Page:Cyclopaedia, Chambers - Volume 2.djvu/845

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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