CYC 
ACER is quadruple of the diameter E P. 
4. If E R be parallel to the base A B, and 
CR parallel to the axis of the cycloid EF ; 
the space EC R, bounded by the arc of the 
'cycloid EC, and the lines ER and RC, 
shall be equal to the circle area E G K : 
hence it follows, if A T, perpendicular to 
the base A B, meet E R in T, the space 
E T A C E will be equal to the semi-circle 
E G F : and since A F is equal to tlie semi- 
circumference EGF, the rectangle EFAT, 
being the rectangle of the diameter and se- 
mi-circumference, will be equal to four 
times the semi-circle EGF; and therefore 
the area E C A F E will be equal to three 
times the area of the generating semi-circle 
EGF. Again, if you draw the line EA, 
the area intercepted betwixt the cycloid 
EC A, and the straight line EA will be 
equal to tlie semi-circle EGF ; for the area 
ECAFE is equal to three times EGF, 
and the triangle EAF = AF XjEF, the 
rectangle of the semi-circle and radius, and 
consequently equal to 2 E G P ; therefore 
their difference, the area ECAE, is equal 
to EGF. 5. Take E6 = OK, drawfiZ 
parallel to the base, meeting the generating 
circle in X, and the cycloid in Z, and join 
C Z, F X ; then shall the area C Z E C be 
equal to the sum of the triangles G FK and 
6 F X. Hence an infinite number of seg- 
ments of the cycloid may be assigned, that 
are perfectly quadrable. 
. For example, if the ordinate C K be sup- 
posed to cut the axis in the middle of the 
radius O E, then K and b coincide ; and the 
area ECK becomes in that case equal to 
the triangle GKF, and EftZ becomes 
equal to F 6 X, and these triangles them- 
selves become equal. 
This is the curve on which the doctrine 
of pendulums and time-measuring instru- 
ments in a great measure depend; Mr. 
Huygens having demonstrated, that from 
whatever point or height a heavy body os- 
cillating on a fixed centre begins to descend, 
while it continues to move in a cycloid, the 
time of its falls or oscillations will be equal 
to each other. It is likewise demonstra- 
ble, that it is the curve of quickest descent, 
i. e. a body falling in it, from any given 
point above, to another not exactly under 
it, will come to this point in a less time 
than in any other curve passing through 
those two points. 
CYCLOPjEDIA, or Encyclopaedia, 
denotes the circle or compass of arts and 
sciences. 
CYCLOPTERUS, the sucker, in natural 
CYD 
history, a genus of fishes of the order Card- 
laginei. Generic character : head obtuse ; 
tongue short and thick; teeth in the jaws; 
body short, thick, and without scales ; ven- 
tral fins united into an oval concavity, form- 
ing an instrument of adhesion. There are 
ten species, of which the principal is C. lum- 
pus, the lump-sucker. The shape of this 
fish is very similar to that of the bream, 
and it sometimes grows to the weight of 
seven pounds. Beneath tlie pectoral fins 
it possesses an oval aperture, surrounded 
with a soft muscular substance, edged with 
small thready appendages, which act as so 
many claspers. By this apparatus the 
sucker is enabled to adhere with extreme 
tenacity to any substance, and in several 
cases it has been found impossible to make 
it quit its hold but by the application of a 
force which has lacerated and destroyed it. 
M. Pennant mentions, that one of these 
fishes, soon after being caught, was flung 
mto a pail of water containing several gal- 
lons, and attached itself in a few moments 
so strongly to the bottom of the vessel that, 
on taking the fish by the tail, the whole ves- 
sel was lifted together with its contents, 
and the fish appeared to shew no disposi- 
tion to quit its hold. These fishes are eaten 
commonly in Greenland, where their oily 
quality renders them particularly pleasing. 
In England they are thought tasteless and 
flabby. In Scotland, near Caithness, suck- 
ers are found in immense shoals. They are 
pursued on that coast with the most de- 
structive havock, by the seals which there 
also abound. During the season in which 
tliese ravages are committed, the spot un- 
der which they take place is distinguish- 
able by the smooth and oily surface of the 
water for a considerable extent. The skins 
of the suckers, which are rejected by the 
seals, are also found in vast abundance on 
the shores. For a variety of this species, 
called C. pavonius, or the Pavonian sucker, 
see Pisces, Plate III. fig. 3. 
CYDER, a well-known liquor, serving in 
many parts of England as a common bever- 
age, though not considered to be so whole- 
some as well-made beer, especially to per- 
sons troubled with gravel, or chronic com- 
plaints of any kind. Cyder is made from 
apples, which should be mellow ripe, and 
gathered when perfectly dry. It was for- 
merly held as a general opinion, that “ the 
worse the fruit the better for cyder ;” but 
such an absurd opinion was in time, though 
slowly, refuted. The best pippins make 
the best flavoured and the wholesomest 
