A Practical Treatise on the Science of Land and Engineering Surveying, Levelling, Estimating Quantities, &e

46 10.015163 10.016427 10.017691 10.018956 10.020220 10.021485 10.022750 10.024015 10.025281 10.026546 10.027812 10.029078 10.030344 43
47 10.030344 10.031611 10.032878 10.034145 10.035412 10.036680 10.037948 10.039216 10.040485 10.041754 10.043023 10.044293 10.045563 42
48 10.045563 10.046833 10.048104 10.049375 10.050647 10.051919 10.053192 10.054465 10.055738 10.057012 10.058287 13.059562 10.060837 41
49 10.060837 10.062113 10.063390 10.064667 10.065944 10.067222 10.068501 10.069781 10.071060 10.072341 10.073622 10.074904 10.076187 40
50 10.076187 10.077470 10.078753 10.080038 10.081323 10.082609 10.083896 10.085183 10.086471 10.087760 10.089049 10.090340 10.091631 39

51 10.091631 10.092923 10.094216 10.095509 10.096803 10.098098 10.099395 10.100692 10.101990 10.103288 10.104588 10.105889 10.107190 38
52 10.107190 10.108493 10.109796 10.111100 10.112406 10.113712 10.115020 10.116328 10.117638 10.118948 10.120259 10.121572 10.122886 37
53 10.122886 10.124200 10.125516 10.126833 10.128151 10.129471 10.130791 10.132113 10.133436 10.134760 10.136085 10.137412 10.138739 36
54 10.138739 10.140068 10.141398 10.142730 10.144062 10.145397 10.146732 10.148069 10.149407 10.150746 10.152087 10.153430 10.154773 35
55 10.154773 10.156118 10.157465 10.158813 10.160162 10.161513 10.162366| 10.164220 10.165575 10.166932 10.168291| 10.169651 10.171013 34
56 10.171013 10.172376 10.173741 10.175107 10.176476 10.177846 10.179217 10.180590 10.181965 10.183342 10.184721 10.186101 10.187483 33
57 10.187483 10.188866 10.190252 10.191639 10.193029 10.194420 10.195813 10.197208 10.198604 10.200033 10.201404 10.202806 10.204211 32
58 10.204211 10.205617 10.207026 10.208437 10.209849 10.211264 10.212681 10.214100 10.215521 10.216944 10.218869 10.219797 10.221226 31
59 10.221226 10.222658 10.224092 10.225529 10.226967 10.228408 10.229852 10.231297 10.232745 10.234195 10.235648 10.237163 10.238561 30
60 10.238561 10.240021 10.241483 10.242948 10.244415 10.245885 10.247358 10.248833 10.250311 10.251791 10.253274 10.254760 10.256248 29
61 10.256248 10.257739 10.259233 10.260729 10.262229 10.263731 10.265236 10.266743 10.268254 10.269768 10.271284 10.272803 10.274326 28
62 10.274326 10.275851 10.277379 10.278911 10.280445 10.281983 10.283523 10.285067 10.286614 10.288164 10.289719 10.291274 10.292834 27
63 10.292834 10.294397 10.295964 10.297534 10.299107 10.300684 10.302264 10.303847 10.305434 10.307025| 10.308619 10.310217 10.311818 26
64 10.311818 10.313423 10.315032 10.316644 10.318260 10.319880 10.321504 10.323131 10.324763 10.326398 10.328037 10.329680 10.331328 25
65 10.331328 10.332979 10.334634 10.336293 10.337957 10.339624 10.341296 10.342972 10.344652 10.346337 10.348026 10.349719 10.351417 24

66 10.351417 10.353119 10.354826 10.356537 10.358253 10.359973 10.361698 10.363428 10.365162 10.366902 10.368646 10.370394 10.372148 23
67 10.372148 10.373907 10.375670 10.377439 10.379213 10.380992 10.382776 10.384565 10.386359 10.388159 10.389964 10.391775 10.393590 22
68 10.393590 10.395412 10.397239 10.399071 10.400909 10.402753 10.404603 10.406458 10.408319 10.410186 10.412059 10.413938 10.415823 21
69 10.415823 10.417714 10.419611 10.421514 10.423424 10.425340 10.427262 10.429191 10.431127 10.433068 10.435017 10.436972 10.438934 20
70 10.438934 10.440903 10.442879 10.444861 10.446851 10.448848 10.450851 10.452862 10.454881 10.456906 10.458939 10.460980 10.463028 19
60'

25'

20'

15'

10'

Deg.

30 2

55'

50'

45'

40'

35'

LOGARITHMIC CO-TANGENTS.

71 10.463028 10.465084 10.467147 10.469219 10.471298 10.473385 10.475480 10.477583 10.479695 10.481815 10.483943 10.486079 10.488224 18
72 10.488224 10.490378 10.492540 10.494711 10.496891 10.499080 10.501278 10.503485 10.505701 10.507927 10.510162 10.512407 10.514661 17
73 10.514661 10.516925 10.519199 10.521483 10.523777 10.526081 10.528395 10.530720 10.533055 10.535401 10.537758 10.540125 10.542504 16
74 10.542504 10.544893 10.547294 10.549706 10.552130 10.554565 10.557012 10.559471 10.561941 10.564424 10.566920 10.569427 10.571948 15
75 10.571948 10.574481 10.577027 10.579585 10.582158 10.584743 10.587342 10.589955 10.592581 10.595222 10.597876 10.600545 10.603229 14
76 10.603229 10.605927 10.608641 10.611369 10.614112 10.616872 10.619646 10.622437 10.625244 10.628067 10.630906 10.633763 10.636636 13
77 10.636636 10.639526 10.642434 10.645360 10.648303 10.651265 10.654245 10.657243 10.660261 10.663298 10.666354 10.669430 10.672526 12
78 10.672526 10.675642 10.678778 10.681936 10.685115 10.688315 10.691537 10.694782 10.698049 10.701338 10.704651 10.707987 10.711348 11
79 10.711348 10.714732 10.718142 10.721576 10.725036 10.728521 10.732033 10.735572 10.739138 10.742731 10.746352 10.750002 10.753681 10
80 10.753681 10.757390 10.761128 10.764897 10.768698 10.772529 10.776394 10.780290 10.784221 10.788185 10.792184 10.796218 10.800288 9
81 10.800288 10.804394 10.808538 10.812720 10.816941 10.821201 10.825501 10.829843 10.834226 10.838653 10.843123 10.847637 10.852196
82 10.852196 10.856804 10.861458 10.866161 10.870913 10.875716 10.880571 10.885479 10.890441 10.895458 10.900532 10.905665 10.910856 7
83 10.910856 10.916109 10.921424 10.926803 10.932248 10.937760 10.943341 10.948992 10.954716 10.960515 10.966391 10.972345 10.978380
84 10.978380 10.984498 10.990702 10.996993 11.003876 11.009851 11.016423| 11.023094 11.029867 11.036746 11.043733 11.050832 11.058048
85 11.058048 11.065384 11.072844 11.080433 11.088154 11.096013 11.104016 11.112167 11.120471 11.128936 11.137567 11.146372 11,155356
86 11.155356 11.164528 11.173897 11.183471 11.193258 11.203269 11.213519 11.224005 11.234754 11.245773 11.257078 11.268683 11.280604
87 11.280604 11.292861 11.305471 11.318456 11.331840 11.345648 11.359907 11.374648 11.389906 11.405717 11.422123 11.439172 11.456916 2
88 11.456916 11.475414 11.494733 11.514950 11.536151| 11.558440 11.581932 11.606766 11.633106 11.661144 11.691116 11.723309 11.758079 1
89 11.758079 11.795874 11.837273 11.883037 11.934195 12.992191 12.059142 12.138326| 12.235239 12.360180 12.536273 12.837304 Infinite
60'

89654

55'

50'

45'

40'

35'

30'

25'

20'

15'

10'

Deg.

LOGARITHMIC CO-TANGENTS.

TABLE IV.-NATURAL SINES AND NATURAL CO-SINES.

012345

.017452

67849

12345

.241921 .243334
.258819 .260224

.246153 .247563 .263031 .264434

.001454 .002909 .004363 .005818 .007272 .008727
.018907 .020361 .021815 .023269 .024723 .026177
.034899 .036353 .037807 .039260 .040713 .042166 .043619
.052336 .053788 .055241 .056693 .058145 .059597 .061049 .062500 .063952 .065403 .066854
.069757 .071207 .072658 .074109 .075559 .077009 .078459 .079909 .081359 .082808 .084258
.087156 .088605 .090053 .091502 .092950 .094398 .095846 .097293 .098741 .100188 .101635
.104529 .105975 .107421 .108867 .110313 .111758 .113203 .114648 .116093 .117537 .118982
.121869 .123313 .124756 .126199 .127642 .129084 .130526 .131968 .133410 .134851 .136292
.139173 .140613 .142053 .143493 .144932 .146371 .147809 .149248 .150686 .152123 .153561
.156435 .157871 .159307 .160743 .162178 .163613 .165048 .166482 .167916
10 .173648 .175080 .176512 .177944 .179375 .180805 .182236 .183665 .185095 .186524
11 .190809 .192237 .193664 .195090 .196517 .197943 .199368 .200793 .202218 .203642
.207912 .209334 .210756 .212178 .213599 .215019 .216440 .217859 .219279 .220697 .222116
.224951 .226368 .227784 .229200 .230616 .232030 .233445 .234859 .236273 .237686 .239098
.244743
.250380 .251788 .253195 .254602 .256008
.261628
.267238 .268640 .270040 .271440
.275637 .277035 .278432 .279829 .281225
.292372 .293762 .295152 .296542 .297930
.309017 .310410 .311782 .313164 .314545
.325568 .326943 .328317 .329691 .331063
.342020 .343387 .344752 .346117 .347481

60'

55'

50'

45'

40'

35'

.282621 .284015 .285410 .286803 .288196 .289589
.299318 .300706 .302093 .303479 .304864 .306249
.315925 .317305 .318684 .320062 .321440 .322816
.332436 .333807 .335178 .336548 .337917 .339285
.348845 .350207 .351569 .352931 .354291 .355651
30'
25'

U 2

24.

.358368 .359725 .361082 .362438 .363793 .365148 .366501 .367854 .369206 .374607 .375955 .377302 .378649 .379994 .381339 .382683 .384027 .385369 .390731 .392070 .393407 .394744 .396080 .397415 .398749 .400082 .401415 .406737 .408065 .409392 .410719 .412045 .413369 .414693 .416016 .417339 .422618 .423936 .425253 .426569 .427884 .429198 .430511 .431823 .433135 .438371 .439678 .440984 .442289 .443593 .444896 .446198 .447499 .448799 .450099 .451397 .452694 .453991 .453991 .455286 .456580 .457874 .459166 .460458 .461749 .463038 .464327 .465615 .466901 .468187 .469472 28 .469472 .470755 .472038 .473320 .474600 .475880 .477159 .478436 .479713 .480989 .482263 .483537 .484810 .484810 .486081 .487352 .488621 .489890 .491157 .492424 .493689 .494953 .496217 .497479 .498740 .500000 30 .500000 .501260 .502517 .503774 .505030 .506285 .507539 .508791 .510043 .511293 .512543 .513791 .515038

.370557 .371908 .373258 .374607 .386711 .388052 .389392 .390731 .402747 .404078 .405408 .406737 .418660 .419980 .421300 .422618 .434446 .435755 .437063 .438371

.515038 .516284 .517529 .518773 32 .529919 .531152 .532384 .533615 33 .544639 .545858 .547076 .548293

.520016 .521258 .522499 .523738 .524977 .526214 .527450 .528685 .529919 58 .534844 .536072 .537300 .538526 .539751 .540975 .542197 .543419 .544639 57 .549509 .550724 .551937 .553149 .554360 .555570 .556779 .557987 .559193 .559193 .560398 .561602 .562805 .564007 .565207 .566406 .567604 .568801 .569997 .571191 .572384 .573576 .573576 .574767 .575957 .577145 .578332 .579518 .580703 .581886 .583069 .584250 .585429 .586608 .587785 .587785 .588961 .590136 .591310 .592482 .593653 ,594823 .595991 .597159 .598325 .599489 .600653 .601815 .601815 .602976 .604136 .605294 .606451 .607607 .608761 .609915 .611067 .612217 .613367 .614515 .615662 .615662 .616807 .617951 .619094 .620236 .621376 .622515 .623652 .624789 .625924 .627057 .628189 .629320 51 .629320 .630450 .631578 .632705 .633831 .634955 .636078 .637200 .638320 .639439 .640557 .641673 .642788 .642788 .643901 .645013 .646124 .647233 .648341 .649448 .650554 .651657 .652760 41 .656059 .657156 .658252 .659346 .660439 .661530 .662620 .663709 .664796 .665882 .669131 .670211 .671290 .672367 .673443 .674517 .675590 .676662 .677732 .678801 .681998 .683061 .684123 .685183 .686242 .687299 .688355 .689409 .690462 .691513 .694658 .695704 .696748 .697791 .698832 .699871 .700909 .701946 .702981 .704015 40' 35' 30' 25' 20' 15'

Deg.

NATURAL CO-SINES.

.707107 .708135

.766044 .766979 .767911 .777146 .778060 .778973 .788011 .788905 .789798 .798636 .799510 .800383 .809017 .809871 .810723

45 .709161 .710185 .711209 .712230 .713251 .714269 .715286 46 .719340 .720349 .721357 .722364 .723369 .724372 .725374 .726375 .727374 .728371 .731354 .732345 .733335 .734322 .735309 .736294 .737277 .738259 .739239 48 .743145 .744117 .745088 .746057 .747025 .747991 .748956 .749919 .750880 49 .754710 .755663 .756615 .757565 .758514 .759461 .760406 .761350 .762292 .768842 .769771 .770699 .779885 .780794 .781702 .790690 .791579 .792467 .801254 .802123 .802991 .803857 .804721 .805584 .806445 .807304 .808161 .811574 .812423 .813270 .814116 .814959 .815801 .816642 .817480

.716302 .717316

.718329

.719340 44

.729367

.730361

.731354 43

.740218

.741195

.742171

.743145 42

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

.819152 .819985 .820817 .821647 .822475 .823302 .824126 .824949 .825770 .826590 .827407 .829038 .829850 .830661 .831470 .832277 .833082 .833886 .834688 .835488 .836286 .837083 .838671 .839462 .840251 .841039 .841825 .842609 .843391 .844172 .844951 .845728 .846503 58 .848048 .848818 .849586 .850352 .851117 .851879 .852640 .853399 .854156 .854912 .855666 59 .857167 .857916 .858662 .859406 .860149 .860890 .861629 .862366 .863102 .863836 .864567 60 .866025 .866752 .867476 .868199 .868920 .869639 .870356 .871071 61 .874620 .875324 .876026 .876727 .877425 .878122 .878817 .879510 .882948 .883629 .884310 .884988 .885664 .886338 .887011 .887682 63 .891007 .891666 .892323 .893979 .893633 .894284 .894934 .895582 .898794 .899431 .900065 .900698 .901329 .901958 .902585 .903211 .906308 .906922 .907533 .908143 .908751 .909357 .909961 .910564 .911164 .911762 .912358 66 .913545 .914136 .914725 .915312 .915896 .916479 .917060 .917639 .918216 .918791 .919364 .919936 .920505 .921072 .921638 .922201 .922762 .923322 .923880 .924435 .924989 .925541 .926090 .926638 .927184 .927728 .928270 .928810 .929348 .929884 .930418 .930950 .931950 .932008 .932534 .933058 .933580 .934101 .934619 .935135 .935650 .936162 .936672 .937181 .937687 .938191 .938694 .939194 45' 40' 30' 25' 5'

20'

15'

10'

0' Deg.

NATURAL CO-SINES.

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A Practical Treatise on the Science of Land and Engineering Surveying ...