## A Collection of Tables and Formulæ Useful in Surveying, Geodesy, and Practical Astronomy: Including Elements for the Projection of Maps |

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angle apparent applied approximate axis azimuth Barometer central Chronometer Co-ordinates comparison compute convert correction corresponding culmination decimal declination deduced deflection denote determined Diff difference distance division double East English inches equal altitudes error experiments feet foot FORM formula French given horizontal hour angle inclination intensity Interval known Latitude length limb Long longitude lower magnet mean moon mean solar measure meridian method metre middle miles minus Minutes moon's noon object Obs'd observed obtained parallax parallel preceding quantities R. A. in Arc radius readings Reduction refraction result scale seconds Sextant side sidereal sin² star station Sun's Survey Table taken tang tang L temperature tenths term Thermometer tion transit true upper vibration weight wire Yards zenith distance бр

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Page 26 - To trace Railroad Curves by means of deflections. General Propositions. 1. The angle formed by a tangent and a chord is equal to half the angle at the centre of the circle, subtended by the chord. 2. The angle of deflection formed by any two equal chords meeting

Page 8 - is a vessel containing 58372.2 grains, (8.3389 pounds avoirdupois,) of the standard pound of distilled water, at the temperature of maximum density of water, the vessel being weighed in air in which the Barometer is 30 inches at 62° Fahrenheit. The bushel is a measure containing 543391.89 standard grains (77.6274

Page 10 - 10 pounds avoirdupois weight of distilled water, weighed in air at the temperature of 62° Fahrenheit's Thermometer, the Barometer being at 30 inches. The

Page 6 - Oblique spherical triangles sin A sin B sin C sin a ~~ sin b sin c cos a = • cos b

Page 8 - The bushel is a measure containing 543391.89 standard grains (77.6274 pounds avoirdupois) of distilled water, at the temperature of maximum density of water, and Barometer 30 inches at 62° Fahrenheit. The gallon is thus the Wine gallon (of 231 cubic inches) nearly, and the bushel the Winchester bushel, nearly. The temperature of maximum density of water was determined by Mr. Hassler to be

Page 8 - are the gallon for liquid and the bushel for dry measure. The gallon is a vessel containing 58372.2 grains, (8.3389 pounds avoirdupois,) of the standard pound of distilled water, at the temperature of maximum density of water, the vessel being weighed in air in which the Barometer is 30 inches at 62°

Page 54 - in yards = 6.8427917. If the three angles of a triangle are assumed to have been equally well determined, the previous determination of the spherical excess is not necessary for the calculation of the sides, though it will be required for estimating the relative accuracy of the observations. For the sides of a spherical triangle may be computed as if they were rectilineal, when

Page 56 - to the level of the sea. Let r represent the radius of the Earth (or better, the normal N,) corresponding to the base b at the level of the sea, and r -\- a the radius referred to the level of the measured base B,

Page 54 - Between latitudes 45° and 25° the spherical excess amounts to about 1" for an area of 75.5 square miles. Hence, if the area in square miles be known, a close approximation to the spherical excess will be had by dividing the area by 75.5.

Page 23 - to that which is formed in excavations or embankments of roads ; terminated by parallel cross sections. Solid content = area of each end, added to four times the middle area, and the sum multiplied by the length