fince, in whatever Part of the World it is used, the Longitude of that Place will be hereby discovered with the utmoft Eafe and Certainty.In fhort, from the Nature of the Thing, it is moft evident, that no aftronomical Obfervations can be made with Eafe and Exactnefs by any other Means than this, which will be fufficient to recommend it to all the Studious in natural Science, as an Object of the greatest Curiofity and Utility to Mankind. Having thus given you a particular Account of all the ufeful Conftructions of optical Inftruments, I fhall endeavour to prepare you, at the next Opportunity, for perceiving the infinite Wisdom in the Conftruction of the Organ of Sight, or Vision, in the. natural Mechanifm of the Eye, by a few previous Speculations on the Nature and Effects of fingle Glaffes or Lenfes.

DIALOGUE XVII.

On the NATURE and USES of SINGLE LENSES, both Convex and Concave, applied as READING-GLASSES, VISUAL-GLASSES, and BURNING-GLASSES.

Euphrofyne.

Τ gives me the greatest Pleasure to find we are approaching towards an Enquiry into the natural Conftitution and Mechanism of the Eye, which you propose to explain to me, by a Diffection of the fame, and a particular Account in what Manner every Part is conducive to fo noble an End :--- -But you tell me, I muft be previously acquainted with the Ufe of fingle Glafies, the better to comprehend the fame; and accordingly I fee you have a great Variety of convex and concave Lenfes, Spectacles, &c. fpread before me on the Table.

Cleon. I have provided fuch an Affortment only as will be neceffary for you to know the Ufes of, as Readingglaffes, or fuch as affift the Sight by a fingle Application of them to the Eye.But here I do not fuppofe

you

you are ignorant of the Nature of a convex Glass in general, or of its Ufes in the Construction of optical Inftruments, which I have exemplified to you in fo many Cafes.———You very well know, that if an Object be placed on one Side of fuch a Lens, at more than its focal Distance from it, the Rays, proceeding from every Point, diverging upon the Glafs, will be retracted through it, converging to fo many Points on the other Side, which form the Image thereof.You have also been taught, that when an Object is placed juft at the focal Distance of the Lens, the Rays will then be refracted parallel to each other, and thereby fitted to produce diftinct Vision of fuch an Object: This you had an Inftance of in those very fmall Lenses which are used in fingle Microfcopes:

But there is one Cafe yet remaining, in which both convex and concave Lenfes become extremely useful to Mankind, which has not yet been explained: And that is, when the Object is placed between the focal Point and the Glafs itself.

Euphrof. This Cafe is indeed new to me, and I fhould be very much pleased to know in what Manner thefe Glaffes are rendered ferviceable to us in this Refpect.. When an Image is formed of an Object, by a Lens, I can easily conceive how that Object may be contemplated in its Image; alfo, I know, that when an Object is placed in the Focus of a Lens, it becomes in itself thereby visible; but when it is placed nearer to the Glafs than its Focus, I have no Idea which Way the Object becomes magnified to the Sight.

Cleon. Yet this you must understand before you can be properly faid to know the Theory, or Rationale of a common Reading-glafs, which, you know by Experience, has a magnifying Power, and may be as properly called a Megalafcope for magnifying large Objects, as very fmall Lenfes are called Microfcopes for magnifying fmall ones. Thus, the Page of a fmall printed Book may, in itfelf, be confidered as a large Object, while the Words and Letters are too finall to be easily read by a good Eye, and not at all by one whofe Sight is rendered in any Degree deficient by Age, or other Accidents: But when a large Convex Glafs, in this Cafe, is applied between the Book and the Eye, the

Page

Page becomes greatly dilated to the View, and the fmall Characters appear as a large and eafily legible Print.

Euphrof. All this I know very well, as I am oftentimes obliged, in Cafe of fuch very fmall Prints, to make Ufe of a Reading-glafs myfelf, but how this magnifying Power is produced, I am still at a Lofs to apprehend, and muft beg of you to explain.

Cleon. This I will do in the beft Manner I can; but it must be by a Diagram, as no real Image of an Object is, in this Cafe, formed any where but in the Eye: To this End, therefore, let ECD be fuch a Readingglass, or Convex Lens, and let F be the Focus in the Axis FN; on C the Center of the Lens, with the Diftance CF, describe the Arch of a Circle QF P, draw the right Lines QC and PC, making any Angle with the Axis FC on either Side; then, in the Line QC, let any Point, A, be taken, and from that Point let the Lines A E, and AD be drawn, to reprefent two diverging Rays iffuing from that Point on the Convex Glafs. Now, you know, it is the Property of a Convex Lens to bring diverging Rays, which fall upon it, nearer together after Refraction, and therefore the Rays A D and A E, instead of pursuing their firft Directions to I and L, will, by the Lens, be refracted nearer together, viz. into the Direction DK and EM:If then these Lines D K and EM, as they are inclined to each other, be continued out, they will meet in a Point G in the Line QC. All this, I fuppofe, is very plain from the Figure, my Euphrofyne.

Euphrof. So very plain, that it can admit of no farther Explication. But what am I to infer from thence?

Cleon. This much, that the Point A, being not far from the focal Distance Q, will caufe the diverging Rays AI and AL, after Refraction into D K and EM, to be not much different from parallel Rays, and therefore will produce diftin&t Vifion of the faid Point A: — But then the apparent Place of the Point A will be much altered; for fince the two refracted Parts DK and EM enter the Eye, as if they came from the Point G, they will there reprefent the Point A; fo that the apparent Distance of that Point will be much greater than the real Distance C A. This, I fuppofe, you can likewife fee from the Diagram?

Euphrof. Nothing is more evident; and at the fame Time I obferve, from your Drawing, that on the other Side of the Axis the Rays proceeding from the Point B will, after Refraction, reprefent that Point at H.

Cleon. Your Inference is juft; and I fee, by that, you have a clear Idea in what Manner the Points A and B are removed to the Distances G and H refpectively from the Glafs; and that therefore all the Space contained between A and B will be expanded into the Length, or Space contained between G and H; and confequently any Objects contained between A and B will be enlarged in Appearance, in the Proportion of the Distance between A B to the Distance between GH, that is, in the Ratio of AC to GC: and confequently, if the Page of a fmall printed Book be placed at the Diftance of AC from the Glafs, and parallel to it, the Words, or Print of that Page, will appear enlarged in the fame Proportion as GC is larger than A C, with respect to their Diame-ters or lineal Dimenfions: But the whole Area, or Surface of the Page, will be enlarged or magnified in Proportion as the Square of A C is to the Square of G C.

Euphrof. This I fee very plainly illuftrated by the Words, God fave the King, in fmall Print between A B, and in much larger Characters between G H. Pray, Cleonicus, is there any general Rule to be observed, for holding the Reading-glafs, with Respect to the Eye and the Print?

Cleon. There is, my Euphrofyne:- -For by the Mathematical Theory we learn this Rule, the Distance of the Object AC and that of its magnified Appearance GC, is always in the Proportion of the Distance of the Object from the Focus AQ, to the Distance QC of that Focus from the Glafs; and, confequently, from hence you will obferve, the lefs A Qis, or the nearer the Object is held to the Focus of the Glafs, the more it will be magnified; and fince the Rays paffing through the Glafs differ but little from parallel Rays, it will give a diftinct View of the Object fo magnified; and by moving the Glass one Way or the other ever fo little, you will immediately find the Pofition of the Object, and the Glafs where the Field of View and magnifying Power will beft fuit the Eye. But this is a Point which we are directed to by

Nature,

Nature, without any Rules of Art.
Rules of Art. And this, I think,
is as much as I can say with regard to the Nature and
Use of a READING-GLASS.

Euphrof. Is there nothing particular with refpect to the Size, or focal Length of thofe Glaffes, by which we may be directed in the Choice of them?

Cleon. Yes, moft certainly; for if it be proposed to read with both the Eyes, then, in fuch a Cafe, the Glafs must be fufficiently large to transmit the Rays from the Object to both the Eyes, and, confequently, ought not to be lefs than three Inches in Diameter: -The elliptic Form is alfo preferable to a round one, in a Reading-glafs and, laftly, the longer the focal Distance, the lefs irksome is the Effect to the Eye. But in this Refpect, the Eye must be confulted, and the magnifying Power of the Glafs must be fuch as is required.

:

Euphrof. What is the Difference between thefe large Reading-glaffes and Spectacles, or Visual Glaffes, as you

call them.

Cleon. The Nature and Effect of both are much the fame, only the Vifual Glaffes, being difpofed in a proper Frame, may be, in different Ways, applied to the Eye, without being held in the Hand; and, therefore, leaving both Hands at Liberty, they are much better fuited to all Occafions of Reading, Writing, Working, &c. than a manual Glafs can be.- Befides, the

Vision is more diftinct and perfect through two Glaffes, than by one alone; because the Axis of each Glafs, when they are properly fixed in their Frames, may be made to coincide with the Axis of each Eye respectively; and therefore the Rays of every Visual Pencil will be much more naturally refracted to the Eye, than they can be through a fingle Glafs, where only the collateral Rays of fuch Pencils can enter the Eye, by which the Vifion can be neither fo eafy or perfect as in the former Cafe.

Euphrof. But what is the Reafon of this black Circle or Ring of Horn about the Glafs?

Gleon. There is more Reafon for this than many Perfons are aware of: the Pupil of the Eye is but small, and no more Light can be of Service to Vifion, than what VOL. II.

Y

enters