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76° 77° 78° 790 800 81° 820 | 0 4:01 07800 14:33 14759 4.70 46301 5.1 445540 5.6 712818 63 1375157.1 153697 60 1 57570 72316 +71 13686 525557 80946 256601 304190 59 2 +02 07446 134 30018 81256 605813 906394 3761261 455308 58 3 57410 87866 4:72 49012 686311 5:7 003663 496092 607056 57 4 11:03 07550 1:35 45861 4.73 16954 767051 101256 616502 759437 56 5 57779 4:36 04003 85083 848035 199173 737359 912456 55 6 4:04 08125 62293 4.74 53401 929264 297416 858665 7.2 060116 54 7 58590 1:37 20731 4:75 21907 5.2 010738 395988 980422 220422 53 8 4:05 09174 79317 90603 092459 494889 6-4 102633 375378 52 9 59877 1:38 38054 4.76 59490 174428 591122 225301 530987 51 10 1:06 10700 96940 4.77 28568 256647 693688 348428 687255 50 11 61613 4:39 55977 97837 339116 793588 472017 844184 49 12 4:07 12707 4:40 15164 478 67300 421836 893825 596070 7.3 001780 48 13 63892 74504 4.79 36957 504809 994400 720591 160047 47 14 4.08 15199 4:41 33996 4.80 06808 588035 5.8 095315 845581 318989 46 15 66627 93641 76854 671517 196572 971043 478610 45 16 1.09 18178 14:42 53439 4.81 47096 755255 298172 6-5 096981 638916 44 17 69852 443 13392 4.82 17536 839251 400117 223396 799909 43 18 4:10 21649 73500 88174 923505 502410 350293 961595 42 19 73569 +44 33762 4.83 59010 5:3 008018 605051 477672 704 123978 41 20 4.11 25611 91181 4.84 30045 092793 708042 605538 287064 40 21 77784 1:45 51756 4.85 01282 177830 811386 733892 450855 39 22 4.12 30079 1:46 15489 72719 263131 915084 862739 615357 38 23 82499 70379 4.86 44359 3486965.9 019138 992080 780576 37 24 1.1335046 147 37428 4.87 16201 434527 123550 6.6 121919 946514 36 25 87719 98636 88248 520626 228322 252258 7:5 113178 35 26 4:14 40519 4:48 60004 4:88 60499 606993 333455 383100 280571 31 27 93446 4:49 21532 14.89 32956 693630 438952 514449 448699 33 28 4.15 46501 83221 4.90 05620 780538 544815 646307 617567 32 29 99685 4.50 45072 78191 867718 651045 778677 787179 31 30 4:16 52998 451 07085 4:91 51570 955172 757614 911562 957541 30 31 4.17 06140 69261 4.92 21859 5.4 042901 864614 67 049667.6 128657 29 32 60011 4.52 31601 98358 130906 971957 178891 300533 28 33 4.18 13713 91105 4.93 72068 21918816.0 079676 313341 473174 27 31 67546 4:53 56773 4.91 45990 307750 187772 448318 646584 26 35 4.19 21510 4:54 19608 4.95,20125 396592 296247 583826 820769 25 36 75606 82603 9474 485715 405103 719867 995735 24 37 4.20 29835 4.55 45776 4.96 69037 575121 514343 85644677 171486 23 38 84196 4.56 09111 4.97 43817 664812 623967 993565 348028 22 39 4.21 38690 72615 4.98 18813 754788 733979 6.8 131227 525366 21 40 93318 4:57 36287

91027 845052 844381 269437 703506 20 41 422 48080 4.58 00129 4.99 69459 935601 955174 408196) 882453 19 42 1.23 02977 64141 5.00 45111 5:5 026446 6.1 066360 547508 7-8 062212 18 43 58009 4.59 28325 5:01 20984 117579 177943 687378 242790 17 44 1:24 13177 92680 97078 209005 289923 827807 424191 16 45 68482 4.60 57207 15.0273395 300724 402303 968799 606423 15 46 + 25 23923 4.61 21908 5.03 49935 392740 515085 6.9 110359 789489 14 47 79501 86783 5:04 26700 4850521 628272 252489 973396 13 49 4.26 35218 4.62 51832 15.05 03099 577663 741865 3951927.9 158151 12 49 91072 4.63 17056 80907 670574 855867 538473 343758 11 50 4:27 47066 82457 5.06 58352 763786 970279 682335 530224 10 51 +28 03199 +61 48031 5.07 36025 857302 6.2 085106 826781 717555 9 52 59472 4.65 13788 5.08 13928 951121 200347 971806 905756 8 53 4.29 15885 79721 92061 5.6 045247 316007 7.0 117441 8-0 094835 54 7210 1.66 45832 5:09 70426 139680 432086 263662 284796 6 55 4.30 29136 167 12124 5.10 49024 234421 548588 410482 475647 56 85974 78595 5:11 27855 329174 665515 557905 667394 4 57 4:31 42955 1.68 45218 5.12 06921 424838 782868 705934 860042 3 58 1:32 00079 +69 12083 8622+ 520516 900651 854573 81 053599 2 59 57347 79100 5:13 65763 61650916-3018866 7.1 003826 248071 1 60 +33 14759 170 16301 5.14 45510 712818 137515 153697 +3464 0 130 120

11° 10° go 80 70

83° 84° 1 850 86° 870 880 890 08:1 4434649.5 143645 11.430052 14:300066 19.081137 28.636253 57.289962 60

639786 410613 468474 360696 187930 877089 58.261174 59

837041 679068 507154 421230 295922 29.122006 59.265872 58 3 8.2 035239 949022 546093 482273 405133 371106 60-305820 57

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837579|9:7 014075 704500 731679 854591 411580 64-858008 53 8 83 040586 321713 744779 795372 970219 683307 66.105473 52

244577 600927 785333 859616 20.087199 959928 67.401854 51 10 449558 881732 826167 924417 205553 31.241577 68.75008750 11 655536/9.8 164140 867282 989784 325308 528392 70.153346 49 12 862519 448166 908682 15.055723 446486 820516 71.615070 48 13 8.4 0705151 733823 950370 122242 509115 32.118099 73.138991 47 14 279531 9.9 021125 992349 189349 693220 421295 74.729165 46 15 489573 310088 12.034622 257052 818828 730265 76.390009| 45 16 700651 600724 077192

325358 945966 33.045173 78.126342 44 17 912772 893050 120062 394276 21.074664 366194 79.943430 43 18 18.5 125943) 10-018708 163236 463814 204949 693509 81.847041 42 19 3401721 048283 206716 533981 336851 34.027303 83.843507 41 20 555168!

078031 250505 604784 470401 367771 85.939791 40 21 771838

107954 294609 76233 605630 715115 88.143572 39 22 989290 138054 339028 748337 742569 35.069546 90.463336 38 22 8.6 207833 168332 383768 821105 881251 431282 92.908487 37 24 427 475 198789 428831 894545 22:021710 800553 95.489475 36 25 648223 229428 474221 968667 163980 36.177596 98.217943 35 26 870088 260249 519942 16.043482 308097 562659 101.10690 34 27 807 093077 291255 565997 118998 454096 95C001 104.17094 33 28 317198

322147 612390 195225 602015 37.357892 107.42648 32 29 542161 353827 659125 272174 751892 768613 110.89205 31 30 768871 385397 706205 349855 903766 38.188459 114-58865 30 31 996446 417158 753634 428279 23.057677 617738 118.54018 29 32 8.8 225186 419112 801417 507456 213666 39.056771 122.77396 28 33 455103 481261 819557 587396 371777 505895 | 127-32134 34 686206 513607 898058 668112 532052 965460 132-21851 26 35 918505 546151 946924 749614 694537 40-435837 137-50745 25 36 8.9 152009 578895 906100 831915 859277 917412 143.23712 24 37 386726 611841 13.015769 915025 24:026320 41.410588 149.46502 23 38 622668 644992 095757 998957 195714 915790 156.25998 22 39 859813 678348 146127 17.083724 367509 42:433464 163-70019 21 40 9.0 098261 711913 196883 169337 541758 964077 171.88540 20 41 337933 745687 248031 255809 718512 43-508122 180.93220 19 42 578867 779673 299574 313155 897826 44.066113 190.98419 18 43 821074 813872 351518 431385 25.079757 f38596 202.21875 17 44

848288 403867 520516 264361 45.226141 214.85762 16 45 3093-18 882921 456625 610559 451700 829351 229 18166 15 46 555 136

917775 509799 701529 641832 46.4488F2 245-55198 14 802838 952850 563391 793442 834823 47.085343 264.44080 13 48 9.2 051564 988150 617409 886310 26.030736 739501 286.47773 12 49 301627 11.023676

671856 980150 229638 48:412084 312-52137 11 50 553035 059431 726738 18.074977 431600 49.102881 343.77371 10 51 805802

095416 782060 170807 636690 815726 381.970999 52 9.3 0599361 131635 837827 267654 841984 50-548506 429.71757 8 53 3154501 168089 891045 365537 27.056557 51:303157 491.10000 5+ 572355 204780 950719 464471 271486 52.080673 572 95721 6 55 830663 241712 14.007856 564473 489853 882109 687.5-4887 5 56 94 090384 278885 065459 665562 711740 53.708587 859.43630 4 57 351531

316301 123536 7 7754 937233 5+:561300 1145.9153 3 58 614116 353970 182092 871068 28.166422 55-411517 1718-8732 2 59 878149 391885 2+1134 975523 399397 56 350590 3437.7467 60 9.5 143615 +30052 300666 19.081137 636253 57.289962 Infinite.

5° 4° 30 2° 10 00

TABLE XV.

CHORDS, VERSED SINES, EXTERNAL SECANTS, AND

TANGENTS OF A ONE-DEGREE CURVE.

X

с

The angles of the table are the intersection angles, I, equal to the total central angle included between the tangent points.

To find the corresponding function for any other curve, divide the tabular number by the degree of curvature.

The unit chord is assumed to be one hundred feet long.

By using radius of 5,730 feet, the chord column of the table can be made serviceable for plotting.

269

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33.33
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43.33
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53.33
56.67
60.00
63.33
66.67
70.00
73.33
76.67
80.00
83.33
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93.33
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100.00
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113.33
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123.33
126.66
130.00
133.33
136.66
140.00
143.33
146.66
150.00
153.33
156.66
160.00
163:33
166.66
170.00
173.33
176.66
180.00
183.33
186.66
190.00
193.33
196.66
199.98

22
24
26
28
30
32
34

0.229
0.243
0.258
0.275
0.292
0.310
0.328
0.346
0.364
0.382
0.400
0.423
0.446
0.469
0.492
0.515
0.538
0.561
0.584
0.607
0.630
0.653
0.676
0.699
0.722
0.745
0.768
0.791
0.814
0.837
0.860

4
6
8
10
12
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18
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0.258
0.275
0.292
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0.401
0.424
0.447
0.470
0.493
0.516
0.539
0.562
0.585
0.608
0.632
0.655
0.678
0.701
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0.747
0.770
0.793
0.816
0.839
0.862

50.00
51.67
53.33
55.00
56.67
58.33
60.00
61.67
63.33
65.00
66.67
68.33
70.00
71.67
73.33
75.00
76.67
78.33
80.00
81.67
83.33
85.00
86.67
88.33
90.00
91.67
93.33
95.00
96.67
98.33
100.00

28.33

36

36
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38
40
42

42

42

30.00
31.67
33.33
35.00
36.67
38.33
40.00
41.67
43.33
45.00
46.67
48.33
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