OPTICS. 
654 
in B ; join j/E ; and draw BO parallel to pE. Then the 
rays which flow from P in the objedt, or p its image, en¬ 
ter the eye, placed at O, in the direction BO. Alfo the 
rays which flow from Q enter the eye in the direction 
EO ; thus, the angle which QP fubtends at the centre of 
the eye, when viewed through the telefcope, is the angle 
BOE, which is equal to pEq. The angle which QP fub¬ 
tends, when viewed with the naked eye from L, is PLQ, 
• which is equal to pEq. And, fince the ^ pEq : the 
pEq (when thefe angles are fmall) :: L q : E<y; therefore, 
The -angle which the objedt fubtends at the centre of 
the eye, when feen through the telefcope: the angle which 
it fubtends at the centre of the naked eye :: Lq : E q. 
Cor. i. If the angle which the objedt fubtends at the 
centre of the naked eye be given, the angle which it fub¬ 
tends at the centre of the eye, when feen through the 
i r ■ E<7 
•telefcope, varies as —. This quantity is ufually called 
the magnifying power of the telefcope. 
Cor. 2. It the telefcope be inverted, the object tnay be 
feen diftindtly; and the vifual angle will be as much di- 
miniflied as it was magnified in the former cafe. 
Cor. 3. To adapt the telefcope to a nearer objedt, the 
eye-glafs mull be moved farther from the objedt-glafs. 
For, if QP be brought nearer to the glafs L, the image 
qp will be formed at a greater dillance from it; and there¬ 
fore, in order that qp may ftill be in the principal focus of 
the glafs E, this glafs mud be moved farther from L. 
Cor. 4.. When QP is brought nearer to L, the magnify¬ 
ing power is increafed. For LQ is increafed, and E^ re¬ 
mains the fame ; therefore ^ is increafed. 
Eg 
Cor. 5. To adjuft the telefcope to the eye of a fhort- 
fighted perfon, the eye-glafs ‘mull be moved nearer to 
the object-glafs. If the eye require converging rays, the 
eye-glafs mull be moved the contrary way. 
Cor. 6. If we fuppofe the eye to be placed between the 
glafs AB and its principal focus, the vifual angle is in¬ 
creafed by adjufling the telefcope to the eye of a fhort- 
fighted perfon. If the eye be farther from the glafs than 
its principal focus, that angleis diminifhed. The con¬ 
trary eft'edts are produced when the telefcope is adjufted 
to the eye of a long-fighted perfon. 
Prot. II. Objedts feen through the aftronomical tele¬ 
fcope appear inverted. 
The image of pqr is inverted upon the retina, and pqr 
is inverted with refpedt to PQR ; therefore the image 
upon the retina is eredt with refpedt to PQR; and, con- 
fequently, the objedt appears inverted. 
Cor. An objedt moving acrofs the field of the telefcope 
from the right to the left, appears to move from the left 
to the right. 
Prop. III. In the aftronomical telefcope, the field of 
view is the greateft when the eye is placed between the 
eye-glafs and its principal focus. . 
The field of view' is the greateft, when the eye is fo 
placed as to receive the extreme rays refradted from the 
objedt-glafs to the eye-glafs. Let MN, fig. 4., be the 
diameter of the objedt-glafs; AB, the diameter of the 
eye-glafs; join N,.B, the correfponding extremities of 
the glafles, and let NB cut the image pqr in p; join pE, 
and fuppofe pE, EL, to be produced till they meet the 
objedt QP in P and Q; join alfo pE, NP; and draw BO 
parallel to pE. Then, if the eye be placed at O, it will 
receive the ray NBO. And this is the ray which comes 
from a point in the objedt at the greateft vifible diftance 
frojn the axis of the telefcope ; for the rays, which flow' 
from any point in the objedt above P, will, after the firft 
refradtion, converge to a point below p, and all of them 
fall below the glafs AB ; therefore P is the extreme point 
vifible in the objedt, and QP is half the linear magnitude 
of the vifible area. Now, when the diameter of the ob- 
1 
jedt-glafs is greater than that of the eye-glafs, which is the 
cafe in the aftronomical telefcope, the rays NB, LE, con¬ 
verge to fome point x beyond the eye-glafs; and there¬ 
fore the point O, to which they converge after the fecond 
refradtion, and where the eye mull be placed to receive 
them, is between the glafs E and its principal focus. 
Cor. 1. If NB and LE be parallel, O is the principal 
focus of the glafs E; and, if they diverge, O lies beyond 
the principal focus. 
Cor. 2. It appears from the figure, that NBO is the only 
ray which comes to the eye from P ; for, any other ray of 
the pencil, as PL7?, after refradtion at the objedt-glafs, 
croffes NB in p, and falls below the eye-glafs. Hence it 
follows, that the extremity of the vifible area is very 
faint. If a point be taken in the objedt nearer to the 
centre of the field of view, more of the rays which flow 
from it will be refradted to the eye; and thus the bright- 
nefs will continually increafe, till all the rays in each pen¬ 
cil incident upon MN are received by the glafs AB; 
when this takes place, the brightnefs will become uni¬ 
form; becaufe the fame number of rays, or very nearly 
fo, is received by the glafs MN from every point in the 
objedt. Here it is fuppofed that the pupil is properly 
placed, and fo large as to receive all the rays refradted by 
the lens AB. 
Prop. IV. If two convex lenfes be added to the formef, 
and placed in a fimilar manner, a diftant objedt may be 
feen diftindliy through the telefcope, and the vifual 
angle will be altered in the ratio of the focal lengths of 
the additional glafles. 
Let CD, HK, fig. 5, be the additional glafles, whofe 
axes coincide with the line LE produced, and the dif¬ 
tance of whofe centres FG is equal to the fum of their 
focal lengths; alfo, let CD be fo placed as to receive the 
extreme rays refradted by AB. 
Then, fince the rays in each pencil, after refradtion at 
the glals E, are parallel (Prop. I.), they will be colledted 
in the principal focus of the glafs CD; that is, in the 
principal focus of the glafs HK; and an image, ahc, will 
be formed there, which may be feen diftindtly through 
the lens HK. 
Again, let BC be the extreme pencil of rays refradted 
by AB; draw F« parallel to BC, and let it meet ahc in a; 
join aG, C a ; and produce Ca till it meets the lens HK in 
H; d raw HV parallel to «G; and at V let the eye be 
placed. Then, NBCHV being the courfe of the pencil 
of rays which flows from P, and LEFGV the courfe of the 
pencil which flows from Q, The angle which QP fubtends 
at the centre of the eye when feen through the four 
glafles: the angle which it fubtends there when feen 
through the firft two :: the^/HVG : the^EOB :: the 
£aGb : the/_a¥b :: F b : Gb. 
Cor. 1. Since the angle which QP fubtends at the centre 
of the eye when it is feen through the two firft glafles 
: the angle which it fubtends at the centre of the naked 
eye :: Eg : Eg ; (Prop. I.) by compounding this pro¬ 
portion with the laft, we have, The angle which the ob¬ 
jedt fubtends at the centre of the eye when viewed 
through the four glafles : the angle which it fubtends at 
the naked eye :>.L^xFi : E qxGb. 
Cor. 2. If Gb and F b be equal, the vifiual angle is not 
altered. 
Cor. 3. The objedt, when viewed through the glafles 
thus combined, appears eredt. For the. axes of the fe- 
veral pencils of rays which flow' from the image pqr crofs 
each other at E ; therefore, the image abc is inverted with 
refpedt to pqr, or eredt with refpedf to the objedt PQR ; 
and, confequently, the image upon the retina is inverted, 
that is, the objedt appears eredt. This is one advantage 
gained by the additional glafles. The inconvenience 
with which they are attended is, that they render objedts 
more faint, by increafing the quantity of the refradting 
medium through which the rays muft pafs, before they 
arrive at the eye. 
Of 
