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of orange peel is squeezed between the fingers. Although the LESSONS IN GERMAN.-XXIV.
SECTION XLV.-PECULIAR IDIOMS. tain cases, belong to the Myrtaceæ, nevertheless it is a very loose Sich erinnern corresponds, in signification, to the English verb sign when taken apart from others. We can only arrive at a “ remember,” as :-r erinnert sich meiner ($ 126), he remembers correct botanical comprehension of the Myrtacec by studying me (literally, he remembers himself of me). Ich erinnere mich some of the generic characters that have been mentioned in our jener schönen Zeit, I remember (remind myself of) that sweet time. preceding list.
In referring to a thing already learned, the verb behalten, " to If the specimen of common myrtle under examination be a keep, to retain," is generally used, as :-3c fann die Wörter nicht sprig, not a single leaf, the student, before he lays it down, (im Gedächtniß) behalten, I cannot retain or remember (keep in should observe that the leaves are opposite, not alternate memory) the words. Er macht so viele Fehler, weil er die Regeln nicht (Fig. 143). Let us now examine the flower. The particular behält, he makes so many mistakes, because he does not retain species under consideration has a calyx of five divisions, and remember) the rules. there are also five petals, but in certain species these floral parts 1. The dative of a personal pronoun is frequently used instead are generally four. The stamens are numerous, as will be of an possessive pronoun, as :- Ich habe mir den Finger abgeschnitten, readily observed; and the reader need not be told at this period I have cut off my finger (I have to me the finger cut off). Gr of our labours that it is necessary to ascertain whether these gab es mir in die Hände, he gave it into my hands (he gave it to stamens grow from the calyx or the receptacle. They grow me in the hands). from the calyx, as will be readily distinguished. The ovary is 2. The phrases et fällt schwer or ed hält schwer are nearly synonyinferior; it contains three little cells, and each cell contains mous, and signify “to be hard, to be difficult," as :-Diesem many ovules; and it shoots up a single style, which terminates armen Manne fällt es schwer, zu betteln, it is hard (it comes hard) for in a small stigma so very minute that it cannot be seen by the this poor man to beg. Es hielt schwer, ihn zu beruhigen, it was diffinaked eye.
cult to calm him. Figs. 141 and 142 are representations of a vertical section of the
VOCABULARY. flower and ovary of a common myrtle, and a transverse section Ankunft, f. arrival. Eigenschaft, f. quality. Hülse, f. help, assistof the ovary with adherent calyx, or rather the fruit with ad- Aus“sehen, to appear. Grinónern (sich), to reherent calyx. If the reader examines Fig. 142, he will observe Berie'nen, to serve. member.
Spielen, to play. that the number of seed-cells in the species of myrtle under Begrei'fen, to compre- Grzählungf.narrative Verbre'chen, n. crime. consideration is three, or, to use the language of Botany, the hend.
Fau'lenzer, m. idler. Wi verwärtigkeit
, f. ad. ovary is trilocular, or three-celled. If the reader now refer to Berau'ben, to rob. Gedächtniß,n. memory versity. the list of characteristics of this family, he will find the expres. Diebstahl, m. theft. Grüntlich, thoroughly, Zuwei'len, sometimes. sion, “ ovary, usually two to six-celled,” which signifies that the Drüden, to press. fundamentally. number of cells may vary between two and six. By well considering the characteristics already discussed, the
RÉSUMÉ OF EXAMPLES. student will be at no loss to recognise an individual of the myrtle Grerin'nert sich noch des alten He still remembers the old tribe, even without taking into consideration minute microscopio
Napoʻleon hatte ein so gutes Ges Napoleon had so good a meLet us now proceed to mention a few particulars in connection dacht'niß, daß er die Namen seiner mory that he could remember with the dimensions, natural habitation, and properties of this meisten Solba'ten behal'ten konnte. (retain) the names of most of beautiful and useful botanical order.
his soldiers. The stem of the Myrtacec is generally woody, the leaves oppo- Er flüsterte ihm etwas in's Ohr. He whispered something in his site or alternate, simple, entire, rarely stipulated; frequently, as we have seen, provided with secretive glandular appendages, Es hält schwer, einen Giógensinnigen It is difficult to convince an embedded in the parenchyma. The flowers are complete, regular, zu überzeu'gen.
obstinate (person). solitary, or irregularly agglomerated. The greater number of Es fällt den meisten Menschen schwer, It is difficult for most people myrtaceous plants have berries for their fruits; but some others, fich dem Schicfal geduldig zu uns to submit patiently to their the principal of them being Australian plants, have a dry hard terwer'fen.
destiny. fruit; these, too, have alternate leaves, which is not usual in the
EXERCISE 86. myrtle tribe. The great districts for myrtles are the intertro.
1. Können Sie sich des Tages meiner Anfunst nicht mehr erinnern? 2. pical regions and Australia ; only a few species existing in o ja, ich erinnere midy tesselben noch sehr gut. 3. Es giebt viele Menschen, temperate climes. The spice sold as cloves is the produce of tie fich lieber ihrer schlechten, als ibrer guten Thaten erinnern. 4. Ei bieff one of the myrtle tribe, Caryophyllus Aromaticus (Fig. 144),
5. G8 balt which cloves are the dry flower-buds. Allspice the berry of another (Eugenia Pimenta). Guava jelly, so valued and fällt tem armen, aber fleißigen Manne schwer, tie Hülfe fremter Leute in
zuweilen schwer, etwas zu glauben, was wir nicht begreifen fönnen. 6. * esteemed wherever it can be procured, is the conserve made of Anspruch nehmen zu müssen. 7. Die englische Sprache fällt mir fidhwerer, the mashed berries of a myrtle which grows in the West Indies. ale tie französische. 8. Vei seinem Gelte, seinen Verwandten und feinen The pomegranate, too, a native of Northern Africa, but which Kenntnissen fiel es ihm nicht schwer, eine eben so gute, als angenehme Stelle now grows in the south of Europe, furnishes another example
zu finden. 9. Warum lernt Ihr Bruter so viel sdneller, als Sie? 10. of a fruit-bearing myrtle. In reviewing, then, the chemical and physiological character. 11. Können Sie sich nicht mehr erinnern, wem Sie die Bücher und tas
Weil er ein besseres Hebächtnis hat, und die Wörter besser behalten faun. istics of the Myrtacea, we learn that none of the tribe are poisonous. The greater number contain an abundance of Papier gegeben haben? 12. Ich fann mich bessen nicht mehr erinnets. fragrant oil. Some yield fruits which are delicious to eat; and 13. Der Faulenzer behält die Regeln nicht, weil er rieselben nicht gründlich all are imbued with a certain, but variable amount of astringent 15. Gr trüdte tem armen Manne einen Thaler in die Hand. 16. In
14. Der Diebstahl ist ein Berbreiten. matter, similar to that contained in oak bark, whence it has been denominated tannic acid by the chemist.
ter Ferne erinnern wir uns gern der Freunde, 17. Junge Leute traget In this country the myrtle requires protection during the zuweilen Brillen, um gelehrt auszusehen. winter months in all districts north of the Thames, but in the
EXERCISE 87. the south of England, and especially along the coast of the 1. Do you remember the day of the arrival of your friend? western counties, it flourishes against a wall, often growing to 2. Yes, I remember the day very well. 3. Most people remenia great height, and covering a considerable space with masses ber the years of their youth with pleasure. 4. There are many of dark-green foliage.
who remember their follies with shame. 5. It is difficult to Many of the species of the myrtle tribe are very large trees. remember every rule of a language. 6. It is not so difficult to The Sapucaya tree, as it is called in Brazil (Lecythis Ollaria), is convince a learned as an unlearned man. 7. Is it diffeult to ne of the tallest trees amongst the very tall ones that grow in submit to the adversities of life? 8. Yes, it is very difficult; "lian forests. In Fig. 136 the reader will find a representa- but the thinking man conquers them. 9. Can you not remem
a branch of this species. How different from a branch ber to whom you have lent my bok? 10. No, I cannot remen. ommon myrtle!
ber. 11. To lie is a sin.
SECTION XLVI.–VERBS GOVERNING THE GENITIVE. der Straße läuft. 13. Wenn den Fürsten das Volt jammerte, so würde er
anders regieren. 14. Aber das Volt wird ihm hierfür noch lohnen, und Some verbs in German govern the genitive ($ 125), while
tann seiner nicht schonen. 15. 68 fönnte wohl der Mühe lohnen, nach those in English of corresponding signification require the objective, as :-Bedenke meiner, remember me (or, think of me). Ich Californien zu reisen. 16. Ich würde gern diese Kleiter schonen, wenn ich
antere hätte. achte seiner nicht, I do not regard (notice) him. Gr bedarf des Gelres,
17. Ich wünsche feine andern Top zu sterben, als den Tob
vor Altersschwäche. 18. Vergiß meine Worte nicht. 19. Vergiß ter he needs (wants) money. Er tenkt or getenkt meiner, he thinks of me. Gr erwähnte unser, he mentioned (spoke of) us. Er berzubte ihn überstandenen Leiten, aber vergiß nicht die genossenen Freuden. 20. Wenn all seiner Schäße, he robbed him of all his treasures. Das Haus tic Fürsten fönnten, so schonten sie weder der Freiheit, noch sonst eines
Rechtes ihrer Völker. entfert de Baters, the house lacks (misses) the father (master).
EXERCISE 89. Der Unglüdliche ḥarrt besserer Zeiten, the unfortunate (waits for) expects better times. Schonet mein ($ 57. 1), spare me. Sie spotten 1. She nursed her father in his old age, and nursed me when meiner, Prinz, you mock me, prince! Vergesset meiner nicht, forget I had the nervous fever. 2. He mocked me, but observed not me not. Er bediente sich der besten Mittel, he used (served himself how the people mocked him. 3. Has he accepted my present ? of) the best means.
4. No, he told me he needed not the present. 5. Do not Some verbs of the above class (§ 125) more commonly take mention his kindness. 6. The teacher dares not spare the the accusative, as :-Vergiß deine Bücher nicht, do not forget your negligence or falsehood of his scholars, but must reprimand books.
them severely when he observes it. 7. Forget not the warning VOCABULARY.
voice of your parents. 8. Remember the Sabbath-day. 9. Al'rcsíchwäche, f. de- Erwähönen, to men. Regiment', n. regi- everybody ? 10. We waited with longing for the arrival of our
Who can believe a man who sneers at everything and scoffs at crepitude. tion.
friends. 11. When thou repentest of thy faults, then shall I Betürósen, to need, Gefälligkeit, f. com- Sehnsucht, f. longing.
remember thee with pleasure. want. kind. Schonen, to spare.
12. Conscientious people make plaisance, Defüm'mern, to grieve,
Spotten, to mock,
no vain speeches, nor make parade of qualifications which they
do not possess. trouble.
Harren, to hope, wait scoff at. Bereu'en, to repent, for.
Sterben, to die.
Appended to this and subsequent lessons the student will regret.
Hierfür, for this, for Strenge, severely. find a Key to the Exercises in German. Our reasons for not Bekhei'ten, modest. it.
Ueberstc'hen, to over- beginning this key before are the same as those which we have Bitte, f. request, pe- Jammern, to distress, come, endure. given for not commencing the Key to Exercises in Lessons in tition.
grieve, lament. Unentbehrlich, indis- French at an earlier period. Californien, n. Cali- Långst, long since pensable. fornia. (ago). Unleid'lich, insuffer
KEY TO EXERCISES IN LESSONS IN GERMAN. Cho'lera, f. cholera. Leib, n, pain, sorrow. able. Dann, then.
Exercises 1 and 2 are on Pronunciation. Exercise 3 is on Handwriting. Lohnen, to reward. Un'wahrheit, f. falseDumn, stupid. Nachlässigkeit, f. neg. hood.
EXERCISE 4 (Vol. I., page 38). Enblic, at length. ligence, remiss- Verwei'sen, to repri
1. Who has bread ? 2. The baker has bread. 3. Has the baker Entbehören, to be in
flour? 4. Yes, he has flour also. 5. What has the miller? 6. The miller want of, dispense Rede, f. speech, Wahr'nehmen, to ob- has flour and grain. 7. Who has meat ? 8. The butcher has meat. with. harangue.
9. Have you beer? 10. No, the brewer has beer. 11. Have you Erbur'men (sich), to Regieren, to govern, Zuleşt', at last. wine ? 12. No, I have coffee. 13. What has the girl ? 14. The girl have pity on. rule.
has tea. 15. Has the brewer grain ? 16. No, he has only beer and
wine. - 17. What has the child ? 18. It has water. 19. Has it bread RÉSUMÉ OF EXAMPLES.
also ? 20. Yes, it has bread and meat also. Bet ürich Sie noch ferner meiner Are you still further in need of
EXERCISE 5 (Vol. I., page 38). Dienste ?
my assistance ? Ja, mein Herr ! ich brauche Gelt, Yes, sir; I need some money,
1. Do you love the child or the man ? 2. I love the child. 3. Have tenn ich entbeh're selbst (Sect. for I am in want even of the you the sugar ? 4. No, the child has the sugar. 5. Does the child LXII.1) ter nothwentigsten
love the girl ? 6. Yes, and the girl loves the child. 7. Who has the most necessary provisions. Pehenemittel.
glass ? 8. The child has the glass. 9. Has the brewer the wagon ?
10. No, the peasant has the wagon. 11. Who has the beer? 12. The Derjenige, der ein Vergnü'gen nicht He that cannot dispense with a
brewer has the beer and the wine. 13. Has the miller the flour or the entbehren kann, zeigt, daß er nicht pleasure, shows that he does bread ? 11. He has the flour. 15. Has the baker the wine or the terstebt", tassel'be zu genie'fen. not know how to enjoy it water ? 16. He has the water. 17. Do you love the peasant ? 18. (the same).
No, I love the teacher. 19. Have you meat or wine? 20. I have the 3h würte feiner gar nicht erwäh'nen, I would not speak of him at all meat. 21. Have you the bread or the sugar! 22. I have the bread. wenn er nicht mein Verwant 'ter
24. He has the book. if he were not my relative.
23. Has the father the book or the comb? wäre.
EXERCISE 6 (Vol. I., page 61). Genie'ße des Lebens, aber mit Ehren! Enjoy (the) life, but with honour !
1. Are you the baker's friend ? 2. No, I am the joiner's friend.
4. He has the peasant's dog and Gr wurde eines Verbre'chens an'ge. He was accused of a crime that 3. What has the butcher's friend ?
horse. 5. Where is the flour? 6. It is in the miller's bag. 7. Where flagt, tas er nicht began'gen hatte. he had not committed.
is the grain ? 8. It is in the peasant's basket. 9. Who loves the Sergeisen Sie meiner nicht. Do not forget me.
teacher ? 10. The scholar loves the teacher. 11. Are you sleepy ? zu vergaß' meinen Bleistift ; geben I forgot my pencil; give me 12. No, I am thirsty. 13. Where is the brother's ball? 14. The Sie mir einen Au'genblic ten yours a moment.
child has the brother's ball in the father's hat. 15. Where is the 3h'rigen.
teacher's horse ? 16. It is in the stable. 17. Does the joiner praise EXERCISE 88.
the carpenter? 18. No, the carpenter's son praises the teacher's son.
19. Where is the joiner's chair ? 20. It is in the teacher's room. 1. Wer alte feute nicht achtet, ist nicht werth, selbst geachtet zu werden. 21. Does the carpenter love the teacher ? 22. Yes, he loves and 2. Wenn man auf jede Rede achten wollte, hätte man sich um viele Sachen praises the teacher. 23. The man is at the table, the book is on the ju bekümmern. 3. Er entbehrte der nöthigen Mittel, um seine Pläne aus, table, and the dog is under the table. zuführent. 4. Wer wird sich meiner annehmen, wenn ich verlassen bin? 5.
EXERCISE 7 (Vol. I., page 62). Wenn er seine Fehler bereut, so will ich ihrer auch nicht mehr gerenten. 6. Id würde noch viel mehr Sachen bevrirfen, wenn ich nicht gewohnt wire, 1. Who has this girl's paper ? 2. This child has it. 3. Whose die Gegenstände zu entbehren, tie (Sect. XXI. 3) viele Leute für unent.
book has this scholar? 4. He has the teacher's book, 5. From whom behtlich halten. 7. Der General erwähnte Ihres Sohnes, als eines der
bave you this leather ? 6. I have it from the shoemaker. 7. For tapfersten Männer in seinen Regimentern. 8. Gewähre meine Bitte, o
whom is this apple? 8. It is for the saddler's child. 9. Whose coat
has the tailor's son ? 10. He has this friend's coat. 11. From whom Vert! und schüße mich vor meinen Feinden. 9. Gerenfe meiner Bitte.
has this hatter's son money? 12. He has money from the father. 10. Muhts ist unleidlicher, als auf Iemanden lange zu warten, der zulett 13. Where is the peasant's wagon ? 14. The teacher's friend has it. gar nicht fommt. 11. Längst schon harrte ich Ihrer mit Sehnsucht, als ich 15. Whose house and garden has the teacher ? 16. He has the Sie entlich fommen fah. 12. Erbarme rich des Kindes, bas verlassen auf mayor's house and garden. 17. From whom have you this liat P
I have it from the hatter, 19. For whom is it? 20. It is for the name was Giotto or Angiolatto, an Italian painter, sculptor, tailor's son. 21. Have you gold, silver, or copper for the teacher ? architect, and engineer, born at Vespignano in 1276. As a boy 22. I have silver for him. 23. Whom does the child love ?
24. It he was employed as a shepherd, but Cimabue, who accidentally loves the teacher's brother.
discovered his innate talent for drawing, took him by the hand, EXERCISE 8 (VOL. I., page 62).
and made him a greater painter than himself. He had learnt 1. Where is the mate's brother? 2. He is with the captain in the
the rudiments of his art in the fields by sketching his sheep on ship. 3. Is the nobleman's son with him also ??
the earth with the end of his shepherd's crook, or with a nail
4. No, he is in Germany. 5. Where is the father ? 6. He is with the captain in the
on any flat piece of stone that might come in his way. These custom-house. 7. Does the captain praise the nobleman's son? small beginnings had great results in Giotto's case, for he went 8. Yes, and he praises the father also. 9, Does the nobleman love the on step by step until he became the greatest Italian painter of captain? 10. Yes, he loves and praises him very much. 11. Is this his time. When Benedict XI. was Pope Rome, artists were man the captain's son? 12. No, he is the mate's son. 13. Is this wanted to work at the decorations of the great cathedral dedi. sailor rich? 14. No, he is poor and merry. 15. How old is this cated to St. Peter, and invitations were sent to the principal inan ? 16. He is not very old. 17. Is he sick ? 18. No, he is painters of Italy to forward specimens of their skill for the hungry. 19. What does this girl give the child ? only sugar. 21. What do you give the servant ? 22. I give him pope's inspection. Giotto contented himself with drawing a money. 23. What does the servant give the horse ? 24. He gives it
circle on a piece of paper with a bit of charcoal, and handing it hay. 25. Does this child love the teacher ? 26. Yes, and the teacher to Pope Benedict's messenger. It was in vain that the mes. praises the child. 27. Is the hunter still in the forest ? 28. Yes, and senger urged that his master required some design as a speci. the nobleman's son is with him. 29. The huntsman goes to the men of Giotto's skill, for the painter refused to send anything forest to the father, and I go to the brother,
else. The circle so hastily drawn was found to be perfect when EXERCISE 9 (Vol. I., page 66).
tested with a pair of compasses, and so struck was the pope
and his advisers with this surprising proof of the artist's 1. Has a man or a child this friend's stick? 2. This man has an
capacity as a draughtsman, that he was immediately summoned enemy's sword, and this child has a friend's stick.
3. What has the to Rome to carry out the work that Benedict wished to con: hunter ? 4. He has a dog and a gun. 5. Who has the peasant's tribute as his quota to the adornment of the finest cathedral plough? 6. The father of this child has the plough. 7. Has this blacksmith the merchant's money? 8. No, he has only iron from a
that has yet been built. merchant. 9. Have you the baker's wagon ? 10. No, I have this
But to return from this digression. The circle, in geometrical wagon from a carriage-maker. 11. Have you this girl's ribbon terms, is a plane figure; that is, a figure drawn on a plane or 12. No, I have cloth from a draper. 13. Have you this friend's coat? level surface, and bounded by a curved line called the circum. 14. No, I have this cont from a tailor. 15. Have you the teacher's ference or periphery. Let us explain these terms; for there is paper ? 16. No, I have this paper from a stationer, and a letter of nothing so well calculated to fix the meaning of a word and the recommendation from the teacher. 17. Is the horse a draught, peculiar property of the figure that it is intended to describe as animal? 18. Yes, and it is also a beast of burden. 19. Is the camel to trace it to the primary source or root from which it is derived. a draught-animal also ? 20. No, it is only a beast of burden. 21. The word plane is derived from the Latin planus, fiat, smooth
, Whose law-book has the nobleman's son ? 22. He has the law.book of level. It is merely another form of the word plain, which we the judge of the superior court.
apply to a level tract of country because it is flat and devoid of hills or any striking inequalities in its surface. A joiner or
cabinet-maker will now see at once the reason why the tool he LESSONS IN GEOMETRY.-XIV. uses to give an even level surface to a piece of wood is called a
plane. The word circumference, which is applied to the line THE CIRCLE AND ITS PROPERTIES.
which is carried round about, or which bounds any figure, is HITHERTO, in our lessons in Geometry, the attention of the derived from the Latin words circum, round, and fero, I bear or student has been directed to the construction of rectilineal carry. The word periphery means precisely the same thing, figures, or figures contained by right or straight lines : we shall but it traces its source to the Greek instead of the Latin, being now enter on what may be termed the "geometry of the circle,” derived from the Greek Tepi (per'-ry), around, and pepw (fer'-ro). or the method of drawing circles and parts of circles under I bear or carry. various conditions; concluding our lessons on this subject Look at the annexed figure. The whole of the superficies or with instructions for drawing regular polygons by the aid surface of the paper that lies within the curved line A C B E is of the circle, protractor, and scale of chords, as well as the called a circle. The curved line A C B E ellipse and other figures bounded by curves or consisting of itself is called the circumference or periphery curved lines.
of this circle. The point o is called its It may be useful to the student if we recapitulate briefly the centre, a word derived immediately from the names of various parts of the circle, and mention its chief Latin centrum, and more remotely from the properties as laid down in the Definitions (Vol. I., page 53), Greek KevTpov (ken'-tron), a sharp point. before explaining one or two other points that will be necessary The position of this point has this peculiar for him to understand before he reads the problems that we are property: it is such that all straight lines about to bring under his notice.
drawn from it to the circumference are Firstly, let us ask, What is a circle? It is a form that meets equal to one another. Thus the straight lines O A, O B, OG the eye often enough as we go about our daily tasks. As we o e, drawn from the centre o to the points A, B, C, E, in the cir pass through the streets of town or city, or along the highways cumference, are equal to one another. These lines are called and byways of the country, it is brought before us in the wheels radii of the circle À C B E, from the Latin radius, a sunbeam of of every vehicle we meet. It is exhibited in the form of the ray of light, and hence applied to any line or any number of lines majority of our cooking utensils. If we turn our eyes to the that radiate in various directions from the same point, as rays face of the clock that stands on the mantel-shelf, or the watch of light seem to proceed from the sun or any luminous centre
, that is carried in the waistcoat-pocket, it is there. Nay, more, as may be seen by looking at a candle or gas-light with halfit is found in every button that we wear on our attire, in the closed eyes, when the rays that seem to issue from it will become cups and glasses out of which we drink, and in the plates off distinctly
visible. Any two radii that proceed from the centre which we eat our daily food. It is the most perfect, the most in opposite directions, and therefore lie in the same straight line
, elegant, the most useful of all forms. Under
the figure of a form together a straight line called a diameter of the circle. In snake holding its tail in its mouth, the ancients adopted it as the above figure (Fig. 49), A B is a diameter of the circle ACBE the emblem of eternity, which had no beginning, and which has Its name, derived from the Greek sta (di'-a), through
, and no end. It is a figure which any one can describe by the aid of uerpely
(met-rine), to measure, implies that it is a line that a pair of compasses with the greatest ease, but one which it measures the circle across its superficies and through its centre wonld be most difficult to draw without the assistance of this Having arrived at the meaning of the word diameter
, we arrive useful instrument.
at the full significance of the term " diametrically opposite." There was a man once, though, who could draw a perfect Thus, when we say that the opinions entertained by any two circle with a simple sweep of his unerring arm and hand, and men are diametrically opposite, we mean that they are as.com mark its centre with the same rapidity and precision. His trary to each other
as it is possible to be as opposite, in fact, in
direction and aim as the two radii proceeding from the centre of Rs in the point c. Straight lines drawn at right angles to the a circle that together form a diameter of that circle.
tangents of a circle intersect in the centre of that circle. Thus Any portion of the circumference of a circle, no matter how great in the annexed figure, the straight lines B 0, C o drawn at right or how small, is called an arc of that circle. Thus the portion Ac angles to the tangents P Q, R 8 respecof the circumference of the circle A C B E is an arc of that circle. tively, intersect in the point o, the cenFor the sake of clearness we will call this portion the arc AM C. tre of the circle A BC. The straight The remainder of the circumference, C B A, is also an arc of the lines B 0, CO are radii of the circle A B C; circle, as are also the portions A C B, B E A, E A C, C B E, etc. and thus, conversely, if a straight line be etc. The straight line that joins the extremities an arc is drawn through the extremity of a radius called the chord of that arc. Thus A c is the chord of the arc that meets the circumference of any ANC, A E is the chord of the arc A N E, and A B is the chord of circle, at right angles to that radius, the the arc A C B or the arc A E B. The student may ask why a straight line thus drawn at right angles portion of the circumference of a circle is called an arc, and to to the radius is a tangent of that circle. this we may reply by two counter-questions—Why is a man who The ratio of the diameter of a circle to
P shoots with a bow and arrow called an archer ? and, What does its circumference is as 1 to 31, or very
Fig. 52. the arc and its chord resemble ? It may not be easy to give a nearly so, expressed in figures in the reply to our first counter-query, but it will suggest a reply to simplest way possible—that is, the circumference of a circle our second, namely, that the arc and its chord look very much is equal in length to three times the length of the diameter, like a bent bow and its string tightened to its utmost tension. and one-seventh of its length; or it may be written as 7 to 22, Let it now be said that the Latin word for a bow is arcus, and which means that if a diameter of a circle be divided into 7 the meaning of the words arc and archer becomes clear enough. parts, the length of the circumference is equal to 22 of those The word chord is derived from the Latin chorda, the string of parts. Expressed in decimals, the ratio is as 1 to 3:14159. a harp or lyre, and hence any kind of string. It is from this Of course a greater degree of exactness may be obtained by word that we have "cord,” a term applied to any small rope, increasing the number of decimal places in the above, but the or thick or closely-twisted string. From this it may be seen number given is sufficient for all practical purposes. how much a letter more or less disguises an otherwise familiar The following remarks have been made on the ratio of the word.
diameter of a circle to the circumference by General T. Perronet A segment of a circle is any part of the surface of the entire Thompson, whose name has been already mentioned in our circle enclosed by an arc and its chord. The word segment is Lessons in Music :-derived from the Latin segmentum, a piece, shred, or paring. “If it is asked, what after all is the proportion between the Thus in Fig. 49, A M C represents a small segment of the circle diameter of a wheel and its circumference? it is as 1 to ACB E contained by the arc A M C and the chord A C. In like 3:14159; eto. etc., to as many figures of decimals as anybody manner, the portion of the circle C B E A, contained by the arc shall think it worth while to discover and add; but, as in the CBE A and the chord c A, is a segment of the circle A C B E, case of the square root of 5, coming to the end, No! As the as is also A C B, contained by the aro A C B and the chord A B. Irish sailor said of the rope, the end is cut off. It is not quite This chord, however, is a diameter of the circle A C B E; and so easy to add figure to figure as in the case of the square root when a diameter is the chord of an arc that encloses a segment of 5, but the conclusion is the same. .... The simplest proin conjunction with it, the portion of the surface thus enclosed portion for common purposes is as 7 to 22. The next, which is called a semicircle or half-circle.
there is very seldom any occasion to go beyond, is as 113 to 355, The figure enclosed between any two radii of a circle and the on which may be given a useful piece of what is called 'artificial arc of the circumference intercepted between the extremities of memory.' The ablest man it was ever my chance to know, the radii that touch or meet the circumference, is called a sector, professor of mathematics in the University of Cambridge, wanted from sectum, a part of the Latin verb seco, to cut. Thus O CE, this proportion one day, and was observed to be fidgeting with the portion of the circle A C B E bounded or enclosed by the radii, a pen and a piece of paper. At last he broke out, “There it is, OC, O E, and the arc C A E, is the sector of that circle, as is also sir. Write down the first three odd figures in pairs, and cut the remainder of the surface; namely, the portion bounded by them in twothe radii o C, O E, and the arc C B E.
113 / 355.' We shall have occasion in the course of future problems to speak of circles touching or meeting one another, and of straight I remember telling this to the driver of a French cabriolet on lines that are tangents to a circle. In Fig. 50, the smaller circles the Pont Neuf, to his great delight. He will never forget it; ADE, C F G touch the larger circle A BC,
nor should any working man to whom it may be ever likely to
be of use." the former in the point A, and the latter in the point c. One circle can touch another in only one point. The circum
READING AND ELOCUTION.-XIV. ference of the touching circles meet in one point only. If, however, the surface
ANALYSIS OF THE VOICE (continued). of one circle overlaps the surface of the x other in the slightest degree, contact is
EXERCISES ON INFLECTIONS.
Fig. 50. destroyed, and the circumferences of the
Rising Inflection. circles are said to cut one another. Thus in Fig. 51, the circum. ference of the circle B C D, which overlaps the circle A C E, cuts Rule 1.—" High rising inflection.” the circumference of the last-named circle in the points c and F. Há !-say you só ? When, therefore, two circles touch one another, they touch or Whát!-confer a crówn on the author of the public calamities ?
meet in one point only. They cannot touch Indéed !-acknowledge a tráitor for our sovereign ?
Rule 2.—“Moderate rising inflection."
In every station which Washington was called to fill, he acquitted of the one cuts the circumference of the himself with honour. other in two points only; it cannot by any As the evening was now far advanced, the party broke possibility whatever cut the circumference
Where your treasure is, there will your heart be I also. Fig. 51. of the other in more points than two.
Though we cannot discern the reasons which regulate the occurIn Fig. 50, the straight line xy which touches the circle A BC in the point B is called a tangent to that the cognisance of Infinite Wisdom.
rence of events, we may rest assured that nothing can happen without circle. Now in speaking of a line in plane geometry as the
Despairing of any way of escape from the perils which surrounded tangent of or to a circle, nothing more is meant than this, that him, he abandoned his struggles, and gave himself up to what seemed it touches the circle. The word tangent is derived from the his inevitable doom. Latin tango, I touch. In Fig. 52, the straight lines P Q, R S, are Had I suffered such enormities to pass unpunished, I should have tangents to the circle A B C, P Q touching it in the point B, and deemed myself recreant to every principle of justice and of duty.
Note and Exception.--" Words and phrases of address." from vice, from evil påssion,-from every corrupting bondage of the
soul! Listen, Amèricans, to the lesson which seems borne to us on the very air we breathe, while we perform these dutiful rights. Ye winds,
If guilty, let us calmly abide the results, and peaceably submit to that wafted the pilgrims to the land of promise, fan, in their children's our sentence; but if we are traduced, and really be innocent, tell hearts, the love of freedom! Blood which our fathers shed, cry from ministers the truth-tell them they are tyrànts; and strain every the ground ;-echoing arches of this renowed håll, whisper back the effort to avert their oppression. voices of other dàys ;-glorious Washington ! break the long silence of Heaven has imprinted in the mother's face something beyond this that votive cànvas ;-speak, speak, marble lips: teach us THE LOVE OF world, something which claims kindred with the skies, -the angelic LIBERTY PROTECTED BY LAW!
smile, the tender look, the waking, watchful eye, which keeps its fond
vigil over her slumbering båbe. - In the heart of man lies this lovely Rule 3.-Note.-"Poetic series."
picture ; it lives in his sympathies; it reigns in his affections; his eye Power, will, sensation, mémory, failed in turn.
looks round, in vain, for such another object on earth.
Rule 1.-" Intensive downward slide.”
Ùp! all ye who love me ! BLOW on BLÓW!
And lay the outlawed selons LÒw !
“MACGRÈGOR! MACGREGOR!” he bitterly cried.
On! countrymen, ON !—for the day,–
The proud day of glory,--is come!
To Àrus! gallant Frenchmen, to ÀRMS!
Oh! SHAME on us, countrymen, shame on us ÀLL!
If we cringe to so dastard a race !
TRÈM BLE, ye traitors ! whose schemes
Are alike by all parties abhorred, -
TREMBLE! for, roused from your parricide dreams,
Ye shall soon meet your fitting reward ! Onward still the remote Pawnee and Mandan will beckon, whither the deer are flying, and the wild horse roams, where the buffalo rănges, Rule 2.—“Full” falling inflection, in the cadence of a senand the condor soars,-far towards the waves where the stars plunge tence. at midnight, and amid which bloom those ideal scenes for the perse- The changes of the year impart a colour and character to our cuted savage, where white men will murder no more for gold, nor thoughts and feelings. startle the game upon the sunshine hills.
To a lover of nature and of wisdom, the vicissitude of seasons con
veys a proof and exhibition of the wise and benerolent contrivance of Rule 4.-"Questions which may be answered by Yes or No.” the Author of all things.
Has not the patronage of peers incréased ? Is not the patronage He who can approach the cradle of sleeping innocence without of India now vested in the crown? Are all these innovations to be thinking that "of such is the kingdom of heaven," or see the fond made to increase the influence of the executive power; and is nothing parent hang over its beauties, and half retain her breath, lest she to be done in favour of the popular part of the constitution, to act as
should break its slumbers,-without a veneration beyond all common a cóunterpoise ?
feeling,-is to be avoided in every intercourse of life, and is fit only for
the shadow of darkness, and the solitude of the désert.
This monument is a plain shaft. It bears no inscription, fronting Exception.—“ Emphasis.”
the rising sun, from which the future antiquarian shall wipe the dúst. Tell me not of the honour of belonging to a free country,—I ask, But at the rising of the sun, and at the setting of the sun, in the blaze
Nor does the rising sun cause tones of music to issue from its summit. does our liberty bear generous fruits ?
of noon-day, and beneath the milder effulgence of lunar light, it speaks, Was there a village or a hamlet on Massachusetts Bày, which did ' it acts, to the full comprehension of every British mind, and the not gather its hardy seamen to man the gun-decks of your ships of awakening of glowing enthusiasm in every British heart. wàr? Did they not rally to the battle, as men flock to a feast ?
I speak not to you, sir, of your own outcast condítion. You Is there a man among you, so lost to his dignity and his duty, as perhaps delight in the perils of martyrdom. I speak not to those to withhold his aid at a moment like this?
around me, who, in their persons, their substance, and their families,
have endured the torture, poverty, and irremedial dishónour. They Rule 5.—“Penultimate Inflection.”
may be meek and hallowed men,--willing to endure. All is doubt, distrúst,* and disgràce; and, in this instance, rely on The foundation on which you have built your hopes, may seem to it, that the certain and fatal result will be to make Ireland hate the you deep and firm. But the swelling flood, and the howling blàst, and connection, contemn the councils of England and despise her power. the beating ràin, will prove it to be but treacherous sånd.
I am at a loss to reconcile the conduct of men, who, at this moment, rise up as champions of the East India Company's charter ;
Rule 3.—“Moderate" falling inflection, of complete sense. although the incompetence of that company to an adequate discharge Joy is too brilliant a thing to be confined within our own bisoms : of the trust deposited in them, are themes of ridicule and contempt to it burnishes all nature, and, with its vivid colouring, gives a kind of all the world ; and although, in consequence of their mismànagement, fàctitious life to objects without sense or motion. connivance, and imbecility, combined with the wickedness of their When men are wanting, we address the animal creation; and, rather servants, the very name of an Englishman is detested, even to a pro: than have none to partake our feelings, we find sentiment in the music verb, through all A'sia; and the national character is become disgraced of birds, the hum of insects, and the lowing of kìne ; nay, we call and dishonoured.
on rocks and streams and forests to witness and share our emotions, It will be the duty of the historian and the sage, in all ages, to I have done my duty :-I stand acquitted to my conscience and omit no occasion of commemorating that illustrious màn; and, till my country :- I have opposed this measure throughout; and I DOS time shall be no more, will a test of the progress which our race made protest against it, as hårsh, oppressive, uncalled for, unjust, -as estain wisdom and in virtue, be derived from the veneration paid to the blishing an infamous precedent, by retalinting crime against crime,immortal name of Washington.
as tyrannous,-cruelly and vindictively tyrannous. Exception.—“Emphasis.”
Exception.—“Plaintive expression.” Let us bless and hallow our dwellings as the homes of freedom.
I see the cloud and the tempest near, Let us make them, too, the homes of a nöbler freedom,--of freedom
The voice of the troubled tide I hear;
The torrent of sorrow, the sea of griet, • The penultimate inflection of a concluding series, or of a clause that forms perfect sense, is the same in kind with that which precedes
The rushing waves of a wretched life. a period, except in verse and poetic prose, which, in long passages of
No deep-mouthed hound the hunter's haunt betrayed, great beauty, retain the suspensive slide.
No lights upon the shore or waters played ;