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lurid are frequently call'd Geographical or Land-Maps, in eontra-diftinc'tion to Hydrographical or Sea-Maps, repre- fenting only the Seas arid Sea-Coafts, properly call'd Charts. See Chart.
There are three Qualifications required in a Map. Firft, That all Places have their juft Situation with regard to the chief Circles of the Earth, as the Equator, Parallel) Meridians, &c. becaufe on thefe depend many Properties of Regions, as well as Celeftial Phenomena. Secondly, That the Magnitudes of the feveral Countries have the fame Proportion as on the Surface of the Earth. And, Thirdly, That the feveral Places have the fame Diftance and Situation with regard to each other, as on the Earth itfelf.
For the Foundation oiMaps, and the Laws of FrojeBion, fee FerfpeBive and FrojeBion of the Sphere: The Applica- tion thereof, in the Conftruclion of Maps, is as follows.
FrojeBion of a Map, the Eye being plac'd in the Axis. Suppofe, v.g. rhe Northern Hemifphere to be reprefented with the Eye in a Point of theAxis, v.g. the South-Pole; for the Plane, whereon the Reprefentation is to be made, we take the Plane of the Equator, and from all the Points of the Surface of the Northern Hemifphere, conceive Lines palling thto the Plane to the Eye; which Points connected together, conftitute the Map required. Here the Equator will be theLimit of the Frojefture; the Pole, the Centre. The Meridians will be Right Lines pafling from the Pole to the Equator; the Parallels of Latitude, &c. Circles concentric with the Equator; and all the other Circles,and Arches of Circles, as the Horizon, Vertical Circles, £5?c. Ecliptic, fi?r. conceived in that Hemifphere, will be Ellip- fes, or Arches of Ellipfes. The better to apprehend the Projefture of the Circles on the Plane, conceive a radiant Cone, whofe Vertex is the Eye, its Bafe the Circle to be reprefented, and its Sides the Rays palling between the Circle and the Eye. Suppofe this Cone cut by the Plane. J Tis obvious, that, according to the various Por- tion of the Cone, there will be a different Section, and confequently a different Line or Reprefentation.
For the Application of thisDoclrine in Practice. In a Plane, v.g. a Paper, take the middle Point P. (Plate Geo- graphy, Fig. 2.) f° r the Pole, and from this, as a Centre, defcribe a Circle, of the intended Bignefs of your Map, to reprefent the Equator. Thefe two may be pitch'd on atpleafure, and from thefe all the other Points and Circles are to be determined. Divide the Equator into 360°, and drawing Right Lines from the Centre to the beginning of each Degree, thefe will be Meridians; whereof that drawn to the beginning of the firft Degree, we fuppofe the firft Meridian.
Now for the Parallels. There are four Quadrants of the Equator; the firft, 0,90; the fecond, 90,180; the third, 180,270; the fourth, 170,0; which, iorthebetter diftinc- tion, we will note with the Letters AB, BC, CD, DE. Taking one of thefe, v. g. BC, from the feveral Degrees thereof, as alfo from 25°, 50', andtftf", 50'. thereof draw occult Right Lines to the Point V, marking where thefe Lines cut the Semidiameter B?C; and from F, as a Centre, defcribe Arches pafling thro' the feveral Points in F C. Thefe Arches will be Parallels of Latitude. The Parallel at 23;o', will be the Tropic of Cancer, and that at <S6"° 30', the ArSic Circle. The Meridians and Parallels thus defcribed, from a Table of Longi- tudes and Latitudes, lay down the Places; reckoning the Longitude of each Place on the Equator, commencing at the firft Meridian, and proceeding to the Meridian of the Place; and for the Latitude of the Place, chufing a Parallel of the fame Latitude : the Point where this Meridian and Parallel interfea, reprefents the Place : And in the fame manner all the other Places may be deter- mined 'till the Map be compleat.
For the Ecliptic, half of which comes in this Hemi- fphere; we have obferved, that it makes an Ellipfis; fo that the Points thro' which it paffes are to be found. The firft Point, or that wherein the Ecliptic cuts the Equator,is the fame with that wherein the firft Meridian cuts the Equator, which is therefore diftinguifh'd by the Sign of Aries; the laft Point of this half Ellipfis, or the other In- terferon of the Equator and Ecliptic, viz. the End of Virgo, will be in the oppofite Point of the Equator, viz. at i8o Q . The middle Point of the Ellipfis is that wherein the Meridian 90 cuts the Tropic of Cancer. Thus we have three Points of the Ecliptic determined; for the reft, viz. for 1 ° , and 1; ° of Taunt s, 1 " and 1 5 ° of Gemini, 1 " of Leo, t Q of Virgo, the Declinations of thofe Points from the Equator muft be taken from a Table, and fet off in the Map. See Declination, &c.
Thus where the Meridian of 1 5 . cuts the Parallel of 5 fi , that Point will be 15*. of Aries. Where the Meri- dian 27 . cuts the Parallel, r 1 \ will be the firft Degree of Taurus, and fo of the reft. Thefe Points being all
join'd by a Curve Line, will be a Portion of an Ellipfis reprefenting the Ecliptic.
Maps of this Projection have the firft Qualification re- quired; but are defective in the fecond : the Surface be- ing ftretch'd further, as it approaches nearer the Equator. For the third, they are ftill further out. By this Method may almoft the whole Earth be reprefented in one Map, placing the Eye, v. g. in the Antarctic Pole, and affuming for the Plane of Projection that of fome Circle near it, v.g. the Antar.flic Circle. Nothing is here required bel fides the former Project ion; but to continue the Meridian draw Parallels on the other fide of the Equator, and com' pleat the Ecliptick; but this dillorts too much for Praflice.
This Projection is of all others the eafieft; but that, where the Eye is placed 'in the Plane of the Equator, is preferr'd for ufe, 'Tis, in effeft, of the latter kind that Maps are ordinarily made. The former are added to 'em, in fmall, by way of Supplement to reprefent the inter- mediate Spaces left between the two Hemifpheres. Fur- ther, as the Situation of the Ecliptic, with regard to the Earth, is continually changing, ftridly fpeaking, it has no Place in the Earth's Surface, but is ufed to be repre- fented according to its Situation fome certain Moment 5 viz. fo as the beginning of Aries and Libra may be in the Interferons of the firft Meridian and Equator.
The FrojeBion of Maps, with the Eye in the Plane of the Equator. This Method of Projection, tho' more difficult, is yet much jufter, more natural and commodious, than the former. To conceive it, we fuppofe the Surface of the Earth cut in two Hemifpheres by the entire Periphery of the firft Meridian, each of which Hemifpheres we re- prefent in a diftinft Map. The Eye is placed in the Point of the Equator 90 diftant from the firft Meridian; and for the tranfparent Plane, wherein the Reprefentation is to' be, we take the Plane of the firft Meridian. In this Pro- jection, the Equator is a Right Line, and the Meridian 90 diftant from the firft, is alfo a right Line; but the other Meridians, and all the Parallels of the Equator, are Arches of Circles, and the Ecliptic an Ellipfis.
The Method is thus. From a Point E, as a Centre, (Fig.3.) defcribe a Circle according to tho intended Bignefs of theMi^. This reprefents the firft Meridian, and its oppo- fite,'; for, drawing the Diameter B 33, there arife two Semi- circles , the one whereof IS A D is the firft Meridian, the other B C D its oppofite, or the Meridian of i8o g . This Diameter B D reprefents the Meridian of 90 Degrees, whereof the Point B is the Arclic Pole, and the Point D the Antarctic. The Diameter A C, perpendic ular to that B D, is the Equator. Divide the Quadrants AB, BC,CD, D A, each into 90 Degrees; and to find the Arches of the Meridians and Parallels, proceed thus. Divide the Equa- tor into its Degrees, viz. 180. (as being indeed only half the Equator;) thro' thefe feveral Divifions, and the two Poles, defcribe Arches of Circles, reprefenting Meridians, as B 1 D, B 2 D, &c. How to find Centres for defcribing thofe Arches, fee under the Word Circle. Indeed, the Ope- ration will be both more eafy and accurate, if performed by a Canon of Tangents. To defcribe the Parallels, the Meridian D B muft be in like manner divided into 180 De- grees; then thro' each of thefe Divifions, and the cor- refponding Divifions of the Quadrants A B, C B, defcribe Arches of Circles. Thus fhall we have Parallels of all Degrees, with Tropics, Polars and Meridians. As for the Ecliptic, it may be defign'd two ways. For its Situation over the Earth may either be fuch, as that its Interferon with the Equator may be over the Place A,j in which Cafe, the Projection of its Semi-Circles, from the firft Degree of Cancer, to the firft of Capricorn, will be a ftraight Line, to be determined by numbering 2; 30' from A towards B, and from the Extreme of that Numeration, drawing a Diameter thro' E; this Line will be half the Ecliptic in this Situation, and may be divided, as before, into Degrees, to which the Numbers, Signs, i$c. are to be affix'd. But if the Ecliptic be fo placed, as that its Interfeclion with the Equator is over the Place A, in the firft Meridian, its Projection in that Cafe will be a Segment of an Ellipfis; whereof two of the Points are AC--, a third that wherein the Meridian 90 cuts the Tropic of Cancer. The other Points muft be determin'd in the manner laid down above, viz. by taking the Declinations and right Afcenfions of r 5 t& Aries, i° of Taurus, 15 of Gemini, &c. For where the Parallels, according to their feveral Degrees of Declina- tion, cut the Merid ians, taken according to the feveral right Afcenfions, thofe Points of Interfecf ion are the Points of the 1 5 of 'Aries, Sic. A curve Line therefore being drawn, thefe will give the Projection of the Ecliptic.
Nothing now remains to compleat the Map, but to take the Longitudes and Latitudes of Places from a Table; and to fet them off on thcMap, as was directed under the former Method. In this Projection the whole Surface of the Earth
may
