(hehistory of tlic Itoyal Academy dfSclcnre*, 
fij'fs a specimen <4 it concerning arithme- 
tical progre-.sionals ; where he skews that, 
because in binary arithmetic, only two cha- 
racters are user], therefore the laws' of pro- 
gression may be more easily discovered by it 
than by common arithmetic. 
All the characters used in binary arith- 
metic, are 0 and 1 ; and the cypher multi- 
plies every tiling by 2, as in the common 
arithmetic by 10. Thus 1 is one ; 10, two, 
il, three; 100, four; 101, five; 110, six; 
111, seven ; _ ! 000, eight ; 1001, nine ; 1 () 1 0, 
ten ; which is built on the same principles 
with common arithmetic. 
1 lie author, however, does not recom- 
mend this method for common use, because 
ot the great number of figures required to 
express a number ; and adds, that' if the com- 
mon progression were from 12 to 12, or 
from 16 lo lb, it would be still more expe- 
ditious. 
Binary arithmetic appears to have been 
the same with that used among the Chinese 
4000 years ago, and left in enigma by Fohi, 
the founder ot their empire and sciences. 
Binary measure, in music, is a measure 
which is beaten equally, or where the time 
of rising is equal to that of falling. This is 
usually called common time, beside which 
there is a binary triple. 
BIND of eels, a quantity consisting of two 
hundred and fifty ; or ten' strikes, each con- 
taining twenty five eels. 
Bind-weed. See Convolvulus. 
BING, in the alum-works, denotes a heap 
of alum throw n together in order to drain. 
BINOMIAL, in algebra, a root consisting of 
two members connected by the sign -j- or — . 
ft bus a -f- b and 8 — 3 are binomials, consisting ( 
ot the sum and difference of these quantities, j 
The powers of any binomial are found by a ’ 
continual multiplication of it by itself. For j 
example, the cube or third power of a -}~k will I 
be found by multiplication to be a 3 -{- ?>a 2 [> -}- ! 
Sab 1 -j- P ; and if the powers of a — 6 are re- ! 
quired, they will be found the same as the pre- j 
ceding, only the terms in which the exponent 
of b is an odd numb dr will be found negative, 
t hus, the cube of a — b will he found to be i 
« -f- Sa 2 b -j- Sab 1 — b ' ; where the second and \ 
fourth terms are negative, the exponent of b j 
being an odd number of these terms. In general, j 
the terms of any power of a — b are positive 
and negative by turns. See Algebra. 
BINOCULAR telescope, a kind of di- j 
(jptric telescope fitted with two tubes joined 
in such a manner, that one may see a distant 
object with both eyes at the same time. 
BIPED, an animal furnished with onlv 
two legs. Men and birds are bipeds. Apes j 
occasionally walk on their hind legs, and seem j 
to be of this tribe ; but their more natural po- | 
sition is on all four. 
I he term is used for a genus of reptiles ! 
that belong to the lizard family. These have S 
a very long body covered with scales, and the | 
'tocsot the two little feet are armed with nails, j 
BIPENNIS, in Roman antiquity, an ax' 
with a double edge, one of which was used in 
Stabbing, and the other in cutting. 
BIQUADRATIC power, in algebra, the \ 
fourth power, or squared square, of a num- 
ber: as 16 is the biquadratic power of 2; for 
2 X 2 is 4, and 4 x 4 is equal to 1 6. 
Biquadratic root of a number, is the 
square root . of its square root: thus the bi- 
quadratic root ot 81 is 3; for the square root 
B 1 li 
of 81 is <}, ami the square root of 0 is 3. See 
Algebra. 
Biquadratic equation, an equation where 
toe unknown quantity of one of the terms has 
four dimensions. 
Any biquadratic equation may be conceived 
as generated by the multiplication of four simple 
equations. Thus, if ,r — a, x — b, x — c , x ~J, 
or x — a — O, a- — b — O, .v _ , 0 ’ v _ d 
— 0 ; then v/ili x — a x x — b x x — - c X 
x — d : o beget a biquadratic equation. Or it 
ma y be forme d of two quad ratic equations, as 
a -j- bx -j- c x -V* -j- dx -j- e — 0 ; or, lastly, it 
may be produced from the multiplication of 
one c ubic and one simple equation, as 
x — a X -V s -j- e x 2 -j- d x — j- £ — O. 
Bi RCII-tree. See Betula. 
BIRD, avis, in zoology, one of the six 
general classes of animals, the characters 
of whicn a i e, that their body is covered 
with feathers, and that tney nave two wings, 
two legs, and a Dili of a firm bony, or rather 
horny substance : add to this, that the fe- 
males are all oviparous. 
1 he knowledge oi birds, of the orders and 
genera into which they are subdivided, and 
ot their nature, uses, figures, &c. constitutes 
a particular science, under the name of or- 
nithology ; in which there are six orders, viz. 
accipkres, pica:, anseres, grallai, galling, and 
passeres. 
Birds, in heraldry, according to their se- 
veral kinds, represent either the contempla- 
tive or active life. They are the emblems 
of liberty, expedition, readiness, swiftness, 
and fear. Birds that are either whole-footed, 
or have their feet divided and yet have no 
talons, are said to be membered ; but the 
cock, and all birds of prey with sharp and 
hooked beaks and talons, for encounter or 
defence, are termed armed. In the blazon- 
ing of birds, if their wings are not displayed, 
they are said to he borne close ; as, he bear- 
eth kn eagle, &c. close. 
BIRD-CATCHING, is the art of taking 
birds or wild-fowl, either for food, or for the 
pleasure ot their songs in cages, or for pre- 
venting the destruction which some species 
ot them occasion to the husbandmen. Sonic 
recur to it as an amusing pastime, and others 
practice it as a profitable employment. There 
are various methods of catching birds: one of 
the most systematic and ingenious is prac- 
tised in the neighbourhood "of London, by 
persons who find a ready market for birds 
ot any kind, which at certain seasons of the 
year change their situation, and hence are 
called birds of flight. The birds usually 
taken on such occasions, are wood-larks, tit- 
larks, linnets, goldfinches, greenfinches, 
&c. which are taken during what is called 
their flight, or while they congregate for the 
purpose of propagating their species. The 
nets used by bird-catchers are about twelve 
yards long, and two and a half wide ; which 
are spread on the ground parallel to one an- 
other, and at such a distance,- that when 
turned over, they shall coincide. The re- 
maining apparatus consists of lines so fasten- 
ed to the nets, that the bird-catcher is able 
by a sudden pull to draw the net over the 
birds that may have alighted in the space 
between the parallel sides. These birds are 
enticed to alight by others usually denomi- 
nated call-birds, of which there are generally 
five or six linnets, two goldfinches, two green- 
finches, one wood-lark, one red-poll, a yel- 
BIR 
low-hammer, a fit-lark, an aberdevine,' end 
perhaps a bullfinch. Resides these, they 
have others which are cAk-d liur- birds: but 
the call-birds are particularly trained for the 
seniee ; and when the nets are laid, these 
are properly arranged, and they appear to 
possess a most malicious desire of ‘bringing 
the wild ones into the same state of captivity 
with themselves. When they perceive the 
approach of the wild birds, the intelligence 
is announced from cage to cage with tire 
utmost extacy. The note by which they in- 
vite them down, has so powerful an ascend- 
g'-v } ovei tile wild birds, that the moment 
tney hear it, they alight on a spot within 
twenty yards of the bird-catchers. If only 
half the flock is caught by the first pull 
of the string, the others that escape will 
soon return to the net, and share the 
fate of their companions ; such is tiie fasci- 
nating power that the call-birds possess over 
those that are wild. 
Birds^re caught in traps of various kinds ; 
and frequently by nooses of hair. In this 
way, great numbers of wheatears are annually 
taken on the various downs of England. 
Small holes are dug by the shepherds m the 
ground, in each of which is placed a noose. 
W henever a cloud obscures the sun, these 
timid birds seek for shelter under a slone, or 
creep into any holes that present themselves ; 
ami they are thus ensnared by the nooses 
which fasten around their necks. Wood- 
cch ks and snipes are taken likewise by nooses 
of horse-hair placed along their paths, in 
marshes and moist grounds. Wild ducks 
in all their varieties are taken in vast num- 
Ixtr every winter on our coasts by means 
of decoys. (See Decoy.) Grouse and 
partridges are taken by means of nets: 
either at night when resting on the ground, 
by observing where they alight, and when 
setted, drawing a net over that part of the 
fit ;d , or, in the day, a very- steady dog is 
used to point at them. The attention of the 
birds being thus fixed, tw’o persons, drawing 
tin tw o extremities oi a large nef, pass il ov<-r 
them, and thus secure a whole pack of 
grouse, or covey of partridges, at once. Phea- 
sants are sometimes taken by night, by 
holding flaming sulphur under the trees on 
w inch they are observed to perch, the suf- 
focating effluvia of which make them fall 
senseless. 
In various parts of the world, peculiar 
inodes are adopted for ensnaring anti taking 
biuls , some of which, whilst they are 
hazardous to those who practise them, excite 
no inconsiderable degree of surprise, and 
even of anxiety, in the spectators. Thus, 
in the Orkney islands, where the birds that 
inhabit the rocks, and the eggs which they 
deposit among the cliffs, supply the principal 
food of many among the poorer inhabitants, 
the intrepid and adventurous fowlers climb 
rocky precipices more than {fifty fathoms 
above the sea, and pass from one shelf or 
ledge, to another, whose breadth is barely 
sufficient for resting-places to the birds 
which deposit their eggs upon them. In 
this hazardous employment, the adventurers 
are commonly lowered from above by means 
oi a rope,. formed often of brittle materials, 
and held by a single assistant. Fastened to 
this lope, the intrepid peasant descends, and 
seat dies all the cavities for eggs; springum 
lrom one projecting ledge to another, by 
