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LESSONS IN BOTANY.-IX.
| a saucer, from 'ho under, and xpatnp a cup), or saucer-shaped
(Fig. 97); campanulate (Italian, campana, a bell), or bell-shaped SECTION XVII.-ON THE COROLLA, ITS PARTS AND
(Fig. 95); rotate (Latin, rota, a wheel), or wheel-shaped (Fig. 98); MODIFICATIONS.
labiate (Lat., labium, a lip), or lip-shaped (Fig. 96); personaie As the calyx may be made up of one sepal, in which case it is (Lat., persona, a mask), or mask-like (Fig. 100); and ligulate termed monosepalous, or of many sepals, in which case it is (Lat., ligula, a strap), or strap.shaped (Fig. 101) flowers. When ir. termed polysepalous, so the corolla may be made up of one or regular corollas are neither labiate, nor personate, nor ligulate, they many parts called petals. In the former case a monopetalous, are sometimes called anomalous, from the Greek a, negative, and in the latter a polypetalous, flower results. Even the most dualos (hom-a-los), equal or similar, as in the fox-glove (Fig. 99). casual observer of flowers must have noticed some of the various SECTION XVIII.-ON FRUITS AND THEIR VARIETIES. modifications of form and arrangement to which petals are We have already remarked that the female parts of a flower subject. Hence have
termed carpels, arisen various botani.
from Kaptos, fruit, be. cal designations, some
cause fruit is the result of which we shall now
of the development. proceed to explain. In
Sometimes the ovary the disposition and ar.
alone becomes dere. rangement of petals,
loped into the fruit, but those which assume the
occasionally other parts cross form are very con.
of the flower attach
91 spicuous. Vegetables 89
themselves to the orary, of the cabbage tribe,
and thus become incorindeed, including tur
porated with its sub. nips, watercresses, and
stance, helping to form many others, have had
the fruit. In the mathe botanical designa
jority of cases fruit will tion cruciform or cru
not ripen except the ciferous (Latin crux,
ovary has been fertil. crucis, & cross, and fero,
101 ised; but many excep. I bear) given to them
tions occur to this rule. from this very circum. 94
Thus certain varieties stance (Fig. 89). The
of oranges, grapes, and rosaceous disposition of
pine-apples ripen freely petals is also very well
enough, although the marked, not only being •
ovaries from which they observable in the wild
spring have never been roses, but being shared
fertilised, and conseby numerous other ve
quently they bear no getables. The straw.
seed. Now, even in or. berry flower, for exam
dinary language, we ple, is rosaceous in the
employ various terms disposition of its petals
to denominate various (Fig. 90). The long
kinds of fruit : it fol. tapering claw which cer.
lows, therefore, that tain petals have is also
since botanists recoghighly characteristic,
nise many growths 23 and gives rise to corollæ
fruits which we in orwhich are said to be
dinary language fail to caryophyllate, from re.
dignify by that pleas. sembling that of the
ing term, many botani. pink Dianthus caryo
cal designations become phyllus. Of this the
There are lychnis (Fig. 91) fur.
two methods of communishes us with an exam.
nicating to the reader ple. The papilionaceous
these distinctions. The (Latin, papilio, a but
first is by telling in 89. CRUCIFORM COROLLA OF THE CELANDINE. 90. ROSACEOUS COROLLA OF THE STRAW. terfly) corolla consti.
what the distinctions BERRI. 91. CARYOPHYLLATE COROLLA OF THE LYCHNIS. 92. PAPILIONACEOUS COROLLA tutes an exceedingly 93. TUBULAR COROLLA OF THE CORN CENTAURI. 94, INFUNDIBULIPORM
consist; the second by well. marked natural COROLLA OF THE BINDWEED. 95. CAMPANULATE COROLLA OF THE CAYPANULA. 96.
showing the various division, the name being LABIATE COROLLA OF THE DEAD-NETTLE. 97. HYPOCRATERIFORM COROLLA OF THE forms which result. PerAcquired from the cir- PERIWINKLE. 98. BOTATE COBOLLA OF THE PIMPERNEL. 99. ANOMALOUS COROLLA haps the latter method comstance that they re- OF THE FOXGLOVE. 100. PERSONATE COROLLA OF THE SNAPDRAGON. 101. LIGULATE will, of the two, be the nemble a butterfly in COROLLA OF THE CHRYSANTHEMUM.
more simple. We shall general appearance. No
therefore give drawings person, we are sure, who has ever seen a pea-flower—and who has of some of the chief varieties of fruit, which are as follow :not P-can have failed to be struck with the marked resemblance Pomes, or fruits resembling apples (Fig. 102); drupes, or in question. Hence the technical name papilionaceæ has been fruits resembling chorries, peaches, plums, so called from falling applied by botanists to plants bearing such flowers. Our dia- from the tree when ripe—the term drupe being derived from gram (Fig. 92) represents the flower of a common garden pea. the Greek Oputra (drup'-pa), an over-ripe olive, or SPUTETTIS
Such are amongst the chief of the modes in which the petals of (dru'-pet-ees), quite ripe, which is derived from Opus (droos), an oak polypetalous flowers are arrangod. Monopetalous corollæ evi. or tree, and TITTW (pip-to), to fall (Fig. 103); the achanium dently do not admit of these variations, since they only consist (from the Greek a, negative, and xaiw [ki'.no), to gape), a term of one organ; nevertheless, so numerous are the forms which applied to hard, dry fruits, such as the fruit of the ranunculus, these one-petaled corolle assume, that many distinctions may be which do not adhere to the shell or pericarp, and do not open drawn between them. Thus, for example, we have tubular, from when ripe (Fig. 104); the caryopsis (from Kapvov (kar-ru-on), a the Latin tubulus, the diminutive of tubus, a pipe (Fig. 93); in. nnt, and OTTW (op'-to), to see), a small, dry, seed-like fruit which fundibuliform (Latin, infundibulum, a funnel), or funnel-shaped coheres inseparably with the seed within, as in buckwheat (Fig. 94); hypocrateriform (Greek, imorpathp (hu-pa-cra-teer], (Fig. 105); the follicle (from the Latin folliculus, the diminutive
OF THE PEA.
of folls, a windball or bag), a frait or seed vessel which splits Seeds, the reader will remember, belong exclusively to on one side only, as in the columbine (Fig. 106); the legume or Aowering plants; and we shall presently discover that seede pod (from the Latin legumen, from the verb lego, to gather), admit of two natural divisions characterised by a difference a seed-vessel which splits into two valves, having the seeds of structure-one division corresponding with endogenous, the attached only to one suture or seam at the union of the margin other with exogenous plants. of the valves, as in the whole pea-flower tribe, example the lotus Did the reader ever remember planting a bean for amuse(Fig. 109); the capsule (from the Latin capsula, a little chest), ment? Most young people have done this, and we will assume & pericarp which
that the reader of may have one cell
this lesson has done only, or many cells,
it. * and which splitsinto
After having repieces by valves, as
mained in the earth in the gentian (Fig.
a few days, the bean 107); the colchicum
throws up a shoot (Fig. 110), the iris
terminating in two (Fig. 111), the lych.
little leaves. These nis (Fig. 117), and
iittle leaves were em
103 the corn-poppy (Fig.
bedded, in miniature 108); the pyris (from
proportions it is the Gr. Tufis (puke'.
true, in the bean, and sis), a box), a fruit
may be recognised which is like a box
there by careful ex. and throws off a cap,
amination; however, as in the pimpernel
by planting the bean (Fig. 118); the sili.
they are rendered qua (from the Latin
much more evident siliqua, a husk or
(Fig. 119). These
107 pod), a pod which
two thick seed. splits into two pieces
leaves are termed of valves separat
cotyledons, from the ing from a frame,
Greek κοτυλη (koand which is longer 111
tu'-le), a cup; and than it is broad, as 112
the bean, from posin the celandine
sessing two of these (Fig. 112); the sili
cotyledons, is called cule (from the Latin
108 silicula), a little pod
plant. or husk, the diminn.
Again, perhaps tiveof siliqua, a pod,
the reader has at which splits into two
some period of his pieces or valves, se
life planted a grain parating from
of wheat, barley, or, frame, and which is
still better, Indian about as broad as it
corn (Fig. 120). If is long, as in the 116
he has done this, he Shepherd's Parse
may have remarked (Fig. 113); the sa.
the result to have mara (from the La
differed from that tin samera, an elm.
noticeable wben the Feed), a fruit which
bean was planted. is hard, thin, and
Instead of two seed. extended into
leaves, or cotyleving, as in the maple
dons, only one in (Fig. 114); the nut 117
this case appears on (from the Anglo
the young plant, Saxon hnut, or the
which, therefore, is Latin nur, nucis, &
said to be a mononat), as in the chest- 102. POME. 103. DRUPE. 104. ACRÆNIUM OF THE RANUNCULUS. 105, CARTOPSIS OF THE BUCK- cotyledonous plant. nat (Fig. 115); and
106, FOLLICLE OF THE COLUMBINE. 107. CAPSULE OF THE GENTIAN. 108. CAPSULL Extending these in. the berry (from the OF THE CORN POPPY. 109. LEGUME OF THE LOTUS, 110. CAPSULE OF THE COLCHICUM, 111.
quiries still further, Anglo-Saxon beria, CAPSULE OF THE IRIS. 112. SILIQUA OF THE CELANDIXE. 113. SILICULE OF THE SHEPHERD'S
it will be found that PURSE. 114. SAMARA OF THE MAPLE. 115. XUT OF THE CHESTNUT. a grape), a succu.
116. BERRY OF THE
all plants whose DEADLY NIGHTSHADE, 117. CAPSULE OF THE LICHNIS. 118. PYXIS OF THE PIMPERXEL. lent or palpy fruit
fibro-vascular sys119. GERMINATION OF THE BEAN. 120. GERMINATION OF INDIAN CORN. Pontaining seeds
tem grows by exter. which have no co
nal depositions, and Tering but the pulp or rind), as in the deadly nightshade, the which possess reticulated leaves—in other words, all exogenous fruit of which is shown in Fig. 116.
plants yield dicotyledonous seeds; and all plants whose stems SECTION XIX.- THE SEED.
grow by internal depositions, and which possess straight-veined The seed, everybody knows, is that part of a plant which,
leaves, yield monocotyledonous seeds.
Thus, then, it follows that even already the reader is so far being sown, gives rise to a new plant. We might write a whole treatise on the nature and varieties of seeds, especially indicate the grand division of the vegetable kingdom to which
master of the principles of botanical classification, that he could 25 concerns their anatomical construction, but much of this information would be out of place in a series of elementary any plant belonged by one of three classes of signs—namely, papers: we shall, therefore, content ourselves with recapitulating
• The germination of a bean may be watched from day to day by some points that have already been adverted to in relation suspending the seed over water in the mouth of a hyacinth-glass, or to seeds, and shall then mention some general facts concerning crocus.glass. The bean should not be allowed to do more than seeds which must not be forgotten,
barely touch the water.
the signs of the section of the stem, the signs of the leaf, | Kaffee. 12. Haben Sie dieselben Bücher, weldie mein Nachbar gehabt hat? and, lastly, the signs of the flower. We may, therefore, divide 13. hat der Matrose seinem Bruder geantwortet ? 14. Nein, ich habe the various members of the vegetable kingdom as follows :- seinen Brief beantwortet. Cryptogamic, or flowers
EXERCISE 55. not apparent.
1. They have recommended the foreigners to me and to you. Endogenous. Monocotyledonous. Leal-veins 2. There lives in Naples a friend of mine; I shall recommend Phænogamous, parallel. Parts of the flower in fours or fives him to you. 3. One of my friends, whom you have seen with flowers apparent. Exogenous. Dicotyledonous. Leaf-veins reti. culated, Parts of the flower in threes.
me, has travelled in America, and has written a letter to me, in which he describes his journey. 4. A man of honour lowers him. self to (vor) nobody, in whatever condition he may find himself.
5. Did you receive the news before us ? 6. I received it after LESSONS IN GERMAN.—XVII.
you; the whole neighbourhood too was informed of it, as we SECTION XXXI.-INSEPARABLE PARTICLES. received your letter. 7. The children promised their father to
be obedient. 8. Advantages may be derived from this inven. BESIDES the separable particles (Sect. XXVI.), there is another tion, which nobody can account for. class (be, emp, cnt, er, miß, ver, etc., $ 94) that, unlike the former, are never used apart from the radical words to which they are
VOCABULARY. prefixed, and hence are called inseparable particles; thus by the Anffangen, to begin. Ausländer, fo-, Feuer, n. fire. union of these particles be, emp, ent, er, etc., with the radicals An'kommen, to arrive. reigner.
Sech, six ($ 44). fehlen, etc., we have the compounds befehlen, empfinden, entbehren, An'machen, to kindle Aus'sprechen, to pro- Trösten, to comfort. erholen, mißfallen, verhören, zermalmen, etc., corresponding in forma- (to make a fire).
Berter'ben, to hurt. tion to the English compounds be-tray, de-rive, dis-may, mis- An'zünden, to light. Grhe'ben, to raise. Vergnügen,n.pleasure take, etc. With few exceptions (as begeistern, beseelen), however, Aufstehen, to rise. Erzei'gen, to render, Wert, n, word. German, unlike most English radicals, may be used as well alone Ausgehen, to go out.
Zweimal, twice ($ 50). as in combination with prefixes; as, stören, to disturb; zerstören, to demolish.
EXERCISE 56. Many particles in German, which are used to modify radical 1. Geht Ihr Herr Vater heute nicht aus? 2. Er ist sten ausgegangen, verbs, have their exact equivalents in English, as :-Deuten, to er ist (Sect. XXII.) heute Morgen sehr früh aufgestanden. 3. Wo ift interpret; mißteuten, to misinterpret; fallen, to fall; befallen, to er hingegangen? 4. Er ist zu seinem Nachbar gegangen, er will auf das befall, etc. ($ 97. 1, 2, etc.)
Land geben. 5. Wo wollen Sie hingehen? 6. Ich muß auf ren Martt, In German, as in English, the inseparable particles never take in den Garten, an ten Brunner: gehen. 7. Sein Freund hat ihm geschrieben, the primary accent. ($ 98.)
raß er in Amerifa angekommen ist. 8. Wann haben Sie angefangen, 1. Por, which is often rendered by the English “ago,” unlike Deutsch zu lernen? 9. Ich habe vor sechs Wochen angefangen zu lesen
. the latter, always precedes the word of time to which it refers, 10. Wann wollen Sie anfangen, französisch zu lernen? 11. Ich habe schon 29:-Gr war vor zwei Stunten hier, he was here two hours ago angefangen zu lesen, und werde bald anfangen zu sprechen. 12. Wollen Sie (literally, he was here before two hours).
mir den Gefallen erzeigen, eine lampe anzuzünden? 13. Ich will es mit Seit (since), when used with words denoting time, often dem größten Vergnügen thun. 14. Hat tas Dienstmatchen das Fener sehen answers to "for” or “during," as :- -Er ist seit einer Woche franf, angemacht? 15. Nein, fie hat es noch nicht angemacht. he has been (literally is, see Sect. XVII. 6) siok for a week.
EXERCISE 57. Ich habe ihn seit einem ganzen Jahre nicht gesehen, I have not seen him during a whole year (a whole year since).
.1. Will you have the goodness to pronounce those words to VOCABULARY.
2. Do you pronounce well P 3. I believe I pronounce
well, but my brother pronounces better. 4. Many an innocent Ant'worten, to answer, Essen, to eat. Stiefel, m. boot. mind has been hurt by reading pernicious books.
5. The (intransitive). Gemit'tet, n. tempest, Storen, to disturb, tempest has disturbed the company in their enjoyments, and Beantworten, to an. thunder and light- interrupt.
has destroyed the house. 6. I have papers to read and letters swer (transitive). ning.
Tragen, to carry. to write. 7. Those persons who set fire to the house ought to Begrün'ten, to consti- Halten, to hold. Trinfen, to drink. be punished. tute.
Nest, n. nest. Versprechen, to promise. Beschreiben, to de- Paar, n. pair. Verste'hen, to under
SECTION XXXII. -VARIOUS IDIOMS. scribe. Reise, f. journey. stand.
Beide (plural) is declined like an adjective, and, unlike its Betraʻgen, to behave. Reisen, to travel. Zeitung, f. newspaper, equivalent (both), comes after the article or pronoun with which Erfin'den, to invent. Schwalbe, f. swallow. gazette.
it is used, as :-Die beiden Hänte, both the hands; meine beiten Grhalten, to receive. Sicy. himself, etc. Zerstören, to destroy, Mänte, both my hands. Alle (all) is sometimes, for the sake of Grnie'r rigen, to lower. I (Sect. XVII. 2.) demolish.
emphasis, placed before beite, and may together be translated, RÉSUMÉ OF EXAMPLES.
both of them,” or simply,“ both,"as :—Alle beite, both of them;
both. Diefen schönen Kana'rienvogel Hat My father gave me this beauti- 1. Beites (neuter singular) is frequently employed to couple
mir mein Vater heute Morgen ful canary-bird this morning. two things different in kind, whether designated by nouns alike gege'ben.
or different in gender, as :-Wem gehört (§ 129. 2) rieses Meffer und Die Freunde haben fich in den Gar. The friends have betakon them. rieses Schwert? Beides gehört meinem Freunde, both belong to my ten begeben.
selves to the garden.
friend. Bat Ihnen der Uhrmacher nur die Uhr, oder auch diesen King Die feindliche Armee hat sich erge's The hostile army has surren gemacht? Er hat Beides gemacht; or, Beite gemacht. Sind Sie mit ben.
ter Uhr und dem Ring zufrieden? Nein, ich bin mit Beitem unzufrieben, Der Lehrer Hat dem Knaben verge'. The teacher has pardoned the denn Veites ist nicht nach meinem Wunsche, no, I am dissatisfied with ben.
both, for both are not according to my wish.
2. For the pronoun “neither” the phrase feines or feins non EXERCISE 54.
beiden is used, as :-Haben Sie das neue orer das alte Buch? 30 bato 1. Will Ihr Sohn mein Pferd halten? 2. Gr hat es gehalten, aber feins von Beiten, I have neither (of the two). er bat einen Brief erhalten, welchen er lesen will. 3. Wie hat sich dieser 3. Recht and Unrecht, like the words "right" and "wrong," are Knabe betragen? Gr hat sich gut betragen, er hat meinen Regenichirm nouns, adjectives, and adverbs. The phrases, however, " to bo getragen. 5. Die Russen haben einen tapfern Helten gefunden. 6. Die right, to be wrong,” are expressed in German by the noun, wit! Deutichen haben viele nüßliche Künste erfunden. 7. Dieser Bettler hat eine the transitive verb haben, as :-r hat Necht, he (has) is right. Stunde an der Thüre gestanden, er hat mich nicht verstanden. 8. Hat Sie haben nicht Unrecht, you (have) are not wrong. ter Schuhmacher Zeit, mir ein Paar (Sect. LXI.) Stiefel zu machen ? 4. Gben so, before an adjective, signifies "just as," as:- Dicies 9. Er hat keine Zeit, Ihnen Stiefel zu machen, er hat Antern zu viel vers Kind ist eben so alt wie jenes, this child is just as old as that. Dieser (brochen. 10. Hat der Bauer mehr Kaffee zu trinfen, als Brod zu essen? Mann hat eben so viel Klugheit wie Verstand, this man has just as 11. Er hat Brod genug zu essen und Wasser zu trinken, aber er hat feinen much prudence as understanding.
5. Wanz wie, with a verb, signifies “precisely," or "just as,' 11. Der Staat Pennsylvanten liefert eben so viel Kohlen, ald ganz England. of " like," as :
-r ist ganz wie ich, he is just as I (am), he is just 12. Arbeitet Gustav nicht eben so viel, wie sein Bruder Hermann? 13. Die like me. Sie dentt ganz wie er, she thinks precisely as he kleine Glise gab ihrer Schwester Pauline eben so viel Pflaumen, wie ihrer (thinks), she thinks precisely like him.
Freundin Grma. 14. Haben unsere Nachbarn noch keinen Garten? 15. 6. Nost, besides meaning “nor," when used in conjunction Nein, sie haben noch feinen. 16. Bleiben Sie noch lange auf dem Lande? with weder, “neither,” is variously rendered by “still some, or 17. Ich bleibe noch eine furze Zeit da, und meine Freunde auch. 18. Geben yet more, another, besides,” etc., as :-Er schläft noch, he sleeps Sie heute noch spazieren? (Sect. LXIV. 1.) 19. Nein, denn ich muß still. Gieb dem Kinte noch Brod, give the child some more bread. noch arbeiten. 20. Die Freudenthränen der lang getrennten Freunde rühtten Bann þat er noch ein Pferd gekauft? when did he buy another die Herzen aller Zuschauer. 21. Kiönnen Sie die Waaren nicht billiger ver. horse ? Ginen Apfel hat das Kind gegessen, aber es hat noch einen, kaufen? 22. Es ist rein unmöglich. 23. Sie müssen dieses anter: machen. the child has eaten one apple, but it has one besides (or 24. Was kann ich anders thun ? 25. Du kannst anders reden und another)
bandeln. . 26. Ich werde Sie besuchen, wenn Sie es erlauben. 27. Er 7. Mehr, connected with a negative word, is used like its erzählte die Sache ganz anders. 28. Es ist etwas anderes, ob ich schreibe : equivalent “more," as :
:-Ich habe feing mehr, I have no more. er ist gelehrt,“ oder „geleert.“ 3d babe nicht viel mehr, I have not much more. Used with
EXERCISE 59. a nonn, the adverb follows, while in English it precedes the noun.
1. Has the teacher taken away the paper or the book? 2. Ho 8. Ander signifies other, in the sense of different; it must not has taken away both; for both belong to him. 3. Both towns be used in phrases like, “ I saw him the other day," which is in are situated on navigable rivers. 4. Thoy may take either way, German, Ich sah ihn neulich (literally, recently); or, Ich sah ihn vor as they have proceeded so far. 5. A great part of the land in einigen Tagen (literally, a few days ago).
America is still uncultivated. 6. He who wants the purpose, 9. The neuter anderes, preceded by etwas (in conversation must will the means. 7. The Rhine steamboat has just started usually contracted to wae), is rendered by the phrase “ another for Holland. 8. You err altogether when you say that you have thing," as :—Das ist etwas anderes, or, das ist was Anteres, that is quite surmounted every difficulty, otherwise all that you have another thing.
stated would be correct. 9. Which of us is right, I or he ? 10. 10. The adverb anders is readily distinguished by its form, You are both wrong. 11. It is quite another thing to say that and is rendered by “otherwise, differently,” etc., as :- -Er spricht he was not well, and could not come in consequence of it. 12. anders, alt er denft, he speaks otherwise than he thinks.
I shall speak no more about it; because I have found upon
closer investigation, that he is neither covetous nor prodigal. VOCABULARY.
13. They do not think themselves better than others. 14. Abfahren, to depart, Gustav, m. Gustavus. Spazie'rengehen, to Emma is just as intelligent as Eliza. 15. The sailor sets sail start.
Handeln, to act, deal. take a walk. for America to-morrow. 16. Do you drink wine or beer ? 17. Anter, other (R. 8). Insgesammt', alto- Staat, m. state. I drink neither wine nor beer, I always drink water. 18. An dered (R. 9).
Thaler, m. thaler (a Gustavus gave the boy a thaler to buy some coals for his Aaters, otherwise, Irren, to err.
German coin, mother. 19. Pennsylvania is a rich and flourishing state in the differently. Kohle, f. coal,
worth about 38.) United States of America. 20. She is just like her sister. 21. Aus bleiben, to remain liefern, to furnish. Trennen, to separate. Give the boy some more plums. 22. I have no more. 23. The out.
Mit'nehmen, to take Un'angebaut, unculti- girl shed tears of joy when she saw her mother. 24. That Beide, both. with.
ware is cheap, and the pattern of it is beautiful. 25. My Beites (R. 1)
Mittel, n, means. Unmögrlich, impossible friend has purchased a new winter coat. 26. This merchant Besuchen, to visit. Mufter, n. pattern. Unrecht, wrong
sends his goods to the town in a wagon. 27. Will you take a Dibleiben, to remain Pennsylva'nien, Verstandig, intelli- walk to-morrow? 28. It is impossible. (there).
Pennsylvania. gent, sensible.
THE THREE ORDERS OF LEVERS.-THE COMMON Elʻle, j. Eliza. fect. coat.
BALANCE. Griau'ben, to allow, Sache, f. thing, af. Wohlfeil, cheap. Of Levers there are commonly reckoned three kinds, of which Kreu tentbräne f. tear fair.
Zu'schauer, m. specta. Figs. 45, 47, and 49 furnish illustrations, in which the bar Sommerrod, m, sum. tor.
extends to equal distances on either side of the fulcrum, F; Geleret', empty.
may not by its weight interfere with the action of the Weight RÉSUMÉ OF EXAMPLES.
and Power. In that case It hat zwei Söhne, aber beide sind He has two sons, but both are
THE LIMUN we must consider the true taubftumm. deaf and dumb.
lever only as so much of the Der Riefe faßte die Keule mit beis The giant seized the club with
bar as is between P and w, den anden both hands.
or p or w and F, the points Sut ber Kaufmann ein Pferd oder Has this merchant a horse or a
of application and the fui. einen Wagen ? wagon ?
crum. These levers are said to be of three orders. Gt bat Beites. He has both.
First Order.—When the fulcrum is between the Power and Die Wahrheit und die Rofe find The truth and the rose aro Resisting Weight. sehr schön, aber Beide haben Dor- very beautiful, but both have Second Order.—When the fulcrum is at one end, and the thoras.
Weight nearer to it than the Power. Pia auf richtiger Mann verabscheut An upright man abhors a lie. Third Order.—When the fulcrum is again at one end, but eine Lüge.
the Power nearer to it than the šak jeder Mensch hat eben so viel Nearly every human being has Weight. Summet als Freude.
quite as much sorrow as joy. First Order.-The Condition of
Equilibrium in this we have
already determined in connec1. Wollen Sie ein Muster von diesem oder jenem Tuche haben? 2. tion with the balls in Lesson
Fig. 46. Son Erinen von beiden. 3. Wir geben ihm einen Thaler für jeden der VI. (Fig. 44). The Resisting betten Männer
4. Trinfen Sie Wein oder Bier ? 5. Ich trinke Weight (Fig. 45) is to the Power inversely as w F to P F, or poster Wein noch Buer (or, ich trinte feines von beiden). 6. Sie haben the weight multiplied by the arm, w F, is equal to the power Petit
, tas Sie ras gethan haben. 7. Ist ef recht, daß Johann so lange multiplied by the arm P F. Of this kind of lever the examples ausbleibt? 8. Nein, es ist unrecht von ihm, da er seine Aufgaben zu lernen are very numerous. In Fig. 46 the crowbar is used as a lever, bat. 9. Wie viel Tuch braucht der fleir:2 Friedrich zu (Sect. LXXIII. 1) by means of the falcrum in the middle, to lift the chest, the clauem Sommerrede? 10. Er braucht eben so viel, wie zu einem Wintertode. push of the hand and the weight of the chest, both parallel
forces, acting downwards. A poker put into a fire to raise he likes by means of the muscles attached to them along their
spade is also a familiar il- greater than the weight before he succeeds in lifting it. If he
Fig. 51. Second Order.—This is a no less important class; but the a large weight by a small Power and Resistance, not as in the former case, act in opposite force is not the only object aimed at in mechanism, natural directions, as in Fig. 47; and this accounts for the fulcrum or artificial. It is as often desirable to give the end of a having both these forces on one side of it, for, as I have shown lever a very rapid motion, and this can be done with most in the last lesson, the forces being opposite, the resultant, which, advantage when it is of the third order. The amount of force for equilibrium, must pass through the fulcrum, cannot lie between put forth in such cases is no consideration in comparison to them. Moreover, as it has been shown there that the distances rapidity of action, especially in animal mechanics. To strike of o from A and B (see Fig. 44, page 250) are inversely as a swift and smart blow with the closed hand, or with a sword the forces, so here the distances PF and we must be inversely in the hand, as it is often necessary to do, a lever of the third as the power and resistance, or, what is equivalent, the power order is the most effective. multiplied by its arm PF is equal to the weight multiplied by Levers of the various orders are often worked together, so as its arm W F. In this order of
to make compound levers, the resistance end of one working levers, as in the former, it should
into the power end of the other. In this way the effect of a be observed that there is a
small power is often very largely multiplied, and a very great mechanical advantage gained
resistance easily overcome. Such a compound lever is that in a larger weight at w is overcome
Fig. 51, where all are of the first order, three fulcrums at F, F, F., by a lesser at P, a result always
a power at Povercoming a resistance at P,, and there multiplied to be secured where the larger
overcoming a second resistance at P2, and this eventually lifting arm can be given to the power.
the still greater weight w. The power is multiplied in the first As an example of this lever, take the crowbar in the illustration lever inversely as the length of the arms, also in the second in Fig. 48, used differently from that in Fig. 46. The workman and so also in the third. Sappose, for example, the power at P makes the ground at the point of his bar his fulcrum, is one pound, and the short arm of each lever a third of the throws the weight of the chest about the middle, and, instead long one, then the 1 pound at P produces at the end of the long of pushing downwards with his hand, lifts upwards. The arm of the second lever at P, a force of 3 pounds. This again mechanical advantage is clearly on his side. The oar of a boat produces at P, in the third lever 3 times 3, or 9 pounds; and is also a lever of the second order; the arms of the oarsman thus 1 pound eventually balances a weight of 27 pounds at w, the furnish the power ; but most persons at first imagine that the mechanical advantage gained by the combination being 27 to 1. rowlock is the fulcrum. This is natural, for it looks very like But suppose that the lengths of the arms were in the proporone, but that it is not such is evident from the fact that tho 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 pis 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, Fig. 49.
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 off of of that unit, or, on making the end. 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, Third Order.—Here again the Resistance and Power, as in and the rule you arrive at is this Fig. 49, are parallel forces acting in opposite directions, and the Rule.—Multiply together the fractions which represent the condition of equilibrium is the same as in the last order, and for ratios of the Power arms to the Resistance arms, and the product
obtained is the number of pounds of the Resistance which ench pound of the Power balances. When the Power is more than i 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 rele 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 denominator 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 Fig. 50.
arms is equal to the Resistance multiplied by those of the Resist
ance arms. a similar reason ; but the mechanical advantage is against the And you thus have a result not unlike that established above power, which from being nearer the fulcrum must be greater for a single lever. And observe that this, thongh prored above than the resistance. The best examples are found in the limbs only for a combination of levers of the first order, holds equally of animals. The leg of a horse is a pair of levers with a joint good of other combinations, mixed or unmixed, all of the second. in the middle, which he can make into one or use separately as or all of the third, or of two kinds, or of all three together.