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preferve and direct the Sight, or to tender it more diftinct, by Angling out the particular Object look'd at, and (hutting out all the foreign Rays reflected trom others, whole Proxi- mity might have render'd the Image lels precife.
This Conjecture is verify'd by Experience; we having often obferv'd, that without a Tube, by only looking rliro' the Hand, or even the Fingers, or a Pin-Hole in a Paper, Objects mall appear more clear and diftinct than otherwile.
Be this as it will, 'tis certain the Optic Principles, whereon Telefaxes are founded, are contain'd in Euclid, and were well known to the ancient Geometricians; and 'tis for want of Attention thereto, that the World was lb long without that admirable Invention ; as, no doubt, thete are numerous others lying hid in the lame Principles, only waiting for Re- flection or Accident to bring them torrh.
Telefcopes are of feveral Kinds, divtinguiflt'd by the Num- ber and Form of their Lens's or Glafles, and denominared from their particular Ules, £S?r. fuch are the Terreflrial or iand Telefcope, the Caleftial or Jftronomtcal Telefcope : To which may be added, the Galilean of Dutch Telefcope, the RefleSing Telefcope, and the Aerial Telefcope.
Galileo's, or the 'Dutch Telescope, is a Telefcope con- futing of a Convex Object-glafs, and a Concave Eye-glafs. See Concave and Convex.
This, of all others, is the molt ancient Form, being the only Kind made by the Inventots, Galileo, l£c. or known, before HuygenS : Whence its Name. Its Conftruction, Per- fections, Imperfections, &c. are deliver'd in what follows.
ConJlruBion of Galileo's or the Dutch Telescope,
In a Tube prepar'd for the Putpofe, (the Structure where- of fee under the Article Tube] at one End is fitted a Con- vex Object Lens, either a plain Convex, or Convex on both Sides, but a Segment of a very large Sphere: At the other End is fitted an Eye-glafs, concave on both Sides, and the Segment of a lels Sphere ; fo dlfpos'd, as to be the Diftance of the Vittual Focus before the Image of the Convex Lens. See Focus.
Theory of Galileo'* Telescope."
Now, in an Instrument thus framed, all 'People, except Myopes, or thofe ftiort-fighted, muft fee Objetls difinSly,i;i an er'cS Situation; and increafed in tie Ratio if the Hi- fiance of the Virtual Feats of the Eye Glafs, to the Diftance cf the Focus 0} the 01 jetf Glafs.
But, for Myopes to fee Objects diftinctly thro' fuch an In- strument, the Eye-glafs mult be fet nearer the ObjecVglals. The Reafon of thefe Effects will appear from what follows :
For, l Q , Since 'tis far diftant Objects that are to be viewed with a Telefcope, the Rays proceeding from the fame Point of the Object, will fall on the Object-glafs, parallel ; and, confequently, by their Refraction thro the Convexity will be thrown Converging on the Eye-glafs. But by their Refraction thro' the Concavity hereof, they will be again render'd pa- rallel ; and in fuch Difpoiition will enter the Eye. See Ray, Concavity, Convexity, and Converging.
But all, excepting Mybpes, fee Objects diftinilly by parallel Rays. See Vision and Parallel. Therefore the firft fPoint is clear.
2° Suppofe A (Tab. Opticks, Fig. 4.1.) to be the Focus of the Object-glafs ; and fuppofe AC the furthelt Ray on the Right Hand of the Object that paffes through the Tube : After Refraction, it will become parallel to the Axis B I, and, confequently, after a fecond Refraction through the concave Lens, will diverge from the virtual Focus. Where- fore, fince all the Rays coming from the fame Extreme to the Eye placed behind the concave Lens, are parallel to L E ; and thofe from the middle of the Object, parallel to E G (as fliewn under the former Article) the middle Point of the Object will be feen in the Axis GA ; and the right Ex- treme, on the right Side, viz. in the Line LN, or parallel thereto : that is, the Object will be ereS ; Which is the fecond (Point.
3 Since all Right Lines parallel to L E cut the Axis under the fame Angle ; the Semi-diameter ot the Object will be feen through the Telefcope, under the Angle E FI ; the Rays L E and G I entring the Eye in the fame Manner, as if the Pupil were placed in F. If, now, the naked Eye wete in A, it would fee the Semi-diameter of the Object under rhe An- gle c Ab or CAB. But fince the Object is fuppofed very remote, the Diftance A F in refpeft hereto is nothing, and therefore the naked Eye, even in F, would fee the Semi- diameter of the Objea under an Angle, equal to A.
The Semi-diameter of the Object, therefore, feen with the naked Eye, is to that feen through the Telefcope as I M to I E. But 'tis demonftrated, that IM:IE::IF:AB; that is, the Semi-diameter feen with the naked Eye, is to that viewed through the Telefcope ; in the Ratio of the 'Diftance of the Vimial Focus of the Eye-glafs F I, to the Diftance of the jFocus of the ObjeS-glafs, ABj Which was the third 'Point.
^Laftly, Myopes have theirRetina too far from the cryftaffirj Humour ; and diverging Rays, concur at a greater Diffance than parallel ones ; and thofethat were parallel become diverg- ing by bringing the Eye-glafs nearer the Objcct-offs; l?y means of fuch Approach, Myopes mil fee boieSs iiftmSh through ^Telefcope ; Which is the fourth 'Point.
Hence, j°, To have the whole Object viiible, the Semi- diameter of the Pupil mult not be lets than the Di ! ; ance of the Rays LE and GI ; and, therefore, rhe more the Pupil is dilated, the greater Field or Compafs will be taken in by the Telefcope, and wee verfa ; fo that coming out of a dark Place, or (hutting the Eye for fome time e'er you apply it to the Glafs, you will take in a greater Field at firft Glance, than afterwards, when the Pupil is again contracted by the Incteafe of Light. SeePrjriL.
2° Since the Diitance of the Rays E L and IK is Greater, at a greater Diftance from the Lens ; the Compafs taken in by the Eye at one View, will be greater as the Eye is neater the Concave Lens.
3 Since the Focus of a Piano Convex Object Lens, and the Focus of a Piano Concave Eye Lens, is at the Diftance of the Diameter ; and the Focus of an Object-glafs, convex on both. Sides, and the virtual Focus of an Eye-glafs concave on both Sides, is at the Diftance of a Semi-diameter ; if the Object- glafs be Piano Convex, and the Eye glafs Piano Concave, the Telefcope will increafe the Diameter of the Object, in the Ratio of the Diameter of the Concavity to that of the Con- vexity: If the Object-glafs be Convex on both Sides, and the Eye-glafs Concave on both Sides, it will magnify in tb.eRatio of the Semi-diameter of the Concavity to that of the Con- vexity ; if the Objeft-glafs be Piano Convex, and the Eye- glafs Concave on both Sides, the Semi-diameter of the Object will be increafed in the Ratio of the Diameter of the Con- vexity to the Semi diameter of the Concavity : And, Laftly, if the Object-glafs be Convex on both Sides, and the Eye- glafs Piano Concave, the Increafe will be in the Ratio of the Diameter of the Concavity, to the Semi-diameter of the Con- vexity. ^
4 Since the Ratio of the Semi-diameters is the fame as that of the Diameters: Telefcopes magnify the Object in the fame Manner, whether the Object-glafs be Piano Convex, and the Eye-glafs Piano Concave, or whether the one be Convex on both Sides, and the other Concave on both.
5 Since the Semi-diameter of the Concavity, has a lets Ratio to the Diameter of the Convexity, than its Diameter has ; a Telefcope magnifies more, if the Object-glafs he Piano Convex, than if it be Convex on both Sides.
6" The greater the Diameter of the Object-glafs, and the lefs that of the Eye-glafs ; the lefs Ratio has the Diameter of the Object viewed with the naked Eye, to its Semi- diameter viewed with a Telefcope; and, confequently, the more is the Object magnified by the Telefcope.
7 Since the Semi-diameter of the Object is increafed in the Ratio of the Angle E F I ; and the greater the Angle E F I is, the lefs Part of the Object does it take in at one View ; the Telefcope exhibits fo much a lefs Part of the Object, as it in'creafesits Diameter more.
And this is the Reafon that determined the Mathematicians to look out for another Telefcope, after having clearly found the Imperfection of the firft, difcover'd by Chance. Nor were their Endeavours vain ; as appears from the Aftrono- rnical Telefcope hereafter to be defctibed.
If the Semi-diameter of the Eye-glafs, have too fmall a Ratio to that of the Object-glafs, an Object through the Telefcope, will not appear fufficiently clear, by reafon the great Divergency of the Rays will occafion the feveral Pencils reprefenting the feveral Pbints of the Object on the Retina, to confift of too few Rays. This, too, is found, that equal Object Lens's won't bear the fame Eye Lens, if they be differently tranfparent, or there be a Difference in their Polifh. A lefs tranfparent Object-glafs, or one lefs accurately ground, requires a more fpherical Eye-glafs, than another more tranfparent, S?c.
Hence, though it be found by Experience, that a Telefcope is good, if the Diftance of the Focus of the Object-glafs be fix Inches, and the Diameter of the Piano Concave Eye-glafs be one Inch and one Line, or of one equally Concave on both Sides, one Inch and a Half; yet is it by no means expedient to recommend to the Artificer, either this or any particular Combination ; but to try feveral Eye-glaffes, both greater and fmaller, with the fame Object-glafs; and take that through which Objects appear molt clear and diftinct.
Hevtfhts.. recommends an Object-glafs Convex on botb. Sides, whofe Diameter is four Dannie Feet ; and an Eye- glafs Concave on both Sides, whofe Diameter is 4 \ Digits or Tenths of a Foot. An Object-glafs, equally Convex on both Sides, whofe Diameter is five Feet, he obferves, will require an Eye-glafs of 5 J- Digits ; and adds, that the fame Eve- glafs will alfo ferve an Object-glafs of eight or ten Feet.
Hence, as the Diftance of the Objea-glafs and Eye glafi is the Difference between the Diftance of the virtual Focus of the
Eye-
