134 
A R C 
ARC 
A R C 
any suit in equity that might be brought 
against them in consequence of their award ; 
also one to enable them in case they cannot 
agree, to call in a third arbitrator, by mutual 
agreement, who is called an umpire. An 
action of debt may be brought tor money 
adjudged to be paid by arbitrators. 
ARBOR, in mechanics, the principal part 
of a machine which serves to sustain the rest: 
also the axis or spindle on which a machine 
turns, as the arbor of a crane, windmill, &c. 
ARBOR! BONZES, wandering priests of 
Japan, who subsist on alms. They dwell in 
caverns, and cover their heads with bonnets 
made of the bark of trees. 
ARBUTUS, the strawberry-tree, in bo- 
tany, a genus of plants with a one-leaved bell- 
fashioned flower, and a berry or fruit resemb- 
ling a large strawberry. See plate 
The strawberry-tree belongs to the decan- 
dria monogynia class of Linneus. The es- 
sential character is, calyx five parted ; corolla, 
ovate, diaphonous at the base ; capsule five 
celled. There are ten species of this beauti- 
ful shrub, all of them tolerably hardy, but 
they will not bear fruit, except when they 
are sheltered from the cold winds. The 
fruit is eatable. 
ARC, in geometry, any part of the cir- 
cumference of a circle, or curved line, lying 
from one point to another, by which the 
quantity of the whole circle or line, or some 
other thing sought after, may be gathered. 
Arch of a Circle , the length of an arch may 
be found by this rule : as 180° is to the number 
of degrees in the arc, so is 3.1416 times the ra- 
tlins to the length : for when radius is 1-half, 
the circumference is 3.14159, &c.,; therefore, 
3.14159 „ , , 
— — , &c. = .01745329, &c. = the length of 
an arch of 1 degree. Hence r X .01745, &c. 
= the length of 1° to the radius r; and there- 
fore r x 0.1745, Sec. X the number of degrees 
in any arc = the length of that arch. 
The length of circular archs may be found 
in the following manner : 
The radius of a circle being 1 ; and of any 
arc a, if the tangent be t, the sine s, the co-sine 
c, and the versed sine v : then the arc a will be 
truly expressed by several series, as follow, viz. 
the arc 
• = t - + - 1 / - y + v* &c - 
1.3 
7 • 
1.3.5 
& c. 
: H d 4- / _L ._m / &c- 
2.3 ‘ 2.4.5 ‘ S.4.6.7 
, , , 1 v. , 1.3 id , 
- \Z-V X f + 2 4^5 • + 
1.3.5 id 
‘ 2 s 
&c. 
180 
- d — .01745329 &c. X where 
d denotes the numher of degrees in the given 
8c — c . 
arc. Also, a — nearly ; where c is the 
3 1 
chord of the arc, and c the chord of half the 
arc ; whatever the radius is. 
To investigate the length of the arc of any curve. 
Put x — the absciss, y = the ordinate, of the 
arc x, of any curve whatever. Put z — 
y 2 ; then, by means of the equation of 
the curve, find the value of x in terms of y, or 
of y in terms of x, and substitute that value 
instead of it in the above expression % ~ 
V at -f-/; hence, taking the fluents, they will 
give the length of the arc z, in terms of x or y. 
See Fluxions. 
Akch of equilibration, is that which is ill equi- 
librium in all its parts, having no tendency to 
break in one part more than in another, and 
which is therefore safer and stronger than any 
other figure. Every particular figure of the cx- 
trados, or upper side of the wall above an arch, 
requires a peculiar curve for the under side of 
the arch itself, to form an arch of equilibra- 
tion, so that the incumbent pressure on every 
part may he proportional to the strength or re- 
sistance there. When the arch is equally thick 
throughout, a case that can hardly ever hap- 
pen, then the catenarian curve is the arch of 
equilibration ; but in no other case ; and there- 
fore it is a great mistake in some authors to 
suppose that this curve is the best figure for 
arches in all cases ; when in reality it is com- 
monly the worst. This subject is fully treated 
in Dr. Hutton’s Principles of Bridges, prob. 5, 
where the proper intrados is investigated for 
every extrados, so as to form an arch of equi- 
libration in all cases whatever. It there appears 
that, when the upper- side of the wall is a 
straight horizontal line, as in the figure (Plate 
IX. fig. 3.}, the equation of the curve is thus 
expressed, 
i . a -f- at -f- 2aX + 
log. of — 5 5 
J ~ /N 
, . a r -4- \/ 2ar T- rr 
log. of — L—JUA Z 
a 
where x — DP, y — PC, r — DQ, h — AQ, 
and a — DK. And hence, when a , h, r, are 
any given numbers, a table is formed for the 
corresponding values of x and y, by which the 
curve is constructed for any particular occasion, 
Thus, supposing a or DK = 6, h or AQ = 50, 
and r or DQ = 40 ; then the corresponding 
values of KI and IC, or horizontal and vertical 
lines, will be as in this table. 
Table for constructing the Curve of Equilibration. 
Value 
of KI. 
Value 
of IC. 
Value 
of KI. 
Value 
of IC. 
Value 
of KI. 
Value 
of IC. 
0 
6.000 
21 
10.381 
36 
21.774 
Q 
6.035 
22 
10.858 
37 
22.948 
4 
6.144 
23 
1 1.368 
38 
24.190 
6 
6.324 
24 
11.911 
39 
25.505 
8 
6.580 
25 
12.489 
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 
35.1 35 
16 
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 
Arcs, similar. If the arc ot one curve 
contains the same number of degrees as the 
arc of another ; or if the radius of one curve 
is to the radius of another, as the arc of one 
curve is to its corresponding one, then these 
two arcs are similar. 
Arcs, equal, those which contain the same 
number of degrees, and whose radii are equal. 
Arc, diurnal, that part of a circle described 
by a heavenly body, between its rising and 
setting; as the nocturnal arch is that described 
between its setting and rising ; both these 
together are always equal. 
Arc of progression or direction, an arch 
of the zodiac, which a planet seems to pass 
over, when its motion is according to the 
signs. 
Arc of retrogradation, an arch of the 
zodiac, described by a planet, while it is re- 
trograde, or moves contrary to the order of 
the signs. 
A RCA, in conchology, a genus of bivalves, j 
the animal of which is supposed to be a 
tethys : the valves are equal ; and the hinge 
beset with numerous sharp teeth, inserted 
between each other. T Jie species are di- j 
vided into two sections; the first has an 
entire margin, and in the other the marg n is 
crenulated. 
ARCADE, in architecture, is used to 1 
denote any opening in the wail of a building j 
forming an arch. 
ARCH, in architecture, a concave build- I 
ing, with a mold bent in form of a curve, | 
erected to support some structure. See I 
Architecture. 
ARCHBUTLER, one of the great officers j 
of the German empire, who presents the j 
cup to the emperor, on solemn occasions. ] 
This office belongs to the king of Bohemia. 
ARCHCHAMBERLAIN, an officer of 
the empire, much the some with the great j 
chamberlain in England. The elector of 
Brandenburgh was appointed, by the golden I 
bull, arehchamberlain of the empire. 
ARC II C HAN C ELLO R , an high officer, j 
who, in antient times, presided over the se- | 
•cretaries of the court. I 'nder the two first 1 
races of the kings of France, when their ter- ] 
ritories were divided into Germany, Italy, J 
and Arles, there were three archchancellors ; 1 
and hence the three archchancellors still sub- ] 
sisting in Germany, the archbishop of Alentz j 
being archchancellor of Germany, the arch- j 
bishop of Cologn of Italy, and the archbishop ] 
of Treves of Arles. 
ARCHDEACON, an ecclesiastical dig-| 
nitary or officer, next to a bishop, whose 1 
jurisdiction extends eit her over the whole J 
diocese, or only a part of it. We have sixty ] 
archdeacons in England. 
ARCHDUKE, a title given to dukes of 
greater authority and power than other dukes. I 
ARCHED legs, a fault in g horse, when! 
his knees are bent arch-wise. 
ARCHER, in the antient military art J 
one who fought with bows and arrows. 
The English archers were esteemed the 
best in Europe, to whose prowess and dex-j 
terity the many victories over the French ■ 
were in a great measure owing. 
ARCH ERY, the art of shooting with a bow ' 
and arrow. This art cither as an instrument] 
in war or an object of amusement, may be 
traced in the history of almost every country.] 
Our own was in its earliest periods highly ’ 
celebrated for its skill in archery ; and it ap-j 
pears that the English monarchs took great] 
pains to encourage the exercise of the long 
bow. Edward III. ordered a complaint to] 
be lodged against the sheriff of London, fori 
permitting other useless games to be pur- 
sued, when the leisure time of his people upon = 
holidays ought to be spent in the recreations 
of archery. In the reign of Ed. 1 V. an act was 
made that every Englishman should have a 
bow of his own height to be made of yew, I 
hazel, ash, &c. : and mounds of earth w ere! 
ordered to l>e made in even township, and | 
the inhabitants to practise archery, under! 
certain penalties. During the reigns of * 
Henry \ II. and VIII. archery was also en-1 
couragcd; in the third of Henry VIII. a I 
statute was made commanding every father! 
to provide a how and tw r o arrows for his son, j 
when he was seven years old. By the found- -i 
