Mathematical Instruments

# Of the Globes.

## Section I.

Globes there are two Kinds, viz. Celestial and Terrestrial. The first is a Representation of the Heavens, upon the Convex Surface of a material Sphere, containing all the known Stars, after the manner that Astronomers, for the easier knowing them, have divided them into Constellations, or Figures of Men, Beasts, Fowls, Fishes, &c. according to the Resemblance they fancied each select Number of Stars formed. The other is the Terrestrial Globe, which is the Image of the Earth, on the Convex Surface of a material Sphere, exhibiting all the Kingdoms, Countries, stands, and other Places situated upon it, in the same Order, Figure, Dimensions, Situation, and Proportion, respecting one another as on the Earth itself.

There are ten eminent Circles upon the Globe, six of which are called greater, and the four other lesser Circles.

A lesser Circle is that which is parallel to a greater, as the Tropicks and Polar Circles are to the Equator, and as the Circles of Altitude are to the Horizon.

### The great Circles are,

I. The Horizon, which is a broad wooden Circle encompassing the Globe about, having two Notches, one in the North, the other in the South part thereof, for the Brazen Meridian to stand, or move round in, when the Globe is to be set to a particular Latitude.

There are usually reckoned two Horizons: First, The Visible or Sensible Horizon, which may be conceived to be made by some great Plane, or the Surface of the Sea; and which divides the Heavens into two Hemispheres, the one above, the other (apparently) below the Level of the Earth.

This Circle determinates the Rising and Setting of the Sun, Moon, or Stars, in any particular Latitude: for when any one of them comes just to the Eastern edge of the Horizon, then we say it Rises; and when it doth so at the Western edge, we say it Sets. And from hence also is the Altitude of the Sun or Stars reckoned, which is their height in Degrees above the Horizon.

Secondly, The other Horizon is called the Real or Rational Horizon, and is a Circle encompassing the Earth exactly in the middle, and whose Poles are the Zenith and Nadir, viz. two Points in its Axis, each 90 Deg. distant from its Plane, (as the Poles of all Circles are) the one exactly over our Heads, and the other directly under our Feet. This is the Circle that the wooden Horizon on the Globe represents.

On which Broad Horizon several Circles are drawn, the innermost of which is the Number of Degrees of the Twelve Signs of the Zodiack, viz. 30 to each Sign: for the ancient Astronomers observed the Sun in his (apparent) Annual Course, always to describe one and the same Line in the Heavens, and never to deviate from this Track or Path to the North or South, as all the other Planets did, more or less: and because they found the Sun to shift as it were backwards, thro’ all the Parts of this Circle, so that in one whole Year’s Course he would Rise, Culminate, and Set, with every Point of it; they distinguished the fixed Stars that appeared, in or near this Circle, into 12 Constellations or Divisions, which they called Signs, and denoted them with certain Characters; and because they are, most of them usually drawn in the form of Animals, they called this Circle by the Name of Zodiack, which signifies an Animal, and the very middle Line of it the Ecliptick; and since every Circle is divided into 360 Degrees, a twelfth part of this Number will be 30, the Degrees in each Sign.

Next to this you have the Names of those Signs; next to this the Days of the Months, according to the Julian Account, or Old Style, with the Calendar; and then another Calendar, according to the Foreign Account or New Style.

And. without these, is a Circle divided into thirty two equal Parts, which make the 32 Winds or Points of the Mariners Compass, with the Names annexed.

### The Uses of this Circle in the Globe are,

1. To determine the Rising and Setting of the Sun, Moon, or Stars, and to shew the time of it, by help of the Hour-Circle and Index; as shall be shewn hereafter.
2. To limit the Increase and Decrease of the Day and Night: for when the Sun rises due East, and sets West, the Days are equal.

But when he Rises and Sets to the North of the East and West, the Days are longer than the Nights; and contrariwise, the Nights are longer than the Days, when the Sun Rises and Sets to the Southwards of the East and West Points of the Horizon.

3. To. show the Sun’s Amplitude, or the Amplitude of a Star; and also on what Point of the Compass, it Rises and Sets.

II. The next Circle, is the Meridian, which is represented by the brazen Frame or Circle, in which the Globe hangs and turns. This is divided into four Nineties or 360 Degrees, beginning at the Equinoctial.

This Circle is called the Meridian, because when the Sun comes to the South part of it, it is Meridies, Mid-day, or High noon; and then the Sun hath its greatest Altitude for that Day, which therefore is called the Meridian Altitude. The Plane of this Circle is perpendicular to the Horizon, and passeth thro’ the South and North Parts thereof, thro’ the Zenith and Nadir, and thro’ the Poles of the World. In it, each way from the Equinoclial on the Celestial Globe, is accounted the North or South Declination of the Sun or Stars; and on the Terrestrial, the Latitude of a Place North or South, which is equal to the elevation or height of the Pole above the Horizon: Because the Distance from the Zenith to the Horizon, being the same as that between the Equinoclial and the Poles, if from each you imagine the Distance from the Pole to the Zenith to be taken away, the Latitude will remain equal to the, Pole’s Altitude.

There are two Points of this Circle, each 90 Degrees distant from the Equinoctial, which are called the Poles of the World, the upper one the North Pole, and the under one the South Pole. A Diameter continued thro’ both the Poles in either Globe and the Center, is called the Axis of the Earth or Heavens, on which they are supposed to turn about.

The Meridians are various, and change according to the Longitude of Places; for as soon as ever a Man moves but one Degree, or but a Point to the East or West, he is under a New Meridian: But there is or should be one fixed, which is called the first Meridian.

And this on some Globes, passes thro’ one of the Azores Islands: but the French place the first Meridian at Fero, one of the Canary Islands.

The Poles of the Meridian are the East and West Points of the Horizon. On the Terrestrial Globe, are usually drawn 24 Meridians, one thro’ every 15 Degrees of the Equator, or every 15 Degrees of Longitude.

### The Uses of the Meridian Circle are,

First, To set the Globe to any particular Latitude, by a proper Elevation of the Pole above the Horizon of that Place. And, Secondly, To shew the Sun or Stars Declination, right Ascension, and greatest Altitude; of which more hereafter.

III. The next great Circle, is the Equinoclial Circle, as it is called on the Celestial, and the Equator, on the Terrestrial Globe. This is a great Circle whose Poles are the Poles of the World: it divides the Globe into two equal Parts or Hemispheres, as to North and South; it passes thro’ the East and West Points of the Horizon, and at the Meridian is always as much raised above the Horizon, as is the Complement of the Latitude of any particular Place. Whenever the Sun comes to this Circle, it makes equal Days and Nights all round the Globe, because it then Rises due East, and Sets due West, which it doth at no other time of the Year. All Stars also which are under this Circle, or which have no Declination, do always Rise due East, and Set full West.

All People living under this Circle (which by Navigators is called the Line) have their Days and Nights constantly equal. And when the Sun is in the Equinoctial, he will be at Noon in their Zenith, or directly over their Heads, and so their erect Bodies can east no Shadow.

From this Circle both ways, the Sun, or Stars Declination on the Celestial, or Latitude of all Places on the Terrestrial Globe, is accounted on the Meridian: and such lesser Circles as run thro’ each Degree of Latitude or Declination parallel to the Equinoctial, are called Parallels of Latitude or Declination.

Through every 15 Degrees of this Equinoctial, the Hour-Circles are drawn at right Angles to it on the Celestial Globe, and all pass thro’ the Poles of the World, dividing the Equinoctial into 24 equal Parts.

And the Equator on the Terrestrial Globe, is divided by the Meridians into 36 equal Parts; which Meridians are equivalent to the Hour-Circles on the other Globe.

IV. The Zodiack is another great Circle of the Globe, dividing the Globe into two equal Parts (as do all great Circles): When the Points of Aries and Libra are brought to the Horizon, it will cut that and the Equinoctial obliquely, making with the former an Angle equal to 23 Degrees 30 Minutes, which is the Sun’s greatest Declination. This Circle is accounted by Astronomers as a Kind of broad one, and is like a Belt or Girdle: Through the Middle of it is drawn a Line called the Ecliptick, or Via Solis, the Way of the Sun; because the Sun never deviates from it, in it’s annual Course.

This Circle is marked with the Characters of the Twelve Signs, and on it is found out the Sun’s Place, which is under what Star or Degree of any of the Twelve Zodiacal Constellations, he appears to be in at Noon. By this are determined the four Quarters of the Year, according as the Ecliptick is divided into four equal Parts; and accordingly as the Sun goes on here, he has more or less Declination.

Also from this Circle the Latitude of the Planets and fixed Stars are accounted from the Ecliptick towards the Poles.

The Poles of this Circle are 23 Degrees, 30 Minutes distant from the Poles of the World, or of the Equinoctial; and by their Motion round the Poles of the World, are the Polar Circles described.

V. If you imagine two great Circles both passing thro’ the Poles of the World, and also one of them thro’ the Equinoctial Points Aries and Libra, and the other thro’ the Solstitial Points, Cancer and Capricorn: These are called the two Colures, the one the Equinoclial, and the other the Solstitial Colure. These. will divide the Ecliptick into four equal Parts, which are denominated according to the Points they pass thro’, called the four Cardinal Points, and are the first Points of Aries, Libra, Cancer, and Capricorn.

These are all the great Circles.

VI. If you suppose two Circles drawn parallel to the Equinoctial at 23 Degrees, 30 Minutes, reckoned on the Meridian, these are called the Tropicks, because the Sun appears, when in them, to turn backward from his former Course; the one, the Tropick of Cancer; the other the Tropick of Capricorn, because they are under these Signs.

VII. If two other Circles are supposed to be drawn thro’ 23 Degrees, 30 Minutes, reckoned in the Meridian from the Polar Points, these are called the Polar Circles: The Northern is the Arctick, and the Southern the Antarctick Circle, because opposite to the former.

These are the four lesser Circles.

And these on the Terrestrial Globes, the Ancients supposed to divide the Earth into five Zones, viz. two Frigid, two Temperate, and the Torrid Zone.

Besides these ten Circles already described, there are some other necessary Circles to be known, which are barely imaginary, and only supposed to be drawn upon the Globe.

1. Meridians, or Hour-Circles, which are great Circles all meeting in the Poles of the World, and crossing the Equinoctial at right Angles; these are supplied by the brazen Meridian Hour-Circle and Index.
2. Azimuths, or Vertical Circles, which likewise are great Circles of the Sphere, and meet in the Zenith and Nadir, as the Meridians and Hour-Circles do in the Poles; these cut the Horizon at right Angles, and on these is reckoned the Sun’s Altitude, when he is not in the Meridian. They are represented by the Quadrant of Altitude, by and by spoken of, which being fixed at the Zenith, is moveable about the Globe thro’ all the Points of the Compass.
3. There are also Circles of Longitude of the Stars and Planets, which are great Circles passing thro’ the Poles of the Ecliptick, and in that Line determining the Stars or Planets Place Or Longitude, reckoned from the first Point of Aries.
4. Almacanters, or Parallels of Altitude, are Circles having their Poles in the Zenith, and are always drawn parallel to the Horizon. These are lesser Circles of the Sphere, diminishing as they go further and further from the Horizon. In respect of the Stars, there are also Circles supposed to be Parallels of Latitude, which are Parallels to the Ecliptick, and have their Poles the same as that of the Ecliptick.
5. Parallels of Declination of the Sun or Stars, are lesser Circles, whose Poles are the Poles of the World, and are all drawn parallel to the Equinoctial, either North or South; and these (when drawn on the Terrestrial Globe) are called Parallels of Latitude.

VIII. There are belonging to Globes a Quadrant of Altitude, and Semi-Circle of Position. The first is a thin pliable Piece of Brass, whereon is graduated 90 Degrees answerable to those of the Equator, a fourth Part of which it represents; with a Nut and Screw, to fasten it to any part of the brazen Meridian as occasion requires. There is, or should be likewise, a Compass belonging to a Globe, that so it may be set North and South.

The Semi-Circle of Position is a narrow Plate of Brass, inscribed with 180 Degrees, and answerable to just half the Equator.

Lastly, The Brass Circle, fastened at right Angles on the brazen Meridian, and the Index put on the Axis, is called the Index and Hour-Circle.

## Section II. Having now described the Circles of the Gloves, I proceed to their Construction.

The Body of the Globe is composed of an Axle-Tree, two Paper-Caps sewed together, a Composition of Plaister laid over them, and last of all globical Papers or Gores (of which more by and by), (luck or glewed on the Plaister.

The Axle-Tree is a Piece of Wood which runs thro’ the middle of the Globe, turned sometimes of an equal Thickness, but oftner smaller in the Middle than at the Ends; where two Pieces of thick hardened Wire are struck in, which is the Axis, that appears without the Globe, on which it turns within the brazen Meridian.

The Paper-Caps inclose this Axle-Tree, and are made in the following Manner. You must have a Ball of Wood turned round, about a Quarter of an Inch less in Diameter, than the Size you intend to make your Globe of, with two Pieces of Wire stuck into it, diametrically opposite to each other, for Conveniency of turning in a Frame, which may be made of two Pieces of Stick fixed upright in a Board, with Notches on the Tops to lay the Wire in. Round this wooden Ball you must paste waste Paper, both brown and white, ’till you judge it to be of the Thickness of Pasteboard; and before it be quite dry, cut it in the Middle, so that it may come off in two Hemispheres: to prevent the Paper from sticking, let the Ball at first making be thick painted, and every time before you paste Paper on it, grease or oil it a little.

The Holes at the Tops of the Caps, occasioned by the Axis on which the Ball turned, are very convenient for the Axis of the Globe to go thro’ in covering of it. Then having fastened the Top of the Caps with small Nails to each end of the wooden Axle-Tree, few them close together in the Middle with strong Twine.

That the Caps may meet exactly, observe two things: 1ft, That the Axle-tree be just in the Diameter of the Ball. 2dly, That before you take the Caps off the Ball, you make Scores across the parting all round, about an Inch asunder, whereby to bore the Holes for sewing them even together, and leave a Mark to direct how to join them again in the same Points: for Instance, make a Cross over any one of the Scores in the upper Cap, and another Cross upon the same Score in the under Cap; and when you close them, bring the two Crosses together, by which means the Caps in sewing will come as close together as before they were parted. This Care must be taken, that there may be no Openings between; in which case, Paper must be crammed in to stop up the Gaps: but whether there be any Gaps or no, there must be Paper pasted all over it’s sewing, to prevent any of the Plaster from falling in.

The Plaster is made with Glue, dissolved over the Fire in Water and Whiting mixed up thick, with some Hemp shred small; the Use of which is to bind the Plaster, and keep it from cracking (as Hair is put into Mortar for the same End): a Handful will serve two or three Gallons of Stuff. There is no necessity for mixing the whole over the Fire, except the Whiting runs into Lumps not easily to be broken with the Hand.

For laying on this Plaster over the Caps in a globular Form, you must have a Steel Semi-Circle exactly half the Circumference you intend the Globe to have, fixed flat-ways in a level Table made for that purpose, with a Notch at each end for the Axis (which must nicely fit it) to turn in, and two Buttons to cover it, to prevent the Axis from being forced out of the Notches, when the Globe is clogged with Plaster, and so requires some Violence to turn it.

Then fixing your Paper-Sphere within this Semi-Circle, lay Plaster on it with your Hands, turning the Globe easily round, ’till it be covered so as to fill the Semi-Circle: But before it comes to touch the Semi-Circle in all it’s Parts, and be equally smooth all round, it will require a great many Layings on of the Plaster, letting it dry between every such Application.

The second or third time of laying on Stuff, it will begin to touch the Semi-Circle in some parts, and to appear round; the fourth time it will touch in more parts, and look rounder; ’till at last it will touch in all parts, and become perfectly round and smooth, like a Ball of polished Marble.

The next thing to be done is to poise the Globe; for it generally happens, by reason of the Plaster lying thicker in one place than in another, that some side weighs still downwards. To remedy this, a Hole must be cut in that part, and a convenient Quantity of Shot put in, in a Bag, to bring it to a due Balance with the rest; after which the Place must be stopped up with a Cork, and covered again with Plaster. The Bag that holds the Shot may be glewed or sewed to the Cap within, or fastened to the Cork: sometimes after one part is balanced, the Weight will incline to another; in which case the same Remedy must be applied again, as often as there will be necessity.

This done, by help of another Semi-Circle, divided into 18 equal Parts, draw the Equator and Parallels of Latitude, placing a Black-lead Pencil at the Graduation, and turning the Globe against the Point of it to make a Line. Then divide the Equator with a Pair of Compasses into so many Parts as there are globical Papers or Gores to lay on, and draw Lines thro’ each from Pole to Pole by the Side of the Semi-Circle. Within each of these Spaces so marked out, you have only to lay one of the Gores, which (being cut out so exact, as neither to lap over, nor leave a Vacancy between them) by the Assistance of the Lines drawn upon the Plaster, may be fitted, so as to fall in with each other with the greatest Exactness. In applying the Gores, you may use a good binding Paste, but Mouth Glue is better.

## Section III. Construction of the Circles of the Globe on the Globical Papers or Gores.

As 7 is to 22, So is the Diameter of a Globe to the Circumference of any one of it’s greatest Circles. The Diameter of the Globe is usually given, from whence it often happens that the Circumference consists of odd Numbers and Parts. Whereas if the Circumference was given in even Numbers, as Inches, it might more easily be divided into Parts. For Example, if the Circumference was 36 Inches, each 10 Degrees of Longitude on the Equator will be one Inch; if the Circumference be 54, each 10 Degrees will be one Inch and a half; if 72, every 10 Degrees of Longitude will be two Inches.

The Diameter of a Globe being given, suppose 24 Inches, to find the Circumference, say, As 7 is to 22, So is 24 to 75.43 Inches, the Length of the Circumference sought.

The Length of each Gore, from the North Pole to the South Pole, will be exactly half the Circumference of the Globe, which is 37.71 Inches, and the Length from the Equator to either Pole will be $$\frac{1}{4}$$, viz. 18.86 Inches.

If each of the Globical Papers contain in their greatest Breadth 30 Degrees of the Equator, 12 of them will cover the Globe, and by dividing the Circumference 75.43 by 12, the Quotient will give 6.28 Inches for the Breadth of the Gore.

If 18 of the Gores go to cover the Globe, the Breadth of each will be 20 Degrees of the Equator, or 4.19 Inches.

If 24, each will contain 15 Degrees of the Equator, or 3.14 Inches of the Circumference.

If 36, each Paper will contain 10 Degrees of the Circumference, or 2.09 Inches.

If the Globe be so large as to take up 360 Papers, that is, one to every Degree of Longitude, then will the Breadth of each Gore be 23 parts of an Inch.

Again, If the Circumference of a Globe be given, suppose 72 Inches, divide it by 2 (for the Length of the Gores from Pole to Pole) and the Quotient will be 36 Inches; and consequently half that Length, or the Distance from the Equator to either Pole, will be 18 Inches: as the Distance from N. to S. taken from a supposed Scale of Inches, is 36 Inches, or one half of the Circumference of the Globe; and the Distance from C to N or S, 18 Inches, or $$\frac{1}{2}$$ of the Circumference.

If each Gore contains 30 Degrees of the Equator in Breadth, or $$\frac{1}{12}$$ of the Circumference, it will take up 6 Inches thereof as IK.

If 18 of the Gores go to cover a Globe of the aforesaid Circumference, each will contain 20 Degrees in Longitude of the Equator, or 4 Inches, as LM.

If your Papers be $$\frac{1}{24}$$ of the Circumference, each will contain 15 Degrees of the Equator, or or 3 Inches, as ab.

If they be $$\frac{1}{36}$$ of the Circumference, each will contain 10 Degrees of the Equator, or 2 Inches, as cd.

If there be 72 Papers for covering the Globe, each will contain 5 Degrees of the Equator, or 1 Inch, that is $$\frac{1}{72}$$ of the Circumference.

If, lastly, the Globe requires 360 Papers, each will contain 1 Degree, or $$\frac{1}{5}$$ of an Inch.

This being premised, I now proceed to give the Manner of drawing the Circles of the Globes upon the aforesaid Gores.

Draw the Diameter WE, and cross it with another at right Angles to it, as NS. From the Scale of Inches set off from C to N, and to S, (the North and South Poles) 18 Inches or 4 of the Circumference, which divide into 9 equal parts, each of which likewise subdivide into 10 more (for the 90 Degrees of North and South Latitude). Upon C, as a Center, describe the Circle NE, SW, and divide each Quadrant into 90 Degrees, numbering each 10th Degree with Figures from the Equator towards the Poles, as 10, 20, 30, &c. Thus the three Points are found, thro’ which the parallel Circles to the Equator must be drawn, viz. two of them are in the Quadrants NE, NW. and SE, SW, and the third is in the Diameter NS.

To find the Centers of any of the said Parallels, suppose of the Parallel of 60 Degrees, set one Foot of your Compasses in the Point 60, or F, of the Quadrant NE, and extend the other to the Point 60, or D, in the Diameter NS; then describe the little Arcs A, B, and removing the Foot of your Compasses to the Point D, describe two other Arcs, cutting those before described, and thro’ the Points of Intersection draw a right Line, which will cut the Diameter CN, produced in the Point G, the Center of the 60th Parallel. Having thus found the Centers of all the Parallels, and drawn them in the Northern Hemisphere, transfer the central Points in the Line CN continued, into the Line CS continued also, and draw the Parallels of the Southern Hemisphere. Note, That whether the polar Papers extend to the 80th or 70th Parallel, those Circles in the meridional Papers, or those that encompass the Body of the Globe, must be described as is here ordered; but in the polar Papers the Pole must be the Center, as you see in the Figure, where one Point of the Compasses being set in the South Pole S, and the other extended to the 80th or 70th Degree of Latitude in the Diameter, strikes those Parallels in the polar Papers. See more concerning the polar Papers hereafter.

Then because the polar Circles and Tropicks are but Parallels 23 Deg. 30 Min. distant from the Poles and Equator; at those Distances describe double Lines, representing such Circles, to distinguish them from other Parallels.

### To draw the Meridians.

Having chosen one of the Proportions beforementioned for the Breadth of each Paper on the Equator, suppose $$\frac{1}{12}$$ of the Equator, which is the common Proportion in globical Papers, and the greatest Breadth that can be allowed them, let the Globe be of what Magnitude soever: then because $$\frac{1}{12}$$ of the Equator contains 30 Degrees, which in the Gores for a Globe of 72 Inches Circumferences, are six Inches in Breadth; from a Scale or Inches take three Inches between your Compasses, and lay them off on the Diameter WCE, from C to K, and from C to I, the Length from I to K being six Inches, or 3 Degrees of the Equator, into which it must be divided, and numbered at each 5th or 10th Degree, with the Degrees of Longitude.

Now because a single Degree cannot be well divided into Parts in so small a Projection, and seeing that any Number of Degrees of Longitude in any Parallel has the same Proportion to one Degree in that Parallel, as the same Number of Degrees of Longitude under the Equator has to one Degree of Longitude; therefore take 15 Degrees of the Equator, viz. IC or IK, in your Compasses, and having divided it separately, as you would a single Degree, into 60 equal Parts, look in the following Table what Proportion a Degree (or 15 Degrees) in each 5th or 10th Parallel of Latitude, hath to a Degree (or 15 Degrees) on the Equator. For example, in the first Column of the Table towards the Left-Hand, are the Degrees of Latitude; over against the 10th Degree, I find 59 Miles in the second Column, and 00 Minutes, or Fractions of a Mile, in the third Column, which signifies that a Degree (or 15 Degrees) in the 10th Parallel of Latitude, contains but 59 Milts 00 Minutes of a Degree (or 15 Degrees of the Equator) which Length I take from the Scale IC or CK between my Compasses, and set off on each side the Meridian, or Diameter NS, on the 10th Parallel.

Again, in the Parallel of 20 Degrees, I find a Degree to contain 56 Miles 24 Minutes, or parts of a Mile, of a Degree in the Equator, and transfer that Length from the aforesaid Scale upon the 20th Parallel; the like is to be understood of all the rest, and those Points being found and joined, will form the Meridians on the Gores. The same Directions must be followed in all other Proportions for the Breadth of the Gores; in chusing of which, observe, that as it is manifest from the Figure of the Globe, that a Paper so large as $$\frac{1}{12}$$ of the Circumference of the Globe, cannot lie upon its Convexity, without crumbling, lapping over, or tearing, in the Application; therefore it will be better to use some lesser Proportion, as LM, ab, or cd: for note, the narrower they are, the more exactly they will fit the Globe. Note also, in drawing the Parallels from 10 to 30 Degrees of Latitude, right Lines will do well enough.

### The Exact Geometrical Way of drawing the Parallels and Meridians on the Gores.

Because in the Method before laid down, the true Centers of the Parallels are not exactly in those Points found as there directed; nor the Points in them the Points by which the Meridians must pass: therefore I think it proper here to exhibit the Geometrical Manner of drawing them truly.

Suppose SB to be the Semidiameter of the Globe, with which describe the Quadrant BI, and continue out the Semidiameter SI, both ways. Make SA equal to $$\frac{1}{4}$$ of the Circumference; the Point A of which, will be the Pole of the Gore. Then divide the Quadrant BI into 90 equal Parts or Degrees, to every of which draw the Tangents i 80, k 70, l 60, m 50, &c. until they meet the Radius SI continued. Again, having divided the Line AS (equal to $$\frac{1}{4}$$; of the Circumference of the Globe) into 90 equal Parts, (I have only divided it into 9) and numbred them as per Figure; take the Length of the Tangent i 80 between your Compasses, and setting one Foot in the Point 80 of the Line AS, the other will fall upon the Point a in the said Line continued out beyond A, which will be the Center of the 80th Parallel passing thro’ the Point 80 in the Line AS.

Moreover, to find the Center of the 70th Parallel, take the Tangent k 70 between your Compasses, and setting one Foot in the Point 70 of the Line AS, the other will fall on the Point b in the Line AS continued, which will be the Center of the 70th Parallel, passing thro’ the Point 80 in the Line AS.

In like manner, to find the Center of the 60th Parallel, take the Tangent l 60 between your Compasses, and set it off from the Point 60 in the Line AS, and you will have the Center c for the 60th Parallel, passing thro’ the Point 60. Proceed thus for finding the Centers d, e, f, g, &c. of the Parallels 50, 40, 30, 20, &c. about each of which Centers respective Arcs being drawn, the Parallels will be had.

The Reason of this Operation for finding the Centers of the Parallels, is this; If a Sphere or Globe hath revolved upon a Plane, in such manner that every Point of the Periphery of some lesser Circle of it, has touched the said Plane, and the Point which in the beginning of the Motion was contiguous to the Plane, became to be contiguous to it again; then the Points on the Plane, that were contiguous to the Points of the Periphery of the aforesaid lesser Circle, will be in the Circumference of a Circle, whose Center will be the Vertex of a right Cone, lying on the aforesaid Plane, the Base of which will be the said Circle; and consequently the Vertex will be determined in the Plane, by continuing a right Line raised on the Circle’s Center perpendicularly ’till it cuts the aforesaid Plane.

### How to draw the Meridians.

Having drawn the Sines 10 p, 20 q, 30 r, 40 s, &c. divide the Radius BS into 360 equal Parts, or make a Diagonal Scale of that Length, whereby 360 may be taken off. Then having assumed SC for half the Breadth of the Gore, suppose $$\frac{1}{48}$$ of the Circumference of the Equator, take Sx (the Sine Complement of 80 Deg.) between your Compasses, and applying this Extent on the Radius BS, or the Diagonal Scale, see how many of those Parts that the Diameter is divided into, that Extent takes up. Then take $$\frac{1}{48}$$ of those Parts, and with the Quotient as so many Degrees make the Arc 10 L off, which will give the Point I. in the Parallel of 10 Degrees, thro’ which the Meridian must pass.

Again, take Sw between your Compasses, and see how many of the Parts that the Radius BS is divided into, it contains; then take $$\frac{1}{48}$$ of those Parts, and with the Quotient, as so many Degrees, make the Arc 20 M off, which will give another Point M, thro’ which the same Meridian must pass in the 20th Parallel.

In like manner, to find the Point N in the Parallel of 30 Degrees, thro’ which the Meridian must pass, take Su (the Sine Complement of 60 Degrees) in your Compasses, and see how many of the Parts that the Radius BS is divided into, it contains; then taking $$\frac{1}{48}$$ of those Parts, with the Quotient as so many Degrees, make the Arc 30 N off.

Proceeding in this manner, you may find other Points in the other Parallels, thro’ which the Meridian must pass. Which Points being afterwards joined, the quarter of the Meridian ANC will be drawn; and therefore one quarter of the Gore; and consequently the other three Quarters of the Gore will be easily limited.

### Method of ordering the Circumpolar Papers.

The Circumpolar Papers were formerly not cut out by themselves, ’till Artists found it hard to make the Poles, or Points of the Gores, fall nicely in the North and South Poles; whence, to help that Inconveniency, they made Circular Papers serve to cover the Superficies of the Globe between the Polar Circles, the Parallels on which Papers are all Concentric Circles, and the Meridians Right Lines: yet finding still so big Papers not to fit the Globe’s Convexity, but wrinkle about the edges, they have extended them from the Poles only to the Parallels of 70 Degrees. But neither will it do yet, because the Longitude decreases disproportionally, the further off the Poles. If the Diameter of a Polar Paper extends to in Degrees from the Pole only, that Paper will lie flat upon the Globe’s Convexity, without any sensible stretching or contracting: But if it extend to or beyond the 70th Parallel, you must take another Course.

Suppose APB to be half of a Gore, 12 of which will cover a Globe. About the Point P with an extent to the 70th Parallel, describe a Circle, which from the Points G or F, divide into 12 equal Parts; or, which is the same, continue every other Meridian in the Parallel 80 to the Parallel 70, and by the aforementioned Table set off on each Side these 12 Meridians, the true Longitude of each 10 Degrees in the Parallel of 80; or, which will save that trouble, transfer the Distance from C to G, or from G to D upon the Parallel of 70 Deg. in the Polar Paper, for that is the extent of 10 Degrees in that Parallel; and, as is manifest from the Figure, there will lie between each twelfth part of the Circumference FG, a narrow slip of Paper which must be cut out, and then the Paper being laid upon the Globe, the Parts will naturally close: whereas, for want of this Care taken, we commonly see the Polar Papers wrap over and wrinkle; besides, the Points of the Meridians on the Polar Papers seldom meet those of the Meridians of the Gores, except now and then by chance.

From this one rough Draught you may transfer the rest of the Gores that are to make up the Surface of the Globe; by which the trouble of projecting a New Scheme for every Gore will be avoided. Observe to do it with great care, For a small Error will, when the Gores are all joined, appear very sensible. Then because the Gores in all make 12, you may divide your Projections upon three Sheets of large Paper, allowing four Gores to each Sheet.

Draw an East and West Diameter thro’ every Sheet, in each of which set off the Distance from I to K, of Fig. 7. with your Compasses four times, without shifting the Points. In the middle of each erect Perpendiculars, and transfer 70 Degrees thereon (allowing the Polar Papers to include 20 Degrees from the Poles) Northwards and Southwards from the Center, which is the Intersection of the Equator with the straight Meridians or Perpendiculars, for Northern and Southern Latitude.

From the aforesaid Semi-gore, take the Distance between the Point of each 10th Parallel in the Perpendiculars, and in the Meridians AC, BD, and in the fair Draught describe Arcs to the Right and Left, upon the Points in the Perpendiculars.

Then placing one foot of your Compasses in the Point A or B, extend the other to the Point of the Meridians and Parallels Intersection; and as you go along, transfer the Distances upon the Copies from the correspondent Points of the Equator into the Arcs, and the Places where they cut will be the Points thro’ which the Meridians and Parallels must be drawn. And that Meridian, among all the Papers which is pitched upon for the first, let be divided equally from the Equator to G, and then in the Polar Papers to the Poles, into Degrees or Minutes, numbering each 10th or 5th Degree, with the Degrees of Latitude, minding to draw three Lines to distinguish it from other Meridians. The same must be observed in describing the Ecliptick or Equator; on which last every 5th or 10th Degree, ’till you come to 180 Degrees, must be figured Eastward and Westward from the first Meridian.

When all the Papers are finished so far as relates to the Meridians and Parallels, you must next draw the Ecliptick; and because that Circle intersects the Meridians in such and such Parallels of Declination, and the Meridians cut the Equator in the Degrees of Right Ascension; therefore by help of a Table of the Declination of those Points of the Ecliptick that cut the Meridian, and the Right Ascension of the same Points, find the Declination over-against the Right Ascension, which shews thro’ what parts of the Meridians the Ecliptick Arcs must pass; and draw Right Lines thro’ the Points of Intersection, which Lines will form the Ecliptick on the Globe.

A Table of Right Ascension and Declination of every 15 Degrees of the Signs.
Deg. Deg. & Min. Deg. & Min.
Aries 1513° 48′5° 56′
Taurus 027° 54′11° 30′
Taurus 1542° 31′16° 23′
Gemini 057° 48′20° 12′
Gemini 1573° 43′22° 39′
Cancer 090° 00′23° 30′
Cancer 15106° 17′22° 39′
Leo 0122° 12′20° 12′
Leo 15137° 29′16° 23′
Virgo 0152° 6′11° 30′
Virgo 15166° 12′5° 56′

Seek the Right Ascension as Longitude, and the Declination as Latitude, and where they intersect is the respective Point of the Ecliptick.

Proceed next to insert the Stars on the Gores for the Celestial Globe, and Places on those for the Terrestrial Globe, by help of most approved Astronomical and Geographical Tables and Maps according to their respective Longitude and Latitude, which may easily be affected by finding the Meridian and Parallel of the Star or Place; and the Point where they intersect each other, will be the exact Situation thereof.

The Rhumb Lines (which always make the same Angles with the Parallels they are dawn thro’) may be inscribed by Wright’s Card, or Loxodromick Tables, found in some Books of Navigation, as those in Newhouse. Trade Winds are best described from Dr Halley in the Philosophical Transactions: the Constellations may be drawn by a Celestial Globe.

Your Projectures of the Heaven and Earth being finished, you may either apply them to a particular Pair of Globes, or have them engraved in Copper-Plates.