CAT 
Shaded" with tceafures. It was obferved that Cato always 
appeared in mourning, and never laid himfelf down ar his 
meals, after the defeat of Pompey, but always fat down, 
contrary to thecuftom of the Romans, as if depreffed with 
the recollection that the fup porters of republican liberty 
were decaying. Plutarch has written an account of his 
life. See Rome. 
CATOCHI’TKS, f. [from Gr. to detain.] A 
precious done of Corlica ; fo called, becaufe, if prelfed 
upon, it dicks to the hand like gum. Pliny. 
CATO'CHUS,y. [from Gr. to detain. ] A ca- 
talepfy. Alfo a tetanus, or fpafmodic difeale, in which 
the body is rigidly held in an upright podure. 
CATOMIS'MUS-, f [from kbto>, below, and 
the lltoulder.] A method of reducing a luxated fhoulder, 
bv railing the patient, over the dioulder of a drong man, 
that by the weight of the b’ody, the dillocation may be re¬ 
duced. 
CATOP'SIS, J. [from xaT07rro^at, Gr. to fee clearly.] 
An acute and quick perception. That acutenefs of the 
faculties which accompanies the latter ftages of confump- 
tion. 
CATOP'TRICAL, ^"..Relating to catoptrics or vi- 
fion by reflection.—A catopuical or dioptrical beat is fu- 
j erior to any, vitrifying the h tided fubffances. A buifinct, 
C ATOP'TRICS, y. [from K«Td3r?go», Gr. a looking- 
glafs.]- The faience'of reflex vifion, or that part of op¬ 
tics which explains the laws and properties of light reflect¬ 
ed from mirrors, or fpecula. The matter or fubjeCt of 
optics being divided into two parts, one.is called dioptrics, 
and the oilier catoptrics. The laws of rejraBion , and the 
effleCts which the refraction of.light has in vilion, are the 
fubjeCt of dioptrics. The laws of reflection, and the 
effects which the reflection of light has in vilion, are the 
fubjeCt of catoptrics. 
The fird treatife extant on catoptrics is tlrat which was 
c-ompofedby Euclid : this was publilhed in Latin in 1604 
by John Pena; it is alfo contained in Herigon’s Courle of 
Mathematics, and in Gregory’s edition of the works of 
Euclid, though it is fufpeCted by fome that this piece was 
not the work of that great geometrician, notwithstanding 
that it is afcribed to liim by Proclius in lib. ii. and by IVla- 
rinus, in his preface to Euclid’s Data. Alhazen, an Ara¬ 
bian author, compofed a large volume of optics about the 
year 1 too, in which he treats very-fully of catoptrics ; and 
after him, Vitello, a Polifit writer, compofed another 
about theyear 1270. Tacquef, in his optics, has very well 
demondrated the chief propofftions of plane and fpherical 
fpecula. And the fame is very ably done by Dr. Barrow, 
in his Optical Lectures. There are alio Trabe’s Catop¬ 
trics; David Gregory’s Elements of Catoptrics^ Woifins’s 
Elements of Catoptrics ; and thofe of Dr. Smith, contain¬ 
ed in his learned and very elaborate Treatife on Optics; 
and many others of lefs note. As this fubjeCt is treated 
under the general term Optics, the lefs need be laid of it 
here. The whole doCtrine of catoptrics depends upon this 
Ample principle, that the angle of incidence is equal to the 
angle of reflection ; that is, that the angle in which a ray 
of light falls upon any furface, called the angle of inci¬ 
dence, is equal to the angle in which it quits it when re¬ 
flected from it, called the angle of reflection; though it is 
fometimes defined ihat the angles of incidence and reflec¬ 
tion are thofe which the incident and reflected rays make, 
not with the reflecting furface itfelf, but with a perpendi¬ 
cular to that furface, at the point of contaCt, which are the 
complements to the others: but it matters not by what 
name thefe angles are called, as to the truth and principles 
of the feience ; fince, if the angles are equal, their comple¬ 
ments are alfo equal. This principle of the equality be¬ 
tween the angles of incidence and reflection, is mere mat¬ 
ter of experience," being a phenomenon that has always 
been obferved to take place, in every cafe that has fallen 
under obfervation, as near at leaf! as mechanical meafure- 
ments can., afeertaia; and hence it is inferred that it is an 
CAT 915 
univerfa! law of nature, and to be confidered as matter of 
fact in all cafe;. 
WitlT reflected as with refraCted rays, it is neceflary that 
feveral rays ffiould aCt at the fame time, in order to make 
an impreflion on our eyes; aid thefe rays may be difpofed 
differently with refpeCt to each other : they may be either 
parallel, convergent, or divergent; and the reflecting fur¬ 
face on which they fall may be either plane, convex, or 
concave. 1 he polifned body that reflects the rays is cal¬ 
led a mirror ; and of thefe there are three principally tiled 
in optical experimentsviz. the plane mirror, GH1, fig. 
1, in the annexed engraving; the fpherical convex mirror, 
G H I, fig. 2 ; and the fpherical concave mirror, G H I, 
fig. 3, The point K, fig. 2, 3, round which the reflecting 
furface of a fpherical mirror is deferibed, is called its cen¬ 
tre. The line KH, drawn from its centre perpendicular 
to its two furfaces, is the axis of the mirror ; and the point 
H, to which that line is drawn, is its vortex. The dif- 
tance between the lines AG and BG, fig 1, is called the 
angle of incidence, and the diffance between BG and CG 
is the angle of reflection. From thefe principles may be 
deduced and collected the following practical maxims in 
catoptrics : 1. In a plane mirror, the image DF, fig. 1, will 
appear as far behind the mirror as the objeCt AC is before it. 
2. The image will appear of the fame fize, and in the fame 
pofition, as the objeCt. 3. Every fitch mirror will reflect 
the image pf an objeCt of twice its ow n length and breadth. 
4. If the objeCt be an opaque body, and its rays fall on the. 
mirror nearly in direCt lines,- there will be only oneimagevi- 
flible, which will be reflected by the inner furface of the glafs. 
But, 5. If the objeCt be a luminous body, and its rays fall 
very obliquely on the mirror, there will appear, to an eye 
placed in a proper pofition, feveral images; the firft of 
which, reflected from tire outer furface of the glafs, will 
not be fo bright as the fecond, reflected from die inner 
furface. The following images, - that are produced by the 
repeated reflections of the rays between the two furfaces-. 
of the glafs, will be in proportion lefs vivid, to the eighth 
or tenth, which will be fcarcely .vifible : 
In a fpherical convex mirror , i.The image D F, fig. 2, 
will always appear behind it. 2. The image will be in the 
fame pofition as the objeCt. 3. It will be lefs than the 
objeCt. 4. It will be curved, but not, as the mirror, Iphe- 
rical. 5. Parallel rays filling on this mirror will have- 
tIre focus or image at half the diffance of the centre K, 
from the mirror. 6-. In-converging rays, the diffance of 
the objeCt muff be equal to half the diffance of the centre, 
to make the image appearbehind the mirror. 7. Diverg¬ 
ing rays will have their image at lefs than half thediftance 
of the centre. If the objeCt be placed in the centre of the 
muror, its image will appear at one eighth of that diffance 
behind it. 
In a fpherical concave mirror, i.That point where the 
image appears of the fame dimenfions as the objeCt, is. file ■ 
centre of that mirror. 2. Parallel rays will have their fociis ■ 
at one half the diffance of the centre. 3. Converging rays 
will form an image before the mirror. 4. In diverging 
rays, if the objeCt be at lefs than one half the diffance ot the 
centre, the image will be behind the mirror, erefl, curved, 
and magnified, as DEF, fig. 3 ; but if the diffance of the 
objeCt be greater, the image will be before the mirror, in¬ 
verted and diminiflied, as DEF, fig. 4. The fun’s rays,. 
falling on a concave mirror, and being parallel, will be 
collected in a focus at half the diffance of its centre, where 
their heat will be augmented in proportion of the furface 
of the mirror to that of the focal fpot. 6. If a luminous 
body be placed in the focus of a concave mirror, its rays, 
being reflected- in parallel lines, will ffrongly enlighten a 
fpace of the fame dimenfion with the mirror, at a great dif- 
tance. If the luminous object be placed nearer than the 
focus, its rays will diverge, and confequently enlighten a 
larger fpace. It is on this principle that reverberators are 
conftrucled. 
Perfons unacquainted with the faience of catoptrics have 
been furprifed at the great illufion of their fight by the ar- 
• tificial 
