O P T 
he placed a microfcope in fuch a manner that the wire, 
with which it was furniftied, apparently coincided with 
the outer furface of the cornea; and then directing the 
fpeftator to look at a nearer object, he found that the cor¬ 
nea immediately projected beyond the wire of the micro¬ 
fcope. This experiment is defcribed by Mr. Home, in a 
very ingenious paper on the fubjeCt, Phil. Tranf. vol. 
Ixxxv. p. 16. 
Now, when the diftance of an objeCt is diminilhed, fup- 
pollng no alteration to take place in the eye, the diver¬ 
gency of the extreme rays of the pencil incident upon 
the pupil is increafed ; and therefore, if the image of the 
objeCt in the firlt iituation be formed upon the retina, in 
the latter it will be formed behind it; but an increafe in 
the curvature of the cornea will increafe the convergency 
of the refracted rays, or bring them fooner to a focus ; 
and thus, by a proper change in this coat of the eye, the 
rays will again be brought to a focus upon the retina, 
and the objeCt be ltill feen diftinftly. 
The leaft diftance at which objeCts can be feen dif- 
tinCtly by common eyes, is about feven or eight inches. 
The greateft diftance cannot be fo eafdy or accurately al- 
certained. It feems that the generality of eyes are capa¬ 
ble of collecting parallel rays upon the retina, or fo near 
to it as to produce diftinCt vifion; and thus, the greateft 
diftance at which objects can be diftinCtly viewed is un¬ 
limited. For this reafon, in adapting optical inftruments 
to common eyes, and calculating their powers, weiup- 
pofe the parts to be fo arranged, that the rays in each 
pencil may, when they fall upon the cornea, be parallel. 
If the humours of the eye be too convex, parallel rays, 
and fuch pencils as diverge from points at any confidera- 
ble diftance, are collected before they reach the retina; 
and objeCts, to be feen diftinftly, muftbe brought nearer 
to the eye. This inconvenience may be remedied by a 
concave glafs, whole focal length is fo adjtilled as to give 
the rays proceeding from a diltant objeCt fuch a degree of 
divergency as the eye requires. 
Prot. I. Having given the diftance at which a Ihort-fighted 
perfon can fee diftinftly, to find the focal length of a 
glafs which will enable him to lee diftinftly at any other 
given diftance. 
If qE (fig. 5.) be the diftance at which he can fee dif¬ 
tindtly, and QE a greater diftance, at which he wifhes to 
view objects; let AB be a concave lens, whofe focal 
length is fuch, that the rays which are incident upon it, 
diverging from Q, may, after refraftion, diverge from q; 
then they will have a proper degree of divergency for the 
eye of this fpeftator. Take F the principal focus of rays 
incident in the contrary direction ; then, lince Q and q 
are conjugate foci, QF : QE :: QE : Q q\ dividendo, 
FE : QE :: E q : Qq ; therefore, FE=-^^—If QE 
be indefinitely great, FE=E^. 
When the humours of the eye are too flat, the rays 
which diverge from a point near the eye converge to a 
point behind the retina. This imperfection may be re¬ 
medied by a convex lens, whofe focal length is adjufted 
to the diftance at which objects are to.be viewed, and the 
degree of convergency in the rays of each pencil which 
the eye requires. 
Prot. II. Having given the diftance at which a long- 
lighted perfon can fee diftindtly, to find the focal length 
of a glafs which will enable him to fee diftindtly at any 
other given diftance. 
If qE (fig. 6.) be the diftance at which he can fee dif¬ 
tinCtly, and QE the diftance at which he willies to view 
objefts ; let AB be a convex lens, whofe focal length FE 
is fuch, that the rays which diverge from Q may, after 
refraCtion, diverge from q. Take F, the principal focus 
of rays incident in the contrary direction ; and, fince Q. 
ICS. 583 
and q are conjugate foci, QF : QE :: QE : Qq ; compo- 
nendo, FE s'QE :s Eq : Qq ; and 
Uq 
Cor. 1. If qE be indefinitely great, or the eye require 
parallel rays, FE=QE. 
Cor. 2. If the eye require converging rays, q falls on 
the other fide of the lens; in this cafe, FE is lei's than QK. 
In the choice of glaftes for long or Ihort lighted per- 
fons, care Ihould be taken tofeleCt fuch as have the leaft 
refraCting power, that will anfwer the purpofe; tor the 
eye has a tendency to retain that conformation to which it 
is accuftomed : and therefore, by the ufe of improper 
glaftes, its imperfection may be increafed. 
Prop. III. If the apparent diftance of an objeCt be given, 
and the angle which it fubtends at the centre of the eye 
befmall, its apparent linear magnitude is nearly propor¬ 
tional to that angle. 
When objeCts are at the fame diftance from the eye, 
and appear to be fo, we learn, by experience, to form an 
eftimate of their linear magnitudes with conliderable ac¬ 
curacy. That is, the apparent magnitudes are nearly 
proportional to the real magnitudes, and the real mag¬ 
nitudes are proportional to the angles which the objects 
fubtend at the centre of the eye, when thole angles are 
fmall ; therefore their apparent magnitudes are nearly in 
that ratio. 
An objeCt, and its image upon the retina, fubtend 
equal angles at the centre of the eye; and, luppoling 
the centre fixed, and the angles fmall, the linear magni¬ 
tude of the image is nearly proportional to the angle 
which it fubtends at that centre : therefore the linear 
magnitude of an objeCt, at a given diftance from the eye, 
is nearly proportional to the linear magnitude of its 
picture upon the retina. On this account, perhaps, we 
learn to eftimate the magnitudes of objects at a given dif¬ 
tance more readily than we ihould otherwife be able to 
do ; but, did the magnitude of the picture upon the re¬ 
tina vary according to any other law, we ihould ftill learn 
by experience to eftimate magnitudes by the fight; that 
is, the apparent and real magnitudes would ftill be pro¬ 
portional. 
When objeCts fubtend confiderable angles at the centre 
of the eye, we judge of their magnitudes by carrying 
the optic axes over their feveral parts; and in this cafe 
alfo, the apparent and real magnitudes are nearly pro¬ 
portional, if we have had l'ufficient experience in eftiinat- 
ing magnitudes of this defeription. The judgment we 
form of the magnitude of an object, depends very much 
upon the notion we have of its diftance; and, fince the 
apparent diftance depends upon a variety of caufes which 
are fubjeCt to no calculation, in fpeaking of apparent 
magnitude authors generally fuppofe the apparent diftanc® 
to be given. 
By the vifual angle of an objeCt, we underftand the an¬ 
gle which the axes of the extreme pencils coming from it 
contain at the centre of the eye ; whether the objeCt is 
viewed with the naked eye, or with the afliftance of reflect¬ 
ing lurfaces, or refraCting mediums. 
Prop. IV. When a given objeCt is viewed with the naked 
eye, the denfity of light in the image upon the retina, 
fuppofing none to be loft in its paflage through the 
air, and the diameter of the pupil to be invariable, is 
nearly the fame at all diftances of the eye from the 
object. 
The denfity of light, in the image of a fmall portion of 
the objeCt, varies direCtly as the number of rays, and in- 
verfely as the fpace over which they are diffufed. The 
number of rays which pafs through the pupil, fuppofing 
its diameter given, and that none are flopped in their pro- 
grefs, varies inverfely as the fquare of the diftance of the 
object from the eye. Alfo, the linear magnitude of the 
picture. 
