OPTICS. 58 I 
place, and therefore the apparent object, and image of it, 
fubtend equal angles at the eye. 
Now, if we fuppofe the pupil to have any fenfible magni¬ 
tude ab ; then the objeft feen by the eye in that fituation 
wiil appear under the angle HXL, which is larger than 
the angle HaK, under which it appeared before ; becaule 
the angle at X is nearer than the angle at a to the line 
JM, which is a fubtenfe common to them both. 
From this Propolition it follows ; that, were the eye 
clofe to the furface at K, the real and apparent object 
would be feen under equal angles, (for the real objedt ap¬ 
pears from that place under the fame angle that the image 
does, as will be Ihown at the end of this fedtion ;) there¬ 
fore, when the eye is nearer to the image than that point, 
the image will fubtend a larger angle at it than the objedt 
does ; and conlequently, lince the image and apparent ob¬ 
jedt fubtend equal angles at the eye, the apparent objedt 
mult necelfarily be feen under a larger angle than the ob¬ 
jedt itfelf, wherever the eye be placed, between the fur- 
face and the image. 
As each point in the reprefentation of an object made 
by reflection is fituated fomewhere in a right line that 
pafles through its correfpondent point in 'the objedt, and 
is perpendicular to the reftedting furface, we may hence 
deduce the following eafy and expeditious method of de¬ 
termining both the magnitude and fituation of the image 
in all cales whatever. Through the extremities of the 
object AB and the centre C (fig. 17, 18, 19.) draw the 
lines AC, BC, and produce them as the cafe requires ; 
thefe lines will be perpendicular to the refledting furface, 
and therefore the extremities of the image will fall upon 
them. Through F, the micldle point of the objedt and the 
centre, draw the line FC, and produce it till it pafles 
through the refledting furface ; this will alfo be perpendi¬ 
cular to the furface. Through G, the point where this 
line cuts the furface, draw the lines AG and BG, and 
produce them this way or that, till they crofs the former 
perpendiculars j and, where they crofs, there I and M, the 
extremities of the image, will fall. For, fuppofing'AG to 
be a ray proceeding from the point A and falling upon G, 
it will tie refledted to B; becaule P'ArazFB, and FG is per¬ 
pendicular to the refledting furface ; and therefore the re¬ 
prefentation of the point A will be in BG produced as 
well as in AC ; conlequently, it will fall on the point I, 
where they crofs each other. LikewH'e the ray BG will, 
for the fame reafon, be refledted to A 5 and therefore, the 
reprefentation of the point B will be in AG produced, as 
well as in fome part of BC, that is, in M, where they crofs. 
Hence the Propolition is obvious. 
If it happen that the lines will not crofs which way 
foever they are produced, as in fig. 20. then is the object 
in the focus of parallel rays of that furface, and has no 
image formed in the place whatever. For in this cafe the 
rays AH, AG, flowing from the point A, become parallel 
after refledtion in the lines HC, GB, and therefore do not 
flow as to or from any point: in like manner, rays, flowing 
from B are refledted into tiie parallel lines KB and GA ; 
fo that no reprefentation can be formed by fuch refledtion. 
From this we learn another circumltance relating to the 
magnitude of the image made by refledtion ; viz. that it 
fubtends the fame angle at the vertex of the refledting fur¬ 
face that the objedt does. This appears by infpedtion of 
the 17th, 18th, or 19th, figure, in each of which the angle 
IGM=AGB, the angles which the imagejubtends at G 
the vertex of the refledting furface, and which the object 
fubtends at the fame place ; for in the two firlt of thole fi¬ 
gures they are vertical, in the third they are the fame. 
The angle ICM, which the image fubtends at the cen¬ 
tre, is alfo equal to the angle ACB which the objedt fub¬ 
tends at the fame place ; for in tne two flrlt figures they 
are the fame, in the lalt they are vertical to each other. 
Whence it is evident, that the objedt and its image are 
to each other in diameter, either as their refpedtive dif- 
tances from the vertex of the refledting furface, or as their 
diltances from the centre of the fame. 
Vol. XVII. No. 1199. 
Prop. VIII. As objedls are multiplied by being feen 
through tranfparent media, whofe furfaces are properly 
difpofed, fo they may alfo by refledting furfaces. 
1. If two refledting furfaces be difpofed at right angles, 
as the furfaces AB, BC, (fig. 21.) an objedt at D may be 
feen by an eye at E, after one refledtion at F, in the line 
EF produced ; afijer two refledtions, the firlt at G, the fe¬ 
cond at H, in the line EH produced ; and alfo, after one 
refledtion made at A, in the line EA,produced. 
2. If the furfaces be parallel, as AB, CD, fig. 22. and 
the objedt be placed at Eand the eye at F, the objedt will 
appear multiplied an infinite number of times : thus it 
may be feen in the line FG produced, after one refledtion 
at G ; in the line FH produced, after two refledtions, the 
firlt at I, the fecond at H ; and alfo in FP produced, after 
feveral fucceffive refledtions of the ray EL, at the points 
L, M, N, O, and P : and fo on in infinitum. But the 
greater the number of refledtions are, the weaker their re- 
prefentations will be. 
For fome entertaining experiments depending on the 
phenomena of refledted light, fee the article Catoptrics, 
vol. iii.'p. 9 iti. 
THEORY of VISION. Plate VI. 
Fig. t. reprefents a fedtion of the human eye, made 
by a plane which is perpendicular to the furfaces of the 
coats which contain its feveral humours, anrfall'o to the 
nofe. Its form is nearly fpherical, and would be exactly 
fo, were not the fore part a little more convex than the 
remainder; the parts BFB, BAB, are, in reality, fegments 
of a greater and a lei's fphere. 
The humours of the eye are contained in a firm coat 
BFBA, called the fclerotica ; the more convex or, protu¬ 
berant part of which, BAB, is tranfparent, and from its 
conliltency, and horny appearance, it is called the cornea. 
This coat is reprefented by the lpace contained between 
the two exterior circles BFBA. 
Contiguous to the fclerotica is a fecond coat, of a fofter 
fubltance, called the choroides. This coat is reprefented 
by the next white fpace, and extends, along the back part 
of the fclerotica, to the cornea. 
From the jundtion of the choroides and cornea arifes 
the uvea, 3 a, Bn, aflat opaque membrane, in the fore part 
of which, and nearly in its centre, is a circular aperture 
called the pupil. 
The pupil is capable of being enlarged or contrasted 
with great readinefs ; by which means a greater or lefs 
number of rays may be admitted into the eye, as the cir- 
cumftances of viflon require. In weak light, too few rays 
might render objedts indiftindt ; and, in (trong light, too 
many might injure the organ. Whillt the pupil is thus 
enlargedorcontradled, its figure remains unaltered. This 
remarkable eft'edt is thought to be produced by means of 
fmall fibres which arife from the outer circumference of 
the uvea, and tend towards its centre ; this circumference 
is alfo fuppofed to be mufcular, and, by its equal adtion 
upon the fibres on each fide, the form of the pupil is pre- 
ferved, whillt its diameter is enlarged or contracted. 
At the back part of the eye, a little nearer to the nofe 
than the point which is oppolite to the pupil, enters the 
optic nerve, V, which fpreads itfelf over the whole of the 
choroides like a fine net; and from this circumltance is 
called the retina. It is immerfed in a dark mucus which 
adheres to the choroides. 
Thefe three coats, the fclerotica, the choroides, and the 
retina, enter the focket of the eye at the fame place. The 
fclerotica is a continuation of the dura mater, a thick, 
membrane which lies immediately under the Ikull. The 
choroides is a continuation of the pin mater, a fine thin 
membrane which adheres clofely to the brain. The retina 
proceeds from the brain itfelf. 
Within the eye, a little behind the pupil, is a foft tranf¬ 
parent fubftance EDE, nearly of the form of a double- 
convex lens, the anterior furface of which is lei's curved 
7 I than 
1 
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