2. If the Side or Sides of the Triangle be compofed of Arches Fig. of fuch Great Circles as are not actually divided (as all Circles XXVI. of Longitude, and other Oblique Great Circles) then, take the Length of fuch Side in a Pair of Calliper Compaffes, and apply it to any of the forementioned Great Circles (as the Aquino Tial, &c.) it thall thereupon fhew you the Quantity of that Side in Degrees. -Or, the Quadrant of Altitude (but rather, a thin Plate of Brafs longer than the Quadrant of Altitude, divided into Degrees, as the Quadrant is) applied to the Side to be Measured, between the Two Angular Points, fhall give you the Quantity of the Degrees of that Side of the Triangle. II. For the Angles. The Angles of Spherical Triangles are Measured upon the Superficies of the Globe, by counting (or fetting off) 90 Deg. from the Angular Point, of the Angle to be Measured, upon both the Sides which contains the Angle to be Meafured: And at the Terminations of thofe 90 Deg. on both the Sides, make Two fmall Marks upon the Globe. Unto thefe Two Marks, apply the Quadrant of Altitude, or thin Plate of Brafs; fo the Number of the Degrees thereof, contained between the Two Marks, is the Quantity of that Angle. Geographical Problems. PROB. I. To find the Longitude of any Place, defcribed upon the Terreftriak Longitude is the Distance of a Place from the firft Meridian reckoned in the Degrees of the Equator, beginning, as was faid, in the New Terreftrial Globe, (made by Mr. Morden) as St. Michael's Ifland in the Azores. Practice.] Bring the Place, (that is, the Mark of the Place) fuppofe London, to the Brazen Meridian; then count how many Degrees of the Equator are contained between the firft Meridian, and that of London cut by the Brazen Meridian, which you will find to be 28 Deg, and that is the Longitude required. And in this manner you find London TH PROB. II. To find the Latitude of any Place, HE Latitude of a Place, is the Distance of the Equator from the Parallel of that Place, reckoned in the Degrees of the Brafs Meridian, and is either North or South, according as it lyes between the North or South Poles of the Equator. To find the Latitude, bring the Mark of the Place, fuppofe London, to be the Brazen Meridian; then count the Number of Degrees upon the Meridian, contained between the Equator and the Place . Thus you fhall find the Latitude, by this new Globe, of London, to be 51 Deg. 30 Min. and of Two Places, which differ only in Latitude, to find their Distance. N this there are Two Varieties of Pofition. IN 1. If both the Places lye under the fame Meridian, and on one and the fame Side of the Equino&ial: Subftract the Leffer Latitude from the Greater, the Difference (or Remainder) reduced into Miles, (by allowing 60 Deg. to One Mile) Shall give you the Distance. Example. London and Ribadio lye both under the fame Me Fig. ridian, but differ in Latitude: For London hath 51 Deg. 30 Min. XXVI. of Latitude, at L, and Ribadio hath 34 Deg. of Latitude, at R, both North the Difference of Latitude is 17 Deg. 30 Min. equal to the Arch LR: And that Reduced into Miles, makes 1050 for their Diftance. 2. If the Two Places lye under the fame Meridian, but in dif ferent Hemispheres, i. e. one on the North, and the other on the South Side of the Equinoctial: Then, Add both the Latitudes together, and the Sum of them is their Distance.. Example. London, and the Ifland Triftan Dacunhu, lye both under One Meridian, but London hath 51 Deg. 30 Min. of North Latitude, at L, and the Ifland hath 34 Deg. of South Latitude, at D; the Sum of thefe Two Latitudes is 85 Deg. 30 Min. equal to the Arch of the Meridian LED; the which reduced into Miles, (by multiplying the Degrees by 60, and allowing for every Minute One Mile) makes 5130 Miles, for their Distance. PROB. IV. Two Places, which differ in Longitude only; To find their Distance. IN 1. If the Two Places lye both under the Equinoctial, and have no Latitude; in this Cafe, Their Difference of Longitude (if it be less than 180 Deg) is their Distance: But, if the Dif ference exceed 180 Deg. Subtract it from 360 Deg. and the Remainder is their Distance, in Degrees. Example. The Ifland Samaira, and Ifland St. Thomas, lye both under the Equinoctial: St. Thomas having 22 Deg. 10 Min. of Longitude at T, and the Ifland Samatra 82 Deg. 10 Min. at S. Now, the Leffer Longitude 22 Deg, 10 Min. fubftracted from the Greater 82 Deg. 10 Min. leaves 60 Deg. equal to the Arch S T, for their Difference in Degrees: Which converted into Miles, makes 3600, and fo many Miles are the Two Iflands diftant from each other. 2. But if the Two Places differ only in Longitude, and lye not in the Equinoctial, but under fome other intermediate Parallel of Latitude: As Hierufalem at H, and Baldo at B; both in the Parallel of 31 Deg. 40 Min. of North Latitude, but differing in Longitude 60 D g. 15 Min. equal to the Angle H PB, to find the Distance of thefe Two Places. Ff 1. By Fig. XXVI. I. By the Globe. Apply the Quadrant of Altitude, or Brass Plate, to the Two Places, and the Number of Degrees thereof contained between the Two Places, is their Distance, which will be found to be 50 Deg. 32 Min. II. By Trigonometrical Calculation.. The Quadrant of Altitude (or Brafs Plate) applied to the Two Places, is reprefented by the Arch HB, and the Arches of the Two Meridians, which pafs through the Two Places, are PBN and P HM; and P B and PH, are equal to the Complement of of the Latitude of both the Places, viz. 58 Deg. 20 Min. So that now you have conftituted upon the Globe an Oblique Spherical Triangle PBH, in which you have given, (1.) The Two Sides PB and P H, both equal to 58 Deg. 20 Min. the Complement of the Latitude. (2.) The Angle BPH 60 Deg.. 15 Min. the Difference of the Longitude of the Two given Places. To find the Side B H, their Distance.. For which this is The Canon for Calculation. By CASE I. of R. A. S. T.. Is to the Co-fine of the Common Latitude (PH or PB) 58 D. 20M.. To to Sine of half the Distance (half B H) 25 Deg. 16 Min. The Double whereof, 50 Deg. 32 Min. is the Distance BH, which in Miles is 3032 Miles. PROB. V. Two Places, which differ both in Longitude and Latitude; to find. their Distance. N this there are Three various Pofitions. IN 1. If one of the Places lye under the Equinoctial, and fo have. no Latitude; and the other under fome Parallel of Latitude be: tween the Equinoctial, and one of the Poles: As London, in 51 Deg. 30 Min. of North Latitude at L; and St. Thomas Illand under the Equinoctial at T, but differ in Longitude 18 Deg. For finding the Distance of thefe Two Places. 1. Ufon 1. Upon the Terreftrial Globe. Fig. Bring London to the Brafs Meridian, and over it, fix the Qua. XXVI. drant of Altitude: The Globe being in this Pofition, bring the Quadrant of Altitude to lye juft over St. Thomas Ifland, and you will find it cut the Quadrant of Altitude, in 54 Deg. 45 Min. for the Distance of the Two Places. II. By Trigonometrical Calculation. The Globe refting in the former Pofition, you will find constituted upon it a Right-angled Spherical Triangle L ET, compofed of, (1.) L Æ, an Arch of the Brafs Meridian. (2.) ÆT, an Arch of the Equinoctial. And, (3.) LT, an Arch of a Great Circle (made by the Quadrant of Altitude) paffing through both the Places: And in this Triangle, you have given, (befides the Right Angle at E) (1.) The Perpendicular LE, the Latitude of London, 51 Deg. 30 Min. (2.) The Angle at L, the Difference of Longitude 18 Deg. 10 Min. To find the Hypotenufe LT, the Distance. The Canon for Calculation. By CASE XIV. of R. A. S. T. As Tang. of the Latitude L Æ, 1 Deg. 30 Min. Is to the Radius So is the Co-fine of EL T, 18 Deg. 10 Min. To the Co-tangent of LT, 52 Deg. 55 Min. Which reduced into Miles, makes 3175 Miles, for Distance be tween London, and St. Thomas Ifland. 2. If both the Places propofed fhall be without the Equinoctial, but both of them, either on the North or South Side thereof: As London in 31 Deg. 30 Min. at L, and Hierufalem in 31 Deg. 40 Min. at H, both on the North Side of the Equinoctial; and their Difference of Longitude 46 Deg: To find their Distance Upon the Terrestrial Globe. Bring one of the Places, as London, to the Brafs Meridian, and over it fcrew the Quadrant of Altitude, and keep the Globe there fixed, then move the Quadrant of Altitude, till it lye over Hierufalem, and you fhall find it to lye under 39 Deg. 32 Min. of the Quadrant: And that is the Distance of the Two Places. |