« 前へ次へ »
ady bcy, and
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, 10. 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 functi 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, solo 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 discessēre superiores. 22. Opis 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, miserőre lapsorum. that the subject of the sentence having the verb is not the 27. Succurite pauperibus. 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 vaning, 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 Sabi nes being subdued, Tarquin in triumph returned to Rome,
the product will be the required denominator of each fraction ; 4. Chilo, filio victore Olympiæ, præ gaudio exspiravit. Chilo, his son BEING conqueror at Olympia, died of joy.
these properly arranged in order will give the answer.
a 3. Apes, ac uleo amisso, statim emori existimantur.
and Bees, their sting being lost, are thought to die at once.
to fractions having a common denominator.
y It will be noticed from the fourth of the above examples,
Here, a xd xy = aly, that the participle, especially when it would be the participle
cx b X y - bey, are the three numerators. of the verb to be (which is not found in good Latin authors), and
т хъха 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.) care 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. harass the Carthaginians by war. 8. The Romans are about to strive. (See Art. 122.]
EXAMPLE. 9. The Romans say that they will strive. 10. The Romans returned
b the favour with increase. 11. The Romans promised the Numidians, Reduce a and to fractions having a common denominator. 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.
which are equivalent to
c' Wise men despise the appearances in a dream. 14. As soon as we have arisen, we despise the appearances in a dream. 15. Aristotle,
b, the fractions having a common denominator.
and 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
dr 2h 6c produced by man against man. 17. I am not born for a corner.
to fractions having a common denominator. 37
9 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 fructions having a common denomiHannibal, having fought with the Romans, always came off conqueror.
3 * d+h
nator, 22. Hannibal, as often as he fought with the Romans in Italy, came
1 off conqueror.
and to fractions having a common denomi.
a+b a-b EXERCISE 115.- LATIN-ENGLISH.
nator. 1. The mind of every most excellent man chiefly strives after im
4. Reduce a, b, and" to fractions having a common denominator. mortal glory. 2. The enemies were wearied by the length of the con.
V fict. 3. The enemies, wearied by the length of the conflict, left the
5. Reduce and (field of) battle. 4. He acquired virtue. 5. In whatever port of the
to fractions having a common denoininator. world a good man is, he will be loved by friends. 6. He who has ac
6. Reduce quired virtue, in whatever part of the world he is, will be loved by us.
to fractions having a common denominator.
56 7. Courage is eager for danger. 8. Courage does not reflect on what
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.
3c 1 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.
3x b 13. The memory of illustrious men, even when dead,
and has influence with us.
to fractions having a common denominator. 14. It is worthy of a king to aid the fallen.
4c 5 15. It is peculiar to folly to perceive the faults of others and to forget
a 5 8x its own.
1 16. We onght to do our best to benefit very many persons.
to fractions having a common denominator. 17. To be angry with those whom we ought to love is wickedness. 18.
44 Friendships, acquaintances, and neighbourhoods contain some pleasure
11. Reduce 17, ", a, and to fractions having a common de(something of pleasure). 19. We understand our advartages better by nominator. being without them, than by enjoying them. 20. What pleasure
12. Reduce and friendships, acquaintances, and neighbourhoods contain, we understand
to fractions having a common denominator, better by being without them, than by enjoying them. 21. Fresh men
1 always succeeded wearied ones.
to fractions having a common + 2 + x + 1
1 EXERCISE 116.-ENGLISH-LATIN.
1 1. Felicitas virtute nititur. 2. Nititur ne hominibus felicitas? 3. 14. Reduce
to fractions having a common Non, felicitas Deo nititur.
ax + ao
x + a 4. Excolere virtutem eniti debemus. 5. denominator.
es are equal to
b + c
a + b
* + a
1 2 3 4
5 15. Reduce and to fractions having a com- 16. Reduce
24xy – 4802
to a whole number, 2ab' 360° 4củ' 5do Gef
12x mon denominator.
ab + e + dr + ax + am 17. Reduce
to a whole or mixed number, 132. To reduce an improper fraction to a whole or mixed
18. Reduce the four next examples to their lowest terms :quantity.
bx + by Divide the numerator by the denominator, the quotient with the
qab (1.) (2.) (3.)
aac remainder in a fractional form is the answer. [See Art. 106.]
ac + abc
ar 133. To reduce a mixed quantity to an improper fraction.
to a common denominator. y
d Multiply the integer by the given denominator, and add the
a given numerator to the product. (See Art. 122.] The sum will
to a common denominator.
g y be the required numerator ; and this placed over the given denominator will form the improper fraction required.
21. Reduce a
to an improper fraction. If the sign before the dividing line is all the signs in the numerator must be changed. (See Art. 124.]
22. Reduce a + b * to an improper fraction.
a C EXERCISE 16.
of of * to a simple fraction.
3 ab + bm +
y 1. Reduce to a whole or mixed quantity.
2c 4dr abc b
to a simple fraction. 2 4x 2a
2d am - a + ady - hr 2. Reduco
to a whole or mixed quantity. a
1 3. Reduce a +
KEY TO EXERCISES IN LESSONS IN ALGEBRA. to an improper fraction.
r + 1
h a 5. Reduco ab to an improper fraction.
EXERCISE 14. 2x
2 + ax + a' 6. Reduco m + d
6 + 8x - 1 to an improper fraction.
" + 8x - 10 3a + 403
40' + ab + 96 7. Reduce a
6. to an improper fraction.
2a + 3b
4r + gar + 1 с
Gay + 3y?
22" 3t - 2
7. 8. Reduce ax + to an improper fraction.
3a + 2y
6x + 1
a - ax + aa
3x + 2 8.
11. 9. Reduce b to an improper fraction.
2x + 2x + 1
3.t + 3 a3 10. Reduce a + ax + a +
to an improper fraction. 2 a
READINGS IN GERMAN.-IX. 7a? 11. Reduce 2x - 4a +
to an improper fraction. & + 2a
10.-Die Nore und die Lilie 25ax 12. Reduce 3a
Deero' zai ont dee lee'. ll.ai. 4x +
to an improper fraction. 40 - 3x
Malvina stand mit ihrem Vater ber ciner Cilic, 13. Reduce 1 to an improper fraction.
Mal-vee'-na shtant mit ee'-rem fah'-ter fore i'-ner lee'-ly-ai, dee & + a
unter einem 134. To reduce a compound fraction to a simple one.
Rosenstrauch blühete. Blendend weiß, wie ein Multiply all the numerators together for a new numerator, and
don'-ter i-nem ro'-zen-shtroud blu”-hai-tai. Blen'-dent vice, vee ine all the denominators for a new denominator.
lichtstrahl, erhob die schöne Blume ihren offnen tuften
lyyt/-shtrahl, err-hope' dee sho'-nai bloo'-mai ee'-ren of-nen doof'-ten. EXERCISE 17.
den Kelch. Ueber ihr hing eine voll aufgeblühte friftige 2 1. Reduce
den kely u"-ber eer hink i'-nai fði out“ gai-bla"-tai kref-ti-gai of
to a simple fraction. 7 b + 2
Rose, und warf einen röthlichen Schimmer auf die jarten 2 4
b + h 2. Reduce
ro'-zai, šont varrf i'-nen rö't-lly-yen shim'-mer ouf dee tsahr'-ten 2a - m
Silberblätter der Lilie, und so floß auch beider Blumen 3. Reduce to a simple fraction.
zil”-ber-blet'-ter dair lee'-ly-ai, dont zo Aðssouch bi'-der bloo'.med. 4. Reduce
duft in einander.
došft in ine-an'-der.
O, welch ein schöner Vund! rief Malvina, unt neigte a:2 + ax + a2
Oh, velý ine sho'-ner bēönt! reef Mal-vec'-da, oont ni'y-tai 3.02 4r + 1 3x + 4 6. Reduce
to a simple fraction.
lächelnd ihr Haupt zu den Blumen, binab.
ley'-yelnt eer houpt tsoo dain bloo'-men hin-ap'.
Es ist der Bund der Uníould unb Liebe! eripiederte
Ess ist dair boðnt dair on-gholt dont lee'-bai! err-vee'-der-tai 8. What is the value of 2aay der Vater. So standen sie schweigend vor dent
Blumen. 9. What is the value of
dair fah'-ter. Zo shtan'.den zee shvi'-ghent fore dain bloo'-men. abcdf
Indes trat Oskar in den Garten, Malvina's ab 10. What is the value of X 4?
In-dess' traht Oss'- karr in dain garr'-ten, Mal-vee'-nass shtil-ler 16xy Beliebter. Da floß ein röthlicher Hauch über
Malvina's 11. What is the value of 4x ?
gai-leep'-ter. Dah foss ine ro’t-liy-yer houch ü”-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'-eu, vee dair ro'-zai glants ü”-ber dee lee'-11-ai, 13. What is the value of
Da sah der Vater fie an und sprach: Nicht wahr, Malvina, 24ar
Dah zah dair fah'-ter zee an dont shprahchy : NYýt vahr, Mal-veer-Dil, 17 abr 14. What is the value of when both numerator and denomi.
die Blumen haben cine Sprache und ein Antlig ? uator are x 20 ? 31a
dee bloo'-men hah'. ben i'-nai shprah'-chai cont ine ant'-lits ? 69hc + 12abr 15. Reduce
Für die linschuld und to a whole or mixed number,
Liebe! feßte Dstar bingu. 216
Fü'r dee oon-shošlt õõnt lee'-bai! zets-tai Oss'-karr hin-tsoo'.
alte Ma u 8.
Dee al'-tai mouse. Lilie, s. lily.
Schimmer,m.glimmer. dig, guilty, in Strauch, m. bush. Silber, n. silver. debted.) [time. Nun ist's zu spät, nun dich das Unglüd schon betroffen. Blenden, to dazzle. Duft, m. odour. Indeß, in the mean- Noon ists tsoo shpeyt, noon diy dass don'-glück sho'ne bai-trof-fen, Strabl, m. beam. Weld, -et, -e, which, Geliebte, m. and f. be- Wer sich nicht rathen läßt, hat Hülfe nicht zu hoffen. Duften, to spread what.
loved, love. Veyr zij niýt rah'-ten lest, hat hül'-fai niýt tsoo hof-fen. odour. Bund, m. alliance. Hauch, m. breath.
dence, splendour. Kaße, f. cat.
like do in do come, Würgen, to choke, open. Unsdult, f. innocence. Sprace, f. language. Maus, f. mouse. pray.)
throttle. Stäftig, strong. (Kraft, (Smuld, f. guilt, Hinzuseßen, to add. Gut sein, to be fond Dich, thee.
Garstig, ugly, horrid. f. strength.) debt, fault; smul. (Seßen, to put.)
Ghrlich, honest, -ly. Schon, already. 11.—Die Kaße, die alte und die junge Maus.
Rathen, to advise. (Ghre, f. honour.) | Betreffen, to befall.
Dir (dative), to thee. Gesicht, n. face. (Treffen, to hit,
(Doch, emphatic. Helfen, to help. Hülfe, f. help. allerliebsted fleines Thier, Doo al-ler-leep'-stess kli'-ness teer,
KEY TO EXERCISES IN LESSONS IN GERMAN. Komm doch ein wenig berju mir,
EXERCISE 128 (Vol. II., page 341). Kõm dod ine vey'-nly heyr tsoo meer, 30 bin dit gar
1. Did you see this neat little garden? 2. No, for I admired that ju
füsse. gut ; tomm daß ich dich nur
pretty cottage. 3. It belongs to two old people, whom I know. 4. lý ba deer gahr tsoo goo't; köm dass Iỷ điy Door küss -sai.
What kind of pretty little animals are those ? 5. There are a great Die alte M a U 3.
many young lambkins in the garden. 6. This girl plays with her little Dee al'.tai
brother. 7. Will you give me that little chest ? 8. Will you have Id rathe bir, Rind,
that one on the little table ? gehe nicht!
9. Look, what a neat little hat. 10. The
little child is delighted with his little kitten and with his gosling. 11. lý rah-tai deer, kint, ghey'-hai niyt!
So arrange it that you may be at my house by Saturday morning. 12.
Do we make it in such a manner that it is useful for both purposes ?
13. He shall so arrange it that he can take his books with him. 14. So komm doc i fiebe, diese Nuise
At all events, I will so arrange it that I shall be with you at ten
o'clock. 15. We will so arrange it that we by no means come too Zo kóm doch; zee'-hai, dee'-zai nüss'-sai
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 dựý ine'-mahl küss'-sai.
will arrive by the last steamboat. 18. A prophet is nowhere less Die iunge Ma u 8.
esteemed than in his native country and in his house. 19. His voice D e e ý 5 ở ng • ai m o u e.
has great influence in the council. 20. What will you bet that in
twenty years the greater part of Europe is republican? 21. The in. O Mutter, höre doce, wie sie so freundlich spricht.
clination to vice is much stronger in us than to virtue. 22. The 0 m8t-ter, hổ mi dốc, vee Zee zo troint-ly spriyt.
recognition of our performances is a powerful impulse to industry. 23. Id geb.
The business of his manafactores increases from year to year. 24. He lý ghep.
lifted up his eyes. 25. Ho jumped for joy, and clapped his hands. Die alte Ma u 8.
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 und andre schöne Sachen rivers and streams has given rise to the highest displays of con. och dee'-zess tsöök'-ker-brote ošnt an'-drai sho'nai zach'-chen structive skill in railway architecture. The bridges formed for Geb' ich dir, wenn du fommst.
this purpose present an infinite variety of detail, but the most gaib' lý deer, ven doo komst.
important may be classified as suspension, tubular, and lattice Die iunge Ma u 8.
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 Was fel is
unsuited to bear the violent strain produced by railway traffic. machen? Vass 281 tỷ ma '-đen?
To construct a substantial railway bridge of such material over D Mutter, laß mich gehn!
a stream of more than the smallest proportions, the piers would O möðt'-ter, lags mlý 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
describe; and by these means it was found possible to give a Rind, folg' mir, gehe nicht very wide span to the arches, with perfect safety to the bridge. Kint, folý meer, ghey'-hai nrýt!
Iron arches were employed for bridges before the introduc. Die iunge Ma u 8.
tion of railways-for example, in the very fine bridge over the De e y8 8 ngai
Thames at Southwark, which was completed in 1819. In their Was wird sie mir denn thun? Welch
adaptation to railway architecture, cast-iron was the material Tags virrt zee meer den toon ? velý eyr'-llý.yess gai-ziýt' ! at first employed, but this was known to be unsafe for arches
of any considerable span. Cast-iron was well enough calculated Die Kate.
to act as a support for the traffic, but unfitted to sustain the Dee kat'.tsa i. Komm, fleines Närtchen, fomm!
thrust and vibration produced by the passage of trains over an Kdın, kli'-ness Derr'-yen, kèm !
arch or span of large dimensions. A method of trussing the
cast-iron girders with wrought-iron bars was then introduced, Die iunge Ma u 8.
the tensile power of the wrought iron partly removing the defect Dee yoở ng'-ai mouse.
produced by the rigidity of the other material. But the failure Ac. Mutter, hilf! Oweh! of one of these trussed girder bridges, with spans of nearly 100
ac, most-ter, hilf ! Oh vey! | feet, on the Chester and Holyhead Railway, in 1847, shook the Sie würgt mich! Ach, tie Garstige!
faith of engineers in the principle, and the use of wrought-iron Zee vurýt miý! ach, doe garr’-sti-gai !
alone then became general.
To return to our classification of iron railway bridges, we | This is a form peculiar to railway architecture, the great engihave first to mention the suspension bridge. Structures of this neer who designed the first having before him no previous struckind are usually built in the following manner. A massive ture similar in kind-although applied to other purposes, as in tower of masonry is erected on each side of the stream, these the case of the suspension bridges—to suggest the idea and guide towers being termed the abutments. Over the tops of the him in carrying it out. The first tubular bridge was that towers are passed chains formed of bars of iron, the ends of thrown by Mr. Robert Stephenson across the Menai Strait, not which chains are sunk to a great depth in the ground, and far from the suspension bridge to which we have before alluded. firmly embedded therein. From these chains iron rods are It was a necessary condition, imposed by the Admiralty, that the hung, to support the roadway which passes from tower to central arches of a bridge across this strait should be of more tower. Among the good examples of ordinary suspension than 400 feet span, and 100 feet above the surface of the water bridges may be mentioned that at Hammersmith, on the at the highest tide, to preserve the freedom of the navigation. Thames; Hungerford Bridge, now removed to Clifton; and the In studying the problem of how to accomplish this end with bridge of this kind across the Menai Straits.
the utmost security, Mr. Stephenson determined, after repeated In the earlier days of railway construction, this form of experiments, to adopt a tubular form for his girders, and to bridge was not considered suitable for railway traffic. The make his bridge, so to speak, a tunnel suspended in the air. A passage of a train over such a bridge would depress the chain further series of experiments convinced him that a rectangular and roadway at either end, raising it at the centre, and so l tube was the most suitable for the purpose, possessing far greater
endanger the security of the entire fabric. But this tendency -strength than tubes either cylindrical or elliptical in form. His was counteracted by various devices to stiffen the roadway; idea, as finally resolved
on and carried out, was, therefore, that and a great engineering triumph was achieved when, in 1848, a of a long
tube, in section an oblong square, made of plates of railway suspension bridge, spanning a chasm of 800
foet, was cast-iron closely riveted together, the chief weight and supportbuilt over the St. Lawrence below the falls of Niagara. In ing power of the material being massed in a cellular form at this bridge wire cables are made to support a rectangular tube, the top and bottom of the structure. Two million rivets were which carries both an upper and a lower roadway, the former for employed throughout the tube. These rivets, when brought to the railway traffic, and the lower for that of vehicles and foot the works,
were formed with only
one end flattened, holes being passengers. A representation of this very remarkable structure punched in the plates to receive them. Each rivet, before being is given in one of our engravings.
fixed in position, was made red-hot in a furnace, then taken op Another kind of suspension bridge is occasionally employed by pincers and inserted in its place, when the unflattened end for railway purposes. In this form the roadway is supported of the hot metal was hammered on the inside until another by chains
and rods which hang from wronght-iron tubes, these head was formed, and the plates were thus securely bound tubes passing from tower to tower or from pier to pier, instead together. of the chains before mentioned. The great railway bridges at The Britannia Tubular Bridge, when completed, consisted of Chepstow and Saltash are formed in this manner. The method four spans over the Strait, the two central spans 460 feet each of their construction will be understood by a reference
to our in length, and the two at the sides half those dimensions. A illustration
of the first-named example, on the South Wales representation of this structure is given in our illustrations. An Railway.
immense bridge of the same character was afterwards erected We come now to the second classificetion of iron railway across the st. Lawrence at Montreal. It consists of a tube bridges—namely, those constructed on the tubular principle. more than 6,500 feet long, divided into twenty-five spans, the
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, ico which in winter
which are set on are brought down
stone foundations. the stream.
Railway bridges The Britannia
of recent construc. Bridge was justly
almost considered, at the
all of this form. time of its con.
The riveting is car. struction, 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, a great im.
Britannia Bridge, provement has
and the same since been made
amount of strength upon it. This im.
which is there afprovement 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 BRITANNIA TUBULAR BRIDGE ACROSS THE MENAI STRAIT.
right angles. open lattice-work
The use of iron formed of bars
girders has greatly or 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 aske 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.