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heaven_n	earth_n	great_a	let_v	6,859	5	4.2631	3	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A51133	Dioptrica nova, A treatise of dioptricks in two parts : wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of humane life, are explained / by William Molyneux of Dublin, Esq. ...	Molyneux, William, 1656-1698.; Halley, Edmond, 1656-1742.	1692 (1692)	Wing M2405; ESTC R3440	201,330	332

Naturalis Lib. 17. Cap. 10. Printed An. 1589. has these Words Si utramque Lentem sc. Concavam Convexam rectè componere noveris longinqua proxima majora clara videbis But Porta's Character is so well known that we may easily imagine he had got this Hint from Holland Franciscus Fontana a Neapolitan in his Observationes coelestium terrestriumque rerum contends that he himself An. 1608. first invented the Telescope composed of a Convex Object-Glass and Convex Eye-Glass For the Tubus Batavus and Galileo's Tube was furnish'd with a Concave Eye-Glass and Fontana confesses it was before his and that An. 1618. he first invented the double Microscope Rheita in his Oculus Enoch Eliae Lib. 4. towards the end pretends to be the first Discoverer of the erecting Telescope of three Convex Eye-Glasses as also of the Telescope for looking with both Eyes called Telescopium binoculum Of which latter Cherubin has writ his whole Volume La Vision parfait c. Thus we see how long the Use of single Optick Glasses was common in the World even about 300 years before M●n rightly understood their due Application in the Composition of this admirable Instrument They had them in their hands they look'd through them now a Convex then a Concave and admired their Effects and the Help they gave to disorder'd Eyes but still were ignorant of the vast Advantage the most acute Eye might receive by them even to the Increase of its Power some Thousands of Degrees beyond its natural Abilities This was reserved for some lucky Chance in a future Age to be discovered by him that should first be so fortunate as to adapt these Glasses at their due Distance for to some such happy Hitt I imagine the Invention is due and not to any profound Thought on the nature and properties of Glasses that first suggested the Contrivance to the Dutch Mechanick that was its Author And this does naturally suggest a Thought to us of some incouragements in natural Enquiries by the method of experimental Philosophy that perhaps we are every day ingaged amongst some particular Things which we commonly see handle use and are conversant with and which have in them some latent hidden Properties which upon a right Application to be discovered perhaps by some lucky Hitt may be of the most useful and surprising Effects And that therefore we should not despair of making the greatest Discoveries about even the meanest Things Who could expect to see such Wonders from an easie Composition of three such plain simple Bodies Niter Sulfur and Charcole as we daily see from Gunpowder And the Property of the Magnet's drawing Iron was commonly known many generations before it was so happily applyed to guiding a Ship Who could have thought by looking upon that dark unpromising stone that future Ages should use it to such a stupendous and advantageous a Purpose far exceeding the Virtues of the most illustrious Gemms Hence may we learn not to despise the Products of Nature even of the meanest Appearance And let us not say that any Discovery is useless since we know not what Time and Posterity may produce from the simplest Truth And this naturally leads me to the discoveries made by Optick Glasses Galileo as is noted before is deservedly reputed the first that raised up this Gigantick Instrument that ventures to climb Heaven and from thence brings down the Stars He first was surprized and struck with wonder to see four little Moons dancing round Iupiter that from their first Creation to the lucky Moment when he first discovered them had never struck the eye of any mortal Inhabitant of this Globe Were these then made for the Use of poor Man from whose Knowledg they were concealed for 5000 years together Vain Man that thus presumes to confine the Designs of the Almighty Creator to miserable Dust and Ashes when his infinite Power can make Millions of intelligent Beings and all intelligent after different ways to serve and praise him And these perhaps are the Inhabitants of these distant Worlds and of those again infinitely extended beyond these 'T is true indeed now these little Planets are discovered we have happily applyed them to an advantageous purpose as shall be shew'd hereafter But this we are to esteem as a particular Benefit of Providence to these latter Generations and respects not all the general Race of Mankind that lived and were busie for 5000 years together and knew nothing of them But in this stupendous Enquiry I stop as not being able to reach it with the longest Telescope To keep therefore to our Subject I shall take the Heavens in order as they lie considering first the uppermost and so descend down to our Earth and shall briefly declare the Discoveries made in each and as far as I can attain it by whom and when with farther References to those Authors where each particular may be found more fully treated of And First for the Fixt Stars That whitish Band or Zone the Galaxia or milky Way that so irregularly incompasses a great scope in the Heavens and of which the Ancients could give no tolerable Account is found by the Telescope to be no other than an heap of very minute Stars thickly set together which by their great Distance Smalness and Closeness appear to the naked Eye as one united whitish Cloud In like manner the Nebulosa Orionis Praesepe Cancri c. are found to be a Congeries of small Stars closely set together but easily distinguishable by the Telescope The Pleiades or seven Stars tho scarce more than six appear are found by an ordinary Glass to be nigh forty And in the single Constellation of Orion the Telescope discovers more Stars than the naked Eye can number in all the Heavens On this Account the Seed of Abraham that was to be made numerous as the Stars in the Firmament may yet for ought we know admit of Propagations through many future Generations before it comes up to its Limits And the number which Archimedes demonstrated greater than that of the Grains of Sand composing this Globe of Earth may perhaps fall short of the Stars in the Heavens For hardly any Corner of the Firmament so dark But the Telescope turn'd towards it descries Multitudes of glittering Spangles therein 10. From the fixt Stars let us contract our Prospect and in a vast long and almost immense Course homewards we first meet with Saturn By his slow Motion he takes State upon him as carrying about him something more weighty than ordinary But the short sight percieves nothing thereof and sees only a plain round Globe as the rest of the Chorus dancing round the Sun All his Equipage and Attendants are hid from our View 'till surveyed more closely by the Telescope And then behold a mighty Ring parallel to the Equator bright as the Planets own Face encompassing round his Body very thin and separated in all Appearance on all

the Focal length of the Object-Glass To the Focal length of the Eye-Glass Which was to be Demonstrated The same may be declared otherwise Thus Tab. 35. f. 2. Let us suppose the naked Eye at h to view the Object Inverted by means of the Distinct Base f e d The Inverted Object shall appear under the Angle f h d by Prop. XL. But the Eye at o through the Glass perceives the Inverted Image of the Object under the Angle g o l equal to f h d by Prop. XXXIII and f h d is equal to f q d and consequently as in the foregoing Demonstration the Proposition is manifest I shall now mention the common Method for trying the Truth of this Proposition by Experiment Having the Focal length of an Object-Glass for Instance 144 Inches and the Focal length of an Eye-Glass three Inches A Telescope composed of these shall make the apparent Diamet●al Magnitude of an Object To the apparent Magnitude of the same Object viewed by the naked Eye As 144 To 3 or 48 To 1. Wherefore such a Glass is said to Magnifie 48 times in the Diameter of the Object and 2304 = square of 48 in the Surface of the Object The Superficies of like Figures being to each other as the Squares of their Diameters or Homologous Sides Wherefore from a convenient Scale take one part and therewith describe a Circle And from the same Scale take 48 parts and describe another Circle Let these two Circles be cut out in Paper or other Conspicuous Material and placed at three or four Foot from each other on a Wall at such a Distance as will require the length between the Glasses in the Telescope but just 147 = 144 + 3 Inches to shew these Objects distinctly Then with one Eye through the Telescope observe the smaller Circle and at the same time with t'other Eye naked look upon the greater Circle these two Circles shall appear equal to both Eyes Perhaps it may be objected That the Comparison is not fair between both Appearances For the Proposition supposes the naked Eye at the Station of the Object-Glass But this Experiment sets the naked Eye Distant from the Object-Glass the whole length of the Telescope This would be a material Objection against this Method of Tryal were not the Distance of the two Circles from the Eyes vastly greater than the length of the Telescope so that the Telescopes length may not bear any sensible Proportion thereto And such we suppose it in this Experiment by advertising that this Distance is to be so great that the Distance between the Glasses may be no longer than for viewing a Distant Object viz. the just Aggregate of the Focal lengths of the Glasses that is 144 + 3 = 147 Inches that is ye + eh = yh I shall now give an Example of a Calculation according to this Proposition Wherefore in Tab. 35. f. 4. let us take the Moon ABC for our Distant Object and let us suppose its Diameter to subtend an Arch of a great Circle of Heaven of 30 ' Minutes Let the Ray a y d proceed from its upper Limb b y e from its Centre c y f from its lower Limb. These cross in the Vertex y or middle Point of the Object-Glass x y z making the Angle f y d = a y e equal to 30 Minutes Let the Focal length of the Object-Glass e y be given twelve Feet = 144 Inches or 144,00 Parts And the Focus of the Eye-Glass h e be given three Inches or 3,00 such Parts Let the Distinct Base wherein the Image of the Moon is Projected by the Object-Glass be f e d and draw f h d h. It is shewn before that the Angle g o h is equal to the Angle f h e. Wherefore in the Right-angled Triangle f e y we have e y = 144,00 and the Angle f y e = 15 ' to find f e = 0,63 Then in the Right-angled Triangle f e h we have h e = 3,00 and f e = 0 63 to find the Angle f h e = 11° 51 ' 40 Wherefore the Semidiameter of the Moon which by the naked Eye would be seen under the Angle of 15 ' Minutes is seen through this Telescope under an Angle of 11° 51 ' 40 Let us now enquire whether the Object appearing under an Angle of 15° Minutes and being afterwards made to appear under an Angle of 11° 51 ' 40 doth not thereby appear 48 times bigger than naturally for so much by what foregoes does this Glass Magnifie And for shewing this let us imagine f e increased 48 times its length 0 63 And then inquire what Angle f y e would be Wherefore f e is now supposed = 30 24 = 48 times 0. 63 Then in the Right-angled Triangle f e y we have f e = 30 24 and e y = 144,00 to find the Angle f y e = 11° 51 ' 40 Which shews that the Semidiameter of the Moon being made by the Glass to appear under an Angle of 11° 51 ' 40 is seen by the Eye as big as if the Semidiameter of the Moon it self were really increased 48 times and viewed by the naked Eye Which is the proposed Design of this Calculation Corollary 1. From hence it follows That the same Object-Glass being at one time combined with an Eye-Glass whose Focus is 1. And at another time with an Eye-Glass whose Focus is 2. The first Telescope Magnifies twice as much as the latter Corollary 2. Supposing two Telescopes of different lengths If the Focus of the Eye-Glass of the shorter bears the same Proportion to the Focus of its Object-Glass as the Focus of the Eye-Glass of the longer bears to its Object-Glass These two Telescopes Magnifie equally And hereupon perhaps it may be enquired To what end then is all the Pains and Trouble in forming and managing Telescopes of 30. 40. 50. 100. 200. 300 c. Feet When Objects may be Magnified as much by smaller Object-Glasses or Object-Glasses of shorter Focal lengths combined with Proportional Eye-Glases I answer First That Object-Glasses of a shorter Focus will not bear proportionably Eye-Glasses of such short Foci without coloring the Object and rendring it dark as Object-Glasses of longer Foci For instance let us suppose that an excellent Object-Glass of twelve Foot Focus will receive an Eye-Glass of no shorter a Focus than three Inches with Clearness and Distinctness I say an Object Glass of 24 Foot Focus of the same Perfection shall receive an Eye-Glass of less than six Inches Focus with equal Clearness and Distinctness And perhaps it may take an Eye-Glass of five or four Inches Focus And then an Object-Glass of twelve Foot with an Eye-Glass of three Inches Magnifies but 48 times But an Object-Glass of 24 Foot with an Eye-Glass of four Inches Magnifies 72 times viz. ⅓ more than the former which is a great Difference and of vast Advantage when it may be obtained with the same Clearness and Distinctness I

confess the longest Telescopes do generally render the Objects more Dark and Obscure yet when shorter Glasses have proportionably as short Eye-Glasses and as close Apertures they are more Obscure than the longer Telescopes I answer Secondly That the Image of the Moon or other Object in the Distinct Base of an Object-Glass of 24 Foot is twice as long as the Image in the Distinct Base of an Object-Glass of twelve Foot And consequently we shall not wonder that the Picture in the former should be much more Distinct and Perfect than in the latter As 't is much more easie to represent every Feature and Line of a Face in a large Piece than in a small Piece of Miniature Corollary 3. And if the Object-Glass be formed on a less Sphere than the Eye-Glass as suppose the Object-Glass formed on a Sphere of six Inches Radius and the Eye-Glass on a Sphere of twelve Inches Radius hereby the Appearance of the Object shall be Diminished And the Appearance through the Glass shall be to the naked Appearance as six to twelve or ½ the Natural Appearance Scholium From hence it is manifest how requisite it is in relating any Phaenomena observed by the Telescope or even by the Microscope to mention not only the length of the Tube in general But to specifie the particular Focus of the Eye-Glass as well as of the Object-Glass as also the Aperture of the Object-Glass For by this means they that intend to observe the same Phaenomena may understand how to adapt their Telescopes proper for the Observation This the Learned and Ingenious Monsieur Hugens in his Systema Saturnium puts down exactly pag. 4. Where also we find this Passage Illud in Dioptricis Nostris Demonstratum invenietur Speciei per Tubum visae ad eam quae Nudo Oculo percipitur hane secundum Diametrum esse Rationem quae Distantiae Foci in Exteriori vitro Objectivo Scilicet ad illam quae in Interiori sive Oculari vitro est Foci Distantiam But hitherto we are so unhappy as to want that excellent Persons Dioptricks In the mean time let that which I have given in the foregoing Prop. LIII serve till a better be offered PROP. LIV. PROBL. To Determine the Angle received by a Telescope of the foregoing Combination The Rule is as the Distance between the Object-Glass and Eye-Glass To half the Breadth of the Eye-Glass So Radius To the Tangent of half the Angle received Tab. 25. f. 2. The Distance of the Glasses is h y. Let half the Breadth of the Eye-Glass be g h. Then as h y To g h So Radius To the Tangent of the Angle g y h which is half the Angle g y l the Angle received That is the Eye at o shall perceive no more of the Object than subtends this Angle before the Object-Glass Scholium 1. But if the Eye Approach nigher to or recede further from the Eye-Glass g h l Tab. 35. f. 1. than its Focus at o it shall perceive a lesser Area of the Object though what it sees shall be as Distinct as at o. For let us suppose the Pupil of the Eye at m The Rays g o l o do not enter the Eye and consequently the Points in the Object answerable to f d in the Distinct Base shall not be visible The same may be conceived if the Eye recede farther from the Eye-Glass than o because all the Rays from the several Points in the Object are mixt together and intersect at o in the Focus of the Eye-Glass and thence flowing forward they separate and Diverge But then the Eye at m receives the Rays that do enter it Parallel or at least a very little Diverging and consequently the Vision is Distinct. Scholium 2. From hence also 't is manifest that the Angle received or Visible Area of the Object is not increased or diminished by the greater or lesser Aperture of the Object-Glass For the Angle g y l continues the same though the Object-Glass were all covered to the very middle Point y. All that is effected by this greater or lesser Aperture is the more Bright or Obscure Appea●ance of the Object But of this more fully in the next Proposition PROP. LV. Concerning the Apertures of Object Glasses By the Aperture of a Glass I mean that part of the Glass which is left open and uncovered And this ought to be various according as we would have more or less Light admitted It also varies according to the various Focal lengths of the Object-Glasses For a ten Foot Object-Glass shall bear a greater Aperture than an Object-Glass of one Foot and a twenty Foot Glass yet greater than a ten Foot Glass But at what Rate or Proportion the Apertures of Glasses alter in respect of their lengths is not yet well setled Monsieur Auzout Phil. Transact N. 4. P. 55. Tells us that he finds That the Apertures which Glasses can bear with Distinctness are in about a Subduplicate Ratio to their lengths Or as the Square Roots of their lengths Whereof he intends to give the Reason and Demonstration in his Dioptrica which we yet want But this Ingenious Person should have told us when he speaks of the Apertures of Glasses whether he designs them for Objects on the Earth or in the Heavens And if in this latter whether for the Moon Mars Iupiter or Venus For each of these Objects will require a different Aperture of the same Glass Because the Strength of their Light is different For to view Venus there is requisite a much smaller Aperture than to view the Moon Saturn or Iupiter However till some better Rule can be found for settling the Apertures of Object-Glasses which at present I shall not pretend to I shall here Present you with Mr. Auzout's Table as 't is to be found in the fore-cited Philosophical Transaction Numb 4. Noting only that his Feet are Parisian Feet which is to the London Foot as 1068 to 1000 and each Inch which is the 112 part of his Foot is subdivided into twelve Lines For it had not been worth our Pains to have reduced the whole Table to our English Measure Vid. Tab. 36. A TABLE of the Apertures of Obiect-Glasses The Points put to some of these Numbers denote Fractions Length of Glasses For Excellent ones For good ones For ordinary ones Feet Inchs Inch. Lines Inch. Lines Inch. Lines 4 4 4 3 6 5 5 4 9 7 6 5 0 8 7 6 1 6 9 8 7 2 0 11 10 8 2 6 1 0 11 9 3 0 1 1 1 0 10 3 0 1 2 1 1 11 4 0 1 4 1 2 1 0 4 6 1 5 1 3 1 5 0 1 6 1 4 1 1. 6 1 7 1 5 1 2 7 1 9 1 6 1 3 8 1 10 1 8 1 4 9 1 11. 1 9 1 5 10 2 1 1 10 1 6 12 2 4 2 0 1 8 14 2 6 2 2 1 9. 16 2 8 2 4 1 11. 18 2 10 2 6 2 1 20 3 0 2