Hydrographic surveying; elementary. for beginners, seamen, and others

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ...Take the simplest case. In fig. 145, O is the true station, and O' the false; 0 A is the zero line. In this case the false station is made directly in that line. A O' B is the observed angle; suppose it to be 60, while A O B is the angle required. AO'B = AOB + OBO'; therefore O B O' is the correction required. O O' is by supposition a short distance as compared to O B or O' B; and O x, drawn perpendicular to BO'i, represents the maximum perpendicular distance subtended by an angle OBx; Ox = O O'. sin O O' X = O O' sin A O' B, the observed angle. From the traverse table (Inman's Tables), 5 feet in the upper column and an angle of 60 gives 2-5 and 43. These values are those of the sides opposite the angles of a rightangled triangle, the greater side being opposite the greater angle. Therefore the side opposite the greater angle = 4-3. The next question is, What angle does 4 feet (near enough) subtend at a distance equal to O'B or OB; OBx being small Ox Og-tan or sin O Re. This may be calculated from the logarithm tables. But, by referring to the table in the Appendix, the angle can be taken out by inspection, and is the amount of the correction required, in this case,-to the observed reading AO'B; if O' is on the other side of O, then the correction would be +. Above 180 the sign is reversed. B is only a single angle taken from O'; but if there are any more, each would have to be corrected. Secondly, when the position O' is not on the line O A, but at O', as shown in fig. 146, then the correction to A O' B = O A O' + O B O', or the angle at A subtended by O y + angle at B subtended by the perpendicular distance O x. From A the perpendicular distance is O Y, and it is O X from B. In this case O X = O O1 sin O O1 X. O O1 is measured, and angle AO1 O observed. S...