465 
CUB 
Ojbe, duplication of, is the finding" the side of 
3 cube that shall double in solidity a given 
cube, which is a celebrated problem, much dis- 
cussed by ancient geometricians. It was first 
proposed by the oracle of Apollo at Delphos, 
which declared that the plague, then raging at 
Athens, should cease when Apollo’s altar, a 
cube, was doubled. Upon this the mathemati- 
cians applied themselves seriously to seek the 
duplicature of the cube ; hence it is called the 
Delian problem. It cannot, however, be effected 
geometrically, as it requires the solution of a 
cubic equation, or requires the finding of two 
mean proportionals, viz. between the side of the 
given cube and the double of the same, the first 
of which two mean proportions is the side of 
the double cube, as was first observed by Hip- 
pocrates of Chios. For, let a be the side of the 
given cube, and z the side of the double cube 
nought ; then it is 2 5 = 2a 5 , or a 1 * z 1 * * z ; 2a ; 
so that, if a and z be the first and 2d terms of a 
-set of continued proportionals, then a 1 * z 2 is 
the ratio of the square of the first to the square 
of the 2d, which, it is known, is the same as 
the ratio of the first term to the 3d, or of the 2d 
to the 4th, that is, of z to 2a; therefore z being 
the 2d term, 2a will be the 4th. So that z, the 
side of the cube sought, is the 2d of four terms 
in continued proportion, the first and 4th being 
a and 2a, that is, the side of the double cube is 
the first of two mean proportionals between a 
and 2a. The thing has been frequently done 
mechanically by- Archimedes, Eutochius, Pap- 
pus, Sac. 
Cube, or Cubic number, in arithmetic, that 
which is produced by the multiplication of a 
square number by its root : thus, 64 is a cube 
number, and arises by multiplying 16, the square 
of 4, by the root 4. 
• Cube, or Cubic quantity, in algebra, the third 
power in a series of geometrical proportionals 
continued ; as a is the root, aa the square, and 
aaa the cube. All cubic numbers may be ranged 
into the form of cubes ; as 8 or 27, whose sides 
are 2 and 3, and their bases 4 and 9 ; whence it 
appears, that every true cubic number, produced 
from a binomial root, consists of these parts, viz. 
The cubes of the greater and lesser parts of the 
root, and of three times the square of the greater 
part multiplied by the lesser, and of three times 
the square of the lesser multiplied by the great- 
er, as, 
aa -{- 2ab bb 
a -}- b 
aaa -j- 2 aab abb 
aab -j- c 2abb -j- bbb 
aaa — |- 3 aab — 3 abb -f- bbb 
Trom hence it is easy to understand both the 
composition of any cubic number, and the rea- 
son of the method for extracting the cube root 
out of any number given. See the following 
article. 
Cube root of any number, or quantity , such a 
number, or quantity, which, if multiplied into 
itself, and then, again, the product thence aris- 
ing, by that number or quantity, being the cube 
root, this last product shall be equal to the num- 
ber or quantity whereof it is the cube root : as 
2 is the cube root of 8, because two times 2 are 4, 
and two times 4 are 8 ; and a -f- b is the cube 
root of a 1 -f- 3a 2 b -f- 3 ab 1 -}- b \ 
Every cube number has three roots, one real 
root, and two imaginary ones ; as the cube num- 
ber 8 has one real root 2, and two imaginary 
roots, viz. if — 3 — 1, and — 3 -f- 1 ; and 
enerally if be the real root of any cube num- 
er, one of the imaginary roots of that number 
a * 4 - a / — 
will be — — , and the other 
a if -WZ' Algebra. 
2 
VOL. I. 
cue 
CUBEBS, cubeba of the shops, in the 
materia medica, a small dried fruit, resem- 
bling a grain of pepper, but often somewhat 
longer, brought into Europe from the island 
of Java. See Materia Medica. 
CUBIC, or Cubical, Equation, in al- 
gebra, one whose highest power consists of 
three dimensions, as a 3 — a' — b\ or a 3 -j- rxx 
= />*, &c. 
CUBIT, in the mensuration of the antients, 
a long measure, equal to the length of a man’s 
arm, from the elbow to the tip of the lingers. 
Dr. Arbuthnot makes the English cubit equal 
to IS inches ; the Roman cubit equal to one 
foot, 5,406 inches ; and the cubit of the scrip- 
ture equal to one foot, 9,8S8 inches. 
CUBErVEUS. See Anatomy. 
CUBITUS, in anatomy, a hone of the 
arm, reaching from the elbow to the wrist, 
otherwise called the ulna. 
CUCKING-stool, antiently called tum- 
brel, an engine invented for the punishment 
of scolds and unquiet women, by ducking 
them. This instrument was a sort of chair, 
placed at the end of a plank, in which the of- 
fender was placed, and so clucked : it was 
formerly made u e of to punish bakers and 
brewers, upon transgressing the laws made 
in relation to their several trades; for upon 
offending in this respect, they were ducked, 
or plunged in some stinking muddy pond, 
by means of this chair. 
CUCUBALUS, berry-hearing chickweed, 
a genus of the trigynia order in the decandria 
class of plants, and in the natural method 
ranking, under the 22d order, caryophvlei. 
The calyx is- inflated, the petals 5, unguiculat- 
ed without ; a nectariferous corona at the 
throat ; the capsule is trilocular. There are 
17 species; the most remarkable of which 
are, 
1. The behen, Swedish lychnis, orgumse- 
pungar, a native of several parts of Europe. 
The empalement of its flower is curiously 
wrought like a network, and is of a purplish 
colour. The leaves have Somewhat of the 
flavour of peas, and proved of great use to 
the inhabitants of Minorca in 1685, when a 
swarm of locusts had destroyed the harvest. 
The Gothlanders apply the leaves to erysi- 
pelatous eruptions. Horses, cows, sheep, 
and goats, eat this plant. 
2. The catholicus, or night-flowering lych- 
nis, grows naturally in Spain and Italy. It 
is a perennial plant, rising with an upright 
branching stalk, a foot and a half high, w ith 
very narrow leaves placed opposite. The 
flowers stand upon long naked footstalks, 
each supporting three or four flowers which 
have long tubes wiflf striped empalements : 
the petals are large, deeply divided at top, 
and of a pale-blueish colour. The flowers 
are closed all the day ; but whyu the sun 
leaves them, they expand, and then emit a 
very agreeable scent. It may be propagated 
by seeds sow n in the spring on a bed of light 
earth, and will flower the following year. 
3. The otites, or catch-fly, is a native of 
Britain and other European countries, ft 
has a thick, fleshy, perennial root, which 
strikes into the ground, whence rises a joint- 
ed stalk three or four feet high. At the 
joints there exudes a viscous clammy juice, 
that sticks to the lingers when handled; and 
the small insects which settle upon those 
parts of the stalks are so fastened that they 
3 N ‘ 
c u c 
j cannot get off. The flowers are small, and 
of a greenish colour. 
CUCUJUS, a genus of insects of the c»- 
leoptera order: antennae filiform ; feelers four, 
equal, the last joint truncate and thicker; lip 
short, bilid; the divisions linear and distant; 
body depressed. There are 1 1 species be- 
longing to this genus. 
CUCULLANUS, a genus of worms of the 
order intestina: body sharp, pointed behind 
and obtuse before ; moutlf orbicular, with a 
striated hood. They are most of them vivi- 
parous. There are eight species, which take 
their names from the animal in which they 
are found. Thus, the cucullanus talprc in- 
habits the common mole, is gregarious, in- 
closed in a membrane, spirally twisted, white, 
and found in the fat about the peritoneum. 
CUCULLARIS, see Anatomy. 
CUCULUS, the cuckow, in ornithology, 
a genus belonging to the order of pics; the 
essential characters of which are : the bill is 
smooth, and more or less bending ; the nos- 
trils are bounded by a small rim ; the tongue 
is short and pointed ; the feet and toes form- 
for climbing'. See PI. N. H. fig. 153. There 
are 46 species. The most remarkable are.: 
I. The canorus, or common cuckow, weighs 
about live ounces, and is in length 14 inches, 
in breadth 25. The bill isblack, and about two- 
thirds of an inch in length. T he head, hind 
part of the neck, coverts of the wings and 
rump, are of a dove-colour, darker on the 
head and paler on the rump. The legs are 
short, and the toes disposed two backwards 
and two forwards, like those of the wood- 
pecker, though it is never observed to run 
up the sides of trees. The female differs in 
some respects. 
This bird appears in our country early in 
the spring, and makes the shortest stay with 
us of any bird of passage. It is "directed hither 
by that constitution of the air which causes 
the fig-tree to put forth its fruit ; though it 
has been supposed that some of these birds 
do not quit this island during the winter, but 
that they seek shelter in hollow trees, and lie 
torpid, unless animated by unusually warm 
weather. Mr. Pennant gives tw r o instances 
of their being heard in February; one in 
1771, in the end of that month; the other in 
1769, on the fourth day; but after that they 
were heard no more, being probably chilled 
into torpidity. There is a remarkable coin- 
cidence between the song of these birds, and 
the mackarels continuing in full roe; that is, 
from about the middle of April to the latter 
part of June. The cuckow is silent tor some 
time after his arrival. His note is so uniform, 
that his name in all languages seems to have 
been derived from it ; and in all countries 
it is used in the same reproachful sense. 
On the natural history of this singular bird, 
we have a very curious paper by Dr. Jenue.r, 
published in the Philosophical 'Transaction 
for 1788, part II. art. 14. The first appear- 
ance of cuckow's in the county of Gloucester 
is about the middle of April. The song of 
the male, which is well known, soon pro- 
claims its arrival. The song of the female 
(if the peculiar notes of which it is composed 
may be so called) is widely different, and j^s 
been so little attended to', that perhaps few 
are acquainted with it; the cry of the dub- 
chick hears some resemblance to it. 
Unlike the generality of birds, cuckows 
do not pair. When a female appears gn 
