OPTICS. 
655 
Of Galileo's Telefcope. 
Galileo’s telefcope confifts of a convex and a concave 
lens, whofe axes are in the fame line, and whofe diftance 
is equal to the difference of their focal lengths. 
Prop. V. A diffant objedl may be feen diftindlly through 
Galileo’s telefcope; and the angle which it fubtends at 
the centre of the eye when thus feen, is to the angle 
which it fubtends at the centre of the naked eye, as the 
focal length of the objedl-glafs to the focal length of 
the eye-glafs. 
Let L and E, fig. 6. be the centres of the glades; PQR 
a diffant objedl, towards which the axis’ of the telefcope 
is directed; pqr its image in the principal focus of the 
glafs L, and therefore in the principal focus of the glafs 
E ; then, fince the rays tend to form an image in the 
principal focus of the concave lens E, after refradtion at 
that lens they will be proper for vidon; or a diftindl 
image of the objedl PQR will be formed upon the retina 
of a common eye. 
Alfo, the angle under which the o'ojefl: QP is feen 
through the telefcope, is equal to the angle qEp ; and the 
angle under which it is feen with the naked eye from L, 
is QLP, which is equal to qLp ; therefore, The vifual 
angle in the former cafe : the vifual angle in the latter 
:: L q : E q. 
Cor. i. The magnifying power of the telefcope is mea- 
fured by (See Prop. I. Cor. i.) 
Cor. 2. To adapt this telefcope to a nearer objedl, the 
eye-glafs mud be moved to a greater diftance from the 
objedl-glafs. For, as QL decreafes, Lq increafes ; there¬ 
fore, in order that the principal focus of the glafs E may 
coincide with q, LE mull be increafed. This is the con- 
ftrudlion of the common opera-glafs. 
Cor. 3. When the telefcope is adjufted to a nearer ob- 
jedt, the magnifying power is increafed; for L q is in¬ 
creafed, and E q remains the fame; therefore is 
E q 
increafed. 
Cor. 4. To adjuft this telefcope to the eye of a Jhort- 
fighted perfon, the eye-glafs mull be moved nearer t6 the 
objedt-glafs; if the eye require converging rays, the eye- 
glafs mull be moved the contrary way. 
Cor. 5. To take in the greatell field of view, the eye 
mull be placed clofe to the glafs AB; and therefore, by 
adjulling the telefcope to the eye of a Ihort-fighted perfon, 
the vifual angle of a given objedl is diminilhed; and, on 
the contrary, by adjulling it to the eye of a long-lighted 
perfon, this angle is increafed. 
Prop. VI. Objedls feen through Galileo’s telefcope ap¬ 
pear eredt. 
For, the image upon the retina is eredl with refpedl to 
pqr ; therefore it is inverted with refpedl to the objedl; or 
the objedl appears eredt. 
Prop. VII. The linear magnitude of the field of view, 
when the eye is placed clofe to the concave lens in Ga¬ 
lileo’s telefcope, is meafured by the angle which the 
diameterof the pupil fubtends at the centre of the objedt- 
glafs, increafed by the difference between the angles 
which the diameter of the objedt-glafs fubtends at the 
pupil, and at the image. 
Let MN, fig. 7. be the diameter of the objedt-glafs ; 
AB, the diameter of the pupil, whofe centre is in the 
axis of the telefcope ; join M, B, the oppofite extremities 
of thefe diameters 5 and let MB meet the axis in x, and 
the image in p ; join LB, L p ; and fuppofe pL, qL, to be 
produced till they meet the objedl in P and Q; alfo, fup¬ 
pofe MP to be joined. Then will PM be refradted to the 
pupil in the diredtion MB ; but, any other ray in the pen¬ 
cil, as PL, and every ray which flows from a point more 
dillant from the axis of the telefcope, and is refradted by 
MN, will fall below the pupil ; therefore QP is half the 
linear magnitude of the greatell vilible area. Alfo QP is 
meafured by the angle QLP, or its equal pL<? = ELB + 
B Lp=E L B + L BM—LpM ; and, by doubling thefe quan¬ 
tities, 2QP is meafured by 2ELB+2LBM—2LpM. 
Cor. The rays M.rB, LxE, which are incident upon 
the glafs E, diverging from x, after refradtion, will di¬ 
verge more; therefore, if the eye be moved to any other 
point in the axis of the telefcope, the ray a-By will not 
enter the pupil; and confequently the vilible area will be 
diminilhed. 
Of Sir Ifaac Newton's Telefcope. 
Let ACB, fig. 8, be a concave fpherical refiedtor, whofe 
middle point is C, and centre E. Join CE ; and this is 
called the axis of the refiedtor , or of the telefcope. Let 
CE be directed to the point Q, in the dillant objedl QP; 
then qp, an inverted image of QP, would be formed in 
the principal focus of the refledtor, at right angles to CE, 
and terminated by the lines PEp, QE<p were the reflec¬ 
ted rays 'fullered to proceed thither; but, before they 
arrive at the focus, they are received upon a plane reflec¬ 
tor ach, inclined at an angle of 45 0 to the axis CE 5 and 
thus an image, mn, is formed, fimilar and equal to pq, and 
equally inclined to the plane refledtor; and, confequently, 
mn is parallel to EC. This image is viewed through a 
convex eye-glafs klr, whofe axis is perpendicular to EC, 
and whofe diftance from the image mn is equal to its fo¬ 
cal length. 
If the refledtion be made at c, by a fmall right-angled 
prifm, one of whofe fides is perpendicular, and the other 
parallel to the axis, much lefs light will be loft than if the 
refledtion be made by a plane fpeculum. 
Dr. Herfchel has fo far increafed the focal lengths and 
apertures of hisrefledtors, that the image qp can be viewed 
diredlly, through an eye-glafs placed between q and E. 
The axis of the telefcope is inclined a little from the ob¬ 
jedl, that the image qp may be formed near the fide of 
the tube which contains the refledtor; and the head of 
the obferver does not intercept"fo many rays as materially 
to affedl the brightnefs of the image. By this conftruc- 
tion, one refledtion of the rays is avoided ; and the ftrong- 
eft and moft effective pencils are preferved, which, in the 
Newtonian telefcope, are flopped by the plane refledtor. 
Prop. VIII. When a dillant objedl is viewed with New¬ 
ton’s refledting telefcope, the angle which it fubtends 
at the centre of the eye, is to the angle which it fubtends 
at the naked eye, as the focal length of the refledtor to 
the focal length of the eye-glafs. 
Let QP be the objedl as before ; qp its image, in the 
principal focus of the refledtor : QEC the axis of the te¬ 
lefcope, cutting acb in c. Draw cnlO perpendicular to 
CE ; make cn equal to cq ; draw run at right angles to 
cn, and make nm equal to qp ; then mn is the image of 
qp, or QP. At l let a convex eye-glafs klr be placed, 
whofe focal length is In, and whofe axis coincides with 
that line ; join ml. Then the image nm, which corre- 
fponds to QP in the objedl, is feen through the glafs klr, 
under an angle which is equal to min; and QP is feen, 
with the naked eye placed at E, under an angle which is 
equal to qEp-, and, fince thefe angles have equal fubtenfes, 
run and qp, they are to each other inverfely as the radii In, 
qE-, therefore, The angle which the objedl fubtends at 
the centre of the eye when viewed with the telefco’pe 
: the angle which it fubtends at the naked eye :: Eq 
: In. 
Cor. 1. The magnifying power of this telefcope is mea¬ 
fured by 
In 
Cor. 2. To adapt the telefcope to nearer objedls, the 
refledtor acb, to which the eye-glafs is attached, mull be 
moved towards E. For, as QE decreafes, <?E decreafes ; 
and, therefore, that qc or cn may remain of the fame mag¬ 
nitude, acb mull be moved nearer to E. 
Cor , 
