A treatise on the principal mathematical instruments employed in surveying, levelling, and astronomy; explaining their construction, adjustments, and use with an appendix, and tables

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. 1844 Excerpt: ... obtained by computation is necessarily very uncertain. Tables containing the dip for various altitudes, allowing for the mean effect of refraction, are to be found in all collections of nautical tables. But these tabular dips are at times found to differ so considerably from the truth, especially in tropical climates, that some experienced navigators have lately been induced to measure the actual dip by means of the sector, when any important determination has depended on the observation of altitudes. In the above diagram, A a represents a portion of the earth's surface, and O the place of an observer; H O H will be his true horizon, O A and O a his visible horizon; these rays being tangents to the earth's surface at A and a; the angle, O A, or H O a, is the dip of the horizon, which it is the of the dip-sector to measure. But the arcs to be measured by this instrument, for the purpose of obtaining the dip, are A Z a and A N a, the former of which is 180 + double the dip, and the latter 180--double the dip, therefore the fourth part of the difference is the measure of the dip. But as the instrument is constructed, only double the dip affected by index error is read from it, and the index error is made so great that the readings are both on the same side of zero, therefore the fourth part of the difference of the readings is the dip angle. In observing, the face of the instrument must be held in a vertical plane, and lengthwise, in a line with the opposite parts of the horizon whose dip is required; the eye-tube, G F, (page 65) will then be horizontal, and the observer will be looking at right angles to those points of the horizon which he wishes to observe. Suppose the instrument to be held as represented in our engraving, with the index uppermost, the obs...