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Perimeter of the Earth to be 20.160 Miles, or 20. 340, according to that Measure.

FROM that Time to this none were folicitous about folving the Problem. The Arabs commonly ufing the Dimensions they had received from their Mathematicians; and the Italians, when they began to study Astronomy, made ufe of Ptolemy's Measure, viz. 180.000 Furlongs (which make 21.600 Italian Miles, or 5.400 German; fo that 60 of the former, and 15 of the later was thought to make a Degree: but they ought to have reckoned 15% of the latter, becaufe 32 Furlongs nearly equal a German Mile thus the Periphery would be 5625. Germ. Miles). But about 80 Years ago Snellius, a famous Mathematician, and Profeffor at Leyden, obferving that the Perimeter of the Earth, commonly made ufe of by Mathematicians (or the length of a Degree, vulgarly fuppofed 15 Dutch Miles), was queftionable, and founded upon no certain Demonstration; he thereupon applied himself with great Industry to it's Menfuration, and happily finished it; demonftrating the Magnitude of one Degree of the Earth's Periphery to be 28.500 Perches (each containing 12 Rbinland Feet) or 19 Holland Miles; and the whole Periphery to equal 6.840 Miles (reckoning 1.500 Perches, or 18.000 Rhinland Feet, to a Mile).

WE thought fit to premife this fhort Hiftory of the Earth's Menfuration, that the Reader may perceive by what Industry it hath been managed, and with what Difficulty effected. Now we shall treat of the different Methods of Menfuration, all founded upon the Discovery of the Earth's fpherical Figure, which we have proved in the preceding Chapter. Therefore, confidering it globular, if it be cut by a Plane paffing thro' the Center, the Section will be a great Circle of the Earth: if not thro' the Center, then the Section will be one of the leffer Circles. Alfo the Periphery of a great Circle upon the Surface of the

Earth,

Earth, is it's Circuit or Measure round. Note, This Periphery is divided (as all others are) into 360 Degr. and because the Extent of the whole cannot be measured at once, we folve the Problem by finding the Length of a Part (viz. of 1 Degr. Degr. &c.) in known Measures; which Neceffity often occurs in other Problems. We alfo frequently take the Periphery of the Earth to be a Meridian paffing thro' the Place of Observation, and the North or Pole-Star; which is more eafy, and lefs fubject to Error.

The first Method; ufed by the Arabians and others for measuring the Earth.

LE Tour Horizon be b HRSs; then the Perimeter of the Terrestrial Meridian (which lies under, and is concentrical to, that in the Heavens abcd) will be ABCD, (Fig. 6.) and R will be the Center of the Earth. Suppofe our Place of Obfervation at B, whofe Zenith is b, and the Terrestrial Pole A lying under that in the Heavens a; then the Elevation of the Pole above our Horizon will be AH, or ab. Let us take another Place in the fame Meridian ABCD under abcd, as G, whofe Zenith is g, and Horizon fFRTt. Now fuppofe the Elevation of the Pole to be accurately obferved in the Place B, viz. ab or AH; and alfo in the Place G, viz. fa or FA. Take FA from HA and the Remainder is HF, equal to BG, the Arch intercepted between the two Places. Laftly the Distance BG equal to the Arch bg, is to be accurately measured by fome known Measure, as a Perch or a Mile. Then by the Golden Rule fay, as BG is to ABGCD, 360 Degr. fo is the known Interval in Miles or Perches, to the Miles or Perches contained in the Periphery ABGCD: or as the Arch BG is to I Degr. fo are the Miles in the Distance BG, to the Miles or Perches in 1 Degree,

NOTE,

NOTE, If you take the vulgar Computation of the Distance B G, without meafuring it, then the Quantity of the Degree will be determined accordingly; as 1 Degr. will equal 15 fuch Miles, as BG equals 10, &c.

Example, Let B be Amfterdam, where the Eleva-. tion of the Pole AH or ab is 52 degr. 23 min. and let G be Schoonhoven, lying under the fame Meridian with Amfterdam, where the Elevation of the Pole AF or af is 51 degr. 54 min. therefore FH or BG will be 29 min. but the Distance between Amfterdam and Schoonhoven is 94 Dutch Miles, or 13875 Rhinland Perches, 12 Foot each; therefore, as 29 min. is to 60 min. or 1 degr. fo is 94 Miles to 19 Dutch Miles: therefore 19 Dutch Miles equal 1 degr. and 6.840 make 360, or the whole Periphery.

O'R if the Distance B G be fuppofed 7 German Miles (each equal to 1900 Rhinland Perches) it will be as 29 min. is to 60 min. fo is 7 to 15 of the fame German Miles, for a Degr. of which 5.400 make the whole Circumference. Thus the Elevation of the Pole at Prague is 50 degr. 6 min. and at Lincium 48 degr. 16 min. the Difference B G is 1 degr. 50 min. and the Distance is computed to be 26 German Miles; from whence the Periphery will be 5.105 Miles.

The fecond Method, that of Eratofthenes.

AGAIN, let there be two Places under the fame Meridian; the one B, Alexandria in Egypt, where Eratofthenes, Keeper of the King's Library, lived; the other G, (Fig. 6.) the Town of Syene, a City in Egypt, under the Tropic of Cancer, and, for that Reafon, chofen by Eratofthenes, whofe Diftance from Alexandria was computed 5000 Furlongs. Let the Distance of the Sun, at Noon, from the Zeniths, g and b, of both Places be

obferved

SECT. II. observed by an Inftrument on the fame Solstitial Day, viz. the 21st of June; when, at Alexandria, gb or GB equals Part of the Periphery by Obfervation (or 7 degr. 12 min.) but at Syene the Sun hath no Distance from the Zenith at Noon, it being exactly vertical that Day. So that the Arch of the Distance B G, intercepted between the two Places is 7 degr. 12 min. but the Distance itself is accounted 5.000 Furlongs (8 of which make an Italian Mile). Therefore by the Golden Rule, as 7 degr. 12 min. is to 1 degr. (or as % to 30, or as 36 to 5) fo is 5000 to 694 Furlongs in degr. Or as is to 1, (or as I to 50) fo is 5000 to 25000 Furlongs, the whole Periphery, according to this Measure. There are divers ways of taking the Meridian Altitude of the Sun, or it's Distance from the Vertex; as by a Quadrant, &c. Eratofthenes found it by a hollow hemifpherical Dial; where the Style BX (Fig. 7.) points to the Zenith, and OXZ is a Ray of the Sun terminating the Shadow of the Style, and fhews the Arch BZ equal to OB 7 degr. 12 min. the Distance of the Sun from the Zenith. But at Syene the Style hath no Shadow; nor hath the Sun any Diftance from the Zenith; being perpendicular to the Plane of the Place. Therefore fince B X Z (Fig. 6, 7.) is equal to the Angle b X O, (whose Measure is B G or bO) BG is equal to BZ 7 degr. 12 min. or so Part of the Periphery, as before.

The third Methad, that of Pofidonius.

POSIDONIUS took two Places under the fame Meridian; viz. B, Rhodes, the Place where he lived, and G, Alexandria in Egypt; and obferved the Altitude of the Star S (Fig. 6.) (a bright Star in the Ship Argo called Canopus) when it came to the Meridian of both Places, on the fame,

or

48

or which is all one, on different Days. This Star did not rife above the Horizon b Hs at Rhodes, but only glanced upon it at S: tho' it was elevated above the Horizon of Alexandria FRT, the Arch ts Part of the Periphery or 7 degr. 30 min. He tells us the Distance betwixt Alexandria and Rhodes is 5.000 Furlongs. Therefore, as 7 degr. 30 min. is to 1 degr. (or as to, i. e. as 360 to 48) fo is 5.000 to 6663 Furlongs in 1 degr, or as 1 : 48:: 5.000 24.000 Furlongs, for the whole Periphery of the Earth, according to Pofidonius.

The fourth Method, that of Snellius.

IN the Methods above delivered we have constantly supposed the two Places to lie under the fame Meridian; but because Places may lie plainer, and more commodious for this Purpose under different Meridians, we fhall propofe an Example in this Cafe which is that of Snellius.

LET therefore ABCD (Fig. 6.) be the Meridian of Alcmair, and B, Alcmair itfelf; where the Elevation of the Pole ba is 52 degr. 40 min. and the Polar Distance BA 37 degr. 191 min. 30 Sec.

LET the other Place P be Bergen-op-zoom, whose Meridian is A PC, and it's Distance from the Pole, or Complement of Latitude (viz. to 51 degr. 29 min.) is AP 38 degr. 31 min. therefore, having drawn PG perpendicular to ABG, the Difference of their Distances from the Pole is BG 1 degr. 11 min. 30 fec.

AFTER Snellius had taken these Obfervations, he accurately measured the Distance BP, between Alcmair and Bergen, and found it to be 34710 Rhinland Perches; and the Angle of Pofition PBG 11 degr. 26 min. 2 fec. therefore in the rightangled Triangle PBG, the Hypotenufe PB and VOL. I. E

the

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