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GENERALIZED STRATIGRAPHIC COLUMN NEAR RED LODGE, MONTANA REGIONAL THICKNESS EOCENE ABSAROKA VOLCANIC SUPERGROUP 8000' MAINLY ANDESITIC, BASALTIC, AND DACITIC VOLCANICLASTICS (INCLUDING BRECCIAS, CONGLOMERATES, SANDSTONES, SILTSTONES, AND TUFS) INTERBEDDED WITH LAVA FLOWS AND VENT BRECCIAS; PETRIFIED TREES AND LEAF FOSSILS COMMON. WILLMUD FM 2300' VARIEGATED UNITS OF GRAY, RED AND PURPLE MUDSTONES WITH OCCASIONAL THIN SANDSTONES. MAMMALIAN BONES COMMON. PLANT REMAINS PRESENT IN TABULAR AND LENTICULAR CARBONACEOUS SHALES. PALEOCENE FORT UNION FM 3,000'-12,000' INTERBEDDED YELLOWISH, LENTICULAR SANDSTONES AND YELLOW-GRAY MUDSTONES; LACUSTRINE BELFRY MEMBER NEAR MIDDLE; COAL-BEARING MEMBER IN UPPER PART; SYNTECTONIC CONGLOMERATES AND BRECCIAS AT TOP OF SECTION ALONG MOUNTAIN FRONT; FOSSIL LEAVES COMMON, BONES RARE. CRETACEOUS LANCE FM 750-1000' THICK AND LATERALLY EXTENSIVE YELLOW SANDSTONES INTERBEDDED WITH GRAY, GRAY MUDSTONES. OCCASIONAL DINOSAUR BONES. MEETETESE FM 1200' BANDED GRAY MUDSTONES WITH INTERBEDDED SANDSTONES AND OCCASIONAL THIN LIGNITES. MUDSTONES ARE ROOTED AND CONTAIN PLANTS, FRESHWATER MOLLUSCS, AND DINOSAUR BONES. A SANDSTONE UNIT NEAR MIDDLE CONTAINS A MARINE TRACE FOSSIL ASSEMBLAGE. JUDITH RIVER FM 500-900' LIGHT-COLORED YELLOWISH SANDSTONES INTERBEDDED WITH YELLOWISH-GRAY SANDY SHALES AND SILTSTONES; FEW BEDS OF DARK GRAY CARBONACEOUS SHALES; OCCASIONAL THIN COAL BEDS; COMMON DINOSAUR BONES AND OCCASIONAL FOSSIL PLANTS CLAGGETT FM 120-500' BROWN TO GRAY SHALE WITH STRINGER SANDS NEAR TOP, GRADING UPWARD INTO MASSIVE RUSTY SANDSTONE. COMMONLY DARK NEAR BOTTOM AND LIGHTER NEAR TOP - PARKMAN MEMBER: THICK BENTONITE BELOW SHALE, NEAR BASE OF FORMATION, EAGLE FM 200-550' INTERBEDDED RIDGE-FORMING SANDSTONES WITH INTERBEDDED SHALES; COAL BETWEEN LOWER SANDS; SANDSTONES NOT CONTINUOUS: MASSIVE, RUSTY, PITTED SANDSTONE AT BASE - VIRGELLE MEMBER. TELEGRAPH CREEK FM 150-400' GREENISH-GRAY SHALE, SOME GYPSUM; SALT AND PEPPER SANDSTONE FORMS SHOULDER-LIKE MOUND IN UPPER PART: TWO PROMINENT RUSTY SANDSTONE RIDGE-FORMERS AT BASE. VERY FOSSILIFEROUS - ELK BASIN SANDSTONE MEMBER. CARLILE - NIobrARA SH 1000-1600' CODY SH VERY THICK SHALE, GRAY ON FRESH SURFACE, WEATHERS ALMOST WHITE; VERY LARGE CONCRETIONS NEAR TOP AS WELL AS LOWER IN FORMATION: LARGE AMMONITES FOUND IN CERTAIN LOCALITIES - EQUAL TO PART OR ALL OF 'CODY SHALE. FRONTIER FM 300-600' MASSIVE GRAY, RESISTANT SANDSTONES INTERCALATED WITH THINLY-BEDDED BROWN SANDY SHALE AND BLACK SHALE: LARGE THREE-FOOT CONCRETIONS NEAR TOP: FEW BEDS OF CHERT-PEBBLE CONGLOMERATE. POWRY SH 350-500' BROWNIISH-GRAY, HARD, RESISTANT SANDSTONE AND SOME BLACK SHALE: NUMEROUS FISH SCALES UP TO ONE AND ONE-HALF INCHES IN LOWER 250 FEET; SIDEITE CONCRETIONS COMMON 150 TO 300 FEET FROM TOP IN BLACK SHALES. THERMOPOLIS SH 500-600' DARK GRAY TO BLACK, THINLY-BEDDED, SOFT SHALES. NON-RESISTANT, INTERBEDDED WITH SEVERAL BENTONITE BEDS: SANDSTONE UNIT BETWEEN TWO AND THREE HUNDRED FEET ABOVE BASE. JURASSIC CLOVERLY FM 150-350' BASAL BLACK CHERT CONGLOMERATES OR PEBBLY, YELLOWISH SANDSTONES: REDDISH SHALES INTERCALATED WITH ANDESITIC AGGLOMERATES AND YELLOW SANDSTONE IN MIDDLE PORTION; GRAY-BROWN SANDSTONE AND SANDY SHALES TOWARD TOP. MORRISON FM 200-350' VARIEGATED REDDISH, GREENISH, PURPLISH, AND GRAY CLAYS AND SHALES INTERBEDDED WITH LIGHT YELLOWISH-GRAY SANDSTONES: RARE OCCURRENCES OF DINOSAUR BONES AND GASTROLITHS. SUNDANCE FM 350-600' BASAL GREEN-BROWN & RED CLAY; SHALES: THIN BEDS OF GYPSUM AND LS; MIDDLE GRAY CLAYS & SANDSTONE WEATHERING GREEN-BROWN: UPPER RESISTANT SS, GLAUCONITIC: COMMON BELEMNITES, CRINOID STEMS, AND THE MOLLUSCS, CRYPHEA GYPSUM SPRINGS FM 40-200' THIN-BEDDED GRAY LIMESTONES AND REDDISH SHALES: THINLY TO MASSIVELY BEDDED GYPSUM TOWARD TOP. TRIASS. PERM CHUGWATER FM 180-600' BRIGHT TO DARK RED SHALES, SILTSTONES, AND SANDSTONES: MUCH GYPSUM SCATTERED IN BASAL TWENTY FEET. PARK CITY FM 10-70' POROUS, THIN-BEDDED, GRAY LIMESTONES: FEW DOLOMITE BEDS AND THIN CALCAREOUS SANDSTONES ("PHOSPHORIA FM") MISSISSIPPIAN-PELM TENSLEEP SS 40-280' GRAY TO TAN, MASSIVE, CROSS-BEDDED, MEDIUM TO COARSE SANDSTONES: RESISTANT TO EROSION; UNFOSSILIFEROUS. AMSDEN FM 80-140' RED SHALES AND SILTSTONES WITH INTERCALATED GRAY LIMESTONE AND DOLOMITE: LOCALLY GRAY, CHERTY SANDSTONE. CAMBRIAN MADISON LS 700-900' CHIEFLY MASSIVE, LIGHT GRAY TO TAN LIMESTONES, COARSELY CRYSTALLINE TO FINE-GRAINED: SOME DOLOMITE AND LOCAL CHERTY ZONES; A FEW THINLY-BEDDED LIMESTONES; A VARIETY OF MARINE INVERTEBRATE FOSSILS FAIRLY COMMON. DEVONIAN THREE FORKS FM 70-140' PLATY, LIGHT GRAY AND YELLOW TO BROWN AND REDDISH LIMESTONE AND DOLOMITE: THICKER CALCAREOUS SANDSTONE AT BASE. JEFFERSON LS 220-375' ALTERNATING THINLY-TO-THICKLY BEDDED LIGHT GRAY TO BROWN LIMESTONES AND DOLOMITES WITH PETID ODOR; FEW FINE BRECCIA BEDS: CALCAREOUS SANDSTONE AT BASE: BRACHIOPODS (AIRYBAS, ETC.) FAIRLY COMMON. ORD. BEARTOOTH BUTTE FM 0-150' LOCAL LENSES OF THINLY-BEDDED RED AND BUFF CALCAREOUS SHALES AND THICKER BEDS OF YELLOWISH-WEATHERING, GRAY LIMESTONE AND INTRAFORMATIONAL LIMESTONE CONGLOMERATE: VERY COARSE BASAL CONGLOMERATE; FOSSIL FISHES AND PLANTS. BIGHORN DOLOMITE 150-400' YELLOWISH-GRAY SANDY DOLOMITE, TEN FEET, OVERLAIN BY MASSIVE, CLIFF-FORMING BUFF, ROUGH WEATHERING DOLOMITE MOTTLED WITH GRAY CRYSTALS; THEN LESS RESISTANT, THIN-BEDDED. FINE-GRAINED LIMESTONE WITH RESISTANT DOLOMITE IN MIDDLE, SIXTY FEET THIS UNIT: TOP EIGHTY FEET SAME MASSIVE, MOTTLED DOLOMITE NEAR BOTTOM: FOSSILS RARE. SNOWY RANGE FM 250-300' INTERCALATED GREENISH-GRAY SHALES AND INTRAFORMATIONAL CONGLOMERATES: LATTER CONTAINS DISTINCT SUB-ANGULAR, FLAT, GRAY PEBBLES; UPPER FORTY TO FIFTY FEET YELLOW TO GREENISH SHALE, GRAY TO BUFF DOLOMITE AND INTRAFORMATIONAL CONGLOMERATE (= GROVE CREEK MEMBER); PEbbles WELL-ROUNDED, GRAY WITH GREEN COATING: STAR-SHAPED FOSSILS IN MATRIX. CAMBRIAN MAURICE FM 90-150' CLIFF-FORMING, THICKLY BEDDED, CRYSTALLINE LIMESTONE, LIGHT GRAY TO BUFF WITH SOME MOTTLING; OCCASIONALLY OOLITIC: TRILLOBITE REMAINS COMMON IN COQUINA ABOUT THIRTY FEET ABOVE BASE AND IN TOPMOST BED. PARK SH 350-475' GREENISH TO PURPLE SHALE INTERBEDDED WITH ONE INCH BEDS AND LENSES OF GRAY LIMESTONE; TOP FIFTY FEET CONTAINS DISTINCTIVE EDGWISE CONGLOMERATES WITH CLASTS AT ALL ANGLES TO BEDDING. MEAGHER LS 40-100' THIN-BEDDED GRAY LIMESTONE, USUALLY IRREGULARLY WAVY-BEDDED: MIDDLE MEMBER, IF PRESENT, MAINLY SOFT, GREEN SHALES. WOLSEY SH 50-200' GREEN, GRAY, PURPLE, PAPERY SHALES GRADING UP TO GREEN, BROWN, SANDY SHALES & SILTSTONES; TRILLOBITES FAIRLY COMMON. PRE-C FLATHEAD SS 0-60' LIGHT TAN TO REDDISH TO WHITE, MEDIUM SANDSTONE, QUARTZITE, LOCALLY CGS: SANDSTONE COARSE & ARKOSIC TOWARD BASE. "BASEMENT" COMPLEX OF GRANITIC GNEISSES AND DARK SCHISTES, INTRUDED BY MAFIC DIKES, ETC. COMPILED BY KELLING DOF H. S. KAUFMAN A. JOHNSON NOTE: RELATIVE THICKNESSES PROPORTIONAL (APPROXIMATELY TO SCALE) WITHIN EACH ERA BUT NOT BETWEEN ERAS. TOTAL PALEOZOIC ABOUT 3000'; TOTAL MESOZOIC ABOUT 8500'; TOTAL CENOZOIC ABOUT 13,000' FEET. 1989
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TABLE I. SLOPE STAKE DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OF ANY WIDTH, SIDE SLOPES 1\frac{1}{2} TO 1. SLOPE STAKE SIDE STAKE C.L. SIDE STAKE SLOPE STAKE 16.05 10.7 16.2 24.3 \frac{1}{2} TO 1 \frac{1}{2} TO 1 | Cut or Fill | Distance out from Side or Shoulder Stake. | Cut or Fill | |---|---|---| | | 0 | .1 | .2 | .3 | .4 | .5 | .6 | .7 | .8 | .9 | | | 0 | 0 00 | 0 15 | 0 30 | 0 45 | 0 60 | 0 75 | 0 90 | 1 05 | 1 20 | 1 35 | 0 | | 1 | 1 50 | 1 65 | 1 80 | 1 95 | 2 10 | 2 25 | 2 40 | 2 55 | 2 70 | 2 85 | 1 | | 2 | 3 00 | 3 15 | 3 30 | 3 45 | 3 60 | 3 75 | 3 90 | 4 05 | 4 20 | 4 35 | 2 | | 3 | 4 50 | 4 65 | 4 80 | 4 95 | 5 10 | 5 25 | 5 40 | 5 55 | 5 70 | 5 85 | 3 | | 4 | 6 00 | 6 15 | 6 30 | 6 45 | 6 60 | 6 75 | 6 90 | 7 05 | 7 20 | 7 35 | 4 | | 5 | 7 50 | 7 65 | 7 80 | 7 95 | 8 10 | 8 25 | 8 40 | 8 55 | 8 70 | 8 85 | 5 | | 6 | 9 00 | 9 15 | 9 30 | 9 45 | 9 60 | 9 75 | 9 90 | 10 05 | 10 20 | 10 35 | 6 | | 7 | 10 50 | 10 65 | 10 80 | 10 95 | 11 10 | 11 25 | 11 40 | 11 55 | 11 70 | 11 85 | 7 | | 8 | 12 00 | 12 15 | 12 30 | 12 45 | 12 60 | 12 75 | 12 90 | 13 05 | 13 20 | 13 35 | 8 | | 9 | 13 50 | 13 65 | 13 80 | 13 95 | 14 10 | 14 25 | 14 40 | 14 55 | 14 70 | 14 85 | 9 | | 10 | 15 00 | 15 15 | 15 30 | 15 45 | 15 60 | 15 75 | 15 90 | 16 05 | 16 20 | 16 35 | 10 | | 11 | 16 50 | 16 65 | 16 80 | 16 95 | 17 10 | 17 25 | 17 40 | 17 55 | 17 70 | 17 85 | 11 | | 12 | 18 00 | 18 15 | 18 30 | 18 45 | 18 60 | 18 75 | 18 90 | 19 05 | 19 20 | 19 35 | 12 | | 13 | 19 50 | 19 65 | 19 80 | 19 95 | 20 10 | 20 25 | 20 40 | 20 55 | 20 70 | 20 85 | 13 | | 14 | 21 00 | 21 15 | 21 30 | 21 45 | 21 60 | 21 75 | 21 90 | 22 05 | 22 20 | 22 35 | 14 | | 15 | 22 50 | 22 65 | 22 80 | 22 95 | 23 10 | 23 25 | 23 40 | 23 55 | 23 70 | 23 85 | 15 | | 16 | 24 00 | 24 15 | 24 30 | 24 45 | 24 60 | 24 75 | 24 90 | 25 05 | 25 20 | 25 35 | 16 | | 17 | 25 50 | 25 65 | 25 80 | 25 95 | 26 10 | 26 25 | 26 40 | 26 55 | 26 70 | 26 85 | 17 | | 18 | 27 00 | 27 15 | 27 30 | 27 45 | 27 60 | 27 75 | 27 90 | 28 05 | 28 20 | 28 35 | 18 | | 19 | 28 50 | 28 65 | 28 80 | 28 95 | 29 10 | 29 25 | 29 40 | 29 55 | 29 70 | 29 85 | 19 | | 20 | 30 00 | 30 15 | 30 30 | 30 45 | 30 60 | 30 75 | 30 90 | 31 05 | 31 20 | 31 35 | 20 | | 21 | 31 50 | 31 65 | 31 80 | 31 95 | 32 10 | 32 25 | 32 40 | 32 55 | 32 70 | 32 85 | 21 | | 22 | 33 00 | 33 15 | 33 30 | 33 45 | 33 60 | 33 75 | 33 90 | 34 05 | 34 20 | 34 35 | 22 | | 23 | 34 50 | 34 65 | 34 80 | 34 95 | 35 10 | 35 25 | 35 40 | 35 55 | 35 70 | 35 85 | 23 | | 24 | 36 00 | 36 15 | 36 30 | 36 45 | 36 60 | 36 75 | 36 90 | 37 05 | 37 20 | 37 35 | 24 | | 25 | 37 50 | 37 65 | 37 80 | 37 95 | 38 10 | 38 25 | 38 40 | 38 55 | 38 70 | 38 85 | 25 | | 26 | 39 00 | 39 15 | 39 30 | 39 45 | 39 60 | 39 75 | 39 90 | 40 05 | 40 20 | 40 35 | 26 | | 27 | 40 50 | 40 65 | 40 80 | 40 95 | 41 10 | 41 25 | 41 40 | 41 55 | 41 70 | 41 85 | 27 | | 28 | 42 00 | 42 15 | 42 30 | 42 45 | 42 60 | 42 75 | 42 90 | 43 05 | 43 20 | 43 35 | 28 | | 29 | 43 50 | 43 65 | 43 80 | 43 95 | 44 10 | 44 25 | 44 40 | 44 55 | 44 70 | 44 85 | 29 | | 30 | 45 00 | 45 15 | 45 30 | 45 45 | 45 60 | 45 75 | 45 90 | 46 05 | 46 20 | 46 35 | 30 | | 31 | 46 50 | 46 65 | 46 80 | 46 95 | 47 10 | 47 25 | 47 40 | 47 55 | 47 70 | 47 85 | 31 | | 32 | 48 00 | 48 15 | 48 30 | 48 45 | 48 60 | 48 75 | 48 90 | 49 05 | 49 20 | 49 35 | 32 | | 33 | 49 50 | 49 65 | 49 80 | 49 95 | 50 10 | 50 25 | 50 40 | 50 55 | 50 70 | 50 85 | 33 | | 34 | 51 00 | 51 15 | 51 30 | 51 45 | 51 60 | 51 75 | 51 90 | 52 05 | 52 20 | 52 35 | 34 | | 35 | 52 50 | 52 65 | 52 80 | 52 95 | 53 10 | 53 25 | 53 40 | 53 55 | 53 70 | 53 85 | 35 | | 36 | 54 00 | 54 15 | 54 30 | 54 45 | 54 60 | 54 75 | 54 90 | 55 05 | 55 20 | 55 35 | 36 | | 37 | 55 50 | 55 65 | 55 80 | 55 95 | 56 10 | 56 25 | 56 40 | 56 55 | 56 70 | 56 85 | 37 | | 38 | 57 00 | 57 15 | 57 30 | 57 45 | 57 60 | 57 75 | 57 90 | 58 05 | 58 20 | 58 35 | 38 | | 39 | 58 50 | 58 65 | 58 80 | 58 95 | 59 10 | 59 25 | 59 40 | 59 55 | 59 70 | 59 85 | 39 | | 40 | 60 00 | 60 15 | 60 30 | 60 45 | 60 60 | 60 75 | 60 90 | 61 05 | 61 20 | 61 35 | 40 |
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TABLE III. TRIGONOMETRIC FORMULAE Right Triangle Oblique Triangles Solution of Right Triangles For Angle A. sin = a/c , cos = b/c , tan = a/b , cot = b/a , sec = c/b , cosec = c/a Given | Required a, b | A, B, c | tan A = a/b = cot B, c = sqrt(a^2 + b^2) = a sqrt(1 + b^2/a^2) a, c | A, B, b | sin A = a/c = cos B, b = sqrt((c+a)(c-a)) = c sqrt(1 - a^2/c^2) A, a | B, b, c | B = 90 deg - A, b = a cot A, c = a/sin A. A, b | B, a, c | B = 90 deg - A, a = b tan A, c = b/cos A. A, c | B, a, b | B = 90 deg - A, a = c sin A, b = c cos A, Solution of Oblique Triangles Given | Required A, B, a | b, c, C | b = (a sin B)/sin A , C = 180 deg - (A + B), c = (a sin C)/sin A A, a, b | B, c, C | sin B = (b sin A)/a , C = 180 deg - (A + B), c = (a sin C)/sin A a, b, C | A, B, c | A+B=180 deg-C, tan 1/2(A-B) = ((a-b)tan 1/2(A+B))/(a+b). c = (a sin C)/sin A a, b, c | A, B, C | s=(a+b+c)/2, sin 1/2 A = sqrt(((s-b)(s-c))/(bc)) , sin 1/2 B = sqrt(((s-a)(s-c))/(ac)), C=180 deg-(A+B) a, b, c | Area | s=(a+b+c)/2, area = sqrt(s(s-a)(s-b)(s-c)) A, b, c | Area | area = (bc sin A)/2 A, B, C,a | Area | area = (a^2 sin B sin C)/(2 sin A) REDUCTION TO HORIZONTAL Horizontal distance = Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance = 319.4 ft. Vert. angle - 5 deg 10'. From Table. IV. cos 5 deg 10' = .9959. Horizontal distance - 319.4 x .9959 - 318.09 ft. Horizontal distance also - Slope distance minus slope distance times (1-cosine of vertical angle). With the same figures as in the preceding example, the following result is obtained. Cosine 5 deg 10' = .9959. 1-.9959=.0041. 319.4 x .0041=1.31. 319.4-1.31=318.09 ft. When the rise is known, the horizontal distance is approximately:-the slope distance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft. slope distance=302.6 ft. Horizontal distance=302.6-(14 x 14)/(2 x 302.6) = 302.6-.32=302.28 ft.
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TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS Angle Sin Tan. Sec. Cosec. Cotg. Cosin. 0 o, 10 .0029 .0029 343.8 343.8 50 20 .0058 .0058 171.9 171.9 .99998 30 .0087 .0087 114.6 114.6 .99996 40 .0116 .0116 1.0001 85.94 85.94 .99993 20 40 .0156 .0156 1.0001 68.76 68.75 .99989 1 o, 10 .0204 .0204 49.11 49.10 .99979 50 20 .0233 .0233 1.0003 42.98 42.96 .99973 30 .0262 .0262 1.0003 38.20 38.19 .99966 40 .0291 .0291 1.0004 34.38 34.37 .99958 20 40 .0320 .0320 1.0005 31.26 31.24 .99949 2 o, 10 .0349 .0349 1.0006 28.65 28.64 .99939 50 20 .0378 .0378 1.0007 26.45 26.43 .99929 30 .0407 .0407 1.0008 24.56 24.54 .99917 40 .0436 .0437 1.0010 22.93 22.90 .99905 20 40 .0465 .0466 1.0011 21.49 21.47 .9892 20 40 .0494 .0495 1.0012 20.23 20.21 .98878 3 o, 10 .0552 .0553 1.0015 18.10 18.07 .98847 50 20 .0581 .0582 1.0017 17.20 17.17 .98831 30 .0610 .0612 1.0019 16.38 16.35 .98813 40 .0640 .0641 1.0020 15.64 15.60 .98795 20 40 .0669 .0670 1.0022 14.96 14.92 .98776 4 o, 10 .0727 .0729 1.0027 13.76 13.73 .98736 50 20 .0756 .0758 1.0029 13.23 13.20 .98714 30 .0785 .0787 1.0031 12.75 12.71 .98692 40 .0814 .0816 1.0033 12.29 12.25 .98668 20 40 .0843 .0846 1.0036 11.87 11.83 .98644 5 o, 10 .0901 .0904 1.0041 11.10 11.06 .98594 50 20 .0929 .0934 1.0043 10.76 10.71 .98567 30 .0958 .0963 1.0046 10.43 10.39 .98540 40 .0987 .0992 1.0049 10.13 10.08 .98511 20 40 .1016 .1022 1.0052 9.839 9.788 .98482 6 o, 10 .1074 .1080 1.0058 9.309 9.255 .98421 50 20 .1103 .1110 1.0061 9.065 9.010 .98390 30 .1132 .1139 1.0065 8.834 8.777 .98357 30 40 .1161 .1169 1.0068 8.614 8.556 .98324 20 40 .1190 .1198 1.0072 8.405 8.345 .98290 7 o, 10 .1248 .1257 1.0079 8.016 7.953 .98219 50 20 .1276 .1287 1.0082 7.834 7.770 .98182 40 30 .1305 .1317 1.0086 7.661 7.596 .98144 20 40 .1334 .1346 1.0090 7.496 7.429 .98106 10 40 .1363 .1376 1.0094 7.337 7.269 .98067 Angle Sin Tan. Sec. Cosec. Cotg. Cosin. 90 8 10 .1392 .1405 1.0098 7.185 7.115 .99027 82 50 10 .1421 .1435 1.0102 7.040 6.968 .98986 50 20 .1449 .1465 1.0107 6.900 6.827 .98944 40 30 .1478 .1495 1.0111 6.766 6.691 .98902 30 20 .1507 .1524 1.0115 6.636 6.561 .98858 20 10 .1536 .1554 1.0120 6.512 6.435 .98814 10 89 9 10 .1564 .1584 1.0125 6.394 6.314 .98769 81 50 10 .1593 .1614 1.0129 6.277 6.197 .98723 50 20 .1622 .1644 1.0134 6.166 6.084 .98676 40 30 .1650 .1673 1.0139 6.059 5.976 .98629 30 40 .1679 .1703 1.0144 5.955 5.871 .98580 20 10 50 .1708 .1733 1.0149 5.855 5.769 .98531 10 88 10 10 .1736 .1763 1.0154 5.759 5.671 .98481 80 50 10 .1765 .1793 1.0160 5.665 5.576 .98430 50 20 .1794 .1823 1.0165 5.575 5.485 .98378 40 30 .1822 .1853 1.0170 5.488 5.396 .98325 30 40 .1851 .1883 1.0176 5.403 5.309 .98272 20 10 50 .1880 .1914 1.0181 5.320 5.226 .98218 10 87 11 10 .1908 .1944 1.0187 5.241 5.145 .98163 79 50 10 .1937 .1974 1.0193 5.164 5.066 .98107 50 20 .1965 .2004 1.0199 5.089 4.989 .98050 40 30 .1994 .2035 1.0205 5.016 4.915 .97992 30 40 .2022 .2065 1.0211 4.945 4.843 .97934 20 10 50 .2051 .2095 1.0217 4.877 4.773 .97875 10 86 12 10 .2079 .2126 1.0223 4.810 4.705 .97815 78 50 10 .2108 .2156 1.0230 4.745 4.638 .97754 50 20 .2136 .2186 1.0236 4.682 4.574 .97692 40 30 .2164 .2217 1.0243 4.620 4.511 .97630 30 40 .2193 .2247 1.0249 4.560 4.449 .97566 20 10 50 .2221 .2278 1.0256 4.502 4.390 .97502 10 85 13 10 .2250 .2309 1.0263 4.445 4.331 .97437 77 50 10 .2278 .2339 1.0270 4.390 4.275 .97371 50 20 .2306 .2370 1.0277 4.336 4.219 .97304 40 30 .2334 .2401 1.0284 4.284 4.165 .97237 30 40 .2363 .2432 1.0291 4.232 4.113 .97169 20 10 50 .2391 .2462 1.0299 4.182 4.061 .97100 10 84 14 10 .2419 .2493 1.0306 4.133 4.011 .97030 76 50 10 .2447 .2524 1.0314 4.086 3.962 .96959 50 20 .2476 .2555 1.0321 4.039 3.914 .96887 40 30 .2504 .2586 1.0329 3.994 3.867 .96815 30 40 .2532 .2617 1.0337 3.949 3.821 .96742 20 10 50 .2560 .2648 1.0345 3.906 3.776 .96667 10 83 15 10 .2588 .2679 1.0353 3.864 3.732 .96593 75 50 10 .2616 .2711 1.0361 3.822 3.689 .96517 50 20 .2644 .2742 1.0369 3.782 3.647 .96440 40 30 .2672 .2773 1.0377 3.742 3.606 .96363 30 40 .2700 .2805 1.0386 3.703 3.566 .96285 20 10 50 .2728 .2836 1.0394 3.665 3.526 .96206 10 74 o, Cosin Cotg. Cosec. Sec. Tan. Sin. Angle Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle
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TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Angle Sin. Tan. Sec. Cosec. Cotg. Cosin. 16 .2756 .2867 1.0403 3.628 3.487 .96126 10 .2784 .2899 1.0412 3.592 3.450 .96046 20 .2812 .2931 1.0423 3.556 3.412 .95964 30 .2840 .2962 1.0429 3.521 3.376 .95882 40 .2868 .2994 1.0438 3.487 3.340 .95799 50 .2896 .3026 1.0448 3.453 3.305 .95715 17 .2924 .3057 1.0457 3.420 3.271 .95630 10 .2952 .3089 1.0466 3.388 3.237 .95545 20 .2979 .3121 1.0476 3.357 3.202 .95459 30 .3007 .3153 1.0485 3.326 3.174 .95372 40 .3035 .3185 1.0495 3.295 3.140 .95284 50 .3062 .3217 1.0505 3.265 3.108 .95195 18 .3090 .3249 1.0515 3.236 3.078 .95106 10 .3118 .3281 1.0525 3.207 3.048 .95015 20 .3145 .3314 1.0535 3.179 3.018 .94924 30 .3173 .3346 1.0545 3.152 2.989 .94832 40 .3201 .3378 1.0555 3.124 2.960 .94740 50 .3228 .3411 1.0566 3.098 2.932 .94646 19 .3256 .3443 1.0576 3.072 2.904 .94552 10 .3283 .3476 1.0587 3.046 2.877 .94457 20 .3311 .3508 1.0598 3.020 2.850 .94361 30 .3338 .3541 1.0608 2.996 2.824 .94264 40 .3365 .3574 1.0619 2.971 2.798 .94167 50 .3393 .3607 1.0631 2.947 2.773 .94068 20 .3420 .3640 1.0642 2.924 2.747 .93969 10 .3448 .3673 1.0653 2.900 2.723 .93869 20 .3475 .3706 1.0665 2.878 2.699 .93769 30 .3502 .3739 1.0676 2.856 2.675 .93667 40 .3529 .3772 1.0688 2.833 2.651 .93565 50 .3557 .3805 1.0700 2.811 2.628 .93462 21 .3584 .3839 1.0711 2.790 2.605 .93358 10 .3611 .3872 1.0723 2.769 2.583 .93253 20 .3638 .3906 1.0736 2.749 2.560 .93148 30 .3665 .3939 1.0748 2.729 2.539 .93042 40 .3692 .3973 1.0760 2.709 2.517 .92935 50 .3719 .4006 1.0773 2.689 2.496 .92827 22 .3746 .4040 1.0785 2.670 2.475 .92718 10 .3773 .4074 1.0798 2.650 2.455 .92609 20 .3800 .4108 1.0811 2.632 2.434 .92499 30 .3827 .4142 1.0824 2.613 2.414 .92388 40 .3854 .4176 1.0837 2.595 2.394 .92276 50 .3881 .4210 1.0850 2.577 2.375 .92164 23 .3907 .4245 1.0864 2.559 2.356 .92050 10 .3934 .4279 1.0877 2.542 2.337 .91936 20 .3961 .4314 1.0891 2.525 2.318 .91822 30 .3987 .4348 1.0904 2.508 2.300 .91706 40 .4014 .4383 1.0918 2.491 2.282 .91590 50 .4041 .4417 1.0932 2.475 2.264 .91472 Angle Sin. Tan. Sec. Cosec. Cotg. Cosin. 74 .4067 .4452 1.0946 2.459 2.246 .91355 50 .4094 .4487 1.0961 2.443 2.229 .91236 40 .4120 .4522 1.0975 2.427 2.211 .91116 30 .4147 .4557 1.0989 2.411 2.194 .90996 20 .4173 .4592 1.1004 2.396 2.177 .90875 10 .4200 .4628 1.1019 2.381 2.161 .90753 25 .4226 .4663 1.1034 2.366 2.145 .90631 50 .4253 .4699 1.1049 2.351 2.128 .90507 40 .4279 .4734 1.1064 2.337 2.112 .90383 30 .4305 .4770 1.1079 2.323 2.097 .90259 20 .4331 .4806 1.1095 2.309 2.081 .90133 10 .4358 .4841 1.1110 2.295 2.066 .90007 26 .4384 .4877 1.1126 2.281 2.050 .89879 50 .4410 .4913 1.1142 2.268 2.035 .89752 40 .4436 .4950 1.1158 2.254 2.020 .89623 30 .4462 .4986 1.1174 2.241 2.006 .89493 20 .4488 .5022 1.1190 2.228 1.991 .89363 10 .4514 .5057 1.1207 2.215 1.977 .89232 27 .4540 .5095 1.1223 2.203 1.963 .89101 50 .4566 .5132 1.1240 2.190 1.949 .88968 40 .4592 .5169 1.1257 2.178 1.935 .88835 30 .4617 .5206 1.1274 2.166 1.921 .88701 20 .4643 .5243 1.1291 2.154 1.907 .88566 10 .4669 .5280 1.1308 2.142 1.894 .88431 28 .4695 .5317 1.1326 2.130 1.881 .88295 50 .4720 .5354 1.1343 2.119 1.868 .88158 40 .4746 .5392 1.1361 2.107 1.855 .88020 30 .4772 .5430 1.1379 2.096 1.842 .87882 20 .4797 .5467 1.1397 2.085 1.829 .87743 10 .4823 .5505 1.1415 2.073 1.816 .87603 29 .4848 .5543 1.1434 2.063 1.804 .87462 50 .4874 .5581 1.1452 2.052 1.792 .87321 40 .4899 .5619 1.1471 2.041 1.780 .87178 30 .4924 .5658 1.1490 2.031 1.767 .87036 20 .4950 .5696 1.1509 2.020 1.756 .86892 10 .4975 .5735 1.1528 2.010 1.744 .86748 30 .5000 .5774 1.1547 2.000 1.732 .86603 50 .5025 .5812 1.1566 1.990 1.720 .86457 40 .5050 .5851 1.1586 1.980 1.709 .86310 30 .5075 .5890 1.1606 1.970 1.698 .86163 20 .5100 .5930 1.1626 1.961 1.686 .86015 10 .5125 .5969 1.1646 1.951 1.675 .85866 31 .5150 .6009 1.1666 1.924 1.664 .85717 50 .5175 .6048 1.1687 1.932 1.653 .85567 40 .5200 .6088 1.1707 1.923 1.643 .85416 30 .5225 .6128 1.1728 1.914 1.632 .85264 20 .5250 .6168 1.1749 1.905 1.621 .85112 10 .5275 .6208 1.1770 1.896 1.611 .84959 Angle Sin. Tan. Sec. Cosec. Cotg. Cosin. 66 .4074 .4535 1.0993 2.433 2.230 .91171 50 .4100 .4570 1.1008 2.418 2.213 .91036 40 .4126 .4605 1.1023 2.404 2.197 .90899 30 .4151 .4640 1.1038 2.390 2.180 .90759 20 .4177 .4676 1.1053 2.377 2.164 .90619 10 .4202 .4711 1.1068 2.363 2.147 .90475 65 .4228 .4747 1.1083 2.350 2.131 .90331 50 .4253 .4783 1.1098 2.337 2.115 .90183 40 .4279 .4819 1.1113 2.324 2.099 .90033 30 .4304 .4855 1.1128 2.311 2.083 .89879 20 .4330 .4891 1.1143 2.298 2.067 .89723 10 .4355 .4927 1.1158 2.285 2.051 .89564 64 .4381 .4964 1.1173 2.272 2.035 .89402 50 .4406 .5000 1.1188 2.259 2.019 .89238 40 .4432 .5037 1.1203 2.246 2.003 .89071 30 .4457 .5074 1.1218 2.233 1.987 .88900 20 .4483 .5111 1.1233 2.220 1.971 .88726 10 .4508 .5148 1.1248 2.207 1.955 .88550 63 .4534 .5185 1.1263 2.194 1.939 .88371 50 .4559 .5222 1.1278 2.181 1.923 .88190 40 .4585 .5260 1.1293 2.168 1.907 .88005 30 .4610 .5297 1.1308 2.155 1.891 .87817 20 .4636 .5335 1.1323 2.142 1.875 .87626 10 .4661 .5372 1.1338 2.129 1.859 .87431 62 .4687 .5410 1.1353 2.116 1.843 .87235 50 .4712 .5448 1.1368 2.103 1.827 .87036 40 .4738 .5486 1.1383 2.090 1.811 .86833 30 .4763 .5524 1.1398 2.077 1.795 .86628 20 .4789 .5562 1.1413 2.064 1.779 .86419 10 .4814 .5600 1.1428 2.051 1.763 .86207 61 .4840 .5639 1.1443 2.038 1.747 .85992 50 .4865 .5677 1.1458 2.025 1.731 .85773 40 .4891 .5716 1.1473 2.012 1.715 .85551 30 .4916 .5754 1.1488 1.999 1.699 .85326 20 .4942 .5793 1.1503 1.986 1.683 .85098 10 .4967 .5832 1.1518 1.973 1.667 .84866 60 .5000 .5872 1.1533 1.960 1.651 .84630 50 .5025 .5911 1.1548 1.947 1.635 .84390 40 .5050 .5951 1.1563 1.934 1.619 .84146 30 .5075 .5990 1.1578 1.921 1.603 .83899 20 .5100 .6030 1.1593 1.908 1.587 .83648 10 .5125 .6070 1.1608 1.895 1.571 .83394 Angle Sin. Tan. Sec. Cosec. Cotg. Cosin. 66 .4067 .4535 1.0993 2.433 2.230 .91171 50 .4100 .4570 1.1008 2.418 2.213 .91036 40 .4126 .4605 1.1023 2.404 2.197 .90899 30 .4151 .4640 1.1038 2.390 2.180 .90759 20 .4177 .4676 1.1053 2.377 2.164 .90619 10 .4202 .4711 1.1068 2.363 2.147 .90475 65 .4228 .4747 1.1083 2.350 2.131 .90331 50 .4253 .4783 1.1098 2.337 2.115 .90183 40 .4279 .4819 1.1113 2.324 2.099 .90033 30 .4304 .4855 1.1128 2.311 2.083 .89879 20 .4330 .4891 1.1143 2.298 2.067 .89723 10 .4355 .4927 1.1158 2.285 2.051 .89564 64 .4381 .4964 1.1173 2.272 2.035 .89402 50 .4406 .5000 1.1188 2.259 2.019 .89238 40 .4432 .5037 1.1203 2.246 2.003 .89071 30 .4457 .5074 1.1218 2.233 1.987 .88900 20 .4483 .5111 1.1233 2.220 1.971 .88726 10 .4508 .5148 1.1248 2.207 1.955 .88550 63 .4534 .5185 1.1263 2.194 1.939 .88371 50 .4559 .5222 1.1278 2.181 1.923 .88190 40 .4585 .5260 1.1293 2.168 1.907 .88005 30 .4610 .5297 1.1308 2.155 1.891 .87817 20 .4636 .5335 1.1323 2.142 1.875 .87626 10 .4661 .5372 1.1338 2.129 1.859 .87431 62 .4687 .5410 1.1353 2.116 1.843 .87235 50 .4712 .5448 1.1368 2.103 1.827 .87036 40 .4738 .5486 1.1383 2.090 1.811 .86833 30 .4763 .5524 1.1398 2.077 1.795 .86628 20 .4789 .5562 1.1413 2.064 1.779 .86419 10 .4814 .5600 1.1428 2.051 1.763 .86207 61 .4840 .5639 1.1443 2.038 1.747 .85992 50 .4865 .5677 1.1458 2.025 1.731 .85773 40 .4891 .5716 1.1473 2.012 1.715 .85551 30 .4916 .5754 1.1488 1.999 1.699 .85326 20 .4942 .5793 1.1503 1.986 1.683 .85098 10 .4967 .5832 1.1518 1.973 1.667 .84866 60 .5000 .5872 1.1533 1.960 1.651 .84630 50 .5025 .5911 1.1548 1.947 1.635 .84390 40 .5050 .5951 1.1563 1.934 1.619 .84146 30 .5075 .5990 1.1578 1.921 1.603 .83899 20 .5100 .6030 1.1593 1.908 1.587 .83648 10 .5125 .6070 1.1608 1.895 1.571 .83394 Angle Cosin. Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle
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TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Angle Sin. Tan. Sec. Cosec. Cotg. Cosin. Angle Sin. Tan Sec. Cosec. Cotg. Cosin. 32 .5299 .6249 1.1792 1.887 1.600 .84805 58 39 .6293 .8098 1.2868 1.589 1.235 .77715 51 10 .5324 .6289 1.1813 1.878 1.590 .84650 50 10 .6316 .8146 1.2898 1.583 1.228 .77531 50 20 .5348 .6330 1.1835 1.870 1.580 .84495 40 20 .6338 .8195 1.2929 1.578 1.220 .77347 40 30 .5373 .6371 1.1857 1.861 1.570 .84339 30 30 .6361 .8243 1.2959 1.572 1.213 .77162 30 40 .5398 .6412 1.1879 1.853 1.560 .84182 20 40 .6383 .8292 1.2991 1.567 1.206 .76977 20 50 .5422 .6453 1.1901 1.844 1.550 .84025 10 50 .6406 .8342 1.3022 1.561 1.199 .76791 10 33 .5446 .6494 1.1924 1.836 1.540 .83867 57 40 .6428 .8391 1.3054 1.556 1.192 .76604 50 10 .5471 .6536 1.1946 1.828 1.530 .83708 50 10 .6450 .8441 1.3086 1.550 1.185 .76417 50 20 .5495 .6577 1.1969 1.820 1.520 .83549 40 20 .6472 .8491 1.3118 1.545 1.178 .76229 40 30 .5519 .6619 1.1992 1.812 1.511 .83389 30 30 .6494 .8541 1.3151 1.540 1.171 .76041 30 40 .5544 .6661 1.2015 1.804 1.501 .83228 20 40 .6517 .8591 1.3184 1.535 1.164 .75851 20 50 .5568 .6703 1.2039 1.796 1.492 .83066 10 50 .6539 .8642 1.3217 1.529 1.157 .75661 10 34 .5592 .6745 1.2062 1.788 1.483 .82904 56 41 .6561 .8693 1.3251 1.524 1.150 .75471 49 10 .5616 .6787 1.2086 1.781 1.473 .82741 50 10 .6583 .8744 1.3284 1.519 1.144 .75280 50 20 .5640 .6830 1.2110 1.773 1.464 .82577 40 20 .6604 .8796 1.3318 1.514 1.137 .75088 40 30 .5664 .6873 1.2134 1.766 1.455 .82413 30 30 .6626 .8847 1.3352 1.509 1.130 .74896 30 40 .5688 .6915 1.2158 1.758 1.446 .82248 20 40 .6648 .8899 1.3386 1.504 1.124 .74703 20 50 .5712 .6959 1.2183 1.751 1.437 .82082 10 50 .6670 .8952 1.3421 1.499 1.117 .74509 10 35 .5736 .7002 1.2208 1.743 1.428 .81915 55 42 .6691 .9004 1.3456 1.494 1.111 .74314 48 10 .5760 .7046 1.2233 1.736 1.419 .81748 50 10 .6713 .9057 1.3492 1.490 1.104 .74120 50 20 .5783 .7089 1.2258 1.729 1.411 .81580 40 20 .6734 .9110 1.3527 1.485 1.098 .73924 40 30 .5807 .7133 1.2283 1.722 1.402 .81412 30 30 .6756 .9163 1.3563 1.480 1.091 .73728 30 40 .5831 .7177 1.2309 1.715 1.393 .81242 20 40 .6777 .9217 1.3600 1.476 1.085 .73531 20 50 .5854 .7221 1.2335 1.708 1.385 .81072 10 50 .6799 .9271 1.3636 1.471 1.079 .73333 10 36 .5878 .7265 1.2361 1.701 1.376 .80902 54 43 .6820 .9325 1.3673 1.466 1.072 .73135 47 10 .5901 .7310 1.2387 1.695 1.368 .80730 50 10 .6841 .9380 1.3711 1.462 1.066 .72937 50 20 .5925 .7355 1.2413 1.688 1.360 .80558 40 20 .6862 .9435 1.3748 1.457 1.060 .72737 40 30 .5948 .7400 1.2440 1.681 1.351 .80386 30 30 .6884 .9490 1.3786 1.453 1.054 .72537 30 40 .5972 .7445 1.2466 1.675 1.343 .80212 20 40 .6905 .9545 1.3824 1.448 1.048 .72337 20 50 .5995 .7490 1.2494 1.668 1.335 .80038 10 50 .6926 .9601 1.3863 1.444 1.042 .72136 10 37 .6018 .7536 1.2521 1.662 1.327 .79864 53 44 .6947 .9657 1.3902 1.440 1.036 .71934 46 10 .6041 .7581 1.2549 1.655 1.319 .79688 50 10 .6967 .9713 1.3941 1.435 1.030 .71732 50 20 .6065 .7627 1.2577 1.649 1.311 .79512 40 20 .6988 .9770 1.3980 1.431 1.024 .71529 40 30 .6088 .7673 1.2605 1.643 1.303 .79335 30 30 .7009 .9827 1.4020 1.427 1.018 .71325 30 40 .6111 .7720 1.2633 1.636 1.295 .79158 20 40 .7030 .9884 1.4061 1.422 1.012 .71121 20 50 .6134 .7766 1.2661 1.630 1.288 .78980 10 50 .7050 .9942 1.4101 1.418 1.006 .70916 10 38 .6157 .7813 1.2690 1.624 1.280 .78801 52 .7071 1. 1.414 1.414 1. .70711 45 10 .6180 .7860 1.2719 1.618 1.272 .78622 50 20 .6202 .7907 1.2748 1.612 1.265 .78442 40 30 .6225 .7954 1.2778 1.606 1.257 .78261 30 40 .6248 .8002 1.2808 1.601 1.250 .78079 20 50 .6271 .8050 1.2838 1.595 1.242 .77897 10 Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle
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TABLE V. TANGENTS AND EXTERNALS TO A 1° CURVE I T E I=10° I T E I=20° I T E I=30° 1° 50.00 .218 + 10' 58.34 .297 20' 66.67 .388 30' 75.01 .491 40' 83.34 .606 50' 91.68 .733 2° 100.01 .873 .001 10' 108.35 1.024 20' 116.68 1.188 30' 125.02 1.364 40' 133.36 1.552 50' 141.70 1.752 3° 150.04 1.964 10°. C. 10' 158.38 2.188 T 20' 166.72 2.425 .06 30' 175.06 2.674 E 40' 183.40 2.934 50' 191.74 3.207 .003 4° 200.08 3.492 10' 208.43 3.790 20' 216.77 4.099 30' 225.12 4.421 40' 233.47 4.755 50' 241.81 5.100 15°. C. 5° 250.16 5.459 T 10' 258.51 5.829 .09 20' 266.86 6.211 E 30' 275.21 6.606 .004 40' 283.57 7.013 50' 291.92 7.432 6° 300.28 7.863 20°. C. 10' 308.64 8.307 T 20' 316.99 8.762 30' 325.35 9.230 40' 333.71 9.710 50' 342.08 10.202 .13 7° 350.44 10.707 E .006 10' 358.81 11.224 20' 367.17 11.753 30' 375.54 12.294 40' 383.91 12.847 50' 392.28 13.413 8° 400.66 13.991 25°. C. 10' 409.03 14.582 T 20' 417.41 15.184 30' 425.79 15.799 40' 434.17 16.426 .16 50' 442.55 17.065 E .007 9° 450.93 17.717 10' 459.32 18.381 20' 467.71 19.058 30' 476.10 19.746 40' 484.49 20.447 50' 492.88 21.161 10° 501.28 21.887 30°. C. 10' 509.68 22.624 T 20' 518.08 23.375 .19 30' 526.48 24.138 E 40' 534.89 24.913 50' 543.29 25.700 .008 11° 551.70 26.500 + 10' 560.11 27.313 20' 568.53 28.137 5°. C. 30' 576.95 28.974 T 40' 585.36 29.824 .06 50' 593.79 30.686 E 12° 602.21 31.561 .006 10' 610.64 32.447 20' 619.07 33.347 30' 627.50 34.259 40' 635.93 35.183 50' 644.37 36.120 13° 652.81 37.070 10°. C. 10' 661.25 38.031 T 20' 669.70 39.006 .13 30' 678.15 39.993 40' 686.60 40.992 50' 695.06 42.004 .011 14° 703.51 43.029 10' 711.97 44.066 20' 720.44 45.116 30' 728.90 46.178 40' 737.37 47.253 50' 745.85 48.341 15°. C. 15° 754.32 49.441 T 10' 762.80 50.554 .19 20' 771.29 51.679 E 30' 779.77 52.818 .017 40' 788.26 53.969 50' 796.75 55.132 16° 805.25 56.309 20°. C. 10' 813.75 57.498 T 20' 822.25 58.699 30' 830.76 59.914 40' 839.27 61.141 50' 847.78 62.381 .26 17° 856.30 63.634 E .022 10' 864.82 64.900 20' 873.35 66.178 30' 881.88 67.470 40' 890.41 68.774 50' 898.95 70.091 18° 907.49 71.421 25°. C. 10' 916.03 72.764 T 20' 924.58 74.119 30' 933.13 75.488 .32 40' 941.69 76.869 E 50' 950.25 78.264 .028 19° 958.81 79.671 10' 967.38 81.092 20' 975.96 82.525 30' 984.53 83.972 40' 993.12 85.431 50' 1001.7 86.904 20° 1010.3 88.389 30°. C. 10' 1018.9 89.888 T 20' 1027.5 91.399 .39 30' 1036.1 92.924 E 40' 1044.7 94.462 50' 1053.3 96.013 .034 21° 1061.9 97.577 + 10' 1070.6 99.155 5°. C. 20' 1079.2 100.75 T 30' 1087.8 102.35 40' 1096.4 103.97 .10 50' 1105.1 105.60 E 22° 1113.7 107.24 .013 10' 1122.4 108.90 20' 1131.0 110.57 30' 1139.7 112.25 40' 1148.4 113.95 50' 1157.0 115.66 23° 1165.7 117.38 10°. C. 10' 1174.4 119.12 T 20' 1183.1 120.87 .19 30' 1191.8 122.63 40' 1200.5 124.41 50' 1209.2 126.20 .025 24° 1217.9 128.00 10' 1226.6 129.82 20' 1235.3 131.65 30' 1244.0 133.50 40' 1252.8 135.35 50' 1261.5 137.23 15°. C. 25° 1270.2 139.11 T .29 10' 1279.0 141.01 20' 1287.7 142.93 E 30' 1296.5 144.85 .038 40' 1305.3 146.79 50' 1314.0 148.75 26° 1322.8 150.71 20°. C. 10' 1331.6 152.69 T 20' 1340.4 154.69 30' 1349.2 156.70 40' 1358.0 158.72 50' 1366.8 160.76 .39 27° 1375.6 162.81 E .051 10' 1384.4 164.86 20' 1393.2 166.95 30' 1402.0 169.04 40' 1410.9 171.15 50' 1419.7 173.27 28° 1428.6 175.41 25°. C. 10' 1437.4 177.55 T 20' 1446.3 179.72 30' 1455.1 181.89 40' 1464.0 184.08 .49 50' 1472.9 186.29 E .065 29° 1481.8 188.55 10' 1490.7 190.74 20' 1499.6 192.99 30' 1508.5 195.25 40' 1517.4 197.53 50' 1526.3 199.82 30° 1535.3 202.12 30°. C. 10' 1544.2 204.44 T 20' 1553.1 206.77 .59 30' 1562.1 209.12 E 40' 1571.0 211.48 50' 1580.0 213.86 .078 T = R tan ½I E = R exsec ½I
Page 72
TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE I T E I=40° 31° 1589.0 216.3 + 10' 1598.0 218.7 5° C. 20' 1606.9 221.1 T 30' 1615.9 223.5 40' 1624.9 226.0 .13 50' 1633.9 228.4 E 32° 1643.0 230.9 .023 10' 1652.0 233.4 20' 1661.0 235.9 30' 1670.0 238.4 40' 1679.1 241.0 50' 1688.1 243.5 33° 1697.2 246.1 10° C. 10' 1706.3 248.7 T 20' 1715.3 251.3 .26 30' 1724.4 253.9 40' 1733.5 256.5 E 50' 1742.6 259.1 .046 34° 1751.7 261.8 10' 1760.8 264.5 20' 1770.0 267.2 30' 1779.1 269.9 40' 1788.2 272.6 50' 1797.4 275.3 35° 1806.6 278.1 .40 10' 1815.7 280.8 E 20' 1824.9 283.6 30' 1834.1 286.4 40' 1843.3 289.2 .070 50' 1852.5 292.0 36° 1861.7 294.9 10' 1870.9 297.7 20' 1880.1 300.6 30' 1889.4 303.5 40' 1898.6 306.4 50' 1907.9 309.3 37° 1917.1 312.2 .53 10' 1926.4 315.2 E 20' 1935.7 318.1 .093 30' 1945.0 321.1 40' 1954.3 324.1 50' 1963.6 327.1 38° 1972.9 330.2 .67 10' 1982.2 333.2 E 20' 1991.5 336.3 30' 2000.9 339.3 40' 2010.2 342.4 .117 50' 2019.6 345.5 E 39° 2029.0 348.6 10' 2038.4 351.8 T 20' 2047.8 354.9 .80 30' 2057.2 358.1 E 40' 2066.6 361.3 50' 2076.0 364.5 40° 2085.4 367.7 .141 10' 2094.9 371.0 T 20' 2104.3 374.2 30' 2113.8 377.5 E 40' 2123.3 380.8 50' 2132.7 384.1 I T E I=40° 41° 2142.2 387.4 + 10' 2151.7 390.7 5° C. 20' 2161.2 394.1 T 30' 2170.8 397.4 40' 2180.3 400.8 .17 50' 2189.9 404.2 E 42° 2199.4 407.6 .037 10' 2209.0 411.1 20' 2218.6 414.5 30' 2228.1 418.0 40' 2237.7 421.4 50' 2247.3 425.0 43° 2257.0 428.5 .34 10' 2266.6 432.0 T 20' 2276.2 435.6 30' 2285.9 439.2 40' 2295.6 442.8 E 50' 2305.2 446.4 .075 44° 2314.9 450.0 10' 2324.6 453.6 20' 2334.3 457.3 30' 2344.1 461.0 40' 2353.8 464.6 50' 2363.5 468.4 45° 2373.3 472.1 .51 10' 2383.1 475.8 E 20' 2392.8 479.6 30' 2402.6 483.4 40' 2412.4 487.2 .116 50' 2422.3 491.0 46° 2432.1 494.8 .68 10' 2441.9 498.7 E 20' 2451.8 502.5 30' 2461.7 506.4 40' 2471.5 510.3 T 50' 2481.4 514.3 47° 2491.3 518.2 .151 10' 2501.2 522.2 E 20' 2511.2 526.1 30' 2521.1 530.1 40' 2531.1 534.2 50' 2541.0 538.2 48° 2551.0 542.2 .85 10' 2561.0 546.3 E 20' 2571.0 550.4 T 30' 2581.0 554.5 40' 2591.0 558.6 .189 50' 2601.1 562.8 E 49° 2611.2 566.9 10' 2621.2 571.1 T 20' 2631.3 575.3 30' 2641.4 579.5 40' 2651.5 583.8 E 50' 2661.6 588.0 I T E I=40° 50° 2671.8 592.3 .227 10' 2681.9 596.6 T 20' 2692.1 600.9 1.02 30' 2702.3 605.3 E 40' 2712.5 609.6 50' 2722.7 614.0 I T E I=50° 51° 2732.9 618.4 + 10' 2743.1 622.8 5° C. 20' 2753.4 627.2 T 30' 2763.7 631.7 40' 2773.9 636.2 .21 50' 2784.2 640.7 E 52° 2794.5 645.2 .056 10' 2804.9 649.7 20' 2815.2 654.3 30' 2825.6 658.8 40' 2835.9 663.4 50' 2846.3 668.0 53° 2856.7 672.7 .112 10' 2867.1 677.3 T 20' 2877.5 682.0 30' 2888.0 686.7 40' 2898.4 691.4 E 50' 2908.9 696.1 .112 54° 2919.4 700.9 10' 2929.9 705.7 20' 2940.4 710.5 30' 2951.0 715.3 40' 2961.5 720.1 50' 2972.1 725.0 55° 2982.7 729.9 .63 10' 2993.3 734.8 E 20' 3003.9 739.7 30' 3014.5 744.6 .168 40' 3025.2 749.6 50' 3035.8 754.6 56° 3046.5 759.6 .84 10' 3057.2 764.6 E 20' 3067.9 769.7 T 30' 3078.7 774.7 40' 3089.4 779.8 .225 50' 3100.2 784.9 E 57° 3110.9 790.1 10' 3121.7 795.2 T 20' 3132.6 800.4 30' 3143.4 805.6 E 40' 3154.2 810.9 50' 3165.1 816.1 .283 58° 3176.0 821.4 10' 3186.9 826.7 T 20' 3197.8 832.0 30' 3208.8 837.3 40' 3219.7 842.7 1.05 50' 3230.7 848.1 E 59° 3241.7 853.5 10' 3252.7 858.9 T 20' 3263.7 864.3 30' 3274.8 869.8 E 40' 3285.8 875.3 50' 3296.9 880.8 .340 60° 3308.0 886.4 T 10' 3319.1 892.0 1.27 20' 3330.3 897.5 E 30' 3341.4 903.2 40' 3352.6 908.8 50' 3363.8 914.5 .340 T = R tan ½ I E = R exsec ½ I
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TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE I T E I=70° I T E I=80° I T E I=90° 61° 3375.0 920.2 + 71° 4086.9 1308.2 + 81° 4893.6 1805.3 + 10' 3386.3 925.9 10' 4099.5 1315.6 10' 4908.0 1814.7 20' 3397.5 931.6 20' 4112.1 1322.9 20' 4922.5 1824.1 30' 3408.8 937.3 T 30' 4124.8 1330.3 T 30' 4937.0 1833.6 T 40' 3420.1 943.1 .25 40' 4137.4 1337.7 .30 40' 4951.5 1843.1 .36 50' 3431.4 948.9 E 50' 4150.1 1345.1 E 50' 4966.1 1852.6 E 62° 3442.7 954.8 .080 72° 4162.8 1352.6 82° 4980.7 1862.2 .149 10' 3454.1 960.6 10' 4175.6 1360.1 10' 4995.4 1871.8 20' 3465.4 966.5 20' 4188.5 1367.6 20' 5010.0 1881.5 30' 3476.8 972.4 30' 4201.2 1375.2 30' 5024.8 1891.2 40' 3488.3 978.3 40' 4214.0 1382.8 40' 5039.5 1900.9 50' 3499.7 984.3 50' 4226.8 1390.4 50' 5054.3 1910.7 63° 3511.1 990.2 10° C. 73° 4239.7 1398.0 10° C. 83° 5069.2 1920.5 10° C. 10' 3522.6 996.2 T 10' 4252.6 1405.7 T 10' 5084.0 1930.4 T 20' 3534.1 1002.3 .51 20' 4265.6 1413.5 .61 20' 5099.0 1940.3 .72 30' 3545.6 1008.3 30' 4278.5 1421.2 30' 5113.9 1950.3 40' 3557.2 1014.4 E 40' 4291.5 1429.0 E 40' 5128.9 1960.2 E 50' 3568.7 1020.5 .159 50' 4304.6 1436.8 .220 50' 5143.9 1970.3 .299 64° 3580.3 1026.6 74° 4317.6 1444.6 84° 5159.0 1980.4 10' 3591.9 1032.8 10' 4330.7 1452.5 10' 5174.1 1990.5 20' 3603.5 1039.0 20' 4343.8 1460.4 20' 5189.3 2000.6 30' 3615.1 1045.2 30' 4356.9 1468.4 30' 5204.4 2010.8 40' 3626.8 1051.4 40' 4370.1 1476.4 40' 5219.7 2021.1 50' 3638.5 1057.7 15° C. 50' 4383.3 1484.4 15° C. 50' 5234.9 2031.4 15° C. 65° 3650.2 1063.9 T 75° 4396.5 1492.4 .91 T 85° 5250.3 2041.7 T 10' 3661.9 1070.2 .76 10' 4409.8 1500.5 E 10' 5265.6 2052.1 1.09 20' 3673.7 1076.6 E 20' 4423.1 1508.6 .332 E 20' 5281.0 2062.5 .450 30' 3685.4 1082.9 .240 30' 4436.4 1516.7 30' 5296.4 2073.0 40' 3697.2 1089.3 40' 4449.7 1524.9 40' 5311.9 2083.5 50' 3709.0 1095.7 50' 4463.1 1533.1 50' 5327.4 2094.1 66° 3720.9 1102.2 76° 4476.5 1541.4 86° 5343.0 2104.7 10' 3732.7 1108.6 10' 4489.9 1549.7 10' 5358.6 2115.3 20' 3744.6 1115.1 20' 4503.4 1558.0 20' 5374.2 2126.0 30' 3756.5 1121.7 30' 4516.9 1566.3 30' 5389.9 2136.7 40' 3768.5 1128.2 T 40' 4530.4 1574.7 20° C. 40' 5405.6 2147.5 20° C. 50' 3780.4 1134.8 E 50' 4544.0 1583.1 T 50' 5421.4 2158.4 T 67° 3792.4 1141.4 1.02 E 77° 4557.6 1591.6 .445 E 87° 5437.2 2169.2 10' 3804.4 1148.0 .321 10' 4571.2 1600.1 10' 5453.1 2180.2 .603 20' 3816.4 1154.7 20' 4584.8 1608.6 20' 5469.0 2191.1 E 30' 3828.4 1161.3 30' 4598.5 1617.1 30' 5484.9 2202.2 40' 3840.5 1168.1 40' 4612.2 1625.7 40' 5500.9 2213.2 50' 3852.6 1174.8 50' 4626.0 1634.4 50' 5517.0 2224.3 68° 3864.7 1181.6 78° 4639.8 1643.0 88° 5533.1 2235.5 10' 3876.8 1188.4 25° C. 10' 4653.6 1651.7 25° C. 10' 5549.2 2246.7 25° C. 20' 3889.0 1195.2 T 20' 4667.4 1660.5 T 20' 5565.4 2258.0 T 30' 3901.2 1202.0 30' 4681.3 1669.2 30' 5581.6 2269.3 40' 3913.4 1208.9 1.28 E 40' 4695.2 1678.1 1.53 E 40' 5597.8 2280.6 1.83 50' 3925.6 1215.8 .403 50' 4709.2 1686.9 E 50' 5614.2 2292.0 E 69° 3937.9 1222.7 79° 4723.2 1695.8 .558 89° 5630.5 2303.5 .756 10' 3950.2 1229.7 10' 4737.2 1704.7 10' 5646.9 2315.0 20' 3962.5 1236.7 20' 4751.2 1713.7 20' 5663.4 2326.6 30' 3974.8 1243.7 30' 4765.3 1722.7 30' 5679.9 2338.2 40' 3987.2 1250.8 40' 4779.4 1731.7 40' 5696.4 2349.8 50' 3999.5 1257.9 50' 4793.6 1740.8 50' 5713.0 2361.5 70° 4011.9 1265.0 30° C. 80° 4807.7 1749.9 30° C. 90° 5729.7 2373.3 30° C. 10' 4024.4 1272.1 T 10' 4822.0 1759.0 T 10' 5746.3 2385.1 T 20' 4036.8 1279.3 1.54 E 20' 4836.2 1768.2 .84 E 20' 5763.1 2397.0 2.20 30' 4049.3 1286.5 30' 4850.5 1777.4 30' 5779.9 2408.9 E 40' 4061.8 1293.6 .485 40' 4864.8 1786.7 E 40' 5796.7 2420.9 .910 50' 4074.4 1300.9 50' 4879.2 1796.0 .671 50' 5813.6 2432.9 T = R tan ½I E = R exsec ½I
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TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1° CURVE I | T | E | I=100° || I | T | E | I=110° || I | T | E | I=120° 91° | 5830.5 | 2444.9 | + | 101° | 6950.6 | 3278.1 | + | 111° | 8336.7 | 4386.1 | + 10' | 5847.5 | 2457.1 | 10' | 6971.3 | 3294.1 | 10' | 8362.7 | 4407.6 20' | 5864.6 | 2469.3 | 5° C. | 20' | 6992.0 | 3310.1 | 5° C. | 20' | 8388.9 | 4429.2 30' | 5881.7 | 2481.5 | T | 30' | 7012.7 | 3326.1 | T | 30' | 8415.1 | 4450.9 40' | 5898.8 | 2493.8 | .43 | 40' | 7033.6 | 3342.3 | .51 | 40' | 8441.5 | 4472.7 50' | 5916.0 | 2506.1 | E | 50' | 7054.5 | 3358.5 | E | 50' | 8468.0 | 4494.6 92° | 5933.2 | 2518.5 | .200 | 102° | 7075.5 | 3374.9 | .268 | 112° | 8494.6 | 4516.6 | .360 10' | 5950.5 | 2531.0 | 10' | 7096.6 | 3391.2 | 10' | 8521.3 | 4538.8 20' | 5967.9 | 2543.5 | 20' | 7117.8 | 3407.7 | 20' | 8548.1 | 4561.1 30' | 5985.3 | 2556.0 | 30' | 7139.0 | 3424.3 | 30' | 8575.0 | 4583.4 40' | 6002.7 | 2568.6 | 40' | 7160.3 | 3440.9 | 40' | 8602.1 | 4606.0 50' | 6020.2 | 2581.3 | E | 50' | 7181.7 | 3457.6 | E | 50' | 8629.3 | 4628.6 93° | 6037.8 | 2594.0 | 10° C. | 103° | 7203.2 | 3474.4 | 10° C. | 113° | 8656.6 | 4651.3 | 10° C. 10' | 6055.4 | 2606.8 | T | 10' | 7224.7 | 3491.3 | T | 10' | 8684.0 | 4674.2 | T 20' | 6073.1 | 2619.7 | .86 | 20' | 7246.3 | 3508.2 | .103 | 20' | 8711.5 | 4697.2 | 1.25 30' | 6090.8 | 2632.6 | 30' | 7268.0 | 3525.2 | E | 30' | 8739.2 | 4720.3 | E 40' | 6108.6 | 2645.5 | .401 | 40' | 7289.8 | 3542.4 | .536 | 40' | 8767.0 | 4743.6 50' | 6126.4 | 2658.5 | E | 50' | 7311.7 | 3559.6 | E | 50' | 8794.9 | 4766.9 94° | 6144.3 | 2671.6 | .15 C. | 104° | 7333.6 | 3576.8 | .15 C. | 114° | 8822.9 | 4790.4 | .15 C. 10' | 6162.2 | 2684.7 | 10' | 7355.6 | 3594.2 | 10' | 8851.0 | 4814.1 20' | 6180.2 | 2697.9 | 20' | 7377.8 | 3611.7 | 20' | 8879.3 | 4837.8 30' | 6198.3 | 2711.2 | 30' | 7399.9 | 3629.2 | 30' | 8907.7 | 4861.7 40' | 6216.4 | 2724.5 | T | 40' | 7422.2 | 3646.8 | 40' | 8936.3 | 4885.7 50' | 6234.6 | 2737.9 | E | 50' | 7444.6 | 3664.5 | E | 50' | 8965.0 | 4909.9 95° | 6252.8 | 2751.3 | T | 1.30 | 105° | 7467.0 | 3682.3 | T | 1.56 | 115° | 8993.8 | 4934.1 | T | 1.93 10' | 6271.1 | 2764.8 | E | 20' | 7489.6 | 3700.2 | .806 | 10' | 9022.7 | 4958.6 | E | 1.09 20' | 6289.4 | 2778.3 | 20' | 7512.2 | 3718.2 | E | 20' | 9051.7 | 4983.1 30' | 6307.9 | 2792.0 | .604 | 30' | 7534.9 | 3736.2 | 30' | 9080.9 | 5007.8 40' | 6326.3 | 2805.6 | 40' | 7557.7 | 3754.4 | 40' | 9110.3 | 5032.6 50' | 6344.8 | 2819.4 | E | 50' | 7580.5 | 3772.6 | E | 50' | 9139.8 | 5057.6 96° | 6363.4 | 2833.2 | .20 C. | 106° | 7603.5 | 3791.0 | .20 C. | 116° | 9169.4 | 5082.7 | .20 C. 10' | 6382.1 | 2847.0 | T | 1.74 | 10' | 7626.6 | 3809.4 | T | 2.08 | 10' | 9199.1 | 5107.9 | T | 2.52 20' | 6400.8 | 2861.0 | E | 30' | 7649.7 | 3827.9 | .108 | 20' | 9229.0 | 5133.3 | E | 1.46 30' | 6419.5 | 2875.0 | 30' | 7672.9 | 3846.5 | 30' | 9259.0 | 5158.8 40' | 6438.4 | 2889.0 | .809 | 40' | 7696.3 | 3865.2 | 40' | 9289.2 | 5184.5 50' | 6457.3 | 2903.1 | E | 50' | 7719.7 | 3884.0 | E | 50' | 9319.5 | 5210.3 97° | 6476.2 | 2917.3 | T | .107° | 7743.2 | 3902.9 | .117° | 9349.9 | 5236.2 | .118° | 9353.7 | 5395.1 10' | 6495.2 | 2931.6 | E | 10' | 7766.8 | 3921.9 | T | 25 C. | 10' | 9567.2 | 5422.1 20' | 6514.3 | 2945.9 | 20' | 7790.5 | 3940.9 | .108 | 20' | 9598.9 | 5449.2 30' | 6533.4 | 2960.3 | 30' | 7814.3 | 3960.1 | T | 30' | 9630.7 | 5476.5 40' | 6552.6 | 2974.7 | .809 | 40' | 7838.1 | 3979.4 | 2.61 | 40' | 9662.6 | 5504.0 | T | 3.16 50' | 6571.9 | 2989.2 | E | 50' | 7862.1 | 3998.7 | E | 50' | 9694.7 | 5531.7 | E 98° | 6591.2 | 3003.8 | .25 C. | 108° | 7886.2 | 4018.2 | .25 C. | 118° | 9727.0 | 5559.4 | .25 C. 10' | 6610.6 | 3018.4 | T | 10' | 7910.4 | 4037.8 | T | 10' | 9759.4 | 5587.4 20' | 6630.1 | 3033.1 | 20' | 7934.6 | 4057.4 | .136 | 20' | 9792.0 | 5615.5 30' | 6649.6 | 3047.9 | T | 30' | 7959.0 | 4077.2 | 30' | 9824.8 | 5643.8 40' | 6669.2 | 3062.8 | 2.18 | 40' | 7983.5 | 4097.1 | E | 40' | 9857.7 | 5672.3 50' | 6688.8 | 3077.7 | .102 | 50' | 8008.0 | 4117.0 | E | 50' | 9890.8 | 5700.9 99° | 6708.6 | 3092.7 | .30 C. | 109° | 8032.7 | 4137.1 | .30 C. | 119° | 9924.0 | 5729.7 | .30 C. 10' | 6728.4 | 3107.7 | T | 10' | 8057.4 | 4157.3 | T | 10' | 9957.5 | 5758.6 | T | 3.81 20' | 6748.2 | 3122.9 | .20' | 8082.3 | 4177.5 | 20' | 9991.0 | 5787.7 30' | 6768.1 | 3138.1 | 30' | 8107.3 | 4197.9 | 30' | 10025.0 | 5817.0 40' | 6788.1 | 3153.3 | E | 40' | 8132.3 | 4218.4 | E | 40' | 10059.0 | 5846.5 50' | 6808.2 | 3168.7 | .122 | 50' | 8157.5 | 4239.0 | E | 50' | 10093.0 | 5876.1 | E | 2.20 100° | 6828.3 | 3184.1 | T | 2.62 | 110° | 8182.8 | 4259.7 | T | 3.14 | 120° | 9924.0 | 5729.7 | 30° C. 10' | 6848.5 | 3199.6 | 10' | 8208.2 | 4280.5 | T | 10' | 9957.5 | 5758.6 | T 20' | 6868.8 | 3215.1 | 20' | 8233.7 | 4301.4 | E | 20' | 9991.0 | 5787.7 30' | 6889.2 | 3230.8 | .122 | 30' | 8259.3 | 4322.4 | E | 30' | 10025.0 | 5817.0 40' | 6909.6 | 3246.5 | .122 | 40' | 8285.0 | 4343.6 | E | 40' | 10059.0 | 5846.5 50' | 6930.1 | 3262.3 | .122 | 50' | 8310.8 | 4364.8 | E | 50' | 10093.0 | 5876.1 T = R tan ½I | E = R exsec ½I
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TABLE VI. INCHES TO DECIMALS OF A FOOT In. 0 1 2 3 4 5 6 7 8 9 10 11 In. 0 Foot .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 0 1-32 .0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526 .8359 .9193 1-32 1-16 .0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885 .6719 .7552 .8385 .9219 1-16 3-32 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 .7578 .8411 .9245 3-32 1-8 .0104 .0938 .1771 .2604 .3438 .4271 .5104 .5938 .6771 .7604 .8438 .9271 1-8 5-32 .0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297 5-32 3-16 .0156 .0990 .1823 .2656 .3490 .4323 .5156 .5990 .6823 .7656 .8490 .9323 3-16 7-32 .0182 .1016 .1849 .2682 .3516 .4349 .5182 .6016 .6849 .7682 .8516 .9349 7-32 1-4 .0208 .1042 .1875 .2708 .3542 .4375 .5208 .6042 .6875 .7708 .8542 .9375 1-4 9-32 .0234 .1068 .1901 .2734 .3568 .4401 .5234 .6068 .6901 .7734 .8568 .9401 9-32 5-16 .0260 .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7760 .8594 .9427 5-16 11-32 .0286 .1120 .1953 .2786 .3620 .4453 .5286 .6120 .6953 .7786 .8620 .9453 11-32 3-8 .0313 .1146 .1979 .2813 .3646 .4479 .5313 .6146 .6979 .7813 .8646 .9479 3-8 13-32 .0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 .8672 .9505 13-32 7-16 .0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 7-16 15-32 .0391 .1224 .2057 .2891 .3724 .4557 .5391 .6224 .7057 .7891 .8724 .9557 15-32 1-2 .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583 1-2 17-32 .0443 .1276 .2109 .2943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609 17-32 9-16 .0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7135 .7969 .8802 .9635 9-16 19-32 .0495 .1328 .2161 .2995 .3828 .4661 .5495 .6328 .7161 .7995 .8828 .9661 19-32 5-8 .0521 .1354 .2188 .3021 .3854 .4688 .5521 .6354 .7188 .8021 .8854 .9688 5-8 21-32 .0547 .1380 .2214 .3047 .3880 .4714 .5547 .6380 .7214 .8047 .8880 .9714 21-32 11-16 .0573 .1406 .2240 .3073 .3906 .4740 .5573 .6406 .7240 .8073 .8906 .9740 11-16 23-32 .0599 .1432 .2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099 .8932 .9766 23-32 3-4 .0625 .1458 .2292 .3125 .3958 .4792 .5625 .6458 .7292 .7917 .8750 .9583 3-4 25-32 .0651 .1484 .2318 .3151 .3984 .4818 .5651 .6484 .7318 .8151 .8984 .9818 25-32 13-16 .0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 13-16 27-32 .0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870 27-32 7-8 .0729 .1563 .2396 .3229 .4063 .4896 .5729 .6563 .7396 .8229 .9063 .9896 7-8 29-32 .0755 .1589 .2422 .3255 .4089 .4922 .5755 .6589 .7422 .8255 .9089 .9922 29-32 15-16 .0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948 15-16 31-32 .0807 .1641 .2474 .3307 .4141 .4974 .5807 .6641 .7474 .8307 .9141 .9974 31-32 0 1 2 3 4 5 6 7 8 9 10 11 TABLE VII. MINUTES IN DECIMALS OF A DEGREE 0' 30" .00833 10' 30" .17500 20' 30" .34167 30' 30" .50833 40' 30" .67500 50' 30" .84167 1 00 .01667 11 00 .18333 21 00 .35000 31 00 .51667 41 00 .68333 51 00 .85000 30 .02500 30 .19167 30 .35833 30 .52500 30 .69167 30 .85833 2 00 .03333 12 00 .20000 22 00 .36667 32 00 .53333 42 00 .70000 52 00 .86667 30 .04167 30 .20833 30 .37500 30 .54167 30 .70833 30 .87500 3 00 .05000 13 00 .21667 23 00 .38333 33 00 .55000 43 00 .71667 53 00 .88333 30 .05833 30 .22500 30 .39167 30 .55833 30 .72500 30 .89167 4 00 .06667 14 00 .23333 24 00 .40000 34 00 .56667 44 00 .73333 54 00 .90000 30 .07500 30 .24167 30 .40833 30 .57500 30 .74167 30 .90833 5 00 .08333 15 00 .25000 25 00 .41667 35 00 .58333 45 00 .75000 55 00 .91667 30 .09167 30 .25833 30 .42500 30 .59167 30 .75833 30 .92500 6 00 .10000 16 00 .26667 26 00 .43333 36 00 .60000 46 00 .76667 56 00 .93333 30 .10833 30 .27500 30 .44167 30 .60833 30 .77500 30 .94167 7 00 .11667 17 00 .28333 27 00 .45000 37 00 .61667 47 00 .78333 57 00 .95000 30 .12500 30 .29167 30 .45833 30 .62500 30 .79167 30 .95833 8 00 .13333 18 00 .30000 28 00 .46667 38 00 .63333 48 00 .80000 58 00 .96667 30 .14167 30 .30833 30 .47500 30 .64167 30 .80833 30 .97500 9 00 .15000 19 00 .31667 29 00 .48333 39 00 .65000 49 00 .81667 59 00 .98333 30 .15833 30 .32500 30 .49167 30 .65833 30 .82500 30 .99167 10 00 .16667 20 00 .33333 30 00 .500000 40 00 .66667 50 00 .83333 60 00 1.00000
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TABLE VIII. MIDDLE ORDINATES OF RAILS Length of Rail (feet) C | R | 30 | 28 | 26 | 24 | 22 | 20 | C | R | 30 | 28 | 26 | 24 | 22 | 20 O / Feet Inch Inch Inch Inch Inch Inch O Feet Inch Inch Inch Inch Inch Inch 0-20 17189 .08 .07 .06 .05 .04 .03 8 716.8 1.88 1.64 1.42 1.20 1.01 .84 0-40 8594 .16 .14 .12 .10 .08 .07 9 637.3 2.12 1.84 1.60 1.35 1.14 .94 1-0 5730 .24 .20 .18 .15 .13 .10 10 573.7 2.36 2.05 1.78 1.50 1.27 1.04 1-20 4297 .31 .27 .23 .20 .17 .13 11 521.7 2.59 2.26 1.95 1.65 1.39 1.15 1-40 3438 .39 .34 .29 .25 .21 .17 12 478.3 2.83 2.47 2.15 1.81 1.54 1.26 2-0 2865 .47 .41 .35 .30 .25 .20 13 441.7 3.05 2.66 2.30 1.96 1.66 1.36 2-20 2456 .55 .48 .41 .35 .29 .23 14 410.3 3.30 2.87 2.48 2.10 1.78 1.46 2-40 2149 .63 .55 .47 .40 .33 .27 15 383.1 3.54 3.08 2.68 2.26 1.91 1.57 3-0 1910 .71 .62 .53 .45 .38 .31 16 359.3 3.76 3.28 2.83 2.40 2.04 1.67 3-20 1719 .78 .68 .59 .50 .42 .35 17 338.3 4.00 3.48 3.02 2.57 2.16 1.78 3-40 1563 .86 .75 .65 .55 .46 .38 18 319.6 4.21 3.67 3.18 2.70 2.28 1.87 4-0 1433 .94 .82 .71 .60 .50 .42 19 302.9 4.45 3.89 3.36 2.86 2.41 1.98 4-20 1323 1.02 .89 .77 .65 .55 .45 20 287.9 4.70 4.09 3.55 3.00 2.54 2.09 4-40 1228 1.10 .96 .83 .70 .59 .48 22 262.0 5.16 4.44 3.84 3.30 2.80 2.29 5 1146 1.18 1.03 .89 .75 .63 .52 24 240.5 5.64 4.92 4.20 3.59 3.04 2.50 6 955.3 1.41 1.23 1.06 .90 .76 .62 26 222.3 6.07 5.29 4.58 3.88 3.29 2.70 7 819.0 1.65 1.44 1.24 1.05 .89 .73 TABLE IX. SHORT RADIUS CURVES Radius | Chord | Central | Deflection | Deflection Feet Feet Angle Angle for 1 Foot 35 10 16-26 8-13 49.3 45 10 12-46 6-23 38.3 50 15 17-16 8-38 34.5 60 15 14-22 7-11 28.8 75 15 11-30 5-45 23.0 100 20 11-30 5-45 17.3 120 20 9-34 4-47 14.3 150 20 7-39 3-49 11.5 190 25 7-32 3-46 9.15 200 25 7-10 3-35 8.6 225 25 6-25 3-12 7.7 240 25 5-58 2-59 7.2 250 25 5-44 2-52 6.9 275 25 5-12 2-36 6.2 288 50 9-58 4-59 6.0 300 50 9-32 4-46 5.7 350 50 8-12 4-06 4.9 376 50 7-40 3-50 4.6 400 50 7-10 3-35 4.3 410 50 7-00 3-30 4.2 To find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.
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TABLE X. RODS IN FEET, 10THS AND 100THS OF FEET Rods Feet Rods Feet Rods Feet Rods Feet Rods Feet 1 16.50 21 346.50 41 676.50 61 1006.50 81 1336.50 2 33.00 22 363.00 42 693.00 62 1023.00 82 1353.00 3 49.50 23 379.50 43 709.50 63 1039.50 83 1369.50 4 66.00 24 396.00 44 726.00 64 1056.00 84 1386.00 5 82.50 25 412.50 45 742.50 65 1072.50 85 1402.50 6 99.00 26 429.00 46 759.00 66 1089.00 86 1419.00 7 115.50 27 445.50 47 775.50 67 1105.50 87 1435.50 8 132.00 28 462.00 48 792.00 68 1122.00 88 1452.00 9 148.50 29 478.50 49 808.50 69 1138.50 89 1468.50 10 165.00 30 495.00 50 825.00 70 1155.00 90 1485.00 11 181.50 31 511.50 51 841.50 71 1171.50 91 1501.50 12 198.00 32 528.00 52 858.00 72 1188.00 92 1518.00 13 214.50 33 544.50 53 874.50 73 1204.50 93 1534.50 14 231.00 34 561.00 54 891.00 74 1221.00 94 1551.00 15 247.50 35 577.50 55 907.50 75 1237.50 95 1567.50 16 264.00 36 594.00 56 924.00 76 1254.00 96 1584.00 17 280.50 37 610.50 57 940.50 77 1270.50 97 1600.50 18 297.00 38 627.00 58 957.00 78 1287.00 98 1617.00 19 313.50 39 643.50 59 973.50 79 1303.50 99 1633.50 20 330.00 40 660.00 60 990.00 80 1320.00 100 1650.00 TABLE XI. LINKS IN FEET, 10THS AND 100THS OF FEET Links Feet Links Feet Links Feet Links Feet Links Feet Links Feet 1 0.66 18 11.88 35 23.10 52 34.32 69 45.54 86 56.76 2 1.32 19 12.54 36 23.76 53 34.98 70 46.20 87 57.42 3 1.98 20 13.20 37 24.42 54 35.64 71 46.86 88 58.08 4 2.64 21 13.86 38 25.08 55 36.30 72 47.52 89 58.74 5 3.30 22 14.52 39 25.74 56 36.96 73 48.18 90 59.40 6 3.96 23 15.18 40 26.40 57 37.62 74 48.84 91 60.06 7 4.62 24 15.84 41 27.06 58 38.28 75 49.50 92 60.72 8 5.28 25 16.50 42 27.72 59 38.94 76 50.16 93 61.38 9 5.94 26 17.16 43 28.38 60 39.60 77 50.82 94 62.04 10 6.60 27 17.82 44 29.04 61 40.26 78 51.48 95 62.70 11 7.26 28 18.48 45 29.70 62 40.92 79 52.14 96 63.36 12 7.92 29 19.14 46 30.36 63 41.58 80 52.80 97 64.02 13 8.58 30 19.80 47 31.02 64 42.24 81 53.46 98 64.68 14 9.24 31 20.46 48 31.68 65 42.90 82 54.12 99 65.34 15 9.90 32 21.12 49 32.34 66 43.56 83 54.78 100 66.00 16 10.56 33 21.78 50 33.00 67 44.22 84 55.44 101 66.66 17 11.22 34 22.44 51 33.66 68 44.88 85 56.10 102 67.32