Practical military surveying and sketching

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1861 - 192 pages
 

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Page 119 - As the sum of the two given sides is to the difference of those sides, so is the tangent of half the sum of the two unknown angles to the tangent of half their difference. Half the difference thus found, added to half their sum, gives the greater of the two angles, which is the angle opposite the greatest side, and subtracted from the half sum, will give the less angle.
Page 144 - ... to the tangent of the angle adjacent to the first side. CASE 3. — When the three sides are given. RULE 6. To find an angle. Subtract the sum of the logarithms of the sides which contain the required angle, from 20; to the remainder add the logarithm of half the sum of the three sides, and that of the difference between this half sum and the side opposite to the required angle. Half the sum of these three logarithms will be the logarithmic cosine of half the required angle. The other angles...
Page 161 - Azimuths, great circles which pass through the zenith and nadir, and are perpendicular to the horizon. The...
Page 132 - Then, if the zenith distance and declination be both north or both south, add them together; but if one be north and the other south, subtract the less from the greater, and the sum or difference will be the latitude, of the same name with the greater.* EXAMPLE I.
Page 41 - ... coincides with the 0 of the graduated scale. If this coincidence occurs, and the observed object be distant fully half a mile. then the instrument is in adjustment, and is ready for use ; but if the two zero points do not agree, the index-arm is moved until they do, and the key is then placed in one of the keyholes, and the reflected image of the distant object is made to coincide with the object seen direct through the lower part of the horizon-gloss.
Page 142 - C, as seen above, are constants, depending upon the latitude of the place of observation and the declination of the star. Tables for these quantities will be found in an appendix to Annual Report US Coast and Geodetic Survey for 1874.
Page 162 - The angular distance of a celestial body north or south of the celestial equator; also, engineering term for magnetic variation.
Page 132 - OOP, will give the zenith distance; to be called North or South, according as the observer is north or south of the star at the time of observation.
Page 116 - In that case, having found the difference as above, add -J^-Q of the result for each degree by which the mean temperature of the air at the two stands exceeds 55°; subtract the like proportion if the mean temperature be below 55°. When the upper thermometer reads highest, for "subtract" say "add," and vice versa in the foregoing rule.
Page 123 - The amplitude of a heavenly body is its angular distance from the prime vertical when in the horizon. It is reckoned from the east point when the body is rising or from the west point when it is setting, and toward the north or south according as the body is north or south of the prime vertical. Amplitudes are seldom used in modern practice. Fio. 3 Referring again to Fig. 3, the celestial body C' is above the horizon an angular distance measured by the arc CC'.

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