ZEEVAARTKUNDIGE TAFELS
VOORZIEN VAN EENE
■
UITGEGEVEN
OP LAST VAN HET DEPARTEMENT VAN MARINE
BEWERKT DOOR
I
TWEEDE DEEL.
’ S GRAVENHAGE — DEPARTEMENT VAN MARINE — 1918.
i KORTE VERKLARING VAN HARE INRICHTING
EN HAAR GEBRUIK
I
P. HAVERKAMP,
LUITENANT TER ZEE DER EERSTE KLASSE,
BELAST MET HET ONDERWIJS IN DE THEORETISCHE ZEEVAARTKUNDE AAN HET KONINKLIJK INSTITUUT VOOR DE MARINE
TE WILLEMSOORD.
\tP\
L . —---——“ '
GEDRUKT TER ALGEMEENE LANDSDRUKKERIJ.
VOORBERICHT.
UI
van
W
illemsoord, September 1918.
der iste klasse, P. HAVERKAMP.
De Luitenant ter zee werden ontleend aan den 3 den
litgebreid tot 300 declinatie
Tafel XXXVIII is gedeeltelijk ontleend
Van de in Deel II voorkomende tafels werden opnieuw- of herbecijferd de tafels XXXII, XXXVI, XLII, XLVI, XLIX« en b, L, Lil en LUI (de laatstgenoemde langs grafischen weg).
Tafel XXX werd verkregen door onderlinge vergelijking van de 5 decimalige tafels van G
onggrijp, met de 7 decimalige tafels die voorkomen in resp. Schat
kamer ofte Konst der Stuurlieden van KLAAS DE VRIES (onder toezicht van B. J. D
ouwes, 1781), Grondbeginsels der Stuurmanskunst van P
yboS
teenstraen J
aCOB F
lorijn(1816) en Tafelen der Logarithmen, alsmede der Sinussen, Tangenten en Secanten ten dienste der Latijn.sche Scholen en andere Collegiën (Amsterdam, Weduwe G
erardH
ulst vanK
eulen, 1828).
Tafel XXXI kon slechts aan onderlinge vergelijking van de drie laatst genoemde werken worden ontleend.
De tafels XXXIII t/m XXXV, XXXVII, XXXIX t/m XLI, XLIII en XLIV druk van B
rouwer’ S Tafels. Daarbij werd tafel XLIII en 720 breedte.
aan B
rouwer’S Tafels, gedeeltelijk aan tafels, die door het Duitsche Departement van Marine worden uitgegeven.
Tafel XLV komt voor in een door het Amerikaansche Departement Marine uitgegeven werk.
De tafels XLVII en XLVIII zijn ontleend aan den 2 den druk van de door het Departement van Marine uitgegeven Hydrografische Tafels, terwijl de opgaven, die vervat zijn in tafel LI, door de Afdeeling Hydrografie werden verstrekt.
en correctie vond op de in het voorbericht van Becijfering, herbecijfering
Deel I genoemde wijze plaats.
Op blz. 144 komt een lijst van verbeteringen voor.
Bij het onderzoek naar de nauwkeurigheid van de A. B. C. tafels is gebleken, dat eenige bladzijden van tafel XII gewijzigd moeten worden.' Men treft deze los achterin aan. Men kan de te vervangen pagina’ s langs de zwarte lijn afsnijden en de losse bladen ter plaatse inplakken.
Bij de exemplaren van Deel I die nog ongebonden zijn, zal getracht worden de vervanging bij het binden te doen plaats vinden.
Mijn mede-corrector, den heer G. C. D
ibbetzjr., breng ik gaarne mijn dank voor de wijze, waarop hij zijn medewerking verleende.
Ten slotte betuig ik mijn bijzonderen dank aan den heer J. VAN ROON, dien ik
steeds bereid vond mij bij de bewerking van de Verklaring enz. van de Tafels ter
zijde te staan.
INHOUD.
Bladz.
Tafel.
23 XXXV.
24 XXXVI.
26 XLIII.
33
XLIXzz.
34 XLIXA
34
74 XLVI.
XLVII.
XLVIII.
XLIV.
XLV.
XLI.
XLÏI.
°P willekeuriger! datum
24 25 25 26
26 2627 3i 1 11 20 22
32
32
3344
58 72 73 XXX.XXXI.
XXXII.
XXXIII.
XXXIV.
XXXVII.
XXXVIII.
XXXIX.
XL.
LI.
Lil.
LUI.
voor diverse plaatsen op aarde
een looding tot L. W. S ...
schijnbare windrichting en -kracht tot ware . Natuurlijke tangens en cotangens
Natuurlijke secans en cosecans ...
Schijnbare kimduiking met vrije en onvrije kim ...
Middelbare straalbuiging
Verbetering van de middelbare straalbuiging voor een anderen thermometerstand
Verbetering van de middelbare straalbuiging voor een anderen barometerstand
Overeenkomstige aanwijzingen van den barometer en thermometer op de meest gebruikelijke schalen
Verschilzicht in hoogte van zon en planeten Verschillende opgaven
Zons halve middellijn
Verbetering van het equatoriaal horizontaal verschilzicht der maan voor de breedte
Verbetering der maans halve middellijn voor de hoogte ....
Verbetering der hellende halve middellijn van Q of C voor de straalbuiging
Uurhoek en hoogte der hemellichten tijdens de gunstigste om standigheid voor tijdsbepaling
Herleiding van geografische- tot geocentrische breedte ....
Kort overzicht van de lengten van 1° van den meridiaan en van i° van de parallel
Herleiding van Engelsche vamen tot meters en omgekeerd . . . Astronomisch argument op 1 Januari
Percentsgewijze verbetering der amplituden voor de verschillende
jaren • ...
Verschil van de waarde van het astronomisch argument 1 Januari ten ou M. T. Gr. met die op een
ten o u M. T. Gr. ...
Becijfering van het tijdstip van H. W. van een partieel getij door , , — V o + K — m X 360
uitvoering van de deeling --- - —! ---- —--- - ---- ; . ; Tafels, die bij gegeven amplitude de rijzing van een partieel getij boven het gemiddelde peil geven op heele en halve uren na het oogenblik van H. W. van dat getij
Getijconstanten Herleiding van Herleiding van
Korte verklaring van inrichting en gebruik der in Deel I en II voorkomende
tafels, met vermelding hunner nauwkeurigheid, benevens eenige theoretische
beschouwingen en litteratuur opgaven
WISKUNDIGE TAFELEN.
0°—5°
o° i° 2° 3° 4°
Cotang.
Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang.
o
i
27,27149
,03987
,04075
37,35789
22,16398
0,02939
,03492 o
Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang.
89° 88° 87° 86° 8$°
2
L
TAFEL XXX.
Natuurlijke tangens en cotangens*
21 22 23 24 25 26 27 28 29 30
0,00175 ,00204 ,00233 ,00262 ,00291
0,01047 ,01076 ,01105 ,01135 ,01164
0,02502 ,02531
,03405 ,03434
29 28 27 26 25
9 8 7 6 5 11
12
*3
>4 15 16 17 18 19 20
30,95993 30,68331 30,41158 . — . 30,14462 ,03346 29,88230
0,03376 29,62450 29,37111 29,1 2200 ,03463 28,87709 28,63625 0,02793
,02822 ,02851 ,02881 ,02910
47,73950 47,08534 46,44886
^02182 45,82935
45,22614 44,63860
32,42129 32,11810 31,82052 31,52839 31,24158
14,30067 14,24113 14,18209
*4>12354 14,06546 14,00786
44 43 42 4*
40
24 23 22 21 20
*9 18 17 16
*5 2
3 4 5 6 7 8 9 10
3i 32 33 34 35 36 37 38 39 40
4i 42 43 44 45 46 47 48 49 50
5»
52 53 54 55 56 57 58 59 60
oneindig 3437,74667
>718,87319 1>45,9*530 859,43630 687,54887 572,95721 491,10600 429,7*757 381,97099 343,7737*
0,02357 ,02386 ,024*5 ,02444 ,02473 0,01746 57,28996
,o*775 ,01804 ,01833 ,01862 ,01891
0,03230 ,03259 ,03288 ,033*7 ,02997 ,03026 ,03055 0,03084
,03**4 ,03*43 ,03*72 ,03201
56,35059 55,44152 54,56130 53,70859 52,88211
52,08067 51,30316 50,54851 49,81573
0,04104 ,04*33 ,04162 ,04*9*
,04220
0,04250 ,04279 ,04308 ,04337 ,04366
0,05124 ,05*53 ,05182 ,05212 ,0524*
,03842 ,0387*
,03900 ,03929
28,63625 28,39940 28,16642 27,93723 27,7**74
49 48 47 46 45 60 59 58 57 56 55
39 38 37 36 35 54 53 52 5*
50
34 33 32 3*
30
*4
*3 12
10
4 3 2 0,06993
,07022 ,07051 ,07080 ,07110 ,07*39 0,07168
,07*97 ,07227 ,07256 ,07285
0,00902 ,00931 ,00960 ,00989 ,01018
20,44649 20,32531 20,20555 20,08720 19,97022
*9,85459 19,74029
*9,62730
*9,5*558
*9,405*3
*9,29592
*9,18793 19,08114 0,00000
,00029 ,00058 ,00087 ,00116 ,00145
0,00320 ,00349 ,00378 ,00407 ,00436
0,00465 ,00495 ,00524 ,00553 ,00582
0,00611 ,00640 ,00669 ,00698 ,00727
0,00756 ,00785 ,00815 ,00844 ,00873
,02589 . . ...
,02619 38,18846 0,02648 37,76861
,02677____ ", ,02706 36,95600 ,02735
22,02171 21,88125 21,74257 21,60563 21,47040
21,33685 2 *,20495 2 1,07466 20,94597 20,81883
19,08114 18,97552 18,87107 18,76775 18,66556 18,56447
'8,46447 18,36554 18,26765 18,17081 18,07408
*7,98015 17,88631
*7,79344
*7,70*53 17,61056
0,07753 ,07782 ,07812 ,07841
■07870
0,07899 ,07929 ,07958 ,07987 ,08017
0,08046 ,08075 ,08104 ,08134 ,08163
0,08192 ,08221 ,08251 ,08280 ,08309
0,08339 ,08368 ,08397 ,08427 ,08456
0,08485 ,08514 ,08544 ,08573 ,08602
0,08632 ,08661 ,08690 ,08720 ,08749
**,99235
**,95037 11,90868 11,86728 11,82617
11,78533 11,74478 11,70450 11,66450 11,62476
11,58529 11,54609
”,50715 11,46847
”,43005 17,52052
'7,43'39 '7,34315 17,25581 17,16934
17,08372 16,99896 16,91503 16,83191 16,74961
16,66811 16,58740 16,50746 164.2828 16,34986
16,27217
■ 6,19523 16,11900 16,04348 '5,96867
'5,89454 1 5,82110 '5,74834 15,67623 15,60478
15,53398 '5.46381 15,39428 '5,32536 15,25705 15,18935 '5,12224 '5.05572 14,98978 '4,92442 14,85962 '4,79537 '4,73'68 14,66853 14,60592
14.54383 14,48227 14,42123 14,36070 14,30067
13.95072 '3,89405 13,83783 13,78206 13,72674
13,67186 '3,61741 '3,56339 13,50980 13,45663
13,40387 '3,35152 13,29957 '3,24803 13,19688
13,14613 13,09576 13,04577 12,99616 12,94692
12,89806 12,84956 12,80142
*2,75363 12,70620
12,65912 12,61239 12,56600
*2,5*994 12,47422 12,42883
*2,38377
*2,33903 12,29461
*2,2505*
12,20672 12,16324 12,12006 12,077*9 12,03462 0,01193
,01222 ,01251 ,01280 ,01309 0,01338
,01367 ,01396 ,01425 .0'455 0,01484
,015*3 ,01542 ,0157*
,01600
0,01629 ,01658 ,01687 ,01716 ,01746
23,53205 23,37*78 23,2*367 23,05768 22,90377 22,75*89 22,60201 22,454*0
0,05241 ,05270 ,05299 ,05328 ,05357 ,05387
0,05416 ,05445 ,05474 ,05503 ,05533 0,05562
,0559*
,05620 ,05649 ,05678
0,05708 ,05737 ,05766 ,05795 ,05824
0,05854 ,05883 ,059*2 ,0594*
,05970
0,07314 ,07344 ,07373 ,07402 ,0743*
0,07461 ,07490 ,075*9 ,07548 ,07578
0,07607 ,07636 ,07665 ,07695 ,07724 312,52137
286,47773 264,44080 245,55198 229,18166
214,85762 202,21875 190,98419 180,93220 171.88540
163,70019 156,25908 149.46502 143,23712 137,50745 132,21851 127,32134 122,77396 118,54018
”4,58865
110,89205 107,42648 104,17094 101,10690 98,21794 95,48948 92,90849 90,46334 88,14357 85,93979
83,84351 81,84704 79,94343 78,12634 76,39001
74,729'7 73,13899 71,61507 70,15335 68,75009
67,40185 66,10547 64,85801 63,65674 62,49915
61,38291 60,30582 59,26587 58,26117 57,28996
0,01920 ,0'949 ,01978 ,02007 ,02036 49,10388
0,02066 48,41208
>02095 ,02124 ,02153
0,02211 ,02240 ,02269 44,o66ll ,02298 43,50812 ,02328 42,96408
, . 36,56266 ,02764 36,17760 35,80055 35>43*28 35,06955 34,7*5*2 34,36777 , 34,02730 ,02968 33>6935*
33,36619 33,045*7 32,73026
0,03492 ,0352*
,03550 ,03579 ,03609 ...
,03638 27,48985
0,03667 ,0369627^0’5656 ,03725 ,03754 ,03783
0,04541 ,04570 ,04599 ,04628 ,04658
0,04687 ,047*6 ,04745 ,04774 ,04803
0,04833 20,69322 ,04862 20,56911 ,04891 ,04920 ,04949 0,04978 ,05007 ,05037 ,05066 ,05095 42,43346 4i,9*579 41,4*059 40,9*74*
40,43584
39,96546 , _ 39,50589 ,02560 39,05677 38,61774
0,04395 ,04424
>04454 ....
,04483 22,30810
>045*2
0,05999 ,06029 ,06058 ,06087 ,06116
0,06145 ,06175 ,06204 ,06233 ,06262
0,06291 ,06321 ,06350 ,06379 ,06408
0,06438 ,06467 ,06496 ,06525 ,06554
0,06584 ,06613 ,06642 ,06671 ,06700
0,06730 ,06759 ,06788 ,06817 ,06847
0,06876 ,06905 ,06934 ,06963 ,06993 26,84498 26,63669 26,43160
0,03812 26,22964 26,03074 25,83482 25,64183 25,45'7°
0,03958 25,26436 25,07976 ,04016 24,89783 ,04046 24,71851 24,54176
24,3675' 24,19571 24,02632 23,85928 23,69454
85°—90°
TAFEL XXX.
Natuurlijke tangens en cotangens.
6° 7° 8° 9°
5°
Tang. Cotang.
Cotang.
Cotang. Tang. Cotang. Tang.
Tang.
Cotang.
Tang.
o
io
o Tang.
Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang.
83° 82° 8i° 80°
84°
80° —85°
21 22 23 24 25
0,08749 ,08778 ,08807 ,08837 ,08866 ,08895
0.10099 ,10128 ,10158 ,10187 ,10216
0,10393 ,10422 ,10452 ,10481 ,10510
o,n57o
,11600 ,11629 ,11659 ,11688 0,10834 ,10863 ,10893 ,10922 ,10952
0,12013 ,12042 ,12072 ,12101 ,12131 0,12160
,12190 ,12219 ,12249 ,12278
0,12751 ,12781 ,12810 ,12840 ,12869 0,12899 ,12929 ,12958 ,12988 ,13017 0,13047
,13076 ,13106 ,13136 ,13165 0,12603
,12633 ,12662 ,12692 ,12722
0,15570 ,15600 ,15630 ,15660 ,15689
6,67787 ,66463 ,65144 ,63831 ,62523
0,16017 ,16047 ,16077 ,>6107 ,16137
5,80953 ,79944 ,78938 ,77936 ,76937 5,75941 ,74949 ,7396o ,72974 ,7'994 5,86051 ,85024 ,84001 ,82982 ,81966 5,91236
,90191 ,89151 ,88114 ,87080
24 23 22 21 20 29 28 27 26 25
»4
>3 12
9 8 7 6 5 16
17 18
>9 20
26 27 28 29 30
4»
42 43 44 45 46 47 48 49 50
56 57 58 59 60
0,09365 ,09394 ,09423 ,09453 ,09482 0,09218
,09247 ,09277 ,09306 ,09335
11,20478 , 16809 ,13163 ,09542 ,05943
10,35383 ,32245 ,29126 ,26025 ,22943
9,90211 ,87338 ,84482 ,81641 ,78817 9,76009
,73217 ,70441 ,67680 ,64935
0,11128 ,11158 ,11187 ,11217 ,11246 0,10981 ,1 ÏOI I ,11040 ,11070 ,11099
0,11423 ,11452 ,11482
J154I
0,11865 ,11895 ,11924 ,11954 ,11983
9,10646 ,08211 ,05789 ,03379 ,00983
8,64275 ,62078 ,59893 ,57718 ,55555
8,22344 ,20352 ,18370 ,16398 ,'4435 8,53402
,5'259 ,49'28 ,47007 ,44896
o,'3'95 ,'3224 ,'3254 ,'3284 ,'33'3 o,i3343
,13372 ,13402 ,13432 ,13461 0,12456
,12485 ,125'5 ,12544 ,12574
7,25310 ,23754 ,22204 ,2066I ,19125 7,84242
,82428 ,80622 ,78825
>77035
0,157'9 ,'5749 ,'5779 ,';8o9 ,'5838 0,14678
,14707 ,14737 ,14767 ,14796 0,14826
,14856 ,14886 ,14915 ,14945 0,14232
,14262 ,14291 ,14321 ,14351 0,14381
,14410 ,14440 ,14470 ,14499
6,36165 ,34961 ,33761 ,32566 ,31375 6,54777
,53503 ,52234 ,50970 ,497io 6,74483
,73'33 ,71789 ,70450 ,69116 7,02637
,01174 6,997'8 ,98268 ,96823 7,”537 ,10038 ,08546 ,07059 ,05579
>04105
0,17213 ,17243 ,'7273 ,17303 ,17333 0,17363 ,'7393 ,'7423 ,'7453 ,■7483 0,16764
,'6794 ,16824 ,16854 ,16884 0,16615
,'6645 ,'6674 ,16704 ,'6734
5,71013 ,70037 ,69064 ,68094 ,67128
39 38 37 36 35 34 33 32 3i 30
19 18 17 16 15 60 59 58 57 56 55
36 37 38 39 40 3»
32 33 34 35 6 7 8 9 10
12 13 14 15
51 52 53 54 55 2 3 4 5
0,08925 ,08954 ,08983 ,09013 ,09042 0,09071
,09101 ,09130 ,09’59 ,09189
0,09658 ,09688 ,09717 ,09746 ,09776 0,09805 ,09834 ,09864 ,09893 ,09923 0,09952
,09981 ,10011 .10040 ,10069
0,10246 ,10275 ,10305 ,10334 ,10363
11,43005 ,39'88 ,35397 ,3'630 ,27889 ,24'7'
11,02368 10,98815 ,95285 ,9'777 ,88292 10,84829
,8'387 ,77967 ,74569 ,71191 '0,67835
,64499 ,61184 ,57889 ,54615 10,51361 ,48126 ,44911 ,41716 ,38540
10,19879 ,16833 ,13805 ,10795 ,07803
9,62205 ,59490
>5679' ,54106 ,5'436
0,11276 ,''3°5 ,"335 ,11364 ,11394 0,10687
,10716 ,10746 ,10775 ,10805
0,11718 ,11747 ,11777 ,11806 ,11836 0,10510 ,10540 ,10569 ,10599 ,10628 ,10657
9,23016 ,20516 ,18028 ,15554 ,13093
8,98598 ,96227 ,93867 ,91520
>89185 9,35724
,33155 ,30599 ,28058 ,25530
8,86862 ,8455' ,82252 ,79964 ,77689
8,42795 ƒ30705 ,38625 ,36555 ,34496 8,32446 ,30406 ,28376 ,26355 ,24345 9,51436 ,48781 ,46141 ,435'5 ƒ40904 ,38307
0,13491 ,13521 ,'355°
,'358o ,13609 0,13639
,13669 ,'3698 ,'3728 ,13758 0,13787 ,13817 ,>3846 ,13876 ,13906 0,12278
,12308 ,12338 ,12367 ,12397 ,12426
7,17594 ,16071 ,’4553 ,13042 ,1’537 7,49465 ,47806 ,46154 ,44509 ,42871
7,33190 ,31600 ,30018 ,28442 ,26873 7,66466
,64732 ,63005 ,61287 ,59575 7,57872 ,56176 ,54487 ,52806 ,5"32
7,4'240 ,39616 ,37999 ,36389 ,34786 7,75254
,7348o ,71715 ,69957 ,68208 8,02848 ,00948 7,99058 ,97176 ,95302 7,93438 ,91582 ,89734 ,87895 ,86064 8,14435 ,12481 ,'0536 ,08600 ,06674 ,04756
0,15124 ,'5'53
>15183 ,'52'3 ,'5243 0,15272
,'5302 ,'5332 ,15362 ,'539' 0,14975 ,'5005 ,15034 ,15064 ,15094 o,'4529
,'4559 ,14588 ,14618 ,14648 0,14054 ,14084 ,>4”3 ,14143 ,14'73 ,14202
6,48456 ,47206 ,45961 ,44720 ,43484 6,61219
,59921 ,58627 ,57339 ,56055 6,88278
,86874 ,85475 ,84082 ,82694 6,95385 ,93952 ,92525 ,91104 ,89688
0,17063 ,17093 ,17123 ,17153 ,17183
0,17513 ,'7543 ,17573 ,17603 ,17633 0,16914
,16944 ,16974 ,17004
>17033 0,16316
,16346 ,'6376 ,'6405 ,16435 0,15838
,15868 ,15898 ,15928 ,15958 ,15988
6,07340 ,06240 ,05’43 ,04051 ,02962 6,01878 ,00797 5,99720 ,98646 ,97576 5,96510 ,95448 ,94390 ,93335 ,92283 6,12899
,”779 ,10664 ,09552 ,08444 6,18559
,174’9 ,16283 ,’5'5’ ,14023 6,24321 ,23160 ,22003 ,20851 ,19703
44 43 42 4i 40 49 48 47 46 45 54 53 52 5i 50
4 3 2 0,09511
,0954’ ,09570 ,09600 ,09629
0,15421 ,’545’ ,15481 ,155H ,15540
6,42253 ,41026 ,39804 ,38587 ,37374 6,81312
,79936 ,78564 ,77’99 ,75838
6,3’375 ,30189 ,29007 ,27829 ,26655 ,25486
0,13935 ,13965 ,13995 ,14024 ,14054 10,04828
,01871 9,98931
,96007 ,93101
o, 16465 ,'6495 ,16525 ,16555 ,16585
8,75425 ,73172 ,7093' ,68701 ,66482
0,16167 ,16196 ,16226 ,16256 ,16286
5°—10°
10° —15°
U°
io°
Ï2°«3°
Cotang.
Cotang. Tang.' Tang. Cotang. Tang. Cotang. Tang.
Tang. Cotang.
o
o Cotang. Tang. Cotang. Tang. Cotang. Tang.
78° 77° 76° 75°
4
TAFEL XXX.
Natuurlijke tangens en cotangens.
21 22 23 24 25 26 27 28 29 30
0,18113 ,18143 ,18173
>18203 ,18233
0,18263 ,18293 ,18323 ,18353 ,18384
0,19016 ,19046 ,19076 ,19106 ,19136
5,56706 ,55777 ,54851 ,53927 ,53007
0,19921 ,19952 ,19982 ,20012 ,20042 0,197/0 ,19801 ,19831 ,19861 ,19891
0,20830 ,20861 ,20891 ,20921 ,20952
0,21134 ,21164 ,21195 ,21225 ,21256
0,21895 ,21925 ,21956 ,21986 ,22017 0,22047
,22078 ,22108 ,22139 ,22169
0,22964 ,22995 ,23026 ,23056 ,23087 0,22658
,22689 ,22719 ,22750 ,22781
4,63171 ,62518 ,61868 ,61219 ,60572
4,47374 ,46764 ,46155 ,45548 ,44942 4,44338
,43735 ,43134 ,42534 ,41936
0,26048 ,26079 ,26110 ,26141 ,26172
0,26359 ,26390 ,26421 ,26452 ,26483 0,26203
,26235 ,26266 ,26297 ,26328
3,90890 ,90417 ,89945 ,89474 ,89004
3,74950 ,74512 ,74075 ,73640 ,73205
24 23 22 21 20 l6
17 18 19 20 12 13 14 15
3»
32 33 34 35
0,17633 ,17663 ,17693 ,17723 ,17753 37783
0,17813 ,17843 J7873 ,17903 ,17933
0,18414 ,18444 ,18474 ,'8504 ,18534
0,18564 ,18594 ,18624 ,18654 ,18684
0,19317 ,«9347 ,19378 ,<9408 ,19438
5,38677 ,37805 ,36936 ,36070 ,35206
5,17671 ,16863 ,16058 ,15256 ,14455
0,20073 ,20103 ,20133 ,20164 ,20194 0,19438
,19468 ,19498 ,19529 ,19559 ,19589
0,20982 ,21013 ,21043 ,21073 ,21104 0,20679 ,20709 ,20739 ,20770 ,20800 0,20527
,20557 ,20588 ,20618 ,20648
4,87162 ,86444 ,85727 ,85013 ,84300
4,80068 ,7937°
,78673 ,77978 ,77286 5,14455 ,13658 ,12862 ,12069 ,”279 ,10490
4,76595 ,75906 ,75219 ,74534 ,73851 4,83590
,82882 ,82175 ,81471 ,80769
0,21256 ,21286 ,21316 ,21347 ,21377 ,21408
0,22200 ,22231 ,22261 ,22292 ,22322
O,228t I ,22842 ,22872 ,22903 ,22934
4,66458 ,65797 ,65138 ,64480 ,63825
4,56726 ,56091 ,55458 ,54826 ,54196
4,35459 ,34879 ,343oo ,33723 ,33148 4,5045'
,49832 ,49215 ,48600 ,47986
4,38381 ,37793 ,37207 ,36623 ,36040
0,24193 ,24223 ,24254 ,24285 ,24316
0,24809 ,24840 ,24871 ,24902 ,24933 0,24655
,24686 ,24717 ,24747 ,24778
4,33148 ,32573 ,32001 ,31430 ,30860 ,30291
4,21387 ,20842 ,20298 ,19756 ,19215 4,18675
,18137 ,17600 ,17064 ,16530
4,08152 ,07639 ,07127 ,06616 ,06107
4,03076 ,02574 ,02074 ,01576 ,01078
0,25118 ,25149 ,25180 ,25211 ,25242 0,25273
,25304 ,25335 ,25366 ,25397
0,25583 ,25614 ,25645 ,25676 ,25707
3,95680 ,95196 ,94713 ,94232 ,93751
3,86208 ,85745 ,85284 ,84824 ,84364
3,77152 ,76709 ,76268 ,75828 ,75388
60 59 58 57 56 55
44 43 42 4«
40
«9 18
«7 16
«5
«4
«3 12 11 10
9 8 7 6 5 6
7 8 9 10
36 37 38 39 40
4«
42 43 44 45 46 47 48 49 50
5«
52 53 54 55
0,17963 ,«7993 ,18023 ,18053 ,18083
0,18865 ,18895 ,18925 ,'8955 ,18986 0,18714 ,18745 ,18775 ,18805 ,18835
0,19166 ,19197 ,19227 ,19257 ,19287
5,67128 ,66165 ,65205 ,64248 ,63295 ,62344
5,47548 ,46648 ,45751 ,44857 ,43966 5,61397
,60452 ,595'1 ,58573 ,57638
5,43077 ,42192 ,41309 ,40429 ,39552
5,21744 ,20925 ,20107 ,«9293 ,18480 5.34345
,33487 ,32631 ,3«778 ,30928
0,19619 ,19649 ,19680 ,i97io ,19740
0,20224 ,20254 ,20285 ,20315 ,20345 0,20376
,20406 ,20436 ,20466 ,20497
5,oï97i ,01210 ,00451 4,99695 ,98940
4,98188 ,97438 ,96690 ,95945 ,95201 5,09704
,08921 ,08139 ,07360 ,06584
5,05809 ,05037 ,04267 ,03499 ,02734
4,9446o ,93721 ,92984 ,92249 ,91516
0,21743 ,21773 ,21804 ,21834 ,21864
0,22353 ,22383 ,22414 ,22444 ,22475 0,22505
,22536 ,22567 ,22597 ,22628
4,70463 ,69791 ,69121 ,68452 ,67786 ,67121
4,53568 ,52941 ,52316 ,51693 ,51071
4,4i34o ,40745 ,40152 ,3956o ,38969
0,23424 ,23455 ,23485 ,235’6 ,23547 0,23087
,23117 ,23148 ,23179 ,23209 ,23240
0,23271 ,23301 ,23333 ,23363 ,23393
0,23578 ,23608 ,23639 ,23670 ,23700
0,23885 ,239'6 ,23946 ,23977 ,24008
0,24039 ,24069 ,24100 ,24131 ,24162
0,24347 ,24377 ,24408 ,24439 ,24470 0,24501
,24532 ,24562 ,24593 ,2462+
4,26911 ,26352 ,25795 ,25239 ,24685 4,29724
,29159 ,28595 ,28032 ,27471
4,24132 ,23580 ,23030 ,22481 ,21933
4,13350 ,12825 ,12301 ,11778 ,11256
4,05599 ,05092 ,04586 ,04081 ,03578
0,25428 ,25459 ,25490 ,25521 ,25552
0,25738 ,25769 ,25800 ,25831 ,25862
0,26515 ,26546 ,26577 ,26608 ,26639
0,26670 ,26701 ,26733 ,26764 ,26795
4,01078 ,00582 ,00086 3,99592
,99099 ,98607
3,98117 ,97627 ,97139 ,96651 ,96165
3,93271 ,92793 ,92316 ,91839 ,91364
3,88536 ,88068 ,87601 ,87136 ,86671
3,83906 ,83449 ,82992 ,82537 ,82083
3,79378 ,78931 ,78485 ,78040 ,77595 3,81630
,81177 ,80726 ,80276 ,79827
49 48 47 46 45
39 38 37 36 35
4 3 2 2
3 4
5
5,52090 ,51'76 ,50264 ,49356 ,48451
4,'5997 ,15465 ,14934 ,14405 ,13877
4,10736 ,10216 ,09699 ,09182 ,08666
0,24933 ,24964 ,24995 ,25026 ,25056 ,25087
54 53 52 5'
5°
5,25880 ,25048 ,24218 ,23391 ,22566
0,21590 ,21621 ,21651 ,21682 ,21712 0,21438
,21469 ,21499 ,21529 ,21560
4,59927 ,592^3 ,58641 ,58001 ,57363
0,25893 ,25924 ,25955 ,25986 ,26017
34 33 32 3«
_3° .
29 i 28 27 26 25
5,30080 ,29235 ,28393 ,27553 ,26715
4,90785 ,90056 ,89330 ,88605 ,87882
75°—80°
4,73170 ,72490 ,71813 ,71137 ,70463 Cotang. | Tang.
0,2373' ,23762 ,23793 ,23823 ,23854
56
58__
Cotang. | Tang.
79°
IV - SXV
wip
'C/Uan;
<W»Ï». ÏW‘.
T«sg.
>302,37
3.464
0.3479' O.2QO2I i
>34922
,32264
O
Cotang. Tang. Cotang. Tang. Cotang. Tang. Tang.
74° 73° 72 0 70 0
70° —75°
5
tafsx , xxx.
Kalwri&kfe ta’ .-4'Ècïs <em ««tawjgm®.
.31019 .31051 13
17 18
■9 20 1:
12 13 14
■5
0,28234 ,28266 ,28297 ,28329 ,28360
3,50279 ,49894 ,49509 ,49125 ,48741 ,55761 ,55364 ,54968 ,54573
•45703 ,45327 ,44951
.3S679 ,38317 ,37955
,14605 ,14288
9 8 7 6 5 41
42 43 44 45
0,28391 ,28423 ,28454 ,28486 ,28517 0,28549
,28580 ,28612 ,28643 ,28675
3,52219 ,51829 ,51441 ,51053 ,50666
0,30287 ,30319 ,30351 ,30382 ,30414
3-42713 742343 ,41973 ,41604 .41236
0.310S3 ,3” 15:
»3«i7S ,31210
3,10532 ,10223 ,09914 ,09606 ,09298
0,34140 ,34173 ,34205 ,34238 ,34270
2,91523 ,91246 ,90971 ,90696
^90421 2,97144
,96858 ,96573 ,96288 ,96004
2,77002 ,76750 ,76498 ,76247 ,75996 2,75746
,75496 ,75246 ,74997 ,74748
)
36 37 38 39 40
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
3,64289 ,63874 ,63461 ,63048 ,62636
3,60181 ,59775 ,59370 ,58966 ,58562 3,58160
,57758 ,57357 ,56957 ,56557
0,28864 .4Ï«95 1 .28927 .2S95S .2S990
,30160 ,30192 ,30224 ,30255
3-44576 .44202 ,43829 ,43456
0.32203 ,32235 ,32267 ,32299 ,32331 0,32363
.32396 ,32428 ,32460 ,32492
3,21722 ,21392 .21063 ,20734 ,20400
2,95721 ,95437 ,95155
■ ,94872 ,9459'
2,92910 ,92632 ,92354 ,92076
>91799 2,94309
,94028 ,93748 ,93468 ,93189
0,36101 ,36134 ,36167 ,36199 ,36232 0,35937 ,35969 ,36002 ,36035 ,36068
0,36265 ,36298 ,36331.
,363641 ,36397 0,35772
,35805 ,35838 .35871
>35904 2,79545
,79289 ,79033 ,78778 ,78523 2,78269 ,78014 ,77761 ,77507 ,77254
34 33 32 3>
30 44 43 42 41 40
14 13 12 1O 47 46 45
23 24 25 S 3
3,30174 ,29829 ,29483 ,29139 ,28795 3,28452 ,28109 ,27767 ,27426 ,27085
0,34303 .34335 ,34368 ,344oo ,34433
,33395 ,33427 ,33460
54 53 52 51 50
4 3 2 3,62224
,61814 ,61405 .6S061 ,67638 ,67217 ,66796
,65957 ,65538 ,65121 ,64705
3,00028 2,99738 ,9944^
2,98580 ,98292 ,98004 ,977'7 ,9743°
3,08991 ,08685 ,08379 ,08073 ,07768 26
%
29 30 6 8 9 10
3,54'79 ,53785 ,53393 ,53001 ,52609
3,35443 ,35087 ,34732 ,34377 ,34023
0,33654 ,33686 ,33718 ,33751 ,33783 0,33816 ,33848 ,33881 ,339'3 ,33945 0,33978
,34010
>34043 ,34075 ,34io8
3 3 i
37 36 35 Il-ung. ‘<Cauin;..
3
27 26 25 ,ss5i'i ,88240 287700
.2,s6o$e, ,85822
.85555 ,85289
>85023
31 32 33 34 35
,35150 .35183 ,35216 ,35248
,29716 ,29748, ,29780
..35314 ,35346 ■
0,3012813,31914 ,31565 ,31216
,3°86
s ,30521 0,27921 !,27952!
,27983.
,28015 ; ,28046I 0,28077 3,56159
,28109 ,28140 ,28172 ,28203
<0.4867$ .3,4874’
.48359
>47977 .47596
>47216 46S37
.30860
>30891 0.30923 1 3,23381
,30955
0.27294 3-66376 ,27326 ,27357 ,27388 ,274'9
.. „ ,'"53 ,32171 | ,10842 . ,15877 ,316901 ,'5558 ,23048 ,22715 .22384 ,22053
.35020 ,35052 ,35085
035118 2,84758 ,84494 ,84229 ,83965 ,83702 3.'75ïC5
<=77’
>72338
>7*9O7
>7’476 .71046
0,32685 .3105950 --- -,051.49 . .05340 .,05049 ,27013
„270.70
„27107 0,2715$ 3.6S485
.27109 ,2/201 ,2/232 .27263
,13341 ,13027 ,12713 ,12400 i 3,12087
■ ,11775
032846 .3,04450
■04152 .03854
•03556
,3'594' . . . .31626 .16197 ,3'658'
■.34563
•.34596
0,34638 -3,88-83
>34661
•,34693
■,34726
■.34758
« 4I
.86892
>86624 .86356 7.3 .3,27685
,26745;
.26406
3,20079 ,19752
; ,19426 ,19100 ,<8775
0,5249=
>3=5=4 .-3=55s
■,3=588 3=6=1 >06554
>3=653: >06=5=
0,39495 ,29526 ,=9558 ,29590 ’ _______
4296=1 | ,37594 0,29653 ' 3.37=34 ,=9685 ,36875 ' ,36516 ,36158 ,35Soo
,3329$ I
Cotang. | ,29U7
o,29ï79 ,29210 ,29242 ,29274 ,29305
• 3,40869
•40502 ,29400 ,40136 -39771 ,39406
•>34530 1
>•
-,*9*55;
0-35445 :
>35477 ' ,355’0, ,35543 •
>35576
0,35608 ,35641 -35674 ,35707 ,35740 0,27451
,27482 ,27513 • ,27545 • ,27576
*27638 ,27670 ! ,27701: ,27732;
0,27764 ,27795 i ,278261 ,=7858 ,=7889I
.317861 ,31818I ,3lS5O ,13972 0,31882! 3,13656
,31914 ,3'946| .31978 : ,32010 I 0.32042
,32=74! . ...
,32106! ,11464 ,32139 '
0,33492, ,335=4 ,33557 ,33589 .33621
0,35=81 2,83439 ,83176 .... .S2914 ,35379I ,82653 ,35412: ,8239!
2,82130 ,81870 ,81610 ,81350 ,81091 2,80833 ,80574 ,80316 ,80059 .79802
60 50 5>!
57
55
„28706
>28.73$
<28769 ; j
<28832
,29432 ,29463 ‘
24
23 1
22 21 i 2° ■
’9 18 17 16
»5
«0^679$
.26A26
•.26920
*,26951
0.25982 ,3.70616 .701 SS
>69761 ,69335 ,68909
ihing. ::
.SW'^il <0,84433 -4,9O4=> ;
„CW>4: „a...|.->5 „00:47 ,0'
71 0
0,31242
>31274 ,31306 ,31338 ,313/0 0.31402 1 3-18451
,31434 ,181=7 ,31466 ,17804 ,31498! ,17481 ,3153°| ,17159 0,31562! 3,16838 ,>6517
3=7 17 >
,3=749 ■
>32782 , ,32814; ,04749
0,31722 ! 3,'524O ,3'754 i ,14922
•3=878 : ,3=9"
,3=943 ,3=975 i ,03260 0.33007! 3,02963 ,33040 „02667 ,33072 ,0237=
,33104. ,02077 _j33'36 1^01783 0,33'69; 3,01489 33201; ,01196
... ,00903 ,00611 ,00319 030764: 3-25055
.30706 ,24719 30828. .24383
,24049
>23714
0,29811 ,29843 ,29875 ,29906 ; ,29938 1
0,29970! 3,33670 ,30001 | ,33317 ,30033' ,32965 ,30065 ; ,32614 ,30097 , ,32264
,30700 >2.5729!
,30.732 ; ,25392
0,30446 ,30478 ,30509 ,30541 ,30573 Cotang. | Tang.
TAFEL XXX.
Natuurlijke tangens en cotangens.
20°—25°
23° 24°
20° 21° 22°
Tang. Cotang.
Cotang. Cotang.
Tang. Tang. Cotang. Tang.
o
■
o
Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang. Cotang. Tang.
69° 68° 67° 66° 65°
6 16
’7 18 20’9 21 22 23 24 2$
12 13 14 15
26 27 28 29 30
2,62561 ,62332 ,62103 ,61874 ,61646 2,67225 ,66989 ,66752 ,66516 ,66281
2,51502 ,51289 ,51076 ,50864 ,50652
0,42139 42173 ,42207 ,42242 ,42276 0,41968 ,42002 ,42036 ,42070 ,42105
2,42218 ,42019 ,41819 ,41620 ,41421
2,28891 ,28710 ,28528 ,28348 ,28167
2,26196 ,26018 ,25840 ,25663 ,25486
2,20961 ,20790 ,20619 ,20449 ,20278
2,16751 ,16585 ,16420 ,16255 ,16090
29 28 27 26 25 24 23 22 21 20
14 13 12 II IO
■
0,36925 ,36958 ,36991 ,37024 ,37057 0,37090
,37123 ,37157 ,37>9o ,37223 0,37256
,37289 ,37322 ,37355 ,37388 o,37422
,37455 ,37488 ,37521 ,37554
2,70819 ,70577 ,70335 ,70094 ,69853
o,39257 ,39290 ,39324 ,39357 ,3939’ o,39425
,39458 ,39492 ,39526 ,39559
0,40267 ,40301 ,40335 ,40369 ,40403 0,40098 ,40132 ,40166 ,40200 ,40234
2,55827 ,556o8 ,55389 ,55’70 ,54952
2,48340 ,48132 ,47924 ,477*6 ,47509 2,49386 ,49’77 ,48967 ,48758 ,48549 2,50440 ,50229 ,50018 ,49807 ,49597
0,40403 ,40436 ,40470 ,40504 ,40538 ,40572 0,40606
,40640 ,40674 ,40707 ,40741
o,4i455 ,4i49o ,41524 ,41558 ,41592
0,423'0 ,42345 ,42379 ,42413 ,42447
2,44230 ,44027 ,43825 ,43623 ,43422
2,41223 ,41025 ,40827 ,40629 ,40432 2,40235 ,40038 ,39841 ,39645 ,39449
2,373” ,37118 ,36925 ,36733 ,3654' 2,38279 ,38084 ,37891 ,37697 ,37504
0,42826 ,42860 ,42894 ,42929 ,42963
0,43343 ,43378 ,434’2 ,43447 ,43481
0,44210 ,44244 ,44279 ,443’4 ,44349 0,44036 ,44071 ,44’05 ,44’40 ,44’75
2,35585 ,35395 ,35205 ,350’5 ,34825 ,34636
2,29801 ,29619 ,29437 ,29254 ,29073
0,45432 ,45467 ,45502 ,45538 ,45573
0,45784 ,45819 ,45854 ,45889 ,45924
0,46136 ,46171 ,46206 ,46242 ,46277
2,20108 ,*9938 ,19769 ,’9599 ,’943o
2,15104 ,’494O ,14777 ,146’4 ,1445’
2,18419 ,18251 ,18084 ,’79’6 ,17749
*9 18
’7 16 15
9 8 7 6 5 4’
42 43 44 45
56 57 58 59 60 31 32 33 34 35
5i 52 53 54 55 2 3 4 5
0,37920 ,37953 ,37986 ,38020 ,38053
0,38253 ,38286 ,38320 ,38353 ,38386 0,37754
,37787 ,37820 ,37853 ,37887 0,37588
,37621 ,37654 ,37687 ,37720
2,69612 ,69371 ,69131 ,68892 ,68653 2,74748 ,74499 ,74251 ,74004 ,73756 ,73509 2,73263 ,73017 ,72771 ,72526 ,72281
2,68414 ,68175 ,67937 ,67700 ,67462
2,66046 ,65811 ,65576 ,65342 ,65109
0,38921 ,38955 ,38988 ,39022 ,39055 0,38587
,38620 ,38654 ,38687 ,38721
0,39761 ,39795 ,39829 ,39862 ,39896
2,59'56 ,58932 ,58708 ,58484 ,58261
2,56928 ,56707 ,56487 ,56266 ,56046 2,58038
,57815 ,57593 ,57371 ,57150
.0,41285 ,41319 ,41353 ,41387 ,41421
0,41626 ,41660 ,41694 ,41728 ,41763 0,41797
,41831 ,41865 ,41899 ,41933
2,46270 ,46065 ,45860 ,45655 ,45451 245246 ,45043 ,44839 ,44636 ,44433
2,43220 ,43019 ,42819 ,42618 ,42418
2,392 53 ,39058 ,38863 ,38668 ,38473
0,42447 ,42482 42516 ,42551 42585 42619 0,42654
,42688 ,42722 ,42757 ,4279’
0,43170 ,43205 ,43239 ,43274 ,43308
0,44384 ,44418 ,44453 ,44488 ,44523 0,43862 ,43897
>43932 ,43966 ,44001
0,44523 ,44558 ,44593 ,44627 ,44662 ,44697 0,44732 ,44767 ,44802 ,44837 ,44872
0/45082 ,45"7 ,45152 ,45187 ,45222 0,45257 ,45292 ,45327 ,45362 ,45397
0,45608 ,45643 ,45678 ,45713 ,45748
0,46312 ,46348 ,46383 ,46418 ,46454 0,46489
,46525 ,46560 ,46595
>46631
2,24604 ,24428 ,24252 ,24077 ,23902 ,23727
2,19261 ,19092 ,18923 ,'8755 ,18587
60 59 58 57 56 55
49 48 47 46 45
46 47 48 49 50 36 37 38 39 40
0,36760 ,36793 ,36826 ,36859 ,36892 0,36397 ,36430 ,36463 ,36496 ,36529 ,36562 0,36595
,36628 ,36661 ,36694 ,36727
0,38086 ,38120 ,38153 ,38186 ,38220
2,72036 ,71792 ,71548 .,71305 ,71062
2,63714 ,63483 ,63252 ,63021 ,62791
0,39089 ,39122 ,39156 ,39'90 ,39223 0,38754 ,38787 ,38821 ,38854 ,38888 0,38386 ,38420 ,38453 ,38487 ,38520 ,38553
0,39593 ,39626 ,39660 ,39694 ,39727
0,3993°
,39963 ,39997 ,40031 ,40065
2,54734 ,545'6 ,54299 ,54082 ,53865 2,53648 ,53432 ,53217 ,53ooi ,52786 2,52571
,52357 ,52142 ,5'929 ,51715
0,40945 ,40979 ,41013 ,41047 ,41081 0,4” ’ 5 ,4”49
>4”83 ,4’2’7 ,41251
247509 ,47302 ,47095 ,46888 46682 46476
2,36349 ,36158 ,35967 ,35776 ,35585
0,42998 ,43032 ,43067 43101 ,43136
043516 ,43550 ,43585 ,43620 ,43654 0,43689
,43724 ,43758 ,43793 43828
2,32570 ,32383 ,32197 ,32012 ,31826 2,31641 ,31456 ,31271 ,31086 ,30902 2,30718
,30534 ,3035' ,30167 ,29984
2,25309 ,25132 ,24956 ,24780 ,24604 2,27088
,26909 ,26730 ,26552 ,26374 2,27987 ,27806 ,27626 ,27447 ,27267
0,44907 ,44942 ,44977 ,450’2
^5047
o,4596o ,45995 ,46030 ,46065 ,46101
2,23553 ,23378 ,23204 ,23030 ,22857 2,22683
,22510 ,22337 ,22164 ,2’992 2,21819 ,21647 ,2’475 ,21304 ,21132
2,17582 ,’74’6 ,’7249 ,17083 ,16917
44 43 42 4’ 40 54 53 52 5’ 50
39 38 37 36 35 34 33 32 3’
30
4 3 2 6
7 8 9 10
0,40775 ,40809 ,40843 ,40877 ,40911 2,60509
,60283 ,60057 ,59831 ,59606 ,59381
2,34447 ,34258 ,34069 ,33881 ,33693 2,33505
,333'7 ,33130 ,32943 ,32756
2,64875 ,64642 ,64410 ,64'77 ,63945
2,61418 ,61190 ,60963 ,60736 ,60509
Tang. I Cotang.
2,15925 ,15760 ,'5596 ,!5432 ,15268
