C—la

70

4r \C Angular centring error ~3t ab B( v Applying this to each station gives the following: — Square of centring error (using rounded-off values)— (1) =( ' l X \ ( M() V 3ii > \3 x 31,11.6/ \390 x 430/ " 10"' (2) = 4 0 5 ( 87 ° V 7 " 18 10" \390 x 530/ ~ 10 10 4-05/ 710 V_ll6B 10 c V-530 x 250/ 10"' 4-05/ 360 V 42-85 10 s V 250 x 140/ *' 10 1 " ... 4-05 / 180 \ 66-95 IO 6 V, 140 x 100/ =: IO 10 405/ 300 V 68-90 (' ~ 10 x 230/ " 10"' _ 405 / 1020 V io ' 2< ' ) "> ~ 10 \230 x 880/ 10"' _ 4-05 / 990 V _ 2 7 7 (0) ~ IO" \BBO x 430/ "" IO 10 ' The second step is to determine the mean error in the traverse angles due to the sighting and reading error of 10". This gives v = + 10" = 10" '' 4848 in circular measure, .'. v' 2 =10 10 x 2350 for each angle. The error in the bearing of each lino is shown in the following table : —

The closing error in the bearing is therefore 10 ' in circular measure or 0' 42" in arc. The last step consists in computing the error in the total length of the traverse due to the coefficient of the chain and the errors in the traverse due to the angular errors in each line. c = 0015, 24 = 2956 links, .'. c 2 M = -006651. The square of the mean error for each line is as follows : — (2-3) 10 "' x 26-96 x 530' 2 = '000757 (3-4) 10 J " x 57-64 x 250 2 - -000360 (4-5) 10 10 x 92-77 x 140 2 = -000182 (5-6) 10" l 0 x 159-12 x 100 2 - -000159 (6-7) 10 1G x 249-57 x 230 2 = 001320 (7-8) 10 l 0 x 341-97 x 880 2 = -026482 (8-1) 10 '" x 375-76 x 430 2 = -006948 Sum = -036208 Mean error of closure — + (-006651 -|- -036208) = ± -207. Expressed in terms of a mile it is '56, or 0-395 in latitude and departure. The errors in the bearing in the above example due to imperfect centring are a little greater than those caused by the error of sighting and reading. This is accounted for by the three short

1. 2. 3. 4. 5. I a". A 1 + 2. Mean (error)' 2 in Bearing. I I Line. 10 10 x 3-46 10 '" x 7-18 10 '" x 1.1-63 10 '" x 42-85 10 "' x 66-95 10 '" x 68-90 10 '" x 10-29 IO 1 " x 2-77 10 '" x 23-50 10 '" x 26-96 10 "' x 23-50 10 '" x 30-68 10 '" x 23-50 10"'" x 3513 10 l0 x 23-50 10 "' x 06-35 10 "' x 2350 10 "' x 90-45 10 '" x 2350 10" 1 " x 92-40 LO l0 x 23-50 10 J " x 33-79 10 »- x 23-50 10 "' x 26-27 — I" 10 '" x 26-96 10 "' x 57-64 10 "' x 92-77 10 '" x .159-12 10 '" x 24957 10-'" x 341-97 10 l0 x 375-76 10'" X 402-03 2 3 3-4 4-5 5-6 6 7 7-8 8-1 L-2 10 "' x 214-03 10 '" x 18800 10 '" x 40203