Elements of Surveying, and Navigation: With Descriptions of the Instruments and the Necessary Tables |
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Page 48
... yards . er parts . A Required the oth- GEOMETRICALLY . 27. Draw an indefinite straight line , AB , and from the scale of equal parts lay off AB equal to 408. Then , at A , lay off an angle equal to 58 ° 07 ' , and at B an angle equal to ...
... yards . er parts . A Required the oth- GEOMETRICALLY . 27. Draw an indefinite straight line , AB , and from the scale of equal parts lay off AB equal to 408. Then , at A , lay off an angle equal to 58 ° 07 ' , and at B an angle equal to ...
Page 49
... yards . TRIGONOMETRICALLY BY LOGARITHMS . To the angle Add the angle Their sum , • taken from leaves C A = 58 ° 07 ' • B = 22 ° 37 ' = 80 ° 44 ' 180 ° 00 ' 99 ° 16 ' , of which , as it ex- ceeds 90 ° , we use the supplement 80 ° 44 ...
... yards . TRIGONOMETRICALLY BY LOGARITHMS . To the angle Add the angle Their sum , • taken from leaves C A = 58 ° 07 ' • B = 22 ° 37 ' = 80 ° 44 ' 180 ° 00 ' 99 ° 16 ' , of which , as it ex- ceeds 90 ° , we use the supplement 80 ° 44 ...
Page 55
... yards , CAB 57 ° 35 ' , and CBA = 64 ° 51 ' . The angle C = 180 ° − ( A + B ) = 57 ° 34 ′ . To find the distance BC . ar . comp . sin C 57 ° 34 ' sin A 57 ° 35 ' :: AB 600 BC 600.11 yards • 0.073649 9.926431 · 2.778151 2.778231 . To ...
... yards , CAB 57 ° 35 ' , and CBA = 64 ° 51 ' . The angle C = 180 ° − ( A + B ) = 57 ° 34 ′ . To find the distance BC . ar . comp . sin C 57 ° 34 ' sin A 57 ° 35 ' :: AB 600 BC 600.11 yards • 0.073649 9.926431 · 2.778151 2.778231 . To ...
Page 56
... yards 2.808544 II . To determine the altitude of an inaccessible object above a given horizontal plane . FIRST METHOD . 36. Suppose D to be the inac- cessible object , and BC the hori zontal plane from which the alti- tude is to be ...
... yards 2.808544 II . To determine the altitude of an inaccessible object above a given horizontal plane . FIRST METHOD . 36. Suppose D to be the inac- cessible object , and BC the hori zontal plane from which the alti- tude is to be ...
Page 58
... have measured the base line , and the two angles of elevation , and AB = = found A 975 yards , = 15 ° 36 ' , DBC - 27 ° 29 ' ; First : ADB DBC - A = 27 ° 29 required the altitude DC . 58 { BOOK L ELEMENTS OF SURVEYING .
... have measured the base line , and the two angles of elevation , and AB = = found A 975 yards , = 15 ° 36 ' , DBC - 27 ° 29 ' ; First : ADB DBC - A = 27 ° 29 required the altitude DC . 58 { BOOK L ELEMENTS OF SURVEYING .
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Common terms and phrases
axis back-sight base line bearing called centre column comp Cosine Cosine D Cotang course decimal degrees determined difference of level direction divided double meridian distance draw east error example feet figure fore-sight given angle given line given point ground half hence horizontal angle horizontal distance horizontal line horizontal plane hypothenuse inch instrument intersection latitude and departure length line of collimation logarithm marked measure method miles multiplied natural sines needle parallel passing perpendicular plane of reference Plane Sail plane triangle protractor quotient radius right angles right-angled triangle rods scale of equal screws secant sector sides sights similar triangles spherical excess spider's lines square chains staff station straight line subtract surface survey Tang tangent telescope theodolite trigonometrical variation vernier plate vertical limb yards
Popular passages
Page 10 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 38 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 45 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 138 - ... the time of revolution is 23 h. and 56 min. To the eye of an observer, this star is continually in motion, 'and is due north but twice in 23 h. 56 min. ; and is then said to be on the meridian. Now, when it departs from the meridian, it apparently moves east or west, for 5 h. and 59 min., and then returns to the meridian again. When at its greatest distance from the meridian, east or west, it is said to be at its greatest eastern or western elongation.
Page 61 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Page 9 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number.
Page 142 - Now, if the elongation, at the time of observation, was west, and the north end of the needle is on the west side of the line, the azimuth, plus the angle shown by the needle, is the true variation. But should the north end of the needle be found on the east side of the line, the elongation being west, the difference between the azimuth and the angle would show the variation, and the reverse when the elongation is east. 1. Elongation west, azimuth 2° 04' North end of the needle on the west, angle...
Page 39 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, 00 is the secant of the arc AB.
Page 44 - CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side...
Page 22 - In a Right-angled Triangle, the side opposite the right angle is called the Hypothenuse ; and the other two sides are called the Legs, and sometimes the Base and Perpendicular.