365 
c I R 
gf his coronation, and to dine at the upper- 
most table ill the great hall on his right hand ; 
;o be exempted from subsidies and other 
lids ; their heirs to be free from personal 
Wardship, notwithstanding any tenure ; to be 
impleaded in their own towns only, and not 
jto be liable to tolls, Sec. 
F Certioraris, to remove indictments taken 
in the cinque-ports, must be directed to the 
fill ay or and jurats before whom they were 
taken, and not to the lord warden ; because 
they hold plea of it as justices of the peace, 
by virtue of their commission, and not by 
their antient character. 
CIPHER, denotes certain secret charac- 
ters disguised and varied, used in writing 
letters that contain some secret, not to be 
understood but by those between whom the 
[cipher is agreed on. There are several kinds 
of ciphers, according to lord Bacon ; as the 
simple, those mixed with non-significants, 
those consisting of two kinds of characters, 
wheel-ciphers, key-ciphers, word-ciphers, 
Sec. They ought all to have these three 
properties, 1. They should be easy to write 
and read. 2. They should be trusty and un- 
decipherable. 3. Clear of suspicion. 
There is a new way of eluding the exami- 
nation of a cipher, viz. to have two alphabets,, 
the one of significant, and the other of non- 
significant letters ; and folding up two writ- 
ings together, the one containing the secret, 
while the other is such as the writer might 
probably send without danger: in case of a 
' strict examination, the bearer is to produce 
the non-significant alphabet for the true, and 
the true tor the non-significant ; by which 
I means the examiner woidd fall upon the out- 
| ward writing,, and finding it probable, suspect 
; nothing of the inner. No doubt the art of 
ciphering is capable of great improvement, 
li is said that king Charles 1. had a cipher 
consisting only of a straight line differently 
inclined: and there are ways of ciphering by 
the mere punctuation of a letter, whilst the 
words of a letter shall be non-significants, or 
sense that leaves no room for suspicion. 
Those who desire a fuller explanation of ci- 
phering may consult Bacon, where they will 
find a cipher of his invention; bishop M il- 
kin’s Secret and Swift Messenger ; and Mr. 
Falconer’s Cryptomenysis Patefacta. 
CIPPUS, in antiquity, a 1ow t column, with 
an inscription, erected in the high roads, or 
other places, to shew the way to travellers, to 
serve as a boundiy, to mark the grave of a 
deceased person, Sec. Those erected in the 
highways to mark the miles w r ere called mi- 
liary columns. 
CIRCT1A, enchanter's nightshade, a ge- 
nus of the monogynia order, in the diandria 
class of plants, and in the natural method 
ranking under the 48th order, aggregate. 
The corolla is dipetaious; the calyx dipliyl- 
lous, superior, with one bilocular seed. There 
are two species, one of which is a native of 
Britain, and the other of Germany. They 
are low herbaceous plants with white flowers, 
and possessed of no remarkable property. 
CIRCLE, in geometry, a plane figure 
comprehended by a single curve line, called 
its circumference ; in which right lines drawn 
from a point in the middle, called the centre, 
are equal to each other. 
The area of the circle is found by multiply- 
ing the circumference by the fourth part of 
the diameter ; or half the circumference by 
11 
C I R 
half the diameter: for every circle may be 
conceived to be a polygon of an infinite num- 
ber of sides, and the semidiameter must be 
equal to the perpendicular of such a polygon, 
and the circumference of the circle equal to 
the periphery of the polygon : therefore hall 
the circumference multiplied by ball the 
diameter, gives the area ot the circle. 
Circles, and similar iigures inscribed in 
them, are always as the squares of the dia- 
meters ; so that they are in a duplicate ratio 
of their diameters, and consequently of their 
radii. . . 
A circle is equal to a triangle, the base ot 
which is equal to the periphery, and its alti- 
tude to its radius circles therefore are in 
a ratio compounded of the peripheries and 
the radii. 
To find the proportion of the diameter ot a 
circle to its circumference. Find, by con- 
tinual bisection, the sides of the inscribed 
polygon, till vou, arrive at a side subtending 
any arch, howsoever small ; this found, find 
likewise the side of a similar circumscribed 
polygon; multiply each by the number of 
C 1 R 
:4 X (1 — 
1.3.5 
2A.G7fe 7 .& 
1 
2.3 " 2.4.5 
Sec). 
The quadrature of the circle, or the man- 
ner of making a square whose surface is per- 
fectly and geometrically equal to that of a 
circle, is a problem that has employed the 
geometricians of all ages. 
Many maintain it to be impossible ; Des 
Cartes, in particular, insists on it, that a right 
line and a circle being of different natures, 
there can be no strict proportion between 
them ; and in effect we are at a loss for the 
just proportion between the diameter and 
circumference of a circle. 
Archimedes is the person who has come 
nearest the truth : all the rest have made pa- 
ralogisms. Charles V. off ered a reward of one 
hundred thousand crowns to the person who 
should solve this celebrated problem. 
Dr. Wallis has given in his Arithmetic of 
Infinites, a series for expressing the ratio of a 
circle to the square of its diameter, as 
. 3X3X5X 5X7 X7 &c 
ie sides of the polygon, by which you will 
iave the perimeter ot each polygon. I lie 
atio: of the diameter to the periphery of the 
circle will be greater than that of the same 
diameter to the perimeter of the circumscrib- 
ed polygon, but less than that ot the inscribed 
polygon. The difference of the two being 
known, the ratio of the diameter to the peri- 
phery is easily had in numbers very nearly, 
though not justly, true. Thus Archimedes 
lixed the proportion at 7 to 22. 
Wolfius finds it as 10000000000000000 to 
31415926033897932; and the learned Mr. 
Machin has carried it to one hundred places, 
as follows; if the diameter of a circle be 1, 
the circumference will be 3.14159, 26535, 
89793, 23846,26433, 83279,50288, 41971, 
69399, 37510, 58209, 74944, 59230, 78164, 
05286, 20899, 86280, 34825, 34211, 70679, 
of the same parts. But the ratios generally 
used in practice are that of Archimedes, and 
the following ; as 106 to 333, as 113 to 3ao, 
as 1702 to 5347 as 1815 to 5702, or as 1 to 
A variety of series have been discovered for 
obtaining the length of the circumference of a 
circle, such as the following, viz. If the diameter 
be 1, the circumference c will be variously ex- 
pressed thus, 
1 r 1 1.1 1 
2X4X4X6X6X8 
9 25 49 
— X — X 
or as 1 
24 
56 
Sec. 
4XLI- T + 
7 9 
11 
i See), 
^ 13 15 ' 
— \/8 x (i *4~ 
. JL _ 
5 7*9 T 11 
_ — Sec), 
13 15 ‘ 
_1,J_ 1 , 1 
c — \/ 12 X (1 3.3 ”4” 5. 3 2 7.3 3 ' 9. 3* 
Sec), 
1 1 1_ J 1_ 
C ~ 8 X ^ 1 X 3 "^“ 1A5 3.5.7 '5.7.9, 7.9.11 
Sec), 
2 1 1 _ 1.3 _ 1.3,5 
c = 8 X 5 F7 4^9 4.6.8.11 
&c), 
( 3- ~ 
1.3 
5.2 4.7. 2 2 
1.3.5 
A&8.1L2 5 
4.6. 9. 2 3 
Sec), 
Circle of the- higher kind, an expression, 
used by Wolfius, and some others, to denote, 
for the most part, a curve expressed by the 
. m m — 1 m .... 
equation y zzz ax — x which in ■ 
deed will be an oval when in is an even num- 
ber; but when in is an odd number, the curve 
will have two infinite legs. 
Circles, druidical, in British topogra- 
phy, a name given to certain ancient inclo- 
sures, formed by rude stones, circularly ar- 
ranged. 
These, it is now generally agreed, tvere 
temples, and many writers think also places ot 
solemn assemblies for councils or elections, 
and seats of judgment.. These temples, 
though generally circular, occasionally differ 
as well in figure as magnitude : with relation 
to the first, the most simple were composed 
of one circle. Stonehenge consisted of two 
circles and two ovals, respectively concen- 
tric ; whilst that at Bottaich near St. Just in 
Cornwall is formed by four intersecting circles. 
The great temple at Abury in Wiltshire, 
it is said, described the figure of a seraph or 
fiery flying serpent, represented by circles 
and right hues. Some, besides circles, have 
avenues of stone- pillars. Most, it not all ot 
them, have pillars or altars within their pene- 
tralia or centre. In the article of magnitude 
and number of stones, there is the greatest 
variety ; some circles being only twelve feet 
diameter, and formed only of twelve stones ; 
whilst others, such as Stonehenge and Abury, 
contained, the first one hundred and forty, 
the second six hundred and fifty-two, and oc- 
cupied many, acres; of ground. All these 
different numbers, measures, and arrange- 
ments, had their pretended reference, either to 
the astronomical divisions of the year, or 
some mysteries of the druidical religion. 
CIKCONCELLIONES, a race of fanatics, 
so called because they were continually ram- 
bling round the houses in the country. They 
took their rise among the donatists in the 
reign of the emperor Constantine. It is in- 
credible what ravages and cruelties these va- 
gabonds committed in Africa through a long 
series of years. They were illiterate, savage 
peasants, who understood only the Punic 
