This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 edition. Excerpt: ...and that they be independent of one another, so that no one of them could be obtained by combining any of the others. If a dependent condition were included, by mistake, it would be indicated during the solution of the normal equations by a derived equation having all of its coefficients zero, or ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 edition. Excerpt: ...and that they be independent of one another, so that no one of them could be obtained by combining any of the others. If a dependent condition were included, by mistake, it would be indicated during the solution of the normal equations by a derived equation having all of its coefficients zero, or nearly so, so that the corresponding correlate would be indeterminate. The necessary number of independent angle and side equations will be given by formulas (107) and (124), namely, Number of Angle Equations = L'--S' + 1 (107) Number of Side Equations =L-2S +3 (124) in which L and S are the total numbers of lines and stations, and L' is the number of full lines and S' is the number of occupied stations. (For a station to be considered as occupied, at least two lines must be unbroken at that station.) The best method of writing the angle and side equations so as to be certain of their independence as well as their number, is to draw a sketch of the system or figure to be adjusted, adding one station at a time, with its lines to the previous stations, and writing the equations introduced by that station and those lines. For each station so added, there will be as many angle equations as new full lines, less one, and as many side equations as new lines, less two. As has been stated, small angles should be used in the side equations where practicable, although it is best to use each but once. In angle equations, on the contrary, they should be avoided. 1 These local conditions are avoided in the figure adjustment by using directions instead of angles, as will be shown later on. For example, the equations for Fig. 22, page 96, will be written. In this case, L = 13, L' =12, S = S' = 7, and there are six angle and two side equations. The complete...
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