CAT 
CAT 
of thick rope for a handle, and liaving three 
knots on each cord, with which the men 
who transgress the orders of their superiors 
are punislied. 
C\T’s-paw, a light breeze of wind per- 
ceived at a distance in a calm, by the im- 
pression made on the suidace of the sea, 
wiiich it sweeps very lightly, and then de- 
cays. The same term is given to a parti- 
cular turn made in the bight of a rope, in 
order to hook a tackle on it. 
CxT-harpings, in a ship, small ropes run- 
ning in little blocks from one side of the 
shrowds to the other, near the deck. Their 
use is to force the shrowds and make them 
taught, for the more security and safety of 
the masts. 
CAT-heads, two strong beams of timber 
projected almost horizontally over the ships- 
bows, on each side of the bowsprit. The 
cat-head serves to suspend the anchor clear 
of the bow, when it is necessary to let it 
go ; it is supported by a sort of knee, which 
is generally ornamented by sculpture. 
CAT AC AU STIC curves, in the higher 
geometry, that species of caustic curves 
which are formed by reflection. 
These curves are generated after the fol- 
lowing manner. If there be an infinite 
number of rays, as A B, A C, A D, &c. 
(plate Miscellanies, fig. 6.) proceeding from 
the radiating point A, and reflected at any 
given curve B D H, so that the angles of 
incidence be still equal to those of reflec- 
tion ; then the curve BEG, to which the 
reflected rays B I, CE, DF, £ec. are tan- 
gents continually, as in the points I, E, F, 
is called the catacaustic curve. 
If the reflected I B be produced to K, 
so that A B = B K, and the curve K L be 
the evolute of the catacaustic BEG, be- 
ginning at the point K ; then the portion 
of the catacaustic BE = AC — AB x 
CE — B I continually. Or if any two in- 
cident rays, as A B, A C be taken, that por- 
tion of the caustic that is evolved while the 
ray A B approaches to a coincidence with 
A C, is equal to the dilference of those in- 
cident rays X the dilference of the reflected 
rays. When the given curve is a geome- 
trical one, the catacaustic will be so too, 
and always rectifiable. The catacaustic of 
a circle is a cycloid, formed by the revo- 
lution of a circle along a circle. Thus, 
A B D, fig. 7, being a semicircle exposed to 
parallel rays ; then those rays which tall 
hear the axis C B will be reflected to F, 
the middle point of B C ; aud those which 
full at A, as they touch the curve only, will 
not be reflected at all ; but any interme- 
diate ray H I will be reflected to a point 
somewhere between A and F. And since 
every different iiicident ray will have a dif- 
ferent focal point, therefore those various 
focal points will form a curve line A E F 
in one quadrant, and F G D in the other, 
being the cycloid above-mentioned. And 
this figure may be beautifully exhibited ex- 
perimentally by exposing the inside of a 
smooth bowl, or glass, to the sun beams, or 
strong candle light; for then this curve 
A E F G D will appear plainly delineated 
on any w'iiite surface placed horizontally 
within the same, or on the surface of milk 
contained in the bowl. The caustic of the 
common semi-cycloid ; when the rays are 
parallel to the axis is also a common cycloid, 
described by the revolution of a circle upon 
the same base. The caustic of the loga- 
rithmic spiral is the same curve, only set in 
a different position. 
CATACHKESIS, in rhetoric, a trope 
which boiTOWs the name of one thing to ex- 
press another. Thus Milton, describing 
Raphael's descent from the empyreal heaven 
to paradise, says, 
“ Down thither prone in flight 
He speeds, and tliro’ the vast ethereal 
sky 
Sails between worlds and worlds.” 
CATACOMB, a grotto or subterrane- 
ous place for the burial of the dead. 
The term is particularly used in Italy, 
for a vast assemblage of subterraneous se- 
pulchres, three leagues from Rome, in the 
Via Appia, supposed to be the sepulchres 
of the ancients. Others imagine these ca- 
tacombs to be the cells wherein the primi- 
tive Christians hid themselves. Each cata- 
comb is three feet broad, and eight or ten 
high, running in form of an alley or gallery, 
and communicating with one anotlier. 
Mr. Monro, in the Philosophical Trans- 
actions, gives it as his opinion, tiiat the ca- 
tacombs were the burial places of the first 
Romans, before the practice of burning the 
dead was introduced ; and that they were 
dug in consequence of these opinions, that 
shades hate the light, and love to hover 
about the place where their bodies were 
laid. 
CATACOUSTICS, an appellation given 
to the doctrine of reflected sounds. See 
Acoustics. 
CAT.ALOGUE, a list or enumeration of 
the names of several books, men, or other 
things, according to a certain order. 
Catalogue of the stars, is a list of the 
