Elements of Precise Surveying and Geodesy |
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Page 4
... THREE - POINT PROBLEM PAGE 59 61 • · 64 67 GENERAL CONSIDERATIONS CHAPTER III . BASE LINES . 25 . PRINCIPLES AND METHODS . 26 . 27 . PROBABLE ERROR AND UNCERTAINTY BASES AND ANGLES . 28 . STANDARD TAPES 71 72 74 76 29 . MEASUREMENT WITH ...
... THREE - POINT PROBLEM PAGE 59 61 • · 64 67 GENERAL CONSIDERATIONS CHAPTER III . BASE LINES . 25 . PRINCIPLES AND METHODS . 26 . 27 . PROBABLE ERROR AND UNCERTAINTY BASES AND ANGLES . 28 . STANDARD TAPES 71 72 74 76 29 . MEASUREMENT WITH ...
Page 17
... three angles of a plane triangle be called x , y , and z , it is necessary that x + y + z = 180 ° and the values to be found for the angles must satisfy this condi- tion . In stating observation equations it will often be found best to ...
... three angles of a plane triangle be called x , y , and z , it is necessary that x + y + z = 180 ° and the values to be found for the angles must satisfy this condi- tion . In stating observation equations it will often be found best to ...
Page 18
... angles around the point N ; but if x , y , z , and w repre- sent these angles , then + y + z + w = 360 ° and the quantities are conditioned . To make the quantities inde- N M pendent only three unknowns should be taken ; thus let CNM ...
... angles around the point N ; but if x , y , z , and w repre- sent these angles , then + y + z + w = 360 ° and the quantities are conditioned . To make the quantities inde- N M pendent only three unknowns should be taken ; thus let CNM ...
Page 24
... three observations give B 56 ° 40 ′ 09 " , and two observations give C = 81 ° 02 ' 10 " . Compute the adjusted values of the angles . = 8. SOLUTION OF NORMAL EQUATIONS . The normal equations which arise in the adjustment of observations ...
... three observations give B 56 ° 40 ′ 09 " , and two observations give C = 81 ° 02 ' 10 " . Compute the adjusted values of the angles . = 8. SOLUTION OF NORMAL EQUATIONS . The normal equations which arise in the adjustment of observations ...
Page 40
... angles with a probable error of one second if proper precautions be taken to ... three repeti- tions . The first and fourth sets are taken with the telescope ... ANGLES . 4I The 40 II . PRECISE PLANE TRIANGULATION .
... angles with a probable error of one second if proper precautions be taken to ... three repeti- tions . The first and fourth sets are taken with the telescope ... ANGLES . 4I The 40 II . PRECISE PLANE TRIANGULATION .
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Common terms and phrases
adjusted values altitude angle equations arithmetic mean astronomical axis azimuth B₁ Bake Oven C₁ circle circle of latitude conditional equations coordinates corrections cosZ d₁ deduced degrees determined difference distance earth elevation ellipse ellipsoid equal Eratosthenes feet figure adjustment formula Geodetic Survey geodetic triangulation geoid given gives hence last Article latitude and longitude Least Squares length linear logarithms longitude M₁ mean measured meridian arcs meters method of Art Method of Least miles normal equations normal section oblate spheroid observation equations observed angles observed values P₁ Packer Spire parallel plane angles plumb-line deflections pole polyconic projection precision Prob probable error probable values quadrant R₁ radius of curvature refraction side equation sinZ Smith's Gap sphere spherical angles spherical excess station adjustment surface Table taken tangent telescope theodolite three angles tion toises tude unknown quantities v₁ v₂ vertical angles weight ΙΟ
Popular passages
Page 15 - Assume that the weights for the following subjects are: English 3, History 2, Mathematics 2, Foreign Languages 2, and Art 1. What would be the average of a student whose marks are: English 80, History 85, Algebra 84, Spanish 82, and Art 90? Solution...
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 12 - In observations of equal precision the most probable values of observed quantities are those that render the sum of the squares of the residual errors a minimum.
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 156 - L' , longitude M', and azimuth Z' . 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...
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 242 - THE word Geoid is used to designate the actual figure of the surface of the waters of the earth. The sphere, the spheroid, the ellipsoid, the ovaloid, and many other geometrical figures may be, to a less or greater degree, sufficient practical approximations to the geoidal or earthlike shape, yet no such assumed form can be found to represent it with precision. The geoid, then, is an irregular figure peculiar to our planet...
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 141 - Astronomeres, in 12 Signes; and every Signe is devysed in 30 Degrees, that is 360 Degrees, that the Firmament hathe aboven. Also, be the Erthe devysed in als many parties, as the Firmament; and lat every partye answere to a Degree of the Firmament: and wytethe it wel, that aftre the...
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.