ? 14. He has had it more than six months. 15. How far is it from Paris to Lyons? 16. It is one hundred and sixteen leagues from Paris to Lyons. 17. Is it farther (plus loin) from Lyons to Geneva than from Lyons to Turin ? 18. It is farther from Lyons to Turin than from Lyons to Geneva. 19. How long did your father live in Germany? 20. He lived in Germany two years, and in England six months. 21. How long did you live in Rome? 22. We lived there more than a year. 23. Have you been learning German more than one year? 24. I have been learning it more than four years. KEY TO EXERCISES IN LESSONS IN FRENCH. 1. Avez-vous les chevaux de mon frère ? 2. Je n'ai pas les chevaux de votre frère, j'ai les chapeaux de votre cousin. 3. Les maréchaux ont-ils de bon fer? 4. Le maréchal a deux morceaux de fer. 5. Avezvous deux paires de bas? 6. J'ai une paire de bas, et deux paires de gants. 7. Votre sœur a-t-elle les bijoux d'or? 8. Ma sœur a les bijoux d'or et les joujoux de papier. 9. Avez-vous les choux dans votre jardin ? 10. Nous avons deux choux dans notre jardin. 11. Avezvous les chapeaux de soie? 12. Les généraux ont les chapeaux de soie. 13. Avez-vous du café ou du sucre ? 14. Nous n'avons ni café ni sucre. 15. Vos frères ont-ils honte ? 16. Mes frères n'ont ni honte ni peur. 17. Qui a deux barils de farine P 18. Le meunier a deux barils de farine. 19. Les oiseaux ont-ils du pain? 20. Les oiseaux n'ont pas de pain. 21. Le marchand a-t-il du thé, du chocolat, du sucre, et du poivre ? 22. Il a du sucre et du poivre, mais il n'a ni thé ni chocolat. 23. Votre sœur qu'a-t-elle ? 24. Elle n'a rien. 25. Votre frère qu'a-t-il ? 26. Il n'a rien. 27. N'a-t-il pas froid? 28. Il n'a pas froid, il a chaud. EXERCISE 17 (Vol. I., page 78). 1. Have you the blacksmiths' hammers ? 2. Yes, Sir, I have them. 3. Have you them not ? 4. No, Sir, we have them not. 5. The workman has them. 6. Has the innkeeper your horses ? 7. The innHow long has your brother been keeper has neither my horses nor yours, he has his. 8. Has the learning Greek? physician books? 9. Yes, Sir, he has good books. 10. Have you not my best pens? 11. Yes, Sir, I have your best pens, mine, and those of your cousin. 12. Has the traveller good guns? 13. He has no good guns, he has iron guns. 14. Has not the sailor my horse-hair mattresses ? 15. He has them not. 16. What has he? 17. He has the cabinet-maker's woollen mattresses. 18. Has the cabinet-maker mahogany tables? 19. Yes, Madam, he has mahogany tables and white marble tables. 20. Have you my chairs or yours? 21. I have neither yours nor mine, I have the cabinet-maker's. 22. Are you not sleepy? 23. No, Sir, I am neither sleepy nor hungry. 24. Has the tinman your iron candlesticks? 25. No, Sir, he has the blacksmith's. It is eight leagues from Calais to VOCABULARY. ter. Maintenant, now. Verger, m., orchard. 1. Combien de temps y a-t-il que M. L. demeure à Paris? 2. Il y a dix ans qu'il y demeure. 3. N'a-t-il pas demeuré à Lyon? 4. Il y a demeuré autrefois. 5. Pouvez-vous me dire où est le fils du capitaine? 6. Il y a un an qu'il est en Angleterre. 7. Savez-vous où demeure M. B.? 8. Il demeurait autrefois à Rouen; je ne sais pas où il demeure maintenant. 9. Y a-t-il longtemps que vous êtes ici ? 10. Il y a plus de deux mois que nous sommes ici. 11. Combien de temps y a-t-il que vous avez ce verger? 12. Il y a un an que nous l'avons. MECHANICS.-XIII. STATICAL FORCES.-FRICTION. We have now mastered the elementary principles of the simple machines, and are in a position to resolve a compound machine into the elementary ones of which it is made up, and thus to find the benefit derived from its use. Our inquiry now is, what are the forces which most generally act on a body or a system of bodies when in a state of equilibrium? We shall consider further on the main "prime movers" or forces which produce motion. There are, then, four kinds of forces with which statics deals. They are: 1. Gravity. 2. Resistance of surface. 3. Tension. 4. Friction. Gravity is the most universal of these, as it acts constantly and on every substance. Hence we ought always to take it into account, though, for the sake of simplicity, we have hitherto neglected it. Most that is requisite was, however, said about it, in our lessons on the centre of gravity. All bodies attract each other with a force proportionate to their bulk. If a heavy weight be suspended by a cord over the edge of an almost vertical precipice, and looked at from a short, distance by a telescope, we shall find that the cord does not hang perfectly vertical, but is inclined slightly inwards by the attraction of the rock for the weight. we obtain, it is very important for us to become familiar with its effects. If we attempt to cause one body to slide or move over another, we find a certain amount of resistance to our efforts. This resistance or opposition to attempted motion is friction. All surfaces have a degree of roughness or unevenness of texture, and the inequalities of two such surfaces fit into one another, the projections of the one catching those of the other. We find this friction more or less in all cases of attempted motion. If two surfaces were absolutely smooth, there would be none; this, however, we cannot obtain, but the nearer we approach to it, the less friction we have. runners, like those of a sledge, we still further reduce friction. In all cases, however, it exists; and as we see, it is only called into play when motion is attempted; and since it prevents the body from moving (unless the force applied be powerful enough to overcome it), its line of action must be contrary to that of the attempted motion, as otherwise it could not neutralise the force applied. Now it will easily be seen that it is of great importance to be able to ascertain the amount of friction between surfaces. On a railway we want to know what force is required to overcome the friction of a train along a level part of the line. We can easily, by the principles of the inclined plane, find the additional force required to draw it up an incline. Many practical questions of this sort are constantly met with, and there are two common ways of solving them. 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 same time keeps the planets in their orbits, and thus lies at the basis of the science of astronomy. When a body is raised from the earth and then left free, this attraction causes it to fall. The reason why it falls towards the earth, instead of the earth rising to it, is the immensely superior bulk of the latter. Strictly speaking, they do move towards each other in the exact proportion of their bulk. If a body of equal size with the earth were allowed to fall towards it, they would meet just half way. This force always acts towards the centre of the earth, and its amount is easily ascertained, being simply the weight of the body. When we say that a body weighs eight pounds, we merely mean that that is the force with which the attraction of the earth draws it. This attraction diminishes as we remove farther from the earth's centre; hence, as the diameter is greater at the equator than at the poles, a substance weighs less there than it does as we travel northward or southward. Of course this must be ascertained by a spring balance; in any other kind, the weight would be altered as much as the substance weighed. We see, then, that gravity acts in a line perpendicular to the earth's surface, is equal to the weight of the body on which it acts, and, as before shown, may be considered to act through its centre of gravity. It is now easy to calculate what allow ance is to be made for the weight of the simple machines, and whether this weight tells in their favour or against them. In a lever of the first kind, for instance, as the power acts at the longer arm, the centre of gravity will, if the lever be uniform, be in that arm, and therefore gravity is here a third force, which helps the power to sustain a greater weight than it other wise could. In the first system of pulleys, on the other hand, their weight acts against the power, one-half of the weight of the pulley next the power being supported by it, one-fourth of the next, and so on. Hence the weight that can be raised is less than theoretically it should be. We now pass to the second kind of force-resistance of surfaces. We shall better understand this by assuming a case. A ball rests on a horizontal table; the force of gravity presses it vertically downwards with a force equal to its weight, and yet the ball does not fall. Evidently there must be some force counteracting that of gravity. This force is the resistance of the table, which presses it upwards with a force exactly equal to its weight; for, if it were not equal, motion would ensue. This resistance acts, too, in a line perpendicular to the surface, for it must be exactly opposite to the line in which gravity acts, or else the two forces would have a resultant, in whose direction the ball would move. We learn, then, the following general principle:-Action and re-action are always equal, and act in exactly opposite directions. When two surfaces press on one another, the line of action of the resistance must pass through the point of contact. If the surfaces be smooth and one be a plane, it will also be perpendicular to that plane. The third kind of force is the tension of strings or fine rods. When an omnibus is drawn by horses, the forces which act directly on it are the tensions of the traces, and by these tensions it is moved. About this kind of force there is little The most usual method is by the apparatus represented in Fig. 82. A slab of the substance over which the other is to slide, is laid horizontally on a table. A block, A, of the second substance is taken, a cord is fastened to it and passed Fig. 82. over a pulley at the edge of the table, so as to be parallel to its surface; at the other end of this cord a scale-pan is fastened. Weights are now placed in this, or, better still, sand is poured into it, until A just begins to move. The weight of the sand in the pan divided by that of A, gives the fraction which expresses the proportion that the friction bears to the weight to be moved. Thus, if the substance weigh 2 pounds or 32 ounces, and a weight of 5 ounces is required to move it, the fraction is. This is called the Co-efficient of Friction. The other way of ascertaining this quantity is sometimes easier. A block, A (Fig. 83), of one substance is laid on a plane, BC, made of the other, and the end c is then lifted till A is just on the point of sliding down the plane. The full amount of friction is now at work, and we may consider this as a case of a body kept at rest on an inclined plane. The forces which act on A are its own weight in the direction A w, the resistance of the plane in the direction AR perpendicular to its surface, and RA E W Fig. 83. the force of friction which acts up the plane along AF. Now, C since there is equilibrium, this last force is equal and opposite to the resultant of A B and Aw, that is, to AE. The three forces, then, D may be represented by the three sides of the triangle WA E, but this triangle is similar 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 CD is communicated to the body moved, and its intensity is measured by the number of pounds it will support. We on to consider the nature and effects of the friction. This has been frequently referred iterferes with the accuracy of the results CD BC the friction, and is the co-efficient of friction. We have, then, the following rule:-Incline the plane till the body is on the point of motion; the elevation of the end of the plane divided by its length gives the required fraction. This suggests the way of making a useful calculation, like the following:-On how steep an incline will a cart stand safely if the co-efficient of friction be? We see that the incline must be somewhat less than 1 foot in 30, as, if it be greater, the cart will run down from its own weight. By these and similar means thousands of experiments have been tried, a few of which are here given as illustrations. You can easily try others yourself. Along a railway friction is reckoned to be from 8 to 10 pounds per ton; on a good road about th of the load; this amount, however, varies very greatly with the character of the road. The coefficient of friction for steel on ice is only, while that of oak on oak or elm is over When a body is kept at rest by the action of any number of forces upon it, if we resolve these forces along any two directions at right angles to one another, their resolved parts in each direction must neutralise each other. If they did not, some motion must ensue. In a similar way we can often find whether any number of forces will produce equilibrium, and if not, what their resultant will be. This mode of solving the question is sometimes more convenient than the polygon of forces. Suppose three forces, represented by A B, A C, and A D (Fig. 84), act on A. Fix on any two lines E F and G H at right angles to one another, and both passing through A. From B, C, and D drop perpendiculars on E F and G H. This may be done with a and thus is the resultant of two forces which are represented by A N and A K. We may therefore resolve it into those two, and, There are, however, certain general rules, discovered by expe- square. Now A B is the diagonal of the parallelogram K A N B, riment, which are more important to remember. 1. Friction is proportional to the pressure. If we place 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 3 pounds. 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 3 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 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 smooth as possible, and oil or grease applied to them. The bearings, too, or boxes in which the axles of wheels turn, are made of a different kind of metal from the axles themselves, and many other expedients are resorted to. Still there is a loss of power from this cause, which often amounts to or even . There are two kinds of friction-sliding and rolling. Sliding friction is that of which we have spoken; but if a body be made round, and allowed to roll over and over instead of sliding, a different kind of friction comes into action. The rudest application of this is when a man, instead of pushing a stone along the ground, puts rollers under it, and thus moves it with far more ease, fresh rollers being put under in front when needed. Wheels are a further advance upon this, as they not only save the trouble of constantly replacing the rollers, but, as they only touch the ground at the sides of the body, and not along the whole width as rollers do, they avoid much of the friction. Sometimes when a large axle has to turn in bearings, frictionwheels are introduced. These are small wheels, on the edge of which the axle turns, and they transfer the friction to their own small axles. Many such appliances to avoid friction are constantly met with. Castors on chairs and tables, and narrow irons on skates, are familiar examples. We must not, however, imagine from all this that friction is always a hindrance. Far from it. If we try and walk along a very glassy surface of ice, we are soon painfully reminded of the absence of the customary friction between our boots and the surface on which we are walking, and hence in frosty weather gravel or ashes are scattered on the paths. All the driving force a railway engine has is from the friction of its wheels with the rails. It was at first proposed that the driving-wheels should be toothed, and notches cut into the rails into which these teeth might catch; but the friction was soon found to be sufficient. On damp days, however, we frequently see the porters at a station putting gravel on the rails, in order that there may be more friction at starting. The brake, also, which is applied to stop a train or machine, acts by pressing a block against the wheel, and thus causing an amount of friction which is soon sufficient to overcome the momentum acquired. So, when a nail is driven into a piece of wood, it is held in its place merely by friction, and the same cause enables the fibres of cotton or hemp to cling 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. We must now look at two propositions which are often very useful, and we shall then be able to trace the application of what has been said to a few common cases. instead of A B acting on A, we shall have the two forces A N acting along E F, and A K acting along H G. In the same way resolve a C and A D into A L and A M, and A O and A P respectively. We have thus resolved all our forces into others acting in the directions we fixed upon. Three of these, AN, A M, and A O, act along EF; and if A N equals the sum of the other two, these will cancel one another, and so of the forces along G H. If there are any residues in either case we mark off distances from A to represent them, and complete the parallelogram, the diagonal of which will be the resultant. The other proposition is as follows: If a body be kept at rest by the action of three forces, their lines of action must, unless the forces be parallel, pass through one point. For if not, since two of them pass through the point in which they meet (and they must meet, not being parallel), the body will turn till this point comes into the line of action of the third. If in Fig. 85 two of the forces act through B, and the third through ▲ in the direction A c, the body will evidently turn till B, A, and c are in one straight line. The cases when the forces are parallel have all been considered except the one when equal and parallel forces act in opposite directions, and we have what is termed a couple. Let AC and BD represent two such forces. In any other case, if forces act on a body, a single resultant can be found, but here no one force that can be applied will produco equilibrium. The motion. however, which these forces tend to produce, is not one of progression through space, but merely one of rotation round a point midway between A and B. This tendency to rotation increases with the distance A B, and is clearly equal to the sum of the forces multiplied by half that distance. The only way to overcome these forces is to introduce another couple having an equal tendency to turn the body in the contrary direction. The application of these principles we shall Fig. 85. see in the next lesson. EXAMPLES. 1. A lever of the first kind, 8 feet long, weighs 10 pounds. What weight will a power of 10 pounds raise, the fulcrum being 15 inches from the end? 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 will 15 pounds support? 3. If friction be reckoned at 9 pounds per ton, what power will be required to draw a train weighing 20 tons up an incline of 1 in 100 P 4. What strain must a horse pull with, to draw a load of 27 cwt. up an incline of 1 foot in 70, the co-efficient of friction being? 5. If the co-efficient of friction be, and the strain on a rope which just moves a carriage be 80 pounds, what is the weight of the carriage ? 6. A horse has to exert a strain of 116 pounds to pull a wagon weighing 1 tons. What is the co-efficient of friction? ANSWERS TO EXAMPLES IN MECHANICS, XII. 1. A power of 201 pounds. 2. He must pull with a strain of of a ton, or 89 pounds. 3. It would support a resistance of 616 pounds, again, resemble nouns in ing, in having (for the most part) an active signification; but the ending ion differs from the termination ing, inasmuch as the former can be affixed only to nouns of Latin parentage: thus, we say the communication, or the communicating; but WE CANNOT SAY the runion (running), nor the rision (rising). Nouns in ion are not so purely active as are nouns ending in ing. For instance, communication may signify either the act of communicating, or the thing communicated, the result of the act of communicating. So devotion may 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 not mean ancient merely or generally, so much as ancient in relation to the immediate past, the age of the Reformation, the Middle Ages. Not seldom has antique the subordinate notion of curious, singular, or odd connected with it; probably because 4. A force of nearly 10 pounds must be applied, the gain being 2x3 antiques are rare. feet divided by inch, which equals 3014. 5. The pressure will be 8,304 pounds. 6. The difference between the threads is of a foot. The gain is therefore 1×2× 3 × 110, or 1,210. 12 × 45 2 or 270. 7. 135 pounds. The gain is In the foregoing, friction was not taken into consideration. LESSONS IN ENGLISH.-XVII. LANGUAGE has many a tale to tell respecting national character and manners. The fact that the English names of animals, when alive, are of Saxon origin-for example, bull, sheep, calfand that the English names of animals, when dead, are of French origin-as beef, mutton, veal-in showing that at one period of our history the Saxon population fed the animals, and the French population ate them, shows also that the former were in hard servitude to the latter; in other words, that our Saxon ancestors were serfs, and the forefathers of the present French were masters on this soil of England. Such a relation was not likely to be durable. A proof of the assertion is found in the words etiquette and coquette, to which reference was made in the last lesson (page 71). Etiquette and coquette are both of French origin. Essentially French are the things the words stand for. Among the French those things had their birth, and on the soil of France they flourished. Hence you learn that lightness, weakness, and vanity are essential features in the character of Frenchmen. Superficial, if pleasing, a true type of the French character may outshine, or for a moment overcome, an Englishman, but he is utterly unable to hold our countryman in permanent subjection. Equally illustrative of national character is the fact that Pantaloon and Punch come to us from Italy. Pantaloon is from the Italian Pantalone, which when written in full is Piantaleone, a word signifying lion-planter. Pianteleone was a surname or name of honour, given in the Middle Ages to a very powerful Venetian, who planted the banner bearing the winged lion of St. Mark, the symbol of the Venetian Republic, on many islands of the Mediterranean. His renown caused Piantaleone to be brought on the stage. Hence Pantaloon, the lion-hearted, who originally bore a nearer resemblance to his prototype than is found in the impudence and hardihood of the modern degenerated specimen. And hence the peculiar dress of Pantaloon (also trousers called pantaloons), which, making due abatement for exaggerations, was the attire of distinguished Italians in former days. Our Punch owes his birth and his name to Italy. Punch is derived from the Italian Pulcinella; and Pulcinella seems to be made up of Puccio d' Aniello; that is, Puccio, an ill made, witty clown of the town Aniello, who gained a livelihood by his antics in the market-places and public highways. The character being transferred to the stage, Punch came to be the recognised symbol of fun and frolic. Ion, from the Latin termination io; as actio, action; quæstio, question ・ motio, motion; visio, vision. Nouns in ion, like e called verbal, seeing they are derived fn. as actio, from the Latin verb ago I do; motio, from the Latin verb motus), I move, etc. Nouns in ion, "Name not these living death-heads unto me, For these not ancient but antique be."—Donne. "And sooner may a gulling weather-spy, By drawing forth heaven's scheme, tell certainly What fashion'd hats or ruffs, or suits next year, Our giddy-headed antique South will wear."-Donne. The word antic, from antique (formerly spelt antick), takes its force from this associated notion of singularity. From the same Greek Testament; as in the word baptise, from the Greek Barrica, Ise, formerly ize, of Greek origin, introduced through the New ending we have dogmatise, methodise, criticise. This terminapronounced bap-ti'-zo, I dip frequently. tion gives rise to others; as from baptizo come baptist, baptism, baptistry, baptismal. "He (the pope) solicited the favour of England by sending Henry a sacred rose, perfumed with musk, and anointed with chrism.”—Hume. anointed; that is, with a consecrated unguent or holy oil. The suffix ise or ize, added to nouns, gives them the force of verbs, thus: to christianise, is to make Christian; to evangelise, is to bring men to the evangel, that is, the Gospel. In the use of this termination authority must be followed. The termination ism is employed to describe religious or social diversities; it is found in Atheism, Deism, Swedenborgianism, Calvinism, Arminianism, Owenism, etc. While ism denotes the sect, ist denotes the sectary; as, Atheist, Deist, Methodist, etc. The adherents to particular modes of faith are also designated by arian; as, Trinitarian, Unitarian; or ian, as Episcopalian. Sometimes the word man holds a similar post, as in Churchman, used in contrast with Dissenter. Ist, too, performs the same office; as in Nonconformist. Another form is found in ste; as Irvingite, Mormonite, etc. Analogy is a dangerous guide in English, for, while we say Irvingite, we DO NOT say Southootite, but Southcotian-probably for the sake of euphony. This ite comes, we are disposed to think, not from the rare Latin ending itus (as auritus, with pricked-up ears), but the scriptural ite; as in Jebusite. Ish, probably from the Saxon ic and the German isch (as in mürrisch, peevish), denotes, as in peevish, quality, and so forms adjectives. Ish has sometimes a diminutive force; as thinnish, thickish. When forming part of verbs, as in punish, publish, ish has a different origin, and may be a softened form of the Greek termination ise or ize. Ite, a patronymio, or father-name-the name that is expressive of a race, like the Greek ides-is very common in the Old Testa ment, from the language of which it may have come into the English; thus, Israelite is a descendant of Israel; so we have Hittites, Hivites, etc. Ive, of Latin origin, from ivus, as seen in captivus, a captive; also in fugitive (Latin, fugio, I flee); natious (Latin, natus, born), a native; votivus (Latin, votum, a vow), votive. This is in French becomes if, whence we have plaintif (French, plaindre, |