Elements of Precise Surveying and Geodesy |
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a₁ adjusted values angle equations arithmetic mean astronomical axis Bake Oven base line bench C₁ circle computed conditional equation coordinates corrections cosZ d₁ deduced degrees determined difference distance earth elevation ellipse ellipsoid equal feet figure adjustment formula geodesy Geodetic Survey geodetic triangulation geoid given gives Greenwich mean hence hour-angle instrument known last Article latitude and longitude Least Squares length logarithms longitude M₁ mean solar measured meridian arc meters method of Art Method of Least miles normal equations normal section observation equations observed values ocean level P₁ parallel plane angles plumb-line deflections Polaris pole precision Prob probable error probable values quadrant r₁ radius of curvature reading refraction right ascension side equation sinZ sphere spherical angles spherical excess spheroid star subtracted surface Table taken tangent tape telescope theodolite three angles tion toises triangle unknown quantities v₁ v₂ vertical angles weight ΙΟ
Popular passages
Page 151 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 156 - The figure of the earth is very nearly that of an oblate spheroid, that is, an ellipsoid generated by the revolution of an ellipse about its minor axis. The...
Page 15 - In observations of equal precision the most probable values of the observed quantities are those that render the sum of the squares of the residual errors a minimum ; and in...
Page 156 - CHAPTER VII. SPHEROIDAL GEODESY. 57. PROPERTIES OF THE ELLIPSE. Since an oblate spheroid is generated by the revolution of an ellipse about its minor axis, the equator and all the sections of the spheroid parallel to the equator are circles, and all sections made by planes passing through the axis of revolution are equal ellipses. Let a and b represent the lengths of the semi-major and semi-minor axes of this meridian ellipse, which are the same as the semi-equatorial and semi-polar diameters of...
Page 153 - Let A and B be two points on the surface of the sphere, L and M being the latitude and longitude of A, and L' and M
Page 40 - ... right. The order in which the characters were to be read, was shown by the direction in which the figures are placed, as their heads are invariably turned towards the reader. A single line of hieroglyphics—the dedication of a temple or of any other monument, for example—proceeds sometimes one half from left to right, and the other half from right to left; but in this case a sign, such as the sacred tau, or an obelisk, which has no particular direction, is placed in the middle of the inscription,...
Page 140 - Sterre, ne apperethe not to hem. For whiche cause, men may wel perceyve, that the Lond and the See ben of rownde schapp and forme. For the partie of the Firmament schewethe in o Contree, that schewethe not in another Contree.
Page 110 - P tbe pole, Z the zenith, Q the celestial equator, and 0 the place of the sun at noon. Let A be the point where the instrument is set, which may be regarded as the center of the celestial sphere. Then the angle PAN or its equal QA Z is the latitude of the place of observation.
Page 142 - ... flatness of the earth, and had begun to regard it as a sphere, their investigations had been directed toward its size alone; now, however, the inquiry assumed a new phase, and its shape came up again for discussion.