Formulas and Tables to Facilitate the Construction and Use of Maps

U.S. Government Printing Office, 1889 - 124 pages

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Page 39 - Tables.] Latitude of parallel. Meridional distances from even degree parallels. Abscissas of developed parallel. Ordinales of developed parallel. 5
Page 19 - Washington, Jr. The length corresponding to any latitude interval is the distance along the meridian between parallels whose latitudes are less and greater respectively than the given latitude by half the interval. Thus, for example, the length corresponding to the interval 30' and latitude 37° (182047.3 feet) is the distance along the meridian from latitude 36° 45
Page 13 - ... central meridian of the area to be projected. The distances along this central meridian between consecutive parallels are made equal (on the scale of the map) to the real distances along the surface of the spheroid. The circles in which the parallels are developed are not concentric, but their centres all lie on the central meridian. The meridians are concave toward the central meridian, and, except near the corners of maps showing large areas, they cross the parallels at angles differing little...
Page 38 - Latitude of parallel. Meridional distances from even degree parallels. Abscissas of developed parallel. Ordinates of developed parallel. 5' longitude. 10' longitude. 15' longitude. 20' longitude. 25
Page 7 - This spheroid undoubtedly represents very closely the true size and shape of the earth, and is the one to which nearly all geodetic work in the United States is now referred. The values of the constants are as follows : a, semi-major axis = 20926062 feet ; log a = 7.3206875.
Page 21 - ... and their application in the construction of maps may be best explained by an example. Suppose it is required to draw meridians and parallels for a map of an area of i° extent in longitude, lying between the parallels of 34° and 35°. Let the scale of the map be one mile to the inch, or 1/63360, and let the meridians and parallels be 10
Page 14 - II 7.3212956 2 0.3010300 x 6.8396581 y 5.989373l x = 6912865 feet y = 975828 feet. The equations (10) are exact expressions for the co-ordinates. But when JA is small, one may use the first terms in the expansions of sin (à), since) and sin2 £ (JA sinif) and reach results of a much simpler form.
Page 14 - ¿(ДХ sin ф)2 . x, and the value of у will be too great by an amount somewhat less than -^(ДХ sin ф)2 . у. An idea of the magnitudes of these fractions of x and у may be gained from the following table, which gives the values of ¿(ДХ sin ф)2 for a few values of the Values of ¿(ДА.
Page 16 - QUADRILATERALS OF THE EARTH'S SURFACE. An expression for the area of a zone of the earth's surface or of a quadrilateral bounded by meridians and parallels may be found in the following manner : — The area of an elementary zone dZ, whose middle latitude is ф and whose width is pm ¿ф, is (see FIG.
Page 13 - In the polyconic system of map projection every parallel of latitude appears on the map as the developed circumference of the base of a right cone tangent to the spheroid along that parallel. Thus the parallel EF (Fio. 2) will appear in projection as the arc of a circle EOF (Fie.

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