## Outline of the Method of Conducting a Trigonometrical Survey, for the Formation of Geographical and Topographical Maps and Plans, Military Reconnaissance, Levelling, Etc: With the Most Useful Problems in Geodesy and Practical Astronomy, and Formulæ and Tables for Facilitating Their Calculation |

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accuracy accurate Additives adjustment altitude angle apparent applied approximate ascertained axis azimuth barometer base boundaries calculated centre chapter chronometer circle compared construction contained contents contours correction course declination depression described detail determined difference direction distance divisions drawn earth elevation equal error evidently feet figure fixed given gives ground half height horizontal hour inches instrument intersection interval known laid land latitude latter laying length longitude marked mean measured meridian method miles minute nature nearly necessary noon object observed obtained operation parallax parallel plane plotted pole portions position practical proportion quantity reading reference refraction represented roads scale screw sidereal sides sketch spherical star stations supposed surface survey taken taking telescope temperature theodolite thermometer tion tracing triangles trigonometrical true vertical zenith distance

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Page 180 - PS, the polar distance, and the angle at P are known, and ZP, the co-latitude, is the quantity sought. The formula given by Baily, for finding the third side, when the other two sides and an angle opposite to one of them are given, is tan a' == cos given angle x tan adjacent side

Page 147 - Both these projections may be considered natural ones, inasmuch as they are really perspective representations of the surface on a plane; but Mercator's projection is entirely an artificial one, representing the sphere as it cannot be seen from any one point, but as it might be seen by an eye carried successively over every part of it.

Page 156 - represent the equinox, rT will be the right ascension, TS the declination, and PS the polar distance of any star or object S, referred to the equinoctial by the hour circle PSTp; and BSD will be the diurnal circle it will appear to describe about the pole. Again, if we refer it to the horizon by the vertical circle

Page 101 - The pot is filled four or five inches with pure water; the thermometer fitted into the aperture in the lid of the sliding tube, by means of a collar of cork; and the tin sliding tube pushed up or down to admit of the bulb of the thermometer being about two inches from the bottom of the pot.

Page 126 - solely to establish the truth of this supposition, the account of which is published in the " Philosophical Transactions " for 1775. A distance of upwards of 4000 feet was accurately measured between two stations, one on the north and the other on the south side of a mountain in Perthshire. The difference of latitude between these extremities of the measured distance was, from a number of most careful observations, determined to be

Page 71 - required for use, is filled with water (colored with lake or indigo), till it nearly reaches to the necks of the bottles, which are then corked for the convenience of carriage. On setting the stand tolerably level by the eye, these corks are both withdrawn

Page 155 - 0 35 These definitions are rendered more evident by reference to the figure below, taken from Sir J. Herschel's Treatise on Astronomy, published in the Cabinet Cyclopaedia. " Let C be the centre of the earth, NCS its axis; then are N and S its poles; EQ its equator; AB the parallel of latitude of the station A on its surface; AP, parallel to

Page 146 - diametral plane ADF perpendicular to EB by the visual line PM E. The stereographic projection of a sphere, then, is a true perspective representation of its concavity on a diametral plane; and as such it possesses some singular geometrical properties, of which the following are two of the principal:—first, all circles on the sphere are represented by circles in the projection; thus the

Page 153 - always additive. This term, as applied in its limited sense to altitudes of celestial objects, is meant to express the angle subtended by the semi-diameter of the earth at the distance of the object observed. Altitudes of the moon, from her proximity to the earth, are most

Page 41 - ac=AC aD=AD To measure the distance between A and B, both being inaccessible :—From any point C draw any line Cc bisected in D ; take any point E in the prolonga'tion of AC, and join ED, producing