38. VERTICAL ANGLES 0 180 90 270 0 180 270 90 Direct Reverse 50 0 310 0 With no index error Z D + Z R = 360 0 = 50 0 + 310 0 Index error occurs when the 0 0 is not in exactly vertical
39. Index Error 0 180 90 270 0 180 270 90 Direct Reverse 50 0 310 0 Index Error Index Error Z D = 54 0 50’ 10” Z R = 305 0 10’ 20” = 360 0 00’ 30” Index Error = = 30”/2 = 15” Corrected Z D = 54 0 50’ 10” – 15” = 54 0 49’ 55” Z R = 305 0 10’ 20” – 15” = 305 0 10’ 05” = 360 0 00’ 00”
46. ความสัมพันธ์ระหว่างมุมและระยะทาง A bisecting error of 1cm over 10m corresponds to an angle of 3’26” A bisecting error of 1cm over 1000m corresponds to an angle of 0’2” Hence, if a bisecting error of 1cm is made and the two legs of a measured angle are 10m and 1000m long respectively, then the measured angle could have an error of 3’26”+0’02”. THE QUALITY OF AN ANGULAR OBSERVATION DEPENDS TO A LARGE DEGREE ON THE PRECISION WITH WHICH AN OBJECT CAN BE BISECTED WHICH IN TURN DEPENDS ON THE DISTANCE BETWEEN THE TELESCOPE AND THE OBJECT
51. Converting Angular Values Convert = 39 0 41’ 54” to radians 2 radians = 360 0 OR radians = 180 0 = (39 + 41/60 +54/3600) degs / (180/ ) ……. radians DMS must usually be converted to D.DD before they can be operated on in a calculator or computer. In some cases (e.g. Excel) angular values must be converted to radians for trig functions. Most calculators will have a hard-wired function to go between DMS (HMS) and D.DD (H) and vice versa.
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