UNITED STATES DEPARTMENT OF THE INTERIOR FRED A. SEATON, Secretary BUREAU OF LAND MANAGEMENT EDWARD WOOZLEY, Director + STANDARD FIELD TABLES AND TRIGONOMETRIC FORMULAS A Supplement to the Manual of Instructions for the Survey of the Public Lands of the United States EIGHTH EDITION 1956 Prepared in the Division of Cadastral Engineering UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON: 1956 For sale by the Superintendent of Documents, U. S. Government Printing Office Washington 25, D. C. - Price $1.50 TABLE H.-CONVERGENCY OF MERIDIANS. SIX MILES LONG AND SIX MILES APART, AND DIFFERENCES OF LATITUDE AND LONGITUDE. Convergency. Difference of longitude Difference of latitude I per range. for- Lat. I On the parallel. Angle. In arc. In time. 1 mt ITp. -- I 0 , , Lks. " " Seconds. 25 33.9 2 25 5 44.34 22.96 26 35.4 2 32 5 47.20 23.15 27 37.0 2 39 5 50.22 23.35 0.871 5.229 28 38.6 2 46 5 53.40 23.56 29 40.2 2 53 [) 56.74 23.78 30 41. 9 3 0 6 0.26 24.02 31 43.6 3 7 6 3.97 24.26 32 45.4 3 15 6 7.87 24.52 0.871 5.225 33 47.2 3 23 6 11.96 24.80 34 49.1 3 30 6 16.26 25.08 35 50.9 3 38 6 20. 78 25.39 36 52.7 3 46 6 25.53 25.70 37 54. 7 3 55 6 30.52 26.03 0.870 5.221 38 56.8 4 4 6 35. 76 26.38 39 58.8 4 13 6 41.27 26.75 40 60.9 4 22 6 47.06 27.14 41 63.1 4 31 6 53.15 27.54 42 65.4 4 41 6 59.56 27.97 0.869 5.216 43 67.7 4 51 7 6.29 28.42 44 70.1 5 1 7 13.39 28.89 45 72.6 5 12 7 20.86 29.39 46 75.2 5 23 7 28.74 29.92 47 77.8 5 34 7 37.04 30.47 0.869 5.211 48 SO. 6 5 46 7 45.80 31.05 49 83.5 5 59 7 55.05 31.67 50 86.4 6 12 8 4.83 32.32 51 89.6 6 25 8 15.17 33.03 ,52 92.8 6 39 8 26. 13 33.74 0.868 5.207 ,53 96.2 6 54 8 37.7,5 34.52 54 99.8 7 9 8 50.07 35.34 .'1.'1 103.5 7 25 9 3.18 36.22 56 107.5 7 42 9 17.12 37.14 57 111.6 8 0 9 31. 97 38.13 0.867 5.202 58 116.0 8 19 9 47.83 39.19 59 120.6 8 38 10 4:78 40.32 60 125.5 8 59 10 22.94 41.52 61 130.8 9 22 10 42.42 42.83 62 136.3 9 46 11 3.38 44.22 0.866 5.198 (j3 142.2 10 11 11 25.97 45.73 64 148.6 10 38 11 50.37 47.36 65 155.0 11 8 12 16.82 49.12 66 1(j2.S 11 39 12 45.55 51.04 67 170.7 12 13 13 16.88 53.12 0.866 5.195 68 179.3 12 51 13 51.15 55.41 69 188.7 13 31 14 28.77 57.92 70 199.1 14 15 15 10.26 00.68 0.866 5.193 199 TABLE 12.-AZIMUTHS OF THE TANGENT TO THE PARALLEL. , TABLE IS.-OFFSETS, IN LINKS, FROll THE TANGENT TO THE PARALLEL. Lat. 1 mi. 2m!. 3ml. 4 mi. 5 mi. 6ml. Lat. ~ 2!1 3% 4~ nu. ImL ~ 2m!. mi. 3m!. mi. 4m!. mL I I 6roLi . I I . I , ~ ~ 25 . 89 59.6 89 59.2 89 58.8 89 58.4 1--- 26 59.6 59.2 89 58.0 89 57.6 58.7 58.3 57.9 57.5 . 27 59.6 59.1 2S 58.7 58.2 57.8 57.4 25 0 0 1 2 3 4 6 8 10 12 14 17 59.5 59.1 58.6 58.2 29 59.5 59.0 57.7 57.2 26 0 0 I 2 3 4 6 8 10 12 15 18 58.6 58.1 57.6 57.1 27 0 1 1 2 3 5 6 8 10 13 16 18 30 59.5 28 0 1 1 2 3 5 7 9 11 13 16 19 59.0 58.5 58.0 29 31 59.5 59.0 57.5 57.0 0 1 1 2 3 5 7 9 11 14 17 20 32 58.4 57.9 57.4 56.9 59.5 58.9 58.4 57.8 33 59.4 57.3 56.8 30 0 1 1 2 4 5 7 9 12 15 18 21 58.9 58.3 57.7 31 0 1 1 2 4 5 34 59.4 58.8 57.2 56.6 7 10 12 15 18 22 58.2 57.7 57.1 56.5 32 0 1 1 3 4 6 8 10 13 16 19 23 33 0 1 1 3 4 6 8. 10 13 16 20 24 35 59.4 58.8 58.2 36 59.4 57.6 57.0 56.4 34 0 1 2 3 4 6 8 11 14 17 21 25 58.7 58.1 57.5 56.9 37 59.3 58.7 58.0 56.2 38 59.3 57.4 56.7 56.1 35 0 1 2 3 4 6 8 11 14 18 21 25 58.6 58.0 57.3 2 39 59.3 58.6 56.6 55.9 36 0 1 3 5 7 9 12 15 18 22 26 57.9 57.2 56.5 55.8 37 0 1 2 3 5 7 9 12 15 19 23 27 38 0 1 2 3 5 7 10 13 16 20 24 ~8 40 59.3 58.5 57.8 41 59.2 57.1 56.4 55.6 39 0 1 2 3 5 7 10 13 17 20 25 29 58.5 57.7 57.0 56.2 42 59.2 58.4 57.7 55.5 43 59.2 56.9 56.1 55.3 40 0 1 2 3 5 8 10 14 17 21 26 30 58.4 57.6 56.8 1 2 44 59.2 58.3 56.0 55.2 41 0 4 5 8 11 14 18 22 27 32 57.5 56.7 55.8 55.0 42 0 1 2 4 6 8 11 15 18 23 27 33 45 59.1 43 0 1 2 4 6 8 11 15 19 24 28 34 58.3 57.4 56.5 2 46 59.1 58.2 55.7 54.8 44 0 1 4 6 9 12 16 20 24 29 35 57.3 56.4 55.5 54.6 47 59.1 58.1 57.2 48 56.3 55.4 54.4 45 0 1 2 4 6 9 12 16 20 25 30 36 59.0 58.1 57.1 56.2 49 59.0 58.0 55.2 54.2 46 0 1 2 4 7 9 13 17 21 26 32 38 57.0 56.0 55.0 54.0 47 0 1 2 4 7 10 13 17 22 27 33 39 50 59.0 57.9 48 0 I 3 4 7 10 14 18 23 28 34 40 56.9 55.9 54.8 53.8 49 0 1 3 5 7 10 14 19 23 29 35 42 51 58.9 57.9 56.8 52 55.7 54.6 53.6 58.9 57.8 56.7 55.6 53 58.8 54..5 53.4 50 0 1 3 5 8 11 15 19 24 30 36 43 57.7 56.6 55.4 54.2 54 58.8 57.6 53.1 51 0 1 3 5 8 11 15 20 25 31 38 45 56.4 55.2 54.0 52.8 52 0 1 3 5 8 12 16 21 26 32 39 46 55 53 0 1 3 5 8 12 16 21 27 33 40 48 58.8 57.5 56.3 55.1 56 58.7 57.4 53.8 52.6 54 0 1 3 6 9 12 17 22 28 35 42 50 56.2 54.9 53.6 52.3 57 58.7 57.3 56.0 58 54.7 53.3 52.0 55 0 1 3 6 9 13 18 23 29 36 43 52 58.6 57.2 55.8 54.5 59 58.6 57.1 53.1 51. 7 56 0 1 3 6 9 13 18 24 30 37 45 54 55.7 54.2 52.8 51.4 57 0 2 3 6 10 14 19 25 31 39 47 56 60 58.5 57.0 58 0 2 4 6 10 J4 20 26 33 40 49 58 55.5 54.0 52.5 51.0 59 0 2 4 7 10 15 20 27 34 42 51 60 61 58.4 56.9 55.3 62 53.8 52.2 50.6 58.4 56.7 55.1 53.5 63 58.3 51.9 50.2 60 0 2 4 7 11 16 21 28 35 44 53 63 56.6 54.9 53.2 51.5 64 58.2 56.5 49.8 61 0 2 4 7 11 16 22 29 37 45 55 65 54.7 52.9 51.1 49.4 62 0 2 4 8 12 17 23 30 38 47 57 68 65 58.1 63 0 2 4 8 12 18 2{ 32 40 49 60 71 56.3 54.4 52.6 50.7 66 58.1 56.1 48.9 64 1 2 5 8 13 19 25 33 42 52 62 74 54.2 52.2 50.3 48.4 67 58.0 .55.9 53.9 68 51.8 49.8 47.8 65 I 2 5 9 13 19 26 34 44 54 65 78 57.9 55.7 53.