ARC
204
ARC
Arcas, in the mythology, the son of Jupiter and Calisto , who Iwas turned into a she bear by Juno.
ARCBOUTANT, [from arc, and boater, to abut, Fr.] inbuilding, an arched buttress.
AR (JEN -RARTvOIS, a town of France , in the department ofCote-d’Or, 35 miles N. of Dijon , Lon. 5. 7. E. Lat. 47. 55. N.
ARCF.SlI.AUti, a celebrated Greek philosopher, born atFitane, in Eolis, about B. C. 300. He founded the academy,called the second school. He was a man of great erudition, andwell versed in the writings of the ancients. He was remarkablefor the severity of his criticisms •, but knew how to accommodatehimself to the age, and pursue the allurements of pleasure.
ARCH, in architecture, a building generally in form of a curve,erected to support some structure or other weight. They are ofvarious figures as, circular arches, which are either exactly semi-circles, or less than semicircles ; elliptical, catanarian, cycloidal,groined gothic or pointed arches, &c. Straight arches are thoseused over doors and windows, having plain straight edges, bothupper and under, which are parallel, but both the ends and jointspoint towards a center. The term arch is peculiarly used for thespace between two piers of a bridge, intended for the passage ofwater, vessels, See. The construction of arches is the noblest andmost difficult part of masonry. The stupendous structures andenormous weights supported by arches, shew that they are notkept together by the force of the cement, but by the equal ba-lance of all their parts. Such an arch having no tendency to onepart more than to another is railed the arch of equilibration, beingthat which is in equilibrium in all its parts; and which is thereforesafer and stronger than any other figure. In such arches everyparticular figure of the extrados, or upper side of the wall aboverequires a peculiar curve for the under side of the arch itself, toform an arch of equilibration, so that the incumbent pressure onevery part may be proportional to the strength or resistance there.When the arch is equally thick throughout, a case that canhardly ever happen, then the catenarian curve is the arch of equi-libration ; but in no other case ; and therefore it is a great mis-take in some authors to suppose that this curve is the best figurefor arches in all cases; when in reality it is commonly the worst.This subject is fully 7 treated in Dr. Hutton’s Principles ofBridges, prob. 5, where the proper intrado* is investigated forevery extrados, so as to form an arch of equilibration in all caseswhatever. It there appears that, when the upper side of the wallis a straight horizontal line, as in the figure (Plate XI. fig. 2.), theequation of the curve is thus expressed,
log. ofl±i±^Z±2f
y = hx - __ —
a-I- r 4- v iSnr rr
log. of---—-
where x = DP, y =;PC, r = DO, h = AO, and a — DK. Andhence, when a, h, r, are any given numbers, a table is formed forthe corresponding values of x and ?/, by which the curve is con-structed for any particular occasion. Thus, supposing a or DK=6,h or At) 50, and r or DO = 40; then the correspondingvalues of KI and IC, or horizontal and vertical lines, will be asill this table.
TABLE FOR CONSTRUCTING THF. CURVE OF EOUIMBRATfON.
Value
of KI.
Valueof IC.
Valueof K l.
Value 1ofIC.
\ alueof K1.
Value |of IC. j
0
6.000 ;
21
10.381 1
36
21.774 j
2
6.035
22
10.858 )
37
22.948
4
6.144 ;
23
11.368
38
24,190
6
6.324 1
24
1 1.91 1
39
25.505
S
6.580
25
12.4S9
40
26.894
10
6.914 :
26
13.106 :
41
28.364 |
12
7.330
27
13.761
42
29-919
13
7.571
28
14.457
43
31.563
14
7.834
29
15.196
44
33.299
15
8.120
30
15.980
45
35.135
us
8.430
31
16.811
46
37.075
17
8.766
32
17.693
47
39.126
18
9.168
33
18.627
48
41-293
19
9.517
34
19.617
49
43.581
20
9.934
35
20.665
50
46.000
The following simple and mechanical method of constructingan arch of equilibration, was first suggested by 7 De la Hire. LetAB, (Plate XI. fig. 1.) be the span, and C 7, the height of thearch, to have a road way EDF. Invert the figure AF.DFB, tothe position A e df B, suspend a chain of uniform thickness fromA and B, so that its lowest part shall be a little below c corres-londingtoC. Divide AB into equal parts, and draw verticalines, cutting the chain in the points 1, 2, 3, &c. to these pointsattacli pieces of another uniform chain, to or from which linksmust be added or taken away, till their extremities coincide withthe inverted roadway 7 e df, the greater lengths towards A and 11will puli down those parts and raise the middle at c a little higher,and thus bring it to its true altitude, and produce the arch of equi-libration ; but this supposes that the weight of the suspendedchain, is to the weight of the sum of the appended bits, as thew eight of the arch stones, is to the w eight ot the matter laid uponthem, very nearly 7 . Therefore to make it answer the purpose, esti-mate the weight of the intended arch stones and of the incumbentmatter, and also find the weight of the suspended chain A c B,this weight of the chain by that of the incumbent mat-
ter, and divide the product by the weight of the arch stones, re-serve the quotient. Then estimate as near as you can the meanlength between A c and cd which are given, multiply this lengthby the number of bits to be suspended, this product w ill shew thelength of an uniform chain, whose weight is to be equal to the re-served quotient, this being divided into parts and suspended fromthe several points 1, 2, 3, &c. links are to be taken from thosewhich hang below the inverted road way and added to thosewhich fail short of it, till their extremities answer to the form ofthe road way. Then will this curve be indefinitely near to thearch of equilibration for the purpose wanted. By this methodany intelligent person, though ignorant ot mathemactis, may easilyconstruct an arch to answer any conditions. The above theory 7supposes that the pressure on the arcii is in vertical lines, but insome cases loose materials, as sand, rubbish, fee. exert a kind oflateral pressure oil the arch, this and some other circumstances, asthe joining the arch stones with mortar, &c.. will allect the theorya little. In the construction of arches these particulars should beattended to, in order to have them on the form. On this subjectthe reader is referred to the excellent Treatises of Dr. Hutton andM. Bossut; and to the word arch in the Supplement to the En-cyclo. Britan.
Arches, Triumphal, are magnificent entries into cities,erected to adorn a triumph, and perpetuate the memory of theaction.
Arch, in geometry. See Arc.
AKCILEOGRAPIHA, [from i?,-, ancient and yjaf®; todescribe,] the science or study of antiques, comprehending a know-ledge of ancient coins, medals, inscriptions, sculptures, statues, Sec.
ARCHAIOLCKtY, [from ancient, and x°ySe, a dis-
course,] a discourse on antiquity.
ARCHAISM , etymologic, is when either an obsolete word,declension, or conjugation is used.
Archaism, syntactic, is an unusual and obsolete construc-tion in discourse.
ARCHANGEL, an angel of the highest order.
Archangel, [ laminin , Lat.] a plant, called also Dead nettle.See Lamium .
Archangel, a cite of Russia , in the province of Dwina, onthe Dwina, about 300 miles N. of Moscow . Lon. 39. 0. E.Lat. (if. 54. N.
Archangel-Gorod, a government or province of Russia , inEurope, comprehending part of Lapland , and the ancient king"dom of Holmogard.
ARCIIAUD, in commerce, a kind of green fruit, pickled in-vinegar, much valued in the East Indies.
ARCHBISHOP. A bishop of the first class who superintendsthe conduct of other bishops his suffragans. Archbishops w<‘Venot known in the east till about the year 320; and though therewere some soon after this who had the title, yet that was only 3personal honour, bv which the bishops of considerable cities weredistinguished. It ’was not till after this that archbishops becamemetropolitans, and had suffragans under them. The ecclesiasticalgovernment of England is divided into two provinces, viz. Can-terbury and York. Canterbury hath the following suffraganbishoprics appertaining to it, St. Asaph , Bangor, Bath and V el