LESSONS IN BOTANY.-IX. SECTION XVII.-ON THE COROLLA, ITS PARTS AND MODIFICATIONS. As the calyx may be made up of one sepal, in which case it is termed monosepalous, or of many sepals, in which case it is termed polysepalous, so the corolla may be made up of one or many parts called petals. In the former case a monopetalous, in the latter a polypetalous, flower results. Even the most casual observer of flowers must have noticed some of the various modifications of form and arrangement to which petals are subject. Hence have 94 á saucer, from no under, and крaтnр a cup), or saucer-shaped (Fig. 97); campanulate (Italian, campana, a bell), or bell-shaped (Fig. 95); rotate (Latin, rota, a wheel), or wheel-shaped (Fig. 98); labiate (Lat., labium, a lip), or lip-shaped (Fig. 96); personate (Lat., persona, a mask), or mask-like (Fig. 100); and ligulate (Lat., ligula, a strap), or strap-shaped (Fig. 101) flowers. When irregular corollas are neither labiate, nor personate, nor ligulate, they are sometimes called anomalous, from the Greek a, negative, and ouaλos (hom-a-los), equal or similar, as in the fox-glove (Fig. 99). SECTION XVIII.-ON FRUITS AND THEIR VARIETIES. We have already remarked that the female parts of a flower 90 91 89 96 100 arisen various botanical designations, some of which we shall now proceed to explain. In the disposition and arrangement of petals, those which assume the cross form are very conspicuous. Vegetables of the cabbage tribe, indeed, including turnips, watercresses, and many others, have had the botanical designation cruciform or cruciferous (Latin crux, crucis, a cross, and fero, I bear) given to them from this very circumstance (Fig. 89). The rosaceous disposition of petals is also very well marked, not only being observable in the wild roses, but being shared by numerous other vegetables. The straw. berry flower, for example, is rosaceous in the disposition of its petals (Fig. 90). The long tapering claw which certain petals have is also highly characteristic, and gives rise to corollæ which are said to be caryophyllate, from resembling that of the pink Dianthus caryophyllus. Of this the lychnis (Fig. 91) furnishes us with an example. The papilionaceous (Latin, papilio, a butterfly) corolla constitutes an exceedingly well-marked natural division, the name being Acquired from the circumstance that they resemble a butterfly in general appearance. No person, we are sure, who has ever seen a pea-flower-and who has not ?-can have failed to be struck with the marked resemblance in question. Hence the technical name papilionacea has been applied by botanists to plants bearing such flowers. Our diagram (Fig. 92) represents the flower of a common garden pea. Such are amongst the chief of the modes in which the petals of polypetalous flowers are arranged. Monopetalous corollæ evidently do not admit of these variations, since they only consist of one organ; nevertheless, so numerous are the forms which these one-petaled corolla assume, that many distinctions may be drawn between them. Thus, for example, we have tubular, from the Latin tubulus, the diminutive of tubus, a pipe (Fig. 93); infundibuliform (Latin, infundibulum, a funnel), or funnel-shaped (Fig. 94); hypocrateriform (Greek, TоxpаTTP [hu-pe-cra-teer], 95 93 98 97 16 92 99 are termed carpels, from kарros, fruit, because fruit is the result of the development. Sometimes the ovary alone becomes developed into the fruit, but occasionally other parts of the flower attach themselves to the ovary, and thus become incorporated with its substance, helping to form the fruit. In the majority of cases fruit will not ripen except the Ovary has been fertil. 101 ised; but many excep. tions occur to this rule. Thus certain varieties of oranges, grapes, and pine-apples ripen freely enough, although the ovaries from which they spring have never been fertilised, and consequently they bear no seed. Now, even in ordinary language, we employ various terms to denominate various kinds of fruit: it follows, therefore, that since botanists recognise many growths as fruits which we in ordinary language fail to dignify by that pleasing term, many botanical designations become necessary. There are two methods of communicating to the reader these distinctions. The first is by telling in what the distinctions consist; the second by showing the varions forms which result. Perhaps the latter method will, of the two, be the more simple. We shall therefore give drawings 89. CRUCIFORM COROLLA OF THE CELANDINE. 90. ROSACEOUS COROLLA OF THE STRAW- of some of the chief varieties of fruit, which are as follow:Pomes, or fruits resembling apples (Fig. 102); drupes, or fruits resembling cherries, peaches, plums, so called from falling from the tree when ripe-the term drupe being derived from the Greek Spuжяа (druр'-рa), an over-ripe olive, or SpuжETTS (dru'-pet-ees), quite ripe, which is derived from 8pus (droos), an oak or tree, and TITTW (pip'-to), to fall (Fig. 103); the achanium (from the Greek a, negative, and xaiw [ki'-no], to gape), a term applied to hard, dry fruits, such as the fruit of the ranunculus, which do not adhere to the shell or pericarp, and do not open when ripe (Fig. 104); the caryopsis (from kapvov [kar-ru-on], a nut, and orra [op'-to], to see), a small, dry, seed-like fruit which coheres inseparably with the seed within, as in buckwheat (Fig. 105); the follicle (from the Latin folliculus, the diminutive of follis, a windball or bag), a fruit or seed vessel which splits on one side only, as in the columbine (Fig. 106); the legume or pod (from the Latin legumen, from the verb lego, to gather), a seed-vessel which splits into two valves, having the seeds attached only to one suture or seam at the union of the margin of the valves, as in the whole pea-flower tribe, example the lotus (Fig. 109); the capsule (from the Latin capsula, a little chest), a pericarp which may have one cell only, or many cells, and which splits into pieces by valves, as in the gentian (Fig. 107); the colchicum (Fig. 110), the iris (Fig. 111), the lychnis (Fig. 117), and the corn-poppy (Fig. 108); the pyxis (from the Gr. Tugis [puke'sis], a box), a fruit which is like a box and throws off a cap, as in the pimpernel (Fig. 118); the siliqua (from the Latin siliqua, a husk or pod), a pod which splits into two pieces or valves separating from a frame, and which is longer than it is broad, as in the celandine (Fig. 112); the silicule (from the Latin silicula), a little pod or husk, the diminutive of siliqua, a pod, which splits in totwo pieces or valves, separating from a frame, and which is about as broad as it is long, as in the Shepherd's Purse (Fig. 113); the samara (from the Latin samera, an elmseed), a fruit which is hard, thin, and extended into a wing, as in the maple (Fig. 114); the nut (from the AngloSaxon hnut, or the Latin nur, nucis, a nut), as in the chestnut (Fig. 115); and the berry (from the Anglo-Saxon beria, a grape), a succulent or pulpy fruit containing seeds which have no co 102. FOME. 108 103. DRUPE. 104. ACHENIUM OF THE RANUNCULUS. 105, CARTOPSIS OF THE BUCKWHEAT. 106. FOLLICLE OF THE COLUMBINE. 107. CAPSULE OF THE GENTIAN. 108. CAPSULE 109. LEGUME OF THE LOTUS. 110. CAPSULE OF THE COLCHICUM. 111. 112. SILIQUA OF THE CELANDINE. 113. SILICULE OF THE SHEPHERD'S PURSE. 114. SAMARA OF THE MAPLE. 115. NUT OF THE CHESTNUT. 116, BERRY OF THE 117. CAPSULE OF THE LYCHNIS. 118. PYXIS OF THE PIMPERNEL, OF THE CORN POPPY. CAPSULE OF THE IRIS. DEADLY NIGHTSHADE. 119. GERMINATION OF THE BEAN. 120. GERMINATION OF INDIAN CORN. vering but the pulp or rind), as in the deadly nightshade, the fruit of which is shown in Fig. 116. SECTION XIX.-THE SEED. The seed, everybody knows, is that part of a plant which, being sown, gives rise to a new plant. We might write a whole treatise on the nature and varieties of seeds, especially 25 concerns their anatomical construction, but much of this information would be out of place in a series of elementary papers: we shall, therefore, content ourselves with recapitulating some points that have already been adverted to in relation to seeds, and shall then mention some general facts concerning seeds which must not be forgotten. After having remained in the earth a few days, the bean throws up a shoot terminating in two little leaves. These little leaves were embedded, in miniature proportions it is true, in the bean, and may be recognised there by careful examination; however, by planting the bean they are rendered much more evident (Fig. 119). These two thick seedleaves are termed cotyledons, from the Greek κοτυλη (κοtu'-le), a cup; and the bean, from possessing two of these cotyledons, is called A dicotyledonous plant. Again, perhaps the reader has at some period of his life planted a grain of wheat, barley, or, still better, Indian corn (Fig. 120). If he has done this, he may have remarked the result to have differed from that noticeable when the bean was planted. Instead of two seedleaves, or cotyledons, only one in this case appears on the young plant, which, therefore, is said to be a monocotyledonous plant. Extending these inquiries still further, it will be found that all plants whose fibro-vascular system grows by external depositions, and which possess reticulated leaves-in other words, all exogenous plants-yield dicotyledonous seeds; and all plants whose stems grow by internal depositions, and which possess straight-veined leaves, yield monocotyledonous seeds. Thus, then, it follows that even already the reader is so far indicate the grand division of the vegetable kingdom to which master of the principles of botanical classification, that he could any plant belonged by one of three classes of signs-namely, The germination of a bean may be watched from day to day by suspending the seed over water in the mouth of a hyacinth-glass, or crocus-glass. The bean should not be allowed to do more than barely touch the water. LESSONS IN GERMAN.-XVII, SECTION XXXI.-INSEPARABLE PARTICLES. BESIDES the separable particles (Sect. XXVI.), there is another class (be, emp, ent, er, miß, ver, etc., § 94) that, unlike the former, are never used apart from the radical words to which they are prefixed, and hence are called inseparable particles; thus by the union of these particles be, emp, ent, er, etc., with the radicals fehlen, etc., we have the compounds befehlen, empfinden, entbehren, erholen, mißfallen, verhören, zermalmen, etc., corresponding in formation to the English compounds be-tray, de-rive, dis-may, mistake, etc. With few exceptions (as begeistern, beseelen), however, German, unlike most English radicals, may be used as well alone as in combination with prefixes; as, stören, to disturb; zerstören, to demolish. Many particles in German, which are used to modify radical verbs, have their exact equivalents in English, as :-Deuten, to interpret; misteuten, to misinterpret; fallen, to fall; befallen, to befall, etc. (§ 97. 1, 2, etc.) In German, as in English, the inseparable particles never take the primary accent. (§ 98.) 1. Bor, which is often rendered by the English "ago," unlike the latter, always precedes the word of time to which it refers, as:—Er war vor zwei Stunten hier, he was here two hours ago (literally, he was here before two hours). Seit (since), when used with words denoting time, often answers to "for" or "during," as:-Er ist seit einer Woche krank, he has been (literally is, see Sect. XVII. 6) sick for a week. Ich habe ihn seit einem ganzen Jahre nicht gesehen, I have not seen him during a whole year (a whole year since). 1. Will Ihr Sohn mein Pferd halten? 2. Er hat es gehalten, aber er hat einen Brief erhalten, welchen er lesen will. 3. Wie hat sich dieser Knabe betragen? 4. Er hat sich gut betragen, er hat meinen Regenschirm getragen. 5. Die Russen haben einen tapfern Helden gefunden. 6. Die Deutschen haben viele nügliche Künste erfunden. 7. Dieser Bettler hat eine Stunde an der Thüre gestanden, er hat mich nicht verstanden. 8. Hat ́der Schuhmacher Zeit, mir ein Paar (Sect. LXI.) Stiefel zu machen? 9. Er hat keine Zeit, Ihnen Stiefel zu machen, er hat Andern zu viel vers sprochen. 10. Hat der Bauer mehr Kaffee zu trinken, als Brod zu essen? 11. Er hat Brod genug zu essen und Wasser zu trinken, aber er hat keinen 1. They have recommended the foreigners to me and to you. 2. There lives in Naples a friend of mine; I shall recommend him to you. 3. One of my friends, whom you have seen with me, has travelled in America, and has written a letter to me, in which he describes his journey. 4. A man of honour lowers himself to [ver] nobody, in whatever condition he may find himself. 5. Did you receive the news before us? 6. I received it after you; the whole neighbourhood too was informed of it, as we received your letter. 7. The children promised their father to be obedient. 8. Advantages may be derived from this inven tion, which nobody can account for. 1. Geht Ihr Herr Vater heute nicht aus? 2. Er ist schon ausgegangen, er ist (Sect. XXII.) heute Morgen sehr früh aufgestanten. 3. Wo ist er hingegangen? 4. Er ist zu seinem Nachbar gegangen, er will auf das Land gehen. 5. Wo wollen Sie hingehen? 6. Ich muß auf ren Markt, in den Garten, an den Brunnen gehen. 7. Sein Freund hat ihm geschrieben, daß er in Amerika angekommen ist. 8. Wann haben Sie angefangen, Deutsch zu lernen? 9. Ich habe vor sechs Wochen angefangen zu lesen. 10. Wann wollen Sie anfangen, französisch zu lernen? 11. Ich habe schon angefangen zu lesen, und werde bald anfangen zu sprechen. 12. Wollen Sie mir den Gefallen erzeigen, eine Lampe anzuzünden? 13. Ich will es mit tem größten Bergnügen thun. 14. Hat das Dienstmärchen das Fener schon angemacht? 15. Nein, sie hat es noch nicht angemacht. EXERCISE 57. 5. The 1. Will you have the goodness to pronounce those words to me ? 2. Do you pronounce well? 3. I believe I pronounce well, but my brother pronounces better. 4. Many an innocent mind has been hurt by reading pernicious books. tempest has disturbed the company in their enjoyments, and has destroyed the house. 6. I have papers to read and letters to write. 7. Those persons who set fire to the house ought to be punished. SECTION XXXII.-VARIOUS IDIOMS. Beide (plural) is declined like an adjective, and, unlike its equivalent (both), comes after the article or pronoun with which it is used, as-Die beiden Hante, both the hands; meine beiten Hände, both my hands. Alle (all) is sometimes, for the sake of emphasis, placed before beite, and may together be translated, "both of them," or simply, "both," as :-Alle beire, both of them; both. 1. Beires (neuter singular) is frequently employed to couple two things different in kind, whether designated by nouns alike or different in gender, as :-Wem gehört (§ 129. 2) dieses Messer und rieses Schwert? Beides gehört meinem Freunde, both belong to my friend. Hat Ihnen der Uhrmacher nur die Uhr, oder auch diesen King gemacht? Er hat Beides gemacht; or, Beite gemacht. Sind Sie mit der Uhr und dem Ring zufrieden? Nein, ich bin mit Beidem unzufrieden, benn Beides ist nicht nach meinem Wunsche, no, I am dissatisfied with both, for both are not according to my wish. 2. For the pronoun "neither" the phrase feines or keins von beiden is used, as:-Haben Sie das neue over das alte Buch? Ich hat keins von Beiten, I have neither (of the two). 3. Recht and Unrecht, like the words "right" and "wrong," are nouns, adjectives, and adverbs. The phrases, however, "to be right, to be wrong," are expressed in German by the noun, with the transitive verb haben, as:-Er hat Recht, he (has) is right. Sie haben nicht Unrecht, you (have) are not wrong. 4. Gben fo, before an adjective, signifies "just as," as:-Dicfes Kind ist eben so alt wie jenes, this child is just as old as that. Diefer Mann hat eben so viel Klugheit wie Verstant, this man has just as much prudence as understanding. 5. Ganz wie, with a verb, signifies "precisely," or "just as," or "like," as-Gr ist ganz wie ich, he is just as I (am), he is just like me. Se denkt ganz wie er, she thinks precisely as he (thinks), she thinks precisely like him. 6. Noch, besides meaning "nor," when used in conjunction with meber, "neither," is variously rendered by "still some, or yet more, another, besides," etc., as:—Er schläft noch, he sleeps still. Gieb dem Kinte noch Brod, give the child some more bread. Bann hat er noch ein Pferd gekauft? when did he buy another horse? Ginen Apfel hat das Kind gegessen, aber es hat noch einen, the child has eaten one apple, but it has one besides (or another). 7. Mehr, connected with a negative word, is used like its equivalent "more," as:- -Ich habe keins mehr, I have no more. Ich habe nicht viel mehr, I have not much more. Used with a noun, the adverb follows, while in English it precedes the noun. 8. Ander signifies other, in the sense of different; it must not be used in phrases like, "I saw him the other day," which is in German, Ich sah ihn neulich (literally, recently); or, Ich sah ihn vor einigen Tagen (literally, a few days ago). 9. The neuter anderes, preceded by etwas (in conversation usually contracted to was), is rendered by the phrase "another thing," as:-Das ist etwas Anderes, or, das ist was Anderes, that is another thing. 10. The adverb anders is readily distinguished by its form, and is rendered by "otherwise, differently," etc., as :-Er spricht anders, als er denkt, he speaks otherwise than he thinks. Spazie’rengehen, take a walk. 11. Der Staat Bennsylvanien liefert eben so viel Kohlen, als ganz England. 12. Arbeitet Gustav nicht eben so viel, wie sein Bruder Hermann? 13. Die kleine Elise gab ihrer Schwester Pauline eben so viel Pflaumen, wie ihrer Freundin Grama. 14. Haben unsere Nachbarn noch keinen Garten? 15. Nein, sie haben noch keinen. 16. Bleiben Sie noch lange auf dem Lande? 17. Ich bleibe noch eine kurze Zeit da, und meine Freunde auch. 18. Gehen Sie heute noch spazieren? (Sect. LXIV. 1.) 19. Nein, denn ich muß noch arbeiten. 20. Die Freudenthränen der lang getrennten Freunde rührten die Herzen aller Zuschauer. 21. Können Sie die Waaren nicht billiger ver. kaufen? 22. Es ist rein unmöglich. 23. Sie müssen dieses anders machen. 24. Was kann ich anders thun? 25. Du kannst anders reden und handeln. 26. Ich werde Sie besuchen, wenn Sie es erlauben. 27. Er erzählte die Sache ganz anders. 28. Es ist etwas anderes, ob ich schreibe: er ist gelehrt,“ oder „geleert.“ EXERCISE 59. 1. Has the teacher taken away the paper or the book? 2. He has taken away both; for both belong to him. 3. Both towns are situated on navigable rivers. 4. They may take either way, as they have proceeded so far. 5. A great part of the land in America is still uncultivated. 6. He who wants the purpose, must will the means. 7. The Rhine steamboat has just started for Holland. 8. You err altogether when you say that you have quite surmounted every difficulty, otherwise all that you have stated would be correct. 9. Which of us is right, I or he? 10. You are both wrong. 11. It is quite another thing to say that he was not well, and could not come in consequence of it. 12. I shall speak no more about it; because I have found upon closer investigation, that he is neither covetous nor prodigal. 13. They do not think themselves better than others. 14. to Emma is just as intelligent as Eliza. 15. The sailor sets sail for America to-morrow. 16. Do you drink wine or beer? 17. I drink neither wine nor beer, I always drink water. 18. Gustavus gave the boy a thaler to buy some coals for his mother. 19. Pennsylvania is a rich and flourishing state in the United States of America. 20. She is just like her sister. 21. Give the boy some more plums. 22. I have no more. 23. The girl shed tears of joy when she saw her mother. 24. That ware is cheap, and the pattern of it is beautiful. 25. My friend has purchased a new winter coat. 26. This merchant sends his goods to the town in a wagon. 27. Will you take a walk to-morrow? 28. It is impossible. Unmöglich, impossible Win'terrock, m. winter tor. Sache, f. thing, af- Wohlfeil, cheap. 3ved,m.aim,purpose. He has two sons, but both are deaf and dumb. The giant seized the club with Has this merchant a horse or a He has both. The truth and the rose are An upright man abhors a lie. Nearly every human being has EXERCISE 58. 1. Wollen Sie ein Muster von diesem over jenem Tuche haben? 2. Son keinen von beiden. 3. Wir geben ihm einen Thaler für jeden der betten Männer 4. Trinken Sie Wein oder Bier? 5. Ich trinke weder Wein noch Bier (or, ich trinke keines von beiden). 6. Sie haben Recht, daß Sie das gethan haben. 7. Ist es recht, daß Johann so lange ausbleibt? 8. Nein, es ist unrecht von ihm, da er seine Aufgaben zu lernen bat. 9. Wie viel Tuch braucht der fleire Friedrich zu (Sect. LXXIII. 1) einem Sommerrocke? 10. Er braucht eben so viel, wie zu einem Winterrocke. MECHANICS.-VIII. THE THREE ORDERS OF LEVERS.-THE COMMON OF Levers there are commonly reckoned three kinds, of which crum. F P W Fig. 45. First Order.-The Condition of Equilibrium in this we have already determined in connection with the balls in Lesson VI. (Fig. 44). The Resisting Weight (Fig. 45) is to the Power inversely as w F to P F, or the weight multiplied by the arm, w F, is equal to the power multiplied by the arm P F. Of this kind of lever the examples are very numerous. In Fig. 46 the crowbar is used as a lever, by means of the fulcrum in the middle, to lift the chest, the push of the hand and the weight of the chest, both parallel P TV Fig. 47. forces, acting downwards. A poker put into a fire to raise P Fig. 48. he likes by means of the muscles attached to them along their lengths. The fulcrum is in the shoulder-joint or the knee-joint, and the resistance is at the hoof when he puts forth his strength to pull a load. If a man stretches his arm out straight, and so lifts a weight, that weight is the resistance; the shoulder is the fulcrum, and he must put forth a strength by his muscles in the middle greater than the weight before he succeeds in lifting it. If he moves only the lower joint, as in Fig. 50, his elbow is the fulcrum, and the power is midway. F F2 E1 PI P2 W Fig. 51. It may be asked, Why ever use a lever in which the power is at a mechanical disadvantage? The answer to be given is, that to lift a large weight by a small force is not the only object aimed at in mechanism, natural or artificial. It is as often desirable to give the end of a lever a very rapid motion, and this can be done with most advantage when it is of the third order. The amount of force put forth in such cases is no consideration in comparison to rapidity of action, especially in animal mechanics. To strike a swift and smart blow with the closed hand, or with a sword in the hand, as it is often necessary to do, a lever of the third order is the most effective. Levers of the various orders are often worked together, so as to make compound levers, the resistance end of one working into the power end of the other. In this way the effect of a small power is often very largely multiplied, and a very great resistance easily overcome. Such a compound lever is that in Fig. 51, where all are of the first order, three fulcrums at F. F1, F2, a power at P overcoming a resistance at P,, and there multiplied overcoming a second resistance at P2, and this eventually lifting the still greater weight w. The power is multiplied in the first lever inversely as the length of the arms, also in the second. and so also in the third. Suppose, for example, the power at P is one pound, and the short arm of each lever a third of the long one, then the 1 pound at P produces at the end of the long arm of the second lever at P, a force of 3 pounds. This again produces at P, in the third lever 3 times 3, or 9 pounds; and thus 1 pound eventually balances a weight of 27 pounds at w, the mechanical advantage gained by the combination being 27 to 1. As an example of this lever, take the crowbar in the illustration in Fig. 48, used differently from that in Fig. 46. The workman makes the ground at the point of his bar his fulcrum, throws the weight of the chest about the middle, and, instead of pushing downwards with his hand, lifts upwards. The mechanical advantage is clearly on his side. The oar of a boat is also a lever of the second order; the arms of the oarsman furnish the power; but most persons at first imagine that the rowlock is the fulcrum. This is natural, for it looks very like But suppose that the lengths of the arms were in the propor one, but that it is not such is evident from the fact that the tion of any other numbers in the several lovers-say 9 to 4 in boat is the thing he wants the first, 7 to 3 in the second, 5 to 2 in the third; what weight to move. To spurt the would 1 pound at P support at w? It is not difficult to discover, water about with the blade if you know something about multiplying fractions. Now, in is not his object, but with the first lever, by the principle of moments, already explained, 9 each stroke he makes a times the 1 pound at P is equal to 4 times the power produced by temporary fulcrum of the that pound in the second lever at P,; that is to say, this second water, by which he imparts power is of a pound. But this force, for the same reason, a smart blow to his boat, is multiplied at P, in the proportion of 7 to 3, and therefore and sends it ahead. The fulcrum is then in the water at one becomes off of a pound, and this eventually balances a end, the resistance in the middle, and the power at the other weight at w of of of of that unit, or, on making the A nut-cracker furnishes another instance- the fulcrum calculation, the 1 pound balances 13 pounds 2 ounces. And, at the joint, the resisting nut in the middle. of course, what is true of these numbers is true of all others, and the rule you arrive at is this end. Τ Fig. 49. Third Order.-Here again the Resistance and Power, as in Fig. 49, are parallel forces acting in opposite directions, and the condition of equilibrium is the same as in the last order, and for Fig. 50. a similar reason; but the mechanical advantage is against the power, which from being nearer the fulcrum must be greater than the resistance. The best examples are found in the limbs of animals. The leg of a horse is a pair of levers with a joint in the middle, which he can make into one or use separately as Rule.-Multiply together the fractions which represent the ratios of the Power arms to the Resistance arms, and the product obtained is the number of pounds of the Resistance which each pound of the Power balances. When the Power is more than 1 pound, multiply this number into that of the pounds and fractions of a pound in it. And this leads us to another result, which expresses the rela tion between the power and resistance without fractions. Since, in the above example, we had the resistance equal to of of of the power, it is evident that the three denominators multiplied into the resistance must be equal to the three nume rators into the power, and thus, extending the principle, we may say that The Power multiplied by the several lengths of the Power arms is equal to the Resistance multiplied by those of the Resist ance arms. And you thus have a result not unlike that established above for a single lever. And observe that this, though proved above only for a combination of levers of the first order, holds equally good of other combinations, mixed or unmixed, all of the second. or all of the third, or of two kinds, or of all three together. |
