444 
COT 
C O T 
C O T 
rs X rn x pf See — / _j_ /, 
and pa x pc x I>E &c — a ;/: .v , viz. a — x , 
c c 
cr X' — a , according as the point P is within 
or without the circle. 
For instance, if c ~ 5, divide the circumfer- 
ence into 10 equal parts, and the point P being 
within the circle, then will 
0A' -f- op’ = bp x cp X fp X hp x kp, 
and oa' — op’ — ap y cp x ep x op X ip. 
[n like manner, if c — 6, having divided the 
circumference into twelve equal parts, then will 
oa' -j- OP* = BP X DP X FP X UP X KP X MP, 
OA 6 —'op’ — AP X CP X EP X GP X IP X IP- 
The demonstration of this theorem may be 
seen in Dr. Pemberton’s Epist. de Cotesii Inven- 
tis. See also Dr. Smith’s Theoremata Logome- 
trica et Trigonometrica, added to Cotes’s 
Harm. Mens. pa. 114; De Moivre Miscel. Ana- 
lyt. pa. 17; and Waring’* Letter to Dr. Powell, 
pa. 39. 
By means of this theorem, the author was 
enabled to make a farther progress in the in- 
verse method of fluxions, than had been done 
before. But in the application of his discovery 
there still remained a limitation, which was re- 
moved by M. Demoivre. 
COTICE, or Coti.se, in heraldry, is the 
fourth part of the bend ; and with us seldom 
if ever borne but in couples, with a bend be- 
tween them. 
COT1NUS. See Rhus. 
COTTAGE, in law, a little house for 
habitation, without lands belonging to it, 
stat. 4 Edw. I. But by a later statute, 31 
Eliz. c. 7, no man may build a cottage un- 
less he lays four acres of land to it, except in 
cities or market-towns, or within a mile of 
the sea, or for the habitation of miners, sailors, 
foresters, shepherds, &c. ; excepting also 
cottages erected by justices of the peace for 
poor impotent persons. The above four 
acres of land must be freehold, and land of 
inheritance ; copyhold, or lease for years, 
are not sufficient tenure by the statute. 
COTTON, a soft downy substance found 
on the gossypium, or cotton-tree. See Gos- 
sypium. Cotton is separated from the seeds 
of the plant by a mill, ancl then spun and pre- 
pared for all sorts of line work, as stockings, 
waistcoats, quilts, &c. With it they likewise 
make callico and muslin ; and sometimes it is 
mixed with wool, sometimes with silk, and 
even with gold itself. The finest sort comes 
from Bengal and the coast of Coromandel. 
Cotton makes a very considerable article in 
commerce, and is distinguished into cotton- 
wool and cotton-thread. 4 'he first is brought 
mostly from the West India islands, and 
Smyrna; the most esteemed is white, long, 
and soft. Those who buy it in bales should 
see that it has not been wet, moisture being 
very prejudicial to it. 
Of cotton-thread, that of Darnas, called 
c.otton-d’ounce, and that of Jerusalem, called 
bazas, have been the most esteemed ; as also 
that of the West Indian islands. But with the 
help of the machines now in general use in 
Britain, we are able to spin it of almost any 
degree of fineness. Cotton of Siam is a kind 
of silky cotton in the Antilles, so called be- 
cause the grain was brought from Siam. It is 
of an extraordinary fineness, even surpassing 
silk in softness. They make hose of it there, 
preferable to silk for their lustre and beauty. 
They sell at from 10 to 12 and 15 crowns a 
pair, but there are very few made unless for 
curiosity. 
The manner of packing cotton as practised 
in the Antilles is thus : The bags are made of 
coarse cloth, of which they take three ells and 
a half each ; the breadth is one ell and three 
inches. When the bag has been well soaked 
m water, they hang it up, extending the mouth 
of it to cross pieces of timber nailed to posts, 
li,xed in the ground seven or eight feet high. 
He who packs it goes into the bag, which is 
six feet nine inches deep, or thereabout, and 
presses down the cotton, which another throws 
in, with hands and feet ; observing to tread it 
equally every where, and putting in but little 
at a time. The best time of packing is in 
rainy moist weather, provided the cotton is 
under cover. The bag should contain from 
300 to 320 pounds. The tare abated in the 
Antilles is three in the hundred. 
Cotton -spinning, the art or process of 
reducing cotton-wool into yarn or thread. 
The most simple method for this purpose, 
and the only one in use for a long time in this 
country, was by the hand, upon the well- 
known domestic machine called a one-thread 
wheel. But as the demand for cotton goods 
began to increase, other, inventions were 
thought of for expediting this part of the ma- 
nufacture. About 60 years ago, one Paul and 
others of London contrived an engine for a 
more easy and expeditious method of spin- 
ning cotton, and for which they obtained a 
patent; but the undertaking did not prove 
successful. Some years after, various ma- 
chines were constructed by different persons 
for facilitating the spinning of cotton, but 
without producing any very material or last- 
ing advantage. At length, about the year 
1767, Mr. James Hargrave, a weaver in the 
neighbourhood of Blackburn in Lancashire, 
constructed a machine by which a great num- 
ber of threads (from 20 "to 80) might be spun 
at once, and for which he obtained his ma- 
jesty’s letters-patent. This machine is called 
a jenny, and is the best contrivance for spin- 
ning woof or shoot that has hitherto appear- 
ed. It is now commonly constructed for 84» 
threads; and with it one person can spin 100 
English hanks in the ddy, each hank contain- 
ing 840 yards. 
Carding of Cotton, as a preparation for 
spinning, used formerly to be performed by 
the hand, with a single pair of cards, upon the 
knee; but this being a tedious method, ill 
suited to the rapid operations of the new spin- 
ning-machines, other methods were contrived 
for affording a quicker and more adequate 
supply. The first improvement for this pur- 
pose was likewise made by Mr. , Hargrave ; 
and consisted in applying two or three cards 
to the same board, and fixing them to a stool 
or stock ; whence they obtained the name of 
stock-cards. With these, one woman could 
perform two or three times as much work as 
she could do before in the common way. A 
still more expeditious method of. carding, 
however, by what are commonly called cy- 
linder-cards, was soon afterwards invented, 
and is that which is now most commonly 
practised : but as several persons lay claim to 
this invention, it is not easy to determine to 
whom in particular the merit of it is due. 
The next and most capital improvements 
which this branch of manufacture received 
were from Mr. Arkwright, a native of Lanca- 
shire, afterwards sir Richard Arkwright of 
Cromford in Derbyshire. He first brought 
forward his new method of spinning cotton in 
1768, for which he obtained a patent in 1 769 : 
he afterwards, in 1775, -obtained a patent for 
engines which he had constructed to prepare 
She materials for spinning; though one of 
these patents, being challenged at law, was 
set aside some years before ft expired. The 
result of Mr. Arkwright’s different inventions, 
and improvements, is a combination of ma- 
chinery, by which cotton is carded, roved, 
and spun, with the utmost exactness and 
equality ; and such a degree of perfection at- 
tained in spinning warp, as is not to be equal- 
led in any other part of the world. To these 
improvements this country is entirely indebt- 
ed for the great extent of its cotton-manufac- 
tures; large buildings having been erected for 
that branch both in England and Scotland), 
many of which contain several thousands of 
spindles, each driven by . one or more larger 
water-wheels; and some of such extent as to 
spin at the rate oftme thousand yards of twist 
or warp-yarn in a minute. 
Other machines have been invented at dif- 
ferent times, and a variety of improvements 
made by different mechanics and manufac- 
turers ; one of which in particular we must 
not omit to mention. It is called a mule, 
being a kind of mixtureof machinery between 
the warp-machine of Mr. . Arkwright and the 
woof-machine or hand-jenny of Mr. Har- 
grave ; and was also invented in Lancashire. 
This machine- promises to be of great use in 
spinning cotton-yarn for muslins to a degree 
of fineness never before known in this coun- 
try, being nearly equal in quality to those 
usually brought from India. 
COTTUS, or Bull-head, in ichthyology, a 
genus belonging to the -order of thoracici. 
The head is broader than the body, and the 
gill-membrane has six rays. There are six 
species, of which the most remarkable are : - 
l.The gobio, or river-bullhead, very com- 
mon in all our clear brooks ; it lies almost al- 
ways at the bottom, either on the gravel or 
under a stone; it deposits its spawn in a hole 
which it forms among the gravel, and quits it 
with great reluctance. It feeds on water-in- 
sects. This fish seldom exceeds the length of. 
three inches and a half : the head is large, 
broad, fiat, and thin at its circumference, be- 
ing well adapted for insinuating itself under 
stones ; on the middle part of the covers of 
the gills is a small crooked spine turning in- 
wards. The eyes are very small, the h ides 
yellow; the body grows slender towards the 
tail, and is very smooth. The colour of this 
fish is as disagreeable as its form, being dusky 
mixed with a dirty yellow ; the belly is whitish. 
The taste, however, is excellent. *2. The ca- 
taphractus (See Plate N. H. fig. 147) is very 
common on most of the British coasts. It 
seldom exceeds five inches and a half in 
length, and even seldom arrives at that size. 
I he head is large, bony, and very rugged : 
the end of the nose is armed with four short 
upright spines ; on the throat are a number of 
short white beards; the body is octagonal, 
and covered with a number of strong bony 
crusts divided into several compartments, 
the ends ot which project into a sharp point, 
and form several echinated lines along the 
back and sides from the head to the tail. 
3. Thescorpius, or father-lasher, is not un- 
common on the rocky coasts of this island ; it 
lurks under stones, and will take a bait. It 
seldom exceeds 8 or 9 inches in length. The 
head is large, and has a most formidable ap- 
pearance, being armed with vast spines, 
which it can oppose to any enemy that at- 
tacks it, by swelling; out its cheeks and gill- 
