not more of those curious Perfons than we find; so very few there are, that I never faw but one of those Binocular Reflectors, yet, in any Gentleman's Collection of aptical Instruments, and yet there is nothing in the Price that is fo very extraordinary, or difficult in its Ufe, that might deter People from having them. Especially as to the Refracting Binoculars, whofe Expence and Use are both very reasonable and easy. Of these there were no less than three or four of different and very curious Construction in the Mufæum of his Grace the late Duke of Argyle.

Euphrof. And was I a Duchefs, I would have as many, and every Inftrument of every Form and Construction that could afford me any different Pleasure and Inftruction; and I fhould always look upon those Inftruments as the principal Furniture of the choiceft Apartments of my House.

Cleon. There is yet another optical Inftrument, which, at our next future Leifure, I shall defcribe to you, and though it has no magnifying Power for diftant Objects, is not without a Variety of Ufes adapted to the Amufement of Ladies and Gentlemen, and with which, I dare fay, you will be very well pleafed.

DIALOGUE XIII.

The DESCRIPTION and USE of an OPTICAL INSTRUMENT for measuring the ANGLE of VISION, the apparent MAGNITUDES, and DISTANCES of Objects; for viewing perspective PRINTS, PICTURES, Intaglio's, &c.

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Cleonicus.

Shall now prefent you, my Euphrofyne, with a small optical Inftrument that is not only defigned for Amusement, but many confiderable Ufes.

Euphrof. It makes but a finall Appearance, 'tis true; but the Value and Ufes of Things, in general, depend

very little on their Bulk.-Pray, what are the Peculiarities of this Inftrument?

Cleon. I fhall relate them to you in Order, and exemplify them by Experiment: One Thing, however, I fhall premife with respect to the Nature and Conftruction thereof, as it is a Property quite peculiar to this Inftrument, and that is this, viz. that it gives you a clear View of difiant Objects, without magnifying them at all, and, at the fame Time, it prefents you with a magnified View of Obj.Ets near at Hand, by a proper Change of Glaffes.

Euphrof. Pray, what, and how many Glaffes have you

in this Inftrument?

Clean. There are effentially no more than two required, and those both of the fame Form, or Figure, and confequently of the fame focal Distance:And, as to the Position, they are placed, as you fee, one at each End of the Inftrument, and from this Conftruction you will easily understand the Nature of the Inftrument, from what I have formerly faid of a Telescope with two Glaffes; for in fuch a one, you remember, I told you that the magnifying Power was in Proportion of the focal Diftance of the Object-glass to the focal Distance of the Eye-glafs. Now, in this Inftrument one Glass is to be confidered as the Object-glafs, by which an Image is formed; the other, as an Eye-glafs, by which it is viewed; but fince thefe Glaffes have an equal focal Distance, the Image will be equally diftant from either Glafs, and confequently there can be no magnifying Power at all with refpect to diftant Objects: For the Image will appear under the fame Angle to one Eye applied to the Glafs, as the Object does to the other naked Eye, and therefore they muft appear equal, as you will find by Experiment.

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Euphrof. Pray, let me try that Experiment.] will place myself on this Side of the Room, and look on the Safh-window on the other Side, and see how the Quarrels appear, in the Manner you formerly directed me by viewing it with one Eye applied to the Glafs, and the other without it. And now I perceive the Truth of all you fay,each Quarrel in the Window is of the fame Bignefs in the Inftrument as to the naked Eye, and, by properly removing it, I make the whole

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Frame

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Frame in the Image exactly coincide with the Appearance of the Win.ow itself to the naked Eye: Which, therefore, fully proves that the Image and the Objećt are equal to each other.

Cleon. You will farther obferve, that in the Conftruction of this Inftrum nt there is a Screw and Cell in the middle Part, for another Glafs; which is to be of the fame focal Distance with the other Two, whose Ufe is to render the Field of View more perfect towards the extreme Part; by which Means the Eye may be applied nearer, and view the Object to much greater Advantage. -You will fatisfy yourself by the Experiment: For I have now put in the third Glafs.

Euphrof. It is really fact: The Images of all Objects that I view, appear in an enlarged, and a much more perfect Field, even to the extreme Circumference; this Glafs is a great Addition to the Diftinctnefs and Perfection of the Inftrument.. But it is fomething

of a Paradox to me, that a Glafs, which, in itself, has fo confiderable a magnifying Power, fhould yet, when placed in the Inftrument, appear to have no Effect of that Kind.

Cleon. Optical Glaffes, applied in different Circumftances, will have different Effects; it's Difpofition in the Middle of the Inftrument gives it no Power of magnifying, but only of perfecting the Field of View.

Euphrof. The Image I obferve is inverted; but that, I prefume, is no Obftruction to the Ufes you would make of this Inftrument :-But, as it neither magnifies nor diminishes, I fhall be glad to know wherein the Ufes of it confift.

Cleon. That I fhall now particularize to you. It is therefore to be obferved, that fince the Object and the Image appear under the fame vifual Angle, that Angle may be eafily eftimated, or measured by this Inftrument, by adapting a MICROMETER to the middle Part, where the Image is formed in the common Focus of both the Glaffes, which Micrometer may be made of many different Forms, viz. (1.) With a Screw having very fine Threads, or (2.) by Means of parallel or equidistant Lines drawn on a circular Piece of plain Glafs very near to each other; or, (3.) by two Hairs moving parallel to each

other

other in a small brafs Frame placed in the middle Part of the Inftrument.

Euphrof. How, by Means of these Micrometers, you measure a visual Angle, be pleased in the next Place to explain to me; for, as yet, I am not acquainted with these Inftruments of Measure.

Cleon. A MICROMETER is an Inftrument of great Ule in the nicer Computations of Aftronomy, which concerns the Magnitudes and Distances of the heavenly Bodies: But, in the Ufe of this Inftrument, great Exactnefs is not required; and therefore a Micrometer made of a Screw will answer this general Purpose as well as any, and will be more fimple and leaft expenfive of all others; and a Screw that has forty Threads in an Inch will be fufficient for this Purpose. Then, if the focal Distance of the Glaffes be one Inch, the Angle, which is fubtended by the Interval between two of those Threads, will be 1° 26', and two will fubtend an Angle of 2° 52′, and 3 Threads will fubtend an Angle of 4° 18', and fo on; the Angles and their Subtenfes being very nearly proportional, when very small, and therefore, by obferving how many of thofe Threads of the Screws the Image of any Object occupies, it will be known from thence what the Quantity of the optic Angle is under which it And if a Screw has a greater Number of Threads to an Inch, as fuppofe 60 or 80, the Accuracy of the Inftrument in measuring the optic Angle will be in fuch Proportion greater.- But though this Uie of the Inftrument may the leaft concern you, yet it may be oftentimes of great Importance to those who are concerned in measuring the Angle under which diftant Objects appear, which are generally very small, in order to form a Calculation, or an Idea of their Diftance, by previously knowing the Dimenfions of the Object, Thus, for Inftance, by knowing the Number of Feet in the Length of the Crofs on the Top of St. Paul's, and obferving, by this Inftrument, what Angle it fubtends to the Eye, a Perfon will immediately find, by the Rules of Trigonometry, what Distance he is from that Object.

appears:

Euphrof. This is an Affair of too mathematical a Nature for me; there are others, I prefume, more adapted to

my Understanding, which may afford me fome Degree of Pleasure and Curiofity.

Cleon. There are, moft certainly; the next I fhall mention is one of them, which is, that by Means of this Inftrument we may eafily judge of the comparative, or apparent Magnitude of Bodies: For when you would compare the apparent Magnitude of any two Objects, you only move the Inftrument in fuch a Manner, as fhall bring the Image in each Object fucceffively upon the Threads of the Screw, and then obferving how many of thofe Threads are occupied by each. Thus, for Example, if the Image of one Object was equal to the Distance of two Threads of the Screw, and another measured three Threads; then their apparent Linear Dimenfions would be in Proportion as 2 to 3, and their Surfaces in Proportion to the Squares of thofe Numbers, viz. 4 to 9, and their Solidities as the Cubes, or as 8 to 27: And thus the comparative apparent Magnitude of all diftant Bodies may be eafily estimated.

Euphrof. This, I allow, is a very pretty and inftructive Ufe of the Inftrument, as nothing is more common than to hear People afk, How large do fuch or fuch Objects appear? whereas, it is impoffible to give any Answer to fuch Queftions, without a Method of comparing their Magnitude with that of fome other Objects that we know, which, by what you have now faid, I find is very easy to be done by fuch a Micrometer.

Cleon. Another Ufe of this Inftrument, equally curious and amufing, is, to measure the Distance of any Object without any Skill in Geometry, or the least Degree of Difficulty: Thus fuppofe you observe the apparent Image of any Object upon the Threads of the Screw, then, if you walk fo far backward 'till the Image of the fame Object occupies but half the Number of Threads, or if you go forward 'till the faid Image measures twice the Number as at firft, in either Cafe you walk just fo far as is equal to the Distance of the Object from your firft Station; for you well know, the apparent Magnitude of Bodies increafe or decrease very nearly with their Diftances inverfely, or, that at twice the Distance, they ap pear twice as fmall; and, at half the Diftance, they appar twice as large.

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