« 前へ次へ »
glory. 15. Honour follows distinguished virtue. 16. He promised Pater filium complexus est. 6. Filius patris mortem ultus est. 7. me that he would return, 17. He has returned. 18. No, he will return Rex præmium pollicitus est. 8. Sorori tuæ regina pollicita estne to-morrow. 19. Boys support each other. 20. Boys ought to support præmium 9. Milites cumulatam gloriam adipisci nitentur. 20. each other. 21. I pity and shall pity the wretched. 22. Never forget Mane experrecti sunt, et discessēre. 11. Bene vitæ officiis functi sunt. thy own faults. 23. I shall set out within a few days. 24. When 12. Aristoteles et Zeno præceptorum officiis fancti sunt. 13. Quando wilt thou return? 25. Boys, reverence the aged.
amici tui domum revertent? 14. Heri domum reverterunt. 15. E Observe, that in the ablative absolute construction there are patriâ profecti sunt, et nunquam revertent. 16. Pestis hæc hominum properly two sentences, and consequently two subjects: for in animis nata est (born). 17. Ubi est patria ? 18. Patria mea est
mundus. 19. In animis mortalibus sunt semina innata vitiorum, 20. example, sole oriente, tenebræ diffugiunt; in the words sole oriente Dux cum hostibus congressus est. 21. Quotiescunque duces Anglici there is a subject, namely, sol; and in tenebræ diffugiunt there cum hostibus congressi sunt, semper discessere superiores. 22. Op. is a subject, namely, tenebre. The former sentence is incom- timi cujusque pueri animus maxime parentes suos amat. 23. Boni plete, nevertheless there is a subject in it.
in salutem animæ nituntur. 24. Lacte pueri et puellæ vescuntur. 25. Now it is an element in the ablative absolute construction, Discipuli officiis suis functi sunt. 26. O Deus, miseröre lapsorum. that the subject of the sentence having the verb is not the 27. Succurite pæuperibus. 28. Proprium est stultitiæ nulli prodesse. same as the subject of the imperfect sentence containing the participle. You may see this fact exemplified and illustrated in these instances :
LESSONS IN ALGEBRA.-X.
REDUCTION OF FRACTIONS. 1. Senescente luná, ostreæ tabescere dicuntur.
130. TO REDUCE fractions of different denominators to fractions The moon waning, oysters are said to waste away.
having a common denominator. 2. Geryone interempto, Hercules in Italiam venit.
Multiply together each numerator and all the denominators Geryon being slain, Hercules came into Italy.
except its own, and the product will be the required numerator of 3. Sabinis debellatis, Tarquinius triumphans Romam rediit.
each fraction; next, multiply together all the denominators, and The Sabines being subdued, Tarquin in triumph returned to Rome. 4. Chilo, filio victore Olympiæ, præ gaudio exspiravit.
the product will be the required denominator of each fraction ; Chilo, his son BEING conqueror at Olympia, died of joy.
these properly arranged in order will give the answer.
mi 5. Apes, aculeo amisso, statim emori existimantur.
to fractions having a comBees, their sting being lost, are thought to die at once.
7 a mon denominator.
Y It will be noticed from the fourth of the above examples,
Here, a xd xy = ady, that the participle, especially when it would be the participle
c X 6 X Y = boy, are the three numerators. of the verb to be (which is not found in good Latin authors),
and m x 6 xd=bdm, is sometimes omitted.
Also, bxd xy = bdy, is the common denominator.
bdm KEY TO EXERCISES IN LESSONS IN LATIN.-XXXII. Hence, the reduced fractions are
bdy' bdy bdy EXERCISE 114.-LATIN-ENGLISH.
The reason of this rule is plain, for the reduction consists in 1. The safety of men depends not only on truth, but also on repu- multiplying the numerator and denominator of each fraction into tation. 2. The citizens, having' made a treaty with the enemies, all the other denominators, a process which does not alter the enjoyed peace. 3. By reflection, we comprehend God and the divine mind. 4. We live on milk, flesh, and many other things. 5. Take value of the fractions. (See Art. 121.] fire that you do not avenge yourselves on your enemies. 6. The Romans
131. An integer and a fraction are easily reduced to fractions promised this to the Numidians. 7. The Numidians continued to having a common denominator, by making the former a fraction. haruss the Carthaginians by war. 8. The Romans are about to strive. (See Art. 122.]
EXAMPLE. %. The Romans say that they will strive. 10. The Romans returned the favour with increase. 11. The Romans promised the Numidians,
6 if they would continue to harass the Carthaginians by war, that they would strive to return the favour with increase. 12. No one has lived
b too short a time who has performed a work of perfect virtue. 13.
Here, a and
which are equivalent to
1 Wise men despise the appearances in a dream. 14. As soon as we have arisen, we despise the appearances in a dream. .15. Aristotle,
the fractions having a common denominator. Zeno, and innumerable others, having gone out of their country, never
EXERCISE 15. returned home. 16. There is no plague so detestable, which is not produced by man against man. 17. I am not born for a corner. 18.
to fractions having a common denominator. This whole world is my country. 19. The seeds of virtue are inborn
1+1 in our nature. 20. Hannibal fought with the Romans in Italy. 21. 2. Reduce and to fractions having a common denomiHannibal, having fought with the Romans, always came off conqueror. nator.
d+h 22. Hannibal, as often as he fought with the Romans in Italy, came off conqueror.
to fractions having a common denomi.
a + b EXERCISE 115.-LATIN-ENGLISH.
nator. 1. The mind of every most excellent man chiefly strives after im 4. Reduce b,
and to fractions having a common denominator. mortal glory. 2. The enemies were wearied by the length of the conflict. 3. The enemies, wearied by the length of the conflict, left the (field of) battle. 4. He acquired virtue. 5. In whatever part of the
5. Reduce and
to fractions having a common denominator.
b'a world a good man is, he will be loved by friends. 6. He who has acquired virtue, in whatever part of the world he is, will be loved by us.
to fractions having a common denominator.
a 56 7. Courage is eager for danger. 8. Courage does not reflect on what it may be about to suffer. 9. Courage is eager for danger, and whither
7. Reduce b, and to fractious having a common denominator. it turns, does not think of what it will suffer. 10. Augustus did not suffer himself to be called a lord. 11. Some animals are destitute of 8. Reduce and to fractions having a common denominator. reason, others use reason. 12. The soul having escaped, the body is
3 worth nothing. 13. The memory of illustrious men, even when dead, 9. Reduce and to fractions having a common denominator. has influence with us. 14. It is worthy of a king to aid the fallen.
a' 4c' 5 15. It is pecnliar to folly to perceive the faults of others and to forget
a 5 8x
to fractions having a common denominator. 17. To be angry with those whom we ought to love is wickedness. 18. Friendships, acquaintances, and neighbourhoods contain some pleasure
11. Reduce , , x, and to fractions having a common de(something of pleasure). 19, We understand our advantages better by nominator. being without them, than by enjoying them. 20. What pleasure
and friendships, acquaintances, and neighbourhoods contain, we understand
to fractions having a common denominator.
a 83 better by being without them, than by enjoying them. 21. Fresh men always succeeded wearied ones.
and to fractions having a common
+ + x + 1 EXERCISE 116.-ENGLISH-LATIN.
denominator. 1. Felicitas virtute nititur. 2. Nititur ne hominibus felicitas? 3.
and to fractions having a common Non, felicitas Deo nititur. 4. Excolere virtutem eniti debemus. 5. denominator.
- ax + a?
Reduce a and to fractions having a common denominator.
y 2 a
1 2 3 4 15. Reduce
and to fractions having a com2ab' 360' 4cd' 5de' 6ef mon denominator,
132. To reduce an improper fraction to a whole or mixed quantity.
Divide the numerator by the denominator, the quotient with the remainder in a fractional form is the answer. [See Art. 106.]
133. To reduce a mixed quantity to an improper fraction.
Multiply the integer by the given denominator, and add the given numerator to the product. (See Art. 122.] The sum will be the required numerator; and this placed over the given denominator will form the improper fraction required.
If the sign before the dividing line is all the signs in the numerator must be changed. (See Art. 124.]
3. Reduce a + to an improper fraction.
KEY TO EXERCISES IN LESSONS IN ALGEBRA. b
h-1 5. Reduce ab to an improper fraction.
6x + 8 - 1 6. Reduce m + dto an improper fraction.
29 + 8 - 10 a + b
3a + 403
423 + 6ab + 9b 7. Reduce a to an improper fraction.
2a + 36
4x + 9x + 1 с
Gay + 3yo
2 - 3 - 2 8. Reduce a +
x2 - 6x +1
- ax + a
11. 9. Reduce b - to an improper fraction.
3.23 -3. + 3 d-y 10. Reduce a2 + ax + a + to an improper fraction.
READINGS IN GERMAN.-IX. 11. Reduce 2x
to an improper fraction. a + 2a
10.—Die Rofe und die Lilie 25ax - 122* 12. Reduce 3a
Dee ro' zai 80nt dee lee'-l1-ai. 4x +
to an improper fraction. 4a - 3x
Malvina stand mit ihrem Vater ver ciner Cilic, 13. Reduce 1 to an improper fraction,
Mal-vee'-na shtant mit ee'-rem fah'-ter fore i'-ner lee'-II-ai, dee & + a 134. To reduce a compound fraction to a simple one.
unter einem Rosenstrauch blühete. Blendend weiß, wie ein
don'-ter i-nem ro'-zen-shtroud blu"-hai-tai. Blen'-dent vice, vee ine Multiply all the numerators together for a new numerator, and all the denominators for a new denominator,
lichtstrahl, erhob die schöne Blume ihren offnen tuften
¥ýt-shtrahl, err-hope' dee shoʻ-nai bloo'-mai ee'-ren of-nen d&$f'-ten. EXERCISE 17.
den Kelch. Ueber ihr hing eine voll aufgeblühte Fräftige 1. Reduce of
ü"-ber eer hink i-nai fði out"-gai-bla"-tai kref-ti-gai
Rose, und warf einen röthlichen Sohimmer auf die jarten b +h 2. Reduce to a simple fraction.
ro'-zai, zont varrf i'-nen rö't'-ly-yen shim'-mer ouf dee tsahr'-ten 2a - m
Silberblätter ber Lilie, und To floß auch beiter Blumen 3. Reduce to a simple fraction.
zil”-ber-blet'-ter dair lee®-11-ai, oont zo foss ouch bi--der bloo'.men. 4. Reduce to a simple fraction,
duft in einander.
dooft in ine-an'-der.
O, welch ein schöner Wund! rief Malvina, unt neigte 2:2 + ax + a2
Oh, velý ine shö’-ner boont! reef Mal-vee'-na, ont ni'y-tai 3.02 4x + 1
3x + 4 6. Reduce
to a simple fraction. 22 + 4x - 3
lächelnd ihr Haupt zu ben Blumen, hinab. 1
ley'-yelnt eer houpt tsoo dain blooʻ-men hin-ap'. 7. Reduce of of
to a simple fraction. 8-a
Gs ist der Bund der Unschuld und Liebe! erwiederte 8. What is the value of Saay
Ess ist dair boðnt dair öðn'-shoot dont lee'-bai! err-veer-der-tai 2aay
der Vater. So standen fie schweigend vor den Blumen. 9. What is the value of aabbccddff
dair fah'-ter. Zo shtan'-den zee shvi'-ghent fore dair bloo'-men. abcdf
Indeß trat Ostar ab
in den Garten, Malvina's stiller 10. What is the value of X 42
In-dess' traht Oss'-karr in dain garr'-ten, Mal-vee'-nass shtiľ-ler 16axy 11. What is the value of
Malvina's Da floß ein röthlicher Bauch über
gai-leep'-ter. Dah floss ine rö't-ly-yer houch u-ber Mal-vee'-nass 16ax 12. What is the value of when the denominator is multiplied Wangen, wie der Rose Glanz über die Lilie.
2a by 4?
vang'-en, vee dair ro'-zai glants a"-ber dee lee'-Il-ai. 13. What is the value of 3ary when the denominatoris divided by bax?
Da sah der Vater fie an und sprach: Nicht wahr, Malvina, 24ax
Dah zah dair fah'-ter zee an ont shprahch: Nyýt vahr, Mal-vee'-nu, 14. What is the value of
when both numerator and denomi- die Blumen baben eine Sprache und ein Antliß?
3la nator are 20 ?
dee bloo'-men hah'-ben i'-nai shprah'-chai cont ine ant-lits ? 15. Reduce 6abc + 12abe to a whole or mixed number.
Für die Inschuld und Liebe! feßte Dólar bingu. 2ab
Fü'r dee oon-shošlt dont lee'-bai! zets'-tai Oss'-karr hyn-tsoo'.
Die alte Ma u 8.
Dee al'-tai mouse. Lilie, f. lily.
Schimmer,m.glimmer. dig, guilty, inStraucy, m. bush. Silber, n. silver.
[time. Nun ist'e zu spåt, nun dich das Unglüd schon betroffen. Blenden, to dazzle. Duft, m. odour. Indeß, in the mean
Noon ists tsoo shpeyt, noon diy dass odn'-glück sho'ne bai-trof-fen. Strahl, m. beam. Weld, -er, -es, which, Geliebte, m.and f. be. Wer fich nicht rathen läßt, hat Bülfe nicht zu hoffen. Duften, to spread what.
loved, love. Veyr zij niýt rah'-ten lest, hat hul-fai niýt tsoo hof-fen.
like do in do come,, Würgen, to choke, open. Unschult, f. innocence. Sprache, f. language. Maus, f. mouse.
pray.) Sräftig, strong. (Kraft, (Schuld, f. guilt, Hinzufeßen, to add. Gut sein, to be fond Dich, thee.
Garstig, ugly, horrid. f. strength.) debt, fault; idul. (Seßen, to put.)
Ghrlich, honest, -ly. Schon, already. 11.--Die Raße, die alte und die junge Maus.
Rathen, to advise. (Ghre, f. honour.) Betreffen, to befall.
Dir (dative), to thee. Gesicht, n. face. (Treffen, to bit,
(Dochy, emphatic. Helfen, to help. Hülfe, f. help. allerliebstet fleines Thier, Doo al-ler-leep'-stess kli'-ness teer,
KEY TO EXERCISES IN LESSONS IN GERMAN. Komm boc ein wenig ber zu mir,
EXERCISE 128 (Vol. II., page 341).
1. Did you see this neat little garden? 2. No, for I admired that
füffe. zu gut; komm baz ich dich nur
pretty cottage. 3. It belongs to two old people, whom I know. 4. lý bin deer gahr tsoo goo't; kòm dass iy diy poor küss'-sai.
What kind of pretty little animals are those ? 5. There are a great Die alte Ma u s.
many young lambkins in the garden. 6. This girl plays with her little Dee al'tai mouse.
brother. 7. Will you give me that little chest ? 8. Will you have 3d rathe bit, Rind, gehe nicht!
that one on the little table? 9. Look, what a neat little hat. 10. The I rah'-tai deer, kint, ghey'-hai nfyt!
little child is delighted with his little kitten and with his gosling. 11.
So arrange it that you may be at my house by Saturday morning. 12. Kage.
Do we make it in such a manner that it is useful for both purposes ? Dee kat'-tsai.
13. He shall so arrange it that he can take his books with him. 14. So tomm doc; siehe, biese Nuñe
At all events, I will so arrange it that I shall be with you at ten
o'clock. Zo kóm doch; zee'-hai, dee'-zai nüss'-sai
15. We will so arrange it that we by no means come too
late. 16. Tell your brother he should so arrange it that it may be Sind alle dein, wenn ich dich einmal küsse.
understood by everybody. 17. I hope you will so arrange it that you Zint al-lai dine, ven lý dij ine'-mahl küss'-sai.
will arrive by the last steamboat. 18. A prophet is nowhere less Die iunge Ma u .
esteemed than in his native country and in his house. 19. His voice Dee yoong'-ai mouse.
has great influence in the council. 20. What will you bet that in
twenty years the greater part of Europe is republican? 21. The inD Mutter höre doch, wie sie so freundlich spricht.
clination to vice is much stronger in us than to virtue. 22. The Omšot-ter, hõ-rai doc, vee zee zo froint'-lvý shpríýt.
recognition of our performances is a powerful impulse to industry. 23. 34 gen.
The business of his manufactores increases from year to year, 24. He lý ghep.
lifted up his eyes. 25. He jumped for joy, and clapped his hands. Die alte Ma ul.
26. The children were jumping up.
Kind, gehe nicht!
LESSONS IN ARCHITECTURE.-XVI.
THE necessity that railways should frequently be thrown across Auch dieses Zuderbrod
rivers and streams has given rise to the highest displays of conoch dee'-zess tašok'-ker-brote odnt an'-drai sho'nai zach-chen structive skill in railway architecture. The bridges formed for cb' ich dir, wenn du kommst.
this purpose present an infinite variety of detail, but the most gaib' lý deer, ven doo könet.
important may be classified as suspension, tubular, and lattice Die iunge Ma u s.
bridges, in all of which iron is the principal material employed. Dee yoo ng'-ai mouse.
Brickwork and masonry, except in the piers and abutments, are
unsuited to bear the violent strain produced by railway traffic. Was soll ich machen ? Vass zol rý mach'-chen ?
To construct a substantial railway bridge of such material over O Mutter, laß mich gehn !
a stream of more than the smallest proportions, the piers would O miot-ter, lass miy gheyn!
have to be so closely set together as seriously to impede the
navigation. This difficulty was removed by the use of iron Die alte Ma us.
girders or beams of various forms, which we shall presently Dee al'.tai mouse.
describe; and by these means it was found possible to give a Kind, folg' mir, gehe nicht! very wide span to the arches, with perfect safety to the bridge.
Kint, fdlý meer, ghey'-hai nrýt! Iron arches were employed for bridges before the introducDie iunge Ma u 6.
tion of railways-for example, in the very fine bridge over the Dee yoong'-ai mouse.
Thames at Southwark, which was completed in 1819. In their Was wird sie mir denn thun? welch ehrliches
adaptation to railway architecture, cast-iron was the material Vass virrt zee meer den toon ? velý eyr'-ly-yess gai-zrýt' ! at first employed, but this was known to be unsafe for arches Die
of any considerable span. Cast-iron was well enough calculated Kate.
to act as a support for the traffic, but unfitted to sustain the Dee kat'.tsa i.
thrust and vibration produced by the passage of trains over an Somm, Fleine Nårechen, fomm!
arch or span of large dimensions. A method of trussing the Kěm, kli-ness nerr'-ýen, kom!
cast-iron girders with wrought-iron bars was then introduced, iunge Ma u 8.
the tensile power of the wrought-iron partly removing the defect Dee yoong'-ai mouse.
produced by the rigidity of the other material. But the failure Ach, Mutter, hilf! weh! of one of these trussed girder bridges, with spans of nearly 100
ach, most-ter, hilf! Oh vey! feet, on the Chester and Holyhead Railway, in 1847, shook the Sie würgt mich! Ach, die Garstige!
faith of engineers in the principle, and the use of wrought-iron Zee vürýt miý! ach, dee garr'-sti-gai!
alone then became general.
To return to our classification of iron railway bridges, we have first to mention the suspension bridge. Structures of this kind are usually built in the following manner. A massive tower of masonry is erected on each side of the stream, these towers being termed the abutments. Over the tops of the towers are passed chains formed of bars of iron, the ends of which chains are sunk to a great depth in the ground, and firmly embedded therein. From these chains iron rods are Thung, to support the roadway which passes from tower to tower. Among the good examples of ordinary suspension bridges may be mentioned that at Hammersmith, on the Thames; Hungerford Bridge, now removed to Clifton; and the bridge of this kind across the Menai Straits.
In the earlier days of railway construction, this form of bridge was not considered suitable for railway traffic. The passage of a train over such a bridge would depress the chain and roadway at either end, raising it at the eentre, and so
endanger the security of the entire fabric. But this tendency was counteracted by various devices to stiffen the roadway; and a great engineering triumph was achieved when, in 1848, a railway suspension bridge, spanning a chasm of 800 feet, was built over the St. Lawrence below the falls of Niagara. In this bridge wire cables are made to support a rectangular tube, which carries both an upper and a lower roadway, the former for the railway traffic, and the lower for that of vehicles and foot passengers. A representation of this very remarkable structure is given in one of our engravings. Another kind of suspension bridge is occasionally employed for railway purposes. In this form the roadway is supported by chains and rods which hang from wrought-iron tubes, these tubes passing from tower to tower or from pier to pier, instead of the chains before mentioned. The great railway bridges at Chepstow and Saltash are formed in this manner. The method of their construction will be understood by a reference to our illustration of the first-named example, on the South Wales Railway. We come now to the second classification of iron railway *ges—namely, those constructed on the tubular principle.
strength than tubes either cylindrical or elliptical in form. His
the top and bottom of the structure. Two million rivets wer
This is a form peculiar to railway architecture, the great engi. neer who designed the first having before him no previous strueture similar in kind—although applied to other purposes, as in the case of the suspension bridges—to suggest the idea and guide him in carrying it out. The first tubular bridge was that thrown by Mr. Robert Stephenson across the Menai Strait, not far from the suspension bridge to which we have before alluded. It was a necessary condition, imposed by the Admiralty, that the central arches of a bridge across this strait should be of more than 400 feet span, and 100 feet above the surface of the water at the highest tide, to preserve the freedom of the navigation. In studying the problem of how to accomplish this end with the utmost security, Mr. Stephenson determined, after repeated experiments, to adopt a tubular form for his girders, and to make his bridge, so to speak, a tunnel suspended in the air. A further series of experiments convinced him that a rectangular tube was the most suitable for the purpose, possessing far greater
idea, as finally resolved on and carried out, was, therefore, that of a long tube, in section an oblong square, made of plates o cast-iron closely riveted together, the chief weight and support ing power of the material being massed in a cellular form *
employed throughout the tube. These rivets, when brought to the works, were formed with only one end flattened, holes being punched in the plates to receive them. Each rivet, before being fixed in position, was made red-hot in a furnace, then taken ul by pincers and inserted in its place, when the unflattened on of the hot metal was hammered on the inside until anothe head was formed, and the plates were thus securely bound together. The Britannia Tubular Bridge, when completed, consisted c four spans over the Strait, the two central spans 460 feet eac in length, and the two at the sides half those dimensions. . representation of this structure is given in our illustrations. A immense bridge of the same character was afterwards erecte across the St. Lawrence at Montreal. It consists of a tub more than 6,500 feet long, divided into twenty-five spans, th
central one of 330 feet; but the masonry of the piers is of much A good example of the lattice-girder bridge is seen in that of greater strength and proportion than in the case of the the London, Chatham, and Dover Railway over the Thames at Britannia Bridge, to resist the force of the great masses of Blackfriars, the girders in this case resting on columns of iron, ice which in winter
which are set on are brought down
stone foundations. the stream.
Railway bridges The Britannia
of recent construc. Bridge was justly
tion are almost considered, at the
all of this form. time of its con
The riveting is carstruction, a great
ried out on the engineering tri
same principle and umph; but, bril
to the same extent - liant as was the
as in the case of the idea, & great im
Britannia Bridge, provement has
and the same since been made
amount of strength upon it. This im
which is there af. provement consists
forded by the cel. in the substitution
lular arrangement of lattice girders
of material above for those of a tu.
and below, is given bular form. In the
in the lattice tubular girders the
bridges by iron. sides are formed of
beams which, at solid plates. In the
frequent intervals, lattice girders, as
cross the principal the name implies,
girders, both at the sides are com
top and bottom, at posed of a kind of
right angles. BRITANNIA TUBULAR BRIDGE ACROSS THE MENAI STRAIT. open lattice-work
The use of iron formed of bars
girders has greatly of rods of iron, which cross each other diagonally. By this facilitated the construction of what are known as skew bridges, means, in the first place, a great saving is effected in the i.e., bridges the line of which runs askew or obliquely to material employed ; next, every portion of that material can | that of the stream. The peculiar formation which it was
be so adjusted as to bear a full share of the strain of the necessary to give to the component parts of the arches in traffic; and lastly, the whole fabric presents a smaller surface stone bridges, on the skew principle, rendered these difficult to the action of the wind and weather, while at the same time it of construction, and they were comparatively unsafe for the can be more easily repainted or repaired.
enormous strain of general railway traffic.