Norie's Nautical Tables [Dieukhientaubien.net]

NORIE'S

NAUTICAL TABLES

WITH EXPLA N ATIO N S OF THEIR USE

EDITED BY

CA PTA I N A.G . BLA NCE B.Sc.

IMRAY LA U R IE NOR IE A N D WILSON LTD

SA I NT IVES CA MBRIDGESH I R E ENGLAND

CONTENTS

]'reface. 7 Explanation a nd use of the Tables. 9

I. COMPUTATION T A BLES Trave rse Ta bles. 2 Meridional Pans . '14 Loga rithms. 103 Logarithms ofTrig. Functions. 11 8 Log. a nd Na tural Havcrsines. 242

al ural Functions of Angles. 34Y Squares of Numbe rs. 364 Cubes of Numbers, 366 Squa re Roots of Numbers, 36R Cube Roots of Numbers. 372

11 . TA BLES FOR USE IN CEL ESTI A L N A VIGATION A B & C Azimut h T'lbles. 380 Amplitudes and Correct ions. 429 Ex-Me ridi an Tables. 432 Change of '-lour A ngle with A ltitude, 449 Chnnge of Altitude in Onc Minute of Time, 451 Di p of Sea Horizon . 453 Monthly Mea n o f the Sun's Semi -diamete r and Para llax in A ltitude . 453

Augmentation of Moon's Semi-diameter. 453 Reductio n o f the Moon's Parallax. 453 Mean Refraction . 454 Additional Refractio n Corrections, 454 Correction of Moon 's Meridional Passage, 455 Sun's To tal Correctio n . 456 SlU r'S Towl Correctio n. 462 Moon's TOIa l Correction Lowcr Limb. 466 Moon 's Tolal Corrcction Upper Lim b. 479

Ill. T A BLES FOR USE I N COASTA L NAV IGATION Day's Run - Average Speed 494 Radar Ran ge . 501 Rada r -Plo th.' r'S Speed and DiSI,lRce. 502 Measured Mile Speed , 503 Distance by Ve rtical Angle. 510 Extreme Range. 5 16 Distance o f the Sea Ho rizon . 51 8 Dip of the Shore Horizon. 5 19 Correction required 10 convert a Radio Great Cirde

Bea ring to Mercatori al Bearing, 520

IV. CONVE RSION AND I)H YSICAL TA BLES Arc into T ime. 522 T ime into A rc, 523 Hours a nd Minutes to a Decimal of a Day, 524 Atmosph eric Pressure Conversion, 525

vi

Te mpe rature Conve rsio n. Degrees El hn:nheit Degrees Celsius - Degree:- Fah renhe it. 526

S I - British U ni ts, 527 Brit ish Ga ll o ns - Litres - Briti sh G,llIo n5, 52') Brit ish Ga lil)!1s - US Gallons - BritIsh GallllIls. 53() US Gallolls - Li tres - US Ga ll ons . 531 internatior l<li Naut ica l Mile s - Kilome tres

Inlc rn;l,io llal Nauti('a l Miles. 532 Intcrnation .. 1 Nautica l Miles - Statute Miles International Nautica l Miks. 533

Sta tut e Miks - Kilomet res - Stat ut e Miles. 534 Fa thom s - Met res - Fatho ms, 535 Decimal Fractions of a Deg ree. 536

v. PORTS OF T HE WORLD Alphabet ical List. 53!'!

huide [rolll COl'er Sun's To ta l Correctio n

Inside /J(I( 'k co!' ('/" Star's '1'01;11 Correctio n. Decimal Fractions or a Degree

PREFACE

Onc hundred "nd eighty years of publication involving many new edit ions and reprints atlord a sea rching test of the usefulness and value of ,my publicat io n designed (0 meet the exacting re· quirclllcnt s o f navigators and the shipping industry. Since J. W. Norie published the first edition of his COMPLETE SET OF NAUTICAL TABLES AND EPITOME OF PRACTICA L NA VIGA TlON in 1803. the tabl es have und ergone a continuing process of change to maintain their usefulness to the modern practical Ililvigator.

During Ihese years many changes 10 the tables have been necessary in both COrilCl1I a nd presclll 'llio n to confo rm with changing techniques of naviga lion. bUI the ai m of the ed ito rs has always bee n to have user fri endly naviglllionai t;lbles which could be used quickly and casily under shipboard condi tions. This has resulted in many changes 10 the tables aimed at removing much of the tedium of interpol atio n. so enabling the nav igator to obtain the answers to navigational prob le ms quickly with the minimum of probab il ity of crror. Ce rtain tables and data arc also incl uded which arc not readil y avai lable on board ship or arc on ly used in the examinatioll room, but th e physica l dimension s o f the book impose stri ct limit s on what can be included with the result that it is impossible to include a ll the tables the editor would wish.

[n the prese nt edition, the Star's Total Correction Tab[e inside the back cover. the Moon's Total Correction Table and the exte nded Slar's To la[ Correction Table have been redesigned to reduce ime rpolation to a minimum.

The ed ito r wishes to thank a ll those who have suggested improvements to the tables. and will we lcome any further helpful criticism which users of the Tables may care to makc .

A. G. BLANCE London [99 1

EXPLANA nON AND

USE OF THE TABLES

I. COMPUTATION TABLES

TRAVERSE TABLE (Pages 2 - 93)

These Tables afford an easy and expeditious means of solving a ll problems that resolve themselves inlo the sohllion of righ t-angled p la ne tria ngles. They can thus be applied to all the forms of Saili ngs cltcept Great Circle Sa iling; but they a re specially useful in resolving a Traverse. On this account they are called Traverse Tabks, and the terms Course, Distance, Djfference of Latitude and Departure are used as names of the different parts involved.

The Traverse Table has now been brough t into line with the requirements of the modern com pass notation by the inclusion. at the top a nd foot of each page, of the number of degrees of the new (0- 360) circular system of reckonin g. correspondi ng to the value printed at centre of tit le in conformity with the older quadrantal notation. the latter form being retained for its application to the so lut ion of certain problems in the Sailings and for its utili ty in the co nversi on of Departure to Difference of Long itude and vice versa, as explained later in thi s article.

The figures denoting th e number of degrees under the new arrangement are placed in the appropriate quadrants of a small diagrammatic symbol, represe nting the cardina l points of the compass, a nd in these posi tions they introduce the equivalents in the new notation corresponding to the number of degrees of the old system, show n at centre o f titles, when pertain ing to the respect ive quad rants. T he arrangement will be better understood by reference 10 an example ; thus, on page 58 - '28 DEG REES'

For old Read new

115r 2080 I or vice versa, and . as examples of the with ca ption '72 DEGREES'-

reverse process, o n page 38, but this time from the foot

Fo r new ~r

Read old I

N7rE

_ 1 _ I logo

S7rE

1 25r I

S7rw

2880 1 I

N7rw

It will be obse rved that , in the new notation of the Traverse Table, the three-figure degrees correspond ing to Easterly courses are placed in the symbol diagram towa rds the right-ha nd side of the pa ge, in contrad isti nction to those for Westerly equivalents wh ich are printed on the left .

The courses, in both the old and new notation, are di splayed at the top and bottom of the pages, whi le the Di stances are arranged in order in the columns marked Dist. The Difference of Lati tude and DeplITwre co rresponding to any given Run on any given Course will be found in the columns ma rked D. Lat. and Dep ., respecti vely, of the page for the gi ve n Course and opposite the given Distance. But it must most carefully be observed tha t when the required Course is fo und a t the lOp of the page, the Difference of Latitude and Depa rture also are to be taken from the columns as named at the lOp o f the page; and when the Course appears at the foot of the page, the relevant quantities too must be taken from the columns as named at the foot of the page.

When a ny of the given qua ntit ies (except the Cou rse which is never to be changed) exceeds the li mits of the tables, any aliquot pa rt, as a half or a third, is to be taken , and the qua ntities found are to be doubled or t rebled ; tha t is, they a re to be multiplied by the same figure as the given quant ity was di vided by. And since the Difference of Latitude and Departure correspo nding to any given Co urse and Dista nce are to be found oppos ite the Di stance on that page which contains the Course. it follows tha t if any two of the four part s be given , and these two be found in their proper places in the tables, {he othe r two will be found in thei r respective places o n the same page.

The fo llowing examples will ill ustrate the appl ication of the tables 10 Plane Sa iling :-

EX PLANAT ION OF TH E TAIJLES 11

1 Example' : Find the difference of latitude and deparlure made good by a ship in sailing 84 miles on a course 112°. (S68°E., Old Style). ~

Co urse I 1 r is found in the Tab le at foo t O f~ Oppos ite 84 in the Distance column on that page we gel:- O. Lat. 31'5, Dep. 77·9.

The D. Lat. is named S and Departure E, bec;:!use it is noted that I lr is shown in the South and East quadrant of the compass sy mbol. ~ Example : Find the course and distance made good by a ship whose difference of lati tude was found to be 431 mi les S, and deoartur~ 132' W.

431 and 132 are not to be found alongside each other, but in the Table on age 37 e find 431·3 and 13 1'9, and these arc sulTicient ly near to the desired value for all practical pur These give 197°, or 17° old styl e, as a course, and 451 as a dista nce. Hcnce-

Cou rse 517° W, or 197°, a nd Distance 451 miles.

These tables may also, as has already been stated, be appli~d to solving problems in Parallel and Midd le Latitude 5a ilings. In solving these problems the Cou rse (old nOlal ion) a llhe top o r bottom of page beco mes the l atitude or Midd le l atitude, the Distance col umn becomes a Diff. l ongi lUde column , and the O. Lat. column becomes a Oep . column. To faci litate the taking out of these qua ntities the D. Long. and Ocp. arc brac ketcd together. and the words D. Long ., and Dep. are also printed in italics at the top o f their respective columns when the Latitude or Midd le Lat itude, as course, is a t the fop; but at the bottom of their respect ive columns when Latit ude or Midd le Latitude, as cou rse is at the b0110m .

.7 Example: In Latitude o r Middle Lat itude 47" the depa rt ure made good was 260' ,5; requi red Ihe diffe re nce of Lo ngitude.

With 47° as course at the bo t/om of the page, look in the co lumn with Dep. printed in italics at the bot/om, just over the end of the bracket; and opposite to 260'-'-5-wiILl2:t found 382 in the D. Long. column, wh ich is the Difference of Longi tude requ ired . ? o3L '6~)

1/ Example: A ship. after sa iling East 260', 5, had chan~hCT"Longitude 6° 22', R~qui red the parallel of Latitude on which she sailed .

6° 22' eq uals 382' . Opposite 382 in D. Long_ column is 260'·5 in Dep, colu mn ente red from the b,,, ,om, aod th, pamlle] 00 wh;ch ,he sa;],d;s LaL 4T'~

MERIDIONAL PARTS (For the Spheroid) ( P~ges 94 . t02)

Th is table is used in resolving prob !~ms by Mercators Sailing and in construct ing charts on Merca tor's projection . The merid ional parts are to be taken out fo r the d~gr~~s answering to the given latitude at the fOp o r bottom, and for Ihe m i n u t~s a t either side column. Thus, the meridional parts corresponding 10 the lat itude 49° 57' are 345]-88.

12 EXPLANATION OF TH E TABLES

LOGARITHMS (Pl>ges 103 - 117)

This ta ble gives correct to fi ve signifi cant fi gures the mantissae (or frac tional parts) of the common logarit hms of numbers. The operator must decide for himseJfthe integral or whole number part of the loga rithm (called the characteri stic) acco rding to the position of the decimal point in th e natural numbe r.

The rules for determining the characteristic can be demonstrated by the following:

10 {)()() 10' 10g.1O 10 {)()() 4 I {)()() - 10' log'HI I ()()() 3

100 10' 10g'10 100 - 2 10 10 ' 10g.1O 10 I I 10' log'l/) I 0 0 -1 10- - 10g'10 0-1 - -I 0-01 \O- ~ \og·)O 0-01 - 2 0·001 10- 1

10g'10 0-001 - 3 0·000 1 IO- ~ 10g. 10 o-{)()() I - 4

T he above, which may be extended infinitely in both directions, shows that the log. of, say. 342 must li e between 2 and 3. Similarly, the log. of 29·64 must be between I and 2. From the table it will be fou nd that log. 34~= ,53403 and Jog. 29·64 = 1·47 188. These statem ents could be ex-pressed liS follows:- rs10':t (?3 1~

- IOU :J.I(13 = 342 I ()1.m M = 29·64

For numbers greater than I the rule fo r finding the characteri stic is- T he characteristic is the nu mber which is I less than the number of figures before the decimal point. If there are five figure~ before the decimal point the characteristic is 4; if there is onc figure before the decimal point the characteristic is 0, and so on. Thus:-

log. 5378 log. 537·8 log. 53·78 log. 5·378

3-73062 2- 73062 1·73062 0-73062

-~

For numbers less Ihan I the ru le for fi nding the cha racteristic i5- The negati ve characteristic of the log. o f a number less tha n I is the number wh ich is I mo re than the number of no ughts between the decim al point and the first si gnificant fi gure. Thus:-

log. 0·5378 1-73062 log. 0 ·05378 - 2· 73062

log. 0{l05378 - 3·73062

log. O{)005378 ~ 4· 73062

Tabular logarithms To avoid the negative characteristics, logari th ms in tabu lar form are obta ined by adding 10 to the characteri st ic.

Example: log 0·53 78 = 1·73062 or in tabu lar form 9·73062

rc)g 0·005378 = )·73062 o r in tabular fo rm 7·73062

In the ta bles of logarithms of trigonometrical function s the ch aracteristi c is given in both form s at the top of eac h co lumn of logarithm s.

Example : log. sin . 5° 30' = '2"98 157 or 8·98 157 / r~ 1~O log. cot. 5° 30' = 1·0 1642 or 11·01642

I:-.XPLAI\.ATION 0 1- TH E r ABL ES 13

1111 er po! (J/ iOIl

When the number whose logari thm is req u ired consists of ro ur si gni ficam figu res o r less the mant issa is ta ken rrom the ma in pa rt of the table. Where there a re fi ve sig nificant fi gures the diffe rence ror the fifth figure is o bta ined from the relevan t sectio n o f the D col um n.

E.rampl t" : log . 140·27 = 2·!4675 f 21 = 2·1 4696 (i'0-5e.. -10'; ) Ir the num ber co nsists or more tha n six sign ifica n t fi gures the approxima te logarithm ca n be round by sim ple proportion.

Example: log. 140·277 = 2·1 4675 (rrom ma in table ) + 21 (rrom D col umn) + 2 (by simp le propo rti on) 2· 1469S

Ta find ,lte nllmht'r, N, IrllOse log. is k ,lOlI"l/ . Ir the number is requ ired to four significant figures o r less al l that is necessary is to fi nd the series o f d igi ts correspo nding to the tabu lated ma m issa wh ich is lIt"an's! to Ihe one given. T he characteristic of the log. will determ ine the pos ition o f the dec imal po int. Th us:-

G;,," log. N ~ 1·87109. ( 11?\ Nea rest tabulated mantissa 87 111 gives digi ts 7432. P.3 :» T he charac tcriSlic being I , there a re two Hgures berore the decimal poin t. Th e requ ired number, N, is therefo re 74 ·32.

The fo llo wing examples will serve to illu strate the procedure whe n mo re than rour sign ifi ca nt figu res a re req uired . Suppose the number, N. co rrect to five significan t figures is requi red whe n log. N is known to be 2 ·27 104.

Example : log. N = 2 ·27 1 04 T he nex t less tabu la ted ma nl issa ·27091 gives the d igit s 1866. ( D~<:e 10 y) But ,27 104 - ·2709 1 = 13 I ..J :. Entering the 18Q-..189 section of the D column the fift h fi gure is 6 ror a D va lue of 12 a nd bv

sim ple proportion the sixth fi gure is the refore 5. -tlle di gi ts o f Ihe n umber are I S6665

The cha racter is t ic of the l og~~ r it hm is 2. :. the number N is 186·665

LOGS. of TRIG . FUNCTIONS (P .. gesI18 · 241 )

Whilst preserving t he basic layou t which has been a rc;~ ture o f ' No rh's', and ' Node's' alone, since J. W. Node produced the o r iglllal ed ition, c hanges have been introd uced which ma ke th e table a muc h more effic ien t instrument in conform ing with the mo dern techn ique o r as tro no mica l na viga tio n. For a ll a nglcs rrorn 0" to 9{)" the ta b le is now comp!etely downward read ing a nd for tha t reaso n alone should be p ractica ll }' blunder-proof. In the ma in pari of the table fro m 4 0 to 86° the log. runct ions of angles are tabulated ror o nc minute interva ls of the angles a nd p ro portional parts ror frac tio ns o f o ne minute (from 0 ' ·[ to 0 ' ·9) a re given. In the rema inder of the ta ble, where that system ceases to be pr;lcticable, log . functions are tabula ted fo r in te rva ls o r 0'· 1 o r 0' ·2 as necessa ry a nd d ifferences betwee n success ive tab lLlation s lITe given. This means tha t, except in special and ra re cases, in terpolatio n is reduced when tak ing o ut a ny log. funct io n oran an gle and there is no need to resort 10 the questiona ble p ractice o r ro und ing o ff a ngles to the nearest m inute in o rder to 'save tro uble'. With this t:able it is no mo re o f a n effort to work accura tely than it is to work roughly. How fa r a navigator is justilied in working to tenths o r a minu te is a m;.tler wh ich C;1Il be argued about indefinilcly.

14 EXPLANATION OF THE TABLES

but since the Nau tica l Almanac gives hour a ngles and decli nat ions 10 tenths ora minute and a modern sex tant with a decima l vernier enables readings to be la ken 10 tenths of a min ute as well, it would seem o nl y logical to use navigat ion tables which. with the minimum of effort. provide fo r the sa me o rder of precision.

The ch aracterist ic of the loga rithm is g iven at the top of eac h function's column in ind icial fo rm with the tabular form in brackets.

Example : log. sin. 5° 09 ' = 2.953 10 or 8·953 10

T hus the na viga tor can use whichever fo rm of cha racteristic is preferred though it must be apprec iated tha t t he two fo rms cannot be interchanged withi n a calcu la tion.

Occasionally, it may be necessa ry to find the logs. of trigonomet rica l funct ions of a ng le~ grea ter than 90°. No difficulty ~hou ld be ex perienced in such case~ as the ~econd . third and fo urt h quadran t equi valents o f the fir~t quadra nt a ngle~ afe pla inly indicated . It ~hou ld be noted . however. that the ta ble is upward reading fo r angles between 90° a nd 180 0 and a lso fo r those between 270° a nd 360°. but dolt'nn·ard readi ng fo r angles between 180° and 270°. In all cases, however. the name of the rat io bei ng used appears at the top of the page. When applying proport ional parts care should be taken to notice in whic h d irecti on the log . functi on is inc reas ing, i.e. upwards or downwa rd s.

Examples: ( f:) 12' }- Iog_ , ;0 - 10 38'·7 = 2·(45754 ..l.. ¥ ) = 2· 45798 0' 8-45798

( ~ 12.3, -log- ta o_ 177" 57'·5 ~ 2'(55240 _ 7~O) 2-55205 0' 8·55205 ~ log. cosec. 26" 04' ·4 ~ 0-(35712 - 10) - 0-35702 0< 10·35702

log. sec. 3330 25'-3 ~ 0-(04852 - 2) - 0-04850 0< 10·04850 log. cos. 138" 17'·6 ~ 1'(87300 + 7) - 1.87307 0 ' 9·87307

log. sin . 62° 19'·8 ~ 1·(94720 + 5) ~ 1.94725 0< 9·94725

log. cot. 11 7° 53'·0 ~ 1·72354 0< 9·72354

log. cos. 8]0 15'·3 - 1-(070 18 - 32) ~ 1.06986 0< 9{16986

To find the angle whose log. functi on is g iven is equally si mple. For instance, to fin d 8 when log. sin . 0 = 1-66305 or 9·66305, no tice that the next less tabulated log. sin . is 1-66295 or 9·66295 which g ives the angle 27" 24'·0. T he excess 10 g ives a n additi onal 0' ·4. Hence. 8 = 27° 24' ·4.

In practice, the above processes will , o f course, be perfo rmed mentally.

HAVERSINES (P~ge3 242 . 348)

To make the tables clearer and 10 make interpolat ion almost com pletely unnecessary the tables are presented as fo llows:-

1. The Log. Have rsines are printed in bold type and the Natura l Haversi nes in light type. 2. In the range 0° to 90° and 270° la 360° (the ra nge most frequently used) haversines are tabu

la ted a t 0·2' interva ls a nd t he proportiona l parts fo r 0-1' a re given a t the foot o f each page. 3. In the remainder o r the table haversines are tabulated a t 1·0' inte rvals and the proportiona l

pa rts fo r 0·2' a re given a t the top of each column_ 4. The ch aracteris tic or the logarithms is g iven a t the top of each colum n in the negat ive index

fo rm together with the tabular form in brackets.

EXPLAN AT ION OF THE TABL ES

ANG LE LOG . HAVERSINE

15'33'-0 2·26249 o r 8·26249

W 33'-6 2-26304 or 8·26304 IS" 33', 7 "2' 26313 or 8· 26313

344° 10' ·0 "2'27807 or 8·27807 3440 10' ·4 2'2777 1 or 8·2777 1 344 0 10',5 2·27762 or 8·27762 95° 25',0 1 ,738 15 or 9·73815

950 25'-6 1·73822 or 9·73822 263" 37',0 1 ·74475 or 9·74475 2630 37',8 1·74466 o r 9·74466

DeriM(iOfl of Haversine Formulae:

cos. a - cos. b cos. c Cos. A = - - _ b ' , (fundamental fo rmula).

Slfl . 510. C

cos. a - cos. b cos. c .. I - cos. A = I - 'b -

510 . SIfl . c

sin. b. sin. c - cos. a + cos. b cos. c i.e. vers A = . b - ,

Sill . SIR. C

:. cos. (b ....... c) - cos. a = sin. b sin. c verso A, or - cos. a = - - cos. (b ...... c) + sin. b sin. c verso A.

By add ing uni ty to each side this becomes-

1 - cos. a = - cos. (b ...... c) + s.in. b sin . c verso A, : . verso a = verso (b ....... c) -I- sin. b sin . c verso A.

NAT . HAV.

0-01830 -0-01832 0·0 1832 0-01897 0-01895 0-01895 _ 0·54720 0-54729 0·55559 0 ·55547

whence hav. a = hay . (b ...... c) + sin . b sin. c hav. A ........ (1 )

By tra nsposi ng we obtain-

haY. A = {hay. a - hav. (b -- c)) cosec. b costt. C • .. •• •• (2) and hay. (b __ c) = hav . a - hay. A si n. b sin . c. ..... . .... . ... (3)

I'

D 2.S8 1/

11

1/

1/

11

P3 B(I I'

" ff

These three versions o r the spherical haversine rormula are rrequ ently adapted for navigat ional purposes as fo llows.

(I) Hav . z = hav. (I ';t d)'" -I- hay . h cos . I cos. d . (2) Hav. h = [hav. z - hav. (I .t cl ;"'] sec. I sec. d. (3) Hav. mer. zen. dist. = haY. z - hay. h cos. I cos. d.

{: :: where d =

b ~

• (I ...... d) when I and d have the same name, (1 + d) when I and d have different names.

zenith distance, la titude, declination, ho ur angle.


Examples

(I ) Find zenith distance when h = 66Q 49"3 , 1 = 3 1° 10',2 N., d = 19" 24'·7 N.

h

d

z

66° 49' -) 31° 10" 2 )9" 24', 7

11 ° 45"5

60° 40'-9

Hav.7. = hay. h cos. I cos . d + haY. (I t d) .

L hay. ]·48 173 o r 9·48 173 L. cos. \·93228 or 9·93228 L. cos. ],97458 or 9·97458

L. haY. 1·38859 or 9·38859 N. hay. 0·24468 N. hay. 0·01049

N. hay. 0·25517

Ca lculated u nith distance = 60" 40'·9 and is used for comparing with the true zenith distance to find the intercept when establishing the position line by the Marc St. HiJa ire or Intercept method.

(2) Find the hour angle when I = 41 ? 21'·6 N., d = 9" 34'·\ S. , z = 63° 45'-8.

z (I + d)

1 d

h

63" 45' ·8 50" 55'-7

Hav. h = {hay. z - hay. (I ! d)] sec. I sec. d.

N. hay. 0-27896 N. hay. 0,18485

N. haY, 0·09411 L. hay. 2·97364 or 8·97364 L. sec. 0·12461 or 10' 12461 L. sec. 0·00608 or JO.OO608

L. hay. 1·10433 or 9'10433

Hou r angle = 41 " 46"9 if body is w. of the meridian, or hour angle = 3 18" 13 '· \ if body is E. of the meridian, and is used for finding the computed longitude when establi shing the position line by the "chronometer method".

(3) Find the mer. zen. disl. when h = 355" 57"2, I = 48" 12' ·5 N., d = 12" 1)' ·7 S., z = 60" 2 1' ·6.

h

I d

z

355" 57' ,2

48" \2'·5 12" 13"7

Hav. mer. zen. disc = hay. z - hay. h cos. 1 cos. d.

L. hav. H)9571 or 7·0957 1 L. cos. \ ·82375 or 9·82375 L. cos. \·99003 or 9·99003

L. hav. 4·90949 or 6·90949 N. hay. (HJOO8 1 N . hay. 0·25273

mer. zen. dist. .. 60" 15' ,2 ..... .. , . • . ..• .. .. N. hay. 0·25192

The mer. zen. disc , 60" 15" 2, when combined with the decli na tion gives the latitude of the point where the posit ion line (at right angles to the di re<:tion o f the body) cuts the meridian of D. R . longitude used to compute h. T his method of work ing an ex·meridian sight is. of course, an alternative to usi ng ex-merid ian tables.

EXPLANATION OF THE TABLES 17

The ha w'rsine formulae and grelll circle sailing calculations

Form ula ( I) is used to find the great circle dista nce rrom one point to another and rormula (2) is used to find the initial and final courses. The vertex or the track and the lat itude or the point where the track cuts any specifi ed meridian can then be ro und by right angled spherical trigono metry.

Example : Fi nd the great ci rcle distance and the initial course on the track fro m A pr 22 ' N ., 25° 2S' W.) to B (40° OS' N., 73° 17' W.) .

To find fht' great circle distance

Hay. AB = hay. (PA "- PO) + hay. P sin. PA sin. PB. P 4r 49'·0 L. hav. 1·21 550 or 9·2 1550 PA 72° 38',0 L. si n. 1·97974 or 9·97974 PB 49" 52" 0 L. sin . ' -88340 o r 9·88340

L haY . ,·07864 o r 9·07864 N. hay. 0 ' 11985 (PA - PB) 2r 46',0 . .. ...... . . ......... N. haY . 0·03896

AB 46° 58' ,2 ........ . .......... N. hav. O· 15881

:. G reat circle d ista nce = 18 18·2 miles.

----To find (he initial cOl/rse

HaY. A = (hay. PB - haY. (PA......, AB)J co~. PA cOse<:. AB. PO 49" 52',0 N. hay. 0· 17772

(PA "- AB) .. 25° 39' ·8 N. hay. 0·04932

N. hay. 0· 12840 L hav_ 1·10856 or 9- 10&56 PA 72° 38 ',0 ....... L cOse<: . 0·02026 or 10·02026 AB 46' 58 ',2 .. . ..... L cosec . 0-1 3609 or 10-13609

A 500 48' ,5 L. hav . 1·26491 or 9·26491 - - -

Initia l course = N . 50° 48', 5 W. or 3090 11' ,5.

NATURAL FUNCTIONS OF ANGLES (P~ 34!J.36J)

In these tables. which are intended fo r use with s imple pocket calcula tors . the na tural trigono met ric functio ns can be o btained to five dec imal places. Exam ples :

I. To find tan . 490 38': 1·17500 (tan. 49" 36 ')

+0 ·001 38 (2 ' from d iffere nce table against 49")

tan . 49° 38 ' == j ·1 7638 l'0 j&( 354- )

" 2. To fi nd cos. soe 27':

O· 16677 -0-00086

cos. 80"27' = 0 ' 16591

3. To find sec. 76° 44' : 4·34689

+ 0·01078

Sec. 76" 44 ' = 4·35767

EX PLANATION OF T HE TABLES

( PCq," ; S2. ) (cos. SO" 24 ') J

(3 ' from diffe re nce table agai nst BO". subtracted)

(sec. 76° 42 ' ) (lhlsec . 76° 42' -sec . 76<> 48' 1; diffe rence must be

obtai ned by this method because the mean diffe re nces are not suffic ie ntly accurate)

4 . To convert 31 " 46' to radians; 3 1° = 0 ·54105 radian s (OO~(L 46' = 0·01338 radians I' ..J

3 1" 46' =0·55443 radian s

5 . To convert 1·648 radians to degrees: 1 radian = 51" 17· 7'

0·648 radia ns = 37" 07· 7'

1·648 radians = 94° 25 -4 '

SQUARES AND CUBES OF NUMBERS (PiJges 364 ·367)

T hese tables wi ll give squa res and cubes of numbers to fou r significant figures.

To obtain rhe squun or cube of a numb..,.'

(a) If the number is betwee n I and [0 and cons ists of three significa nt figures (o r less) the sq uare or cube is taken from the ma in pa rt of the tables, but if there a re fo ur significant flgu res the Mean Difference section is a lso used.

Example:

2.8242

7·63 J3

= 7·9 52 (fro m main ta ble) 1- 23 (from Mean Di fference) 7·975 58· 22 (from main table) - 2 (from Mean Difference) 58·24

(b) All other numbers are converted into scien tific notat ion a nd the square or cube ob tained for the significant fi gures as before.

Example:

46J ·8t

0 ·000 0725 J3

(4·638 x 1O:)t = 2 1·51 x I(P 2' 15 1 x I(}> or 215 100

(7'251 x 1O-~ )~ = 381 ·3 X 10- 1;

3·813 X 10- 13 o r 0·000 000 000 000 38 13

EXPLANATION OF TH E TABLES 19

SQUARE A N D CUBE ROOTS OF NUMBERS (P~gfU 368 . 377)

These tables, which give the square and cube rools o f numbers to four significa nt figures, are in the following fo rm :

(a) Square roots of numbers between I and 10 and between 10 and 100. (b) Cube roots of numbers between I and 10. between 10 and 100 a nd belween 100 and 1000.

The following examples illustrate the method of obtaining square or cube roots using the tables:

,1839-2 ,14523 ',178620000 ' ,10-000 7247

I. Change Ihe nllmber inlO scielllijic nOlation.

= v'4·523 x jCP = 'v'7·247 X 10- 1

2. Adjust Ihe position of rhl! decimal point to make the index of 10 exactl), divil'ible by Ihe rool being found.

= v'45·23 )I' HP = 'v'724·7x 10-=4

3. Enter lhe lab/~s shoK'n below and ~xlral'1 Ihe required rOO I of Ihe signijil'OnI figures.

TABl.E Of SQUARE

ROOTS 1- 10

~ 2-897

TABl.E Of SQUARE

ROOTS 10-100

""" 6·725

TABLE OF CU8E

ROOTS 10-100

= 4·284

4. Delt'rmint' the square or l'u~ root of the poK't'r of 10.

,1 ,0' _ 10

__ ,1839-2 = 2·897 x 10 or 28-97

V IOl = 10 :_ ,145-23 _ 6·725 x 10 or 67-25

3v'1()G = 10~

: . 3 Y78 620 000 = 4·284 x IQ! or 428·4

TABLE OF CUBE

ROOTS 100-1000

- 8-982

'v' 10-- = 10-1

:. 'YO-OOO 7247 = 8·982 x 10- ' or 0·08982

Mean Difference columns are not required in the table of square roots of num bers between 5·5 and 9·9 nor in the tables of cube roots of numbers between 1-0 and 10·0 and between 55-0 and 100·0. When any of the above tables are bei ng used 10 fi nd the roolS of nu mbers wi th four significant figures in terpolat ion ca n be carried out mentally.

11. TABLES FOR CELESTIAL NA VIGA nON

A, B & C AZIMUTH TABLES (Pages 380 - 428)

To conform with the method of present ing data in the Nautical Almanac the hour angles in Tables A and B are given in degrees and minutes of arc from OC 15' to 359" 45'.

If the H.A. is between 0" and 1800 the body is west of the meridian and its hour angle will appear in the upper row of H.A.s at either the top or bottom of the page. If the H.A. is between 180C and 3600 the body is east of the meridian and ils hour angle will appear in the lower row.

The A, Band C values and the azimuth are derived by employ ing the well known formula which connects four adjacent parts of a spherical triangle. It can be shown, for instance, that in spherical triangle A B C:-

cot. a sin. b = cot. A sin. C + cos. b cos. C. cot. a sin : b - cos. C cos . b = sin. C cot. A.

x.

"

p

, o

,,, • • (j

f :V. : '11' Z

The figure shows the astronomical triangle PZX with the four adjacent parts PX, P, PZ and Z representing, in that order, polar distance, hour angle, co-latitude and azimuth.

Applying the above formula to this particular case, we have:- -

cot. PX sin. PZ - cos. P. cos. PZ = P. cot. Z. Divid ing by sin. P. sin. PZ, this becomes--

cot. PX . sin. PZ cos. P cos. PZ sin. PZ

sin. P

sin. P

i.c. N

sin . P

cot. PX tan. dee!.

In the tables;-

sin. PZ sin. P

cosec. P - cot. P cot. PZ = cot. Z cosee. PZ, cosec. H.A. - cot. H.A. tan. lat.

= cot. azi. sec. lat.

cot. Z sin. PZ

cot. H.A. tan. lat. is tabulated as A, and tan. decl. cosec. H. A. is tabulated as B. Hence (A ;!; B) cos. lal. = , cot. azimuth.

(A ;!; B), referred to for convenience as .C' , forms the primary argument in Table C with lat. as the secondary argument. With these two arguments the azimuth is found.

As an example, consider the case where hour angle = 48°, lat. = sr N., and deel. = 15° N.

lat. H.A . decl.

EXPLANATION OF THE TABLES

5ZO 00' N 48" 00' 15° 00'N

L. tan. 0' 107 19 L. cot. 9.95444 L. coscc .

+ L. tan. 0·12893 9·42805

Log. A 0·06 163 Log. B 9· 55698

(?oy 3%. 3~5 ') _:._A_~_I_'1 5_3_S. (A is named oppos ite to lat.; B has the same name as decl.) (A .:t

name as A which is numerically greater than B.).

'C' 0·792 S.

fOJ" M~ Azi. 64" 00'

Log. L. cos.

L co l. (

)

la l. 52" 00' N.

.". Azimuth = S. 64o(£Jor 244".

8 ) ~ 'C' - 0· 792 S.

21

(Same

(The az imuth ta kes the names of t he 'C' factor and hour anglc.) ( -pc;/_ 394 - 345 ) Reference to the tables wi ll show tha t fo r the above data A = J.\ ~ Sand 8 = 036 N. T he

combination of these is 0·79 S., wh ich in Table C with la l. sr gives azim uth S. 64°·2 W. The rules for naming and combi ning A and B a nd for nam ing the azi mut h are given on each

page of the ap propria te w ble. It is imponant that they shou ld be applied corre(;tly.

umgilllde Correction The quanti ty (A t B) or 'C', besides being one of the arguments for finding the azimuth from

table C, is a lso the ' longit ude correct ion fac to r' o r the erro r in longitude d ue to an e rror of I' of latitude. This ca n often be very usefu l to those accUSlOmed to working sights by the longitude method.

A simple sketch showing the di rect ion of the position line will at once make it clear which way the longitude correction should be applied. It will easil y he apparent tha t when work ing a sight by the longitude method :-

(a) when the position li ne lies N.E.jS.W. (body in N. W. or S.E. quadrant), if the assumed lat itude is too fa r north the com puted lo ngitude will be too fa r east, and if the latitude is too fa r south t he longitude will be too fa r west ;

(b) when the position line lies N.W.jS.E. (body in N. E. or S.W. quadrant) the reverse holds good.

Example: Suppose a sight worked with lal. 49° 06' N. gi ves longit ude 179 0 46',0 W. and azimuth S. 70°·5 E., the value of 'C' bei ng 0·54. If the correct la t it ude turned oul 10 be 49° 46' N., i.e. 40' error, the e rror in longitude would be 40 x 0 ' ,54 or 21'·6. We should Iherefore have:-

Com puted long. 179° 46"0 W. Correction 2 1" 6 E.

Correct long. 179 0 24" 4 W.

This is a case where the latitude being too far sou th, the com puted longi tude is 100 far west.

Examples on 'he use of the tables In each of the fo ll owing cases find the longitude correct ion factor and the t rue azimuth .

22 EX I)LA NATION OF TH E TABLES

Example I: H.A. 3 10°, la!. 48° N., ded. 20" N. From Table A with H.A. 310". lal. 48° N., A = 0-93 S. poqe. ?/J4 - 'y::y 5 From Table B with H.A. 310· , decl. 20" N., B = 0-48 N. ...)

Lo ng. corr'n. factor = A - B = C = 0-45 S.

Fro m Table C with C 0-45 S .• la t. 48° N. , T. Azi. = S.73°·2 g ~A ~s ;.,e.Jw ('..('/\

1'1//- 360 0

A is named S. opposite to lat. because H.A. is 1101 between 90° a nd 270°, B is named N. beca use the decl. ;s N. C = A - 8 as A a nd B have d ifferent names, and is named S. as the grea ter quant ity is S. The azimuth is na med S. beca use C is S .• and E. beca use H.A. is between 180" and 360",

Example 2: H.A. 244", la l. 41 " S .. decl. 5" S. From Table A wi th H.A. 244", lat. 4 1" 5., From Table B with H.A. 244", decl. 5" 5.,

Long. corr' n. factor = A + B =

A = 0-42 S. B = 0·10$.

c ~ 0· 52 S.

From Table C with C 0·52 S., lat . 41 ° S., T. Azi. = S. 68°·6 E.

A is named S. same as lat. because H.A. is between 90° a nd 270°. B is named S. because the decl. is S. C = A + B as A and B have the same name (both 5.). The azimu th is named S. because C is 5., and E. because H.A. is between 180" a nd 360°.

Example 3: H.A. 108°, 1at. 61 " N., decl. 20° N. From Supplementary Table A with H.A. 108", lat. 61 ° N., From Table B with H.A. 108", decl. 20" N.,

Long. corr'n. factor = A + B =

A ~ 0·59 N. B ~ 0·38 N.

c ~ 0·97 N.

From Table C witn C 0·97 N., lal. 61" N., T. Azi . = N. 64"'8 w.

A is named N. same as lat. beca use H.A. is between 90" and 270". B is na med N. because the decl. is N. C = A + B as A and B have the same name (both N.). The azimuth is named N. because C is N., and W. because H.A. is between 0" and 180".

Use q( A BC Tables Ior Great Circle Sailing These tables provide a ready means of finding tne initia l grea t circle course from onc point (0

another. Suppose, for example, the in itial course from P (49° 30' N., 5° 00' W.) to Q (46° 00' N., 53° 00' W.) is req uired. The procedure is simply to treat d. long. as hou r angle, lat. of P. as lat itude , and lat. ofQas declinnlion. Th us:- HA::::: 5~_5;:;.UD"

From Ta ble A with H.A. 48°, lat. 49° 30' N. , A = 1·06 S.l.f'Il'10 \ ! _ I QO ?,O~ From Tnble B wi thH.A.48", decl. 46° ()(),N. , 8 = 1·)9N.\j 1.,5} 01'_ '-JI (I I

- ( eke ; 4 b DO A - B ~ C ~ ~-=- N' \P34fI!

From Table C with C 0·33 N" lat. 49" 30' N., T. Azi. = N. 77°·9 W. i.e . Initi al a.c. Course = N. 77°·9 W. or 282°·1.

The final co urse, if requ ired, may be obta ined in a similar way by fi nding the initial course from Q to P and reversing it.

EXPLA NATION OF THE TA BLES

AMPLITUDES and CORRECTIONS (Explan'tion wilh rabla)

(pages 429 . 431)

EX-MERIDIAN TABLE I (P'ges 432 · 443)

23

• A' is the change in the altitude of a b<XIy in seconds of arc during the minute of time immediately preceding or following meridian passage. It is tabulated for latitudes to 83° and declinations to 63°.

This table is in two seclions:-

OJ Latitude and DecJ;nat;on SAME NAME. On page 432 - 435 there are bands ;n whkh the value of'A' is omitted. This is because' A' changes too rapidly for accurate interpolation to be possible, when the body is near the zenith.

Oi) Latitude and Declination DIFFERE NT NAME. ' A' for Lower Transit observation is tabulated on the lower parts of pages 440 - 442 of thi s section and on page 443 , although the latitude and declination are of the same name.

'A' is computed using the fonnula:-

1.9635 X cos lat X cos dec A~-------

sin ( Iact dec)

In the denominator the latitude and declination are:-(a) subtracted at Upper Trans it if of the same name; (b) added at Upper Transit if of different name; (c) subtracted at Lower Transit.

EX-MERIDIAN TABLE 11 (Pilg'u 4 44 • 447)

The Reduction is the product of' A' from Table I and the square of the time in minutes that the body is East or West of the meridian. To obtain the True Meridian A ltitude, the Reduction is added to the True Altitude of Upper Transit observations and subtracted from the True Altitude of Lower Transit observations of circumpolar b<XIies.

The table is entered with ' A' and the Local Hour Angle for Upper Transit observations o r ' A ' and ( 180 -- LHA) for Lower Transit observations. Ifthe interpolated value of' A' from Table I is toone or two decimal places. the Reduction can be obtained to a corresponding accuracy by moving the decimal point the appropriate number of places as shown in the example below:

'A ' = 2.45 ; Local Hour Angle = 354" 00' F rom the column he aded 354" 00':

Reduction for 2.0 = 19.2 0.4 = 3.84 (extract the value for 4" and move the decimal point one place) 0.05 = 0.48 (extract the value for 5" and move the decimal point two places)

Reduction for 2.45 = 23 .52

EX PLANATION 0 1- HI E TABLES

Example I: In O. R. Lat. 48c 13' N ., D.R. Long. 7" 20' W., the True Altitudeofthe sun was 19° 52'. Sun' s LHA 356" 00' . Declination 2 10 39' S. Detennine the Position Line.

Table I (Different Name)

La L 48° I) ' N. Dec! . 21° 39' S.

A = [ "·3

(yy 4 3/':, )

Tabl" /1 LHA 356 0 00'

A = I ~')

Red for. I ~ 'O = 4'·) .) = [ ' ·3

Reduct ion = 5'·6

T. Alt. Reduct ion

T . Mer. AIL T . M er. Z. Disl. DecL

Lac True Azi mut h

19° 52',0 S. 5'·6

19° 57',6 S. 70° 02 ' -4 N. 21 ° 39'·05.

48 ° 23'·4 N.

( 'fey 41[1-1) from Az. Tables 176°

Posit ion Line passes 086° and 266° through L1.t. 48° 23',4 N., Long. 7° 20' W.

Example 2: D .R. Lat. 4r 12' N., D.R. Long. 24° 32' W. , the True Altitude of Antares was 21 0 28'. St:l r's LHA 3570 00' . Declination 260 18' '0 5. Determine the Position Line.

Table I TaM- 11 T. All. (Different Name) LHA 357" 00' Reduction

Lat. 42° 12' N . Oecl. 26° 18' S.

A = 1"'4

A = 1· ·4 Red . for 1"·0 = 2' -4

-4 = 0',96

Red ucti on = 3',36

T . Mer. Alt. T. Mer. Z . Dist. Dec!.

La!. True AzinHuh

2 1° 31' -4 S. 68 0 28' ,6 N. 26 0 [8 '·0 S.

42° 10' ·6 N.

from Az. Tables 177°

Position Line passes OSY and 267~ through La c 42° 10" 6 N. Long. 24° 32' W.

Although the latitude and declination of a circumpolar body are always of the same name, 'A ' for Lower Transit observations is tabulated in the lower part of the " Latitude and Declination Different Name" sectio n of Table I ,

When near its Lower Transit the Local Hour Angle is less than 180 0 when west oh he meridian and more than 180° when east of it. The Hour Angle to use when entering Table 11 in this case is (1 80°....., LHA).

Example 3: D.R Lat. 42 0 10' N. , Long. 21 0 30' W., the True Altitude of D ub he was 14° 20'. Star's LHA 176 0 30' . D eclination 62" 0 1' N . Determine the Position Line.

Table I Table 11 T. All. 14° 20' ·0 (Same Name) LHA 176° 30' Reduct ion - 2'· )

= 3" 30' --~~

Lat. 42'" 10' N. A = 0"· 7 T. Mer. All. 14~ 17'· 7

Oecl. 62'" 01' N . Reductio n ~ 2'· 29 Po la r Dist. 27" 59',0 For Lower T ra nsi t- 2'· ) A= 0" '7

Lat. 42" 16',7 N. "True Azimuth fro m Az. Ta bles 3580

Position Line passes 088" a nd 268° th rough La!. 42" 16' ,7 N. , Long. 21° 30' W.

EXPLAN;\TI ON OF TH E TABLES

Example 4: D.R Lat. 50" 02 ' S., D.R Long. 67" 20' W., the True Altitude of Achemar was 17° 20'. Star' s LHA 184" 20'. Declination 57° 29' S. Determine the Position Line.

Table I Tahle II T. Alt . Ir 20',0 (Same Name) LHA 184" 20' Reduction - )',5

= 4" 20' ----A = 0-' 7 T. Mer. Alt. 17° 16', 5

= 3' ,5 Polar Dist. 32" 31 ' ,0 Lat 50' 02' S,

Red uctio n Dec!. 57" 29' S. For Lower T r:L llsit- 3"5 A ~ 0"'7 Lat. 49° 47 ',5 S.

True Azimuth from Az. Ta bles 177·5"

Position Line passes 087"·5 and 267"·5 through 49° 47' ·55., Long. 67" 20' w.

EX-MERIDIAN TABLE III (P~ge 448)

This Table contains a Second Correction. wh ich, when the amount of the Main Correct ion is considerable, enables the process of Reduction to Meridian to be applied wit h advan tage on much larger hour angles than could otherwise be the Cdse.

Example: D.R Lat. 3 I 0 00' N., D.R long. 124" 00' W. , the True Altitude of the Sun was 55 ~ 01' . Sun's LHA 347 0 30' . Declination 2° 00' S. D etermine the Position Line.

Table I Table /I T. AIt . (Different Name) LHA 347° 30' 1st Co rrection

Lat. 31° 00' N . Dec!. r 00' S.

A ~ 3", 1

A = Y' I 2nd Corrttt ion Red. fo r Y·O = 125' ,0

·1 = 4', 2

1st Correct ion = 129' ,2

T. Mer. Alt. T. Mer. Z. Di sl. Dec! .

55" 01'·0 S. 2' 09"2 +

3"6-

57" 06"6 S. 3r 53" 4 N. 2' (I()'.(I S.

Entering Table I11 with 129' as First Correct ion and 560 as Altitude we have 3·6' Subtracti\'c for Second Correction.

Lat. 30" 53'-4 N. True Azimuth from Az. Tables 1580

Position Line passes 068° and 248" through La L 30" 53',4 N., Long. 124° 00' W.

EX-MERIDIAN TABLE IV (Pig, 44$)

This Tab le gives the limits of Hour Angle or T ime before or "fter the time of the Meri dia n Pussage when an Ex-Meridi an observati on can be taken . When the observation is taken within the lime li mit prescribed by this Table the Second Correction from Table I1I is negl igible. The Table is entered with 'A' ta ke n from Ta ble L

Given Lat. 3]<> N., Declinat ion ISO N., find the lim its of Hour Angle for taking an Ex-Meridian observation.

For LOlL 37" and Declination 18°, 'S"me Name', Table I gives 4~'6 for 'A'. Entering Table IV with 4' ·6 as 'A" th e lime li mit abreast is found to be 24 minutes.

,)'


CHANGE of HOUR ANGLE with ALTITUDE (Pages 449 - 450)

The formula used in calculating the values tabulated is:-

Change of H.A. (in mins.) due to I' change of Alt. = cosec. Az. sec. Lat.

The table gives in minutes of arc the error in hour angle resulting from an altitude I' in error. This is of particular value to those navigators who work their sights by the 'Longitude by Chronometer' method. It will be seen that the error is least in the case of a body on the prime vertical and that it increases as the azimuth decreases-very rapidly as the azimuth becomes very small. From the table the observer can readily find the least azimuth on which the altitude of a body should be observed in order that the resulting longitude may not exceed a chosen lim it of error. Another use to which th is table can be put is to find the correct longitude when a sight has been worked using an altitude in error by a known amount.

, Example I: In latitude 18° what should be the lowest value of azimuth in order that ail error !.ill of I' in the altitude may not produce more than 2' of error in the computed longitude'!

Under lat. 18° and against azi. 32°, the error for I' of alt. is found to be 1',98. Accordingly, the observation should be taken on a bearing greater than 3r.

(In lat. 36°, it will be seen, an azimuth of about 390 would constitute the limit. In lat. 63 ° the error would exceed 2' even when the body was on the P.V.)

Example 2: A sight worked in lat. 54° by the 'Longitude Method ' resulted in a deducted longitude of 64° 14',5 W. and azimuth N. 65° E. Afterwards it was discovered that the sextant index error of 2' 30w off the arc had been applied the wrong way . Find the correct longitude.

Since the longitude is found by comparing the L.H.A. of the body with its G.H.A., it is evident that the error in the L.H.A. will be the error in the computed longitude. The index error of 2"5, which should have been added, was subtracted , so that the altitude used was 5' too small.

The table shows that in lat. 54°, when the azi. is 65", the error in H.A. is 1',88 per I ' of alt. For 5' , therefore, the error will be 5 x 1'·88 = 9',40.

As the real altitude wa3 greater than the value used, the observer must be nearer to the body than his computed longitude would lead him to suppose. With an easterly azimuth this means that the Westerly L.H.A. should be greater, and therefore the observer's west longitude should be smaller. Hence:-

Computed long .... ......... . . 14'·5W. Error 9',4 to subtract

Correct long.

It will be appreciated that this is much quicker than re-working the sight.

CHANGE OF ALTITUDE IN ONE MINUTE OF TIME (Pages 451 _ 452)

This Table contains the change in the alt itude of a celestial body in minutes and tenths of arc in one minute of time. It is useful for finding the correction to be applied to the computed altitude of a heavenly body when the time of observation differs from that u~ed in the computation of the altitude. When the star is East of the Meridiar.. the correction from the Table is subtractive from the computed altitude if the time of observation is earlier than that used in the computation of the

EXPLA NATION OF TH E TABLES

altitude; it is additive if the time of observation is later. When the star is West of the meridian the correct ion is additive if t he time of observation is before that used when computing the altitude, it is subtractive if the lime o f observation is after.

Formula Change of altitude in one minute of time = 15' Sin. Az. Cos . Lat. The change in 6 seconds of time is found by shifting the decimal poi nt one place to the left. The change in I second of time is found by ca ll ing the quantities in the Table seconds instead of

minutes.

Example: In La t. 51 " 30' N. on the Meridian of Greenwich on October 261h, 1925 a t 8 h. 0 m. p.m. the computed altitude of the sta r Altair was 31" 09 '·2. Find the true altitude at 8 h. 10 m. p.m., the Az. being S.49° 37' W. Opposite 520 in the Lat. Col. and under SO" in the Az. Col. is

l7"IJof arc which is the change of a ltitude in I min. of time, and 7'· 1 x 10 minutes gives 71' or I " 11', which is the correction to apply to the com puted altitude.

~ / \ Com puted All. .. ... . . 37" 09"2 Prs- y52 ) COH.toSubt. ....... I' WO

True All. required 35' 58',2

DIP of the SEA HORIZON

The tabu lated values are derived from the formu la-Dip (in minutes) = 1'76-vh where h = height of eye in metres. Thu s, for example, when h = 30 m (98 ft), dip . = 9"6.

Heights of eye are given in metres, ranging from'O· 5 m to 50·0 In and also in the equivalent feet (1'5 ft to 164 ft ).

MONTHLY MEAN OF THE SUN' S SEMIDIAMETER AND SUN' S PARALLAX IN ALTITUDE

(Pag/il 453)

Correction fo r para llax is to be taken ou l opposite the Su n's Alt itude and is always addithe.

Example: The sun 's parallax corresponding to 51" of a ltitude is 0'· 1.

AUGMENTATION OF THE MOON'S SEMIDIAMETER (Pagtl453)

REDUCTION OF THE MOON'S PARALLAX (P~(}e 453)

EXPLA NATIO N OF TH E TAB LES

MEAN REFRACTION (Page 454)

This table contains the Refraction of the heavenly bodies, in minutes and de.::imals at a mea n state of the atmosphere, a nd correspond ing to their appa rent a lti tudes. Th is correction is always to be slIbrrocled from the apparent altitude of the object.

Example : The mean refraction for the apparent al titude 10° 50', is 4· '9.

Caution: For low altitudes all refraction tables are more or less inaccurate.

ADDITIONAL REFRACTION CORRECTIONS (PJg e 454)

The mean refract ion values given in the Mean Refraction table a re for a n atmospheric pressure of t ,000 mb (29·5 in) and anairternpe rature of IO"C (SO°F). If the atmospheric pressure or temperature differ from these values additional co rrect ions mu st be a pplied to the a pparent altitude. These co rrections a re conta ined in the ta bles' Additional Refraction Correcti ons for Atmospheric Pressure' and 'Additiona l Refract ion Corrections for Air Temperature'

Example: Find the true altitude of the sun when the observed altitude of the sun's lower lim b was 6" OC)', height of eye 16 m (85 ft), atmospheric pressure 1020 mb (30' 1 in), a ir temperatu re 0° C (32° F).

Observed alt itude sun's lower limb - 6° 00' Total correction ~ 0"- 01'S'

- ---True altit ude 5' 58S

Correction for temperature -OA' Correction for pressure -0'2'

Corrected altitude ~ 5° 57-9'

If the altitude is greater than 50 00' th e error due to appl ying these corrections to the true alt itude can be ignored in practice.

N.B.-To convert baro meter readings fro m mercury inches to milli bars, o r vice-versa, see page 499 . To convert temperatures rrom Fah renheit to Celsius, or vice-versa, see page 494 .

The adjustment or mean refraction as shown above is important only when the alt itude is small. It should be borne in mind that on account or uncertai n refraction positio n lines obtained from sights taken when the altitude of the body is less than lO° or so sho uld not be relied upon implicitly. Moreover, due to the effect of atmospheric refraction on dip it is unwise to place too much reliance on sights taken , whatever the alt itude. when there is cause fo r abnormal refraction to be suspected.

EXPLANATION OF TH E TABLES " CORRECTION of MOON' S MERIDIAN PASSAGE

(PiJge 455)

The correction obtained from this ta ble is to be applied to the time o f meridian passage given in the Nau tical Almanac (i.e. the time o f transit at Greenwich) in o rder to find the time of the local tr.lnsit according to the obse rver's longitude.

D X longitude Correction = where D is the d iffe rence between the times o f successive transits.

360

When the observer is in £OS( longitude, D is the difference between the time of Inlnsil on the day of observation arxf the time of transit on the preceding day. When in West lo ngitooe it is the difference between the times o n the day of observa tion a nd the /oJlQwing day.

£xamplt·: From Nau!. Aim. L.M .T . of moon's upper transit a t Greenwich ls:-

h. m. I Si July 18 44

diff. 48m. 2nd July 19 32

diff. 5Jm. 3rd July 20 25

Find G.M.T. of moon's uppe r tra nsit o n 2nd July (a) in longitude 1560 E., (b) in lo ngitude 63" W.

Jul y (a) LM .T. of transi t a t Greenwich ..... ... ... . . ... . . .... . . . ..... .. .. 2

Corr·n. for 0 48m .. long. 1560 E .... .. ... • •. . _ .. . .... . ..... . .. . . .

L.M .T. of loca l transit East longitude in ti me units

G.M.T. of loca l transi t ( 1560 E.) ..... . .. .. .......... .. . . ... . ... .

(b) L.M .T. of tra nsit a t Greenwich Corr' n. for D 53 111 ., lo ng. 630 W.

L.M .T. of loca llransi t ........ . . _ . . , . West longitude in t ime un its . .. .... .. . _ .. • . .

a .M .T. of local transit (630 W.) ... . .

2

2

J uly

2

2

2

h. m. 19 32

- 20·8

19 11 ·2 - 10 24

8 47·2

h. m.

19 32 +9'2

19 41 ·2 +4 12

23 53·2 -


SUN'S TOTAL CORRECTION (Pages 456-461 and Iniith Front Cover)

This is a combined table for the correction of both Lower Limb and Upper Limb altitudes of the Sun. To simplify interpolation for intennediate altitudes and heights of eye, the tabulation is based on columnar and linear correction differences of 0.2.

The corrections in the main table give the combined effect of dip, refraction, parallax in altitude and an assumed semi-diameter of 16.0 . Subsidiary corrections at the foot of the table give the monthly variations of the semi-diameter from the assumed value of 16.0 . The corrections and subsidiary corrections are added to or subtracted from the observed altitude as show in the table.

Example J Obs. AIL Sun's L.L

0(--"\ Corm. for obs. alt. 25 f J 'b I and H.E. 12.0m

\. lA) True Alt. of Sun's centre

24 57.2

+ 8.0 + 0.1

2505.3

Example 2 Obs. AIL Sun's U.L Corm. for obs. a lto 34

and H.E. 19.7m Subs idiary corm. for June True A lt. of Sun 's centre

STAR'S TOTAL CORRECTION ( I""SIL (Pages 462-465 and InSIde S,ck Cover)

33 45.6

- 24" + 0.2

3320.7

y53 )

This table corrects the combined effects of dip and refraction . To si mplify interpolation for intermediate alti tudes and heights of eye. the table is b;:lsed o n columnar and linear correction diffe rences of 0' .2.

This table can also be used for the co rrectio n o f observed altitudes of the planets, bu t in the case of Ve nus and Mars the small additional correction given in the Nautical Almanac for para ll ax and phase may he necessary. T he size of these corrections vary with the date and the altitude of the planet.

MOON'S TOTAL CORRECTION (Lower Limb -p8ge:s466-478; U~ Limb - pages 479-49IJ

This table corrects the combined effects of d ip. at mosphe ric refraction . augmented se midiamete r and para llax in alti tude. '1l1e dip component used in lhe main tahle is ,. constant 12'.3. therefore the subsidiary correction given at the foot o f the pages must be added to the main correction. T he argument for this subsidiary correction is the observer 's height of eye .

No account has been taken of the red uction with latitudc of th e moon's horizo ntal parallax, bu t in ge neral this is of no practica l significance. in cases whcre a hi gh degree of accu racy is rcquired it will be necessary to appl y th e corrections scpa rately toge the r wi th the ad justm ent of the ret"raction correctio n fo r the prevailing atmosphe ric pressure and tempe rature .

T he main correctio ns ~Ire AL W A VS added 10 bot h the lower limb and upper limb obse rved altitudes of the moon , the dip correction is then ~Idded and for upper li mb observations 3(]' must be subt racted from the result.

Example I

Moon 's Hor . Pax. ( from N. Aim.) = 57'.5

Obs. All. moo n's lower lim b Co rrection from main tuble Co rrection fo r heigh t o f eye 13.5m T rue altitude o f moon

= 3K~47' .4

= + 47'. 1 = + 5'.8 = :lif'40' .. "\

Example 2

Moon 's Ho T. Pax. ( from N. Aim. ) = 59'0

O hs. All. moon 's upper limb Correctio n from mai n tabl e Correction fo r heigh t of eye 33m

T rue altitude o t moon

= 69"36'. 0 = + 22'.0 = + 2' ,2 70"00' .2 - 30' ~ 69"30'.2

Ill. TABLES FOR COASTAL NAVIGATION

DAY' S RUN - AVERAGE SPEED TABLE

This table provides a rapid means of finding the average speed directly from the a rguments 'steaming time' and 'd istance run', It wi ll be apprecialed that there is no necessity 10 convert minutes into decimals of a day, a nd that no logarit hms or co- loga rithms a re required. Sim ple addition is all that is needed .

The scope of the table has been made wide enough to cover cases of high speed vessels (up to 40 knots or so) on easterly or westerly cou rses in high latitudes where cha nge o f longitude between one local noon and the next may amount to some 30°, or 2 hours of time.

Distances a re tabulated as multiples of 100 miles. Increments of speed for multip les of IQ miles and multiples of 1 mile are obtained simply by shifting the decimal point one or two places to the left , rtsptttively.

£xanrp/(' ; Give n steaming time 23 h. 29 m., distance 582 miles, find the ave rage speed .

Distance in miles 500 80' 2!

582

Speed in knots 21 ·29 1 3-4066 0·08517

24·78277

That is. av.:rage speed correct to two places of decimals, which a re g.:nerally considered suffici.:nt, is 24·78 knots .

• Enter with 800 miles and shift d.:cima l point I place to the left t Ent.:r with 200 miles and shift decimal po int 2 places to the left

RADAR RANGE TABLE {Pag9501}

RADAR PLOTTER'S SPEED AND DISTANCE TABLE (P~gfl 5021

MEASURED MILE SPEED TABLE (P~ 503-509J

This table is a rranged in 'crit ical table' form and gives speeds correct to th.: nearest hundredth of a knot without interpolatio n. If the time argument is an exact tabulated value, the speed immediately above it shou ld be taken.

32 EXPLANATION OF TH E TABLES

I. If the time recorded for the measured mile i5' 9 m. 16·2 s., the speed is 6·47 knots. 2. If the time is 4 m. 55·3 s., the spttd is 12·19 knots. 3. If the time is 3 m. 52·3 s. , the speed is 15·49 knots. 4. Suppose a ship on trials makes six runs over a measured mile, three against the tide and three

with the tide, such th at the timings by stop-watch are as follows:-

First run against tide .. . First run with tide . . . Second fun agai nst tide ... Second fun with t ide Third run against tide .............. .. . • ... . Third run with tide .. . ........ ... . . . .... • ....

Then total time for 6 miles is ..

:.Average time for 1 mile is

m. s. 3 28·8 3 18·4 3 30-0 3 1J.8 3 3 1" 3 16·7

20 2H

3 2H

From the fable the average speed for rhe six runs is 17·66 knots.

Strictly speaking, the average speed should be computed by finding the 'mea n of means', in which case the work would be arranged as follows.

RUN SPEED 1ST 2ND 3RO 4TH MEAN OF

m. s. KNOTS MEAN MEA N MEAN MEAN MEANS

ISI 3 28·8 17·24 17· 690

2nd 3 18A 18' 14 IH650 17·640 17·66000

3rd 3 30·0 17· 14 17·6550 17·655625 17·670 17·65 125 17·6528125

4th 3 17·8 18·20 17·6475 17·650000 17·625 17·64875

5th 3 31· 1 17·05 17·6500 17·675

6th 3 16·7 18·30 - --

6) 106·07 4) 70·6175

IH8 17·6544 'I' Ordinary Ordinary mean True mean

mean speed of second means· speed

At speeds greater than about 191- knots it will be not iced that in certain cases a change of a tenth of a second in the time will make a d ifference o f mo re tha n one hundredth o f a knot in the tabu lated speed. For example, if the ti me for o ne mile is between 2 m. 38·7 s. and 2 m. 38·8 s. the speed. correct to two places of decima ls, could be either 22 ·68 or 22·67 knots.

In very high speed vessels the recorded t ime fo r a measured mile may be $ 0 sma ll as to be beyond the scope of the table. Even so, a reasonably accurate speed is easily obta ined by entering the table with double the recorded t ime, a nd then doubli ng the speed so obta ined. For instance, if a mile is run in I m. 55·25 .. enter with 3 m. 50·4 s. Thi s gives 15·62 knots which is half the required speed of 31·24 knots (and this wi ll be correct wit hin 0·02 of a knot). By calculat ion th,e correct speed is actually 31·250 knots .

• Th is is usually regarded as being sufficiently accurate

EXPLANATION OF HIE TABLES JJ

Besides its orthodox use for speed trial purposes, the table will be found useful to navigators for other purposes.

For example, suppose it is decided to alter course after the ship has run 6 miles on a certain heading from a position line obta ined at 1432, the speed of the ship being 11·75 knots. The table shows that at this speed the ship will run one mile in a li ttle ove r 5 m. 6 s. , or 6 miles in about 30t minutes. Therefore, the course should be altered at 1502t.

In certain circumstances it mi ght be considered convenient to pl ot the radar target of another vessel at regular intervals corresponding to one mile runs of one's own vessel. Suppose the speed to be 9·70 knots, which the table shows to correspond to a mile in about 6 m. 11 s. Then, if the stop-watch is started from zero at the t ime of the first observat ion , successive observations should be taken as nea rly as practicable when the watch shows 6 m. 11 s. , 12 m. 22 s .• 18 m. 33s. , 24 m. 44 s., a nd so on.

DISTANCE BY VERTICAL ANGLE (Pages 5'~515)

This table gives the distance of an obse rver from objects of known height when the angle betwee n base and the summit is known. The ta bles are for distances up to 7 miles so that the whole object from base to summit will be in view when the hei ght of eye is more than 12 metres (39 feet) Observers whose height of eye is less than th is must apply a correcti on for Dip if their distance from the object exceeds the distance of the sea horizon given for their height of eye in the table Distance of the Sea Horizon (page 486).

The distances given are from the pos ition of the observer to a po int at the base vertically below the summit, and it is to this point that the angle should be measured . In places where there is a big rise and fall of tide it would be necessa ry to make an allowance for the state of the tide, as heights are always given above Mea n H.igh Water Springs or Mean Higher Hi gh Water. In the case of light-vessels there is no allowance fo r the state o f the t ide. as the water plane is always at the sa me distance wi th refe rence to any part of the vessel.

Tojind the Distance Measu re the angle from summit to base and note the angle ; then under the given height find the

observed angle, and opposite the angle will be found the di stance off in Mi les in the left hand column.

Example: The vertical angle between the base and summit of a li ght-house situated 61 m (200 feet) above sea level was 0 0 57'. Required the distance. fI.)

Under 61 m (200 ft) and opposite the given angle is 2·0 miles, the distance. l.!;Y~ 5 12-

To jintl the Angle /0 place on Ihe Sexlant to pass at a gi\'en distance f rom a Point of Known Hdght Opposite the given distance and under the known height wi ll be found the required a ngle 10

place on the sextant.

Example: Wishi ng to pass a po int situated 150 m (492 ft) above sea level at a distance of 4 miles, required the angle to place on the sexta nt.

Oppos ite 4 miles in the distance column at the side, and under 150 m (492 ft) at the lOp. is 1° 10' , the angle required to place on the sex tant.

J4 EXPLANATIO OF TH E TABLES

EXTREME RANGE TABLE IPages 516-517)

This table has b«n compiled fo r the purpose of determining the maximum distance at which an object may be seen at sea according to its elevation and that of the obse rvtr's eye. Heights are given in metres with thei r equivalents in feet .

The arguments with which the table is ord inarily entered are the height of the observer's eye a nd the height of the distant object which last, however. need nol be a terrestrial one bu t may be the masthead of a vessel. or some other easi ly defined detai l thereof, provided always that the hei ght of the feature or object observed be definitely known. The arguments, too, can be made interchangeable, thus, should the lookout, sta tioned at the masthead a t an elevation exceeding 30 metres observe a low-lying rock having a height of less than that amou nt, then the terms can be subst ituted for each other and the ' Height of Eye' can be sought in the 'Height ofObjecf column, and vice versa .

The tables are computed on the basis of normal at mospher ic condit ions, refractio n and visi bility, and, in the case of li ghts, the quantity taken out as ' Extreme Range' presupposes that the light possesses sufficient power to be discernible at such a distance. It must be remembered also that the heights of lights and shore objects a re referred 10 Mea n High Wa ter Springs or Mean Higher Waler therefore due a llowance should be made when the time of observation does not approximate thereto, part icularly if the elevation or distance should be small .

Example I : At what distance will a tower 60 m ( 197 ft ) high be visible to a n observer whose eye r?t-\ is elevated 20 m (66 ft ) above the water? 51b ) Take 60 m (197 ft) as the ' Height of Object' in the ma rginal column and in the column under

20 m (66 ft) ' Height of Eye', a t the top of the page, will be found the 25·6 miles dista nce.

Example 2: The officer of the watch. whose eye is elevated 16 m (52 ft) above the water, observes a shore light, with an elevation of 45 m (148 Il). just dipping. At what dist .. ,nce is the ship from the light?

In the column he,:lded 16 m (52 ft) ' Heigh t of Eye' and abreast of 45 m (1 48 ft ) 'Height of Object' will be found the distance 22·4 miles.

DISTANCE of the SEA HORIZON (PII99518)

The tabula tions a rc derived fro m the fo rm ula- Distance of the sea horizon in nautical miles = 2·095 vh, where h = height of eye in metres. Thus for exam ple, when h = 50 m (164 ft)thedistance of the sea horizon is 14·8 n. miles.

The following examples show how the table can be used .

Example I : At what distanc~ in good visibil ity should an observer whose height of eye is 16 m (52 ft) be a ble to sight a terreSlrial object of height 170 m (558 ft )'!

Distance of horizon for height 16 m (52 ft) = 8·4 miles .. 170 m (558 ft ) = 27·3 miles

Sum = 35·7 miles -Hence, (he object should be visible a t a distance of 35·7 miles,

EXPLANATION OF THE TABLES J5

Example 2: The range of visibi lity of a light is stated on a cha rt to be 21 M . At wha t distance from the light will an observer be a t the moment when the light has just dipped below the horizon if his height of eye is 50 feet?

Charted range, i.e. for 15 feet height of eye ..... ...... . Subtracting distance of horizon for height 15 feel

Range of light at sea level .. .. ..... . .. ........ . Adding distance of horizon for height 50 feet ......... .

Dipping distance, or maximum r,tnge (0 observer .....

21 miles 4'55

16·45 8·30

24· 75

N. 8.- This method is applicable o nly in the case of a light of adeq uate power, and the accuracy of the result will probably be affected by the fact that the charted height of a light never includes a fraction of a mile. Abnormal refraction will also affect the accuracy of distances obtained by using this table.

DIP OF THE SHORE HORIZON (Page 519)

When the part of the horizon immediately under the sun is obstructed by land and the o bserver is near the shore. the D ip for a n observed a ltitude wi ll be greater than tha t shown in the Dip of the Sea Horizon table. When correcting the altitude the dip should t>e taken from this table when obtaining the apparent altitude.

Example: The observed altitude of the sun's lower limb above the shore horizon (distance 1·6 miles) was 2r 30', Height of Eye 12 m (39 ft).

Observed altitude ... Dip of Shore Horizon ....

:. Apparent a ltitude .....

(H.E. = 12 m, distance = 1·6 miles)

If the refraction is believed to be abnormal the table should be used wi th caution.

The table can also be used to obtain the approximate range of a sh ip by measuring the angle between the ship's waterline and the sea horizon.

Example: The sextant angle between a sh ip's waterline and the sea horizon is 5·0'. Height of Eye = 25 m (82 ft).

From dip of sea horizon table. Dip ...... .... ..... .. . Observed angle

c~~~~~_~~ :. From the dip of the shore ho rizon table, Range

8·8' 5·0'

14·8 3·5 miles

CORRECTION REQUIRED TO CONVERT A RADIO GREAT CIRCLE BEARING TO MERCATORIAL BEARING

(Page 520)

EXPLANAT ION OF THE TAB LES

IV. PHYSICAL AND CONVERSION TABLES

TO CONVERT ARC TO TIME AND TIME TO ARC (Pages 522-523)

HOURS AND MINUTES TO DECIMAL OF A DAY (Page 524)

ATMOSPHERIC PRESSURE CONVERSION TABLE (Page 525)

' FAHRENHEIT - ' CELSIUS - 'FAHRENHEIT (Page 526)

SI - BRITISH UNITS (Pages 527-528)

BRITISH GALLONS - U.S. GALLONS - LITRES (Pages 529-531 )

NAUTICAL MILES, STATUTE MILES, KILOMETRES (Pages 532-534)

FATHOMS - METRES - FATHOMS

DECIMAL FRACTIONS OF A DEGREE (Page 536 and Inside Bad( Caverl

EXPLANATION OF TH E TABLES

V. PORTS OF THE WORLD

PORTS OF THE WORLD. LATITUDES AND LONGITUDES (Pages 538-595)

This section is an alphabetical list of all the ports of the world used by commercial shipping, the positions given to the nearest minute of latitude and longitude being those of the port area, not the centre of the towns or cities. Every effort has been made to ensure that the names and positions given are correct by checking with charts and reliable official sources and publications.

The user should note the following points: -1 The order of listing is strictly alphabetical and if two or more ports have the same name they are

listed in the sub-order of their countries, alphabetically. 2 A port which has several commonly used names or whose name has been changed recently is

entered under each name with the alternative names in brackets. 3 Ports whose names consist of two or more words are entered under each word.

e.g. Port Chalmers is entered under P as Port Chalmers and under C as Chalmers, Port. 4 To assist in locating a port its country is given in Anglicised form and where it is considered useful

the name of the bay, island, river etc. on which it is sited is given in the form used in its country. 5 Accents and diphthongs have been omitted.

37

~:l: f TRAVERSE TABLE f017' l h 08m

17 Degrees 163'

D. Lon en . D. ,~ D • . D. Lon D • . D. Lon D • . O. Lon D • . Oist. D. Lat. De Dist. O. lat. DeD. Dist . O. lat. DeD. Oist. D. Lat. DeD. Dist. O. Lat. DeD. » 1 287 8 880 361 3452 1055 .21 4026 123 1 '81 460-0 1406 541 517 4 1582 302 2888 88 3 382 346 ,2 1058 .22 4036 123·4 '82 4609 140,9 542 518,3 1585 303 289 8 88 6 363 347 1 106·' 423 404 ,5 123,7 '83 461 ·9 141 2 543 519 3 1588 >l4 2907 88 ·9 384 3481 106·4 '" 405 5 1240 '84 462-9 14 1 5 54' 5202 159 1 305 29 1 7 89 ·2 365 349 1 106,7 426 4064 124 3 485 463 8 141 8 545 521 2 159 3 300 292 6 89 -5 366 350 ,0 107,0 '26 4074 124 ·6 .ea 464 8 142 -' 546 522 1 1596 307 293 6 898 367 3510 107 3 427 40B' 3 1248 '87 465,7 1424 547 523 1 , 59-9 308 294 5 90-' 368 351 9 1076 428 4093 125 1 '88 468 7 1427 548 524 1 160 2 J09 295 5 903 36' 352,9 1079 .29 4103 1254 489 4676 1430 54' 5250 1605 310 296 5 906 370 353-8 1082 430 411 2 125 7 '90 4686 143-3 550 5260 1608

311 2974 909 371 354-8 1085 431 412 2 1260 491 4695 1436 551 5269 1611 312 2984 912 372 355-7 1088 432 4131 1263 '92 4705 1438 552 5279 16' 4 313 2993 915 373 3567 1091 433 414-' 1266 '93 471 5 144-' '53 5288 161 7 314 300 3 91 ·8 374 3577 1093 .34 4150 1269 '94 472 4 144 4 554 5298 1620 315 301 ·2 921 375 358-6 1096 435 416 -0 127-2 '9' 4734 144 7 555 5307 162 3 316 302 2 924 376 3596 1099 '36 4169 1275 '96 474 3 1450 '56 531 7 162 6 317 303 1 92- 7 on 3605 1102 .37 41 7 9 1278 497 4753 1453 557 532 7 162 9 318 304- 1 93-0 378 361 -5 11 05 438 418-9 1281 498 476-2 145 -6 558 533 6 163 1 319 306- 1 93-3 379 36 2-4 110 -8 '39 4198 1284 '88 477 2 1459 '59 534-6 163 -4 320 306-0 936 380 363 -4 111-1 440 420 8 128 -6 500 478-2 146 2 560 535-5 163-7

321 3070 93 -9 361 364 4 111 4 441 4217 128 -9 601 479 1 146 5 561 536-5 1640 322 3079 94 I 382 3653 111 7 442 422-7 1292 502 4801 1468 562 537 -4 164 3 323 3089 944 383 366 ·3 1120 443 423-6 129-5 503 4810 1471 563 5384 1646 32. 3098 947 384 3672 112 3 444 424 6 1298 504 4820 1474 564 5394 1649 325 3108 950 385 368·2 1126 44' 425-6 1301 50' 4829 147-6 56' 5403 1652 326 311 8 953 386 369 I 1129 .... 426-5 1304 506 4839 147-9 566 541 3 1655 327 312 7 956 387 3701 113 1 .47 427 5 1307 507 4848 1482 567 5422 1658 328 3136 959 388 371-0 1134 448 428-4 131-0 508 4858 148-5 568 5432 166 1 329 314 6 96 2 389 372 ·0 1137 449 429-4 131 3 509 4868 148·8 569 5441 1664 330 315 5 965 390 3730 1140 .50 430·3 131 6 510 487-7 149 ·1 570 545 1 166-7

331 316 -5 96 8 391 373 9 11 4-3 '51 431 3 131 9 '" 488-7 149 -4 '71 546 1 166-9 332 317 5 971 392 3749 114-6 452 43 2 2 132 2 512 489 6 1497 572 5470 167 2 333 318-4 97 4 393 375 -6 11 4-9 '53 433 2 132 4 613 4906 150-0 573 5480 167 5 334 319-4 97-7 394 376 8 11 5 2 '54 434 2 132 -7 51' 491 5 1503 574 548 9 167-8 335 3204 97-9 395 377 7 11 5 5 455 435 1 1330 51' 492 5 150-6 57' 549 9 168-' 336 321 3 982 396 378 -7 1158 .56 436 1 133-3 518 493 5 150 -9 576 5508 1884 337 322 3 98·5 397 379 7 1181 '57 437-0 1336 '17 494 4 151 2 '77 551 8 1687 338 3232 98·8 398 3806 1164 '58 4380 1339 518 4954 151 4 578 552 7 1690 339 324 2 991 399 381 6 116 7 .59 438-9 134 2 519 4963 151-7 579 5537 1693 340 3251 994 '00 382 5 1169 .60 4399 134 5 520 497 3 1520 580 5547 1696

341 326 \ 99 7 .01 383 5 \17 2 481 4409 1348 521 4982 152·3 581 5556 1699 342 327 1 100 0 .02 3844 117 5 462 1141-8 1351 522 499 2 152-6 582 5566 1702 343 3280 1003 .03 3854 117 8 .63 11428 1354 523 500 I 1529 563 557 5 1705 34. 329 -0 1006 '04 3863 118-1 454 4437 135 7 52. 501 1 153-2 584 558 5 1707 345 329-9 100-9 '05 387·3 11 8-4 '65 444 7 1360 526 502 1 153 5 58' 559-4 171 0 346 330-8 101 2 .06 388 3 11 8-7 '86 445 6 136 2 526 5030 153 8 586 560-4 17 1 3 347 331 8 101 5 '07 389 2 11 90 '67 446 -6 136 5 527 5040 154-1 587 561 -4 171 6 348 332 8 101 7 408 3902 119 3 '68 44 7 6 136 8 528 504-9 154 4 588 562 3 ' 71 9 34' 333 S 1020 .09 391 1 119 6 '6' 448- 5 137 1 529 505-9 1547 589 563-3 172 2 350 334 7 102 3 410 392 1 1199 "0 449 -5 137 4 530 506 -8 1550 590 564 -2 172 5

351 335 7 102 6 .11 3930 1202 471 450-4 137 7 531 507·8 155-2 591 5652 172 8 352 336 6 1029 412 394-0 1205 472 451 4 1380 532 5088 155-5 '92 566 1 173 1 353 3376 1032 413 3949 1207 473 452-3 1383 533 5097 1558 593 567 1 173 4 354 338 5 1035 .14 395-9 121 0 '" 453-3 1386 534 5107 156-1 594 5680 1737 35' 339 5 1038 '15 3968 121 3 475 454 2 1389 536 511 6 1564 59' 5690 1740 356 3404 1041 416 397 8 121 6 "6 455-2 139 2 536 5126 156-7 596 5700 1743 357 341 4 1044 417 3987 121 9 477 4562 1395 537 513 5 1570 597 5709 1745 358 3424 104- 7 418 3997 122 2 "8 11571 1398 538 514-5 1573 598 571 9 174 8 359 343 3 1050 419 400-7 122 5 . 79 458 1 1400 53' 515-4 157 6 599 572-8 175 1 360 344 3 105-3 420 401 6 122 8 480 459 0 140-3 540 516-4 157 -9 600 5738 1754 Dist. Dep. D. Lat. Dist. Dep. D. Lat. Dist. Dep. D. Lat . Dist, DeD. D. Lat. Dist. Dep. D. Lat.

D. Lon D • . D. 'on D • . D. ,~ Dep. D. Lon Dep. D. Lon D • .

287' v

73 Degrees ~ ~5J- 107" 4h 52m

46

22 ~ TRAVERSE TABLE f022' lh 2am

0 202' 22 Degrees 158 '

D. Lon D, . D. ion D, . D. Lon D, . D. Lon Dep. D. Lon D, . Dist. O. Lat . Dep. Oist. D. Lat. Dep. Dist. D. Lat. Dep. Oi5t. D. Lat. Dep. Dist. D. Lat. Dep.

1 00' 00' 61 566 22-9 121 112 2 453 ' 8' 167 8 678 '" ~ 223- 5 903 2 019 007 62 575 23-2 . 22 113 1 457 182 1687 682 "2 224-4 907 3 028 O •• 63 58 , 236 123 1140 '6 • ' 83 169 7 686 243 2253 91 -0 , 037 O' 5 6' 593 240 12' 1150 465 . 84 1706 689 244 226-2 91-4 5 046 019 65 603 24-3 125 1159 '68 ' 85 171 5 693 245 2272 91-8 6 056 022 66 6. 2 247 ' 26 1168 '72 186 172 5 697 246 228 1 921 7 065 026 67 621 25-' ' 27 11] 8 476 '87 173 <I 701 247 2290 92-5 8 0" 030 68 630 255 128 1187 '79 .88 1743 70 , 248 2299 92' , 083 034 6. 640 25-8 12' 11 96 483 189 1752 70B ". 230-9 93-3

. 0 093 037 70 649 26-2 130 1205 487 '90 1762 712 250 231-8 93-7

11 102 041 71 658 266 131 121 5 491 ." 177 1 71 5 251 232-7 94 0 12 111 045 72 668 270 132 122 4 494 192 1780 '" 252 2337 '" 13 121 049 73 67·7 273 133 1233 498 193 1789 723 253 2346 948 14 130 051 74 686 277 134 124 2 502 194 1799 727 25' 2355 95, 2 15 139 056 75 695 281 135 1 25 2 506 195 1808 730 255 236 4 95,5 16 14·8 06·0 76 70·5 28 5 136 1 26 1 509 196 181 7 734 256 2374 959 17 15 8 06-4 77 714 28 8 137 127 0 51 3 197 182-7 738 257 2383 96 3 18 167 06-7 78 723 29 2 138 128 0 51 7 198 183-6 742 258 239 2 966 19 17-6 071 79 73 2 29-6 13' 1289 52 1 19' 184 5 74 5 259 240 1 970 20 185 075 80 742 300 140 129 8 524 200 185 -4 749 260 24 1 1 97 -4

21 195 07-9 81 75 1 30 3 141 1307 528 201 186-4 75 3 261 242 0 97-8 22 10 , 08-2 82 760 307 142 131 7 532 202 187 3 757 262 242 9 981 23 21 3 08-6 83 770 31 1 143 132 6 536 203 188 2 760 263 243 8 985 24 223 0' 0 84 77' 31 5 144 1335 539 204 189 1 764 264 2448 9B -9 25 232 094 85 78. 318 145 134 4 543 205 1901 768 265 245 7 993 26 241 097 86 797 32 ·2 146 135 4 54 ·7 206 1910 772 266 2466 996 27 250 101 87 807 32-6 147 136-3 551 207 191 9 775 267 2476 1000 28 260 105 88 816 330 148 137 2 55 ·4 20B 192 9 779 268 2485 1004 29 269 10' 89 825 333 14' 138-2 558 209 1938 783 26' 2494 1008 30 278 11 2 '0 83' 337 150 1391 562 210 194 7 787 270 250-3 1011

31 287 116 " 84' 34-1 151 1400 566 21 1 1956 790 271 251 3 1015 32 297 120 92 853 34-5 152 1409 56 , 212 1966 79' 272 252-2 1019 J.3 306 12' 93 862 348 153 141-9 573 21 3 1975 798 273 253-1 1023 34 31 5 127 94 872 35-2 154 1428 577 214 1984 802 274 254-0 1026 3. 325 131 95 881 35-6 155 1437 581 215 1993 805 275 255-0 1030 3. 334 135 96 890 360 156 144 6 584 21. 200 3 809 276 2559 1034 37 343 13' 97 89' 36-3 157 1456 588 217 201 2 813 277 256-8 1038 38 352 142 98 909 367 158 1465 592 218 202 1 81 7 278 257 ·8 1041 39 362 146 99 918 371 15' 1474 596 219 2031 820 279 2567 104 5 '0 371 150 100 927 375 160 1483 599 220 2040 824 280 2596 104 9

41 38-0 15' 101 93 . 37-8 161 1493 603 221 204 9 828 281 2605 1053 42 38-9 15- 7 102 946 382 162 1502 607 222 2058 832 282 261 5 105 6 43 39-9 16-1 103 955 386 163 151 1 61 1 223 206-8 83 5 283 262 4 1060

" 408 16 -5 104 964 39 -0 164 152 1 61 , 224 2077 839 284 2633 1064 45 41 -7 16-9 10. 97 A 39 3 16. 153 0 61 8 225 208-6 843 285 2642 1068 ,. 42 -7 172 106 98 -3 397 166 1 S3 9 622 "6 209 5 847 286 265 2 107 1 47 4 3-6 17 -6 107 99 2 40 1 167 154 8 62 6 227 210-5 850 287 266 1 107 5 48 44 -5 18-0 108 100 -1 40 -5 168 1 S5 8 62 9 228 211 -4 85 4 288 2670 107-9 49 45-4 18-4 109 101 1 408 16' 156 7 63 -3 229 212 3 858 289 268 0 1083 50 46 -4 18-7 11 0 1020 41 2 170 157 6 637 230 213-3 86-2 290 2689 108 -6

51 473 191 111 1029 416 171 1585 641 231 214 2 865 291 2698 109-0 52 '82 195 112 1038 420 172 1595 644 232 215 1 869 292 270 7 1094 53 491 199 '" 1048 423 173 1604 648 233 2160 873 293 271 7 1098 54 501 20·2 ." 1057 427 174 1613 652 234 2170 877 294 272 6 110 1 5. 510 206 115 106 6 43 -1 175 162-3 656 235 2179 880 295 F35 1105 56 519 210 116 1076 43·5 176 1632 659 236 2188 884 296 274 a 1109 57 528 21' 117 1065 '38 177 164-' 663 237 219 7 888 291 2754 111 3 58 538 21 7 11 8 109 4 44-2 178 1650 667 238 2207 892 298 2763 111 6 59 54 7 221 11. 110 3 "6 '79 1660 671 239 221 6 895 299 277 2 1120 60 556 22. 120 111 3 450 180 1669 6" 240 222 5 89' 300 2782 1124

Dist. Oep. D. Lat. Oist. Dep . O. Lat. Disc. Oep. D. Lat Oist. Oep. O. Lat. Disl . Dep. D. Lal D. Lon Dep. D. Lo" D, . D. LOll Dep. D. Lon D, . D. Lo" Do. , . ,

v , • 292' ~ ~ 68 Degrees 4h 32m 68 0

89

31Tl TRAVERSE TABLE ~

2h 52m

223 ' 43 Degrees 137' .----A------ ~

O. Lon D, . D. Lon Dep. O. Lon D, O. Lon D, . D. Lon D, .

Dist. D. Lat. Dep. Dist. D. Lat . Dep. Dist. D. Lat. Dep. Dist. D. lat. Dep. Dist. O. Lat. De

"" 2201 205 3 361 2640 2462 421 3079 287 1 481 3518 328-0 541 395 7 369 ,0 302 2209 206,0 362 264 -8 2469 422 3086 2878 482 352 5 328 -7 542 3%4 3696 303 22 1 6 2066 353 26 55 247 6 423 3094 288,5 483 353,2 329-4 543 39 7-' 3703 304 22 2 3 207 3 364 2662 248 ,2 424 3101 289 2 484 3540 330-1 544 397 ·9 371 0 305 223 " 2080 365 2669 2489 425 3108 289 ,8 485 354,7 330 ,8 54. 398 6 371 7 306 2238 208 7 365 2677 249 ,6 426 311 6 2905 486 355 4 331 5 645 399 ,3 372-4 307 224 5 209 -4 367 268 -4 2503 427 3123 29 1 2 487 3562 3321 647 400 -' 3731 308 2253 210 1 358 269 1 2 51 ,0 428 3130 2919 488 3569 332 8 548 4008 373 ,7 309 2260 2107 369 269 ,9 251 ,7 429 3138 2926 489 35 7-6 3335 549 401 ,5 374 -4 310 226 7 211 -4 370 270 ,6 2523 430 314 -5 2933 490 3584 3342 550 402 ,2 375 1

311 22 75 212 1 371 271 ,3 253 ·0 431 315 ·2 2939 491 3591 3349 551 403 ,0 375 ,8 312 228 2 212 ,8 372 272 ·1 253 ·7 432 315·9 2946 492 3598 335 ,5 552 4037 3765 313 228 ,9 2135 373 272 ·8 254·4 433 316 ·7 295 ·3 493 360·6 3362 553 4044 3771 314 2296 21 4, 1 374 273·5 255 ·1 434 31 74 296 ·0 494 361 ·3 336 ,9 554 405 2 3778 315 2304 214,8 375 274 ·3 255 ·7 435 31 8·1 296 ·7 495 362 ·0 3376 555 405 9 378·5 315 231 1 2155 375 275·0 2564 436 318·9 297 ·4 496 362 ·8 3383 556 406 6 379 ·2 317 231 8 216,2 377 275 ·7 257·1 437 319 6 298 ·0 497 363 5 339 ,0 557 407 4 379 ·9 318 232 ,6 2169 378 276 ·5 25 7· 8 438 320·3 298 ·7 4Sa 364·2 3396 558 408 1 380·6 319 233-3 21 7 6 379 277 ·2 258 ·5 439 321 1 2994 499 364 9 3403 559 408,8 381 ·2 320 234 ·0 218,2 380 277 ·9 259 2 440 3218 300·1 500 365'7 341 ,0 560 409 6 381 ·9

321 234 ·8 2189 381 278 ·6 259 ,8 441 32 25 3008 501 3664 341 ·7 561 4103 382 ·6 322 235 ·5 2196 382 2794 260 5 442 323 ,3 3014 502 367 1 3424 562 41 1 0 383 ·3 323 236 ·2 2203 383 2801 26 1 2 443 3240 302 1 503 367 9 343 ·0 563 411 ,8 384 ·0 324 237 0 221 ,0 384 2808 2619 444 324 7 302 ,8 504 368,6 343 ·7 564 412 5 384 ·6 325 237 ,7 22 1 6 385 281 6 2626 445 325 ,5 3035 505 3693 3444 565 413 ·2 385 ,3 326 238 4 2223 386 282 ,3 263 ,3 445 32 6 2 3042 500 370 1 345 ,1 565 4 13·9 3860 327 239 2 223 ·0 387 2830 2639 447 3269 304 ,9 607 370,8 3458 567 4 14·7 386 ,7 328 2399 223 ·7 388 283 ,8 264 6 448 32 7 6 305 5 508 371 5 346 ,5 568 4 15 4 387 4 329 2406 224 ·4 389 2845 2653 449 328 ,4 306 ,2 509 372-3 347 1 569 4161 388 ,' 330 24 1 3 225 ·1 390 28 5 2 2660 450 329 ,1 306 9 510 3730 347 8 570 4 16 ,9 3887

331 24 2 1 225· 7 391 2860 266 , 7 451 3299 307 6 511 373 7 3485 571 4176 3894 332 242 8 226 ·4 392 286 , 7 2673 452 3306 3083 512 374 ·5 349 2 572 4183 390 1 333 243 ,5 22 7 1 393 28 74 2680 453 331 3 308 9 513 375 ·2 3499 573 419 1 3908 334 2443 227 ·8 394 288 ,2 2687 454 3320 309 ,6 514 375 ·9 350 ,5 57' 4198 391 5 335 245,0 22 8·5 395 288 9 2694 455 332 8 310 3 515 376 ·6 351 2 575 420 ,5 392 1 336 245 7 2292 395 289 ,6 270 ,1 456 3335 31 1 0 516 3774 351 ,9 575 421 3 3928 337 246 ·5 2298 397 290 3 2708 457 334 ·2 311 7 517 378·1 352 6 577 422,0 393 ,5 338 247 ·2 2305 398 291 1 271 ,4 458 335 ·0 3124 518 3788 353 ,3 578 422 7 3942 339 247 ·9 23 1 2 399 291 8 27 2 1 459 335 ·7 313 ,0 519 3796 354 0 579 4235 394 ,9 340 248 7 23 1 9 400 292 ,5 27 2, 8 450 3364 313 ·7 520 3803 354 ·6 580 424 2 39 5 6

341 249 4 232,6 401 293 ,3 273, 5 461 337 2 3144 521 381 ·0 355 ,3 581 4249 3962 342 2501 233 2 402 2940 2742 452 3379 315 ·1 522 381 ·8 356 0 582 425 ,6 396 ,9 343 2509 2339 403 2947 2748 453 3386 315 ·8 523 382 ·5 356 7 583 4 264 3976 344 251 6 234 ·6 404 295 ,5 275 ,5 464 3393 3164 524 383 ·2 357, 4 584 427 1 3983 345 252 ,3 235 ·3 405 29 6 2 2762 465 340·1 317 ·1 525 384 ·0 3580 585 427 ,8 3990 346 253 ·0 236 ·0 406 2969 2769 466 340 ,8 317 ·8 526 384 7 358 , 7 586 4286 399 7 347 253·8 2367 407 2977 2776 457 341 5 318 ·5 527 385 4 3594 587 429 3 400,3 348 254 ·5 237 3 408 2984 278 ·3 468 342 ·3 319 ·2 528 386 '2 3601 588 4300 401 0 349 255 2 2380 409 299 1 278 ·9 459 343 ·0 319 ·9 529 386 ,9 360 ,8 589 4308 401 ,7 350 2560 238 7 410 2999 27 9· 6 470 343 ·7 320·5 530 387 6 361 ·5 590 43 1 5 4024

351 256 ,7 2394 411 300· 6 280·3 471 344 ·5 321 ·2 531 3883 3621 591 432 2 403 ,1 352 2574 240,1 412 301 ·3 281 ·0 472 345 ,2 32 1·9 532 389 1 362 ·8 592 4330 403 7 353 258 ,2 2407 413 3020 281 ·7 473 3459 322 ·6 533 3898 363 ·5 593 433 ,7 404 ,4 364 2589 2414 414 302 ·8 282 ·3 474 346,7 323·3 534 390 5 364 ·2 594 4344 4051 355 2596 242 ·1 415 303·5 283 ·0 475 347 4 323-9 535 391 3 364 ·9 595 43 5 2 405·8 356 260·4 2428 415 3043 283 ·7 476 348 ,' 324 ·6 535 392 ,0 3656 596 435 ,9 406 ·5 357 261·1 2435 417 305 ·0 284 ·4 477 348 9 3253 537 392 7 366 ,2 597 4366 407·2 359 261 ·8 2442 418 305 ·7 285 ,' 478 349 ,6 326 ·0 538 393 ,5 3669 598 437 ,3 407 ·8 359 2626 244 ,8 419 3064 285 ·8 479 3503 326 ·7 539 3942 3676 599 438 ,1 408 ·5 360 2633 24 55 420 307 ·2 2864 480 351 ,0 327 ·4 540 3949 368 ,3 500 438 ,8 409 ·2

Dist. Dep. D. Lat . Dist. Dec. D. Lat. Dist. Dec. D. Lat. Dist. Dec. D.Lat. Dist. Dec. D. Lat. o. Lon Dep. D Lon Dep. D Lon Dep. D. Lon D, . D. Lon D •.

313' v

ill- 47 Degrees ~ 3h 08m 133'

98

Terrestrial Spheroid MERIDIONAL PARTS 1 Compression 293 465

M 41 ' 42' 43' 44' 45' 46' 47' 48' 49' 50' M

0 2686·24 2766·05 2847-13 2929-55 3013·38 J096-70 3185·59 3274-13 336H l 3456·53 0 1 2687-56 2767·39 2848<9 29.1093 3014·79 3100·14 3187·05 3275·62 3365-93 3458<J8 1 , 2688-88 2768·73 2849·85 2932-32 3016 -20 3101·57 3188·51 32THl 336NS 345%4 , 3 2690-20 mo·(fl 2851·22 293:HI 3On61 3103-01 3189·97 3278·60 336897 3461-19 3 • 2691·52 2711·41 2852·58 2935-09 J019-Q2 31(}H 4 3191-44 3280-09 3370·49 3462·74 • , 2692·lH Z17'HS 285.3-9\ 2936<. """<3 3105·88 319'2,90 3281·58 33n.Ol 3464·29 , • 2694-16 277H O 2855·31 ?!JJ7'fn 302185 3107-32 3194<36 =-07 3373·54 3485-85 • , 2695·49 2775·44 2856·67 2939-26 = -26 3mH6 3195·83 3284·57 3375·06 3467·40 , • 2696·81 2'n6·78 2858-'" Z9lO-64 J024 '67 3110·19 3197·29 3286-06 3376·58 346896 • , 2698·13 zna·13 285940 29<12·03 3026-00 3111·63 3198·76 328N5 3378·11 3470·52 ,

10 2699-45 mg'47 ""'-77 294342 302750 3113 ·07 =-'" 3289-05 3.:ng·63 3472·07 10 11 270(}78 2780·81 2862·14 2944·81 3028·91 3114·51 3201·69 ""-54 3381-16 3473·63 11

" 2702· 10 2782·16 ""' -50 2946·20 3030·.,32 3115·95 3203·16 3292·04 ""'-68 3475·19 " 13 270.3042 2783·50 2864 -87 2947·59 3031·74 3117·39 3204·63 329354 3384·21 3476·75 13

" 2704 ·75 2784·85 2866·24 2948·96 3033·15 3118 ·83 3206·10 3295·03 3385·73 3478·30 14

" 2706·07 2786-19 2867 ·00 2950·37 3034·57 3120·27 3207 ·56 3296 ·53 3387 ·26 3479 ·86 " 18 2707·40 2787-54 _ -97 2951·76 3035·99 3121 ·71 3209·03 3298 ·03 3388-79 3481 ·42 16 17 2708·72 2788·89 2870·34 2953·15 3037·40 3123-16 3210 ·50 3299·52 3390·32 3482-98 17 18 27 10·05 2790-'" 2871·71 2954·55 3038·82 3124·60 3211·97 3301·02 3391·85 3484 ·54 18 19 2711 ·38 2791 ·58 2873·08 2955·94 3040·23 3126·04 3213·44 3302·52 3393·38 3486·11 19

" 2712·70 2792 ·93 2874·45 2957·33 ml·65 3127·49 3214·91 ""' 02 3394·91 3487·67 " " 2714 ·03 2794·28 2875·82 2958·73 3Ot3·07 3128·93 3216 ·38 3305·52 3396·44 3489·23 " .. 2715'36 2795-62 2877-19 296<H 2 3044-49 3130·37 3217·86 3307·02 3397·97 3490·79 " " 2716·68 Z196-97 2878·56 2951·51 3(W5·91 3131·82 3219 ·33 3308·52 3399·50 3492·36 " .. 2718 {)1 2798·32 2879-93 2962·91 3047·33 3133·26 322<1-80 3310·02 3401·03 3493-92 2A

" 2719·34 2799·67 2881 ·30 2964 -30 3()t8'75 3134·71 3222·27 3311 ·53 3402-56 3495·49 " .. 2720·67 2801 ·02 2882·67 2965·70 3050·17 3136·15 3223-75 3313·03 3404·10 3497·05 .. " 2722-00 2802·37 2884-05 2967·09 .3051·59 3137·60 3225-22 3314·53 3405·63 3498·62 " " Z12l-33 'SO"" 2885·42 2968·49 3053·01 3139 ·05 3226·69 3316·03 340'7-16 350018 " " 2724'66 2B05-07 2886-79 2969 ·89 J054·43 3140-49 3228· 17 3317·54 J406·70 3501·75 " 30 2725-99 2806·42 2888·17 2971 ·28 3055-85 3141 ·9'\ 3229-64 3319 ·0 4 3410 ·2,3 350]32 30 31 2727-32 2fJl1/-77 2889-54 297268 3057-Z/ 3143 ·39 3231·12 3320·55 3411 ·77 3504-89 31

" 2728·65 2009·13 2890·91 2974·08 3058·70 3144·84 3232·60 3322-05 3413·30 3506·45 " 33 2729-98 2810 ·48 2892-29 2975·48 3060·12 3146·29 3234 -07 = -56 3414 ·84 350802 33 34 2731·31 2811 ·83 ""'-66 2976·88 3061 ·54 3147·74 3235-55 3325·07 3416·38 3509·59 " " 2732'64 2813·18 2895-(}1 2978·28 3062-97 31<19·19 3237·03 3326·57 3417·92 3511-16 35 ,. 2733·97 281<1 ·54 2"}6<2 2979-68 3064 ·39 3150·64 3238·51 3328-08 34 19 ·45 3512·73 36

" 2735·31 2815·89 ""-79 2981·00 3065·81 3152·09 3239·98 3329·59 3420·99 3514·31 " '" 2736·64 2817·25 2899·17 2982·48 .3067·24 3153·54 3241·46 3331-10 3422·53 3515·88 '" 39 2737 ·97 2818·60 2900-54 ""'-88 306866 3154·99 3242·9'\ 3332-60 3424·07 3517-45 39 .. 2739·30 2819·95 2901·92 2965 28 J070 {19 3156·45 3244 ·42 3334·11 3425·61 3519 ·02 eo .. 2740·64 2821·31 2<J03-30 2'166 68 3071 ·52 3157·90 3245·90 3335-62 3427-15 3520·60 41 .. 2741 ·97 2822·67 290468 2988-08 3072 ·94 3159·35 3247·38 JJ3H3 3428·70 3522·17 " 43 2743·31 282402 2906-06 2989-48 .)()74·37 3160·81 3248·87 3338-65 3430·24 3523·75 43 .. 2744·6<1 2825-38 2907-43 299088 3075 ·80 3162·26 3250·35 3340·16 3431·78 3525·32 .. " 2745 ·98 2826 ·73 2908·81 299229 3077-23 3163 ·71 3251·83 3341-67 3433-32 3526·90 " .. 2747-31 2828 09 2910·19 2993-69 3078·66 3165·17 3253·31 3343-18 3434 ·87 3528-47 .. " 2748 ·65 2829-45 2911·57 2995-09 308009 3166·62 3254 ·80 3344·69 3436·41 3530 ·05 " .. 2749·98 2830·81 2912 ·95 2996-50 3081 ·52 31GS'OS 3256·28 3345·21 3437 ·95 3531·63 .. " 2751·32 2832·16 2914·33 2fff7"IJ 3082 ·95 3169·54 3257·n 3347-72 3439·50 3533 ·21 " 50 2752 ·66 2833·52 2915·72 2999·31 3004 -38 3170·99 3259·25 3349·24 3441 ·05 3534·79 50

" 2754 ·00 2834 -88 2917·10 3(X)(}71 3085 ·81 3172 ·45 3260·74 3350·75 3442·59 3536 ·37 " " 2755·33 2836-24 2918·48 3002·12 3087·24 3173·91 3262·22 3352·27 3444-14 3537·95 " 53 2756·67 2837·60 2919·86 3003·53 3088·67 3175·37 3263·71 3353·78 3445·69 3539·53 53

" 2758·01 2838-96 29'21·24 30)4·93 3090· 10 3176·83 J265'ro 3J55.3Q 3447·23 3541-11 54 55 2759 ·35 2840·32 2922-63 3006 34 .309153 317S'28 3266-68 3356-82 3448·78 3542·69 55 56 2760'69 2841 ·68 2924-01 3fXjl·75 3092 -97 3179·74 3268·17 3358-33 3450·33 3544-27 56 57 2762·03 2843·04 2925·39 3009·16 309> 40 3181·20 3269·66 3359·85 3451·88 3545·85 57

" 2763·37 ,.4H) 2926·78 3010·56 3095-83 3182·66 3271-15 3361·37 3453-4.3 3547« " " 2764·71 2845·77 292f·16 3OU ·97 YH/-Z/ 3184·13 3..."72·64 336289 3454·98 3549-02 " .. 2766·05 284H3 2929·55 3013·38 J098·70 3185·59 3274 ·13 ""'<I 3456·53 3550-00 60

M 41 ' 42' 43" 44' 45' 46' 47' 48' 49' 50" M

104

LOGARITHMS

No. 1600 2199 20412 34223

0 1 2 3 4 5 6 7 8 9 5th

0 fig.

'60 20412 20439 200466 20493 20520 20548 20575 20602 20629 20656 lOO 16' 20683 20710 20737 20763 20790 20817 20844 20871 20898 2092S 16' , 3 '62 20952 20978 21005 210)2 21059 21085 21112 21139 21165 21192 '62 2 5 '63 21219 21245 21272 21299 21325 21352 21378 21405 21431 21458 '63 3 8 '64 21484 21511 21537 21564 21590 21617 216-'13 21669 21696 21722 '64 4 11 '65 21748 21175 21801 21827 21854 21880 21906 21932 21958 21 985 '65 5 13 '66 22011 22037 2206) 22089 22115 22141 22168 2219-'1 22220 222"'6 166 6 16 '67 22272 22298 22324 22350 22376 22402 2H27 22453 22479 22505 '67 7 18 '68 22531 22557 22583 22608 2263-4 22660 22686 22712 22737 22763 '68 8 21 '69 22789 22814 22&40 22866 22891 22917 22943 22968 22994 23019 '69 9 24

170 23045 23070 23096 23122 23147 23172 23198 13223 23249 23274 170 171 23300 23325 23350 23376 23-401 23426 23452 23477 23502 23526 171 , 2 172 13553 23578 13603 23619 23654 23679 13704 13729 23754 23780 172 2 5 173 13805 23830 13855 23880 23905 13930 23955 13980 14005 24030 173 3 7 174 24055 H080 14105 14130 H155 14180 14104 24229 14154 24279 174 4 10 175 24304 24329 24353 24378 2+403 1#18 14451 24477 14501 24517 175 5 12 176 24551 24576 14601 24625 H650 14675 14699 24714 24748 14773 176 6 15 177 24797 H822 14846 24871 24895 14920 14944 14969 14993 250HJ 177 7 17 '78 25042 15066 25091 25115 15140 25164 25188 25213 15137 15261 '78 8 20 '79 15185 15310 15334 25358 25382 25406 15431 25455 15479 15503 '79 9 22

180 15527 15551 15576 25600 15624 25648 25672 25696 15710 157# 180 18' 25768 25792 25816 25840 25864 25888 25912 25936 25959 15983 18' , 2 '82 16007 16031 26055 26079 16103 26126 26150 26174 16198 16221 '82 2 5 183 16145 26269 16193 26316 16340 26364 16387 26411 16435 16458 '83 3 7 '94 26482 26505 26529 26553 26576 26600 16623 16647 26670 16694 184 4 9 185 26717 16741 26764 26788 16811 26834 26858 16881 16905 16928 185 5 12 '86 16951 16975 16998 27011 17045 27068 17091 27114 17138 17161 '86 6 14 187 17184 27107 27231 27254 27177 27300 27323 27346 27370 27393 187 7 16 '88 27416 17439 27462 27485 27508 27531 27554 27577 27600 27623 '88 8 19 '89 27646 27669 17692 27715 17738 27761 17784 27807 17830 17853 '89 9 21

190 27875 17898 17921 17944 27967 27990 28012 18035 18058 28081 190 19' 181 03 18126 18149 28172 18194 18217 28240 28262 28185 18308 19' , 2 '92 28330 28353 28375 28398 28421 26+43 '&466 '&488 28511 28533 '92 2 , 193 28556 28578 28601 28623 28646 28668 28691 28713 28735 28758 193 3 7 194 28780 18803 18825 28847 28870 18891 18914 18937 28959 18981 184 4 9 195 '900' 19026 19048 29070 29093 19115 29137 29159 29181 29203 195 5 11 196 29226 19148 29270 29292 29314 29336 29358 29380 29403 19425 196 6 '3 197 29447 19469 29491 29513 29535 19557 29579 29601 29613 29645 197 7 16 '98 29667 19688 29710 29732 29754 19776 29798 29810 29842 29864 '98 8 18 '99 29885 19907 29929 29951 29973 29994 30016 30038 30060 30081 199 9 20

200 30103 30125 30146 30168 30190 30111 30233 30255 30276 30298 200 20' 30320 30341 30363 30384 30406 30428 3<k19 30471 30492 30514 20' , 2 202 30535 30557 30578 30600 30621 30643 30664 30685 30707 30728 202 2 4 203 30750 30771 30792 30814 30835 30856 30878 30899 30920 30942 203 3 6 204 30963 3"&4 31006 31027 31048 31069 31091 31112 31133 31154 204 4 8 205 31 175 31197 31218 31239 31160 31281 31302 31323 31345 31366 205 5 11 206 31387 31408 31429 31450 31471 31492 31513 31534 31555 31576 206 6 13 207 31597 31618 31639 31660 31681 31701 31723 317+4 31765 31785 207 7 15 208 31806 31827 "&46 31869 31890 31911 31931 31952 31973 31994 208 8 17 209 31015 32035 32056 31077 32098 32118 32139 32160 32181 32201 209 9 19

210 31222 32243 32263 32284 32305 32325 32346 32367 32387 32408 210 21' 32428 32449 32469 32490 31511 32531 32552 31572 32593 32613 21' , 2 212 32634 32654 32675 32695 32716 32736 32756 32777 32797 32818 212 2 4 213 32838 32858 32879 32899 31919 32940 32960 31981 33001 33021 213 3 6 214 33041 33062 33082 33102 33123 33143 33163 33183 33203 33224 214 4 8 215 33244 33264 33284 33304 33325 33345 33365 33385 33405 33425 215 5 10 216 33445 33466 33486 33506 33526 33546 33566 33586 33606 33626 216 6 12 217 33646 33666 33686 33706 33726 33746 33766 33786 33806 33826 217 7 14 218 33846 33866 33886 33905 33925 33945 33965 33985 3 .... 5 34025 218 8 16 219 34044 340 ... 3;os, 34104 34124 341+4 34163 34183 34203 34223 218 9 18 ,

0 1 2 3 4 5 6 7 8 9

106

LOGARITHMS

No. 2800-3399 Log. 447U 531 35

0 1 2 3 4 5 6 8 9 51 t1

0 7 fig .

280 "''''716 +4731 +47<47 +4762 +4778 "'''793 +4809 +4814 ,- "4855 280 281 +4871 ...... +4902 +491 7 +1932 +19"8 +4963 +1979 +199" "SOlO 281 1 2 282 45025

,_ ''''56 45071 'S<l87 " 5102 45111 45133 45148 15163 282 2 3

283 ""5179 45194 45209 "SllS 45240 45155 15271 45266 'IS301 "'5317 283 3 , 284 -'15332 -45347 45362 4S)78 45)9] 45408 "S'42~ 454]9 ",,5'154 "5-'169 284 4 0 28' "5485 15500 45515 -45530 45545 45561 45576 45591 '56" 45621 28' 0 8 286 45637 -45652 45667 <15682 45697 4571) 15728 -457"'3 45758 "'5773 286 0 9 287 45788 45803 45818 "'5834 45849 45864 45879 "'5894 45909 45924 287 7 11 288 459J9 "'5954 45969 45985 46000 46015 16030 460"'5 46060 46075 288 8 12 289 46090 46105 -46120 46135 46150 46165 46180 16195 -'16210 -'16225 289 8 14

290 46240 46255 46270 ..0285 400C 46315 -'16)30 463 .. 5 46)59 4637-4 290 291 -46389 ...... ... ,,' %434 ..... , ...... .... " ..6<194 46509 4(52) 291 1 1 292 46538 1655) 46'60 "6SS) ""911 .... 13 %627 46642 46657 16672 292 2 3 293 ..... , .046702 46716 46731 46746 %761 -46716 46790 46805 0\6820 293 3 • 294 4&E13S '60'" ... " 46879 ",,9< 46909 46923 46938 46953 46968 294 • 6 295 46982 46997 47012 .. 1026 47041 47056 47070 47085 47100 47115 295 • 7 296 47129 "71# .. 7159 47173 47188 47203 47217 47232 41246 47261 296 0 9 297 47276 47290 47305 47320 "'7334 .. 7349 47363 47378 47393 "7407 297 7 10 298 47422 47436 47-451 47465 47480 47494 47509 475lJt ,,7538 47553 298 8 12 299 'i7567 47582 47596 4161 1 47625 +7640 47654 47669 47683 17698 299 • ., 300 47712 47727 47741 47756 47770 17784 47199 47813 "7828 1 7&42 300 301 47857 4787 1 "'86 <1900 4791-4 41929 47943 479 58 47972 47986 301 1 1 302 4Bool 4B015 ... " , .... 48058 4807) '8087 48101 " 6116 48130 302 2 3 303 481# 481 59 -48173 481 87 "'S202 04821 6 48230 48245 18259 4827) 303 3 • 3D' 48287 48302 48316 -48330 48345 48359 48373 "8387 48402 48-416 304 • 0 30. 4&430 48#-4 "8"58 48473 48487 -48501 -48515 48530 485044 48558 3D. • 7 300 48572 48586 "8601 -48615 -48629 -48M3 -48657 48671 48686 48700 306 • 9 307 48714 -48728 -48H2 48756 4877C 48785 -48799 .048813 ... " ..... , 307 7 10 308 48855 -48869 -48883 48897 48911 48926 48940 -4895-4 -48968 -48982 308 8 11 309 48996 -49010 4902-4 .049038 -49052 "'" ,- -4909-4 49108 .0491-22 309 • 13

31 . 491)6 49150 -491 6-4 49178 49191 49206 49220 49234 492-48 49262 310 311 49276 49290 49)04 493 18 49332 -4'13% -49360 4937 -4 49)88 -49-402 311 1 1 312 49416 49-429 -4944) 49-457 49-471 49485 49499 -49513 .049527 49541 312 2 3 313 -49554 "568 49582 49596 4961 0 -49624 -49638 -49651 49665 49679 313 3 • 314 49693 .049707 .049721 49734 -49748 49762 -49776 -49790 -49804 49817 31. • 6 315 -49831 .0498-45 49859 49872 49886 49900 .049914 .049928 -49941 -49955 315 6 7 316 .049969 49982 49996 50010 50024 50037 50051 50065 50079 50092 310 • 8 317 50106 50120 50133 501-47 50161 50174 50188 50201 50215 50229 317 7 10 318 50243 50156 50270 5028-4 50297 50311 50325 50338 50352 50365 318 8 11 319 50)19 50393 -, 50·nO 50004 50441 50-461 50-4H , .... 50501 319 • 12

320 50515 50529 S05-42 50556 S0569 50583 505% S0610 50623 5O611 320 321 50651 "', .. 50678 50691 50105 5071 8 S07l2 SOHS 50159 50772 321 1 1 322 50186 50199 50813 50826 508-40 50853 SOS66 50880 50893 50907 322 2 3 323 50920 50934 50941 50961 5097.04 50981 51001 5101-4 51028 51041 323 3 • 32. 51055 51068 51081 51095 51 108 51122 51135 51 1-48 51162 51 115 32. 4 , 32S 51188 51201 51215 51228 51242 5125S 51268 51281 51295 51 308 325 6 7 326 51322 51335 51348 51361 51375 51388 51.0402 51-415 51-428 51442 326 • 8 327 51-455 51468 51.0481 51495 51508 51521 515 14 515-48 51561 51574 327 7 9 328 51587 51601 5161-4 51 621 516<0 51 654 51667 51680 5169) 51706 328 8 11 329 51720 5173] 517% 51759 51n 2 51786 51799 51 812 51825 51838 329 • 12

330 51851 51865 51878 51891 51904 5U17 519]0 5U·O 51951 51970 330 331 51 983 51996 "000 520n 52035 52048 52061 52075 52088 52101 331 1 1 332 52114 52127 52140 52153 52166 52179 52192 52205 52218 52231 332 2 3 333 52244 52258 52271 5228-4 52297 52310 52323 52336 523-49 52362 333 3 • 334 52375 52388 52-401 52414 52-427 52-4-40 52-453 52466 51-479 51-492 334 • 5 335 52505 52517 52530 52543 52556 52569 52582 52595 52608 52621 335 5 0 336 52634 52M7 " ... 52673 "686 52699 52711 5272-4 52737 52750 330 0 8 337 52763 52176 52789 52802 52815 52827 52840 52853 52866 52879 331 7 9 338 52892 52905 52917 52930 529-4) '''56 52969 52982 52994 53007 338 8 10 339 5)020 5]03) ,- 5]058 53071 'lOS' 530'.17 53110 5)122 531)5 339 9 12

0 1 2 3 4 5 6 7 8 9

107

LOGARITHMS

No. l400 3999 Log. 531 48 60'95

a 1 2 3 4 5 6 7 8 9 5<" 0 lig .

34. 53148 53161 5317) 5)186 53199 53212 53225 53237 SllSO 53263 34. 341 53275 53288 S3301 53314 53326 53339 53352 53365 53377 5))90 341 1 1 342 5)103 53"'5 SJ428 53441 53453 51-466 53479 53491 5350; 51517 342 2 3 343 53529 5) 5 .. 2 5]555 5) 567 53580 5)593 53605 53618 53631 5)613 343 3 • 344 5)656 53069 536$1 53694 51706 5)719 53712 5)74" 53757 5)769 34. • 5 345 53782 SJ795 53807 53820 53832 53845 53857 53870 53883 53895 345 5 6 346 53908 Sl'nO 5)9)) 539-45 SJ958 53970 5]983 53995 ,- 504020 346 6 8 347 54033 5040"6 S40'8 S.oW71 '4083 54096 54108 54'21 54133 5'''45 347 7 • 348 541SS 54170 54183 54,95 54208 54220 54233 5-4215 S'l2SS 5"'270 34' • ,. 34. 5'1283 54295 54307 5-4320 54332 543-45 54357 54370 5-4382 5-4)9-4 34. • 11

35. 54-407 5-4"'9 5<4432 5"'''44 54456 54469 54481 54494 5<,.. 5'1518 350 351 54531 5 .. 54] 54SSS 54568 54580 54593 54605 54617 54630 54M2 351 1 , 352 54654 5-4667 54679 5-4691 54704 54716 54728 5-'1741 5-4753 54765 352 2 2 353 54778 54790 54802 5-4814 5-4827 54839 54851 54864 5-4876 54888 353 3 • 354 54900 5491) 54925 5"'937 54949 54962 549].4 54986 54998 55011 364 • 5 355 55023 55035 55047 55060 55072 55084 55096 55108 55121 55133 35. 5 6 356 55145 55157 55169 SS1B2 55194 55206 5.5218 55230 55243 55255 366 6 7 357 55267 55279 55291 55303 55315 55328 55340 55352 55361 55376 357 7 9 358 55388 55400 SS413 5S'US 55437 55<149 55461 55-473 55-'185 55497 358 • ,. 359 55509 55522 55534 555"'6 55558 55570 SSSB2 55594 55606 55618 359 • " 36. 55630 55642 55654 55666 55679 55691 55703 55715 55727 55739 36. 361 55751 55763 55775 55787 55799 55811 55823 55835 55&41 55859 36' , , 362 55871 55883 55895 55907 55919 55931 55943 55955 55967 55979 362 2 2 363 55991 '6003 56015 56027 56039 '60SO 56062 5607'" 56086 56098 363 3 • 364 56110 56122 56134 56H6 56158 56170 56182 56194 56206 56217 364 • 5 365 56229 56241 56253 56265 ",on 56289 56301 56313 56324 56336 365 5 6 366 56348 56)60 56372 56384 56396 56407 ,..." 5&01 S6443 56455 366 • 7 367 56467 56478 56'190 56502 56514 5"6526 56538 "',.., 56561 56573 367 7 8 368 56585 56597 "608 56620 56632 'MM 56656 "'667 56679 '6691 368 8 I . 36. 56703 56714 56726 56738 56750 56761 56773 56785 56797 56808 36. • " 37. 56820 56832 " .. , 56855 56"7 56879 "'''' 56 .. ' 5691 4 56926 37. 371 56937 56949 5696.1 56973 " .... "'" 57008 57019 570)1 57043 371 , , 372 57054 57066 57078 57CM 57101 57113 57124 571)6 57148 57159 372 2 2 373 57171 57183 57194 57206 57217 57229 57241 57252 sno< 57276 373 3 • 374 57287 57299 573 10 57322 57])4 57345 57357 57368 57380 57392 374 • 5 375 57403 57415 57426 574)8 57449 57461 57473 57484 57496 57SC17 37S 5 6 376 57519 575)0 57542 5755) 57565 57577 57588 57600 57611 57623 376 6 7 377 57634 576'16 57657 57669 57680 57692 57703 57715 57726 57738 377 7 • 378 57749 57761 57772 57784 57795 57907 S7818 57830 57&41 57853 378 8 • 379 5786'1 57875 57887 57B98 57910 57921 579]) 579+4 57956 57967 379 • 10

380 57978 57990 58001 59013 59024 58036 '80<7 59058 58070 58081 38. 38' 58093 58104 58115 58127 58138 58150 58161 58172 581&4 58195 J81 1 , 382 58206 58218 58229 58240 58252 58263 58275 58286 58297 58309 382 2 2 383 58320 58331 5834) 58354 58365 58377 58388 58399 5&411 58422 383 3 3 384 58433 58+44 58456 58467 5&478 58-490 58501 58512 58524 58535 394 • 5 385 58546 58557 58569 58580 58591 58602 58614 58625 58636 58648 385 5 6 300 58659 58670 58681 58693 58704 58715 58726 58737 58749 58760 300 6 7 387 58771 58782 58794 58805 58816 58827 58838 58850 58861 58872 387 7 8 388 58883 58894 58906 58917 58928 58939 58950 58962 58973 58984 388 • • 389 58995 '900' 59017 59028 '9040 59051 '906' 59073 , .... 59095 38. • ' 0

390 59107 59118 59129 59140 59151 59162 59173 !m&4 59196 59207 390 391 5"218 59229 59240 59251 59262 59273 592&4 59295 59306 59318 391 , , 3.2 59329 59)-40 59351 59362 59373 59384 59395 " ... 59417 59428 392 2 2 393 59439 59-450 59461 59472 59483 59495 ",.. 59517 59528 59539 393 3 3 394 59550 59561 59572 59583 59594 59605 59616 59627 59638 59649 394 • • 395 '%60 59671 ,%" 59693 59704 59715 59726 59737 59748 59759 . 395 5 6 396 5.,.,70 59781 59791 59802 59813 59824 59835 , .... , ' .. 51 , .... 396 6 7 397 59879 " ... "901 5991 2 ,m3 59931 59945 "." 59967 ,,.n 397 7 8 398 "'" "'" 6001. 600" 60032 ..... , 600,.. 60065 600" 60086 398 • • 399 60097 60108 60119 60'30 6OH' 60152 60163 60173 6OIS1 60195 399 • ,.

a 1 2 3 4 5 6 7 8 9

110

LOGARITHMS

No. 5lOO 5799 Log. 71600 76335

0 1 2 3 4 5 6 7 8 9 5" 1ig. 0

520 71600 71609 71617 71625 716H 71M2 71650 71659 71667 71675 520 521 71684 71692 71700 71709 71717 71.725 717]4 71742 71750 71759 521 1 1 522 71767 71 775 71784 71792 71800 71809 71817 71825 71834 718<42 522 2 , 523 71850 71859 71867 71875 71883 71892 7>900 71908 71917 71925 523 3 3 52. 71933 719<41 71950 71958 71966 71975 71983 71991 71999 72008 52' • 3 525 72016 72021 72033 120041 720.49 72057 72066 12074 72082 72090 525 5 • 525 72099 72107 721 1S 72123 72132 72HO 721.048 71156 72165 72173 525 5 5 527 72181 71189 72198 72206 72214 72222 72231 72239 72247 72255 527 7 6 528 72263 72271 "' .. 72288 72296 72105 72313 72)21 723" 72])7 528 8 7 529 72>16 7235-4 72362 72)70 72318 72387 72395 72403 724" 72-419 529 • 8

530 71-428 72436 72 ...... 72452 7H50 72469 72477 12485 72 .. 93 72501 530 531 72510 72518 72526 72531 72S42 72550 72559 72567 72575 72583 531 1 1 53' 725<)1 72599 72608 72616 72624 72632 72640 726<18 72656 72665 532 2 2 533, 72673 72681 72689 72697 72705 72713 72722 72730 72736 72746 533 3 3 53' 72754 72762 72770 72779 72787 72795 72803 72811 72819 72827 53' • 3 535 72835 72844 72852 72860 72868 72876 72884 72892 72900 72908 535 5 • 536 72917 72925 7293) 72941 72949 72957 72965 72973 72981 72989 535 , 5 537 72997 73006 73014 73022 73030 7 3038 73046 73054 73062 73070 537 7 6 538 73078 73086 73094 73102 731 11 73119 73127 73135 73143 73151 538 8 7 539 73159 73167 73175 73183 73191 73199 73207 73215 73223 73231 539 • 8

540 73239 73247 73256 7l2M 73272 7)280 71288 73296 7330-4 73312 540 541 73320 73328 73136 71344 73352 73360 17368 73376 17384 73392 541 1 , 542 71<00 73408 73416 71424 71432 73440 73 ... 73456 ".,., 73472 542 2 , 543 73480 73488 73496 73504 73512 73520 73528 73536 73S44 73552 543 3 2 544 73560 73568 73576 73584 73592 73500 7l508 73616 73624 73632 544 • 3 54' 73610 736048 73656 73 .... 73672 73680 7J687 736'15 73703 73711 54. 5 • 546 73719 73727 73735 73743 73751 73759 73767 73775 73783 73791 546 5 5 547 73799 73807 73815 73823 73831 73838 73846 73854 73862 73870 547 7 6 548 73878 73886 73694 73902 73910 73918 73926 73914 73941 73949 548 8 5 54. 73957 73965 73973 13961 73989 73997 74005 74013 74021 74028 54. • 7

550 74036 74044 74052 74060 74068 74076 74064 74092 74099 74107 550 551 7411 5 14123 74131 74139 74147 74155 74162 74170 74178 14166 551 1 1 552 74194 74202 74210 74218 14225 14233 74241 74249 14257 14265 552 2 , 553 14273 74280 74266 74296 74304 14312 74320 74328 74335 14343 553 3 2 654 74351 74359 74367 74375 74382 74390 74)98 7440' 74414 74422 554 • 3 555 74429 74437 7,.., 7445] 14461 7«68 74476 7 ..... 74492 74500 555 5 • 556 74508 74515 74523 745]1 1453'1 74547 14554 74562 74570 74578 556 5 • 557 74586 745')) 74501 74509 74617 74625 74632 746040 7<.,8 74656 557 7 5 558 14663 74671 74679 74687 74695 74702 74710 74718 74726 74713 .58 8 6 55' 74741 74749 74757 14765 74772 14780 74788 74796 7 .... ' 74811 559 • 7

560 74819 74827 74834 74842 74850 74858 H'" 74873 74881 "'59 560 561 74896 ,,90< 74912 14920 14927 14935 7494] 74950 74958 74966 551 1 1 562 74974 14981 74989 74997 75005 75012 75020 75028 75035 75043 562 2 , 563 75051 75059 75066 75074 75082 75089 75097 75105 751 13 75120 563 3 , 56' 75128 75136 75143 75151 75159 75166 75174 75182 75190 751 97 56' • 3 565 75205 75213 75220 75228 75236 75243 75251 75259 75266 75214 585 5 • 566 75282 75289 75297 75305 75312 75320 75328 75335 75343 75351 556 6 5 567 75358 75366 75374 75381 75389 75397 75404 75412 75420 75427 567 7 5 568 75435 75«' 75450 15458 75465 75473 75481 75488 75496 7550. 588 8 5 56. 7551 1 75519 75527 75514 75542 75549 75557 75565 75572 75580 56. • 7

570 75588 75595 7560' 75610 75618 75626 756]) 756041 75648 75656 570 571 75661 75671 75679 75686 75694 75702 75709 75717 75721 75732 '71 , 1 572 75740 75717 75755 75762 7IDO 75n8 75785 75793 75800 75808 572 2 2 573 75816 75823 75831 75838 75846 75853 "'" "'" 75876 " .... 573 3 , '74 75891 75899 759 .. 75914 75921 75929 75937 75944 75952 75959 .74 • 3 575 7596" 75974 75982 75989 75997 76005 76012 76020 76027 76035 57. 5 4 576 7 .... ' 76050 76057 76065 76072 76080 76088 76095 76103 761 10 576 • 5 577 76118 76125 76133 76140 761 i8 76155 76163 76170 76178 76185 577 7 5 578 76193 76200 76208 76215 76223 76230 76238 76245 76253 76260 578 8 5 57. 76268 76275 76283 76290 76298 76305 76313 76320 76328 76335 57. • 7

0 1 2 3 4 5 6 7 8 9

113

LOGARITHMS

No. 7000 7599 Log. &4510 88076

0 1 2 3 4 5 6 7 B 9 6<' 0 fig .

700 84510 8-4516 84522 84528 8-4535 84541 .... 7 84553 84559 .. ,.. 700 70' IH572 &4578 84,... 84590 &4597 .... , ..... ... " 64621 Sot628 70' , , 702 816).4 .... 0 ..... ... " ... SS ...., 8-4671 ... n .... , ..... 702 2 , 703 ... % &4702 "'08 &4714 ..,,. 84726 &4131 84739 ..,,, &4751 703 3 2 704 &4757 6476] .mo 8-4776 &4782 "'88 &4194 ... 00 .... , ..." '04 • 2 705 ..." ... " 8483' "'" ..... ... 50 ... 56 .... , ..... ... ,. 705 , 3 706 .... , .... 7 ... " ..... "90' 8<4911 8-4917 .. ,,. &4930 &4936 '06 • • '07 ... ., 84,..8 ..... ..... .. %, 84973 84979 .. OS, .... , .... , 7ID 7 • 708 '500' 85010 85016 85022 .502' 850)" .- ..... 85052 85059 708 • , 709 '506' 85071 85077 '508' .SOS. '509' 85101 85108 85"" 85120 709 • 5

710 85126 85132 85138 851+1 85150 851 56 85163 85169 85175 85181 71 0 711 85187 85193 85199 85205 65211 85216 85224 85230 85236 85HZ 711 , , 712 85248 8S1S4 85260 85266 85272 85279 8528S 85291 85297 8530) 712 2 , 713 'SlO'> 85315 85321 85327 8Sll3 853]9 85346 85352 85358 8536-4 713 3 2 714 85370 85376 85382 85388 SS," ' .. 00 ...... 85412 8~19 85<" 71. • 2 71' 85-431 85007 ,5+1, ,5+1' 8Y1SS .... , .... 7 85-471 85479 .,." 715 5 3 71. 85491 85497 85503 85510 85516 85522 85528 8553-4 SS'" " .... 716 • • 717 85552 85558 SS564 85570 85576 85582 SS588 855~ 8_ 8S606 717 7 • 71 . 85612 85619 85625 .,." 85637 '56" 8 .... 8S655 8566' .5667 '18 8 , 719 85673 85679 85685 85691 .,.., 85703 85709 85715 85721 85727 719 9 , 720 85733 85739 857"5 85751 85757 85763 85769 85775 85782 85788 720 721 8579" 85800 85806 85812 85818 8582" 85830 85836 858"2 85&48 '21 , , 722 8585" 85860 85866 85872 8 5878 8588" 85890 85896 85902 85908 722 2 , 723 859H 85920 85926 85932 85938 859+4 85950 85956 85962 85968 723 3 2 72. 8597.of 85980 SS986 85992 "998 ..... 860" 860,. 8602' .. 028 724 • 2 725 860,.. 860<0 86046 860" "OS, ..... 860" 86016 ...., ..... 725 5 3 7,. ...... "'00 "'06 86112 86118 8612" .. ,,, .. ,,, 86H2 861"8 726 6 • 727 86153 86159 86165 86171 .. m 86183 .. ,,. 86195 .. ,., ",.7 727 7 4 728 86213 86219 .. 225 .. ", .. ", 862"3 862"9 .. '" 86261 .. '" 728 8 , 729 86273 86279 86285 .. ,., .. ,., 86303 .. '" 863,. "'20 .. ". 72' 9 , 730 86332 86338 863"" .. ,SO "'56 .. ,,' .. ,.. 86l7.of .. , .. .. , .. 730 731 86392 86398 ..... 86"'0 864,. 864" 86"27 86"33 86"39 86445 731 , , 732 8M51 3M57 86"63 ...... 8M75 8M81 86"87 8M 93 8M99 86505 732 2 , 733 86510 86516 86522 86528 8653.of 865"0 865"6 86552 86558 8656" 733 3 2 ' 34 86570 86576 .. ", .. ", 86593 "'99 .660' 86611 86617 866" 734 • 2 '35 866" 866" .... , .... 7 866" 86658 8 .... 866" 866" .... , 73' , 3 736 ..... ..... "700 " 706 86711 86717 .. ", .. 729 86735 86Hl 736 • • 737 867"7 867 53 86759 "764 .. no .. no "7" "'88 8679" 86800 737 7 • 738 ..... ... " 8681' "'" 86829 ... " .... , .... 7 ... " ...59 738 • 8 5 739 ..... ... " ... " ...., ..... ..... 86 ... ..... ..." 86917 739 9 , 740 86923 86929 86935 .... , 869"7 86953 ... 58 ...... 86970 86976 740 '41 ... " "OS8 ..... ..... 87005 87011 87017 87023 87029 87035 ' 41 , , '42 870"0 870% 87052 87058 870M 87070 81076 87081 87087 87093 742 2 , '43 87099 87105 871 11 87116 87122 87128 8713" 87HO 871"6 87152 743 3 2 744 87157 87163 87169 87175 87181 87187 87192 87198 8720" 87210 744 4 2 74' 87216 87222 87227 87233 87239 872"5 87251 87256 87262 87268 74'

, 3 ' 4. 872H 87280 87286 87291 87297 87303 87'" 87315 87320 87326 74. 6 • 747 87332 87'" "'4< 873SO 87355 87161 81367 87373 87379 873&4 747 7 4 748 87390 87396 87 .. ' 87408 87"'3 8H19 87"25 8701 8H37 874<' 748 8 5 749 87448 8745<4 87460 87 .... 87471 87477 810483 87489 87495 87500 , .. , , 750 87506 87512 87518 87514 87529 87535 87541 87547 87552 8"'. 750 751 87564 81570 87516 87581 87587 87593 875" 87605 87610 87616 751 , , 752 87622 87628 87633 87639 87645 87651 87'56 87662 87668 87674 752 2 , 753 87680 87685 87691 87697 87703 87708 87114 87720 81726 87131 '53 3 2 75' 87737 87743 87H9 87754 87760 87766 87772 87777 87783 81789 754 4 2 755 87795 87800 87806 87812 87818 87823 87829 87835 87841 87&46 755 , 3 756 87852 87858 87864 87869 87875 87881 87887 87892 87898 "904 ' 56

, • 757 87910 87915 87921 87927 87933 87938 8794<4 87950 87956 87961 757 7 • 758 87967 87973 87978 87984 87990 ."'. 88001 8800' "'" 88019 758 • 5 759 88024 880)0 88036 .... , .... 7 88OS' 88059 ..... 880" 880" 759 9 ,

0 1 2 3 4 5 6 7 B 9

127

1° lOGS. OF TRIG. FUNCTIONS 18/ 0

, Sine Diff. Cosec. Tan. Diff. Cotan. Secant Dift. Cosine

,. .• 2. (11) 44594 90 t .(1') 55~ 1 .(8) '"611 90 1.(11) 55389 0.(1 0) '00017 1 .(9) 99983 ". ., ..... 91 55316 44701 91 55299 000" 99983 ., 44715 55225 44792 55208 000" 9998 3 ., 448 .. 90 55135 ... " 9Q

55118 000" 99983 ., 44954 89 55046 44971 89 55029 000" 99983 90 90 37·0 ..... 90 54956 ..... 90 54939 000" 99983 23' ., 45114 89 5 ..... 45151 89 5-484' 000" 999S3 ., 45123 89 54777 4U40 90 5 .. 760 000" , .. ., ., 45311 89 5<688 <&5330 89 ""7' 000 .. ..,,,

. , """ 88 54599 4541 • 88 54581 000 .. m" " .. ."" 89 54511 455,)7 89 54493 000 .. 99982 22' . , 45518 88 54422 45596 88 5+<0. 000 .. 99982 . , ,- 88 5-433-1 ..... 88 54316 000 .. 99982 . , 4$754 88 54246 .. S7n 88 54228 000 .. 99982

·s 45'42 88 54158 ..... 88 54HO 000" 99982 3g.o 45910 88 54070 ..... 88 54052 000" 99982 21' . , ...... 87 53982 46036 87 53964 00018 99982 ., 46105 88 53895 46123 88 53877 000 .. 99982 ., 46193 87 53807 46211 87 53789 000 .. 99982 ., "'OO 86 53720 46198 87 53702 000 .. 99982 .... .., ..

87 53634 ,.,,, 86 53615 000 .. "'" 2~ . , .... ,

87 53547 464" 88 53529 000 .. "98' ., .. 540 Il6 53<60 46559 Il6 5)441 000" ...., ., .. ". 86 5337<4 ..... Il6 53355 000" ..,,, ., 46711 86 53288 46131 86 SJ269 000" m "

41 -0 .. 79. 86 53202 m" 86 S3183 000" 99981 19' ., ..... 86 53116 "90' 86 53097 000" ..,,, ., 46970 86 53030 ..... 86 5)011 000" 99981 ., 47056 85 529+4 -47075 85 52925 000" 99981 ., .. 71 .. ' 85 52859 .. 7160 85 528 .. 0 000" 99981 .... .. 7216 85 52771 ~n"5 85 52755 000" 99981 1" , "7311 85 52689 "7330 85 52670 000" 99981 , .. 7396 85 5260-4 .. 7-415 85 52585 000" 99981 ., .. 7 .. 81 85 52519 .. 7500 85 52500 000" 99981 ., "7566 .. 5HH .. 7585 .. 5H 15 000" 99981

'H .. 7650 .. 52350 .. 7669 85 52331 000" "981 17' ., '"" 84 52266 '"54 84 522<+6 0002. " ... ., -47818 .. 52182 "7838 84 52162 0002 • ..... ., 4790l 84 52098 41'" 84 52018 00010 " ... . , .7986 8.1 52014 ..... ID 5,9'}4 000" " ... .... ..... 84 51931 ..... 84 5191 1 000" " ... 16' ., 48153 8.1 51841 48173 III 51827 000" ", .. ., 48lJ6 8.1 511M "'50 8.1 511 .. 4 0002. ",,, ., 48319 8.1 51681 .. 8339 III 51661 0002. 99980 ., .... , 8.1 51598 4"22 III 51518 0002. 99980 .... 48<85 82 51515 .. SSD5

82 51495 000" 99980 ". ., 48567 8.1 51433 48587 83 51413 000" 99980 ., ..... 82 51350 48670 83 51330 000" 99980 ., -48731 82 51268 48753 82 51241 000" 99979 ., .... 14 82 51 186 48835 82 51165 000" m79 .... ..... 82 5110-4 -48917 82 51083 000" m79 14' ., 489" 82 51022 ...., 82 51001 0002. 99979 ., ..... B' ,.,40 "908-' 8' "'19 00021 ..,,,

• .. 91 ... 82 SOB59 ..9161 82 SOB38 0002' 99979 ., mu 8l 50717 .. 92 .... 8' 50756 000" 99979

47·0 .. 930 .. 8l 50696 49'" 8l 50675 00021 99979 /J ' '2 49385 8l 50615 49406 8l 50594 000" "''' . , ..... 8l 505H 49 .. 87 8l 50513 000" 99979 ., "95 .. 7 80 50453 .. 9568 80 50432 000" 99979 ., "9627 81 50313 .. 9648 81 50352 000" 99919 .... .. 9708 50292 "9729 50271 000" 99979 12'

1780

358 0

129

2° LOGS. OF TRIG. FUNCTIONS 182~

, Sine Diff. Cosec. Tan. DifI. Cotan . Secant Oilf. Cosine

"., 2.(8) 54212 1 .(11).045718 2.(8) 54308 1.(11)-45692 0.(10) 00017 -

72 73 1.(9)99914 60' , 54354 45646 5011 45619 00017 "''' • 544]6 72 45574 .... , 72 45541 00017 "''' • 54498 72 moo 54'" 72 45475 00017 "''' •• 545" 72 -45,430 545" 72 45..03 00017 "''' '1'2 72

01 ·0 .- 72 -45358 .....

72 45331 00027 99973 W ., 54714 "'5286 5474' 45259 00027 99973 ., 54786 72 -4521-4 54813 72 45187 00017 99973 ., 54851 71 45143 54884 71 45116 00017 99973 " 54928 71 "5072 54955 71 -45045 00027 99973

71 72 , ... ..000 72

4S001 55011 71 -44973 00027 "''' '8' " SS011 .... ," ..... "'-4902 00017 99973 " SS10a 71 ... '" 55170 72 ... ,. 00028 99972

• S51tl 70 . " .. m .. 70 .... 760 0001' "''' " 5528) 71 .. 4717 SSJtt 71 .... , 00028 99972 71 71 ",' 55354 70

+16 .. 55)82 70 44618 00021 99972 '" " 5542-4 44576 55452 44548 00028 99972

• 55495 71 44505 SSSl) 71 4-4-477 00018 99972 " 55565 70 4+135 SSS,] 70 4<4407 00028 99972 " 55615 70 "-4365 55661 70 -+4337 00028 99972

70 71 .,,' 55705 70 +t295 557].4 ., .... ,,, 0001' "''' U' " .. ns 44225 55803 +4197 0001' "''' • ..... 70 44155 ..'" 70 404127 00018 "''' • 55915 70 +108, 55944 71 +40" 00019 "''' " 55984

., ... 16 5601) 6' 0987 00019 "''' 70 70

05' 56054 6'

-439046 5608) 6'

<43917 00019 99971 '" " 5612] <43877 56152 43848 00019 99971 " 5619) 70 <43807 56U2 70 43778 0001. 99971 " 56262 6' <43738 56291 69 <43709 0002. 99971 , 56)]! 6' 43669 56360 69 4]640 00019 99971

.9 6' .... ..... ., <3'" 56<429 6'

43571 00019 "''' 54' " ..... 43531 56<498 43502 00019 99'171 " S6538 6' -430462 56567 69 -4J433 00019 99'171 " ..... 68 41394 ,66,. .,

4))64 OOOlO 99'170 ., 6' " 56615 68 43325 56105 68 43295 OOOlO 99'170

ON 56143 68 -43257 56773 68 43221 00030 99970 53'

" 56811 69 43189 5684' 69 43159 00030 99970

" 56880 68 43120 56910 68

43090 00030 99970 " 50 ... 68

-41052 56918 68 4J022 OOOlO 99970 'S 51016 68

42984 "046 68 ~2954 OOOlO 99970

01' 57'" 67 -42916 57114 .7 m .. 000]0 99970 ,,,.

" Sltst 68 <1.49 5118t 68 -42819 OOOlO "'70 • 5nf9 42781 sn49 42751 OOOlO 99'170 " sn81 68 -42713 57311 68 42683 00030 99970

67 68 " 57354 .7 426-46 57385 67

42615 00031 99969

09·0 57421 68 42579 57452 68 42548 00031 99969 :;1' " 57489 -4251 1 s7520 42-480 00031 99969 " 57556 67 42-4+1 51581

67 42-413 0003f 99969

'. 51623 .7 42377 57654 67 42346 00031 99969 " 57690

67 42310 S1nf 67 42279 00031 'm. . 7 67 10·0 57157 67

42243 "'08 .. 42212 00031 ,m, "" " 51823 . 7 42177 51854 67 42146 00031 "''' , S1890 67 42110 5792f 67 42079 00031 "''' " 579S7 -42043 S7988 42012 00031 "''' " 58023

.. 41977 58054 .. 41946 00031 99969 .. 67

11 ·0 58089 .. 41911 58121 .. 41879 00032 99969 '" " satss 67 -41845 58187 67 41813 00032 99968 , 58222 41778 58254 41746 00032 "".

" 50'" .. -41712 58310 .. ., ... OOOJl ''''' 65 65 " 58]53 .. 416-47 'Ol" .. 41 61 S OOOJl ''''' lU 5a..19 41581 584S1 41549 OOOJl ''''' 48'

1770

3570

140

5° lOGS. OF TRIG . FUNCTIONS 185'

- Sine Parts Cosec. Tan. Parts Cotan. Secant ParIs Cosine

00·. 2 .(8) 94010 - 1,(11 )05970 2 .(8) 9.,95 - 1 ,(1'1 05805 0.(10) 001 66 1.(9)99334 .. 01·0 94174 ·1 14 05826 94)40 ·1 I • OS660 00167 99833 02·0 94]17 ·2 28 05683 .... , ·2 29 05515 00168 99832 03,0 94461 ., 43 05S)9 94630 ., 43 05371 00169 998]1 04·. 94(0) ·4 57 05397 94773 ., 57 05227 00170 99830 05-0 94146 ·5 71 05254 94917 ·5 72 05083 00171 99829 SS' .... 94887 ·6 85 OSI1) 95060 ·6 86 0-4940 001n 99828 07·0 95019 ·7 99 CH,)7' 95201 ·7 100 04798 00173 99827 .... 95110 ·B 114 04830 """

·8115 ... " 00175 99826 .... 95110 ·9128 ...... " ... -9 129 04514 00176 mH

10 -0 95450 ·1 14 omo 95621 0073 OOIn 99821 W' 11 -0 95589 0«" 95161 '1 14 0<231 00178 99821 12·0 9sns ·2 28 04272 "908 ·2 28 0<4093 00179 99821 13·0 95867

., 41 (41)) ..... , ., 42 0)953 00'" 99820 14·0 ' 600' ·4 55 03995 961 81 -4 55 03813 00181 99819 ·5 69 ·5 69 15·0 96143 ·6 83 03857 96326 ·6 83 0367S 00181 99817 /.{j' 16·0 96280 ·7 96 03720 ...... ·7 9? 03536 00184 99816 17-0 96417 -8 110 03583 96602 -8 III 03398 00185 99815 18-0 96553 -9124 03+47 96739 -9 125 03261 00'86 99814 19-0 9668. 03311 96877 03123 00187 99813 ,.., 96815 ·1 13 03175 9701 3 02987 00.88 99812 W 21-0 96960 03040 911 50 ·1 13 02850 00.90 99810 "., 97095 ·2 27

02905 9121U ·2 27 02715 00191 99809 23-0 97219

., 40 02711 91421

., 40 02579 00'" , .... 24-0 97,.) ·4 53

02637 97SS. ·4 54 ., .... 00193 "807 ·5 67 ·5 67 ,.., 97 .... ·6 '" 02504 9169t ·6 81 '2309 OOt94 99806 '" 26-0 91629 ·7 " 02371 91825 ·7 9\ 02175 OOt96 9980' 21-0 97762 -8107 02238 91959 -8 l OB 02041 00191 '980) 28-0 91894 -9120 02106 .8092 -9 121 01908 00198 '980' 29-0 98026 0197 .. . 8225 01775 00i99 99801

30-0 98151 018 .. 3 98358 ·1

01642 00200 99800 ,. 31 -0 98288 ·1 13 01712 98490 13 01510 00202 99798 32-0 98419 ·2 26 01581 98622 ·2 26 01378 00203 99797 33·. 98549 ·3 39 01451 98753

., 39 01247 00204 99796 ,.., 98619 •• 52 01321 ..... ·4 52 01116 00205 99795

.8808 ·5 65 01192

·5 65 ... " "'.7 99794 35" ·6 78 99015 ·6 78 '" 36-0 989)7 '7 91 01063 99145 ·7 91 006" 00'08 99791 37 -0 ..... -8103

..,,. "''' -8104 00725 002., 99791 ,. .• 99194 -9 116 00806 9940' -9 ll7 00'96 002 •• 99790

39-0 99m 00678 995" ...... ..,11 99789 ... , 99" • 005SO ... " 00318 002U 99787 20-41-0 99577 ·1 13 00423 "'91 ·1 13 00'09 ..,1< 99786 42-0 99'04 ·2 25 00296 99919 ·2 25 00081 00215 99785 43-0 998* ·3 38 00170 - - ·3 38 0 -(10) 9995 .. 00217 99784 .... 999" .. 50 ~

1 _(9) 00041 ·4 51 99826 002.8 99782 -- ·5 63 00114 ·5 63 45-0 1.(9) 00061 ·6 75 0 .(10) 99918 00301 ·6 76 99700 00219 99781 Ut ... , 00207 ·7 88 99793 004" ·7 89 99573 0022. 99780 47-0 00]]2 -8100 99668 00553 -8101 99+47 oom 99778 .. ,. 004 .. -9 113 99'+1 006" -9114 99321 00'" 99777 49 -0 ... 81 99 .. 20 0080' 99195 0022< 99716 .... ..,04 "''' 009,. 99070 00226 99775 10' 51 -0 ...,. ., 12 99172 •• 0<5 ·1 12 98945 00227 99713 52-0 009<. ·2 24 ..... , 01179 ·2 25 98821 ..". 99nI 5,.. 01074 ·3 37 98926 ono] ., 37 996" 0022. 99771 ,.., OU K .. 49 ,.... 01 411 ·4 49 98573 00211 99769 55-0 01318 ·5 61 98682 01550 ·5 62 98'SO 00211 99768 ,-... , .. - ·6 73 98S60 01673 ·6 74 98321 002)) 99767 51 -0 01561 ·7 85 98"]9 01796 ·7 86 98204 00215 99765 58 -0 01681 ·8 98 98318 01918 ·8 99 98082 00216 997M 59-0 01803 -9110 98197 02040 -9 III 97960 001]7 99763 60-0 01924 98077 01161 97838 00219 99761 0'

IH~

354'

258

15°1 HAVERSINES L-~-r-----r-----T~~=T----~-----.4

.0 .2 A .6 B -Log. Nat.

I -2.or (S. ) o 00

" 02 03 04 05 00 07 08 09 10 11

" 13 14 15 16 11 18 19 20 21

" 23 24 25 26 27 28 29 30 31 32 33 34

35 36 37 38 39 40 41 42 43 44 45 .. 47 .. 49 50 51 52 53 54

" " 57 58 59

231-40 01704 11115 01707 Ill)f 01711 23427 01715 23523 01719 23618 01123 23713 01726 2]809 01730 23904 01734 2399'.1 01738 2409" 01742 24189 01745 2<4283 01749 24378 01753 24472 01757 24567 01761 24661 01764 24755 01769 24850 01772 24944 01776 25037 01780 25131 01784 25225 01788 25319 01791 25412 01795 25505 01799 25599 01803 25692 01807 25785 01811 25878 01815 25971 01818 26064 01822 26156 01826 26249 01830 26341 01834 264]4 01838 26526 01842 26618 01846 26710 01850 26801 01854 26894 01858 26986 01861 21077 01865 21169 01869 27261 01873 21352 01877 27443 01881 27534 01885 27626 01889 27717 0189) 27807 01897 27898 01901 27989 01905 28080 01909 28170 01913 28260 01917 28351 01921 28441 01925 28531 01929 28621 01933

PARTS for 0' .1:

Log . Nat. Log Nat. Log. Nat. Log. Nal.

2.or(S.)

23159 23255 23350 23446 23542 23637 23712 23828 23923 24018 24113 24208 24302 24397 24491 24586 24680 24n4 248" 24962 25056 25150 25244 25337 25431 25524 25617 25710 25804 25897 25989 26082 26175 26267 26360 26452 26544 26617 26729 26821 26912 27004 27096 27187 27179 27170 27461 27553 27 .... 2nn 27826 27916 28007 28098 28188 28278 28369 ,.. .. 28549 28639

o.

01704 01708 01712 01716 01720 01723 01727 01731 01735 01739 01742 01146 01750 01754 01758 01761 01765 01769 01773 01777 01781 01784 01788 01792 01796 01800 01804 01808 01811 01815 01819 01823 01827 01831 01835 01839 01843 01847 01850 01854 01858 01862 01866 01870 01814 01878 01882 01886 01890 01894 01898 01902 01906 01910 01914 01918 01922 01926 01930 01934

.8

LOGS 9

2.or(S.) O.

23178 23274 23370 23<6' 23561 23656 21751 23847 23942 24017 24132 24227 24321 24416 24510 24605 24699 24793 24887 24981 25075 25169 25262 25356 25449 25543 25636 25729 25822 25915 26008 26101 26193 26286 26378 26471 26563 26655 26747 26839 26931 27022 27114 27206 27297 27188 27480 27511 27662 27153 27844 27934 28025 28116 28206 28297 28387 28471 28567 28657

.6

01705 01709 01713 01717 01720 01724 01728 01732 01735 01739 01743 01147 01751 01755 01758 01762 01766 01770 01774 01777 01781 01785 0178'1 01793 01797 01801 01805 01808 01812 01816 01820 01824 01828 01832 01836 01840 01843 01847 01851 01855 01859 01863 01867 01871 01875 01879 01883 01887 01891 01895 01899 01903 01907 01911 01915 01919 01923 01927 01931 01935

2.or{S.) 0.

23197 23293 23389 23484 235ao 23675 23711 23866 23961 24056 24151 24245 24340 24435 '14529 24624 24718 24812 24906 25000 25094 25187 25261 25375 25468 25561 25655 25748 25841 25934 26026 26119 26212 26304 26397

2 .... ' 26581 2667l 26765 26857 26949 27041 27132 2n24 27315 27407 27496 27589

"'80 27711 27862 21953 2804' 28134 28224 28315 "<0, 28495 28585 28675

.4

01706 01710 01713 01717 01721 01725 01729 01732 01736 01140 01744 01148 01751 01755 01759 01763 01767 01771 01774 0~778

01782 01786 01790 01794 01798 01801 01805 01809 01813 01817 01821 01825 01829 01832 01836 01840 01844 01848 01852 01856 01860 01864 01868 01872 01876 01880 01884 01888 01891 01895 01899 01903 01907 0191 1 01915 01919 01923 01927 01931 01935

2.or(8.) O.

23216 23312 23408 23503 23599 23694 23790 23885 23980 24075 24170 24264 24359 24454 24548 246042 24737 24831 24925 25019 25112 25206 25300 25393 25487 25580 25673 25766 25859 25952

2"" 26138 26230 26323 26415 26508 26600 26692 26784 26876 26967 27059 27151 27242 27334 27425 27516 27607 27698 27189 27880 27971 28061 28152 28242 28333 28423 28513 28603 28693

.2

01707 01710 01714 01718 01722 01726 01729 01733 01737 01741 01745 01748 01752 01756 01760 01764 01768 01771 01775 01779 01783 01787 01791 01794 01798 01802 01806 01810 01814 01818 01822 01825 01829 018n 01837 01841 01845 01849 01853 01857 01861 01865 01869 01873 01876 01880 01884 01888 01892 01896 01900 01904 01908 01912 01916 01920 01924 01928 01932 01936

NATURAlS negligible

Log Nat.

2.or(S.} 0

2J235 23331 23427 23523 23618 23713 23809 23904 23999 2409' 24189 24283 24378 24471 204567 24661 24755 24850 24944 25037 25131 25225 25319 25412 25505 255'i9 25692 25785 25878 25971 26064 26156 26249 26341 26434 26526 26618 26710 26802 26894

01707 01711 01715 01719 01723 01726 01730 01734 01738 01742 01745 01749 01753 01757 01761 01764 01768 01772 01776 01780 01784 01788 01791 01795 01799 01803 01807 01811 01815 01818 01822 01826 01830 01834 01838 01842 01846 01850 01854 01858

,

" " " ~ 55 ~

" " " " ., ., 47 ., 45 ., 47

" ., .. 39 39 31 39 35

" 33 32 31 30

" " " " " " " " 21

" 26986 01861 19 27077 0186S 18 21169 01869 17 I 27261 01873 16 27352 01877 15 i 27443 01881 14 27534 01885 13 27626 01889 12 21717 01893 11 27807 01897 10 27898 01901 09 27989 01905 OS 28080 01909 07 28170 01913 06 28260 01917 05 28351 01921 04 28441 01925 03 28531 01929 02 28621 O19JJ 01 j 287"001~~4;

334

HAVERSINES 91 ' 92 ' 93 ' 94 ' 95 ' 96 '

Log. Nat. Log. Nat. Log. Nat. Log. Nat. Log. Nal. Log. Nat. - , ., , ., , , , ., , ., , , , ., , , , ., , , , ., , ., ,

O V .2 a; ., 5 ., , ., 5 ., , ., 5 ., , , 5 ., , , 5 ., , ., 5 ., , • . . " , , N ., , ., , ., , ., , ., , ., , , , ., , ., , ., , ., , ., , • .. . -• 0 , 10 ., 11 ., 10 , 11 , •• ., 11 , • , 11 . , • , 11 . , • ·8 ." - 0 , . , 1 .or{S. ) o. 1 oriS ) o. l. or{9. ) 0 l .or(S.) o. 1.o r{9. ) o. l.o r(9. ) o. ,

00 '06" 50873 71)81 5t H S nftl 52617 12815 53<188 13516 54358 14215 55226 .. ot '066' S0887 71399 S~760 12124 52631 72817 53502 US)8 5072 ,.". 5.5241 " 02 70673 50902 71411 51714 72136 52646 7284' 53517 7354' 5.087 74137 55255 " 03 , .... 5091 6 7'423 51789 111-48 52660 '186' 53531 7)561 ,<60' 7424' 55270 " 04 70698 50931 71436 51 80) 71160 52675 72813 5)546 "'" 54-i16 74160 55284 " 05 10710 50945 71+48 5181 8 11172 52689 "886 5]560 13584 5040430 14211 55299 " OS 10723 50960 71460 51832 11184 527CH 72896 53575 "' .. 54445 74283 55313 " 01 70735 50914 11472 518-'17 71196 52718 72908 53589 13607 54459 741" 55328 " OS 70748 50989 71484 51861 11208 52733 12920 5360-4 7J619 5+4704 74306 553'12 " .. 70760 S1004 714'6 51876 11nO 52H8 71911 53618 73630 , ... , 74317 55357 " 10 70711 51018 71509 51890 122ll 52762 72943 53633 73641 54503 74328 55371 .. " 70785 51033 71511 51905 "'" 52776 72955 53617 73653 5451 7 74]40 55386 .. t2 70797 51047 71511 51919 1115' 52791 72967 53662 73665 54532 74351 55'" .. 13 70809 51062 71545 51934 mM 52806 72978 53676 73676 54546 74362 554'" 41 14 70811 51076 71557 51948 12180 52820 12990 53691 "698 54561 74374 55429 .. " 70834 51091 71569 51963 12291 .52835 13001 53705 73699 54515 741BS 55 ..... 3 45 18 70841 51105 71581 51978 12104 52849 not4 53720 73111 54590 74396 55458 .. 11 10859 51120 71594 51992 12316 52864 73015 53734 7J721 54604 ,- 55472 43 18 70871 51134 71606 52007 71Jl8 52878 13031 53749 73734 54619 7 .... " 55-487 .. 19 70884 51 149 71618 52021 71340 52893 13049 53763 73146 5463) , .... 30 55501 .. 28 10896 51 163 716)0 520)6 71351 52907 "060 53778 7J151 54647 , ... , 55516 40 2t , ... , 51 178 71641 52050 71363 52912 73012 5)792 73769 ,<66' ,.," 555JO JO

" 70921 5119) 71654 52065 12375 529J6 "086 53807 7)780 566" , .... 55545 31 2J 70933 51207 "'" 51079 71387 52951 'J096 53821 13791 54691 7 .... 75 55559 31

" 70945 51212 71679 52094 m .. 52%5 71107 53836 'J80' 54705 "'" 55573 38 .. 70958 51236 71691 52108 12411 52980 7Jllt 53850 718tS 54720 ", .. 55588 35 28 70970 51251 71703 5212) 1241l 52994 nlll 53865 ,,.,, 54734 ,- 55602 " 21 '098' 51265 71715 52137 nos "000 711 41 53879 7.)118 54749 "'" 55617 31

" '099' 51280 71727 52152 nw 53023 7]154 538').4 ~ 54763 74532 55631 32 29 11007 51 294 71739 52166 12459 5)038 73166 53908 'J860 54178 "5" 55646 " 30 11019 51309 71151 521 81 1l61. 53052 1]117 5)923 'J81l 54792 74554 '5660 30 3t 110]2 51323 1116) 52196 12482 5]067 7] 189 5)937 ,,.., , ... , "'" 55675 29

" 71044 51338 71715 52210 "''' 53081 73201 53952 ']89' 54811 74517 , .... '" 33 11056 51352 11781 52225 11506 530% 73211 53966 "906 548)6 ,,, .. 557G4 " 34 1 1068 51367 11800 51239 11518 53110 13n4 53981 71918 , .. SO , .... 55718 " 3S 11081 51382 11812 52254 71530 53-125 lJ2J6 S)9<}5 73929 , ... , 74611 55732 " 38 71093 51 396 11814 52268 11542 53140 73241 54010 73941 54879 74611 55747 " J1 71105 51"11 71836 52283 71554 53154 7)159 5-4024 73951 54894 746)3 55761 " " 71118 5H2S 11848 52297 71565 53169 73171 5-4039 73964 54908 "". 55776 " " 11130 51440 71860 52312 71571 53183 73281 5-4053 1)975 54923 74656 55790 " 40 71142 51454 11872 52326 71589 53198 73194 , .... , 7J987 54937 "'61 55805 " .. 71154 51469 71884 52341 12601 53212 73306 54082 13"8 54952 74618 55819 19 42 71167 51483 11896 52355 12M3 53227 73311 54097 " ... 54966 74690 55834 " 43 71119 51498 11908 52370 12625 53241 73)29 54111 74011 $4980 74701 55848 11 .. 71191 51512 11910 5238<1 12637 53256 73]41 54126 74031 54995 74712 55862 16 4S 7120) 51527 11932 52399 12648 53270 1])52 5'1140 ,- 55009 7472] 55877 " .. 71216 51541 71944 52413 '1660 53285 7])64 54155 74055 55024 74734 55891 " 41 71218 51556 11956 52428 12672 53299 13375 54169 '606' 55038 74146 55906 1l .. 71140 51571 11968 52+42 12684 5331'1 73387 54184 14018 55053 74751 55920 " .. 71251 51585 71980 52457 72696 53328 73399 54198 14089 '506' 74168 559)5 11 so 71265 51600 71"2 52472 12108 53343 73410 54213 74101 55082 74719 55949 10 51 11171 51 614 "004 " ... 721t9 53357 73422 54227 14112 '509' 74791 55964 " " 71289 51629 72016 52501 121Jl 53372 730J 54242 14114 55111 ,- 55978 .. 53 7UOl 51643 12028 52$15 12743 5)]86 73 .... 5 54256 74135 55125 l.fl1U 55992 07 54 11114 51658 "060 52530 11155 53-401 73457 54271 74146 55140 14114 5600' .. ss mu 51672 non 52544 12167 5)415 " ... 54285 14158 55154 14'" 56021 .. 56 lU)8 51681 11 ... 52559 11118 5)4JO ,,- ",OO 74t69 55169 ", .. 56036 .. " 71350 51701 72076 52571 m .. 534+1 71491 5'1114 14181 55183 "'58 56OSO 03 56 71362 51716 n ... 52588 11801 51459 73S03 54329 14192 55197 ''''' '606' .. 59 ltJ15 51730 "'00 52602 72214 5347) 73.515 54143 '610, 55212 ,- 56079 ot so ltl87 51745 72112 51617 11815 " ... 13.516 54358 74115 55226 ,,89' '60'1' GO

268 ' 267' 266 ' 265 ' 264 ' 263 '

354

NATURAL FUNCTIONS OF ANGLES /----------.- --- - -------------1

NATURAL TANGENT S

0'

u ' -001l0(I """" 47 -07237 48 ·1106' 49 -15007

SO 1-19175 51 ·25490 52 ·2799-1 53 -32704 54 -3763a

SS '- 42815 56 ·48256 57 ·53987 58 60033 59 ·S&t28

60 1-73205 61 ' ·804OS 62 J.88073 63 ' ·962£1 &I 2·05030

65 2·14451 66 2·245().1 67 2·35535 68 2·47509 69 2-60509

70 2·14748 71 ,·9IM21 72 3-0n68 73 3·21085 74 :1-48741

15 3·13205 76 ( ·01078 n 4·33148 78 H0463 79 5·'44!>6 .. " " " "

5-67128 6-31375 711~7

8-14435 9·51436

85 11-(30 86 14·301 67 19·061 86 28-636 89 57·290

'" .

" """ ... " "''' 11452 15443

"'" '''''' "'" 33187 38145

4l3H 48816 54576

"'" "'" 1-73905 J.81150 , ,88867 1-97111 2-05942

2·15432 2·25663 2·31m3 2·48753 2-61874

2·76247 ,.,.-3-29139 3-51053

H5a28 4·04061 4·36623 4·74554 5, 'M93

5·72'974 6·36587 7· 20661 6-26356 9·6768

11 ·~

14·669 19·740 30-'45 63-657

'" .,"', '"'' -118'4

"'" 2002' 24375

"''' "''' "'53

"'" 49376 55170 6' 283 67752

' ·74610 ' ·81 900 ' -89&67 1 · 97~7 , . ..., 2-,&o! 2Q 2<26730 2·3789' 2·50018 am2 2·m61 2·937' 8 3-1 14601 ;)·;)1216 ,..,"" 3-78-185 . ·01127 4040152 4-78673 5·24218

5·78938 5·45961 7·30018 8·38625 9·8448

1101109 15·056 20·445 31·821 71 ·615

'" ''''53 0 ....

""" "'" "'" "'''' """ "'" '''''' "'" 44418 ."". 55767 81914 88419

, ·75319 1·82654 1 ·~72 ,·98828 2·01785

2·1741 6 2·27806 2-39056 2·51289 2·64842

2-79269 2·95437 ;) · 1~1

333317 3·55761

;)·81117 4·10218 4·43735 H2U2 5·29235

5·8S024

''''''' 1·3gel8 8·51259

10·019

I 2· I 6:l 15·464 21·205 33·694 81 ·847

,.' 0"'" "''''" 06749

"'" , .. n

""" '"'' "'53 """ 39679

44958 5-0512

"''' 62546

"'''' 1·76032 1·83413 1·91262 1·99695 2-06716

2·1 8-119 2·28691 2 .(1)235

2-52$71 2·66046 , . .." 2·971 •• 3·15240 ;)·35-443 3·56160 , . .,.. 4·13350 4·. 7374 4·87162 5·3-'345

5·91236 6·61220 7·49465 6·64275

10· 199

12· 429 15·895 22 ·022 35·601 &5· 489

"" 01 761

""" 09131

"'" ,,"" 2 1310 25717

""" 35142 40195

45501 51084 56969 63165 89766

1·76749 1-114177 1·92098 2·00569 2·09654

2·1 9430 ,,,... 2·41421 ,.-2·67462

2·82391 ,.""" 3·17159 3·37594 ,.""" 3·86671 4·165-30 4·51071 491516 5 ·39552

5·&7576 6· 69116 7-59575 8 ·77689

10·385

12706 16·350 22·904 38·188

114·60

'" 02117 05747 .... 13428

"'00 21742 26169 307&5

"53' 40714

46046 51656 57675 63826 71)446

1·77471 1·84946 1·92920 2·0U'9 2·10600

2·20449 2·31086 2·42618 2·551 ro 2·68892

H13965 3·00611 3·19100 3·39171 , ..... 3·fl9.t74 4· 19756 4·54826 4·95945 5·4455 7

HI4051 6·77199 7-69957 8·91520

\0·579

12·996 1!3-832 23 ·859 40·917

143·24

'" 02474 06117

""" "'" 17916

"", "''' '"'' 3Il134 41235

46595 52235 58194 64471 71 I 2"9

1-78198 16572(l

193746 2·02335 2·11552

2-21 475 2·32197 2· 4382$ 2·56487

'''''''' 2-85556 3·02372 3·21063 3·41973 3·65538

3·92318

."""" 4·58641 5~51

5_

6·11)66.( 5·85475 7·80622 H15789

10·780

,.' '"'' ...., 102~

'<2" "",. 2lel2 mm 31745

"'" 41759

47146 526 16 58797 65 120 7161 7

1·7892"9 1·86500 1·94579 2·03227 2·12511

2·22510 2·333 17 2045043 2·57815 2·71792

2·87181 3·(14152 3-23(1.18 3·u m 3-68061

3·95196 4·26::152 4·62518 HS037 5·55777

6·1H19

E·93952 7·91582 9·20518

10·966

13·300 13·617 17·343 17-S86 24 ·898 le ·031 44·1)66 47·740

HIO·98 286·46

54'

" " " " " 03192 56 118 177 237 296 06B62 61 123 1~ 245 307 10672 &3 127 191 255 319 14&32 66 132 199 2ti5 331 18754 69 138 Z07 276 344

23050 72 143 216 288 359 27535 75 150 225 300 375 32224 76 157 235 314 392 3710.. 82 164 247 32"9 41\ 422&6 88 172 259 345 431

47700 91 181 272 362 453 53400 95 19 1 266 382 477 59414 TOO 201 302 403 S04 85?? 2 105 213 319 426 533 72509 113 226 339 452 564

1·79665 12(l 240 360 481 &10 1·87283 128 255 363 511 639 1·95411 136 273 409 546 6a3 2·04125 146 292 438 584 731 2·13417 151 314 471 629 7116

2·23553 2·34447 2-46270 2-59156 2-73263

2·88783 ,,-, "'" 3·460156 3-70616

393111 4·29724 4·66-458

"'-5·6 1397

6· 24321 1·02&37 8·02548 9·35724

11 ·205

13·95 1 16·454 27-27 1 52·cal

512·96

HI9 338 >06 677 546 183 366 549 732 915 199 391 596 795 ~

Mean d,ffe<ences no longer $Ull,eie ntly accurate.

352

NATURAL FUNCTIONS OF ANGLES

NA TUR AL COSIN ES

$ ubtrael · M • • n Olfferenc •• • , 0' " 12' 16' '" 3D' 36' 42 ,"' 54 ' • " "

, "

, " 0·707" ",,, 70463 70339 70215 ''''''' ''''' 69'" 69717 69591 " " 52 S3 ,~

" ·6946E 69340 69214 , ... "'" """" """ 68582 "." "'" " " " " 'M

" "'" "''' 679'- 61816 '"'' 67559 67430 67301 61172 ,,,,, " " .. " '" ., ·66913 "'" .." "'" "'" "'" 66131 ""'" "'" "'" " .. " " ' 00

" "'" 6So174 '5'" 66210 "''' '"'' "''' ,,,,,

'"'' &1412 " .. " " '" " 0·601279 6414$ ""''' "''' "'" """ ,,'" "'" '''''' """ " ., "

., '" " ,"'"' "'" """ "". "'" "''' 62115 81978 81 84 1 'H" " " " " , ..

52 ·61566 61429 6 1291 61153 61016 .. " . ,," "'" ..... .. ," " .. 69 " '" " ·60181 '''''' """ 59763 "'" "'" 593<12 ,m, , .. , ""'" " " " ,.

'" " ·5a119 "'" "''' "''' "''' 54'" ,,,,, 57786 57643 57501 " " " " '" " 0-5 7358 57215 57071 56926 "". "'" 56497 ..,,,

"'" "'" " ., n " '" " -55919 55775 """ 55464 55339 55194 ",., 54." 5H~6 54610 " " " " '" " ·54464 54317 54171 54024 53877 53730 53583 53435 S32S8 53140 " " " " '" " ·52992 52844 '"'' 52547 52399 52250 52101 S1gs2 51803 51653 " " " " '" 59 · 51~ 51354 """ 510501 ""'. S0754 ''''''' 50453 5Ol02 50151 " " " "" " " " ,SOOOO "'" 49697 49546 493904 49242 . .,., .,," 46786 "'" " " " '"' .. " ·4&461 "'" 46175 "." "'" 47716 (751)2 47409 47255 47101 " " " '" ,~

" ·4~1 46793 OS,"~ ..... .,,'" 46175 .""" ",S> 45710 .,,~ " " n '"' '" " '."" 45243 """ .. '" U776 .. '" 44464 44307 44 151 "'''' " " '" '" "" " ·43837 "'''' "'" "'" """ "OS, " ... .,," 42578 42420 " 53 " '"' '" os 0·4l2(l2 421G4 "'" 41787 41628 ... " 41310 41151 "'" """ " 53 " '00 m .. ·f0674 4(1514 ... " """ ""'" , .. " 39715 "~SS, "'" "'" " 53 .. '"' ,~ ., ·39073 "''' 38752 "''' """ "'" 38107 "'" on" "'" " " " '" '" .. ·37461 "'" 37137 "''' "''' " .. , "''' "'" "'" """' " ,. " ". '" 69 ·35837 350674 35511 35347 35184 ''''' 34857 34694 '''''' '"'' " " " '09 '"

" 0·34202 3,"" "''' 33110 33545 33381 33216 "'" 32S87 32722 " " " "" '" " ·32557 32392 32227 "00' 31900 31730 3151)5 3 1 3~ 31233 """ '" " " ''" .. " ... , "',,, 30570 "''", 30237 JOO71 """ 29n7 "''' 294()4 '" " " '" '" " ·29237 '''''" "''''' 28736 28569 28402 28234 "''''' 27899 2773 1 '" " " '" '" " ·27584 27300 27228 "M» "'" 26724 , .. " ''''' 262 19 ,,...

'" " " '" '" " 0-25&62 25713 ,,,OS 25376 25207 ''''' "'" 2HOO 24531 24362 '" " ss '" '" " ·2U92 20'" "'" "'" 2351 4 ",,, 23175 ,- "'"

,,, .. '" " .. "3 '" n ·22495 "'" 22155 "'" 21814 21644 21474 "'''' 21132 "'" '" " .. '" '" " ·207'91 """ ,,,OS,, "'''' "'''' "'" "'" 19595 "." 19252 " " " '" '" " ·19081 18910 ''''' 18561 "'" "'"

, .. , """ m'" 17!>37 " " " '" '" .. 0 ·17365 17193 11021 "'" 16677 """ '''''' 16160 "'" 151116 " " " '" ". " · 1150643 15471 ''''' 15126 '''50 14781 .. "" 14436 '"'' """ " " " '" ... " ·1 3917 137 .. 13572 ,,,,,

"'" "OS, """ "''' 12S33 "'OO " " " '" ... " ·12167 12014 11840 11667 11 494 1I 32Q 1 \I ~ 7 10973 "'''' , .. " " " " '"

,., .. · lo.t53 10279 101 1)6 09932 09' " """ ",on 09", "'" _.

" " " '" '" " 0·06716 oas" "''"' 08194 - 07846 07672 07498 0732~ 071 50 " " " " a '" as ·06976 -, """ 06453 06279 06105 0593\ 05756 05582 ~"a " " " '" '" " ·05234 """' """ 04 711 04536 04362 "' ... 04013 """ "'" " " " '" '" " ·03490 """ 03141 """ 02792 02618 02443 02U9 """' 01920 " " " '"

,., " ·01745 01571 01396 o.m 0 l().l1 """ """ 00520 0030' 00175 " " " '" ,os .,

"""'"

362

RADIANS TO DEGREES

• c • • • • 000 -002 ·004 -006 ·00'

0 0 0 0 0

·50 28 36·9 26 45·7 26 52·6 28 59·5 29 ... 51 29 13·3 29 20· \ 29 27·0 29 33·9 29 40-8

·52 29 47·6 29 54·5 30 01 ·4 30 08-3 30 15 · \ 53 30 22·0 30 28-9 30 35 ·8 30 42·6 30 49·5

" 30 56· 4 3 1 03·3 31 10 ·\ 31 17·0 31 23·9

55 31 30·8 31 37·6 31 44 ·5 3 1 51· 4 31 58·3

" 32 05" 32 12-0 32 18'9 32 25-8 32 32·6 57 32 39 ·5 32 46·4 32 53·3 33 00 1 33 07·0 56 33 13·9 33 20 ·6 33 27·6 33 34·5 33 4 , ·4

·59 33 48·3 33 55·' ,. 02·0 ,. 08·9 ,. 15·8

·60 ,. 22·6 34 29·5 ,. 36·' ,. 43- 3 ,. 50·2 ·61 ,. 57·0 35 03-9 35 10·8 35 17·7 35 24 ·5 62 35 3 1·4 35 363 35 45 ·2 35 52·0 35 58 ·9 63 36 05-8 36 12·7 36 19·5 36 26·4 36 33·3 6. 36 40 -2 36 47 -0 36 53'9 37 006 37 on 65 37 14 ·5 37 2 1·4 37 28·3 37 35 ·2 37 42·0 66 37 48·9 37 55 -6 38 02·7 36 09·5 36 16· 4 67 36 23·3 38 30·2 38 37-0 38 43·9 36 50-8 6. 38 57·7 39 04·5 39 11 ·4 39 18-3 39 25·2

·69 39 32·0 39 36·9 39 45·8 39 52·7 39 59 ·5

70 40 06'4 ' 0 13·3 40 20·2 .. 27·0 .. 33·9 71 40 40-8 .. 47 ·7 40 54·6 41 01·4 41 06·3 72 41 15·2 41 22· ' 41 28·9 41 35 ·6 41 42 ·7 73 41 49, 6 41 56·4 42 03·3 42 10· 2 42 17 · , 74 42 23 ·9 42 30·8 42 37·7 42 44·6 42 5 1 ·4

75 42 58 ·3 '3 05·2 43 12·1 <3 18·9 43 25 ·8 76 <3 32 ·7 43 39·6 <3 46·4 <3 53 ·3 44 00 ·2

·77 44 07-1 .. 13·9 .. 20 ·8 .. 27·7 44 34 ·6 ·76 44 4 1·4 .. 48·3 44 55·2 " 02· 1 " 06·9 ·79 45 15·8 " 22·7 " 29' " 36 ·4 ., 43·3

80 45 50·2 " 57 ·1 46 03·9 46 10 ·8 " 17 ·7 61 46 24 ·6 46 3 1· 5 46 38·3 46 45 ·2 46 52· 1 62 46 59 ·0 47 05·8 47 12·7 47 19·6 47 26·5 83 47 33 ·3 47 40·2 47 47· 1 47 54 ·0 48 00·8 04 48 07·7 46 14·6 48 21·5 48 28·3 48 35·2

·85 " 42·1 46 49·0 " 55 ·8 49 02· 7 49 09' 66 49 16·5 49 23·3 49 30·2 49 37·1 49 44 ·0 ·87 49 50·8 49 57·7 50 04 ·6 50 11·5 50 18·3 ... 50 25·2 50 32·1 50 39·0 50 45 ·8 50 52·7 69 50 59·6 51 "·5 51 13·3 51 20·2 51 27· 1

90 51 34·0 51 40·8 51 47·7 51 54·6 52 0 1·5 91 52 08 ·3 52 15 ·2 52 22 ·1 52 29 ·0 52 35·9 92 52 42·7 52 49·6 52 56·5 53 03·4 53 10 ·2 ·93 53 17 · ' 53 24 ·0 53 30·9 53 37·7 53 44 ·6 ·94 53 5 1·5 53 58·4 54 05 ·2 54 12· 1 54 19·0

·95 54 25 ·9 5' 32·7 5' 39·6 54 46·5 54 53· 4 96 55 00·2 55 07·' " 14·0 55 20·9 " 27·7

·97 55 34 ·6 55 41·5 55 46·4 55 55·2 56 02· ' ·96 56 09·0 " 15·9 " 22·7 56 29·6 56 36·5 ·99 56 43·4 " 50·2 " 57 · , 57 04·0 57 10·9

' ·00 57 17 ·7

363

DEGREES TO RADIANS

• • ! ~ • Q 0 , 2 3 4 5 • 7 , 9

Radians

0 0·00000 0·01 745 0 ·03491 0-05236 0 -06981 0 ·08727 0· 10472 0,12217 0-13963 0, 15708

10 ·17453 ·19199 ·20944 ·22689 ·24435 ·26160 ·27925 ·29671 ·31 41 6 ·33161

20 ·34907 ·36652 ·38397 040 143 ·41 888 ·43633 ·45379 A7 124 ·48869 ·50615

30 ·52360 ·54 105 ·55851 ·57596 ·59341 ·6 1087 ·62832 ·64577 ·66323 ·68068

40 ·69813 ·71558 ·73304 ·75049 ·76794 ·78540 ·80285 ·82030 ·83776 ·85521

" 0·87266 0 -890 12 0 ·90757 0·92502 0 ·94248 0 ·95993 0-97738 0·99484 ,·0 1229 ' -02974

60 ' ·04720 ' ·06465 '-08210 ,·09956 ,., 170 1 ',13446 ' , ' 5192 '- ' 6937 ' ·18682 '·20428

70 -22173 ·23918 -25664 ·27409 ·29 154 ·30900 ·32645 ·34390 -36136 ·37881

80 ·39626 ·4 1372 -43 117 -44862 ·46608 ·48353 ·50098 -51 844 ·53589 ·55334

90 -57080

MINUTES OF ARC TO RADIANS

• ~ < i 0 , , 3 4 5 • 7 , 9

Radians

0 0 ·00000 0 ·00029 0·00058 0 ·00087 0 ·001 16 0·00145 0 ·00175 0 ·00204 0·00233 0·002£2

10 ·00291 ·00320 ·00349 ·00378 ·00407 ·00436 ·00465 ·00495 ·00524 ·00553

20 ·00582 ·0061 1 ·00640 ·00669 ·00698 ·00727 ·00756 ·00785 ·00814 ·00844

30 ·00873 ·00902 ·00931 ·00960 ·00989 ·01018 ·01047 ·01076 ·0 1105 ·01 134

40 ·011 64 ·01 193 ·01222 ·0125 1 ·01280 ·01309 ·01338 ·01367 ·01396 ·01 425

" ·0 1454 ·01 484 ·01513 ·01 542 ·01571 ·01600 ·01629 ·01658 ·01687 ·01716

60 ·0 1745

394

l>

• ~ • o J: o C "

.

.

A

r • ,

• 1 2 , • • • 7

• 9 10 11

" 13 .. 15

" 11

" " " " " 23 .. 25 .. 21 .. 29 30 31 32 33

" 35

" 37 38 39 .. 41 .. ., 44 45

4' 41 .. 4. .. " " 53 54 55

" 61 OB 59 .. §

45' 46' 47' 48'

315' 314 313 0 312 ·00 ·00 ·00 ·00 ·02 {)2 ·02 ·02 . ., <J3 <J3 <>.l -05 -05 -05 -05 -00 {f/ ·en <l6 ·09 . .,. <J8 <J8 ·n ·10 ·10 «l ·12 ·12 ·n ·n ·14 ·14 ·13 ·13 ·16 ·15 ·15 ·14 ·18 ·17 ·16 ·16 .l9 '1' ·18 ·18 ·21 ·21 ·20 ·1' ·23 ·22 ·22 ·21 ·25 ·24 ·23 ·22 ·27 ·26 ·25 ·24 ·29 ·28 ·27 ·26 ·31 ·30 ·29 ·28 ·32 ·31 ·30 ·29 ·34 .3.3 32 ·31 ·36 ·35 ·34 .3.3 ·38 ·37 ·36 ·35 ·'0 ·39 ·38 ·36 . 2 'I "0 ·38 . 5 ·43 ·42 .. .7 .5 ·44 .2 ·49 47 ·46 -44 ·51 ·49 ·48 ·46 ." ·51 ·50 "8 ·55 ·54 ·52 ·50 '58 ·56 ·54 ·52 ·60 ·58 56 ·54 ·62 ·60 ·58 ·56 65 ." ·61 ·58 ·67 ·65 ·63 ·61 ·70 ·68 ·65 ·63 ·73 ·70 ·68 ·65 ·75 ·73 ·70 ·68 ·78 ·75 ·73 ·70 ·81 ·78 ·76 ·73 ·84 ·81 ·78 ·76 ·87 ·84 81 ·78 ·90 ·87 ·84 ·81 ·93 ·90 ·87 ·84 ·97 ·93 90 ·87

1·00 ·97 93 ·90 I'" 1·00 97 ·93 1 ·07 1·04 100 ·97 1·11 1,07 104 1·00 1-15 I,ll 1 -07 1·()\ 1<19 115 HI ),07 1·23 1-19 1-15 1 ·11 1·28 ) ,24 1-19 1-15 1·33 1·28 1 ·24 1-19 1·38 1·33 1·28 I ·'" ) ,43 1·38 1·33 1·29 1-48 lA3 1·38 1·34 1·54 1-49 ),44 1·39 1·60 1·55 1-49 }·44 1-08 }'61 1·55 1·50 1 ·73 1-67 162 1·56

IlS" 114 1330 112

2250 126 227· 228

TABLE A HOUR ANGLE

49' SO' SI ' 52' 53' 54' SS' S6'

311 0 310 309' 308 307' 306 305Q 304 ·00 ·00 ·00 ·00 ·00 ·00 ·00 ·00 ·02 ·01 ~1 ~1 ·01 ·01 ·01 ·01 . ., . ., <J3 <J3 <J3 . ., ·02 {)2

·05 .", '" '" .", .", .", <>4 ·06 ·06 <l6 -05 -05 ·05 ·05 -05 .()8 ·en ·en {f/ {f/ ·06 ·06 ·06 «l ·09 ·09 <J8 <l8 .()8 ·en {f/

·n ·10 ·10 ·10 «l ·09 ·09 ·08 ·12 ·12 ·n ·n ·n ·10 ·10 ·09 ,1' ·13 ·13 ·12 ·12 ·12 ·n ·n ·15 ·15 ·14 ·14 ·13 ·13 ·12 .]2.

·17 ·16 ·16 ·15 ·15 '1' '1' ·13 ·18 ·18 ·17 ·17 ·16 ·15 ·15 ·14 ·20 '1' ,1' ·18 ·17 ·17 ·16 ·16 ·22 ·21 ·20 ·1' '1' ·18 ·17 ·17 ·23 ·22 ·22 ·21 .,., ·1' '1' ·18 ·25 ·24 ·23 ·22 ·22 ·21 ·20 ,1' ·27 ·26 ·25 ·24 ·23 '22 ·21 ·21 ·28 ·27 ·26 ·25 ·24 ·24 ·23 ·22 ·30 ·29 ·28 ·27 ·26 ·25 ·24 ·23 ·32 ·31 ·29 ·28 ·27 ·26 ·25 ·25 .3.3 ·32 ·31 ·30 ·29 ·28 ·27 ·26 ·35 ·34 ·33 ·32 ·30 ·29 ·28 ·27 ·37 ·36 ·34 ·33 ·32 ·31 ·30 ·29 ,3' ·37 ·36 ·35 ·34 ·32 ·31 ·30 " 1 ·39 ·38 ·36 ·35 ·34 .3.3 ·Jl

·42 "1 ·39 ·38 ·37 ·35 ·34 ·33 ·44 ·43 "1 " 0 ·38 ·37 ·36 ·34 ·46 ·45 ·43 ·42 "0 ,3' ·37 ·36 ·48 ·47 ·45 ·43 ·42 .4{) ·39 ·37 ·50 ·48 ·47 ·45 ·44 ·42 "0 ·39 ·52 ·50 4' . 7 ·45 ·44 ·42 ·40 ·54 ·52 ·51 4' ·47 ·45 ·44 ·42 ·56 ·55 ·53 ·51 ., ·47 ·45 ·44 ,5' ·57 ·55 ·53 ·51 ·49 ·47 ·46 ·61 ·59 ·57 ·55 ." ·51 ·49 ·47 ·63 ·61 ·59 ·57 ·55 ·53 ·51 ·49 ·66 ·63 ·61 59 ·57 55 ." ·51 ·68 66 ·63 ·61 ·59 ·57 ·55 ." ·70 68 ·66 ·63 ·61 59 ·57 ·55 ·73 ·70 ·68 ·66 ·63 ·61 ·59 ·57 ·76 ·73 ·70 ·68 ·66 ·63 ·61 ·59 ·78 ·76 ·73 ·70 ·68 ·65 ·63 ·61 81 ·78 ·76 ·73 ·70 ·68 ·65 ·63 ·84 81 ·78 ·75 ·73 ·7. ·68 65 ·87 ·84 ·81 ·78 ·75 ·73 ·70 ·68 ·90 ·87 84 ·81 ·78 ·75 ·73 ·70 ·93 90 ·87 ·84 ·81 ·78 ·75 ·72 ·97 ·93 ·90 ·87 ·84 ·81 ·78 ·75

1·00 ·97 ·93 ·90 ·87 ·84 ·81 ·78 1·'" 1 00 ·97 ·93 ·90 ·87 ·83 ·80 10'7 1·'" 1·00 97 ·93 ·90 ·86 ·83 1-11 1·07 I ·'" 1 00 ·96 ·93 ·90 ·86 1-15 H I l·en I ·'" 1·00 ·96 ·93 ·90 1·20 1-15 l ·ll 1·()8 1·()\ 1~ ·96 ·93 1·24 1·20 1-16 1-12 1·()8 1()\ 1~ ·96 1 29 ) ·24 1·20 1-16 1-12 108 104 1~ 1·34 129 } ·25 1·20 U 6 1-12 1·08 1·()\ }·39 }·34 1 ·30 }·25 } ·21 H6 1-12 1 ()8 }·45 1·4{) 1·35 1·30 1·25 1·21 1-17 1-12 1 ·51 } ·45 1 ·40 1-35 } ·31 1·26 1·21 1-17

131 0 110 129' 128 127° 126 115° 124

129" 230 231 " 232 233' 234 235" 236

HOUR ANGLE

57' 58'

3W 302 ·00 ·00 ~1 ·01 <>2 ·02 <J3 . ., ·05 .",

<l6 ·05 {f/ ·07 <l8 .()8 <J9 ·09 ·10 ·10 ·n ·n ·13 ·12 ,1' ·13 ·15 ·14 ·16 ·16 ·17 ·17 ,1' ·18 ·20 ·1' ·21 ·20 ·22 ·22 ·24 ·23 ·25 ·24 ·26 ·25 ·28 ·27 ·29 ·28 ·30 ·29 ·32 ·30 ·33 ." ·35 .3.3 ·36 ·35 ·37 ·36 ·39 ·38 ·41 ·39 ·42 . 1 ·44 . 2 ·45 ·44

·47 ·45 ·49 ·47 ·51 ." ." ·51 ·55 ·52 ·56 ·54 ·58 ·56 ~1 ·58 ·63 ·60 ·65 ·63 ·67 ·65 ·70 ." ·72 ·69 ·75 ·72 ·77 ·75 ·80 ·77 83 ·80 ·86 ·83 . ., ·86 ·93 . ., .", ·93

'·00 ·96 1·04 100 1·()8 I ·", 1-12 1()8

11r In

237' 238

59' 60'

301 0 300° ·00 ·00 ·01 ·01 ·02 ·02 . ., <J3 .", <>4 ·05 -05 ·06 <l6 ·07 '0'7 ·08 ·08 ·10 ·09 ·n ·10 ·12 ·n ·13 ·12 ·1' ·13 ·15 ,1' ·16 ·15 ·17 ·17 ·18 ." ·zo '1' ·21 ·20 ·22 ·21 ·23 ·22 ·24 ·23 ·26 ·25 ·27 ·26 ·28 ·27 ·29 ·28 ·Jl ·29 ·32 ·31 .3.3 ·32 ·35 .3.3 ·36 ·35 ·38 ·36 ·39 ·37 .<1 ·39 ·42 ·40 ·44 ·42 ·45 ·44 ·47 ·45 ·49 ·47 ·50 ·48 ·52 ·50 ·54 ·52 .,. ·54 ·58 ·56 ·60 ·58 ·62 ·60 ." ·62 ·67 ·64 ·69 ·66 '72 ·69 ·74 71 ·77 ·74 ·80 ·77 ·83 ·79 ·86 ·82 . ., ·88 ·93 . ., ·96 ·92

100 ·96 1<>4 1·00

121 ' 12.

239" HO

£ ,

• 1 • , • • • 1

• • 10 11

" 13 .. 15 18 11

" 19

" " 22 2'

" 25

" 21

" .. 30 31 32 33 34 35

" 37 38 39 .. 41

" 43 .. .. 4. 47 48 4. 50 51

" " 54 55 58 51 OB 59 .. " ~

" o o J:

e ~ ~ o u • E • z

5' • ~ 3 • • •

0 ~ , 0 1 2 3 • 5

• 7 • • I. 11

" 13 14 15 16 17 IS 19 20 21 22 23 24 25

" 21 28

" 30 31

" 33 34 35

" 37 38 39 .. 41 42 43 44 45 46 47 48 CO 50

" 52 53

" 55 .. 57 58

" .. 0 • a

45' 46'

315° 314 ·00 ·00 ·02 ·02 ·05 ·05 ·07 ·07 ·10 ·10 ·12 ·12 ·15 ·15 ·17 ·17 ·20 ·20 .Z2 ·22 ·25 ·25 ·27 27 ·30 ·30 ·33 ·32 ·35 ·35 ·38 ·37 ·41 ·40 ·43 ·43 ·46 ·45 ·49 ·48 ·51 ·51 ·54 ·53 ·57 .5G ·50 ·59 ·63 ·62 ·66 ·65 ·59 ·66 ·72 ·71 ·75 ·74 ·78 ·77 ·82 ·80 ·85 ·84 ·88 87 ·92 ·90 .% ·94 ·99 ·97

U)3 1-01 1 -07 1·05 HI UJ9 1-15 1-13 1-19 1·17 1·23 1 ·21 1 ·28 1·25 1·32 130 1·37 1 ·34 1-41 1 ,39 1-47 1·44 1·52 1 ·49 1 ·57 1 ·54 1·&3 160 1·69 Hi6 1 ·75 1·72 1·81 1 ·78 H8 1·84 1 95 1·91 2·02 199 2·10 206 2·18 2·14 2·27 2·22 2·36 2·31 2·45 2·41

135" 1340

2250 226

47' 48'

3l JO 312 ·00 ·00 ·02 ·02 ·05 ·05 ·07 ·07 ·10 ·09 ·12 ·12 ·14 ·14 ·17 ·17 ·19 ·19 ·22 ·21 ·24 24 ·27 ·26 ·29 ·29 ·32 ·31 ·34 ·34 ·37 ·36 ·39 ·39 ·42 ·41 ·44 ·44 ·47 .4£ ·50 ·49 ·52 ·52 ·55 ·54 ·58 ·57 ·61 ·60 ·64 ·63 ·67 ·66 ·70 ·6' ·73 ·72 ·76 ·75 ·79 78 ·82 ·81 ·85 ·84 ·89 ·87 ·92 ·91 .% ·94 ·99 ·98

1 03 1-01 1·07 H 5 1 ·11 H9 U S 1·13 1-19 1-17 1 ·23 1·21 1·26 125 1·32 1 30 1 ·37 U S 1 ·42 1·39 1 ·47 1·44 I -52 1 -49 I-57 1·55 1 ·&3 160 1·69 Hi6 1 ·75 1·72 1·81 1·79 1 ·88 1·85 1·95 1·92 2·03 200 2 ·11 2·07 2 ·19 2·15 2·28 2·24 2·37 2 ·33

133' Ill'

2270 2280

TABLE B HOUR ANG LE

49' W 51 ' 52' 53' 54' 55' 56'

311 0 31 0 309' 308 3070 306 305' 304 ·00 <JO ·00 ·00 ·00 ·00 ·00 ·00 ·02 ·02 ·02 ·02 ·02 ·02 ·02 ·02 ·05 ·05 ·04 ·04 ·04 ·04 ·04 ·04 ·07 ·07 ·07 ·07 ·07 ·06 ·06 ·06 ·09 ·09 ·09 ·09 ·09 ·09 ·09 ·08 ·12 ·11 ·11 ·11 ·11 ·11 ·11 ·11 ·14 ·14 ·14 ·13 ·13 ·13 ·13 ·13 ·16 ·16 ·16 ·16 ·15 ·15 ·15 ·15 ·19 ·18 ·18 ·18 ·18 ·17 ·17 ·17 ·21 ·21 ·20 ·20 ·20 ·20 ·19 ·19 ·23 ·23 ·23 ·22 ·22 ·22 ·22 ·21 ·26 ·25 ·25 ·25 ·24 ·24 ·24 ·23 ·28 ·28 ·27 ·27 ·27 ·26 ·26 ·26 ·31 ·30 ·30 ·29 ·29 ·29 ·28 ·28 ·33 ·33 ·32 ·32 ·31 ·31 ·30 ·30 ·36 ·35 ·34 ·34 ·34 ·33 ·33 ·32

·38 ·37 ·37 ·36 ·36 ·35 ·35 ·35 ·41 ·40 ·39 ·39 ·38 ·38 ·37 ·37 ·43 ·42 ·42 ·41 ·41 AO ·40 ·39 ·46 ·45 ·44 ·44 ·43 ·43 .. 2 ·42 ·48 ·48 ·47 .4£ ·46 ·45 ·44 ·44 ·51 ·50 ·49 .. 9 ·48 ·47 .. 7 ·46 ·54 ·53 ·52 ·51 ·51 ·50 ·49 ·49 ·56 ·55 ·55 ·54 ·53 ·52 ·52 ·51 ·59 ·58 ·57 ·57 ·56 ·55 ·54 ·54 62 ·61 ·50 ·59 ·58 ·58 ·57 ·56 ·65 ·64 ·63 ·62 ·61 ·60 ·60 ·59 ·68 ·67 ·66 ·65 ·64 .&3 ·62 ·61 ·70 ·59 ·68 ·67 ·67 ·66 ·65 ·64 ·73 ·72 ·71 ·70 ·6' ·59 ·68 ·67 ·76 ·75 ·74 ·73 ·72 ·71 ·70 ·70 ·80 ·78 ·77 .7G ·75 ·74 ·73 ·72 ·83 ·82 ·80 ·79 ·78 ·77 ·76 ·75 ·86 ·85 ·84 ·82 ·81 ·80 ·79 ·78 ·89 ·88 ·87 ·86 ·84 ·83 ·82 ·81 93 91 .CJQ ·89 ·88 ·87 ·85 84

96 ·95 ·93 ·92 ·91 ·90 ·89 88 HJO ·98 ·97 ·96 ·94 ·93 ·92 ·91 1 .<J4 1 02 1 ·00 ·99 ·98 ·97 95 ·94 1-07 106 1·04 1 ·03 1·01 H O ·99 ·98 Ul H O HJ8 HJ6 ,.,5 1 04 1·02 1 ·01 1 -15 1-13 1-12 1 -10 "'9 1-07 1·06 1·05 1-19 H8 1·16 1·14 B3 H I H O 1 09 1·24 1 22 1·20 1 ·18 1·17 1·15 1-14 1-12 1 28 126 1·24 1·23 1·21 1<19 ua US 1·33 1·31 1 ·29 127 1 25 1·24 1·22 1 ·21 1·37 US 1·33 1 -31 HO 1·26 1·26 1 25 1-42 -lAO H8 1 -36 1·34 1·33 1·:n 1·29 lA7 lA5 1 ·43 1Al 1·39 1·37 1 ·36 "'4 1·52 1:50 1 ·48 H6 1·44 1·42 1·40 1·39 I-58 1·56 1 ·53 1·51 1 ·49 1 ·47 1·45 1·44 1·64 HI 1·59 1·57 1 ·55 1 ·53 1 ·51 1-49 1·70 1,67 H5 1·62 1·60 1 ·58 1 ·56 1·54 1,76 1·73 1·71 H 8 1·66 164 1·62 1 60 1·82 180 1·77 1·75 1·72 1-70 1·68 1 66 H9 H6 184 1-81 1·79 1·77 1·74 ,.,,2 Hl6 "'4 1·91 H8 1·86 183 1·81 1·79 2<J4 2·01 198 1·95 1·93 1·90 H8 H6 2·12 209 2 06 2·03 2·00 1·98 1 ·95 1 ·93 2·21 2·17 2,14 2-11 208 206 2 ·03 2·01 2·29 2·26 223 2·20 2·17 2 ·14 2-11 2·09

131 0 130 1290 128 1270 126 125' 124

2290 230 231 0 232 233" 234' 235' 236

HOUR ANGLE

57' 58'

303' 302 ·00 ·00 ·02 ·02 ·04 ·04 ·06 ·06 ·08 ·08 ·10 ·10 ·13 ·12 ·15 ·14 ·17 '17 ·19 ·19 ·21 ·21 ·23 ·23 ·25 ·25 ·28 ·27 ·30 ·29 ·32 ·32 ·34 ·34 ·36 ·36 ·39 ·38 ·41 ·41 ·43 ·43 .. 6 ·45 48 ·48

·51 ·50 ·53 ·53 56 ·55 58 ·58 ·61 ·60 .&3 ·63 66 ·65 ·59 ·68 ·72 ·71 ·75 ·74 ·77 ·77 ·80 ·80 ·83 ·83 87 ·86 ·90 ·89 ·93 ·92 ·97 ·95

1 ·00 ·99 1 ·<J4 1·03 107 1 06 1·11 HO H 5 1-14 1·19 U 8 1·23 1 ':" 1 ·28 1·26 1·32 l.:n 1-37 1·36 1·42 1 ·41 1·47 1·4£ 1·53 1·51 1 ·58 1·56 1·64 1·62 H O 1·68 1·77 H5 1·84 H2 1·91 1 ·89 1 ·98 1 ·96 2·07 2·<J4

123' 122

2370 238

59' 60'

30 1" 300' ·00 ·00 ·02 ·02 ·04 ·04 ·06 ·06 ·08 ·08 ·10 ·10 ·12 ·12 ·14 ·14 ·16 ·15 ·18 18 21 ·20

·23 ·22 ·25 ·25 ·27 27 ·29 ·29 ·31 ·31 ·33 ·33 ·36 ·35 ·38 ·38 ·40 ·40 ·42 ·42 ·45 ·44 ·47 ·47 ·50 A' ·52 ·51 ·54 ·54 ·57 56 ·59 ·59 62 ·61 ·65 ·64 ·67 ·67 ·70 69 73 72 ·76 ·75 ·79 ·78 82 ·81 ·85 84 88 87 ·91 .CJQ

·94 ·94 ·98 ·97

HI 1 00 1·05 1 <J4 109 108 1-13 1 -12 1-17 H5 1·21 1·20 1 ·25 1·24 1·30 1·28 1-34 1·33 U9 1·38 1 ·44 1·43 1·49 1·48 1 ·55 1·53 1·61 1·59 1 ·67 1·65 1 ·73 1·71 1·80 1 ·78 1·87 1·85 "'4 1·92 2·02 2·00

121 ' 120

2390 240°

0 • e ,

0 1 2 3 4 , • 1

• • 10 11

" 13 14 15 16 17 IS 19 20 21

" 23 24 25

" 21 28

" 30 31

" 33 34 35

" 37

" 39 40 41 42 43 44 45

" 47 46 4' 50 51 52 53 54 55 56 57 50

" 50

~ a

• • • E ~ • "

B

395

412

TABLE C A. a •. CORRECTION.

± ... ·30' '31 ' '32' '33' '34' .,,' .,.' '31 ' I '38' '39' '40 ' '~1 ' -42 ' -43 ' .« ' .". ' ± ~ AZIMUTHS ~ • • ~ • • • • • • • • • • • • • • • • • • 73·3 72·. 72·3 71·7 71·2 70·7 70-2 69·7 69·2 68·' 68·2 67·7 67·2 66·' 66·3 65·. • , 73-4 72·. 72·3 71·8 71·3 70-8 70·3 69·8 69·3 68·. 68·3 67·8 67·3 66·. 66·4 65·9 , 10 73-5 73·0 72·5 72·0 71·5 71-0 70-5 70,0 69·5 69·0 68·5 68·0 67·5 67·0 66·6 66·1 10 ,. 7:H 73·2 72·7 72·2 71 ·7 71·2 70·7 70·2 69·7 69·3 68·. 68·3 67 ·8 67·4 66·9 66·4 14 11 74·1 73·6 73-1 72·6 72·1 71-6 71-1 70-6 70·1 69·6 69·2 68·7 68·2 67 ·8 67·3 66·. 18 .. 74·3 73·8 73-3 ", .• 72·3 n ·. 71·3 70·8 70'3 69·9 69·4 689 68·5 68·0 67·5 GH .. 12 74·5 74-0 U 5 73·0 72·5 72'0 71-5 7H 70·6 70·1 69 -7 69·2 68·' 68·3 67·8 67-4 .. lA 74-1 74·2 73·7 73-2 72·' 72·3 71·8 71·3 70-9 70-4 69·9 69·5 69-0 68·6 68·1 67·7 .. .. 74·9 744 74·0 ?,H 73-0 72·5 72·1 11-6 7l'1 ~ 70·7 70-2 69·8 69·3 68·9 684 68~ .. .. 75·2 74·7 74·2 73·8 73-3 72·. 72· • 71·9 ?L'') 71·0 70·5 70,1 69·7 ,69·2 68·. 68·3 .. '. .. 75·4 75~ 74·5 74·1 73-6 7H 72·7 72·2 71 ·8 n·, 70'9 70-5 70·0 69·6 69·] 68·7 ,. " 75·6 7H 74·7 74·2 73·8 7.H 72·9 72·' 72·0 n·5 7H 70-6 70·2 69'S 69·3 68·9 " ,. 75·7 75·3 74·S 74·4 73-9 73-5 73·0 72·6 72·1 71-7 71-3 70,S 704 70-0 69·5 69·1 32

" 75·9 75·4 75,0 74·5 7401 73,6 73·2 72·. "'., 71·9 71 ·5 7H 70·6 70-2 69·7 69·3 " .. 76·0 75·6 7H 74·7 74 ·3 73-8 73·4 72·9 12·5 72·' 71-7 71'2 70·8 70,4 70·0 69·5 34 ,. 76·2 75-8 75·3 74,9 74·4 74-0 73·6 73·1 72·7 72·3 71·9 71-4 71-0 70·6 70-2 69·S '" .. 76·4 75·9 75·5 75·1 74·6 74·2 73·8 73·3 72·9 72·5 72·1 71-6 71·2 70-8 70-4 70·0 " ,., 76·5 76·1 75·7 75·2 74·8 74-4 74·0 73·5 7H 72·7 72-3 71·9 71·5 71·0 70·6 70·2 37

" 76-7 76-3 75·8 75-4 75·0 74'6 74·2 73·7 7J.3 12·9 72·5 72-1 71-7 71 ·3 70·9 70·5 31

" 76·9 76·5 76·0 75·6 75·2 74·8 744 74·0 73·5 73·1 72·7 72·' 71-9 n '5 71-1 70·7 ,. .. 77-1 76·6 76·2 75·8 754 75·0 74·6 74·2 73·8 73<4 73·0 72·6 72·2 71·8 n4 71~ .. ., 77-2 76·8 764 76~ 75<> 75·2 74·8 744 74-0 73·6 73·2 72·. 72-. 72·0 71-6 71·2 41

" 77-' 77-0 76<> 76·2 75·8 75·4 75-0 74·6 74 ·2 73·8 n. 73·1 727 723 n ·9 71-5 .. .. 77<> 77·2 76·8 764 76·0 15·6 75·2 74 ·9 74·5 7401 73·7 73-3 72·9 72·5 72·2 71·8 ., .. 77-. 774 77·0 76·6 76·3 75-9 75·5 75·1 74-7 74·3 73-9 73·6 73-2 ""8 72·' 72·1 .. .. 78·0 77-6 77·3 76·9 76·5 76·1 75·7 75·3 75~ 74<> 74·2 U8 73·5 7H 727 72·3 .. .. 78 'l 77 ·. 77·5 nl 76·7 76,3 76·0 75·6 75-2 74·8 74·5 7401 73·7 734 U O 12·6 .. Cl 78·4 78·1 n7 77-3 76·9 76·6 76·2 75·8 75·5 75·1 74·7 74-4 74·0 73·7 73·3 72·9 Cl .. 78'6 78·3 77·9 77·5 77·2 76·8 76·5 76·1 75 ·7 75-4 75·0 74·7 74·3 73·9 73'6 73·2 .. .. 78·9 78·5 78·1 n8 77-4 7H 76·7 76·4 76·0 75 ·6 75 ·3 74 ·9 74·6 74·2 73-9 73·6 .. .. 79·1 78·7 78-4 78·0 77·7 77-3 77-0 76·6 76·3 75·9 75·6 75·2 74·9 74-5 74 ·2 73-9 .. " 79·' 79·0 78·6 78·' 77-9 77<> 77·2 76·9 76·6 76·2 75·9 75·5 75·2 74·9 74 ·5 74·2 " 52 79·5 79·2 78·9 78·5 "'·2 77·. 77·5 77·2 76·8 76·5 76-2 75·8 75-5 75·2 74-8 74·5 51 53 79·. 79·. 79·1 78·. 7.4 78-1 77·. 774 77·1 76·8 76·5 76·1 75·8 75·5 75·2 74·8 " .. eo·o 79·7 79·3 79~ 78·7 784 78·1 77·7 774 77·1 76·8 76·5 76·1 75·8 75·5 75·2 54

50 80·2 79·9 79<> 79·' 79<) 78<> 78·3 78-0 77-7 77-. 77-1 76'8 76·5 76·1 75·. 75·5 50 .. ""5 "'·2 79·9 79·5 79·2 78 ·9 7.<> 78·3 78·0 77-7 77-. 77·1 76·8 76·5 76·2 75-9 50 67 80-7 ", .• "'·1 79·. 79·5 79·2 78-9 7.<> 78·3 78·0 77·7 77·' 71-1 76·8 76-5 76·2 ., 51 8H 80·7 80·' 80-1 79·. 79·5 79·2 78·9 78·6 78·3 78·0 77-7 77-5 77·2 76·9 76<> 51 59 81·2 "'9 80·6 eo·. "'·1 79·. 79·5 79·2 78·9 78·6 78·. 78·1 77-. 77-5 77-2 77-0 51

OD 81-5 81·2 80·9 80·6 80·. 80·1 79·8 79·5 79·2 79·0 78·7 78·4 78·1 77-9 77-6 n3 .. 01 81·7 81·5 81·2 80·9 80·6 80·4 80·1 79·8 7% 79·3 79·0 78·8 78·5 78·2 78·0 77-7 " .. 82·0 8H 81-5 81·2 80·9 80·7 80·4 80·1 79·9 79·6 79·4 79·1 78·8 78·6 78·3 78·1 .. " 82·2 82·0 8H 81·5 81·2 81 ,0 807 80·5 80·2 80·0 79·7 79·5 79·2 79·0 78·7 78·5 " .. 82·5 82·, 82·. 81·8 81·5 81·3 81 -0 80. 80·5 80·' 80,] 79·8 79·6 79·3 79·1 78·8 .. .. 82·. 82·5 82·, 82·1 8] .• 8106 81·3 8 H 80·9 80·6 804 "" 2 79·9 79·7 79·5 79·2 56 .. 83·0 82·. .,.. 824 82·1 81 ·9 8H .14 81·2 .,~ 80·. 80·5 ",., 80·1 79·9 79 6 .. " 83·' 83·1 82·9 82·7 824 82·2 82·0 81-8 81·6 81·3 8H 80·9 80·7 eo'5 80·2 8O~ " .. .3<> 834 83·2 83·0 82·7 82'5 82·' 82·1 8B 8H 81·5 81 ·3 8H 80·. 80·6 804 58

• j ~

± 8_ -30' -31 ' .,.' '33' '34' .,.' '31' 'JT' .,.' '3t' '40' '41' '42' '43' .... ' '45'_A±

A & B s ame NameS} RULE TO FIND { A & B D ifferent names take um. (add) . C CORREC TI ON take ifference (S ub.)

C CORRECTI ON. (A t B) is named t he same as the greater of th ese quantities_

c AZIMUTH ta kes combined names of C Correction and Hour Angle

414

TABLE C A & 8 OORRECTION

±a _ ·80' ·82' ,84' .... ·88' ' 70' ,72 ' ·74' ·78' ,71' ·80' ·82' .... .... ·as' ·90 ' ''' A.j: r AZIMUTHS r ~ ~ • . . . . . . . . . . . . • . . . . 0 59·0 ,.., 57·4 56·6 SS'8 55·0 54·' "·5 52 ·8 52·0 51-3 SO·6 SO'O 49-3 48·7 48-0 0 5 59·1 ",3 57·5 56·7 55·' SS I 54·3 " .• 52·9 52·2 51·5 SO'8 SO'1 49-4 48·8 48· 1 5

\0 :>9 ·4 ,.. 57-8 57·0 56·' SS , 54·7 "., "., 52'5 51·8 51 -1 SO·, 49·7 49-1 48·' \0

" 59·8 59 ·0 ,.., 57·4 56·. SS·8 55·1 54'3 " .• 52·9 52·2 51·5 SO·8 SO·, 49·5 48·9 14 18 60·3 ')9·5 "'7 57·9 5H ",3 55·6 54·, 54·1 "., 52·7 52·1 51·4 SO·7 SO·1 49·4 " 20 60·6 59·8 59·0 58·' 57·4 56,7 55·9 55·2 54·5 53·8 53·1 52·4 51·7 51-1 :0·4 49·8 " 22 60·' 60·1 59·3 58·5 57·8 57·0 56·3 55·5 54·8 54>1 53-4 52·8 52·1 51-4 SO'8 50·2 22 24 61·3 60·5 59·7 589 58·' 57·4 56·7 55·9 55·2 545 53·8 "., 52·5 51 ·8 51·2 SO'6 24

" 61 ·7 60' 60·1 59·3 58·. 57·8 57·1 ,.., SS" 55,0 54 3 ". 52·9 52·3 51 ·7 51·0 21 21 62·1 61·3 60·5 59·8 59-0 58·3 57·6 568 56-[ 55-4 548 54·1 53·4 52·8 52·' 51·5 ,. " 62·5 61·8 61 -0 60·' 59·5 ",8 ,,·1 57-3 56·. 56·0 55·3 546 "·0 "·3 52·7 52·1 ,. 31 62·8 62·0 61'3 60 5 59·8 59·0 " ,3 57·6 56·, 56·' 55·, "., "., " ·6 " ·0 " .. 31 32 C3'0 62·3 61·5 60·8 600 59·3 58·. s7·9 57·2 56·5 55·8 55·2 54·5 "., SJ3 52·7 32 33 63-3 62·5 61·8 61·0 60·3 59·6 ,.., ,.., 57·5 56·8 56·1 55·5 "·8 54·2 "·6 " ·0 33 34 6H 62·8 62·1 61·3 60·6 59·9 59·2 " ,5 57·8 57·1 56-4 55·8 55·1 54·5 53·9 "·3 ,. 35 63-8 63·1 62·3 61·6 60·9 60·' 59·5 58·8 58·1 57 ·4 56·8 56·1 55·5 54·8 542 SJ·' 35

" .... 63· ' 62·6 61'9 61·2 60·5 59·8 59·1 ,. .• 57 ·7 57 ·1 ,.., 55·a 55·2 54. '" ,.

37 ,,-4 63,' 62·' ",., 61·5 60·8 60·1 59·4 ",7 ",1 5N 568 ,,·1 55·5 54·9 "·3 37 38 "., 54·0 63·' "'·5 61·8 61-1 60·' 59·a 59'1 58·' 57·a 57·1 56·5 55' SS·3 "., '" " 65·0 "·3 63·. 62·8 62·1 61·5 60·8 60·1 59·4 58·8 58·1 57·5 56·9 56·2 55-6 550 " .. 65·3 " .• 63·' 63·2 62·5 61·8 61·1 60·5 59·8 59·1 58·5 57·9 57·2 56·. 56-0 55·' .. 41 65-6 64' 64·' 63·5 62·8 62'2 61·5 60·8 60·2 59·5 ,.., 58·' 57-6 57-0 56' 55·8 .. " ,,·0 65'3 oH 63' 6'" 62·5 61·9 61·2 60·5 59·9 59·3 58·6 " ,0 57·4 568 56·' .. " " ·3 65 ·6 "., ,,·2 63·' 62·9 62·2 61·6 60·' 60·3 59·7 59-0 ,.., 57·a 57·2 56·6 43 .. ... , .. 0 65'3 "·6 63·' 63·3 62·6 62-0 61·3 60,' 60·1 59·5 58·9 583 57·7 57.' .. 45 67-0 .. ·3 65,' 65·0 ,,·3 ",7 630 62·' 61·7 6B 60·5 59·9 59·3 58· 7 58·1 57·6 45 .. 67·4 ... , ..0 65· • "., "·1 63·. 62·8 62·' 61·5 60·, 60·3 59·7 59·1 58·. 58·0 .. " 67·7 67·1 .... 65·8 65·1 "·5 63·8 63·' ., .• "" 0 61·4 6<}8 60·' 59·6 59<> " ,5 " .. .. ·1 67·5 " ·8 .. ·2 65·5 "., "·3 63-7 " ,0 62·4 61·8 61·2 60,' 60·1 59·5 58·, ca .. .. ·5 67·9 67 ·2 " ·6 "·0 65·3 "., .... 6B 62·9 ",., 61 ·7 61-1 60·' 60·0 59 ·4 .. 50 ... , .. ·3 6706 67'0 "., 658 65·2 ,,·6 64-0 63 4 (2-8 62·2 61 ·6 GH 60·5 600 50

" 6N .. , 68·1 67·4 ,,·8 66·2 65 ·6 65·0 ,,-4 63' 63·' 62·7 62-1 61·6 61-0 60·5 " " 69·7 159'1 .. ·5 67·9 67·3 66,' .. ·1 65·5 ,,·9 .1-4 63·8 63·2 62·7 62·1 61·6 H-C 51

" 70·1 69·5 68' 68' 67·7 67-2 .... "·0 65-4 "., "·3 63·7 6'" ., .• 62·1 61·6 " .. 70·6 70·0 69·4 68·8 68·2 67·6 67-1 665 65·, 65·4 &H 64-3 63,' 63·' 62·6 62·1 .. " 71·0 70 ·4 69·8 69·3 .. ·7 .. ·1 67·6 67·0 66' 65' 65·4 " ·8 ,, ·3 63,' 63·' 62·' SS

" 71·5 70 ·9 70·3 69·7 69·2 68·6 ,,·1 67·5 67·0 66·' 65·' 65·4 .... , ,, ·3 63·8 6'" .. 57 71 ·9 71-3 70 ·8 70·2 69·7 69·1 68·6 .. ·0 67·5 67·0 .. ·5 65·' 65·4 " ·9 ,,·4 63·, 51 58 72-' 71-8 71 ·3 70·7 70·2 69'6 69 ·1 68·' .. ·1 67·5 67·0 "·5 .. ·0 65·5 65<> ,,·S .. 51 12·8 72-3 11·8 71 ·2 70·7 70·2 69·7 59·1 68·6 .. ·1 67·6 67-1 66·6 661 65·. 65·1 .. .. 73·,3 12·8 72·3 71-7 71·2 70·7 70·2 69·7 69·2 ... , 68·' 67 ·7 67 ·2 66' 663 658 00 61 73-8 73·3 72-8 12·3 71 ·8 71·3 70·8 70·3 69 ·8 69·3 "·8 68·3 67 ·8 67·4 .. 9 66·' .. " 74·3 73-8 73·3 12·8 72·3 11·8 71·3 70·8 70·4 69·9 69-4 68·' 68·S 68·0 67-6 67·1 .. 03 74 ·8 74·3 73·8 73·3 72-8 72·4 71·9 71·4 71 ·0 70·5 70·0 69·6 69·1 68·7 .. , 67·8 13 .. 75·3 74·8 74·3 73·9 73·4 72·9 725 '12 ·0 71-6 71-1 70·7 70·2 69·8 69·3 68·9 ,,·5 M

" 75·8 75·3 74·9 74-4 74 ·0 73·5 73-1 72& 72-2 71 ·8 71·3 70·9 70-5 70·0 69·6 69-2 .. .. 76-3 75·8 75·4 75-0 74 ·5 74·1 73·7 73·2 72·8 72·4 72·0 71 ·6 71-1 70·7 70 ·3 69·9 .. 8T 76·8 76·4 76 ·0 75·5 75·1 74 ·7 74-3 73 ·9 73·5 73-1 12-6 72·2 71·8 71·4 71-0 70·6 " 68 ,7-3 76·9 76·5 76·1 75·7 75·3 74·9 74·5 74·1 73·7 73·3 72·, 72·5 72·1 71·8 71·4 .. " j ~

±B_ ·6Q' -12' .... ·18' .... ' 70 ' -72' -14' '71' ,11' ·so· ,12' .... .... ." . 'SO"= A :!:

A & B s ame NameS } RULE TO FIND { A & B D ifferent names lake urn. (add ) C CORRECTION take Iflerence(Sub_)

C CORRECTION, (A 7 B) is named Ihe same as the greater of these quantities .

c AZIMUTH takes combined names of C Correction and Hour Angle

431

TRUE AMPLITUDES r Declination

Amplitude Corrections ,

25t' 26' 26f 27' 27t' 28' 2Bt' 29' 0 • . . . , . . .

r Declination , 0' 5' 10' IS' 20' 25'

2 25-5 26·0 26-5 27-0 27·5 28-0 28-5 29-0 4 25-6 26-1 26·6 2N 27·6 28-1 28-6 29-1 • 25-7 26 -2 26-7 27·2 27·7 28·2 28-7 29-2 • 25-8 26-' 268 27·3 27·8 28-' 28·8 29-'

10 25-9 26-4 26-9 27·5 28-0 28-5 29-0 29-5

0 , 0 • . , • 0 0-0 0-0 0-0 0-0 0-0 0-0 , 0-1 0 -1 0-1 0-1 0-1 0-1

10 0-1 0-1 0-1 0-1 0-1 0-1 15 0-2 0 -2 0-2 0-2 0-2 0-2

12 26·1 26-6 ~H 2N 28-2 28-7 29-2 29-7 14 26-3 26-9 27-4 27-9 28-4 28-9 29-5 300 16 26·6 27·1 27-7 28-2 28-7 29-2 29-8 30·3

- 16 26'9 27·5 28-0 28·5 29-0 29-6 30-1 30-7

" 27·3 27·8 28-' 28-9 29-4 30-0 30-5 31-1

20 0-2 . 0,2 0-2 0-2 Or 0-'

25 0-' 0 -' 0-' O~3 --'o~. .0-3) 30 0-' 0-4 0-' 0-4 0-' 0-4 35 0-' 0-5 0-5 0-5 0-5 0-5 40 0-5 0-6 06 0-6 0-6 0-7

22 27-7 28·2 28-8 29-3 29-9 304 31·0 31·5 .. 28-1 28-7 29-2 29-8 30-4 30-9 31·5 32·1 .. 28-6 29-2 29-8 .30'3) 30-9 31·5 32·1 32-6 28 29-2 29-8 30-4 30-9 :)1-5 32-1 32·7 ,,-, 30 29-8 30-4 31·0 31-6 "-2 32·8 '" ,4-1

42 0-6 06 0-6 0-6 0-7 0-7

44 0-' 06 0-7 0-7 0-7 0-7 46 0-7 0-7 0-7 0-7 0-8 0-8 48 0-7 0-8 0 -8 0 -8 0-9 0-9 50 0-8 08 0-8 0-9 0-9 1-0

31 30-1 30-8 31-4 "-0 32-6 3,)<2 i 33·8 "-5

" 30-5 31-1 31-7 ,,-, "-0 33·6 J4·2 "-9 33 30·9 31·5 32·1 " -8 ,,-, "-0 34·7 35-' 34 31·3 31·9 32·6 "-2 "-8 34·5 35·1 35·8 35 31·7' 32-' "-0 "-7 ,,-, 35·0 35·6 36-'

" 0-8 0-9 0-9 0-9 1-0 I-I

54 0-9 0-9 10 1-0 I-I 1-'

" 0-9 0-9 1-0 1-0 1,2 1-5

" 1-0 1-0 1-1 1-2 1-' 1-7 so I-I 1-2 1-2 1-' 1-5 2-1

36 32-2 32·8 "-5 "-I "-8 35·5 36-1 36-8 37 32·6 33·3 "-0 " -6 35·3 36,0 36-7 37·4 36 "-I "-8 "-5 35-2 35·9 36·6 37·3 "-0 39 ,,-, ,,-, 35-0 35-8 36-5 37·2 37·9 '" 40 "-2 "-9 35·6 36-' 3H 37·8 "-5 39·3

62 1-2 1-2 1-' 1-4 1-8 2-9

COMPASS ERROR BY AMPLITUDE

The true amplitudes given in the main table are calculated for the

41 "-8 35-5 36-2 37·0 37·7 " -5 In 40-0 42 35-4 36-2 36-9 37·7 ,,-4 39·2 39·9 40-7 43 36-1 36-8 37·6 "-4 39·2 39·9 40-7 41·5 44 36-8 37-5 ,,-, 39·2 39·9 40-7 41·6 42-4 45 37·5 ,,-, 39·1 39·9 40-8 41'6 42·4 ,,-, 46 ,,-, JH 400 40·8 41·7 42·5 43·4 44-' 47 39-1 40-0 40-9 41·7 42·6 "-5 44-' 45·3 48 40-0 40-9 41·8 42·7 43·6 44-5 45·5 46-4 49 41·0 41-9 42·9 43,8 44-7 45·7 46·7 41·7 50 42·0 4J-O 44-0 44-9 45·9 46-9 47·9 49-0

instant when the true altitude of the body is precisely 0' 00'. In the CMe

of the sun (owing to the effech of dip, relraction and parallax) the lower limb at this instant will appear to be approximately half a diameter above the visible horizon. If the compass bearing is taken at that moment there will be no need to apply any correction.

However, should the bearing be observed when the sun's centre

50, 42·6 ,,-, 44-5 45·5 t'-5 47·6 48-' 49·7

" 43·2 44-2 45·2 46-2 7-2 48-2 49·3 so-, 51, 43·8 44-8 45·8 46·8 47·9 49·0 so-o 51·2 52 44-4 45-4 46·4 47·5 48-' 49·7 SO-8 52·0 521 45·0 46-0 47·1 48-2 49·3 SO-5 51·6 52·8

appears to be in the visible horizon, ,h, correction obta ined from ,h, subsidiary table should be 7fplied by being added to the observe azimuth reckoned from the elevated pole as shown in the exa.mple below. (ut.

53 45·7 46_7 47·9 49-0 SO-I 51·3 52·5 537 53, 46·4 47·5 48·6 49·8 SO-9 52·1 53-3 546 54 47·1 48-2 49·4 so-' 51·8 53-0 54-' 55·6 54, 47·8 49-0 SO-2 51·4 52·7 53'9 55-' 56-6 55 48·6 49·8 51-1 52·3 53<6 54-9 56-' 57·7

55, 49·5 SO-7 52-0 53·3 54-' 56-0 57 4 58-9 56 so-, 51·6 52·9 54-' 55·7 57-1 58-6 601 56, 51·3 52·6 53'9 55-' 568 58-' 59·8 61·4 57 52·2 53'6 55 ·0 565 58-0 59·6 61·2 62·9 57, 53·2 54 ·7 56-I 57·7 59·2 60-7 62·6 65-0

62' N., decL 20' S.). Obs'd. Azi. ' S_ 41°·5 E. From clcv. pole N. 138°·5 E. Con'n. + 1",8 Som N. 140" .'3 E. Corr'd. obs'd. Amp. E. 50°'3 S. T. Amp. from table E_ 4\>"·8 S. Comp. Error 3°·5 W .

Observations of rising or setting stars and planets are seldom prac· ticable but. if obtained, should be treated in the !lame way as those of

58 54 ·3 55·8 51<4 58·9 60-' 62 ·4 64-2 66-2 58, 55·5 57·0 58-6 GIJ-' 62·1 64·0 66-0 681 59 56-7 58' 600 61·8 "-7 " -7 57·9 70·3 '91 58-0 59·7 61·5 "-4 65 -5 67·7 70·1 ne GO 59-4 61·2 032 65-2 67·4 69·9 72·6 75 ·8

the sun's centre. In the cas<: of the moon that body

will be approximately one-third of a degree below the horizon at the moment whe n its t rue altitude i, 0" 00'. If observed when its centre

GO, 61·0 62·9 65·0 67·2 69·7 72·4 75·7 79·9 61 62·6 647 67-0 69·4 72·3 75·5 79 ·8 90-0 611 64-5 " -7 69·3 72 ·1 75·4 79·7 900 -62 "-2 69·0 71'9 75·2 79·6 900 - -62, 68-8 71 ·7 75·1 19-5 90-0

appears in the visible horizon, two-thirds of the correction from 'h, subsidiary table should be subtracted from t he observed azimuth reckoned from the ele'-ated pole .

439

EX-MERIDIAN TABLE I Latitude and Declination DIFFERENT NAME

Change of Alt itud e in one minute from Meridian Passage : A

r DECLINATION .: , 15" lG" ," ,.- ,," 20" ,," 22" 23" ,," 25" 26" 27" 28" 29" 30"

" . . . . . - - . . - - - . . - - " 0 7.3 G.8 G.4 G.O 5.7 ' .4 ' .1 4 .' 4 .G 4 .4 4 .2 4 .0 3.' 3.7 3.5 3.4 0 1 G.' G.' 6. 1 '.7 ' .4 '.1 4.' 4.7 4.4 4 .2 4 .1 3~ 3.7 3.6 3.4 3.3 1 2 6 .5 6 .1 .2 ••• '.2 4 .' 4.7 4.' 4 .3 4 .1 3~ 3.8 3.6 3.' 3.3 3.2 2 3 6 .1 5 .8 ••• '.2 4~ 4 .7 4.' 4.3 4.1 3~ 3.8 3.6 3.' 3.4 3.2 3.1 3 4 '.8 ••• .2 5.0 4 .7 4.5 4.3 4.1 4.0 3.8 3.7 3.5 3.4 3.3 3.2 3.0 4 5 5.5 - '.2 5.0 4 .8 4 .• 4.3 4.2 4.0 3.8 3.7 3.6 34 3.3 3.2 3.1 3.0 • G '.3 5.0 4.8 4.6 4.4 4.2 4.0 3.' 3.7 3.6 3A 3.3 3.2 3.1 3.0 2.' • 7 '.0 4 .8 4 .• 4.4 4 .2 4.0 3.' 3.7 3.6 3.5 3.3 3.2 3.1 3.0 2.' 2.8 7 8 4 .8 4 .6 4 .4 4.2 4 .0 3.' 3.7 3.6 3.5 3.4 3.2 3.1 3.0 2.' 2.8 2.7 8 , 4 .6 4.4 4.2 4.1 3.' 3.8 3.6 3.5 3.4 3.3 3.1 3.0 2.' 2.' 2.8 2.7 • 10 4.4 4.2 4 .1 3.' 3.8 3.6 3.' 3.4 3.3 3.2 3.1 3.0 2.' 2.8 2.7 2.6 10

11 4.2 4 .1 3.' 3.8 3.G 3.5 3.4 3.3 3.2 3.1 3.0 2.8 2.8 2.7 2.6 2.5 11 12 4.1 3.' 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.' 2.8 2.7 2.G 2.G 2.5 12 13 3.' 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.' 2.8 2.7 2.7 2.6 2.5 2.4 13 14 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.' 2 .8 2.7 2.7 2.8 2 .• 2A 2.4 14 15 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.' 2.8 2.8 2.7 2.8 2.6 2.5 2.4 2.3 15 lG 3.5 3.4 3.3 3.2 3. 1 3.0 2.' 2.8 2.8 2.7 2.6 2.' 2.' 2A 2.3 2.3 16 17 3.4 3.3 3.2 3.1 3.0 2.' 2.8 2.8 2.7 2.6 2.5 2.6 2.4 2.3 2.3 2.2 17 18 3.3 3.2 3.1 3.0 2.' 2.' 2.8 2.7 2.6 2.' 2.' 2.4 2.4 2.3 2.2 2.2 18 19 3.2 3.1 3.0 2.' 2.' 2.8 2.7 2.6 2.6 2.' 2A 2.4 2.3 2.2 2.2 2.1 19 20 3.1 3.0 2.' 2.' 2.8 2.7 2.G 2.6 2.' 2.4 2.4 2.3 2.3 2.2 2. 1 2.1 20

21 3.0 2.' 2.8 2.8 2.7 2.6 2.G 2.' 2.4 2A 2.3 2.3 2.2 2.1 2. 1 2.0 " 22 2 .' 2 .8 2.8 2.7 2.6 2.G 2.' 2.4 2.4 2.3 2.3 2.2 2 .2 2. 1 2. 1 2.0 22 23 2.8 2.8 2 .7 2.6 2.6 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 23

" ,. 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2. 1 2.1 2.0 2.0 I.. 24

25 2.7 2 ." 2 5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 21 2 .0 2.0 I.' I.' 25 26 2." 25 25 2.4 2.4 2.3 2.3 2.2 2 .1 2.1 2.1 2.0 2.0 I., I.. I., 26 27 2.5 2." 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.1 2.0 2.0 I., I.' I.. 1.8 27 28 2.5 2.4 2.3 2.3 2 .2 2.2 2.1 2.1 2.1 2.0 2.0 I., I., I.' 12 12 26 29 2.4 2.3 2.3 2.2 2 .2 2.1 2. 1 2.0 2.0 2.0 I.. I.. I.. 1.8 1.8 1.7 29 30 2.3 2.3 2.2 2.2 2 .1 2.1 2 .0 2.0 2.0 I.' I.. 1.8 1.8 1.8 1.7 1.7 30

31 2.3 2.2 2.2 2.1 2. 1 2.0 2.0 2.0 I.' I.' 1.8 1.8 1.8 1.7 1.7 1.7 31 32 22 2.2 2.1 2.1 2.0 2.0 I.' I.' I.' 1.8 1.8 1.8 1.7 1.7 1.7 I." 32 33 2. 1 2. 1 2.1 2 .0 2.0 I.. I.' I.' 1.8 1.8 I.' 1.7 1.7 1.7 1.6 1.6 33 34 2.1 2.0 2.0 2.0 I.' I.' I.. 1.8 1.8 1.8 1.7 1.7 1.7 1.8 I." I." 34 35 2.0 2.0 2 .0 I.' I.' 1.8 I.. 1.8 1.7 1.7 1.7 1.7 I." 1.6 I." 1.5 35 36 2.0 I.. I.' I.' 1.8 1.8 1.8 1.7 1.7 1.7 I." 1.6 1.6 I." I.' 1.5 36 37 I.' I.. I.' 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.8 I.' 1.5 1.5 37 38 I., 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 I.' I.' I.' I.' 1.5 38 39 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 I.' I.' I.' 1.4 1.4 39 40 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 I.' I.' I.' 1.6 1.4 lA 1.4 40

41 1 .7 1.7 1.7 1.6 1.6 1.6 I." 1.5 1.5 1.5 I.' 1.4 1.4 1.4 1.4 1.4 41 42 1.7 1 .7 I." 1.6 1.6 1.6 1.5 1.5 I.' I.' 1.4 1.4 1.4 1.4 1.4 1.3 42 43 1.6 1.6 1.6 1.6 I. ' 1.5 I.' I.' 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 43 44 1.6 1.6 I.. I.. I.' I.. I.. 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 44 45 I.' I.' I.' I.' I.. 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 45 46 I.' I.. I.' 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 46 47 I.. 1.4 1.4 1.4 l A 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 47 48 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 48 49 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 4. 50 1.3 1.3 1.3 1.3 1 .3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 50

51 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 51 52 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 52 .3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 53 54 1.2 1.2 1.2 1.2 1.1 11 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 54 55 1.2 1.1 1.1 11 11 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 55 .. 1.1 1.1 1.1 11 11 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 .. 57 1.1 1.1 1.1 11 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 57 58 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0 .' 58 59 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.' 0.' 0 .' 59 60 1.0 1.0 1.0 1.0 0 .' O~ O~ 0 .' 0.' 0.' 60

444

EX-MERIDIAN TABLE 11 Reduct ion Plus 10 True AUiwde a l Upper Transit

HOU R ANGLE

o· s' 0" 1" O· 15' 0" '" O· 25' 0" 30' a· 3 ,j' 0" t o' a· IS ' 0" 5<1' O· ,M' '" " A A 359°,5,'/ 359Q o$O ]5'· "5' 359''40 )59' 3,';' 359°30 JSr2.~' 359"20 ' lS9"J,j' 359°.10' 35'· 6' 359· 0'

· , , , , , , , , , , · I O~ 0-0 0-0 O~ 0-0 0-1 0-1 0-1 0-2 0-2 0-2 0-' I 2 0-0 O~ 0-0 0-1 0-1 0-1 0-2 0-2 0-' 04 04 0-' 2 , O~ O~ 0-' 0-1 0-1 0-2 0-' 04 0-' 0-6 0-7 0-8 3 • O~ O~ 0-' 0-' 0-2 0-' 04 0-' O~ 0-7 O-g H • • O~ 0-0 0-' 0-1 0-2 0-' 0-' O~ 0-. O~ H ,-, • • ~ ~ 0-1 0-2 0-, 04 0-' 0-7 O-g H ,-, H • T O~ 0-' 0-1 0-2 0-, 0-' O~ 0-. H 1-' I~ 1-' T • 0-0 0-1 0-' 0-2 04 0-' 0-7 0-' ' -2 1-' 1-. 2-1 • • 0-0 0-1 0-2 0-' 04 O~ 0-8 I -I '4 1-7 2-0 24 •

, . S' 1° 10' 1° Ni' ,°20' ' " 2S' 1° 30' ' · 35' ' " 10' , " 4// IQ 50' , . /;5' l~ 0' A A

358°6.:; ' 358°50 358""5' JSS· ,,/)' JSBoJS' 35&°30' ]SS"'?';' 358°20' 358' 15' 3580 1(1 3580 &' 358' 0'

· , , , , , , , , , , · 1 0-' 04 04 0 -' 0-5 O~ 0-7 0-7 0-. O. 1-0 I -I 1 2 O~ 0-7 0-. 0-' H 1 -2 1-' 1-' 1 ~ 1-8 1-' 2-1 , , 0-' H 1-3 1-5 1-7 ,.. 2-0 2-2 2-5 2-7 3-0 3-2 3 • 1-2 14 1-7 1 ~ 2-2 24 2-7 '-0 ,-, H H .., • • ,~ '" 2-l 24 2-7 ,-0 '4 3-7 4-1 ' -5 4-' 5-' • • 1-' 2-2 2-5 2-' ' -2 '-6 4-0 44 ,-. ' 4 ,-. 64 • T 2-2 2-5 2~ 3-3 3-7 ' -2 4-7 ' -2 5-7 6-' .~ 7-' T • 2-' 2-' ,-, ,-. .., ,-8 54 5-' 6-' 7-l 7-8 . -5 • • 2-8 3-3 J.8 ,-, ,-. '4 '-0 6-7 7- ' .-1 .-8 H •

2° 5' 2° 10' 2" J{/ 2° 20' 2' 2.>' 2' 30' 1° JS' 1° 10' 1° 4::" r SO' l~ /i.';' JOO' A A

U P S';' 15T'.)Q 1ST'"s' JSJO.,o 357"35' 357"JO' 357"26' 357":1(1 357° I;;' 357"10' 157" .,,' 3570 0'

· , , . , . , , , , , , · 1 1-2 1-' 14 1-5 1 ~ 1-7 ... B 2-0 2-1 2-' 24 1 , 2-' 2-5 2-7 2-' H 3-3 ' -5 ,-. ' -0 '-2 ' -5 ,-. • , 3 ·5 ' -8 4-l 44 '-7 , -0 5-' 5-7 6-1 6-5 .~ 7-2 , • 4-7 5-0 54 5-8 ' -2 '-7 7-l H 8-' 8~ ' -1 H • • 5-8 .-, .-8 7-J 7-8 8-' .~ '-5 10-1 10-7 114 12-0 • • 6-' 7-5 8-1 8 -7 .-, 10-0 10·7 114 12-1 12-8 13~ 144 • T 8-1 8-8 ' -5 10·2 10~ n '7 12 ·5 13-, 14-1 14 ·9 15·8 16-8 T • '-2 10·0 10·8 n·6 12·5 13-' 14 ·2 15-1 16'1 17·1 18·1 19·2 • • 10·4 11·3 12·2 13-1 1H 15·0 16 ·0 27-1 18 ·2 19·3 20-5 21·6 •

) " 5' ) 010' ) 0 U( J0 20' ) " 25' 1" 30' l e 3 .. ; ' 1" ,11/' 1" I.;' ) " 5IJ' ) . ,;.'j' ~O' A A

1S'C.:i5' )56"60 )56°46' 356°10' )56"3.:i ' 156°30 156°t ,s' 356"20 ' )S'0 l ,s' )56"11)' )560 6' 1S" 0'

· , , , , , . . , , . , · 1 2-5 2-7 2-8 2-' H 3-J 3-5 ,~ J-8 4-0 4-l 4-J 1

• ' -I 5-' H 5-' ' -2 '-5 .-8 7-l 7-5 7-8 .~ 8-5 • 3 7-6 8-0 . -5 8-' '4 .-8 10·3 '0-8 11 ·3 U-8 12-' 12-8 , • 10 ·1 10·7 11 -3 11 ·9 12 ·5 13-1 13-7 144 15-0 15-7 I'~ 17·1 • • 12·7 134 14-1 '''' 15~ 16·3 IN 17~ 18·8 1% 2O~ 21-' • • 15·2 '6-0 16 ·9 17-8 18·7 19·6 20-5 21-' 22-5 23-' 24-5 2H • T 17·7 18·7 19 ·7 20-7 21·8 22-' 24-0 ,,-1 26-' Z/-' 28-7 29-' T

• 20-' 21·4 22-5 23-7 2 .... 26 -' Z/4 28-7 3O~ 31·3 "-7 " -I • • 22-. 24-1 ,,-, 26·7 28-0 29-4 30-. ,,-, 33-8 35-' 36-' 38-' • Reduction Minus 10 True Altitude a l l ower Transit

448

EX-MERIDIAN TABLE III Second Correction Subtractive from First Correction

First Altit ude FirSI Corr Corr ,,' 30' 35" 40' .. ' .0' .3' 56' .. ' .,. .. ' .8' ,,' ,,' ,,' 80' , , , , , , , , ,

15 0.0 0.0 0.0 0 .0 0.0 0.0 0.0 0.1 0.1 0.1 0. 1 0.1 0.1 0.1 0. 1 0.2 15 30 0.0 0. 1 0.1 0.1 0 .1 0.2 0.2 0 .2 0.2 0.2 0.3 0.3 0 .4 0.' 0.6 0.7 30 35 0. 1 0 .1 0.1 0.2 0.2 0.2 0.2 0 .3 0.3 0 .3 0.4 0 .4 0.' 0.6 0.8 1.0 35 40 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.' 0 .• 0.7 0.8 1.0 1.3 40 45 0. 1 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.' 0.6 0.6 0.7 0.' 1.0 1.3 1.7 45

50 0. 1 0.2 0 .3 0 .3 0.4 0.4 0 .' 0 .' 0.6 0 .7 0 .8 0.' 1.1 1.3 1 .• 2.1 50 55 0 .1 0.3 0.3 0 .4 0 .4 0 .' 0 .• 0 .7 0.7 0 .8 0.' 1.1 1.3 1.. 1.' 2.' 55 . 0 0 .1 0.3 0.4 0.4 0.' 0 .• 0.7 0.7 0 .' 1.0 1.1 1.3 1.' 1.8 2.3 3.0 60 •• 0.2 0.4 0 .4 0.' 0 .• 0 .7 0 .8 0.' 1.0 1.2 1.3 1.' 1.8 2.1 2. 7 3.' 55 70 0 .2 0.4 0.' 0 .• 0 .7 0.' 0.' 1.1 1.2 1.3 1.' 1.8 2. 1 2.' 3. 1 4.0 70

75 0.2 0.' 0 .• 0.7 0.8 1.0 1.1 1.2 1.4 1.' 1.8 2.0 2.4 2.' 3.6 4 .• 75 80 0.3 0.' 0.7 0 .8 0.' 1.1 1.2 1.4 1 .• 1.8 2.0 2.3 2.7 3.3 4.0 6.3 80 8' 0.3 0.6 0.7 0.' 1.1 1.3 1.4 1.. 1.8 2.0 2.3 2.6 3.1 3.7 4.' 6.0 85 90 0.3 0.7 0 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.5 2.' 3.4 4 .1 5.1 6.7 90 93 0.3 0.7 0.' 1.1 1.3 1.5 1.7 1.. 2.1 2.4 2.7 3.1 3.7 4.4 5.6 7. 1 93

.6 0.4 0.8 0.' 1.1 1.3 1.. 1.8 2.0 2.2 2.5 2.' 3.3 3.' 4.7 5.8 7 .• •• 99 0.4 0.8 1.0 1.2 1.4 1.7 1.' 2.1 2.4 2.7 3.1 3.' 4 .1 5.0 • . 2 8. 1 99 102 0.4 0.' 1.1 1.3 1.' 1.8 2.0 2.2 2.' 2.' 3.2 3.7 4.4 5.3 ••• 8.6 102 105 0.' 0.' 1.1 1.4 1 .• 1.' 2.1 2.4 2.7 3.0 3.' 4.0 ' .7 ••• 7.0 '.1 105 106 0.' 1.0 1.2 1.' 1.7 2.0 2.3 2.' 2.8 3.2 3 .• 4 .2 ••• 5.' 7.3 ••• 106

111 0 .5 1.0 1.3 1.5 1.8 2.1 2.4 2.7 3.0 3.4 3.8 4.4 5.2 6.3 7.8 10.2 111 114 0.' 1.1 1.3 1.. 1.' 2.3 2.' 2.8 3.2 3 .• 4. 1 4 .7 '.5 •. 6 8.2 10 .7 114 117 0 .' 1.1 1.4 1.7 2.0 2.4 2 .• 3.0 3 .3 3.7 4.3 49 '.8 ••• 8.6 1 1.3 117 120 0.6 1.2 1.' 1.8 2.1 2.5 2.8 3.1 3.' 3.' 4 .5 '.2 6.1 7.3 '.1 11.9 120 123 0.6 1.3 1.' 1.8 2.2 2.6 2.' 3.3 3.7 4.1 4.7 5.' 6.4 7.6 ••• 12.5 123

126 0.6 1.3 1.6 1.. 2.3 2.8 3 .1 3,4 3.8 4 .3 '.0 ' .7 6 .7 8.0 10.0 13. 1 126 129 0.7 1,4 1.7 2.0 2,4 2.' 3.2 3.6 4 .0 4 .6 '.2 6.0 7.0 8,4 to.5 13.7 129 132 0.7 1.' 1.8 2. 1 2.' 3.0 3.4 3.8 4.2 4 .8 6,4 6.3 7,4 8.8 11 .0 14.4 132 135 0.7 1.5 1.' 2.2 2.6 3.2 3.5 3.' 4,4 5.0 ' .7 6 .6 7.7 '.2 11 .5 15,0 135 138 0 .7 1.6 1.' 2.3 2 .8 3.3 3.7 4. 1 4.6 '.2 5.' 6.' 8.0 '.7 12.0 15.7 "8 141 0.8 1.7 2.0 2,4 2 .' 3.' 3 .• 4.3 4.8 • .4 6 .2 7.2 8 ,4 1.0 12.5 16.4 141

EX-MERIDIAN TABLE IV Limits of Hour An gle or Time 'before or after' Merid ian Passage

I Ho", -;1 Ho", A H our A Hour A Hour A Angle Angle Angle Angle A ngle

, , m . m . m . m m 52·2 • 7·54 17 3·37 30 1·92 43 1·21 56 40·2 5 6-94 18 3·20 31 1·85 44 H 7 57 31·4 • 6·44 19 3 ·05 " H8 45 H 3 56 25·4 7 600 " 2 ·92 33 1·72 •• 1·09 " 2 1·2 8 564 21 279 J4 1 66 47 106 60 18-0 9 ,·26 22 2 ·67 35 1·60 48 1·02 " 15· 7 10 4·94 " 2·55 38 1·54 49 0 ·99 " 13·8 11 4-60 " 2 ·45 J7 1 ·49 50 096 63 12·2 " 4-40 " 2·35 38 1'43 51 0-93 .. 10·9 13 4-17 " 2·25 39 1 ·38 " 090 " 9 90 " 3·94 27 2·16 40 1 ·34 53 0·87 " 9'02 15 3·73 .. 2·08 41 1 -29 54 8·22 16 3·54 .. 200 42 1 ·25 "

449

CHANGE of HOUR ANGLE :I: with ALTITUDE >-:0 :;; LATITUDE -N

" 0' 3' 6' 9' 12" IS' 18' 21' 24' 27' 30' no 36'

0 , , , , , , , , , , , ,

1 57·30 57·3$ 57'61 58·01 58·58 59·32 60·25 61·38 62·72 &1·31 66· 16 68'32 70·83 2 28'65 28·69 28·81 29·01 29,29 29,66 30·13 :5(H,9 31·37 32 -16 33,09 34·17 35·42 3 19·11 19·13 19·21 19·35 19·53 19'78 20,09 20·47 20·92 21·44 22·06 22·78 23'62

• 14-34 14·36 14 ·41 14'51 14·66 14·84 15·07 15·36 15·69 16'09 16'55 17·09 17·72

• 11-47 11·49 11·54 1H2 n '73 11·88 12'06 12-29 12'56 12·88 13·25 13·68 HIS

• 9·57 9 ,58 %2 %9 9·78 9,90 10·06 10·25 10·47 1O·74 11·05 11'41 1l·83 7 8·21 8·22 8·25 8·31 8·39 8'SO 8·63 8·79 8·98 9·21 9-48 9·78 10-14

• 7-19 7·20 7,23 7,28 7'35 7-44 7·56 7'70 7·87 8,06 8·30 8·57 8·88

• 6·39 6'40 6·43 6·47 6·54 6'62 6·72 6,85 7,00 7-17 7-31l 7-62 7,90 10 5·76 5·77 5·79 5·8] 5·89 5·96 6·06 6 ·17 6,30 6·46 6·65 6,8'7 7-12

11 5·24 5,25 5·27 5·31 5," 5-43 5·51 5·61 5·74 5,88 6·05 6·25 6·48 12 4·81 4,82 4-84 4-87 4,92 4·98 5,06 5-15 5·27 5·40 5·55 5·74 5·95 13 4·45 4-45 4·47 4'SO 4'55 4-60 4·67 4-76 4·8'7 4·99 5·13 5,30 5'50 14 4·13 4·14 4·16 4 ·19 4,2.3 4,28 4,35 4·43 4·53 4·64 4-77 4-93 HI 16 3,86 3·87 3-89 3-91 3-95 4·00 4,06 4-14 4·23 4·34 4-46 4·61 4'78

11 3·63 3·63 H5 3·67 3·71 3'76 3-82 3·89 3·97 4-07 4·19 4,33 4-48 17 3-42 3-43 3 ·44 3·46 3'SO 3·54 HO 3·66 3·74 3'", 3-95 4,08 4·23 11 3-24 3·24 3-25 3-2f 3-31 3·35 3-40 347 3·54 3,&3 3-74 3·86 4,00 It 3-<11 '3 ·08 3·09 3-11 H4 H8 3-23 3,29 3·" 3-45 3-55 3,66 HO .. 2,92 2·93 2·94 2·96 2,99 3,03 3-07 H3 3·20 3,28 3-3Il 3-49 3-61

21 2·79 2·79 2-81 2,83 2,85 2-89 2-93 2,99 3·06 H3 3,22 3,33 3-45 22 2-67 2-67 2,68 2·70 2-73 2-76 2-81 2·86 2·92 3-00 3-08 H8 3-30 24 2·46 2·46 2-47 2-49 2-51 2-55 2-59 2,63 2·69 2·76 2,", 2,93 3,04 21 2-28 2·28 2,29 2-31 2,33 2,,, 2·40 2-44 2'SO 2'56 2'&3 2,72 2,82 21 2·13 2-13 2·14 2·16 2-18 2·21 2-24 2-28 2-33 2·39 2,46 2·54 2,&3 .. 2·00 2·00 2-01 2'03 2·05 2-07 2-10 2-14 2-19 2·25 2-31 2·39 2-47 32 1·89 1-89 1,90 1-91 1-93 1,95 1·98 2·02 2·0'/ 2·12 2-18 2·25 2-33 34 1·79 1·79 HO 1·81 1·8] 1,85 1,88 1,92 1,96 2·01 2-07 2-13 2-21 .. 1-70 1-70 1-71 1-72 1·74 1-76 1·79 1·82 1·86 1·91 1-96 2-03 HO 38 H2 1·63 1 ·&3 1·65 1·66 H8 1-71 1-74 1-78 1·82 H8 1·94 2-01

CO 1,56 1·56 1 ·56 1,58 I-59 HI 1,64 1-67 1-70 1·75 1 ·80 1·86 1·92 42 1-49 l'SO 1·50 I -51 1·53 1·55 I -57 HO H4 1·68 1-73 1·78 1·85 .. 1-44 1·44 1-45 1·46 H7 1·49 I-51 1,54 1,58 1-62 1-06 1·72 1 ·78 .. 1·39 H9 HO HI H2 1·44 1-46 1-49 I-52 1'56 1-61 1·66 1·72 .. 1-35 1·35 1·35 1·" 1·38 HO 1-42 1-44 H7 I-51 1·55 HO H6 .. 1-31 1-31 HI 1-32 1·34 1·35 1·37 1-40 1-43 1-47 1·51 1'56 1-61 .2 1·27 1-2'7 1·28 1,29 1·30 1·31 1,33 1,,, 1-39 H2 1-47 I-51 I-57 .. 1,22 1,22 1 ,23 1-24 1-25 1·26 1,28 1·31 1·34 1-37 1 ·41 H6 1·51 eo H6 1·16 H6 1-17 H8 1·20 1-21 1·24 1·26 1,30 1·33 1,38 1·43 .. HO 1·11 1-11 H2 1-13 H4 H6 H 8 1·21 1·24 1·27 1-32 1·"

70 1·06 }'07 1·07 1·08 1-09 HO H2 1·14 1 ·17 H9 1·23 1-27 1·32 76 1,04 H)4 H)4 1·05 1-06 1-07 1-09 HI H3 H6 H9 1,2.3 1-28 .. 1,02 1,02 1·02 1-03 1,04 1-05 1·07 1·09 HI H4 H7 1-21 1·26 .. 1,00 1-01 1-01 1·02 1,03 1·04 H16 1,08 HO H3 1-16 1,20 1·24 to 1,00 1,00 1·01 1-01 1-02 1·04 I-OS 1·07 1,09 H2 H5 1>19 1,24

450

CHANGE OF HOUR ANGLE J: with ALTITUDE .... ::l :;; - LATITUDE N

" ] 9" 42" 45° 48° 51" 54° 57" 60° 6)0 66" 69" n °

° . . . . . . . . 1 73·73 nlO 81·03 85-63 91-05 97-48 105·2( 114·60 126·21 \ 40·88 159·89 185·43 , 36-87 "'-56 40-52 42·82: 45'53 48·75 52'61 57-31 63·11 70-45 79-96 92·73 3 24·59 25·71 27-02 28-56 30-36 .32·51 lS·oe 38-21 42·09 46-98 53·32 61·83 , 18·45 19·29 2(}27 21·42 22·78 24-39 26·3( 28·67 31·58 35·25 40-00 46·39 5 14·76 15·44 16·23 17-15 18·23 19·52 2H7 22·95 25·27 28·21 32·02 37-13

• 12·31 12·87 13·53 14":50 15·20 16·28 17-57 19·13 21-04 2.H8 26-65 30·91 7 10·56 11 -04 U ·60 12-26 13-'" 13-96 15'0'1 16-41 18·07 20·17 22-90 26-55

• 9-2.5 9'67 10·16 10·74 11·42 12-22 13·19 14'37 15-& 17-67 21)-05 23-25

• 8-2J 8-60 9-'" 9-55 lO·16 10·88 IH4 12·78 IH)6 15-72 17·64 21)-69 10 7·41 ns 8·14 8·61 9-15 9-8() 10·57 ll·52 12·68 14·16 16-()7 18-64

11 6·74 7-05 7-oH 7-& 8-33 8-92 9-62 10-48 11·54 12-89 14·63 16·96 12 6·19 6'47 6 -00 7-19 7-64 8·18 8 -& 9-62 10-59 n·&) 13·42 15-56

" 5·72 5-98 6-29 6-64 7-06 7-56 8·16 8-89 9-79 10·9.3 12·40 14'39 14 5'32 5-56 5·85 6·18 6·57 7-(" 7·59 8-27 9·11 10·16 11 ·53 13·38 15 4-97 5-20 5-4<' 5-77 6 ,14 6·57 7-09 7-73 8·51 9-50 10·78 12-50

16 4 '67 4-88 5-13 5·42 5-77 6· 17 6-66 7-26 7-99 8-92 10·12 11·74 17 4-40 ' -60 '-84 5-U 5-<4 5-82 6-28 6-84 7-53 8·41 9-54 11·00 1& 4·16 '-36 . -se '-84 5·14 5·51 5-" 6-47 7-13 7-96 9-03 10·47

" '-95 4013 '-34 4·59 '-88 5-23 5-64 6· 14 6-7/ 7-55 8·57 9-.. to 3·76 '-93 4-14 4 ·37 ' -65 '-97 5-37 5-85 6-44 7-19 8·16 9-46

21 3·59 3·76 ' -95 4 ·17 .-43 4·75 5·12 5-56 6·15 6-86 7-79 9-03 22 '-<4 3·59 ,HS ' -99 4 ·24 ' -54 '-90 5-34 5-88 6-56 7045 8 -64 24 3'16 3·31 3-48 3·67 3·91 4-18 4-51 '-92 5-42 6-04 6-86 7-96 28 2-94 3-07 3-2, H I , -&] '-88 4'19 ' -56 5-02 % 1 6·37 7-'" 28 2-74 2-87 3·01 3018 3-39 3-62 3·91 ' -26 4·69 5·24 5-94 6-89

30 2·57 2-69 2-83 2-99 3·18 '-40 3·67 '-00 4'41 ' -92 5-58 6·47 32 2-43 2-54 2-67 2-82 3-00 3·21 3·47 3-7/ 4·16 '-64 5-27 6·11 34 2-30 2'41 2-53 2·67 2-" ,-'" '-28 '-58 ,-.. .-4<l ' -99 5-79 36 2-19 2-29 2·41 2-54 2·70 2-89 3-12 3-40 3·75 4018 4·75 5·51 31 2-09 2·19 2-30 2-43 2-58 2·76 2-98 '-2.5 '-58 '-99 '-53 5-26 .. 2-00 2-09 2-21) 2-33 2'47 2-65 2 -86 .l·ll 3-43 '-82 '-34 5<)3 42 1-92 2·01 2·11 2-23 2-38 2-54 2'74 2-99 3-29 3·67 4·17 4·84 .. 1-85 1-94 2-04 2·15 2-29 2-45 2-64 2-88 3-17 3·54 ' -02 ' -66

" 1· 79 H 7 1-97 2-08 2·21 2-37 2-55 2·78 3-06 3·42 3-88 '-50 .. 1·73 H I 1-90 2·01 2'14 2-29 2·47 2·69 2-96 .HI 3-75 4-35

,. 1-68 1-76 1-85 1-95 2-(11 2-22 2-40 2·61 2-88 3-21 3-" '-22 52 1-63 1-71 1-80 1-90 2-02 2 ·16 2-33 2-54 2-80 3-12 3-54 4 ·11 .. 1·57 1-" 1'73 1-82 1-" 2-re 2·24 2-44 2-69 3-00 3-41 3-95 60 1'49 I -55 1-63 1·73 1-" 1-96 2-12 2,31 2-54 2-" 3-22 3·74 65 1·42 1-49 I -56 1-65 1·75 1-88 2-03 2-21 2·43 2'71 3-08 3·57

70 1·37 1·43 1·51 1·59 H9 1·81 1-95 2· 13 2-34 2-62 2-97 3·44 75 1-33 1·39 1-46 I -55 H 5 1·76 1-90 2·07 2·28 2-55 2-89 3-35 80 1·31 1·37 1·44 1·52 1 ·61 1'73 1-86 2-03 2·24 2-50 2-83 3-29 15 1-29 1-35 1-42 I-50 H O 1-71 1-84 2·01 2·21 2·47 2-8() 3-25 .. 1-29 1 -35 1 ·41 1·49 1'59 1-70 1 -84 2-00 2-21) 2-46 2-79 3·24

452

CHANGE OF ALTITUDE IN ONE MINUTE OF TIME

AZIMUTH

..... 40" 42%G 45" 47%G 50" 52%0 55" 57%0 50" 62%" 66" 67%0 70· 75" so" .. " Lat .

0" 9.6 10.1 10.6 11.0 11.5 11.9 12.3 12.7 13 ,0 13 .3 13.6 13.8 14.1 14.5 14.8 15.0 o· 4" 9.6 10.1 10.6 11.0 11.5 11.9 12.3 12.6 13.0 13 .3 13.6 13.8 14.1 14.5 14 .7 15.0 4' 8 ' 9.5 to.O 10.5 11.0 11.4 11 .8 12 .2 12.5 12.9 13 .2 13.5 13.7 14 .0 14.4 14 .6 14.9 8· ,,' 9 .. 9 .9 10.4 10.8 11.2 11.6 12.0 12.3 12 .7 13.0 13.3 13.5 13.8 14.2 14.4 14 .7 ,,'

18· 9.3 9 .8 10.2 10.6 11 .0 11.4 11.8 12.1 12.5 12.8 13.1 13.3 13.5 13.9 14 .2 14.4 16·

,," 9.1 9.5 10.0 10.4 10.8 11.1 11.5 11.8 12.2 12 .5 12.8 13.0 13 .2 13.6 13.9 14.1 ,," 24" 8.8 9.2 9.7 10.2 10.5 10.8 11.2 11.5 11.9 12.2 12.4 12.6 12 .9 13.2 13.5 13.7 24' 26" 8.7 9 .1 9.5 9.9 10.3 10.6 11 .0 11.3 11.7 12 .0 12.2 12.5 12.7 \ 3.0 13.3 13.5 26" 2s" '.5 9 .0 9 .. 9 .7 10 .1 10.4 10.8 11.1 11.5 1 1.7 12.0 12.2 12.4 12.8 13.1 13.2 28" 30" '.3 .B 9 .2 9.6 9 .9 10.2 10.6 10.9 1 1.2 11 .5 11.8 12.0 12.2 12.5 "B 13.0 3D'

,," ' .2 8 .6 9 .0 9 .4 9 .7 10.0 10.4 10.1 11.0 11.3 11 ,5 I1 B 12.0 12.3 12.5 12.1 3i' ,." 8.0 8.4 ••• 9.2 9.5 9B 10 .2 10.5 10.8 11.0 11.3 11 .5 11.7 12.0 12.3 12.4 ,." 36" 7.' '.2 8.6 9.0 9.3 8.6 9 .9 10,2 10.5 10.7 11.0 11.2 11.4 ' 1.7 12 .0 12.1 36· 38· 7.6 '.0 8.4 8.7 9 .1 9.4 9.7 10 .0 10.2 10.5 10.7 10.9 11. I 11.4 11.6 11 .8 38" 40' 7.4 7.7 8.1 8.5 ••• 9.1 9 .4 9 .7 10.0 10.2 10.4 10.6 10.8 11.1 11 .3 11 .5 40'

42" 7.2 7.5 7.9 ' .2 8.5 8.8 9. 1 9 .4 9.7 9 .9 10. 1 10.3 10.5 10.6 11.0 11 .1 42· 44· 6.9 7.2 7.6 8.0 8.3 '.6 8 .' 9.0 9 .3 9.6 9 .' 10.0 10 .1 lOA 10.6 10.8 44· 46' 6.7 7.0 7.4 7.7 '.0 '.3 '.5 8.7 9.0 9.2 9.4 9.6 9 .8 10.1 10.3 10.4 46· 48' 6.5 6.' 7.1 7.4 7.7 '.0 8 .2 8.5 8.7 8 .9 9. 1 9.3 9.4 9.7 9.9 10.0 48' 49" 6 .' 6.6 6.9 7.2 7.6 7.' '.0 ' .3 '.5 ' .7 8.9 9. 1 9.2 9.5 9.7 9 .' 49'

50" 6 .2 6.5 6.' 7.1 7.4 7.6 7.9 8.1 8.3 ' .5 ' .7 '.9 9. 1 9.3 9.6 9 .6 SO" 51' 6 .0 6.3 6.6 6B ,.2 7.5 7.7 7.9 ' .1 ' .3 8.5 '.7 .9 9.1 9 .3 9.4 51" si' 5.9 6.2 6 .5 6~ 7.1 7.4 7.6 7.' ' .0 ' .2 8.4 8 .6 8.7 8.9 9 .1 9 .2 !it' 5'- 5.' 6 .1 6.4 6.7 7.0 7.3 7.5 7.7 7.9 ' .1 '3 '.4 '.5 '.7 ' .9 9 .0 5'-54" 5 .7 60 6.2 6 .5 6.' 7.0 7.2 7.4 7.6 7.' 8 .0 8.2 8.3 8.5 8 .7 •• 54"

65" 5.5 5.8 6. 1 6.3 ' .6 6.8 7.0 7.2 7.5 7.6 7.' 8.0 ' .1 8.3 8.5 8.6 5s" 56" 5.4 5.7 5.9 6.2 6.4 6.7 6 .9 7. 1 7.3 7.4 7.6 7.8 7.9 8.1 .. , 8.4 56· 67· 5.2 5.5 5.8 6.0 6.3 6.5 6 .7 6.9 7.1 7.2 7.4 7.6 7.7 7.9 8.0 8.2 57· 58" 5.1 5.3 5.6 5.8 6.1 6.3 6 .5 6.7 6.9 7.0 7.2 7.4 7.5 7.7 7.' 8.0 58· 59" 5.0 5.2 5.5 5.7 5.9 6. 1 6 .' 6.5 6 .7 6.9 7.0 7.2 7.3 7.5 7.8 7.7 59·

60" 4.' 5.1 5.3 5.5 5.7 5.9 6.1 6.3 6.5 6 .7 6.' 6.9 7.0 7.2 7.4 7.6 60' 51 ' 4 .' 5.1 5.3 5.5 5.7 5.9 6.1 6.3 6 .5 6 .6 6.7 6.8 6.9 7.0 7.2 7.3 6 1' 62" 4.5 4.7 5.0 5.2 5.4 5.6 5.' 5.9 6. 1 6 .2 6.4 65 6.6 6.7 6.9 7.0 62" 63" 4.3 4.5 4B 5.0 5.2 5.4 5.6 5.7 5.9 6 .0 6.2 6.3 6.4 6.5 6.7 6.' 63" 84' 4 .2 4.4 4 .7 4 9 5. 1 5.2 5.4 5.5 5.7 5.' 6.0 6 .1 6.2 6.3 6.4 6 .5 64" ... 4.1 4.3 4.5 4.7 4.9 5 .0 5 .2 5.3 5.5 5.6 5.' 5.9 6.0 6.1 6 .2 6 .3 6s" .. " 4.0 4. 1 4.3 4.5 4 .7 4 9 5 .0 5 .' 5.3 5.4 6 .5 5.6 5. 7 5.9 6.0 6 .1 66"

6" 3.8 4 .0 4.1 4.3 4 .5 4.7 4.' 5.0 5. 1 5.2 5.' 5 .4 5.5 5.7 5.' 5.9 6" 68" 3.6 3.' 4 .0 4.1 4.3 4.5 4.6 4.8 4.9 5.0 5.1 5.1 5.2 5.4 5.6 5.6 .. " 69· 3.5 3.6 3 .' 4.0 4.1 4.3 4 .4 4.6 4 .7 4 .' 4 .9 5.0 5.0 5.1 5.' 5.4 69'

70" ,., 3 .5 3.6 3.7 '.9 4.1 4 .2 4 .' 4.5 4 .6 4 .7 4.7 4 .8 4.9 5.0 5.1 70· 71" '.1 3.' 3.5 3.6 ' .7 '.9 4.0 4.1 4.2 4.3 4 .4 4.5 4.6 4.7 4.' 4.9 ". 7i' 2.9 3 .1 3.3 3.4 '.5 '.7 3 .' 3 .9 4 .0 4 .1 4.2 4.2 4 .3 4.4 4.5 4.6 72· 7'- 2.' 3.0 3.1 3.3 3.4 3.5 3 .6 3.7 '.8 3.9 4.0 4.1 4. 1 4.2 4.' 4.4 73' 74" 2.6 2 .8 2.e 3.1 3.2 '.3 3.4 3.5 ' .6 3 .7 3.' 3.9 3.9 3.9 4.0 4.1 74' 75" 2.5 2.6 2.7 2.9 3.0 '. 1 3.2 3.3 3.4 3.4 3.5 3.5 3.6 3.7 3.8 3.9 75·

Lit . 40· 4"," 45" 47Y..° SO" 5lY.." 5s" 57Y.." 60" 62 Y..° ... 67%" 70· 7s" 80" .. " Lat.

453

AUGMENTATION OF THE MOON'S DIP OF THE SEA HORIZON

SEMI" DIAMETER

m h Dip m h Dip , , App. Al t. Moon 's S6m;-OiClmeter

"- 0.' 1.5 - 1.2 20.5 67 - 8.0 , 1.0 3 -1.8 2 1.0 69 - 8.1

14.5 15.0 155 16.0 16.5 17.0 1.5 5 - 2.2 21.5 71 - 8 .2 2.0 7 -2.5 22.0 72 - 8,3

• 2.' 0 - 2.8 22.5 74 .... . 3

10 0.0 0.0 0. 1 0.1 0.1 0. 1 3.0 10 -3.0 23.0 75 - 8.4 3.5 11 - 3.3 23.5 77 - S.5

20 0. 1 0. 1 0. 1 0.1 0.1 0.1 4.0 13 - 3.5 24.0 79 - 8.6 4.5 15 -3.7 24.5 BD -8.7

30 0.1 0.1 0.1 0.1 0.2 0.2 5.0 15 - 3.9 25.0 82 - 8.8

40 0.1 0.2 0.2 0.2 0.2 0.2 5.5 18 - 4.1 25.5 84 - 8.9 6.0 20 -4.3 26.0 OS - 9 .0

60 0.2 0 .2 0.2 0.2 0.2 0.2 6.5 21 -4.5 26.5 " - 9 .1 7.0 23 - 4 .7 21.0 89 - 9 .1

60 0.2 0.2 0.2 0.2 0.3 0.3 7.5 25 -4.8 27.5 90 - 9.2 8.0 26 - 5.0 28.0 92 - 9.3

70 0.2 0.2 0.3 0.3 0.3 0.3 8.' 28 - 5.1 28.5 94 - 9.4 9.0 30 . - 5.3 29.0 95 - 9.5

80 0.2 0.2 0.3 0.3 0 .3 0.3 9.5 31 -5.4 29.5 97 - 9.6 10.0 33 - 5.6 30.0 98 - 9,6

90 0.2 0.2 0 .3 0.3 I 0 .3 0.3 10.5 34 - 5.7 31 102 - 9 .8

I 11 .0 36 - 5.8 32 105 - 10.0 11 .5 38 - 6 ,0 33 108 - 10.1 12.0 39 -6.1 34 112 - 10.3 12.5 41 -6.2 35 115 -1 0.4

REDUCTION OF THE MOON'S 13.0 43 - 6.3 36 118 - 10.6 13.6 44 - 6.5 37 121 - 10.7

HORIZONTAL PARALLAX 14.0 4' -6.6 38 125 - 10.8 14.5 48 - 6.7 39 128 - 11 .0 15.0 49 - S.8 40 131 - 11.1

15.5 51 - 6.9 41 135 - 11.3 16.0 52 -7.0 42 138 - 11 .4

La t. H ori~ont'" Parallax 16.5 54 - 1. 1 43 141 - 11 .5 17.0 .. -7.3 44 144 - 1 1.7 ,

54 58 62 17.5 57 - 7.4 45 148 -1 1.8 18.0 59 - 7.5 46 151 - 11.9

• 18.5 51 - 7.6 47 154 - 12.1

10 0.0 0.0 0.0 19.0 62 - 7.7 48 157 - 12.2 19.5 64 - 7.B 49 161 - 12.3

20 0.0 0.0 0.0 20.0 66 -7 .9 50 154 - 12.4

30 0.0 0.0 0. 1

40 0.1 0.1 0. 1

50 0 1 0. 1 0.1 SUN

Para llax if' Alt itude M ean Sem i Diameter 60 0. 1 0.2 02

70 0.2 App.

Parlx . Month Mean S.D . 0.2 0.2 '" 80 0.2 0.2 0.2 ,

• , Jan. 16.3

0 + 0.2 hb. 16.2 10 + 0.2 March 16 .1 20 + 0.1 April 16.0 30 + 0. 1 Moy 15.8 40 + 0.1 JuM 15.8 50 + 0.1 July 15.8 60 + 0.1 Aut· 15.8 70 + 0.1 s." •. 15.9 80 + 0 .0 00 •. 16.1 90 +0.0 N~. 16 .2

0.,. 16.3 ,

454

MEAN REFRACTION ADDITIONAL REFRACTION CORRECTIONS FOR AIR TEMPERATURE

Atmospheric Pressure l 000mbs (29.5109) 70 be applied /0 the App8renl A ltitude Temperature lOT (SO' F)

~~pAIt. Air Temperatu re -'C App. All . Relr. App. All. Refr, A pp. AI!. Refr.

-6 ' O' 5 ' ' 0 ' 15 ' 20' 25' 30' 35' . . . . . . . . o 00 -lA -2.0 -\.O 0.0 -+ 1.0 -+1.9 +2.8 +3.7 +4.7

20 2.7 1.S 0.' 0.0 0.' 1.5 2.2 3.1 3.7 o 00 - 33.9 4 00 - 1 1.5 12 00 - 4.4 40 2.4 I.S O.S 0 .0 O.S 1.3 2.0 2.7 3.3

05 32.8 10 11.1 20 4.3 1 00 2.0 1.4 0 .7 0.0 07 1.2 I.S 2.4 2.' 10 3 1.8 20 10.8 40 4.2 20 I.S 1.2 O.S 0 .0 O.S 1.0 1.5 2.0 2.S 15 30.8 30 10. 5 13 00 4.0 40 1.5 1.0 0. 5 0.0 0.5 D.' 1.3 1.S 2.2 20 29.9 .0 10.2 20 3.' 25 29 .0 50 ,., 40 3.'

200 - 1.3 - 0.9 - 0 .4 0.0 +0.4 +0.8 +1.2 +1.5 +1.9 20 1.2 O.S 0,4 0.0 0,4 0.7 , 1 1.4 1.7

o 30 -28.2 5 00 -9. 7 14 00 -3.8 ' 0 1.1 0.7 0,4 0 .0 0,4 0.7 1.0 1.2 I.S 35 27.4 10 ,,4 20 3.7 300 1.0 0.7 0.3 0.0 0.3 OS ' .0 1.2 1. 5 40 26.S 20 '.2 40 3.S 20 1.0 O.S 0.3 0 .0 0.3 O.S 0.' 1.1 1.4 45 25.9 30 S.' ' 5 00 3.5 40 0 .' OS 0.3 0.0 0 .3 O.S O.S 1.0 1.3 50 25.2 40 S.7 20 3.' 55 24 .6 50 S5 40 3.'

4 00 - 0.8 - 0.6 -0.3 0.0 +0.3 +0.5 +0,8 + 1,0 +1.2 5 0.7 0.5 0.2 0.0 0.2 0 ,4 0 .7 O.S 1.0

1 00 - 23.9 6 00 - 8.3 16 00 - 3,3 S O.S 0,4 0.2 0.0 0 .2 0,4 O.S 0.7 0.' 05 23 .3 10 S. l 17 00 3 1 7 0 .' 0 .4 0 .2 0.0 0 .2 0.3 0 .5 O.S OS '0 22 .7 20 7' 18 0 0 2.' 6 0.5 0.3 0.2 0.0 0. 1 0.3 0,4 0.' 0.7 15 22. 1 30 7.7 19 00 2.7 , 0,4 0.3 0 .1 0.0 0. 1 0.3 0,4 0.5 O.S 20 2 1.5 40 7.5 2000 2.S 25 21.0 50 7,4 21 00 2.5

10 00 - 0.4 - 0 .3 - 0 .1 0.0 +0. 1 +0.2 +0.4 +0.4 +0.5 20 0.2 0.1 0.1 0 .0 0.1 0.1 0.2 0.2 0.3

1 30 - 20.5 7 00 - 7.2 22 00 -2.3 30 0.1 0 .1 0.0 0.0 0.0 0. 1 0.1 0.1 0.2 35 2 0 .1 ' 0 7.0 23 00 2.2 .0 0.1 0. 1 0.0 0.0 0 .0 0.1 0.1 0. 1 0.1 40 19.6 20 6' 24 00 2.1 50 0. 1 0.0 0.0 0.0 0 .0 0.0 0.0 0. ' 01 45 19. 1 30 SS 25 00 2.0 SO 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 50 18.7 40 6.6 2S 00 I .' 55 18 .3 50 S .5 27 00 I.S

2 00 - 11.9 600 - 6 .4 26 00 -1.8 05 17. 5 10 S.3 29 00 1.7 ' 0 17 .1 20 S .2 30 00 1.7 ADDITIONAL REFRACTION CORRECTIONS 15 16.8 30 S I 31 00 I.S FOR ATMOSPHERIC PRESSURE 20 16 .4 40 S .O 32 00 1.5 25 16. 1 50 5.' 33 00 1.5 f o be applied to the App,U6IJ( A llitude

App _ All . Atmospher ic Pressure - millibars 2 30 - 15.S 9 00 - 5 .S 3400 -1 .4

960 980 1000 1020 '030 35 15.5 10 5.7 3500 1,4 40 15 .2 20 5.S 3600 13 . . . . . 45 14 .S 30 5.5 37 00 1.2 000 "" .7 "'0.8 0.0 -(J. S - 1.7 50 14 .6 40 5,4 38 00 1.2 30 1,4 0.7 0.0 0.7 1,4 55 14 .4 50 5.3 3900 1.2 , 00 1.2 0 .6 0.0 O.S 1.2

30 1.0 0 .5 0.0 0.5 1.0

3 00 - 14.1 '0 00 - 5 .2 40 00 -1. 1 05 13.S '0 5.2 45 00 0.' 2 00 +0.9 .0,4 0.0 -0.4 - 0.9 ' 0 13.6 20 5. 1 50 00 O.S 4 O.S 0.3 0.0 0.3 O.S

" 13.4 30 5.0 5500 0.7 6 0 .4 0.2 0.0 0.2 0,4 20 13.1 40 4.' SO 00 0 .5 S 0.3 02 0.0 0.2 0.3 25 12.9 50 4.' SS 00 0.4 10 0.3 0. 1 0.0 0.1 0.3

3 30 - 12 .7 " 00 - 4 .8 10 0 0 - 0.3 15 00 "'0.2 .0.1 0.0 - 0 .1 - 0 .2 35 12.4 '0 ' .7 15 00 0.3 20 0. 1 0.1 0.0 0 .1 0. ' 40 12 .2 20 ' .7 80 00 0.2 25 0. 1 0' 0.0 0 .1 0.1 45 12. 1 30 4 .S SS 00 0.1 30 0.1 0.0 0.0 0.0 0. 1 50 11 .9 40 ' .5 90 00 0.0 35 0. 1 0.0 0.0 0 .0 0. 1 55 11.1 50 4 .5

• 00 -1 1.5 12 00 - 4.4 .0 00 0 .0 0.0 0.0 0.0 0.0

455

CORRECTION OF MOON'S MER. PASS. Corr. Plus to Mer. Pass_ in West Long .

~ Difference between times at successive trans.ts. ~

0 0 , ~

~ 39 m. 42 m . 45 m. 48 m . SI m . 54 m . 57 m . 6Om. 63 m . 66m.

. m_ m_ m_ m_ m_ m m. m. m_ m. • 3 03 O. 04 0-4 O. 0-' 0-5 0 ·5 0-5 0-6 3 6 0-6 0 -7 0-8 0-' 0-8 0-9 1-0 1-0 1'·0 1-1 • • 10 1 0 I- I 1-2 1-3 14 14 1-5 1-6 16 I

" 1 3 1 . 1-5 1-6 1-7 1 8 1-' 2-0 21 2-2 11 15 1-6 1-8 1-9 2-0 2-1 22 24 25 2-6 2-8 " 18 2-0 2-1 2-2 2-, 2 6 27 2-8 3-0 3-2 3-3 18 21 2-3 2-, 2-6 2-. 3-0 32 3-3 3-5 3-7 3-8 21 24 2-6 2-8 3 0 3-2 3' 3-6 3-8 '-0 '-2 44 24 21 2-' 3-2 3-, 3-6 3-8 , 0 '-3 ' -5 ' -7 5-0 11 30 3 -2 3-5 3-8 ' -0 '-2 ,-5 ' -8 5-0 5-2 5-5 3' " 3 6 3-8 ., ,-, ' -7 5-0 5-2 5-5 5-. 8-0 " " 3' ' -2 ' -5 4-. 5-1 5-' 5-7 6-0 6-3 6-6 " " .2 '-6 4-9 5-2 5-5 5-. 6-2 6-5 6-. 7-2 " " 4-6 . , 5-2 5-6 6-0 6-3 '-6 7-0 7-4 7-7 .. "

., 5-2 5-6 6-0 64 68 7- 1 7-5 7-' 8-2 .. .. 52 5-6 60 6-4 68 7_2 Hi 8-0 8-, 8-8 48 51 5-5 6-0 6-4 6-8 7-2 7-6 8-1 . -5 8-' 9-4 .. .. 5-8 6-3 6-8 7-2 7-6 8-1 .-6 '-0 ,-, ,-, 54

" 6-2 6-6 7-1 7-6 8-1 86 '0 '-5 10·0 10·4 " .. 6-5 7-0 Hi 8-0 . 5 '-0 ' -5 10·0 10·5 U·O .. " 6-8 7-' 7-' 8-' 8-' ,-, 10-0 10-5 11-0 11·6 " .. 7-2 7-7 8 -2 8-8 '4 ,-, 10 ·4 11<0 11-6 12-1 .. .. 7-5 8-0 .-. ' -2 ' -8 10·4 10-9 IB 12-1 12-6 .. " 7-8 8-' ' -0 ' -6 10-2 10·8 I H 12-0 12·6 13-2 " ,. 8 -1 8-8 ,-, 10 ·0 10-6 U -2 11·9 12·5 13-2 13-8 T5

" 8' '-1 ,-. 104 11-0 I H 12-' 13-0 13·6 14·3 71 81 8-8 ,-, 10-1 10·8 lUi 12·2 12·6 13·5 14·2 14·8 81 84 '-I '-8 10·5 11·2 11·9 12·6 13·3 14·0 14·7 154 •• 87 '-4 10·2 10-9 11-6 12·3 13·0 13-8 14·5 15·2 16·0 87 .. ,-. 10-5 11·2 12-0 12·8 13 ·5 14·2 15·0 15·8 16·5 I.

" 10·1 10·8 11 ·6 12-4 13-2 14 -0 14·7 15·5 16-3 17-0 " .. lOA 11·2 12·0 12·8 13-6 14-4 15·2 16-0 16·8 17·6 .. .. 10·7 11·6 12·4 13·2 14·0 14·8 15·7 16'5 17·3 18·2 .. 102 11-0 11·9 12·8 13'6 14A lS":S 16·2 17·0 17·8 18·7 102 105 11 ·4 12·2 1H 14 ·0 14-9 15-8 16·6 17·5 18·4 19-2 .05 .08 11-7 12-6 13-5 14·4 15·3 16 ·2 17-1 18-0 18·9 19-8 .08

"' 12·0 13·0 13-9 14·8 15-7 16-6 17-6 18-5 19·4 20-' 111 .14 12-4 13-3 14-2 15·2 16·2 11-1 18·0 19-0 "'-0 20-9 "' '" 12·7 13-6 14-6 15-. 16-6 17 ·6 18-5 19' 20-5 214 '" '20 13-0 14·0 15·0 16 -0 17-0 18 ·0 19·0 "'-0 21-0 22-0 .20

123 13·3 14· 4 15-4 16·4 17-4 18-4 19·5 2O·S 21 ·5 22~ I;,/.~

126 13·6 14·7 15·8 16-8 17·8 18·9 200 21·0 22·0 23·1 126 .29 14·0 15·0 16-1 17 ·2 18-3 19·4 20·4 21-5 22-6 23·6 129 132 14 ·3 15,4 16·5 17·6 18·7 19·8 20·9 22·0 2H 24·2 132 13. 14·6 15 ·8 16·9 18·0 19·1 20·2 21-4 22-5 23 ·6 24 ·8 '" 138 15·0 16·1 17·2 18·4 19·6 2<)-7 21 ·8 23-0 24·2 25·3 .38 .41 15·3 16·4 17·6 18-8 20 ·0 21·2 22-3 23-5 24·7 258 14. .44 15·6 16·8 18·0 19·2 20-4 21·6 22·8 24·0 25·2 26-' 14. 147 15·9 17·2 18·4 19 -6 20-. 22·0 23·.3 24·5 25-7 "'-0 147 . SO 16-2 17·5 18·8 200 21·2 22·5 2.3-8 25·0 26-2 "'-5 .SO

I5l 16·6 17-8 19·1 20-' 21-7 23-0 24-2 25·5 26-8 28-0 153 156 16-9 18-2 19-5 20-8 22-) 23-4 24 -7 26·0 27-3 28-6 156 ." 17-2 18·6 19·9 21·2 22-5 23-8 25·2 26·5 27-8 29-2 '" 162 17·6 18·9 20-2 21·6 "-0 24·3 25·6 27·0 28- ' 29-7 ... 165 17·9 19·2 20-6 22-0 23 4 24·8 26-1 27·5 28' 31)-2 165 .68 18·2 19·6 21·0 22- ' 23-8 25·2 26-6 28-0 29-' 30-8 16. 171 18-5 20·0 21·4 22-8 24·2 25·6 27-1 28·5 29·9 .31·4 171 IT4 18·8 20·.3 21·8 2.3·2 24·6 26-1 27·6 29·0 .30·4 31·9 IT4 In 19·2 20-6 22·1 2.3-6 25-1 26 ·6 28 ·0 29-5 31 ·0 32-4 177 ... 19-5 21-0 22·5 24-0 25·5 27·0 28·5 .30-0 .31·5 33·0 ...

Corr_ Minus to Mer_ Pass. in East Long _

458

SUN'S TOTAL CORRECTION To be applied to the Observed Altitude of the Sun 's Lower (L) or Upper (V) Limb

Height of EVe . Obs. l O.Srn 11 .2m 12.0m 12 .8m 13 .6m 14.SM 15.4 m 16 .3 m

All , (34ft) (3 7ft) (39ft ) 42 ft) (4 5 ft ) (48ft) (50ft ) (53 ft )

L U L U L U L U L U L U L U L U , , , , , , , ,

0600 + 19 - 30, / + 1.7 -30.3 + 1.5 -30.5 +1.3 - 3 0 .7 ., .1 -30,9 +0.9 - 31.1 <{1 2 -31.3 +0.5 -31.5 10 2.1 29.9 1.9 30.1 1.2 30.3 1.5 30.5 1.3 30.7 11 309 09 31, , 0.2 31 .3

20 2.3 29.7 2.1 29.9 1.9 30.1 1.2 30.3 1.5 30.5 13 3 0 . 7 1.1 30.9 0.9 31. 1

30 25 29.5 2.3 29. 7 2.1 29.9 1.9 30.' U 30.3 1.5 30.5 1.3 30. 7 1.1 30.' .. 2.2 2 9.3 2.5 29.5 23 29. 7 2.1 29_9 1.9 30. , U 30.3 1.5 30. 5 1.3 302

50 2. 29.1 22 29.3 2.5 29.5 23 29.7 2.1 29. 9 1.9 30. 1 1.2 30.3 1.5 305

01 00 +3.' -28 .9 +2.9 -29. 1 +2. 7 - 29.3 +2.5 -29.5 +2.3 - 29.7 +2.1 - 29.9 + 1.9 -30. 1 +1.7 -30.3

15 3.3 28.7 31 28.9 2.9 29. 1 2 2 29.3 2.5 29.5 2 .3 297 2 .1 29.9 1.9 30. 1

30 35 28.5 3.3 28.7 3.1 28. 9 2.9 2 9 . , 2.2 29.3 25 29.5 2 .3 29.7 2.1 29.9

" 32 28.3 3.5 28.5 33 28.7 3. 1 28.9 2.9 29. 1 2.2 29.3 2 .5 29.5 2.3 29. 7

08 00 39 28.1 3 2 28.3 3.5 28.5 3.3 28.7 3.1 28.9 2 .9 2 9. 1 2.2 29.3 2.5 29.5

16 '. 1 27.9 3.9 28. , 3.2 28.3 3.0 28.5 3.3 28. 7 3 1 28.9 2 .9 29. 1 2.2 29.3

30 " 2 7. 7 " 27.9 39 28. 1 3.2 28.3 35 28.5 3.3 28. 7 3 .1 28.9 2.9 29. 1

45 ' .5 27.5 4 .3 27. 7 4 .1 27.9 39 28. I 3.2 28.3 3 .5 28 .5 3 .3 28,7 31 28.9

09 00 ... . 2 - 27.3 +4.5 -27.5 +4.3 -27. 7 ... . 1 - 27.9 + 3.9 -28.1 +3.7 -28.3 +3.5 -28.5 +3.3 -28.7 20 4 .9 27.' 4 .7 27.3 4 .5 27.5 4 .3 2], 7 ' .1 27.9 3.9 2B. I 3 .2 28.3 3.5 28.5 .. 5.1 26.9 4 .9 27. 1 ' .7 27.3 4 .5 27.5 ' .3 27. 7 4 .1 27.9 3 .9 28. 1 3.2 28.3

1000 5 3 26.7 51 26.9 ' .9 27. 1 .., 27.3 '.5 27.5 '3 27.7 4 .1 27.9 3.9 28. 1

30 5.5 2 6 .5 5.3 26. 7 5.1 26.9 4 9 27. I 4 .7 27.3 '.5 27.5 ' .3 27.7 '.1 27. 9

" 00 P 26. 3 5. 0 26.5 5.3 26. 7 51 26.9 ,., 27. 1 .., 27. 3 ' .5 27.5 ' .3 27.7

30 09 261 P 26.3 05 26.5 5 .3 26.7 5.1 26.9 4 .9 2 7. I .., 27.3 4 .5 2],5

12 00 6 .1 25.9 0.9 26. 1 0.2 26.3 55 26. 5 5.' 26.7 0 1 269 ' 9 27. f 4 .2 27.3

30 6 .3 25.7 6 .1 2 5.9 59 2 6. I 5 .2 2 6 .3 5.5 26.5 0 3 2 6 .7 5.1 26.9 ' .9 2 7. I

1300 +6 .5 - 25.5 + 6.3 - 25.7 +6 .1 -25.9 + 5.9 - 26.1 +5.7 - 26.3 +55 -265 + 5.3 - 26. 7 +5 .1 -26.9

14 00 6 .2 25.3 6.5 25.5 '3 25.7 6 1 25.9 5.9 26, I 52 26.3 55 26.5 5.3 26.7

" 00 69 25.1 6 2 25.3 5.5 25.5 6.3 2 5 . 7 " 25.9 59 2 6.1 5.2 26.3 55 26.5

16 00 2.1 2 4 .9 ' 9 25.1 '.2 25.3 6.5 25.5 ' .3 25. 7 ' . 1 25.9 5.9 26. 1 52 26.3 17 00 2.3 24 .7 2.1 24.9 ' .9 25. 1 ' .2 2 5.3 ' .5 25.5 ' .3 25.7 6.1 2 5.9 5 .9 26. 1 1800 2.5 24.5 2.3 24. 7 2.1 24.9 6 .9 25. 1 ' .2 25.3 '.5 25.5 ' .3 25. 7 6 .1 25.9 19 00 2.2 24.3 2.5 24.5 2.3 24. 7 2.1 24.9 , .• 25. 1 6.2 25.3 65 25.5 ' .3 25.7

2000 + 7.9 - 24.1 +7.1 - 24.3 +7.5 -24 .5 + 7.3 -24 .7 +7 .1 - 24.9 ..... - 25. 1 +6.1 -25.3 +6.5 - 25.5 22 00 " 23.9 2.9 24. 1 2.2 24.3 2.5 24 .5 2.3 24 . 7 2.1 24.9 ' .9 25. 1 ' .2 25.3 24 00 8.3 23.7 '.1 23.9 2.9 24 . 1 2 2 24 .3 2.5 24.5 23 24 7 2.1 24.9 ' .9 25. 1

26 00 85 23.5 83 23. 7 8 .1 2 3.9 2.9 24.1 22 24 .3 2.5 24.5 2.3 24.7 2.1 24.9 2900 8 .2 23.3 8.5 23.5 8.3 23. 7 8 .1 2 3.9 2.9 24 . I 2 2 24 .3 2.5 24.5 2.3 24. 7

3200 ' 9 23. 1 8.2 23.3 8.5 2 3.5 83 23.7 8 .1 23.9 2 9 24 1 2 2 24.3 2.5 24.5

3600 9.1 22.9 89 23.1 82 2 3.3 8 5 23.5 83 23. 7 8 1 23.9 2.9 24. 1 2.2 24.3

.. 00 +<>.3 - 22. 7 +9.1 -22 .9 -+6.9 -23. 1 -+-6.7 - 23 .3 +8.5 -23 .6 +8 .3 -23. 7 + 8.1 -23.9 + 7.9 -24 . 1

45 00 9.5 22.5 9.3 22. 7 9 .1 22.9 89 23. 1 8 .2 23.3 8 .5 23.5 '.3 23.7 '.1 23.9 ., 00 9 .2 22.3 9.5 22.5 9.3 22.7 9.1 22.9 8 .9 23. 1 8 .2 23.3 8 .5 23.5 8.3 23.7

'000 9 .9 22. 1 9.2 22.3 9.5 22.5 9.3 22.7 9 .1 22.9 8.9 23. 1 8 7 23.3 8 .5 23.5

" 00 10.1 21 .9 99 22. 1 9.2 22.3 95 22.5 9.3 22. 7 9 1 22.9 89 23. I 8 .2 23.3

go oo 10.3 21 .7 10 .1 21.9 9 .9 22. 1 9 .2 22.3 95 22.5 9.3 22. 7 9 1 22. 9 89 23. 1

ADDITIO NAL MONTHLY CORRECTION

J," ,,' M" A" M .. J une July A'8 S e pl 0 " No. 0.0 LL <{1.2 <{1.2 <{1 .1 0 .0 -0.1 -0 2 -0. 2 -0.2 -0.1 00 <{1.2 <{12 U, -0.2 -02 -0. , 0 .0 «1. , «12 «12 «1.2 «1. , 0.0 -0.2 -0.2

459

SUN'S TOTAL CORRECTION To be applied to the Observed Altitude of (he Sun's Lower (L) or Upper (U) Limb

Height of Eye

Ob • . H .2m 1,8.2m 19 .2m 20.2m jZl.zm 22.2m 23.3m ! 24.4m Ah (56ft) [ (60h) (63ft) (66ftl 1 (7011) (73ft) (7711) I (80ft) , U , U , U , U , U , U , U , U , , , , ,

0600 ;{).3 -31.} ;{). , -:31.9 .,,,, -32. 1 -0.3 -32.3 -0.5 -32.5 ...{I.7 -32. 7 -0.9 -32.9 -1.1 - 33. 1

" 05 31.5 0 .3 31.7 ;{) , 3/.9 ..JU 32.1 0 .3 32.3 0.5 32.5 0 .7 32. 7 09 32.9 20 0 .7 3/.3 0 .5 3 1.5 0 .3 31. 7 ;{)., 31.9 ...Q1 32. 1 0.3 32.3 0 .5 32. 5 0. 7 32.7 30 0 .9 31. 1 0.7 3 / .3 05 3 1.6 0.3 31.7 ;{) , 31.9 ...Q1 32. ' 0 .3 32.3 0.5 32.5

'" '-' 30.9 0.9 31 , 1 0.7 3/.3 0 .5 31.5 0 .3 31. 7 '"" 31. 9 -lU 32. I 03 32.3 5. '-' 30.7 '-' ZO.9 • . 9 31. I • . 7 31.3 .5 31. 5 •. 3 3/ . 7 ;{). , 3/. 9 ...ill 32.1

0700 + 1.5 -30.5 +1.3 -J()] + 1. 1 -30.9 -+0.9 -31. 1 ;{).7 -31.3 ;{).5 ---31 .5 +0.3 -31.7 ;{)., -31.9 15 '-' 30.3 "5 30.5 '-' 30. 7 '-' 30.' • . 9 31 . 1 • . 7 3/.3 • . 5 31.5 •. 3 3/.7 3. " 9 30. ' '-' 30.3 " 5 30.5 '-' 30.7 •• 30.' •. 9 31, 1 • . 7 31.3 •. 5 3/.5 .. 2.' 29.9 "9 3D. ' '-' 30.3 "5 30.5 , .3 30. 7 " 30.9 •. 9 3T.I • . 7 3/.3

0800 2.3 29.7 2.' 29.9 ' .9 30. 1 '-' 30.3 "5 30.5 '-' 30.7 .. , 30.9 09 31. 1

15 25 29.5 2.3 29. 7 2 . , 29.9 "9 30.1 , .7 30.3 • . 5 30. 5 ' 3 30.7 " 30.9 3. 2.7 29.3 2.6 29.5 23 29. 7 2.' 29.9 ' .9 30. , " 30.3 ' 5 30.5 '-' 30.7

" 2.9 29.1 2.7 29.3 2.5 29.5 2.3 29.7 2. ' 29.9 '9 30. 1 '-' 30.3 "5 30.5

0900 +3. 1 -28.9 +2.9 - 29. I +2.7 - 29.3 +2.5 29.5 +2.3 29. 7 +2.1 - 29.9 +1 .9 -30 . 1 +1.7 -<73.3 20 3.3 28.7 3. ' 28.9 29 29. I 2.7 29.3 2 .5 29.5 2.3 29.7 2. , 29.9 ' 9 30.'

'" 3.5 28.5 3.3 28.7 3.' 28. 9 29 29. I 27 29.3 2.5 29.5 2.3 29.7 2. ' 2 9.9 ,.00 37 28.3 3 .5 28.5 3.3 28. 7 3. , 28.9 2' 29. 1 " 29.3 2.5 29.5 2.3 29. 7

3. 3.9 28. , 3 .7 28.3 3.5 28.5 3.3 28. 7 3. , 28.9 2.9 29.1 " 29.3 2.5 29.5 11 00 , .. 27.9 39 28. 1 3.7 28.3 3.5 285 33 28.7 3.' 28.9 2.9 29.1 " 29.3

3. ' 3 27. 7 " 27.9 3.9 28. 1 37 28.3 35 28.5 3.3 28.7 3. ' 28.9 29 29. 1 12 00 ' .5 27.5 '-' 27.7 ,. 27. 9 3.9 28. 1 37 28.3 35 28.5 3.3 28.7 3. ' 28.9

3. ' .7 27.3 '5 27.5 ' .3 27. 7 ••• 27. 9 3.9 28. 1 37 28.3 3.5 28.5 3.3 28. 7

13 00 .... 9 -27. 1 +4.7 - 27.3 +4.5 -37.5 +4 .3 -27. 7 .... , - 27.9 +3.9 -28. 1 +3.7 -28.3 +3.5 -28.5 1400 5. ' 26.9 ' .9 27. 1 . 7 27.3 ' .5 27.5 ' .3 27. 7 " 27.9 3.9 28. I 3.7 28.3 1500 5.3 26.7 5.' 26.9 '.9 27. I .7 27.3 ' .5 27.5 '.3 27.7 .. , 27.9 3.9 28. 1 16 00 5.5 26.5 5.3 26.7 5. ' 25.9 ., 27.1 ' .7 27.3 ' .5 2 7.5 '.3 27.7 , .. 27.9 1700 5.7 26.3 5.5 26.5 53 26. 7 5. ' 2 6.9 '.9 27. 1 ' 7 2 7.3 ' .5 27.5 ' 3 27. 7

" 00 5.9 26. 1 5.7 26.3 5.5 25.5 5.3 26.7 5. ' 26.9 '9 27. I ' 7 27.3 ' .5 27.5

," 00 6 ' 25.9 5.9 26. 1 5.7 26.3 5.5 26.5 5.3 26.7 5.' 26.9 ' .9 2 7.1 ' .7 27.3

2.00 +6.3 - 25. 7 +6.' - 25.9 .... 9 - 26. 1 +5.7 - 26.3 +5.5 - 26.5 +5.3 -26 . 7 +5.' - 26 .9 +4.9 -27. I 2200 6 .5 25.5 5 .3 25. 7 5.' 25.9 5.9 26.1 5.7 26.3 5 .5 26.5 5.3 26.7 5.' 2 6.9

" 00 6 .3 25.3 6 .5 25.5 63 25. 7 5 ' 25.9 59 26. 1 5.7 26.3 5.5 26.5 5.3 26. 7

2600 6.9 25.1 5 7 25.3 6.5 25.5 5.3 25.7 5 ' 25.9 5 .9 26. 1 5.7 26.3 55 26.5 2900 7. 24. 9 6.9 25.1 6.7 25.3 '5 25.5 53 26.7 6 . ' 25.9 5.9 26. 1 5.7 26.3 3200 7.3 24. 7 7 , 24 .9 6.9 25. 1 57 25.3 65 25.5 6.3 25. 7 ,., 25.9 5.9 26. 1

" 00 7.5 24 .5 7.3 24 .7 7. ' 24.9 6 .9 25. 1 57 25.3 65 25.5 ' .3 25.7 6. ' 25.9

'" 00 + 7.7 -24.3 +7 .5 -24.7 + 7.3 24. 7 + 7.1 -24. 9 +69 - 25.1 +6.7 - 253 6 .5 - 25.5 6.3 - 25.7

,"00 7.9 24. 1 7.7 24 .3 7.5 24.5 7.3 24.7 7.' 24.9 6.9 25. 1 '7 25.3 6 .5 25. 5 5200 •• 23.9 7.9 24. 1 7.7 24.3 75 24.5 7.3 24. 7 7 . 24 .9 6 .9 25. 1 57 25.3 so 00 .3 23.7 , .. 23.9 7.9 24. 1 7 7 24. 3 3.5 24.5 7.3 24. 7 7. ' 24 .9 6 .9 2 5. 1 7500 ' .5 23.5 '3 23.7 ,. 23. 9 7.9 24. 1 77 24.3 7.5 24.5 7.3 24. 7 7. ' 24 .9 90 •• '7 23 .3 ' .5 23.5 '.3 23. 7 , , 23.9 79 24. 1 77 24.3 7.5 24.5 73 24. 7

ADDITIONAL MO NTHLY CORRECTION

J~ , .. M .. A" M., Jun" J uly A", S"pl 0" Nw ... " ;{).2 ;{).2 ;{). , 0 .0 .,,., -<>2 -<>.2 -<>.2 -<> .• ••• ;{)2 ;{).2 UL -<>. 2 -<>2 -<>. , • . 0 ;{). , -;0.2 -;0.2 -;0.2 ;{) , ••• -<>.2 -<>.2

463

STAR'S TOTAL CORRECTION To be SUBTRACTED from the Observed Altitude of the Star

Height of Eye

Metres 9.1 9.' 10.S 11.2 12.0 12.8 13.6 14.5 15.4 16.3 17.2 18.2 19.2 20.2 21.2

Feet 30 32 34 37 39 42 " 48 51 53 56 60 63 66 70

Ob • . All. . • . . • . . . . . . . . . 6' 00 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15.8 16.0 16.2 16.4

12 13.4 13.5 13.8 14.0 14.2 14 .4 14.6 14.8 15.0 15.2 15.4 15.6 15.8 16.0 16.2 24 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 ],4.8 15.0 1S.2 15.4 15.6 15.8 16.0 36 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6 15 .8 48 12 .8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15.6

7 00 12. 6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.0 15.2 15.4 15 12.4 12.6 12.8 13,0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15 .0 15.2 30 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14. 4 14.6 14.8 15.0 45 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14 .2 14.4 14.6 14.8

• 00 11.8 12.0 12.2 12.4 12.6 12. 8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.5 20 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 40 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2

9 00 11.2 11.4 11.6 11.8 12.0 12. 2 12.4 12.6 12 .8 13.0 13.2 13.4 13.6 13.5 14.0 20 11.0 11. 2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 40 10.8 11. 0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6

10 00 10. 6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 30 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 13.2

1100 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.0 30 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12 .2 12.4 12.6 12.8

1200 9.S 10 . 0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6

30 9.6 9.S 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4

13 00 9.4 9.6 9.' 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2

30 9.2 9.' 9.6 9.' 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0

1400 9.0 9.2 9 .• 9.6 9.' 10.0 10.2 10 . 4 10.6 10.8 11.0 11.2 11.4 11.6 11.8

1500 '.S 9.0 9.2 9.' 9.6 9.' 10.0 10.2 10.4 10.6 10. 8 11.0 11.2 11.4 11.6

16 00 '.6 '.S 9.0 9.2 9.' 9.' 9.' 10.0 10.2 10 .4 10.6 10.8 11.0 11.2 ',1.4

1700 ••• S.6 ••• 9.0 9.2 9.' 9.' 9.S 10.0 10.? 10.4 10.6 10.8 11.0 11.2

1800 '.2 S.' '.6 ••• 9. 0 9.2 9.' 9.6 9.' 10.0 10.2 10.4 10.6 10.8 11.0

1900 S.O S.2 ••• ••• ••• 9.0 9.2 9.' 9.6 9. ' 10.0 10.2 10 .4 10.6 10 .8

21 00 7.S '.0 .. , ••• ••• ••• 9.0 9.' 9. ' 9.' 9.S 10.0 10.2 10.4 10.6

23 00 7.6 7.S '.0 '.2 ••• ••• '.S 9.0 9.2 9 .• 9.' 9.' 10.0 10.2 10 .4

2500 7.' 7.6 7.' '.0 '.2 ••• '.6 S.' 9. 0 9.' 9 .• 9.' 9.' 10.0 10.2

2700 7.2 7.' 7.' 7.S '.0 '.2 '.4 S.' ••• 9.0 9.2 9 .• 9.6 9.' 10.0

2900 7.0 7.2 7.' 7.6 7.S '.0 '.2 S.' '.6 '.S 9.0 9.2 9. ' 9.6 9.' 3300 6.S 7.0 7.2 7.' 7.6 7.S '.0 '.2 ••• '.6 S.' 9.0 9.2 9.' 9.6 3600 6.6 6.' 7.0 7.2 7.' 7.6 7.' S.O ' . 2 ••• '.6 ••• 9.0 9.2 9.' 41 00 6.' 6.6 6.' 7.0 7.2 7.' 7.6 7.' ' .0 '.2 S.' ••• ••• 9.0 9.2 4800 6.2 6.' '.6 ••• 7.0 7.2 7.' 7.6 7.' '.0 S.2 ••• '.6 ••• 9.0

55 00 6.0 6.2 6.' 6.6 6.S 7.0 7.2 7.' 7.6 7.' S.O '.2 ••• '.6 ••• 6500 5.' 6.0 6.2 6.' 6.6 6.S 7.0 7.2 7.' 7.6 7.' '.0 '.2 ••• '.6 7500 5.6 5.S '.0 6.2 6.' 6.6 6.' 7.0 7.2 7.' 7.6 7.' '.0 '.2 ••• 8500 5.' 5.6 5.' '.0 '.2 ••• ••• 6.' 7.0 7.2 7.' 7.6 7.' '.0 '.2 9000 5.3 5.5 5.7 5.9 6.1 6.3 6.5 '.7 '.9 7.1 7.3 7.5 7.7 7.9 S.l

A shortened table of the Star's Total Correction is given inside the back cover

471

MOON'S TOTAL CORRECTION - LOWER LIMB Add to the Observed Altitude of the Moon 's Lower limb

Observed Altitude H.P. 38' 00' JO' 39"00' 30' 40'00' JO' 4,°00' 30' 42·00' 30' 43"00' JO ' 44000' 30' 45"00' . ".0 43.7 43.5 43. 2 42.9 42. 6 42 . 3 42. 1 41.8 41. 5 41.2 40.9 40.6 40.3 39.9 39.6

". 2 43,9 43.7 43.4 43.1 42.S 42.6 42.3 42.0 41. 7 41.4 4 1. 1 40.8 40 .S 40 . 1 39 .8 .... ".2 43.9 43 . 6 43.3 43.0 42.8 42.5 42.2 41 .9 41.6 41.3 41.0 40. 6 40.3 40.0 ... , .... ".1 43.8 43 . 5 43.2 43.0 42 .7 42.4 42.1 41.8 41.5 41.2 40.B 40.5 40.2

".B ... , ".3 44.0 43.7 43.S 43.2 42.9 42. 5 42. 3 42.0 41.7 4 1. 4 41.0 40.7 40. 4

55.0 " .B ".5 ".2 43.9 43.7 43.4 43.1 42.8 42.5 42.2 41.9 41.6 41.2 40.9 40.6

55.2 4S. 0 ".7 .... ".2 43. 9 43.6 43.3 43.0 42. 7 42.4 42. 1 41. 8 41.4 41.1 40.8 55.4 4 5.2 .... , «., .... 44 . 1 43.8 43.S 43. 2 42.9 42. 6 42.3 41. 9 41. 6 41.3 41.0

SS., 45. 4 45. 1 ... , 44.6 ".3 .. . 0 43. 7 43.4 43. 1 42.8 42.5 42. 1 41.8 41.5 41.2 SS. 8 45.6 4 5.3 45.1 44.S 44.5 44.2 43.9 43.5 43. 3 43.0 42 . 7 42.3 42. 0 41.7 41.4

56.0 4 S.S 45.5 45.3 45.0 44.7 .... 44.1 43. S 43. 5 43. 2 42.9 42.5 42.2 41.9 41.6

55.2 45.0 45.B 45.5 45. 2 44.9 44 .5 44. 3 ".0 43. 7 43. 4 43.1 42.7 42.4 42.1 41.S

56. ' 46.3 45.0 45.7 45.4 45.1 " . B 44.5 44.2 43.9 43.6 43.3 42.9 42.5 42.3 42.0

55. 6 46.5 46. 2 45.9 45.6 45.3 45. 0 ". 7 44.' ". 1 43.8 43.5 43.1 42.8 42.5 42. 2

56.8 46.7 46.4 46. 1 45.8 45. 5 45.2 44. 9 ... , ". 3 44.0 43.7 43.3 43.0 42 .7 42:.3 57.0 45.9 46.5 46.3 46.0 4 5.7 45.4 45.1 44.8 .... 5 ". 2 43. 9 43.5 43. 2 42.9 42:.5

57.2 47.1 " .B 46.5 46.2 4 5.9 45.5 4 5.3 45.0 44.7 .... ".1 43.7 43. 4 43.1 42.7

57.4 47.3 47 . 0 46.7 .... 46. 1 45.B 45.5 45.2 ... , 44.' ".3 43.9 U. 6 43.3 42.9

57.6 47.5 47.2 46.9 46.6 46.3 46. 0 45. 7 4 5. 4 45.1 ".B " .5 ".1 43.8 43.5 43.1

57 .8 47.7 47.4 47. 1 46.8 46.5 46.2 45.9 45.6 45.3 45.0 ... , 44 .3 " .0 43. 7 43.3

58.0 47. 9 47.6 47.4 47. 1 46.7 46.4 46. 1 45. 8 4 5.5 45.2 44.8 ".5 ".2 43.9 43.5

58.2 48.1 47.9 47.6 47.3 47.0 45.6 46.3 46. 0 45.7 45. 4 45.0 " .7 .... ".0 43. 7

58.' 48.4 ".1 47 .9 47. 5 47.2 46.8 46.5 46.2 45 .9 45.5 45.2 ... , 44.' 44.2 43.9

58.' 48. 6 ".3 ".0 47 .7 47.4 47.1 46 . 7 46.4 45.1 45.B 4 5.4 45.1 44.8 .... 44.1 58.B ".B ... , ".2 47.9 47.6 47.3 46. 9 46.6 46.3 46,0 4 5. 6 45.3 45 . 0 44.6 44. 3

59.0 49.0 ".7 .... ".1 47.8 47.5 47.1 46.8 46.5 46. 2 45 .B 45 .5 4 5.2 44.8 ... , 59.2 49.2 ... , ... , 48.3 48.0 47.7 47.4 47 . 0 45.7 46.4 45.0 45.7 45 .4 4 5.0 " .7 59.4 49. 4 49.1 ".8 ".5 ".2 47.9 47.6 47.2 45.9 46.6 45.2 45.9 45.6 45 .2 ... , 59.6 49.6 49.3 49.0 ".7 .... ". 1 47.B 47.4 47.1 ".S .... ". 1 45.8 45. 4 45. 1

59.8 49.8 49.5 49.2 ... , 4B.6 ".3 ".0 47.6 47.3 47. 0 ... , ".3 46. 0 45.6 45.3

60.0 SO.O 49.7 49.4 49. I 48. 8 ".5 ".2 47 .8 47.5 47.2 46 .8 46 .5 46.2 4 5.8 45.5

60.2 SO.3 49.9 49.6 49.3 49 .0 ". 7 .... ".0 47. 7 47,4 47.0 46.7 46.3 46.0 45.6 60. 4 SO. 5 SO.2 49 .8 49.5 49.2 .... ... , ".2 47.9 47.6 47.2 46.9 46.5 46.2 4S.S

60.6 SO.7 SO .• SO .1 49. 7 49,4 49.1 ".8 .... " .1 47.8 47.4 47.1 46. 7 45'- 46.0

60.8 SO .• SO., SO.3 49 . 9 49.6 49.3 49.0 ... , ".3 ".0 47.6 47.3 46.9 46.6 46.2

61.0 51.1 SO.B SO.5 SO.2 49,8 49 . 5 49.2 ... , ".5 ".2 47.8 47.5 47.1 46.8 45 . 4

61.2 51. 3 51.0 SO . 7 SO . • SO.O 49.7 49.4 49.1 ".7 .... ".0 47.7 47.3 47.0 46.5

61.4 51. 5 51.<' SO. , SO., SO.2 49.9 49.6 49.3 ... , ... , ".2 47.9 47.5 47,2 46.S

51.5 51.6 51.3 51.0 SO. 7 SO .• SO.O 49 .7 49.4 49.0 " . 7 .... ".0 47.7 47.3 45.9

Height of Eye Correction Always ADDED to the Observed Altitude

Metres 2 2.3 2.7 3. 1 3. 5 3. ' ••• .. , 5.' 5. , '.5 Feet 7 B ,

" " " " " " " 21

Corrn ' '.8 ,., , .. '.2 '.0 8.B 8.' 8.' B.2 B.O 7.8

502

RADAR PLOTTER'S SPEED AND DISTANCE TABLE

SPEED Miles Miles Miles Miles Miles Mi les Miles SP EED IN In In In In In In In IN

KNOTS I m in. 2 m in. 2i' min . 3 min. -4 m in. S min. 6 min. KNOTS ,., 0-07 0-13 0- 17 0·2<) 027 0·33 0 -40 ,., " 0·08 0-15 0-19 0·2.3 0·30 0·38 0·45 ,., , 0 0·08 0 -17 0-21 025 0·33 0·42 0·50 ... ,., 0·10 0 ·18 0·2.3 0·28 0-37 0·46 0·55 ,., ,., 0·10 0·20 0·25 030 0 -40 0·50 0·60 ' ·0 ,., 0,11 0·22 027 0·33 0·43 054 065 ,., ,., 0 ·12 0·2J 029 0-35 0 ·47 0·58 0·70 " " 0 '13 0·25 0-31 038 0·50 063 0-75 ,.. ,., 0,13 0·27 0·.).3 040 053 0 -67 0 80 ., " Q' I4 0·26 0·35 0·43 0·57 0-71 0 ·85 a, H 0-15 0·30 038 0·45 0·50 0-75 090 , ·0 ,., 0·16 0·32 0040 0048 063 080 0,95 ,.,

10-0 0-17 0·33 0042 0·50 0·67 063 1 00 10 -0 10 ·5 0·18 0,35 0-44 0·53 0-70 088 1 ,05 10,5 11 ·0 0·18 0·37 0·46 0-55 0·73 0,91 110 11 ·0 11-5 0 -19 038 0 ·48 058 0.77 0% H 5 lHi 12-0 0·20 0040 0·50 0·60 0·80 1·00 UO 12·0 12·5 0·21 0-42 0·52 063 0·83 10. 1·25 12·5 13 ·0 0·22 0-43 054 065 0·87 108 1·30 13·0 13·5 0'23 0,45 0·56 0·68 0·90 1-13 1·35 13·5 14·0 0·2.3 0-47 058 0 -70 0·9.] 1<17 HO 14·0 14'$ 0·24 0048 0·60 0 ·73 O ·~ 1 21 l AS 14-5 15·0 0·25 0·50 0·63 0·75 100 1 25 1·50 1!1 'O 15·5 0·26 0-52 065 0 -78 1·03 1·29 1·55 15·15 HI·a 0·27 053 0·67 080 1·07 1·33 HO 16·0 18 '$ 0·21\ 0·55 0·69 083 H O 1·38 1·65 18-5 11 '0 021\ 0·57 0·71 085 H 3 1-42 1·70 11 ·0 17-5 029 0·58 0 ·73 0·88 H 7 1,46 1<75 11'S 18·0 0·30 060 0 ·75 0·90 HO 1·50 1·80 18·0 18 -5 0-31 062 0·77 0·9.] 1·2.3 1·54 1·85 18·5 19·0 0';12 0·63 0·79 0·95 1·27 1·58 ,.,.0 19-0 19-5 0·33 0·65 0 ·81 0·98 1·30 1·63 1·95 19-5 20 ·' 0·33 0·67 0 ,8.) 100 1·33 1-67 2·00 20·' 20 ·, 0·34 0·68 0·85 1·03 1·37 HI 2·05 20 'S 21·0 0<35 0 ·70 088 105 HO 1·75 2-10 21 ·0 21 ·5 0 ·36 0·72 090 1·08 1-43 1·79 2-15 21 ·5 22·0 0,37 0 ·73 092 H O 147 1·83 2·20 22-0 'N 0·38 0-75 0·91 1·13 1·50 188 2·25 2U 23-0 0·38 0·77 096 1-15 1·53 1·92 2·30 23·0 23-5 0,39 0-78 098 H8 1·57 "'l6 2·35 23·5 24·, 0·40 080 100 120 1·60 0.00 2,40 24·0 24·5 0-41 082 102 1·2] H3 2·04 2·45 24·5 25'0 0·42 0·83 J.()' 1 25 1·67 2·08 2·50 25 ·0 25·5 0 -43 085 1 06 1·28 1·70 2·13 2·55 25 ·5 26'0 0·43 0·87 1 08 1·30 1 ·73 2-17 2 'f:,() 26·0 26·5 0·44 088 HO H I 1·77 2·21 265 26·5 27-0 0·';5 0·90 H3 1·35 ).80 2·25 2-70 27 ·0 27 ·5 0,46 0·92 H 5 1·38 1·83 2·29 2-75 21-5 28 -0 0-47 0 ·9.] H 7 1 ·40 1·87 HI 2·80 28 ·0 21-5 0-48 0-95 H 9 1·43 1·90 2·38 285 28-5 29-0 048 O~ 1·21 1 ·45 1·9.] 2·42 2·90 29 ,0 21-5 0-49 0·98 1 2.3 1-48 1·~ 2,46 2·95 29 ·5 30·0 0 50 1·00 1·25 BO 2·00 2·50 300 30-0 30·' 0-51 H" 1·27 1·53 2<>3 2·54 3·05 30·' 31 -0 0 52 1·03 ' ·29 I·SS 2<11 2·58 HO 3H 31 -5 0·53 1 05 1-31 1·58 2·10 2·63 3015 3Hi 32·0 0·53 ' ·07 ' ·33 1·60 2·13 2·67 ;"0 ,H 32-5 0·54 H. '·35 1·63 2 -17 2 -71 3·25 32·5 33·0 OSS H O 1·38 1·65 2·20 2·75 3·30 33·. » ., 0·56 1-12 HO 1<8 2·2.3 2'/9 3·35 ,,.. " ·0 0 ,57 HI 142 ' ·70 2·Z/ 2·83 340 ,,~

RADAR RANGE TABLE

T he accompanyi ng l~ble gives the approx imate distance of the 'r~d8r horizon' cor responding to different heigh ts 01 the radar aeria l or targe t from whi<:;h Br'! echo is returned , and is b ,15ed on the formula'-

horiwn din. in n.mls .. 2.2h/11 where h .. height o f aeria l o r target in metres

In similar mannllr to light waves, radio waves are refracted in passing throu gh the atmosphere. T h is nil the e ff ect 01 making ,he d istance o f the , ad .. , hor izon for 3cm. waves. under certain sta ndard conditions of Ihe a tmosphere, about 15 per cent . grea te r tha n the d istar\Ce of the geometrical horizon . Hence, lak ing Ihe lalter in nau tica l m ites to be 1.92../h, the d istance 01 the radar horizon becomH 2 .2 1.j h. T his w ill be correct only under the standard cond itions, and fNefY departure from such sla nda rd wi ll cause the d istaJl(:e$ 10 ~a ry ~omewhal. T he !itanda rd referred to is as follows :-

Atmospher ic pressure 1013mb. d ecreasing with height a l the rate of appro x imately 100mb . per 1000m.

Air temperature a l sea leve l 30"C. dl.lCreasing with heigh t allhe rate 01 6.50 C per 10oom.

60 per cent. rela tive humidity remain ing connarot wi th he i9ht.

Apart from var ia t io ns from Ihe above standard , the range al which ta rge t echoes can be seen o n Ihe P.P.I. sc reen wi ll depend 10 a consid erab le ex le nt o n Ihe c ha rac le ristics 01 the par t icu lar radar installat io n and o n the I.IC hoing q ua li t ies o f the target.

Used with discre t ion, however, the information gi ven in the table can be of much va lue to the radar observer.

No te : - T he su m of t he radar hor izon d istances o f aer ial and ta rge t res pl.ICt i~ el y gives the maximum distance from which t hat targe t can re turn a n echO.

1. A 1arge l o f heigh t 120m (390ftl should begin to ap pear on the P.P.I. of an inS laUation Wilh a n aerial mounted IOm (33ft l a bove sea level at a range o f approximately 24+7 " 3 1 miles

2. If an echo l irSI appears o n the P.P. I. (aerial 10m (33 ft) above $fa level) at a range of 26 miles, the probable he ight 01 Ihe lerga t il of the o rde r of a bout 70m (230ft!. This may anist in ident ifying it.

CAUTION: - TO 8E USED WITH 3am. WA VE RADAR ONL Y.

m , , 6 8 10

15 20 25 30 35

40 45 50 55 60

70 80 90 100 >1 0

h .

7 13 20 '6 33

49 66 8' 98 m

131 148

'" 180 197

230 ,., 295 328 36IJ

501

Range R,_ M" m. h . MI.

3 .1 110 360 23 '.4 120 390 24 5.4 130 430 25 6.3 140 '60 '6 7.0 150 490 27

8 .6 160 530 ' 8 9.9 H O 560 29 1 1.1 180 590 30 12.1 190 6" 31 13. 1 200 660 31

14 .0 no 720 33 14 .8 240 790 34 15.6 '50 850 36 16.0 280 920 37 17 .1 300 980 38

18.5 320 1050 40 19.8 340 1120 41 21.0 36IJ 1 180 " 22.1 380 1250 43 23.0 400 1310 44

5,2

DISTANCE BY VERTICAL ANGLE

Height of Object

• m 46 47.5 .. SO.5 52 53.5 E 55 56.5 58 59.5 6' 62.5 64 65.5 • I1 151 ' 56 .6. u e '66 171 176 180 185 190 " 5 200 205 210 215 • " " . , • , • , . , . , . , . , . . , • , · , • • .

0.1 13 57 14 23 14 49 15 15 ' 5 41 16 07 16 32 1658 17 23 17 •• 18 14 18 39 1. 04 1929 .2 705 7 18 7 32 745 759 8 13 8 27 8 40 8 54 .08

• 21 • 35 • 48 10 02

.3 444 4 53 5 02 5 12 521 5 30 539 5 48 5 58 • 07 6 16 6 25 .34 .43

.4 333 3 40 347 354 4 01 408 4 15 422 429 4 3. 442 • •• 5 4. 5 03

0 .5 2 51 266 3 02 3 07 3 13 3 18 3 24 329 3 35 3 41 346 3 52 3 57 4 03 6 222 227 2 31 2 3. 2 41 245 2SO 2 55 2 5. 304 309 3 13 3 18 3 22

.7 2 02 206 2 10 2 14 2 18 222 226 2 30 234 2 38 242 2 4. 2SO 2 54

.8 147 1 51 164 1 57 2 01 204 2 08 2 11 2 15 2 18 2 21 2 25 2 28 232 •• 1 35 1 38 1 41 1 44 1 47 1 50 1 53 1 5. 200 2 03 206 2 o. 2 12 2 15

10 1 25 1 28 1 31 1 34 1 3' 1 3. 1 42 1 45 1 48 1 50 • 53 1 5. 1 5. 2 02 .1 1 18 1 20 1 23 1 25 1 28 1 30 1 33 1 35 1 38 1 '0 1 43 1 .5 1 48 1 50 .2 1 11 1 13 1 16 1 18 1 20 1 23 1 25 1 27 1 30 1 32 1 34 1 37 1 3. 141 3 1 06 1 08 1 10 • 12 1 14 1 16 1 18 1 21 1 23 1 24 1 27 1 29 1 31 134

.4 1 01 1 03 1 05 1 07 1 09 1 11 1 13 1 15 1 17 1 19 1 21 1 23 1 25 127

1.5 o 57 o 5. 1 01 1 02 1 04 1 06 1 08 1 10 1 12 1 14 1 15 1 17 1 I. 1 21 .6 o 53 o 55 057 o 5. 1 00 102 1 04 1 06 1 08 1 09 1 11 1 12 1 14 1 16 .7 050 o 52 o 53 o 55 o 57 058 1 00 1 02 1 03 1 05 1 07 1 08 1 10 1 12 .8 047 04' OSO o 52 054 o 55 0 56 0 58 1 00 1 01 1 03 1 04 1 06 1 08

•• 045 046 048 04. o 51 o 52 054 o 55 0 57 o 58 1 00 1 01 1 03 1 04

2.0 043 044 045 047 048 050 051 052 054 055 057 058 05. 101 .1 041 042 043 045 046 047 04. OSO 051 053 054 o 55 057 058 .2 039 040 041 043 0 44 045 046 048 04. 050 051 053 054 055 .3 037 038 039 041 042 043 044 046 047 048 04. OSO 052 0 53 .4 036 037 038 0 39 0 40 041 043 0 44 045 04. 047 048 04. 051

2.5 034 035 036 0 37 039 040 041 042 043 0 44 045 04. 048 04. .6 033 034 035 036 0 37 038 039 040 041 042 044 045 046 047 .7 032 033 034 035 036 037 0 38 039 040 041 0 42 043 044 045 .8 030 031 032 033 034 035 036 037 038 03' 040 041 042 043 •• 029 030 031 032 033 034 035 o 36 037 038 039 040 041 042

3.0 028 02. 030 031 032 033 034 035 036 037 038 o 3. o 40 0 41 .2 027 028 o 2. 029 030 031 032 033 034 035 035 o 36 037 038 .4 025 o 26 027 028 028 029 030 o 31 032 032 033 034 035 o 36 • 024 024 025 026 027 o 28 028 o 2. 030 031 o 31 032 033 034 .8 022 023 024 025 025 o 26 027 028 028 029 030 031 o 31 032

'.0 o 21 022 023 023 024 025 o 26 026 027 o 28 028 029 030 030 .2 020 021 022 022 023 024 024 025 028 o 28 027 028 o 28 029 .4 o 19 020 021 o 21 022 023 023 0 24 024 025 o 26 o 2' 027 o 28 .6 o 19 o 1. 020 020 0 21 022 022 023 023 0 24 025 025 026 026 .8 o 18 o 18 o I. 020 020 0 21 021 022 022 023 024 024 025 025

5.0 017 0 18 0 18 o 19 0 1. 020 020 o 21 022 022 023 0 23 024 024 .2 o 16 0 17 0 17 o 18 0 19 o I. 020 020 o 21 o 21 022 022 023 023 .4 o 16 0 " 0 17 o 17 0 18 o 18 o 19 o I. 020 020 021 o 21 022 023 •• 015 0 16 0 16 0 17 0 17 o 18 018 o I. o 19 020 020 021 o 21 022 .8 o 15 0 15 0 16 o 1. 0 17 017 o 18 o 18 o 1. o I. 020 020 020 021

6.0 0 14 0 15 0 15 o 16 0 "

0 17 0 17 0 17 0 18 o 18 o I. o I. 020 020

Tan. h

El ' (j" " Where El · venical angle, h ' heighl of object, and d • distance .

516

EXTREME RANGE TABLE

Elevation Height of Eye

m 1.' 3 4.' • 8 1. 12 14 16 18 2. 22

m " 5 1. 15 20 2. 33 39 46 52 59 .. 72

• • 2 .• 3 .• 4A 5 .1 5.9 ••• 7.3 7.8 8A 8 .9 9.4 9.8 2 7 5.5 ••• 7 A 8 .1 8.9 9 .• 10.2 10.8 11 .3 11 .9 12.3 12.8 4 13 .~ 7~ 8 .• 9.3 10.1 ,.~ 11.4 12.0 12.6 13.1 13.6 14,0

• 20 7.7 8.8 9 .• 10.3 11.1 11.8 12.4 13,0 13.5 14.0 14,5 15.0 8 2. B.5 9.6 10.4 11 .1 11 .9 12.6 13.2 13.8 14.3 14.8 15.3 15.8

10 33 9 .2 10.3 11.1 11.8 12.6 13.3 13.9 14.5 15.0 15.5 16.0 16.5 12 39 9.B 10.9 11.7 12.4 13 .2 13.9 14.5 15.1 15.6 16.1 16.6 17.1 14 46 10.4 11 .5 12.3 13,0 lU 14.5 15.1 15.7 16.2 16.7 17.2 17.7 1. 52 10.9 12.0 12~ 13.5 14.3 15.0 15.6 16.2 ,.~ 17.3 17.1 18 .2 18 59 11 .4 12.5 13.3 14.0 14.8 15.5 16.1 16.7 17.3 17.8 18.3 18.7

20 66 11 .9 13.0 13.B 14.5 15.3 16.0 16.6 17.2 17.7 18.3 18.7 19.2 22 72 12.4 13.5 14.3 15.0 15~ 16.5 17.1 17.7 18.2 18.7 19.2 19.1 24 79 12~ 13.9 14.7 15.4 16.2 ,.~ 17.5 18.1 18.6 19.2 19.6 20.1 26 SS 13.2 14.3 15.1 15.8 16.6 17.3 17.9 18.5 19.1 19.6 20. 1 20.5 2B 92 '3.7 14.7 15.5 16.2 17.0 17.7 18.3 18.9 19.5 20.0 20.' 20.9

30 98 14.0 15.1 15.9 16.6 17,4 18.1 18.7 19.3 19.9 20,4 20.8 21 .3 35 115 15.0 16.0 16.8 17 .5 18.3 19.0 19.7 20.2 20.8 21.3 21 .8 22.2 40 131 15B 16.9 17 .7 18.4 19.2 19~ 20.5 21.1 21.6 22.1 22.6 23.1 45 148 16.6 17.7 18.5 19.2 20.0 20.7 21.3 21.9 22.4 2B 23.4 23.9 50 164 17 .4 18.4 19.2 19~ 20.7 21.4 22.1 22.7 23.2 23.7 24.2 24 .6

55 180 18.1 19.2 20.0 20.7 21 .5 22.2 22.8 23.4 23 .9 24.4 24.9 25.4 60 197 lBB 19.9 20.7 21.4 22.2 22.9 23.5 24.1 24.6 25.1 25.6 26.1 65 213 19.5 20.5 21 .3 22.0 22.8 23.5 24.1 24.7 25.3 25B 26.3 28.7 70 230 20.1 21.1 21.9 22.7 23.5 24.2 24~ 25.4 25.9 26.4 26.9 27.4 75 246 20.7 21.7 22.5 23.3 24.1 24.8 25.4 26.0 26.5 27.0 27.5 28.0

80 262 21.3 22.4 23.2 23.9 24.7 25.4 26.0 26.6 27.1 27.6 28. 1 28.6 SS 279 21.9 22.9 23.7 24.4 25.2 25.9 26.6 27.2 27.7 28.2 28.7 29.1 90 295 22.4 23.5 24.3 25.0 25.8 26.5 27.1 27.7 28.3 28.8 29.2 29.7 95 312 23.0 24.0 24.8 25.6 26.3 27.0 27.7 28.3 28.8 29.3 29~ 30.2

100 328 23.5 24 .6 25.4 26.1 26.9 27.6 28.2 202 29.3 29.8 30.3 30.8

110 361 24 .5 25.6 26.' 27.1 27~ 28.6 29.2 29.8 30.' 30.9 3 1.3 31.8 120 394 25.5 26.6 27.4 28.1 28.9 29.6 30.2 30.8 3 1.3 31 .8 32.3 JOB 130 4Z7 26.5 27.5 28.3 29.0 29.8 30.5 31.1 31.7 32.3 32.8 33.3 33.7 140 459 27.4 28.4 29.2 29~ 30.7 31.4 32.0 32.6 33.2 33.7 34.2 34 .6 150 492 28.2 29.3 30.1 30.8 3 1.6 32.3 32.9 33.5 34.0 34.5 35.0 35.5

160 525 29. 1 30.1 30.9 31 .6 32.4 33.1 33.8 34.3 34.9 35.4 35.9 36.3 170 558 29 .9 30.9 31.7 32.4 33.2 33.9 34.6 35.2 35.7 36.2 36.7 37.1 180 591 30.7 31.7 32.5 33.2 34 .• 34.7 35.4 35.9 36.5 37.0 37.5 37.9 190 623 3 1.4 32.5 33.3 34.0 34.B 35.5 36.1 36.7 37.3 37.8 38.2 38.7 200 ... 32.2 33.3 34.1 34.8 35.6 36.3 36.9 37.5 38 .• 38.5 39.0 39.5

210 689 32.9 34.0 34.8 35.5 36.3 37.0 37.6 38.2 38.7 39.2 39.7 40.2 220 722 33.6 34 .7 35.5 36.2 37.0 37.7 38.3 38.9 39.5 40.0 40.4 4O~ 230 755 34.3 35.4 36.2 36.9 37.7 38.4 39.0 39.6 40.1 40.7 41.1 4 1.6 240 7Ir1 35.0 36.1 36.9 37.6 38.4 39.1 39.7 40.3 40.8 4 1.3 41~ 42.3 250 820 35.7 36.8 31.6 38.3 39.1 39B 40.4 41.0 41.5 42.0 42.5 43 .0

2.0 853 36.3 37.4 38.2 38.9 39.7 40.4 41 .0 41.6 42.2 42.7 43.2 43.6 270 B8. 37.0 38.1 38.9 39.6 40.4 41 .0 41.7 42.3 42.8 43.3 43.6 44.3 280 919 37.6 38.7 39.5 40.2 41.0 41.7 42.3 42.9 43.4 43.9 44.4 44.9 290 95 1 38.2 39.3 40.1 40.8 41 .6 42.3 42.9 43.5 44.1 44.6 45.0 45.5 300 ... 38.9 39~ 40.7 41.4 42.2 42.9 43.5 44 .1 44.7 45.2 4 5.7 46.1

519

DIP OF THE SHORE HORIZON or Dip at Different Ranges Heighl of Eye

m , .• 3 4.' • 7.' 9 10 .5 '2 13.5 15 17.5 20 Mites " 5 '0 15 20 2. 30 36 39 44 49 57 56

• , . . , • , . . · , • • , . . , • , o. , - 27.9 - 55.7 -=-.L 23.5 - 1 5 1.3 - 2 19. 1 - 2 46.9 -3 14.7 - 3 42.5 - 4 10.3 -4 38. 1 - 5 24.5 -6 10.8

.2 14.0 27.9 ~55.7 , 09.6 , 23. 5 , 37.4 , 51.3 :2 05.2 2 19.1 :2 42.3 3 05.5

.3 9.4 18.7 27.9 ~.: ;~~ ~; '.~ I ~8:8 , 14.3 , 23 .6 , 32.8 , 4B.3 :2 03.7

.4 7.' 14.1 21.0 28.0 g~:7 ~"3 1 ~~"8 1 ~~:t 1 tt:: •• 6.8 11.3 16.9 22.4 28.0 33.6 39.1

••• - 4.9 - 9.5 -14.2 - 18.8 - 23 .4 -28.1 -32 .7 - 37.3 - 42.0 - 46 .6 - 64.3 - 1 02.1 .7 4.3 8 .2 12.2 16 .2 20.2 24.1 28.1 32.1 36 .1 40.0 46 .7 53.3 •• 3.8 7.3 10.8 14.2 17 .7 2 1.2 24.7 28.2 3 1.6 35.1 40.9 46.7

•• 3.' ••• '.7 12.7 15 .8 18.9 22.0 25.1 28.2 31.3 36.4 4 1.6 1 .• 3.2 ••• 8.8 1 1.5 14.3 11.1 19.9 22.7 25.4 28.2 32.9 37.5

' .2 - 2.8 - 5.1 -1.5 - 9 .8 - 12 .1 - 14.4 - 16.7 - 19.0 - 2 1.4 - 23.7 - 27.6 -31.4 .4 2.' 4.' '.5 8.5 10.5 12.5 14.5 16 .5 18.5 20.5 23.8 27. 1

•• 2.4 4.' 5.' 7.' • .4 11.1 12.9 14.7 16.3 lB. l 21.0 23.9 •• 2 .3 3.' 5.4 ••• '.5 10.0 " .6 13.1 14.7 16.2 18.8 2 1.4 2 .• 2 .2 3.' 5 .• • .4 7.' '.2 10 .6 12.0 13.4 14.8 17. 1 19.4

2.5 - 3.3 -4 .4 - 5.5 - 6.6 - 7.7 -8.8 - 10.0 - 11. 1 - 12 .2 - 14 .0 - 15.9 3 .• 3.' 4.' 5 .• 5.' 6.8 7.' 8 .7 ••• 10 .5 12. 1 13.6

.5 3.' 4 .7 5.5 ' .2 7 .• 7.8 B.' '.4 lQ.8 12. 1 4.0 3.8 4.' 5.2 5.' ••• 7.3 7.9 ••• ••• 1 1.0

. 5 4.4 5 .• 5.' 6.2 '.8 7.5 8. ' •. , 10.1

5.0 . ••• 5.5 •. , • •• 7.2 7.7 8.' ••• ••• 5.3 5.8 '.2 ' .7 7.2 7.' 8 .7 7 .• .., '.5 ••• 7.' 83 ••• 7.4 8.0 ' .0 7.'

Heighl of Eye

m 20 22. 5 25 27.5 3. 32.5 35 37 .5 40 42.' 45 47 .5 Miles " 56 74 82 90 98 ' 07 115 123 ' 31 139 ' 48 '56 . , . , , . , • . · , • , . , , , • , . •. , -. 10.8 -6 57.2 -7 43.5 - 8 29.9 -. 16,2 ·10 02.6 · 10 4 8 .9 · 11 35.3 -12 2 1.6 ·13 08.0 -13 54.3 -14 4 0.7

.2 3 05.5 3 28.6 3 51.8 4 15.0 4 38.2 5 01,4 5 24.5 5 47.7 6 10.9 6 34 .0 • 57.2 7 2004

.3 2 03.7 2 19.2 2 34 .6 2 50.' 3 05.5 3 2 1.0 3 36.3 3 51.9 4 07 .3 4 2 2.8 4 38.2 4 53.7

.4 1 ~~:; 23:6 ~ n:9 ~ ~2 : 2 ~ !,?~ :2 30.8 2 42.4 2 54.0 3 05.6 3 17 .2 3 28.7 3 40.3

.5 , 1 51.4 .l. VU.I • '0.0 ,,.. • ' 0. 0 2 37.8 :2 47 .1 :2 56.3

0.' -, 02.1 - I 09.' - , 17.5 - I 25.2 -, 33.0 - 1 407 - , 4&4 - 1 56.' -2 03.9 - 2 11 .6 - 2 19.3 - 2 27.0 .7 53.3 59.' , 06.5 , 13 . 1 , 19.8 , 26.4 , 33.0 , 39.6 , 46.2 , 52.8 , 59.4 :2 06. 1

•• 46.7 52.5 58.3 , 04. ' , 09.' , 15.7 , 21 .5 , 27.2 , 33.0 , 38.8 , 4 4 .6 , 50.4

•• 41.6 46.7 5 1.9 57.0 , 02.2 , 07.3 , 12.5 , 17.6 , 22.8 , 2 7.9 , 33.1 , 38.2 , .• 37.5 42.1 46.8 51.4 ,.. , 00.7 , OS.3 , 09.' , 14.6 , 19.2 , 23.9 , 28.5

' .2 - 31 .4 - 35.3 - 39.1 - 43.0 - 46.9 -50.7 - 54.6 - 58.4 -, 02.3 - 1 06.2 -, 10 .0 - 1 13.9 .4 27.1 30.4 33.7 37.0 40.3 43.6 46.' 50.3 53.9 56.9 , 00.2 , 03.5

•• 23.9 26.8 29.7 32.6 35.4 38.3 41.2 44. 1 4 7.0 49.9 52.8 55.7 .B 21.4 239 26.5 29. 1 3 1.7 34 .2 36.8 39.4 42.0 44.5 47 .1 49.7

2 .• 19.4 2 1. 7 24.0 26.3 28.7 3 1.0 33.3 35.6 37 .9 40.2 42 .6 44.9

2.5 - 15.9 - 17.8 - 19.6 - 21.5 - 23.3 -25.2 - 27.0 - 28.9 - 30.7 - 32.6 _ 34.4 - 36.3 3.0 13.6 15.2 16.7 18.3 19.8 21.4 22.9 24 .4 26.0 27.5 29. 1 30.6 3.5 12.1 13.4 14 .7 16.0 17.4 18.7 20.0 21.3 22.7 24 .0 25.3 26.6 4 .• 11.0 12. 1 13.3 14 .4 15.6 16.8 17.9 19 .1 20.2 21.4 22.5 23.7 4.5 10.1 11.2 12.2 13.2 14 .3 15.3 16.3 17.4 18.4 19.5 20.4 2 1.5

~. - 9 .6 - 10.5 - 1 1.4 - 12.4 - 13.3 - 14.2 - 15. 1 - 16 .1 - 17.0 -1 7.9 - 18 .8 - 19.8

••• 8. 7 • .5 10 .3 11.0 11.8 12.6 13.4 14 .1 14 .9 15.7 16.4 17.2 7 .• 8 .3 B.' ••• 10.2 10.9 11.6 12.2 12.9 13.6 14.2 14 .9 15.5 B .• 8 .• 8.' '.2 '.8 10.3 10.9 11 .5 12.1 12.6 13.2 13.8 14.4

••• 7.' B.4 ••• 9.5 10.0 10. 5 11.0 11.5 12.1 12.6 13.1 13.6

10.0 - 8.9 - 9.3 - 9.8 - 10.3 - 10.7 - 11 .2 - 11.6 - 12.1 - 12.6 - 13.0 11 .0 '.7 10. 1 10.5 11.0 11.4 11 .8 12.2 12.7 12.0 10.9 11.3 11.6 12.0 12.4 13.0 11.2 11.6 11.9 12.3 14.0 12.2

518

DISTANCE OF THE SEA HORIZON

Height Dis!_ Height Ois t. Height Dis!

m " ml, m " Miles m " M iles

40 131 13.3 200 656 29.6 0.' 1.6 1.5 '2 13B 13.6 205 6" 30.0 1.0 3 2.1 44 144 13.9 210 68' :lOA I .' 5 2.6 46 161 14.2 215 705 3<).7 2.0 7 3.0 48 157 ,4 ,5 220 722 31.1 2.' B 3.3 50 164 14.8 225 73B 31 .4

3.0 10 3.6 52 171 15.1 230 15. 31 .8 3.' 11 3.9 54 177 15.4 23. 771 32.1 4.0 13 4.2 56 184 15 .7 240 781 32.5 ••• 15 4.4 .. "0 16 .0 245 804 32.8 5.0 16 4.7 .. 197 16.2 250 820 33. 1

5.5 18 49 62 203 16.5 260 853 33.8 6.0 20 51 64 210 16. 8 270 886 34.4 6.5 21 5.3 .. 217 17.0 280 919 35.1 7.0 23 5.5 .. 223 11.3 290 951 35.7 7.5 25 5.7 70 230 17 .5 300 984 36.3

B.O 26 5.9 72 236 17.8 310 1017 36.9 8.5 28 6.1 7. 243 18 .0 320 1050 37.5 9.0 30 6 3 76 249 18.3 330 1093 38.1 9.' 31 6.5 78 256 18.5 340 111 5 38.6

10.0 33 6.6 80 262 18 .7 350 1148 39.2

11 36 6.9 B2 26' 19.0 360 1181 39.8 12 39 7.3 84 '76 19 .2 370 1214 40.3 13 43 7.6 86 2B' 19.4 380 1247 4 0.8 ,. 46 7.8 BB 289 19.7 390 1280 41 .4 15 49 8. 1 90 295 19 .9 400 13 12 41 .9

16 52 8A 82 302 20. 1 410 1345 4 2 .4 17 66 86 94 308 20.3 420 1378 42 .9 18 50 8.9 96 315 20.5 430 1411 43.4 19 62 9 .1 98 322 20.7 440 1444 43.9 20 66 9A 100 328 21 .0 450 1476 44A

21 69 9.6 105 344 2 1.5 460 1509 44.9 22 72 9.8 110 361 22.0 470 1542 4 5.4 23 75 10.0 115 377 22.5 480 1575 45.9 24 79 10.3 120 394 23.0 490 1608 46.4 25 B2 10.5 125 410 23.4 500 1640 46.8

26 85 10.7 130 427 23.9 51 0 1673 47.3 27 89 10.9 135 443 24.3 520 1706 47 .8 28 82 11.1 140 459 24.8 530 1739 48.2 29 95 11.3 145 .,6 25.2 540 1772 48.7 10 98 1 1.5 150 482 25.7 550 1804 49. 1

31 102 11.7 15. 509 26.1 580 1837 49.6 32 105 11.9 160 525 26.5 570 1870 50.0 33 108 12.0 165 541 26.9 580 1903 50.' 34 112 12. 2 170 658 27.3 590 1936 50.9 35 115 12.4 17' 57' 27.7 600 196' 51.3

36 118 12.6 180 591 28.1 610 2001 51.7 37 121 12.7 185 607 28.5 620 2034 52.2 38 125 12.9 190 623 28.9 630 2067 52.6 39 128 13.1 195 640 29.3 640 2100 53.0 40 131 13.3 200 6 .. 29.6 6" 2133 53.4

520

CORRECTION REQUIRED to CONVERT a RADIO GREAT CIRCLE BEARING to

MERCATORIAL BEARING

.~ DIFFERENCE OF LONGITUDE OF SH IP AND RADIO STATION r ~

rr •• ,...~ -. 4' 6' 8' 10" IT 14' 16" 18" 20" ll' 24' 2l>' 28" le!" ,

-" • • • • • • • • • • • • • • • , .. I~ 2~ H 4~ S~ 6~ H 8~ ,~

-~ 10·9 II~ 12~ IH 14·9 .. " I ~ 2-0 2-_ ,~ ,~ 5-_ 6-' H 8-' ,-, 10·9 11 ·9 12 ·8 13·B IH 11

" I~ 2~ .., 3-' ,-, 5-' 60 7-8 8-8 ' -8 10. 11-7 12·7 13-7 14 ·7 71 75 ,~ 1-' 2-, H ' -8 50 60 H 8-7 ' -7 10 ·7 11~ 12~ 13·5 ". 75

" H I~ 2-' H H 5-7 6-7 H 8~ '" 10·5 11. ' 2' 13·3 IH ,. .. O~ I~ .. H 4-7 ... 6 • H 8' H 'O~ 11~ IN IJ.l ,,~ .. .. 0 -' " 2. ,., H .. 6 • 7. 8' 91 10~ 11~ 11' 12. lH .. " O~ " 2-' H ... 54 6-3 H 8~ 8-' ,. 10·7 II~ 12. 1.1-3 13 .. 0-' H H ,.. ' -3 5-2 6-1 6~ H H ,. 10. '" IN 12~ .. 57 0-8 H B 34 4-2 S~ S~ 6' H 8' n 10~ 10 ' lH 12' 57 54 00 1-6 2' H H ,-, 5-7 6-5 '3 8 I 8-' ' -7 10-5 IH 12-1 54

" 0 -8 I< 2-3 31 3-' 4-' 5 -5 G-2 7~ H 8-5 '-3 10 I 10·8 IIG " .. 08 IS 2-2 3~ 3-7 ' -5 5-2 5-' 6-' 74 8-2 8-' ' -6 10 ·4 11-1 48 .. 0 -7 14 H 2-8 ,.. ... ,-, H 6-3 H 78 8-5 ' -2 ,-, 10 .. .. et 0-7 14 2~ .., 34 H .., 54 6~ 6-7 74 8~ 8 7 ,. 10~ .. " O~ ' -3 ,-, B J.2 ,.. .. S~ 5-7 G-3 6' H 8 I 8. ,. " " O~ 1-2 " 2. 3~ ,.. H ,-, 5-3 5-' 64 ,~ 76 8-2 8-7 " " O' H I< .. 27 H .. .. ,~ •• G~ 6-5 71 H 8 I " 30 0 -5 I~ 10 2~ 2-5 3~ 35 ,~ ... H .. 6~ 6-5 7~ ,. ,. IT 0 -5 0-' 14 " 2-3 2-7 32 H H ,. .~ 54 S~ G-3 60 IT .. O. 0-8 ' -2 I< H 2. 2' H H H .. ' -8 5 -2 H GO H

" 0-3 0-' H 14 " 22 2 -5 2-' 3-2 H H ' -3 ' -6 H S~ " 18 0 -3 0 -6 0 -' 1-2 I< 1-' 2-2 2-' 2-8 H 34 H ' -0 H H tI

" 0 -3 0 -5 0-8 I~ ,~ I< I. H 2-3 ... ... H H ,.. .. " " 0-2 O' O~ O' I~ I . 1-5 1-7 '" H 2~ .. 2-' 2-' 31 12

• O~ o. 0-5 0-6 0-8 I~ H 1-2 14 I< H 1-_ 2~ 2-2 2. • • 0 -' 0-2 0 -3 O. 0-5 O~ 0-7 O. O~ 10 H I • I ~ B 16 • , 0 -1 0 -1 0-2 0-2 O~ 0-3 O. O' OS 0-5 O~ O~ 0 -7 0-7 08 3

T 4' 6' 8" 10' 12' 14" 16" 18" 20' 22" 24' 2l>' 28' W

In both North and SoYth lati tudes liways allow t he above cor rection, toward, the Equator from the Radio Grnt Clrct, bearln, to obtaJn the correspondln, Mercatoria] li~ of burln,.

N .8 .-The Burin,. must alw.t.ys be bid 01'1", on the ch~. from the Radio Station.

EXAMPlE I. A ship In D.R. position Lu.. lr 37' N .. Lon,. 56- 25' W .• (<<.Ivu from l Radio

Statloo In Lat. IS· I'" N .. Lone. 7Sg 32' W., u.e Radio beanne 07 .. G• Find tlMo correction and the correlpondln, Meraotorial bu r ing.

Men Lilt . I. t (39' 37'+35" 14' ) o r t (7"· 51 ' ) - 37·· ...

O. Lone. I1 75· 31' _ S6G 25' _ 19'· 1.

For Mun lat. 37" ... and D. Lone. 19"·1 the Table "ves .. corrc«lon of 6· (approx.).

Allowin, th ll correction towards tJle Equator t hoe correspond ;n, MerutorlaJ budne Is found to be 07 .. 'r 6- _ 080-.

EXAMPLE 2. A ship In D.R. position ut. 37· 26' S .. Lone. 84" 35' W., finds, with her own appantus, thoe Radio bearln, of a uatiorl In Lat. 360 37' 5., Lon,. 73" 0) ' W ., to be 089' . Find the correction and t he correspondln, H,rC:iltor ial bear In, .

for' Mbn u t. 37" and D. Lone. 110.5 tJlc Tablc ,ives a correction of ) 0·5 (lpproX.) .

Allowin, thl, correction towards tkle EquatOf' tkle correspondin, M,rcatoria! beanne is b.lnd to b, (189'-) 0·5 _08SG.S,

522

A" Time A" 0 h.m.

0

, m. $.

• .00 60 1 00< 61

• • 08 62 3 012 63 4 '16 64

5 02. 65 , 024 66 , 028 67

• 032 68 • '36 69

10 040 7. 11 .... 71 1 • • 48 n 13 052 73 14 '56 74

16 '00 7S 18 , O. 76 17 108 77 18 112 78 19 116 79

•• 120 80 ., 124 81 •• 128 82 .3 132 83 24 , 36 8< .5 , 40 85

•• 144 86 .7 '48 87

•• , 52 88

" 156 89 30 200 90 31 20< 91 3. 208 92 33 212 93 34 21' 94

35 22. 95 36 22. 96 37 228 97 38 232 96 39 236 99 4. "0 100 41 ". 101 42 248 102 43 252 103 44 256 104 45 3 O' 105 4, 30< 106 ., 3 08 107 48 312 lOO 4. 3 16 109 50 32' 110

" 32' 111

" 328 112 53 332 113 54 '" 11.

55 HO 11S

" 344 116 57 H8 117 58 352 "' .. 356 119

80 .00 120

CONVERSION OF ARC TO TIME Time A" Time A" Time A" Time A" Time A" Time

Parts h.m. 0 h.m. 0 h.m. 0 h.m. 0 h.m. 0' .,

" 400 120 800 18. 1200 240 1600 300 2000 ' ·1 0'4 404 121 804 181 1204 241 1604 301 2004 408 122 808 182 1208 2" 1608 302 2008 '·2 08 4 12 123 812 183 1212 243 16 12 303 2012 416 124 816 18< 1216 24' 1616 30. 2016 . ·3 1·2 420 125 820 185 1220 245 1620 3" 2020 ••• H 424 126 824 186 1224 246 1624 306 2024 428 127 828 187 1228 24' 1628 307 2028 •. , 20 432 128 832 188 1232 24. 1632 308 2032 436 129 836 189 1236 249 1636 309 2036 .,' 2·4 440 13. '4{) 190 1240 25. 1640 31' 20 40 444 131 .44 19£ 1244 '" 1644 311 2044 .., 2·' 448 132 .48 192 1248 252 1648 312 2048 452 133 852 193 1252 253 16 52 313 2052 . ·8 3·2 456 134 '56 19. 1256 254 1656 31. 2056 500 135 900 '95 1300 l5S 1700 315 2100 ',9 36 504 136 904 196 1304 25, 17()1 316 2104 508 137 908 '" 1308 257 1708 317 21 08 5 12 138 912 198 1312 258 1712 318 2112 516 139 916 199 1316 259 17 16 319 2116 520 140 920 200 1320 260 1720 320 2120 524 141 924 201 1324 261 1724 321 2124 528 142 928 202 1328 262 1728 322 2128 532 143 932 203 1332 263 1732 323 21 32 536 144 936 204 13.36 264 1736 32. 2136 540 145 940 205 13 40 265 17 40 l2S 214{) 544 146 944 206 1344 266 1744 326 2144 548 147 948 207 13 48 267 1748 327 2148 5 52 148 952 208 13 52 26 • 17 52 328 2152 556 149 956 209 1356 26' 1756 329 2156

600 150 1000 21' 1400 27' le (l(J 330 2200 604 151 1004 211 14 ()I 271 18 ()I 331 22 ()I 608 152 1008 212 1408 272 1808 332 2208 6 12 153 10 12 213 14 12 273 1812 333 22 12 616 15. 10 16 21. 1416 27. 1816 33. 2216 620 155 1020 215 1420 275 1820 335 22 20 624 156 1024 216 1424 276 1824 336 2224 628 157 1028 217 1428 277 1828 337 2228 632 158 1032 216 1432 276 1832 338 2232 636 159 1036 219 1436 279 1836 339 2236 64{) lOO 1040 220 144{) 28. 1840 340 22 40 644 161 1044 221 1444 281 1844 341 2244 648 162 1048 m 1448 262 1848 342 2248 652 163 10 52 223 1452 263 1852 343 22 52 656 164 1056 22. 1456 26. 1856 344 2256 700 165 1100 225 1500 285 1900 34' 2300 7 ()I 166 1104 226 1504 286 1904 34' 2304 708 167 1108 227 1508 267 1908 347 2308 712 168 1112 228 15 12 288 1912 348 2312 716 169 1116 219 1516 269 1916 349 2316 720 17. H2O 230 1520 290 1920 350 23 20 724 171 1124 231 1524 291 1924 351 2324 728 172 1128 l32 1528 292 1928 l52 2328 732 173 11 32 23J 1532 293 1932 353 2332 736 17. 1136 23. 1536 29. 1936 35. 2336 740 175 1140 235 1540 295 194{) 355 23 40 744 176 1144 236 1544 296 1944 356 2344 748 m 1148 2J7 1548 297 1948 357 2348 7 52 176 11 52 236 1552 296 1952 358 23 52 756 179 1156 239 1556 299 1956 359 2356 800 180 1200 240 1600 300 2000 360 2400

A"

· • 1 2 3 • 5 , 7

• 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2. 25 26 27 28 29 30 31 32 33 34 35 36 37 36 39

40 41 42 43 44

45 46 47 48 49

50 51 52 53 54

55 56 57

" 59 60

Time.

., 0·00 0.Q7 0 ·13 0·20 0·27 0;].3 0-40 0·41 0·53 060 0-67 0-73 0·80 0·87 0·93 1·00 H7 H3 1·20 1·27 1·;].3 1-40 1-47 1·53 1·60 1·67 1·73 1-80 1·87 1-9, 2·00 2·07 2-13 2·20 2·27 2·;].3 2·40 2·47 2·53 2·60 2·67 2·73 2·80 2·87 2,93

'·00 3·07 3-13 '·20 3-2'1 3'33 ,·40 347 ,,53 3·60 3·67 3'73 ',00 ,.8'/ ',93 4,00

I !

-SUN ' S TOTAL CORRECTION

To be epp/ifu} to (he Observed A lrirude of the Sun's Lower (LI 0' Upper (U) Limb

H"ig~t of Eve

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" 14. ' " ,n '. 24.5 " " , " '4.' .. , 15. 1 .. , 26.J .. ". AOOITION M. MONTHLY CORRECTIO N

'M ,~ M. .. M .. ~". ,., . ~ ••• ~ .~ o~ u ~., ~., ~. , 00 ~. , ~ , ~., ~, ~ . 00 ~, ~.,

~ ~, ~ , ~. ., ~, W., ~, W., ~. 00 ~, ~,

7.7", ('5~1

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-+-7.3 ~24, 7 ) .5 24, ~

) .7 ]4, 3

7.9 24.1 a., 23.9 8 . ) 23. 7 a . ~ 23.5

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~,' 22.9 ~, 3 22. 7 9 ,! 22.5 9 ,1 1).3

9 ,9 22. I

+5.9 - 26. 1

6.' 25.9 e. 3 25. 7 M 25.5 e.7 25.3 6 ,9 25, I

H ,' - 24 .9 7 ,) 24.7 7.! 24.5 7.7 24.3 7.9 14. 7 8 .1 2:1.9 8 .3 2J. '

+ 8 .5 - 23.5 $.1 23.3 8.9 23. 1 9.' 22.9 ~. 3 n.7 9. ~ 21.5 P 21.3

9.1", (JOII)

~ 5, ) -26,3 5 .9 26. I 6 .1 25.9 6 .3 25.7 6.5 25.5 6.7 25 .3

# .9 - 25. 1 7J 24. ~

7. ' 24. ' ) .5 24.5 7. ) 14,3 7.9 24, 1 8.1 23.9

9 ,8", (32ft)

+5 ,5 - 26,5 5 ,7 26.3 5 ,9 26. 1 6 , I 25.9 6 .3 25. ' 6 .5 25 .5

# .7 - 25.3 6 .9 25. 1 1.1 24.9 ) .3 24. 7 ) .5 24 ,5 1,1 24.3 ) ,9 24. 1

+8 .3 _23. 7 +8 .1 _23.9 8.5 23.5 8.3 23. 7 8 .7 13.3 6 .5 23.5 6.9 13. 1 8 .7 23.J g .' n .9 6.9 23. 1 9 .3 22. 7 g . ' 12.9 9.5 2:1.5 g. l 22. 7

+' 0.1 -:11.9 +{I ,g - 22. 1 10.3 21.7 'o,, 21 .9 10.~ n5 '0.3 2'- ' 10.' n3 10 ,5 2) ,5 10.9 nl 10. ) 21.3 , '-' 20.9 10 ,9 21 I

+11.7 - 22,3 9 .9 22. 1

'0,1 21.9 10,3 21 . ' 10 .5 21 .5 to, ) 21 ,3

-+-9.5 - 22,5 9 . ) 22.3 9.9 22. 1

10 ,1 21 .9 10.3 21 . 7 10.5 21 .5

lQ,lm (10011) , " ,) - JCl.l

' .5 i/O.5 '-' 30.3 1.9 30.1 V 19.9 :1.3 29. 7

+. ,5 - 29.5 l ,7 29.J 2,9 29, I 3.1 ]8,9 3 .3 28. 7 3.5 28.5 3.7 28,3

+3.9 - 28, 1 . , ]7.9

4 ,3 2 7.7 4 ,5 27.5 4,) 27.3 4 ,9 21.1 5. ' 26.9

3 1.em 1 32 .9 .... (104ft1 (10all)

, " _' .1 -30,9 -0.9 -JI I

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- 0 .1 - 31 .3 0.9 31 . 1 1.1 30.9 1.3 30.7 1.5 30.5 L7 30.3

+2 .3 - 29, 7 +2 . ' - 29.9 + 1 .9 -30. 1 2.5 29, ~ l .3 29.7 2 .' 29.9 l, 7 29,3 2, ~ 29.5 2. ) 19.7 2 ,9 29. / 2 ,7 29.3 2,5 29.5 3,1 28.9 2.9 29. 1 l, 7 29,3 3 ,1 28.7 3, ' 28.9 2 ,9 ]9, 1 3 , ~ 28 ,5 J ,3 28. 7 l .' 28.9

H ,7 -28 ,3 3.9 28, I 4 .' 27,9 4 .3 27, 7 '. 5 27,5 ' .7 27,3 '. 9 27. I

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+3 .3 -28 . 1 3.5 28.5 3 .7 28.3 3 .9 2~. 1

4 .' 27.9 4 .3 27.7 ~ . 5 27.5

+5 ,3 -26.7 +5 .' - 16.9 -H.9 - 27.1 5 ,1 28.9 ~.3 26. 1 5 .5 26.5 5.' 26.3 5.9 26. I

-H .7 27.3 ' .9 ]7, I

~ .' 26.9 ~ . J 26. 7 ~ . 5 26.5 5 .1 26.3

5 ,5 26.5 5,) 26.J 5,9 26. I 6, ' 25. 9 6.3 25. J

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_ 5,3 - 26. 7

5.5 26.5 5. 7 26.1 5 .9 26. 1 6 .1 25.9 ~. 3 25. '

11.2 .... (31ft)

, " +5.1 -26.9

$.3 26.7 $. ~ 26.5 5 .1 26.3 5.9 26.7 6.1 25.9

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12 .0m (39 ft)

H .9 _27. 1 S .1 26.9 5 .1 26. 7 $ .5 26.5 5 .1 26.3 5 .9 26. 1

'2.em 4 2ft)

, " +4 .7 - 27.J

4 .9 27.1

~ .' 25.9 ~ . 3 25. 7 5 .~ 26.5 ~ . 7 26.3

-+15 .1 ~n. 9 +5 .9 - 26. 1 G.3 25. 7 e.' 25.9 6.5 25,5 6 ,J 25.7 6 ,) 25.3 6 .5 25.5 6 ,9 25.1 6.7 25.3 7 ,1 14,9 6 ,9 25. 1 7 ,3 14.7 7.1 24.9

-+-) ,9 - 24 .1 8.' 23.9 8 ,3 23.7 8 .5 23.5 8 .7 23.3 8 .9 23.1 9 .' 22.9

+7 ,) - 14.3 +7 .5 _24 .5 + 1 .3 _14. 7 ) .9 24. 1 7 .7 24.3 7 .5 24.5 8 .1 23.9 7 .9 14. 1 ' .7 24.3 e .] 23. 7 8 .1 23.9 7 .9 24.1 8 .5 23.5 8.3 23. 7 e.' 23.9 8 .7 23.3 8 .5 23.5 8 .1 23.7 8 .9 23.1 8 .7 23.J e .5 2J.5

' 4, 5M (4all) , ,

15,4m (SOli)

, " 16.3m (53ft) , ,

+4. 5 - 27.5 4 .7 27.J 4 .9 27.1 5.' 26.9 5 .3 25.7 5 .5 26,5

H .3 -27. 7 4 .5 27.5 4.1 27.3 4.9 27. 1 5, ' 26.9 5 ,3 26. 7

H .l -27,9 _3 .9 -28. 1 " .3 27, 7 4,' 27.9 4, 5 27,5 4,3 27. 7 ",1 27, ] 4 ,5 27.5 " .9 27. 1 4 .7 U .:! 5 ,1 26.9 4 .9 21. 1

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+7.1 - 14.9 7.3 24, 7 ' .$ 24.5 '-' 24.3 1 ,g 24, I 8 .1 23,9 8 .3 23, 7

+!l ,g - 25, I 1, t 24,9 ) .3 24.7 ) , ~ ]4,5 ),7 14.3 ) , ~ ]4, 1 6,' 23.9

<-<3 ,7 - 25.3 6 ,9 25.1 7,1 24.9 7 .3 24 . 7 7 .5 24.5 7 ,7 24.J 7 .9 24.1

-HI ., - 26.9 5.3 25. 7 5 .5 26.5 5 ,7 26.3 5 ,9 26. I 6 ,' 25.9 6 ,3 25.7

<-<3 .[; _25.5 e .7 25.3 6 .9 25. I 7 .' 24.9 7.3 24.7 7.5 14.5 ,., 24.3

+9 .3 _22 .7 +9 .1 _22.9 +8 .9 - 23. 1 +8 .7 - 23.3 +6.5 - 23,5 +8,3 - 23.7 +6.1 - 23.9 + ) .9 - 24. 1 6 ,1 23, 9 6 ,3 23, 7 8,5 23,5 8 . ) 23.3 8 .9 13, I

g .5 17.5 9 .3 22. 7 9 .' n ,9 8 ,g 23. 1 8 . ) 23.3 8 .5 23.5 8 .3 23. 7 9.7 17.3 9 . ~ n.5 9 .3 n , 7 g ,' 22.9 8 .9 23. 1 8 .1 23.J e .5 23.5 9.9 n.1 9.' 11.3 9 . ~ n " g ,J 22. 7 9 .1 22.9 8 .9 13.1 e .7 23.3

10.1 21 ,9 9 ,9 22, 1 9.7 22,3 9 ,5 22.5 9 .3 22. 7 9 . ' 11.9 8 ,9 23, I 10.3 21.7 10 , ' 21 ,9 9 ,9 22, 1 9 ,7 22.3 9 .5 22.5 9 .1 22. 7 9 .' 2:1.9

35 .S", (117ft)

, " -O.S -31 . ~

0.1 31 .3 0 .9 31.1 , ., 30.9 1.3 30.7 '. 5 30.5

+1 .7 -30.3 1.9 30. 1 2.' 29.9 2,J 29. 7 2,~ 29.5 2,7 29.3 l .9 29, I

H .' -18 ,9 3 .3 28, 7 3.5 '8,5 3.) 28.3 3.9 28, 1 4 .' 27,9 ' .3 27.7

.... . ~ - 27.5 • . ) 27,3 ' .9 27, 1 ~ .' 26,9 ~ .3 26, 7 ~ . 5 26.5

J7 ,O ... :121ft)

I (~~iffl , ,

.0.3 _31 .7 -IQ., -31.9 0 .5 31 .5 0 .3 31.7 0 . ) 31 .3 0 .5 31.5 0 .9 31 . 1 0 .7 31 .3 '-' 30.9 0 .9 31.1 1.3 30. 7 1.1 30.9

~1 .5 -30.5 Ll 30.3 1.9 .10. 1 • . 1 19.9 ~ .3 29. J

2.5 29.5 2 .7 29.3

+2 .9 - 29. 1 3 .' 2e.9 3 .) 28. 7 3 .5 28.5 3 .7 28.3 3 .9 2e, 7 ~ ., 27.9

+1 .3 -30.7 1.5 30.5 1.7 30.3 ' .9 30. 1

" " +2.7 - 29.3

2 .9 29.1 3.' 28.9 3.3 28. 7 H 28 .5 3 .) 28 .3 3 .9 28 . I

4O .0m (13111)

" ' 0 .1 ' 32. 1

-IQ. ' 31 .9 0 .3 JI . 7 0 .5 31 .5 0 .1 JI .3 0 .9 JI . I

+1.1 _30.9 1.3 30.7 1.5 .10.5 1.1 30.3 1.9 30. 1 2.1 29.9 2 .3 29. 7

+~.5 - 29.5 2 .7 29.3 2 .9 29. 1 ) ., 28 .9 ).J 28.7 3 .5 28.5 3 .7 28.J

-H .3 _27. 7 -H .' - 27.9 H .9 - 28.1 4 .5 27.5 ' .3 27. 7 4 .' 27.9 4 .7 27.3 '. 5 27,5 4.3 27.7 4 ,9 17. 1 ' .1 ]7,3 4, ~ 27,5 5 .' 2~. 9 ' .9 ]7. 1 4 .7 27. 3 5 .1 26. 7 5 .1 26.9 4 .9 27. 1

41 ,5m (13511)

43.0", (1401I)

, " · 0 .1 -32.J ' 0 .5 -32.5 -0.7 ' 32. 7

0 .' 32.1 0 .3 32.J 0 .5 32.5 -IQ . I 3UI 0 .1 32. 1 0 .1 32.3

0 .1 31 . 7 -IQ .' 31 .9 0 .' 32. 1 0 .5 37 .5 0 .1 31-' +O:i 31.9 0 .7 31 .3 0 .5 37 .5 0 .3 31.7

-IQ.9 _31 .1 1.1 .10.9 1. 3 30. 7 1.5 3O,~

\.1 30,3 >.9 30.1 2.1 29.9

+2.3 - 29. 7 2 .S 29.5 2. 7 29.3 2.9 29. I 1.' 2e.9 3.1 28. 7 3.5 28.5

H.7 - 2e. 3 3.9 28. 1 • . , 27.9 ',3 27. 7 ' .5 27.5 ~ . 7 27.3

-IQ.7 _31 .3 0 .9 31 . 1 1.\ 30.9 1.3 30. J 1. ~ 30.5 1.1 30.3 1. 9 30.1

+2 .1 - 29.9 2.1 29. 7 2.5 29.5 2 .1 29.3 2.9 29. 7 3.1 28.9 3.J 28.7

+3 .5 - 28.5 3.1 28.3 3.9 28. 1 '.1 27.9 '.J 27.7 4 .5 27.5

-IQ .5 -31 .5 0 .7 31 .J 0 .9 37 .1 1.1 30.9 1.3 30.7 '. ~ 30.5 1.1 30.J

+'. 9 - 30. 1 2.' 29.9 2.1 29. 7 2 .$ 29.5 2.? 29.3 2.9 29. 1 3.1 2S.9

+1.3 _2S. 7 3.5 28.5 3.1 2e.3 3.9 28. 7 4.1 17.9 4 .3 27.7

4e,Orn ( 1 50ft)

, " -0 .9 ' 32.9 0 .7 32. 7 0 .5 32.5 0 .3 32.3 0 .1 32. 1

+<l.1 31 .9

-IQ.3 _31 . 7 0 .5 JI .5 0. ' 31 .3 0 .9 3 1. I 1.1 30,9 ' .3 30. 7 ' .5 30.5

+1 .7 -30.3 1.9 30. 1 2.' 29.9 2 .3 29.7 2.5 29.5 2 .7 29.3 2 .9 29. 1

H .I _28.9 3.3 28. 7 H 28 .5 3 .7 28.J 1.9 28 .1 4 . 1 27.9

17.2,., (56ft)

'3 .7 _28.3 3.9 28.1 4 .1 27.9 4 .3 21.7 4 .5 27.5 4 .7 27.3

.... . 9 - 27, I 5.1 26.9 5.1 26.7 5 .5 26.5 5 .7 25.3 ~ . 9 26. I e.' 25 .9

.. tU -25.' 6 .5 25,5 6 .3 25.3 6 ,9 25.7 7 ,' 24.9 7,J 24. 7 7 ,5 24.5

-+-7 ,7 -24.3 7 ,9 24. 1 8,1 23,9 8 ,3 23, 7 8 .5 23,5 6 .7 23.3

4, ,5m (15511) ,

.1.1 ' 33, 1 0 .9 32,9 0 .1 32.7 0 .5 32,5 0 .3 32,3

...!2J. 32, 1

+<l.1 ~31 , 9

0.3 31.7 0 .5 31 ,5 0 ,1 31 ,3 0 .9 31 . 1 1. 1 30,9 1 ,3 30.7

+' ,5 - 30.5 1,7 30.3 >. 9 30. 1 2. ' 29.9 2 .3 29. 7 2 . ~ 29.5 2 .7 29.3

H .9 -29. 1 3 ,' 28,9 3,3 28. 7 3 , ~ 28.5 3 ,7 28.3 3.9 1S. I

-DECIM"'~S OF THE DEGREE

STAR'S TOTAL CORRECTION

, .0 . 2 ·G •• Metres ,., u ", ,. , '" ", ••• ••• , .. , .. U ",

Fee, , , • 00 " " ,.

" " " " " 0 0.000 0.003 0.007 0.010 0.013 Ob ..... 't. , , , , 1 .017 _020 ,023 .02 7 .030 .000 ,., ,., .., ,8 .4 ... ... .. , .., ... ••• .. , 10. 0

2 .033 .037 ,040 ,043 .047 " ". , ., .., ,. , , .. , .. ... .., .., ... ••• ... 3 .050 .053 .057 .060 .063 "00 ". ". '"

,., ,., , .. , .. ... .. , .., ••• ••• 4 .067 .070 _0 73 . 077 .080 " ", ". , .. ,., ,., .., , .. , .. ... .. , .., ••• 5 0 .083 0 .087 0.090 0 .093 0 .097 "00 ", ,., ". ". ,., ,., .., , .. , .. ... .., .., 6 .1 00 .103 .107 .110 .113 " .. , ", ", , .. ". , ., .., .., , .. ... ... .. , 7 .117 .120 .123 .127 .130 n oo ••• .. , ", ", , .. , .. ,., ,., ,., , .. ... ... • .133 .137 .140 .143 . 147 " ••• ••• .. , ", ,. , ". ". , ., ,., .., , .. , .. 9 .150 .153 .157 .1 60 .163 " 00 .., ••• ••• .. , ", ", , .. , .. ,., ,., ,., , ..

"00 .. , .., ••• ... ... ", ", ". ". '" ,., ..,

10 0. 167 0. 170 0.173 0.177 0.180 "00 ,., .., .., ••• ••• .. , ", ", ". ". ,., " " .183 .1 87 .190 .193 .197 " 00 , .. ,., .., .., ••• ... ... ", ", ". , .. ,.,

12 .200 .203 .207 .210 .21.3 "00 , .. , .. ,., .. , .., ••• ••• .. , ", ", ". ". 13 .217 .220 .2 23 .227 .230 "00 ,., , .. , .. ,., .. , .., ••• ••• ... ,., ", ". ,. .233 .237 .240 .243 . 247

15 0.250 0 .253 0 .257 0.260 0.263

" .267 .270 .273 .277 .280 17 .283 .287 .290' .293 .297 18 .300 .303 .307 .310 . 313

" .3 17 .320 .323 .327 . 330

" 00 ,., .., , .. , .. ,., .. , .., ••• ••• ... ,., ",

"00 ... ,., .., , .. , .. ,., .. , .., ••• ••• .. , ,., ,"00 ••• .., ,., ,., , .. , .. ,., .., .., ... ••• .. , "00 ••• ••• ... ,., ,., , .. ... ,., .., .., ••• • •• "00 .., ••• ••• .. , ,., .., , .. , .. ,., .., .. , &: 4

"00 .., .., ••• ••• ... ,., .., , .. , .. ,., .. , .., 20 0.333 0.337 0.340 0 .343 0.347 21 .350 .353 .357 .360 . 363 22 .367 .370 .373 .377 .380

"00 '" .., .., ••• ••• .. , ,., ,., , .. , .. ,., ..,

"00 H ,., .., .., ••• ••• ... ,., ,., , .. , .. ,., '"00 , .. , .. '"

.., .., ••• ... ... ,., .., ... ... 23 .383 .387 .390 .393 .397 24 .400 .403 .407 .410 .413 ,"00 ,., ". ". '"

.., .., ••• ... .. , ,., ,., , .. "00 ", ,., , .. ". '"

.., .., ••• ••• .., ,., ,., 25 0.417 0.420 0.423 0.427 0.430 '"00 ,., ", .., ". ". '"

.., .., ••• ••• ... ,., 26 .433 .437 .440 .443 .447 "00 ". ,., ,., .., ". , .. ,., .., .., ••• ••• .. , 27 .450' ,453 .457 .460 .463 0000 ,., ,. , , .. ,. , ", ,., ,., ", .., .., ... .., 2. ,467 .470 .473 .477 .480 29 .483 .487 .490 .493 .497

Me tres 22.2 23 . 3 24.4 25.5 ~., 27.9 29. I ~., 31. 6 '32.9 M.' 35.5 30 0.500 0.503 0.507 0.510 0.513 Feet " "

., .. .. ~ " ;, W. 00' m '" " .517 .520 .523 .527 .530 32 .533 .537 .540 .543 .547 33 .550 .553 .557 .560 .563 34 .567 .570 .573 .57 7 .580

Ob, . .oJt , , , , .000 13. 6 13. 9 14.0 14.2 1'.4 14.6 14.9 15. 0 15.2 15.4 15.6 15.8

" 13.4 13. 6 13.9 14. 0 14.2 14.4 14.6 14. 8 15.0 15.2 15 .4 15.6

" 00 D.2 13.4 13.6 13.9 14.0 " .2 1 ••• ,'.6 " .8 15.0 15.2 15.4

35 0.583 0 .587 0.590 0.593 0.597 " 13.0 13.2 13.4 13.6 D.8 ".0 ".2 "., 14.6 ".B 15.0 15.2

" .600 .603 .607 .610 .613 37 .617 .620 .623 .627 .630 38 .633 .637 .640 .643 .647 39 .650 .653 .657 .660 .663

"00 12.9 13.0 13.2 13.' 13.6 13.8 14.0 14.2 ".4 14.6 ". 9 15.0

" 12.6 12. 8 13.0 13.2 D.' 13.6 13.8 " . 0 ".2 14.' ,' .6 ,'.8 noo 12. ' 12. 6 12.9 13.0 13.2 13. ' 13.6 13.8 14.0 ".2 ".4 , '.6

" 12.2 12.4 12.6 12.8 13.0 13.2 13.t 13.6 D.8 14.0 " .2 1 •. •

40 0 .667 0 .670 0.673 0.677 0 .680 '"'' 12.0 12.2 12.' 12. 6 12.8 13.0 D.2 13.' 13.6 13.6 14.0 ".2 41 .683 .687 .690 .693 .697 "00 11.B 12.0 12.2 12.' 12.6 12. 8 13 . 0 13.2 13.' 13.6 13. 8 14.0

4' .700 .703 .707 .710 .713 "00 11.6 11.8 12.0 12.2 12.' 12.6 12. 8 13. 0 13.2 13.4 13. 6 13.9

43 .717 .720 . 723 .727 .730 "00 11. • 11 .6 11.8 12.0 12.2 12.4 12.6 12.8 13. 0 13.2 13.' 13. &

44 . . 733 .73 7 .740 .743 .747 "00 11. 2 11 . ' 11.6 11.8 12.0 12.2 12 . ' 12. 6 12.8 13.0 13. 2 13.' "00 11.0 11.2 11.' 11.6 11 .8 12.0 12.2 12. t 12.6 12.8 13. 0 13.2

" 0.750 0.753 0.757 0 .760 0 .763 46 .767 .770 .773 .777 .780 "00 10.8 11. 0 11.2 11.t 11.6 11.8 12.0 12.2 12.' 12.6 12.8 13.0

47 .783 .787 .790 .793 .797 ,,00 10.6 10.8 11.0 11.2 11.' 11.6 11.6 12. 0 12.2 12.' 12.6 12.B 4. .800 .803 .807 .810 .813 "00 10 .• 10. 6 10 . 6 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12. 6 49 .817 .820 .823 .827 . 830 "00 10.2 10. t 10.6 10.8 11.0 11.2 11.' 11.6 " . 8 12.0 12.2 12. 4

"00 10.0 10.2 10.' 10.6 10.8 11.0 11. 2 11.t " .6 11.6 12.0 12. 2 50 0.833 0.837 0 .840 0.843 0.847 "00 ... 10.0 10.2 10.4 10.6 10.9 11.0 11 .2 11.. 11.6 11.6 12.0 51 .850 .853 .857 . 860 .863 52 .867 .870 .873 .877 .880 53 .883 .887 .890 .893 .897 54 .900 .903 .907 .910 .913

"00 ... .. , 10.0 10.2 10.' 10.~ 10.8 11.0 11 .2 11. t 11. 6 11.8

" 00 ... ••• ... 10.0 10.2 10.t 10.6 10.9 11.0 11. 2 11.4 11. 6

'"00 .., ••• ... ... 10.0 10. 2 10.' 10.6 10.6 11.0 11.2 11.4

55 0 .9 17 0 .920 0.923 0.927 0.930 56 .933 .937 .940 .943 . 947 57 .950 .953 .957 .960 . 963 58 .967 .970 .973 .977 .980 59 .983 .987 .990 .993 . 997

,"00 .. , .., ••• ... .. , 10 .. 0 10.2 10.4 10.6 10.8 11.0 11.2

"00 ... .., .. , ••• ••• ... 10.0 10.2 10.' 10.6 10.8 11.0

'" 00 , .. ,., .., .. , ••• ••• ... 10.0 10. 2 10 •• 10. 6 10. 8

"00 ... , .. ,., .., .. , ••• • •• .., 10.0 10.2 10.' 10.6 0000 ,., ,., ,., , .. .. , .. , ... .., ••• 10. I 10.3 10.5

"

To be SUBTRACTED from the Observed Altitude of the 5t8r

Height of Eye ,., ••• .. , ••• lO.S '1.2 12.0 12 .8 13.6 '4,$ 15.4 n.l 17.2 18.2 19. 2 "., 21. 2

" " ~ ~ ~ " " " .. .. " " " " " .. ~

, , , , , . 10.2 10. ' 10. 6 10.8 11 .0 11 .2 11 .' 11 .6 11.8 12.1l 12.2 12. ' 12.6 U . I 13.0 13.2 11. 4

10.0 10. 2 10. ' 10. 6 10. 8 11.0 11.2 11 . 4 11. 6 11.8 12.0 12.2 12.4 12.6 12.8 13. 0 1l.2

••• 10.0 10. 2 10. ' 10. 6 10. ' 11 .0 11 . 2 11 .' 11.6 11 .8 12.0 12.2 12.' 12.6 12 .8 13.0

••• • •• 10.0 10.2 ID. ' 10.6 la.' 11 .0 11 .2 11. ' 11 .6 11 . 11 12.0 12.2 11.' 12.6 12. '

0.' ••• ••• 10.0 10 . 2 10 • • 10.6 10. 8 11.0 11.2 11 .' 11. 6 11.8 12. 0 12. 2 12 .• 12 .6 .., ••• ••• ••• 10.0 10. 2 10. ' 10.6 10. 8 11.0 11 .2 11. ' 11 .6 "., 12.0 12.2 12, ' .. , .., ••• ••• ••• 10. 0 10. 2 10. ' 10.6 10.8 11 .0 11 . 2 11 .' 11 .' 11 .8 12.0 12.2

••• .. , .. , ••• 0.' '. 1 10.0 10. 2 10 . • 10.6 10.8 11. 0 11 .2 11 . ' 11 . 6 11 .8 12. 0

I.' ••• .. , .., ... ••• ... 10.0 10. 2 10. ' 10.6 10.8 11.0 11. 2 11. ' 11 .6 11 . 8

••• •• • ••• .., .., ••• ... ••• 10.0 10.2 ID. 4 ID.~ ID.8 11. D 11.2 11 .' 11 . ' .., ••• ••• • •• ••• .., '.' ••• ... 10.D lD.2 10. ' 10.6 10. 8 11.0 11 . 2 11. ' .. , .., ••• • •• 1.1 .. , .. , ••• ••• ••• lD.O 10. 2 10.' 10.' 10.8 11 .0 11. 2 , .. .. , .. , ••• ••• 1.1 .., .., • •• ••• ••• 10.0 10.2 10. 4 10.6 10. 8 11. 0

'" ' .1 .. , .., I.' ••• ••• .., .., ••• ••• ... 10.0 lD.2 10: ' 10 .6 · ID.'

'" , .. ' . 1 .. , I.' ••• ••• ••• .. , .., ••• ••• ... lD.O 10.2 10 . • l D. 6

'" , .. , .. ?' .. , I.' ••• • •• ••• .., .. , ••• ••• ••• 10. 0 10. 2 lD . 4

?' '" '" ? ' ?I I .' I.> I. ' I.' ••• .. , .., ••• ••• ••• 10. D lD.2

". ?' '" ? .• , .. ?I .. , .., ••• ••• 1 .1 .. , .., ••• ••• ' .1 10 . 0

••• ••• M '" '" ?' ?' .. , .. , ••• ••• ••• .. , .., ••• ••• • •• ••• ••• ••• ? ' '" '" , .. ?' I . ' .., ••• ••• ••• .., .., ••• ••• .. , ••• ••• ••• M '" , .. , .. ?' .. , .. , ••• ••• 1. 1 .. , .., 0.' .. , .., ••• ••• '.1 ?' '" ?' ?' ? ' .. , .., I.' I . ' 1. 1 .., .., ••• .., .., ••• ••• • •• ?' '" ?' ?' ?' .. , I.> I . ' ••• ••• .. , , .. ••• .. , .., ••• ••• ••• ?' '" ?' '" ?I I. ' .., ••• • •• ... , .. ••• ••• .., .., ••• ••• ••• ?' '" ?' ?' ?' .. , .., •• • I .' .., ••• ••• ••• .. , .., ••• ••• ••• ?' '" ?' '" ?I I . ' .. , • •• ,., .. , ••• ••• ' .1 .. , .., ••• ••• ' .1 ,., '" ?' '" ?I ... I.> ... .. , .., ••• .. , ... .. , .. , ••• .., • •• ? , U ?' '" ?' I . ,

JI . D " .. ~ .. '1 . 5 ·3.D " .. ... , n .s '9. D

'" ". '" ". '" , .. '" '" '" , , , , 16.D 16. 2 16 . ' 16.6 16. 8 17. D 11. 2 11.' 11. 6

15.8 16 . D 16.2 16 . ' 16. 6 16. S 11.0 11.2 11.' 15.6 15.8 16 . 0 16 . 2 16 . ' 16. ' 16.8 I1.D 11.2

15.' 15.6 15.8 16.0 16. 2 16. 4 16.6 16.8 17. 0

15.2 15.' 15. 6 15.8 16.0 16.2 16. ' 16.6 16.8

15. 0 15.2 I S. ' 15. 6 15.8 16.0 16 . 2 16. 4 16.6

".8 15.0 15.2 15 . • 15 . 6 \5 .8 16 .0 16. 2 16. ' 1(.6 14.8 15. 0 15, 2 15. ' 15. ' 1$.11 16.0 16.2

1( . • ".6 14 .8 15.0 15.2 15. 4 1$.' 15.8 16.0 " . 2 14 .• ".6 14 . 8 15. 0 15.2 15.4 15.6 IS.B ,.,0 14. 2 1 •.• 14 . 6 " . 8 15. 0 15.2 15.' 15.' 13.8 ".0 11.2 14.4 " .6 14.8 15.0 15.2 15.'

1l.6 lJ.9 14.0 11. 2 14 . • 14.6 14.8 15.0 15.2

\l.' I l.6 13. B 14 .0 14. 2 14. ' 14.6 14.8 15.0

13. 2 n .' 13. 6 13.9 14 . 0 14 .2 ,. .. ,..6 14.8

13.0 n .l 13.' 13. 6 13. B " .0 14.2 ,. .. 14.6

12.9 13.0 n.2 I l .' 13.6 13.8 ,..0 ".2 1 •.•

12.6 12.8 l l.0 13.2 13.' 1l.6 13.8 ".0 14.2

12.' 12. 6 12 . 9 13.0 13.2 13. ' ll. 6 13. B " .0 12. 2 12 . ' 12 .6 12. 8 l l . 0 13. 2 ll.' 13.6 13.8 12. 0 12.2 12. ' 12. 6 12. 8 13.0 13.2 \l.' 1l.6

" • 12. 0 12 . 2 12 . ' 12,6 12.' Il. O 1l.2 \l.' 11.6 11.' 12 .D 12.2 12. ' l l. 6 12. 1 13 .0 13.2

11 .' 11. 6 11 . 8 12.0 12. 2 12. ' 12. 6 12 . 8 13. D

11. 2 11. ' 11 .6 11 . 8 12 .0 12. 2 i 2.' 12. 6 12 . 8

I 1. D 11 . 2 11 . ' 11.6 11. 8 l l. 0 12.2 12. ' I l . 6

10.8 11.0 11 . 2 11 .' 11 . 6 11.8 12. 0 12. 2 12. '

10.7 I D. 9 11. 1 11 .3 11 . S 11 .1 11 .' 12. 1 12.3

Norie's Nautical Tables [Dieukhientaubien.net]

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