TEL
[ 188]
TEL
Eye-glafs, and the Diftance of the Focus of the Objea- giafs 5 the Length of the Telefcope is had by fubftracting that from this. That is, the Length of the Telefcope is the Difference between the Diameters of the Object-glafs and Eye-glafs, if that be Piano Convex and this Piano Concave ; or the Difference between the Semi-diameters of the Objecf- glafs, and Eye-glafs, if that be Convex on both Sides, and this Concave on both ; or the Difference between the Semi- diameter of the Objea-giafs and Eye-glafs, if that be Con- vex on both Sides, and this Concave on both ; or the Diffe- rence between the Semi-diameter of the Objecf-glafs, and the Diameter of the Eye-glafs, if that be Convex on both Sides, and this, Piano Concave ; or the Difference between the Dia- meter of the Objea-giafs, and the Semi-diameter of the Eye-glafs if that be Piano Convex, and this Concave on both Sides.
Thus, e.gr. If the Diameter of an Objecf-glafs on both Sides, be four Foot, and that of an Eye-glafs Concave on both Sides, be Four and a Half Digits or Tenths of a Foot ; theLength of the Telefcope will be one Foot eight Digits.
Aftronomical Telescope, is a Telefcope confifting of an Objecf-glafs and an Eye-glafs, both Convex. See Con- vexity.
It has its Name, from its being wholly ufed in Aft ronomical Obfervations.
ConftruBion of the Aftronomical T:
ELESCOPE.
The Tube being prepared, an Objedf-glafs, either Piano Convex, or Convex on both Sides, but to be a Seament of a large Sphere, is fitted in at one End. At the other End, an Eye-glafs Convex on both Sides, which is the Segment of a fmall Sphere, is fitted into the other End, at the common Diftance of the Foci.
Theory of the Aftronomical Telescope]
Now, an Eye placed near the Focus of the Eye-glafs, will fee Objects diftinffly, but inverted; and magnify 1 d in the Ratio of the Diftance of the Focus of the Eye-glafs to the Diftance of the Focus of the ObjeS-glafs.
For i° Since 'tis very remote Objects are viewed through Telefcopes, the Rays from any Point of the Object, fall parallel on the Object-glafs ; and, confequently, after Re- Iracfion, will meet in a Point behind the Glafs, which Point is the Focus of the Eye-glafs. From this Point they begin to diverge, and fall diverging on the Eye-glafs, where being refract ed, they enter the Eye parallel.
Hence, as all but Myopes fee diftincf ly by parallel Rays, a Telefcope, thus difpos'd, will exhibit remote Objects di- ftintlly.
Suppofe the common Focus of the Lens's in F, (Fig. 42.) and make A B = B F. Since one of the Rays A C, proceed- ing from the Right Side of the Object, paffes thro' A ; the Ray C E will he parallel to the Axis A I, and therefore after Refraction in the Eye-glafs, will fall in with it in its Focus G. Since then, the Eye is placed near it ; and all the other Rays proceeding from the fame Point of the Object with E G, are refracted parallel thereto ; the Point in the Right Side of the Object , will be feen in the Right Line EG.
After the like Manner it appears, that the middle Point of the Object is feen in the Axis G B fb that the Object appears Inverted.
3 From what has been already fhcwn, it appears that the Semi-diameter of the Object will be feen through the Telef- cope, under the Angle E G I, which to the naked Eye placed in A, is feen under the Angle bAc. Suppofe, now, IF equal to the Diftance of the Focus I G ; fincc the Right Angles at I are equal ; EGF = EFI. Therefore drawing FM parallel to A C, we fhall have I F M = B A C. The Semi- diameter, therefore, viewed with the naked Eye, is to that viewed through the Telefcope, as I M to I E. Draw K E parallel to FM ; we fhall have I M : I E : : I F : I K. But by re.fono fthe Parallelifm of the Lens's ; CE=BI=:BF + F I = AB+ F I ; and by rcafon of the Parallelifm of the Right Lines CA, and EK; C E = A K, therefore B I = A K, confequently, A B = I K. And, therefore, I M : I E : : I F : A B ; that is, the Semi-diameter feen with the naked Eye, is to the Semi-diameter vieiv'd through the Telefcope, in the Ratio of the Diftance of the Focus of the Eye-Lens I F, to the Diftance of the Focus of the Objetl-zlafs AB. C^e.d.
Hence, i°, As the Agronomical Telefcope exhibits Objefls Inverted; it ferves, commodiouily enough for obferving the Stars (it mattering little, whether they be feen Erect or In- verted) but for Terreftrial Objects, 'tis much lefs proper, as the Inverting mutually prevents their being known.
2° If between the Eye-glafs, and its Focus G, be a plain well-polifh'd Metal Speculum L N, of the Length of an Inch, and of an Oval Figure, inclined to the Axis under an Angle of 4.50, the Rays'E P and M Q_will be reffefled in fuch Manner, as that concurring ing, they make an Angle P g Q_,
equal toPGQ_: And therefore the Eye being placed in F will fee the Object of the fame Magnitude as btfoie only Tn an erect Situation. By the Addition, therefore, of f uc h a Speculum, the Aftronomical 'lelefcofe, is render'd fit to ob- ferve Terreftnal Objects. See Mirror.
3° Since the Focus of a Glafs Convex on both Sides, i s diftantfrom the Glafs itfelf, a Semi-diameter; and that of a Piano Convex Glafs, a Diameter ; if the Object-glafs be Con- vex on both Sides, the 'Telefcope will magnify the Semi- diameter of the Objeft, in the Ratio of the Semi-diameter of the Eye-glafs to the Semi-diameter of the Objea-giafs ; but if the Object-glafs be a Piano Convex, in the Ratio of the Sem.-diameter of the Eye-glafs, to that of the Objea-giafs
4° Wnerefore, fince rhe Semi-diameter of the Eye-glafs has a greater Ratio to the Semi-diameter of the ObjecMafs than to itsDiameter ; a telefcope magnifies the Semi-diameter of the Objea more, if the Object-glafs be a Piano Convex, than it Convex on both Sides.
S° The Ratio of the Semi-diameter of the Eye-glafs to the Diameter or Semi-diameter of the Objeft-glafs, is' the Ms, as the Eye-glafs is a Segment of a lefs Sphere, and the Ubjeit-glafs of a greater. A Telefcope, therefore, magnifies the Diameter of the Objea more, as the Objea-glaf? is a Segment of a greater, and the Eye-glafs of a leffer Sphere. And yet the Ratio of the Semi-diameter of the Eye glafs to the Objea.glafs mull not be too fmall : If it be, it will not refraa Rays enough to the Eye from each Point of the Objea ; nor will it feparate thofe coming from different Points fufhciently: by which means the Vifion will be render'd obfeure, and confuted. To this maybe added, what we have ihewn, of the Ratio of the Objea.glafs to the Eye- glafs in the Dutch Telefcope.
De Chales obferves, that an Objea Lens of 2 a Feet will require an Eye-glafs of 1 \ Digit or Tenth of a Foot ; and an Objea-giafs of eight or ten Feet, an Eye-glafs of four Digits ; in which he is confirm'd by Euftachio de Divinis
Huygeus's great Telefcope, wherewith Saturn's true Face and one of his Satellites were firft difcovered, confifts of an Objea-giafs of 12 Feet, and an Eye-glafs of a little more than Ihree Digits. Though he frequentiv ufed a Telefcope 23 Feet long, with two Eye-glaffes joined together, each in Diameter 1 -| a Digit ; fo that the Two were equal to Oi.e of Three Digits. The fame Author obferves, that an Objea- giafs of 30 Feet, requires an Eye-glafs of 3 ^ Digits ; and gives us a Table of Proportions, forthe Conftrucfing'V Agro- nomical Telefcopes -, an Abridgment whereof, we fhall here give the Reader.
Dift. of Foe.
Diam. ol Dift. of F
Matin,
jDift. of Foe
u ~ —
Aperture
it E.GIdl
Dim.
ofObj.Ghfs
Apeimre.
ofE.GI»6IDiam
Rhinlind
Digits &
Feet.
Dec.
Dec.
l !
2 2
4f 74
2 3
7°
OT
72 89
ICO
I
° SS
61
20
V
6 9j
8y
28
30
3
00
3
- °
109
3
4 f
I Of
-14
40
3
46
3
r°
,26
1 25
I 3f
40
44
i £°
1 60
4 4
87
- 4
4 4
26
66
141
T4
6
1 34
' 47
49
70
4
fi*
r
04
ifV>
7 8
9
10
1 4f
1 60
Si
80
r
90 y
30
nR
1 £'
• 73
1 7i 1 80
1 co|
if 60
«; 1
S°
100
r s
°s\s 48J9
S&
03
183
3
_ If in Two or more Telefcopes, the Ratio between the Ob- left and Eye-glafs be the fame ; the Objea will be magni- fied the fame in both. °
Hence fome may conclude, the making of large Telefcopes a needlefs Trouble. But it muft be remembered, what we have already laid down : An Eye-glafs may be ,,n a lefs Ratio to a greater Objea-giafs, than to a fmaller: Thus e or in HuygensS Telefcope ot 25 Feet, the Eye glals is Three Digits Now, keeping this Propornon, in a Telefcope of 5 o Feet the Eye-glals fhould be Six Digits ; but the Table fhews Four and a Half are fufficient. Hence, from the fame Table it ap- pears, that a Telefcope of 50 Feet magnifies in the Ratio of 1 : 141 ; whereas that of 25 Feet, only magnifies in the Ratio of 1:100.
Since the Diftance of the Lens's is equal to the Aggregate of the Diftance of the Foci of the Objea and Eye glaffes - and the Focus of a Glafs Convex 011 each Side is a Semi- diameter's Diftance, and that of a Piano Convex, a Diame- ter's Diftance from the Lens ; the Length of a Telefcope is equal to the Aggregate of the Semi-diameters of the Lens's, if the Objea-giafs be Convex on borh Sides ; and to the Sum of the Semi-diameter of the Eye-glafs, and of the Diameter of the Objea.glafs, if the Objea-giafs be a Piano Convex.
But as the Semi-diameter of the Eve-glaft in vety ffnall in refnea of that of the Objea-giafs, the Length of the Telefcope is ufiially eftimart-d from the Diftance of rhe Objea-giafs, i. e. from its SetaSdiameter, if it be a Convex on both Sides j or its DiameKJ if Piano Convex. Thus a
Telefcope
