was explained before; for fhewing the Situation of places, and their Distance more accurately.

THE Method is this: There must be found by mathematical Inftruments, the Angle of the Pofition of one place from another; which is to be transferred to Paper. For Example; Let there be five places of a Country to be laid down, according to their Situation and Distance, which we call A, B, C, D, E. (Fig. 46.) And let us choose one, as A, from which the reft, or most of them, may be seen; and with an Instrument observe how they lie from you, or from the Meridian in which you are. Then taking, on the Paper, a Point as A, defcribe a Circle on it (which yet may be omitted if you have a Protractor) and take one Diameter of the Circle for the Meridian of A, as HAK; the other perpendicular to it, as HAK, will show the Eaft and Weft Point; F being the North, and G the South. Suppofe then that A looked from B thirty Degrees between South and East; count fo many Degrees on GH, and draw a Line thro' the thirtieth Degree: this fhows how B lies from A; and thus the Points the places D and E lie in are to be fet down. Then going to one of the other places, whofe Distance is known from A, with an Inftrument obferve the other three places C, D, E. This being done; Let there be drawn on the Paper a Scale of Miles, great or small, as you would have your Map; and on the Line between B and A, fet down their Distance known; which will give the place B; and thro' B draw another Meridian, parallel to the former; and making a Circle about B, as about A, draw from it Lines fhowing the Points that C, D, and E lie in; and where thefe Lines cut the Lines from A, will be the Places of C, D, E. And the fame is to be done, if there had been more

places.

The

The fourth Method; by the Globe.

WE may, with the help of the terrestrial Globe, represent Places remote from one another, and know their Situations and Distances: yea the whole Superficies of the Earth may be thus laid down; fo that the given place, or any place be in the middle of the Map, as in the fixth general Method; fo that this Method may be brought in among those for general Maps: but 'tis better not to extend the Map beyond an Hemifphere. For Example; Let it be proposed to fet down all the Places about Amfterdam, in their due Situation and Distance. First choose a Point in the Middle, as A, (Fig. 46.) and defcribe a Circle about it; and let FG be the Meridian Line, and HK the Eaft and Weft; divide each Quadrant into ninety Degrees.

THEN, on the Globe, bring Amfterdam to the Meridian, and elevate the Pole for it's Latitude, fix the Quadrant of Altitude at the Zenith, and bring it about to every Place you would have fet down; as to the Bounds of Spain, France, &c. and obferve in each the Angle made by the Meridian, and the Quadrant, i. e. the Angle of Pofition, with the Meridian of Amfterdam; and also the Degrees on the Quadrant between Amfterdam and each place; then draw on your Paper Lines from A, according as their bearing is between the four Cardinal places (we shall show afterwards how the Trouble of drawing Lines may be fpared); on these Lines are to be fet down their Distances by the Quadrant from a Scale, large or fmall, as you would have your Map; and you will thus have the feveral places.

BUT if the Map is to be large, and the Places at a great Distance, the Line may be divided by the Laws of Perfpective; by fuppofing the Eye at

the Antipodes of Amfterdam; and for the Map, we take the Plane of the Horizon for repreprefenting an Hemisphere; but if a greater or leffer Part of it, then we take a Plane for the Map, that fhall be parallel to that of the Horizon, which is to be distant from it the farther, as what we would lay down is above an Hemifphere. Draw then in another Paper a Circle, whofe Center is M, and NO a Diameter, and PQ_another, perpendicular; divide NQ into ninety Degrees, and take below. Q Degrees in proportion to the excefs of what you would reprefent above an Hemisphere, and thro' R draw a Line to MO parallel to QM, and from O draw Lines to each Degree of the Quadrant NQ or NQR, if a greater Portion than NQ; which will divide MQ or SR, into Parts which will be Degrees: then choose a Line of fuch a Length as we would have to reprefent the furtheft Distance from Amfterdam, which will be about half the Breadth of the Map; that Line is to be divided as MQ or SR, and mark the Parts 1, 2, 3, 4, &c. from that, as a Scale, take the feveral Distances, and fet them on the Lines that go to the places; and you have the Map finifhed, But the Lines need not be drawn to the places; if you have a Scale, or Ruler, divided as MQ or SR; apply one end to A, and the Scale on the Ruler being brought to Points that fhow the bearing of the places, you may fet off cir Distance, counting from A, on the Ruler.

The fifth Method; for Sea-Charts.

SEA-Charts are ftrait lined, and have the Meridians all parallel; otherwife than was shown in the laft Part of the fecond Method.

THEY are two-fold; the Degrees on the Meridians being either equal or not: they are made

the

761 the fame way as in the fourth and fifth Method of general Maps, only they represent but little, and have more Sea-Compaffes on them for finding the Bearings. We fhall fhow their Ufe hereafter, for failing. The Degrees on the Meridians are nearly equal when a small Part only is exhibited; as the Mediterranean: and if the Latitude be great, or the North and South Parts of the Country far diftant then they are made unequal.

CHAP.

CHAP. XXXIII.

Of the Distance of Places.

PROPOSITION I.

Having tawo Points, or Places, on the Globe, to draw from the one to the other an Arc, which shall be the Part of a great Circle on that Globe.

Co

NONCEIVE a right Line drawn from the one Point to the other; and from both, two Lines to the Center; these three make a Triangle; which if extended, will cut the Superficies of the Globe, and the Section will be the Periphery of a great Circle; and the Arch between the two Places will be what is wanted. Or take with your Compaffes a Quadrant of a great Circle, and fixing one Foot at each Place, defcribe two Arches cutting one another; where they interfect will be the Center of a great Circle, that will pafs thro' the two Points given.

PROPOSITION II.

The shortest Distance between two Places on the Superficies of the Earth, is only one Line, (excepting the Places of the Antipodes) which is the Arch of a great Circle, intercepted between the two Places.

THE