Compass Rule and Transit Rule | Compass

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  Compass rule  The compass or bow ditch rule which has named after the distinguished American navigator Nathaniel bow ditch (1773-1838) The compass rule is based on the assumption that all lengths wee measured with eual care and all angles ta!en with appro imatel# the same precision$ %t is also assumed that the errors in measurement are accidental and that thetotal error in an# side of the traverse is directl# proportional to the total length of the traverse$ The compass rule ma# be stated as follows& the correction to be applied to the latitude or departure of an# course is eual to the total closure of latitudeor departure ' multiplied b# the ratio of the length of the course to the total length or perimeter of the traverse$ These correction are given b# the following euations$  1    * (d+,)  d  , (d+,) here&1  correction to be applied to the latitude of an# coursed  correction to be applied to the departure of an# course*  total closure in latitude or the algebraic sum of the north and south latitudes (.N*/.0,),  total closure in departure or the algebraic sum of the east and west departures (.0,/.,)d  length of an# closure, total length or perimeter of the traverseAll computed corrections should be added to chec! whether their respective sums eual the closures in latitude and departure$ To determine the adustedlatitude of an# course the latitude correction is either added to or subtracted from the computed latitude of the course$ A simple rule to remember is& if the sum of the north latitudes e ceeds the sum of the south latitudes ' latitudes corrections are subtracted from north latitudes and added to corresponding south latitudes$ 2owever ' if the sum of the south latitudes  e ceeds the sum of the north latitudes' the correction are applied in the opposite manner$ A similar procedure is used when adusting the departures$ After all corrections have been applied properl# to the latitudes and departures of the traverse$ it will be e pected that a perfect closure will be obtained$   Adusted length and directions *  √  lat  2 + dep 2  Tan 4  De p '   Lat'  here&*  adusted length of a course*at  adusted latitude of a course,ep  adusted departure of a course4  adusted hori5ontal angle between the reference meridian and a course6A99 :;*0(problem)<iven the accompan#ing tabulation are the observed data for a traverse obtained from a transit-tape surve#$ ,etermine the latitudes and departures of each course and balance these uantities b# emplo#ing the compass rule$ Also determine the linear error of closure' bearing of the side of error and the relative error of closure$ tabulates values accordingl# 6;:90,%9TAN0=0A:%N<6;T0, *AT%T;,06;T0, ,0A:T;:0/N-9/0-A=>?@$8@N @ 3 0>?3$@7>7$@3  =8@$BCN >B C 0@?$@3B1C$C3,8@@$>@9 B7 38 03C@$@37?1$?,01C$879 1C C@ 0??B$??C1?$@10D1117$CB9 83 >> 1C1$?B111$@8DABB$8N @@ ? 377$1?@>1$79;9@$13 (m)/1>B1$C?-1>>>$>8/1B7$3B-1B@C$C8 a)omputing *atitudes&*at  length cos 4b)omputing ,epartures,ep  length sin 4 c) ,etermining Total losure in *atitudes and ,epartures.N*  />?3$@7 / @?$@3 / 377$1?  /1>B1$C?m (summation of north latitudes).9*  -3C@$@3 E ??B$?? E 1C1$?B- 1>>>$>8m (summation of south latitudes).0,  />7$@3 / B1C$C3 / 7?1$? / C1?$@1 /1B7$3Bm (summation of east departures).,  -111$@8 E @>1$7- 1B@C$C8 (summation of west departure) *  .N* / .9*  /1>B1$C? / (-1>>>$>8) /1B$81 m  ,  .0, / .,  /1B7$3B / (-1B@C$C8) /18$8m ,  d1 / dC /d3 /d> /d@ / dB  d),etermining corrections for latitude F  1 CL D   F  1 16.815000.13 = 0.00336  A=   $33BG >?@$8@  1$B7  =  $33B G8@$BC C$8B  ,  $33B G8@@$>@ C$88  ,0  $33B G1C$87 3$>3  0D  $33B G1117$CB 3$7@  DA  $33B GBB$8 C$CC96*;T%6N 20F&1$B7/C$8B/C$88/3$>3/3$7@/C$CC  1B$811B$811B$81?(20F9)
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