Mathematical Instruments
Book VI. Additions. Ch. II.

# Of Astronomical and Geographical Definitions, and the Uses of the Globes.

Before I lay down the Uses of the Globe, it will be proper to exhibit the following Definitions, necessary to be known in order to understand their Uses.

Definition I. The Latitude of any Place, is an Arc of the Meridian of that Place, intercepted between the Zenith and the Equator; and this is the same as an Arc of the Meridian intercepted between the Pole and the Horizon; and therefore the Latitude of any Place is often expressed by the Pole’s Height, or Elevation of the Pole: the Reason of which is, that from the Equator to the Pole, there always being the Distance of 90 Degrees, and from the Zenith to the Horizon the same Number, and each of these 90 containing within it the Distance between the Zenith and the Pole; that Distance therefore being taken away from both, must leave the Distance from the Zenith to the Equator equal to the Distance between the Pole and the Horizon, or the Elevation of the Pole above the Horizon.

Definition II. Latitude of a Star or Planet, is an Arc of a great Circle reckoned on the Quadrant of Altitude, laid through the Star and Pole of the Ecliptick, from the Ecliptick towards its Pole.

Definition III. Longitude of a Place is an Arc of the Equator intercepted between the Meridian; or it is more properly the Difference, either East or West, between the Meridians of any two Places, accounted on the Equator.

Definition IV. Longitude of a Star, is an Arc of the Ecliptick, accounted from the beginning of Aries to the Place where the Star’s Circle of Longitude crosseth the Ecliptick; so that it is much the same as the Star’s Place in the Ecliptick, accounted from the beginning of Aries.

Definition V. Amplitude of the Sun or of a Star, is an Arc of the Horizon intercepted between the true East or West Points of it, and that Point upon which the Sun or Star rises or sets.

Definition VI. Right Ascension of the Sun, or of a Star, is that part of the Equinoctial reckoned from the beginning of Aries, which riseth or setteth with the Sun or Star in a Right Sphere: but in an Oblique Sphere it is that part of a Degree of the Equinoctial, which comes to the Meridian with it, (as before) reckoned from the beginning of Aries.

Definition VII. A right or direct Sphere, is when the Poles are in the Horizon, and the Equator in the Zenith: the Consequence of being under such a Position of the Heavens as this (which is the case of those who live directly under the Line) is, that the Inhabitants have no Latitude nor Elevation of the Pole; they can nearly see both the Poles of the World. All the Stars in the Heaven do once in twenty-four Hours rise, culminate, and set with them; the Sun always rises and descends at Right Angles with the Horizon, which is the Reason they have always equal Days and Nights, because the Horizon doth exactly bisect the Circle of the Sun’s Diurnal Revolution.

Definition VIII. A Parallel Sphere, is where the Poles are in the Zenith and Nadir, and the Equinoctial in the Horizon; which is the Case of such Persons, if any such there be, who live directly under the North or South Poles.

And the Consequence of such a Position are, that the Parallels of the Sun’s Declination will also be Parallels of his Altitude, or Almacanters to them. The Inhabitants can see only such Stars as are on their side the Equinoctial; and they must have six Months Day, and six Months continual Night every Year; and the Sun can never be higher with them than 23 Degrees, 30 Minutes, which is not so high as it is with us on February the 10th.

Definition IX. An oblique Sphere, is where the Pole is elevated to any Number of Degrees less than 90: and consequently the Axis of the Globe can never be at Right Angles to, nor in the Horizon; and the Equator and Parallels of Declination, will all cut the Horizon obliquely, from whence it takes its Name.

Oblique Ascension of the Sun or Stars, is that Part or Degree of the Equinoctial reckoned from the beginning of Aries, which rises and sets with them in an oblique Sphere.

Ascensional Difference, is the Difference between the right and oblique Ascension, when the lesser is substracted from the greater.

## On the Terrestrial Globe.

Definition X. A Space upon the Surface of the Earth, reckoned between two Parallels to the Equator, wherein the Increase of the longest Day is a quarter of an Hour, is by some Writers called a Parallel.

Definition XI. And the Space contained between two such Parallels, is called a Climate: These Climates begin at the Equator; and when we go North or South, till the Day becomes half an Hour longer than it was before, they say we are come into the first Climate; when the Days are an Hour longer than they are under the Equator, we are come to the Second Climate, &c these Climates are counted in Number 24, reckoned each way from the Poles.

The Inhabitants of the Earth are divided into three sorts, as to the falling of their Shadows.

Definition XII. Amphiscii, who are those which inhabit the Torrid Zone, or live between the Equator and Tropicks, and consequently have the Sun twice a Year in their Zenith; at which time they are Ascii, i. e. have no Shadows, the Sun being vertical to them: these have their Shadows call to the Southward, when the Sun is in the Northern Signs, and to the Northward when the Sun is in the Southern Signs reckoned in respect of them.

Definition XIll. Heteroscii, who are those whose Shadows fall but one way, as is the Case of all such as live between the Tropicks and Polar Circles; for their Shadows at Noon are always to the Northward in North Latitude, and to the Southward in South Latitude.

Definition XIV. Periscrii, are such Persons that inhabit those Places of the Earth that lie between the Polar Circles and the Poles, and therefore have their Shadows falling all manner of ways, because the Sun at some time of the Year goes clear round about them. The Inhabitants of the Earth, in respect to one another, are also divided into three Sorts.

Periæcei, who are such as inhabiting the same Parallel (not a great Circle), are yet directly opposite to one another, the one being East or West from the other exactly 180 Degrees, which is their Difference of Longitude. Now these have the same Latitude and Length of Days and Nights, but exactly at contrary Times; for when the Sun riseth to one, it sets to the other.

Antæci, who are Inhabitants of such Places, as being under a Semi-circle of the same Meridian, do lie at equal Distance from the Equator, one towards the North, and the other towards the South. Now these have the same Degree of Latitude, but towards contrary Parts, the one North and the other South; and therefore must have the Seasons of the Year directly at contrary Times one to the other.

Antipodes, who are such as dwell under the same Meridian, but in two opposite and equidistant Parallels, and in the two opposite Points of those two Parallels; so that they go Feet against Feet, and are distant from each other an intire Diameter of the Earth, or 180 Degrees of a great Circle. These have the same Degree of Latitude, but the one South, the other North, and accounted from the Equator a quite contrary way; and therefore these will have all things, as Day and Night, Summer and Winter, directly contrary to one another.

### Use I.To find the Latitude of any Place.

Bring the Place to the Brass Meridian, and the Degrees of that Circle, intercepted between the Place and the Equinoctial, are the Latitude of that Place either North or South.

Then to fit the Globe so that the wooden Horizon shall represent the Horizon of that Place, elevate the Pole as many Degrees above the wooden Horizon, as are contain’d in the Latitude of that Place, and it is done; for then will that Place be in the Zenith.

If after this you rectify the Globe to any particular time, you may by the Index know the time of Sun-rising and Setting with the Inhabitants of that Place, and consequently the present Length of their Day and Night, &c.

### Use II.To find the Longitude of a Place.

Bring the Places severally to the Brass Meridian, and then the Number of Degrees of the Equinoctial, which are between the Meridians of each Place, are their Difference of Longitude either East or West.

But if you reckon it from any Place where a first Meridian is supposed to be placed, you must bring the first Meridian to the Brazen one on the Globe; and then turn the Globe about ’till the other Place comes thither also: reckon the Number of Degrees of the Equinoctial intercepted between the first Meridian, and the proper one of the Place, and that is the Longitude of that Place, either East or West.

### Use III.To find what Places of the Earth the Sun is Vertical to, at any time assigned.

Bring the Sun’s Place found in the Ecliptick on the Terrestrial Globe to the brazen Meridian, and note what Degree of the Meridian it cuts; then by turning the Globe round about, you will see what Places of the Earth are in that Parallel of Declination (for they will all come successively to that Degree of the brazen Meridian); and those are the Places and Parts of the Earth to which the Sun will be Vertical that Day, whose Inhabitants will then be Ascii; that is, their erect Bodies at Noon will cast no Shadow.

## Of the Celestial Globe.

### Use IV.To find the Sun’s place in the Ecliptick in any given Day of the Month, by means of the Circle of Signs on the wooden Horizon.

Seek the Day of the Month upon the Horizon, observing the Difference between the Julian and Gregorian Calendars; and then against the said Day you will find, in the Circle of Signs, the Sign and Degree the Sun is in the said Day. This being done, find the same Sign and Degree upon the Ecliptick on the Superficies of the Globe, and the Sun’s place will be had. Note, If the Sun’s place be required more exactly, you must consult an Ephemeris for the given Year, or else calculate it from Astronomical Tables.

### Use V.The Sun’s Place for any Day being given, to find his Declination.

Bring the Sun’s Place for that Day to the Meridian, and then the Degrees of the Meridian, reckoned from the Equinoctial either North or South to the said Place, shew the Sun’s Declination for that Day at Noon, either North or South, according to the time of the Year, viz. from March the 10th to September the 12th, North; and from thence to March again, South.

### Use VI.To find the Sun’s Amplitude either Rising or Setting.

Having rectified the Globe to the Latitude of the Place, that is, moved the brazen Meridian ’till the Degree of the Latitude thereon be cut by the Plane of the wooden Horizon, bring the Sun’s Place to the said Horizon either on the East or West side, and the Degrees of the Horizon, reckoned from the East Point, either North or South, give the Amplitude sought, and at the same time you have in the Circle of Rhumbs the Point that the Sun rises or sets upon.

### Use VII.To find the Sun’s Right Ascension.

Bring the Sun’s Place to the brazen Meridian, and the Degrees intercepted between the beginning of Aries, and that Degree of the Equinoctial which comes to the Meridian with the Sun, is the Right Ascension; which if you would have in time, you must reckon every 15 Degrees for one Hour, and every Degree four Minutes.

Note, The Reason of bringing the Sun’s place to the Meridian in this Use, is to fave the trouble of putting the Globe into the Position of a Right Sphere: for properly Right Ascension is that Degree of the Equinoctial, which rises with the Sun in a Right Sphere. But since the Equator is always at Right Angles to the Meridian, if you bring the Sun’s place thither, it must in the Equinoctial cut his Right Ascension.

### Use VIII.To find the Sun’s Oblique Ascension.

Having rectified the Globe to the Latitude, bring the Sun’s Place to the East-side of the Horizon, and the Number of Degrees intercepted between that Degree of the Equinoctial, which is now come to the Horizon and the beginning of Aries, is the Oblique Ascension. Now the lesser of these two Ascensions being taken from the greater, the Remainder is the ascensional Difference; which therefore is the Difference in Degrees between the Right or Oblique Ascension, or the Space between the Sun’s Rising or Setting, and the Hour of six. Wherefore the ascensional Difference being converted into Time, will give the time of the Sun’s Rising and Setting before or after six.

### Use IX.To find the time of the Sun’s Rising or Setting in any given Latitude.

Having first brought his Place to the Meridian, and the Hour-Index to twelve at Noon, bring his Place afterwards to the Horizon, either on the East or West-side thereof; then the Hour Index will either shew the time of his Rising and Setting accordingly. Now the time of the Sun’s Setting being doubled, gives the Length of the Day; and the time of his Rising doubled, gives the Length of the Night.

### Use X.To find the Sun’s Meridian Altitude, or Depression at Midnight, in any given Latitude.

Bring his Place to the Meridian above the Horizon, for his Noon Altitude, which will shew the Degrees thereof, reckoning from the Horizon; and to find his midnight Depression below the North Point of the Horizon, the Point in the Ecliptick opposite to the Sun’s present Place, must be brought to the South part of the Meridian above the Horizon, and the Degrees there intercepted between that Point and the Horizon, are his midnight Depression.

### Use XI.To find the Sun’s Altitude at any time of the Day given.

Rectify the Globe, that is, bring the Sun’s Place to the Meridian, and set the Hour-Index to twelve, and raise the Pole to the Latitude of the Place above the Horizon. This being done, fit the Quadrant of Altitude, that is, screw the Quadrant of Altitude to the Zenith, or in our Latitude screw it so that the divided Edge cuts 51 Deg. 32 Min. on the Meridian reckoned from the Equinoctial. Then turn the Globe about ’till the Index shews the given Time, and stay the Globe there; after which, bring the Quadrant of Altitude to cut the Sun’s Place in the Ecliptick, and then that Place or Degree of the Ecliptick will shew the Sun’s Altitude on the Quadrant of Altitude.

### Use XII.To find the Sun’s Altitude, and at what Hour he is due East or West.

Rectify the Globe, and fit the Quadrant of Altitude. Then bring the Quadrant to cut the true East Point, and turn the Globe about ’till the Sun’s Place in the Ecliptick cuts the divided Edge of the Quadrant of Altitude; for then that Place will shew the Altitude, and the Index the Hour.

### Use XIII.The Sun’s Azimuth, or when he is on any Point of the Compass being given; to find his Altitude and the Hour of the Day.

Set the Quadrant of Altitude to the Azimuth given, and turn the Globe about ’till his place in the Ecliptick touches the divided Edge of the Quadrant; so shall that Place give the Altitude on the Quadrant, and the Hour-Index the Time of the Day.

### Use XIV.To find the Declination, and the Right Ascension of any Star.

Bring the Star to the brazen Meridian, and then the Degrees intercepted between the Equinoctial and the Point of the Meridian cut by the Star, gives its Declinations. And the Meridian cuts, and shews its Right Ascension on the Equinoctial, reckoning from the beginning of Aries.

### Use XV.To find the Longitude and Latitude of any Star.

Bring the Solistitial Colure to the brazen Meridian, and there fix the Globe; then will the Pole of the Ecliptick be just under 23 Deg. 30 Min. reckoning from the Pole above the North Point of the Horizon, and upon the same Meridian; there screw the Quadrant of Altitude, and then bring its graduated Edge to the Star assigned, and there stay it: so will the Star cut its proper Latitude on the Quadrant, reckoned from the Ecliptick; and the Quadrant will cut the Ecliptick in the Star’s Longitude, or its Distance from the first Point of Aries.

### Use XVI.To find the time of any star’s rising, setting, or culminating, that is, being on the Meridian.

Rectify the Globe, and Hour-Index, and bring the Star to the East or West part of the Horizon, or to the brazen Meridian, and the Index will shew accordingly the Time of the Star’s rising, setting, or culminating, or of its being on the Meridian.

### Use XVII.To know, at any time assigned, what Stars are rising or setting, which are on the Meridian, and how high they are above the Horizon; on what Azimuth or Point of the Compass they are; by which means the real Stars in the Heaven may easily be known by their proper Names, and rightly distinguished from one another.

Rectify the Globe, and fit the Quadrant of Altitude, and set the Globe, by means of the Compass, due North and South; then turn the Globe and Hour-Index to the Hour of the Night assigned; so will the Globe, thus fixed, represent the Face or Appearance of the Heavens for that time: whereby you may readily see what Stars are in or near the Horizon; what are on or near the Meridian; which are to the North, or which to the South, &c. and the Quadrant of Altitude being laid over any particular Star, will shew its Altitude and Azimuth, or on what Point of the Compass it is, whereby any Star may easily be known; especially if you have a Quadrant to take the Altitude of any real Star supposed to be known by the Globe, to see whether it agrees with that Star which is its Representative on the Globe or not.

### Use XVIII.The Sun’s Place given, as also a Star’s Altitude, to find the Hour of the Night.

Rectify the Globe, and fit the Quadrant of Altitude; then move the Globe backwards or forwards, till the Quadrant cuts the Star in its given Altitude: for then the Hour-Index will shew the Hour of the Night. And thus may the Hour of the Night be known by a Star’s Azimuth, or its Azimuth by its Altitude.

### Use XIX.To find the Distance between any two Stars.

If the Stars lie both under the same Meridian, bring them to the brazen Meridian, and the Degrees of the said Meridian comprehended between them, are their Distance.

If they are both in the Equinoctial, or have both the same Declination, that is, are both in the same Parallel, then bring them one after another to the brazen Meridian, and the Degrees of the Equinoctial intercepted between them, when thus brought to the Meridian severally, are their Distance.

If the Stars are neither under the same Meridian or Parallel, then either lay the Quadrant of Altitude from one to the other (if it will reach), and that will shew the Distance between them in Degrees; or else take the Distance with Compasses, and apply that to the Equinoctial, or to the Meridian.

This Method of Proceeding will also shew the Distance of any two Places on the Terrestrial Globe in Degrees. Wherefore to find how far any Place on the Globe is from another, you need only take the Distance between them on the Globe with a Pair of Compasses, and applying the Compasses to the Equator at the Beginning of Aries, or at the first Meridian, you will there find the Degrees of their Distance, which multiplied by 70 (or 69 $$\frac{4}{11}$$ English Miles), and that will be their Distance in Miles.