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IrantponadM
Uferaiy
my-
%
THE
CIVIL ENGINEER'S
FIELD-BOOK
• I
f •:
I ' .'
THE
CIVIL ENGINEER'S
FIELD-BOOK:
DBSIONBD FOR THB USB OF THB
LOCATING ENGINEER.
COMTAININO
TABLES OF ACTUAL TANGENTS, AND ARCS EXPRESSED IN
CHORDS OF 100 FEET FOR EVERY MINUTE OF INTER-
SECTION, FROM 0« TO W, FROM A !• CURVE
TO A lO* CURVE, INCLUSIVE;
ALSO
TABLES OF FORMULAS APPLICABLE TO RAILROAD CURVES
AND THE LOCATION OF FROGS;
TOOBTHBR WITH
RADn, LONG CHORDS, GRADES. NATURAL TANGENTS, NATURAL 8INE8,
NATURAL VERSED SINES, NATURAL EXTERNAL SECANTS, ETa
.,1. I i tr ^
;.■-'■.
BY
HDWARD BUTTS,
ClYIL KNGINBKB,
THIRD AND REVISED EDITION,
TOTAL ISSUE, TEN THOUSAND
NEW TORK :
JOHN WILEY hi ^O^^.
LojmoK : CHAPMAN & H AlA., l^iwwwk.
' ■ • " ■' : : ^ /■ ■ ;. J ! / I'J
r ■ f ;
V
9/26
Copyright. 1586,
By John Wiley & SoNft.
Copyright Renewed, 1914,
By Epwabd, i^yrrs.
Printed in U. 8. A. • > •
PKtMl iOf .
BRAUNWORTH & CO., INC.
BROOKLYN. NCWYOMK
<.'
3- *-i. a- \^ -* i<^ vT.
1
PREFACE.
In preparing this book it has been the author's design to
present a volume based on the most economic principles ot
•iC'
field engineering.
Many good books of the kind are in print, yet none of them,
it is believed, have presented the subject to the full extent of
a labor-saving medium.
Considerable time is spent in making mathematical field*
calculations, thereby delaying the party and increasing the
expense of the survey. To eliminate many of the errors that
occur in these calculations, and advance the progress of fields
operations, extensive, hitherto unpublished, tables have been
added to this work, and others previously published have
been enlarged to prevent the field-work extending beyond
their bounds. The formulae are comparatively arranged in a
more systematic manner.
Tlie work of computing the tables has been thoroughly
done, and it is believed will be found strictly reliable.
An effort has been made to make the problems general, and
therefore applicable to any case that may arise in a long
practice. Thrbugliout the work each problem is arranged
with reference to the last preceding figure.
Should this volume prove itself an assistant to the field-
engineer, and fill the space for which it iS' de8i^tv«i^^ ^^^
author's wish will be fully realized. ^* ^*'
Kanbas City, Mo., August, 1886.
;i t
; * ) /
I '
CIVIL ENGINEER'S FIELD-BOOK,
CURVE FORMULA AND PROBLEMS.
V '■'/•■
>/
ABBREVIATIONS.
T = Tangent, BA or BC.
72 = Radius, AD or CD.
I = Intersection, angle FBC or KBA,
D — Deflection, angle for 100 ft. chords, BAa or BCe,
d = Sub-deflection, angle for any chord less than 100 h,
BAfov BCy.
E = External Secant, Be,
M= Middle Onlinate, Je.
C = Chord, or Long Chord, any chord. ot IQft W «t -o^ss^^x
Aa or A C.
e = Sub-chonJ, any chord less l\\ati \0^ IX.., AJ ot «^* ^^^^^,
J = Arc, the /engf h of the cur^e in c\\ot^% ol \^ ^^-^ ^
A
'/
CIVIL engineer's field-book.
TABIiE I.
TO FIND THE TANGENT.
GIVEN.
A/
E,I
F0IU1UL.A.
60 tan \I
T =
sin D
Ecotil
ir- ■^^-^
GIVKN.
BJ, AD, AJ
FORMULiB.
^
. stKisi/;
r =
vers i/
BJx AD
AJ
TABIiE II.
TO FIND T^ RADIUS.
OIYBN.
FORMULJS.
orvKN.
FORMU1.JE.
D
E,I
R= TcotiJ
" ~ sin Z>
72 ' ^
M,I
AJ, AB, BJ
R- ^
R- ^
vers |I
" exnecil
TABLE III.
TO FIND THE DEFLECTION.
GIVEN.
FORMULA.
GIVEN.
FORMULA.
GIVEN.
FORMULA.
B
M T. 60
8inD=^
T,I
dfnDi^^**^*''
A, I
D=100^
A.
<• ■!<'
GIVEN.
rABIiE IV.
TO FIND THE EXTERNAL SECANT.
B.I
T,I
Jf,7
FORMULA.
E= R ezsec i/
X^Tttinkl
M
E^
cotil
PORMUUB.
iC
.exsec if
WnU
-A
CURVE FORMULAE IND PROBLEUGU
TO FIND THE MIDDLE QRDINATE.
• r
OIVBN.
VOBMVhA
oiymr.
WQt^lDJhM.
R.I
r,/
M= R vers i/
If = rcoti/vers^J
Jlf = JK cos i J
c,/
J?; J
M=kCta,niI
M=R-{M\fOB^I)
^- R-\- E
TABLE VI.
TO FIND THE CHORD.
OIVIN.
FORMULA.
GIVEN.
FORMULA.
R.I
T,I
C=^2R9\n i/
C = 2rcos4/
E,I
C = WcotJ/
exsec \I
TABIiB Vn.
TO FIND THE INTERSECTION.
OIYBN.
FOEMULS.
OIVXN..
FORMULA.
D,A
T,R
R,C
M,R
E,R
vers i^ = ^
exsec Ji = —
TO FIND THE ARC.
Problem 1.
OiT^n the i, FBO s '^l*, and the J), BAh = 2% tp fl^d th«
A, AabedeC,
Formula. Example.
il = ^100
i> = 2' ±= IW \^
_ ■ ^ I —
BeBult, A = ^^^^^^
4* OITIL ENGHSTEHR's PI^l^P-BOOK.
TO FIND THE aUB/DEFLECTlON.
Problem 2.
Given the c, Af = 75 ft., and the B, BAa = 4' 18', to find
tbe d, BAf.
Formvla, Example. '
._Be 2) = 4" 18' = 258'
100 . ^= 75
1290
1806 Result,
100. I 19850. I 193.50 = 3** 13' 30" = d.
.Problem 3.
Many sub-deflections may be calculated quickly by tbe fol-
lowing method; Multiply tbe degree of the given curve by
0.3, and multiply the produci (fhuji oibtained by the length of
the given subcliord, and then reduce the second product one
denomination; the result will be the required sub-deflection.
Given the c, ^^C = 30 ft., and the degree of curve aBb = 3",
to find the d, BGg.
Example,
Degree of curve = 2*
.3
.6
<j= 30.
Second product = 18**
Reduced one denomination = 18'0 = <?.
Explanation. — Wlien it is required to run a curve very
accurately the above formulae, although generally used, are
not correct. This will be readily understood by considering
that the shorter the chords ;the nearer the approach to the
circumference of the circle, and the longer the chords the
nearer the approach to the diameter' of the circle.
The base of most field-work and calculations is one hundred
feet. Therefore when a chord is shorter than this base it
should be proportionally longer tlian would be indicated in a
deflection calculated by the above method, and vice verm when
a chord is longer than this base.
T//e deSection must first be calculated as indicated hy Prob-
feiw ^or 8, after which correct the sub-chord \>y l\\c IcAXon^vcx^.
GUBYJS FOBHULiE A^D PSOBLBUa. 5i
Problem 4.
Given the (?, BAf = 6% and the E; AD = 359.265, to find
the c, 4/1 "
Formula. Example.
c-2li6md. 212= 718.58
rf = 6° si n 0.10458
215559
859265
287412
. ■-; 71853
Product c= 75.1079409
Problem 5.
Given the i, FBC = 45% and the J2, -4/) = 687.275, to lay
out a curve by ordinate^ when the curve begins 60 ft. beyond
a station and ends 60 ft. back of a station,
By Table I. the 1\ BA and 5C = -B Ian \I = 268.97
By Table III. siu 2> = ^ = 4* 80'.
By Problem 1, ^ = ^100 = 500.
Denote BAa' by d. Denote a'Aa by x.
*• BAh' '• D'Efi. *\ b'Ab ** «iBfo.
- Aa' '* <j. '' ' ** Aa ^^ M-
'^ Ad' ** CfSc, '' Ab *> >t^^
" iut' ** o. ** >*f ** ^'*
6 <7ivtt ekoikkbr'b field-book.
By Problem 2, d = ^ = V 4B\ &nd D' = d -\^ D = V 48'
+ 4" 30' = 6° 18'.
Then x = ^F - d = 22"" 30' - 1*^48' = 20*43', and x' =
^r- D' = 22" 30' - 6" 18' = 16* 12'.
By Problem 4:, c ^ 2Rhiu d = 40.03. and C --= 139.8e;ftj.
TotiudyKc.
Formula, Example.
y = ccosx, X = 20* 42' cos 0.93544
e= ■ ■■ 40 03
280688
374176
Product y = 87.4456632
To find oEe.
Formula. Example.
o=zC9\iiX. a? = 20** 42' siu 0.35347
c= 40.03
"^ . 106041r
141388,.
Product = 14.14^4041
Problem 6.
a/rea the Z J^BC = 45\ and the R AD = «»T.!5Tb, to lay
i^n^a curve from pbinta on the tangenU AB and OB N«\\feu \A\^
GURYB WOBMUhM lAHO PAQBUOfS. 7
curve begins 00 ft. beyond a station and ends 60 ft. back of a
station.
By Table I. the T, BA and 5(7 = B tan iJ = 268.96
By Table III. sin D = ^ = 4' 30'.
By Problem 1, A = ^iOO = 50a
Denote BAa by li. ^ Denote Aa by e.
BAb •* ly.
BAc " D\
Aa' " X.
AV " ^,
A<£ ." af.
J6 " a
^c •* (7'.
oa' ** y.
Tie : "
By Problem 2. d = j^ = 1* 48', and /^ = ,d + i) = 1' 43'
+ 4- 80' = 6- 18'. and2)'' = (i + 2D = r4d' + 9* = 10^48'.
By Problem i, q = 2R sin d = 40.0^, and C = 189.86, and
C" = 288.88 ^
To find a?.
!c =1 c cos d. d = 1* 48' cos 0.99951
e= 40.03
299863
399804
Product X = 40.0108868
Use the same method to find x' and x",
.»
To find y.
Formula. Bxample.
y = c sin (f. d-V 48' sin 0.08141
c= 40.03
9423
12664
Product y = 1.2678423
Use the same method to find yf and y".
Then, for locating the other half of the curve, begin at
and run towards B, using the same formulae «Ji^ ^vs^w \;x^^^-
8
OITIL BirOIKXEB'S BIBLD-BOOK;
»» • 1
' I . •
I •
• I ' ; ■ i
Problem 7.
i
Given the i^, AD = 1432.69 of a located curve AabeC, it is
desired to run another curve A'a'b'c'G' parallel to it at a given
distance of AA' = 75 f t;
The chords Aa^ ahKc are 100 ft. long.
Denote the chords A'a\ a'h'Kc, by x.
Denote AD by -B', then li' = AD - AA' = 1432.69 - 75
= 1357.69
By Table III. sin D = ^ = 2".
To find a?.
M
Foiinula,
X = 2^' sin D.
Example,
2i2'=r 2715.38
J) = ^" si n 0.03490
24438420
1086152
814614
Product X =
94.7667620
If it is desired to run the curve A'a'b'c'C, add the distance
A A' to the Rt AD, and use the above method.
It ••
CU&YS tOBVUL^ AlETP FBOBLBICS.
'.! .;?
Problem 8.
Given the -B, ^D = 2864.93, to locate a curve when the
point of intersection R is inaccessible.
Make the offset AN =■ 12 ft. = a, and run NR parallel to
AG intersecting the tangent Rll at P, and turn the angle
RPU = OB 1 1 = W = L
By Table I. the T, RA and J?(7 = i?tan ^7 = 351.76
Denote FO by x, and PR by z.
Determine tlic unknown sides of the triangle RPO by the
following formulae:
To find a?.
Formula. ' ExamplS,
« = a cot /. / = 14' cot 4.01078
a= 12.
802156
401078
Product a; = 48.12936
To find z.
Formula. ■ Example.
_ a I :c W'~\ a = rQuotient e =
~" si" ^ sin 0.24192J 13.0000L49.60
96768
.. 232820
.... 217728
145920
NO = AR =z 351.76, and NP(= KO -V OP - ^t^n^ Ar
48.13) = 899.89 from 1\ a point 12 it. «lI t\s\iX. «i\^^^ ^-^ ^^'^
point of curve A.
10 OI¥IL BITQIKXEB'S PISLD^BOOK^ i
The point of tangent 0{:=B0- BP^ 861.76 - 49.60)
802.16 from P.
By Table III. sin D = ^- = V.
si
By Problem 1, A ^ ^100 = 700,
Problem 9.
Qiven tbe R, AD = 287.939, and the distance atound the
curve, AC = 200 ft., to locate the point Gftom a pdint on the
tangent AO. ' "
The R, AD being that of a 20° curve, the angle FBC =
40° = /. and by Table VI. the chord AO = 2R sin K =
196.962 = G. SI..
Make the distance AG = AO. Then invariably the angle
AGO and AOO = ilz^lO\
Calculate the distance G€ = a; by the following:
Formula. Example.
a? = 2(7 cos iL 20 = 898.924
il = 10° co g 0.98481
898924
3151892
1575696
8151892
8545816
Product X = 887.94029444
CU&VK MQBHVhJB AKO FBOBUJfS. 11
Problem lO.
Given the B, AD = 168d.40, to locate the beginning and
end of a curve when tiie |Mlnt of intersection B is inaccessible.
Continue the tangent BA to li, also the tangent HC to P.
Measure the distance IfP = 359.20 = a, and turn the angle
iTPy = 38' 43* = ft. and the angle fl^^P = 28' 35' = c; then
the angle GBP =b + e = 33' 48' + 28**35' = 62' 18' = /.
By Table I. the T, BA and £(7 = i^ tan i/ r= 986.67
Denote BN hy x, and BP by «.
Determine the unknown sides ot* the triangle 21BP by the
following formulae:
To find a?.
Formula. Example,
a sin 6 ft ^ 33° 43' sin 0.55509
iiiotso
499581
277545
/ = 62* 18n 166527 TResult x =
Bin O.88539J199.3883280L225.I9
177078
223108
177078
460252
442695
12 OIVIL B39aiKS£B^8 FtfiLD-BOOJIt.
To find e.
Formula,
asm c
■" sin/
V
Sktample.
c-28''35' sin 0.47844
a = 359.20
956890
430586
239!^Sb
/ = 62' 18"] 1 43632 FResult z =
sin 0.88539_jl71.855648oLl94.10
88539
• • ' ' . ,■ ■
833166
863154
854166
»
89988
88539 ..
14490
i^.4 = T -r jj = 986.67 - 225.19 = 761.48. the distance
from N to the pofni of curve A,
PC ^T -- t = 986.67 - 194.10 = 792 57, the distance
from P to the point of tangent (7.
Problem 1 1 .
Given the /, FB(' = 68", to locate a curve tlirough a given
point //.
Find tlie point O on tlie tangent BA where the angle BOH
= i/ = 29^
Measure the distance OH = 40 ft. = a, also the distance
^^=500 ft, =d.
denote GJ^ by x, and HK fj y, and QA by z.
GUBYB FORHirL^ AND PBOBLBXS. 18
Calculate « and « by the following f Ortnites
To find X,
Formula, Example,
x = 2b cos if. il^ 29^ cos 0.87462
26= 1000 .
Product a; = . 874.63000
Then y = x - a =: 874.62 - 40. = 834.62
To find 2.
Formula, Example,
z = ^m. j/ ==' 834.62
a= 4a
83384.80
111
28l288
224
Result e =
182.71
862 I 984
724
"\a647 I 26080
- -- 25529
86541 I 55100
86641
The tangent 5^ and BG =rb + z = 600. + 182.71 = 682.71
By Table II. the li, AD = Tcoi i/= 1231.64
Problem 12.
Given the /, FBG = 4V 86', and \he d\8.Vw\^<i C J ^^.^'^ — ^>
to determiDe bow far toward G, A' mv\&\. \>ft Uoth A. n» ^n»sX
the curve AV, v^liich is similar to AC.X.^^^^^^^^^^'^'^'*^'^^'^'^^'^
magent C^^ parallel to CH at the giNen dXaVwwi^ a.
14
XSrPlL BN^IKKBB'S i FIRl<D4B00K.
Denote the distaaee AA' by ipand calculate it l^.thfi foUawiog
FormvXa. EocampU.
a / = 41* son a = rQuotient x =
X =
sin /
sin o.aesodj 8.6200 Li^ds
66398
198070
182786
652840
697537
658030
Problem 13.
GKven the i?, AD = 1432.69. and the /, FBG = ^2** 30', of a
located curve ^ C7 to find the K, AD' of another curve to start
from the same point A and end in th^ tangent C"^ parallel to
OH at a given distance QC = 4^.60 =3 a.
Denote the distaupe ,t)jy by x and calculate it .by the fol-
lowing.
F(yrmula,
sin i/
■^"-v...
X =
i/= 31' 15n Ja ^^/TOuotient x =
sin 0.51877j«li06oL41.05
207508
<l4fl26^
51877
■■"I
a0480Q
Tbes Jj^^ Urt-iff ^ 1432.69 + 4105 * Ul^.U
OURTIB WOBMVhM AafTO PBOBLBMS.
16
Problem 14.
Given the B, At) 2= 1910.08, and the /. FBO = 81 80' of a
located curve AG, to find the R; AI^ of Unpthef curyei to
start from the same point A, and end in the tangent C^X par-
allel to QH9X a given distance, OC = 14 Ft. = a.
Denote the distance DD' by a;, and calculate it by the lol-
lotting:
Example.
Formula,
a
X =
vers/*
/ = 31° 80'"| « =r TQuotient x =
vers O.U^dO J 14.0000^5.00
18 26214
73760
73680
8000
Then IT » i? + a? = 1910.08 4-^96.00 = 2005.08
COMPOUND CURVES.
Problem 16.
Having run the curve A G with the R, AD — ^XsXs^R^ vs^
the /, FBG = 64* 80', it is desired to ^«LUeii V\i<i e\«^fe ^^» ^^^>
end, a distance of AG and CH = 150 U. ^\X\x «^ \^^v^^ ^"^ ^*^
and ai?" = 1910.08 = R,
16
OIYIL BNGISTBEBfS TIELI>-B00i:.
Required the radius Qiy and ED" = r, to Join the two
curves A O and OJI at G and i21 • i
The ir. AD', and OD' being that of a SVcurve, the angle
:42>'Gf = 4"30'. also Ciy// = 4^80'.
The angle e^2>"4.==:/- (^-D'G^ + QJ^'M) = 54** 80' - 9'
= 45" 30' = J'.
Denpte Ji' - E by a; , then a == 1910.08 - 955.866 = P54,7J4.
Denote the distance D"iy by a;, and calculate it by the tpl-
lowing:
Formula,
a sin i/
Sin ^1
, • Example,
, .a, = 954.714 .
jj = 27" 15' si n 45787
6682998
7687712
6682998
4778570
iJ' = 92' 45'"[ 381 8856 PResult x
sin 0.88671 J437.13489918L1130.39
38671
50424
-88671
117538
116013
152599
116013
365861
Then r = iT •* a? = 1910.08 - 1180.89 =s 779.
VN
GUByi FQBMULiB AKD PB0BLBM8. 17
Problem 16.
Given l^e chord AG = 600 f t. = C, and the angle BAC
= 45% and the angle B(J' A = 67' 36', to find the radii CD and
CD' to lay out the compound curve ACC
The angle GAC = iJ5A(7 = 23' 80' = a, and the angle
CCA = iJJCT'^ = 33' 48' = h.
The angle A CV = 180' - (32' 30' + 83' 48') = 138' 43' = e.
Denote the chord AChy or, and the chord CC by y, and cal-
culate the two sides, x and y, of the triangle ACC by the fol-
losing formUlaB:
To^da?
Formula, Example,
Csin h ^> = 33' 48' sin 0.55630
C7= 600.
t =
Bin 6
e = 128'42'n 333.78000 plesult x =
8in0.88195j???^??^L401.20
100000
83195
168050
18 eiYIL bkoinssb's fivld^booe.
To find y.
Ibrmula, Example,
Csin a a = 22' 3(y sfu 0.88268
^ = "asT" o = : goo-
= 123" 42'-1 229:^800 FResult y =
ain 0.83195J ^^^^^ [275.98
632180 ,
582365
498150>/
:, . 415ytf
821750
748755
729950
The angle GAO — \BB'C = i/to the curve AG, and sim-
ilarly the angle GO A = WB"G' = i/ to the curve GG'.
Having thus found the chords AG, and GG' the R, GD, by
Table II. = tt-^-tt = 624.20, and the B, GD r= 248.05
2 6IB i/
Problem 17,
Given the angle FBO = 112'* 86', and the di^tiMlcei 4^
= 600.870 = a, and the distance OB = 459.557 = 6, to find
the radii GB and GU to lay out the compound curve A GO,
Denote the angle BAO by a?, and the angle BOA by y, and
the distance ^(7' by 2.
The angle ABO = 180*" - 112' 36' = 67" 24' *= c, and »
+ y = 112'86'
Calculate x, y< and z, by the following forifaulaa-
To find half the difference between x and y.
formula.
. ,/ V (a — 6) tan i(« + y)
tan i(y — a;) = ^^ — --|i— L-s/
CVBVB VOJOitlLm AK» PROBIIMB. 19
a-'b = 141.318
4(3? + y) =r 56M8' tanJL4ft044
565252
565253
1271817
1271817
566252
a + b ="[ 141813 r Result tan i(y-a;) =
1060. 427J 211.^9086472 LA^82 = 11" 18'
T060427
10584766
9548843
10409234
9548843
86S8917
8488416
1705012
Tk^fl a? =2: i<a? + y) - ^(.v-. x) = SdMS' ~ 11' 18'= 46*
aU y = i(» + y)+ i(y - ir) = 56" 18' + IV 18' = 67" 86'.
Ti. dud «.
Formula,
a
z = -. sin c.
wtiy
Mtample.
y = 67" 86'"! a ^ F/^ _.
sin 0. 92455 J 60Q.870 L^o L
5347^0 ^^-^
461400 <J = 67" 24' sin 92321
915800 129980
194970
129980
584910
Result 0i=i 599.9941790
Then by Problem 16, the chord AG — 401.20 and the chord
CC = 375.98
By TaWe II. the B, CD = — £-- = X^'iA!^, wi^ \3tta B»»
2sln^I
CJy =248.06.
eo
Qirih SKGill^E^'a FISLD-BOQ«[<i >
REVERSED CURVES.
Problem 18.
Given the angle C'AFz= 20" = a, and Ibe distance AC
= 400 ft. = C, to find the iJ, GD and Ciy to join the two paral-
lel linles ili^and EO* with the reversed curve ACC.
R
Formula.
sin a
Example,
a = 20n iC = rQuotient. R
sin 0.34202J 100.000 L292. 880
68404
815960
307818
81420
68404
130160
102606
275540
Problem 19.
Given the angle C'AF = Z" 31' = a, and the distance A E
= 14 ft. = d, to find the R, CD and Ciy to join the two par-
alleJ ViDes AFknd EC with the reversed curve A GC
Culculate the distance AC = C by Ihe toWoviVn^v
GUB7S FORM UL;£ AKD PROBLEICS. ^
fhrmula. Example,
^ ~ sia « ^ 0.06184 J 14.000 ^28.286
12268
17820
. 12268
I I
50520
49072
14480
12268
22120
18402
87180
Then by Problem 18, the B, CD and CV = 4^ = 980.206
sin a
Problem 20.
Giyen the distaBoe AF= 196.11 = b, and the distance AE
= 14 ft. = d, to And the iJ, CD and C^Z^ to join tlie two par-
allel lines ^i^and EC with the reversed curve A CO',
Calculate the angle C'AF = ahy the following:
Formula, Example,
d b ="] d= PQubtient, tan a =s
196.1lJl4.000oLo7189 = 4° 05'
187277 .
27280
19611
tan a =
76190
56838
173570
Then by Problem 19 the distance AC = -$— = 196.605
•^ sm a
And by Problem IS the B, CD and GB = 4^- ^ ^^.'^'^
^ a\ix a .
2:1
CIVIIi l&KOtKfiER's FIELD«>BOOK.
Problem 21.
Given the 12, CD and CU ^ 819.03 and (he Kn^t O'AF
— • 3** 15' = a, to find the distance AF=b,
Formula, JSSxample. .
b=:2B sin 2a. 2R = 1638.04
2a = 6" 30' si n 0.11320
8276080
491412
163804
163804
Product b =5
185.4261280
Problem 22.
Given the angle 0'AF= 3" 45' = fJ, and the IH, CD =
941.60, and the distance AM = 14 ft. = d, to find the H, CD
of the curve CC to join the tangent ISC, which is parallel to
AF at the given distance, and complete the reversied onrve
ACCK
Denote ^Cby (7, and ^(7' by C", and CC by C.
Calculate CT' and C by tl^e following formulae:
To find C\
JSxample.
2E ^ 1883.20
il = 3* 45^ si n 0.06540
7632800
941600
1129920
Formula.
a = 2R sin i/.
Ptoduct O =
123.1612800
GirktS TOnUtJLM AVI) PBOBLfiM.
To find C'\
Formula,
d
C'=:
sin \I
Bscample,
U = 3* 45n d = rQuotient. C =
sin 0.0654oJl4.000L2U.067
18080
9300
j540
26600
26160
44000
89240
47600
Then C = C" - a = 214.067 - 123.161 = 90.906
Having thusJoiuid C by Table II. R = -^-^1 = ^^^'^
k Bin "^A
Problem 23.
Oiven the /, GBF = W 42', and the distance Bff = 548.5
■= a, f^nd /', OBJI ^ 10" 80, to find the i?, C'Z) and CZX to
Join the two lines ^j? and ^i/ with the reversed qyrv^ ACC
M
. Giy(i;i. ^K otHJ^EB'a iriiiLiJhBpQK. .
i2 =
Formula,
a
tan il+ tan i/'
, Eosampls,
iJ = 7' 21' tan 0.1«899
iF = 5' 15' tan 0,09189
-^ I a = FResult. E
tan i/+ tan i/' = .22088 548.50 2i83.24
J44176L
106740
88352
188880
176704
'7»760
66264
54960
44J76^
107840
3>U'-:
. Problem 24. ,
Given the ^, AD = 1661.0 and the k, AD' = 941.6 auA
the i2", CD' = 235 4. and the distance Aa and eC = 20 ft. =
d, to join the two parallel curves Ae and aC with the re-
versed curve ACC. ■ \ > ■• .
Required the /', ADD", and the J", D'D"C\ to determmo
the Ic^ngth of the curve A C, and the length of the curve Cd\
Find al) the sides of the triangle DD'D" by the following
method: The (distance
D'D" = U' + R' = 941.6 + 235.4 = 1177.0 = a,
and D'D = R + d - W = 1661.0 + 20. - 235.4 =
1445 6 = b,
and DD' = R+R z= 1661.0 + 941.6 = 2602.6 = e.
i(a + d + e) = 2612.6 = «.
CUKTE rOHUVLA kND PROBLKlfS. %i
Then calculate /' and /" by tbe following fonnule:
Tofind/'.
Formula,
■ I I
8068960.2
sini/' =4/(llL^Hi:il)
f <3KJ
Example,
(« — a) (« — c) = p Quotient = p Result,
14856.0060 .0046865101 sin U' =06846
122580408 Lg]; 8g L =3* 55' 30" v
210295920 128 1086 /' = 7" 51'
188705612 I 1 1024
265003080 1364 6251
245060816 5456
199422640
- 188795612
154270280
158163010
H1072700
80682602
18686 79501
44009600
Tofind/"*
Formula. Example.
. -., sin Fe T = r 51' sin 0.18658
sini =— J — ^ _,, 2602.6
81948
27816
81948
27816
6 =
1445.6
855.468108 Result, sin F =
28912 ^.24589= 14n4'02'
66848
57824
85191
72280
129110
115648
184628
m
OITIL BNeiNBEB'S VIELD-BOOK.
. »•
FROG PROBLEMS.
ABBREVIATIONS.
N = Prog number.
S = Length of switch-raiL
D — Degree of curve.
E = Radius, AD.
C = Chord, AG.
T = Tangent, BA.
F =;: Frog angle, MEG,
I = Intersection, FBC.
L ss Distance, JE,
— Gauge of track, JK.
Problem 25.
Given the frog measurements EN = 8.55 =-a, and HO
0.95 = 6, to find the frog number JV.
Foitnula. Exam'pU.
^ = F
b ="1 a = rQuotient. N =
O.95J8.55L9.
8.55
Problem 26.
Given the frog measurements EN = 8.55 = a, and HG
0.95 = 6, to find the J?*, MEG.
Formula.
tanii^ = ~
a
Example.
a =n iJ = rQuotient, tan \F =
S.55J0.4750L05555 = 8" 10' 47"
4275
4750
CURVE FORHULJB AXO PROBLEMd. 27
Problem 27.
Given the frog number N, - 9, to find the F, HEG,
Formula. Kxtimple.
,^ 0.50 N=~\ FQuotient, tan i^ =
tan iF= -^rzr-
^ 9 J 0. 50 L 05556 = 8' 10' 47"
45
50
Problem 28.
Given the iJ, AD = 150.656, and the 0^, JK = 4.708, ami
(lie L, JK = 87.664, to find the F, HEG.
Foifnula.
L
\AnF=
B-iG
Example,
iJ-4Gf=nx= PQuotient, tan i^ =
;]
148.802J37.6640L.25397 = 14** 15'
296604
800360
741510
/
588500
444906
1485940
135 471^
10122^0
28 GIVIL ENGIKREB'S FIKLD-BOOK.
Problem 29.
Given th§ i?. AJ) = 150.656, aiul ihe F, HEG = 14° 16', to
find the C7, AC.
Formula.
C=21ismiF
• Example.
2i?= 301.812
iF= T 07' 30" sin 0.124035
1506560
903936
1 205248
602624
301312
/
Product C = 37.373233920
Problem 30.
Given the F, UKG = 14' 15'. and the iJ, AB =r 150.656.
and the G, JK = 4.708 to find the L, JE.
Formula.
L = {It - iG) tan F.
Example.
E-^G^z 148.302
F= 14^15' tn n 0.25397
1038114
1334718
444906
741510
296604
Product L = 37.66425894
Problem 31.
Given the G, JK = 4.708, and the frog numher iV = 4, to
find the L, JE.
Foi'mula. Example.
L = 2GJ^. 2G = 9.416
iV^= 4
Product L = 37.ttQ4
CVKVR FORMULJfi AKD PB0BLBM6.
2d
Problem 32.
Given the A ^^ = 87.664 to find the length of the switch-
rail-S.
Emmple.
"I Z = rQuotient. S =
8.36J37.664L11.209
386
FormiUa,
L
8 =
3.36
406
336
704
673
3200
The above formula is for a gauge of 4.708; for a three-foot
gauge. ^ = 5-
TO FIND THE TANGENT OR RADIUS.
To find the T, BA or BC, or the 22, AD. The F, IIEG =
FBG = 7. Tlien by Table 1. T= R tan \l and by Table
II. 22= Tcoti/.
— '^
to
Problem 33.
Given the R, AD =z 762.696, and the Q, JK = 4..'706, to
flad thei^, GKlIoi the middle frog in a three-throw switch.
Formula,
G
vera iF =
2{R -\- \G)
so
CItIL 15NGH1«6BR*S WBLD-BOOK.
Example.
2{E -f hO) ="]<?= FQaotient, vers ^F =
r68oLo03076 = 4' 29' 45"
1530.1 J 4.7(
45903
117700
107107
105930
Problem 34.
Given the iJ, AD - 762.696, and the F,
to find the distance AE I.
IlKG
Formula,
i = JS tan ^F.
R-
i2^=4°
Example,
762.696
29' 45" tan 0.078628
6101568
1525392
4576176
6101568
6338872
= 8** 59' 30'
Product I =
59.969261088
A J
%
Problem 35.
To find the frog angle when the main track is curving in the
same direction as the proposed turnout.
Oiven tlie curve of the main track, AF = 5** , «ixiA V\\^ cvwn^
of the turnout AL = 9" 30'. Subtracting the \ea»ex cuxn^ Itom
CUBVS FQBHUL^ AND PBOBLBHS. 31
the grdater, ^e bare a departure of 4*d0\ with a, relative
radius of 1273.57 = R,
Then given R = 1278.57. and the G, JK = 4.708, to f ud
the /; MEG.
Formula,
R -{-^='1' G = rQuotient, vers F=:
1275.924 J4.7O8OO0L00368 = 4r 55'
3827772
8802280
7655544
11467360
Problem 36^
Given the R, Aiy = 603.805, and the R. AD = 1146.28, and
the JP; BEG = 4*55', and the (?, JK = 4.708, to find the
<ihcMAa-G.
' By the following method solve the required parts of the
triangle -&i)i)': • ; .
The distance
DD' = R - R = 1146.28 - 603.805 = 542 475 = a.
The distance
D'fS = iJ + i(7 = 603.805 + 2.354 = 606.159 = 6.
To find the angle EDD' = I'.
Formula. Example.
. r, b sin F h= 606.159
sin r s= —J — j^_ 4* 55. gijj 0.08671
> ■
' . •-
606159
4243113
3030795
4849272
642.475
51.95388789
4882275
>
3131137
2712375
. •. ■ * ^ • '
Result, sin /' =.-
.09577 = 5°29'44"
^60^0^^
32 CIVIL EKQIKBEiEt'S FIBLD-BOOK.
' Th6n the angle ADO =± /' J^F = 5* 39' 44" + 4'55'
10" 24' 44 ' = /.
• Bj^Table VI. (7= aUsin iJ= 109.58.
.^
.^f
.-»"
Problem 37.
To locate a frog when the main track is curving in a direc-
tion opp<>isite to that of the proposed turnout.
Given the curve of the main track AF = 8*, and the curve
of the proposed turnout AL = 9**, and the (?, JK = 4.708
: 'Adding tiie lesser curve to the greater, we have a departure
of 12" with a relative radius of 478.839 = 22'.^
To find the F, HEG,
Formula,
Example,
R +^G = n (7 = rvers. F =
480.698j4.70800oLo0979 = 8" 01' 30'
4826287
8817680
8364851
4527790
4826287
2015580
Then relatively the angle CITA = 6" 01' 08" = /.
Then, given the -B, AD' = 687.275. and the /, ADC = 6'
^V'^ ; to Sad the chord AG =^ G.
Bjr Table VL (7= 2Ji sin il = 66.91
GUBVE FOBHUIJB A^STS^ /P^OBJ^J^UB.
i8d
ui
o
H
o
H
QQ
o
525
O
o
O
d
•J
M
a
I
BO
I
h
O
o
g
O
o
o
H
O
3
o
s
liNii
o
to
I
e
«0
o
t-
^g'
o
o
CO
m
• > •
^^ 9j ^^ s?
So*
J" • " *
e
t-©l(
e
0(
9
O CO
00
l«Si
0)1
eo so ®» i>: ^"
O 090 OOf-iO
Op '<»• ri
;? P;^fis^^^cDA
I
a
Q
a
M
Si
So
n
e
GO
^3
e
00
oco
^o&
o
3:
?5S
is
^
^
&'
^
$
09
^S
s
I
»
^v4
QQ
09
8
NNs
o o
o» to
o»a»<
tO*-i(
r?!7»SP^
»- CO
09
to
t.o)^e
«-<o'Sdcde9
O iO^35r^09
09 o ■v
r^ CO
1-^ I-
Q0<
00
2» * &» *^ "^ »f
^QO^OCCSO
"^ fi *^ »S '- »
e ^o 3SS
09 r"
s -^ • • •
2k • «B| • • •
o 8 o S * oi
5? SJ
S
Q
C^T^^^tH^
IN
e
00
* _< •
o
00
8iS
S©E
S!^co
§1^
-5I0
00
09®;-
CO
09**O»
84
CIVIL BKGlirteBft'S tTELD-BOOK.
TABIiE IX.
BiaHT TRIANQLEa
TO FIND A,
TO FIND B.
TO FIND a.
SiTKN.
FORMULA.
GIVBN.
FORMUUB.
6,C
6, a
tan^ = -
c
sin il = -
a
C.6
c, a
cot .4 = ^
. c
COS ^ = -
a
a
a
h
cos B
c
sin B
TO FIND 6.
.^, c
wi, a
b = c tan A
b — a cos B
^ = c cot A
TO FIND c.
^a
-^^
e = a COS A
c =: b Got A
e s: a Bin B
c = i» tan 5
CUBYB J70BH,UI<jat AXTD ]PE03J['EAIS.
36
TABLE X.
OBLIQUE TKIANGLE&
TO FIND a» 6, c.
TO FIHD ^, P, C.
GIVEN.
FORinTUB.
aiv«K.
FORMULA.
A,b,C
A, B, c
A,B,b
6slnC
*"" sin ^
c sin ^
*"= sfni^
& sin iB
C = — : T
Sin A
a,b,C
Ayb^C
A, a, 6
*.« = <= "f-*
TO FIND A, B, C.
s = \{a-\-b-{- c).
OIVSN.
. FORMULA.
a, c, 8
«■- M = /" - °:J' - ''
a, 6, 8
"-MB^/l^^^l^
6, c, ff
^,c=/.^-^il^
-'«ITtI.' BKalHBE&'d VtBljD-BOOE.
TABLE XI.
LONO CHORDS. DETLECnOHS, AND ORDINATEB.
p
HOHDB. 1 TIOKS.
^^
'
aoo 300
400 1 500
600
TOO 1 1 «
i
1
BB.
BO.
T
Httl.»fla.'99.970
399.934 JDB.RtS
599.73-3
609.571 .873
^
~^
"^
e
iiffl.oro
SOO.BTB
MB
fl95 49B.39]
508.934
SOS
SB 1,745
8
4*0
.8S7
486
3
109.931
SDft.TSfl
39B
315'498.C130
507.604
606
IflS, 3,618
t.
236
.491
^6
4
OT.K8
SW.B13
308
-[«»
505 744
603
106 3,190
B
080
,666
873
R
lira. 810
aBsaao
108
099JM,a)i
508.858
689
3B6 4.36^
8
7!i4
.818
oei
S
ISBiBO
•JDH.HM
197
294 i04.534 5il0.«9
084
745 S.SIM 10
467
-982
309
7
IflBBET
:i98.5D9
396
278 493.568 087.031
079
285 6 ,05 12
310 1.148
598
8
1SIU.5I3
^054
306
„.„«u.„
613
DI9 6.976
13
9511-310
746
9
199.388
m.ssB
193
BfiT487.T49ST8 633
6B5
950 7.846
15
6J,.474
965
10
iBO.aao
■ioe.'xs
Wl
4S44S4.Boan;3 BscleaH
105 8.716
431.^2
IS8
n
iMors
M6.3S6
390
Bis' 181-763 668,245 049
496 9.B8,-
,;
l4,80.|.
40S
la
l!)S.9(M
«g5.sa9
389
„J.»,„»,™-
143 10 «3
«
906 1 967 2
830
13
IBS.T14
4B4.371
387
m,,,.J^.«L
062,11,330
„
6412.181,2
839
14
18B.S0B
294.050
as5
225 470.049 519.058 619
278'l2.1BT
„
058
10
m.m
208 185
388
™,„,»j„,J»,
8lV,3.06«
1052.46i!b
377
10
IS8 054
592.253
880
763 461.8M 533 918 595
888 18.917
"
8352.6258
496
17
iur.803
m XI
ST8
s2aU;.ue(iWi.n«58!
988 14,781
»
68f7918
716
18
lor.sse
iiooaii
O
739 4B9.01,','51T,100 5«9
67115,648
.,
^2.9568
985
10
,«»...,„
3T3
CIStl46.T08'noe.l39ll!»
68418.505
»
0,08.124
155
20
lea BfK CRT rag
370
107-141,147 438,724 541
147 17.885
-
™i'-H*
87<
CUKVE FOKHLXjE AKD PBOULEICS.
CUBVIfi FOBHULJS AlTD PROBLEMS.
89
TABLE XIII.
GRADES.
Grade
Rise
Grade
Rise
Grade
RiFie
Grade
Rise
per
100 ft.
per
Mile.
per
100 ft.
per
Mile.
per
100 ft.
per
Mile.
per
100 ft.
per
Mile.
.05
2.640
.59
81.152 !
1.13
60.664
1.67
88.176
.06
8.168
.60
81.680 !
1.14
60.192
1.68
88.704
.07
8.696
.61
82.206
1.15
60.720
1.69
89.232
.08
4.224
.62
32 786
1.18
61.248
1.70
89.760
.09
4.752 '
.68
83.264
1 17
61.776
1.71
90.288
.10
b.iOO
.64
88.792
1.18
62.804
1.72
90.816
.11
5.808
.65
84.320
1.19
62.832
1.73
91.344
.12
6.886
.66
34.848
1.20
68.360
1.74
91.872
.18
6.864
.67
85.876
1.21
63 888
1.75
92.400
.14
7.892
.68
35.904
1.22
64.416
1.76
92.928
.15
7 920
.69
86.432
1.23
64.944
1.77
93.456
.16
8.448
.70
86.960
1 24
65.472
1.78
93.984
.17
8.976
.71
87.488
1.25
66.000
1.79
94.512
.18
9.S04
.72
38.016
1.26
66.528
1.80
95.040
.10
10 082
.78
38.544
1.27
67.056
1.81
96.568
.ao
10 560
.74
89 072
1.28
67.584
1.82
96 096
.SI
11.088
.75
89.600
1.29
68.112
1.83
96.624
.28
11.616
.76
40.128
1.30
68.640
1.84
97.152
.23
12.144
.77
40.656
1.31
69.168
1.85
97.680
.24
12.672
.78
41.184
1.82
69.696
1.86
98.208
.f&
18 200
.79
41.712
1.33
70.224
1.87
98.786
.26
18.728
.80
42.240
1.34
70.762
1.88
99.264
.27
14 256
.81
42.768
1 85
71.280
1.89
99.792
.28
14.784
.82
48.296
1.86
71.806
1.90
100.820
.29
15.312
.83
48.824
1.37
72.386
1.91
100.848
.80
15.840
.84
44.352
1.88
TO.864
1.92
101.876
.81
16.368
.85
44.880
1.39
73.392
1.93
101.904
.82
16 896
.86
45.408
1.40
78.920
1.94
102.432
.S3
17.424 ;
.87
45.936
1.41
74.448
1.95
102.960
.84
17.952
.88
46.464
1.42
• 74.976
1.96
103.488
.85
18.480
.89
46 992
1.43
75.504
1.97
104.016
.86
19.008
.90
47.520
1.44
76.032
1.98
104.544
.87
19.586 ;
.91
48.048
1.45
76.560
1.99
105. 0?2
.88
20.064
.02'
48.576
1.46
77.088
2.00
105.600
.89
20.592
.93
49.104
1.47
77.616
2.10
110.880
.40
21.190
.94
49.682
1.48
78.144
2.20
116.160
.41
21.648
.95
50.160
1.49
78.672
2.30
121.440
.42
22 176
.96
50.688
1.50
79 200
2.40
126.720
.48
28.704
.97
51.216
1.51
79.728
2.50
182 000
.44
23.282
.98
51.744
1.52
80.256
2.60
137.280
.45
28.760
.99
58.272
1.53
80 784
2.70
142.500
.46
24:^
1.00
52.800
1.54
81.312
2.80
147.840
.47
S4.H16
1.01
53.328
1.55
81.840
2.90
158.120
.48
25.844
1.02
53.866
1.56
82.868
8.00
158.400
.49
25 872
1.08
54.384
1.57
82.896
8.10
168.680
.60
26.400
1.04
54.912
1.58
83.424
3.20
168.960
.51
26.928
1.05
55.440
1 59
88.952
8.80
174.240
.62
27.456
1.06
55.968
1.60
84.480
3.40
179.520
.68
27.984
1.07
56.496
1.61
85.008
3.50
184.800
.54
28.512
1.08
57.024
1.62
85.536
3.60
190 .Q»l
.65
29.040
1.09
57.550
1 63
86<»\\
>v ^.1^
\\<«S!»KS
.66
29.568
1.10
58.080
l.ft4
\ ^^;&
Vv ^.^^
\«»»X>ASi
.67
30.086 i
90. m
1 11
68.608
1.65
\ ^l.l^Ck
\\ ^-"^
.« /
1.12
59.136
\\ ^'^
\ W.^
.\ ^..
40 CIVIL engineer's field-book*
EXPLANATION OF TABLE XIV.
MmuTES Expressed in Decimals.
In the third column, under the heading of *' 1" Curve, Arc,"
will be found the minutes given in the first column under
"0°," expressed in decimals of a degree, by simply putting
the decimal point two places to the left. For example:
6' = .10 and 54' = .90
Proof: 6' + 54' = 1% and .10 + .90 = 1.00 = l^
In like manner all arcs to a one degree curve are expressions
of their intersections decimally.
TO FIND THE TANGENT.
Given the 7, FBC = 42** 88', and the degree of curve AC =
5% to find the T, BA and BO,
Find the number corresponding to the number of whole
degrees in the given i, at the top of the left or right hand
column, after which descend the column until the correspond-
ing minutes in the given 1 is reached, then on the same line
to the right or left under the heading ** 5** Curve, Tan./' will
be found the required T = 447.301
Problem 38.
Given the /. FBC = 24" 50', and the degree of curve AC —
4" 12, to £ud the T, BA and BG,
Select the t»u. to the given J f rp?n the c^t^^ c^oVvvtaxi ^oxx^
CUSYE FOBMULiB A;SD PROBL^M^. 4Jk
spoiiding to the number of whole degrees in tbe given curve.
Multiply this by tbe number of whole degrees in tbe given
curve, and divide tlie product by tbe given curve expressed
decimally.
Kxample.
1= 24" 50'. 4" Curve, Tan. = 815.485
Number of whole degrees = 4
•Result, T =
Given curve = 4* 12' = 4.20
1261.740
1260
3W,41
1740
1680
600
TO FIND THE ARC.
Given tbe /, FBG = 56° 40', and the degree of curve AC —
9% to find tbe A, AfabcC.
Find tlie number corresponding to the number of whole de-
grees in the given / ai tbe lop of the left or right hand columu,
after which descend the column until the .^prresponding
minutes in tbe given i is readied, then on the same line to tbe
right or left under the beading ** 9** Curve, A,rc" will be found
the required A = 629 680
Problem 39.
Given the /, FBO = 96° 18', and tbe degree of curve AC =z
2° 15', to find the A, AfabcC. '
To tbe number of whole degr|es in the given / affix the
fractional part expressed deciiiially; also to the number of
whole degrees in the given curve affix the fractional part ex-
pressed decimally, and divide tbe fornd^r by thb'latter. The
quotient will be the required A,
Example.
Given curve =*!/ = 96° 18' = fQuotient, A =
curve =*1
V = 2.25 J'
2° 16' = 2.25J 96.30 L42.80 =;= 428Q ft.
900 -
630
450
1800
4d CiyiL BNGINBER'S FIEUy-BOOK.
TO FIND THE SUB DEFLECTION.
Given the c, Af = 90 ft., and the degree of curve AC = S^,
to find the d, BAf.
Take half the given c = 45, and find the number correspond-
ing to it in the coluton headed *' 5"* Curve, Arc." Then in the
upper right or left hand corner of the table will be found the
degrees, beneath which on a line with the corresponding num-
ber will be found the minutes of the required d.
Thus the d, BAf = 2* 15'.
Problem 40.
Given the (7, Jlf = 60 ft., and the degree of curve AC = 4:"
80', to find the d, BAf,
Multiply the degree of the given curve expressed decimally
by half the given c, and find the number corresponding to it
in the column headed "1** Curve, Arc." Then in the top
right or left hand comer of the table will be found the degrees
beneath which on a line with the corresponding number will
be found the minutes of the required d,
JSxamjde.
Given curve = 4" 30' = 4.5
|c= 30
Product 135.0 = r 21' = d
TO FIND THE INTERSECTION.
GIVEN THE CURVE AND ARC
Given the degree of the curve AC = 10°, and the A, AfabcC
= 485.000, to find the J, J^'J?^^.
Find the number corresponding to the given A in the
column headed ** 10° Curve» Arc." Then in the upper right
or left hand corner of the table will be found the degrees, be-
neatli which on a iiiie with the corresponding number will be
/bund the minutea of the required I = ^° SO' .
CUKVE FORMULA AND PROBLEMS. 43
GIVEN tHB CURVE AND TANGENT.
Given the degree of the curve AG = 7°, aud the T, BA and
BG = .171.601, to find the /, FBG.
Find the number corresponding to the given Tin the column
headed "7° Curve, Tan." Then in the upper right or left
hand corner of the table will be found the degrees, beneath
which on a line with the corresponding number will be found
the minutes of the required I = 23° 40'.
TO FIND THE DEGREE OF CURVE.
GIVEN THE INTERSECTION AND TANGENT.
Given the /, FBG= 37° 33', and the T, BA and BG= 195.03,
to find the degree of the curve AG.
Find the number corresponding to the number of whole
degrees in the given / at the top of the left or right hand
column, after which descend the column until the correspond-
ing minutes in the given / is reached; then on the same line
to the right or left seek a number under the heading "Tan."
corresponding to the given T\ ai ihe top of the column in which
the corresponding number is found will be found the required
degree of curve = 10°.
GIVEN THE INTERSECTION AND ARC.
Given the /, FBG = 42" 18', and the A, AfabcG= 528.750,
to find the degree of the curve A G.
Find the number corresponding to the number of whole
degrees in the given /at the top of the left or right hand col-
umn, after which descend the column until the corresponding
minutes in the given /is reached; then on the same line to the
right or left seek a n\imber under the heading " Arc" corre-
sponding to the given A ; at the top of the column in which
the corresponding number is found will be found the required
degree of curve = 8°.
TABLE XIV.
rUAL TANGENTS, AND ARCS EXPRESSED IN CHORDS OF
100 FEET FOR EVERY MINUTE OF INTERSECTION.
FROM 0« TO 90<», FROM A !• CURVE TO
A 10» CURVE. INCLUSIVE.
TABLE XrV.— ACTUAL TANGBNTfl, ETC.
1° Curve.
M.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
»0
21
22
23
24
25
26 21
Tan.
.830799
1.66160
2.49240
3.323>0
4.15400
4.98480
5.81559
6.64639
7.47719
8.30799
Arc.
1.66667
3.33333
5.00000
6:66667
8.33333
10.0000
11.6667
13.3333
15.0000
16.6667
9.16744 18
10.0269'20,
10.S577I21,
11.6885123
12 5193
13.a501
14.1809
15.0117
15.8425
16.6733
17.
18.
19,
19.
20.
27
28
29
30
31
32
33
34
35
36
37
38
22
23
24
24
25
26
27
28
29
30
30
31
39 .32
40 33
41
34
42 135
43 35
44 86
45 37
46 138
47 39
48
49
50
39
40
41
5041
3349
1657
9965
8273
6581
4889
3197
1505
.9813
8121
6429
5023
3618
1926
0234
8542
6850
,5158
.3466
.1774
,0082
.8390
,6698
,5006
,3314
.1622
.9930
.8238
.6546
25.
26.
28.
30.
31.
83.
35.
36.
38.
40.
41.
43.
45,
46
48
50
3333
0000
6667
3333
0000
6667
3333
0000
6667
8333
0000
6667
3333
0000
6667
33*5
0000
6667
3333
0000
51.6667
53.a333
55.0000
56.6667
58.3333
60.0000
61.6667
63.3333
65.0000
66.6667
68.
70
71,
73
75,
76,
78,
80,
81
83,
a333
0000
6667
3333
0000
6667
3333
0000
6667
8333
51 42 4a54 85.0000 21.2435 42
62 43 3162 86.6667 21.6589 43
63 44.1470 88.3338 22.0743 44
64 44 9778 90.0000 22.4897 45
55 45 . aS72 91 . 6667 22 . 9194 45
56 46 . 6966 98 . 3333 23 . 3492 46
^Z 4r.5J^4i95.000023. 7646 47
£f£ 48. 3683 96. 666724. 1800l48.
^» 49. 1800. 9S. 333324. 5954 49.
f jr.
2» Carre.
Tan.
.415415
.830830
1.24624
1.66166
2.07707
49249
90790
32332
73873
15415
4.58389
5.01363
5.42904
5.84446
6.25987
6.67529
7.09070
7.50612
7.92158
8.83695
8.75236
9.16778
9.58319
9.99661
10.4140
10.8294
11.2449
11.6603
12.0757
12.4911
12.9065
13.3219
13.7517
14.1814
14.5968
15.0122
15.4276
15.8481
16.2585
16.6789
17
17
17
18
18
19
19
19
20
20
0893
5047
9201
3356
7510
1664
,5818
.9972
4126
8280
Arc.
.833383
1.66667
2.60000
3.38383
4.16667
5.00000
5.83a33
6.66667
7.50000
8.83883
9.16667
10.0000
10.8883
11.6667
12.5000
18.8388
14.1667
15.0000
15.8888
16.6667
17
18
19
20
20.
21.
22.
28.
34.
25.
25.
26.
27.
28.
29.
80.
30.
31.
32.
83.
34.
35.
35
36
87
88
39
40
40
41
,5000
,8383
,1667
0000
,8333
,6667
.5000
.3333
.1«67
,0000
8333
,6667
,5U00
3333
,1667
,0000
8333
,6667
,5000
.8383
.1667
.0000
.8333
.666'
,5000
8338
.1667
.0000
.8a33
.6667
.5000
.3333
.1667
0000
.8333
.6667
.5000
3333
J667ll6
3® Curve.
4" Curve.
Tan.
.276962
.553923
.8:50885
1.10785
1 .38481
i.66irr
1.93878
2.21569
2.49265
2.76962
3.05618
3.34264
61960
89656
17852
45049
72745
5.00441
5.28137
5.55838
,83829
11226
88922
66618
94814
22010
49706
774aS
06009
32795
8.60491
8.88187
9.168:58
9.45490
9.73186
10.0088
10.2858
10.5627
10.8397
11.1167
11.
11.
11
12.
12.
12.
13.
13.
18.
18.
14.
14
14,
14
15
15
15,
16.
Arc. Tan.
.555556
1.11111
.207740
.415480
.628220
.830960
1.66667
2.22222
2.77778 1.03870
8 333331.24644
3.88889 1.45418
4.44444 1.66192
5.00000 1.8(3966
5.55556 2.07740
1^2
11111^.29230
666672.50721
22222|2.71495
77778 2.92269
a3333 8.13043
88889 3.38817
44444 8.54591
10.0000,3.75365
10.5556 8.96189
11.11114.16918
3936
6706
9476
2245
5015
7784
0554
3324
6098
8868
11.
12.
12.
18.
13.
14.
15.
15.
16.
16.
17.
17.
18.
18.
19.
20.
20.
21.
21.
22.
23.
23.
24.
25.
25
26
26
27
27
66674
22224
77784
3333,5
88895
4444*5
00005
5556
IIU
6667
2222 6.
7778 6.
a333 6.
8889 7.
4444 7,
0000
5556
nil
6667
2222
.87687
.58461
,79235
00009
,20783
.41557
,62381
.&3105
,08879
.24658
46427
66201
.87691
.09182
29956
60780
71504
92278
18052
33826
Arc.
.416667
.838888
1.25000
1.66667
2.08833
2.50000
2.01667
3.33383
3.76000
4.16667
4.58333
5.(HX)00
5.41667
83333
.28000
66667
08333
,50000
,91667
8.33338
8.75000
9.16667
9.58333
10.0000
10.4167
10.8833
11.2600
11.6667
12.0833
12.6000
1632 28
4402128,
7778 8.54600
3333 8.75374
8889 8.96148
4444 9.16922
000019.37696
5566 9.68470
1111
6667
7778
29
30
7172
9941
2806 30.
5672! :«.
8441! 31
1211132
8980,33
46
9.79244
10.0002
10.2079
10.4167
12
13
13
14
14
15
15
15
16
16.
17.
17.
17.
18,
18.
19.
19.
20
20,
20
9167
8833
7500
1667
5838
0000
4167
8333
2500
.6667
.0833
.5000
.9167
.3333
.7500
.1667
.5833
0000
4167
8338
6<* Ourv«.
Tan.
.166211
.332421
.498632
.664842
.831053
.997264
1.16347
1.82968
1.49590
1.66211
88405
00599
17220
8:5841
60462
67088
2.83704
3.00325
8.16946
8.88567
8383 10.6284 21.2500 8.49967 17.0000
8889 10.8311 21.6667 8.66588 17.3338
4444 11 .0389 22.0833 8 83209 17 6667
0000 1 1 . 2466 22 . 5000 8 . 99a30 1 8 . 0000
5556 11.4615 22.9167 9.17024 18.3333
1111;11 6764 23 3a33 9.34218 18.6667
6667 >1 1.8842 ,28. 7500 9.60839 19.0000
60189
66810
83431
00052
16678
88294
49916
66636
83157
99778
16399
33020
60214
67409
84080
00661
17272
38898
50514
67135
83756
,0a377
,16998
33619
,50240
,66861
.83482
.00103
16725
.38346
Are.
.388888
.666667
1.00000
1.88888
1.66667
2.00000
2.88883
2.66667
8.00000
3.88883
66667
00000
88383
66667
00000
33838
66667
00000
83833
66667
00000
a3888
7.66667
8.00000
8.38883
8.66667
9.00000
9.38383
0.66667
10.0000
10.3333
10.6667
11.0000
11.8838
11.6667
12 0000
.3388
.6667
.0000
.3388
12.
12.
13.
13.
18.6667
14.0000
14.a333
14.6667
15.0000
15 3338
16.6667
16.0000
16.3388
16.6667
\
TABLE XIY. — ACTUAL TANGEKT8, ETC,
6" Onrre.
Tan.
Arc.
.138589
.877057
.415586
.554115
.698643
.881178
.9097101
1.10883
1.84676
1.38589
1.58859
1.67190
1.81043
1.94895
8.06748
8.22601
8.S6454
8.50807
8.64160
8.78018
8.91866
3 05718
8.195n
3.S3484
3.47877
3.61130
3.74983
3.88836
4.08888
4.16541
4.30894
4.44847
4.58578
4.78908
4.86V61
5.00614
5.14467
5.88380
.877778
.555556
1.11111
1.38889
1.66667
A • trrrarw
8.88888
8.50000
8.77778
3 05556
3.33333
3.61111
3.88889
4.16667
4.44444
4.78828
5.0000C
6.87778
ft.55566
7® Curve. 8» Carve.
Tan.
Arc.
5.48178 10.8333
6.66085
6.69878
6.83781
6.97584
6.11487
6.85890
6 89143
6.68995
6.66848
6.80701
6.94554
5.88333
6.11111
6.38889
6.66667
6.94444
7 ?»^^
7.50000
7.77778
8.06566
8.33333
8.61111
8.88889
9.16667
0.41444
9.72S2Si
10.0000
10.8778
10.5566
.118768
.887516
.856874
.475038
.593789
.718547
.831805
.950068
1.06888
1.18758
1.81043
1.48889
1.55804
1.67080
1.78956
1.90638
8.08707
8.14583
8.86469
8.88335
8.60811
8.68066
8.73968
8.85838
8.97714
3.09690
3.81465
S.88341
3.45817
3.67093
.888096
.476190
.714885
.958:180
1.19048
1.48856
1.66667
1.90476
8.14886
8.38095
8.61906
8.85714
3.09584
3.83333
3.57148
3.80958
4.04768
4.88571
4.683S1
4.76190
6.00000
5.88810
5.47619
5.71489
5.95838
6.19048
6.48856
6.66667
6.90476
7.14886
11.1111
11.8889
11.6667
8.
3.
3.
4.
4.
4.
4.
4.
4.
4.
68969
80844
98130
05415
17891
89166
41048
58918
64794
76670
.38095
.61905
.86714
.09584
83333
,67143
80968
.04768
88571
,58381
4.88546
6.00481
11.9444 6.18897
18.8888,6.84173
18.6000 5.86049
18. 7778'6. 47934
18.0556 5.59800
18.8388:6.716.6
I8.611l!6.83.'ir.8
13.8889 6.96488
7.06407 14.1667 6.07303 18.1489 5.31498
7.88860 14.4444 6.19179 18.8810 5.41880
7.86118 14.7888,6.31055 18.0191 6.58279,
7.49966 15. 0000;6. 48931 12.8571 5.68678
7.64896 15.8778 6.65816 13.0052 6.73424
7.78687 16.6666'6. 67501 13. a^33 5.84176
7.98479 13. fflS39;0. T9877 IS. 571415. 94^9
8.aS88i^ie.lUll0.9l2S8l8.8O96\(i.(yi96Si
8.SOl86lje.8889,7.08U9ll4.0476l6.15a56
9.76190
10 0000
10.8381
10.4768
10,7143
10.9524
11.1905
11.4286
11.6667
11.9048
Tan.
.108983
.807866
.311799
.415738
.519666
.683599
.727588
.831465
.935398
1.03933
1.14686
1.85487
1.35880
1.46883
1.66616
1.67010
1.77403
1.87796
1.98190
8.08683
Arc.
9» Curve.
Tan.
208338
.416667
.685000'
.8333?}8'
1.04167,
1.85000,
1.45883!
1.66667
1. 875001
8.08333,
Arc.
.098404
.184808
.877218
369617
.462081
.554485
.646889
.789833
.831687
.984041
8.89167 1
8.500001
8.708381
8.9166711
3.18500 1
3.33333I1
8.54167|1
3.760001
3.958831
4.16G67 1
8.18976 4
8 89370:4
8.39763 4
8.50166'5
8.605&0'5
8.7094S;5
8.81336,5
8.91789 6.83:^!8.
37500
58333
79167
00000 8.
808338.
,416t78,
62500 2
3.08183*6.
3. 1851616.
04167
85000
46838
6G667
87500
3.6480617.08333
3.6519917.89167
60000
3.829096.
3.833036.
3.440646.
I
3.76593 7
3.85986
3.96379
4.06773
4.17166
87569
37953
.01963
.11588
.80763
.30003
.39843
.48484
.67724
.66966
.76806
.86446
.94686
.03986
.1316'
82407
31648
40888
50188
59369
68609
77850
,70883'3
,91667 3
18500
33338
8.64167
8.75000
.488468. 95833;3
58789,9. 16667
6918319.37500
79586'9. 58333
89919
00318
10706
81099
9.79167
10.0000
10.8083
10.4167
10.6260
I0.a-J33
87090
96331
05890
15449
84689
33989
43170
58410
61651
70891
.80188
89872
.98612
.07S53
.17098
.86334
.35574
.44814
.54055
.68296
.186185
.370370
.556556
.740741
.925986
1.11111
1.89C3U
1.48148
1.66667
1.85185
03704
40741
59859
77778
,96896
,14815
.33333
.51858
.70870
,88889
.07407
.26926
44444
.68963
.81481
.00060
.18518
.37037
.56566
.74074
,98593
.11111
.89630
.48148
,6666'
85186
08704
88222
,40741
.59259
,77778
.96296
14815
,83333
61858
70370
88889
07407
85986
10« Curve.
Tan.
.083185
.166870
.849555
.338740
.415985
.499110
.582895
.665480
.748665
.831861
.917904
1.00396
1.08714
1.17033
1.85361
1.33670
1.41988
1.5030713
1.586253
1.66944 3
Arc.
.166667
.333383
.500000
.666667
.833338
1.00000
1.16667
1.33383
1.50000
1.66667
1.75268
1.8:^581
1.91899
8.00818
8.08586
8.16855
8.25173
8.33492
8.41810
8.50189
6844'
06766
75371
83977
92895
00614
08988
17251
25569
33888
42206
60526
58843
67162
75480
83799
92117
00436
08754
17073
.83333
00000
16667
,83383
50000
.66667
.88333
.00000
.16667
.33333
3.50000
3.66667
83333
00000
16667
4.33333
4.50000
4.66667
4.83833
5.00000
1666'
33333
50000
6666'
83333
00000
16667
33333
50000
66667
83838
00000
16667
33383
50000
66667
83383
00000
16667
33333
8.60000
8.6C.G67
8.88333
4.72536 9.44444 4.25391
4.81776 9.02068 4.38710
11. 0417'4. 91017,9. 81481 4.42028 _„ .
11 . a'iOO'S. 00257 10. 0000l4.6a%'v\<J> .v5RftRSi\'5»^. \
1 1 . 4.^88 5 .oaftimo .\waU .tiWKaNSi A'?^^'^"^^^^
11 .8750 R.«fcM\0.«m\4.^^«a^^^
12."20n 5.A7090\\0.^^'«\4.'»'»A5^^^1
"is
l" l" Onrve. 8" Curve. 3° Curve.
4° Cnrre.
M. Tao, 1 Are. Tan- Arc. Tan. Arc.
au. aiuaiioa.oDoss.oios 50,0000 IB, a7ea^.33S3
1 M.SMaioi.etrso.JsasBO.saasifl.assoM.sssft
a 51. 88141103.38835. S4I7 51. flSB7l7.saBBM. 4444
3 ss.siaiios.ooDss.iifiTiikS.GOoaiT.soeHsn.noaa
4 s8.3430]06.oeTag,BTiS5a,as33i7,Tsaa3s.»o«
5 M.iraa 108,83387.0878 5*.l«e7 18.<»«j 80,1111
e sa.0O4fl]io.oo027. 5033 55, 0000 18, 3.MH 36. eaff
8 5fi!60e211s!33338!834^5S!lie6TIs!8»0737!77Tl
S 67,4970 115,000 38,7498 57.5000 18,1677 88,8333
lO 53,3273 n6,W 1!B,1<»0 58,S3-1» 19,4448 8e,$gEI
!3 ISifflsSSli
14 61.6510 128,338 30.8286 81.6887 80.6535 41.111:
16 63!3136ll28!88 i:65T5 88!333Sil!loe4 43:22a
Tan. Arc,
13:5574^:0050
13»^MS33f
13:8833 36:866;
13,5461 27.0333
18,7638 37,6000
14:3770 38:7501
14 534S 39.1661
ltt:3080|30:416;
ia:0481 133:0831
10.0070 30.0000
10, 1732!20 .3-133
10,3394 30.8867
li:33ST 33:6687
11.5039 33,0000
ills
12:6064 si'.aaaa
12,8388 35,6867
IHMBhbm
sa ro:847
ST ra,Mia
as ?a.3395
SB 74.1703
30 re. 001
3L 73,831
33 78.6647
33 77.4936
34 :B.ai4
36 T9!llB»
37 80,8167
35 SI 647
40 83.3664
41 M,197
ill
4S 90,0128
49 B0.8436
fi3 wlieai
Ms
IS:SiS;SS:Sg:a!!!!SE:S
148.3.1335.8403 71,6867 i3,8Bfil 47,7778 1T.9-J30
145,000 .3S.S557 72.5000 24.1731 48.38.^ 18.1307
146. M7 38.6711 73.8333 24.44S0 43.3830 13,3334
148,3.33 37.0889 74.1867 M,7!60 *B,4144 18,0468
im:333 la^fsk TflieosT 35:a569 silin? wiieol
155.000 38.7483 77.5000 25.8338 51.8867 10.3771
168.667 30. 1638 73.3333 26.111)3:53.23^ 19.5349
iiillsiflilil
163,e67|4I. 6347 83,8333 27.7917! 55. 6556 ^ ^^
ITSiSsa 43:3464 SeieaW 38:H67:^ 3i;6T66
17S.000 43.7613 87.6000 30.1765 S8.S3SS SI .SS«
ibo:ooo'45:do3i 00:0000 3a:oaT4t6o:oooo 23:ai>76
1B1.887J45.4335B0.8S33 BO.awg M.6S6« 23.7158
l||||slffi||l|
93:334'48:33I4 96:6667 8^:3^30 64:4444 34:ie!»
/fW.MOW.fMSim-.MOO 33.5000 6.1.0000 34.3773
»r.flfl-*S,7a33(B,.ra.*?«,7770«.-S.565eM.!»O
(W.aB^.sflfsw.iaaras.oBSSiee.mm.TBBO
1
TABLE Xrr.— ACTUAt. TAHQEMTS. BTQ
,.0„™. B.On»..
0' c
.„e.
.•
Tan 1 ATO
Tan 1 Vr,- Tb.,
Arc
Tdi.
~&V
Tiu"
»
M~
r"M5l
6SH»r
BOU831
4-8ai 18 out
W*»I4 r-Jts6 *H 111.70(0
11 29si
-oM7 17 MOO
,l!IU 15 HI" H UM t«05B
11 6B8
8PM8
BjOH 1 )h
11 8,M1
I MJM )S M?
03308
leOBM
4Sffl 1 1 3.
nse
S (3*
5 60-4S11 0001
3I00S
IB 40-.
44681
) r,3si
B B-a-Bll 338J
68^4
19 1M-
amsr|iBi
b Hseii 6000
8safls'ifl«8B
il9«aL 14 &83d 41-11
("DflSO
HSMttl
19 -*a
1 4. i!38 IB got)
4110-S
n i4»i
6 Bi336!l 8338
lOOOST
iOOOOU
SMBS
13 333!
BOOGWl (0)0
10 1413
a>^-9
tesuoi 3SL(
wm
I6 20«3
B Oe»-S 1 186T
lOJ-K
OfiSM
t MiJBO 17 (1101
fl949M
13 §881
10 5SW
JT 3tWJ
iu»i ism
80^
UWl^
041B3
13-4-
il4i5a31JS33B'l7
1 twa
1 s!iW« 18 r |.
a 4UB3 18 BOSS
a i3soa
4!»4.
WBiKfl
11 1XJ5
-. jaa
s&aasB vott
8 3433!.
ISBM
41-ft,
I4B14»
»6"rB
113S31
U llMn » 38B«
8 44"T(5
M0«3
BO»f
11 3»fl
*( — B
B oei SB^
1 (Tb-ll
aam
iai8E^
13 686
H^l
^U5S8
» 8HM7| H Bl»
10 ooeibo (WO
mm
IS 870.
Bs-ai
13 8333
asm
« awft
dooo
7 Tr44
OlMI
14 0001
2) eiii
10 IB J at -as
1 068
r984
a wea
10 ■Hsslao 4 6!.
1 B16'
- B-aa
IBB3M9
1 681
I4 33S
1 090-
34 IBB
sma
IB lu:
10 4>t3S JO w
18 m
aisoa
10 393;
343a
1*668
une^
M^
18 541
BS4He
]3Gnss
9soooa
10 eioei 4386
9383116
IB -BOO
9 34188
HBS67
760060
IB 0000
30
10 m Li i«6
msBsft
IflSW
9 4349-
18B51B
7BBirB
1M6S
1" -h*i»|-a 'j^M
10 nshs' I Mil
g BMM
tsm
L"^
. BflK
16 333:
1 i hIj w)
8«B44e
niififlgjii 111!
:i li«kiei.B8H
B7B8S8
]RB8Sa
7 40-.
16 86*
n iBHi
■0 iSHJ
;i dt4-i jj Hisi
taoa
»-Bl
7BBsa
16B331
18 33-1
1 JM. fe-ifil
Mono
7-S
Booa-i
11 BBjal^ oBse
Dsoai
' seso
S7 lidSS
llB710 28S8Sa
10 il41
si4se
1BSS3S
18 673
■7 6000
U -MB|83 B-14
10 3219
»0»0
18 8833
B1»1I4
IflBOOO
38
]8 90«
:! 11197 "3 Win
■m BBS1
^UM
8 4303 1(1 SiM
14^168 n jr
S'
U lil&.
B 11104 1^ sas;
""*
n Mil ni
■"
fl 4-11 i'« h^
ni
"s^
j
V yi*"*
/
/ois J ( -ft
4 1 Jt ■iUU 41 4 01 V\ 1
\v c *
■aas.
TABLE XTV. — ^ACTUAL TANGENTS, ETC.
9<
1** Carre.
Tan.
100.040
100.8710
101.701
10-3.532
103.963
104.194
105.034
105.855
106.686
107.517
108.
100.
110
110.
111.
112.
113.
114.
114.
115.
116.
117.
118.
119.
120.
120.
121.
122.
123.
124.
125.
125.
126.
197.
128.
129.
130.
130.
181.
132.
1&3.
134.
135.
135.
136,
137.
138.
189.
140.
140.
348
178
009
810
671
502
33-2
163
994
825
656
515
375
205
036
867
698
529
859
021
852
683
513
Ui
176
006
837
667
386
21
048
879
709
Arc.
200.000
201.667
203.333
205.000
206.667
206.338
210.000
211.667
213.333
215.000
216
218
220
221
223
225
226.
228.
230.
231.
233
236.
236
238.
240.
241.
243
245.
246
190 248.
250.
251.
253.
255.
256.
258.
260.
261.
263
,667
333
000
667
333
000
667
333
000
.667
333
.000
.667
33:3
000
667
333
000
667
333
000
66T
a33
000
667
333
000 65
527 266
266.
268.
270
271.
273.
540 275
371276
202
033
2^8
280
863 281
667
383
000
667
383
000
66'
333
000
667
333
000
667
141.694 283.333 70.8497141
142.625 286.000 71.2051 142.600 47
143.856 286.067 71 .6805 148. a33 47
144.187 288.333 72.0960 144.167
146.017 290.000 72.5114 146.000 48
145.848 291.667 72.9268 145. R33 48
14». 679 293.333 78.3422 146.667 48
£it//^- ^^^^!^. OO0 73. 7578 147. 60049
jSf//^-^^- ^*^74. 1780 148.
^»/l4 0,»»39e. 383 74. 6028 149.
%^ Gurre.
Tan.
50.0217
50.4371
50.8525
51.2679
51.6833
52.0988
52.5142
52.9296
53.3450
53.7604
54.
54.
56.
55.
56.
56.
56.
57.
57.
67.
58.
58.
59.
60.
60.
60.
61
61.
62,
62
68
63
64
64
66.
66.
66
66
67.
67.
67,
68,
68,
69,
69,
ro.
70,
1758
5912
0067
4221
8375
2329
6683
0837
4991
9146
3300
7697
.1895
6049
0203
,4357
,8611
.2665
.6819
,0974
.5128
.9282
.3436
.7590
.1744
.5898
.0053
.4207
.8361
.2658
.6966
1110
5264
9418
35?2
7726
1881
Ga36
0189
4343
Arc.
100.000
100.833
101.667
102.500
103.333
104.16'
106.000
106.833
106.667
107.500
3® Cnrv*.
Tan.
Arc.
106.
109.
110.
110.
111.
112.
113.
114.
115.
116.
116.
117.
118.
119.
120.
120.
121.
122.
128.
124.
123.
126.
126.
127.
128.
129.
180.
180.
131.
182.
133.
134.
135.
135.
136.
137.
138.
189.
140.
140,
333
167
000
833
667
600
333
167
000
833
657
600
333
167
000
833
667
500
333
167
000
833
667
600
333
167
000
883
6(rr
600
338
16
000
833
667
500
333
167
000
833
667
38.3500
83 6270
33.9039
34.1809;
34.4678
34.7348
36.0118
35.2887
35.5667
35.8427
36.
36.
36.
86.
37.
37.
37.
38.
88.
38.
38.
39.
39.
39.
40.
40.
40.
40
41.
41.
41.
41.
42.
42.
42.
43.
48.
48.
43.
44
44
44
46.
46
45
45,
46
46
46
46
47
1196
3966
6736
9506
2275
6044
7814
03a3
3353
6123
8892
17^7
4623
7392
0102
2931
5701
8471
1240
4010
,6779
9649
2819
1 0068
7858
0628
,3397
6167
.8986
.180088.
66.6667
67.2222
67.7778
68.8333
68.8889
69.4444
70.0000
70.6666
71.1111
71.6667
4» Curve.
Tan.
72
72.
73.
78.
74.
75.
76.
76.
76.
77.
77.
78.
'8.
79.
80.
80.
81.
81.
82.
82.
83.
88.
84.
86.
86.
86.
86,
87,
87,
4667
7436
0206
2976
5745
8515
1284 92
4054'92
6824 93
9693 98
89
90
90
91
91
48.067S
2363
.5132
7902
0672
.3441
.6211
.8980
1750'
83S49.
157/49.7885 99
94.
95.
95.
96.
96.
97.
97.
98.
98.
2222
7778
8333
8889
4444
0000
5556
nil
6667
2222
7778
3333
8889
4444
0000
5566
1111
6667
22.!2
7778
8833
8889
4444
0000
6566
nil
6667
2222
7778
3833
8889
4444
0000
5556
nil
6667
2222
7778
3333
8889
4444
0000
5556
nil
6667
2222
7778
3333
26.0148
25.2226
25.4302
26.6880
26.8467
26.0636
26.2612
26.4689
26.6767
26.8844
Arc.
60.0000
60.4167
50.8333
61.2500
61.6667
62.0833
52.6000
52.9167
53.3333
63.7500
27
27
27.
27.
27.
28.
28.
28.
28.
28.
29.
29.
29.
29.
30.
30.
30.
:».
30.
31.
31.
31.
31.
31.
32.
32.
32.
32.
32.
33.
33.
33.
33.
:«.
34.
34,
34,
34.
36
36
35,
36.
35.
36.
36.
36.
86.
36.
0922
2999
5076
7154
9231
1300
3386
6403
7541
9618
1696
3845
5994
8071
0149
2226
4303
6381
8458
0586
2613
4690
6768
8846J
0923
3000
5077
7155
9232
1381
3630
5608
7685
9762
1840
3917
5995
8072
0149
,2227
4304
6882
84.59
0636
2614
4691
6769
8846
5» CuTTe.
Tan.
54
54,
55.
55.
56.
56.
56.
67.
67.
57.
68.
58.
59.
59.
60.
60.
60.
61.
61.
62.
62.
62.
68.
63.
64.
64.
66.
66.
65.
66.
66.
67.
67.
67.
68.
68,
K9.
69,
70,
166'
6833
OUOU
4167
8333
2500 22
6667
0833
6000
9167
3333
7600
1667
5833
0000
4167
8333
2500
6667
0833
6000
9167
3333
7500
1667
5833
0000
4167
a338
2500
6667
0833
5000
9167
3333
7500
1667
5K33
0000
4167
20.0140
20.1803
20.3466 40
20.5127
20.6789141
20.8451
21.0113
21.1776
21.3437
21.6099
Arc.
40.0000
40.8383
.0667
41.0000
8383
41.6667
42.0000
42.3383
42.6607
43.0000
6762 43.3333
8424 43.6667
0066 44.0000
1748 44.3333
21.
21.
22.
22
22! 3410:44. 6667
22.
22.
28.
23.
23.
23.
23.
24.
24.
24.
24.
24.
24.
25.
25,
26,
25,
25.
26.
26,
26.
26.
26.
26
26,
27,
27
27,
27
27,
27.
28,
28,
607346.0000
6734 45.3333
8396146.6667
0068 46.0000
1721 46.8333
,3383 46.6667
,5102 47.0000
6821 47.3333
8484 47.6667
0146 48.0000
1808 48.3333
3470 48.6667
5182 49.0000
6794 49.8333
8456 49.6667
0118 50.0000
1780 50.3833
3443 60.6667
6105 61.0000
6767 51.3833
8429 61.6667
0091 52.0000
,1753 62.3333
,3415 62.6667
,6185 58.0000
.6864 63.3833
,8516i53.6667
,0178:54.0000
,1840.54.3388
, aw* 1 54. 6667
,51R5 55 0000
,6827'66.3833
84891.55.6667
,0151 56.0000
.1813 66.3383
28.
28.
70.8a33
71.2500
71
72.0633128
72.5000 29
6667128.
88S9i37.0923\74.\W
4444 87
3475 56.6667
513757.0000
6799!57.a338
8461157.6667
0128 58.0000
72.9167 29. 1786'68.33S3
73 . 3dS3| 29 . 3448 58 . 6667
73.7BOO'29.5nO'59.0000
50
TASLB XIV.— ACTDAI. TANOBMra, KTC.
,«.
<y c
w.
U, A
Tan. 1 Arc,
T" 1 ■"
"" 1 "°
Tan
«
Tfli»'33.38t3
14300 a"^
^w-asase
a.B1>S,38,B]]l
4a8S«S01B
E9 40-
t-asmta.eaai
•sai
£81
I. oaas 34.1(07
9aGl.i«S85b
JS 6-10
asm
20 son
T.aMaM.4M4
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aw-
iS8B3J
1IIMH968
34W
20 860-
7. 873434. «ffi
8939U
68»t«S 8
4328
20 833;
oijasooooo
ser
!G!£UI
17 !bmB 33-2771
ui aossB
i4S&
^6 458.
rf^
S08S
J7. raw 85, MO
ic
asusso tt.
3464
36 868
ata
17. 8!(7B 86.8338
3u«iao 43
Jh SO
J8.OS60.S6.1111
IB
4^" 30
0-
^
21 88-
aMMM.am
BOM
^w
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1S.S43trRe.Mi);
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]8.«aKi 7.2!aa
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lB.I5»7iS7.N»u
OS
w»
22 50 J
IB.BSra. 7,J77«
wfiefr
iB.oasrjSS.Qun
288
esTJSSBTfc
4308
18.1743 38. B33S
3858
S-6O0
a 7900,85 UM
40
is.aias
38.6111
18
»*5|33 0flW
8 8824 £9 407
23 86-
U.4SI3
n.83H
16
OT30
»
1
^
i9.ba*B
11
6^^3333
Tsoou
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D- SSSOSS
I»!87»5
089TS4 04-b
10
30.0150
40;000(
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a,
ta.iiaa
40.2778
17
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205
86-
m.soii
40.6fiS6
17
896034 8
3333
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tOBSSI
IT 47 35 own
•684 OOOO
mmi
r 8336 3» 888
43-
aM|2-40-
3! , 8fl
lu'ora
17 83335 -63
8 04
8188 hrw^
84 "4 8333
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41 Mff
.7^ I35 48
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1
1
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n SM"
1 BM8»
21 ijsa
21 a6iH4iMoo
18 -rssfi
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18^80 31,
21 S3G8|4.1 OT^'M
18 4648 8'
ii 8~a 43 S3sa
21 8ise 43 bin
SI ffwW SHSt
!8«. a" BO
K 09" 41 ia<7
18 0439 87 86
S79 33 MO
S6S4 hfl MOO
as a41o'44 4444
1B0B08 98OB5S
6earU3383
m\-^^
8 «bsb|'>6 6r
40
a s-KSM-sa,
£2 5ISI 4B DDTM
saexe^sa-n
BE ■«14SM
M Bsy 45 a*!.
83 0^46 1 1
as 810- 48 Sbm
SS WB- 48 (UK
ss4tra4s iHHiX)
JO
M64 -^L-
7960 SB
■WW
r 28 8333 ao
M ai«4 soma
wnm S50
85Bll 606
OS 28 6000 51
83 9034 r "T
34 0419 « PC ■" f
M 1«M 4S WW
S4 SICT 4« E 1
U l/n 4H B«
M BOfiolsn jft
W7W
TABIA ZIT.—
L TANQBXTB, KTO,
M.
1- Curre,
»' Carre.
4° CurTe. 5° Curve.
Tan.
Are.
~T»o.
Are.
mooii
T«i-
lOO.iXW
lua.
7B0000 60.0811
sOooo
SOOJJOO
rii
U7V
iGu.aiu
M.Boao
100. Ba
a7.7«S
JB
33»
am
151.667
M.BTHB
87,BS76
76
8333 61
83S:
6a!««8T
Ml
Tt
Km
IG^.MU
M.83S9
Stl.l46i
76
S6O0S0
6187
70
bi.iaa
imlim
78
6667 30
6888
0l!8S83
77
!M:ifl-
m.TK
ga.Moi
77
18838
8531
018667
n
wm.
M.mi
ioa.333
83.7886
77
01 s
7
867
103.889
38.97K
1107 81
vu'.iasi
it
M:ro(
as
7i
8539
5i!aioi
104.444
31S3S1
3MU
83.6607
»
»16
79
7713
israoo
Ba.fii7fl
106.000
39:8911
7(
76CCJ61
B170
63.00DO
iGS.aea
SIS
807
1967
1G8.SS3
W.699(
■8.3333
m.m
1(
s»
sa^oTii
Uf
88.61167
1»
isa.oea
*
leoiooo
96.8486
loaieoi
4o:oi«
xwo.st
0151
61.0000
iso.sao
11
iO
tm
180.836
W.a3M
107.44
40.e^
64.8333
aea
!tB3
t
8486
161,66;
M.SIKi
107.778
40.4SIS
i333:ll:!
IW-SW
s
on
aaai
108.33)
40.6383;81
SaKSi
ISS.SBt
M.iBO^
4o.8iaa>si
0667 ilB
8804
«i:8a38
iM-aiE
lOW
084*
41 06068, lB83*t85M
doo
i
6386
m;^
41 e- jb aj 6U01 33 o«a
1«I>.I)«
m
867
B340
41 433B8«S16'33 1905
ao
186.7*
MSS
ae.fissa
111 111
78IB
167; Boi
M.8BW
111 66- J H«M
•aam
warn
168 SK
66 IB-!
US 2£. 4 M
laoeiB
S38 333
irooM
BMOOO
98 0311
170 001
36 6!)ll
iroas:
341 my
aB4us
D6 9«8:
113 880 1 Id
M5 W3
Ksm
171 6b:
I7i S4I
mm-
173 3?
iiflsir
88 688" 31 6884 09 8383
iO
3J8 -isa
87 ins
174 167
58 0780
lie 111 43 6609
8 08^184 Saae 88 686
ssoooo
87 62W
8* eooo'ss 0189
1)0000
51 mi
97 Min r - > ■■ 1 -
ir^
87 Bie^iSS lUl
178 -M
1S4>
assaa^^Ms
8 "800 83 B^aa
"1 0009
8 ler % 696^
B 6833iss 8614
IKI (114- 1
<^
Booooojeoi^fl
■^0000
ISO B14
31.1 Id.*
SO 4IMi 1S.I b
n tj J3S
80 418 % 1938
-8 3333
3IM »«
» HTsa ill ( 0-
4'>'Mi
«0 8333 36 3300
-3 666
3CSOO0
01 i»io iBJ am
46 eaa-
91*500
36 6363
40
itaiM
aea bb7
»1 ?t)64 189 3«
61 HI
mnna
4fiBeM
91 666"
36SBU
-a 8333
814181
isa~8
46 0881
Hi 0688
36aaB8
-3WM
<. ,- I.-"-. -> >. '^ .isjooa
iaS33!
40 sTsa
63 8000
3. aMa..4 0000
4 11 1-45 B.H
81 BTSI
133 888
48 4836
3 9167
1 1 ]■-, d?
62 use
134 444
46l»l<
98 8333
61 rmt
twooi
93 7900
67 6336 76 0009
47 lOtt
B4 inm
37 8887 76 3383
11 II IMI IfiT
47 3146
94 6883
37 8569 78^
47 630 96 0000
88 (ten 76 0000
imi fs3 w MP
«.4;,1|,»833
63 6343
IS? as
47 TMlloS 4167
68 1883 78 3333
IBl 711 383 WS
M MM IBI 667
68 611;
127 771
47 S378 96 R333'38 SUilrO 6067 1
iQ-i V4 3at 000
dO W03 IW WO
%rWmi n
J'
— Fl.fi7
TjLBLX riV.— AcrtUAli TANGZMTB, BIG.
7° Curve.
M,
6
13
T«,.
as.Mii
£S. 43(17
a5;&3
1!6.71.M
2«:i2M
ai.2679
IS
27. wot
3S!D7»
.4939
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.(MSO
■» iBflf
is
» w
■asem
Mor3
W18.W
30 804;
iO *14
30-189
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30 99*11
gs
31 413
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■a 960
ii
Are.
?;S
i .B«7
Is
i;i
CS.BBdS
54.1«67
M.4444
S4.rM3
5.0000
BB.J77S
MI.G65I
iSllll:
U.SfiS9
56. «W
57:T77i
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60 8838
81 ■»«
61 886
is
68 air
MS8SB
si
Taa.
H:450i
ii
sIbibo
3!l121
!S!:473I
ainss
im!is»
M.BOSS
i!4.4a78
24 540
M.7939
M.BOES
S3S
25 sa>«
26 3814
2!i 6011
SfiffiM
95 reo<
•1 9-B3
96 -m
iB4'i4J
■6 6-31
»«919
pi
s:b7h
iS.flOM
14! 2866
14:7811
II
11
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4n.6a3s
60.0000
»™
II
l'"
6.
B4 flifl
is
9.3961138.7500
i;SS
B-8}'8M.6B33
Jo:oi97i4o;axio
20.1238 40. ;iae3
M. 2275:40, 41 lit
». 8316 140. 6261
»:650141.2'i0<
20.7544 41,4683
20.8583 4t .Bee"-
21 :oa62 42!okl
ji.i;or42.«i)i'
ai.8970l4B.750l
"■ aa0544 6t«3
!!S4**6 44 -01
ai J)3|i5 413
1J8 9SS5
IJ'S
IH.MTil
17.0697
I7.1M1
iJiBaii
II
III
II
is
9 40(
'!S
vli
XISOW
3113990
11
wliiSB!
isioooi
16,186:
35.K15i
38:6i«
39:074;
39 2591
39 6J9I
19 8 48
1000a
luBBBI
40 40-
iB:t«4B
15:2741
16.3671
16:890!
IB. 7 738
l!:a
Ifi.OllBi
le.srai
i«:442<
17:3591
IT. 4430
IJ.6SK
r'89»
1 8847
1 MT
1SS8«
IB 3638
TIMIUJO
w.iee;
i;i
11
31.5000
31.6667
31.8893
38.0000
92.1667
32.3333
39.6000
32.8667
3il,S333
T.
ii'.rm
34.6867
34.8333
iS;S
35 3333
3Be»r
3eooo(
58 3:3!
tf 9439 M 48^
38 *tl4 » 9WP
SI "11-
1.'
TABLK JCIV.-
■ ■» B7B,418 33S
10. IDS «».()oa
11.788.4^.833
1.1Ml|*»!oi»
o >% 4h3 46S ee
•5 DOnjsB 1 44|ll
r.Bir«.it
t.SSS 43.36% Be
> 46 0JWB"
I ■» "065 It
id 4fl 3-8S S'
» ID JtlUBl 6t
B 41 "mW SM
I 48 8.1485 000
t 13 Kin 486 Sli
i .'41. Ml 1 488. »1.
I 345.173 490.00(1
aoioAtu I
330 Ha lioa'w B9 ol
8ST09fl BM
a B450|irof-
8 M D- a;
TABLB ZIT.— ACTUAL TANQBItTfi, BK,
S7 53W
r 6760
r 8186
SBfl-T!
J9 ;%ii sa SJ38 '
leoooou
■6 37^
eUG6
~fi833I
■Biin
TSSB6S
Sit oeoG
33 1-W
92 8980
saTTai
SS 8918
33 014
saiiTs
IS TB
£s isssiao soraut h<ad u ease
« sa-s w i c 4 I'j.
as MW\ft e I ^^l
26 w*.
I tnsaLj' SHI hia tn
6596 4 oa-tl
._ (MBB4 SST
DB 383,47 40
47S8i.
47"?^
\n ssasi'ie a>s6
sasMO
1 os-B
37 iao4.
w 4jae m im8 s8 uw as 6~{ia si «e<7
m n3M,4a u(
»S 13E4 4H 1(
23 E11S4B 3C
w u^ u w^lne
TABLE XIV.— ACTUAL TANGENTS, ETC.
5« 1» Carre.
M. Tan. I Arc
A
250.087
^1.818
252.649
253.480
254. 3.^
255.199
256.029
256.860
267.691
«• Carre.
500.000
!501.667
508.3:^8
505.000
506.667
506.383|
510 000;
511.6671
518.a3:i:
515.000.
258
259
260
261
261
262.
268
264
265
266
266.
267.
269
270
271,
271.
272,
278.
274.
275
276
276,
277,
27S,
279
280,
281,
281,
282
288
284,
285
286
286
287,
288,
289
290
291
522
358
188
014
845
676
507
837
168
028
887
718
540
379
210
041
872
708
538
364
195
055
914
745
576
406
2:JI7
068
899
730
560
391
222
a53
884
748
Tan.
m068
125.498
125.914
126.829
126.745
127.174
127.604
128.019
128.485
128.850
518,
518.
520,
521.
528
525.
.526.
528.
.530
531.
533.
.5:W.
538.
540.
541
543
545.
546.
548.
560.
551.
563.
5.55.
556.
558.
560.
561.
.563.
565.
566.
568.
570.
571.
578,
575
667! 129
833129.
,000 180.
667 130,
3*3 180
000 181,
««7 131,
8:i3 182
000132.
667183,
383183
000 133
667; 181
333 134
000.135
««7|135
3:«'l35
000136
602 576
4:«|.578
264
095
291.926
292.756
298.587
294.418
295.249
86,
86,
86
87,
87.
87.
87,
88.
88.
88
88.
89
89.
89.
90.
90.
90
90.
91.
91.
91.
92.
92.
92.
92.
93.
93.
93.
ft3.
94.
94.
94.
95.
95.
95.
95.
96.
96.
96.
97.
97.
97.
97.
98
590.000 147.680 295.000 98
667
883
000
667
333
000
136
137
137.
138,
188.
las.
667 139
3:« 139
000140
667il40
838,140
000 141
667
3a3
000
580
681
141.
142
142.
6671143.
338 143.
000143.
6671144,
838144.
000145.
667J145.
266
681
096
512
927
343
758
174
589
019
.448
.864
.279
.6a5
.110
.526
.941
.356
.772
.187
608
032
462
877
298
708
124
539
955
870
785
201
616
Arc.
250.000
250.883
251.66
252.500
253.338
254.167
255.000
255. 83:^
256.667
257.600
268
259
260
260,
261
262.
263
264
265
265.
266.
267.
268
269
270.
270
271.
272.
278.
274,
275.
275.
276.
277.
278.
279.
280.
280.
281.
282
288
284
285
0321285
447286
877 287
8071288
7221289
137290
558J290
833
167
000
833
66
600
838
167
000
883
667
500
833
167
000
833
667
500
833
167
000
a^3
667
500
a33
167
000
a33
667
600
833
167
000
833
66
500
3:W
167
000
833
667
583.838 145. 968*201
585.000 146.8t» 292.500
586.667 146.799 298.333
588.3;i3 147.214 294.167
3« Carre.
Tan.
83.3941
83.6711
83.9480
84.2250
84 5019
84.7885
85 0750
H5.&519
85.6289
a5.9058
Arc.
166.667
167.222
167. ''TH
168.:i3d
168.889
169.444
170.000
170.5.'i6
171.111
171.667
1828 172
4598
7867
0137
2907
5676
8446
1215
3945
6850
9715
2485
.5254
8024
0794
8568
6838
9103
1872
4642
7411
0277
3142
5911
8681
1451
4220
6990
9759
2529
5299
8068
0838
8607
6877
9242
2107
4877
7647
0416
3186
5956
172
173
173
174
175
175
176
176
177
177
178
178
179
180
180,
181,
181,
182
182
188
183,
184,
185,
185,
186
186
187
187
188
188.
189.
190.
190.
191.
J91.
192.
192.
193.
198.
194,
195
222
.778
V»
889
444
000
5.T6
111
667
222
778
333
889
444
000
556
111
667
222
778
333
889
444
000
556
111
667
222
,778
3a3
,889
444
.000
,556
.111
.667
222
778
833
889
4" Curve.
Tan.
^5512
62.7590
62.9667
68.1745
63.&S22
68.5971
68 8120
64.0108
64.2276
64.4862
Arc.
6* Curve*
Tan.
64
64
65
65
66
65
65
66
66
66
66.
66.
67.
67.
67.
67.
87.
68.
68.
68.
68.
69.
69.
69.
69.
69.
70.
70.
70.
70.
70
71
71
71
71
71
78
72
72
?2
296.0S0 591 .667 148.045 295.833 98
jSStf.9J0:5»3.S:iS )4Q.4m 296.6<'>7 98
^J'/SPT. 77V/505. OOn 148. 890 297. SOOm
ffj^. 400/301*. 838 149. 786.299. 167 99.
.8725196.
.1495 196,
.4264 196
.70:«'197,
.98ft3 197,
2669.198
6534' 198
8308; 109
444
000
556
111
667
222
778
im
.889
6430
8507
0586
266d
4739
6817
8894
0972
3049
6196
7347
9424
1502
8579
5657
7784
9811
1889
8966
6044
8121
0270
2419
4496
6574
8651
0729
2806
4883
6961
9038
1116
8198
6270
7848
9497
1646
8723
5801
,7878
126.000 60.0466
125.41750.2128
125.883 60
250.60
667i60
088 60
126
126
127
127
127
128
500
91
833
128.750
129
129
130,
130
180,
181.
181.
182.
182.
182.
183.
188.
134.
184.
135.
135.
185
186
186.
187.
187.
137.
138.
138.
139.
139.
140.
140.
140.
141.
141.
142.
142.
142.
143.
143.
144.
144.
145.
145.
51
61
51
61
61
51
52
52
52,
62
52,
52.
68
68
58.
.58
58.
63.
ooo;64.
417 54.
838 54.
167
688
000
417
833
250
667
088
600
917
838
750
167
683
250
667
088
500
917
338
750
167
688
000 66
64
54
64
56
56
56
65
56
66
72
73.
73.
73.
73.
74.
74.
74.
74
417
a38
260
667
083
500
917
3:^
750
167
583
000
417
66.
66.
66.
66.
66.
57.
57,
67.
67.
57
57,
68
58
.8700
.6452
.7114
.8884
.0668
.2216
.8877
.6630
.7202
.8864
.0526
,2188
,8850
.6612
,7174
,8836
0408
2218
8037
5509
7261
8024
0586
2248
3010
5572
7234
8896
0658
2278
8007
5660
,7321
8088
,0646
,2806
.8070
.5632
.7204
,8056
.0618
.2280
.8042
.6662
.7881
0048
0706
2868
Arc.
100.000
100.838
10U.667
101.000
101.838
101.667
102.000
102.888
102.667
108.000
103 888
108 667
104.000
104.838
104.667
105.000
105.883
105.667
106.000
106.888
106.667
107.000
107.838
107.667
106.000
106.838
106.667
100.000
100.888
100.667
110.000
110. 8:»
110.667
111.000
111.838
111.667
112.000
112.833
112.667
118.000
118.833
118.667
114.000
114.838
114.667
116.000
115.833
115.667
116.000
116.888
0956 145.8.38 58.4080 116.607
2033 146.250 58.5602 117.000
4110 146. 667;58. 7854 117.338
6188 147.083 58.0018 117.667
82651 147. 500 50.0678 118.000
0343:147.017,59.2340 118.388
2420; 1 48 . 333 .50 . 4002 1 18 . 667
4WN« \4S .IHS Ml .5722;U9 .000
.67\H'' A4« . \'^'; fA .1V4\\\\^ .«»
. 444174 .ft7«5\ \4ft .BWi rA .^\Qi \\^ ,WR
\
56
TADLB XTT.— ACTUAL TANOEKTa, ETC.
32M !m
« IHtU'U 666*
MS 5 I
__ 06 S M C.
H 344W <
Ma -BMiSl
aesons 11 >(
SB smsL at
jt> e u ^
"" MWtBOi
eaiMuK
ie OB 3 us 0000
4g -80 9- aaa
T.— ACTUAL TAMQKKTS, ETC.
..
1= c
»r.«
,.c™
1" Cone 1 4* Cane
..eo»e 1
M Tan 1 An
Tail 1 Arc
Tail 1 An; Tan
Air?
Tan
Are
TofTur Moooo -B ibts
W0-6B
1 m i^aWu 1* wwoe^
100 SM U MeK asfo
160 ii;
60a427
100 333
W IIW
1 "h '' J? Vl"^"*'*' '"!ii"Jl''^H?' ciVl"^
121 333
r "si
VOb.'
00 9U-0
leiBBT
. !'r
810-18
b\ Moa
193 333
« 4J1.
01108a
iasB87
I'^i r-fl
Bi a-sa
113 000
II) iuHMBmSM71M8MW9 8W
IW896
«05 E66|7r 1*90
IB4 1G-
SI -501
123 333
11 W9« W9aiaiM71BMllBl
108 173
Mill
77 8888
15)583
ijsar
13 no sib'mo ow 156 los'aio 000
103 1»
gOBBB-
TJBBIB
55 000
ai08js
155 SBOlVO 83!
103 W7
W7Sa
r7 Boa
tlJJlW
IfHMBSIl Birr
104 OM
ls»7-78
ai 414B
124 08-
In ilS-!!!
BSiOOO
IM»I
aosass
rasi-
5flffl0
liSSI^
1S5 000
628 8B;
M«.889
;b.4B65
5fl.867
135. sua
157 :»t!
imIbs!
an. 414
135. CO?
88o!oai
157. 8B7
108 I1«
138.000
19
aiBJaa
631.887
158.087
sis! 83!
Ufi.BM
sio:&M
7B:oB58
16?! 917
Ba:BS17
lae.aaa
air.cns
los.tas
SB .870:
(I3,4i!a7
191.687
3lT.!U3!ea.^o(»'l5B.0s^
itB.aaa
sniflw
-B.ires
sa.ssK
IWOOO
aia (183; S39 tw7 i!j»,347
los.eafr
aia.as!
:37.S33
819.5:1838.33*
m.tin
lOfl.eio
SltJTTB
■s'kmo
a.iass
«JI).M.S6«.(X>1
108.793
213.333
80.1017
M.ae85
iss'ooo
107.071
n3,88t
(osog
180.417
81 3917
:!8.SS3
3w:oo6]tm,3si
100.893
81.4-Mg
Ml 83- 645 000
aiBOOD
IBl 160
t 88
iso'ooo
MT BOC
219BfiS
nner
1«1 BS~
139 333
.9,334 11»IMflM
IN amm ia7
108 177
m 111
B114M
laaoffl
t BISB
Jf' x^ o
»1B0B-
8 Ifl 8 K
JLOM
J
6 iur i ma
J8 «- u. 1* 3.M| oeoiiBai fit) |)i ftffln iumolHi m twi
68 4«mi B2 M
J» .Ml aw »65 fflW IM «S|3M MO^MO XS\m M- 83 SWl 1« oo
8B ED81 133 DOS
40 'aw wnlflM nnriM wiliis ■!<«' i nn'"" ""'iii ^m' w wr
88 -Tim'lSl 333
;, ... ^,, ,.--,„,...,
Vt g. S ^887
1.- , . , ... .„,. . , . »i
i»asa
ro 3M «o'^ ^n nae'iM m^ih oae|'«r -n ra Bstfl|i-o bssU isw
133 107
3-000
37 333
S3 3M ftei.ess S3S n Mr|844 10-14 s 9a-a
M 'sis 111 fliw ono ire ra-'w ooo ii .y lo*
SB 34C B"iIb91 bit l"a 14 we 8331 ^ —M
JiT*! /^oa»»wi-3M aw«e-i 44 8
£7vS ««»*«'«» /«in« WW 1 a in-9
fj^ ""swiw-' < *«?JHM3i B j~* \»wrV
■\af»wi
»\-»wi
TABUt XIT.— ACTUAL TAMQRNTB, KTO.
Q* C
7 t
s C r
•> tur
T«
6
Tan An
M ITHIOO )00« wiat
60 aoss 100 ■-« rt u, 'i'<
MSlBOilOl VI43 e J»
» 488»| OU Wi » -B
vi 6ae
»i 34© 10^, soT u jj
» a^
ds iw
1 4e5Bi(M-7alM iKoa
88 09W
3S *«
91 6043 JOB l).i(l44aSM
M333:
38 IG
U 4^103 <i»S44 iWl
38 taOK
il tMl4 103 nil 44 4-B9
uo9»ia»s>»
MftBBB
DflW-S
311 ■j-e f
W»l«9
'mi.M -o
v-ax,
04 "sa
MB7*I
woec
»0-OTMtiuOl
•taJ144 8
»nTa
lȣT8
«iBaa90J3h
n 9-^
!».B«IM
loaiet
IS 31M M 4
K9WI
mm
El isr
i^fi
M«-«i
mafs
9S414
otfxr,
fS-BHB
lisssae
41Ml»Li» u.
Mens
Mtao.
^M, 1 -A
U —8 ffl flfli i i" 4JI' SI
H. hI i
M 10--!
Ul dli -9
WU,i-4MM.ii
»
M 4. «
' '
1 L X^
^om
^^333
H BH XKX
M„
t) isu B-^i a
US
8SSS
M ^^ lib 3383
33sa86,IW5W»
is
»bSiio«s
^37oaah
SBS4OTHI
■rl^iJi
0^41
a 411 L ™
40
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5B 1^4
jfi W^J 1
M tta iJ
«8in H
87 035*1 ]S^
,
LHS^
BTOMSllS 1
\.
37 Tare 116 >-
n 8^116
U 0148 US «»
V*
aeisst
if4«
—
w-v
■6
[T. — AtTTIIAIi TAHOENTB, ETC.
7-
w7
%' Carre.
3.C
rv«.
S* Cnrr
■n
Ton.
Arc.
Tflu. 1 Are,
T"- 1 A"^
T^n. 1 A,,;.
Tan, 1 AK.
-0
700.O06;i75.ai9iiW,0O(
116. 8« 338.888 87 83.33 17A. OIK 1
io:iOUG
Tuaaasnelosu's-iiWi;
40
3sa:os7
iit'874 i3i.44i'eH'.os8B iraisss
70:43Ht
41
387
3M.9M
TOS. 000 178.480,862.500
17.681 a«.000 B8.«S37 176.260
85S-B0I!
708 687
176.901
368.38:
17.947 V^.656;88 4686)78.867
133
3u.es;
708 K8J
18 WM286.tli;»8,876S 177,081
887
6
ib:778'3S7:3*(|8b:o9]8 miwi
V&.7»
71 LW
133
Bsr.iai
71S.3S1
178 S71
358,867
I19.06S S37,77S8»,399« 178,883
14:;
i67
IJB,S87
367,600
119.88* a8,8S8 8S,SOJ8;i;B,760
35s.T9i!7iB.e(r
1IB.609'338.8S»:80,TI60 179.167
71.7801
388
MB.flaiiria.a3s|i:9.8n
14S
S67
S60,4S2 ?J0.000!lH0.«89 360.000
»:i03aw:ooow:i305j80,o«
30.450 340.M8,90.34M 180,417
a>.738 341, lu'W-SWa 160,83)
687
aosioffi
7i5.ooo,i8i.so8aas.5oo
«
000
sas.B*
728.687 181. fli3iS8S.83.i
ai:S90 343:3a3'9o:9758iBi:B61
983
798.333' lH-i.Sa8:8B4.iaT
2K6fl7|349.T7B[ai,18S81Ba.0K
730.000,l8i.764 385.000
4C
19
■m.^
731, 8871 188. IflBses.MS
33:iaija43:88eifli;5B9oi8s:»n
78:3874
46
333
^.Jig.Jmajg
13g_aB8 344.444 9! ,S0B8'l8a. 883
I4r
1S3. 676 IMS, 000, 32. 01 45 183,7^0
368!m18
133.053 346. &S6N.3:EaiB4. 187
7S:7860
S-HS
asB.flT'
lSS;33»18i:815|36»:i8r
isa-3S>
448.111 83.4373,T8».68S
73.9580
143
667
740.000 las.aTelara.ooi
348.BB7 93.8531185.000
I4E
347.333 93.8608 18S. 417
MS
llaisaslasiioeaTi:^
194 ! Oil
447,778 93.0675186.838
I4»
667
373049
74s.000188.6ai
373,600
iai.35t
149
000
S78.8B0
748.687 188.011
(78.83!
Ms!^ 93:4830 mew
149
333
374. SW
349.444 03,8008^187,083
149
Sra.BSl
TllO.noO 187,788
ITB.OOI
1*5.187
!50,000
93 8986
187.6rt)
75 ISra
150
000
378.38:
m:i13(
r5:wRi
9-33
7SS"333 188! 637
H.338t
88:333
667
55,000 189.043
75:8S7!
wo
.178:9I>.
T6, 667 189.458
tTSis*
36!ai4
m.^ti
)4:743(
189! 16:
37B.;a;
5S.aa.l, 188.87:
11.9511
180.88)
DUO
381 !3»
368.880 95.3870
i«o:4r
IS)
388
3ae.3^
B.?:33a'lfli:iI9
381 !«a-
iM.445 9B„1747
100.83.3
B87
388.066
785.000191.533
382.600
366.000
95.78K
101. KM
in
383.88?
786. 8671 1 91 .9B0
95.9901
191,867
fS!
v&
768,.133 193.S80
i3s;3e3
3^.666
93.083
667
770.000 19S.810
38S.00O
lffl.6i8
iBoisW
Hi.&i
W.600
771.«87;IW.:MS
Sa'i.BM
138.836
SB7.1«»
93.917
77:aio»
386 86-
119.103
357.778
M.S38
77.4771
r?5:«oo;iB»:o68
776,887194.471
887,600
130.3TB
«a.83a
»S,7S0
-6433
000
■m.m
188,333
1S9.866
388.881
97.aai(
94.187
77.81*95
sa
3S9.7SB
778.338104.887
»9.ie:
139.081
97.4587
94.58!
77. im;
:no.5SO
m.m
97,868.
301.4M
97.8814196.417
T8:8isi
1S8
8»3
7*.3 3-33 196.193
101. p
lao 788
381 111
98,0063105.8.33
7R.48i(
IM 667
3«J0«
7M«v;ipn5T-
461.68;
98,8041.; 108,350
98,5118 98. 687
■I»:bibi
157
3!U
382: 77)
98,nM' 97.083
78.B84-!
n4
M.'i.Mo
368.388
98.9373 97.500
mo
3»6«3
283. 889
ni:8'i«(
/ ag mT.S94T<l<-'- 14.'
264.444
79.4WII
\f
/^T 3Bs.mkm„.> , .....,,;■/■:., -jKnoo
m'.imb «'.™i
79.8498
'^ ?^.m7im.tl.): ,. :^-. ... ! ■ ;■> WiSW -fiSlflB.TWimAinVTO.MW,
\x> '>wia* 11
-WS-
TABLR XIV.— ACTDtL TAKOBHTB, ETC
S* Carra.
1' C
r«.
8^0
«,e.
9» C„r.e.
10= Curve.
1"
T»n. 1 Arc,
X^--
~M^
Tao.
a™.
Tan.
a™.
:i^:
^-
M.miiia.H;
islSS
WOTN
77.7771
H.08S8
o.uoo(
M. 5090 1111.844
su'aiouioo.auB
t8.94«
B7.a»i
BB-007*
l.lTOl
M.TOTSlllT.iM!
so. BS88 100.478
i7.«i;
11 18a
78!l4S!
M, 46111 ini.TM
78.3383
7alfioai
iiT.Tnt
iO.BTMll».»
H.aea
»;36i.
W.MBfi
70.8867
!is!iita
iis.ow
u.aat
W.B417
80.4138
I8.7W
70.BSa
IISSH
o^Biw m.*»
M.4t00
W.TSOI
u.asei
118.811
o.Kmiot.at
u.srso
s!874t
71 ! 186:
ss.usi
iiH.sa
1. 0490 101 .lO
)4,B7«t
ll,7«(
tbIsso
i.lBSl
n.assa
aii.Bw;
U. 1888 KB .143
44.7808
BO.STM
8>.ai34
70.4444
71.MO0
fa ears
Ttuam os.tai
44.8848
30.00(18
■8,SMG
71.8887
SB aeati
lil.40M OS. BIB
U.nt87
90.9968
s.oon
71.8889
1
aa.ioas
Bi.sais ou.Bo:
411 00«
00 0000
40.0008
as.ooa
n.oooo
a
so sun
ai ejT4' M OK
4S.HI01
W.SDR
40 188!
MT«
i.iec;
eo 3HM iw.&M
M.TTO£i OB.SiU
4S.J107
80.870
en.sarsiiw.BS*
5i.8awnw»7i
30'82si
3741
9.848]
5
Bo.S(M)a:]:ii.iii
J.OCBllOB.BK
4fi:si!iJ
90.833;
40.4sai
38.4898
18.8887
«
w.tjMam 3HS
B6 6tH
78.8388
Hu.Maaiiui w
ui4M104:wl
08 8087
78.0000
m.dsieiai.eM
M.38« 104.684
ib'ssh
9i;4MB
40'74SB
ai;s98B
»™
78.1687
a
ei £», m,2»
!U.48aB'i04 ns
i&.BSlS
Bi.BSo;
40 8881
I.4S1I
38.7880
il^
ao
SI 3EmIi£!.«(M
i2 SOIS.IOG.OOO
40.0SA:!
38.84118
61,«T2|l«77a
iw.7so8ioB.rai
4».ia91
MiOS*
ro8i;
liSBIl
36.0881
'.a' am;
6) fi4aB!ia OH
4a,»fi«
M.aii7
41.1187
l.OBJl
Ta.SKK
ei.7BW!i9i.iu:
M^eeoo !!»>].
M.SMS
K.taa
41.9138
58.08M10a.BK
4B.4WI
41,8048
)'«^
ia.es
M.iiOis'ios iw
4SM»
41.8071
5s.3aia|HM.4ai
4B.6660
as.iiB.
41.4fl«
iIttti
»7,SW1
av
en^KiTe
ia*Ai'
4e.78»!iis sass
i!.Be3i
BT.4838
S8
w.tn*
m.T-s
4ll,8rjS|B3,Sll7
4i;0T«
3r.BI6a
«;B33i
»
N.nta
issoBo
M.B7B81W.148
M.K1S,flS.750O
41.768-
Ba.assa
37 5008
rsoo™
30
U.Ttttt
ia.x\
». 801(107.881
47.0^68 IM.BMI
4l.BSiS»n ^'^^'"fr''^ ■BBT'ai
IS.DOK
ia».A»
1».8S
I07.8»'
la^a-.i/s-' '■'■ '"'i' :t3
niiiw
108.000
47.400"
M.fiSff
s>i.b:7I
iw!m
itH.aaa
4JW46
n,«»t
iM.er
108. an
47,8088
48^8JT;i.'-i iw. ■■' -ij; ]-; i;i;(«i; 38
IM.W
4.GIS)
sz
17.7I»
47,8184
ulsoa
BP.4r8T
70^3338
M.eris
IW.M
47.1801
BS.a9B0
ilisM; BBiOOOO
BB,^
™.6000
SD
IU.ODSS
m.TTO
H.BT4S
ia».6»4
48.0W8
KS33S
ta.svn Lb.ibu
38.4878
78.8687
40
H.IBSI
188.091
H.Bm
loa.Tw
48.U1B
Be:n4i7
M SM4
48 laosfl" ;t.(->'i- ■■■■"'^ " r-^r.'.'-.' m^Kr ">»«
49
M.U4I
iw:8i:
uiinf
IIO^KV
)S.84.i;»i r.-'i !■ ."i . -- -.!■ ..- "I- r. ];:-.
H.STSS
US.BSS
110.471
4S.44;i'iN ■! :■ 14
u.nta
in.KT
SS'.47»
H.ssoa
I».M4
as.Kwi
m'.m
HMK
lae.Tsa
4i'.7^9<iv: :■'■ : 1.. ^.i':-'. i-'- ■■■' ■■:.-.; r. '-i
iso.noo
4H.8829.liT.:««i.. ^.i+i,= , M. (iA-
«:j7m
m.e-.a
SB.BiWUl M7
ia,B704;or.^oe3 13 ;,3t«|Su.i«iB
49
U.4I4S
IX. Hie
40 0771)107 9187 48 B3S0
S7.0«7(
30 880)
78.3383
SO
u.u^isa.im
31.3831
7B.B000
kalsi.^n'm^wi
w!407^
78.6887
KiBesslisriwi
M1.4S4(Illiafli0
40 NW:flB.M174fl'9tr
78.8833
M.«a8a;ifli.ii«T
40 49117 nfl.7.Wfll44. 0(181
":7^
H.ioefiisi.t)*'
ss'BTsiiiiHna-
RT .«S»VW1 .WI«SWi .\'BSl .W.
M.rawin:) 3ffl
|Ei:sa'Sts>^?>^^s?
M'.HaBB im'.Kt
Komem.r.n
M.UCM
MMar
'S:Sl
i::SI
SoioiB!
ao'.W
\t,A^
as
iwr\«'
ffi^
^
TABLB Xir.—AOTTTAI. TAHOEKTS, STa
JOI) «0 DD 83S
B atsa
438 083
<H 61. wr 91
B3SS8B
'OO00 94 _^
OflSS
_ 66-
na 0S3,85 3S
ns ODOiSS HBH ra 000
"16 §fl 1*50 S i8
fl6S9S6 I -^B«T
LB SSOiBA G9S. n 000
Its 01 'so 8«l -B »
66 2« BT 40
3 833 eel 1874160" Si S34 44\ K \iSa B3a|B8 6%" "U 66"
S 000|W1 "TB 8 600 8 8 396 — —
E 3tIT,— ACTUAL
W.MT5 '
».9a]
M.sea- a
»!bt«b a
TO.Ifltt 4
70, sr ■
8- -KM
U44 JW Bl
i 14! -T Bl
14a Mm
n.lKSl
I4S *>B fia
[4<lh8 u
14a B44ra
K 7^184 SI
lai 100
» WOO
4
atBi
losia,
W<>4H
1 I 1
1 wi
e H869 4J 3«ia|84 auc( s
IB IQO » lltl 43 38B1..IU
^4 »Bfiu Mt BOoo' n
IS) Vi/tlK 4AWA* «*»*''
w asBA.ea 6M6w ^„*;
TABLE TIT.— ACIDAL TANOBNTS, ETC.
91
Cur
„
„
S Oar
»n 1 r.-
A
-5
««raS)0"Too
4M0I»
50 3X1 wo nx
ras
^m6
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BO mo
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TABLE TIT.— AOTUAl. TANOBNTS, STa
6-0
Onr
Tan.
a™. 1 Ta.. 1 .
iOma
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ooo'ST
ra.sM
ST)W
70.404
TB.MW
IB.TB N
Tt.BSn
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n.iwo (
80.360 <.
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80.84-8 (
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Ba.BBS 180
n.otio 80
i 8e « HI E B4 eOD :
TABI.R xiT. — acthaij tanoemtb, etc.
M
4C
ran
41,
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r n
A
Ta 1 Arc
Tun. 1 An.
'0^
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338 333
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211 OOB 500 USB
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100 451 aoo 333
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126 ^hno bss
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100 KBS ail 333
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168 sir
331 111
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101 ]:» a)l 067
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338 8SS
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101 D6 1 "03 333
1 \i 018 13
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330 4H
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1 ri osooo
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455 UUO
10" JTO JW 000
JSA 1 LO SIO 8»!
laao-
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1 1 OS!
341 111
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54804 D«e6
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103 480
806 333
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104 161
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104 923
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133 3»W 88)
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916 667
'114 iie.iosfl 00
108 861
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TABLE XIV.—
I. TAKOENTB, ETC.
B.siraiiu.MTTi.ei
r iin.iH(> 7).SK3s 14
.2M1M.311»1M.1
u.ooo 68.«fi»i; 1^ .»;& M. Mis
im.as7ii\t3u
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r7.aatre.2iBn:i5
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rT.HmilM.WieT.H
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il.'sSiSi
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f.nwJ/iB.nuoi J(ltl.1S»68,TOSl ■"" ""'
__. ran/™, awe, iB«. 687^88. SI OB
IBS (««/rS.r«7/I58,fl068S.814H
11.111 .U.lWl
100.
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5BB ■iSOlWl
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TIBLB ZIV.— ACTUAL ■rAKOBHTfl, I
e- Curve. 1 7 Cnir
« 8 C"'ve
9° Onns
lO C
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M.
W J
liF^
bTSm-
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088:
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6
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198 811
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TABLB XrV.— ACTUAL TANGBNT8, ETC.
ie<
M.
O
1
603.046
2 1603.905
3J604.736
605. 5(57
606. 4 J6
607 380
eO-S-llO
608.947
609.778
610
611.
613.
613.
613.
614.
615.
616.
617.
618.
619.
619.
680,
631.
633.
63:i.
634.
634.
635.
636.
037.
638.
63;).
33 ;630.
630.
641
&33
633
634
635
A
609
468
338
158
989
849
708
539
370
229
089
919
750
581
413
271
131
963
793
653
511
343
173
033
893
733
553
413
•373
103
1300.i«
1J0I.67
1303.3:i
1305.00
1306.67
lr208.33
1310.00
1311.67
1313.33
1315.00
2° Curve.
1216
1318.
1230.
1321.
1333.
1335.
1*336.
1238.
1830.
1331.
1233.
1335.
1236.
1238.
1340.
1341.
1343.
1345.
1246.
1248.
1850.
1251.
1253.
1255.
1356.
1358.
1360.
1361,
1363
1365
1366.
1368.
1370.
635.934
636.765
637.595
638.456J1371.
639.314 1373.
640.145
640.976
67
83
00
67
33
00
67
33
00
67
33
00
67
3i
00
67
33
00
67
3:^
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
1375^00
1376.6
641.8351378.33
642.695 1380.00
643.526
1381.67
Tan.
301.104
301 531
301 9<i4
303.379
:«)3 794
:i0:i.334
3)3 654
301.069
304.485
:ja4.900
Arc.
305
305
306,
306
:wr.
307
307
:«)S.
308.
309.
:«)9.
309.
310.
310.
311.
311.
313.
313.
313
313.
313.
314.
314.
315.
315.
315
316
316
317
317
317
318
318
319
319
316
745
175
590
006
600.000
600.8:^
601.667
603.600
603.333
604.167
605.000
6a5.833
606.667
607.500
30 Carve.
Tan.
60S
609
610.
610
611.
436613
865 613
381614,
696:615
136 615
556 616.
971617.
:«ri618.
8<)3 619.
217 6-30.
647 620.
077,631.
493 633.
90s' 633.
337 634.
767 635.
183 635.
598636.
0381637.
457 638.
873639.
.3HH6:»,
.71«i(a0,
.148!«31
.563 633
979
394
809
633.
634.
635.
239,6:i5
669 636
330.08416:37
330.500!6:«
330.939 639
331.359 610
831.775640
333
3-3->
333
I
644.356 1283.33
645.216 12a5. 00
646.075 1386.67
646.906 1288.33
647.73711290.00
648.5961291.67
649. 456j 1293. 3:1
^7/d30. 287P^95 001325. 155 647
J^/pi 117/1296. 67355. 571 648.
^fO/asi. 977,1298 331326. 000 649,
190,641
630 643
050 64:^
333.465 644
:j33.880,&45
:i34.310 645
3 i4. 740 646
33:)
167
000
8*3
667
500
333
167
000
8:J;3
667
500
3:i3
167
000
a33
667
500
333
167
000
833
667
500
333
167
000
8:33
667
500
333
167
.000
.8:33
.667
.500
.333
.167
.000
.833
.667
.500
.3*3
.16
.000
.833
.667
.500
333
167
300 749
201.086
-301 333
301.599
301.876
203.163
303.449
•303.7-36
20:3.003
303.280
Arc.
•303
308
-304.
•304.
304.
304.
305.
•305.
•305.
•306.
206.
306.
•306.
•307.
•307.
•307.
-303.
•208.
-308.
•308.
•309.
•309.
309.
310.
310.
310.
310.
•311.
311.
211.
213.
312.
•312.
312.
•313.
213.
213.
•313.
214.
•314.
214.
•315.
315.
215
315
216
216
316
217
217
557
844
130
407
684
971
257
5:34
811
09:t
400.000
400.556
401.111
401.667
402.2-32
403.778
408.333
403.889
404.444
405.000
405
406
406,
407.
407.
408.
408.
409.
410.
410.
384 411
6611411
938 413
315
493
779
065
343
619
905
413
413
413
414
415
415
416
193:416
469
746
a33
417
417
418
319:418
596 419
8?3 4'30
159.4-30
446 431
?33 431
4-32.
4-33.
4-33.
000
377
554
840 4*3:3.
137 4'34.
404 425
681 425
967 426
254 426
581 437
556
111
66
.778
,338
,889
444
.000
.556
111
667
2-33
778
333
889
444
000
556
111
667
233
778
333
889
444
000
5.56
111
.667
222
778
3-33
889
444
000
556
111
667
232
4° Curve.
Tan.
150.576
160.791
151.006
151.213
151.4-31
151.6:36
151.851
152.059
153.266
153.474
152
153
158
153.
153.
153.
153.
154.
154.
154.
154.
155
155.
155.
155.
155.
156.
156.
156.
156.
1.56.
157.
157,
157.
1.57
157
158,
158.
158
158
1.59.
159.
159.
159.
159.
160.
160.
160.
160.
160.
Arc.
300.000
:3U0.417
300.8.33
301.350
:301.6tf:
303.083
3t)3.500
802.917
:308.d33
30:3.750
5« Curve.
Tan.
130.474
1-30.646
120.818
130.984
131.150
r31.3-33
1-31.494
121.000
1-31.827
121.993
683
897
113
310
527
74.';:306.
957;306,
16.5:307.
:304
W4
:305,
105
:305.
373
587
807
307
,803 308
010 308
318i-309.
435;:309.
638,310.
848
063
271
478
693
908
116
3-24
539
753
961
169
384
.599
,807
:310.
310.
311.
:311.
312.
:312.
313.
:313,
:313
314
314
315
315
315
316
014 316.
808 427.
094*428.
381438.
658 4-39.
935 430.
231430.
508 431.
785 431 .
061 433
348 432
778
838
889
444
000
556
111
667
233
480
645
317
:317
317
860 318
067
275
490
318
:3l9
:319
705 .330
913 330
161.120
161.385
167
5*3
000
41
838
3.50
667
083
51 K)
917
3:i3
750
167
583
000
417
8:33
•350
667
oa3
500
917
3:33
750
167
583
000
417
8:38
•350
66'
.083
,500
917
333
.750
.167
.583
.000
.417
1-33.
132.
lii.
133.
132.
133.
1*33.
1-38.
123.
133.
123.
124.
1*34.
134.
124.
124.
124.
125.
125.
125.
125.
135.
125.
126.
126.
126.
126.
126.
126.
127.
1-37.
127.
127.
127.
127.
128.
128.
128.
128
128.
159
331
.508
660
835
0ft7
179
:il5
512
Are.
8IO.OO0
240.888
240.667
-J41.000
241.884
241 687
242.000
242.888
243.867
^48.000
664 d46.
a56
022
188
854
520
692
864
080
197
869
541
707
2I1
888
549
721
893
050
«48
243
244
244.
'345.
■345.
245.
246.
888
667
OQO
888
667
000
333
667
000
246.667
•347.000
247.Sn
347.667
•348.000
•348.838
248.667
240.000
849.838
249.667
250.000
850.838
8781250.667
0451251.000
851.883
251.667
352.000
258.3%
268.667
258.000
3-30.8.33
831.350
161.550 331.66
161 758 322.088
161.966 3-33.500
826
392
556
730
902
068
284
406
578
744
163.181
:333.917
162.895 333.833
162.603 838.750
1-28.911
129.083
129.265
139.421
129.587
129.759
129.881
180.007
868.888
868.667
354.0(10
«M.888
854.667
256.000
855.888
35ft.667
866.000
856.888
856.667
267.000
857.888
[867.667
858.000
85R.883
256.667
850.000
778;i63 Qm\'i£t\ xmX^ASO^^OA:
m
7€
TASLB XIT.— ACTUAL TAIiaEMTII, VIO.
rve. T Curve. 8* Cnrvs. »• Cui-f*. Hf
An. Tan I Arc Tan I Arc Tan I Arc I Tan
toi eso-wi 6<>
B WiS «- JI158 1
a 611 T 84-* n
a 8M IT BOJ 1
7N Tt HIOl I
IBS »»se
IRS luete
153 1S5RI
111 lit n
M 140 uwra
IS SM.aiO B33 m "843 ISO 714 N If
MBS "V^hi
«. M5I* BUSl
SB <MI8I isai
TABLB XIV. — ^ACTUAL TANGENTS, ETC
180 1* Carve.
M. Tan.
r Met
658.886
653.667
654.498
655.329
656.160
657.019
657.878
658.709
659.540
660.899
661.259
662.090
662.921
663.780
664.639
665.470
666.801
667.160
668.020
668.851
669.681
670.541
671.400
672.231
673.062
673.921
674.781
675.612
676.442
677.302
678.161
678.992
679.823
680.682
681.512
682.373
683.203
684.063
684.922
685.753
686.584
687.443
688. sas
689 134
689.964
690.824
691.683
692.514
693.845
694.204
695.064
695.895
696.725
697.585
696.444
699.275
700.106
Arc.
d<* Carre.
Tan.
800.00
301.67
303.33
305.00
306.67
308.33
810.00
311.67
313.33
315.00
316.67
318.38
820.00
321.67
823.33
325.00
826.67
328.33
330.00
331.67
338.38
835.00
386.67
388. as
340.00
341.67
343. as
345.00
a46.67
348.88
a'lO.OO
^51.67
353.33
355.00
a")6.67
*i8.83
360.00
361.67
368. as
365.00
366.67
368.83
370.00
371 67
378. as
375.00
876.67
378.33
380.00
881.67
383.33
385 00 347.960
386.6
388.83
890.00
391
398
348.375
348.805
349.285
67 349.650
88 mi.OM
667 231,
.500 231.
.333 232
.167 832.
.000 232
8aS288.
, , , 667 888.
£'J/7VO. 965 1895. 00S50. 496:697. 500 238.
£^£/l!^ '§^1^396. 671350. 92Sl698.3S^ 288.
167 284.
826.430
826.846
827.261
327.676
328.092
328.522
328.951
329.367
329.782
830.212
380,
asi
asi.
asi.
332.
332
*«.
333.
aS4.
384.
642
057
472
902
832
747
\m
592
022
438
Aro.
3<> Carve.
Tan.
OW.OOO
650.833
651.667
652.500
653. aS3
654.167
655.000
655.833
656.667i
657.500
384.853
385.283
335.712
336.128
3:^6.543
336.973
837.403
aS7.818
aS8.234
338.668
339.
339.
as9.
340.
340.
341.
341.
34i.
342.
342
343
343
344
344
344
345
345
846
346
347.
093
509
924
354
7as
199
614
044
474
889
805
73 »
164
579
995
425
a54
270
685
115
347.545
658
659
660
660
661
662
663
664
665
665
666
667.
668
669.
670.
670.
671.
672.
673.
674.
675.
675.
676.
677.
678.
679.
680.
680.
681.
682.
6as.
684.
685.
685.
686.
687.
6as.
689.
690.
690.
691.
217.635
217.911
218.188
218.465
218.742
219.029
219.315
219.592
219.869
220.156
.838 220
167 220
.000 220.
.833 221
.667,221.
.500 221.
.aJ3 222.
.167 228.
.000 222.
.833 222.
667
500
442
719
996
283
569
846
123
410
696
978
Arc.
223.250
228 537
338'223.823
167 224.100
000
883
667
500
224.377
224.664
224.950
225.227
3:^2^5.504
167 225.791
000 226
8aS226
667 226
500
as:i
167
000
883
667
500
226
227
227
227
228
228
228
8aS228.
167 229.
000 229.
8aS229.
667230.
500,230
ass 230
167 330
000 231,
8aS231.
077
854
6:31
918
204
481
758
044
381
608
8a5
171
458
735
012
298
585
139
425
433.333
483.889
434.444
4a5.000
435.556
436.111
436.667
437.222
487.778
438.333
488.889
439.444
440.000
440.556
441.111
441.667
442.222
442.778
443.833
443.889
444.444
445.000
445.556
446.111
446.667
447.222
447.778
448. 3S8
448.889
449.444
4<> Carve.
Tan.
167.
167.
167,
168.
168.
168,
168.
168.
169.
169.
169.
169.
169.
170.
170.
170.
170.
171.
171
171.
171.
171
172.
172.
.778! 172.
.aJ8 172.
.889 172.
862;459.444:178
.000173.
.566,178,
450.
450.
451.
451.
452.
4.52.
453.
453.
454.
455.
000
556
111
667
222
778
aas
889
444
000
455
456
456
4.57
457
458
4.58
.566
111
667
222
163.241
16:3.448
I168.&56
,163.864
164.072
164.287
164.501
164.709
164.917
ia5.182
166.847
165.554
165.762
165.977
166.192
166.400
166.608
166.822
167.037
167.245
Aro.
712
692.
693.
694.
695.
696.
696.
^»/7t».a56/lH98.33l851.8ill6a9.
266
552
839
116
898
679
966
460.
460.
461
461
462
468
468
468
464
465
465
,463
668
.883
090
298
513
728
986
143
358
573
781
989
204
418
626
834
049
264
478
679
894
109
317
585
739
9.54
162
870
585
825.000
325.417
1325.888
326.250
326.667
327.083
327.500
327.917
328. aas
828.750
829.167
329.588
380.000
a30.417
330. as3
381.250
331.667
aS2.U83
332.500
332.917
338.383
3*3.750
334.167
aS4.588
aS5.000
aS5.417
aa5.833
aS6.250
336 667
337.083
5* Carve.
Tan.
111178. 800
,667174.007
222 174.215 346.667
337.
•337.
a38.
a38.
a39.
:3;39.
340.
340.
340.
841.
341
342
342
342
348
348
344
:344
345
845
600
917
333
750
167
588
000
417
833
250
.667
.088
.500
.917
a38
750
.167
.583
.000
.417
345.838
346.250
843|466
- - ^ ■ -.. ' !.,... ^ ."t_
778 174.480 847.088
ass 174.646 347 600
889;i74. 868 347.917
444176.060 848.388
,000176.275 848.760
. 560 175 m Vk^ .\v:\\4(;^ .am&V^;;^ .»«&
.uiii7& .Qa&\M<d .c«ft\\4(;^ .misn^ .«si
180.607
130.778
130.940
131.106
1:31.872
131.444
131.616
131.788
131.948
182.180
132.298
188.458
132.626
132.797
138.968
133.186
133.801
133.478
138.646
183.811
188.977
184.149
184.381
134.487
184.664
134.826
134 997
185.164
185. aso
135.508
Are.
ia5.
185.
136.
186.
136.
136.
136.
186.
137.
187.
137.
187.
187.
137.
138.
138.
188.
138.
138
138
674
840
006
178
350
516
682
864
086
198
860
631
708
869
035
207
379
646
711
888
189.055
139.281
189.388
139.660
189.788
189. 8B6
140.064
140.286
860.000
860.338
260.607
861.001)
261.833
261.607
868.000
868.883
868.607
863.000
868.888
868.667
864.000
864.888
864.667
865.000
866.888
866.667
266.000
866.838
866.667
867.000
867.833
867.667
868.000
868. a»
868.667
860.000
860.388
860.607
870.000
870.838
270.667
8n.000
871.883
271.667
278.000
878.883
278.667
878.000
878.888
878.667
874.000
874. aS8
874.667
875.000
276.883
875.667
876.000
876.888
876.667
877.000
877.888
877.607
878.000
878.888
878.667
879.000
\
r/cs.
TABLB XIV.— AOTUU. TAMGEHTB, ETC.
,.0.,...
,.e«™
8= tnrre.
»■ Curre,
10° Carve.
13"
Tan. 1 Art.
T«.i. 1 Arc.
Ton. 1 A.-0,
T«Ji,
Are,
T«. 1 Arc.
10«.8M»l8ft.;
Kl.iim 1H.1 TI4
nWamHiv
7*8106
is.aeoa lao.ooo
108.99.1 aiH.B4-
93.43:11 ISB.BBi
11.57881111! ton
Ta.TOiS
«S0
in).»e8 iiM.im
sit
130 saa
»
9a 87M IM 1«9
iiffi
711.8871
000
130.501
iwiioi
317 7TH
9g,;Wi! 180,(1117
888
i«
aiH.OW
911.9170. IW.KK
n.itmm
870
es!7B»
tm'.'eai
^8.8SJ
alBooriitt
78
7»:i711
14(
868
B6.8nt
isi.'ooo
109. HM
»H.I111
H:^iii7:9ei
«. 4048 18)
968
ra.B8ST
T41
68. 964!
181.187
lue >!3
»H.sai
9t.£n'4IBT.0ia
187
73.8M1
9X
181,888
IIO.IIB
«9.1flT
...4««1BT.8JT
BsisiOlllft
;^.48iT
I4(
m
x'.tai
181.800
»
iio.au
94.8«l|lim.0H
BS.7SSe:l8t
66
ra.Mtl
14t
998
88.9098
131 .88T
110.89a
ItlsiTU
»4.iitiy iM.am
BH.HTfiUM
481
68.9927
181.888
IIU.ASI
IK.7«ue IKi.S71
Ki. 93141186
00
141
ee;
H.876B
139.000
w!s;t
M.KsssmBiu
B8.089D:186
ao
;3:6«r
146
66.4BaD
ISt.lST
3
iio!r^
B.OOM IMI Mf
st.i4K.nei
14;
86.8480
1»!.SS3
4
110. Ml
88.681:1
181.600
iii.im
Slim
aisMsiw
83
74:ioe:
407
88.7144
181.BS:
88. 481 9. IBB
r4,gosT
86.8006
isa.m
T
lll!»K
m.aet
eS. 8894186
3i
74.S9W
";
7T8
6«,8885
Ul.MB
m.m
bb:«ws msss
83.B7Sail86
46B
96S
88.M)T
188.107
I1I.C64
£«.!5S
H W71 199 470
ga.T7re!iBB
se;
74.4841
148
148
8T.0«9
133 813
no
atil.SOO
h$'h4W iwIti'
ia.B84B.I86
74.6507
la
838
B7-1SBB
laasDu
IlliSSt
iMf.TTtI
kC.R7dS t90.9fig
H8.BBI818r
OK
74.8768
SI(
ST.SS50
183, 88T
iiaon
«8.flM
BO.W1B,191,11IO
S4.0B8S1S7
tK
T4-T87T
er.aogK
laa.Baa
]]«.SOT
»3.IBI
Wi.il01tl91.4W
4.»»Me;
600
74 8801
14S
BEI
07.3914
134. OOU
84
HI!. 371
•M.saim.VJ7
74.0607
141
074
87,4774
184.187
:Sa!8«
9(i.4.'>IH)19I.DUn
;8.0iil8
859
iT.saar
ao
lK4.1Br
M.ftTinw.M;
MBiBi'iai
T0.14S7
134:600
ii*!t»i
MBSnom
7(1,SM1
149
K0fl7.TSB8
m.mi
aMlia
84. 7306.188
ut
78.8817
149
816 87.8158
uaoTB
aas.ooi
98.0891! 194. w;
««,U:,o
i™i.oi»'fl7 boid'im.oo"
30
m.aii
97. 0^S0 198.096
M.waoic^ ■■■■- -■' ■■■■: ■■" :■■■' ■■''< y ■ "^
na.SK
Ks'uu
97 871 98 TS
56 04 ' ■ 'Dl IJ
118.496
at88.
IT WSI 93&
07 4„4 98
^8fa WD
9 64 £ M U4H
S03^ li
ua.9 f
£»B(r
r mn a isa
aa 61* A
iH.tm
ossw
B--NK8I 94 3H
» 84
U4.a0li
terui
B-BOM W S
n 8839
K4.MI
«-»
noHi 98 000
»'«"8
'0B»'eJ~i|8 88eee8s sesoo
39
114 4n
»r^
M liat 98 SOS
as 89
-0 KM -B SM 1 6 86eU 4m 80 SB-
e»ON
Wiewl 9841
95 9998
l\*.%
nA9)
114.907
08 WTB 9a9r..
iis.Dwan xmi
llttS»4 96 9U
Xe 8 44
118.189 MB S-
DO Da Bfl 4ai
llG.SStl9B4t4
Bsa-Tj 98 6tr
IIS. IT «» ti
BMoe on Bof
iis.ton^ «
M-TT u- "
iis.Taisa 2-§
WiftB u-W
B«846, 08 flW 9 5C8J a «
lu.ffle'sw Mfl
99 8,^8 9~BB
B8 fl 30 -a 9 rk ws ea -04fl9 694b' as sas
SO
110.031 ^ KIS
IHI4 1-9B
troBWil 3 -s~ 3996 BSHWflear'ai S8B00
na.i-aa
iis.sssn ssn
118.460 «s es
misss. *
ws,ss.
19 9.71
00 0^
^
itK.emettixv
00 08 \>
iir.oasisa'*' OOM- ■«»
71- IM
TABLE nv.— ACTUAL TAnOEHTB, BTC.
1*'
I' CDr»
4" Carve
3=Ont™
m"
Tn 1
Taa, 1 Arc
*,
sr
H 140 740 2HI ODO
4.1 OIJ J80 *«
l-i N
141 4^ 381 333
141 toilm ta
'.40000
["iNilssssno
141 leoiot no
«4T)6.«
i~ %8|aM »i-
141 BSt IMi 183
i4-l HI
1~ 611 TBS 338
388 887
4 1 P«-
-aiBISS 60
148 J71
88S0UD
143 437
fxsm
883 66-
14S 781
884 000
14«941
884 388
-N8-185BM3
884 687
qostuMSM
143 av
«
I M
mMten
SB8S<
71-80.
o-mlanfex
143 f»
iMtar
a
718 W-
r as7 wo
143 "»
8saan
-,B«-|
3.i^»-B.r
141 1161
8W3S8
ao
144 I'M
8MIMr
iir
3l J"
+1486^ 333
44 BSaJS- HB-
34
^St
44 siu as )oo
7M8S
«fi
-M48H 1
4 -■! ft.). 4S 142 M8 Bff-
TBsawi-H 11 1 1 I' -a "
48 114 laa 000
r an- L44S r MS Bi i-^ asa
i4IWil4!ttflK
isi arijsi er
148 438 aiB 138
a»
7sa M7 1«8 33 w w -34 ur
IMBTmWTM
iMwaUcsi
'««",*»«-
i;^ Jw ^
^4» J^«n
,140 IWiM) Bfl-
1 18 334 ^1 XW
V WlJSl 338
48 g-2 «9i an
■■ 48 iSS 19* MU
1 14 010 «W Ki
147 isa iM «r
39
ta S18 i«5 iw
m^-^m
34.5B14BSa3d
M IwiSJ ^
14- 349 J03 ODD
«o
7^ 349 HSG (T
ssbj"
iMfnn'^aiHa
tBisrauflW!
-w awijw 1^
ienff^-«»«
13 031 9H 38:1
^ W--MflO-
41 61 H-5 X
IN W -^ 338
irt o-j«a tiB-
48 30- 14-8 13 1 J 80- -« lfl-
44 18- IMO 00 r' I«- 41 101
49
14 1»»!|1461 fi '■J U 40 nil
4« 1SN1 (NtB
«.i«r 4, 4BM5^8M
-lHra6«IM4
iM «8 im i>3H MS «ti awt BS*
4SO-J3 4»iO0a
8« 'mri rao'us 333«fiT oon
iwftnVi Giri4> A!»aB-3s3
Jl rsiB *
■BIH-3 Wr 140 SSSSBflOnO
W08h|lll I
».-! i Bi 1 n) JM aw «8
~fl s-jmIhw I
wr-i isaivi fflisoB 8r
iM-rs M
3ABOII0
« ar-4 Ma \»j ita^w «r \
TABLE MT.— ACTUAL TAKaSHTa, KTO.
6 Curve Curv
e «.C™
8 Cnn
ecu
M
_r«,n_r^ j^T~
T« JA
I ^
T»
An;
ami ws' » us am
oottasooffil worn
^^04f7
-OTO
J3K88 W JOh
-8 198 i
40 «
W-'a» (WW »u
TS ' *
eom
"^ ^
« «
*
294 -a,
M
a
w
TJSf
-9
■D
r' —
Ha 100
Tfl
»
M-
■UBS
r-ni
Hfl ttO
-BS3.
eg
» J^ 1 >M
W BOTO
-«S4*
sw
ssa
9 (14 -HiS. VI
JHU
-«
■SBM 688W
osr
000
«. W Hh
aooa 907
-8 019-
ra 30S GBSS9
BO-jr 9«
BO 9680
-2 30-
»
ft 0" B8
BOSOM W«10
BOSSI
sw, 03 »yi j>it
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TABLE Xir,—
L TAKaBKTB, ETC.
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1= Curve.
a- Curve.
3° Car*B.
4° Carve.
5= Cai
mT
Tan. 1 Arc.
Tan.
Arc.
Tan.
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TW.aifl
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188.814 ks.OOO
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na.iBt
377.59(1
760.B3»
Ml 746
wo.aa
iBS.8a8Hls.4i:
151 ,080 a
878- (W8
751. 0B7
SU.U35
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318.441
aw.aiB
7St!681
leos-O?
753!333':352.5HU
lai.-it
15i:5B4!8l
;58,34f
1M8.B)
traisai
J54.1tt7|Sl5a.S7B
161.758
a
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879.71t
765.000 863.10*
r«3S3i
IBB.BBBlan'ilO.
151. 9g(
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380.148
T65.S33l2a3.4tU
503. 888
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380.67;
758.067
501.444
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152:271
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1«5.00
380. BBS
767.600
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5116.000
190,6».87B.7W)
152.488
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381. MS
254. SH
190. ra4 STB, Iff
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381.838
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760:000
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laiiiuiiaaoiboi
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383.083
780.83!
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191,37!! 380.417
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255.416
507,771
191.570,880.833
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382.600
153.968 3(
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335.!i33
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103,85.
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154,817 31
774.700
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387.S01
155.097!ai
TBO.BOS
105.100
781 .4B7
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105.405
183:331
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793. sse
105.610
388.750
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389.187
38
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198.013
389. 5K3
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800. 00(
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198.466
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I6fl.680i
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15738181
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«ii.50:i5S1.667
108.806
157,6888.
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197.109
801.687
I57.J31
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107.317
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43
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394.B88
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363.343
533.331
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85.B33
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97.74(
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88.6871363.018
103:33!
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168:886 31
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3117.538
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128. ow
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401.007
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16(8. as
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404.7BT
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930.444
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163.367 SaS.OW
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183 189 8*1.000
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14
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408! 590
3T«!410
1104 330 408.833
188.469
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888 000
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410 41
189 »]
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411 m.1
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[ts.auim.sM
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140.000
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348.000
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1-70.00
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178.471
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178:991
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888. 3S
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366.667
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360.333
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1788.33
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180.013 367.009
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180.688 356.000
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i39 iSSifiB OOSlll? 4
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03,805 600,65
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181 :bw
380 667
1806.00
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881 .nm
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303 6861809:32^
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182 281
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J38:629
468:388
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468.750
188.095
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451.187
183 367
368 8S8
ma, 88;
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388 1187
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458:878
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364.000
1881,87
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910,83
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884,338
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306.611 6ftT.i7H
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307.081 K18.8S.
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307.370
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913 833
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467:917
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868.388
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308,330
468.888
886.667
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308. 616
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458. 7KI
367,000
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281.838
459.187
188:819
887.333
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119.16
809.080
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459.688
183.485
887,667
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1810.00
464.004
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460. «W
888,000
4SI.434
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309,643
^33,363
460,417
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868.388
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164,834
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460 838
186.096
188,067
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185.S»
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KB, 688
48186(1
186.167
860.009
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933.33
233 891
380 333
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310 : 789
880.867
30
983 131
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9K.00
311.076
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185.688
870,000
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483,917
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3n:649
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18M.0I
488:750
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138:333
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118:S8fl
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464.167
187:871
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168,731
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187,5«
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37
9M.119
1881.67
m.bn
930:33
630.5.Se
485.417
372:333
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1863.38
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sis:3«
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466. 83S
188 04;
873.687
940.909
1865. («
470.4*8
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813.885
631, w:
3!B.24a
468.350
373.000
611,688
33.1.463
468.867
138 391
373 338
171' i81
934,16
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133:778
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167,08)
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1W,785
43
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1871 :8r
314. ;B1 1833.888
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236 5.371468,760
876.000
its'.%H
173,430 B88,3.-ia
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236.753469.167
189:4M
375,88.?
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18™:S3
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Sft. 947 626, 111
936,037 469,^83
180,501
876. 6R7
1880, 0(
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337. IBS 470. onn
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474:719 910:83
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377,383
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100.631
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470.888 94B.0C0
817. 93;l 630. 000,288.471 47S,fl00
BM.581
iBPi.ar
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101 : 131
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31b: 713 m ; aiii^.TO'tS".^
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870,000
819,080 BSi aaa2aa.si'3\4';t.\w\vi\,«niw» «*
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310.346 Baa.itW'aa sa\\*-;\,««'\w .«,■;.?[» asi
TABLE Xir.— A<rruAI. TAMQENTS, KTC.
U-Currs.
..e„™
8- C
iam
10> Curr«.
18'
^i^
x«.
T«, 1 An>.
Tail. Air.
Tan. 1 Are.
WiraTi
aooMO
iai.ii(i'ws?-i43m:wi
iDo,i»t noo.ooo
IW.OOt
IM.4W
aoa.^n
E2B.83ii;K7.BaMTS.e8i'a!U i«w
101 IB»«aO 186
00.0471
151. MB
sw.sfia
itt.oei,»T.()ia 118.73:1:3^.41;
lUI,ia:a>!(IO.»70
01,0831
180,33!
m.aa
iao.085ia67.B67,ii8.ii^ia,'a.ffii5
101.H1MU0.5M
ll.llBi
180 WO
151 TJl
iio.ifoa8se.oo5iia.B54sa5.M3
.00,741
1(41 H7
»i »
ia),8si!e58.sssiii,.:',-,iia!8.w!
»a.s9i!
180. BS8
imtATt
aai.wr
■Mt 111
181,000
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W1,M4
iaa:si^^HioiN:^i>l£B~wl
101 :«»
«U1.WI
li:4B34
181 167
KM.**
liJO.tiwiaB.owiu.sM
iW.667
101 .Bill
181 StB
163.1)01
i!ai.S76
901 .'867
b1:S
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m.n\
ISO. 845 350. 5«
1I4,5BB
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Ml .85*
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181 867
lU
m.e»t
114703
m.m
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Ii4.80^
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II SfH
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131 :ao&;aea!s88
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aM:69«
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1«!,33:|
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18a., 00
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1S1.074
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115. as;
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109.40-
an 068
ISa 667
i»i :»
90*.?B
lai.TOi
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H 8in
\»i.SS3
115 'ts:
&fi 7D0
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sm.xs»
K,404J
1M.0«
m.m
ts!04i
m'.m
115,560
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1011.741
908.610
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181.167
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109. B86
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183.838
swiw
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»i,148
118,77^
«!0!S7S
10i!,B8H
■loi.m
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188,600
154!48(
MM. Ill
i»a.«i
les.sm
llS.Kil
aii.58a
103.O*;
(04 074
18.7485
l!M.!«B
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m.sm
lias.eii
116 DM
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110. OW
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184.000
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806. IM
luini
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380. ne
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184 167
159 nil
sor.aa
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184. S33
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100,481
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08.1780
184. MO
lulsnr
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930. ««:
106.185
S8,S59D
184 687
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30B.UU
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aH.o48
1 wills;
lai.ofit
loiliwi
ttG.870
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806.668
1S.4SI1
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30
me.Ki
m.m
804. ns4
!ai 458
lisslen
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lOT.Bs;
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186'ssa
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101. on
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186.6011
lU.IB
130 K*
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104.101
nxm
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185.60;
34
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»5.47«
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186 BS3
810.00
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117,860
satnou
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117.484
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l».08l
1:7 688
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«7.087
180.833
38
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181,483
117.605
au7.3^
18B.B00
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184, BH
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lir.BTB
sR8,ssa
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186 667
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186.888
IXT.tM
811. er
ifir 111 "0 "i'.-™i r-.ii '"1 i.-jii'-ji^.Trs
187,000
157. MI
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187.16;
sis.asi!
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187,838
iK.Ta
aii.sDO
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W.7HK
187.600
m.m
ll(.77)>
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94. BOM
187,667
4«
im.mt
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IB7 B83
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m'.doi
818.011
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W8, BIO 1,8. 770^35. ««
106.506 aw.m
»:0804
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8ISSM>
135, 8»4
»S,M« nS.RR 186 417
»a).s8«'ii8,B8Bi!aa,ea.i
106.601 log !69
188 838
ai4.i6T
13B.0B1
106 787 900.444
is'.SBa
14, *+
i»in8niiflB,6'i<,iiB.0B.si!3,is«
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15fl!878
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188.883
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ision
IS8:8Mj«o:onoi]0:B0ei,W^-r. rr';:.-... I-. .i»i;
IBB.OOO
Bis.irs
I».44S*H),i8S110,41-»i'. 1 . ■ ■ . :,"W
\9i,\W\«6.
isaisM
ai5,swia.«ffl,ero.4rBii»,Bin'.::i'. ■■ ■ - >■-
^>^^^**
in9 449
81B.«WlM,fl8»«ro.JHll9,0i!a'Wi'. ■. ■" "'^
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/ffse:ii;asg;:Sii!-3iEiVi,uu:«^s^^
TABU XTT.— ACrCAI. TAKGRKTS, ETC.
...
x=e„™.
».«™.
M.
Tan. 1 Ai-c.
Tna. 1 Arc.
Tan. 1 Are.
Tsn. 1 Am
T.„.J^re.
"iTuwTHiiuirwiiroo
47B.4ir'U6U.CiU0
iil6.*)3.S63X.S«8
ma .746 4T6.o(N)
OI.8l8»a0.uao
1 !r>8
6.->»,iwi.e7
471
(H71W>
861
961,476.417
*IC
a Deu
ii8|iuaa.K
SM
auttiiai
lTa;476.8SS
1107
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m
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tataat
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S4(
881
478. Mfl
M
81
4 tun
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661
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fl».6«7
02
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481
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167
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waest
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477.068
Of
S7t
881
a M>a
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lai
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B.-B(6«
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88^
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81
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481
m
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667
0B66
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188
met
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688
888
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ns.rao
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866
m
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!41.tJ96
170.167
108 688
88S388i
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man
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HW 640 480 41
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51 66
«M 06480 888
104 331
884 60-
48&8a
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aui u-D 481 ISO
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MS IWtSl 66
04 Ml
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646 ftU
MS 016 481 auo
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487 6611
mvia
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643 8HV
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106 UW
880188
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886 se-
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964 1
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a i"^
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116 r"
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44 6 e 4M 606
stTBsa
887 86
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m 8001486 000
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BtteOUD
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14 litt.
^1 ]0S|48S 41
IIH) IW
888 saa
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188 66
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39
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983 6W»30 'H8 6»IM(
101 £60
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10166
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4» IMS nSV M,i» i!£x
218 9-
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44 WW flsa - 66 -T9
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403 8.18
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658 8H!
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daaesit
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16 — 9J61 1 «. JH IM IT- «r
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noa sw
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A6S msasi S! m ii<o,jut m- aos odd
Wl 6
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601 414 »] '11 498 sst toi 4S6 m ar
" * -iimMBoaesi
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J noB^iitrng i-il/KM -4am 16
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TABLK XIV.—
[i TANOEKTH, ETC,
0* Curve.
c
a Cur
C
rr C
M
Tan 1 Arc
"t
ro
ij».ir»a «r
sT^r^
;«
WG
"or64
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s- -^8-
1«
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48
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iw.au too
8- 123
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wsoo
H».4«8 "8
siu
ltiO.H«8 8 0W
IT eo8
im.m s a m
B--W
2!M
96
iw.a-
if
40"
96 808
161.01 aSBW
M s=
96 689-
sg B
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8 4.
88 J83"-3
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96 86
181 .«8
g
iB Ift
4»
IBt.U
8a) OIK
m
240 out
asoa-
a44
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4o
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mm
w 1
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i6i.ie4
ea
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iK.aotJ
sam
tr 64S
IT (&1
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be
8- m.
1W.M0
mat*
^^1
ObC
sa
Ub454
GSO
«■ iOt
sa
9
in.Tas
mm
SB
08 546
e B-
B7 71B6
IBS.ffi'
ewT
000
iroos-
98 600
-»
06
B- B8B"
06
IM.IW
eN»
~(
9a B3I
ina.iu
tarn
168. «49
w
94 tr
ibs.ssh
luS »»
SB JM
9i ss;
an
iia.Ts
844
US 90
iiM.sr
8i4 44
16
A Ul
A nn
!« W6(
94 88
1U4 2d
1
<ida
-d«
iWMJ
OB4U0
U8
»4daj
so
iM.ie
saooo
*»
witw
sunoe
m.mt
WHM
1«.7»4
us
iwioe
■etw
4«U
1»1«4
fvun
lU.SOtI
83- *«
iK.ie
BiTfiOO
18SBW
s^ -s
se
9f to
o
la.Tss
828 W
1M.8B
838 H8B
lU.OM
HIS
IK. It) SffitW
lu.st »-9 r
IIM.«14,«3S 444
Itfl.M-lsai ti
ii>a
m.74 880 OOO
U H ^K.
IM.W18)»0
iaOt»|J83
1_; j;
It. Ho UU
i.;.ar|3»(W
« )«L'»).
£S
NO ro (ws»
»H SS3
itr.i7 SHOftsa
43 lj>=a
i5 lis
ic.ai n
]«T.4n in 989
m.at ■« en
\
iMSrii
^
iw.jf suf-n
iK.ai.
WOM
TABLE CtV.— AOrDAL TASOBHT8, ETC.
lOM.tTMS.Rn
1 097. GO BIS. tn
lou.w MT.ora
BTT.aatfe.Toe
MT.TTS
ffl7"9M
«T.7B4
iisesg.esr
^.MHIHT.ia!
318.8881090.000
UB.194|flOD HW
n0.8B9:EB8.88e
/as,,,',,
Ma S8S nao.sss
' .M« uMii. 1'; ;)M.Ta8 899.*MiB».sosa*.wa\
a.TtiiaM.OBiaiK.
iBos.flooaw
|»Jfi.41T(M.
H)s!l»Od<H
)«
TABLE XIV.— ACTUAL TANGENTS, ETC.
6* Onrve.
Tan. Aro.
168.480
laS.flOl
108.747
168.890
1(».084
100.177
iflo.aso
109.468
100.607
160.760
160.888
170.087
170.180
170.888
170.467
170.6101887
170.71S8
170.807
171.040
171.188
171.896
171.470
171.618
171.756
171.000
178.048
178.186
178.880
ira.478
178.018
178.760
in.908
178.046
in. 189
178.888
178.470
m.610
178.768
1T8.906
174.049
174 108
174.886
174.470
174.6»
174.766
174.909
175.002
175.106
175.889
175.487
175.
175.
175.
175.
175.
m
176.
175.
m.
m.
885
778
888.888
611
167
444
72s!
000
.878
656
688
888
884
884
884
885
885
886
886
886.
886.
8S6.
886.
887.
887
888
888.
Ill
8B0
667
(M4
2«S
600
778
066
888
611
889
840.
840.
840.
840.
841
841.
841.
841.
348
849
348.
848.
848.
848.
848.
844.
844.
845.
846.
345.
846.
848.
846.
846.
846.
847
847
847
848
848
066
806
868,848
406 848
688 848
799:849.
>/U9.
167
444
TH
000
878
656
888
111
889
687
<M4
600
778
056
»t8
611
oov
167
444
728
000
278
656
888
111
880
667
222
600
.778
066
888
611
.889
.167
V* Carve.
8* Carve.
Tan. Ara Tan. Arc.
144.
144.
144.
144.
144.
146.
146.
146.
146.
145.
146
146
145
146
146
146
146
146
146
146
418
641
663
786
909
082
155
278
401
528
285.
285
286
286
286
286
287,
287
287
287.
646 288
769288
892
015
138
261
288.
289
289
388;289
506J289
629 290
146
146
147
147
147
147
J47
147
147
147
148
148
148
148
148,
148,
148
148,
149.
149,
149.
149.
149.
149.
149.
149.
150.
160.
160.
150.
.752
.875
.998
.121
.243
Dnti
.ouD
.489
.612
.785
.858
108
226
340
472
595
718
840
963
086
209
290.
290.
290.
290
291,
291,
291
291
292
292
292
292
298
298,
293
293.
294.
294.
294.
294.
296.
882 295
455
678
700
828
946
069
192
816
442
205
295
295
296
296
296
296
297
297
150.569 297
160.691|297
160.814296
150.987,298
151.060 298
151.183 208
151.306 299
151 499 299
444!l5l.5iil999.
1151.674 999.
714
952
190
429
DOi
905
143
381
619
857
096
338
571
810
048
286
524
762
000
238
476
714
952
190
429
,667
,905
143
881
,619
.857
.095
.838
571
,810
,048
286
524
762
000
288
476
n4
952
190
429
667
905
143
.881
.619
.857
.095
.333
.571
.810
.048
.286
524
126.
126.
126.
126.
126.
126.
127.
127.
127.
127.
127.
127.
127.
127.
127.
128.
128.
128.
128.
128.
128.
128.
128.
128.
128.
129.
129.
129.
129.
129.
129.
129.
129.
129.
130.
180.
180.
180.
130.
180.
180.
180.
130.
131.
131.
181.
131.
131.
131.
181.
131
131
131
132
182
132
132
182
132
390 250.
497,260.
606 2.')0.
712 250.
820
927
085
142
250
857
465
672
680
787
805
008
110
218
325
433
540
648
755
868
970
078
185
293
400
508
615
T?3
830
988
045
158
260
868
475
568
250
251.
251.
251.
251.
251.
252.
252.
252.
252.
252.
253.
253.
253.
253.
253.
254.
254.
254.
254.
256.
255.
255
255
255,
266
256
256
256
256,
2.'>7
257
267.
257.
257.
258.
690 258
798 2.58
905 258
0131258
121 1259,
228 259,
836 259
443'259.
561
662
778
880
088
095
203
310
418
260
260
000
208
417
625
888
042
250
458
667
875
068
292
500
708
917
125
833
542
750
058
W
875
583
792
000
208
,417
,625
,838
.042
.250
.458
.66:
,875
Am
,292
,500
708
91
126
833
542
750
958
167
375
588
792
000
208
.41'
261.
as8i
042 1
8.501
9» Carve.
Tan. Arc.
112
112
112
112
112
112
112
113
113.
118.
118.
113.
113.
113.
113.
113.
113.
113.
114.
114.
114.
114.
114.
114.
114.
114
114
114
115
115
115
115
115
115
115
115
115
115
116
116
116
116
116
116
116
116
116
116
116
117
370
,465
,561
.667
,752
.848
.943
.039
.134
.280
222.222
222.407
222.593
222.778
222.963
228.148
223.388
223.519
228.704
228.889
826 224.074
421224.269
5171224.444
6121224.680
708 224.815
804 225.000
899 21^.185
095 225.370
225.556
226.741
090
186
282 225.926
377
478
568
664
760
855
951
046
142
IQo Carve.
.287
.888
.429
.524
226.111
226.296
226.481
226.667
226.852
227.087
227.222
227.407
227.598
778
963
118
883
519
704
227
227
228
228
.620 228
.715 228
.811 2^.889
.907 229.074
.002229.259
.008,229.444
198 229 680
.289 229.815
.885 230.000
.480 280.185
.576 230.370
.671 280 556
.767,280.741
.863 280.926
.958 231 111
.067 231.296
260.417117.156 281.481
260.625 117.251 281.66
280
261
17.347 281. a52
17.442 232.087
-7.538 282.222
01.159
01.245
01.381
01.417
01.503
01.589
01.675
01.761
01.847
01.938
Tan. Arc.
200.
200.
200.
200.
200.
200.
201.
201.
201.
201.
02.019 201.
02.105'201.
02.191 202.
02.277 202.
202
902
02.368
02.450
02.536,202
O2.622I202.
02.708J203.
02.794j203.
02.88o'203
02.966 203,
08.052 20:1
08.138
03.224
03.310
03.8)16
03 482
08.568
08.654
08.740 205,
03.826 205
208
204
204
204
204
204
204
108.912
103.998
.065
.171
04,
04,
04.
04.
04.
205
205
205
205
257 206
843 206
429 206
04.515 206
04
04
04
04
04
05
05
601 206
,687 206
207
207
778
859
945 207
081 207
117207
05.208,207
05.280 208
05.378.206
000
167
883
500
667
883
000
167
383
500
667
833
000
167
388
500
667
833
000
167
883
500
667
a38
000
16
338
600
667
883
000
16
383
500
66
838
000
16
333
500
667
838
000
16
883
500
667
883
000
167
05.467 208.388
05.5.58 208.500
05.639 208.667
05.725 208.833
05.811 209.000
05 .eat 'iQRk .\^%
SO"
1^
1
2
3
4
5
6
7
8
9
10
11
12
18
14
15
16
17
18
19
»0
ISl
»S
S3
»4
S6
26
87
28
»9
SO
81
38
88
84
86
86
87
88
89
40
41
48
48
44
45
46
47
48
49
50
51
52
58
54
525 261
-.-. 638 262
7621182.7401262
261 .458:1 17.634 282.407, -- .
261 .667\\A7 .VWk ^"i .WS?i\VJfh 'W&*»*J^ "^^^^t
.87R 117 .«K> -aaa .'i'«s\v» .^S.^c^^^^'fe
.0»VA17 .%2ft ^l ^^^-^^s.^^^^^
87
TABLB XIV.— ACTDAI. TAHeBKTB, 'StO.
«.
4-C.™
,.c.™
SL
Tan.
Aro.
T»a.
Arc.
Tan.
Are.
Ttw.
Are.
Tan. 1 Arc.
aS4.8M
ros.oDu
MT.IBS
^lO.m
10
«*m
11»
im-&i
-""-«'
S38.180
1065.88
IIO.BSB
aefl-BSa
4M.m
a!-s
49
^mM
B(».BU
no. Ill
m.m
iwn.lM
«7.«S
tn.cer
1^7 W
UR<um
1«B.K
lefi.au
rai.toT
■JSt.Ml
H1.2S0
low 41
±«).ei1:43S
tins 08
3183 S3 M8.SW l»I.B7'.Wfl,B!fr!7S7.™
-.'■/l 048
488
s
a:
TABLB XIV. — ACTUAL TANGENTS, BTO.
6« Cnrre.
7«> Carre.
Tan. Arc. Tan. Arc.
m.OttH
lT7.ai2
177.8&5
177.498
177.641
177.786
m.flees
178.071
178.815
178.868
860,
%0.
860.
860,
:«1.
851.
861,
851,
8SS
86ef
000161
178.601 852.
178.646 868.
178.788 868
178.888 868
179.064 858
170.827:8.M
170.871 ;aM
179.614;854.
179.667
179.801
179.944
180.087
180.881
180.874
180.617
180.660
180.804
180.947
181.090
181.888
181.886
181.680
181.678
181.816
181.960
189.106
18e.846
188.880
188.688
188.876
i8s.no
188 968
188.106
188.854
188 408
188.640
188.680
188.888
188.976
184.110
866
866
878
566
888
111
888
607
044
888
6UU
778
056
888
611
880
167
444
728
000
878
856.666
865.888
856.111
a56.889
8.'M.607
866.044
857. 83«
867.600
857.778
858.066
868.
858.
868.
868.
858.
868.
yJBO.
860.
860.
860.
88S
611
88tt
167
444
728
000
878
556
861.111
861.888
861.667
861.044
862.222
862.500
868.778
868.056
868.888
868.611
151.
152,
152.
152.
152,
152.
152.
163,
168.
158,
153,
158
158
158
158
158
158
154
154,
797 800.000
0*^0 800.288
048 800.476
166 800.714
28U.800.952
411801.19U
584 301 .429
6571801. 6«i7
78O|8O1.0Or)
908 302.148
I
026 802.881
148 3U2.til9
271 802.857
898 808
525 808
648 8U8
771808
894 304.048
017 804.286
140.804.524
o«je
»88
5^1
810
8° Carve.
154.868
154.885
154.508
154.631
154.764
154.877
154.009
155.122
165.245
156.872
155
155
156
155
155
156
156
156
156
804.762
806.000
805.288
805.476
805.714
805.952
806.190
306.429
306.667
806.005
888156
400 807.148
622 807.881
745 307.619
.868 807.85
,090 306.095
,118 808.»Jd
,286 806.571
.859 808.810
,482 8(^.048
,606.800.886
184.868 868.880
184.406 864.167
184.640 864.444
184.088:864.788
184.886:866.000
184.968 865.878
185.188 865.556
186 876 865.888,
166
166
156
157
157
157
157
157
1.57
167
728 809.524
850 SOD. 768
978 810.000
.100 810.288
,227 810.476
.850 810.714
,478!8l0.95-.i
596 811.190
,719 811.429
,841811.667
157.964 811.905
158.087 812.148
158.210 812.881
158.888 812.619
158.456 812.857
158.583 318.095
158.710 813.388
158.882 818. /.71
195.418 866.1111B8.96a 818M0
Tan.
186. 661 866. 8891159. 078 814.048
82.848
82.955
83.063
33.171
38.278
83.886
88.493
33.601
38.708
38.816
Arc.
262,
202
262
263,
203
263
268
263
264
264
9*» Curve.
Tan.
83.023 264.
34.031 264
84.138 265
34.249
34.860
84.468
84.575
34.683
34.790
84.698
266.
265.
265.
266.
266.
206.
266.
85.005
35.113
85.2-JO
85.828
35.436
85.548
:^.661
85.758
35.866
35.077
36.088
36.195
86.803
36.410
86.518
36.625
86.788
86.840
36.048
87.066
266.
266.
267.
267.
267.
267,
}i67
268
268
268,
500
708
017
125
833
542
750
058
167
875
588
792
000
208
417
625
883
042
250
458
66'
875
088
202
5(i0
708
917
125
888
642
268.750
268.958
269.167
269.875
269.588
269.798
270.000
270.208
870.417
870.685
118
118
118
118
118
118
118
118
118
118
119
119
119
119
119
119
119
119
119
119
120
120
120
120
120
120
120
120
120
120
120,
121,
121
121
121
121
121
.112
207
803
.398
.494
.590
.685
.781
Alt;.
283
238
28a
238
284
234
234
234
.876 234
.07<!,285
.333
.519
.704
.889
.074
.259
.444
.680
,815
.000
067 235.185
1631235.870
259 235.556
87.168
87.270
87.878
37.489
87.600
37.7081271
87.815,272
870
271
271
271
271
87.928
88.080
88.188
272
272
872
883
042
250
.458
667
875
088
292
500
708
.245;278
.358i278
.460 273
..•>68 273
.675 273
.786 273.
.898 274.
139.005 274
189.118 274
189.820 274
88.
88.
38.
38.
88.
38.
88.
017
125
883
542
750
958
lft7
.857
.456
.552
.647
.748
.83ii
.934
.080
.125
.221
.817
412
508
608
699
.794
.898
992
088
188
279
874
470
566
IQo Curve.
Tan.
106
106
106
106
106
lOQ
106
106
107
107
Arc.
210.
210.
210.
828
414
500
586:210
,672.210
,758:210
844 211
980:211
016
102
211
211
107.188 811
2:i5.741
235.026
236.111
236.896
286.481
286.667
286.868
121.661
121.757
121.868
287.
•8i .
237.
287.
287.
287.
288.
288.
238.
288.
288.
239.
289
239,
289
289
240
240
240
840.
121.
128.
122.
122.
122.
122.
122.
122.
122.
182.
048
044
189
238
087
222
407
598
778
968
148
838
519
704
889
074
259
444
680
.815
,000
,185
,870
,666
107.274
107.860
107.440
107.688
107.684
107.710
107.796
107.882
107.068
108.
108.
108.
108.
106.
108.
108,
108,
108
108
108
109
109
109
109
109
109
109
109
109
840.741
240.926
241.111
241.206
»J7,241.481
482 241.667
628 241.852
6281242.087
719 242.822
815:848.407
122.910
128.006
128.101
123.197
128.293
123.391
242.598
242.778
242.968
248.148
248.838
248.519
054
141
227
813
399
485
571
657
748
882
.021
.007
.008
.179
.265
.861
487
528
609
.606
100.781
109.867
109.058
110.042
110.181
110.217
110.303
110.389
110.475
110.661
211
212
212
212
212
212
212
218
218
218.
218.
213.
218.
214.
214.
214.
214.
214.
214.
215.
215.
215.
215.
215.
215
216.
216.
216
216.
216,
216
217
217
217
217,
217
217
218,
218,
000
167
&33
500
667
838
000
167
883
500
667
000
167
888
500
,667
.838
.000
.16'
883
500
66'
888
000
167
888
500
667
888
000
167
883
500
667
888
000
167
888
600
667
838
000
167
883
500
667
833
000
167
«!•
110.648 218.888
218.500
21 8. 6(S7
218.883
219.000
110.784
110.820
110.906
110.992 _- .__ .
vl2a . AWY^"^ .I^NVW A'^^^^V^"^^^
875\\2?i .5)^ftW Vm\\\\ .^^:i^^^A^^^
80
TABLB Xir.-
L TAHGENTB, BTO.
lu.aa-saa'.
isasssU
.l»5Tii,*r011M.OO
wfl.Baa.Mu.ow
■-o.oos.M
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!WI,B6o'RM,lSr
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384.761 1582. DBS
879. 9.M
dW.HnOBS4 16T
940.710 see. ssa
ass.M^K-i.asoMi
TASLK XIT.— ACTUAL TAKBKHTH, BTC.
S Ca II
c
s fc
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M
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000.^ e-i
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moi 3sl s
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dwoir
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TABLE XIT. — ACTUAL TANOBKTS, I
83°
1° Curve.
a- COtTB.
3= Oorve.
.■r„.-v«.
Ta
Kn.
TAn
An
Tan 1 *rQ
T
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T 1 A
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bF^
mooo
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llfl6 89
^1 a
B8S^1^
1150 83
assuo- fi i
J1 03
m W|*» n
B8S aB
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»1 ftj
558s;
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1108 ■a
jso3a(
sg4 lau
389 481 as IS--
as -» 461 dOL
1169 Ifl
am a
KU B18
lea 33
aif «i
58 68-
.J3 910 481 xa
110 05
jsoaa
K3 04
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57^08:
2310W4«1 «
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JBO 844— 000
* -81
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lao &w ~o 5, u
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Il-SM
J3IS33
S3a387
150 3
jai 5M4ftt 86
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air 00
580-81
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234 7-6 403 OB
687 "W
391 W9 —a » J
mm
!S4 .5a 463 ii;
an 3^
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1159 1 TOl B6 -7 —8
23.5 & 46.1 08
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rfw H.1 1 «_l58i ea
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1180 48
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11 ao-lll -.IIM 1 S HI 0- I'M MS
586^50
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S86M
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4flq3«
ta
1190 fll
j3iBaaws4 fllLi 4 1 iiyuioi-8 sl-o te
tnOHS
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30
1131 —
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5S- 500
2S8<96
mm
lift, tL
\ 1 14
11 mi
1 i-osssiij
1 ll^K ■i,!
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10 » 4 1 6ST
19 469'4 i M
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197 81
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fSS-TOO
m 045 110- 5
r^
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7/
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tai.-i«
—ACTUAL TABOKKTB, WO.
aoc™.
T Corre.
a- c
.rve.
0= CiiTva,
10. Cnr«..
■a
T™. I Are.
Ton.
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Arc.
Tan. 1 a™.
m:
iits^sralsj
lUMD
S38.S7]
IIS.S^
l«7:606l».IS*3i«S,aS«
118.7iriB«.000
IM.TW
«a.8i(
14a. 840
B87,I08, 120-731
iifl.8uBiao.iaj
m.ws ^a'.ast:
IM.B83
S«.04l
jSr.BlTlSe.BW
026
9
IH. aw 884. 1ST
146' 1,M
ass.ias 1*0.946
lIS.Mt 2W.SO0
IM.tKSim.'MI
ieii-a
UM
117.087^30.0117
IK <XM 3M4.T«i
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s5u 7tc;
J5(
481
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j*i"7sui»i:^j
667
117.S30,13I.0tt
I».3H»8)ti.«TH
lB7,41W
v(w.95s lau.sa-
T
m.fUMati.'s.ufl
an..iB7iau.4!j4
0.17
ii7;4ii|^i:ki
f
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S30.71.
«7
22!
m.KU 386.111
187,874
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Mfl.BlB
3SB.BBa
180.631
m
407
IT.B80 231.M7
10
lH,B(l.~i.SH6.fl»l
iDT.sa?
891 .18U
147. IW8
tSS.THi
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IW-lOISMBflBT
]M,iaia8i.42»
147.188
200.000
itti nntai.wr
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1M.B08W17
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lT.iM7|«»a.lB-
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181.004 08
I7.eas 282.883
1W.5W DHT.GUU
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181. ion UH
331
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(88.M.
I
JM emjWT.TTH
loe.tMO
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twiissi
181. Wl SAH
iM.HSAiawt.oH
l».748
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891.041
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147. tW
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880
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i
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18
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148 OM
!M.BB7
131 .581199
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288 833
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148 ns
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283.88-
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148.830
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148.481
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884. 7fl!
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871
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281.33:
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148. r;a
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170. ssa
886.47(1
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112,241
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170, 3U
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140.74.
236.000
lHI.T80S93.eil
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23
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100.792 ms »u
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MM
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7X- . »4 m t 8M
120 886
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m.n x to
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TABLB STV.— AOTOAL TAKSENTB, KTO.
Cnrr )l° Cbrv
BUH 00 BOB »-0 JOI u
ew^M 00
aw BO « fl- ae BOS K
™le«'
960 6 ai8 r-
8 a uts a«)
^^
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MS
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■MM-
TABLS nv.— ACTOAl. TAM0BKT9, ETC.
«' Cime.
T.C„™
^■■..
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9" Cnrre.
10° Carre.
84*
Twi
An:
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T 1 Arc
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1 4 001 S4 ee
aociooo
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m 94sWrooc)
1 4 814 S<a 09B
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lis nRoU4n \ln
MS Ml)
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WBW3
100 ass
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8*4 01 iiSi,
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nam
m SS9
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101 BOO
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i41 £00
SMKX
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138 4ET 368 B1D
mtHw
408 OM
6S6Bfl|30ai»
isa SOI
404 S»S
75 681
1"9«t
a«B80
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1-5-08
63 4 TO. -OS
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sssKtsc
tnsiffi^
4U1 167
(0 4.9
sa soaW 1 1 M NX.
S»KI
HO 00
404 -U
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S46 00S
806 (»
406 000
rTia«
M 143
iwssso
406 STB
176 464
B4T381
IM 4B- 303 P
^^3,.,10|
a»oM
406 660
70 681
347 610
ro a-olfi fiss
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B47 86
IM64SS04 8-5
18-4»1
n)£68
awM4
100 111
70 BM
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IM 68804 588
IB-68T
lESSOl
MS 80
M« ffi
48 883
804 -B8
llt8 341
209 601
MOM
548 6"!
306 000
aOB-w
48 810
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m%
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am 84
4B048
166 la
lf"l 481
124 »{
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49 m4
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WW
tosose
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BOOM,
188 Mf
mor
1M4-8
214 838
sm«o
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30
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408 811
SOB 889
l'.3S3
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409 444
4^ 6B 34
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908 B96
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168 502
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40 388
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808 1S6
189 sr
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1«6S46
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158 TIT
IBB 838
186 4B9
£46 60-
411 B8»
BMflie
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180 481
lis BliO
H6SSf
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411 60
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158 981
189 681
1E6 eoi
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111 944
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11 ^
180 7*
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167 SB(
80D8J5
189 SH
lSSB-(
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9M fl
41 ~M
!l «■ 1 8, 9 810
MS 681
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1W04S
tH Wl
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nooof
40 (
26 81
no iBo
41,611
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167 TM
40 m
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MS
m»4
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40 808
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l«44n
58^onn
1 0"!
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4 4 444
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11IB23N
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1 4 "93
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Bll o-T
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W.3!M,«66.W.ll
tii.dsg
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1SB~0
r
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TABIA SIT.— ACTUAI, TAffaKKTB, ETC.
as IB
Bis BUT
3aw»
a 189 w ri -i"!! 16
iw 4ra-4 (H8
XI147 l>e|»8 88013
'4 m 5!M 360 16
[«2T!8?ie>33
m„
aai MB
M? JOI
i]
iM HSU a
16fi-«
T ,<
'■" " "
13.1 03ip3 DO 1
!SS9S8
aai i« ...
SM STH44 16-
193 9S9^ 714
lim S—ltSl BBS
a- «
446
1" 014 aw !■« 1M 848 M
TABLE KIV.— ACTDAL TAKOBNTa, KTC.
M
1 c.„. ,
Cur« 3 Cu,v. 4 Cu»«
1 lAr
T„ 1 i
hjIbsooi
I igluoDoo
Mas Bda
rs AM MO W
3 4 UOO
t3 Hi J^
fl 8-6*3000
,
g
aBfl4 43^13
ol
SI-
pJiE
M 25U
^
00 468 aaalDooa
3 (T
jsaax
f8 93^6U
'
83 W ISflBOM
JJ8 B
083 383
'^5U540S3d
O
bM -60
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-^ nU51 338
la-
asoa
>-tl l-^ -18 000
li HOD 54S 3- J
08S HK
518 Ob
OM
548 000
&!,\m, si>4,u 5fie 3«i <»
i!«Ba
J80 as
54BSSa
46 10 » 350 dS
KT 08a
54D W
'J i-, T,.
MO 496
RjOOOO
A.0 333
"^^
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w 3«
fo
J8 00.
iO
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i 00 3WB(U]S» iSO
jsaosi
SSI 000
q
" — M -Wl'eS Bfl-
283 aeo
553 333
9. ih M
"^
1 s ^ a^ oe "l^ --^
4 6fl' An
1 w ' 3 3fw ns- -a 351 oon'on sb|384 o^lwa bs-
6 tl,
J6
f/
jH 9 n
» 4
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TABLB XIV. — ACTUAL TANGENTS, KTC.
6* Carve.
Tan.
tai.om
SM.948
sao (m
280.844
^80.80^
:fl)U.540
280.088
880.896
880. 9h6
881.184
881.870
SSI. 419
881.507
881.715
881.868
8S8.018
8itt.l60
888.808
8&i.4'i6
888.004
888.747
888.b»0
898.039
888. 1S7
888.885
888.488
888.081
888.779
888.987
884.075
884.888
884 871
884.515
884.658
Arc.
450.000
450.278
450.556
450.888
461.111
451.8t<0
451 067
451.944
458.888
458. 50U
458
463.
458
458.
453
454.
454.
454.
455.
456.
455.
455.
450.
456.
456.
450
457
457.
457.
458.
458
458
456.
459.
459
459
460
884.8U6 460
834.954:460
285.103 460
885.850 461.
235.896 461.
885.540 461.
835.695 401.
885 848 462.
836.991 468.
886.189;408.
886.888 4«{8.
886.486 463
886.578 463.
778
050
383
Oil
107
444
W8
000
278
666
883
111
880
007
944
2ii:i
600
778
056
388
611
889
167
444
722
000
2^8
566
888
111
380
667
944
7" Carre.
Tan.
190.630
196.767
196.884
197.007
197.180
197.867
197.884
197.611
197.638
197.705
286.782
886.870
887.018
837.100
887.314
287.468
287.610
887.758
297.900,
/3198.054 m
197.
198
198.
198.
198.
198.
198.
198.
198.
199.
199.
199.
199.
199.
199.
199.
199.
800.
dOO.
800.
200.
800.
800
800
800.
801.
801
801.
801.
801.
201.
801.
801.
808.
8821808.
5001808.
778!-20a
050-808
833 80'.»
Oil 208
Arc.
885.714
385.958
886.190
886.489
886.667
886.905
887.143
387.881
387.619
887.857
888.095
388.333
388.571
388.810
389.048
389.880
389.584
8b9.708
8991390.000
086 390.838
898
019
145
808
391
518
045
778
153i390.476
880 890.714
407 390.958
530'391.190
658 391.489
779'891.667
9001391. 905
033'398.14d
100<398.881
887 808.619
414 892.857
541 393.095
008.393.338
795 393.571
988 393.810
045 394.048
108 394.880
895 394.584
488 394.708
548 895.000
803
8()3
8i)3
803
463.899
464.167
464.444
404.788
465.000 803
405.8781803
465.5501 808
465.833J808
468.1111208.
08.0541466.3891204
675 395
808 3{l5.
989 395
050 895
183 390.
310 390
.437 390,
.5<{()3i)6
.683 397.
.810 397.
I
.987 897
•KM 397
.1911308
.318 3J«
.445 308
.571 398
.098 399
.825 399.
958 399.
070.399.
838
476
714
958
190
489
667
905
143
881
619
857
005
333
571
810
(VtH
880
584
768
8« Carve.
Tan.
78.
78,
78
78.
78
78
78
78
78.
78.
78.
73.
78
73.
73.
73.
73.
73.
74.
74
084
190
307
414
588
633
744
855
900
077
188
899
411
518
080
737
848
959
070
181
74.892
74.403
74.514
74.088
74.780
74.841
H.958
76.003
75.174
75.285
76.
75.
75.
75.
75.
75.
76.
76.
70.
70.
76.
70.
70
76.
70.
77.
77.
•»■(*
1 1 .
i i .
t i .
I I .
77.
I < .
( I .
78.
78
78
78.
78.
78.
896
507
018
789
K40
948
055
167
,878
389
500
Oil
738
833
944
055
166
874
381
,493
Arc.
387
337.
337.
:i38.
338.
338.
3:38.
338.
339.
389.
339.
339.
340.
340.
340.
340
340.
841.
341.
341.
341.
841.
348.
348.
348.
348.
348
348,
348
348.
343
348
344
344,
344,
344
345
345,
345,
345.
346.
346.
340.
840.
346.
346
347.
347.
347.
347.
604
715
886
937
048
159
870
381
500
708
917
185
333
548
750
958
167
875
583
798
000
808
417
685
833
048
850
458
667
875
083
898
500
708
917
185
383
548
750
958
167
376
583
798
000
208
417
685
833
042
850
458
667
875
063
898
500
708
9° Carre.
Tan.
158.996
153.095
15.3.193
153 889
153.384
l.Vi.483
153.588
153.081
153.780
153.878
Arc.
lO* Carve.
Tan.
800.000 137
300.185137,
Arc.
137
187
138
158
154
154
154
154
154
154
154
154
154
154
155
155
155
155
155
155
155
155
155
155
156
150
156
150
150
15G
156
156
150
156
157
157
157
157
,157
'l57
157
157
157
300.870
800.556
800.741
800.920:188
301.ni!l38
896 138
481 138
607 188
301.
301
301,
.977 301
.076 808
.1751308,
.270:302
es2
037
188,
138,
731870.
880,870.
909|::70.
995870.
081 270.
170,870.
859.271.
848 271 .
4871871.
586 871.
I
615 271.
000
167
838
500
667
883
000
167
333
500
.300
.465
.503
.002
308
302
30'>
303
.70Ii303
.800 303,
8281138
407 138
593! 138
778139
903 189
148:139
3381189
5191139
704
793
879
905
054
143
V38
381
871
878
872
272
272
272
872
273
959
057
150
858
847
446
545
,644
748
.841
303,
308
304
804,
304
804
304.
805
805
805
704
889
409 873
667
833
000
167
833
500
667
833
000
167
87«
M.
189
189
347.917
348.185
348.3:i3
.940 805,
.039 306
.137:305
.230;300,
.335;300,
.431|300
.580-300,
.085 300,
.784:307
.883 807,
.921 307
.080 307,
.119:31»7
.818,307
.810 308,
.415 808
.514 308,
.610 308,
.705 808.
.804 809.
157.903
158.001
158.100
:i48.548'158.199
3 48. 750
348.958
349.1tt7\
158.298
158.397
074139
259 139
444:139
630 139
815140
000*140
185 140
370 140
556 140.
74l'l40
980,140.
Ill!l40.
890 140
481 140
667,140
a*i2'140,
037.141,
2i2 141,
407 141,
593 141,
778 141,
903 141
148!l41,
3331141
519141
704 141
889:141
074 148
.4981273 833
.587:273.500
.676:873. 667
762 873.883
848,1274.000
987 274.107
274.338
274.500
274.607
274.883
275.000
275.167;
27
.026
.115
.204
.893
888
471
500 275.333
049 275.500
738:275.007
824 275.83:3
910276. WHJ
999 276.107
088
176
265
276.333
270.500
276.
270.
t'.»irrr'
809.259
309.444
309.630
.4432;,
.532 277
.681 277
.710 277
.799 277
.885 277
.971 278
000 278
6C7
833
000
167
333
500
607
WJ3
(HX)
167
O
1
2
4
({
7
8
9
10
11
1»
13
14
15
10
17
18
19
20
21
22
23
24
25
2«
27
28
2r
30
31
32
33
34
35
30
37
38
30
40
41
42
43
44
45
40
47
48
49
142.149 278.333
142.23H 278.500
142. 8v;7 278.067
309.815:142.410 278.838
310.000 142. 5a5 279.000
310. 185' 142 .59a ai^A .\<«rv^^
CJAift .?avi^ W^i .'Wa. "Tv^ .*?K?\^>*^
:V4ft .a7r>\^r* .rM^^'^ -^^^ ^^'^ .t;\^^^ x«KK^n.
6041340 .v^A\^^ .vm^\^ "^^ ^'^ -^^^
50
51
52
53
54
101
TABLE XIT.— ACTtTAI, TASoENTB, KTC.
„.
> c
„v
3 Corv
^
Arc
r n
5
T'yAir
I'm!
*
T
Are
1438 G7
14 318
00
iT^oe^wMs
"OOOM
^"803
BeoTBo
HS9 4B
2901 8
1400 63
4 8 iM 9ai !*y
lo 4B
00 41
mt 980
660 588
1430 SS
.3803 38
715 801
1401
a
1 8 R3il931 441
-00 83)
i8«13
180 667
60
4_ 128 H3B 00(J
15 8-9
at* 335
l^l ID
33
01 m
i!B6 613
'^61 388
1483 01
JSOSSi
1404
4~ - 1 ola m
158 333
03 083
661 667
atiooo
16 9~7
140:
4~« 01 836 68
3BBM6
702 600
186 888
163 000
.811 6 17 40-
4 a sod'oa ati
■B8-60
r03 9i
3813 B3j 1 83T
81 no 18 81
4-8 5B0|03- -TH
358 9"r
1430 51
J JO
i>
4 8 S88'bS8 333
36B19-
03 50
387 3B0
508 000
»0 41l
^«
563 388
7M 583
568 667
0^000
664 000
Ml S40 S5B
jaiiosr
05 41
388 100
Xl 333
woso-
Oa833
388 278
388 456
M
480 9^8|B^
OflSB-
288 833
66.1333
144.! b;
1
411 254'94i 8
3811978
11 083
^811
565 687
^awoo
00
«1 195
70-500
666 000
144d3I
83
381418
"0-91
566 888
1446 a
imaa
as 16.
.418 87
488 143[o44 444
sai 640
08 383
389 344
568 687
was 01
60
381 8U£
-OS 750
389 5S2
S3
1S3 -89'949 BAB
883 084
09 IS-
389 899
56-338
iMa»
i83S«
ran98
183 iniim 111
tn3 30fl
700 583
889 8r
1*40 S3
saw 00
-34 941.
0(
483 33 |fl48 k:
710 001
290 055
sesmo
14S0 -"
JS118:
-asssB
149
190 381
"35 830
133 Bie,94 77)
TW*-4
U^
484 S15l9« 339
IISSO
!B0'i8(
569 000
1153 as
»w«
M 18
33
484 511, S48 889
11 6ff
390 765
56S3S3
1848 83
7^ IK
484 80- 949 M4
H8eS8
290 943
689 687
145j 18
2A3OO0
"S-80fl
H^
00
4a.™Uooo
3r5 88i
1 lOO
"W ^;
5 1000
U'iBOi
2si)i6;
J8 05I
iia,
89
4ffiaB9flS0 55(
r
48.-^ 9»i mi m
ItJS !H
48e38 ft £.
1480 4"
ss
-^«s-
1431
;.
1 ' 1
»I0
IPbi 6
u
41- I ■) 9« 8»!
J 1 1 ,J3
-31 151
r
43 4-2 951 4I<
35. m
IR ftM
^ 667
1483 15
»3, 01
-^1 903
143^
50
385 859
298 ~M
5^000
jsan a;
ISS 064 95.^ -06
716 86-
1 401 m.
Jl^'ifiO')^. (11 !IA, W
1 ISS
■93 0-1
5-3 667
n
"*
"
lO
3WS5S
Wl 000
UJSB3 38r!6 488 14
I 13 BOX W4 687
-w 175 000
) 9B4 ^^ 83.1
■ftlSlRIBOOO
JO 41 |3SI4 4fl-|&~6 883
n 8.93 391 874 Sra M7
?,?/.
«'
TABLE Xrr.— ACTUAL TAMOKKTB, BTC.
M 468.811 BOB OG
n4ae.e8»H)fisi
n4sg.iBr«»tM
» 471 .944
«« itse MS I
Me 4811 4M .
90S flIO 404 I
8 carve
Tan \
Sl-S ' '
90 l-n '( i 1
SHT|ii
iisii
-r
181 m\m
Ji
:« ^,U
IMpHS UWjSM
r
ins iKs'isB
4M 1SB fi'-HSlS «
-iw 180 a«s 314 it
M 144 A44 Sftj B9a 1
888 180 61 814 SHI 141 739 «89 11
W 818 aS3 14
M in "W 14
nil 11 111 04 ini lie 300026 14 4G88»I B
IM "inMI lOlllW 1118 131 111 14 8BISS8
S 1H4 BIRlaai 4.'M{II14 417 8"1 £1)6 )4 828 989 1
aiH4 »*fl1Bl m 164 4Ifl3Sl 4HllL4»01SW9 s
1 itB 04nl%i «^^^^M bii^'ftv wn\\'i^ \wv »•
) i«B iBi aaa 08^\i6* awan M«\\*ft ^*''»|
i iSB «a a&. jmHm m sa wn\\* "^^ »
TABLE XIV. — ACTUAL TANGENTS, ETC.
99"* 1° Curve.
M. Tan.
1481.80
1482.69
1488.58
1484.47
1485.35
1486.24
1487.13
1488.0*
1488.91
1489.79
1490.
1491.
1493.
1493.
1494.
1495.
1496.
1496.
1497.
1498.
1499.
1500.
1501.
1502.
1503.
1504
1504
1505
1506
1507
1506
1509
1510,
1511.
1512.
1512.
1518.
1514.
1515,
1516.
1517.
1518.
1519.
1520.
1520.
1521 .
1522.
1523.
15»4.
1525.
68
57
46
35
24
12
01
90
79
68
.56
.45
.34
.26
.17
.06
.95
.84
.73
.61
50
39
,28
.17
05
94
,83
72
61
,50
.38
30
22
10
99
88
77
66
55
43
Arc.
2900.00
2901.67
2903.33
2905.00
2906.67
2908.33
2910.00
2911.67
2913.33
2915.00
2916
2918,
2920.
2921
2923.
2925.
2926
2928,
2930,
2931,
:?933.
2935.
2936.
2938.
2940.
2941.
2943.
2945.
2946.
2948.
2950.
2951.
2953
2955.
2956.
2958.
2960.
2961.
2963.
2965.
2966.
2968.
2970.
2971.
2973.
2975.
2976.
2978.
2980.
2981.
67
33
00
67
33
00
67
33
00
67
33
00
67
as
00
67
33
00
67
33
00
67
33
00
67
83
00
67
83
00
67
33
00
67
m
00
67
3:3
00
67
1526.32 2983.33
1527.21 2985.00
1528.10 2986.67
1528.99 2988.33
1529.87 2990.00
1530.79 2991.67
1531. 71 1 2993. S:i
a7/f532. 6029m. 00.
^//.5«?. 48/S996. 67 766. 770. Um
^0/1534. 3712998. 331767. 214 1499
20 Curve.
Tan.
740.928
741.372
741.816
742.260
742.704
743.149
748.593
744.037
744.481
744.905
745.
745.
746.
746,
747,
747,
748,
748.
748.
749,
749.
750.
750.
751.
51.
752.
752.
752.
753.
753.
754.
754.
755.
755.
756.
756.
756.
757.
757.
758.
758.
759.
759.
760.
760.
760.
761.
7«1.
762.
762.
869
813
257
701
145
589
033
477
921
365
809
254
698
156
614
058
503
947
391
835
279
723
167
611
055
499
943
387
8.^)1
275
719
178
636
080
524
968
412
857
301
745
763.189
763.633
764.077
764.521
764 965
765.423 1495.
765.88211496.
766.326 1497.
Arc.
1450.00
1450. 8:{
1451.67
1452.50
1453.33
1454.17
1455.00
1455.83
1456.67
1457.50
1458.
1459.
1460.
1460.
1461.
1462.
1463.
1464.
1465,
1465.
1466.
1467.
1468.
1469.
1470.
1470.
1471.
1472.
1473.
1474.
1475.
1475.
1476.
1477.
1478.
1479.
1480.
1480.
1481.
1482.
1483.
1484.
1485.
1485.
1486.
1487.
1488.
1489.
1490.
1490.
1491,
1492
1493,
1494.
1495,
33
17
00
.83
.6
50
33
.17
.00
83
67
50
33
17
00
83
67
50
33
17
00
83
67
50
33
17
00
83
67
50
83
17
00
83
67
50
as
17
00
83
67
^^
17
00
as
67
50
as
17
3" Curve.
Tan.
493.985
494.281
494.577
494.873
495.169
495.465
495.761
496.0.57
496.353
496.649
496.
49T.
497.
497
498
498,
498.
499
499.
499.
499.
.500.
500.
500.
501.
."501.
501.
501.
.502.
502.
502.
508.
503.
.503.
504.
504.
504.
504.
505.
505.
505,
506.
506.
506.
507.
.507.
507.
507.
508.
.508.
.508.
509
.«i09
509.
510.
510.
510.
510.
511
511
972
972,
973
973
974,
975,
975,
976,
976.
9
I I
946
242
538
as4
130
426
722
018
314
610
906
202
498
804
109
406
702
998
294
590
886
182
478
774
070
366
662
958
254
550
846
1.52
458
754
0.50 991
Arc.
966.667
967.222
967.778
968.as:i
968.889
969.444
970.000
970.556
971.111
971.667
977.
978.
978.
979.
980.
980.
981.
981.
982.
982.
988,
983.
984.
985.
985.
986.
P86,
987,
987.
988,
988.
989.
990.
990.
346
642
938
991
992
992
234 993
580 993
826
122
418
714
010
316
622
918
214
510
994.
995.
995.
996.
996.
997.
997.
998.
998.
9^)9
4" Curve.
Tan.
370. 522
370.744
370 966
371 . 188
371.411
371.633
371.855
372.077
372.299
872.521
Arc.
725.000
725.417
725.833
726.250
26
727
667
.083
;27.500
727.917
728.333
728.750
.748 ;29.
.96.51729,
.187,730,
.4091730,
.631 rao,
.853 731,
372
872
373
373
373
873
374
374
374.742 732.917
.075
.297
.519
374
375.
375.
375.
375.
376.
376,
376.
376
376
377.
377
377,
377
378,
378
378.
378.
378.
379.
379
379,
379.
:i80.
.S80
380.
•S80.
380.
381.
381.
222
778
333
889
444
000
556
111
667
222
778
as3
889
444
000
556
111
667
222
778
833
889
444
000
556
111
667
222
778
333
889
444
000
5.56
111
667
222
778
aas
889
444
000
5,56
111
667
222
778
sas
.889\5»S\.44!^
781
732
732
16'
583
000
417
838
2.50
667
500
91
964
186
408
637
866
088
310
532
754
977
199
421
643
865
087
309
.531
753
975
197
419
649
878
100
322
544
766
988
210
432
733
733,
784.
734.
7:i5.
735
735
736,
736
737
toi .
737
738,
738.
739,
739,
740,
740,
740,
741.
741,
742,
742,
742.
743.
743.
744.
744.
745.
745.
aas
750
167
583
000
417
833
250
667
083
500
917
3as
750
167
583
000
417
888
250
667
083
500
917
as8
750
167
583
000
417
381.6.54
381.876
382.098
382.320
382.543
.382.772
383.001
3S3.223
745. aas
746.2.50
746.667
747. oas
747.. 500
747.917
748. 8aS
748.750.S06
t4^.\6'rla06.
5° Curve.
Tan.
296.451
296.629
296.806
296.984
297.162
297.839
297.617
2^.695
297.872
298.050
298.
298,
298
298.
298
299
299,
299.
299,
299.
300.
800.
300.
300.
300.
30«).
301.
301.
301.
301.
301
301.
302.
302.
302.
302.
302.
803.
803.
303.
303.
303.
308.
304.
304.
304.
304
304.
805.
305.
Arc.
580.000
580. ass
580.667
581.000
581. a«
581.667
582.000
582.333
582.667
588.000
588.a38
583.667
584.000
.838
228
405
583
761584
9381584.667
116
294
471
585.000
5K5.833
585.667
649 586.000
827 586.333
004
182
860
543
727
904
082
260
437
615
793
970
148
326
508
681
a59
036
214
392
569
753
98C
114
291
469
647
586.667
587.000
587.333
587.667
588.000
588.. S33
588.667
589.000
589.333
589.667
590.000
590.333
590.667
591 000
591. as8
591.667
592.000
592.833
592.667
593 000
383
667
000
333
667
305.
305.
305.
306.
306.
306.
593
503
594
.594
.594
.595.000
595. 3aS
825 595.667
002,596.000
180:596.333
667
Olio
sas
667
000
333
667
000
338
a58 596.
535.507.
713'597.
891 :. 597.
068 598.
252.598.
4a5 .598.
613 599.
790 599.
:!!L^
104
TABLE XIT.-— ACTCAl, TABGBNTS, STC.
1 6< CnrvB.
'• C»r».. 1 8
«""«■ «• Curve.
10° CuriB.
1 1 Ac
w
1 7^ Arc
Ta 1 A c r
3rir8<B8S89
j-wTuTiu
~0
trffiBlKt 011
. J74KB8B9
411 1
Jt7 iSi' *M iir
!i2ib;
. Doaint
MT flTHW 444
■WW
at) KM
il7BH)4as0UU
auy-
MS W
jwasas
^91 IMIO
»« IM 485 S-8
nam
415 UM
188
303 1)5(1
lb. Bir
1-1619
4'*B»(
ioi ir
»I8«£4HSGU
884 IH-
aai-oi
99! !ra
W41D4SSgBa
IK 4.11
1)64 39
iisaHse
891 BOO
9
USBSBIBSIII
nsosi
iiaue
MASf,
864 6«
16* -W)
SS4r4
40 M
SI 68-
10
its -or *m ssa
410 m
4B34U
«8Bae48fl su
lisl^
lUB 1106
4S4V
"09 000
IB
94«IX)8Me»14
■^1411
W&SUb
166 im&
SLiuaa
I4sa4
sea I6~
s« isi «r *a
m^Bw
IBD 41
lOU 194
■W4B5
14B 611
i98MB
Hti «» iir eui
US'!)!
>W6(JU
tlU aw 4KH DfWI
Id B-;
4IS3»1
'„'
Te^
lee 4J0 1? a'o
14R 90
49 B-l
'9' 66
1» H33
16
siu 4a[488asii
«n la
IIK *ll3-^i.(
JfllOOU
uam\ma,
w ir
N t 1 II 4 1
i' 1 ri
!M St 1- 9--«
150 U(
aaiiai
ao
393 aw
1 11 "ou
IBO S ^
as
T
' iVi
IW Kll
J94 0IX1
*04 11
H
"M 1«
»>4 6(ll
gu- ii« 3iKi 10 taaiar 4(r-
iwsw
am 66
Boa a,8 «t 10- BSa nr 69S
'•WlM!
-•0
Tinos -w i(r -solsw "s
■OBdno
3<l
ai rs
>.-,■* 'il.H t, IB «-a t-- 968
IM tS
891 IB-
iH14(
«lrt 3-«
!5I 9^
161 aosiso. SIX
41>- -"
IBl 39 hii» m
w'a^
16 W-MFS!
inm
16 ft 6|»B6 ««
IB -W«l)8 133
a^siH
4e4 la
.,e .|«s»ii^
11 a-D 0!tt IBB OflU C» 444
IS (MljSlMWO
m
151 flM|l!9fl M
•vm
S3 116
»14((1
4M on
] "^' "'"
I JH 1 1 1 1 m
1 IIJ ( "*' -j^
If
1B.1 1-1 1
J '
-S13S3
496 344
1- ! ,r«
M ir IHIM. 1 SI IM
1 30 1* ID 4U
8M Wl
Itr jn-
IS jj^-^ m
1W>
'■lir'91 169 ll"'331 4§1
IBS aitii "98 HSS no
054 n 1»1PBH6]|8»1M
l-UBMMHMKI RI
ins ! 1 "ihi") nfll'ti f"
4ftS0W
4QS ■«.(
iSSflM
99 -!M
TABLR XIV,— ACTUAL TANGENTS, BTC.
3 Cnrre 4 .
KS saoaowia - ._
ss Ml IB wia aa s
so 56 n- !(™ no -s r
a)sa cui'M OS sa
TOBjOOTIOi
TABLE XIV.— ACTUAI. TAMORNTe, ETC.
ase.wi U».(BG MB.
Hfl.lW
aeWB
(tl7.T7B BM.MH KOI
■SS.SM BOD. nx «!.(«.
MO. 911
an!sn9Bio.3i
SBi.eK
sei.sos
Sfii'.HW
H'
BBslia.Biu.iM.r
i.uBiiat.Tu
lt».5Uej376.8n 1
i.aeai
.000 aw wt.«4i.4^
Mt'Txlsielsael^ . i>m '
3.iw8sn.
iiia,735,3n<,i£
.sniTi.o
.Oti 17t.S90
:ae in. MS
..|H IT1.4S]
.es7in.ws
.8TG1T1.SM
ITl.IBr
ITl .M*
.WOITI.MH:
— IM.W! ;
IK.t«:
iiK.fs: mi .«*>
loe.sMant.lue
7.osgJa8!i.4]
r.TTOsas.si
7 998 3Be.O<
4.104 3m.9
K.aia ajcir
iM.sitti.sai.
tH.ais,
»I6.«6T
73.141 Ktr.IU)
..uc iin iMi»<7.'ini
«i.aK17i1.!M::.n;.!HU
- -" -iB.wjasH.iiK
B.A41|88K..MV
l^.»
)3vii.':o4
|J^4.1«i.iM!iHCI
I74!»lu
.Hn iTB.aai
.nn ITS. MS
TABLE XIV.— ACTUAL TAKaBMTS, ETC.
3
1 c
™
.r,e
flT
Tan
Arc
B> Aro
1^^"
■c
1
Art
Tau i
ISw
a * n
-5000
S BmSbsJuijo
liSftsu
0. » iffl w
BH -oasa
8103 W
I34» W 6
w
aus ou
ft Hsa
884 0. «M
jO-M
aoo b
H80
BSOKT
MSB
_saa
aaeffliw ais
Bsa a .t
-ue fi
fi,i4
is aM
818 78*
65B0(
»] 49)1
0300
rrca
53 BH
os-fc
seMO
-7 g
IBM
aa -ea
se h 3 «
M :
566 6-
}32
-BSMlsflsa
B«B«T
•™ W » SI
^^40.
038 3-
W(^
SlBBOe
Sir w'a
SV8 HU
tine
Bjxam
980 e 00
590 -f
BOi to
m \
60
jsoa
1 -^ «i
8S&3!«
J
60 "4 JS «)■ B 1 W
-B s a-oM
ere G ti oum- a 1 5fle a
ts at. iMooo
3 80
naioDO
BOB 0. 3 3 808 OB 5M SS
^4B
03«,»li«0 B^B
82 ^
use 883
n
A
1 ,a
im 48a
tx ar
Sfis
B Olio
^ Sf
b Stt
a M
u^joo
S^iXOOO
1KB
0-8 %a
3S t
ex 60
f. >0
iu
fl>«ooo
M«r
w m
aaissa
sw-h as
aa OK
8«B8
to
a V) nok
•Kf ~V /»
>^ K
030 ono
m
*"
. i
J»
0. 04 t»00
MjiOSO
5IS. J)
a. sirnwooo
ns aisiu A
fiiW
«» Vi 00 3 1-^ <vr
i»BO(i asam
4
ji -n «
■^ -n (W
»
X
40
6 >.
JO « ai 0-5*1388
no
Bsq sa,^ sn 18
BlBiH)- » « ^44«n
Oe OB MO -^ flSI ISB SR «W liST
tm »)«•« V
81 M ifl WM «
fi6 0-I40S -m s- ftL negeirma
la. Ihsbb
i S-O 1 OT1
IMH ft, >« T
-S n IK. 3- 8. 00-
W 9n00>«
»
>
. I «• CuriB.
r siT.w
k:«m bis! Of
Ki ; Hsa I^SD : flsi Va . mol «i I ' Ai u SM.'
T.BSiHD.aaiiB
1W;«MS4a,5tBI
i'i>.tai> 818. ;m 1
o.wssis.ia? 1
B9T'3l3.33:t a
0,98ti 31S.500 S
i7B.MeS4>.e3nie
IS.IIIOjSld!Mi| 39
la.sesaiB.seT 40
ii.7Brl.ll 0.833 M
iSLBBis:^ ftia 11.
730 SM. 704 1(1
HH gra fgS IS
iUMHM.OrtK^
.tiin'irti.i»;>M'M4ie
IBHSMIB
ssii>ii«.au m
.a^lsis.Asi D
.siilsiB.oon n
.aMaia.iiiT..n
TABLE Xrr.— ACTUAL TANOKNTS, ETC.
nr
1 e
a Cu va
3 C
4 c
S CUTT*
1 M
J"- 1 -^
~Ttt
A Tan
ir
"FT^
At
"t
Are
9MU lO
mTsTb
3^~696
ieij8
Kai sua
ItUI t«S4»01i
411 041
3^83
640 334
«-« w
IfHil B-
SIS sua
liitr-H
411 an
woaj!
i*9 051
640 66
aao. 01
SJ3 we
i«n^!H
M8 6ia
1008 IM 111 4fl-
3jJ6ffi
austiu
MB BIB
lOOH BB.IIl T«
1061 44I411 V43
184 4
s*i7n8
IMS ai
»im
S29 GBI
641 6ST
m 1
iiiu.^00
MB fill
1O0O0 41J1 1
i» I
642 000
iwwat
HBOir
10 SO 4U 3Bg
4 M3
10 1 11 iu 8IS
803 338
642 B0
1661 06
«16 00
^aiiSM
wurw
B5U401
1071 67llSai4 80D -50
S».l
04JOOO
lOOS^J
mm
siB -1 I'm 1
160 6U
-.1 laio i ijii ■am ooo
130 88
144 000
181 040
S » |l 11 B l&ll Mb
Ito'' 1) 1 01
811 101
*w -^
;flH13
■HI 1181
145 88^
•«g IS
1M H-'
4I4 0.'«
so- 086
m en
»iooo
H-SUW
10-8 6
B07 5110
131 B4U
iwo 1
mi D
SWOBS
IBl SD
^Si42
10— Ai
SO Bl
saiiiffl
646 383
30
IBfil 08
9J3S 13
H80S43
1610 67
ws -SI
icr- Ti
4115!-
808 188
ja*3o
648 66
toa *
t.M li
CKOS^
14 813
1501
i-W 3-1
ail tin
10 1 14 4IB01Utk)B6MJ
laais
64 66
1 10 »1
H 14B
3Sd0i9
i4'»ftiO
t-li U
S10 4t
■f-nia
«.■« 16
l.'i B NIOHI 111416 BBl
.M8B5
»i 50
^laiaiKti 6 Wbis
IJBOOIl
\6niiii09 ^.n i4«
81186
iii'T.i
149 iB
mass
Ml sr
56«S10a -8 41 3U
812 OBJ
30
10-0 >
1_A, rv.' I nil
G no
^^ „ 10^ J„ SB6
811600
IS* 106
ISO 000
t 1 i xn M \>mm\*\ 815
812 Bl
184 law
mass
150 68
aa
1(4 6ai
65100(1
iS
■:ii! i i "i J
111 16
114 58.1
■184 Baa
ESI 383
661 KT
652 000
l-HB-B
65il 188
IB— WJAJ HH S («■ 1 jl 9 ImIiOS- -S 418 406
tISBSS
w,^
653 am
16-a iBJBM uu.ijaii ui iss euifisn 453|10bb iB|4iB e*
las 40
653 000
TBTii 0- am r HS8 5«8 1633 9)1 sse ru lOfts 39 kifl bso
BIS 667
■nt Bl
668 388
11 iwi-oasi'sfo j^'iB-Hi 1^0, Iwrm'j-oo-j
ti oea
HfllOl
653 6B
6S4 Oi>0
6>4 aia
1 <i^
m86
818 so
,1B16
186 8Ki
tM ai8
!■« 11 JBB
B6oao
104 S ^ 4 1 l)'i(W4 1 8B1
a* 41
^6 388
loesnissisj
8«)8»3
3ir -SB
666 06-
H4 63S
831 250
66 000
ft.1 66
138 0»
15 388
;o«)«3SR8i
K4, i\
1644 1 5H8 8 4 1096 11 4Ji -M
&sffst
888 2-8
338 451
snsooo
Nil !,>(
IBIS m 'W4 i-6 inii- J- 4s» w. ai
8SM 634
668 333
l«4a 67604 SHI lOB "H 441 l"^, -S Wl
138 81
658 66-
/ ?~ '
SJ (II Mil 8B- 10B8 1W4^1 rwlB^ 60
I4S0DI
668 ocn
(I
' /fl-
« *'a
"^i,*,
4*^j"
tIMS»
8*0 17
H6 19B
565 4Se
4a wa
KMS8
'■^■«
as
TABLR XI7.— ACTUAL TAKQEHTfl, ITC.
. c
„
— ^
834— '48— 43
ap
rslw
UODOl
3^~fiS8
Swaa) 1
OK S8
400 KW
64M4aSO
y
m
S8fi
afisiKs
«4«8S3l!a!l88'
40
INHWS
saw
^35
Xd BB8
100 88.
85 ae
5S4 «S
joeove
40 04.
IfiO 48
B4 968 83-1
W B»
US IMU
83sas
Kti
Sfi8
&»
^
08
WblU
« «■
^W
SSfi 5U
2»8^
4(I»I>1
»SXl»
:lSaODB
^w*
40
t)3B3<i
SS )!^
&t m
« 45,
«s
,30
««B«-
06
3^ «c
to 84
as
IS Bsa
M
3S
BO
*souu
rsftoc
5js| wags
ar
bsb'
W WB
HIS
81
3S8
3M98J
eitsu
8K3S3
3£^6D0
(NT
3«
4(10 >»
2r sj
068
1U W
5iiHuue
» ou
Ht 44
U8 M
38 Ot
m«s
sas^
as
40 Ul
jo"!*
SO
e4u
3MM8D
38 ii
asaooo
SdS
as 30B
48 «e
ao-asu
0^968
9fe.
5S8>*8a
EaT«4
48 SOS
80 'Ui
m
M 41
BMSGO
88
^S33
c-
S89
^K
43
W-M6
v»
B&S444
BB a: M
N»444
Hn DBS
38
>»e
359 Utt
li
S37 Bl
d&g
w 000
on
J0SS4
WBooo
8fl 4(
80 000
54
^
oaoss
iUBWt
ueaoK
Hfi W
M 5S(
2«80
iua39
!0g U>
30 8-0
86
i3S33J
«» A83
HS «
380 5Aa
30 944
irs (56
a>8sga
406 831
SfiM
3W
038
SSI 38
-^
M 3((B
1)38 »
84048
aoeam
4efi(>t)!
SfiMO
USO BSS
r M
aa4 83d
278 40
a*8 -BO
W »H
04
M ^
iTB
OS
ton OH » 80 81
fflO JS8
w
H 84
» IB8M
» SS9
IS SB
Kim
S8S,i!3S
M 500
MX OM
H» 33-
M 3fliHa
MKIi i04 » (IB 93 I
M8fW '1
T8T..
An..
W
W
n^
w
; io 'Tf<'«fl ea'
Ml n 87^483 fB^m
U aws 09ST -B8 Bfr W Bfi M 3R -IBS BIW SIS iW 1*B fl-^
SS M« ST) bo' TB I IW'
TABLE XrV. — ACTUAL TANGENTS, ETC.
6<» Carre.
Tan.
U8.348
Kll.396
iftt3.449
tf8.7
284.061
S4.9U8
i84.8ri6
900i550.000
560.278
560.566
560.883
661.111
601661.389
561.667
661.944
568.222
552.500
)84.509
t84.657
S4.805
84.958
S5.111
SK.264
9)6.417
85.565
86.718
85.866
86.019
86.171
86.824
86.47^2
86.621 i5.')6
86.7781556
86.9-i6!557
Arc.
552
553.
553.
553.
563.
5.'54.
554.
554.
555.
555.
778
066
7° Carve.
Tan.
242.602
242.733
242.864
242.995
248.126
243.268
243.380
243.511
243.642
243.778
Arc.
243
244
244
611|244
88»|244
167
444
244
244
722:244
655.
655.
566.
556
87.079
87.282
»7.a85
^".588
187.686
»7.884
287.967
888.140
«B.292
888.445
288.698
888.751
»0.O47
»0.9OO
»0.868
889.506
889.659
889.811
889.964
890.112 568
890.860.563
890.418 568
.557,
557,
668.
568
5j8.
5.58.
550.
559.
539.
560.
560.
560
000
278
556
883
111
389
667
944
222
.500
778
056
fm
611
880
244
245
245
245
245
246
245
245
245
246
246
246.
246
246
246,
.904
.031
.15«
.289
.420
.551
,682
.809
.9:i6
,067
198
329
.460
587
,714
845
976
107
471.429
471.607
471.905
472.143
472.381
472.619
472.867
473.095
473.333
473.571
8° Carve.
Tan.
212.817
212.432
212.547
212.661
212.776
212.887
•212.998
213.113
213.228
218.842
Arc.
473.
474.
474.
474.
474.
475.
475.
475.
475.
475.
476.
476
476
476
477
177.
477
477
238,478
369|478
167 24H
899 560
661
561
561
561.
562
562.
562
444
728
000
278
556
838
111
880
667
944
222
500
247
247
247
247
247
247
247
247
248
248
248
248
778 248
0.161248
833:248
61i:248
.■MX)
627
754
885
016
.147
.278
.410
.541
.668
.794
.926
.057
.188
.819
.460
.681
.708
.835
.966
890.566!563.889!249.007 483..333
478,
478.
470
470.
470
470
480.
4R0.
480.
480.
480.
481.
481.
481.
481.
482.
482.
482.
482.
488.
810
048
286
524
762
000
238
476
714
952
190
429
667
905
143
381
619
857
005
333
571
810
048
28()
524
762
000
238
476
714
952
190
429
667
906
143
381
619
857
095
890 719
290.872
891.025
891.178
891.826
»1.474
891.627
564. 167 240. 22H 483.. 571
564. 444; 240.. 350 4a3. 810
564.7221240.490,484.048
.565.000 240.621484.286
565.278 240.748 484.524
5«6.656;240.875J4R4.702
.565.838 260. 00»'4H5. 000
5fi6.Jll250.]S7 4H5.
213.
213
213.
213.
213.
214,
214
214.
214.
214.
214.
214.
214.
214.
215.
215.
215.
215.
215.
215.
216.
215.
215.
216.
216.
210.
216.
216.
i16.
216.
46
679
794
909
023
188
249
360
475
.500
704
810
030
412.500
412.708
412.917
413.125
413. 3:^
413.542
413.760
413.958
414.167
414.875
9® Carve.
Tan.
414.
414.
415.
415.
415.
415.
415.
416.
416.
416.
416.
416
417
417,
0411417
1561417
270 417
385
500
615
720
840
051
0(J6
181
205
410
.52:)
»40
751
216.862
216.976
217.091
217.206
217.320
217.436
217.650
217.661
217.772
217.887
218.
218.
218,
218.
218.
218.
218,
218,
001
116
231
845
460
571
418,
418.
418.
418.
41H.
410.
410,
419,
410.
420,
420,
420.
420.
588
792
000
208
41
625
8:»
042
2.5<»
458
6«7
W5
083
202
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708
017
125
333
542
750
958
167
375
583
792
000
208
417
625
420.833
421.042
421.260
421.458
421.667
421.876
422.088
422.292
422.600
422.708
.542
1S8.766
188.868
188.970
189.072
189.174
189.2^
189.371
189.473
189.575
189.677
Ai'C.
189
189
189
190
100
100.
190,
MK).
ino.
190.
190.
190.
100.
101.
101.
101.
101.
101.
191.
191.
191.
101.
191.
192.
102.
102.
102.
192.
102.
192.
102
102
198
193
193
193
193
198
193
193
.779
.878
,977
,078
,180
282
384
483
582
684
786
888
990
089
187
2»0
391
4a3
366.667
366. a52
367.087
:^67.222
367.407
367.693
367.778
867.963
368.148
868.383
868
368,
368.
369.
369.
369.
369.
369.
370.
370.
370.
370.
370.
370.
371.
371.
371.
371.
5951371
697 372
,799
808
097
,090
201
.303
.405
,506
,608
,707
806
.908
,010
.112
.214
.316
.418
,617
615
.717
372.
372.
372.
372.
372.
373.
373.
373
373.
373.
374
374.
374
874
374.
375
375
375
375
376
.519
.704
.889
,074
259
444
630
815
000
186
370
556
741
926
111
206
481
667
a52
087
222
407
593
778
963
148
333
.510
704
889
074
259
444
630
815
000
185
370
556
741
10° Carve. ,33°
Tan.
169.933
170.024
170.116
170.208
170.300
170.889
170.478
170.569
170.661
170.753
Arc. IM.
198.819 375.026
193. 921 1376.111
422.917
423 126
423*833 194. 023'376. 296
423
423
423.
194.125 376.481
750194.227 376.667
.958104.326,876.^52
170
170
171
171
171
171
171
171
171
171
171
171
171
172
172
172
172
172
172
17^.
172.
172
172,
172
173
173
173
173
173
173
173
173
173
173
173
174
174
174
174
174
830.000
330.167
830. a33
830.500i
830.667!
330.833
831.000
331.167i
a31.333
881.500
845 331
.934 SS\
.023 832
.1141332
.206 382
.298
.390
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.568
.659
332
332
332
338
333
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.333
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.83:3.
.0«K),
.167'
O
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
36
17
18
19
.751 383 a33 20
.843 333 500 21
.935 333.6671 22
024 333.833 23
113 334.000 24
204 334.167, 26
206 334.333' 20
888 334.500 27
480
5?2
663
752
841
9^i
025
117
2<»8
300
302
481
334.
334.
335.
335.
3.35.
:i35.
3a')
3S5
M36.
3:^6.
336
336.
667 28
833 29
OOo!30
167 31
aS3 32
.500 33
667 34
aS3 35
000 36
167 37
333 38
500 39
570 336.667 40
662 336.a33 41
753:337
.845
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.020
.121
.210
.298
.390
.000
.167
333
.500
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337.
337.
837.
337
337
a38.
338.167 49
42
43
44
45
46
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1. 000 48
174.482 338. a33 60
174.574 338.500 51
174.666 338.667 52
174.757,338.833 53
174.H10|330 000 54
1 74. 9;i8 330.167 55 i.
. 682 424 . 167 104 .425 877 .^xftt'^m .^iv ^^ •'^'^^^^
.797.424
.2381218. 012424
VI. 9921666. :m 2fi0. 268 485. 476 i21 9 . 026 424
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TABLE XIV.— ACTTAL TAKOENTB, KTC.
34
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TABLa XlV.— AOTOAL TANSKKTB, ETC.
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TABLE TOT.—UrTUAh TANOENTfl, BTC.
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TABLE XTV. — ACTUAL TAlJai!ST9,ETe.
Car*
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TABLE Xiy.— ACTUAL TAKOBMTH, ETC.
M.
1- Cocie. 1 a° Curve. 1 3° Curve.
4^ curve.
»=Cu„,.
Tan
A L 1 Tan 1 A Tw Ar
ra
Art
Tin 1 A c
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TABLE mr.— ACniAI. TAMOBKTB, ITO.
TABLE XIV.— ACTCAl TAFSMITB, ETC.
7° Cnrn. tl Cm
4irB588M ir
B^ {»■
j« tsaUsi oDc
*M TBI 4K m
ja6 BS4 4^ ssj
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26 lutl 4Rd SS.
^.^7 ses 483 OH
us eM»r K iflfl n !it.5»~a
6Jfl!89J11M "-si* 6W.JH
TABLE xrr. — AC
L TAHOSITTS, BTO.
M.
Cr,.
4 Cnrre
5 Cnne
Tan
a™
Tan 1 Are
Tan Arc
T&u Arc
"ri^
Arc
~0
180000
jWraSwa
J1) 481 IttSa BS
BsaBwmOOO
4floi r
TO 81B 1033 SH
8S8 iTi leaia
880 333
4!iaS33
■ri 148 ies4 44
3Sa 4K1 IHS (tt
59^ -95
880 331
llkl'iU IWJ U| 4v,
081 030
1 J ' 1 I 1 1 L49
Nlia 1 1 II r OT
««) an 1 1 i MO
2^1 !0
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B i -C! laj, bU B55 is-
i-ffli
3U 400 083 333
49iHaa
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siMou-flBsar
auiHae
HWOM
1311 »
4311 K
8 4 511 1040 0(
ijaooo
tUM 813 884 000
asMir
imi B-
400 H.i
1930 4^
»ffi 018 BBt S3B
aufiitr
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353 444
1180 8)1
[l»»4 884 00-
tei03-
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mas
l»MW
1SL4 1.
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1. 191
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5SG 818 066 str
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1043 83
1883 60
!U6 010 883 000
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1343 BB
IS mi
l.!82 0S
5M I 083 333
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358 jOO
1*38 71
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TABLE XtV.-
[. TAK0KHT8, ETC.
s ■« I t 3.W aat 1
lO C
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*
Tau
Arc
]
::.
a 400
>fl. s
0? S3.
000
I Kj 1X19 380 314 at! 54J»
sr
44 45
t4aa£3i4d
ua (Ht 9
448 130 «
44SSM8J
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i8 6SU|-w a- Mu
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TABLE XIT.— ACTDAt TANGBMTH, KTO.
M
0.
» Ca e
* nrro
fl Cor ■.
1
"t
re
-
Are
m. »s|.,50u<ii
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0"
JWOO
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<»»
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a» 0° ««
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asbBfLso
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M8 3.
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sa «
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sa 3sa
6-0 088
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s3B« ooaoo
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6. m«-
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6 , ' ne uDssa
sa (44 WW 8" r w
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iS 50
Sd8 IS
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a, l» r ^ H A xal-w at a,ir »»
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539 WW
940
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6- W
sm
Moes
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mv
M0.SO
00
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67
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BOailO 688 3-
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B04M flfWSft
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68 .MM WW
w
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TABLE XIY.— ACTUAL TANGENTS, ETC.
0« Curve.
Tan.
446.489 883
445.000
44D.883
440.006
440.177
440.844
440 611
440.07B
410.840
447.018
447
! 447
447
447
447
448
448
448
448
448
190
.867
,&M
090
.808
005
»>:£
.074
MO
448.881
449.1^
449. ftM
449.0Usi
449.659
449.781
449.90<i
450.075
450.447
45U.414
450.681
450.768
450.9a»
461.09ai
451. 459
461.481
461.008
461.771
451.908
4&i.llO
4se.2se
45:!.4&4
4».6a!0
452.798
46^.900
468.18ai
458.804
453.471
458.088
468.810
468.962 847
454.154 847
4.^4. aaO 847
464.498 848
454.061 H48
454.832 848
456.004 848
45A.170 849
4S5.S4S840.
4B0.SS0'849
Arc
888
838.011
883.889
834.10
881.444
885.000
885.978
836.560
885.838
7* Curve.
Tau.
880.111
880.389
830.007
830.944
837.22;i
887.500
887.778
b38.050
838.&t8
888.011
838.889
889.107
839.444
089.722
tMO.OUU
840.278
840.536
840.833
841.111
841. 38U
841.
841.
842.
842
842.
848.
843.
848.
848.
844.
944 1
844.
845.
845.
845.
845.
840.
840.
840.
840.
067
944
222
500
,778
050
883
611
889
107
444
r2i
000
278
560
883
111
389
007
944
.222
.500
.778
.056
.338
.611
.8K9
.107
Arc.
714
714
714
881.917
882.000
382 204
382.351:715.
3»J.49J»:715
882.64',':713
882.7W715,
382. 9» 71 5
3H:J.072 710
280
524
7U;
0(X)
8° Curve.
Tan.
sai
334.
334.
3&1
Arc.
238 334
383.219
383.367
383.510
383.053
383.801
388.918
3ai.092
384.235
384.882
884. 53U
384.073
3»4.816
284.904
385.111
385.255
385.898
385.545
385.093
385.840
385.988
886.131
380
a%.
3ri0
380.
380,
387.
887.
as7,
887.
887
887.
387.
888.
88K.
388.
388.
388.
388.
388.
389.
380.
389
389
389
389
389
390
390
710
710
710
717
717
717
717
718
718
718
718
719
719
719
719
720
720
720
720
720
721
470
.714
952
190
.429
007
905
143
,381
019
,857
<H&
333
571
.81U
048 33G
3.^5.
335.
335,
385
3:15.
3:15.
335.
385.
im.
330.
330.
mi
330.
330.
242,025
307025
49:^025
022 025
751 025
870 020
01)1 U20
127 020
252 02U
381020
000
208
9» Curve. 10* Curve.
Tan.
297
Arc. i Tau
4171297.
025"2»7,
833 297.
.042
.458
.007
.875
510 627.083
030 027.292
701 627.500
890 027.708
917
125
333
019 tJ27,
145tS28
270 0•^8.
3!M) 028.
.'>2« 028.
051 028.
297
297
297
298
298
298
298
298
298
298
298
298
&12
750
958
274 721
4221721
509 721
713
850
0(13
151
291
487
585
782
880
027
170
814
401
009
752
'722.
722.
722
722
723
72:1
723.
280
524
702
UOO
238
4^0
714
952
190
429
(W7
905
143
381
019
:j30
a37
337
337
:«7
:«7
3;i7
3:^7
337
.338
.'38
3:«
aw
338
3:«
8.57: :i38
095':338
3.33 339
571 339
728
724
?24
724
724
725
725
725
810
(M8
280
.524
702
,000
2:J8
,470
.339
.3«>
339
3:^9
.339
.33«.i
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.340
895|725,
043 725
.190
.387
.485
714 340
952 3 to
720
72(J
72(J
028=720
.7721727
.919'727
.000 727
214 727
30/728
7221890.609 728.
.190
.429
.Wi7
.779 029
.908 029
.0.37 629
.1(»029
.288 0.30.
.417 0.30.
510 6.30.
.075 vm.
.81)4 030.
.929 631.
.055 6.31,
.184 0.31.
.313 081.
.438 6.S1
50l(J32.
.098 0.32.
.822 0.32,
.947 632.
073 682.
.202 083
S:)] 03:f
.4WMW3
.589 033
.714 6.33
.810 634
.90U634.
.U1WI034,
.22:i!034.
.3»9!«»;J5.
.478:«85.
299
299
299
1671290
375
.588
792
000
208
417
625
299
2i)9
299
2{)9
299
mo
300
833 300
042 300
250
4.'>8
300.
:i(H).
007 3<Mi
875. 3(K)
l)8.S|.301
292|3()1
.'iOO .301
708 301
917
125
.301
301
333 301
.M2!:«)l
958
107
301
302
302
340
340
340
.375 .H02
583:302
7J)2l302
(N)0j302
208 302
105 555
277 '5.55
388 5.V)
.5<«.V)0
018.">.'j<;
.729 550
841 550
.952 .V)<}
004 5.57
.179 &)7
I
293! 5.57
405557
510 5.57
0:il 557.
740.558.
857' 5.58,
iWy 5.58,
OW 5.58.
198 5.58.
810.559
421! 5.59.
.5301559.
6611.559.
702.5.59.
874 500.
988. .500.
103;,56().
2181500.
333.5()0.
444 .500.
.55<i .501 .
670 .501 .
785 501 .
897 .501
008 561 .
123.502.
237 .5<W
349 .562
401 .502
575 502.
690.502
8()5 5(i3.
919 ;m.
iSi\ 'm.
142 5<'i3,
257 :Mi.
872 WH
488.501
59.5.501
710 .5«M
I
550 267
741 207
920 207,
111 207
290 207
481 208
067,268,
852 208,
087 208.
222 208.
407'2«8
.593 208.
778 2tW.
963 2JJ8.
118 208.
.3.33 201»
.519 20J).
704 20S).
889 209.
074 20.9.
.2591269.
.444'209.
.6.3OI2OO,
.815 209.
.000 209.
. 185270.
.370 270.
.5.50 270.
.741 270.
.920 270.
.111 [270.
.290 271)
.481 270
007 270
.8.52 270
.037 271
222 271
.407 271
.50:J271
.778 271
.963 271
.148 271
..3:«271
..519 271
.704 271
.889 272
074 272
.2.59 •.J72
144 272
.030 2?^
Arc.
517
018
718
821
925
()25
125
226
:i20
430
58:^
633
7:W'.502
>«7 502
910.502
010 502
141 502
214 502
347;.50:i
448,503
500.
500.
500,
.500.
500.
500.
501.
501.
501.
501.
.501.
501.
M.
.648
.0.51
755
.855
9.50
0.59
102
205
mi
409!
509
073
770
870
977
.080
.508
rm.
rm.
503
.501.
504.
.501.
504.
.504.
504.
.505.
.505.
505.
.505.
505.
505.
1H3 500.
284'.500,
3H4:.50(i
487 500.
591 500.
,094.50(i
.797 507
897J507,
,998 507.
101 '507.
2iw.vr7.
30.51507 ,
4a5l.508,
,508 508.
,000
.107
.833
,500.
(10
,8;w
,000
107
333
500
007
8:i8
000
107
.333
.500
007
833
000
107
3.^3
500
007
M3
000
107
3:»
500
007
833
000
107
3.33
500
007
883
000
107
a33
500
007
8.3S
000
107
.3.33
.500
007
833
000
107
.W).5.:«0
. I4:J :i41
O
1
3
4
5
6
7
8
9
10
11
19
13
14
15
16
17
18
19
SO
91
»»
93
94
25
96
87
2H
89
SO
31
39
33
34
35
36
37
38
39
40
41
49
43
44
45
46
47
48
49
.381
.019
:M1
;«i
444390
8.57 .341
m».5;:i41
.383!311
607 685.4171302.824 504.815 272.012 508.833 60
. 7361035. 625j302.93(» .505.000 272.715 508.500 61
.805 635.8;« 3ft3.054 ,5<i5.1ft5 272.818 .508.0(J7 59
. 9iM) im . 042 ma . 1 05 .505 . 370 272 . 9 1 9 5O8 . 833 53
.110 030.2,50 30:^.277 .51^5. .5.50 273.019 50J).000 54
. 245 ♦i.36 . 4.5813:):^ . .391 .5<>:, . 741 273 . I2i 5*V,\ .\.«v\«fc
..374 030 .«S7V.^>ft .W» T*St> .'JfiSfc-rr?* .SSrifc W>^ "'^^^
. .503 oan .H7^ Wft .r.-ix w*^ .\\\ ^rr?» "^^^^i^]^.:- ^Ji
. («I 6^7 .(^ 7i.^\ .TiV» t*AS .'»«» *2r^^, "^^i^^^^t
.701 0:^7 .-Wi :W^ KA^ '*J^» ^'^^ '-^^ '"^^ ;^°^ ^^ -!—
lATT
TABLE XIT.— &CTDAL TANSBNTe, STC.
Bl
1 Curve S Cn VB
6 Curre
T.« 1 a™ 1 T«n
Are
"rii^
A
Tan
A c
Tun 1 Are
-0
•"Sj sa'sioo 00
i3W5I
o-i
3H3 304
mT^mTaa
1|S-M93
13S oe
tisaeis
i\r-u9!
iioa*
130 S3
Bsajw
l!r5 S
4 IMlCBoe
13SSW
S^l
01 '
OS
1 01 r
1 If IB
181 1*
l>-fl Ji
it 558 10- 1 w
o'^wot
liw%
—01 ou a
iiiuoo
186168*MftO0
B11
1141-lM v
IH4 89"
iir-M
147 9^10 0.
li-UOdiBMBS
)i;
418 1 03 a
385 148
13WB*
54« 180 lOa- Ai
185 899
I3r6ti
MH 380 llttH 6 1
0!«10
SUB 00
la^ loij^ So
ma 05
itsn
54a 5H- loaa 0(1 ,
10 U. a
iiieo
i^n ai |MS8 S8
9)'
4-11 1"0.5 W
EH1 91
larsi
Ms^oa'i^^
ii^-uie
isaai i
li^^r It
080 4W
5W1 a-
13T la &I10 »i
eSbSKd
S4B 4I« im ffl
>i«asi
stsia~~>
esu 9411
1280 aa
649 61S 1B4 6
180 1 oa»
68-2U4
1281 25
WOe-JIO* JO
18 r49 3
\\x fl-
1» 4 1 .MS 3D
IT rtw«
ti«ri »
la a 11 »i:i 1
88- 1!
lAuoe
SOlil ID 00
1284 60
660 4-W lOM OC
91
545 1 10 E6
MHSiJ]
l«i9-
550iJ9 10lWa3
^0 >■« 38
650 84 10» 67
*1 1 '"54 41
lis.
I2H3 5
>5I(B1 10-7 00
38 |J ji5 4j
Ml a- jo-ja 13
o5*083i0i8 1
j=Li :
&i2 2B-110S1I 00
«8
aa
IMUl 1 5U
t, X 484 1029 S3
ae
tuai
i4sai
13H1 aa
J54 I
m M4|, 10 n
890 M
m 08
562 owiuffl r 1
3?
zei H
Sj^M
1581 87
is?
1
Til " '
!" ^
25 M
i(en J3
9 1
^1 1 w ■*»
i«Ma7
■-6a i
lasiti
9
>)51B
0-
1%.
9-)
^9-2a
If:
103^ 00
-OK
1386 «
JsaoK
«4a4i
»■
01
9-4
*e
IHI 25
loajoo
40
r-8ii
16.16
m oa
258,133
934 748
i-aa*.
998 8-1
i«gi r
Vj4 9B0
lowM
2-4 ao
188-54
«2a
OBO
HBS 881
9 -S
434
ifl5 r)
i
25B5ai
9Ul
"■
IS94 m
1^ tRj
1031 US
51 3 3!
138flOB
aujBBT
e«
0114 65.
B.T6 -S5
TIW
1189 6!
258-60
^M 988
258a»
Md
605 151
Jrti 11
fti-
095 411
086 6
■ilBOOl
1301 1.
2590 01
B^4~8
iwa
691 6 1
lOWOO
►-S3 la
&iai B-
out*
naaw
ar
m
ITS^M
eft; vxt
l^%4
oUSOO
1038 83
no
■>-84 si'sisa aa
isaais
»fli r
1-^ -8
690 IT
10)6 8'
rH. *i siss 00
139^8
»9sa(
w
KX
1-*H»
891, 443
la* jfl6 ai8
lOJ-M
i aa OTisiBn a
im ij
(IW- Ml iftfl 4-i5
•ra SDsiH 1
94
rssM^in 1
i oni
n
/tf/-w *
IT
Jir/re, va /
kil
%
MJ
^^v
TABLE XIT. — ACTUAL TANOEdTB, ETC.
6 COTT
1 T Carre
8 Curve | S Cnrre
HfO
™
Bl
Tan I
^
^
Arc
45o69 H)
xrataA oodo
SUM e^ 788
V
4.* If »5l
os-a-SBM
0SS3
4Sfl JBS50
JT K2- a-3MS
OMO
45Bo43>l,
M 4U «^4 04«
frji|B8 sasa-f ti
WT
4* 1*
5t J04 w as- -tiir4.as
4.WH&'k^
HM UiM W M e83jS74 »S
a-
+ IM -V,
e wt iro S68 4B n4 4u
m Bt«5«i3.j'r4 6B
B0(
om
5
sar
-Hfl s rs a'^
s:€
BS2'SHtS
d«X
1
u ro 2-8 OS
3 38.
t.iS (45.
M
M owiwbSo^
rs «,
b?
*-B
4.1»« ■«
M .JK. loe l«l 6 93«
am
M4| ■" 1 " "
w* MJ sue «s a
re X
2-6 Ii.
T
IfK 4S
ITB llltt
4 J33
W J. |B.
6 w 8-fl4(r
a*
J « 411. H.
NB ra wr
4 «e
4^«|^
c^Y »«|
'"1 n
Oon
o
4U 3IU (JDD (t33|aM
iir
B i3»- ssaeuisa
Xi SS)9 ^t
» l!8S4BSSj
00 in
1737 TSJTOO a»
,
10 M
WISK
938 I5S
^"i 8*
11 )l
941 803
'
1 UJa efl|"fl40 93 948 1)1
9 9«S S« Bi88 »
I E847 s!>'seRs a
t J818 38 IJHfi !
J 2849 -III •"
1100 83 9ft
1301 6-Bd
180S BOM
W ■■W 320 10
MSOT B'ein
1 M6 "58 10
jiosaoo
^» /esaa egsae
«,R SIT.— ACTUAL TANGKNTa.KTC.
Mass:
8« MT
8«i tan
ifr GOO
B87 -78
M7SH
' tKKO
«8BV
IO° Carre 68°
OH 8 6 ^S-SBw'u HI
10 9aoB~ 9e!i|8-» 90BS30 ib
m 4Mi r-4Bft5
t sn4BMm
B4t)BB444|
tea 6-9 880 aw
» 5W0« ■81
174 9J8 H-
ITS an wi
*"5 464Sl 1
4^«40W
tTBStssse >!
ou an 8
— i 181 »
5 6S) J W 4W J2i 887
o'-is ^^^l »i 8— te asa
*i 68-*! DMisassoo
5H2 &HW SIOWl ODO
M ■>8.«-J»tS«8i«4 I8T
M Wi 1198 «■ 4W( 1*1 KM
B W -8 *««•■- ■ —
.. fe4 1L ,
ft W4 «;
MUflSBSSSSUl
4 l-W. m !f>S MB.ISB
S5 SW S-O J91 OTp) Il»
5»Ki 41 J(u 913 «- isr
H ' •*DD»aHlM-6«7»S
A >H6 «-XHt H0HH0(n:4H
4 ^se IXiMt 888 BtU 187: 41)
~ .R- mrm m noi sss no
t iS-iensKnHnwBauIni
WH Ls- 40- a« IW W 8871 B2
IT KM a% 80S W> KSS n3
LH"t) JMH 40r G«» mo B4
,j| >S- DM JW (llUfcN 1«. ^* \
—ACTUAL TAN<lKITTa, BTO.
«(j la WIS H
%i3a9! «s 3!j
e.w8(«!
83(1148
o i^jsg fljfiwaa ji
"^ aasi'
-ai n8|i^4 08
TABLE XIV.— ACTUAL TANGENTS, ETC.
6* Cnrre.
7° Curve.
Tan.
4T6.!»8
4T6.600
476.079
476.
477.086
477.19S
477.870
477.64(5
4W.7
477.806
Are.
840884
78S885
888.888
888.611
888.889
107
884.444
884.728
886.000
885.278
566
886.888
478.0ff7
478.eSU
478.411
478.588
478.705
478.980
470. lOh
470.280
470. 45:^
479.0S0
479.806
479.078
480.160
480.8--'7
4K).&a8
480.676
480.847
481 0si4
481.201
481.878
481.646
481.721
481.898
48S.070
482.aMS
48--.*.4IO
4MiS.696
48S.76K
482.089
488.116
488.208
488.466
488.687
488.814
488.990
484 16S
484.884
484.611
484.688
484.860
'J I.
485.083 897
485.208 807
485.885 807
486.662 80K
486.780 808
485.911 8»8
486.088 808
486.250 890
486.4ff6;899.
486.018899
900.
886.
886.
886.
887.
887.
887.
888.
888,
888.
Ill
667
044
222
500
056
888
611
Tan.
408.847
408.494
408.642
406.793
408.945
409.002
409.240
409.891
400.54^
409.690
Arc.
8® Carre.
Tan.
757.143
757.881
757.619
757.867
758.095
758.383
758.571
758.810
759.048
750.286
857.872
857.501
357.680
857.763
857.895
858.024
358.153
358. 28U
358.41U
%)8.548
888.889
889.167
889.444
H«9,722
890.(00
800.278
89U 566
890.888
801.111
801.889
409.
400.
410,
410
410,
410.
410.
410.
411.
411.
411.
411.
411.
411.
411.
412.
412.
412.
412.
412.
891
801
892
892
808
898
8i)8
898
667
944
222
500
778
056
888
611
889
167
894.444
894.722
895.000
805.278
895.556
895.838
896.111
896.389
806.667
896.944
8S8
985
132
284
435
583
780
878
026
177
828
,476
.628
,775
,926
,078
,221
.872
524
671
412.819
412.970
418.122
413.269
418.417
413.568
413.720
418.867
414.015
414.166
414.
414.
414.
414.
414.
416.
415.
415.
415.
415.
818
465
612
764
915
063
210
862
513
661
.222 415.808
.500:415.960
,778
(»5B
383
416.111
416.263
416.414
.611416.562
.889 416.709
.W7 416.861
444 417.0121770.
722 417.1641771.
759.
59.
760.
60.
760.
760.
60.
61.
61.
761.
761.
762.
62.
762.
762.
763,
763,
763,
763,
764
764
764
764
765
765
7r)5
765
766
766
766
766
766
767,
767
767.
767.
768.
768.
768
768.
760.
769.
769.
769.
770
770
770
770
Arc.
O" Curve.
662.500
662.708
662.917
663.125
663.333
063.542
663.760
663.958
664.167
664.875
Tan.
Arc.
lOo Curve.
624
762
000
288
476
714
952
190
420
667
905
143
.381
619
,857
,095
,383
.571
.810
.048
.286
.524
.762
.OlM;
.288
.476
.714
.952
.190
.429
.667
,905
,14:j
,381
,619
,857
,095
,383
,571
,810
<M8
2S0
524
762
.000
358.
358.
358.
359.
359.
359.
359.
359.
359.
359.
359.
360.
360.
360.
360.
860.
860.
360.
861.
361.
361,
361,
361.
361,
361
361,
862.
362.
362
862.
862.
362
362
362
363
863
d6:i
363
363
368
363
364
364
364
864
817.730
317.845
817.959'
318.077
818.195
818.810
318.425
818.543
318.660
318.775
677664.
806 664.
935 665.
067 665.
200^665.
329 665
458 eft's,
587,6f.6
716 666
849 666,
08i;660
110666
:.'30;r.67
872:667
.504 667
633;6C.7
762 667
895
028
157
286
41S
551
680
809
942
074
208
882
465
.597
.726
.855
.988
.121
.250
.379
.511
.(J44
.773
668.
668.
668.
668.
668.
669.
669.
669
669.
670.
670.
670.
670.
670.
6n.
671
671
671
671
672
672
672
672
583
792
000
208
41
625
833
042
250
458
66'
875
08:3
292
500
lOf
M
,125
3:^
542
750
,958
,167
875
.588
.792
000
208
417
625
.838
.042
.250
.458
.66
.875
.083
.292
.500
.708
.9r
238 364
.4761864
.714 364
952 '86-4
1901865
902 672.yr«
Mm 673.125
,167- 678. 833
800'673.542
,482 678.750 324.007
.561673 958 324.122
690 674. 1«
688.889
589.074
589.259
589.444
589.630
589.815
590.000
590.185
590.870
590.566
318
319
319
319
319
319
319
319
319
319
820.
320.
320.
320.
320
;i20.
320.
320.
320.
821.
Tan.
286.080
286.184
286.247
286.848
286.449
286 552
286.656
286.762
286.868
286.9n
Arc.
821
321
321
321
321
821
821
322
822
822
822
322
322
822
322.
322
:ii3.
328.
328.
828
890
005
119
287
,855
470
.584
,609
.814
,932
.050
164
.279
.807
515
.630
.744
.862
.980
.095
.210
.327
.445
.560
.675
.798
.911
.02£
.140
258
590.
590.
501.
591.
691.
591.
591.
592.
592.
592.
592.
592.
592.
593.
593.
598
5!)3.
593.
594
594
594
.'^94.
594.
595
595
595
596.
596,
595.
596.
741
926
111
530.000
530.167
530.883
530.500
580.66^
530.888
581.000
531.16
631.383
581.500
53<
M.
287.
287,
287,
206 287
370
490
605
7-.'8
841
956
070
481
667
852
037
407
593
778
963
148
338
519
704
889
074
259
444
630
815
000
870
556
741
926
111
596.296
596.481
596.667
596.852
597.087
597.22
597.407
1881597.593
306 597.778
421 597.963
323.586
:323.653
828.771
323.889
287.
287.
287.
287.
287.
288.
288.
288.
288.
288.
288
288.
288.
288.
288.
289.
289.
289.
289.
289.
0741631 ,
178,581
2811532
387 532
493 532
596;532
700!532
8031532
906
012
533
538
119 533
222;583
325I533
431:533
537i534
186 289
289
289
289
290
290
641
744
850
956
059
163
269
37.->
478
581
688
794
897
000
106
534
534
534
534
534
535
5;)5
535
r..35
rm
586
686
536
586
290.213
290.316
290.419
290.525
290.681
290.785
290.838
290.944
291.050
291.158
598.148 291 .257 588.833 50
598.333 291.868 538.5a) 51
598 . 51 9 291 . 469 588 . (>67 52
598 . 704 291 . 575 538 .833 53
598.889 291.681 r>39 0(H) 54
o*-*. i«.599.074 '^W .•X>S\\\&^ .\^V "^^^
9A\ .^l\Wfi .^>WJk'^ift\ .>«J»^*cS» .V;>K ^5;
667
a33
000
167
383
f>00
667
833
000
167
.833
.500
.667
.833
.00(1
.16
.833
.500
.667
.833
.00('
.167
.333
.500
667
.83JI
.000
.167
.333
.500
686.667
586.888
587.000
587.167
587.383
537.500
537.667
537.883
538.000
538.167
O
1
2
3
4
5
6
7
8
9
10
11
12
18
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
828 674 .5yrrA?i'a4 .^'bWj .^\\\j»\ .^*^3l^^ -^^
088 674 .79aW4 .?>W W«ft .%\^^ "2^^ .^ttJfc^^
TABLE XIV. — ACTUAL TANGENTS, ETC.
1° Curve.
Tau. Arc
2919.43
2021.49
2922.55
2923.61
2924.67
;J925.r3
2926.76
2927.79
2928.85
5400.00
|5401.67
,5403 33
54a5.0U
5406.67
5408.38
5410.00
5411.67
5413. 3:^
5415.00
2929,
2930.
2y:W,
293.1.
14 12934
15 2935.
16 •»936
17
18
19
»0
21
2»
'^3
»4
35
26
37
38
>* .>o«r
293;
2938
2939.
2940.
2941.
2942
2943.
2944
2945.
2946,
2947.
■2948.
91 5416.
97i5418
0;J:5120
07,5421
10 542;^
16o42.),
2-2 15426
2S,:>42S
34!>130
37 5431.
40 54^3,
46'54a5
52'.>136.
39 2949
30
2950.
31 2952.
33 2953.
33 2954.
34 2955.
35 295().
30 -2957.
37 2958.
38 2959.
39 2960.
5S
64
70
76
82
8«
91
94
00
06
12
18
40
41
43
5438
5440
5441
5443
5445
5446
5448
5150
5451
545:^
5455
5456
24 5458
3015460
36,5461
42.5463
48|5465
2961.
2962.
•2963.
67
38
00
67
3.3
00
67
:«
00
67
3ii
00
67
a-i
00
67
00
07
33
00
.67
.33
.00
.67
33
00
67
33
.00
54.>406
57I5468
43:2964.
44 ,2965.
46
40
47
48
49
•2966.
2967.
2968.
2969.
2971.
67
33
00
67
an
00
67
33
00
02 5481.67
60^
66
?2
78
Si
90
96
5470.
M71.
5473.
5475.
5476.
5478.
5480.
1486.10
/.
50 2972.08 5483.33
51 2978.14i.5485.00 1486.63
63 2974.20 5486.67 1487.16 27'
63 2975.26 5488.38 1487.69
54 2976.32 .•>490. 00 1488.22
55 2977. 38 5 491 . 67; 1488. 75
a€f ii97H. 44 .«/W..*V/i489.28
3° Curve.
Tau.
1459777
1460.28
1460. 80
1461.33
1461.86
1462 39
1462.92
1163.43
1463.95
1464.48
Arc.
1465.
1465.
1466.
1466.
1467
1467.
1168.
1468.
1469.
1469.
1470.
1470.
1471.
14T1.
1472.
1472.
1473.
1473.
1474.
1475.
1475;
1476.
1476.
1477.
1477.
1478.
1478.
1479.
1479.
1480.
1480.
1481.
1481.
1482.
1482.
1483.
1483
1484.
14^5
1485.
01
54
07
59
10
63
16
69
74
25
7H
31
84
37
90
43
96
49
01
52
05
58
11
64
17
70
23
76
30
83
34
86
39
92
45
98
51
04
57
2700.00
2700.83
2701.67
2702.50
27a'J.33
2704.17
2705.0*.
2705.83
2706.67
2707.50
2708.
2709.
2710.
2710.
2711.
2712.
2713.
2714.
2715.
2715.
2716.
2717.
2718.
2719.
2720.
2720.
2721.
2722.
2723.
2724.
2725.
2725
2?26.
2727.
2728.
2^29.
2730.
2730.
2731.
2732.
2733.
2734.
2735.
2735.
2736.
2737.
27.38.
2739.
2740.
2740.
3° Curve.
Tan.
073.^43
973.587
973.931
974.284
«74.637
974.991
975.344
975.688
976.032
976.385
Arc.
33
17
00
83
67
50
33
17
00
83
67
50
33
17
00
83
67
50
33
17
00
83
07
50
33
17
00
83
67
60
33
17
00
83
67
50
33
17
00J990
976.
977.
977.
977.
978.
978.
978.
979.
979.
979.
980.
980.
980.
981.
981.
982.
982.
982,
983.
983.
983.
984.
9t».
9&4.
985.
985.
985.
986.
986.
986.
987.
987.
987,
988.
988
989.
989.
989.
1800.00
1800.56
1801.11
1801.67
1802.22
1802.78
1803. a3
180:3.89
1804.44
1805.00
739 180).
092 1806.
4451806.
78911807.
1.331 1807.
486,1808.
840|l808.
193,1809.
546
890
234
587
941
294
G47
001
354
708
061
405
749
102
455
809
162
516
869
222
575
929
626
970
323
677
030
383
737
090
1810.
1810.
1811.
1811.
1812.
1812.
1813.
1813.
1814.
1815.
1815.
1816.
1816.
1817.
1817.
1818.
1818.
1819.
1820.
1820.
1821.
1821.
56
11
67
22
78
:»
89
44
00
56
11
67
22
78
33
89
44
00
56
11
4» Curve.
Tau.
729.999
7:i0.256
7;i0.514
130.779
731.044
731.309
731
731
r**:
67
574
832
32.090
732.855
732.620
732.8851
r33.150'
:33.408i
733.666
73:3.931
734.196
734.461
ra4.726
7^4.984
735.242
7:35.507
735. 7?2
736.087
7:36.802
736.567
786.832
737.098
787.:303
737.620
282 1822.
1822
182:3
1823
1824
1825
1825
1826
1826
83 990.443 1827
S 7 :at7V. 50 549n. 0011489. 81
SS Ji^y. 50 .UOff. 671490. 34
2741
2742
2748
•2744
2745
2745
2746
2747
2748
2749
737.878
r38.143
78ir38.40«
33! 7:38. 673
891738.9:39
447:39.204
00 739 469
56 7:39.734
11 739.999
67 740.264
22 740.629
78 740.787
33 741.045
89 741.. 310
44. 741.. 575
00.741.840
56 742.105
11:742.370
671742.635
22 742.900
67 990.797 1827.78 743.165
.50991. 1.50 1828.33 743.4801
,.33;991.503 1828.89 743.695!
,17 991.8.57 1829.44 743.960'
,00 992.210 18:30.00 744.225
83 992.564 1830.56 744.490
.67 992.917 1831.11 744.755
.'»0:993 ,270 18:i\ .67 7^.020
, 8:3 993 . C24 iSaa .52 145> .^SM* \T»\ .V* ^.V^ .*»(S
Arc.
350700
350.42
.350.83
351.25
:351.67
352.08
352.50
352.92
3.58.83
353.75
854.17
354.68
355.00
a55.42
355.83
856.25
:356.67
857.06
867.50
857.92
858.88
368.76
869.17
869.68
860.00
860.42
360.88
361.26
861.67
862.06
362.60
362.92
863.33
363.76
364.17
:364.58
365.00
865.42
.365.88
366.26
866.67
367.06
867.60
867.92
.368.88
.368.75
3(59. 17i
3<)9.58
370. OOi
5'> Curve.
Tan.
564.064
564.270
584.477
584.689
584.901
.585.118
585.825
585.531
585.788
585.950
I
586.162
586.374
586.586
586.792
586.999
587.211
587 423
587.685
687.647.
688.053
688.259
688.471
686.664
588.896
589.108
.589.. 320
689.6:32
589.744
589.966
590.162
590.869
370.42
.590.661!
590.793
591 .00)1
591.217
591.429;
591.641 1
591.853:
592.065.
602.277
602.489
592.6061
692.902
593.114,
598.326'
508.538
.598.750
.59:3.062
504.174
604.860
870.83 504.698
371.25.594.810
371.67 505.022'
,872.08 695.235:
872..50 605.447:
872.02 .506.6.50'
.373.. 38 505.871.
.373.75 696.088
Arc.
060.00
080.88
080.67
081.00
081.88
U61.67
082.00
082.88
082.67
068.00
068.88
083.67
084.00
084.33
064.67
065.00
065.88
085.67
066.00
066.83
066.67
087.00
067.88
067.67
088.00
088.38
088.67
089.00
080.38
060.67
090.00
090.83
090.67
001.00
001.8S
001.67
002.00
002.88
002.67
003.00
003.88
003.67
004.00
004.88
004.67
006.00
006.88
006.67
006.00
006.88
006.67
007.00
007.88
007.67
008.00
008.88
006.07
00000
000.88
154
V-. — ACTUAJ. TAMOSirTB, RTO.
Cbtm. 1 Our>
8 C
„,
Cr™
1
9ou-:jss| — j«
Ks^ |'~oooai4~ eoT
Ma~
B&
jH.^
»r
Kw
M. 'Wfc tux
W
w
ama-
iM lue ouo
BBUJte. BT
auouiw
JIM ai
ailll<W 64
OS W em
1 50 m
H^
«w««
-0 J*
\ 5«
Jb.«~*
^^
UUBUfiU
m
DM at
19 flUB J33
it
m-KH 6W
^
31)8 IB- Tlf
««»IM4+l
J
3b UM
IB BUflTt
■» IB M.
^
Ob
HOt
m
sij D8«tre
w
4M B&
vta
»- .fl-B»6B
JM3U9
M
m
9uas6U
77 a
887 »H «- ar w
2M
MaB33
tt
Hl&ItSa
80 404
« B~tm)SJ M
!W
343 sua
UU
ee
sue OBB-Bfiwa*-
^nu
M B6
M)38U
UU
rvaa
MJim -M!t 3W
MM -80
U3«Kt
W3
BU6 W
£») 836
M4 Out
St) wti ur (KM aw iir iu«
■W M
54
SIX *if
s*.
— ■SBMIHlStM Ii- 41,
mm
54 38S
«i\m mva»rm
M4 5t»
^
HT
WTl
-M iwsl )u< tws WW jasiiir mh
M
a>
«.3M
Ml 647
M4
W)b ^
Ban
m lift sm's*
54 00(1
341
!»
3U JW 1[^
HUH HUM
«
7-9«
^
«
goo
UK WW (M. JUt
uu te.
iiM
& aa.
m
Has
8fi
m ^^ |«r
a!ata4«JM 60.
sa.
89
naJ^^L
U^^ ^
l»
M
<S.
m
».
S
)!!■
JOU
W
«fflS0.3«
Wfl' B8 M 1
a- SWUHT 3S( B6B
an «1M
w S04 HB
04 H (Uisl^ BR3 |t09
1
m M- i«3aaD sw
M oe
lUM. KB MUt'
:riSSiSff«
w mlM M
(10l)4»«ft-B*iW
M ea
M
ant
4ffi«)il
TWBM
STI4-
ISSSF
Ma42t-II "84 11.
BS4 4U 908 iu an :
3m«»MI~8S
wionwtsa
8-!i ■% am v«\t&
TABLE XIV.— ACTITAL TASOmiTS, ETC
1 (CtJ K 48 M
mtiK
,s..
™rHr,
m-^.
mm
«3«WiK
fl 4 ros R 1 no CM W3 "fl
em «
vnssb
DO -!■■) -s w sn »: )
JMOO 1
DM B hw jinosiw
i« 4»nl wi fl on s
TABLE XIV.— ACTUAL TANGENTS, ETC.
6° Carre.
7° Curve.
Tan.
497^7
487.614
497.690
497.867
498.044
498.221
498 897
498.571
496.751
498.928
499.
4ii9.
499.
499.
499.
499.
WO.
fiOO.
600.
500.
Arc.
916.
910.
917,
917
917.
918.
918.
918.
918.
919.
667
944
2^i
Tau.
426.
426.
426.
857
509
Arc.
785.
785,
8o Curve.
Tan.
Arc.
500 42G
7781426
066 427
101 919.
281 919.
458
62i5
811
988
16.')
S42
518
695
500.872
501.049
.'iOl.225
501.402
501.579
601.755
501 982
502.101)
502 280
5ae.46i
502.640
502.826
508.002
508.179
5(18.856
508.582
506.7U9
608.886
504.008
504.28U
504.416
504.. 598
504 779
504.956
505.138
505.809
605.480
.V)5.H68
505.810
506.021
.•^.208
506.879
.'S06 RHiS
ijn«.7S:J
506.910
.•>o;.o««
507 268
920.
920.
yjo.
920
921.
921.
921.
921.
923.
922.
922.
928.
928.
92:3.
928.
9*^.
924.
924.
925
925.
925
925
926.
926.
926
926.
927.
927.
927.
928
928
928,
928,
929
929
929
930
980
383
611
889
167
444
722
000
278
556
888
111
389
667
944
222
500
778
056
388
611
889
167
444
722
000
278
556
838
111
889
667
944
222
500
778
056
8-83
6il
889
i«:
444
722
000
278
9*0.566
031.111
an.s««
981.067
981.941
982.222
/
427.
427.
427.
427.
427.
428
428.
42:*
428.
42f<.
428.
428,
429,
429.
429.
429
429
429.
429,
480
430,
480,
480,
430.
480.
431.
481.
431.
481.
481
4:}1.
431
432.
432.
432
432
4:K
432
48:1
4:}8
4:«
4:33
43:i
6601786
8121786
9G3'786
115':86
266 787
41b
56!)
721
T87
787
714 878
952 3:3
190.378
429 378.
667:873.
9051:37:3.
148!:373.
881:374.
872 788
02Ji7S8.
175,788
827 788
478!78ft,
6:30 7«9,
78! 1.789,
9:i3 789
085
236
61ii
857
09.*)
:t3:3
874
374
874
:374
57 r 874
Hl«»:;374
04H,:374
79t)
790
888'790.
589,790.
691 '790.
8421791.
9941791.
145,791.
297' 791.
4481792.
6l)0!792.
755 792.
911 792.
06J;798
793.
793.
798.
286
524
762
xm
2:38
476
714
952
190
429
66^
905
143
•175
875
:375,
:375,
OlO.
375,
875,
;376
376,
:376,
376
376,
:376,
134 687.
.'M7 687.
899 687.
.5:32 688.
.665 688.
,797J)«8.
,9:30i688.
,062 688.
,195,689.
,82H|689.
460 689.
,598 689.
725 690.
858|6»0.
901 '690.
12:3 690.
25'; 690
:388!691.
.V2l!691.
654 691.
786 691.
919 691.
051 692.
184 692.
9° Curve.
Tau.
500 331,
708 831.
917 831 .
125 .882.
.838 3:32.
542 aari,
750
958
167
o75
332
:332
832
832
583:;332
79y
(HX)
208
417
625
8:38
042
250
458
3:33
83:3
33:3
3:>8
338
8:38
:3:33
338
388
Arc.
667 834
875 884
317
449
692
692
214
860
517
6691794
:381 :376.
619 376.
857 :377.
09.') :377.
:13:3 377,
582 692
714j693
847 698
98:3 693
82U
9?2
123
275
794
794
794
?J5
426 795
582i79.-)
795
7:37
889
r95
040 79(J,
lJ»2;71Hi
318|7%
495.796
«>46'797
.571
810
048
2HU
.•>24
762
0U»
238
476
714
9r)2
MM)
■I'M
01 ( .
01 1 .
■il i .
377.
87S.
878.
878.
.878.
:378.
878.
:378,
87K.
879,
:179.
.802
4:38
434
434
4.84
484
134
484
.9.58 797
.109 797
r97'
!HK")!:J79
118
381
^
.261
.412
.564
.715
798
798
798
798
507. 4 45! 982.. 500 _
wr.tio3l9S3.(ml4sri.
867' 790
.022-790
, jrs/roo.
880/799."
619
8.57
09.*)
.838
.571
810
048
2S(>
524
762
879
879
:J79
:3H0
m)
:J«0
:3S0
.880
m\
.8S0
119 698.
2:»2,6{):3.
:385 694.
517'694.
,6r)0l694.
,782' 694.
915.695.
048 695.
180 69.5,
313 695.
445 695.
.582 65Hi.
.71H61Hi.
,850,696
988 6JK3.
116 696,
,'J48 697.
:381 697.
.513 697.
650 0J)7,
088
292
500
708
917
125
888
542
750
958
:3.84
:i84
3.84
834
834
:3:34
.8.85
835
a85
.835
:385
167
37.5 835
588
792
000
385
8:35
8:35
208 :386
417 ,.8:36
62513:36
8:38<.836,
042:336
2.50
4.58
667
87.5
083
:336
:3:)6
8:36
.337
:387
744
861
979
097
215
883
.451
.569
.(ih7
.805
928
040
.1.58
276
:394
512
680
.748
866
M\
.101
219
:337
455
578
601
809
927
045
166
287
405
528
640
7.58
876
(M>4
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611.
611.
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612.
612.
612.
612.
612
613.
618
618.
613
613.
614.
614.
614.
614.
614.
615.
615.
615.
615.
615.
615.
616.
616.
616.
616.
616.
617.
617.
617.
617.
617.
617.
618.
618.
618.
618.
10® Curve.
Tau.
111298.
296i298.
481:298.
667:298.
852 299.
037 299
222:299.
407 299.
Arc.
646 550.(
7.52 550.;
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1
2
3
4
6
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7
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9
10
11
12
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14
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16
17
18
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8.88 20
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185:300
870 801
801
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926301
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2961301
4811301
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34
35
36
37
38
39
40
41
42
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620.926 304.288
621.111 304.. 894. 559. 000; 54
621 . 296 .804 .MW Wfi» .V?rv\ 'W*
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TABLK XIT.— ACTDAL TAKOENTB, ETC.
,• curve. ; «~ curve.
B" Curve.
10»Cur»8.
S6°
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Tan.
A«,
Tao 1 Arc Tan. 1 A c
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Tan 1 Arx;
tmam
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measisousa&jgi mj-oows
338 931
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80B14S580 1B
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305 joafiOMS
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305 358
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381 S57 700 83a
339 3n
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660 831
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306 534
568 388
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341 4B.
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311 583
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TABLE XIV.— ACaOAL TAHOBHTB.KTC.
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B" C«r»B,
Taa 1 Arr
Tun 1 Are
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5 C«v^
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TABLR TTV.— ACTUAI, tAHOEKTS, ETC.
an 1 Arc
I G~i see OE
I 9SI^ 33:
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Tui Al£.
Tui
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OOC B.^ a4a 344 444
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TABLK ZIV.— ACTUAL TAttOEKTS, VtO.
«9-
i«e
^e.
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4»0
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M
Tan
Are
T.U Are
Tan
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Tan
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1:'
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5903 83
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BIB aas
BIB KB
B18 8S4
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14 a 00 8IS Ml
10 42 818-64
I4TS 83 B48 »-8
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117B B Blfl 113
11- 08 819 «J
11-8 SKSGOSBI
H-^ 6 BSO 511
11-9 1 QW -3
1140 ou sei 1 [
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Ha,OH&>, j-1
IIB. 50 0^^49
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1189 -isaa iB^
1181 IT BM 3811
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1188 ^0 6M 815
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TABLE XIV.— ACTDAI. TAHQEHTS, I
..c™.
8- Cnrve.
.. <»„., j ,0. Cr...
6»'
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Tan. 1 Arc.
T»n.
Are.
TM. 1 a™.
Tan.
Are. Tan.
a™.
M0.uiw3.iag
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406 686 797,600
iol^
590^000
BW.tUtt 981.011
166.687
Ke
67)1767.706
I6S!741 884'6t«
590.167
Mo.au wa-iMi
8W,7117.917
190.866
iviias^
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948
68.1'i
v.o. 1 1 1 '■■m'^y.
64i:»sw4:m4
464.0W
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819
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064
Ml-*W9tH.iat
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Mi.wiw&.^n
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4«.au6
644
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M9.SM«SS.III
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6*11,7*7 BM8.MT
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M3:«:BHr;!r(
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5i«.60;
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466.(166
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593.633
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016 741.^0
668.680
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503.000
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MU.eu
466. 6;u
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lBi:741.4B8
36*;87;
669.07*
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BBS.IOT
in
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166.661
917
108.^741.06'
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648 866
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948 671
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409 jeoi 4.4 las
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409 69SI 4.1 363
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409 680 48 M.
1160 996^7-816(11636
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960 000
409 6-fl, 48 TOO
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409 BIS 46 966
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9XI»
IDS 4^
960 4ni
400 H8'74* itr
US.Ul
mm
408 663
960 14
*10 088| *4 8TI
304 JJ 1
618.5™-
nf!-i
468 41
»]9S>
410 U~ 4* 686
864 1 U
A46.IW.
468 901
410 80 44 'ft.
998 663
169 061
161 49
110 60* 46 000
098*11
95106
110 618 49 .108
365 m 1 ^ 1
6*T.518 9BSHtW
469 6
«i9a
110 ~9| 4S 41
305 16
M aialica —a
d8
6*7.e9g W4 IS
469 a&L
110 919 4.0a
tassr
6OJ "l^l&OI 681
696 60U
BO
M7.8861BM *4*
■69 OR.
B5K881
411 OSb' 40 863
366*0.
66. 90.l'3B9 000
696 BB-
40
U8 0e UM^U
09 84
86* 619
uca 1*8 320 101
696 868
3U. Hi
S9- 000
Me!*d6W3 ra
"O W
111 4 1 40 4^1
385 8iH
lil^l fl9 1,l J*
43
MS.Ui »« ssa
NWi&i
■u V
4 4»1. 808 6 1
411 51 40 fr-
OU NNJ 3.J 1.^! 9- JJ.
MS m IMS 111
! 1 t,i .SiS Ml
ataiwuue ?eu
4nMI^WM6
664 ..5( a^ H H.mI 4T
ua.»6e»M H
8M»W
3<*44U
6C4 444 d 9 BH IW UIO 48 1
MB.M8|!«0 »M
3MBIU
11*606 *T 06
366 jO
40
Ma. Tan IN 2^
4>a-«
864 IS
41X 442 ~47 91
664 816 330 10-698 686
Me.BiSM siu
use mw
lis 68* 48 Ifift
366 811
660. 1* M ~B
14 SJ
H.WM8
411.-*. 48 AtW nil|ic It Jii 11 W W
BS
6S0.«H«98ti™
1 ] 6
8W4-6
03
6S0.* 1BBN tsa
4ngii
8M ]<
411 16. "i 1
6M1:b»8 8« SHU
A aaaa-yt ig>
418 r-i 1*
66i,t«iBiiii la
4'BSWSS6 4J9
4H4I1 ^ '•^
B6i.»;<»»*j*
4-«fi* ase 06-
"•""•^
2-^ieMsa
*iaBja 1 \ "
—
TABLE XIT.— ACTHAI. TAHCISITTe, BTA
90'
ML
S
21
29
36
3»
40
43
44
46
1. Cur,..
3» Cu^,.
..c,„.
Tan.
Are,
Tan.
Aro.
Tan.
Arc.
TMl.
Are.
Tan,
Arc.
BB08.0I
aw 30
333a, 95
ann.m
IS4I.43
III
SI
1363. B9
31159. SB
ma'.ot
::::
iDia.si
11
60^.33
=s
S048,33
II
UGO^OO
Hiia!sa
il
1075.00
iosn:oo
9UB3.33
la'w.oo
ISS
lees.w
[GS0.B3
IflBO.lB
leao-T.
1061 :«
laua.w
ions OS
1S6^.S4
lou.oo
1631.65
iiwn.BU
:UUU.80
:tw!."98
I873:«
1973.00
II
III
If
!ooo:b-
3007.00
Sf
soio.o
111
JOIA.OU
30IB.83
3018.07
1017.110
JOIM 33
30do!oo
80aj.8a
wai.o;
30U.DD
S;S
8ft«,B0
uag.sf
11
WW. II
S:S
=1
3«0.83
Mil .07
llOd.71
SI
IIM.S-
1104.04
1109.011
I10& 8-
1 106.7.1
110».4!
iio7;«
I108.3;
1109.4;
1110. ai
II
iiiiJ
illl
11
llM.s!
iiai.Bi
aooo.oi
«S!:»
4002 a:
II
SI
m'.s
aooH.a
aoioloi
aoio.56
aoii.ii
SI
sow. 44
aois.oo
!0i6.Ge
i:
aoi7.a
aoiT.T)
aiifl,33
aois.sg
S:S
aoBoso
aei.ii
oei.oT
soaa.ae
2082. IB
S3
a»*,4'
MBoli:
aose.o-
11
aoao.w
»ai.i:
SI
827, IM
II
829! la
SIB.SM
B29.W4
9*9,941
saolaoi
»30.w;
m'.w
BS1.S91
B33.17B
8iBS.4a7
R3e.737
HS3,U0e
sss.asi
Fiaa Boi
Si
SS4,e78
837.751
888-031
838,810
siM.sas
ssfr
39.4*
HI
840.839
ii'ii
S4a:s39
843, M6
842.7«
m.tfn
r.s
609,00
6O0'SI
50!!, 08
60i.60
S;i
SOS. 76
II
6«»!8i
iBosifl;
IM7.01
1607! 9i
ISUSilT
II
iflialoM
I51S>J
1513.8
IBlB,^
Ifil4!6
6in!4
iM7:»
I622!60
I6ca.8;
MS,I»8
612.262
U2.47G
is
MS. sac
1104,029
ffil
B66!l4l
m.ov
uea.2M
0(18.482
zs
637.140
if
«.«
rs
639.198
889, sae
si
170, an
(CT,TOB
S1:SS
S:S
■»■"•
g'S
17^!641
h;3.)«4
174.081
1200,00
1*01.00
if
ia»8.as
j||
isueias
uorioo
ffi:S
il
iii
210.00
210.88
210,67
211.00
il
2ia!38
ss
1213.33
1213,(17
214,00
214,33
2iG!ao
?ia
1218,00
1210,87
1817.00
III
El
\
TABU! XIT.— ACTTIAL TAMGENTa, BTa
1 Ou B. 8 Oar
» tiB DO e
553 OM 00- Si . _
MS »o DO M) 3m
M W5 am
» t«H uui
IKS8UH4 UK
Kssro
m -it'm -
woonas
fiDUiM osoc
iBo(n>
Bttmoetaks m>\tn q
8- IS STt 988 836 B « M" I BO
3° Carve. 4° Ciirre.
i lasa Maoea hs hi
i9|fl)ii "s H
alOM HUM
R I2S0 00
3IS31 S9
0I«.00
■ J SalS43M ifl 1
TABLU XIV.— ACTUAL
s o»»
7 Curve | 8° Corrs 1 S* Curve
IOC
„r,.
61.
3H:
Al
T»n 1 An. Tan
T^
Are,
M. IM
4(Wttiiain m ji. i. 04i
no t«-
tm lu
no SIS
8
BBS au
SIDfiOO
SiS
toi It
483 ti3|K 881 4^ i 380
4HU 34« al tllS t„ g K b. CH b » >4 MN 4S1
BIO 66-
610 SH
5
EOS Hli
lUlHW
4H8 iO-'a » 4^ gt* BJ -W|S7B lai
fl7s»W.W60t
MU oos
483Mi8-8 0«i4Sa BH-ed9M3«^
V
HH 231
1018 8B
«M .( ir-i-mt'^eT w la s-u ra
9M4ti
4wa»jtr8 ,1 4 «3 j^oBoo
611 MO
B04eaa
10IB44
WW!*'- %
880
3SnOB6
nil 86
SM81>
IWB'^J
184 M»
sasDM
1041)01
» ooi
12 08>
Mm
btV ]gS
«u iir
BasjTs
KMQStl
4Mfl8BF »
» T(
■«; Bw
6 888
M&5e
lOWBd
184 84 tr
Han 611
1^600
MS -51
IDll 11
esu 41
aaesti
y ye
WIO B»l
sua 842
sea 134
4e5 8a5«Ts inM 4»
tXJSO
a" OSS
m 111
SMBS
aM8t»
lUlM
«»**p»^l^»»
oeiw
r--5e
681 «9S
840 oes
618 16
D
MS MM
lOMsa
-flew
a— Bss
681 4S
ins»)
«0
iS5 8Ma-6 4ja4ji,iw
«,8-S
J-SOOI
C«I6«-
SI
SI**" 0- -B
485 9 4
68 B5t
JJ 408
SB
■« UOjI 0-- (H
M^ ttUS 4a 45
18 Ksa
-I MO
■>«««,
68:. J^l
AlOtt
4M4U
■iam
K* 40
s— mg 4_ B-5
uses-
BS. B9a
WORW
H388
Its
511 B lOil J
B— sa? ijb oil
6b. ~l
MH «B 0- 1 <J
-ea m
rsHs
MH U 1(RII
IH IW
S-M BBS 4M Sflt
asMn
8TI010
UM 1«
Ml 186
014 Baa
SB
G,*TO fv^nr
fl fl."
!■ ono
J7
^q H - ■.18
BO HI 0. « |4->f< 1 ISN. ,A J^|«1B MO
,>«
5-^ro|,™^^l4KB«U.. 4-. 4««6«>
40
i]H83)
48
m
il S88
'iH
n se"
46
n B8B
. |»S!
48
40
118 sss
80
s^.msouH'I'Iha ,r2a«34i)iwb
V- . H s ■)« 1 (.»i as j
^
B IIV.— ACTDAI, TANOEHTB, KTO.
«»'] 1» Onr** 3° Onrre 1
0„„ 1 4
o
r« 0- Curr,
Tin 1 Are
- yw-MiaiToo
^ omIiwo »i
B llfl 1 00
8 3»l St\m8 3j|l«5 J
1 8 !>■ i 1 J'i 3.1
Kja Him
SB. DO Ml tS-
J44fl0
B+,
^ 1 OU ?ll
litlSS
11 11 r 1 V
m^oo
10 in >« ~ 1 jl ^ 1 ii«i
1 b-a
1 1.8 «i|BjaaM|i7aios«iii ii
i-Mta
18 WH 1 fl«) 00 1-31 M 3115 00
IMUOO
lD{ail)4»lMSl r- l-3i « ?115 83 IL
1.48 -a
' 19 «n
1 * 4fl«7
00
00
1 «
1 PIH 1 m
m sasaesi*
an H Businiaiii «
-r*»« 8S6.
091
u 08 ass 3.11 laiii a
^mv>m
1. inm nasooo
B7
00
00
i H tf 1 « 1^ er
40 wss taiK
g»
MH a aires i&>ii do
4«1W«i lflSMBTlMl»klSlM1IB3
»«>^U
MflB-TO Sr JS3M
4l'lir llrw = 'i 11 -'j 1 1 1
^
J wibflsow ASS
698 WB WM M
U» 2tl' Km U
" lU)B 480 IIU 07
IN ttM eSB «« 00
■ "<»!
4.
em BIB 1SH u
no 9499 ST(B8IS3 1-4S W8141 AT IIM («\xnt 41 WA
omia oaa
*oo 14S i9sa B
« |35«» («W 00|1 M ^|lU- M llff;
tB^jg, tcw-s r-4
1 1 «
-oor-ia 00
ll'wi wls-
(*»
■i 1 6
ooaieiffl S3
a-t iAi -j-t ^ « J
Of
% JBL
-0UB3I1]» «■
-01 KU 1«« V
-«»l6-3«
-01 sa i«M r
T)i M laa 00
B,"
nt
\[i w
a\».
\»flffl 1
TABLE Znr.— AcntAL TAHasnTS, ETC.
liVUi XIV.— ACTCAL TABGKKTB, STC.
63
""'
3 On 4 Cu B 1 Cnn.«
H
"t "a
Ta re Tun
A Tan
Are
85 sewuuo
~6n8a"suuo
a 50 00 00 H IKK.
00 -TW 440
"Sua
^imwu
sa joWMsa
-OS BT>
"M "sa
"" » *""l "^ M
SB'xwan
JOOB-
l"*"fflMOO
IM 88
« OS ffl
luasd %
» '8S09U
03 85
sa4 M
KO- 8
-nato
"^B^^aBaol
» 03».
-»s
«f "1
Q 03
uiMSMiia
03 m
If 04045
J8.
8* M
eoit 8 M
TM
860
■m
88 W
«T "
'Stt
MUSOI
HBO 5.
1^|SJ504|1«.
musB
76 J «<t
i105 BO
BSOBl
-1, k-^'a.«
aimt
^sSs
-« an 59
£00
18 04 wa -u-
va BB
laaooo
-M so'hm 00
iO«B'
VK 01 on
msoe
NMaieoBs
&
Bfi BUS
j» 4. 05 J8
UriH
g-^ IS
-es688 B n
Bfl 0- -8
S8 ITb
6WS BB
Uj8 »8
Aa. <w
(i Asue sa
nSi! .45
58 »-Wi8»
m'.m
B tDS E- SI
-« B8<0a HU
ftHK
OB
IM8J8
^ IMIOUM
IM (IB
M mS^
i««50'tw -X
JBBOO
051
88S
-a il
688 898 588 83 0- 08
tHBB
»8aB84aM8-5ir»l JBOO
884 S" 5B1 ». aa J3
88 81 ■toOO
■<1
58fl TIN tC
■8. »
HI 8 fl X
585 JT.nN
31 saa
8 3181 50
880 00
B8B B « St-
iU4tiKM8a«
".wa
mta
ar 08-09
jwe-
„
tMsaa no
1
^
j-m
r-noo
™ -u. «
^
iK
&> 4s|«s B- 889 1 * Bl ra 00
S3 Ssjitll n 88ft 'as 045' «n ^
1» -ts
1 1 1)0 flj sa
no 956. esss in
1^ 88 r
SSI an 3- TBM S5 Me S3 s imo re b
a ass Hfijuss m
-8 ™|S (. 9,
TABLE XIV.— ACTUAL TANGENTS, ETC.
6^ Onrre.
Tew. Arc
S85.461
966.642
5».888
W6.024
586.215
586.406
586.597
S86.7U8
686.979
B87.170
887.861
687.553
687.744
687.969
588. 1%^^
688.820
688.517
588 7<M
688.90U
689.091
669.282
589.476
689.664
589.855
500.046
690.247
»90.428
5ilO.G24
590.820
991.011
591.202
S9I.898
591.584
691.775
591.964)
am. 162
.'W.740
59-J 9«1
693.1'22
d!i6.61H
598.51^1
5««.705|
5US.K90
.'i9».0H7i
594. 27K
394.474
.594. 071 >
594.861
595. OTi-'
595.248
595 4:)!
995.680
599.826
596.017
596.208
596 899
!m.S90i
596.7m,
7* Cnrve.
Tan. Arc
5'
060.00 501.
090.28 602.
05U.56I50-2.
090.881602.
051.11902.
091.89 902.
051.67j502
051.94 508
052.22|508.
052.50.r)08.
899
099
228
8«7
591
714
052.78(903
098 Ofi'*tS.
058.88i908.
0^.611904
058. H9 504
054.17
054.44
054.72
a>5.(i0
055.28
aV9.56
055.83
056.11
096.89
a56.6
056.94
057 22
057.50
057.78
058.06
098.83
058.61
058.89
099.17
059 44
Or)9.7-,»
060.00
OHO.sW
060.5(1
060.83
061 11
061. :W
001.67
Oin.»4
062. 2J
002.. V)
002.78
0»H.(H)
068.. 8:J
06:). 61
063.89
064.17
064.44
064. ?2
066.00
065.28
065.56
065.83
006.11
904
904.
.504.
901.
905.
905.
.509.
.509.
90ft.
5<e
909
506
906.
906.
506.
906.
906.
5(»7.
507.
907.
507.
.507.
.507.
.50H.
508.
508
90H
.50S
.508
.509
.50J)
.509
500
909
910
.510
.510
910
.510
.510
911
511
611
900.
9(J0.
900.
}|00.
9.0.
901.
H78 901.
042 901.
'H)6 HOI .
370: JW2.
538 902
697 902.
861 9(«.
(W«,90:l
vr,,\m.
:Wl|903.
924,908.
688,904.
8.52'904.
016 904.
1H0 904.
843 909.
907!909.
671 1909.
839'909,
999'H09.
168906.
000
288
470
714
992
190
429
66T
906
148
381
619
857
095
833
571
810
8<> Carve.
Tan. Arc
489
489.
189
489
489,
489
440
440.
440.
440,
440
440
440
441.
441.
441
441,
243,787.
386i787.
9291787.
673 788.
816788.
960 T8S,
103 ;88
788,
789.
7S9.
8(K)
9:^
048 441
28«
924
762
0(K)
238
476
714
441.
441.
442.
44J.
442.
442.
412
830
498
662
9.52 442
190 442
906
906,
906.
826 907.
990
151
317
481
907
907
907
908
649'»i)8
8171908
9S1 i»08
808 909
4?,»
.((40
009,
!I09.
80H;i>lO
9?2.910
186I910
299
488
631
799
968
.127
.290
.454
.622
.790
.994
.118
.281
445
'611.445
1511. em
910
910
911
911
911
911
912
912
912
912
913
913
913
91S.
066.891511.6181914
42{)
667
909
143
881
619
857
099
838
571
810
286
524
76.'
000
2:18
476
714
952
190
429
667
905
148
381
619
897
099
a38
971
810
048
448
448
448
443
448
448
448
444
444
444
444
444
441
444
145
44r.
445
445
445
145
446
44(i
446
416
446
44(i
446
447
447
447
447
417
447
I
676 789.
820 789.
963 790.
110 790.
257 790.
,400 790.
,944 790.
,687 791.
830 791.
974 791.
I
117,791
260'791,
404 792
947 792
690 792
,8.34 792,
977 7«2,
124 79:1
271 798.
414793.
I
558 7*3
701 793,
844 794.
988 71M,
131 794,
278^794.
425 795
.568 75)5,
712795,
855 795,
900
708
91
125
388
.542
7.5t»
958
167
875
.583
792
000
208
417
625
8:«
042
2.50
458
667
875
088
9<* Carve.
10<» Curve.
Tan. Arc. I Tan. Arc.
390
390
890
390
391
891
391
891
391
391
891
am
392
892
:)92
392
892
:)92
892
892,
393
398
893
.919 700,
.646,700
.7741700,
.9011700
.029i700
196
.284
.411
.939
.666
.794
.921
048
179
310
437
969
692
TOO
701
701
701,
701,
701,
7ie
702
702
702
702
702
000 391
189 3.51
.370 891
556 891
741 8.52
926 892
111 352
296 8.52
481 3.52
667J852
,70:1
820 708
947 708
.852 892
.087 352.
.222 3.V2
.407 .358.
.998 853
.778*58.
.908 3.53.
.148 358
.838:i53.
.919 358.
557 630.000
672 630.167
787 630 383
901 630.500
016 680.667
181 680 883
246 681.000
860 631.167
475 681.8.33
590 631.900
705 681.l>67
819 631.888
itSi 632.000
052 632.167
169 632.338
2^4 682.500
899 632.667
513 632.833
628 638.000
748 683.167
03*
M. ;
292 898
.5001893
708:198
917
129
074 708.704,a53.P98 683
2021708
829! 704
,4571704
984
712
898,
898,
.383 894
542 ;194
998
145
292
795
796
796
4.36 '796
57<J?J(i
722 796
75)7
797
797
797
86(i
018
160
308
750
9.58
.167
,375
fm
792
(K)0
.208
417
625
a38
,042
,25(J
,458
.667
,875
,088
292
,.5a)
,708
440
.590
.rm
.880
.027
.170
.314
457
.flOOV
.7471
797
98
•98
798
798
98
99
799.
799
799
9r«
125
839
97(J
100
228
394
894,
:m.
894.
891.
894.
895.
895.
:it»5,
8i»5,
395,
895,
895,
896,
.31W
896,
896,
896
8*K},
704
704
704
705
705
705
a59 709
,488 709
610
738
,865
,996
,126
254
881
.909
636
767
898
025
152
280
407
,^38
6(i9
796
889 858,
074'3'V4
259 35*
444 3.V4
(>.30 894
8l5,&-)4,
000 351
1«)8.54
,870 354,
I
.5.56 355
.741 .3.V)
,926.355
.111,355
.290'a55,
.481;355
.667.395,
9?2i688
087,633
202 6.38
817 6.34
481 6:J4
546 6:14
664,6.34
6.34
896 6.34
383
900
667
833< 23
000 24
O
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
'705,
706,
706,
70«
706
706.8.52-8.55
707
707
Oil 6.35
126 6.35
240 6:i5,
8.55 6.35,
.037
.222
.39(J.924
.35)7.051
3:18:197.178
,542:197.809
7.50:197.440
958.397.-567
167 8t)7.««5
707,
707.
707
707,
708
708,
708,
708,
708,
709,
355
396
407.3.56
.593'356
778 .3.56
96:1 m)
1 48 :l5<i
.3:i3 35«i
9]'.t:.35<S
704.356
889|:i57
074 .'.357
,470
,987
705
,820
934
049
164
282
.39<)
,914
629
748
8.58
976
1)9:1
208
709 . 2551 8.57 . 828 6-38 . .383 50
6a5
635
636
636,
636
636
6.36
6:16
6,37
<>.37,
637
6.37
6.37,
6:17,
688,
6.38.
167
.3.38
50(»
667
8.38
000
167
:i38
.500
667
833
000
167
.3.38
600
667
a33
000
167
.338
.500
667
838
000
1U7
25
20
27
28
29
30
31
32
33
34
35
30
37
38
39
40
41
42
43
44
45
40
47
48
49
709.444 357. 488, 0.38.. 500 51
7()5» . 680|8:)7 . 55:i|o.38 . 0(57 52
709 .815 357 . 670 6-38 . 883 53
710. 0«X)! 857. 787 6:19 0(M) 54
710. ia5;.3.57. 902 6.39.167 55
ar4r>W.^ .^*iVi\Q .««;\«*. •'^'^'^'^^^Ik
.7«iW .WftV^Q .'8«^«» --^A !i»^^^^
lift
TAaX-B XIV.— ACTOAI, TAHOENTB, ETO.
c
B Curv«.
"mom
6oSm
-a
at ou
04
m
f
w
nfl
"'•"
8
TABLB ZIV.— ACTUAL TAKGENTS, BTO.
6* Onrre.
Tan.
606.980
697.178
697.a64
697.500
697.766
697.94
698.188
696.S84
696.580
698.7'21
698.912
690.106
699.304
699.496
699.686
699.882
600.077
600.378
600.469
600.660
600.851
601.047
601.948
601.434
601.685
601. 8S1
803.O17
608.818
608.408
608.600
608.701
6l>-a.987
608.182
603.878
603.574
603.795
603.066
604.162
604.848
604.544
60».740
604.035
605.131
605.322
605.513
605.709
605.005
606.101
606.297
606.498
600.680
606 884
6t)7.080
607.271
607.462
607.658
607.854
608.060
d08.246i
008.4421
Arc.
066.67
066.04
067.22
067.60
067.78
U68.06
068 88
068.61
068.80
060.17
060.44
069. ra
oro.oo
070.28
070.56
070.88
071.11
071.80
071.67
071.04
072.2V
072.60
072.78
073.06
073.88
078.61
078.80
074.17
074.44
074.72
076.00
075.88
075.66
075.88
076.11
076.39
076.67
076.04
077.22
077.50
077.78
078.06
078.33
078 61
078.80
070.17
070.44
070.72
060.01)
060.28
060.56
OHO. 8:^
081.11
061. 3»
061.67
081.04
082.2-2
082.50
062.78521.
068.061521.
7<> Curve.
Tan.
Aro.
511.781014.
511.0451014
512.100 014.
512.876015.
512.444:016
612.608:015.
512.7721015
512.040!015
513.106
513.272
513.485
513.608
513.771
513.935
514.009!0I'
016
016.
016
016
017.
917,
514.267
514.435
614.608
514.770
514.034
.M5.008
515.266
515.434
515.508
515.761
515.020
516.007
516.265
516.433
616.507
516
616
517
517
517
517
517.
517.
618.
518.
518.
518.
518.
518.
519.
519.
510.
519
519.
.MO.
520.
520.
520
520
520
.'^20
521
.^21
761
020
006
264
43Ti
506
760
028
006
264
431
609
767
0:^1
095
268
431
590
76«
034
017,
018
918
018
018
010
010
919
919
920.
980
980.
990.
920.
921.
921.
921.
9-21.
922.
922.
922.
922.
923.
923.
928.
923.
924.
924.
924.
924.
\m.
925.
925.
925.
925.
102 926
270 020
.438 926
.60-.' 92(t
.766 927
9:)4,927
.101|927
.269 027
437/988
605/088
886
.684
762
000
238
476
.714
952
.190
.489
667
.905
.143
.381
.619
.85'
.095
.333
.571
.810
.048
.286
.584
.762
.000
.888
.476
.714
.968
190
429
667
906
143
381
619
857
095
3:^
571
810
048
28(i
524
702
000
238
476
714
968
.190
.429
.667
.905
.143
.381
.619
.857
095
333
8° Carve.
Tan.
447
448
448.
448.
448.
448
448.
448.
449.
449.
449.
449.
449
449
449
450
450
460
450.
450
450
450.
451.
451.
451
451.
451.
451.
,894
038
,181
Arc.
9° Carve.
Tan.
800
900.
800.
328:800
475 800
618
762
909
055
199
801
801
801
801
801
000 398.
208 398.
417398.
625 398
833 398
0421398.
250I39S
812 802.
489 802
636 802
,779 802
.923 802
.070 803
.217 803
364 803
,511 'Has.
664 803.
458
(567
875
083
292
399.
399
399.
399.
399.
211
338
46(5
596
727
854
982
113
243
371
Arc.
711.
711.
711.
711.
711,
712
712
712
712
712.
500|399.
708 399
797
944
091
804
804
804
234|804
378 805
525 805
6W,805
819 805
45
451
2.
452
452
452.
452.
452.
452.
4.53.
453.
453.
453.
453.
453.
454.
154.
454.
454.
454.
454.
4.54.
455.
455.
4.55.
4.^5.
455.
455.
455.
456.
456.
466.
456.
.966
.109
252
399
546
693
840
983
127
274
421
668
715
861
006
158
895
442
589
786
888
030
177
324
471
614
757
904
051
198
805.
806.
806.
806.
806.
806.
807.
807.
807.
807.
807.
608.
808
808.
808.
808,
809.
809
809
809.
810.
810.
917
125
383
.542
750
058
167
375
583
792
000
208
417
625
833
042
250
458
667
876
083
292
500
708
917
125
333
.542
50
958
167
376
.588
792
000
208
810.417
810.625
811.2.50
ftll .Wh
400
400
400
400
400,
400.
400
400.
401.
401.
401.
401.
401.
401.
401.
401.
402.
402.
402.
402.
402.
402.
402.
402.
403.
4U3.
403.
403.
4a3.
403.
403.
404.
404.
4(U.
404.
404.
498 712
629 713.
759 713
887713
014 713.
145 713.
276 714,
406 714.
537 714.
664.714.
792 714.
92J715.
063 715.
181 715.
308 715.
439715.
509,715.
700 710.
716.
716.
831
958
085 716
216716
347i717
477-717
608,717,
7a5 717,
863 717
994717.
1241718.
255 718.
385
516
647
774
902
032
163
294
424
555
404.686
404.816
8l0.K38 4ai.947
811.042 405.074
40). 202
811.4.58 405.3.32
811.667 405.463
718.
718
718,
719,
719.
719
719.
719.
720.
720,
111
296
481
667
852
037
222
407
593
778
963
148
.333
.519
.704
.889
.074
.2.59
.444
.630
,815
,000
.185
370
,55K
741
926
111
296
481
667
852
037
222
407
593
778
963
148
833
519
704
889
074
259
444
630
815
000
185
100 Curve.
Tan.
358.
358.
:-i58.
358.
:J68.
:159,
:m.
369.
a59.
359.
a59.
359.
359
359.
3(50.
360.
360.
3(50.
360.
360.
:M0.
am.
361.
361.
361.
361.
361.
361.
361.
361.
361.
362.
362.
362.
362,
362.
362.
362.
362.
363.
363.
363.
3G3.
363.
363.
3(53
363.
3(53.
:^64
364.
482
596
711
829
946
061
.176
.293
.411
.526
,640
.758
876
990
.105
228
,340
458
576
690
,806
923
040
155
270
:«7
505
623
740
855
97t)
087
205
322
440
555
670
787
905
022
140
258
375
4{)0
605
722
K40
957
075
193
Arc.
640.
640.
640.
640.
640.
640.
641.
641.
641.
641.
641.
641.
642.
642.
648.
642.
642.
642.
643.
643.
643.
643.
643.
643.
644.
644.
644
644.
644.
644.
000
167
333
500
667
838
000
167
888
600
667
838
000
167
833
500
667
833
000
167
383
500
667
838
000
167
333
500
667
833
64<
720.370 364.810
?20 556 .364.428
720 741 364.546
?20.92('> 364.660
7^21.111 364.775
721.296 364.893
X'l\ .A!i»v\\W«S .^VJ^SA^ .'?®5^^bfe
645.000
645.167
(545.333
645.500
645.667
645.833
646.000
646.167
646.333
646.500
646.667
646.838
647.000
647.167
647.333
647.500
847.667
647.833
648.000
648.167
648 3:^
648 500
648.(567
648.833
649.0(k>
649 167
M.
"o"
1
2
3
4
6
6
7
8
9
10
11
18
IS
14
16
16
17
18
le
20
ei
92
28
84
86
»«
87
88
89
30
81
38
33
34
36
36
37
38
30
40
41
48
43
44
46
46
47
48
49
60
61
68
63
64
65
Asx^ .?»wri\ .^"W* As«yjA\^«^s^;:v
845 812".0^40r> i'T^W -««5^J*5^5J^^
4921812 .«»2\405 .«&\'«a .^'•\'?af«> .^R^^^^^
1'3^^
— 40TUAI, TANeENTa, ETC.
I I'C
.,„.
a.o
.™
3»C
.™.
4.C
«„e.
».c
„„.
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^A^
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Are
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Tau
a)Mi8a25ooo
Bie-»
161J0I
760 Ml
iaoooo
■ifii w
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1300 s
m 0=
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lei ft
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"10?31
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sa« K
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168 e
1818 J
30 966
1301 00
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{S0H33
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saass
JU4S(
162-80
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1302 8.1
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6518 8-
1831 Ci
3K3 3»
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915 86!
1839 1
39 BIO
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1654 3*
canoo
i«.l B.'
1630 IJ>
iwioo
«hij4;
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mi-80
1 381
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IJHW
3861 67
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1824 88
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1308 6
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12K0S
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!18 8«
1883 f
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180-00
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-1.430
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I'ffiBt
119 l-B
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130 6"
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6S10 00
lSWi6
1 000
a«*5
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1308 00
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930 066
-^8 165
1808 SJ
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1635 S
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3 50
1636 15
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l\K.^
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■M940
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5'-4 1
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36X6 Hi
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1810 33
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BaS.'J OU
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1^41(1
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1% 11
B3 011
1089 68
T8 4B1
16W B.
u.waou
3>so -CII i
IBM 01
~s8-a*
1818 (r
' 1 605
18 98
< sm
1840 81
'3»*ni
watt 05
6565 00
181BI
1 193
1611 SQ
3B«
131100
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6,566 8
1 486
W9»n.i
1314 10
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1 'li Pirn's
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IM 41 BST 4S8 1611 W
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1 '^ ''.S ? IS'' %
4 41II3I r
la '*S|''"* M
TABLE XIT.— ACTUAI, TAKGKKTfl, KTC;
SOS H33
W 11138 8 4.W SB 8 U -08 409
iti wW 0(8 se me o 4oe
-S. SIB )« 'W
TABLE XIT.— 4CTUA1.
TABI.B XIT.— ACTCAI. TASOKNTS, BIC.
TABLB XIT —ACTUAL TANGBKTl ETC
sr
1 Curve
8 Cu V
4 C
S Curve
Tan 1 Ac
Tan
Ar«
Jl_
A
Tm An-
Ta Arc
i^olTl^woo
BSS^
Tg^aiTsoo
18M Bfl
aaaova
948 6" IB a 4.
18 940
810 33
18B7 44
Msim
120.1 0!
2ii34 4
59 181
1 13-» B3 fl-00 00
1898 04
1 ■05 4,1
-flB42-
311 0I>
isesos
18M* saM 1
l2Ub iS 236 1
9i'> "slie;;; »
759 90.1
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isiwMSissoo
1 <oa Q. S^H 6
01M4J
7IS800 80 II B
1BO0 4 MN,Si
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00 J85
14,33
950 S-&\iiS'S 3;
00 6.0
3t 8
Isol m^ S
«0 8B«
lolra04S7fl IBB
1^ 35-238 89
951 Bifi-Dl
01,0
343 33
1.1 3805 58 ria 33
i90:j 96 -taw 1
■B8BB Jan 4.
ii^
1^ 38oa -80 «oo
1903 46 8380 00
951 (rg lOHO 01
844 00
lOOl 06 ilBO M
96 1% 1S30 4
01 1-20
14 (TOO IBB -I ]n i;, tidi 1 WM „1L 11
OL
6 311
MS 00
IB Wn 69C b— « A,
-B 5.51
17 301 K 1 i-,4 -8
B -9-
IS (Kl-1 01 t 1 l( .24d »
B3U!1J
310 UO
BJ "-3
346 34
iSIB41
n J. 1 J
2844 44
™J.«»
B3B14
340 6
^45 01
bJ-H
14 OO
9>5 183 1684 58
B 40 00 1910 68 33 00 1-^18
-^6B
34BO0
»-Jl 6)1 lull ~(M Jsjll-I
■^ U
704 IS
848 «
Mfflie n-cliii 1- 1 1 1 ,
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8480
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IW a»j 1688 S5
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an 994 1687 08
KOSl
8496
lo 38as lA -fli 1
TKS est
tl^UMb 1 , 1 > ^W19R M
flOltti
300 33
i« «W0 81
111 4 1 K9- 1B88 33
60 403
aSOB"
issmm
[916 If 19 168H 5
~68 644
t4's983ai
60 881
851 S3
1 58 33
"6- \Ji
331 87
l-BOOO
6-3IK
1918 ^i J w 40111690 4
•vav
163*
1919 10 3<M ,1 14, 1 44 1 ) Ct 1600 83
-r &1
atue
39 'was a
tB19 UiJS. J)1-9&._M0 J960 003 18911B
08 089
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66 6-
1920^1 1iS3 33 1'SO 29 " 56960 BOs'lSBl fi
68 3^
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69 5)4
355 00
46 tel IJ3
^9 84
135.5 83
47 9nia J II 424
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1695 00
1)281
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49S85I586-81. ,._ [«9, ^ , -^i . , . J ,|»«. 02«
1693 4«
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1306 33
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imisss
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HI 3853 -BBTBOO
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1696 25
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:1B8 6T
n" A * \M« s
"" 4M
9 (
i -Sa
,'i,
n
-^iK
\'»tt!»l
TABLR XIT.— ACTtlAl. TAUOWITfl, KTC
..0
.™ 1 , 0„„
« 4«rv. 10 C.„.
"•
Tan
a™ T«n Are
ran Apl
r» Arc Ta
An.
eSTsw
-mt-iiumwTL
474 4'!)I^~S004 1 8M 17144 i~9~a
10 UOI
aa 54fl
1 467B,ea 084 iW 44 6.108988-
M -te
1- sa34a« 957 SI!
4 4 -saJBS 9 4^ 064 44 SIS S 9 BM
1 03s;
in so M2 SOB 99 Bb
fiSi 1«
1117-804! BieSSOW
475 a» H s m
tosa
1118 06 ML. II»j()&8S«
4 5 1 ^h,
(aaM4
I11B1SM9 l»IW8G7]
458L5h 1
i?oni
i«~«
lll8S16ia»lBa8 810
475 4 11 M
«8!»+i
lll8ffilM34«)flM(HI
46 OBB H
. I 33:
SM lid
BU84
niBUMsa ^masM
t a a»
H. s. IM 4h -
S80 919
an 86
10
IS4M7
lllUTSSWQBSTOK B-
830 79 4J3 --OH
B71 83;
IM 4t
iisoeoM! 13 iwioooo
4 b &«
81 0004 HO-J
JB 6B
181 180
uMSSMJvlmm
4 B8-U
•MO 1W4SJ5W
88 J80
4 h B3U 84( 41 4 16-0
4 US
Kl 401 6 S-13
w aso
"f ^EOEb^
4 « B« MO Bl, 4 i 6W
4 2^
16
la. BAO
1 831 840 88.1 4^ 93
«1 w! 6^ 80
Ml IN
4 SM
1 1"! 07 546 IBB
Ml 4J9
4 -8
<M ^ 6 1001
MB IM
lUI w ^ aBi
UBl 687
47aU
841 4B8
mm
4 908
3«i0ua
B-3 1Br
le
1 " aw B3S
061 900
1~4S1
8«l SB
8-SB33
w
Il^BOMS 'OS
sex 14S
1.4 ear
_48a3!
%;.E44
673 BOO
11' 8M5B~
m-».
4^'*
fern
B3B8
ass e&
um x\m o4»
iS 4BB
873 836
IIJK S3 540 2llt
4 BOSi
48 BBS
SB^BOK
074 000
lias Bi Bje ?9»
mo«>
84^ -Ot
4JS 141
74»0"4
882 i6
6 4 16.
im 98 616 ^
mm
4B^
B4S01
4« re
749 »9
S,B46
143*
ao
er -B
11^ 1 B46 i
oeaBi
1-8 486
4i5 4I0
4BM«
im 44'm6 909
9«»B10
84.) S»
4»Ma
883 08-
BSS 1«
lU4 7i|64 081
M4MH
4-8 8-
843 641
t«B~
48 BIB
883 SD8
b4883
SB
638 358
.■95 Jm i^^
064 186
84i -3(
4SSBI|
W3B-a
IS&iBO
1 i5 I18,B4 4 5
1164 BU
MB "BO
I a.-. U B47 59
0« IS
4-9 23.
814 16
4.6 0-i
60 371.
MB HI
1 SS 8S'fi4 69
aesftw
814 3-1
SOBS.
83 691
B-^ SOO
Misa
UM 11 &4 Ml
e6S2«
4-9 M
UBSflS
1 se W.MB lid
965 4 B
814 -9- 4S6 4S(
B»GSS
1 SB (r S4B J85
S«« 14
SM OBI B 6 OIK
SSBTSS
1 SB 94 MS 4S
BBS B5J
49B9!!
84r soBJie 41
B129.
3M 1 i'o-6 a
J7
MS »4
1 4- » ' -18 «»
9«« IM
4S0 14,
M0 18B
lir JOiMB 801
OBB 4J9
Bin aes
I187-8MH9-B
afl8 6B
180 448
S41 mU m
■il B.«
884 SJk. e *
40
\'
L
I!-^
T^LlsIL^ Bi'ujJ^isiV -1.
l'»
W 'i'^
11 1 4 1^ 1 1 .4
\
flji WJ
1 1^^
641 Kl
Hi -,
■U
m.&
!"t|:J":i-| x.\-
^Irl-h M«!-I^Hi
TABtB XrV.— ACTHAI,
1
,c.
. « rnr.
~
Tw.
Art.
Ta 1 A
1
Bii n.
HI) 1
hTw-
Tm
i^wrs^
-•0 48—^^
HI "ealTa "m"56«
WB neo eSuDoo
as «
M OOBO-
>(W W9 B to
Htr osoaw B-
s; XD
■n
r 30 BB0 88S
W£ U S
K 680 00
flUU fl-
bWl HSS
bs oou
»ut
»< too
ns «
lO
«
1
^^
•w-s w 00
4it. oKi] m Bin
is« 004 ns, MT
43^ ISn 6« CM
3ft) {i»l 08^ 8S3
lis ra' SB m
aw 14BF»S«W
6te a-
iflO ■BB 683 16-
Mt 45
n- B!>3 SS3
1 w
wa WO
»»»(«!
1 ^ij J
mfxr
xl
MJ JBl
Hy 4^0
SMIfl"
M9 6?l
«M«W
MU 8T(
aKi m
oBoatr
n4i
|»84«W
SD
es B9f|ii4i
6.M SoJ'll - H
i
c"m ni*iir ^ ss H IN
H ( f « a 1
j'.
u; 38-j H 1 ill r -
, |4 ly-
J r 1 r nr ini rsb iw6 oe-
80
R- RBS
4 k
mifii'
114D
6H5fiB
1 4 "
)
BM -BS
654 !>7a
am 178
1 4H
«B»<H
1 4H
* 1
ORB-Nf
1 4S
/ lUe 19611411 41
4 40 4~'4B0
^ 1" -A A^ ■■
j^
TABLE Xir. — ACTUAL TANGENTS, ETC.
69*
M.
O
1
2
3
4
5
7
8
9
10
11
1'^
13
14
15
16
17
18
19
SO
21
22
S3
24.
S5
SO
S7
S8
S0
30
31
3S
33
34
35
30
37
38
39
40
41
4S
43
44
45
46
47
48
49
1° Carve.
Tan.
8987.87
3949. 11
3940 84
3941.57
894-i.80
8944.03
8945.27
3946.50
8947 73
8948.93
8950
39r)l,
395i,
3953.
3955.
3951).
3957.
395.S.
8959.
3961.
3962.
3903.
3904.
8900.
8iH)7,
3908.
396'.».
3971 .
397;*.
8973.
8974.
3970.
3977.
8978.
8979.
8980.
3982.
3983.
8984.
8985.
3987.
3988.
3989.
3990.
8992.
3993.
3994.
8995.
3997.
8998.
14
8r
00
88
00
29
53
70
99
2i
45
0'.)
92
1")
H<
01
85
OS
31
54
77
03
29
53
70
99
22
45
09
92
15
88
61
87
13
37
60
8:^
06
29
Arc.
6900.00
6901.67
0903.88
6{H)5.00
6906.67
6908.33
6910.00
0911.07
0913.33
0915.00
6916
6918.
0920.
0921.
09 J3.
0925.
0920.
092S.
09:i0.
0931 .
0933.
0935.
0»;iO.
09:iS.
0910.
OtUI.
0943.
0iJ45.
0940.
0948.
0950.
o951 .
0953.
0955.
0950.
0958.
6960.
6961.
696:^.
0905.
0966.
6968.
0970.
0971.
6973.
0975.
0970.
0978,
6980,
6981,
67
3:^
00
67
33
00
07
33
00
07
as
00
07
33
00
07
33
00
o;
33
00
07
33
00
07
00
07
33
00
67
33
00
67
33
00
67
a3
00
67
a® Carve.
Tan. Arc.
1969.01
1969.68
1970.24
1970 86
1971.47
1972.09
1972.70
1973.32
1973.94
1974.54
1975.
1975.
1970,
1970.
1977.
1978.
1978.
1979.
I9S0.
1980.
1981.
1981.
1982,
19S3.
1983.
19.S4
1985,
1985.
1986.
1986.
1987.
19.S8.
1988.
1989.
1989.
1990
1991 .
1991.
1992.
1993.
1993.
1994
1994
19U5,
19U6,
1996,
1997
1997,
1998
1999
14
76
34S0.00
8450.83
8451.67
3452.60
34.53.88
3454. IT
3455.00
3455.8^1
3456.07
3457.50
34.58.
3459,
37 3460.
99 3460
603401.
22 3402.
84:3403.
45
07
08
3)
92
3404
3405
3465
3466.
<467.
.53 3408.
. 15^3409.
70i34rO.
.38!3470.
.(KJ.U7I.
U72
3473
01
23
84
46
09
72
84
95
57
18
80
42
03
a5 34S3
20 3484.
88 34H.-J.
51 3485.
143480.
70; 3 487.
37 34S8
99 3489.
00i3490.
22:«90,
88
17
00
8.3
67
50
33
17
0.1
8:i
67
50
3;3
17
OJ
83
67
50
33
50 3999.52 6983.33 1999.84 3491 .
5 1 4000 . 76 6985 . 00 2000 . 45 34»2 .
5S 4001 99 0980.0:2001.07 3493.
53 4003 . 25 098S . 33 20«)1 . 7l) 349 4 .
54 4004.51 0990.00 2002. :« 3495.
, 55 14005.74 6991. 67|2i)02. 94 3495.
£';ff /4(m.9r 699S.3lj'J00:iMmm.
J?J/fS^-^'r^^^- OOI'^U. 18:i497.
sS U^iiSS^- ^^'-^OOi . 79 3498 .
3474.1;
3475.00
3475.83
3470 07
3477.50
3478.33
3479.17
U^O.OO
3480.83
3481.07
3482.50
33
17
00
8:3
50
33
1
00
83
6
50
a3
1
00
83
67
50
88
17
3<> Carve.
Tan.
1312.76
1318.17
1818.58
1313.99
1314.40
1314.811
1315.22
1315.03
1316.05
1816.45
Are.
1316.
1817.
1317.
1818.
1318.
1318.
1319.
1319.
1320.
1320.
1320.
1321.
1321.
1322:
1322.
1323
1323.
1323.
324
13i4.
1325.
1325.
1325.
13-20.
1320.
1327.
1327.
1327.
1328.
1828.
1329.
1329.
1330.
I33J.
133J.
l:Wl
1331,
133-'
1332
1332
13.33
1333
13:^4
1334
1334
1335
13:^0
188T
85
20
67
OS
49
90
31
72
13
54
95
30
78
19
00
01
42
83
24
65
06
48
90
31
72
13
54
95
37
78
19
60
01
43
85
20
,07
08
,49
90
.31
.72
2305
2300,
2800.
2307.
•2.307.
2308.
2808.
2309.
•2310.
•«10.
•2311.
mi
2313
2:^13
•i3l4
2315
.'315
2810
13
.55
9;
38
80
8300.00
2300.56
2801.11
2301.67
2;«2.22
2802.78
2308.83
2303.89
2304.44
2805.00
4" Carve.
Tan. I Arc.
,964.059
9S4.907
985.275
985.583
985.891
986.199
9H6.507
986.815
987.1-28
987.424
2316.
•»317.
2317.
•2318.
-2318.
•2319.
•23-W.
•,»3i0.
2:«1 .
•2821.
•2322.
23-23.
2.323.
2324.
2325.
•2:U5.
•23-20,
23-20
2827.
56
11
07
2i
78
33
89
44
00
50
,11
07
,78
M
,89
44
.00
.50
,11
,67
•22
,78
33
,89
44
00
56
11
67
22
78
33
89
44
00
56
11
67
22
•2328.83
•2:i28.89
•23-29.44
•23:iO.OO
•2:^:10.56
•2331.11
987,
988.
988.
988.
mi
989,
989.
989.
990.
990.
990.
991.
991
991
9.12
992
992
S)92
993
9J8
993.
994.
994.
994.
995.
995.
995.
990.
990.
996.
996.
997.
997.
997,
998
998,
998
9i>9
999
999
725
038
.341
.649
.9.5;
.265
.573
.881
,189
.497
805
113
421
730
0;w
340
054
902
•270
,578
,880
,201
MO
,824
132
.440
.748
.0.-16
.304
.672
.980
.288
.590
912
227
535
843
151
4.59
707
1725.00
1?25,42
1725
1726
1726
1727
1727
1727
1728.33
1728.76
.83
.25
.67
.Ort
..%
.92
2327.78 1000.07
1000.38
1000 09
1001
1001
1001
.01
3
1729.
1729.
1730.
1730:
1780.
1731.
1731.
17.32.
17.32.
1732.
17.3:^.
1733.
1734.
1734.
1735.
1735.
1735.
1730.
1780.
1737.
1737.
1737.
I73S.
173S.
1739.
l?39.
1740.
1740.
1740.
1741.
1741.
1742.
1742.
1742.
1743.
1743.
1744.
1744
1745
1745
17
58
00
42
83
25
07
08
50
92
33
75
17
58
00
42
83
25
07
08
50
92
3:^
75
17
58
00
42
25
67
08
50
92
33
75
17
.58
00
,42
5<> Carve.
Tan.
787.815
788.062
788.808
788.556
788.801
789.048
789.294
784.540
789.787
790.U-28
Arc.
,1880.00
1880.83
! 1380.67
1881.00
11.381.83
11881.67
il882.00
1882.83
1382.67
1888.00
79'>.
790.
i90.
791.
791.
791.
791.
791.
792.
792.
268 1&<«.88
515; 1383.07
1384.00
1384.33
1384.67
1385.00
l:iK5.83
1885.67
1886.00
1386.83
761
008
254
.501
747
994
240
486
792
792
793.
793,
793.
793.
.94.
794.
794.
794.
733
979
2-26
472
719
965
212
4.58
704
951
795.197
795.4.50
795. 7 J2
795.948
790.195
796.441
790.688
796.934
797. 180
797.427
797.673
797.920,
7JI8.166;
:98.418
798.671
798.917i
799.163
799.410
799.656
799.908
1386.67
1387.00
1387.38
l:«7.67
1388.00
1888. ;«
1888.67
1389.00
1889.83
1389.07
1890.00
1390.33
1890.67
1391.00
1391. .38
1891.67
1892.00
1.392.33
1.39-2.67
1398.00
1393.38
1.393.67
1894.00
1394.88
1894.67
1395.00
1.395.33
1895.67
1896.00
1896.a3
1745. as 800.1491896.67
1746.25 800 896 1897.00
1746.67 800.642 1897. as
1747.(J8«00 894 1897.67
1747.5<» 801.147 1898.00
63 1747. i42 801 .898 1898.88
_,. ,HI01 .94 1748. ai 801 68l» I39S.67
2 \ \2:%l . tt7\\(»-i .%\\~ \>»> ."^WNV .SftR 1899 . 00
.62 -233-i.4J \CKVi.?55\\';Aa.\';WYi.\'?a vaj^.tj^ \
0412882 .tttwooi^.gtU'i^a .^\%fri m v^y^.y. \
184
—ACTUAL TANOBNTB, BTC.
7° CtirvB.
a= Cnrre.
9° Cnrre.
10" C»rv..
69-
m"
Arc
Tbq I Arc
Tan a™
Tan 1 At
Tun 4re
sx eo!
56^ Was. 714'4Er ej9 HB 500
iT'ffil'^rSfi
SM sso'bsoooo
~o
IM Bl
160^
503 »»9>k!49j KS'tHi. -V»
I3H IJUI 8« «
W 409 6B0 IB
u 01
BOJ 4'' B8U IB. 4^ 1(8 IN) ei
194 5BJB90 33;
m awl
5UJ4 IBS0 4'94Ba0(l l»63 1 1
iw wi a isv
6I.J UIX WM WT 4W 24 IBS l»l
1194 969UB0
5ei -H urn MM 493 H99 WS 54
43B WWl 6 SW3
394 9O169I S33
et, HSU
MM 9M DH- 143 IWJ BMWil 5U
I.SS 806 B ~t
B95 OiaoOMIUf
mou
IISI W
6W I -O HtT Idl 493 (*i aw
196 149.BB1 16-
0.W «0 IIM 4;
6B4 STO BS- BIH 493 SB KlU IB
•m ■^i\m ix
439 "ISj 60 W
«
ti J11 3L IsiH -a-
439 If 1 1
IdBO 1
iWffitoHB^a*
I 1 91 BHfi„41
H t, -HI jfl4 BS.1|8(ir 8_
440 IS. <,» 44 U- X M H 1 1
ttij Hj J u w". oir
MI5S33
440 109 Bl a H, V b
J9S*4I
»«<)»»
440 SOB «9 815 »9fl a- B9!. 83S
(KW 'BJ n tx
1/i "yooix
495 SM
wwaio
440 443 7) 000 tnO MK Btti OUO
'*'^|"^ *
49SG4II
WB46S
440 JWO "V ISE IM «33 UBS 16-
5«w 4 olaao j-B
49» «
nnr nr
" " -w f m-iSi
so
Sin
-:«d'W8e(» 14
UU B93 50"
uei 1 H
9M> «,199Ua5.
'MB OSh'sOI IDA
-leil 160
" 6MJ sa-i
oh' r>-
W 114 991 4«
1 094 noo
w t.
11 .1 S4
IB -Jl
Ml MB
m »»
1 5 i
5« 4M
Ml von
496 0^
mi4i
49H T
mr M8
115 T
atrsis
WSBdl
496 9%
sisssa
iu Bn-1 arj
filCSM
1168 l»
60-B94
9»i6l9
49-090
WSM^
—5 IB
49" Bl.
MB'^
4«0S
"sas
^ esoLono
1I5M6
SOHSSI
m yn
IISS96H
44^ 2r
IIIH liBbl 16-
Tit )1 9T. ilM[49 rfX
18S IWW 501
M)9SB3
3M 4-9 B5 «6
19 1" 1 )4(i,49S oa.
IBS TO m Sa3
9 -i 9UI JSfl 4)W 1 U
44-'915
MB-^BBOOOO
W4 dO llw ^
:>e9 41 994 ia4'4IIS S^
H Jlf
(4105!,
3as 849,690 10
flb4 4i lla(l^e
09 68 994 fr 4BB 4W
3BS 9 4 Be 333
609 -88 095 I(Xj,19M WW
141 aa
-8 888
I'ra 0% BBO 60(
«i m urn V
509 HO ^ tsR 4g» -m
TO 831
141 46S
—4 0-4
B9B->lBSBe BO
4(1
MS «4 j'bI " 1 \
(KB aw m
4K
1 6J S S ■ilH S T 14-] 1 IN i , 1 l4fl
m B8U
iflji 1 1- -ifl Bo'ooosi r 9 444840-s^S8^nn4^1|BM<13^ 60
1 M H.*l HS 500 495 S fl IJ5I444 9~")'^0 111 400 5t+2 69W JlO 51
M or
liw 4 ,m fisvuM ■- . -J B'B'cw aa
ttr 71B
1165 > 4 IDH-, 50. W « K|UH9 0(« 54
W ftiS
iitWJh ^J^ll.hlt. Ml iIh9i sti
^
M» )!»
1105 51 -I'lii IIH-, ^*» * ■»*
IJffiM 9iUm -U ■Wl 4-- >'«*^
i'^
TABLE XIT. — ACTUAIt TUIOENTB, BTC,
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w
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93
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—
TJLBLK XIV.— ACTUAL TANOBNTB, BTa
7f
I" COTT..
a= c
ur...
3° Cnrrs.
4^ C.„.. 1 »• Cur,-
■E»n
Afc
^n 1 Are
Tan
Are
Tan 1 Aro 1 Tan
Arc,
mTTm
r«oo5«58r|gfsr«>
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10TGUlSr«lB63^
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i4aB-e
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148a!si
1440 8:
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1480.67
£488X1
1UH0 5I
IKl JS8M6
1481,00
UA81
msaa
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1851 « 8M 8H
13*114
ma**
186^ <M 808 09C
1481 !s7
4ai 1:
1441 a
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186-90 865 350
148^. SO
185. 9:1 865 611
14eU,33
4d^OI
4nss3L&i iis-w B
I46S.87
41 ft)"llll"3TI-6u
1443 28
lowas
1853 ^860 mH
1488,00
1 H loss
IMiSe
1483. M
iira-i
1063 Jl
w-iat
1033 &3
1855 00869 HO 1484!oa
144SC
10S3BeiB35 4JB87 1ti4ll4S1.33
1084 ltt,l8&'t 83 86-44 11484.87
JI-SOO
l(B4MI8Sfla,8b 111485,00
ijui iwss^issa
1448 !«
M Bsa
084S5ll8.a8-Ha-9-B'l48S.S3
muiiT
4«aHa<!i ()uia"n 1
^4 6 11
UHS IBllSS <l8SBt< J3S1485.GT
mi IB
4» 00 .1-0 a 8-ia cm
144 2)
0U5|I|» 50 8814 5011483,00
IB
1IUS4
4S1 6 «ri SiriG H9
■■4— «
losseaass wafls ao
1480.89
iMS-^
4S3^i 1 1 J.I.'.
1488,8;
4aiBi»
4.i 1 1 1 1 4BI81* 5 868JSI
1487. DO
IMS 40
4 V ■jHS.,9 1 SUBSJB
I4S7.ta
134 -«
■1 1 14 1)139 WBeS DOS
1487.87
i3iao3
41 4
1BC0 00 8TIO".
1488 00
4!UU3o
111 m
1800 42 8-0 380 1488.33 1
«o* ittS " " '"'"''
ar
isuas
l-MU Mj
1861 ^i8 8^ itlnioD
as
laatao
WBB-
am at
aTjBSB
■Mt a
1861 6 1871 1^
1489. a»
tauw
418 «l
ii~8e
JiTMl-
148! O.
~t» -»
10!» 11.
1883 08 871 a»1
1489, K
30
UetM
7«0(I)
B-aiss
<rr»<»
USStI
*«1S.1
1089 46
186^80^654
1490.00
*as8a
?*Blffi
»raui
S-WiSS
145a ao
1089 e
18&.S4 8n 918
ss
isaSAS
M-Ba-
3TM6-
*4«14^
1090 11
1863 33 8-8 188
iiiBota
S-B-M
I4B3-1
«S3W
1000 43
1863-5 8-8 446
1491 !oo
84
43IU J]
468 8-
a_j8ai
1454 a
J48gS6
IO90 8
1861 l-|8-a IW
1491, «S
35
48I13M
«iai«
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1454 08
11)01 on
1864 5e'8^ 9-)
1491,01
36
i»ai»
400 DO
3 uoa
iIWi 0-
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1865 00 8-8 Ka
1499,00
iBUfl n
8-80 83
48 S-J
1091 B
1865 49 8-3 801
191)7 48
a 11 u
.AH e,
loaauB
1499 '67
woaw
18, 00
"11148! 3 SO
lri8 8J
1868 85 8-4 CB-
1493.00
40
■wo u
■leu a-
m 14I3-33 11
14&StM
-4e8M
I09« 4
1868 fl-'B-4 SSI
1498 33
14e3'87
1 1 ■( jOK.
1
1495:00
149i)!87
1490 in
if.1 u ui r4ut UbOhii loaBiiuga ill j 4 a a uos
H98.8S
&0 43M ao
483 83 eifll S tril « l«l BS S«4 14 lOH w irO 98 S 8 IW
1498 87
4Ba0O,19«89 8T4SMl48lflB!MB6aill»8B-lHl KM- 191
1497. HI
ma 1 irai J3i3i46"i3ii95E«iMfl )'ih-i a 8~ «4
1497.83
isKiiitPi I'iui Mr-rrliii*.] m it «mt7i8
1497.67
1 1 1 1 XIH M
1498.09
I4M.S3
■> naoi
1498.(r
-sT-a
1499 90
I ■^%^Mft^^Mft.»l 1
,.im«
»X«.«.\
TABIJl XIT.— ACTUAL TANGEST8, ETC.
TABLB XTT,— AOTDAI, TANOEMTS, KTC.
M
l-C
,„..
»» c
■.™.
a-c
rv«.
4<- Cor»e.
.»c
.r.e.
Tui
4a»»as
"aoooo
i^^la^oo
uisKi
Are
Tan
An.
"tT"
~A^
iriii«a.s
W~«l
ivSToO
ilTO Ol|3 XI *
l4«tllU
iWOK
18-11-
rosaa
1600 38
i»«i
Tsoa*
JIM « 8-51 e
-Wl II
\frhK
141)0 40
i4Be(i8
-1401 SI
^ w|?^ »
14^ u
iH-fl er
iwi ■m
iaii U4'r-M 1
14« 8H
iff -M
18-" OS
S80 80.)
\m e
44M«
TilOUU
V 8i 8 5. on
148S80
.503 3-
MOS T
.» R
1498 5
.joa S5
B81 GDI
e
I4IW4I
6IS0U
J3M81
B-fl Dl
1489 88
i*6 00
IW «
18 8 ■<
B81 m
150SIW
rwsa
18-9 1
88! ESS
1«09 38
4411 OR
no 1
883 4r
1508 r
44U4a
Tsjoon
aw!*'
lAom
2506 (.
103 81
IH80 00
Baa so
1604 on
•aoesa
1880 *i
88 o«
141 10 ua*
1880 HH
1604 8"
1881 Si
isw 00
"l" ^' ws r
w«
1 1 M
1881 8-
BSSSlfl
1606 8.1
n
18(fi08
»4 08U
18
I8«a W
IB
H 1 1
Ml f
^10 u
1 S^
isKSJ
)M6ia
1608 aj
.0
44W0I
1 B8
1883 88
884 889
88G 146
iao~«
«6 41
Nasi
(IS1H84 58
I5U 8
44ja5i
\m,m
iS. W8
1491 ft.
m 4 6
S4S0O
„i6 Jir 5oi4-ei|asi oi
1108 81
41*1''
axa B4 j-a ss i4 8 ou isis ae
1108 84
1896 6
« Uli
443^04
M8l»
^1 tfU8'74 1 14-HG0|Uie 1)
88-2-8
dS
tif^«
BSD on
,,,y, J,, ,' ,
iim*
lBM-»
« Bll
mow
1510 8.
>i
J8S8 83
BWU8I
4440 ^
^1
888 OOt
inn IB
888 8-
18B0O0
889 I4H
4445 li
8<4II 41(1
180}^
8WSS&
isidr
iV
444B a.
1 J „ il B
11 U 81
IBSl £9
889 W»
iBiaoo
4449
1618 S3
1-*W0B
ifti^ir
•< i*ti ati^^ M
I8WM
1614 00
V -0 Bi 1 t 83 14« - J5-J 8H
\fai9i
li H J.
148 lHir^4 4
18U8 33
(SI sn
1614 r
IMl W
14H5 61 M UO
-SOS
_MHI1 1 88 15
1488 08 Sffi !«
18W1*
*r
rsi
^Jfl 6 1 81 1
1 116-
4<ea4
A,*] in-so 00
im S!.
IBBSOC
1618 Oi
*n
44<l]
681 tt
jsojB^nwfs
148 41|>»iri(
188^4^
8!l 8^
7188 1.
,4-rB8L,r 8
m 8^
a> «)n
1118 IT
4I«4 41
111 (Kl
"1
44IW'"
'
'
■»» U~J It
«7 J-l-V 4-i 1
g» VV-S«,T„
-ill
! -a
EWaa
i.i
W 1
I4Q1 Ht
.ihi-.
\1W
^«y,»
to mis'
TABLK IftV,— ACTUAL
I Currs. 7 Carrt 8 Cnrv 9 C
Otf-W 50U,4rt8 1)»8S3Sa3 wo SOB 50 000
I ids l«l4M9 H1«W 'ilfl wo SJl|*^l IS-
r ua i& M nw
"x:,
.i. u.
Mao MM
sa (187
ma
TABLE XIV.— ACTUAL TANGENTS, ETC.
76*
M.
~0
1
2
3
4
5
6
7
8
9
10
11
la
13
14
15
16
17
18
19
20
HI
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
52
53
1* Carve.
Tan. Arc
4476.52 7600
4477.84 7601,
4479.15 7603.
4480.50 7605.
4481.85 7606,
4483.19 7608
4484.54 7610.
4485.89 7611.
4487.23:7613.
4488.58 7615
4489,
4491
4492,
4493.
4495,
4496.
4498,
4499
4500.
4502.
4503.
4504.
4506.
4507.
4508.
4510.
4511.
4512.
4514.
4515.
4516.
4518.
4519.
4520.
4522.
4523.
4524.
4526.
4527.
4529.
4530.
4531.
4533.
4534.
4535
45:^7.
i5m.
♦.t39.
4541.
4542.
93
27
62
97
31
m
00
35
70
04
89
74
08
43
78
12
47
82
16
54
91
26
61
95
30
64
99
34
68
06
43
78
13
47
82
20
67
92
26
61
4546.71
4548.05
7616
7618,
7620
7621,
7623,
7625
7626,
7628,
7680,
7631.
7633
7635
7636
7688.
7640.
7641,
7643.
7645.
7646.
7648.
7650,
7651,
7653
7655.
7656
7658,
7660.
7661
7663,
7665,
7666
7668,
7670
7671
7673
7675
7676
7678
7680
7681
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
67
33
00
.67
.33
.00
.67
.33
.00
.67
33
00
67
50 4543.96 7683.33 2272.06 3841.
51 4545.33 7685.00 2272.75 3842.
"^ -7686.67 2273.44 3843.
7688.33 2274.113844.
.67
.50
34 J£i9."40j769o!00 S74!78 3845.00
/_.._. j-/22r5.4r 384.5.83
.67
..5(1
,83
2° Carre.
Tan.
2238
2239
22.39
2240
2241
2241,
^42
2243
2243
2244
2245,
2245
2246
2247,
2247.
2248.
2249.
2249.
22.T0.
2251.
22.51.
2252.
2253.
2253.
2si54.
.34
.00
66
.33
.01
.68
Arc.
3800
3800,
3801,
3802,
3803,
3804,
35 3805.
03 3805.
70;3806.
37 8807.
89
06
74
41
08
76
43
10
06 3808,
72 3809,
3810.
3810,
3811,
3812
asi3.
3814,
3815.
3815.
00
83
67
.50
3:^
17
00
83
67
60
83
17
00
83
67
50
33
17
00
83
2255.
2256.
2257.
2257.
2258.
2259.
2259.
2260.
2261.
2d6l.
2262,
2263.
2263.
2264.
2265.
2265.
2266.
3267,
2267.
2-268,
•2269
2270
2270
2271
78 3816.67
4513817.50
33
17
00
83
,67
,50
12
80
47
14
82
49
16
85
3818.
3819.
3820,
;i820.
im\ .
3822.
3823.
3824,
54
21
89
56
23
91
58
25
92
61
30
97
65
32
99
68
37
04
71
3825.
3825.
3826.
3827.
3828.
:«29.
3.S30.
3830.
3831.
3832.
3833.
3834,
:«35,
3835,
3836
3837,
3888
3889
3840
3840
33
17
00
Sd
67
50
3:3
17
00
83
67
50
33
17
00
83
67
50
33
17
,00
,83
30 Curve.
Tan.
1492,
1492,
1493,
1493.
1494.
1494.
1495.
1495,
1495,
1496,
1496.
1497.
1497.
1498.
1498.
1499.
1499.
1499.
1500.
1500.
1501.
1501.
1502.
1502.
1503
1.503.
isas.
1.504.
1504.
1505.
1.505.
1506.
1506.
1507.
1507.
1.T08.
1.508.
1508,
1509.
1509.
1.510.
1510.
1511,
1.511
1512
1512
1.513
1.513
1513
1514
Arc.
33 2533
77
21
65
10
55
00
45
90
85
80
24
69
14
59
04
49
94
39
84
28
73
18
63
08
53
98
43
88
33
79
24
69
14
59
04
49
93
38
84
30
76
20
65
10
55
01
46
91
36
2533
2534
2535
2535
2536
2536
2537
2587
2638
2538
2589
2540
2540,
2541,
2541.
2542,
2542,
2543.
2543
2544
2545.
2.545
2546.
2546
2547.
2547.
2548.
2.548.
2549.
2550
2560,
2551,
2551.
2.552,
2552,
2553
2553
2564
2565
2555
2556
2.556
2557
2567
2568
2658
2.559
2560
2660
1514.81
1515.27
1.515.72
1516
1616
1517
1517
I.M7
1518
.17
.62
.08
33
89
44
00
56
11
67
22
78
33
44
00
66
11
6^
22
78
83
89
44
00
56
11
67
22
7^
38
89
44
00
66
11
67
22
78
.33
89
44
00
.56
.11
.67
.22
.78
.33
.89
.44
.00
.56
40 Curve.
Tan.
1119
1119
1120
1120
1120
1121
1121
1121
1122
1122.
1122
1123
1123
1123
1124
1124
1124,
1125,
1125,
1125.
1126
1126.
1126.
1127.
1127.
U27.
1128.
1128.
1128.
1129,
,86
.68
,01
.34
,68
.02
Arc.
50 Curve.
Tan. Arc.
1900
1900
1900
1901
1901
1902
8511902
69 190-2
00 895.577
42 895.841
.88,896.104
896
03
36
70
04
37
71
05
38
72
06
39
73
07
40
74
08
41
75
09
42
76
10
11-29.45
1129.78
1130.12
1130.46
1130.79
1131.18
1131.47
1131.80
1132.14
1132.48
11.32.
1133.
1133.
1133.
1134,
1134,
1134,
1135
1135
1136
88
16
60
84
17
52
86
20
64
87
1903
1903
1904
1904
1905
1905
1905
1906
1906
1907
1907
1907
1908.
190(4.
1909,
1909,
1910.
1910
1910.
1911,
1911.
1912.
.25
67
.08
.50897
.92,897
.83:897
.76 897
896.874
896.048
918
.182
.451
.721
.990
I
.850
898
.&8i898.S2»
.00,898.796
.42 899.008
83 899.837
25 899.0U6
67 899.870
.08
.60
.92
33
75
17
58
00
4-2
83
25
67
08
1912.50
1912.92
1913.83
1913.76
1914.17
1914.68
1915.00
1915.42
1915.88
1916.25
1916.
1917.
1917
1917.
1918.
1918.
1919,
1919,
1920
1920,
67
08
60
92
3:)
76
17
68
00
42
il51H
2561.11 1136.21 1920.88
2561.67 1136.55 1921.26
2562.2211.36.90 1921.67
2562.78 1137.23 1922.0K
2563.33 11H7.57 1922.50
2563.89 11.37.91 1922.92
54\25ft4 .44\lA?a.2ft\\*«.8a
99 25€>-i m\V^ .?>9 \«£S\ .-liViX^ .SmVvWft A!0
, 90 2566 . \ \\\\^ MAVlik .«i\%V\ .tti&\\ti!^
900.146
900.414
900.684
900.963
901.228
901.492
901.761
902.081
902.800
902.509
902 889
908.108
903.888
903.858
903.928
904.197
904.467
904.786
9a5.006
906. S75
905.644
905.818
906.068
906.864
906.088
906.902
907.172
907.441
907.710
907.991
908.261
908.A80
WRS.iW
909.069
909.844
909.019
909.868
910 IGH
910.488
910.706
620.00
520.83
5ai0.07
521.00
521.88
521.67
5fi22.00
522 88
522.67
5-28.U0
528.83
523.07
524 00
524.38
524.07
525 00
625.38
525.07
526. UO
5ai6.88
526.67
527 00
527.88
687 67
6j».00
6fi».88
1528.07
509.00
629.88
589.07
580.00
580.88
580.07
081.00
581.83
581.07
588 00
682.88
682.67
588.00
583.88
588.07
584.00
534.88
544.07
585.00
586.88
585.07
580.00
680.88
586.07
587.l«
587.88
587 Ii7
588.00
588. >8
M8.07
14\Q
L TANaBMTa, BTO,
D
™
1 Cii •
8 Gun*
..
orr*.
10 C
«„.
A« , Tan 1 a™ 1 T.n
Ara
T«i
^Aro"
Tan
Are
S66 ii?aa9 8w'iD» iWoi?
49~8SS
MSTlS
»oooo
1JI» MMD OHOIIOVI SG,MO 1-8
)MW>
408 088
448 360
TflOlS"
.28 iti«o*iii|ioeaioi5Bns«
498 186
448 M
00 338
maae
60 500
N
s« 's'moSm
lORH B
iSOW
498 486
60 63
iiWR ue <Ho «e
iiHweo
498 636
BO BS3
lies AiwrnsB
lOB 1'
»1«
i9a-86
449 091
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531.57!
BBS. 185
478.84.^
708.33
■97,181
DSS.Ot
508. oni
MW.U4^
BK.870
ire 387
798.38
■K.m
■us.as
598. (MO
990.^0
aas.Aoe
478, 8St
-K,«
UH.ttI
98:7ik(ii3H:»i
M8.4S6
998.468
BW:OB
es.74i
'^.H8
U8.8;
S83.I)W
.138.313
99B.687
saj.iio
88s.9a)470.tn
'w.ioe
sst.aoi
ii3b:iii
588,™
993. 8IS
Sfti.SM
880.111 479.S»:»T.,K»
-M.34S
98t.4«
593.070 W7.UB3
S83,S0e47Tl.aBHT»7.M0
■W.STfl
tsa'.Ti
m.ooB
1189:71
500.143 9g7.2tht
888.481 479, MdItK, 83.
■88.813
WO.K
Oe4.9[r7
mo.QOl
596.331 997,M(
viieiA
883,887 4711.671) 7»<,iwn
-n.oig
oaa.ooe
nw.s4
SSi.OBT
89C,8M479,Wi;ilB,IB
TW.asa
3W.M
BKJ.WH
8ej.M7l479 080 793,33.
TU.MU
lffi.41S
114071
m.fa-iim.-iiik
W3:3ia
897.223 480, 104 7il«,.Vll)
W.TM
1140.95
000.0:11008.333
WI.47I
887,407,480 24;|7l«.68
n.Bsa
I^ISsiHi.ifi
iOO »XII)98.SI3
l«7.Bl«'4«0.38htlW.».3ii
03
Hu.ttr
:s3i,'ar
sHA.ain, 1141.43
300.382 908.:^
1187 , 778 : 480 . 533 1 7110 .«»', &v \
W.466
831.94
888 a« 1141. S7
300.531 IH«,958
n>& Wmi .WR \8i .«;-j:,-.ws ■">«"'V^_
338. dU
mi.4S»\mi.9a
6oo,7d9i».i<r,m,\M,^,\«»i«ft.*w\5Si'S^'S
UD.'fHIl
m.'?H
iSB.06ie.
f:A
■:sl
SOI, 093
301 371
999,58.
099.79
4\ea&
\a«\
S?
ftj^
TABI.IE XIT.— ACTUAL TAKOENTfl, BTO.
IM.JUIIDl.BAI
I14T.38|liOI.BSK
IW.MjSUS.Sau
iDau.oaKUTisBusH.B
n3s.8M8B9.tS0
IK. », II, KM ges4iJi.[i«i|iwi.aH;
IK.S;B|HI0.14il'ltl4.ltU3l«U.lt)H
lOOO.MJWU.U^iJHBl.lIbB 48.1. K
II lOUT.MUU.TIUHIM.S
<«ii=o.i.;
486.SSi:80G!
17:806. «17
jar.ewiis); iisi
ja8.8H8oe.isi
488.^v8lM.aa)
4tW.WI 808. MC
48C,8*4 f08 ew
TABLE iriT.— ACTUAL TASOKKT8,
8..
!■ Cnrve.
3=C
»„e.
4° Onrre.
B' CnrvB.
"ST
Tan 1 a™
Tan
U4e B8
t^uou
TUQ
in.
Tan
Apd
T^n
Are.
4giri -M HiiM n
1^:00
«».■) U 8 01 B-
844 1*1
4050 S3
-00 50
lis 90
16iO,53
>IM8»I
1^4 3,1
XtJ, «> 9-9 BN8
leai.ej
JOie j9 9880
621.00
-0- i.
20»b 980 1 8
MSO«
-0- t-
20— 08 980 459
m\.m
nj-i S3
1^81
20-^980 4fl
-03 Vh
20— B- 981 03-
wsi.ri
11
mo M8JIJ 00
«a J- ,406 SO
1US5 03
osoi
li.6 8S
■ftM -iTOl 61:
IfllM.OO
.>»H Xm 6
3-05 W
is*';^
liW 4 aiiH»
12— ISO
iti88!e;
wiu»
•IM M W«0 00
jar jj
ro««
l—W.
1644 00
«M JB 1080 88
163-0.
n i
203. 4 WW hi
iBM.sa
MM og iOfll 8~
rtU) a
robS
2031 m (K! -Ml
J^ 43 4083 %
1639 B
Z-WBO
1339 41
OlSl 07 088 044
loaias
wan 88
roo*
1W9-
S0a2 OS 983 94-
ltel.B7
Hiiuaa
18
IB-l 0^
SI3I B-
.100 80,4065 63
B405
now
1230 41
iOa- 9* 984 608
iBi»:a3
llf M
IB 3- jooa 6
misaW na
1231 2- im SSIiBlKI
101 ee
2-1 A
I2.I 58,2084 I M(5 •\
Ma 4;
1231 B12031 Msssoan
i62r;6T
10 JOU
I KBIjiKWjOOlltWOd
IfcM.OO
l!4>4 M
40083
Wis, 33
tU3 1 |f<141 Uj
J 16,1 6-
1^« 03 >0-i 83 HBO f
|B'J8.U7
VMi m 8143 00
HW140
mtvs
1814 a
]^i 40 2II8U 35 0811 8ii
iBua.oo
UH OB 8Hd H
^6-13
40 H»
123.) I
2.306
1B«.»8
•11
ia 8"
208 08
98 111
lUiiB.B;
30
r re I
'408 W
40" 0(
1641 81
no 6
1231 49
IS8-50
98 TW
1630.00
98-990
18*1,33
«1 -8
*M *
0H8 27-
risas
988 SSS
■1 I '89
IM 7
iISS
I2» M
988 8B1
lB3i;si
4914 1
1048 Jt
ijsoao
989 154
u J m 4080 (W
MO 01
989 448
1 5 «" 4080 88
201(1 4"
989 -*
ItlTl 38,4081 e
X40 8;<
iBai^B?
JU
JBSOW
siuaoo
(1-B 11 tOS- 50
ibooib
-Jl Q 123 5
2M190
BSOSi:
IBS-i.OO
eBoa»
204 ft
H ! -Ilai )H85
aw so
991 181
1834:00
4 NH 1 ja SBliaig "i
8048 1(1.
991 481
1SS4.S8
111 tSi 1 |-^4 Ml DM
1634. «7
JflHsl l-a-.no 1239 B4
9eae(u
1886.00
4»U J H -^ Bflll 40 il
«OII 1
1686,38
W,B6(
1635.6!
201 00
9W M«
1098.00
9019 42
903 «M
no
IMBl
8188 83
was la 4001 « law 64 -"n s iwi r »i.i w
983(18-
laae.flT
S1S5 00
-jiiisjijin .1 i -~ i 1 4 ]4xiw3a
903 Btt
\m.-Si
1037, 67
4tt-| W
91WI10
«% ii04 *»4BM
1088.W
^^ja ?# «»/ B ojsb ^ .14 OiMi ESS
1038,93
"/ *•
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Wi 5.
»
^"l?
••as SNl
« ei9b a ,.48n DO 41. 1
'^WflS M'iJMfl 2JU9a 1
TABI^ XIV.— ACTD4L TAFOSKTS, ETC.
1311.89
7.4U6iasi.i-
7. 1144 l^l.l
7.H)M laut.i
IB 870 lavi.ra
TI«!lS7
too! 641
T«),7«
TUU.SSO
701 !3M
roi.a^
ruiiwi
TD^'OIS
918. VTO lOia.n
tJSMii 1013. ge
118. IKe I0H.17
aiS.SMI0I6.Ot
S.UU901.
!,88S!l»1,
6.M5,«ilit.
iwn.K);u?.UiUii
(9^.7«&iai8.ie7
is.wt
18.300
l4!l6T
TABUS XIT.— ACTUAL TAROBtm, BTO.
am.K
i«uo.4i ms.si
e.wnos.M'
~ - Bitace.rs
t.UlTSS.I
S.Eu'ltlT.)
jjiiow.wtM.uoliato.
1H&,7S90Ba.4:f.lM.T«''
'- — T7wr siBiMi.
uen.uii.iMi.
4 nn.DiMiiMi.
d|gH.4M!lMI.
jiHM.n«.isu.
MBa.ni«i».i»D|iHt.
I eus. BO .aria. as
9.(M«riS,IMl«d.
IB71.irii7J5.MI
itM.n
l£>4 M
\-XI .M.ari .»
Bl IVM.
-.10 1604.
1009 Miim.
I one. w ism!
itWH.uiwt-s.Miy
— AOTDAL TAMGHST9, I
V Cum.
8" Curve.
»• CBrve. ' IC Carve.
SB'
1 Tu. 1 An:,
Tu. 1 Are.
^ii^
KK-
Tin. : Are. Tan. Aro.
<«a,494'iaBe.«7
ni.gss 1171.43' flia.ota
i<«s,aa
H3:^'flrm4flO«t^<m)
na.lTS 1171 .07,893. m
loaa.a
9M.l»n»I .«M 4<M.Slfl RiO 107
fti
Tia.sM iin M o!3.*»
1{B5 4!
BBJ.aD7(ll .4!1149M,»90,8i»,33S
BO
7ia aw n73.54'(K3.Ma
iA4,4uiim ,v67 4M,MS't)«anao
T8
-w.80ilii7S.39ass.8i;i
W4, 3^111 ,N!W4M.i!t«>'ftl0.ee7
mLTIflSffi
oe
7i3.aiu|ti7s.iiiie:M.ocM
BM.nHll)1«.(l37l4M,434 8VD.8)R
713.318 1I7-J.«S««J tW
loatia
»4.<)47.1ll3,!ftS4M.GHIH3l,<<OI
Si:lS!8af
7l3.438lll73,10fl»l36»
IfTMM
^l.llOilia.lOr 409,727 SSI. 167
8
7ia.BS7|1173.3S(W4,6M
\ftx.v:
NU,lt7U'll]3,aB8 4S8.B;8 8il ,838
Ku.sMiiai
i;
713.Mnlll7S.B7'ae4.73S
\axM
»M.43S|IMS,7™«»(«I8S1.1>00
Rj.fOollMg
M
T14.054I11T3 Sim w.
US G07'fl1«.«8SH».]0«Wl.6«7
m.\w.iwi
iftna
5U 7630 3.148Mn,315'S31,Kt
HM.w:t^
'■\Am\ 74:m^:»;
lCW7.flt
BOBTOilSTO
«
71J.SRB'l 4.WaM.4T3
^.■ifl.'iMlo 8:7IMiH)«ra7«a!8'!.-
MSiilSTC
S6
714.8981 4 78:0^,1658
89
7iBii)iiu b.oo'bss.ssh
656. 416913. H8SI .too. eOalRei 600
sii:«i|i8ri
7[6.«(B|n 6 MIBM.OJI
io-J8:s,'
H6.ri7!l;914.074 IWl 049 83*. BUT
i«i,M5iia7i
a
7IS.044 11 .'i.48B3fl.3ai
65n.74l'914.36aKII.iee8S2.633
'»).««' 1871 K
ns.Tsa'ii 5.718^8 »■;
656l>m914 444IS0I.843'HS8.0a9
loainu
667.070 914. 630 »Ul_.49l(H8,ie7
Ms.wslisM.ai
Tis.iMTirfl.in'Bafl.TM
!i,'.T.3U'9 l.KiaS01.B4oW.«a3
IB.V<UB']]|7lt.ll
7ia.ws'ii78.4a>3H.ii4ii
KC.tmt :s,nDuiKii,T8;')*^,6ai
. n.->.tiT]i;is».ni
7io.iin.ii7e.B7aa7.iJf
[!«:»
UT.uuoa.iMMii.m'ikn.gcaa
IBn.OB
l7ifl,7WiiTS.aia37.an8
K>7.ra>'i S.STO8O8 oni«».i»
»»
imtw)
im»,>j-iH.i(S5|nTT.i4'Ba7,«i
U7.l«69 A.nMMl ttnRW.on
B4
'Ma. BUN
ISM.OliTII.iWajllTT WlBST.BTl
Wl OMB 5,T4I ACn.Sn'lHl.igT
'HU.MM
10*:*
U8.»7'9H.>»I>01B94;r»I.S33
N6
iaH:iT.riTft»1177;JS'^,IS
6.%8,37!J 6.111 604.079 8*1.601
«■!
,«s:.SM
nt.-«,44rir.(flN
li™.IOIlBHii-,-U
^'.8.M:i[9 6.1196 608.8161804.667
\w.mt
im.ia
ris.tHi
1]78.3»IU8.4I.1
668.707 BO. 481 SOSWliKM. 83.1
.wt.m
isram
riBBW
tiTB.sTBas.ote
loai.a
65a.B7a'o 6,607 603.liaB4'l. 001
30
moBt
I8T5,»
718.473
1178 HIlniM 781
^mt.03.^ 9 6,t<6su3.igi'iKa.iii7
i«w.s«e
7JS.«&!
117ft.0filtt».Ba7
loai^fi;
MB. 1989 T.OS7<IOS.4«7IKft.883i »»
Mj.Kn)
7)BS»:>
)17(l ^1 IW9 I.M
X.9 864^ -.*u.-us.nM iw Eou as
ilWB^
i8T6:ti
71BI«
117(1 N!|IW9 341
55U6a)917.407Mn.Si0(>'ila.B6; H4
Ir»wb
ISTBSB
ift*;.a
MB GJI«9 T.-in 308.869 Its. an 95
, mg Biaiiare.BT
UB VhiV T.TTH li03.99H|gi»,0ra
30
i ^isill-w
loaS'-i
.WO.OISI'B 7,968 i»4,14T»!6,l«r
»i
7ifl,flai,iiso,4a(wo.o™
10S3.W
640 180 918.148 S04.!i«ljSlM.3SI
No:oM'!l=i:S
T!».iBo;iiao.jHi3o.wi
'wJrs^.iB
7«o.ssH;iLaa.t»W.«4
1089. »»
900,611 1118,519 504 6g9|H£6.607
'SMM4J]37S.0g
7*0,688
1181.1 HMD. B30
1033. M
M«.!»J|1SM,M
7«l.7lll
llM1.43|ffl.«l,SlT
1081.7,'
6flu,Ki;;l91H!wt9 5O4!687hf7,0On'4a
«1.04ll|S».Bl
)a«.Bn
661.0181919. a;4«».033ACr. 167 4H
|M).»«
IS78.W
iiaiiootcii^ist
1031,17
6£l.]741>ig,«59W6,lgo'»I7,383 44
S»fi83
1879.17
rai!4su
ll8i.M;SS1.871
10:14. 3(
681 .*« 919.444 .105, a3a'«i1. .■!""' 4»
1M1.7T8
laTOM
r-ji.BSs
601 499'6t9. 680 006. 4;8'8-J7. 66^ 4H
M.OS,
I87BTS
I]%VS3;(>,'Il!74I
561 .6041919.816 606. 637, 8:17. 8»l. 4 T
Wt.KS
i»».oo
ti&rmlcai.ms
loasloo
W .830 Kin.OOO 60S.TTT 8W.UU0' 48
HiBH
IS8a.«8
73^1877
118a. JOISM 114
1036.81
6oi.B9o'9ai.iBS6a5.Baift».iu; 4B
m-m
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1038,43
M!.161 930,870 603.075 8SM.833| M)
m.Qu
nulnm
1035.63
56d S» 901.6.16 606.331 8:M. 600 ni
au.«;Ti»>i.ii
7S-J.WR11l«,«l!«W5M
1035.83
W3.4S6:»«(..741 B06,9e7«a8.667 B«
Stl.SOBllSSI.Sn
063.6B3l930.g96KW.91TK».K33|n»
8W.;.M1SKI. «;:■-■; ■■.i 'i-i .-. :: Wi0.»
flftt.aiHwi.iii .w.aet'saa.cou m
ftliawi*'! \»::- ■ ...KM
563.9H393i.nsm.BinHW.i8; no
K3 . 149 Ml .4Hl KK .M MSk .«»,.%«.
iti4joni*w..'ji-- ■■ • i.iiie'.W
ftsa .mil «v .WR wn \ViW» .t**! .*^
TABLB XIT.— ACTUAL TANGENTS, ETC.
Tan I An? Tan | Arc | Tmi I
3 IBM) M],-
Aim Vi HiiN la Um H.141114 i iws i» j-ii i]|ii!~s twAXK. vii in
sifj? 44 HNi fl Itna SI 4iBa S9 [6S« B^r* lu iir« 01 Usi <l|ioii i
«»3 Hill's as
musi
5113 w
ii«i 4u Bra «
140 w aitM a
ftl44 SI ss^ HS ^
IIIH W !»« F ._
514)4 4iiB9»i t^a,
—ACTUAL TAKOKNTS, ETC,
6° Carve.
8' C
»,.
S° CUTVB.
lO" Onrve.
83"
"Xftn.
a™.
^^
Ai-o.
"Tan,
Al^
Te.. 1 a™.
Ton.
Arc.
m:«4
TM.fll!
uSsyri
»ns7
S^tTbo
MS^sfem
830. 00(
Ma.48(
741. aso
iB6.es
B«3.974ll»^,4rr;
SR.:^
rao.on
83u'83:
MS.BSO
138*: ir
7S5,j«
'm'.Ai
uaiitoo
io38:i-
6a4!ao3 9i2!7n
woloir
830.501
He. 238
745 *K
.m.v.
BW.flW
10.18.*
Sdl.4t(8 9W.96!
830t*33
Sin! 7^
iia'.sii
1^348
508:451
831 .im
W6.BT4
i:»6:i«
T«.W4
isv'.-at
63,^,454
1038:91
S64.»6i;9aa'sio
508.M(
l8B5.5t
r^BiK
11B7.IW
B*i.Mll
SW.lSl (1S8.T04
m.xm
1)35 8^
685. £97
g«1.889
631.500
84i.718
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;!M.raiii8fl.io
IMB.013IO3B.58
MS.4K
921.074
509,04-
BSI.Ofl'
10
B47.M7
l3S8.aH
■Ka.WOllSB.^;
924.861
B48.^ll)
iwe.tir
m.TSt
K«:Dni
MS .464
l).M:T5ltlllM0:4;
386.161
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509:49:
sie.-.ii
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BW,8li
609. H:
925.001
8*i:60n
Bsa Bfl-
m.-Kn
7!».m3 ijbu!t<i
S»6'W
610.09'
832.833
M.-.M
1388:*
7aa.436 iiw.ft)
M7:»l IWKSS
w«-7ei
JSsisBI
510.«0
833 0110
9U-BM
7iB.fM» iiao.si
637,1190
510.889
sw.ais
I3BgRS
7^ H6«'ll!)0 48
937 87-
1041 .r
507.119
ftffl.OSS
S10.6JW
8g»8?9
90
m.fx
[»SB.l'
?.'9:i)7bii9o;ti
63«:oei
m.lll
610.891
833 500
jao.suB uw.ijft
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5BV.437 936. aw
833.86-
m.isi
i»n)>:
lUl^J^W
(W7,&a
610 :t9
833. B33
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Ki.aoii
law-wi
fia!7-4(UBl!4:
1013.51
567.788
«6.8a-
834.001
«4
•«1.I61
ia9o.i«
667.96:
926. 8W
Birstt
834.16;
ei.Tos
laou.si
fwi:i4S,iiui'ai
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511.431
ao
Kl.Sfjl
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511. 73'
831 :b6-
Ha.44B
[891 iiu
rdO.J87
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io43:m
M8!817
Ba-:593
611.886
834.833
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sa.tm
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7S .Ott
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689,748
S68.7H
619.08.1
916. OW
eu.wso
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iini'.»
«7!96l
sa.iis-
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lasaia
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B89:ia
B48.148
6ll:8*
836.33;
7B .MT
1193.67
mo: 81'
mi.s
66fl.)W
9*3. tHI
Bia.481
ffi)i!aai
;» .860,1103.81
MO, MO
lOM.M
aK).a48
jaiiiiM
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340 .£87
1044.79
i>89!er
IK8!7(V
5is:7tr
H3S 833
EH.iee
iai3 33
TW.SSOllW.W
B40.K3;(04.^UO
569.783
m.m
B1i,99U
PSB.OOU
KiMa
13U».31
7a:J.61M119t.&
Ml. 0(W 10411. S
M9.BiK
613 m
SSB.Ifl-
tu.Tua
]»93.8»
m'.»i
8,36.8-33
<U,K1
13111. jr
wli^jlM
911.444
Bis:3a
SB6.5O0
ntl.lM
MKiA-
7aa,i4aiiM.2*
fl41.8JfiHMS.a
S70.4SI
HS.39
618.589
IW8.M-
40
V^
T.-js awiifi.viK
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s«.»4n
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ss
ISM.M
lSllj.83
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4S
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laOO.BU^awi mi !,...,. ■,, .■■,. ............ : , .-,u
Htr.aw
13BU.UT
"67.464
IIIM.M
671. 9561931 .i-J6
514.898
838: 167
B97.M
■net wa imr.adlMa.eoi iD47.m
67V. ia> 981.481
>fif!y.ie
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TABTiB XTV.— ACTUAL TANGENTS, ETC?,
6^ Curve.
Tan.
875.434
675.602
875. 0»0
876.Si08
876.456
876.714
876.97:3
877.5825
877.479
877.737
Arc.
1416.67
1416.94
1417.S2
1417.50
1417.78
1418.06
1418.33
1418.61
1418.89
1419.17
750.496
760.714
750.986
761.168
751.360
51.590
751.811
55}.Oa8
52.5M5
752.466
877.095 1419.44
878.252 1419.72
878. 51U 1420.00
878.764' 1420. 28
879.OI7ll420.5U
879.275 1420. 8:J
879.533,1421.11
879. 791 1 1421. 89
880.049|1421 67
880.307 1421.94
880.564 1422.22
860. 822! 1422. 50
881.0«0,14«2.78
881.334 1423.06
881. 5«7 1423.83
881.845 1423.61
882. 108, 1-1 23. b9
882.30111424.17
882.6191 1424.44
882.876 1424.72
888.134
883.302
883.650
883.908
884.160
884.424
884.682
884.940
885. IIW
885.456
1425.00
1425.28
1425.50
1425. 8;J
1426.11
1426
1426
142H
1427
1427
.81)
.6
.94
.22
.50
885.714 1427.78
885.972 1428.06
886.280 14-^.3:^
886.48811428.61
886. 746' 1 428. 80
887.008,1429.1
887.271! 1429.44
887.52911429.72
887.787 1430.00
888.0451480.28
888 30Sil430
888.661 1430
888.819 1431
L
56 761.525 1226.19
88 761.746 1226.48
.11 761.967 1826.67
889.077 1431.89 762.188 1226.90
889.335 1431.67 762. 409' 1227. 14
889.598 1431.94 762 635 1227.88
889 860 1482.22 762.860,1227.62
890.118 1482.50 763.08111227.86
890.376 N.92. rS 763.302 1228. 10
800. 69911438. 061768.537 1228. 38
7® Curve.
Tan.
Arc.
8® Curve.
Tan.
1214.29
1214.52
1214.76
1215.00
1215.24
1215.48
1215.71
1215.95
1216.19
1216.43
752
752
758
758
758
758
754
754
754
754.
754.
755.
755.
755.
755.
755.
756.
756.
i"56.
756.
757
757.
757.
757.
757.
758
758.
758.
758.
759.
750.
7.59.
759.
7.'J9
760.
760.
76<).
760.
761.
761.
688
909
130
347
564
785
006
227
448
670
,891
112
,338
550
.767
.988
,209
.430
.652
,878
094
815
586
757
978
20()
421
(Hi
863
084
805
526
747
9(S9
190
415
640
861
082
804
1216.
1216.
1217.
1217.
1217.
1217.
1218.
1218.
1218.
1218.
1219.
1219.
1219.
1219.
1220.
1220.
1220.
1220.
1220.
1221 .
1221.
1221.
1221.
1222.
1222.
1222.
12d2.
1228.
1223.
12273.
1223.
1224
1224
1224
1224
1225
1225
1225
1225
1225
Arc.
656.807
657.000
657.194
657.884
657 574
657.767
657.961
658.151
658.341
658.534
658.728
658.921
659.115
659.805
659.495
659.686
659.882
660.075
6(K).269
660.463
50
71
.92
.18
.83
.54
9» Curve.
Tan. I Arc.
67
90
14
88
62
86
10
33
57
81
05
29
52
76
00
24
48
71
95
19
43
67
90
14
38
62
86
.10
38
,57
81
,05
,29
52
76:665
,00!665
24 665
48 665
660.
660.
661.
661.
661.
661.
661.
662.
662
662.
662,
662
662,
66:1
668
Whi.
663.
668.
664.
664.
664,
664,
664.
665,
1062
1062
1062
1063
1063
1068
1063.75
1063.96
1064.17
1064.88
1064.58
1064.79
1065.00
1065.21
1065.42
1065.68
1065 83
1066.04
1066.25
1066.46
583.950
584.1221
584.294
584.463
584.681
584.804
584.976
585.144
585.318
585.485
656
85()
048
288
428
617
810
004
197
1066,
1066.
1067,
1067,
1067,
1067,
1067,
1068,
1068,
391 1U68
,684
778
971
165
1008,
1068,
1069,
1069,
3581069
5521069
745:1070
989 1070
1070
1070,
1070.
1071.
1071.
71
95
666
666
182
826
520
718
907
I()0:i071.
294 1071.
491 1 1071.
688 1072.
881 1072.
075 1072.
268,1072.
6'
88
08
29
.50
71
92
18
33
54
75
96
1
88
58
79
00
21
42
68
as
04
25
46
6
88
06
29
50
71
666.462 107T8. 92
666.6.56 1078.18
666.849 1073.38
667.048 1078.54
667 286 1078.75
667.488 1078.96
667 6801074.17
667.824 lW4.aa
944.444
944.630
944.815
945.000
945.185
10* Curve.
Tan.
525.689
5^.844
525.999
Arc.
945.370526.458
945.556
945.741
945.926
946.111
585
585.
586.
586.
586.
586.
586.
586.
587.
587.
587.
587.
587.
.587.
588.
588,
588,
588,
588,
588,
589
589
589
.589,
589
589,
590.
590,
590.
590.
.590,
590.
591.
591 .
.591 .
591.
591.
592.
592.
592.
657
830
002
170
339
511
683
856
0.i8
200
372
544
716
885
054
226
398
570
742
914
086
,2,58
430
,602
774
946
118
290
462
635
807
979
151
323
495
670
845
017
189
946.
946.
946.
946.
947.
947.
947.
947.
947.
947.
948.
948.
948.
948.
948.
949.
949.
949.
949.
949.
9.50.
950,
950.
950,
950.
950.
951.
951.
951.
951.
951
952.
952.
952.
952.
952.
952.
958.
953.
362 958.
296
481
667
852
03
222
407
593
778
968
148
383
519
704
889
074
259
444
680
815
000
185
870
556
741
926
111
29(;
481
667
852
08
222
40
593
778
968
148
a33
519
592.684 953.704
592.706:958.889
592.878 954.074
598.050:954.259
598.222 954.444
598.897 9.54.680
526.151 850
850.
850.
S50.
526.303
626.613
526.765
526.917
527.072
527
527
527
527
527
627
528
528
528
528
528.
528.
629.
529.
.529.
529.
529,
529,
530.
530.
530.
580.
580
530.
530.
581.
581 .
581.
531.
581.
531.
582.
582.
582.
532.
582.
f.82.
582.
.588.
588.
.227
.882
.587
.689
.841
.996
.1.50
.305
.460
.615
770
925
080
282
384
589
694
849
008
158
313
468
628
778
988
088
243
398
552
707
862
017
172
827
482
640
797
952
107
262
860.
850.
851.
851.
851.
851.
851.
851.
852.
852.
852.
852.
852.
852.
fm.
858.
858.
853.
853.
858.
854.
854,
854,
854,
854.
854.
855.
855.
855.
855.
855.
855.
856.
856.
856.
856.
856.
856,
857,
857,
8.57
857,
857,
857,
858,
858.
588.417
533.572
538
727
85<
000
167
883
500
667
883
000
167
838
500
667
833
000
167
.333
500
667
838
000
167
333
500
667
888
000
,167
,888
500
667
888
000
167
338
500
667
888
000
16
a38
500
667
833
000
167
333
600
667
838
OOO
107
858.333
858.500
858.667
533.882:858.888
584.036 859.000
584.194 859.167
M.
O
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
87
38
89
40
41
42
43
44
45
46
47
48
49
50
51
62
53
54
65
M\ .?sa*«t«i^ .'?fie\^'^
598 . 572,954 .8m
668.216 \Cn4.';^W.Q9ft\«fc.^'l^^V-^«»^]^
an
TABLE XIV, — AOTDAL TANOEKTB, 1
TABLE XIY.^ACnjAL TANGENTS, RTO.
6« durre.
Tan.
891.160
8i*1.417
891.675
8»1.9d8
892.196
89:2.459
892.717
892.975
898.287
Arc.
70 Curve.
Tan. I Arc.
1483.83 763.
1488.611763.
1488.80764.
1484.171764
1484.44:764
1484.72 764
1485.00 765
1485.28,765
1485.56;765
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893.600
893.758
894.016
894.279
894.542 148V
894.804!1487
895.067 14:^7
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895.583
895.846
896.108
896.871
896.684
896.892
897.150
897.412
897.675
897.988
898.201
898.468
896.726
896.984
899.242
899.505
899.767
900.080
900.298
900.A56
900.818
901.081
901.844
901.607
901.869
902.182
902.895
902.657
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908.183
903.446
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1489.17
1489.44
1489.72
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1440.28
1440.56
1440.88
1441.11
1441.89
1441.67
1441.94
1442.22
1442.50
1442.78
1443.06
1448.88
1448.61
1448.89
1444.17
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1445.
1445
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1446
1446.
1446.
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766.
767.
767.
767.
767.
767,
768.
768.
768.
768.
769.
769.
769.
769.
770.
770.
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416
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309
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770.460
770.681
770.
771.
771.
771.
771.
772.
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128
858
578
808
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772.254
772.479
772.704
772.980
778.165
778.880
773.605
778.881
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44
72
00
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94 1774. 781
1228.57
1228.81
1229.05
1229.29
1229.52
1229.76
1230.00
1230.24
1280.48
1280.71
1230.
12:^1.
1281.
1281.
1281.
1232.
1282,
1282
1282
1288
1288
1288
1288
1284
1284
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1284
1286
1285
1285.
1285.
12a5
1286.
1286.
1286.
1286.
1237.
12;37.
1287.
1287.
8» Curve.
Taa. Arc.
668 412
668.605
668.799
668.992
669.186
669.888
669.580
669.774
669.967
670.164
95
19
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1289.76
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904.289 1447.50 775.186 1240.7
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904.769 1448.06 775. «41 1241.19
906.082 1448.1)8 775.866 1241.48
905.294 1448.61 776.091 1241.67
905.557 1448.89 776.816 1241.90
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670.
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672
672,
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673
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674.
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674.
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675
675
676
676.
861
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260
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676.246
676.448
676.640
676.887
677.084
677.282
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678,
678
678
679
679
679
679
679
679
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1075.00
1075.21
1075.42
1075.68
1075.83
1076.04
1076.26
1076.46
1076.67
1076.88
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1077.
1077.
1078.
1078
1078
1078
1078
1079
1079
1079
1079
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1080
1060
1060
1080
1061
1061.
1081.
1081.
1081
1082.
1082.
1082.
1062.
1082.
1088.
1088.
1088.
1088,
1088
1084.
1084.
1084.
1084.
1085.
1085.
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Tan.
06
29
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18
38
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594
594
594
594
594
595
595
595
595
595
596.
596.
596.
696.
596.
596.
597.
597.
597.
597.
597.
597.
598.
598.
598,
698.
598.
598.
599.
599.
599.
599.
599.
600.
600.
600.
600.
600.
600.
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267
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960
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965.556
956.741
955.926
956.111
956.296
956.481
956.667
956.852
967.087
957.222
957.407
957.598
967.778
957.968
958.148
958.838
958.619
968.704
958.889
969.074
10* Curve.
Tan.
684.977
585.132
585.267
586.442
586.597
585.765
585.912
586.067
686.222
586.380
586.588
686.698
586.848
587.006
587.168
587.821
587.479
687.634
587.788
587.946
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602.
602.
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282
408
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109
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969
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969.
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960
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960.
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961.
961.
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962
962.
962.
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96:3,
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860.000
860.167
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860.500
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861.000
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862.000
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588,
588.
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688,
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689.
589
589.
589,
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540,
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1)89.671
651 913,
877.833
TW. 161
689,774
M3.07B
878.000
uivieasiiisii.fii
■KAtai
WM.Itl
8»9,BT1!| 1097-7)
613,«U
II76;741
893.384
878.167
49
fllB.BOT I4(B.S!I
788 818
975.926
ise.sgfi
878.833
■W8.B4;
6m'-m'.nii.in
878.500
M
aoM-s im.*-
78B.07T
"13 ^1 '■■■: ■<•>■
W0.iWl«4.t|
78B.!»u'i-jr..-, ,-..■..■ ,-..■..■- Mo.i r,.,;.^., :■,: -...■: -:..■..■< i:b
7S9.5a'i !:;-/■ ... ■ '"V^S:-
Kliuaiiiesiut
T8n.7eB i;.v. ... . ■■S^S,
TSO.Dterj.-.; ■.\'^^
sS
TW.ati
■"t '-
';'"■'
.ir^'i-,-.
,urf;=.>
ja
, Biti one j'i6».ii!T!io.4ei
I f:s.ai4 1406. saiToo. ago' \
TABLE XIV.— AC
L TAMQEHTS, XTO.
89-
.= e
»r,».
S° Vnrve.
S' Cnr^e.
*=c™.
S- Cima. 1
T«.. 4ro.
Are.
Tua.
Arc.
T«., ■ Arc.
"ri^
Arc.
MtOi
za).^.3i
imMMoo:*
«ioa.4a
BSM.IT
4401 !s^
»ffi4!4<
1984^84
swo.sa
i;eo:B7
ttB7.8t
MSillOlSTM:*
HOJ.H
lS46:i(
i!9S,1.00
1331.74
aan.BS
107;w
itai.oo
4403. »
iJ9S.1.S«
IBS*. 14
laoi.Br
los.aa
SMI ill
BgwiwliTTDW
lW3G 11
1881k M
^oix
1108.60
17>l!«7
SMJ-S
SffiDOO
4409 oi
U8BB?
lauoa
smx
1108.80
S644«S
Bsiir
ar B
4408 81
1848 8:
iM7 Ji.
1886 80
ffloaoa
HOB .a
vm.a
MAW
DSIJSS
r-5«f
«a "T^
1386 7B
«)3 8l
UOO.K
BBlfi 00
87^ BH
1840 81
n8Hsa
1887 le
iToaioo
ID
SStfl 1
wno er
>"J BH
1408 88
1849 01
9088 8!
1S87M
awn
111U.I7
1700.88
SSftUW
ssiss.
r-5Bl
44U» 1
1830 41
188- ir
«104D8
iiio.a
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UKMOa
a~bdM
(410 00
1488 38
iiuBiia
1764.00
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4410 89
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IIIS8 m
two 40
1704 .3S
ai^34
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IBM 0~
wi n
1889 18
tmm
1764.87
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1413 110
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1880 50
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1766.00
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sssmr
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20)2 w
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l«^3I
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IH00 4U
JIO 08
iTts.tr
4415 00
[1S4 a
J043 88
ISOOBl
C«7fl0
1766 00
IK
bfiBSTD
Wiir
e-8198
MIS 88
jMasg
1301 Jl
*!O7 08
iiiiiag
i7iH.a
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ssa-ias
HIBO:
isss bl
MU8SI
1766. ST
Nwa w
SH81CU
JOI 01
IBOOO:
1-B-OO
seea m
MM 01
4418 81
(UB 41
I1W4J
im 1
1114 o>
1 67«l
W9«
SBSsa
TH**!
8M B8
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,JU0 6M
1-67
A 1 81
BMOOU
J-86 08
H57 H
laiioftj
1-08 00
i5
2'wga
44JU8B
i»iT as
1 6BBS
M
Mil*
B8I3S3
iTsras
838 Bl
^047 78
itiios)
1-B8 8"
BS49al
WPS 40
441MM
«M)n
W48SI
1804 «
unit Si
1-60 00
as
tir* 9
tJS4SB?
-89*-
ttasBB
I8SR SB
W4Bsy
m\ 6
1 69 33
|«.
ss-sw
SMS 33
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uat 1
IBW IS
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1110 33
1769 B-
so
U8I fUl
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J, nn
1110 66
1-0 00
(*
>6nH -!< HI K
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1 llllIX
1,1)1 ^H
s^B■ u
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1*4 ,- MiMH
IJ-UW
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HHiis ua W7 40 i4» e-
tBUt 00 >S64 44
177^8"
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awa <jg|i!T« iw hu so
IBMflOJBSSOO
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r 1
45
^ Ik
V. J!<|
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Itri 4N ■9B0 0O14t C 1 „iJ7flM
M SI
SWtl WMtm W M4U K)
18-1 08 MOO OS
t4UC 40ljaill«i(
xj w irtA
50
WN 14
WRJ w'ao I 4441 8-
18 1 6 aWl 11
HOB 8 U*0 SB
SB 1"7B V
l*teO0«ril9 444gBO
18-3 IK MSI <(
1404 «N M
JH M 1-7 Dl>
^01 41
Ei8gii e- ,xoH HI i4tB sa
ism 08 2BBJ £i
IIW B' 2« fl-
1 la fti i— n
bi
t8IIHH'>(8HSMB8C1U W4444 I
IH-8 31 iOIti B
lil r'i~7 07
»*
Sfli!Otlll«WOI)«10 44L-H45 0(l
18-8 B,We3B3
14116 44 *-MS
\ H*f, -KM!
18 4 SoWl H9
i4n&ns8i«ja«
1 iM m ruM
Iir4 a4.au 44 l«H W iM. B8U« S|1'8J-|
IS & Beiat»«)U4(A(r3)t» ^ nbw^mcDi
IS G » jMKi mWvi miEiMv uBi»i "<>»
-J_
"_ ""W
unaan
14 as
U4H 1
18 4
\a»6i
\\ 4(r
"Wt
* »
1 -»«
TABLE XrV. — ACTTJAl. TATISBKTB, KTC.
MS BSl 14W fl" TO
tXH BS9 14M fl4 a
IB 405 9- 7-8,1
- "<l,tl" 993,
mi ffii 14
H9I sia u
Ml TB8 14
WU DSS14
9«^80' 14
994 &80I4
M-W S05 1J
' flS 538 U
{So Ml'
S e.^ M IS
_a-9ii m la
S3 ^ 164 I*
N-SH'lHIIWg IS OB
: bfl" "1611 IS ISBl
r 89e 0% iiua es ai
IM HT BSD 000
iM 1871880 187
i&i snam) 83S
iM 4se HS( wo
i.M MB B8" 607
jM BIS 88U sua
&M im Bgi 000
H M f*a
I 91fl Ml 806 M
« 999 eei ISl 50
tSBCrhMK
a 698 982 407
!o croBsa ses
» 158 982 778
» 440 tea 908
508 061
BSSCO?
S8SB8S
884 DOO
'884 M3
_. A58 OaoISM 66
« SflB T« 884 xaa
rr ses
OMe«i
To WW
liLrikiisffis^
™, Jl
n» H^ LMBMn^'^&WB'
888 66
t-HBOW
lOIlW M
sosiioo'
NO- 74
'JJ' s/W4 SP4
IJS3 W/SW 817
1 ,nH1
1
i«eBi
I110 4tl8M 4iS[9B~
86 681 W h
etWHl HI 8
OBtIbOS 184 B
TABLR Xir.— ACTUAL TAKaBKTfi, ETC
/,'•:-'
1= Cnrve
U"
.rv,.
3"C
.„..
,.o
™.
B" Curve.
Tan Arc
Tan
Art 1 Taa | Are
Tan.
1^
T™ ] Arc
MSOfiSBKOOOC
STs^
4430 DO IKT 04 W6B 87
1407 91
M!6 0(
1181 4 1780 00
saw iBttsoi
BT
^6
18
44.10 83 isTT 56 amr «!
aaaa TH saos 3»
*:
00
1408 71
eea»
S«3»lSil«IK»
W
(b
t4ttja
1878 671 J90N «
40D 13
KM 15
1137 43 1T8I 00
Maroe'sKw
«i(
4468 33
1879 il aiBB 8S
409 54
la* (17
lliTTTBireiM
MaSflfliSllOSM
«i»
4ft
4404 17
IBTl TsLoMtl 44
409 95
e«7 o»
hm mIsb u
ilHO
ar
4455 01
IH80 8oL«70 00
410 85
\m f 1^ DO
M41 K E » 1
J)W
10
1880 86 Urru 66
l£.'7 9:
1116 74 1788 38
MStams
JtUI
U
41MK
isai 41 .«71 11
1411 it
nJ9 0- 1J81 B7
M4fi«SSSS
ft.
Jius
T*
44B7W
1881 B6 J9T1 87
,4,159S«8 76
sue Bi mis
B7
u
1989 uLsT^ at
1411 DO S«ai 17
1788 33
M»
a
MM) 17|IA91 04lW< 7S
MIS 41 41W 68
180 05
00
4480 001 18M HttTa «S
1411 SI\:taO DO
iwjan
■msi 818WI
o;
jsa
4460 B3 1084 14 MTO SI
14IB «3 iffiW 4i!
IW 71
WW HUBS*
Hfl 4461 6? ll«4 70 l»r4 4t
14ll)BS«i«K3
181 K
1784 e;
U" 44U:i HI IHSS J4|a)76 OD
1414 0|
issi :&
13] 3'
1785 00
yntt rr h^
4B4463 3allB8n;8,Jff76M
iat 87
*J44W17|1Wfl34J((7fl 11
naaoB
l7S5fiT
>UIU) 00 HI).)!
n.M65 ouiBsa Ba'«7a 6?
1415 H
JUil:! 50
11^38
Wbi ?j hsdi
B7
JUJO
7b'4«8 67'iS87 as
J9T7 a
eastti
183 tH
1786 3»
urtTS
ewsM
113»01
1786 «T
oOffi (Ci M^',
8JI44b7 SO IdSa BS
JKIiiS
nea 75
17S7 00
W* BS d '■It
44 U6H jsissooa
19T8 89
l-^Bl IT
1787 8J
M 44SU IT lasg m
(isIhto oU|1Hbo 18
1070 44
US! 58
i»80 0(
1417 tl
1«5 00
[18184
Ul 4470 B3'lS9U n
1860 56
mUbii
118167
-1 U7I 6711891 SS
1981 11
1418 N
1185 8)1
1788 07
<> i47« u'leui S3
1981 67
UIBOD
i!>EI6tl&
1183 33
I7HB0O
1 4473^311808 3;
aeniii
1119 41
USBBT
1185 85
"ii74 1?18WW
>!9&iT8
1419 St
1187 OH
i 147S Oo'l8S3 48
1989 83
nao«
«ta7 50
uaess
17»)DD
■-. 4476 83 18»4 04
1988 88
14^88
iMSTIte
1186 8fi
IT90U
H78 87 1894 W
198144
I4il 07
IB38 98
1186 98
171ID6T
>.l 4477 GO lUaS 14
19HS W
I4«l 49
1791 DO
tew «
1*£1 BO
li«N i;
1 37 65
I7«»
17 44TBlTiBOe»,
IW181
9189 se
137 98
MSO 00 I89e 79
tmv.
14^7.
IMOOO
1 36 80
UM-iOl
8;
4480 IS 1897 »
1967a
nam
1792 33
14«gGi
iMS»
1793 07
seSL,;a|tlM5 WII84T 48
4482 dO.lSW 4i
«88 8!
1183 911
DUltt
iiiuau
;>e96 ^alxDes
D7]jM8 81
4483 38 1SB9 00
1988 89
14!!4 St
^41 ST
1119 63
1793 33
IHl 08
1130 Be
ine«
1- in 1 V)i I T-i;wi
S4J50
1140 80
- iijs B;
1341 K.
1140 GS
ITMSl
.1243 33
1140 96
1794 «t
l]''l! 44
1H3 71
1141 SB
iniBcn
J 11 87
1141 6
1795 31
1 -1K1S9
^44 61
1795 87
14.J7 70
2HS00
1798.00
11 iVpUHi
1418 IS
aa4a
IIWK
1798 83
;ii? ^ '^ ^1'*'^
6a4491 Br'lWM54E8M44
1438(4
tusa
11^ W
179«S7
0714 TOSBtS
00 185-
4S|l41«BO190S0»|ai96 0I
1418 96
max,
i;»oe
,~lC ib -(.■.1
(, Ij^vS
I7DTM
. n44Mii;«B»
1144 BS 1788 07
\\«> « \™i w
--"'
"-.4,M. lAn, --i-M. n .-- . 4,.^ -iWB, ■«,•;-,'« w\
b TAHBKNTa, ETC.
8 C rre 9 Ci
U.S ,US888 8W
ua stvwio B»i ^M lej nsi HSa
ma MtaS U3U
TABLB XV.-NATURAL SINdS AND COSINBS.
M
o
Sine
Cosin
.00000
One.
1
.00029
One.
2
.00066
One.
3
.00087
One.
4
.00116
One.
5
.00146
One.
6
.00175
One.
7
.00204
One.
8
.00288
One.
9
.00262
One.
10
.00291
One.
11
.00820
.99999
12
.00349
.99999
18
.00378
.99999
14
.00407
.99999
15
.00436
.99999
16
.00165
.99999
17
.00495
.99999
18
.00624
.99999
Id
.00558
.99998
20
.00682
.99996
81
.00611
.99996
22
.00640
.99996
88
.00669
.99998
84
.00698
tWaaO
86
.00727
.99997
86
.00756
.99997
87
.00765
.99997
88
.00614
.99997
89
.00844
.99996
80
.00873
.99996
81
.00902
.99996
82
.00931
.99996
88
.00960
.99995
84
.00989
.99995
85
.01018
.99995
86-
.01047
.99995
87
.01076
.99991
88
.01105
.09991
89
.01184
.99994
40
.01164
.99998
41
.01198
.99993
42
.01222
.99998
48
.01251
.99992
44
.01280
.99992
45
.01309
.99991
46
.01388
.99991
47
.01867
.99991
48
.01396
.99990
49
.01425
.99990
60
.01454
.99989
51
.01488
.99989
58
.01518
.99989
53
.01542
• U99ot}
54
.01571
..99988
55
.01600
.999o7
56
.01629
.99987
57
.01658
.99986
P»)
.03687
.99986
, S0 .017161.99086
£Ol.01745 i.99965 \
'Coaihisine
Sine
.01745
.01774
.01808
.01832
.01862
.01891
.01920
.01949
.01978
.02007
.02036
.02065
.02094
.02128
.02152
.02181
.02211
.02240
.02269
.02298
.02327
.08356
.02385
.02414
.02448
.02472
.02601
.02530
.02560
.02589
.02618
.026^
.02676
.08706
.02734
.02763
.02792
.02821
.02850
.02879
.02906
.02938
.02967
.02996
.08025
.08054
.03083
.03112
.03141
.08170
.03199
.03228
.03257
.03286
.08816
.03345
.08374
.03103
.03432
.0S461
.m90
CosiD
Cosin
.99986
.99984
.99964
.99963
.99983
.99962
.99962
.99981
.99980
.99980
.99979
.99979
.99978
.99977
.99977
.99976
.99976
.99975
.99974
.99974
.99973
.99978
.99972
.99971
.99970
.99969
.99969
.99968
.99967
.99966
.99966
.99965
.99964
.99963
.99963
.99962
.99961
.99960
.99959
.99959
.99968
.99957
.99966
.90955
.99954
.99053
.99952
.99952
.99951
.99950
.99949
.99948
.99947
.99946
.99945
.99941
.99943
.99942
.99941
.99940
.99939
Sine
SB*
2«
Sind
.03490
.03519
.03&16
.03577
.03600
.oaea^i
.08664
.03698
.08723
.08758
.oarrsi
.03810
.03839
.08868
.03897
.03926
.03956
.03964
.04013
.04042
.04071
.04100
.04129
.04159
.04188
.04217
.04246
.04275
.04304
.04333
.04362
.04391
.04420
.04449
.04478
.04507
.01586
.04566
.04594
.04623
.04658
.04682
.04711
.04740
.04709
.04798
.04827
.04656
.04685
.04014
.04943
.04978
.05001
.05030
.06059
.06086
.06117
.05146
.06175
.05205
.05234
Cosin
^99^
.99938
.99987
.99936
.99935
.99984
.99933
.99982
.99981
.99980
.99989
.99927
.99926
.99925
.99924
.99923
.99922
.99921
.99919
.99918
.99917
.99916
.99915
.99913
.99912
.99911
.99910
.99909
.99907
.99906
.99905
.99904
.99902
.99901
.99900
.99896
.99897
.99894
.99893
.99892
.99890
.99889
.99688
.99885
.99883
.99882
.99881
.99879
.99678
.99676
.99875
.99873
.99872
.99670
.99669
.99667
.99666
.99664
.9gBK»
8*
Sine Cosin
.05234
.05263
.05292
.05821
.05850
.06379
.06406
.05437
.05466
.05495
.05624
.05553
.05582
.05611
.06640
.06669
.05698
.05727
.05756
.05785
.05814
.06S44
.05873
.05902
.05931
.05960
.05989
.06018
.06047
.06076
.06106
.06184
.06163
.06192
.06221
.06250
.06279
.06306
.06337
.06366
.06396
.06484
.06453
.06482
.06511
.06540
.06569
.06598
.06627
.06656
.06685
.99668
.99861,
.99860'
.99858!
.99657
.99655
.996541
.99652!
.998511
.99649!
.99647j
.99846'
.99644
.99642
.99841
.99689*
.99686
.99686;
.99634
.99638'
.99881;
.99829
.99827
.99626
.996^
.996221
.99621;
.99619'
.99617)
.99615;
.99613^
.996I2!
.998101
.996061
.99606
.99604'
.99608
.99601
.99799
.99797,
.99795
.99793!
.99792
.99790,
.99788;
.99786'
.99784'
.99782
.99780
.997781
.99776
Sine Cosin
.06714 .99774
.067481.99772
.06773 .99770,
.06802
.06831
.06860
.06889
.06918
.06947
.0^«
.99768
.99766
.99764!
.99762:
.997601
.99758.
.99756
\^
.t)6976
.07005
.07064
.07063
.07092
.07121
.07150
.07179
.07808
.07287
.07860
.07295
.07324
.07853
.07882
.07411
.07440
.07469
.07498
.07527
.07556
.07585
.07614
.(r7643
.07678
.07701
.07730
.07759
.07788
.07817
.07846
.07875
.07904
.07963
.07968
.07991
.06020
.06049
.06078
.06107
.06186
.06165
.06194
.06223
.06258
.08281
.06810
.06339
.06368
.06397
.06426
.06455
.064&1
.06513
.06642
.06M1
.06600
.06689
.06656
.06687
.06716
.99756
.99754
.99758
.99750
.99748
.99746
.99744
.99748
.99740
.99738! 51
.99786 60
60
59
58
57
56
66
54
58
58
.09734
.99731
.99;^
.99787
.99785
.99728
.99781
.99719
.99710
.99714
.99718
.99710
.99706
.99706
.99703
.99701
.99696
.99694
.99698
.09680
.99687
.99665
.99088
.99680
.99678
.99670188
.99078188
49
48
47
46
45
44
48
48
41
40
87
86
86
84
88
8S
81
80
87
86
86
84
.99671
.99668
.99660
.99604
.99661
.99659
.99657
.99664
.99668
.99649
.99647
.99014
.99648
.99687
.99685
.99682
.99680
.99627
.99626
.99688
.99619
Cosinl Slno \\Coa\a\^Vxi<i Mf>wtoi\^Vtia
81
80
19
18
17
16
15
14
18
18
11
10
9
8
7
6
6
4
8
8
1
87'
%«>
OOA
TABLE XV^KATURAL SINIS AND COSINES.
L
^
h
p
9
«iie
OoBin
"o
.08n6
.09619
1
.08745
.99617
2
.08774
.99614
8
.08803
.99612
4
.08881
.99609
5
.OHHfiO
.90607
6
.nHH89
.09604
7
.08918
99602
8
.08947
.99509
9
.08976 .99596
10
.09005
.99594
11
.09031
.99601
12
.06063
.99568
13
.09003
.99566
14
.00121
.99563
15
.00150
.99560
16
.00179
.90578
17
.09008
.99575
18
.09S37
.99572
19
.09966
.0^70
ao
.09995
.99567
SI
.09834
.09564
22
.00853
.99562
23
.09883
.99559
24
.00411
.99556
26
.09440
.99563
26
.09469
.99551
27
.09498
.90548
28
.09Ba7
.99M5
29
.09566
.99542
80
.09685
.99540
81
.00814
.99687
82
.09842
.99534
33
.09671
.09631
84
.09700
.99628
85
.09729
.00686
86
.09758
.09623
87
.09787
.99520
88
.09816
.99517
30
.09645
.99514
40
.09674
.99511
41
.00903
.09508
42
.09982
.99506
43
.09961
.99503
44
.00990
.99500
45
.10019
.99407
46
.10048
.99494
47
.10077
.99401
48
.10106
.994H8
49
.10135
.99485
fiO
.10164
.99482
61
.10192
.99479
52
.lOSSl
.99476
53
.IQISO
.99473
54
.10879
.99470
55
.10808
.994<57
66
.10887
.994<U
57
10866
.09461
58
.10805
.994^
59
.10424
.99455
60
.10463
.90462
Sine'
Codn
§
,
i
A
y 11
6»
Sine
.10453
.10462
.10511
.10540
.10569
.10507
.10696
.10655
.10664
.10713
.10742
.10771
.10600
.10829
.10658
.10887
.10016
.10945
.10073
.11003
.11031
.11060
.11080
.11118
.11147
.11176
.11205
.11234
.11263
.11291
.11320
.11349
.11878
.11407
.11436
.11465
.11494
.11523
.11562
.11580
.11609
.11688
.11067
.11090
.11725
.11754
.11783
.11812
.11840
.11869
.11808
.11927
.iiavj
.11985
.12014
.12043
.12071
.12100
.12129
.12158
.12187
Cosiii Sine
Oodn
799462
• Vlfsvv
■ VtrHO
.99443
.90437
.90431
.90128
.99424
.00121
.99418
.99415
.09412,
.90409!
.9040GJ
.094021
.99390
.09396!
.093931
. WtJWJ [
.99383
.90380
.99077
.99374
.99370
.99367
.99364
.99360
.90357
.90354
.09351
.90347
.9a344
.90341
.99337
.90334
.90331
.99327
.99324
.99320
.99317
.90314
.09310
•90307
.90303
.99300
.99297
.99293
.90290
.99286
.09283
.99279
.99376
.99972
.99269
.99965
.99S62
.99255
7»
Sine
"2187
2216
2246
2274
2302
2381!
2360
2889
2418
2447
2476
2504
2533
2562
2591
2620
2619
2678
2706
2735
2764
2793
2822
2851
2880
2908
2987
2966
2995
3024
3053
3061
8110
3189
3168
8197
3226
3254
3283
3312
3341
8370
3399
3427
3456
3165
3514
3543
3572
3600
3029
3658
3687
8716
3744
8773
3802
3831!
8860
3889
3017
Cosin
Coain \ &me
.09966
.99351
.99348
.09344
.99340
.99287
.99283
.99380
.99226
.09292
.99219
.09215
.99211
.90208
.90204!
.09200
.99197
.99103
.99189
.99186
.09182
.99178
.90175
.90in
.99167
.99168
.99160
.99156
.99152
.99148
.99144
.99141
.99187
.99183
.99129
.99125
.99122
.99118
.99114
.99110
.99106
.99102
. V9U00
.99094
.99091
.99087
.90079
.90075
.90071
.09067
.09063
.99050
.99055
.09051
.99047
.99043
.09039
.99035
.99031
.9!K)27
$•
.14284
.14363
.14292
.14320
.14340
.14378
.14407
.14436
.14464
.14493
.14622
.14551
.14680
.14606
.14687
.14666
.14095
.14723
.14752
.14781
.14810
.14838
.14867
.14896
.14925
.14054
.14962
.15011
.15040
.15069
.16097
.15126
.15165
.16164
.15212
.15241
.15270
.15299
.15327
.15366
.15885
.15414
.15442
.ir>171
.15500
.15529
.15557
.15586
.1.')615
.15643
Bine^ Oosin
Tl89i7
.13046
.13975
.14004
.14083
.14061
.14090
.14119
.14148
.14177
.14205
.09027
.99023
.99019
.99015
.99011
. VoUUti
.99002
. i^^W*!
QAQOn
QAQR9
.98978
.96973
• HCwOv
.98961
.98957
.98053
.98948
.98044
.96981
.06927
.96923
.98919
.98914
.98910
.98906
.96902
.vfxSvi
nofiOQ
Qfififtl
.08880
.96876
.98871
.96863
.96854
.98849
QMU1
.98836
.98882
.06623
.98818
.98814
.98809
.98805
.98800
.98796
.98791
.98787
.98782
.98778
.98773:
.98769
e<
Sine Cosin
.15643
.15672
.16701
.l«y730
.16768
.1M«7
.15616
.15645
.15873!
.16902
.15031
.16969
.15068
.16017
.16046
.16074
.16103
.16132
.16160
.16169
.16216
.16846
.16275
.16304
.16383
.16361
.16390
.16419
.16147
.16476
.16505
.16583
.16562
.16591
.16620
.16648
.16677
.16706
.16784
.16763
.16792
.16620
.16849
.16878
.16906
.16935
.16961
.16992;
.170211
.17050
.17078
.17107
.17186
.17161
.in93
.17222
.17250
1.17279'.
1.17808,
.17336
.96769
.98764
.98760
.08756,
.96751!
.96746
.96741 1 54
.96737: 53
.96732! 62
.96728' 61
.96723 60
60
69
68
67
66
65
49
48
47
46
46
44
43
.96718
.98714
.96709
.96704
.08700
.96695
.96600
.98686142
.986811 41
.96676j40
.96671' 80
.06667,36
.98662 37
.98667186
.98662,86
.98618 34
.96643 38
.96688 88
.96683 81
.96629 80
.98624 99
.96619; 88
.96614! 27
.98609196
.98600
.96606
.98600
.96566
.98560
25
34
28
22
21
20
.98575< 19
.98570! 16
.96565
.98561
.98556
.98551
.08546
.96541
.98536
.98531
.96626
.98521
.98516
.98611
.96506
.96601
.96496
.98491
.98486
.98A&V>
17
16
16
14
18
12
11
10
9
6
7
6
5
4
3
2
1
<\
%3^
TABLE XV—NATORAl BINB8 AND COSINES.
L
§
15» 1
ie» 1
17«» 1
18» 1
19«
•
60
Sine
Cosin
Sine
Cosin
Sine
Cosin
Sine
.30902
Cosin
Sine
Cosin
.25883
.96693
.27564
.96126
.29287
.95680
.95106
.82557
.94562
1
.25910
.96585
.27592
.96118
.29265
.95622
.80929
.95097
.32584
.94542
59
2
.25938
.96578
.27020
.96110
.29293
.95618
.30957
.95088
.32612
.94583
56
8
.25966
.96570
.27648
.96102
.29321
.95605
; .30985
.95079
.82689
.94528
57
4
.25994
.96562
.27676
.96094
.29348
.95596
.31012
.96070
.32667
.94514
56
6
.26022
.96555
.27704
.96086
.29376
.95588
.31040
.95061
.32694
.94504
55
6
.26060
.96547
.27731
.96078
.29404
.95579
.31068
.96052
.32722
.94495
54
7
.26079
.96540
.27759
•96070
.29432
.955n
.31095
.95043
.32749
.94485
53
8
.26107
.96532
.27787
.96062
.29460
.95562
.81123
.95088
' .82777
.94476
52
9
.26135
.96624
.27815 .96054
.29487
.95554
.31151
.95024
.32804
.94466
51
10
.26163
.96517
.27843 .96046
1
.29515
.95545
.81178
.95015
.82882
.94457
50
11
.26191
.96509
.27871
.96087
.29643
.95536
.81206
.95006
.32880
.94447
49
12
.26219
.96602'
.27899
.96029
.29571
.95528
.31283
.94997
.82887
.94488
48
18
.26^7
.96494,
.27927
.96021
.29599
.95519
.31261
.94968
.82914
.04428
47
14
.26275
.96486
.27955
.96013
.29626
.95511
.31289
.94979
.32942
.94418
46
15
.26303
.96479
.27983
.96005
.29664
.95502
.31816
.94970
.82969
.94409
45
16
.26331
.96471;
.28011
.95097
.29682
.95493
.31344
.94961
.82997
.94399
44
17
.26359
.96463
.28089
.95989
.29710
.95485
.31372
.94952
.83024
.94300
43
18
.26887
.96456
.28067
.95981
.29787
.95476
.31399
.94943
.33061
.94880
42
10
.26415
.96448
.88005
.95972
.29765
.95467
.81427
.94983
.33079
.94370
41
20
.26443
.96440
.28123
.95964
.29793
.95459
.31454
.94924
.33106
.94361
40
21
.26471
.96433
.28150
.95956
.29821
.95450
.31482
.94915
.83134
.94351
89
22
.26500
.96425
.28178
.95948
.29649
.95441
.31510
.94906
.83161
.94342
38
23
.26628
.96417
.28206
.95940
.29876
.95433
.31587
.94897
.&S189
.94832
37
24
.26666
.96410
.28234
.95931
.29904
.95424
.31565
.94888
.83216
.94322
38
25
.26684
.96402
.28262
.95923
.29982
.95415
.31593
.94878
.38244
.94313
35
26
.26612
.96394
.28290
.95915
.29960
.95407
.31620
.94869
.33271
.94303
34
27
.26640
.96386
.28318
.95907
.29987
.95398
.31648
.94860
.33296
.94293
33
28
.26668
.96379
.28346
.95898
.30015
.95889
.31675
.94851
.38326
.94284
82
29
.26696
.96371
.28374
.95890
.80043
.95880
.31703
.94842
.33353
.94274
31
80
.26724
.96363
.28402
.06882
.30071
.95372
.31730
.94832
.38381
.94264
30
31
.26752
.96855
.28429
.05874
.30098
.95863
.31758
.94823
.33408
.94254
29
82
.26780
.96347
.28457
.05865
.80120
.95854
.81786
.94814
.83486
.94245
28
88
.26808
.96840
.28485
.05857
.80154
.05345
.31813
.94805
.83463
.94285
27
84
.26836
.96832
.28513
.05849
.80182
.05887
.81841
.94795
.83490
.94225
26
85
.26864
.96324
.28541
.05841
.80209
.05828
.31868
.94786
.83518
.94215
26
86
.26892
.96316
.28569
.05882
.80287
.05319
.81896
.94777
.88545
.94206
24
87
.26920
.96308
.28597
.0581»
.80265
.05310
.31923
.94768
.33573
.94196
23
88
.26948
.96801
.28625
.05816
.80292
.05301
.81951
.94758
.33600
.94186
22
89
.26976
.96293
.28652
.05807
.80320
.05293
.81979
.94749
.33627
.94176
21
40
.27004
.96285
.28680
.05799
.80848
.05284
.82006
.94740
.38655
.94167
20
41
.27032
.96277
.28708
.05791
.80876
.06275
.82084
.04730
.83682
.94157
19
42
.27060
.96269
.28786
.05782
.30403
.05266
.82001
.04721
.88710
.94147
18
48
.27068
.96261
.28784
.05774
.80481
.05257
.32069
.04712
.83737
.94137
17
44
.27116
.96253
.28792
.05766
.80459
.05248
.82116
.04702
.88764
.94127
16
45
.27144
.96246
.05767
.80486
.05240
.82144
.04603
.83798
.94118
15
46
.27172
.96238
^»47
.05749
.30514
.05281
.82171
.04684
.88819
.94108
14
47
.27200
.96280:
!28875
.95740
.30542
.95222
.82199
.04674
.38846
.94098
13
48
.27228
.96222
.28903
.95782
.80570
.95213
.3222';
.04665
.83874
.94068
12
49
.27256
.962141
.28931
.95724
.80597
.95204
.82254
.04656
83901
.94078
n
50
.27264
.96206
.28959
.95715
.80625
.95195
.32282
.04646
.33929
.94068
10
61
.27812
.96198
.28967
.05707
.80653
.95186
.82809
.04637
.38956
.94056
9
52
.27840
.96190,
.29015
.06698
.30680
.95177
.32337
.94627
.33983
.94049
8
58
.27868
.96182
.29042
.95690
.80708
.95168
.82364
.94618
.34011
.94039
7
54
.27896
.96174
.29070
.95681
.80736
.95159
.82392
.94609
.34088
.94029
6
56
.27424
.96166;
.29098
.95678
.30763
.95150
.32419
.94599
.34065
.94019
5
56
.27452 .96158;
.29126
.95664
.30791
.95142'
.32447
.94590
.34093
.94009
4
57
.27480 .96150;
.29154
.95656
.30619
.95133
.32474
.94580
.84120
.93999
3
58
.27608 .96142
.29182
.95647
.30646
.95124
.32502
.94571
.84147
.98969
2
59
.275861.96134
.29209
.95639
.30674
.951151
.32020
.94561
.34175
.93979
1
60
.27564 .96126
.29237
.95630
.80902
.95106:
.82667
.94562
.34202
, .oawftl <\ V
§
Cosin Sine
Cosin
Sine
Cosin Sine \
'
74
• //
71
!•
1
a*
2%a
TABLB ZV.-lf ATDSAL SINS8 AND COBINBfiL
25« ... 1
96^ 1
«7* 1
86- 1
88* 1
60
Bine
Cofiln
.9di^i
Sine
.48847
Ck>sin
.89879
Sine
.45899
OoBin
'89101
Sine
.46047
Oosin
Sine
Gosln
.87468
.48808
.88885
.48481
1
.488881.90618
.48863
.89667
.45485
.89087
.46078
.88281
.48606
.87448
59
8
.48315 .90606
.48889
.89864
.45451
.89074
.46090
.88867
.48588
.87484
68
8
.48841 ' .90694
.48916
.89641
.454rr
.89061
.47084
.88854
.48567,. 87480
57
4
.48867 .90082
,.48948
.89888
.456031.89048
.47050
.88840
.48583 .87406
66
6
.48894!. 90569
.48968
.80816
.45529!. 80035
.47076
.88286
.48606 .87391
55
6
.4^180,. 90557
.48994
.89803;
.45554 .89081
.47101
.88813
.48684 -.87377
54
7
.48146 .90546
.44080
.89790
.45580
.89006
.47187
.88199
.486691.87863
53
8
.48178 -.90538
.44046
.89777
.45606
.88995
.47153
.88185
.48684 .87849
68
9
.48499
.9(»80
.44072
.89764
.45638
.88981
.4n78
.88172
.48710
.87885
51
10
.48685
.90507
.44098
.80752
.45658
.88908
.47804
.88158
.48785
.87881
GO
11
.48658
.90495
.44184
.89789
.45684
.88965
.47880
.88144
.48761
.87806
49
18
.48678
.90483
.44151
.89726
.45710
.88048
.47856
.86180
.48786
.87898
48
18
.48604
.90470
.441771.89713,
45736
.88988
.47881
.88117
.48811
.87878
47
14
.48681
.90458
.44803 .89700
.45768
.88915
.47306
.88103
.48887
.87864
46
15
.48657
.90446
.44229!. 89687'
.45787
.88908
.47888
.88089
.48868
.87850
45
16 .48668
.90433
.44855
.89674 j
.45813
aoooa
.47358
.88075
.48888
.87885
44
17 .48709
.90481
j .44881
.89668,
.45839
.88875
j .47383
.88062
.48913
.87881
43
18 .48786
.90408
.44807
.89649
.45865
.NK868
1.47400
.88048
.48968
.87807
48
19
.48788
.90396
.44833
.89686'
.46891
.88848
.47484
.88034
.48964
.8n08
41
80
.48788
.90883
! .44859
.80683
.45917
.H8H35
.47460
.88080
.48069
.87178
40
81
.48815
.90871
.44885
.89610
.46043
.KRR88
.47486
.88006
.40014
.87164
89
88
.48841
.90858
.44411
.88507
.45968
.iXXMo
; .47511
.87908
.49040
.87150
88
88
.48867
.90346
.44487
.89584
.45994
.88705
.47537
.87970
.49065
.87136
87
84
.48894
.90834
.^464
.895711
.40080
.88788
.47568
.87965
.49090
.87181
86
86
48980
.90881
.44400
.80558
.46046
.88768
.47588
.87961
.49116
.87107
85
86
!48946
.90309
.44516
.69545
.46078
.88755
.47614
.87987
.49141
.87093
9i
87
.48978
.90896
.44548
.89588
.46097
.88741
.47630
.87983
.49166
.87079
83
88
.48999
.90884
.44568
.89519
.46183
.88728
.47065
.87909
.49198
.87064
88
89
.48085
.9»71
.44694
.89506
.46149
.88715
.47600
.87896
.49817
.87050
81
80
.48061
.90859
.44680
.89493
.46175
.88701
.47716
.87882
.49M8
.87036
80
81
.48077
.90846
.44646
.89480
.46801
.88688
.47741
.87868
.49868
.87081
89
88
.48104
.90833
.446?i
.89467
.46886
.88674
.47767
.87864
.49898
.87007
88
88
.43180
.90881
.44698
.89454
.46858
.88661
.47793
.87840
.49818
.86093
27
84
.43166
.90808
.44784
.89U1
.46878
.88647,
.47818
.87826
.49844
.86978
86
86
.43188
.90196
.44750
.89488
.468M
.88634
.47944
.87818
.48369
.86964
85
86
.48809
.90183
.^776
.89415
.46880
.88680
.47809
.87708
.49694
.86049
84
»r
.43885
.901711
.44808
.89408
.46365
.88607
.47895
.877&4
.40419
.86935
83
88
.43861
.90158:
.44888
.89389
.46881
.88603
.47020
.87770
.48445
.86081
88
89
.43887
.90140;
.44854
.80876
.46407
.88580
.47»46
.87756
.40470
.86906
81
40
.48S13
.90133
.44880
.89863
.46433
.88666
.47071
.87743
.49496
.86898
80
41
.48840
.90180 '
.44906
.80860
.46458
.88553
.47007
.87729
.40681
.86878
19
42
.43366
.90ias
.44938
.80337
.4(M&4
.88539
.48028
.87715
.40646
.86863
18
43
.43398
.900U5
.44«38
.89884
.46510
.88686
.48048
.87701
.40671
.86849
17
44
.43418
.90088
.44984
.80811
.46536
.88518
.48078!. 87687 i
.40606
.86834
16
45
.43445
.90070
.45010
.89898
.46561
.88409
.48090
.87673!
.40628
.86880
15
46
.43471
.90057.
.45036
.80885
.46587
.88485
.48124
.876591
.40647
.86805
14
47
.43497
.90045
.45008
.89878
.46613
.88478
.48150;. 87645 i
.40678
.86791
13
48
.43583
.90038.
.4*5088
.80850
.46639
.8&458
.48176
.876311
.40607
.86777
12
49
.43549
.90019
.45114
.8g»45
.46664
.88445
.48801
.87617
.40788
.86768
11
50
.43575
.90007
.45140
.80838
.46690
.88431
.48826
.87603
.40748
.86748
10
61
.48608
.89994
.46166
.80810
.46716
.88417
.48858
.87689
.48778
.86788
9
62
.43088
.89981
.45198
.89806
.46748
.88404
.48877
.87575
.40708
.86n9
8
53
.43654
.89968'
.45818
.80103
.46767
.88890
.48808
.87561
.40684
.86704
7
54
.43680
.89956
.45848
.80180
.46796
.8887?
.48888
.876461!. 40649
.86690
6
56
.43706
.89943
.45869
.80167
.46819
.88863
.48854
.87588
.49674
.86675
5
56
.43783
.899:^
.46895
.80153
.46844
.88349
.48879
.87518
.49899
.86661
4
67
.43759 .89918
.45321
.80140
.46870
.88336
.48406
.875041
.49984
.66646
3
58
.43785,. 89905
.45347
.80127
.46896
.88388
.48430
.87490
.49950
.86638
8
59
.43811 .89808,
.45873
.80114
.46981
.cXKMIw
.48456
.87476
.49975
.86617
1
60
i
.43887
CoAin
.89879
.45399
Coflln
.89101
Sine
.46947
.88895
Sine
.48481
.87468
.50000
.86603
_0
Sine
|Ck>8in
^Co«l\ii^«afe ^
^Q/CW&SXX^dOkSb
■^\ *
ii
\'
es» I
1 Qlo
W f
iV
\ ^1^ \
23X
TABLB ZV.— NATURAL SINES AND COSINES.
1
2
8
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
28
24
26
26
27
28
99
80
81
82
83
84
85
86
87
88
89
40
41
42
48
44
45
46
47
48
49
60
51
52
53
54
55
56
57
58
59
60
80*
Sine Oosln
.50000
.50025
.50060
.50076
.50101
.50126
.50151
.60176
.50201
.50227
.50252
.50277
.50902
.50327
.50352
.50377
.50103
.50128
.50453
.50478
.50603
.60628
.50553
.50678
.50008
.50628
.50654
.50679
.50704
.50729
.60754
.60779
.50604
.50829
.50854
.50679
.50904
.50929
.50954
.50979
.51004
.51029
.51054
.51079
.51104
.51129
.51154
.51179
.51204
.51229
.51254
.61279
.51804
.51329
.51354
.51379
.51404
.51429
.51454
.51479
.51504
.86608
.86588
.86573
.86669
.86544
.86580
.86515
.86501
.86486
.86471
.86457
.86442
.86427
.86413
.86398
.86381
.86869
.86854
.86340
.86325
.86810
.86295
.86281
.86266
.86251
.86237
.86222
.86207
.86192
.86178
.86163
.86148
.86133
.86119
.86101
.86069
.86074
.86059
.86015
.86080
.86015
.86000
.86986
.86970
.86966
.86941
.86926
.86911
.86896
.86881
.86866
.86851
.85836
.85821
.85806
.85792
.85777
.85762
.85747
.85732
.85717
81<
Sine
.61504
.61529
.51664
.51579
.51604
.51628
.51653
.51678
.51703
.51'ra8
.51753
.61778
.51803
.51828
.51852
.51677
.51902
.51927
.61952
.51977
.52002
.62026
.52061
.52076
.62101
.52126
.52151
.52175
.52200
.62225
.52260
.62275
.52299
.62324
.52349
.52374
.52399
.52123
.52448
.52473
.52198
.52522
.52547
.52572
.52597
.62621
.52646
.52671
.52696
.52720
.52745
.62770
.52794
.62819
.62844
.52869
.52893
.52918
.52948
.52967
.52992
Oosin
CoBin
.8M17
.85702
.86687
.86672
.85657
.85642
.a5627
.86612
.86597
.85582
.85667
.85651
.85536
.85521
.85506
.85491
.85476
.85161
.85446
.86431
.85416
.85401
.86385
.85370
.85365
.85310
.85825
.85310
.85294
.85279
.85264
.85219
.85234
.86216
.86203
.85188
.85173
.85157
.86142
.85127
.85112
.85096
.86061
.85066
.85061
.85035
.86020
.86005
.81989
.84974
.849691
.84943!
.84926;
.84913
.84897
.84882
.64866
.84851
.84836
.648201
.84605
Sine
32»
Sine Coflln
52992>
53017!
530411
58066
53091
53115
53140
53164
53169
53214
53238
58263
53268
53312
53837
53861
53386
53411
53485
58460
58484
68609
53534
53658
53663
63607
53632
53656
53661
53705
53730
53754
53779
63804
53828
53653
53677
63902
53926
53951
53975
54000
54021
54019
54073
54007
54122
54146
54171
54195
54220
54244
54269
54293
64317
54312
54366
54391
54415
54440
54464
Cosin
.84805
.84789
.64774
.64759
.84743
.64728
.84712
.64697,
.61661
.61666
.81650
.61635'
.61619
.616041
.84588
.64573
.61557
.64542
.61526
.645111
.61495!
.84460
.84464
.64446
.64433
.^417 1
.»1402!
.84366
.84370
.64355
.&1889
.84824
.61306;
.84202
.84277'
.84261
.61215
.64230
.61214
.61196
.64182
.84167
.64151
.64135
.84120
.64104
.64072
.81057
.61041
.61025
.84009
.63994
.63976
.83962
.83046
.63930
.&3915
.63699
.63683
Sine"
8S«
Sine Ck>8in
54464
54486
54513
54537
54561
54566
54610
54635
M659
51683
M708
54782
54756
54781
54805
54829
54654
54878
54902
54927
54951
64975
54990
65021
55046
55072
56097
55121
55145
55169
65194
65218
56242
55266
55291
55315
55339
55363
55386
55412
55436
55460
554^
56609
56533
55557
55561
55605
55630
55654
55676
65702
65726
56750
66775
55799
55823
55847
55671
55695
M919
Cosin
57^
232
w
84*
Sine Cosin
.88867
.63851
.63835
.83819
.63804
.63788
.637^
.63756
.83740
.63724
.837U6
.83602
.88676
.63660
.68645
.83629
.68613
.83597
.63561
.83565
.68549
.83533
.63617
.63501
.63485
.83469
.63453
.68437
.83421
.63405
.88369
.83878
.63356
.83840
.83821
.63306,
.632921
.832761
.83260
.83244
.63228
.88212
.83195
.83179
.83163
.83147
.63131
.63115:
.63098
.63062
.83066 I
.63050 I
.83084 I
.83017 >
.63001
.82985
.82969:
.829531
.62936
.62920
.82904
Sine I j Cosin
.66019
.55948
.55966
.55992
.56016
.56040
.56064
.56068
.66112
.66136
.56160
.56184
.56206
.56282
.56256
.56280
.56805
.56829
.56853
.56877
.66401
.66425
.56440
.56473
.56497
.56621
.66645
.56669
.66693
.66617
.56641
.66665
.66669
.66n3
.56786
.56760
.667M
.56806
.56632
.66856
.66860
.56904
.56928
.56062
.56976
.57000
.57024
.67047
.57071
.57095
.5ni9
.67148
.57167
.5n91
.57815
.57236
.57262
.57286
.57810
.57834
.57358
.82904 60
.82887,60
.828n 58
.82865 57
.82689,56
.826S2'55
.82606,51
.627901 53
.62773 52
.82757, 51
.627411 50
.82724149
.82706 48
.82692 47
.82675' 46
.82659 45
.62648 44
.82826 43
.82610 42
82593 4.
.62577.40
.82561' 80
.82544 88
.82528,87
.82611 86
.82495 85
.88478:84
.82462! 88
.62446 82
.82129,81
.82418 80
29
28
.82896
.82860
.82868' 27
.82847,26
.82380 25
.82814 iU
.82297123
.82281122
.62264121
.82248 20
.82231 19
.82214 18
.82198 17
.82181116
.82165 15
.82148. 14
.82132: 13
.82115! 12
.82098; 11
.82082 10
.82065
.82018
.62082
.82015
.61999
.61982
.81965
.61949; 2'
.81982; r
.819151
Sine'l*^
9
8
7
V
4
8
««*
w
\
i
TABLE XY.— NATURAL SINES AND C08INX8.
t
S5«
86<>
zv
zt*
ad« 1
60
Sine
Cosin
.81915
Sine
.58779
Cosin
.80902
Sine
T60182
Cosin
Sine
.61566
Cosin
.78801
Sine
Cosin
"O .67358
.62882
.77715
1 ! .67381
.81809
.58802
.808851
.60205
.70646 !
.61689
.78783
.62965
.77606
68
2 . .57405
.81882
.58826
.80867
.60228!. 79829,
.61612
.78765
.62977
.77678
68
8 .57429
.81865
.58849
.80850:
.602511.79811
.61636
.78747
.63000
.77660
57
4 .67453
.81848
.58873
.80633;
.60274
.79793
.61658
.78729
.68022
.77641
56
5 .67477
.81832
.68896
.80616:
.60298
.797761
.61681
.78711
.68046
.77628
55
6 • .57501
.81815
.58920
.80799;
.60;«1 .79758!
.61704
.78694
.68066
.77606
54
7 .57524
.817981
.58943
.80782
.60344
.79741
.61726
.78676
.68000
.77586
68
8 .57548
.817821
.58967
.80765
.60367
.79723
.61749
.78658
.68118
.77866
62
9 ' .57572
.81765
.58990
.80748
.60390 .79706
.61772
.78640
.68186
.77560
51
10 1 .57596
.81748
.59014
.80730
.60414
.79688
.61796
.78622
.68166
.77581
50
11
.57619
.81731
.69037
.80713;
.60487
.79671
.61818
.78604
.68180
.77518
40
12
.57643
.81714
.59061
.80696'
.60460
.79658
.61841
.78686
.68906
.77484
48
13
.57667
.81698
.59084
.80679
.60483
.79635
.61864
.78668
.68225
.77476
47
14
.57691
.81681
.59108
.80662
.60506
.79618
.61887
.78660
.68848
.77468
46
15
.57715
.81664
.59131
.80644
.60529
.79600
.61909
.78683:
.68871
.77489
45
16
.57738
.81647
.69154
.80627
.60553
.79583
.61982
.786141
.68293
.77481
44
17
.57762
.81631
.59178
.80610
.60576
.79666
.61966
.78496
.68816
.77408
48
18
.57786
.81614
.59201
.80593
.60599
.79547
.61978'. 78478!
.68888 1.77884
42
19
.57810
.81597
.59225
.80576
.60622
.79530
.62001
.78460'
.68861
.77866
41
20
.67833
.81580
.59^18
.80558
.60646
.79512
.62024
.78442
.68883
.77847
40
21
.67857
.81563
.69272
.80641
.60668
.79494
.62046
.78424
.68406
.77828
88
22
.57881
.81^46
.592&5
.80524
.60691
.79477
.62069
.78406
.63428
.778101 38
23
.57904
.81530
.59318
.80507
.60714
.79469
.62092
.78887
.68461
.77292 87
24
.57928
.81513
.59342
.80489
.60738
.79441
.62115
.78869
.68473
.77278 86
25
.57952
.81496
.59365
.80472
.60761
.79424
.62188
.78861
.68496!. 77856 185
26
.57976
.81479
.59389
.80455
.60784
.79406
.62160
.78888
.68518!. 77286
ai
27
.57999
.81462
.59412
.80438!
.60807
.79888
.62188
.788161
.68640;. 77218
83
28
.58023
.81445;
.59436
.804201
.60630
.79871
.62206
.782971
.68668 .77199
82
29
.58047
.814281
.59469
.804031
60653
.79358
.62229
.78279
.685851.77181
81
30
.58070
.81412
.59482
.80386|
.60876
.79836
.62251
.78261
.68606 .77162
80
31
.68094
.81395
.59606
.80368
.60699
.79318
.62274
.78248
.68680
.77144
89
32
.58118
.81378
.59529
.80351
.60929
.79800
.62297
.78825
.68668 1.77125
28
33
.58141
.81361
.59552
.80334
.60946
.79282
.62820
.78206
.68675
.77107
27
a4
.58165
.81344
.59576
.80316'
.60968
.79264
.62342
.78188
.68696!. 77068
26
35
.58189
.81327
.59599
.80299
.60991
.79247
.62866
.78170
.687201.77070125
86
.58212
.81.310;
.59622
.80282!
.61015
.79229
.62388
.78152;
.68748J. 770511 24
87
.58236
.81293!
.59646
.80264!
.61038
.79211
.62411
.781841
.68765. 77038 23
88
.58260
.81276'
.59669
.80247.
.61061
.79193
.62433
.78116;
.68767 .77014 22
89
.58283
.81259
.59693
.80230;
.61084
.79176
.62466
.780061
.68810 .76996' 21
40
.58807 .81242
.59716
.80212
.61107
.79158
.62479
.78079J
.68882 .76977 j 20
41
.58330 .81225
.59789
.80195
.61130
.79140
.62502
.78061'
.68864
.76859, 19
42
.58354
.81208
.59763
.80178
.61153
.79122
.62524
.78043
.68877
.76040 IH
43
.58378
.81191
.69786
.80160'
.61176
.79106
.62547
.78025
.68899!. 76921 17
44
.58101
.81174,
.59809;. 80143
.61199
.79087
.62570
.78007
.63922. 76903 16
45
.58425 .81157,
.59832 '.80125
.61222
.79069
.62592
.77988
.63944;. 76884 115
46
.58449|. 81140'
.598561.80108
.61245
.79051
.62615
.r/970
.63966 .76866
14
47
.58472,. 81 1231
.59879 .80091
.61268
.79033
.62638 .77952
.689891.76847
13
48
.58496
.81106,
.599021.80073
.61291
.79016
.62660
.77934
.640111.76828
12
49 .58519
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.599261.80056
.61314
.78998
.62683
.77916
.64038 .76810
11
50 .6854.S
.81072
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.61337
.78980
.62706
.77897
.64056 .76791
10
51
.58567
.81055
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.61360
.78962
.62728
.77879
.64078
.76772
9
52
.58590
.81038
.59995
80003:
.613a3
.78944
.62751
.77861
.64100
.76754
8
53
.58614
.81021
.60019
.79986!
.61406
.78926
.62774
.77848
.64128
.76786
7
54
.58637
.81004
.60042
.79968:
.61429
.78906
.62796
.77824
.64145
.76717
6
55
.586(S1
.80987
.60065
.79951!
.61451
.78891
.62819
.77806!
.64167
.76698
5
56
.58684
.80970
.60089
.79934
.61474
.78873
i .62842
.77788,
.64190 .76679
4
57
.58708
.80953
.60112
.79916
.61497
.78856
1.62864
.77769'
.64212 .76661
3
58 .58731
.80936;
.60136
.79899
.61520
.78837
.62887
.77751!
.64234 .76642
2
59 .58755
.80919,
.601581.79881
.61543
.78819
.62909
.7'7733
.64256 .76628
1
60 ; .58779
.80902
Sine
.60182
Cosin
.79864
Sine j
.61566
.78801
.62932
.77715
.64279
.76604
/
Cosin
Cosin
Siuft (^yc«>«ta3L^
\^b«<&sv
V^Scas^
5
_/
«• w
53» \
\ Q
a*'
w ^
\
^K*
««
a^v
TABLB ZT.-NATnSAL 8INBB 1
' — M 18
1 .TStlTl
I .78998
s .Ttam]
'.KTSa '.1
.tKSl .1
.8W03 .1
■n .loan .1
il .tma .n
■ .toss .1
.NKT,.1
1 .-mil .
L'.TSMS .
iLtkio .
) .71003
} .urns'
Msaa .',
wnar ,1
etaa .:
/7I
\ .7400S .
) .T49se .
! .74897 ■ .. . ..
i .74548 ,67914 .;
i .74028 ,BT9«5 .',
r .74n09 .«7987 .I
' ,887181. 744BB l.WOce ,1
.887401.74470 ."
.867821.74451 ,
' . 86788'. T4431 ._
I .eseoB .74412 I .«xns .;
.ffiMlO .7
.8iH4a:.7
I .flesHi 1 .7
!8M34i:t
.W445:.7
I XVI,— NUTtlRAJ, TAirOENTfl i
C0TASBBNT8.
0- II
S" r
a-
60
_T«.B_
iDliiute.
ranf(_
Cotang
r«iK_
Co«nK
rane 1 ooi
5^
ftT,IJUUd
2M.tH63 1
OKii' T"
0811
aia7.75
BO.SSOe
»Gil
S8.BBW
05!.'70
0765
09
1718-87
01804
M.441S
iH.I«64
oaaoB
Wll
«
ins.sa
]I9S3
M.SUIS
03079
ar.vm
JSSM
DSKH
03838
s:^:9fl7
08607
«7:i!715
oMie
46i5
04
.ooati
4B1.10(3
omt
51.3033
03698
»r,0M6
35MI1
3655
53
. .oom
nmt
^'^?
2877
DOSOS
< ioKdl
8ia:774
SiOSA
13783
ae!43i6
0B6S3 8
.008M
Sia,BS!
030M
48.1191
0S813
96,8806
»S6S
980!
49
: .00*19
a«.47a
>Mfl5
BSH
8863
48
47!o8ra
47
46.4469
95610
46
; '.oam
K9:iH2
oaisa
4fl-BS&l
OTO»
SS.4.W
8103
4F
. .oam
aii.BsB
own
46.20)1
oasss
KMO
41.R3H0
03987
4S
04013
9] 18078
3432
4S
1 '.oosiS
180:932
43!SS1
31,71M
05795
£358
i OONS
171.885
oaasa
4s.a»i
MT5
24.5118
05(B4 ir
leea
0S357
42.433S
mr
yism
41.0108
St! 1957
: :om»
m'.iei
0)168
S4,M68
ffioia i(
0160
.OOI»S
i4S.33r
Mlill
BBJO
13I7S
tis'.e^i
I27;a2i
no.sm
OtS79
S8,3T18
5674
3 -«i8ia
IW.774
OKBW
OISOS
8B,»187
00068 t
5076
} .00844
M589
0IM7
42S8
3 .C»873
01306
3499
110.8B2
oasiS
B7.7088
23,™0
06145 f
sns
29
I .00031
mr?
38
1 .OOS60
sslosoo
27
( .00989
101 ! J 07
36.5057
saiaoBi
08338
0130
38
) .01018
99.8179
037ft
38, 1770
W.M3
S3,l(!40
MS6S !
06S7
5 .01017
96. 4895
ame
3045
.OlOTS
9i.e083
J!»i
33!4313
siisnis
8211
SS
M.4A33
35.061)5
21.7128
06S.'ia !!
7483
88.1438
31.7H1
21,01)58
36379 !
6Mi
» .01194
83.0398
oaiio
31.8078
01058
0048
si.»3no
m87 i;
6340
19
1 '.otsss
«i:Kiro
ffi9G8
01710
S1.8WB
4838
le
1 .ouai
TS.W34
0SB97
ai.am
W7«
78.1*83
MOM
Dosas 5
3351
', !d1309
so.mra
06%4 5
15
S .C13S8
U'.-iWi
noM
siAm i
ao,6i®f
08flM ,'
18K
r .oiaoT
73,1390
C«114
3*.11S1 i
jisia
20,Bfl9l
12SS
1 .oisaa
71.B1B1 1
Kua
70,1.WJ
jwvri 4
9808
68,7301
siituie 1
01049
ao:ao50
0344
10
.0148*
67.401B
ossao
3o.«mi
1I9JB
fiO.OWE
8506
omaa
S0.6833 1
lil.B70B
OOTSO ,|
S
Oft^
80.4116
0.8046
56788 i
7S17
4 .01S71
u;i,<iii«7
80.1440
»nfl«
0.7408
fl0S5
K .oieoo
Ba,4B9a
MSIB
en.stes
1 .mtsa
0:4051
OCOOB t,|
481!3
1 iotflw
bsiaifiii
03481
siijsao
0M82
l!lli9M
00931 H
4aw 3
B -0171B
BN.ana
01W3
jsaia
ISi.lrtTS
06963 14
.01748
OS4W2
otane
-T«^^ C
06993 14.
V^
~ CoUOK
T«w [C
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oQlim^V
i«j*
^
<
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ST
\ w
P
TABLE XVI.— NATURAL TANQENTS AND COTANGENT
I .07110
; !0T1«8
' '.masr
.otnra
.wta7
.08837
.0B453
.03511
! 09070
.06079
.DBlOl
.0S134
.osiar :
.OSisa :
.0R4BB :
.08514 :
/, /f>otiu,gl Tang hQt
_1 «-J- //~
D.TOMI
b1m93S
B.MWflO
9.M7fll
1I.B4109
(l.&UtS ,
48781
41)141
40904
157S4
.lunn 9
bim'
W05S
Iiosos s
S5WI
.lOBM B
BBOIS
.ia«3 B
.10893 fi
.lOBZt B
IBSU
.100S3 £
isms
05788
.1J07O 9
oaara
.noua 9
: iirA
. 1187
9SBC7
. iai7
:11^
ftl651
'.im\
.11423
TMas
:ii5ii
68701
.llHl
ewffi
.11570
6ia;3
03078
:uS5
56655
.iiTia \
.11747 I
BiaBfl
491S8
!ii83e 1
.11866 J
10705
38(05
illBSS B
.13013 f
32443
30406
S8S78
SB8S5
Aim I
.isaio E
18370
1B898
Cirtang'
^
.137^
! 13781
!72SW
TABLE IVI.— NATURAL TANGBNTB AND COTAKGEHTB.
B"
9°
1 ^^
11*
:
_T«nB_
^i?5|.
Tang
.IStSB""
Cotang
Tang C
uiaug
J^B_
Cotang
B.S1S75
.171)38 1
5!l36oe
!jT803 1
esiMG
!lM9fl
5 1^
53
.una
070SB
6,278»
.17723 1
64348
57
.14173
.15968
esm
5 11S70
5.10190
! 1601 7
5,0!mM
.14»K1
.16017
B.sniOO
.1^43 fi
80452
.1084B
.14SS1
.16077
B.awoa
.57973 !
.18107
6^07300
.'llSM
08883
e! 10708
;i9740
6.DS5M
.waei
95385
.1B167
.18558
.17068 B
66706
5.05809
40
tSOul
.ITWn 1
05777
.10801
6.060S7
48
!iBsa
64851
.13831
.04967
Atm
!lB131
:i8«SS !
639B7
.19661
.OHOO
46
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.mm 5
63007
.10901
.osasi
.lOSlB
.18339
.18113 E
B20B0
.ISDtl
Mm
.10346
.10059
.01910
.14CISS <
90264
-looaa
.00451
.14018
woaa
:]6405
:i8M3 [
49360
.20018
41
.11W8 e
a2BM
.1M3S
.18233 E
48451
4:38M0
.07340
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4.08188
39
0D3S
.0U3I0
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46048
;ilO103
38
. 4T37
■S3M
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.18353 B
45751
87
■ *l^'^
771 M
.18363 6
4:05646
SB
Tessa
!02903
.18384 e
43DBB
4.9BaOI
'. 4323
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43077
4.BUW
64
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8133
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4«Ba
39
. 4SM
-09730
.18474 B
. 49IS
ro4so
40430
. 4H3
mils
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395511
:S0349
4:91516
80
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87787
.16761
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18BT7
.S037«
4.9oras
ee
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,30403
!8
85144
llfiS21
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. 50M 8
63831
.18Sit
.186D4 B
B8070
13523
.9EJ88
.180^ S
36306
4:87833
.18714 B
S4345
24
19021
.18745 E
13487
4:8M44
1 SI83
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.18775 B
;!0S88
4.85IOT
. Bflia 6
i7S39
.17034
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I1T78
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4.85013
a
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ma
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4.84300
20
. EBTl 6
!4777
.17063
fi-BflOfli
.18895 S
30090
.30679
4,63500
. KKH <t
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saaii
12384
.18845
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7
! 536'j B
MttTO
4:8147)
. sasi B
4WI0
:i7183
:]8B8»
iB716
4.60700
48459
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4.80008
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4.79370
! 5181 a
!9I8»1
4.7SB13
. 5sn B
b! 77936
joioo
.20021
4-77978
43484
.17333
6.7BB3T
-isiae s
mte
.20053
4.77966
H.nSMl
m»
4.76506
llMOO s
41020
;i73»3
:i9iii7
12 013
4.7590G
.1*630 B
srau4
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4.75919
S85B7
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4,7J5S4
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87S74
s!tI99S
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:i7si8
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jwjg B
MMl
.17643
sItocot
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16803
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4.734M
580064
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4.71813
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t-as'
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Ci.taiiKr'
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*;7*5^
X
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80*
TO
\
IV
\
S XYI.-NATtntAL T
i
I
■'■ m
I
I
IB* \\ -Hi
I
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TABLE SVI.-NATURA.L TANGENTS AND COTANUBlf
r-
flO»
sa' 1
32^
2S-
TiirK
CotftnK 1
TlinR
1 ■i.iunu ;
riDK 1 (
tan^'l
raag^
c
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Mi
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1
a
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2.74«S]
404T0 a
47005 ;
42518
a
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11.74IXM
2:69831
40888|
B.TajSB
:»B90
2,69006
40538 I
42S83
408T3 S
4«r8
42619
isosus
42651
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2>d01T
issoao
2,58389
40040 i
46065
43ues
S.raTTl
.380.M
2,5ST0S
40671 2
45880
iseiiM
.88087
40707 :
45l«fl
.ae7U7
siTsasi
,E875tl
sisaaoi
4B4G1
43791
a
s.ra«M
.3mM
S.CiSOSS
4077B 3
la
a.7i?TO
•asrer
a.Bj8i5
40809 a
45043
It
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9.71S1B
40^3 f
41B39
42804
a
.30830
3.7iac6
iassH
aisTSTl
4)oae
42929
2
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S.7106B
.88869
a.STlM
40011 S
4M3S
43963
If
.S89al
3.66038
40015 a
11390
43908
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.88059
B.eeTOT
4007S S
44037
.sseni
.88388
ISBSS
430C7
IE
.Trmt
b!700D4
.89039
siKsoe
iM
.80055
2.56046
41061 a
41132
3.(iDin2
2.60837
43520
43170
2
'.sn^
S.aU371
!.1S)123
3,5Sfl08
■X
2.03181
.80108
2.6B889
41103 3
41217 S
4!»18
3i
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a!oBit^
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2!54953
42418
at
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2.08)14
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8.M7S1
.BT25B
S.6S17S
.89399
2.54518
41319 S
4337B
IS
.39831
2.54990
4I3B3 3
41819
^sraNs
.30367
2.54083
41S8T '.
41030
Bt
.87388
2:07183
.80891
43181
2
31
a.OTaas
.804Sa
a.53M8
431)10
Si
IsTAW
3.00039
414IW S
41025
43050
as
.87488
2.00753
!SM93
4ueaT
a
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.SOflSS
aisaooi
43020
S5
2.59786
w
^87BR8
!sUfiS3
9.53571
41020 3
4033S
43689
3.62357
41600 S
40068
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S.BSI49
43738
2
3S
2.519£S
4t
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41783 a
39149
.BTIM
3.04875
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S.SI503
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4!
.89790
2.BW89
4.ie'J7
«
.89839
2.51076
41665 2
isisia
. 30863
41699 S
S'0.194fi
.39890
88473
M
a037H
.39930
ainoMo
18270
nose
41
2.50289
Is^RO
43038 2
4t
.mw
! 40031
43070 S
37697
44140
SO
»: 8*7^1
.40005
2.49880
42130 2
«175
:;
M
lasiao
sieaaaa
!4oi3a
48173 S
J7118
61
s.mtB
.40108
»IC»
S.B1S74
.4om
4IM3 S
30783
14314
4K7B 2
36541
44310
! 3835.1
al 01418
!40B8T
42910 a
36849
3Sfi6
s.eiiM
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9.4S1S8
80158
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B.flOBOa
2.47084
43979 £
35D67
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3.4JT1B
43113 2
44488
aasse
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CotanK
2.47509
43M7 a
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A
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Tang C
tnaoB
THTIC
J
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ffl
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TABLB XVL-NATDRAL TAHGBMTS AHD COTAHQBirni.
_TBng _.
. '.tlSOR
l.tUMip
.'gout
.fiS3SI
j.stai
/^
"w/ T
1 1^05
"/.'ttoWtig I Tuig
r«ifi»
.SSfilS
.lOBOl
.fiea»
Boaw
59661
.8TWI
87411
mrw
JOUOK
Tb.«
.an 21
TiBLB XVt.— HATDRAL TAHQEKTS AND COTANQKNin.
.
36"
37"
38=
39*
W
i:
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length.
1 .0174638
2 .0349066'
8 .0623599;
4 .0698132
6 .0872665
6 .1047196
7 .1221730
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9 .1670796
10 .1746329
11 .191
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18 .22689281
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18 .3141593;
19 .33161-J6!
20 .3490659
21 .3665191
22 .3839724
23 .4014257
24 .4188790
25 .4363323
26 .4537850
27 .4712389
28 .4886922
29 .5061465
30 .5235988
81 .5410621
82 .6585054
33 .57595871
34 .5934119
35 .610865-^
36 .6283185
87 .6457719
88 .6632251
89 .6806784
40 .6981317
41 .7155850
42 .73;«»88|
48 .7504916!
44 .7679449;
45 .78539821
46 .802S616
47 .8203047!
48 .8377580
49 .8552113
60 .8726646
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1.0l2-J910i
1.0i07443i
1.04719?6i
Deg.
Lexig1;h.
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
83
84
86
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
103
103
104
105
106
107
108
109
110
1.0646608
T.0821041
1.0995574.
1.1170107,
1.13446401
1.1519173
1.1693706'
1.1868239
1.2042772:
1.2217305
1.2891838
1.2566371
1.2740904
1.2915486
1.3089969
1.8264502,
1.8139035'
1.3613568
1.3788101
1.3962634
1.4137167:
1.4311700
1.4486233
1.4660766
1.4835299
1.5009832
1.5184364
1.5358897
1.553:34:^
1.5707963
1.5882496,
1.6057029,
1.6231562
1.6406095!
1.6580628
1.6755161
1.6929694
1.7104227
1.7278760,
1.7453296
1.7637825
1.78023581
1.79768911
1.8151424!
1.8325957;
1.8500490
1.8675028
1.8849556
1.9024089
1.9198622
1.9873150
1.9547688
1.9722221
1.9896753
2.0071286
2.0245819,
2.0420352
2.0594885'
5.0769418
5.0»4d951
Deg
121
122
123
124
126
126
127
128
129
130
131
182
183
134
185
136
137
188
189
140
141
142
143
144
145
146
147
148
149
150
161
152
153
164
165
166
157
168
169
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
176
176
177
178
179
180
Length.
2.1118484
2.1298017
2.1467550
2.1642083
2.1816616
2.1991149
2.2166682
2.2340214
2.2514747
2.2689280
2.2868813
2.3038846
2.3212879
2.3387412
2.3561946
2.3786478
2.3911011
2.4065644
2.4^60077
2.4484610
Min.
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6629005
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6878070
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2.
2.
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8274834
8448867
8623400
8797938
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9321531
9496064
9670697
2.9846130
3.001966S
8.0194196
3.0868729
3.0543262
3 0717795
3.0892328
3.1066861
3.1241^
8.1415927
1
2
8
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
80
31
82
88
34
35
86
87
38
89
40
41
42
48
44
45
46
47
48
49
60
Length,
.0002909
.0005818
.0008727
.0011636
.0014644
.0017458
.0020862
.0023271
.0026180
.0029089
.0031998
.0034907
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.0078540
.0081449
.0084358
.0087266
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.0095993
.0098902
.0101811
.0104720
.0107629
.0110538
.0113446
.0116355
.0119264
.0122173
.0125082
.0127991
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.0189626
.0142.535
.0146444
.0148863
.0151262
.01.'54171
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.0159989
.0162897
.0165806
.0168716
Sec.
\
1
2
8
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
28
24
25
26
27
28
29
SO
31
83
83
84
86
86
87
88
39
40
41
42
43
44
45
46
47
48
49
60
61
52
68
64
66
66
57
68
60
«^
Length.
\
.0000048
.0000097
.0000145
.0000194
.000024-.J
.0000291
.0000339
.0000388
.0000436
.0000485
.0000633
.0000682
.0000630
.0000679
.0000727
.0000776
.0000824
.0000873
.0000021
.0000970
.0001018
.0001067
.0001115
.0001164
.0001212
.0001261
.0001309
.0001357
.0001406
.0001454
.0001503
.0001.551
.0001600
.0001648
.0001607
.0001746
.0001794
.0001842
.0001891
.0001939
.0001988
.0002086
.0002085
.0002183
.0002182
.0002230
.0002279
.0002327
.0002376
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\*
271
EASEMENT CURVES.
By J. L. Stubblbjfielo, C.E.
The following tables are for easement curves corQposed of
a series of compound curves with degree of curvature in-
creasing at a constant rate with each chord.
Table XX. has three different rates of increase.
The degree of curvature used for the central curve fixes
the length of the easement (jurve, the easement curve stopping
at the point where the degree of curvature la next less than
that of tl\e central curve.
To locgite the P.C. and P.T. take tangent from Table XIV.
for J/, and degree of curvature of central curve, plus ease-
ment tangent "E.T." from Table XX. in the line of the point
marking the end of easement curve, plus the number in column
O on same line multiplied by tangent of J7.
Total tangent= *' actual tangent " -f "E.T." + 0x tan JZ-
Run in the curve from P.C. with chord lengths given
at top of table, turning the deflection angles given in column
"D.A." to point for end of easement curve, then set up at
P.C.C. and set back on vernier the angle in column " T.A."
on same line au last "D.A.", which will bring thi^ vernier to
zero for tangent.
After running in the central angle the P.T. must be set
by long chord or tangent measured from P.I. and the ease-
ment curve at tangent end run back from that point.
The ordinates from tangent for each point are given in
column "Or.", and any point niay be fkced by them.
If obstructions prevent laying out the whole curve from
the P.O., the instniment may be moved up to any point
and set to tangent, then run the remainder of curve as
simple curves, mcrving up for each chord.
The quantity "O tan J/" may be approximated to the
nearest tenth, in nearly all cases, by dividing with the
numbera; in Table XXI. niore easilv than by looking up
' 272 '
EASEMENT OIIBITB8. Z73
tan J/ and multiplying by it. The result is nearly correct,
varying in most cases le^s than one tenth of a foot from
the true value.
Ill Table XX. the coliunn headed Pt. gives the number of
points around the easement curve. Column headed L
gives the length of curve measured in chords. Colmnn
headed D gives the degree of curvature ©f last chord. Column
headed D.A. gives the deflection from tangent at P.C. Column
headed T,A. gives the angle to tangent at P.C.C. from chord
to P.C. Column headed E.A. gives total angle of easement
curve. Column beaded E.T. gives eas^imcnt tangent from
P.C. to O.
Column headed E.T. giveit the tangent of easement curve
from P.C. to O. Column headed O gives the offset of P.C.
of central curve produced. Column headed Ab. gives the
abscissa from P.C. along tangent. Column headed Or* gives
the ordinates from tangent. Column headed O gives the
lei^h of chords from P.C.
274
BASSAiBNT CUBYES.
Ji 4:-^ -::J/ '
£.5. ■
' Ah.