Mathematical Instruments
Suppl. Ch. V.

# Of Perspective Glasses, and Refracting Telescopes.

I. The least Kind of perspective Glasses, are about 4, 5, or 6 Inches long, having only two Lenses within the Tube; the Object Lens or Glass, being a double Convex, or Plano-Convex, being a Segment of a greater Sphere: and the Eye-Glass, a double Concave, being the Segment of a lesser Sphere, placed before the Focus of the Object Lens, by the Distance of the virtual Focus of the concave one.

The Objects appear through these Perspective Glasses distinct, erect, and magnified in Diameter, in the Ratio of the focal Distance of the Object-Glass, to the focal Distance of the Eye-Glass: and for purblind Persons to see the Object distinctly, the Eye-Glass must be brought nearer to the Object-Glass. There are few of these Perspective Glasses now made that exceed 18 Inches long, because you see through them a part of the Object so much the lesser, as it’s Diameter is the more magnified. Formerly, indeed, there were Telescopes made with only a double convex Object-Glass, and a concave Eye-Glass, from 18 Inches long, to about 3 Feet; which was the Length of Galileo’s best Telescope, so famous for the great Discoveries he made with it. Hevelius says, a good Telescope of this sort may be had when the double convex Object-Glass is 4 Danzick Feet in Diameter, and the double concave Eye-Glass in Diameter is 4$$\frac{1}{2}$$ Inches. So likewise will it be, when the former is about 5, 8, 10, or 12 Feet, and the latter about 5$$\frac{1}{2}$$ Inches. But, as I said before, the Field which these Telescopes take in at one View, is too narrow when they exceed 3 or 4 Feet in Length; they have long since been disused, excepting the Perspectives of 4 or 5 Inches in Length; where Mr Huygens recommends the Ratio of the Semi-diameter of the Object-Glass, to that of the Eye-Glass, to be quadruple, or not more than double.

II. There are Perspectives from 18 Inches, to 4 or 5 Feet in Length, chiefly for viewing Objects at Sea or Land, consisting of four convex Lenses or Glasses, viz. an Object-Lens A, and three equal Eye-Lenses, C, D, E; so placed in the common Axis AF, that B is the common Focus of the Object-Glass A, and the Eye-Glass C; the Eye-Glass D is so far from C, as that the Distance CD is equal to twice the focal Distance CB of the Eye-Glass C; and the Eye-Glass E is as much distant from D as C is from D; and the Eye must be placed beyond this last Eye-Glass E, by the Distance BC.

By these four Lenses, and such a Disposition of them, very remote Objects will be distinctly perceived, erect, and magnified in the Proportion of AB, the focal Distance of the Object-Lens, to BC the focal Distance of either of the equal Eye-Lenses; there is a small Annulus, or Ring, placed within the Tube of this Perspective, either at the common Focus of the two Lenses D and E, or at B, the common Focus of the Object-Lens A, and the Eye-Lens C next to it; by which contrivance is cut off those irregular Rays which are not collected near enough to the two common Foci of the Lenses, and so are not by means of the succeeding Lenses sent parallel to the Eye: also the Colours near the Margins of the Lenses are taken away, which otherwise cannot well be avoided.

This is reckoned one of the best Compositions of the four Lenses of a Perspective, and is thought to have been invented by Campani, a famous practical Optician, who lived at Rome many Years ago. There are also Telescopes to view the Celestial Bodies through of this sort, having four Glasses, and of greater Lengths. But a Telescope of two Glasses only, is sufficient for this purpose.

There may be other Compositions of other Species of Lenses than all four double convex ones of equal Convexities, and three of them equal, that may do as well as these; and the best way to find them out is, by Trial: for Example, Suppose the Object-Glass a Plano-Convex, and the three Eye-Lenses equal Plano-Convex.

There have been also Perspectives with three Lenses, which invert the Object, and make it appear coloured. But these are not much esteemed.

There are also Perspectives and Telescopes, made with six Glasses, shewing Objects very distinct, enlightened and magnified. Such a Telescope may consist of five equal Eye-Lenses of equal Convexities, placed in the Axis of the Tube equally distant from each other, by twice the focal Distance of either of them; and the outermost: Eye-Lens next to the double convex Object-Lens is distant from the Object-Lens by the Sum of the focal Distances of the Object-Lens, and one of the Eye-Lenses; for by this Disposition of the Lenses, the Rays that come from a very remote Object that fall upon the Object-Lens, being as it were parallel, will become again parallel after their Refraction by the fifth Eye-Glass; so they will again, after their Refraction by the third Eye-Lens, and: so will they once more after their Refraction by the first Eye-Lens: therefore since the Rays coming from the Object fall parallel upon the Eye, the Object will be distinctly seem. I am not certain whether these six Glass Telescopes are actually made with such Lenses, so disposed, as I have said; for I have not seen their Structure; but I know that according to the Theory, at least, such a Telescope may be so made, although, perhaps, there may be Inconveniences in this Method not to be discovered, unless by actual Practice: for in the Construction of Telescopes, though the Theory and Practice should always attend, and support each other; yet the Practice most conveniently takes the Lead, is the best Guide, and most to be depended upon.

Traber, in his Opticks says, That Anthony Maria de Reita, a Roman Optician, made a Tube with five Convex-Lenses, which was reported to be an exceeding good one: he likewise mentions one Fontana, another Roman Artist of this Kind, who made a Tube with 8 Convex-Glasses, clearly exhibiting the most minute Object, at the Distance of a German Mile, which was bought by Cardinal Nepos, for 800 Crowns, and presented by him to the Great Duke of Florence; but, says he, by reason of the strong and too violent Refraction, the Objects viewed through it appeared coloured, so that the Tube could not be much used without hurting the Eyes. He, moreover, says, that he was told one Eustachio, a Neapolitan, made a Telescope having 19 Convex-Lenses, in Tubes altogether of 19 Cubits long, that would shew the Pictures of Objects less coloured, by reason of the Interposition of some of the nicer Glances (neither magnifying, nor diminishing the Objects), which took away the Colourings of the Objects. Hence (says he) we may see what a great Mystery there is in the apt Composition of Lenses.

But how true this is, what are their particular Constructions and Effects, I know not: for unless the Composition of the Glass, wherewith the Lenses are made, be exceeding fine and pure, free from Veins and Spots, and the Lenses be most exquisitely figured, and polished, and besides, very thin, such a multiplicity of them must hinder the Passage of so many of the Rays that come from the Object to the Eye, as will cause a very obscure View of the Object.

It is as easy in Theory to contrive a Disposition of the Lenses for an 8, 10, or 12, &c. Glass-Telescope; as for one of four Lenses. It is but taking as many Equal Eye-Lenses, except 1, as the Telescope is to have Glasses, and placing them in the Axis of the Object-Lens (being a double Segment of a greater Sphere, which is in all Cases supposed), at equal Distances from one another, each equal to twice the focal Distance of either: the last Eye-Lens next to the Object-Lens, being so far from the Object-Lens as is the Sum of the focal Distances of the Object and Eye-Lens.

III. The Astronomical Telescope, viz. one through which the Heavenly Bodies are viewed, consists of but two double Convex-Lenses, the Object-Lens and the Eye-Lens; these shew the Object inverted, and magnified in the Ratio of the focal Distance of the Object-Lens to that of the Eye-Lens; the focal Distance of the Object-Lens being always much greater than that of the Eye-Lens; these two Lenses being so placed in the common Axis as that their Distance is equal to the Sum of their focal Distances, or, which is the same thing, that their Foci unite in one Point.

Telescopes have been made with other Species of Lenses, besides double convex ones, and Honoratus Fabri in his Synopsis Optica, says, That Eustachius Divini, a famous Roman Optick-Glass maker, made the Eye-Lens of his Telefcopes to consist of two equal, narrow Plano-Convex-Lenses, touching one another’s Convexities in the Axis, and so placed, that the Centre of that Plano-Convex-Lens next to the Object-Lens, was in the Focus of the Object-Lens; by which means the Rays that came parallel from the Object, would fall parallel upon the Eye: and, says Fabri, some of the Advantages of this Telescope are, that the Colours of the Rain-Bow are excluded from it. The Angle of Sight is augmented. A greater Field is taken in at one View. The Object appears more lively and bright. Lastly, He would have Water included in the Vacuity between the Convexities of the two touching Plano-Convex Eye-Lenses. See a more particular Account of all this in the 46th Proposition of Fabri’s Opticks.

If two equal Lenses be joined together so as to touch, the Focus will be removed to a Distance double to that of one of them. Dechales takes Notice, that an Object Glass of 2$$\frac{1}{4}$$ Feet focal Distance, fits an Eye-Glass of 1$$\frac{1}{2}$$ Inch. Eustachius Divini joins an Object-Glass of 8 Feet, to an Eye-Glass of 4 Inches. Mr Huygens’s Telescope, by which he first observed the true Phases of Saturn, and one of his Satellites, consisted of an Object-Glass of 12 Feet focal Distance, and an Eye-Glass a little letter than 3 Inches. Afterwards he observed the same Phenomena by a Telescope of 23 Feet, with two Eye-Glasses of 1$$\frac{1}{2}$$ Inch Diameter, touching one another, and producing the same Effect as one only, viz. collecting the parallel Rays at about 3 Inches Distance. He likewise observed the same with an Object-Glass of 30 Feet joined to an Eye-Glass of 3$$\frac{3}{10}$$ Inches; and in his Dioptricks gives the following Table for the Construction of Telescopes, though here contracted.

Table for Telescopes
The focal Distance of the Object Lens, or the Length of the Telescope The Diameter of the Aperture of the Object Lens The focal Distance of the ocular lens The Proportion of the magnifying considered as to Diameter
Rhinland Feet Inches, and Decimals Inches, and Decimals
1 0,55 0,61 20
2 0,77 0,85 28
3 0,95 1,05 34
4 1,09 1,20 40
5 1,23 1,35 44
6 1,34 1,47 49
7 1,45 1,60 53
8 1,55 1,71 56
9 1,64 1,80 60
10 1,73 1,90 63
13 1,97 2,17 72
15 2,12 2,33 77
20 2,45 2,70 89
25 2,74 3,01 100
30 3,00 3,30 109
35 3,24 3,56 118
40 3,46 3,81 126
45 3,67 4,04 133
50 3,87 4,26 141
55 4,06 4,47 148
60 4,24 4,66 154
65 4,42 4,86 161
70 4,58 5,04 166
75 4,74 5,21 172
80 4,90 5,39 178
85 5,05 5,56 183
90 5,20 5,72 189
95 5,34 5,87 194
100 5,48 6,03 199

Which Table he thus constructs; he multiplies the Number of Feet in the focal Distance of the Object-Lens by 3000, and the square Root of the Product will give the Diameter of the Aperture in Inches and Decimal Parts: and the same augmented by a tenth Part of itself, will be the focal Distance of the Eye-Lens; and the apparent Breadths of the Objects are as the Diameters of the Apertures.

Because two Telescopes where the Ratio of the focal Distance of the Object-Lens of the one to that of it’s Eye-Lens, is equal to the Ratio of the focal Distance of the Object-Lens of the other to that of it’s Eye-Lens, do equally magnify the same Object; some may be apt to think, that the Trouble of figuring and polishing the Object-Glass of a long Telescope may be spared; and that two such Telescopes are equally good: but in this they are mistaken, for the Object in the short Telescope will appear more confused, dark, and indistinct than in the long one, all things else alike. What doth it avail to magnify an Object very much, if it cannot be seen distinctly; this is all we want, and long Telescopes will always do it best.

Sir Isaac Newton has proved in his Opticks, that the Perfection of Telescopes is impeded by the different Refrangibility of the Rays of Light, and not by the spherical Figure of the Glass, the Diameter of the little Circle or Focus, through which the Rays are scattered by the unequal Refrangibility, being about the 55th Part of the Aperture of an Object-Glass, whose Length was 12 Feet, and Aperture 4 Inches: so that the Error arising from the spherical Figure of the Glass, will be to the Error arising from the different Refrangibility of the Rays, as 1 to 5449, which being so little in comparison to the other, deserves not to be considered. He says also, If the Theory of making Telescopes could at length be fully brought into Practice, yet there would be certain Bounds, beyond which Telescopes could not perform, by reason of the perpetual Tremor of the Air, through which we look, at the Sun or Stars; even though long Telescopes may cause Objects to appear larger and brighter than short ones can do, yet they cannot be so formed, as to take away that confusion of the Rays which arises from the Tremors of the Atmosphere; the only Remedy is, a most serene and quiet Air, such as may, perhaps, be found on the Tops of the highest Mountains, above the grosser Clouds.

Since the first Invention of Telescopes, which is now almost 150 Years ago, there have been many made of all Lengths and Goodnesses, in Italy, England, France, and Germany. Several ingenious Persons having imployed their utmost Care and Pains to procure the best and clearest Glass possible, and used their greatest Skill and Dexterity in figuring and polishing the spherical Lenses. Sir Isaac Newton and Mr Huygens took to this Business, but the former made no great Progress in it, rather for want of Inclination to continue the Pursuit, than Abilities to excel in it, if he had. But Mr Huygens went further, and made very good and long Telescopes of 23, 25, 30, and 123 Feet, which last has been in England many Years; the late Doctors Derbam and Pound, made Observations with it at Wansted in Essex. Hevelius of Dantzick, had a Telescope of 140 Feet; and Eustachius Divini, and Jofeph Campani at Rome (long since deceased), made Telescopes of various Lengths, viz. of 23, 24, 30, 33, 45, 50, 60, 70, Roman Palms; the longest of Campani’s was 150 Roman Palms, and Francis biancbini, the Pope’s domestick Prelate, made Observations with it, in the Year 1725. The Telescopes made by these two Italians have been generally esteemed the best in the World. Cassini too had very good Telescopes, the longed being 136 Feet; and the longest that ever I heard off, is one of Artouquellius’s (see the Philosophical Transactions, Numb. 92, 181.), of 220 Feet. There are very good Telescopes of Mr Petroni’s made in Italy.

Mr Huygens wrote a Treatise about grinding Glasses for Telescopes, wherein he supposes the Glasses to be double Convex ones of equal Convexities, and the focal Distance to be given; then the Radius of the spherical Surface will be found, by taking it in proportion to that focal Distance, as 12 is to 11; the focal Distance being given, the Aperture of the Glass is also given by the Table above. When the Radius of the Convexity of the. Glass is very great, and so the said Convexity cannot be described from a Centre, he finds Points through which that spherical Convex is to pass, by laying off in Effect, upon a Tangent to the Pole of the Convex, some of the first Figures of the several Sines of very small Arches (near one another), taken from the Tables of Sines, &c. and that by means of a Pair of Compasses, and an accurate Diagonal Scale of Inches, subdivided into centesimal Parts; and afterwards taking the same Number of the first Sines of the several correspondent versed Sines of those Arches, and laying them off respectively upon Perpendiculars drawn from the Extremities of those Sines that are upon the Tangent-Line; the Radius of the Tables being reduced by cutting off the Figures to the Inches expressed in the given Radius of the Convexity. Mr Huygens’s Concave-Tool, or Plate, or Dish, in which an Object-Glass is ground, was Copper, or cast Brass fastened upon a cylindrical Stone, with a. Composition of Pitch and Ashes; and these Tools were applied to a turning Lathe, in order to turn the concave Surface exactly spherical; then he polishes the Tool by an Incrustation of Pitch and Emery, and afterwards with blue Hones. In the Choice of Glass, he says that is best which looks some what yellow, red, or green when looked through against the Sky-Light, or laid upon a Sheet of white Paper: that which is perfectly white, though it transmits more Light, is generally fuller of Veins, and is often subject to grow moist in the Air, which in Time destroys it's polish; that such Glass was pretty good wherewith Drinking-Glasses was made. That he ordered Pieces of Glass to be made for his Use, of half an Inch, or three Quarters thick, in the same Manner as they make Looking-Glasses, viz. by cutting off the Top and Bottom of the round Globe they blow up, and by slitting the Side of it, and then by flattening it upon the Hearth of the Furnace, and afterwards it was ground to an equal Thickness by a Stone-Cutter, by the Contrivance wherewith he polishes Marble, or ground to an equal Thickness, and polished a little by a common Glass-Grinder. Then having found how free from Veins this Glass was, by looking very obliquely against a small Light in a Room otherwise dark, or by Reflexion with a Candle in that Room, and made choice of the best for his Purpose; he rounds his Glass-Plate, by first describing upon the two Surfaces two Circles directly over each other, with a Diamond pointed Compass, representing the Circumference of the Object-Glass; and also two more concentrick Arches with a Radius about a tenth or twelfth Part of an Inch bigger. This done, he seperates the longer Part of the Glass from the outward Circle by a red-hot Iron, or by a strong broad Vice, opened exactly to the Thickness of the Glass. The remaining Inequalities may be taken off by a Grind-Stone; then having warmed the Glass and cemented a wooden Handle to it, and in a common deep Tool for Eye-Glasses, with white clear Sand and Water, he ground the Circumference of the Glass exactly true to the innermost Circle on each side of it. The Glass being made in figure of a Cylinder, it is ground upon the Tool with Emery (some use common, clean, fine, white Sand), and made fit for polishing; then it is polished (with a Mixture of fine Tripoly and blue Vitriol wetted with Vinegar), by means of a polishing Machine, which he describes. This is but an imperfect, scanty Account of what Mr Huygens says about the figuring and polishing Glasses, yet it may be sufficient for a Hint to satisfy those who are desirous only to be acquainted how the thing is done in general. See the Account at large at the beginning of the Second Volume of Dr Smith’s Opticks.

As spherical Figures for Optick-Glasses will not collect all the Rays coming from one Point of an Object into another Point or Focus, Des Cartes, and some other of his Geometrical Followers, about the middle of the last Century, recommended hyperbolick and elliptick Glasses, instead of spherical ones; according to which, if the Glasses were figured, these would collect parallel Rays into one Point or Focus, and by that means Telescopes with such Glasses would be better than those with spherical Glasses; this is all fully explained by Des Cartes in his Dioptricks, where he gives an Instrument for describing hyperbolick Glasses; but the Difficulty of the figuring such Glasses deterred some, and the Objection of Sir Isaac Newton (who has given a long Proposition in his Opticks, proving to them that fully understand it, who I believe are but few, that it is not the spherical Figure of the Glasses, but the different Refrangibility of the Rays that hinders the Perfection of Telescopes), discouraged others from trying to make Optick-GIasses of hyperbolick and elliptick Figures. There is certainly great Respect to be paid to Sir Isaac Newton in this Matter, who was, doubtless, the greatest Optician in the World; but yet I do not take his Proof to be absolute Conviction, and that such hyperbolick Glasses would not be better than spherical ones: nay, he himself in his Optical Lectures, Section I. says, that Glasses cannot perform more than twice as well as Spherical ones, though they were formed into Figures, the best that could be devised for that end, and both figured and polished exactly alike. From whence one may certainly infer, Sir Isaac thought that it was possible for some Glasses not spherical, to be as good again as spherical ones; therefore, if hyperbolick Glasses will double the present Perfection of Telescopes, it will be worth while to try to make them. I am sure it may be done by those who have a sufficient Skill in Geometry and Mechanicks.

The Tubes of perspective Glasses are of several Sorts, and made of various Matter. Some are made of stiff Paper glued together, covered with Parchment or Shagreen; some consist of single Tubes, made of light dry Wood; others of several lesser Tubes, sliding one within another. The Glasses are fastened in the Tubes to wooden Rings, yet so as to be easily taken out and put in again, by means of Screws various ways, in order to wipe the Dull: or Moisture oil from them, with which they are more or less continually covered; and this should always be done before the Perspective is used. At the End of everyone of the inward Tubes is fitted a wooden Ring, to hinder the lateral spurious Rays from coming to the Eye, which is found by Experience to be of more Use than could be thought; these Rings are generally furnished with female Screws in those Places whereat the Glasses are fitted. The Perspectives of three or four Feet, which have but one wooden Tube, are most handy, especially, if at each End, instead of Covers that screw and unscrew, they have thin Hiding Pieces of Brass for such.

Short Telescopes may have one single Tube, or several Sliding-Tubes; but if the Telescope is more than 20 Feet in Length, these will be too heavy, and apt to bend when the Telescope is using. When the Telescopes are long, there have been many Contrivances to manage and use them, as may be seen in Hevelius’s Machina Cœlestis; Father Cherubin’s Works; de la Hire’s, and others; all very expensive, complicated, and troublesome; but Mr Huygens happily freed Astronomy from this expensive Lumber, in his Astroscopia Compendiaria Tubi Optici Molimine Liberata, printed at the Hague, in 1684; who placing the Object-Glass upon a long upright Pole, contrived to direct it’s Axis towards any Object, by a fine Silk-Line coming down from the Glass above to the Eye-Glass below; which Invention was successfully practised both by himself and others; particularly the late Dr Pound, and Mr Bradley, with Mr Huygens’s own Object-Glass of 123 Feet focal Distance, presented with it’s Aparatus by Mr Huygens to our Royal Society. His contrivance is this:

ab (Fig. 12.) is the Mast or Pole set upright in an open Place, nearly as long as the Telescope itself, having one side of it made flat almost all it’s whole Length, upon which is nailed two Slips of Wood forming a long Dove-tail Channel; in which is fitted a moveable Board cd. On the Top of the Pole there is placed a Pully a, over which goes an endless Rope, near half an Inch thick, and as long again as the Pole. All way up the Pole, are fixed triangular wooden Steps to go up to the Top upon Occasion, not marked in the Scheme. This Rope serves to draw up or down the moveable Board cd, with a steady easy Motion, and to the Middle of this Board cd, there is fixed a wooden Arm e, extended a Foot from the Pole; and the Middle of another Board ff a Foot and a half long, is laid horizontal, and at right Angles, over the End of that Army and fixed to it; the Object-Glass must be placed upon one End of this cross Board, and the whole must be lifted up and down by the Rope above-mentioned, the Ends of it being tied to the Top and Bottom of the sliding Board cd, and the whole must be counterpoised by a leaden Weight b, of a conical Form, fixed to the Rope on the other Side of the Pully in such a Place, that the Weight may be at the Top when the Object-Glass is at the Bottom, and contrariwise.

The Object-Glass is fixed within a Tin or Brass Tube i, four Inches long, and to the Outside of this Tube is fixed a strait Stick kl, about an Inch thick, at the Distance of 8 or 12 Inches from the End of the Tube; the whole is supported by a Brass Ball m, as big as a Marble, fixed to the said Stick by a short Neck, lodged in a hollow Socket, in which it may play very freely without dropping out; let the Socket and it’s cylindrical Pedestal. be slit into two Leaves, and held together by a Screw passing through both, but not so close as to pinch the Ball. By this means the Object-Glass and the Stick annexed are moveable every way, and to keep them in Equilibrio, an equal Counterpoise of Lead n is fixed to the under Part of the Stick kl, by a stiff Brass Wire l; so that by bending this Wire to and fro, the common Centre of Gravity of the Weight, the Lens and Parts annexed may be easily placed in the Centre of the Brass Ball, and then the Compound will be moveable with the least Touch, and will rest; in any given Position; and in this consists the Judgment of the whole Invention. Having stuck the Pedestal of the Ball and Socket m into a Hole in the End of the cross Board ff, a Silk Line is tied to the Bottom of the Stick kl, annexed to the Object-Glass, whose Length is longer than that of the Telescope, as that the other End of it may be brought to the Eye-Glass; so that when the Object-Glass is raised up to the Top of the Pole by gently drawing this Thread, while you are moving round the Pole, the Object-Glass will readily obey it’s Motion, and be directly opposed to what Star you please. Which could never be performed without placing it in the State of Liberation abovementioned: now since it is absolutely necessary that the Stick kl should be parallel to the Silk Line ln, a short Brass Wire is placed at the Tail of the Stick, and is bent downwards To far ’till the End of it, where the Silk is tied, be as much below the Stick as the Centre of the Ball and Socket is.

The Eye-Glass is included in a short Tube o, joined to a Stick p, which may also have a Ball to rest upon, or rather a little transverse Axis q, and a Weight below the Stick to balance the Tube and Eye-Glass. The Observer takes hold of a Handle r, fixed to the transverse Axis, and holds the lower Stick p, directed towards the upper one kl, by means of the Line that connects them, and winds about a Peg or Spool t, fixed in the lower Stick p; so that by pulling gently to extend the Line, the two Glasses will become parallel to each other; the lower Part of the String comes through a small Hole made with a Wire, at the farther End of the lower Stick p, like the Pin of a Fiddle, shortening or lengthening the String at pleasure, ’till the Distance between the Glasses be brought to a just Length requisite for distinct Vision.

Note, At u are the Pins stuck cross each other to make a Hole for the Line to pass through.

In order to keep the Eye-Glass steady, the Observer, whether standing or setting, should Support his Arms upon a wooden Rest x, with only two Feet, holding the Eye-Glass in one of his Hands, which is a readier and more commodious Way than to fix the Eye-Glass upon a three-footed Rest.

When the Nights are dark, and a Star is to be found in the Telescope, a Lanthorn y is used, which collects the Light into a Stream, either by Transmition through a convex Lens, or by Reflection by a concave Speculum; for by directing this Stream of Light ’till it falls upon the Object-Glass, and makes it visible, it is easy for the Observer to change his place, ’till he finds the Star is covered by the Middle of the Object-Glass, and then to apply his Eye-Glass, which is sooner done than by a Telescope with a long Tube. By Moon-Light the Object-Glass is visible without a Lanthorn. But in viewing the Moon through the Telescope, a Paste-board Umbrella should be put about the Object-Glass, of such a Diameter as to cover a Space in the Sky above twice as broad as the Moon, to intercept that Light from coming to the Eye, which would pass by the Sides of the Object-Glass, and by mixing with the Light that comes through the Telescope, and would dilate the Appearance of the Lights and Shades in the Face of the Moon.

This is the Substance of that excellent Contrivance of Mr Huygens for viewing Objects without long Tubes; those who want the full Account, may consult Mr Huygens’s little Treatise abovementioned, or Dr Smith’s English Translation of it, in the Second Volume of his Opticks.

Of all the Instruments invented by Mankind, there are none that ever exceeded Perspectives and the Telescope, for the vast amusive Pleasure, and real Use afforded by them. How is a Person delighted with clearly viewing distant terrestrial Objects through these Instruments, but faintly, or not at all, appearing with the naked Eye, by reason of their great Distance? And how great is their real Use upon many Occasions for Instance, in discovering the Enemy at Sea or Land, in time of War, to which all the good Consequences derived from such Discovery, are to be attributed? How poor, scanty, obscure, and imperfect, was the State of Astronomy, in it’s physical Part, before the Use of the Telescope, which wiped off from it the Dull of Obscurity, cleared away the Rubbish of Error, and opened and widened the narrow clogged up Passage of Sight, leading into the bright, and delightful Mansions of the heavenly Bodies, so vastly distant placed, and imperfectly and minutely seen by the naked Eye. By this they are distinctly seen with Wonder, and pleasing Amazement, enlarged in Bigness and Distinction; and many things are discovered, which now are become familiar to us, that mortal Eyes never before saw, or Men could ever have thought of. This is the Instrument which has brought us into a perfect Acquaintance with those surprising Parts of the Creation, far separated horn our Globe of Earth, and with which we are allowed no other Commerce but looking and observing, and admiring the delightful Mechanism of the Works of the Creator, thereby giving us the greatest and most respectful Notions of his Wisdom and Power; and the first Inventors of this Instrument, whoever they were, ought always to be highly esteemed, as well as looked upon to be great Promoters of Human Happiness.

But enough of this. Some of the particular Discoveries of the Telescope are these.

I. Spots in the Sun first discovered by Galilæo and Scheiner, a Jesuit, about the Year 1611, of various Shapes, Bignesses, and Durations, they all consist of a black Part in the Middle, of some irregular Figure, encompased with a cloudy Border of a colour less Dark. Hevelius says it sometimes happens, that after the gradual Decay and disappearing of the black Part, it's place seems brighter than the rest of the Sun, and continuing so for two or three Days, but Mr Huygens could not observe this. Scheiner, in his Book called Rofa Ursina, tells you he made 2000 Observations of solar Spots for 20 Years together, and sometimes saw above 50 at once; but betwixt the Years 1650, and 1670, he saw none; sometimes they have been seen with the naked Eye. I myself saw one Spot at London in the middle of November, some Years ago. There are many Observations of solar Spots to be found amongst Authors, such as Galilæo, Scheiner, Hevelius, Huygens, Cassini, and in the Transactions of the Royal Societies of London, Paris, Berlin, in my Opinion not worth particularizing. By means of these Spots it is found the Sun revolves about his Axis in about 25 or 26 Days. 2. Galilæo, with his little Telescope, first discovered the Phases of Venus; he first saw Venus perfectly round, neat, and distinctly terminated, but very small; after which her roundness decreased, ’till she appeared semi-circular, and then horned, less and less, ’till they became so thin as to vanish at her Occultation in the Beams of the Sun, imitating all the Phases of the Moon. Mr de la Hire says, that he never failed of seeing the Transits of Venus through the moveable Telescope belonging to the Mural Quadrant at the Royal Observatory at Paris, though within two Degrees of the Sun. He observed her Transit in August 1700, with a sixteen Foot Tube, which magnified her Diameter of one Minute about 90 Times, when she appeared in the Form of a fine slender Crescent, with her Horns in an horizontal Line, and her Back upwards; that in the interior Arch of the Crescent he saw some Inequalities more considerable than those of the New Moon, by which he judged she might have Spots upon her, like those of the other Planets. In November 1691, he saw her at Noon, very near her superior Conjunction with the Sun, appearing round and very small. Mr Cassini several Times observed two Spots on Venus, and in the Year 1666, on the third of March at Bologna, with a Telescope of 16$$\frac{1}{2}$$ Feet he saw four Spots, and on February 24th he discovered two others larger, which were seen at Rome with a 35 Foot Telescope by Mr Campani. Mr Blanchini, in the Year 1726, at Rome, with Campani’s Glasses of 70 and 100 Roman Palms local Distance, discovered several dark Spots on the Disk of Venus, from whence he concludes that a Revolution of Venus, about her Axis, was not finished in 23 Hours, 20 Minutes, as Cassini imagined, but in 24$$\frac{1}{2}$$ Days.

The Phases of Mercury are exactly like those of Venus, or the Moon; but the Telescopes must be pretty good, and properly managed, to observe them well, by reason of the excessive Brightness, and short Digression from the Sun of this Planet. Kepler once took a large Spot in the Sun for Mercury; and Gassendus at Paris took Mercury in the Sun to be a Spot: on October 29, 1723, there was a Conjunction of Mercury and the Sun, when the Diameter of Mercury was then observed by a very good Micrometer, applied to the Huygenian Telescope of 123 Feet, to be 10″$$\frac{3}{4}$$. On the 24th of November 1629, our Horox saw Venus in the Sun, by projecting the Sun’s Image upon a white Paper in a dark Room, whereon she appeared to be a fine round dark Spot. The Particulars about the Phases of Mercury and Venus, are to be found in Gassendus’s Mercurius in Sole visus, & Venus invisa; and in Hevelius’s Mercurius in Sole visus. See the Treatise of this last, entituled, Selenographia. Also see the Memoirs of the Royal Academy of Sciences at Paris for the Year 1700, &c. There is nobody that ever could discover Spots in Mercury.

Dr Halley tells us, that Mercury in 46 Years, makes 191 Revolutions about the Sun; that he appeared the 28th of October, in the Year 1631, on the Sun’s Disk; seen by Gassendus at Paris afterwards, on the 28th of October 1677; seen by himself at St Helena. He says also, that Mercury appeared in the Sun on the 23d of April, 1661. On the 26th of April, 1674. On the 24th of April, 1707. And on the last Day of October 1726. The Doctor also says, that on the 26th of May (O. S.), in the Year 1761, near Six o’Clock in the Morning at London, Venus will appear in the Sun’s Disk, not above four Minutes South of its Centre; and observes, if proper Observations be made upon the then transit of Venus with good Clocks and Telescopes, in different distant Parts of the World, the Sun’s Parallax may be determined, and Distance from the Earth to the Exactness of the 100th Part of the whole, (see the Philosophical Transactions, Numb. 348.) whereas by the best Observations hitherto made, says he, we are not absolutely certain of those Quantities to less than about the 7th Part of them.

That we are not certain of these Quantities I always thought, and ever shall; the Sun’s Parallax is too small a Matter to be obtained by Observation to any Exactness that can be depended upon. The Doctor himself owns it to be exceeding small, but says, upon many repeated trials Dr Pound and Dr Bradley, by a Micromoter apply’d to the Focus of a Telescope, found it to be not more than 12″, and less than 9″. Now, setting aside the Inaccuracy in the Structure, and Smallness of the Radius, &c. of the Instruments used for this Purpose, the Error in defect arising from the Refraction alone may be so great, as even to exceed 9″. If so, what becomes of this slender Parallax, and how immensely farther off must the Sun be distant?

Indeed Dr Halley, in the Philosophical Transactions, at Numb. 368. would have the Air’s Refraction to be so little, that none but nice Instruments can perceive it’s Effects; and that Sir Isaac Newton was the first who ascertained it, and made a true Table thereof, which is set down in that Transaction. But the Air’s Refraction is so unconstant as not to be ascertained, and is always greater than many able Astronomers are willing to allow and suppose. Sir Isaac Newton’s Table makes the horizontal Refraction to be 33′ • 45″ • viz. fix’d, when nevertheless it is known to be very inconstant at different Times, and in different Places. The Dutch formerly wintering at Nova Zembla, found there the horizontal Refraction to be 4 Degrees. Sir Isaac’s Table takes the Refraction at Altitudes above 75 Degrees to be so small as not to be worth Notice. But De la Hire’s Table of Refractions is extended to 89 Degrees of Altitude, making it there to be one second. And the famous Mr Cassini says, it extends quit up to the Zenith. Dr Halley, in the Transaction before mentioned, says, all Distances of Stars are contracted by Refraction, when they are parallel to the Horizon, by the same confront Quantity, be they nigh or low, viz. one second to a Degree; because (says he) the Chords of the real and visible Arches, are in the constant Ratio of the Sine of the Angle of Incidence to that of the refracted Angle. But herein, I think, lies a Fallacy, for he takes the refractive Power, of the Air at all Times to be constant at equal Altitudes above the Horizon. Whereas this is known to be otherwise. For in Mr Hawkesby’s Physico-Mechanical Experim. pag. 175. it is shewn, that the refractive Power of the Air is proportional to the Air’s Density, and since this Density is found to be variable, that refractive Power must by consequence be so too. Moreover, Sir Isaac Newton, in the tenth Proposition of his second Book of Optics, says, that the refractive Power of Air, and all Bodies, seems to be proportional to their Densities, or very nearly, excepting so far as they partake of sulphureous oily Particles, and thereby have their refractive Powers made greater or less; whence, says he, it seems rational to attribute the refractive Power of all Bodies chiefly, if not wholly, to the sulphureous Pares with which they abound. Consequently, as I said above, Dr Halley’s taking the Refraction of the Air at equal Altitudes to be always the same cannot be true, because the Air’s Density at those Altitudes varies, as is found by the Barometer. Whence the denser the Air is, the greater is the Refraction at a given Altitude; and it will be still the more so, as it abounds with sulphureous oily Particles. Hence it should seem, that in dry Weather, when the Mercury in the Barometer is highest, and the Air is the fullest of such Particles, the Refraction will be the greater at a given Altitude. But whether the Air in Summer has not more such Particles in it than in the Winter, in the same parallel of Latitude; or whether in very cold frosty Weather there are not more than in warmer Weather, are Things that should be more inquired into than the Astronomers have hitherto done, in order to determine and ascertain the true Quantity of the Refraction of the Light coming from an observed celestial Object, at a given Time, Place, and Altitude.

But to observe a little farther on this Subject. Dr Nettleton, in the Philosophical Transactions, Numb. 388. says, in taking the Altitudes of some Hills, the Observations were so disturbed by the Refractions that he could come to no Certainty. Having measured the Height of one Hill in a clear Day, he found it, by repeating the Operation on a cloudy Day, when the Air was somewhat gross and hazy, to be different, and the small Angles to be so much augmented by the Refraction, as to make the Hill much higher than before, though they were carefully taken each Time by good Instruments. That pointing the Quadrant to the Tops of some Mountains, they would appear higher in the Morning before Sun-rising, and also late in the Evening, than at Noon in a clear Day. That one Morning in December, when the Vapours lay condensed in the Vallies, and the Air. above was pure, the Top of a Mountain appeared more elevated by above 30′ than it did in September at Noon en a very clear Day. Hence, says he, Refraction is sometimes greater than at others, but, probably, it is always very considerable, and there being no certain Rule to make allowance for it, all Observations made on very high Hills, view’d at a Distance under very small Angles are uncertain, and scarcely to be depended upon, generally erring in making the Heights greater than they really are. Thus Far Dr. Nettleton. Mr. Huygens long since, in his Treatise of Light observes, that the Refraction of the Air changes every Hour, though indeed his Experiments were made upon very small Altitudes on Objects at Land. And father Laval (as appears in the French History of the Royal Academy, for the Year 1710.) observed the Sun’s meridian Altitude on the 22d of June (N. S.) 1710, to be 70° • 25′ • 50″. And on the 23d of June, at the Pittance of 36 Hours from the Time of the Solstice, he found the meridian Altitude to be 70° • 26′ • 00″. greater by 10″, when it ought to be less. And having oftentimes observed such before, he suspected the Refraction varied according to the Difference of the Quarters from whence the Wind blew. Tycho Brache makes the Refractions of the Sun, Moon, and fixed Stars, to be different, and would have that of the Sun to end at 46 Degrees of Altitude, that of the Moon at 45, and that of the fixed Stars at 20 Degrees; he makes the Sun’s horizontal Parallax to be 34′, the Moon’s 33′, and the fix’d Stars 30′, which are all too little. But de la Hire and Cassini makes it to be 32′ in every Star. He makes that of the Sun at 33° to be 55″, and at 52°. to be 58″. See his Table in his Progymnosm. Lib. I. pag. 79, 124, 280.

Hence amidst so much Difference and Uncertainty about the Refraction of the Air, one would be almost led to be doubtful of the Truth of many astronomical Conclusions, entirely depending upon and deduced from Observations, which Doubts must last ’till the Nature and Quantity of the Air’s Refraction at all Times and Places, are better known and settled. How can one believe the apparent Diameters of the Planets, which are so very small, are such as the Astronomers make them, when the true Refraction, at the Time and Place of Observation, is not well known; and how can any great Degree of Belief be fixed upon what they say, as to one of these very small apparent Diameter’s being less at one Time of the Year than at another. Indeed, if the Observations were made near or under the Line, where the Refraction is by all allowed to be the least, especially of the meridian Altitudes, these would be the most to be depended upon, and accordingly so would the Consequences deduced from them. The late Dr Halley had too slight an Opinion of the Air’s Influence upon the Light moving through it, just as he had of it’s Influence upon the Motion of Projectiles, which he would have to move nearly in a Parabola, though now it is really found by Experience they do not. All this by the by. But to return from this seemingly out of the way Digression to the Telescopick Discoveries in the Moon.

It is discovered by the Telescope, that the Moon’s Surface is rough, like our Earth, distinguished into innumerable Mountains, Caves, and Vallies; because at the new Moon the Line joining her Horns, and passing between the bright and dark Parts of the visible Hemisphere appears to be composed of many crooked Turnings and Windings. That many small bright Spots appear in the dark Portion, standing out at several small Distances from that common Boundary. And at some Time after they grow sensibly larger, and apparently nearer to, and at last unite with, the bright Portion of the Hemisphere, just as the Rays of the rising Sun shine first upon the Tops of our high Mountains, then descend gradually to their Bases, and at last into the Vallies. There are many small Spots observed interspersed all over the bright Portion of the Disk, some of which have their dark Sides next to the Sun, and their opposite Sides very bright and circular, which shews them to be round Cavities, whose Shadows fall within them; and some of these are surrounded with Ridges of Mountains. That those larger and less luminous Tracts, which are visible to the naked Eye, appear smoother in the Telescope, and more depressed than the ambient brighter Regions; as is evident by a greater Regularity and Evenness of the part of the Boundary of Light and Shade which passes through them at certain Times, and by it’s Protuberances at both it’s Extremities; and these Tracts are not quite free from smaller Inequalities, especially of Light and Shade.

Now these darker Regions may be compared to the Receptacles of our Seas emptied of their Water, for that they contain none appears from those permanent bright Spots observed in them by short Telescopes; and because larger Telescopes plainly not only discover small Eminencies, but Cavities within them, which seems quite repugnant to the Nature of Seas, and the Obscurity of their Colour may proceed from some sort of Matter that reflects less Light than the other Regions do. There may be Soils in the Moon very different from any we are acquainted with on the Earth.

The Magnitude of the Moon’s Mountains is found to be much higher than any of the Earth’s. When only the Tops of them are enlightened by the Sun, they appear as bright Specks in the dark Part of the Moon’s Disk; and the apparent Distance of several such Specks from the Limit between the dark and bright Parts of the new Moon, has been found to be about the 20th Part of the Moon’s apparent Diameter, and from thence it has been concluded, that the Height of those Mountains is above five Miles. Ricciolus reckons the Height of one of the Moon’s Mountains called St Catherine, to be nine Miles.

It could never be discover’d by the best Telescopes, that there were any visible Changes in the Colours, Shapes, and Situation of the Moon’s Spots; their Appearances being always the same, Allowances being made for their different Lights and Shades in different Ages of the Moon; for the different Goodnesses of Telescopes, and the Clearness of our Atmosphere; nor can it be fairly concluded, from any Observations hitherto made, that the Moon has an Atmosphere, although many Astronomers would make one believe it has. Cassini, in the Memoirs of the French Academy, for the Year 1706, says, he has often observed the spherical Figure of Saturn, Jupiter, and the fixed Stars, at their Occultations near the enlightened or obscure Limb of the Moon, to be changed into an oval Figure; and at other Occultations he has discovered no such Alteration in their Figure, just as the Sun and Moon in a vapourous Horizon appear to be ovular at their rising or setting. Hevelius, in his Cometogrophia, Page 363, says, that he has observed several Times in the most serene Air, wherein he could discover Stars of the sixth and seventh Magnitude, when the Moon had the same Altitude and Distance from the Earth, and with an excellent Telescope, that the Moon and her Spots did not appear equally bright and distinct, but at sometimes did so much more than at others. Sometimes in a clear Air, when Stars of the sixth or seventh Magnitude were seen, the Moon has quite disappeared, so as not to be seen by the best Telescopes; such a thing was seen by Kepler in the Years 1580, 1583, and 1620; as also by Hevelius and by Ricciolus, the 14th of April 1642. See Kepler’s Optical Astronomy, Pag. 227, 297. his Epitom. Astron. Copernican. Lib. v. Pag. 825. Hevelius’s Selenogr. Pag. 117, and Riccolus’s Almag. Nov. Lib. iv. Cap. 6. Pag. 203.

It has been discovered by the Telescope, that the Hemisphere of the Moon visible to us is not at all Times quite the same; at one full Moon we see a small Gore, or Segment, in the Margin of her Disk that was quite hid at another; so that her Body appears to us as if it librated to and fro; sometimes eastward or westward, sometimes northward or southward, and sometimes in a Direction between both. See concerning this in Hevelius’s Book de Motu Lunæ Libratorio.

Langrenus and Hevelius were the first who published Maps of the Moon’s Spots, as they appear through a Telescope, with Names of the most remarkable Spots and Regions, as well for the more immediate astronomical Purposes, as for Posterity to observe what Changes may happen in them.

Now we are upon the Moon, I believe the following short Digression, concerning her Light, will not be disagreeable. Dr Smith, in the first Volume of his Opticks, Pag. 29, 30, says Day-Light is about 90000 Times greater than Moon-Light. And in his Remarks, Vol. II. pag. 16. tells us, one Mr Bouguer, in a Treatise of his entituled, Essai dioptrique fur la gradation de la Lumiere, finds the Light of the full Moon to be about 300000 Times weaker than that of the Sun, at a Medium of several Trials: and the Doctor says, just after that, he himself found it by Theory, not much above 90000 Times: the Difference may arise chiefly (continues he) from the loss of Light in the Moon’s Body, which could not be allowed for in the Theory. But, I neither take the Sun’s Light to exceed that of the Full-Moon near so much, as either of these Gentlemen here make it, nor the Experiments and Theory upon which they have proceeded, and deduced these their Conclusions, to be depended upon, and free from Error: for

1. the Doctor’s Proof is upon the Supposition that all Day-Light is much the same, i. e. equal, he says it, at Pag. 30, Vol. I. which is most: evidently not so; for the Day-Light of a cloudy Day in Winter is most certainly many Times less than that of a clear Day in the Summer.
2. The Doctor would have Moon-Light to be no greater than the Light of a white Cloud, which I take to be another Mistake.
3. Mr Bouguer supposes two Lights to be equal, when he thinks he sees them so, by looking at them; which at best is but a sort of guess-work, liable to great Uncertainty: the seeing minute Objects equally distant from two Lights with the same Distinction, would be better than this, though not certain neither.
4. That Light decreases as the Square of the Distance, I am doubtful of, and have been so many Years; there is no Proof of it by actual Experiments as I know: indeed, it has been long made out by Theory to be so; but the practical Proof of these things is best, and most to be relied upon; and I have often thought, that Light in some cases, as well as Pleat, may decrease, rather as the Cubes of the Distances, than as the Squares; be this as it will, I am sure neither the Doctor nor Mr Bouguer have made out their Assertions to my Satisfaction.

I could say a great deal more about this, but at present have not Inclination. If any body has a Mind to defend these Gentlemen in this Point, I shall then be urged on to proceed to farther Particulars. But to return to the

## Telescopick Discoveries.

The Diameter and Parallax of Mars are said to be above five Times greater in his Opposition to the Sun than in his Conjunction. In both these Positions his enlightened Hemisphere is fully exposed to the Earth, as well as the Sun: but not so fully in his Quadratures with the Sun, where he appears through a Telescope to be a little gibbous, like the Moon about three Days from the Full. Dr Hook and Mr Cassini first discovered Spots upon Mars of determinate Figures, by which it has been found that he revolves about his Axis in twenty-four Hours and forty Minutes. One of these Spots appeared like a Joyner’s Square, or obtuse-angular Bevel; these Spots change their Colours, Shapes, Situations, and vanish at different Times. Mr Miraldi says, that one of the bright Spots upon Mars appeared for near 60 Years, and that it was the only permanent Spot upon his Body. Mr Cassini says, he observed a fixed Star in the Water of Aquarius, which at the Distance of six Minutes from the Disk of Mars, became so faint before it’s Occultation, that it could not be seen with the naked Eye, nor with a three Foot Telescope. The like Diminution of it’s Light after it’s Occupation, was observed by Mr Reaumeur at Paris, who could not see that Star with a large Telescope in a very clear Air, ’till it’s Distance from Mars became equal to $$\frac{2}{3}$$ of it’s Diameter, and yet Stars of that Magnitude are plainly visible, even in Contact with the Moon: by a Comparison of several Observations then made upon that Star, it was judged that it varied it’s Distance from the neighbouring Stars; and by some it has been therefore concluded, that Mars has a very extensive Atmosphere. See more particularly about these Spots in du Hamel’s History of the French Royal Society, pag. 97, 107. Edit. 2.

In the Philosophical Transactions, at Numb. 128, Dr Halley shews how to find from three given Distances of Mars from the Sun, his mean Distance and Excentricity, which in effect amounts to the Construction of a Geometrical Problem, viz. one of the Foci of an Ellipsis passing through three given Points being given: to describe such an Ellipsis, thence find the other Focus, as also the two Axes. Now the Doctor’s Construction is by the Intersection of two Hyperboles, which will be in the other Focus required; but this is only a plain Problem, constructable by right Lines and Circles, without the actual Description of two Hyperbolas, although, indeed, the doing it by two Hyperbolas is the most short and natural way possible; the plain Problem in effect is, to find the Centre of a Circle (which will be the other Focus), that shall touch three given Circles: and a more elegant Computation of this than what the Doctor has given in that Transaction, may be obtained from Lemma 16. Sect. 4. Lib. i. Princip. Mathem. Philos. Naturalis of Sir Isaac Newton.

By the Telescope it is discovered, that on Jupiter there are two Belts lighter than the rest of his Disk terminated by parallel Lines, which are sometimes broader, sometimes narrower, and not always situated on the same Part of the Disk. And Mr Huygens says (In his System of Saturn, pag. 7.), that he saw in March, in the Year 1656, a much broader though obscurer Belt, in the Middle of the Disk of Mars.

About the End of November, in the Year 1609, Simon Marias (see his Preface Ad Mundum Jovialem), first Mathematician to the Elector of Brandenburgh, first discovered three Stars moving about Jupiter, and attending him; and in February 1610, he saw a fourth: and in Italy, Galileo saw the same Stars the 7th of January, in the Year 1610, and published his Observations upon them in a Treatise, entitled, Nuncius Sidcreus. These four Stars, called Satellites, moving about Jupiter, are at different Distances from him, and the periodical Times of the Motions of the first, is one Day and about 18$$\frac{1}{2}$$ Hours; of the second, three Days, and about 13 Hours; of the third, seven Days, and almost 14 Hours; and of the fourth, sixteen Days, and about 16$$\frac{1}{2}$$ Hours. Mr Cassini, and others, discovered Changes in Jupiter’s Belts. Spots upon the Satellites. Jupiter’s Figure to be spheroidical. The Ratio of his Axis to his equatorial Diameter being according to Cassini as 14 is to 15; and according to the late Dr Pound, as 12 is to 13. Transits of the Body and Shadows of the Satellites, in Form of black Spots over the Disk of Jupiter. There are a great many Particulars about these Spots, to be found in astronomical Writings, especially in the Transactions of the French Royal Society, scarcely worth mentioning here, as I think.

Tables of the Motions of Jupiter’s Satellites were first published by Mr Cassini, then Mr Flamstead, and by Dr Halley, and afterwards by Dr Pound. There are ethers too who have given Tables of them. But these may be looked upon as little more than bare Transcribers. Dr Pound particularly has endeavoured to rectify the Motion of the first Satellite next to Jupiter, and to make the Calculation easy of it’s Eclipses in the Shadow of Jupiter, thirteen of which happen in a Month, thereby affording very frequent Opportunities of determining the Longitude of Places, especially at Land, by Time-keepers, and Telescopes of proper Lengths, viz. those of 12, 16, or 20 Feet at least; it being found, that with shorter Telescopes the Times of the Emersions cannot be so well determined as with longer.

This Way of finding the Longitude of Places at Land is practicable, and sufficiently exact, but at Sea it has been found to be ineffectual, by reason of the Length of the Telescope, which Cannot be managed with sufficient Steadiness and Dexterity in a Ship, during it’s various Agitations by the Winds and Waters. The Way of finding the Longitude of Places, by the Observations of the Times of the Eclipses of the Satellites of Jupiter is certainly ingenious, but liable to some Disadvantages; for were the Telescope, by which Jupiter and his Satellites is observed, never so good, and well managed, there are none but Astronomers, and those who have been a good while accustomed to celestial Observations that could do this Business without being liable to mistakes. Though almost every Body knows Jupiter, and can distinguish him from the rest of the Stars near him, a Person not used to Observation may take one Satellite for another, or fixed Stars for Satellites, as did Antonius Maria Schyrleus de Rheitá, a Capuchin of Cologne, who thought he had discovered five more Satellites moving about Jupiter on the 29th Day of December, 1642, which for the Honour of Pope Urban the Vlllth he call’d by the Name of Sidera Urbana Octaviana. See Gassendus’s Letter to Gabr. Naudæum de novem Stellis circa Jovem visis, which turn’d out to be only five fix’d Stars. Besides all this, the Influence that the Satellites have upon each other are observed to disturb their Motion in some measure; and that of the first is said to be liable to Inequalities that will cause Effects not easily reduced to any Rule, but from a long Series of Observations. See the Philosophical Transactions, Numb. 394. Also in these Transactions, are to be seen Observations of Eclipses of the Satellites of Jupiter, in many Parts of the World.

One Mr Reaumeur, a foreign Astronomer, many Years ago, from the Difference between the calculated Time of one of these Eclipses, and the observed Time, will have it that Light is about ten Minutes in its Passage from Jupiter to us. Sir Isaac Newton and his Followers will have it to be in but seven or eight Minutes. Others have said, the whole is doubtful. See the Memoirs of the French Royal Society for the Years 1707, and 1729. of which last Number I myself am one. For I think no Man ever knew enough of the Nature and Motion of Light, to be certain how it really moves and acts. Dr Barrow was a very great Man, as well as Sir Isaac Newton. He says in his Opticks, that the Arguments for and against the direct Propagation of projected Light, and it’s Propagation by the small Impulses of some elastick fluid Medium were so equal, that he durst not venture to assert which was right; they might be partly both, says the Doctor.

I have lately thought, that the Sun’s Light and Heat too is not only greatest where it is most reflected and refracted, but in the vast Space between the Sun and the Planets, where there is little or no reflective or refractive Matter, the Sun’s Light and Heat is least, whether the Distances be nearer or farther from the Sun. That his Heat is most in Vallies, and low sandy Situations, is well known by Experience; and that on the Tops of many Mountains, even near the Line there is Snow to be found at all Times of the Year. (See Varenius’s Geography.) And I take many of our upper Clouds to be chiefly Snow or Hail, both Summer and Winter. Hence, at a small Distance from the Earth’s Surface the Sun’s Heat must needs be considerably lesser than at the Surface itself, and at greater Distances upwards towards the Sun, it is not unreasonable to suppose the Sun’s Heat to be still less, and that it may decrease to certain Limits, either towards the Sun or from it. Consequently, if this be the Case of the Sun’s Heat, I should think it must be so of his Light too, which is greatest at the Surface of the Planets, by reason of the Refraction of their Atmospheres (supposing them to have such) and the Reflections at their Surfaces, &c. and therefore from these, and many other Considerations, I am doubtful whether the Sun’s Light at the several Planets, be the greatest, the nearer the Planet is to the Sun; and whether, if a Person were a thousand Miles, for Instance, above the Earth, towards the Sun, the Light that he would perceive there would not be very weak and faint. These foreign, short, and rude Suppositions, may perhaps serve as a Bar in the Way to hinder the taking Conjectures for Certainty, and making Conclusions founded upon the imaginary Nature of Light, which no Body truly knows (nor perhaps never will) be taken as indubitable Truths. Sir Isaac Newton’s Proposition, about the Time of the Motion of Light from the Sun to the Earth is very short. It is Prob. XI. of Part 3. Book 2. of his Opticks. He says, when the Earth is between the Sun and Jupiter, the Eclipses of the Satellites happen above seven or eight Minutes sooner than they ought to do by the Tables; and when the Earth is beyond the Sun, they happen about seven or eight Minutes later than they ought to do, the Reason being, that the Light of the Satellites has farther to go in the latter Case than in the former, by the Diameter of the Earth’s Orbit, &c.

In the Philosophical Transactions, Numb. 406. there is a curious Account of Dr Bradley’s to prove, that Light is eight Minutes coming from Jupiter to us, chiefly from Observations of the Declinations of the fixed Stars being different some Times of the Year, from what they are at other Times, by some Seconds, though never exceeding 40″ or 41″. The Particulars of his Observations are there set down for two Years, viz. 1727, and 1728. Upon the whole of which I shall briefly observe,

1. The taking Angles to Seconds are very nice Things, oftentimes subject to Uncertainty, especially by reason of the Difference of the Refraction in the Air at the Time of the Observations, not yet settled as it should be, by any Rules or Tables that ever yet has appeared in publick.
2. There is besides another Doubt with me, viz. whether upon the increasing or lessening the Magnitude of the Pupil of the Eye, the Magnitude of the Optick-Angle will not be accordingly increased or decreased. And if this be the Case, since the Pupil increases as the Light falling upon it decreases, whether small Distances and apparent Diameters of Objects in the Heavens, though these Objects be equally distant from the Eye, will not at one Time appear more or less by some Seconds, than at another Time, viz. generally less in the Summer, when the Light is greatest; and greater in the Winter, when the Light is least. And whether the apparent Diameter of the same distant Object, at the same Distance, will not appear greater, if by any Cause it becomes less bright, or more obscure, than when it is more shining or white.
3. It seems to require several Years Observations, at several Places, by several People, to fix the Truth of this ingenious Gentleman’s great Conclusions beyond Dispute. He is certainly a fine Observer, and great Astronomer; but the Love of Truth, and that only, has made me advance these Doubts, not out of any Ill-nature, or Disrespect, or with any View of acquiring the least Praise thereby. If I am but right, that is all I care for. And no Man can justly be blamed for reasonable Suspicions in Science especially, which should always be clothed in Truth.

There is another ingenious Discourse of the Doctor’s in the Philosophical Transactions, Numb. 485, for the Year 1747, on the apparent Motion of some of the fixed Stars.

Saturn has the most extraordinary Appearance through a Telescope, of any of the rest of the Planets. Galileo, with a bad Telescope, took him for three Globes, a larger between two smaller, almost contiguous to one another. Sometimes the middle Globe was lest quite alone. Then they seemed to stick to the middle Globe; to put on various Shapes, appearing sometimes round, sometimes oblong, like Acorns, sometimes semicircular, then lunar, with Horns pointing towards the Globe in the middle, and growing by degree so long, and so wide, as to encompass it with an oval Ring. These monstrous Appearances puzzled the Astronomers at first to account for them. Hevelius, in his little Tract, De nativa facie Saturni, reckons Saturn,

1. To be Mono-spherical.
2. Tri-spherical.
3. Two-handled-spherical.
4. Elliptical-handled.
5. Spherical-horned.

And these Phases he has again sub-distinguished. But Mr Huygens, in his System of Saturn, evidently made it appear, that these wonderful imperfect Appearances were owing to the want of good Telescopes. For with better ones he discovered a Ring about Saturn, which was the true Cause of all those surprizing Phænomena; and besides that, a Satellite revolving round Saturn every sixteen Days, or thereabouts, in the Plane of the King produced. This Satellite was first discovered by him in March, 1655, by Telescopes of 12 and 23 Feet; and afterwards Cassini, at different Times, found out tour more Satellites, viz. the two nearest to Saturn, with the Telescopes of Campani of 100 and 136 Feet, in March, 1684. The third in December, 1672. with one of Campani’s Telescopes of 35 Feet; and the fifth (viz. that of Huygens’s) in October, 1671. by a Telescope or 17 Feet. Afterwards he saw the two inward ones, with Telescopes of Campani of 47 and 34 Feet; and by Telescopes of Borelli of 40 and 70 Feet; and at length, by Telescopes of Artouquellius’s of 80, 155, and 220 Feet. See the Philosophical Transactions, Numb. 92, and 181. Mr Huygens, with a 12 Feet Tube, saw Saturn with two Arms oppositely extended from his Globe, and a darkish Zone or Line passing straight over the Disk, between the upper Sides of the Arms was visible. He saw Saturn quite round sometimes, and that Zone was parallel to our Equator. He makes the Space between the Globe and the Ring to be equal to, or rather bigger than, the Breadth of the Ring, and the greatest Diameter of the Ring is to the Diameter of the Globe, as nine is to four, but Dr Pound makes it to be as seven is to three. That there is empty Space between the Ring and the Body is evident, from seeing the fixed Stars sometimes through it. The broad side of the Ring has sometimes appeared bisected quite round by a dark elliptick Line, divided as it were into two Rings, of which the inner one appeared brighter than the outer. The Ring continues invisible all the Time that it’s Plane produced passes between the Sun and the Earth. Mr Cassini says, he could see all the five Satellites of Saturn with a 34 Feet Tube; whereas Mr Hadley owns, he never could have the Fortune to see them all five with his Reflecting Telescope. The periodical Times of the Satellites are of the first, one Day and about 21 Hours; of the 2d two Days and about 17 Hours; of the 3d four Days and about 12 Hours; of the 4th fifteen Days and about 22 Hours; and of the 5th seventy-nine Days and about 7 Hours. There are many other curious particular Phænomena of Saturn and his Satellites, observed by Huygens, Cassini, Muraldi, Dr Pound, &c. with the Telescope. See the Second Vol. of Dr Smith’s Opticks, from page 438, to 447. and our Philosophical Transactions, as well as thole of the French. I shall only add here, that it might somewhat strengthen the Truth of the Assertion already mentioned, viz. that Light is about seven or eight Minutes in it’s Passage from Jupiter’s Satellites to us. If from the like Observations of the Eclipses of Saturn’s Satellites, the Difference of the observed Times, from the Times by the Tables, were found to be proportional to that seven or eight Minutes, as Saturn’s mean Distance is to Jupiter’s. But this I leave to Astronomers, having neither Inclination nor Abilities to attempt it myself. It may, perhaps, be impossible, though indeed, at present, I do not see that it is.

The best Telescopes do not at all magnify the apparent Diameters of the fixed Stars, nor can it be discovered that the fixed Stars have any sensible Parallax. Mr Cassini, in the French Memoirs for the Year 1717, says, that he saw Sirius under an Angle of 5″ or 6″, with a 36 Foot Telescope, and then with a 3 Foot Telescope. But Dr Halley, in the Philosophical Transactions, Numb. 369, has shewn the Fallacy of this his Assertion. The Radius of Cassini’s Instrument of 3 Feet being too small for such a nice Observation, and the Difference of the Refractions of the Air, which may be 7″ or 8″, being greater than this whole Parallax, 5″ or 6″ supposed to be observed.

The best Telescopes have discovered nothing extraordinary in the fixed Stars; you only see vast Multitudes of them hid from the naked Eye, excepting indeed, that Mr Huygens, in his System of Saturn, tells us, he saw three Stars in the middle of Orion’s Sword (marked θ by Bayer) together with four more, shine out, as it were, through a whitish Cloud, much brighter than the ambient Sky, which being very black and serene, caused the lucid Parts to appear like an Aperture that gave a Prospect into a bright Region. He found it to continue in the same Place, and not altered in Shape. See another of these in our Philosophical Transactions, Numb. 347.