650 
OPTICS 
Cor. 3. As the objeCI is brought nearer to E, the mag¬ 
nifying power of the telefcope is diminifhed. For, E q 
decreafes and In is invariable ; therefore 5 ? decreafes. 
In 
Cor. 4. To adjuft the telefcope to the eye of a fhort- 
lighted perfon,the refleCIor «ei> mull be moved towards C. 
For then the image mn will be at a greater diftance from c, 
or nearer to the eye-glafs; and, therefore, the rays in 
each pencil, after refraction at the glafs hlr, will diverge. 
If the eye require converging rays, the refleCtor acb mult 
be moved the contrary way. 
Prop. IX. ObjeCls viewed with Newton's telefcope ap¬ 
pear inverted. 
Let QP lie in the plane of the paper; and, when the 
eye of theobferver is applied to the glafs hr, let the plane 
•which pafles through both his eyes alfo coincide with 
the plane of the paper. Then, the rays which flow from 
P, the right fide of the objeCt, converge to m, the left fide 
of the image. Alfo the rays which flow from a point 
in the objeCt above the plane of the paper, converge to a 
point in the image below that plane ; thus the image mn 
is inverted ; and, lince it is in, or near to, the principal 
focus of the convex lens through which it is viewed, it 
appears inverted. 
Prop. X. To determine the field of view in the Newtonian 
telefcope. 
Join t, h, the correfponding extremities of the plane 
refleCtor and the eye-glafs 3 and let Ik cut the image mn 
in m: take qp equal to nm ; draw/jE, and produce it till 
it meets the objeft in P. Then, a fmall pencil of rays 
flowing from P will, if acb be not fo large as to intercept 
them before they are incident upon the refleCtor ACB, be 
reflected at b to the extremity of the eye-glafs, and re- 
fraCled thence to the eye at O j the point P will therefore 
be vifible. Alfo, this point is the extremity of the field 
of view : for, if a point be taken in nm, farther from the 
axis of the lens than m, any ftraight line drawn through 
it, will either fall without ab or without hr-, that is, no 
ray belonging to a point in the objeCt QP beyond P, can 
be reflected from acb to the eye-glafs. 
Cor. In order that the field of view may be circular, acb 
niuft be the tranfverfe feCtion of a cone, or cylinder, ge¬ 
nerated by the revolution of bh about the axis cl ; and 
therefore it mull be an ellipfe, whofe major and minor 
axes depend upon the nature of this folid. 
Gf the Gregorian Telefcope. 
In fio-. 9. let ACB, acb, reprefent two concave fpheri- 
cal reflectors, a greater and a fmaller, whofe axes are co¬ 
incident, and whofe concave furfaces are turned towards 
each other; E and e, their centres ; T, t, their principal 
foci of which T lies between e and t. In the middle of 
the larger refleCtor is an opening, nearly of the fame di- 
menlions with the aperture of the fmaller, to admit a 
movable tube, containing a convex eye-glafs FGH. 
When the axis of the telefcope is directed to the point 
q i n a diftant objeCt QP, an inverted image TV of this 
objeCt, terminated by the lines QET, PEV, is formed in 
the principal focus of the refleCtor AB. The rays which 
diverge thence, and fall upon the concave refleCtor acb, 
after "reflection, form an image qp, terminated by the lines 
Te<?, Vcp ; which, becaufe T is between e and t, is inver- 
ted with relpeCt to TV, or ereCt with refpeCt to QP. The 
rays are then received by the eye-glafs FGH, whofe axis 
coincides with the axis of the telefcope, and whofe focal 
length is Gq ; and therefore the image qp may be feen dif- 
tinClly. 
If the diftance Cc be diminifhed, the diftance f<?will be 
increafed. For, as Cc decreafes, Tt decreafes, and Tt : 
t.e :: te : tq, in which proportion te is invariable; there¬ 
fore', tq increafes. By a proper adjuftment, then, of the re¬ 
flectors and eye-glafs, the image qp may b<?formed in the 
principal focus of the lens FGH; orinfuch afituationas 
may be neceflary fordiftinCl vifion. 
This telefcope may be adapted to nearer objeCls, by in- 
creafing the diftance Cc. For, as QP approaches towards 
E, TV alfo approaches towards E, or towards t ; therefore 
the diftance tq increafes, or q is nearer to the eye-glafs 
than before; which inconvenience maybe remedied by 
increafing the diftance Cc, as above. 
ObjeCls feen through this telefcope appear ereCI. For 
qp is an ereCI image of QP, and in or near to the princi¬ 
pal focus of the convex lens through which it is viewed; 
therefore, it appears ereCt. 
As fo much has been faid upon the field of view in 
other telefcopes, the reader will find no difficulty in de¬ 
termining it in this cafe. Join F, a, correfponding extre¬ 
mities of the fmall refleCtor and the eye-glafs ; let F« cut 
qp in p. Draw pc, and produce it till it meets TV in V. 
join VE, and produce this line till it meets the objeCt QP 
in P; then is P the extremity of the field of view. For, 
if «VB be drawn, the rays which flow from P, and fall 
upon the large mirror at B, after reflection converge to 
V, and fall upon the refleCtor acb at a; thence they pro¬ 
ceed in the direction apF, and are refraCled to the eye in 
the direction FO, which is parallel to pG. But no ray 
which belongs to a point in the objeCt above P, can be- 
reflected from acb to the eye-glafs FH. 
Since qp is much nearer to the eye-glafs than to the re¬ 
fleCtor acb, the field of view will depend more upon the 
aperture of the former than of the latter. 
Prop. XI. To determine the angle which an objeCt fub- 
tends at the centre of the eye, when feen through 
Gregory’s telefcope. 
The conftruCtion being made as before, the angle un¬ 
der which QP is feen through the telefcope is equal to 
pGq; and the angle under which it is feen with the naked 
eye is equal to TEV. Now, when the angles are fmall, 
The /_pGq : the Z_peq{TeV) :: eq : qG; and alfo, The 
/_Te\ : the ,/TEV :: ET : eT; by comp. The Z_pGq 
: the ^TEV :: ec/X ET : i/GXeT; that is, The vifual 
angle when the objeCt is feen through the telefcope : the 
vifual angle when it is feen with the naked eye :: egxET 
: qG X eT. 
Cor. Since T t : te :: eT : eq; inverfely, te : T* :: eq 
: eT ; therefore, teXET : TtXqG :: eqXET ■. q GXeT; 
and, The vifual angle when the objeCt is feen through 
the telefcope : the vifual angle when it is feen .with the 
te V FT 
naked eye :: feXET : TtXtfG :: - : T t. 
qG 
Gf Cajfegrain's Telefcope. 
In this telefcope, the fmaller refleCtor acb, fig. 10, is 
convex, and fo placed, that T falls between t and c. In 
other refpeCts, it is fimilar to the Gregorian telefcope, fig. 9. 
Let GCE, fig. 10, the axis of this telefcope, be directed 
to the point Q in a diftant objeCt QP; then, an inverted 
image, TV, of this objeCt, would be formed in the prin¬ 
cipal focus of the large refleCtor, and terminated by the 
lines QET, PEV, if the rays were fuffered to proceed 
thither. But, before they reach the focus, they are re¬ 
ceived upon the convex refleCtor bca ; and fince, by the 
conftruCtion, TV falls between the furface c and princi¬ 
pal focus t of this refleCtor, an ereCt image qp of TV is 
formed, and terminated by the lines eT^, eVp. This 
image is viewed through the lens FGH, whofe axis coin¬ 
cides with the axis of the telefcope, and whofe focal 
length is Gq. 
The diftance of the image qp from t may be determined 
by the proportion T t : et :: et : tq. Alfo, by diminish¬ 
ing the diftance Cc, the diftance T< is diminifhed; and, 
fince te is given, tq is increafed^ Hence it is manifeft, 
that, by a proper adjuftment of the refleCtors and the eye- 
glafs, the image qp may be formed in the principal focus 
of the lens FGH; or in fuch a fituation, that the emergent 
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