OPTICS. 
f)57 
rays may have a proper degree of divergency, or conver- 
gency, for the eye of the obferver. 
Objedts viewed through this telefcope appear inverted. 
For the image qp is eredt with refpedt to TV, or inverted 
with refpedt to the object; and it is in, or near to, the 
principal focus of the convex glafs through which it is 
viewed ; therefore the image upon the retina is eredt, or 
the objedt appears inverted. 
The field of view may be determined exadtly in the 
fame manner as in the Gregorian telefcope; and the de- 
monftration given there may be applied, in the fame 
words, to the preceding figure. This telefcope may alfo 
be adapted, in the fame manner, to nearer objedts; and 
the vifual angle is expreffed in the fame terms. See 
Prop. XI. 
On the divided obje£l-glafis Micrometer. 
This micrometer confifts of a convex lens divided into 
two equal parts, C, D, fig. u, by a plane which paifes 
through its axis; and the fegments are movable on a gra¬ 
duated line CD, perpendicular to that axis. Let C, D, 
be the centres of the fegments ; and P, Q, two remote ob- 
jedls, images of which will be formed in the lines PCE, 
QDE, and alfo in the principal foci of the fegments. 
Let the glaffes be moved till thefe images coincide, as at 
E; then the angle PEQ, which the objedts fubtend at E, 
the principal focus of C, or D, is equal to the angle 
which CD, the diftance of the centres of the two feg¬ 
ments, fubtends at the fame point; and therefore, by 
calculating this angle, we may determine the angular dif- 
tance of the bodies P and Q, as feen from E. Draw EG 
perpendicular to CD; and, becaufe the triangle CED is 
ifofceles, CG^GD, and the ^CEG=the ^/GED; alfo, 
GD is the fine of the angle GED, to the radius ED; 
therefore, knowing ED and GD, the angle GED may 
be found by the tables; and confequently 2GED, or CED, 
may be determined. 
The angle CED is in general fo fmall, that it may, 
without fenfible error, be confidered as proportional to 
the fubtenfe CD. And, being determined in one cafe by 
obfervation, it may be found in any other, by a fingle 
proportion. 
If the objedts be at a given finite diltance, the angle PEQ 
will ftill be proportional to CD ; for, on this fuppofition, 
the diftance CE, or DE, of either image from the corref- 
ponding glafs, will be invariable; therefore, the angle 
CED will be proportional to CD. 
The divided objedt-glafs is applied both to refledting 
and refradting telefcopes ; and thus fmall angular dif- 
tances in the heavens are meafured with great accuracy. 
In this place we may introduce the mention of an ad- 
jundt to the telefcope, for which the world is indebted to 
Mr. Breguet, a French aftronomer. In the focus of a ce- 
lellial eye-glafs, two hands, like thofe of a watch, are 
feen to pals with an uninterrupted motion, and in their 
paffage to correfpond to the divifions of an immovable 
circle, feen alio in the field of the eye-glafs. The corref- 
pondence of thefe hands with the divifions of the circle, 
marks feconds and tenths of feconds ; and, as the eye 
can follow them at the fame time that it obferves the liar 
which goes through the field of the telefcope, in the fame 
diredtion, the duration of its paffage can be determined 
with much more accuracy than by the ufual method. 
What is further remarkable in this inftrument is, that an 
uninterrupted motion is produced by means of an elcape- 
ment. One of the wheels, which communicates motion 
to the hands, has a round hole in the centre, and is held 
upon a round arbor by means of a fpiral fpring, the cen¬ 
tral point of which is fixed to the arbor, and the other 
extremity to the wheel. The vibrations of the balance 
are very rapid, and keep the fpring in a continual ftate of 
nearly-equal tenfion ; by which means the motion pro¬ 
ceeds without any vifible interruption, although feen 
through a powerful lens. 
Vol. XVII. No. 1205, 
Of fingle Microfcopes. 
If the angle which an objedt fubtends at the centre of 
the eye, when at a proper diftance for diftindt vilion, be 
diminilhed beyond a certain limit, the image upon the 
retina is fo fmall as to convey to the mind only the idea 
of a fingle phyfical point, not diftinguilhable into parts ; 
refpedting which, therefore, no judgment can be formed 
by the fight, except what relates to its colour. If we en¬ 
deavour to increafe the image upon the retina by bringing 
the objedt nearer to the eye, the extreme rays which enter 
the pupil will diverge too much, and the image become 
confufed. If the extreme rays be Hopped, to leffen the 
indiftindtnefs produced by the lateral rays, the image will 
be indiftindt for want of light. But, if the objedt be 
placed in the principal focus of a glafs fpherule, or lens, 
whofe focal length is fliort, it may be feen diftindtly; the 
vilual angle, as well as the quantity of light admitted 
into the eye, will be increafed ; and thus, the feveral 
parts of what before appeared only as a fingle point 
will be fubjedled to examination. Thefe glaffes are called 
fingle microfcopes. 
Prop. XII. The vifual angle of an objedt, when feen 
through a fingle microfcope, is to its vifual angle when 
viewed with the naked eye at the leaft diftance of dif¬ 
tindt vifion, as that leaft diftance to the focal length of 
the glafs. 
Let QP, fig. 12, be an objedt placed in the principal 
focus of the lens, or fpherule, AE, whofe centre is E ; 
LQ the leaft diftance at which it can be feen diftindtly 
with the naked eye. Join LP, PE. Then the angle un¬ 
der wdiich the objedt is feen through the glafs is equal to 
PEQ; and the angle under which it is feen with the 
naked eye, is QLP ; alfo, when thefe angles are fmall, 
fince they have a common fubtenfe QP, they are nearly in 
the inverfe ratio of the radii EQ, LQ; that is, The vifual 
angle when the objedt is feen through the glafs : the vi¬ 
fual angle when it is feen with the naked eye at the dif¬ 
tance LQ :: LQ : EQ. 
Example. If the focal length of the glafs be of an 
inch, and the leaft diftance of diftindt vifion eight inches, 
The vifual angle of the objedt when viewed through the 
glafs : the vifual angle when it is feen with the naked 
eye :: 8 : :: 400 : 1. In this microfcope, the objedt 
appears eredt. 
The filar microfcope is a fingle convex lens, ufed in the 
fame manner as in the magic lantern. The movable tube 
is adjufted to a hole in the window-lhutter of a darkened 
chamber, and the objedt to be examined is ftrongly illu¬ 
minated, and placed a little farther from the lens than its 
principal focus; an inverted image of the objedt is thus 
formed, at a confiderable diftance from the lens, and re¬ 
ceived upon a fcreen placed at the concourfe of the re- 
fradted rays. The angles which the image and objedt 
fubtend at the centre of the eye, when viewed at the leaft 
diftance of diftindt vifion, are proportional to their linear, 
magnitudes, that is, to their diftances from the centre of 
the glafs. 
Of the Double Microfcope. 
The aftronomical telefcope, when adapted to near ob¬ 
jedts, becomes a double microfcope. 
QP, fig. 13, is an objedt, placed a little farther from the 
lens MN than its principal focus F ; qp the image of QP, 
formed on the other fide of the lens, and at a confiderable 
diftance from L, its centre. AEB is a convex eye-glafs, 
whofe axis coincides with the axis of the lens MN, and 
whofe diftance from L is equal to the fum of Lq, and its 
own focal length qE ; confequently, the image qp is in the 
principal focus of the eye-glafs, and it may therefore be 
feen diftindtly by a fpectator whofe eyes are able to colledt 
parallel rays. 
Since the conjugate foci, Q and q, move in the fame di¬ 
redtion upon the indefinite line QLO, if the glaffes be 
S E fixed 
