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Full text of "The Civil Engineer's Field-book: Containing Tables of Actual Tangents, and Arcs Expressed in ..."

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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operations, extensive, hitherto unpublished, tables have been 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 




-7B129B238 


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 




^88* 




1S.S43trRe.Mi); 




•IK 












i8.4aia'se.9444 












« 68- 




]8.«aKi 7.2!aa 












«3333 




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 






»!444^ 




D- SSSOSS 














I»!87»5 






089TS4 04-b 


10 








30.0150 


40;000( 




S8&MS8B6 


a, 








ta.iiaa 


40.2778 


17 


«~a84 6a3S 


205 




86- 




m.soii 


40.6fiS6 


17 


896034 8 








3333 




X4m 


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 




KMBS 


41 Mff 


.7^ I35 48 


« 




1 


1 


■iO 


n SM" 




1 BM8» 








21 ijsa 












21 a6iH4iMoo 


18 -rssfi 








214003 4*-^ 


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 
.8324 

.(MSO 
■» iBflf 

is 

» w 
■asem 
Mor3 

W18.W 
30 804; 

iO *14 
30-189 

aosMs 

30 99*11 

gs 

31 413 
«^ 

■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 

iS 

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 

is 

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 


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00 9U-0 


leiBBT 


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810-18 








b\ Moa 


193 333 


« 4J1. 




01108a 


iasB87 




I'^i r-fl 


Bi a-sa 


113 000 


II) iuHMBmSM71M8MW9 8W 


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«05 E66|7r 1*90 


IB4 1G- 


SI -501 


123 333 


11 W9« W9aiaiM71BMllBl 


108 173 


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77 8888 


15)583 




ijsar 


13 no sib'mo ow 156 los'aio 000 


103 1» 


gOBBB- 


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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 






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aosass 


rasi- 


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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 


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sa.ssK 


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aia (183; S39 tw7 i!j»,347 




los.eafr 


aia.as! 








:37.S33 




819.5:1838.33* 




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a.iass 






«JI).M.S6«.(X>1 




108.793 


213.333 


80.1017 




M.ae85 


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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 


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IN amm ia7 


108 177 


m 111 


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8 Ifl 8 K 




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J 




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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 




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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 




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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^ 


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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--! 




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» 




M 4. « 


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1 L X^ 































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H BH XKX 






M„ 
















t) isu B-^i a 


US 
8SSS 


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33sa86,IW5W» 


is 




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SBS4OTHI 


■rl^iJi 


0^41 


a 411 L ™ 


40 




S5-8« 11 












5B 1^4 










jfi W^J 1 




















M tta iJ 








































«8in H 










87 035*1 ]S^ 






, 




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\. 


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 


M iB 


BO mo 




43 -urn M 








MW 


uo 




80 3sa 




45.58S|W3 B 




M 


6087-11 


S8S 


aiSKJi 


HO SU 










9« 


-JB l» 


WSBBti 


8 i-iS 


















w 






^a* 


387- 
WJ4 


aaMrr 




8- 










83 000 


« 


£^ 






1 


"US 


flS ^ 




«3 








H4nO0| 






















83 Gh 








«0 DM 


•« U 








04 


SB 383 




^ 






g 


w 






■« 




58 


»J Ul 


» HU 








-Jtl-cU 










W Od 


31 


saa 


SB 95 W 


ai- 


juaiw- 


M -0 








M8«33 


3-«Q 




58 8:. 


814 


«87K« 




SO US 




0— 








loa 6s- 




«-«o 




00 000 
















an lai 










e 


^ 


v«- w w 1 










SHO 


■« jO 


ffii 1 
























1 


■OOffii 


jas vo 














JOW 




08 :». 


9tm 












Kia 


«1 9- 




» 


sj una 


9fi 81 


^ m 








98 000 




00 




1 






ft«4 


08 IAS 






- 








» IM 




la 




084 


OH ur 


Oi 


13- fiJ c:ffl — 


oa. ja jh AS M ass 






ssassq 


44 


en w TOSK-rs 


!s ufl M 8XI 08 man es w 






OR. 00a 


« 


IblVin 04 £02 »H SS) 


St tGGsts 2WW) 1 91 ae 


















m B 












090001 












OH ua 


48 






BUI •rao-OB. & js 






* / 





















60 r 



TABLE TIT.— AOTUAl. TANOBNTS, STa 



6-0 








Onr 


Tan. 


a™. 1 Ta.. 1 . 


iOma 


"60" 


ooo'ST 




ra.sM 




ST)W 




70.404 








TB.MW 








IB.TB N 








Tt.BSn 
















reliMi 








M.30W 








n.4vr 








w.osa 


B- 














fs^Sbe 
















friiM 
















77!4i»- 






-SI 


T7.6S89 




*, 






TT.TOHl 




DOO 










2-e 












« 








<83 












r 










fi 





TB.srbl 5 Ob. a 

JB.BOa £ - 

n.iwo ( 



80.360 <. 
9D.MXIIJ ( 
80.84-8 ( 



n.T4W 60 
Ba.BBS 180 

n.otio 80 



i 8e « HI E B4 eOD : 






TABI.R xiT. — acthaij tanoemtb, etc. 



M 








4C 




ran 


41, 


Ta i^rc' 


r n 


A 


Ta 1 Arc 


Tun. 1 An. 


'0^ 




"SiooS 


S065S5iiOOOO 




338 333 


U 816 850 OUO 


ioo ass BOO 000 








211 OOB 500 USB 




S8-iS81 




100 451 aoo 333 




5(ti!»t9 




»1 484 'Wl 66 


16 SB 




126 ^hno bss 


100 6a0»»66- 




M~9 




Ji rail 50* 500 


"^ St 


33S0UI 


ijs 9BB'.ei «o 


100 -B- Boi wo 




M Bl( 


1006 6 


^>. 314 WS JS. 




ias ^=8 


i« i"|a5i fcB 


100 KBS ail 333 








a. 44 504 lb 


168 sir 


331 111 


IM 3W so 083 


101 ]:» a)l 067 




mnim 


loiow 


j^i 1 4 soa uoo 


168 -M 


33b 66 


MblXl\vitXO 


10 «m»tooa 




•m \a 


1011 fl" 


J53 589 Bin 833 


leau 




II»81SiRaitl 


101 468 au 3S8 






ion S3 


»i oos m m 






U <r>SMS333 


10 e«l>!18B6- 


9 


^^101 00 


^««l^ ^ 




338 393 


is-aao 


JB3TM 


10 9S«8 00I. 




■m sua' iota e- 


»4W»H133 


160 w 


338 8SS 




iSt 16 


101 D6 1 "03 333 




1 \i 018 13 


Ml x&fmw 


ID 188 


330 4H 


ir BM 


jMWa 


^>K 1i4 2U3M 




1 ri osooo 


.j5 BBS 510 000 








455 UUO 


10" JTO JW 000 






JSA 1 LO SIO 8»! 






laao- 


Jna4i 






n 3 ^' ^ a9 


.^ SX 511 66" 


1 1 OS! 


341 111 


1^ so 




111- 03t<,JO4 06 




SSSS4 oaioo 


ax B41 B12 SOT 


nao. 




!l« 4BI 


.ffl6-.M 


lou m^iK, 000 




54804 D«e6 


&1V, 613 833 




B4 J* 


1«0KI 


»fl 118 






fi S jSti 0» 3K 


!ffl -WSU 167 




MS— 8 


IBS SI! 








^ S «tK ou w 


JOS n6 BIS HK 


1 161 


J43 3BS 




la 501 






lU 






1 *M 


343 8811 


laoaai 


«9 91 


103 480 


806 333 




















1^ Bs*a8"B0 




tOTOBO 






ija 95e,«i9 161 


mv\ 


207 3SS 








104 161 


aresT 


-■ 


1 1 J 1 llilfl 


Isn 6pl««o 41° 


104 923 
104 481 


aoeaoo 

M» 333 




[^14! 1 1 1, 1 1 3!)U|J1 -8 






l»8«»~ 




JWIW U Til THl ^ oUOII <Bfl ?4Ha« 




104 sa. 






4 B 1018 1 di^jBs-jaajuHMiisssi 




IU4 981 


4)9 333 


in 




1X1 4&>'W W3 




HW667 






HI B50'62 500 


lOBssi 










III6 4S8 




11 


"•■^ 'giHO 'wLeJ?'' 


:"i™f 


10,1 6A4 
105 B30 


11000 








106 W 


11 331 






H tuBl^lf^ 




ni wr 






J.~0111e6^0OO 


103 341 


812 OOU 




■^ 3^11061 « LiM 19 ^A S3 1 4 1:3 SMJ 




106 so- 


SIS 333 




wi ioilioea aliM wobsi oe ii-j tm.sm 4M 


133 3»W 88) 


los 671 


iM8<e 




%34 03811066 oope OMMJMOlTKWSa^oOO 






KB 000 


4o 


,4=«U fj ,nU,4.^^^%,'t 


13.1 la'wfl b6: 


10- 006 


SIB 339 










S13 661 


{ 




'[""m* 


214 3SS 


j' 




[1 l)« 








HIS Ob 










1 on 








U 41i -1 lui 


108 V* 


910 Old 


4D 


MB 465.0818 


B-l eO-IHO 883 1M BriB60 556 


lSBB(0|ini4l 


lOHBM 






^43^1089 93 








916 667 




'114 iie.iosfl 00 






108 861 


81 000 




H4 WJ 1080 fl 




iwawm M" 


101 oa 






145 SOh'iOHS 38 




r ir 4-8 r-i 0B3 








•M flUB low IW 




imr BO 


109 36 


iiaooo 




w jt 1091 » n ^ 


1 mi -^ 01 


lOB BS3 


816 333 




108 >-3 as3 


log AM 


818 6» 


' /.^■' '■^loim Ml 4 «« 




1mm Ml 


nswo 


Am 




SS" 












v« 


.^^\ 



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 






re.SK rs.nawlis 
r7.aatre.2iBn:i5 



Wl.SIfiW. 



rT.HmilM.WieT.H 



.RsmiGfl.awtiH.iTvniii.BSS 



il.'sSiSi 



uo.fliiTii' isa.BK 

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. 






























,2.778!0.»«S 




lEMn'si.ffio; 




































»,«B|61.«« 


lUI. 


n.Rja'M.nmt 


Tm 


































ia.4Bi».(W>ii 


IM. 


iO.J«.,7.«l 


ion 
















































































inH 



















.BMn\'.a 

.0Mi\H1 ^ 






a XIV.— AOTBAL TAMGBMTB, BTC. 



,>. 




.™ 




3 C P 


i C rre 


C r B 


~o 


Tan 1 Aru 


Tan Ap<. 






Tan 1 A c 






5BB ■iSOlWl 


a-fils-w 000 




s^assi 










548 aw 3.3 


* 


TMitX 




ro "■ W. 




08 ATOM 
OHHO^ 000 


* 


:> OMs 






09.1^- lUS 
« J- 60" 


« 


^5 






aw J-a w» 










ixa M 


9 


iiB 








*fsooo 












soeu 


eusaa 




W0 9S 


8S3 


"» tl &. » Q W UW T 




laiT 


£i!)««7 




56 -9i 










ItMUUO 








«'™°^^ ^^1 ^ 






^a^ 




MS4E^ 


IS 83 


JS -j w w sd 


4089 A0IW3 




KM tWT 


IS 


MISS 


» DU 


J8J 




M9- 


tsaouo 








*S 






±tGSH3 




Msaooa 


»» 


« 




assi 


an (JOT 




aoass 






-TbiH aw 


«40 


fmooo 


IB 


M7 8W 


31 B- 


■"(S 


■» 




1? 


UBW 






"n 


ss 


60 






" 


30 


a-a-ai 






^ 


3« 


5-HS9a 












j4 se 








u*. "uooo 






4s 1) w Biw B-1 aa 


»i~-a»aB-„ 


13 t. BU 


XTlf^ WW 




saow 


tf a»«i)H<e4&4 a 


B MflBltl'TI 






lO 


H 8 


^ y, 


9- IH 


ll_ 


-JO 000 




















w 










" 


J 










i^aiJ 




«*)0-il 








u -ai-WBBT 






601 -S- -flt Sffi 6U11 


y 85 Jh8 3W 


4a M-9 ^ 


«9a«L«ooo 








1^ sn 


(! ^ '--n 


r^\^S3i 












1 fi» 












IJ 


s- s 






s 


In 








V 








4a,A AU 


Hiuaitsasia 






«}'%-"« 


4N 4 Ul^ 8. 


fiT»i!36 6a 








"" 


MssraS 

P J88 0110 








J3HS-» 








a'iwtasEOT 








S 9 6 fflO 000 


*« 














aau* 



TIBLB ZIV.— ACTUAL ■rAKOBHTfl, I 























e- Curve. 1 7 Cnir 


« 8 C"'ve 


9° Onns 


lO C 


""•■ 


M. 




W J 




liF^ 


bTSm- 


*"' 


Tai. 1 


a™. 


lis** 


9B940S' 


iOMO 




fS.lSlI 


13» 1 






SI 4Jl'Sl IW 40- 


U3ffl8 


10 18- 












11 M 51^991 


HSIUTD 


0183 










118 lis 




W488a 


OM 










1 iwswBi Tt8-ia.Bis 


MB-91 








1S4 "1. 






Mnift'^'m mm'*s^ 


Km% 


088: 






1»OO0 






OS 


■A 4» 




6 


«l!«7It 




fl 0«IM 


sit 


BB 


134118 9M«a 01*8 1*3 619 


RABsm 






U.IIM 


18fi HI 






B9 




w ioe« i»i -iw 




11 SS; 




».»>7 


18» ssa 


^ Mu let 


sw 


08 »Me,i39 r& 


taJUS8J.i8 889 


»«^| 






».»70 


issni 


so WTi'lW S«l 


-V 


OrM 189 588 


MS9IB161074 


hJ 


11087 


10 


tt.BSas 


laiwii 


so ISBi ISB 




T 


1-M 189 -B* 


IKWIB3-4 1W 


H 10 1 


11 sa; 




St.S74< 


IBS So 


MSMfiltn 




-0 


!Mn'l4Dt»U 


IU4ftn])M444 


58S6US 








1MM4 


mtuneo 


sv 


*a siutnM IK 


Nfinri 1 w 


KSSSt 


1 18' 






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Mifi ii40Ba 


re 44 mi oo( 


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una 




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B9 8SUS1IU ISfi 


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M.KttX 




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17 




188 »»l 


41 O^'lOl 




( 


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M SSI 


IS 001 






188 H1I 










la 14W-|135 741 




13 1B7 




M.eOM 


188 »" 








li'i4t «r 


easmiam 


18 08n 


IS sat 


30 


W.93W 


1S9 1 1 




141 8-J. 


83 wriaiin 




13 MM 




SI. 0784 


180 14 




14 oea 


684 in -8 MS 


5 DgM 


IS 087 




K.jioa 


180 




lU M 


6SniKllSB4H 


S7 1-08 


IS 888 




^mn 


9i 






88 OIISW J J6 06- 


It -WO 


14 0110 




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142 T( 


es -oils i«e 8sa 


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14 167 


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wirsn 


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14 500 


87 


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14 «r 


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M38fl 1« 64« 


84 0-4S|ir 593 




14 888 




SB.HKI" 


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w.oDsa 




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198 811 


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99.IJU3 


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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 










W9J* aw MOTajoo 










-, ^ 1^ «r iM % 






" 


w 
























a, 'M 




















^«*|*" 1 1 


SHb ■« 385 88 •* 8 B 79 83 778 








3^«| 1 1 


U JmenU ' w» 


-1 iR- 














* 










uS m « M, 


M 


« ^ 86m^«0 ftlM, ^ 




4» 


ai wow js-loiiii ' 


MH 


ga aw S5 te b.w m 8 67-" 








13 


fls ohI 8. 04 Ka fMti) w m «, 










98 M a pa 111 


^ n 1 






1 
















Mtr Hn 




JSSM 








8 "^ 











TABLE Xir,— 



L TAKaBKTB, ETC. 





.». 


1= Curve. 


a- Curve. 


3° Car*B. 


4° Carve. 


5= Cai 




mT 


Tan. 1 Arc. 


Tan. 


Arc. 


Tan. 


Arc. 


J^„,|^™^ 


Tan. 


s 




TW.aifl 




SifjBS 


raorSffi 


m:m 


soiFIoao 


188.814 ks.OOO 


iBoTgra 






na.iBt 




377.59(1 


760.B3» 


Ml 746 


wo.aa 


iBS.8a8Hls.4i: 


151 ,080 a 










878- (W8 


751. 0B7 


SU.U35 














ISDSioO 


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 






T6fl,4» 




879.71t 


765.000 863.10* 


r«3S3i 


IBB.BBBlan'ilO. 


151. 9g( 


* 










380.148 


T65.S33l2a3.4tU 


503. 888 














isia'ss 


380.67; 


758.067 




501.444 


isoisiB sraiasi 


152:271 








rfliinsa 


1«5.00 


380. BBS 


767.600 


awioia 


5116.000 


190,6».87B.7W) 


152.488 


a 






rt3 78» 




381. MS 




254. SH 




190. ra4 STB, Iff 










;S3.S4{ 




381.838 


















iWao; 


i(wq:o( 


3*i.a88 


760:000 


^80! 




laiiiuiiaaoiboi 


i5a:wi 








?Bs.iBa 




383.083 


780.83! 


BSS.13B 


MW.aa 


191,37!! 380.417 


1!J3 in 








;W.169 




:J83.0» 




255.416 


507,771 


191.570,880.833 










70?. [«a 


i.-ia:(W 




'■m.f*i 


£66.70* 




191 .794 381 -8W 








16 


T«,Ka 


Luas; 


■tSBSt 


703 3S 


S66,980 




19S. 009 381.06: 


153:fia4'81 






7US.T41 




a84.38b 




aso.s?; 


509.41^ 


\ii.^ 382 083 


i53.7l«a 










3S(.9IT 








194.4* 


382.600 


153.968 3( 






170:48! 




335.!i33 


755:333 


35a:s3t 












ao 


771. 2M 


isRSaa 


3Sli.H( 


-60 687 


BST.llt 


Bll.lll 


103,85. 


38.3.38: 


154,S01'8l 












■^i.m 


















1538 :e: 






857 :6« 


<i\i.-i& 






154:045 8( 




as 


rTa:84T 


IS38.* 




"fa'M; 


^7.875 


5ia ITS 


1B3:491 


384:58! 


154,817 31 






774.700 




9T:361 




*58.*ea 


513.333 


:!13,11- 




151,980 81 






775. S37 






7o!twl:as :m 


->13 nau 












77fl.SBS 










3S5:e3!< 


155:321 IS( 






rrr.aj? 


I54S:0I 


aaa:!!-*-.;,; -.■■(.-.> i-;..:' .«^. im W4 


388.W0 


165,483 31 




as 


r78.08f 




W.057^. ...i;>l.S5i 


888.68; 




















30 


nB,S4fl 


ip.oc 


mlji^r' ■}1Z 


387.S01 


155.097!ai 






TBO.BOS 








105.100 










781 .4B7 




M'fl 






105.405 


183:331 


I50:3lll3l 






793. sse 










105.610 


388.750 


!.'iO,6l8,SI 






;sa,i8( 




m.m; 


778.'*« 


alt'osiilMSWJ 


1BS8.'H 


389.187 






38 




15.18.3! 








198.013 


389. 5K3 












m.m 


T8o!oo( 


iiiLfnasajiooi 


IM.KO 


800. 00( 








7i«.'7l« 




SM.Sfll 






198.466 










rsa.oM 


laos;^: 








I6fl.680i 


3»0:S3! 


15738181 




39 






3B8;j« 


Tsa.soo 


«ii.50:i5S1.667 


108.806 




157,6888. 




10 


-98.285 






rss.3« 


^na.rea 


5K.a-a 


197.109 


801.687 


I57.J31 








iaaaisa 






»i3,0B6 


5-N,:7i 


107.317 


3B3.0B3 


]67.srii8: 




43 


9B:W5 


I070.W 


394.B88 


9.^:oo« 


363.343 


533.331 


1B7.R35 


3BS SOO 


ISS.OSBtl 






7B0.8« 




mA\i 


85.B33 


aes.aao 


jii.ssi 


97.74( 








«4 


m.sss 




ifi.B4; 


88.6871363.018 






103:33! 


1»<:3S3SI 






■fti,#V 






87-.W0,'sfl4.in3 




9h!i6I 




ir>8.548ffi 




46 


K.m 


iSTflier 


witJT) 


"88.3181264.470 






mH:™ 






4T 


W.I8T 


;678.ai 


OT.109 


-89.167 aH.758 


r^ill) 


B8..W5'304.Bra 


168:886 31 






7w.04e 




3117.538 


ea.oa0|365.043 




BS. 800-835. 000 


15a<K>8 31 






79S,90fl 






-B0,s3aa85.a!M 




BS.0I6 3S5.41T 


169.33031 




BO 


7flfl.7a: 


:BS3.a^ 


3ne..197,7Tll.867]s85.flia 


B??.rjs 


109.B3o'»05.Ha3 


iso.Wsi 










1^8.813 79a.500]s«S.TO3 


Ma, -333 


IB0 488 3!'U.*5aiF,O..WS3I 
















fS3 


790.388 


r.sai.'B 


m'.nfi!' fni'iV ~Mi Wi r'-?n ji. 








(00, MB 


.™.oo 




















■5113 ^a-i 






,w.).«)*)i..ii.:' ;■■ -.ii.) ri3flos.7soliBn sshIsi 


/^s.'^it.-^iam.erlm.-H -.■!■, ...... - .. ■: ■;i.™ '.iaiB™.m\\TO.-w.\iL' 






/.^MWM 


ttw.**;^ 












MS .Ml 


Ww.w 


M 



TABUS XIT.— ACTDAl. TAsaEHlV, VTO. 



128. ow 
iDS.asG 



Tod. Are. Tan, 



jsi.weiMo.e 

lai.MOiSBl.l 



in. i»i s 

l8S.27<e 

in.«T i 

in. 704 a 
in.B4a» 



108. nil 
»a.8tw 
t».i« 

MO.OIW 



BIT M.U4fa 1117. 






iefi.383 84.eaua 



loo.esi; Hs.4UHt 

.lil.042,(15,(WSS 
31 .a&0,86.B98I 

'-.4fiB8fi.C0aa 

.M7 8S,7Sa> 

tu.oua sa.B;4i 



.M:2 8t.t>»31 
...TMSe.TWI 



iu,iei&8T.Mau 



l9(t.lH:j|E7.7UgO 



BB.SflW 



Ti.afifTS.OiSS 
;rJ.41)7 TB.IBBS 



ITS.ODD ;».34W 

",18B7B.4»81 

.STO 7B.B1BS 

.sse Tn.flofii! 

.T41 TV. 0913 



ITfl.ll 



iTe.aoaTg.MSTii 
iTe,4Hi m.cegs ii 
. ._ ._._ -ITO.MrSO.llMlV 
m BS8BII.0908V.ft.Ml*».^K'WV5*»'^^\* 
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im.n«l'B9.K!irt\AVi ««w»-'£^!^^ 



TABLB XIT.— ACTDAI. TAKSENTS, ZTa 



16° 


l-C 


„». 






* 


OU». 




hT 


Tan. 


AreT 


^^^. 


Tun. 


i.™. 


l-^,. 




Tub. 


Are. 




«Oa.UU 






ew.WJ 


iB».a» 


WIUO 


ra 


ioToei 


wOBo 




KH.lM 








«a8.7«a 
















too. DM 


iwsis-i 






HO. Die 












8«)!b07 






imjB.oo 


i)3:«i!i 


Bwisx 


sun. ESS 










iBrooi 


aai.ooo 




tOBifidI 


isoe-tn 


4Ma«M 


W3.33a;!M9.57( 




iOi 




401.007 


1(1. 7T4 


aai.sss 






16(8. as 

El 


404.7BT 
IM.OIT 










1^-SS 


IBI.HO 331.087 

IBS. lis sas. 000 
leii.ioDaiassa 


7 


(oa"8»3a7o;4» 


^;^ 


w 


I« 


J^:SS 








KI0.04T 


SOS. BO? 


STO.Tlfl 




«lt 


COB403.83S 


]BM.40a 3*1.087 




tUsiSM 




WB.Ui 


ao7.M» 


em.ws 




«B 


ae3 408.7HI 


18^.8838^.000 


lO 


sia.Ks 


lBIfl.B 


woBn 


»».»» 


2n 870 


sw.sse 


JOB 


*n'4oni!T 


1B..793U.3.3 








wi.am 


tos.ia; 


STI.BOf 


930.444 


!« 


088 404.6HS 


163.367 SaS.OW 




SIS^Mt 














BOO 405.000 


183 189 8*1.000 




Hia.aoa 


\ta.\.m 










!M 


)is40n.4iT 


1Bi|.311,3M.3«S 


14 


MTUB 


vm.'& 


408! 590 




3T«!410 




1104 330 408.833 


188.469 






S17SM 


libffiUl 


N.DIJ 




r,i.m» 




aM.B3H400.SM 


183,04) 


BMOOO 




«iea» 








eissri) 




l>M74B 


40l!fl87 




wo 333 


17 


BJSe84 


IBSt ^ 




HU IS 


risw 




aMwi 


4U7a« 


163 w; 


man 


la 


iUM 


laseoo 


110 as- 


B11000 


i^3*3 


.143 330 


«6t-B 


40-300 








S^ 403 


rnaid- 


110-10 


sises 


irsaaj 




«B»0 


«7ttl 


104 » 


130 331 


m 




1033 3.1 








>44 4M 


«>5 0» 


4(eO!» 




met- 


ai 


24 ]Ji 


isa (ID 


411 STj 




-4 4ft. 


MolWO 


2CISBaU 


4011-80 




8»nao 


as 


iaset 


loses 




■tlM'M) 




145 558 


«)«a» 


40S10 


164 Btf 


S«-SS3 




MSlt 








•-4 JM 


MB III 


*oas4s 




























888 000 


as 


RH ao- 








J- u« 






410 41 


189 »] 








1043 j; 




IKl BO 


pBlll 




TO HBO 


411 m.1 




aw 607 










4«aGao 








411 JtO 


165 BSi 


aw 000 


38 








3d3 33a 


roBSi 






411 «fl 




S89 333 




tMSll 


ia4B3a 


414 B 1 


«»■ 


i78«B 


M9 444 


ar ai8 


11 0H3 


108 033 


snoo- 




S3(l 4 








ar-so 


41 mX IBfl 19! 


530 000 
















^ 4<3 






330 06 




aasBi 








^1 000 










188 »r 


SSI 333 




lesoLi 








341 06" 




)t.u&ti 








aaooo 


37 


tea 01 


10610 


lT8K-.t»8.%J 








83*338 




SB a« 


1003 3: 


4IBTU5W1 bS; 




41SB33 




332 087 










Sro Gft.kiS DOO J09 340 


410 360 


167 -BB 


333 060 


40 


R3ff '^ 


iseeoT 


4111 a^B ma 33X 


"70 *% SQ.'i RH ^oa Dm 


418 BT 


iroir 


«3 333 






iflosss 


4J() 0® 'oi ir 




41 083 


i8go-g 


833 06" 








III 1 10 390 


417 300 




334 000 


13 Ml -t 


1 I ^ ll>J9t 


41 017 IBN 41 


KM 333 






4i8mi6«w)5wor 




41B"Vl'lfl8-W33a000 




41t ir.lWW- 330 333 






n ^10 


4)0 WlHaO»B33!)«S- 


48 


Mil otf law 0. .23 ue4|'«o ow jKt oo wo ooo 




4» 000 lOB i-1 BSfl 000 


4ft 


84b IMS tSSI li U3 4H0.»40 H33 -K. ^B 900 6U 


m^ 


4«.41 i0«4«-3»333 


SO 


947 TGB IC89 as 428 gSS^SH «r 2HS AI 161 til 
BM BIN 10H5 00 1- 4 1'_lW VKI >^ 11 W) M7 


3UW 


410 Winn 804 3)10 or 




t m4 1 »w:bi -033 ooo 




W»4BIBtW i 11 W 4idU «.S l-<H II „ 1 4(14 1 Off-lflO W IS3-B38 














ae 






















ttfor 



TABLE nv,— AOTDU/ TAXfiBSTfi, STO. 



[ts.auim.sM 



insists H4 



.«KIXB-!Kn.SK4 



XB'-!K 



V06W. 

mf9.am 

IMitMI.OSBB 
.350 80.— - 
.4H90. 

.i^xi.vn'm'.tm 

ana.oss.M.sosi 
«tti.!»9 so mr. 
sw.Buo.Bu a9e3 

xates 



n.oT^ 






aoj.iffi 



210 4i; M Kioe 

SIO^WHWiwifl 



ag.7?8I2S.ltTI!MS.3Bl 11 






n.BSGS 

81.475* 

.OOU 81 MW 



)tt.41B8 
IS.58M 



14S8B.0WI 

3SBBS.I7BS 

--SSSOIH 

88.3514 

B3.4a:6 

ssoesiTTM. 
SIS Bs.saw I 






TABLE Zrr. — ACTDAL TASSBNTS, ETC. 



i 




a- Curve. 






5. Curve. 




Tan. 


a™. 


Tan. 


an;. 


Ta... 


Ara. 


Tan. 


Are. 


Tan. 


Are. 






iiB.S 






S.H^.OOO 


£8.1.461 






arooo 


"TTSia 


140.000 








liDi.fn 


4aB!sw 


too.saf 


J83.7-1S 


M7;aa 




4S5.4n 












1708.3-1 


4i«.D:j3 




iSBfl-IBl 
















VIS Iks 


iros.oo 


4«B.4E3 




m.m 


m.m 














S5B.m 


iriMBT 


s-s 


»b:S83 




m.m 




iseiae? 


iTiiess 


■M.m 






wa.Hfi 


JOBS 


«4.1fl1 


i86'.884 


m444 




437.088 




111. 667 






IM1.3IN1 




wo. 714 










iBT.BOO 








T 


wi.^ss 




481,14! 


nsissi 


iH7;448 


)7o!m( 




437.917 




t4i:33a 




8 


Hftl.lU 


\7\3.S 


131. 67B 


aM.OOT 


a7.734 




sisisa 


4-ja.838 


i7a;67e 


iia.M7 






M3 BT4 




Oi.im 


88T.609 


m.m 


'iW.W 




1».7B0 


ltS.S4S 


348.000 






S6J i¥a 




184.433 


8M.333 




ira.aas 














mm 




tW-882 


asB.iw 


m.'av4 


^™.77S 


3)b:46; 


4^'^ 


173! 191 


dsiuw 






sooaaa 




m.^ 


B60.0M 


asB.sau 






480.001 










SliT.-WS 






isB.m 


iSB.lST 














16 




iri«!a 


131. 5S 




■!»».Wi 


J74!44.i 

S7B.11UI 


inisH 


48i:3Sl 


173. WH 


MBiooO 




16 




ITSfliW 












131.607 


174. OJC 


■MS .333 












«4JB1 








433. 0B8 














4!«:^S4i 










48a. WO 




HSiOOO 




1» 


era! oil 


ITflliflT 


43«.«M 


^:J^ 


HM.aen 


sTTias 


il8170 


43^.917 


i7*:bm 


3*B.ssa 






SiS.STl 


iTsa-aa 


438.701 


888.667 


J!U.1B3 


577.778 


S18.886 


433.33) 




Ma. 607 






S74.3cn 


17*1.00 






^1.180 


378.388 














s?s,08-; 


liBfl.ST 




MSiSSI 


iBl,707 


578. ■<8g 


118.801 




fn'.um 


H-isa 






STB.8B3 


1738.88 


tsr'.9ts 


869.187 


491. »4 


179. 44' 


iiB oi; 


181.5S) 


i76.a3a 


34T.BW 








1740.00 


i8S.3a 


8T0.000 


iw.aso 










348.600 






srrisio 


I741.8T 




(70.881 


iOii.Ber 


m'.xt 


313 441 






44S.38S 






§7B,470 








193 sss 


SSI. Ill 


eia.mio 




1 75^748 318.667 




37 


878. :SB 


174.1 loo 


iwiesi 


fiii.wi 


m.im 


181.667 


3ia.s7.' 




17.1. 930 SKI.OOO 








1740.67 






■.W.428 


wj.aa 






176 oia 


149.338 




»9 


li8l!CEiU 




410.5a 


mooo 




f^'tS W3 


2'Z 


137.6110 


178. 368 
178.434 


S50.ono 






98U.71( 






s^.vsa; 




r,83 HBB 


3».7a 






»0.883 




3>! 








87(i ■167 




SS4.44I 


iao.U85 






8.1D.067 






884! 4S! 


IW.VliU 










isi.iso 


438.750 


iii.Mi 


aBi.ooo 






98S,a*i 










s»:mi 


<S1.86I» 


1S9.I67 


IJ7.11S 


8B1.388 






888.148 






«7;) Iff 


m.iia 


:«6.lll 


131. Ml 


439. 5B! 


177. S84 


3S1.967 




:IB 


Ba7 tn; 








isj.tm 


58*. 6«: 






177 4S( 


8ia.n<o 








i7iii!a7 




rsoIbs 


49-1. 98" 




33-2 ion 






^.338 












Wi.8fl7 






33^.2^1 


440!f)91 


I77!7II! 


^.nor 




39 


S8»:»7 


17ub!oi 


Hi:?9B 


ssa.soo 


iK.M 


I188;3B» 


aM.iSi 


441.ai0 










800. ass 


17118. ST 




ss3.a.33 


896 «» 




'JS3.640 


441 .er 












1 us. 33 








323.8N 




ITSW 


3U!68T 








1-70.00 






397899 r.aolO'H 


W3. 0701143.. WO 


178.471 


354.009 






899. 9M 


1'71.!17 


m.m 


R8.i:8;B 


iOTNMSBO.KM 


8at.ai.i'i43 91- 




SH.sas 






SOT.sa 


1 73.».1 


i4B.na» 


388.66- 


aB7.»7a^Bi.iii 


aas.BOoma.Bffl 




S54.6S7 








I7TS.I« 


147. aw 


,'«7.SU0 


2^1H.KB5fll.e8- 


SiS. 7^148.75" 


178:991 


866.000 










417. 78B 


888. 3S 


398 Ma «e. LIS: 






S55.333 




47 


S9e:4ft 




HS.S18 






*J4'i44 444:B8! 


17fl!33l 


366.667 




48 


asT.aas 




(18.RH 


8so!ooi 




3-.'4.a.1««B.i»(_ 




SH.OOO 






see.DH 


I'SUN 










170 iWi 


360.333 




SO 


8B8.M5 


1788.33 


149,471 


ssi.ae- 


399.873 r.W. 444 


a4.7Tfll45.im 


I79.aio'3B8.«87 




sa 


m.m 


nss.o._ 


iwait 




3n9.959,1K0(10:3i'4.fl90 44«.2S( 
-IIW.S151.™.1 Mll2a5.S0fl416.lie- 


180.013 367.009 
IW. 184 357.333 












a<4;i(!7]-TO,Mi!MHIliaffl.4t9 147.l« 


1«l).ai8 3S7.687 






asm. 363 








180.688 356.000 






aw-jas.'inii B7 


j.-,i (128 fill,-, wl :*n :iis,'in7 ■jaiia.'. 8iBi47.Br 








180'8T«368!e87 




J?//W.w/yrs!;w,«sWmr..vxii™ruvmw»;!Ml-i-i6'-nflW.-;t. 


\«\ 018 xa mn 




■fl^^v^/'™*- '''■'■'■'-'■ ■'""■*'" *«'«" '"■■■'1^*" »i9*ift.iswA«.\«:\i.w.4w.3«i.«a 




<',«w.«'//7,T«.as;j.iv.,-cj-jM» IWT..30-J Luvi:OT,M-t,-i-i6-;M*«.:*a\w\.»w««.w\ 



— ACTTAI. TAneENTB. KTC. 



6' Carre. 


7° Curve. 


8.C„„e. 


»■ Cnrre. 


I0» Curve. 


^ 


Tan. 


Arc. 


Tan. i Arc. 


Tan. 1 A«. 


Tan. ■ Are. 


T^T 


Arc. 


lU.Ta> 


sw.s«aTa:4M,a«:MT 






u:^ 


M:aoa 




m.aa 


wi.ati 


ui.B99:a4i.oti!> 


lor'.tao^ii.TDi 


wi's8M,iso!u;< 


a.esn 


m.im 




m.im 


aa.m 


va.M 


34».m 


107 ssskie.BiT 


W 4312' im SM 


Moim 


IfO.SH 




14S.SI0. 


»t.w 












iu.su 


au.444 


m.ea< 








141.4Mau.Ttt 




a4-„,.':: --■:/-■:: ■■-■ .-_,; ■;'.:■ ™ 


ITO^SS 




i«.wo«s-«» 










m.T!4,aiii.an 










118.917^ Mt-XM 


lasisjT 








i«.o«iu i».m 


l«8.B00S46.(«^> hi- ii~-L'':i iT,-.'ii il.i-!'. , «i ..-.i.-i, r«JO? 


m.ta 




iH.aoatUAu 


las.ius a4a.238 


ide.isi 


214. eus 










i44.siTsssa» 


1*8.746 B4a.«a 


108.SW 


1(14 JB! 


tsicBSl 100:1;^ 




iTisa 




144.401) IM WT 


]in.8iiBit4B.;i4 






9e.s80Tlol.1II 


W.TUO 






i44.eia.!Mi.9« 


ixa.sBTrJiB.uBi 


lOBMI 




00 4;31 101. iw 


•<8.tUB; 






H4.7ffT,«T.W» 


J«4.i(»a4e.iw 


iM,ei4 


l!l.1.41^ 




BS.HBIl 






144.V10 ^V.WO' 


liM.iS0iM8.4a0 


lOS.nil 


£16 62; 


saiuflii loiiom 








i4s.nM»)r.nH 


l«4.3K.3»«,fl6T 


)flS» 




oe Tsor 101 8B9 




17B MI7 




i45ira«ow 


134 4TI J4S M6 






oaHM^iioaar 


17 I80- 


1~9£3I 




i4i>s40jai3a 


IM MTlMT 744 


Kig OMIiitl »0 


oa B4-?'i9E as 








146 484 WB eil 


IJt 7W( 947 Wl 


I0(.!Bll91fl4W 


or <y.M 10" 40- 


<rmv 


171 IB; 




14$ 6r MS 888 


ImJm , III ^,^ 


m w 




i4.^-B6j«iir 








14» 9M JHO 444 






148 04 jcn) -« 


in JM 4 m 


n Hja 




i4« 11.1 jgu om 


IKB 91M1 41 




1 4 38) 


i 


1£?^ 


«om 


lUIITl 


MB l«K IPS W) 1 11 








148 881 


ifflOW 


laasA 


uajHu 


nuuu IK i« a Miif iMjtWfl 








14B-M 


m 111 


mail 




11U iii»B 11S8 r fW"4 104 <r4 


ssiwi 


1 468 




148 904 


01889 




US fS 


iionsmeM B7t8g6m»s 


88 9134 


I 4888 


S(P 


14 Wi 


»i«r 


lUOM 


aooDo 


110 aw IS I If- iw 444 








III 


»I944 


lis ITS 


lEOStt 






"i-wie 


t' 








]W4«4 




no 04 -5 50 




14 8H 


m 71 




moK) 


no ^ « Gii 


34 


14 -B 


SttOSI 


iMa-o 














leu ~» SI 4"! 








148 044 


jsseii 


W Vt6\- 4 








14«I8 


mm 


m ossU ^* 


-S UPfil 


8 SK 


38 


148 SM 


mu 


19- 15 _ « 1,1 


S0U689 




i» 


4S4Bt 


04 444 


inJ^ 'S'^ 








^KaWAM".^ 






48 SliaBflOl 




48 sw'jw e-B 








4B asNijtH ue 




Jl 


49 191 JWi BW 4 


49 S£4 JSe 11 1 


49 4883W«8n , 




S'«««4 ^/ " lw|».JS|Ti 6V*9 


149t«8'>irS=» 


iJ«4«e sa 14S BO ocos -s saa BO 


iwmiiarMO 


iJSBflj w sw m onral T wori 


iMi-fl'a- "K 




ao aifl.ant im 




iM 481 aw ws 


ISB MB- -* 4 V- i 


iweo4 

TlM-48 


«w«n 






1 1 " 










«i 



iw 891 aw la 

f K OH at 4441 



i39 iSSifiB OOSlll? 4 



lABtA XIT.— AOTTTAl, TtXOlWTb, «TC, 



,.. 


X-Cu„. 


a= Curve. 


3.C 


TV.. 


..c™. 






Tan. 


Arc. 


Tan. " 


Are. 


Tftnri a™. 


Tan, 1 Arc. 


Tnn. 


Arc. 






807. «: 


\m7w 


iM74S 


iiooTooc 


soTBliioirMO 


S6:909!4m:006 


181.541 










1801 87 


4B4.177 


)00.M 


03,805 600,65 


M7.1S4'4M.«7 












1803.^ 


4M.t»r 






JS7. 339,160, 88! 


181 :bw 


380 667 








1806.00 










IBS.UM 


881 .nm 








ISM.Il^ 


OAAS. 




303 6861809:32^ 


!37.:B9 45i'6K 


182 281 






s 






«5,80t 


(w:iB 


503,»sl.U0tt.I78 


M7,a84 462,083 


















*M 3881603.333 














»]3U;s 








04.5^008,889 














914.3a. 






9oe:8e 




J38:629 


468:388 


182 l«tn 


86^:687 




« 




ibis: 00 




swr.wio 


3OS:o»7i6U6:0W 


J39.S41 


468.750 


188.095 


883 OUO 














3(>S.3M|a06.6n6 




451.187 


183 367 


368 8S8 






ma, 88; 


ibis:* 






3w:S(»fl:wl 


339:9n 


Sff 




388 1187 






BIT.71f 


JBW.OO 


458:878 


9io:ooo 




JM,47. 


INJ.WI 


364.000 








1881,87 


49B.30( 


910,83 


a08.B341607.aN 




46a.4r 




884,338 




1« 










306.611 6ftT.i7H 


«»:9U 












^x'.m 


1825. « 






3n6.797lH08.3B8 




4r>6:^ 




8B5:UO0 






Kl.lW 


1B3B.S7 


m'.^ 


!ii3:-s 


307.081 K18.8S. 


J3ir3a 




184281 


356.333 














307.370 




Ji!0..648 


4B7:0R 














411], 4U 




307.6.17 














10 


m.-iM 


i8si:or 




913 833 


30T.B43 


bio: 559 


3o:b7< 


467:917 


184:H08 


868.388 




ao 




18U.33 




918. SS 


308,330 






468.888 




886.667 






t&'.ita 


less.oo 


i%■i^^f 




308. 616 




^l!4UI 


458. 7KI 




367,000 




3a 


s«.ai» 


iKss.sr 


W8.178 


"Ik 


W8 80S 




281.838 


459.187 


188:819 


887.333 








ISS8.33 


4«.B89 


119.16 


809.080 


iia77t 


ai.881 


459.688 


183.485 


887,667 






ta'.vn 


1810.00 


464.004 




!)0»,857 




liSi.OIW 


460. «W 




888,000 










4SI.434 


mff& 


309,643 




^33,363 


460,417 


I8a:83f 


868.388 




aa 


Htm 




164,834 




W9,».<I0 




i33,46e 


460 838 


186.096 


188,067 








I8*S.OO 


185.S» 


m.fa 






KB, 688 


48186(1 


186.167 


860.009 






\z\.m 


IWB.K 




933.33 






233 891 






380 333 






BS3.271 




m.'iti 




310 : 789 










880.867 




30 


983 131 


IHSO.DO 


4M.SBS 


9K.00 


311.076 


imss: 


jss,3as 


4S»,500 


185.688 


870,000 






swiooo 


IBS1.6T 


S7.011 








il&.Mi 


483,917 










SH.asa 


IBBa.M 






3n:649 










87o:Ga; 






DK.TOS 


18M.0I 












488:750 




Tl.OlC 






Mt.US 




111830I 


138:333 


3ia,sw 


118:S8fl 


i34 1^B 


464.167 


187:871 








B!T,«a 




168,731 


)29.I8 






&i.Vri 




187,5« 








BM.Sm 


i8m:oo 






3iii:T»s 






*t^m 








37 


9M.119 


1881.67 


m.bn 


930:33 




630.5.Se 




485.417 




372:333 






ass.HB 


1863.38 


ifa.v^ 


m.w 


sis:3« 


(Bi.in 


S3s:o83 


466. 83S 


188 04; 


873.687 






940.909 


1865. (« 


470.4*8 


B33.HW 


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 


814.1W 


133:778 


«,1,678 


167,08) 


1»l,5«« 


8^,867 




48 


H3.3Hi 






(36.00 


si4.4a^ 




.■3.1.802 




1W,785 






43 


SM.Wfl 


1871 :8r 






314. ;B1 1833.888 


!38,10" 




188, W 






44 


91S.1W 


187S.31 






^.9231468.388 




874:087 










47a: 000,937: M 


3 5:364«ij6:o(v 


236 5.371468,760 




876.000 






its'.%H 




173,430 B88,3.-ia 


a f .641,6aS,SM 


236.753469.167 


189:4M 


375,88.? 




4T 


BtT.BSi 


18™:S3 


7B.BS9 93B.16 


Sft. 947 626, 111 


936,037 469,^83 


180,501 


876. 6R7 








1880, 0( 




8 6.314 633.687 


337. IBS 470. onn 








4S 


Hflido; 




474:719 910:83 


a 6,5oo,B!?r.i»! 


«7.39;.471>,4i; 


iwwi 


376:383 




SO 


9M.S8! 


1883.33 








378.687 








188(1. a 




817:0J8 838:838, 387:8!W 471 :3S1 




877 ono 










i7o:boe948:ai 


SI7 380 «S«.BHB'33«,041 '471 ,837 


1»:4V 


377,383 






BSS.WI 


1888,3: 


O.4.38M4.10T 


817. &(6 63fl.444;S38. 8561473, 0S3 


100.631 






M 


9M,700 


1890.00 


470.888 94B.0C0 


817. 93;l 630. 000,288.471 47S,fl00 










BM.581 


iBPi.ar 


*77.*8SMS,«J 


3[8.aTnB30.55«;39e,6r(i47s,9r 








■3«JilH.»?^;S93.33 






101 : 131 


878,087 




*"^7- «'/'«». erAre.SM sw.sm 


31b: 713 m ; aiii^.TO'tS".^ 


191. MS 


870,000 




819,080 BSi aaa2aa.si'3\4';t.\w\vi\,«niw» «* 


\. 




■'»«i'8a8.3ai47S.Ben:mAG! 


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 






IMSIS 


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 








IM.T46 


m.n\ 


ISO. 845 350. 5« 


1I4,5BB 


^»a 


im-Bff 


Ml .85* 


«.7»,8 


181 867 


lU 




m.e»t 






114703 


m.m 






MS(W7 








iM.oa 


asisii 




Ii4.80^ 


fc.,MI 






II SfH 








ias.is 




131 :ao&;aea!s88 




















3U3:I« 


i]|i.«M,d«o.4ni 


iisio^ 


i^.ii: 


ice.'aea 


aM:69« 


'i.mi 


1«!,33:| 






1W.461 




m.55i,aii0.7U 


nz.m 


aw.ias 


iw.ass 


ae.TTS 




18a., 00 






IMMKi 


smIm^ 


1S1.074 


WO.BbI 


115. as; 


ies.sss 


109.40- 


an 068 




ISa 667 






i»i :» 


90*.?B 


lai.TOi 


aii.iM 




us. MS 






H 8in 


\»i.SS3 














115 'ts: 


&fi 7D0 


ios!mi 


sm.xs» 


K,404J 








1M.0« 


m.m 


ts!04i 


m'.m 


115,560 


VU.BW 


1011.741 


908.610 


0^.4008 


181.167 


JB 




iM.im 






HI. 005 






109. B86 


«e.n>4 


SS.571M 


183.838 








swiw 


ISKWI 


»i,148 


118,77^ 


«!0!S7S 


10i!,B8H 


■loi.m 


B«,«Sd4 


188,600 






154!48( 


MM. Ill 


i»a.«i 


les.sm 


llS.Kil 


aii.58a 


103.O*; 


(04 074 


18.7485 








l!M.!«B 


we. SHU 


m.sm 


lias.eii 


116 DM 


»B7B9 




8W,»0 




ina sga 






IM.TW 


ine.es' 






110. OW 


eSO.IOO 








184.000 






IM.MS 


806. IM 


luini 




iiBie; 


380. ne 


loaiijM 


XM.esB 




184 167 






159 nil 


sor.aa 


>m BOt 


B««9 


llOSM 


!aa.4ii 


iDS.4a<, 


m.m 


ta'.mt 


184. S33 


e« 








ISS.OIl 








100,481 


W6000 


08.1780 


184. MO 






lulsnr 


«w!!^ 




ieaisii 




930. ««: 




106.185 


S8,S59D 


184 687 






i».«a 


30B.UU 


is'.Ts 


aH.o48 


1 wills; 


lai.ofit 


loiliwi 


ttG.870 


^.m 




*8 




IH.HS 


XK.sm 


Ma.ve 


^.»o 




ssi.»o 


in.7» 


806.668 


1S.4SI1 


j85«|0 


30 






me.Ki 


m.m 


804. ns4 




!ai 458 














lisslen 


MS.Ht 


lOT.Bs; 


AH.TS* 


iie;»5i 


«8i.se; 






»:mi 


186'ssa 






iH.on 


soa.iff 




KM.OOD 


IIT.061 


Wl.Kft 


101. on 


M.m 


m.ttm 


186.6011 






lU.IB 




130 K* 


Mn.ew 




OM.na 


104.101 


nxm 


H.TTW 


185.60; 


34 




iH.aot 


BosiTa 


ini.mn 


»5.47« 


ii7!ffn 


Bffi.flf 




Wi.W. 




186 BS3 








810.00 


IM.ia 


A5.TI4 


117,860 


satnou 


t04!&'M 












ihImi 


luo.m 




4W.B6! 


117.484 


«a«.7c« 






<4oeo; 








iM.Tite 




l».08l 




1:7 688 


isaoi; 


io4:m' 


«7.087 




180.833 


38 




IM.WS 


m'.esi 


181,483 




117.605 






au7.3^ 




18B.B00 






,,- (J,. 


„) ],, 


184, BH 


amiwr 


lir.BTB 


sR8,ssa 


1W.T3I 


eo7 4(r 


04.SM0 


186 667 


40 




isrliH 


aiiisw 




MO 9l«ill7 !H0;«« .M-, 




■jcrrieOB 




186.888 






IXT.tM 


811. er 




ifir 111 "0 "i'.-™i r-.ii '"1 i.-jii'-ji^.Trs 




187,000 






157. MI 


SIl.Mt 


IIM'OT' 


af.T MJ"! ;■- -■'■ :■'■■ I'SS-m .Via 




187.16; 








sis.asi! 


1«,0K 


WTi'.l" ii>:M.14R 


e4.esoa 


187,838 






iK.Ta 


aii.sDO 


ISfllSO 


WTN,-, : ■i;-.iiS.88S 


W.7HK 


187.600 






m.m 


ll(.77)> 


)»S,M8 




94. BOM 


187,667 


4« 




im.mt 


iis.nu 


I».4M 




M.BBRI 


IB7 B83 








iia.sm 


IWS.BHB 


WS,^.!,!;,^.^-^-;.!.-..!.^ ,L.'.,.-A«,J(«:w» 










m'.doi 


818.011 


i»6.n* 


W8, BIO 1,8. 770^35. «« 


106.506 aw.m 


»:0804 


iBsijo; 








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« 






ixb'oo; 






15fl!878 








« Wf 


188.883 






IM.OKI 


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'. ■. ■" "'^ 


'.'^>m,™U^ 


/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 


s uui 








m 




aa 


tataat 


ow 


S4( 


881 


478. Mfl 


M 




81 




4 tun 




]i]oe.6T 














661 




HOI 


fl».6«7 


02 


fiOl 


S81 




r. X-1 




IWB.BS 


481 


HM 




167 


iBl 


waest 




M( 




477.068 


Of 


S7t 


881 




a M>a 




iDiaoi 


lai 


W 




OIH 


Sill 


B.-B(6« 


6(r 




aaaj«n.EiOD 






88^ 




T OM 






48> 










ess 








SHMTT.BII 






81 


ass 


8 WA 




'rnslx 


481 




m 


Bffi 


B« 


S3! 








4«t 


tm.sss 


OS 






667 


0B66 


SM 


1M6.0U 


188 


met 


WJ 




B2D 


«i 


688 


888 


Ul 


CHO 


ns.rao 


<« 


866 


m 


ooo 


.o'tjsraw 


1«6V 


MS.T11 


m.m 


^498 


«a8.88e 


!41.tJ96 


170.167 


108 688 


88S388i 












USD 444 


1141! 110 


1 0689 


108 nolges aer \ 




IftUOl 


484 67- 


KOM 




040 000 


M.3aa4fuo(Ki 


108 88) 


MOOD 


13 MUUH 


IIWIK- 


man 


xm 


»iS36; 


JMSfil 


HW 640 480 41 








imai 


4aB4St 


51 66 






«M 06480 888 


104 331 


884 60- 






48&8a 




aeisx 


ill txr 


aui u-D 481 ISO 




BSSOOO 




lOKtr, 


4M aa 






m-sa 


MS IWtSl 66 


04 Ml 




nlH-ajiu 


1B«W 


m « 


M iir 


SMMf 


MS--8 


«aioo48iiofti 


104 41 




i8fl--ii-u 


IBTOW 


48 1S3 


WSOtf- 


IB* Wet 


646 ftU 


MS 016 481 auo 




JMOOV 


It) 5 ll» 




487 6611 


mvia 


tOM 


643 8HV 


M8 miAia Si 


106 UW 


880188 


' 




m 06 


^S44 


M4 44- 


«J.»». 


06^ 


886 se- 




H 1 IMU 




Bit ftl5 4W TlO 


964 1 


as* CUD 


a i"^ 


a* JM 


116 r" 


X44 460 4M IE 
44 6 e 4M 606 




stTBsa 

887 86 






SM -IM 




m 8001486 000 


IB.-. Oil 


BtteOUD 






I'M t) 


14 litt. 


^1 ]0S|48S 41 


IIH) IW 


888 saa 






u 1 o<r 


iriJed 




«S !*)'485 IWl 




188 66 














-46 6«f4t>C i'il 


'sSgffi 










B-asaa 






^IS 4il'4Wi 08 




UtUHW 






^4 16 


M Wa 


04B4W 


JU8ai48 ooa 


m wi|W»w) 


30 


»IS1 


l(fi( IK 


lU M 


S Ok 


»i ■flfl 


i,jnfti» 


IC 1 i« n 


,J-™ 






■> ill 




J0d U 






aj iiH AH 




Hr-Bfl4 j 




wa H 1 u 














ugi -wiiiwu Id iB-j ij 


•U iO ^ UJI J14 




39 


M»«>ljlMn>4»14U 


983 6W»30 'H8 6»IM( 




101 £60 


IBS GISasS CM 


40 




m sa Ml rilflss ,^ 


sisaa 


10166 


.J»,« 










40- 0H3 


108 «6 smes^ 




DM tC» f 4 >W 60- 






9« HDSM4 ouo 


4» IMS nSV M,i» i!£x 


218 9- 




IU»J<]804 338 


44 WW flsa - 66 -T9 


^fl m 


403 8.18 




4r ifl !__ 'wHswj 




■loa w 


tU 041 m ODD 




658 8H! 




im m W8 


*T l»8 81, 








48 HUH »» 










iUIIOWfo 


Wti b 


^iX) liuiuuu IU3 


daaesit 


MO sen ^ i»>j 




1963 S3 


uos-hImi bst 




KOI 11 






WITO 


nsMO 




»I66 H» 




IBI»6~ 




xMsan 








»«»a 






SS4 w 


16 — 9J61 1 «. JH IM IT- «r 




B90 6U 


noa sw 




nates 


A6S msasi S! m ii<o,jut m- aos odd 




Wl 6 






assss 


B«3 88>|»iie6a4trMTaiHi4slss3 




0IMS4 


W8 4* 




»H15M 


601 414 »] '11 498 sst toi 4S6 m ar 


" * -iimMBoaesi 






ow uoo'j&i sHis 498 -fiuhwi «w sw ooe 


■','',**' ' uai Boi8Mmaa» 


tm ^1 


era KM un m 4m \«nW ^ iga m 


J noB^iitrng i-il/KM -4am 16 


aiOMseBBiiii «\m^oi»,\«aa»MnN 



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 




H OD 


UOOOO 








s- -^8- 






1« 


OS '81 


IN) 












87 3U0 










48 


» -* 


SO 






iw.au too 


8- 123 










Ofl 


H^ 


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 




















ISI.M» 


8 4. 


88 J83"-3 






,aa 




Doa 


96 86 








181 .«8 


g 


iB Ift 




4» 
















IBt.U 


8a) OIK 






m 


240 out 
















asoa- 






a44 




»«3 














CE!Oe» 






4o 
















iwioa 


mm 


w 1 












» 


« 






i6i.ie4 


ea 












0- 










iK.aotJ 


sam 














tr 64S 


IT (&1 






lUM 








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 

._[i.aoH 

!WI,B6o'RM,lSr 
.994SGS.41T 






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 




ft CUTVt. 


I« Cr.^ 


M 




T» 


An, 


^^~ 1 1 T«. 






asTB 


KTnr 


M JO iwe IB .B8 r wu 


m* Hutu 


G MU« O 




aesw 


!ifie &H 


sa -u -i^ei M< 


a iie&iu BK 


000.^ e-i 




a» 






moi 3sl s 




W Id 


an si" Hiici 


U HI24 oa( 


-Ti 








MJKUi M 


BW 


dwoir 








itM\aavy 


M 








N JOB ^a 


ttiie'»aaM 


u(ni 


u'nS 








^miM 4 


s w 








MM) DW IW 


um 


MSSW, 


vw 


at B3it 






srowami iff 


iur» 


HS 11 


1SS» 


KIBIIO 






[ 


60 sp mm s (wi 


ijsss 


MS 998 


t38( 


m er 






iinw 


w»-i« 


no M 




8it~«- 


iMoao 


^48 




a Bsa 






M4 






43 


MtCtoS' aou 


JSMt 


Meet 


s ta 


luauM 






ma 


r 






40-83^ UK 


am 


!4e8K 




ttd S- 










WIM 


H 


«(i4i|a~B 


»! 


M-OS- 


L. J< 
















■w Ini 30 


usaa 


U7m 












■r 






00 331 


«S4S 


M 40* 


moi 


tteoB- 






K Rt 


r 3HU 








JftSO 


UTfiW 


usa 


uit» 






KMM 




*l 8 




as out 


M 7* 


)D-. 










17 M4 




3B. >78 1<BH 


KB 01 


ttiaa 


luiao 


Mir 






g 


«.J 


M8MB 


luua 


01888 


M 






am 


MB 38) 


m 




a 




W8 


aKH 


»BSt 


1941 


Mec- 


its 




a 


tioiw 


MBTM 


ano- 


cnt« 


»s 






% 3U 


UHW 


3<W 


wou 


a* 




M 


» J8 


M8 0- 












* 3- 


HUlilw 


-w 


i«a33 


»u 








i4U44 




sou 


41 




MM Sij 


WKMK 


MB 630 




^MVB 






mm. 


B '^ 


M 804 


£4031. 




tusm 


Stt 






3^ 




«"Bfl 


HOOOU 


4 8 


unuoi 


3V 




^m 


B 


^ «s 


tfUitl 


ma Bii 














03 Ki Biiai or 


«Bn 


uom 


UMW 


MDSB 










m J*. JW^ 




■bo'™ 


US74 


HB901 


33 






3- 


0- iH l8»<«i 






44« 


MSB- 


84 












ssHM 




«WIW 










mow 
















d»UU 






M. 


3 d »M 


ns ~fl ae. 06 


» W 




8- -13! 


«a w« 


4 J 


JW 8T 






68 


a *t 




U3 4«t 


i«»9 


fjaa 


w. 4a 




J»i383 








S- MU 


^wj^gaMB 


4BH8 


aau« 


urwB 


£9 M 


083 


iKW BOO 






f 


8- -8 


M 4832 RI 


aoB 


^«3« 


■^-M 


e5 BW 


B-fl 


«6 0<r 


40 




6J3 


S-BON 


04 IT 8.4 WB 




StfSIVL? 


-"* 


«W08 


W8 


tuns' 














SHS « 




maati 




ar wu 












«as9ei 






1 ^»4t 


■r tr 












»«a 


» ( 


luraa 


lU 


ariaa 


44 




KJO 






<84l« 


a<»t 


«w--> 


a B 


er BCU4a 








M B«l 


wsmtfuBot 


w 


M*UB 4K 






>0^» 


ai4ood«s 4H 


BW 


trsai 41 






»I4SI JA3N33 


OT8 


leeNooo Ik 




» -w 1 aoh 


aMOi. U 


a, 


m 41* 






in B80A -04 




»SS3S'0O 




Mr a>!u iiaii 


^'Mi.'bWtl BtM-^SWS 






jsw !»4 0(K*-»6e- Hi 




-mm 


» i~Ia4«w ODftiHgsa sj 

■Va~8|»4 444 U tn.«B) 000 64. 






M Aueu uiMl^a <& i>f> 


3X. '«e HR 


■»» s-(K&* ^^^^. t ■!?*■»» w. «n 


Kaum. SB ffiM •» »w\s». w« «,!«»»»«■■«'■ 


war 


!«i 








» 


». 


\^ 


* "^^ 


IST 


■rsa 





TABLE XIT. — ACTUAL TANOBKTS, I 



83° 


1° Curve. 


a- COtTB. 


3= Oorve. 




.■r„.-v«. 


Ta 


Kn. 


TAn 


An 


Tan 1 *rQ 


T 


A 


T 1 A 


-6^ 


iiK~0 


.Soooo 


bF^ 


mooo 


SsBMSeTe 






.^jiilioooo. 




llfl6 89 


^1 a 


B8S^1^ 


1150 83 


assuo- fi i 


J1 03 




m W|*» n 








B8S aB 




JS9 19 (i s 


»1 ftj 


558s; 


« 5Ml|480 68 




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 




aw Qo' -89 ijl 




57^08: 


2310W4«1 « 






aiooo 






JBO 844— 000 


* -81 




!!M3(H4«aOO( 












lao &w ~o 5, u 






«H4ja483 3C 




Il-SM 


J3IS33 


S3a387 


150 3 








jai 5M4ftt 86 


» 


maw 


air 00 


580-81 




S'lipS' 


WISB 


5-S -« 


234 7-6 403 OB 








687 "W 




391 W9 —a » J 


mm 




!S4 .5a 463 ii; 






an 3^ 


•m a.M 


1159 1 TOl B6 -7 —8 




23.5 & 46.1 08 


la 


nan 


SiOOl 


WO* 


1160 00 in- m TOsai 


ifll 0881580 001 


«)15 S9 464 001 




"3* 






IIOOM^S- *0-TW. 


^ wiliSi) 4i; 


J35-(0»4M3* 






JCii 13 HR B14 






-•W Ml *H 66 






24,^00 




ei5 S18 4SB om 


ifl 


ii"fl« 




rfw H.1 1 «_l58i ea 


J3 00040033^ 




1180 48 


ID'S a 




ja\f»i^a, 










iS6 1M4™00l 








591 1 , «r58 « 




1? 


1183 06 


Hi 00 


B8I 'l 




« GUISa B8 




in SM 18- 000 


i% 


'Is'fl^ 


MS M 


'IS- 1 1 ossiier S33 

W >14WMT 




iisfia 


•140 ff 


5J1 p -r iHSiBaooo 








^j! 1 1 , II 1 ^'i liaa SM 








^!H 15 11 1 1 1 1 HI 11 i'6 




IW r 468 667 








11 ao-lll -.IIM 1 S HI 0- I'M MS 


586^50 


.^90 469 000 








W5 0WI1 ^IS'*" 1 W 'H 5-0 


S86M 


iwOK, 


4flq3« 


ta 


1190 fll 


j3iBaaws4 fllLi 4 1 iiyuioi-8 sl-o te 


tnOHS 


..as ^4 


m&r 


30 


1131 — 


<3,Ono 1 'W II ii 1 1 i!i IS 000 


5S- 500 


2S8<96 


mm 




lift, tL 


\ 1 14 










11 mi 


1 i-osssiij 










1 ll^K ■i,! 




1 1 nm 








iO 1 ,1 1 SM 








10 » 4 1 6ST 








19 469'4 i M 


J7 


197 81 




=9 (Mil-'' la 








! Hll'l 66 








I 


*o 


wxt 


«.«U 






aoi SI ^ ii H 1 1 4) nn i bsi 








!30! w 1 m 8iw|4 4 »<a 




:Jil3 nRfiH4-l«n 












'.aw b. \ 1 1 1 4 nr 








13 IIKI)- 








.^1 a 




1 ia 


so 






B04 an 119! 6~ 






i 10 01 


fSS-TOO 


m 045 110- 5 






















r^ 






'^ ' 1 42 n -tlTt MT 


7/ 


' ' U I'fiJ-BlW 


















■* * 


tai.-i« 



—ACTUAL TABOKKTB, WO. 



aoc™. 


T Corre. 


a- c 


.rve. 


0= CiiTva, 


10. Cnr«.. 


■a 


T™. I Are. 


Ton. 


_Aro^ 


Tan. 


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 


IKT »'U 


s5u 7tc; 






J5( 


481 


iiJ.iMsao.saa 




1K.S3B3W.0U0 


IBT.BTS 


*iii.iim 




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 


]i».eT4i»e.ttad 


:eT;74a 


S30.71. 








«7 


22! 






m.KU 386.111 


187,874 


»^.»» 


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 




«7 


dOf 






IW-lOISMBflBT 


]M,iaia8i.42» 


147.188 


200.000 












itti nntai.wr 




an. on 


1M.B08W17 


Ml 


lT.iM7|«»a.lB- 




JX.Sm :IH7!£tf 


IM.SUi 


ai.ga 


njlau 




181.004 08 




I7.eas 282.883 




1W.5W DHT.GUU 


Iffi 4W1 








181. ion UH 


331 


is.fta 


(88.M. 


I 


JM emjWT.TTH 


loe.tMO 


»t!«8: 




twiissi 


181. Wl SAH 










iM.HSAiawt.oH 


l».748 


ssa.sig 


H7:b78 


891.041 


iai.»;,£S8 




ib:i»: 


2S2!m 




iM.t);H.arw.38n 


IM.M) 


MS, nor 


147. tW 




iai.S3«.ia8 


880 


IIB.IK! 




i 


i«,jaiaB8.Bii 




ua.OM 




m.4S 


i8i.4<Mirai 


OT4 


I1B.888 




18 


iK.Bmlffls.SM 


IM.Ill 


H^.»8a 


148 OM 


!M.BB7 


131 .581199 


SSB 


I1B.4U 


288 833 


SO 






148 ns 


BI.KTI 


131 ,«M 308 


** 


118.644 






lS7's)tlJ18»!Mt 




148 tSt 




si.reiise 


«ao 


11B.83I 


283.88- 


g) 


ivr.TtMasM.i^ 


iei)^4Hi!B»ru«s 


148.830 


eia!«9i 


Hl.BTTaiB 


811 




233 BS; 




)l>7,S«t»90.0«) 

ivr.MiiSUo.an 


laD.eii 


aw.ao 


148.481 


SK.BOO 


41.07!) »a 












*14 MM 




a*. 701 


8«.oiwuua 




llfl.BBI 






lH.I34 3W.I»e 




884. 7fl! 






aa.mm 


871 


11B.071 


281.33: 


at 


tS6.»<ia«a.H3» 


'i«'«m 




14S';«- 


m.isi 


St.-XSWi 










l)e.4«IS91.11l 


IM.tK 


su!:;.^ 


148. r;a 


iwi.sa 


-W.,W1 i!60 






2a4!8«' 


21 


W.IkMWl.aM 


170. ssa 


886.47(1 


I4S.I)K3 


iD8.Mt 


>^.«,-.^ 




112,241 




«» 


iK.n;sH.«7 


170, 3U 


Itt9.7l4 


140. OBO 








s< 


nB.B(w'8B1.1M 


iTO.«g 


»->.■>« 


I4B1(W 


lwi<i> i..: M--'-. ■■ n 


■iBJB- 




IM.OM|a«.» 


Ln-iM 


m.iw 


140.801 






IM.lHiaU.fllll 




BM.4W 




iM 's.- ■ ■-■'■■ia'.HK 






tnisH 


W.<e7 




■m -■■-. ■ ■.■::':jss 88- 


84 


m'.m\aia.<Ki 


iw.im 


nt.soi 


1411 aw 








iw.gealwB.M 






140.74. 




236.000 




lHI.T80S93.eil 




(w'ss 




ffl!5 soHi" --i-en 4.1- 


11" BBO 


233 10- 


a' 


lW.mW3-ANS 




•or a 






tStt»ltl).MI8 


mita 


23e& 




(w.wiaM.ier 


i7i:4 


M7a5 


w m 


ssew 


xnamea 'v 






31 


II»,1MW<.4H 






■n w 


"ft BM 


saisiseioo. 


» M 


238 88 




ni.si^lsM.rai 








« D)!«8 41 


aosBi 






BO 456 -tos. lion 






(OS-S 






UO.MHBM.^ 






20 48 


23 


«] 


100.792 ms »u 


fj 1 w a aa -04 


MM 




44 


■n.eta Bn.%.^ 


7X- . »4 m t 8M 


120 886 


« lU 




»i.in8»9H 111 


:■; M !»i 07 


20 ji 








7-1 S4 uo >64 aw 


00 808 






■)l!s:^^w<i.««T 




ITBOO g JIf S04444 


SO 804 


USB 000 


48 


1M.4J3W0.IM* 




s se 


017 08 84 so 204 eao 


ISO 068 


888 B 


48 


m 021 W7 £29 




2<» 








BO 


»)i.;»s9T.5iio 






tw 84 *. as, oro "1 « 




Ul.tKMSSTTn 










n.<»i soH OM 


m.n x to 




«S8Ma 84 


wuMme.sn 


J7g.Sr S4 «l 


MW 


'W Bl 84 




m.4B 14 «r 


80 


<gRt^8 34 




m.wiai HH 




mas, 




(7>.r SN «. humi 


a»TB 


U:7friK»'444l 


ra,« S i». K 


tB.mm.!m 


-3.89 a*, « a. 



'"I 

^91 J« 



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«) 



^^ 
























US1! 






MS 


"S 


■MM- 



TABLS nv.— ACTOAl. TAM0BKT9, ETC. 



«' Cime. 


T.C„™ 


^■■.. 


"""■ 


9" Cnrre. 


10° Carre. 


84* 


Twi 


An: 


J^|_a™ 


Tan 1 Arc 


T 1 Arc 


WSO-B 




1 4 001 S4 ee 


aociooo 


lasTaS'sMM 


m 94sWrooc) 






1 4 814 S<a 09B 


IS 40el3l>0 JU813&S64l>tsa FA. 


lis nRoU4n \ln 




MS Ml) 




:74 aa- 345 tj-H 1 lU n i w c os i_ iial lo ssa 




WBW3 


100 ass 






■esM 










»B7Kt 






8*4 01 iiSi, 




3WSU 


»IM7 




M4 »• 1 Jl in 




sMceo 


nam 








m SS9 


ftsfa 








«MITT 


101 BOO 


i am 


UfiOoa 


1.,. ~ ^ 


1 -, Wi .»> 




i41 £00 




SMKX 


Wi-B 


-BUM 






138 4ET 368 B1D 








mtHw 


408 OM 






6S6Bfl|30ai» 




isa SOI 








404 S»S 


75 681 








1"9«t 






a«B80 


4ua on 


1-5-08 




63 4 TO. -OS 










«M# 


4<a8S» 


.rasBt 




sssKtsc 










tnsiffi^ 


4U1 167 




(0 4.9 


sa soaW 1 1 M NX. 




S»KI 






HO 00 






404 -U 


■OM* 


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 






aoaiii 


«6 B8S 


T«-04 


B47 86 


IM64SS04 8-5 


18-4»1 


n)£68 








awM4 


100 111 


70 BM 


ISD» 


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 




W20S 






m% 




ss 


am 84 






4B048 


166 la 






lf"l 481 


124 »{ 


e44 388 


se 


an W6 


ur? soo 




49S86 








117100' 








ar i« 


W-77B 




49 m4 






IS8 17! 


e-185. 








WW 


tosose 




m m 




BOOM, 


188 Mf 


mor 


1M4-8 


214 838 




sm«o 


uessa 


~i«<n 




^ 


,nfl w 


q 


»-n 


„, 




30 


SOT 0-1 


408 811 








SOB 889 




l'.3S3 




am M( 






13 MO 




»8uia 


409 444 




4^ 6B 34 


a)8 ifii 


40g79l 






a»w» 








smax 




1i (w" 
















908 B96 




ma» 


KItOG 


168 502 






nsToi 




40 388 


se 


ste-ae 


(ID ess 


[7«M 


■St 148 


iWbog 


808 1S6 


189 sr 


irflB89 


1«6S46 


Me BOO 


sg 


ioews 






BK381 


158 TIT 




IBB 838 




186 4B9 


£46 60- 






411 B8» 




BMflie 


i>6an 




180 481 




lis BliO 


H6SSf 




"OB l-H 


411 60 


-9 JS4 




158 981 




189 681 




1E6 eoi 






aM «!■ 


111 944 


-S44 


1 IKH 


















11 ^ 








180 7* 












n >« 


-TtfirCiV 671 


167 SB( 


80D8J5 


189 SH 




lSSB-( 


i 60( 




9M fl 


41 ~M 


!l «■ 1 8, 9 810 




MS 681 






i»oso 






















1W04S 








tH Wl 


HOOTO 






nooof 


40 ( 




26 81 






no iBo 


41,611 




)S4 6M 


167 TM 




40 m 




«8S«I 


MS 




m»4 


\\7 


H0 8S4 








40 808 




»»)9 










l«44n 


58^onn 


1 0"! 




b' 








4 4 444 


.80 6611 


11IB23N 


\ai*«i 








gO-78 


1 4 "93 


leOBM 




"10 ns- 


4 BOOO 


TOssnsw II 


Bll o-T 




SOtMflSMl 






Bi omiaw ] 


?II Ml 






Wl.iWfltfW. IH/ 


W.3!M,«66.W.ll 


tii.dsg 


M.SSBIJ 


S/.4«/ 


ue.HU 


1SB~0 






r 










A, 



. . l^ 



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 


-HBO 54 OUI 
-^ 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 






"^^ 


* Cb 








w 3« 






fo 


















J8 00. 




iO 


-k w. 


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 




.^ ^ ^w 



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 
.500 
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 
.479 
.568 
.659 



332 
332 
332 
338 
333 



.667 
.833 
.000 
.167 
.333 
.500 
.067 
.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 
.937 
.020 
.121 
.210 
.298 
.390 



.000 
.167 
333 
.500 
.667 



337. 

337. 

837. 

337 

337 

a38. 

338.167 49 



42 
43 
44 
45 
46 



.833 47 
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 



.58a\m.G2ft?i'n ^w\\';v^\v^^^v*^^^>*;, 



.375h 
.7921 






ixd 



TABLE XIV.— ACTTAL TAKOENTB, KTC. 



34 






3 cnrv. 


4 On e 


S Co 


m" 


T 


Are 


T 


Arc 


T 11" 




Ta 


Are 


Tin"" 


Arc 








r&KW 


1 00 00 


m ftffii 


m 


418 018 


KOMO 










nam 




584^-4 


11*18! 


-iwnu 




50 6»( 


880 »33 










W4sai 


1134 44 


fS84E 




50 811 




3 I1-54 il 




t— s-o 


1 0190 


«4 ssa 


1115 00 








981 800 


4 1-SS 39 


wa 8- 




1-OTSa 




iiassn 








B81 339 


B 1-SB31 


joasa 




1-04 1 




1186 11 


439 IBJ 


852 083 




BBlBff: 




mni 








SK^W 


im« 


419 I* 


NM500 


SI Bsa 


SSiMO 


7 


17B8 11 






waWB 




439 814 




1M ~StA»K S3B 1 




ITWOO 




ST) 534 l-Ofl B- 


5W »i 


113 -8 


4-19 88B 




1RI H8 


66SBII7 





lS8fr 




S-4 W ITT Bl 




imas 


440 063 


85d 50 


1MD91 


68jm 










is-ooi 




ISfJSi'Sa 


15. 2^ 


988 «3> 












1110 4i 




i.'U45a 
















IV. B4a 


884 000 










1411 9S aji41 J-SBM 


884 389 


J*!] "^ f\\ ^ ^j 


S Ti 1' w 




III! V 




^19? 




10 1 FH ■nl34'«(l 




WB-iJB 






153 *T^ 


US 133 


17 1 r- ^lii-rt « 




Sm 14i 




441 809WT«( 










ll« I' 




353 4 680 UOO 






SS9T4- 






1M 9i0 




B9 0-i'jm91 


•w Of", 1 i« fl- 


W0 04-i 


"«« 


443S-«aW133 


»4 l» 


6W68- 






91 848 


114. 00 


44S « 1 11^ 7S0 




68 000 






SW fl* 


1145 50 




)54 184 












443 'BO M9 M3 


154 648 


98 m~ 


£4 1 I BliUU IXI 


HSB Na9 i^» 00 


91 tt' 


1146 S- 


443 480 800 OIM 


154 831 






w '9-i^»'<i 


■5BI S 1 


















3W I « «>» BB' 


aTlijewiiia » 


l»t 14 1 J^ W 






144 1 MUl -■* 






igS 6~i 1723 Id 




ll4><Htl 






"9 


1-8 »l«4« 98 


W9 lai 17U 1 


«a-TO 


1140 -14 


444 85. 8HJ 08.4 


165 4BWn WT 




i-79nl«/fH 






}l/1 00 




i 911 PBO oon 




1-^) {W !1M 










l> in 1^41 <ttl 


it 


i-wy !4 1 II 11 1 w « eff- 




1 fl il 4X- B.1 DUO 


35 


1-U! 1 

1-w I 1 






30 


1 HI 61|11 1 i. (l*,(iB- OHO 








1-86 Sa iieS i fli _r 1 11 P "ill 14 4i IH4HH.rl.i3! 387 «M flfl" 




i~g 3i34US(»ie9sseei'». so»ffi8a)|iisaa)4M gisswaso 


IB s-iBB3 0oa 


40 


i-wt *i^w (i «94 itti-M ss-ise iwliiM iseMT i«'»« iw 


3B--M6q3 113 




l-M M itWil 


s-uHOsriii w 1. iwiiu* i-:«jwo(W 


aBT9OT8«isr 






«»M)fih-i 1 1.1 iioige-BOi 


>»9I«BM OKI 




l-W 9 |!4 t '1 




smmmva 






<9 1 1 1 iiwsBssn 


»«4»8HM *r 




SOd )i a<98B8-W 


iiRMmBwnw 


*a 1 M itma 


89B 1 n MHSmlis- 


IMSM 885 333 


47 ni B4int w*B s i 1 II < iwnws 


KWIBNaiH IK 


48 11 ftmllStSU WWS hi 1 1 JtHO-fltm 1)0 


159 t«i,n6an 


49 i-M* 5«i a 


H9S '^1 I 4<) Kl Jt-n J^Kb 1 lliU SB 44a «« g^ 11 


«9«5«»M3 


5o'|-97 8914S! 3- 




359 wassa fir 


HI |1T9S 31 SJft tn 




1/1 —iioi-mi 


B-'l-TOSSHtWU 


Hfl9B4.M 4,1 M (KluO-VllI 44')HMR 1 flh 1, 9 UWlflO- (33 


5t lWni4 S4HH M 


1100 nil n " ™ « 1 « HwiwWnr 


^4 isni on^wik 






'iv^'m 


HDI «" 


Wl 












i s« 


nmar 



— ACTPAI. TANaSMTB. ETC. 



jas £«3 -les 1MB 



an lUAX 
e&3 sss koo 
tea 'U* 4Bi IK 

a-i em\m 

■^ U0|4JI 
^54 ]SB|49:i 6;U 



«») SSI k:n OK) 

«» 610 lir soo 



wo joiiraiT 



-. 1 jjii M^ 



9" Curve. 




^ 




Tftn 


















uucuo 




























































«7«!m.w 




Ml sou 




B5JSTD<»0 










































































1 - 13U IIS lt,7 




W<ili 









STI W ™ 1 


liSi 


«-,4l.l 4.,,! 


R 1)1 US HOI) 




,; ^^ ^1 



!MM 


«, 




v« 






















S!!i 


^ 



TABLR XIV.— ACTUAI, 



TOW* SIB 1 

a MB 7-1 1 

IS 90S -301 
U 4)0 S4T t 



(4 »~fl ee ifU 156 TOt 9SS 

■^ (TT «B ID. aw 01 M- 

03 B~ 500 sfli SJS oaooo 
fetr" »i BWT06 it. ass 

Bl K-a 3M SM SBe ^>■ 88- 

w trs ai sua 0-3 os ooo 

19IR9 Ifl-'MS aS6 08 338 



A IM HHl .iSO 384 r 

a H^,^ Nsi is« s«4 S! 

6 SM l«^ 600|381 T._ . 

le 0S3 i#u »i 384 wr "v 



"iKw onoies S;4 o 



II e-|45 »i8aH8 i^ w 
Riee'4^ i4Bn86U« se 

IIK -8,4(18 87S 887 OSa 18 



18 UT9IB 89K r 

iSMfliB we- 
st 9500 00 HIS 8I4 

«5 aM3 1.1 »ffi eo 



-B.san ociu ins oi» 1 

le'flSO 41 Hbn il4 I 

1 8B0 SS3 itw 4(a 1 
aiiwi W.W8 s6fl 1 



TABLE XIT.—ACTUAL TANGKNTB, I 



i Kte,ooi> jSB.cea 90i.4«9 S! 






s! ISO 441 ! 



•o.siiewi.^ 

II 111 XI u 



( BOH «ii an 4111 BIS OBvaw sa-tix i 
^s8M««fts(HGin»nais 4^-440 1 



9° C 


„e. 


10., 




.. 


3 


Tail. 1 Arc, 


"tZ^ 


Are, 


M 
















lu: 




fllj'lrt',iSBll>J,^U 


vj'.oei 




3U1 




3H.aa7l.lHl*.44. 
















so; 




2ni"44riSI:sij 










aoi.M-isaiooo 










iUI.M.'iSMI.lBC 






167 




Mi.7«m3:( 


18i:B!1 




m 




aoi. Bib, 800.666 


.M.711 




600 




1 


\t\S\ 


flsr 






m.m 








303 "iiT.riyi aiiD 


m.m 




lar 




20J.,ffiil3ai.4B 


m.m 


(Si 


w 




joa.401 


a81.6U7 


iss.sei 








iCC.fKIS 




IK.SM 




9o: 




KK.tHili 


sftsios' 


ift;.445 








aa.TBT 


aK.aa 






ua 




9(».saB 


aiei.4»: 


lai:^ 




167 






SK.p 








S 


asicij 




iw;9w 


W 


so( 




Mi's;! 


II 


183 lis 


l^ 


167 


' 






iR3.*:i 












mm 


W4 600 




iUa -¥lilM4 0-4 








xaaes 


891 AB 


mm 


SHB3S 




ana ew 




IBSBsa 




3 


w ooa 




1H3TD 




a 


wm 


894 8)1 


18S«!S 


MSWH 


d 


aoiesK 


SBMm 


1H3 91B 


556 SOU 


8 






184 006 




3 




StKSt 






WMB 


aTO6» 






9D4 0- 


395-41 


iaiifl4 1M16 


3 




S9G 931 


184 1 RjlW M 


a 


j04 aC 








mm 


89B SSIS 


184BSa3»66 






l(M 5.>1 356 tUl 












IM 83 !b IB 






l«4 01<%1 W8 






m 0-1 -B fiuo 




"i t^a 


IK m'as B6 




' "' "^.^fJ^. 




1*' l-ii 








iH ^-ijiH Mw oim 




Jnfl^,,*Kln4lll^BB44l.1nu 






P'^i*'" ■«^«'*^'^'^^ 


mw 


l\\W4 V 


»,%. 







U 9W S14 (M8 «8« ~81 441) - 



TABLa XlV.— AOTOAL TANSKKTB, ETC. 



ifiBSiaeoi s asi m\ a 
- ..sa BisMs Tina "oo' « 
s 1964 lalsBor 1" s * 



I as UO 939 h»0 K 46 













l-I 































































































































HMBOD: 
law 817 

'uosssa 

Ml IB" 

904 »» 

905 000 

905 838 

900 66- 

"IT OSS 

._ .) 500 

MM" 917 



STi 1 

trt rv 
neaa 

d71 B45 

rsoss 
3"s as 
rs ssa 

75 564 

8-a -74 

rTiss" 



jsom 

■BBOOO 



3048 33 944 £9e 



K 18U SO 6S2 8 

T I<*m S3 (B? ft 



41 


J 


1 «. 


^ 




















)-i TOO 




3-r BO- 


iS[Be- 














ass 
























































laio 








i~.,« 












t M 


3< 11 



B~ 438 V9 000 



TABLE XtV.— ACTOAI, TANOKNTS. 1 





C rr 


• 






B arv 


^ 


















BOOOTO 






SBi 


MOSriM 


Ol ooo 


"sTmosS 


BOO "-a 






01 1 




Un H6 


88 aasei 


BOO 668 








3B1 


400 8" 




BBO 


8~ 


8« 8SS 








ea 




00 5» 


Be -B 








aeim 


a3>> 


jsa<i& 




Kaa 






88 "Tl 






W 889 




-B 


«3 T 






jo- 


u we 




880 


dS6 


101 Ml 


awfHW 








sea 






MflM 


as 00 


Hi 




« OS" 


WW 


>»■ Ol 




468 


207 771 


JM 




a« 








Be DO 






887 


J07BN4 






w » 


80 


BO^fiOO 


ae-ao- 


89 


ssasBs 


16 




^986 


« 86" 


8"i3S 




36 


KH-fi 


a»"«5 


fie 






088 


X8 0e8 


to 852 




SB 66 






je EBB 


uoa 


iSi sn 




SBi 


SOS M 


tceoa 




1h K 


aes 


1 aiH 


HT flu iS 


a '^ 




600 




iai2sti 








WW 
10BB89 


■fl"8rfl 3K 


834 Sk 


46 


-TO 


J*^ 


wtw 

HUSK 


Iff 












«»oeo 




J34 OL 
















m 44 






JS "38 


463 


8811 




«»Bai 




M 






■B8 VJ 




M 


*s 




^eoB 


m 








WfiOOO 










T* 




408 388 


88 00 












136 nts 


^968 


as 01 


US 9 






9S 


SOS >6 






3a. "04 




01 


W9 


ton -Of 


88 »r 


SB. 5 


















tDan» 


SS14 
















at 


HH or 


88 14 
















i0B4ii 


vHsm 


8SfiJ> 








■8. Bl 






SO" 






an 


















«£ 




«»54« 
















BOO 


aa 






J" 




^B( 


GWgw 


•m £ 






880 


SOB 066 
608 S& 


mrni 


63 W) 










60H 


XI 


«( 










mm 


























BM 












wr 




V, 










BBO 


OIK 


■vim 


S_tv, 


IS oau 










JT1997 


sssiwn 


m m 












*- 38 


ws«» 


wsua 










883 


« SU) 


(M^^6^ 


28" 89" 


UB 


™ 




■KS 


















SI 





















» ML am 5691480 JM 



88 J^ sa6 1 



U TAUaENTB, ETC. 



9 68W7M» 



)tr an 

aBTsm 



J5S DD «« uje M .M aao 



US4 M 8n 
BM s«8-Bn 



—ACTUAL tahgrnts, sto. 



I" Cdttc. S° Cm 



e-oasi 

KB )Bl 
ITS VIS 
B-B 4B 



TWIIS 

ijs ei8 oiB 



w/«j s^/a 



O" Curve. 3^ 



rsooaj 



a-s8St 

riDOD 



TABLX XIT.— ACTDAI. TAHOKKTS, KTO. 



... 




a Cuire 


3 Cnn-B 




Ian Are 


T A 


a A 


Tai 


Are Tan 


Aro 




la^TraSiuooo 




B. M8,"S5T 




SGo DaaiiB4 BSB 


"wTooo 




19^8 ISO 6~ 


wi»wo uoow 


BM «3l *- A! 


B3%4 


BBo^ roiB* 


bouaa 






or IBS w B~ 


(bH*« SS 


U. — 


U Sa BBS DBS 














B. saoffi 














» 66- BBS 44 


6 333 












Bfl-uasituo G 067 




Jn io |iOO( 


mnx 


B5, 'MO Ik, h OHO 






man 


BW3 Bd M a. 1 






^ r 


M 8 


amai. tai, b a ee 


« ; 1 aa a 


i» BB arxp 


•^ ««' 


« ^ "- 








11 illM MHSatltt fi 9l)S 




13,1 ■MUU kt-l] X|W (I6S BOOO 


BO X 


la.lBHT, JB Ibs- M D083 


IH, 


itlim 1 














IB 


mf.^ 








BB- 




era 




DM a- 




wum 






t« 




aw 


»5 IM bilmm 


oa (33 


LsaUwaW 


tlBl«- 


'« U fflH 




« -tsr 


0333 






0* 


3S 




6«- 




3- 








se- 




jouB3u»ituua|iiu S|«b.eaiKi8S3fih«es3 


so- 4£ DOS «50 10 (MS 


-^000 




joasflMMfrloDa bi«3S3H~d s^Uhsks 






* 




402 s. 


^ooo 


M -8 33S 


oon 


4 4H. C«8 


4» « 4, fl W 




J , IN Si l^ «b 


|0S85-BfflB 




>o 59 aiea aa dob 63 h va-^misM * 


WBd&Bos* WW ~eae- 




i,M 'SHS. 00 »1 wj so ITS aw] SBs 00 


W5sa B JO 04iso--<»o 








n 


1 +. i(H 1" — fle~ 


'■' . " A 



















TABLE zir.— AcrnAL takobktb, i 



39° 




2" Curre. 


a° Curve. 4= Curve. 


... 


Tan 


^rc 


Tan 1 A« 


'''"" 


Arc llan 


Are 


Tan 




teuuoD 




anax 


noo oolsu? S41 


fTooo 


4(1 9t 










ea la 


soojuao-Bai 




400 11 




josos- 


iv(»S3 




a— m 








406 99 




X3 8 


1905 1)0 


lUja 93 W W 


B~S» 




MB 048 




106 48 








1018 as 19B8 W 


ir^isBi 


80- S3 


ousrs 


9-8 ««7 


406 88 




iD33 fi9 


taaesa 








doa-n 


508 BW 


rroei 


106 86 




M3ISI 


39000 




»&6 0( 


19*8 im 


soasa 


M8 48 




10- 04 






3911 r 


101 81 




B-8E89 


808 89 


608 985 


mi 


40 sa 






saigas 




IMBb 


B~BBO0 


SM44 


509**] 


9-8 833 


iu-« 




soar IS 




1018^ 




0-9 sia 


lauooo 


W9 45I 


9-8 60 






^03^38 


gold g- 




IBS8 S3 




1805 G6 


509 894 


9-9 18 








1019 K 


W91 


079 881 


1806 11 


y»va 


9-9 683 


40-98 




iB"0 « 


lOflOH 




080 141 


iso*r 


misi 


HBO 000 


408 18 






IftjOS 




680 iM 


180- a 


mom 


980 4) 






3lk>S 33 










10S£5 


980 1131 


408 54 




lOr 00 


10" W 


1902 B 


es) 08 


1308 31 






WW -8 








Oil 04 




J8[ W 


isosa 


61098 


981 Ml 


4UH B^ 


















(0,08 






^out m 


3030 l)( 


imss 




68 OS 








409 30 




204sas 




10:18 45 


l91iS83 




ai0 68 


BIl 80- 


»>i) 


409 49 












- 043 


183 1-1 




' 




4UU 86 
4004 


■w 






05 


WBDOO 


















4081 




a Wi 




1099 


4S u. ^ a ahij i wflta iss 3 5 ^ 


18 wo 


«8d W 












30 '0 1) > imii'TkUiie 


14 -Vt 


(B .Of 


4156 










1 1 98 




4 M 


















JS MA lAiJO- 1 b, W Ml C OS ■!» 1 3 

3D jOffieJ«wsoo|io3asj|is^sae8g 512 18^ 




51« 5061091 **l4.3ia 


losms'^m mm aa iBsa as 6S8 kh'ism 2S 


m «U«,4n« 


41 *^ 5 ■< tu*' m 1 33fl ■) 1 -^ 


B 9 1 •» JK3[4 i OS 








i tr 


4h ^ 4 i 94 


4« ■> n 1H 1 1991 6, IJl 1. lU _ Et. -1 


4 5 13 


HO 'W^ 07 MRS is'ioss oe imi a aa, oso i8B7 Ts'-sih ob U s^m 


41B 38 


SI ara si3»i ouioaH49i3)«'K)a9i8'Rirj^ ASM nnsM ,1 




o«jo— SHTOWO laaH imi ai'as bbi'ism si 3 t^ j- 






88 



























^ 








10= Carve. 


39- 

m7 




S. 


Are. 


Tan. 


567.148 




isflao 


Tnu. 


Arc. 


Tan. 


Arc. 




1B5.«70 




20S.165 


390,000 


~0 




sw.ira 




*to.m 


BiTMl 


rat. 044 


4H7 70tt 


!i25.r7( 




303.350 


190.167 


1 




M.«I 




iOO.S* 


Hi7.6II 


l!54,06! 


487.017 














m.nu 


uio!eE 










»&'.m 


tasisso 


3113.436 








■88.987 




i»:B«. 


11"-^ 




■jse.ae* 


4S4.074 




t90:6B7 






iM.ast 


«i:3Bi 


wo. BBS 


4ea;6« 


aw. 189 


434. B6I 


303:63; 


tB0.8S3 






SM.3BI 








234, sai 


4B8.76( 


:i26.aK 




aia,7i7 




e 


* i 






im'.xa 




^M.MT 








203.812 


i9i:ifl7 




r ' 


aaoifiBT 




soi.iw 








hsbIsoi 


434:815 


203.907 


t91.3e8 






la-tia 


tU2-»U 


m.aaa 


aoiaw 


^'.m 


4B9.375 


ai6.610 


435.000 


204.U01 




e 


3 


vo.eea 




m.sn 


56l).5» 




4B9.5»3 












MU.O» 


ess'.tm 


m.&K 


659.;^ 


J55:11B;4»0,7B2 




485:37* 


304:i88 


i9i;838 






sw.ist 


US.SS3 


all. 617 


560.000 


a65,!!3ll41HJ.0O0 


tfflioia 


435.561 




392.000 




3 




KS.fill 


HI. 772 


560.^ 


K5,349l4U0,a« 


■sn.co' 




304:874 


393,167 






BSS.IJdtl 




5«0.470 








304.460 


392.383 








OM.KIT 


!g«!o42 


36U.711 


:»3!5H6 






480:il] 




393.600 


s 


B 


wulsii 


BM.W 


aw.ij? 


ieo.sM 


25.1, JM 


4iw:B3a 


«7:3i( 


486.39<, 


304:6« 


392.607 






BM.rji 


iSi.aiJi 




itWftS 


4BI.041 




436,481 


304.753 


193.83) 




h 




Bne.aoQ 


i!Ua.447 


>ei:4a 


a5B,B41 








a)4.B47 






wiiaw 


DfiG.^ 


iasi.a^ 


661. 667 


£56,050 


m'.-m 


227!856 


480:862 


ai4.9til 


B03;i6i 


» 






sas.Gfia 


n^.m 




06.177 


491 .607 








998 383 


ao 


i' 
















437! 33! 


30e:i3i 


M8.6O0 




















30G.220 


893.66; 






w«!aw 


*<is:]i; 






Jii-j:2g-, 




43f:6iii 


205.315 


893. B33 


xs 




Ma.070 


om.bb; 








228.17' 


437,771 


306. 4I( 


884. OOO 






SU.OM 




iBSiw 


503.005 


*5fl::6l|43^^T«f| 








894.167 






su.ae 




:!93.&» 


eea 3-13 


■^•m.mj'ioi.mr 






30b:5BI 


894 333 




'i' 


su.ua 


657:500 


■ioa.Ki 


063.571 


256.euijl4<l3.1» 


228:490 


438:33; 


20S,G»4 


894.600 


HI 


ais-701 


»7.?T8 


aai.79; 


5M 810 


i»7,116.4S8.3SJ 


228.695 




30B.7SS 


BW.667 




m.me 


BB8.(Hfl 


ai3.»i(i 


564.048 




228.700 




205,883 


894. B83 




« 


mois 


a.'is.asa 


304. oat 


564. ase 


257.85alj93.7S0 


ffl8.805 


4fl8.8BB 


205,978 


896.000 


30 


Ms:i'' 


BSM.IiLJ 


IW.IW 


664,5;!^ 


267,471^4ea-05B 


ise.oii 


438.074 


306,073 


395.16; 




i; 




BS8.KW 






a7. 580 494.167 


229,011 


439. 3SI 


206, I6T 


3K.S33 






690.167 






267.701494.375 






3£6.«6B 


396.601^ 








IISa.444 




.W6:!3i 


ii67. BIB 494.588 


22»:2« 


439:681 


206,851 


896.66! 






S13,7te 




39t.:a 


SM.478 


357,937;4B4,71ia 


329.8^1 




3ue.446 




as 




814. BX 






SM.71' 


S58.05B'4BS,001 


229,130 




200.540 


8961001 
















320,585 




306,684 


306.167 


37 




m.aa 




mii^ 


eoojei 


a5S:«|-.'4BS;41' 


2!iB.640 


t40'871 


306 729 


896 331 


18 




M1.«U 


660-833 


^.isg 


666.428 


2M.410 41B,B1!5 


329, 46 


440 566 


306 824 




10 








!»J.404 


566.607 




339,850 






396 66" 






m4:t4< 




jus.nao 


5UC.(W 




2-J9.flJ' UK 0^ 




i-B Ka 






M4,8B8 


MIM7 


■J96,67. 


567.148 














ia.061 


Bfl1.M4 




;i67,sei 










W2.:ax 




667.613 


2,-iO:iH)l i'i. . ' 41 1 




ia'.ST! 


BBM.SaO 


■iK'.oaa 




am.ft' 1" , ID 




M.sao 


m.-ns 


M6.21S 


B6fl:ooi 






aiO.BH: 


a&i.m 


^.U6 


56S.W; 










m-sgi 


290.477 




3A9.4S': I":.-" ,,;■■. 1 










^.613 




«B.f*B4Br.7M^. B0J14 40 


IT b. 


i98 IB 


40 


c 


JM.150 


eea.esi 


396,747 


56B.04S 


K.M. 704 491, 917880, S|i«44« S03 


80-859 


398 388 


flO 


il4«.307 




3im.es 


MB 2B0'25».MK|4a8.1»a»l.((<1144i "8 


30-964 


898 500 




5 








m 5-34'Mn.04o'4Wi.M.i!3!ii.iofl|442 ee 




898 06i 




jmImi 


Mi'.7« 






308,111 


398.831 


03 




BM.IBO 


eea.wo 


m.m 


5711 .'!ii."i,.: ,-.'. !■!- ?.'":;;. iir6:44a!3a: 


i08,2a 


399.000 


S4 


?; 


SM.93S 


J66-27I 






308.333 


aoa.ir 




ur.ou 




aofiiw 


5711 ! ■■ ■ : ->■;-, A*a>.w.vx«..=awaftsiw,"h* 




H-.sn 


les'-ss 


207. 693 


y/o: .1 ivai4H.Ma\^i«.iseSsifi.wK\*.:\ 


r 


W7,«i/«M.i/i/»r.8aiitoi .1-. .,..■ 1... . . ,.■ Ml isi'.^H wwV'Sfc-wa'^.WL':^'' 


W-aMW,Ww-9M(5ri.i!,M ;,,,.;,;;, uJ.V.:iil.«*i\Wk.««^ 





— ACTOAL TAKOlOnH, KTO, 



*•• 


1 Onmi 


s c 

Ts 


„. 


c 




4 Cn ™ 




Tu 1 An: 






An, 
"OOOOO 


Tan Are 

IB 900000 












MSesruo si 


043 1!- 6H3 










04» -g 


000 88 






sanasMuoi 


044 m 










044 64 Ju 40" 




B6S8U sa 




xno iBMoan 




B4i Hb iJ 638 


OOlDK 


48 3 80 66 




EM'S 


045 S8 


an&w 


BB- 103 aab 


6!3 8-6 


OOSM 


.8SI6« 000 




0«0< 


ioOBBa 


69748 88 K 




00-- B2 






aOM 98,4013 S3 




sow fl- 


BB- -^ as 1 


DBS 34 


OOl 38 


i a -IBB 80" 6«T 




ama St 


tOGDD 




axTBo 






003 n 


18B4803 000 




>n9 B7 


war 


48 


^008 33 


998 Sas' 338 8il 


BMSa) 


not 


A B D3S08 833 




van » 


4aR33 






9B8 6791 339 44 


684 051 


004 M 


1 y JBBBU3 or 




««g r 


4iMioa 




nooo 


988 9941 840 00 




00^00 


49481804 000 




wm 


Mil (T 


I8» 


■^088 


3BBa09 BlOSfl 


W4&fl 


0054 


4 9 6-0S04'JS3 




jMwoa 


40* 3: 




■D 6 


MOM 84 


B» 66 


Wj 88 


4 SSBBOI 6fiT 




aowoa 


4085 00 


OtBB4 








52S 00! 




90 MB 809 000 






4086 0- 




nsss 




34Sa. 






4-0 IBS 808 3S3 




10 49 


1048 83 


a»T8 


401 


-00 5-0 


^ ~a 


«f.1l 


00-08 


120 1 iMis oe 






4030 01 


OD at 


t0500 


-00 881 


343 B3 




00- w 


420 6 6 BOB 000 




ioasa 










348 89 


5SSB43 


00-94 


20 806 806 333 




aCB no 
















io9 B a 


Z8 




















OW 9S|20!S M 1 - m\m 333 
OM 4S sou SL DMiOB OS- 




1 84 


1013 33 


30 


B 3-( 










1QS fl 






581 


40333 




aa 


a Bu 






34 


2 7M 










405B3 






»4I1 


1060 01 




87 


MM 40 




oeo S33 




lii 3! 


««. 31 




30 






Oe 8 M. W SM 356 10 530 l!76] SsjlM BWlSIS WD 


4< 


KMW 


4063 S 


M flfl w 3 0- 8 B 35. sesno 9 2 6 0-14 i-TSis ns 




e 4 s 




W ".18 3»- 




das 3 






iieir 83 


4 


S'Tff 








nss B 




aiKB r 




8 ansa B. 000 






10S 


0- 9 


^ « 1 r"'" 


SO 


swvs 


4083 31 


006 4 k) fl- 


-1 osg' 8 Ib33 -w' 020 ssliae eso's e er 




233 61 




ood Ki^ XI 


30*|36B^33-P«1 «8BB3 TO 








08-^' 






smei 


lOfWS- 








i«5S 




Oft mol 






«flx 


*»,Ww l4,n 


w 


f//^'^ » / « ft n, „ 




/"^S 


mitl 


' 












S,\ 



tABLtt XTV. — ACTUATE TANGENTS, ETC. 




847.796 
M7.8B4 
848.041 
848. 19» 
848.857 
848.514 

848 e» 
848.ffi9 
848.967 
819.145 

849.802 
849.400 
849. 61H 
819.775 

849 ysa 

850.091 
8S0.;i48 
360.406 
8fi0.56d 
860.7SS1 

850.879 
851.036 
851.194 

851 .%•<; 

&M.609 
Sil.667 
851.825 
861 98-2 
36:2.140 
86«.;i97 



666.007 
666.944 

667.600 
667.778 

uOO.UuD 

668.388 
668.611 
668.889 
669.167 



T Curve. 



Tan. I Arc. 



8<> Oiifve. 



9° Oul-ve. 



Tan. ; Arc. | Tan. 



398.099 
:e98.^4 
:t98.869 
398.504 
398.689 
398.774 
398.909 
399.045 
399.180 
399.315 



660. 
uvv. 
670. 
670. 
H70. 
670. 
671. 
671. 
671. 
671. 

673 
673 
673 
678 

«rs 

6^3 
673 
674 
674 
674 



444 399. 

73^399. 

000 3»». 

37H399. 

556 399. 

838.800. 

111,300 

3t»!300. 

667!800. 

944 300. 

333 300. 
500 800. 



571.439 
571.667 
571.905 
5?i.l4:J 
573.381 
573.619 
673.857 
573.095 
578.333 
573.571 



360. U86 
361 005 
;3UI.138 
',361.341 
'361.359 
361 .478 
361 596 
361.714 
361.833 
361.951 



450 578. 

585.574. 

7301574 

855;574 

991574 

1361575. 

v'6l'!575 

396 575 



531 

AAA 



810 
048 
386 
534 
763 
000 
33S 
476 



500 (KX) 
500.308 
500.417 
600.635 

500 888 
501.043 

501 350 
501.458 
501.667 
501.875 



3:31. :M7 
38 J. 063 
333.157 
333.363 
333.368 
383.478 
333 578 
333. (S83 
333 788 
333.893 



Arc. 



10« Oiirre. 40«> 



Tan Arc. i M. 



363. 
363. 
363. 
363 
363 
363 

363 



575 
575 



714 363 



778 
066 
833 
611 
889 
167 
444 



801576. 
987 576 



.073 

307 

843 

.477 

.613 

747 

883 

733 803.018 



301. 

801. 

801 

301. 

801 

301 

301, 



8S2.455 675 

86i.6l3675 

353 

8V3 



7701675 
938 675 



h53 086 676 
853.343'676 
363.401:676 
353.559 676 
a'a. 7161677 
358.874:677 



854.031677 
854.18fl;678 
854.847078 
854.504 678 
854.663 678 
854.834 679 
854. 987679 
855.144 679 
855.80.2 OHO 
865.460,680 



.000 803. 

.3781303. 

..'>56!«I3. 

.8:«'803. 

.111J303 

,3891303 

.667'303 

.944:303. 

.3331303. 

500 803. 

778 303 
056 303. 
333; 308. 
61l!30:i. 
H8«:3IU 
167i:W4. 
444 304 
73-J3n*. 
000 801. 
37H:W4. 



15:3 
388 
433 
558 
693 
838 
964 
099 
33.4 
369 

504 

(m 

774 
910 581 
045 '581 
184 583 
33:3:583 
458 '588 
59:3 583 



576. 

576 

577. 

577. 

577 

577. 

578. 

578. 

578. 

578. 

579, 

579. 

579. 

579 

580. 

580. 

580, 

580 

580. 
581. 
581. 



^3?) 



/ 



855.617 680.5.56:304 
865.775 680.833:301 
856.963 681.1 11 1:3a5 
866.090 681.380 3«tt 
866.848 681.667 305 
866.406 681.944 305 
866 563 688. 3-i3 305 
856.731 683.500 305 
980.878 683. 77»Sm 
$07,086 688.056 im. 



.8(54 
.909 



583 



95« 

190 
439 
667 
90') 
143 
381 
610 
857 
095 
333 

571 
810 
048 
386 
534 
763 
000 
338 
476 
714 

953 
190 
439 
667 
905 
143 
381 
619 
857 
095 



363 

363 
36:3 
:.^3 
363 
363 
363 
363 
364 
364 
364 

364 
364 
364 
364 
-•64 
365 
365 
365 
365 
365 

365 
365 
365 
365 
366 
366 
366 
366 
366 
366. 



583. 
588. 



333 
571 

.131 58:3. HIO 
04H 
38»J 
534 
763 
000 
338 

080/585.476 



Mm 

.404 
.53H 
.r)75 
PWy. 
94rAl 



5H4. 
5S4. 
584. 

:m. 

5R5. 



060 602. 
187 503. 
806 503. 
434 503. 
543 503. 
660 503. 
779 503. 
897 503. 
015 503. 
183 50:3. 

i 

353 '504. 
3;0'5O4, 
, 488:504 
6071504, 
7351505, 
,843 505, 



.444.444 
444.630 
444.815 
445.000 
445.185 
445.370 
445.556 
445.741 
445.936 
446.111 



308-80«> 4W 
30t 901 400. 
30t 995 400. 
3Ul .090 400. 
aot.185 400. 

379400. 

874 '401 . 

469 401. 

563 401. 



S0£ 
309 
309 
309 



08:3 233. 
293 333. 



309.658:401 



000 
16^ i 
833 
500 
667 
83:3 
000 
167 
:33:3 
500 



961 
080 
198 
316 

434 
553 

on 

789 
906 
036 
144 
263 
881 
499 



505 
505 
505 
506 

506. 
506. 
506. 
506. 
507. 
507. 
507. 
607. 
507. 
508. 



500 
708 
917 
135 
333 
543 
750 
958 

167 
375 
583 
793 
000 
308 
417 
635 
833 
043 

250 

458 

667 

875 

083 

293 

500 

708 

91 

135 



366 
366 
367 
«)7 
367 
267 
367 
367 
367 
307 



.617 606.333 
.735 508.543 
,854)508.750 
973 508 958 
,090 509.167 
213 509.375 
3S4'509.583 
452'509.798 
570 510.000 
689 510.206 

I 
807 510.417 
935 510.635 837 



383. 

28:3. 

333. 

333 

3:33. 

3:33. 

333. 

383, 

334 

334. 

334. 

3:34, 

334, 

334 

384. 

384. 

334. 

384. 

385. 

385 

335 

335 

335 

335 

335 

335 

335 

336 



999 446. 
104,446. 
309 446. 
314 446. 
419 447, 
5341447, 
630!447 
735I447, 
840 447, 



945 

050 
155 
360 
866 
471 
576 
681 
786 
891 
996 

103 

207 

313 

417 

533 

627 

Tf 

838 

948 

048 



386.158 
336.358 
336.863 



386 
336 
386 
386 



.469 
574 
683 
790 



336.896 
337.001 
887.106 



287 



7 044 510.8;i3 



.168 
.280 
.398 
.517 
.035 



511.043 
511.3.W 
511.45<i 
511.667 



447. 

448. 
448. 
448. 
448. 
448. 
449. 
449. 
449. 
449. 
449. 

450. 
450. 
450. 
450. 
450. 
450. 
451 . 
451. 
451. 
4.51 



296 209. 

481 309. 

6671309. 

8531310. 

0371310. 

333|210. 

407|310. 

593!310 

778i3l0, 

903 310. 



753 401 
847.101 



O 

1 
«> 

4 
5 

i« 
i 

8 

9 



667 10 



943 
036 
131 



403 
403 
403 



838 
000 
167 



11 
12 
18 
14 



236 403.500 15 



33(« 
415 
510 
604 



118 
333 
519 
704 
8^9 
074 
259 
444 
630 
815 

000 
185 
870 
556 
741 
936 
111 
396 
481 
667 



211 

316 
337.431 

•.'37 53<5 454.250 
337.63' 



451.858 
453.087 
45;? 232 
453.407 
453.593 
453.778 
453.968 
453.148 
453.383 
453.519 

453.704 

453. S"^* 

074 



454 



210, 

310 

310. 

310 

311 

311. 

311 

311 

311, 

311, 

811. 
311. 
311. 
311. 
212. 
312. 
312. 
312. 
212. 
312. 



403 
403. 
403. 
403. 



699 403, 
794:403. 
888 403. 



983 
078 
173 
367 
363 



408 
404 
404 
404 
404 



456 404 
551 404 



646 
740 
835 
930 
034 
119 
214 
808 
403 
498 



212.592 
212.687 
312.783 
218.876 
312.971 



405. 

405, 

405, 

405, 

405, 

405, 

406, 

406, 

406 

406. 



667 
833 
000 
167 

a33 
500 
667 
833 
000 
167 
838 
500 
667 
883 

000 
167 
:333 32 



16 
17 
18 
10 

20 
21 
22 
23 
24 
26 
26 
27 
28 
20 

30 
31 



500 
66: 
833 
000 
167 
333 
500 



406.667 
406 8:33 
407.000 
407.1671 
407.388 



213.068 407.5001 
213.106 407.667! 
318.361407.833: 47 
313.855 408.000' 48 
313.460 408.167, 49 



.545 



408.000 
408.167 

408. a33! 



813 

13.639 408.500 
313.734 408.667 
313.839 408.883 
813 938 409.000 



33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 
46 



r»o 

51 
52 
63 
54 
R5r> 



.- ♦.'■>4.444 -.- .- 

37 73:|4.M.(aO'314.01H 409.tHt , 

UO.T 5n .«75V»'r ,^vi\\^r^ .v>K«N\i\\ ■^»^\^\^^^;;^ 
87i\5ia .ms^^ .\w\^ .^K^Vi-v^ ,^»^j^_^:^ 



TASLB Xir.— -ACTDAL 



H. 


1' Oorre. 


S" Cnrve. 


3° Cnrve. 


..c„.,.[..c„,.. 


^"° 


Are. 


Tun, 1 Are. 


Taa. 


Arc. 


Tan. 


Arc. 1 Tan. 


m^ 


»«-«> 


iWm 


on.uaoso.oo7i4.Mi 


iseO; 


S3p,8,^ 


M5.0«:4g.571 


1 


1048.1; 


4 01 


87 


ori.oi 


«O0.88 714.485 


1867.*J 


savsm 




ai.aaa 








» 








1367. 7W 




oas!83J4i!8!9ei 


ao.aei 




ai45!i( 










715. loe 


1388.89 




U%.%4-J9.15a 


s^.ooo 




3]«.04 


tot 






sossis 


715,4*0 


1388,811 


536;8I( 


lOiB.BT 4i».a80 


Bfl.SSS 


s 


ai4fl.w 


4tt 




OS.K 




715.788 


IS69.4. 


53B.8M 


ioa7.08!4iB.,w8 


881 .(ki7 




!)14T.83 










nfl.061 




M7.087 


I037,au|4a9.si7 


iH.UOO 




iI4a.MI 




tr, 






713.381 




S37.aS3 


10«7.M|430.907 






i\i9.fti 






1011 ! OS 






i37i:ii 


M7.;,Bl 


10^.831 430. (MS 


««^n37 





(150,77 


41 li 


m 


10 5.4i 


au57!(w 


l\t:m^^.m 61 




1 "-.■». 75. 430. aw 






Ji.ii .ii 




87 








Ha,s3a 


11 


3133.69 


fill 




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l:U 


HI 
















l.l7a:*'30«2M;71S,fiW|l.l.^isi 




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lla 




lO^B.re ■Jii>w..i3iTi» a-«|i3.Tj.5i 


.Mil m: 


I'lai.tlT 411.6*1 


ss.asa 










iuTo.aaii(Mi.i;ir]BM7|iS7ti.ii 








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1O70.7 


aUCi.a)l719.8.W 1376.87 


58!l"n3B 








le 


^iwia* 


11 Bl 


B- 


IOSU-18 


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liW.lli; 1377,16! 


510,174 


luaiiiii; 


I3i!. 188 


81M.838 


ao 




4183 3! 


lOBO.ffi 


>»efl.07 


a0.4HS1877.JS 








H-».687 


81 








a»7.rio 


Tai.airiiaia 33 








M;r,O00 


as 


■iita'.i: 


4196 s: 




^068 .3-1 


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jr.B3B 






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B0UB.17 


■SI.447ia7U.44 












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488^834 


H:!S,333 






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Miiei^i 




483 5if8 


8-J8.1187 




«Br,» 






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aoTa.w 


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ijwi:b7 


1412.01* 


lowiifl 


4-^.711 






















1086 B7 












« 






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laailTO 


ui.m 


1087.08 


tM.m 




so 


a 70.71 


4160 


01 


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l4S>J.a8 


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aii'.»i 




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aiTKifll 










4S4!a« 


B30,M7 




■073,81 




01 




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Maism 


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m.BSf 


SI .9X1 




8174.57 




87 


l"87.ai 




jiM.Bsa 


1S8S.58 


i4a.74» 


I08».I7 


435.04R 






a7a,Bi 




3» 


1087.81 


aoTiiai 


?,lfi.lM8 


isss.n 




1030.38 




S8l!6»T 








01 




^■W.Ol) 












ted.oiM 


■" '^^■*' 






ims.78 


■iU80.83 


7m:8» 


S8 7f 


*44'4a5 




£'£ 


8-1:1,11*5 

B. m 










39 -B86 


fla DO 




i08 M|i6ai» 










mm 




aiBoao 














30 B4 


8$ 


4 


S181 JB 


88 13 




m 


486 88. 


^» m 






-ODO 






S3 1X» 










ha 333 


44 




sa 


09- 43 98 


83 M 




8BIM 


00 


OBS 48- 


sasoflO 




faoa 




093 48-841 






•am K 


•g S3 


OB- B3 


ts- W 


4X 


SliT BS 


» 00 






840 0X1 




saw 


tr 


m 1 


1 


838 38. 






sa^ 


oS'^'w -^ °4S 


» 


38» 


" 


B0H8 






iBool IS irMjroail 
» iaeB3-3M 






rel8. M 1 






)H 869 RSX ODD 




ow BBSSsa 


W »1|83S M- 1 


M ss M4|8»9 000 1 






















«a^ 


»»w 



TABLR XtT, — ACTDAL TANOKMTa, ETC. 



*0 DBll' 
KM 366 



J3C MJ 

>i8i-s'«fl sue 
•sattm-ys III 
^ egy-iH SUB 

4Mm; 



4^ , 



iifl ISO 
aisaiH 

■ns 849 



%l 500 

3U mo 






TABJ.B XI¥,— ACTUAL TANOENT8, KIO. 





4»° 1" Cucve. 


»" c 


«™. 1 3= C„rve. 1 ,. C.r... 1 5- Curv^ 




M. Tao. Arc. 


T^n" 


"a .■ 1 .1. ■.■ ■; . M.- Tflii," 


Am. 




O jai99.38 4liUO.u6 


iu9977: 


.■!.. :. ■ . ..KiMd'Oii 


Bjo:ooo 




i^tsKMmi.er 




-■11..^ ■ . . ■ ■ i.'.itiJ.aoii 


S40.iE« 




^ KOi.MIMS.S 


nm'\l 




810.867 
N4I.000 








Wi.SM 




i! 


':7s:!ii 


Ml. OK 

Bu.ooa 






■'-■Ihl.mb 


B«l.3Sa 










B4S.S8; 








(4i.:Ba 


843.000 




io'^.J,ad.B7n«.M 


.10«.8C 




ui an 


MS San 




11 ;a»».e3 42ia.«3iiwi.oo 


sioa.ir 








IS WMljtiO.MllMIl 


2110-00 


73T:o«W0a:8TiMeSi!lD5r,:lx 


mliifSum 






aiiDM 




















'■.;-''..■. .-.(.1- -.1- 111-. i-MU-J MSSJMS.OOO 




]i^ 


. ■ ■ ■■ "■■;■'"'' l™'**"**^ 




z ' ; ■■ 


■ " ' jig 


M.m 




sii " ■ ', 


... 'HIAK 


Is 




;;;?'- ■;;■:, 




4.H.BW 


MB.OOO 
B<S.33S 




V: ■ . '.'"'.. 


■ ■ ■ , ; , ■:■;: |:^; I'^i ^i 


4M?8fl 


SIS. CUT 
WB.OOO 




^u : ; : , ' : 


■ v!.l«?iMi;uV 


H.vsre 


t4».m 
S49,ee7 

(50.000 












;!■! -; ■'■''.. ... 


. ' ■■ ■■■'llul" 


turtjoo 






. ■' ;.'|Mb"m! 


851, SBS 








«i,e«7 
















t^ia-ts 












3« ^.^'A^i ■■ . 


,. .". ■!. . . .■:! iii Wl 


03.000 




JoWt:',.,'. .. -. 


..; iiT.sso 


SS3.S33 




n :^i ^r i-!'^ ; , 


:■ ■ ' ■" ';^ii^ 


its 

MS 


853,687 

RM,ocia 

864.887 




:!;";■,,,; 


_ „ ,', ,,; ,. ;, ,„,. [;'X 


m 


BGs.oao 








m 


HES.tWT 








^iji .in 








BM.DQO 




4a,K4B..kl|jil.li7lll«S,W 


■ai0.iar46:s:a\ite7.ei 


Ml,™ 


im.-a 


148 


416 


BM.iaa 




r,''^^^vdi^'Sij^;' 








HB,OflS 


ssg.aoT 








bea'.ivf 




ua wo 


BST-OOO 






;iw:3^t4b:hioi^,si 


562,431 


1071,97 


*Jfl995 


SS7.8S5 








saaoa 


1072.01 


♦SO.IHI 


SS7.6fl7 














BD8.00D 












i!->o sfNSsii.aaa 1 










1073!33 


4.^ 763 SSfl Sa7 


A 




'. .-.1 1S5 1«1> 


Ma,atri\\a:;a.-n,',«a aaslsse oon 1 




n-- ^ ;-.i.7iijii3i.*a\n6a,«w\ii!f;A.\-;\«.\,u\\««»ft\ 










-W iK-rvlWiT 








.as 


BW».W, 



TABLE TIV.— ACTnaL TANGKNTS, BTC. 




—ACTUAI. TANOENTB, I 



c 


' 


2 C 


.. 


Tbd 

3M4 
tX5 Oj 


1093 

■isoaoo 

f°f 

mi- 

» 01 




AT 

^JToo 

■>B83 
M 



iJ MIT-" 

4 ei»[ w. a 



B 0-1 «8i 6 

<r8 0~4s 



« as B 888 B7T or 

fl 'B77« 
96 ,STS(H 

=4 lnTa on. 
» wa san CT w \ 




p:L:t|:|:1:3f:|:J:j: 



4. 



TABLE XIT.— ACTUAL TAMaBMTS, B 



c 














^ 






iT 




izr 












6.iaaiooo7~i730 


^M~ 




~~ 00 saoloo 


a » 


440 


£100 as 778 MS 






33 H80 333 


a 8: 


408 31 


as 41 


£20 TTBaSO 


18- -8 




UO 03 8801* 








aat 3D7»a85 


«g 




25 88 OUO 








aoiss'ya 009 








1409 33 


8" 


.2W 831 


69 44 581 OS. 


08 64 J4 


88 m 




00 






00 580 va 


aiso uiea 


mm 




41 e- 




_J0 83~3 98 


56 580 510 


4)11484 


tarn 








006 908 




5S0-H1 


03 33 4e4 




68 


14 n 


8- 


iWMI OSJ 


07 


58 OS 


03 48487 


tssooo 


B3 










58 


*46|^ 


888 333 










^Si 








<83«6 






ess 














a. 5( 


44a 


w 


^ 33 


83- 




58J00' 


05 4tt. BB; 


(84 33S 


iaasK 


44ssaa. 




33 






12S1J 


W 6S 48884 04- 




44% DO 










la. yt 


00 6e<)43B&.oao 




warn 






906 






46« » 


885 883 


M3 


44S!8» 






r- 




5B- 




885 667 


2832 






iJ 01 






598 JW 


50 43 


(86 000 


3333 34 


443 












w 




2334 18 


1433 31 


JO 




7-8 86 




583 


^33! x« 


S86 66- 










~8 


33 


j8J 


00 ao 


88 000 


» 








~8 835 


~9 8» 






40 3H 


<8~331 










ra do 










(87 66- 




44< 


MOO 


7-9 186 


* 01 


wioa 




fl7 7S! 


188 000 






^ ~990U 


*0 5fl 


384 




4B7BB0 


888 338 






-BO 


le 




83 


4S3 


888 667 








J^ SO W15 








4«8 -0 


889 000 








Jf -80-83 


48 






68 SIB 


888 3S8 


0. 


^ 


Stf 




-8 08 


48!. 


B35 88 


08 


468 7(H) 


889 367 


OR 


u. 






■8 433 


S3 33 


583 «8 




438 956 


800 000 






5b 


88 




^3 89 






436 


(90 333 




33 




XT 


-saoa. 


481 4< 


iS« 


33 


OS 844 


<90S6 










THiO- 


485 00 


■iBHSSS 


T 


460 589 


S9 000 






iS 33 


-«3 ras 


485 OS 


SB- m 




430-34 


89 333 








-B3 05e 


4S6 




58 


468tt39 


(9 667 




d9 -ii oo 


-B3 3S 


480 8- 


e- jsfl 


01 


-0 ^ 


i9«000 






7S3-08 


48 M 


|8-83S 






(BS333 








48- -8 






~0 


wes 


1 


-3-50 


S4*>5 




■88 &. 






moot 




' ^33 


34 eeo 


48. sa 


=88 503 






893 333 










■9B 


193 067 








488 


194 8.33 








08. 
B-B 


SZ 










895 DSS 








9G 


193 06 










196 000 




13 


40 W) 








-S05 




^» 


44* 


18 L TT^ 


M44 


590 99 


£0 83 


85 896 6. 


zau 


83 00 


80SSI4 S0J88B5, 


95 00 


^ 




01 arm 




«»■ 


-B 




"Sm 













TABUt XIT.— ACTUAI. TiUiasKTB, BKI. 



0° Com 1 7 Cnrvfl 


«Cu„e 


ac.»ve. 


lO' Curve. 


M. 






*"- T«, ] Are. 

7saaMS»0 9»8a(STi 


!«. 1 a™ 


9^^78 


J^ 


I'lUL 


Arc 




(68 W 


nOM 


«0«0 








■aSBl M 044 




m itJXOXB 


» £81 


489 0-4 


981-88) 


440 








BSeisii 


■TfS 88* !til ITS 


ll9S0t8 


USB 88- 






489 a» 


«i.»n 


MO 


88! 


» 




ue.4Ta 


~S4 ir aa as 








lOTTM 


489 444 




44( 








a86.SB8 


-34 444iBI« 


IWM 






BB 908 


189 SW 






k; 






3«a.Ba 


TIM TtiK 99 


BSSTM 


2110 908 




neon 


10) BIS 


884.870 


44( 


sa 






38S.9Sa 






jiioa.M 




HS81M 


laaoa 


989.807 










187. las 


559-888 8- 


Ego 938 


iaout 








»1.4SI 










3w.aae 


TSBSS6 531iO< 


^*0 


taOKS 




OSSM 


190 t» 






SS! 






887. «0 


T3S(W»3J -.iWi ■« 00 






uotu 












187.018 


TSI 




BBS US 


no Tit 






OOT 






887.771 




nsea; 


4B0W 


889:881 


443 


881 










U8TT( 




B89.1B1 




oa 








-H i m 




tBI 99) 


ts.oei 


Mi 








wa.aei 


















ws.ni 






ImS- 


aaiiHi 


44i 










7B7TW 




11 S43 


USS33 




401 SU 


388.848 


Mt 




IS 






nsw 




m on 


U8MI1 






18.481 


449 










mm 




NiTa 


eea-m 




Me OK 




(48 








38S:0K 


tnni 




«>01 


taasB 




MI MR 




4(8 








1189. S«-l 


7Wt<W 




« n*t 


^^4 lar 








(48 








3M.XW u MUB 








448 








WLIiSi .W! 


aasHT 


Wise) 




H8B0I 






SB*. 714 




maxa 






443 888 


83 








no OK 






444 901 


>4 




NO use 
















sw.aw 


40 ~i 1 ^ .i.^i1~ 




»I1T» 




444 311 


»e 




.100 384 






408 880 




444 000 


87 










(MD74 


MOOT 


(44 097 


as 




390:689 


4 ast SM mlm m\aK w ua on 


maeoB 


«4» 


nooe 


444 813 


as 




nosfii 






(U444 


984 "0! 


446 000 


so 




191.014 






1*1 two 


44S1B1 


31 




SB. IT. 










tn.331 


* !1 ' 




33 








44. UflT 






wrw 


48 ■ 








nt.sH 


«■» ■>■ 


448 000 






Mi.oa 




ua 16? 










M»4ft( 


440 888 


S8 






744 iriasfl au 887 « Ism «M B88 man m «e iii 


»M» 


110 000 


TO 




ire 475 


744 4(4 sat 46t MS OK 9M 4B0 KB m »1 IT tK SK 


wen 


HO 087 


«l> 




jir fiK n't M m iss ■(14 wefiw 54a]J0 »«,m 4R 


iJ5 7-S 


440 888 






WAV fl-lim-n-^JiU mjl 


«« Pt-1 


44 m 


49 








43 


















144 MT 


4B 
48 










JJ.I .11 


UJ >08 


«^"^«^« 


i»0 66S 


148 ..T 


«t 








WS80 4ni48 


180 tS 


j48^ 


M 




W4 S 




960 989 498 asa 










W 44 




9fiS0ff-4W^l) 










3M -itr 








4)« *W 






3M 4t 


?flSP1W 4 1* 




»4 9ia 


TJSfl U 'K .1 




WlO-1 


4H Sxn « M '^*-^ 


»S J^ 


3W «M 44 44.f i RH (VI 1BK U 


1 Mseil 49 aim o~64 m 









TABLE XIT.— AOTUAI. TAHOBNTS, STC. 



4&° 


I» Curve. 




».„.,„. 


4.C 


,.„.. 


5.car,e. 


mT 


Tan, 


Aro. 


Tsa, 


a™. 


Tm,~ 


a™. 


Tan. 1 Arc. 


Tm. 


Ara. 






UW.OO 


1188.88 


^Oo 




16O0« 


™:48fi 


IIC5.00 












4501. 67 




2JM.83 






^a^.Ki 


II»,«I 


174 i 980 


800.833 




<sn 


!1 


4S(i3.aa 




siM.er 


7Bl!8» 






11«S.83 








M7B 


^ 


4sas.ua 


UBSilB 


il^.W 


7M.1M 


iboi.b: 


Bwiin 


iiffl.sas 


tn.m 


BOKOOO 




an 


3! 


4S06.a7 


1188.86 


A!&3.8; 


7Bg.4!W 




5B4.4fflJ 


11«,87 


4T5.fiW 


901.883 










jise.is 




71B.817 




5H.EB: 


111(7.08 


47S 780 5101.687 




i!3?1 


It 


4Sio:iio 


llHIt.BS 










11:^.50 


475.981 H«. DUO 




2880 




4811. BT 




ffl5G!88 


rBs'4S8'1603.89 


505! 15 




478.178 903.338 




■iBSi 




451,183 




W6fl.S7 


W.TIII 1S04.4^ 


5M.S117 


Ilii8:» 


470.871 mia.BOT 




mi 






1191 !0B 


jssr.so 




iKMl 


11^.75 


47B. 568 903. 000 




388) 


(B 


WIB.87 


,.■...58 


eiSB.33 


Z''!^'ZZ 


5B5.884 


11=9.17 


476.781 908 33S 








4518 88 


\IKM 


a»ni7 


T91.7«5;lr«J.il 




11^..^8 


470 9.^903 881 




eAS: 




4s«].oa 




HBO. 00 


T9S.090 1,W6 87 




UBU.O0477.151flO4 0OU 1 




















LlS0 4a'477, 316 1104,833 




i»Xf 


9: 


^'.% 


im.bi 


afiiiai 






nuoiSM 


llS0.n8|477. 540804. 087 1 




asK 




151H.W 






71l8:0in 


lM8:is 


587.10-^ 
















i»Ba'8i 


7S6.38B 


IIMI8.8B 


»>7.»IB 




477.930 908.839 




i3!H 


a 


4G»):a8 






7»«.TI3 


1509 .4t 


507.581 


11*J08 


(78.125 905. em 




^90 


8? 


1530.00 






rB7,asg 






im.t. 


478.330 908.000 




W1 




1581. a: 


nti.vs 


OM'.ai 


7W.8W 


lUOM 


KM 








^303 




1683 38 










WS33 


1133.83 


478. 781 ' 008. 887 


ai 


aa 


B! 


4JWB.00 








47S.916 90T.000 




nam 


aa 


4S8e.B? 




113411T 


479.111907.338 




■OK 


» 


4588.83 


ii«7:oi :■■ . ■ -■■.»m 


1184.58 


479,305 907.687 








iUU.OO 


I1H8 4:1 ,-■. ■ i ■ v«i s-n 


1185. oa 


479.500 908 000 


as 


aa; 




4541. BT 






479 B9590S.338 


u 


ex 


n 


4MS.3I 


ilM.iuii-Ja ^.' ijj.i;,-^.i:!i4 Jii.iilU^TW 


ivn'.aa 


479.690,908.687 






u 




uBg.sewT^iwTHu.iiau 




I!0U.U!IU 


1188. «5 


480,0W 909.000 


as 






iHi,K 


1WI1.S8 8*78.88 900,31)1 


IB16 M 


(foo.as 


I18U.87 


480. S80, 909.383 


m 


mi 


» 




ia».B8 £174.17 seo.sia 




wo, KB 


1187.08 




M 


aiOB 


Bl 


4S50.00 


iafll.3-}«T.V()0BO0.»l 


1518,87 


600,770 


tisr.so 


480 «ro'9io,ooo 






B4 






151 T.W 


iOI.WI 




<K0.870|910,3W 


at 


M04M'4i,'.'' ■ -->! iSai 


IM- 7X 




1138.88 




sa 


j«u 


888 




3H.7t 


181.968 91 lioOO 


a* 




889 


la -58 




4fll,481|Bll,*a 


as 




44 


eoaou 


80!5B 


<81 «5l'911.687 


36 




B«aa 


BO- ue 


40.00 




31 






saou 


HCtt4«l 


40.41! 




38 


M M 


5G8 






aoi-8» 


40.83 


«3i40,Bia 887 


39 


« 


4505 00 


«mi3«aMeKMBM 




8(»983 


■** 


48i,44.^91S.«« 


40 




4668 87 


»M 38 ^289 38 904 »! 


sazH 


K»»tt 


.87 










W — J34 rt04 M4 




80 "B 


4d.0S 


48:1: 838' bis! 887 


4a 












50 


483,031,914.000 


43 




oa; 


.« 


488.S«'»t4,88a 


44 










4S 


!4 


w. 


875 


483:810 fll5;3«1 




; i. 






184.011815.687 


48 




9- 






4» 


^ w 










Iw:««,Sl!I"^ 


Mt 


Mmr 




5a- 7B 


805 884 




4H4.H01 910 887 




■Ma»i 






mm 




484 798 017-000 


BS 


tmti 








48 87 


481.001017.839 






6W44 






(85.lSaB17.887 






680 01 






485.888 B18.O0O 




J *~ « 




8089 




485,487.818.8*) 


4»<7,- 




807 80 


48:3} 


488.789 818.887 


a!A» 




80- 08 


48.75 




t*/llJl 


58x&\un u 




s/ai. 














SUTf 


\wnMi 


M.N 


S,fflB,»fiWi.W(\ 



•TABLB XIV.— ACTDAI. lASOXXm, BTO. 



8* Cmre. 


T Cur... 


8° Curre. 3° Curve. 


10. €=„„«. 


M 




3«"^ 


a™ 


mhi 


Arc 


Taa 


Arc 1 Ta 1 arc 


T*n 


Arc 




fiouou 




ifflffi" 


waV: 


Ml 501 aU 964 500 000 


sr na 








SBi stw 


■wrB 








MS OSaMO^MO B9 




SO 6 1 




SM 04S 


IX KM 






17 4 










Mil 


50H38 


ism 




iS- 'B 












mm 




m& 




a»-8w 










SHIMS 


"3 SHU 


'un i» tw d H 




50 8S3 






B» IX 


eu 


MooeuM J86 










MS8-U 


B w 


40.^044 AL 










BBTOK 


-68 a. 


10 3IBB44 a. 














jesou ^ G cuo 






807 85 


-W 8 


14064 L ^ 


J9S J3 «4^1,aO^ 


M 3&i 


.i38iioe 


45 K 


10 




jfr oao 


-S*(W 




IB 664-*.^ Bi 


waoB- 


tss-TT 


45 BIS 






3ft- HB 






■98 at 506 -00 


assn 


N)a2& 


1ISSBD4 


4SSD00 








■* n 




JW Bil rOS SOS 






J38HKI SS ir 








-ilKW 






JUS ^ 


JOj 48 


HNfiBa 




4S3BS3 






JUS -0 


TH H- 




G40 il 


aw 3150 sa 


ai5M6 




EBBW 


4 MO 






must. 










i»5 1): 


fm 


938 U 


468 68- 












A6 ft 




MS B 






















JO. Ikn 


503 H3. 










^eu 


-5i2B 


U DM 


64 38 


^'^l'^^^ 


118 03 




«e BO 


458 6 








-SjfiSB 


14 01 






^333 






tan at 








^SK 5U0 






SW36 








iM U 






ma -B 


rwBtw 


t 8. 




« Bim 












M W ^100 














3/ D8B 


^asi 


a" 












W 4.3 


oh 8J» 


»» 












W ta 








400 gu 








W ! 
















UI 43* 








40 MC 








« 76. 


00 8 44 & ea lu ^ 


W S6 


w ^ 






401 »■ 


00 B.%11 M Ju,6o MCrA. 540 ,.1^ Ml 


aj OJ 










ISO B3^ 144 viSit IS 301 (rBja «a\ies a 


soras 


91 4fi.4SB»0 


30 




401 3&>l 


■» W8W13SB w son-nf»lw«SK 


W*r 


i4 KSJ }S 08 


40 














.,. 


40 




a iw ' MBas 






W(15 WWM 








» 




* 






^ 


* 























TABLE TOT.—UrTUAh TANOENTfl, BTC. 



r> 






-" i 


6S33 






































«S« 






mm 































se%9 5 

008 BOBS 5 

83 8 T niB e 

t3 B 6~ 8 T S4 5 



1 9 £333 AO.Sa 5«| SSS 00 e "M 



M B~19 



/ ss /jMg' seuaB. sn 



■3 S3*) i H B -i 66. * 
-33 D 830 «-i 5flB 



TABLE XTV. — ACTUAL TAlJai!ST9,ETe. 





Car* 


« 


8 € 


"• 




« 




u e 


M 


^ 


™ 


U Mtl 


i^ 


^ 




1^ 


T^ 


irT 




"ToooposSJii 




i«¥ 




4(»e99 




34 -HI 


ST 


sfl nn r 


s-^^o«■nlBSB 


"sa 








405 SSO' 


■W3M 


3 B3I 




aB'*n wf 


5 4 «-or^B 


48 


Ssm 


460 3a 




409 033 


•87 500 


W8 0-B 








M 


4sa I 






40e 8B 


-a r» 
















4 


*MS5S 












ir 








«»fi « 


-08 333 










J- 


v4 






409 osa 


-eee 


S48 04 










^4 me, 






400 844 


-6SS89 












Q44 308 








■M B 






778 


403 


6 501 





07 BO 










D& 








W 




» 


i- -1 1 




44 no 














3 3.); 














00 


SZ9I 




24 09 b. e 




40- S^ 








/- oshs 




WW i. 




U7 99 


-osaas iki« 






"-S 4fl5 




U4 M e ,« 




08 58 


-1 uu eud,iAi u>j 




333 


£-l£Ma 


4 D? 






tm s«y 


71 389 SSa (MS SB 




WCSK 


8 w r" Mflla 








oa4SH 


60 380 8SM 


m 




T- 508-2 4- 




MSSO 6 OOr 




40BSM 


-^ «4 BM SM M 




aoBBW 


^MSir^Ws 




asoo a 




nn 




ioa -1 


-n U09I 














»3-Mra9oi- 










30CS6S 








* 




s2 


-0 11- a-stt. 
5Sooooi-B 3 
so w*^ 


















401 BW 


*< 


bn 




SI % 




2« 


4 DSB3 




I .c 


■0 




" 


^ 


-no 














^ 


^£ 


K-ME 






1 




"7 




& tm 




1 


«a ^flb 






-7 600 


o U 




r ^ 


TO W «« 




41 OS 


^^ 


»! »^l«, 




1 .ml 


1 r ^ 





























90 5* jS 



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 








00 IK) ijit j£M ou tui 58- lase tr 




11 noo 


J9B 414 WO 000 












ll"S4- 


408 01^ B4D SU 








ua wi IB JS^si B 


m iM iM ; 


W3 44! 


11-B83 








M34 «U 


t-wiooi^i um e> 






11 8iS 


m 010 941 000 






.^WW 


4-08 a- IJ) UK 


asata 






118 6 


4M SOS 941 333 






-iMr 


-08MH.a» 


JSMl 


i3£ 1 4 1MB * 












S49 *■ 




JIISSIX 


iM hhIig 01 




in SO 








Avar 










11-7 M 


499 807 


WiSas 




8 


AKir 


n 38 l'49 UH 


jssiib: 






11-8 83 


BOO 00 


B4S BO- 






em^ 


ns « lawi 


-J5 M 


t«d BO- Ij 1 B 


bJBlHS 




sooiin 


MS ODD 




1? 


■JO- n 








ilK 


Sffi 


43 aa? 




4TI8 n lus 1 














HX -B8 










Jm 87 iSi ■• n 


nso 4. 


1«>9W 


44 S3S 






■«taii 


-fflSSli. «. B4W 


1180 es 


W139S 








smi\ 


4 ^ 00 ll»3 lA 




«>bfl-» 


1181 » 


001894 


(6 ODD 








-ao8 i£s3 0- 




JU9I6 




WlB8fl 


M-sau 










an 830 14 13 u 1 


G, 18 


iiBdoe 


501 791 


946 au 












(.■-418 


IBiSf 




948 000 




10 


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B3-88. 


1182 GQ 


502 191 


MBSsa 
















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^ 


















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4 IB B 1150 60Ll~) »-i\liiJ Hi 1 5a. ilUQ 8JB 1188 6 




049 833 




39 


.auo lu 


1748 88,1*80 IdLm 4 1 840 iv\,^ "8 630 14 lir 08 


S«I4 


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4,0X BOBOi (111 " «/ iWlB 51 










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40 r^ ). « 




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c 


rv 


8 nrv 


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Cnrr 


K 


an 1 A 


T 


Arc 


1 


T 1 ™ 


1^ ™ 


w'laaaa 






31 Bft 587*00 


"? ofil Biea 


B. 


^uoiw 


■V. 






>H8Mr iw 








tWTO Bfi 






















a06i-W44 








ffsa -84 








aHWSs 








DGIB N5 










flS65t> 








teas 


-as as 














Oft 


-Ba 


85 15 


-5 


gOBSSfl .iSS -8 B4 S4 0~ 








£24 


-88 BSD 


56 B-B 




■UBHI-9- -SIOBi^a 


■^68 






SB 


7B« eer 


a. 631 


SS« 


n 54 uooou nt 


aocs 


ooo 




















"sa 












BKU 




B88 


-BTM 


aS8S4 




000 


.«)o»e 






BOS 


-8 T 


358 Bg 




8S 


ij^ 


-S IW 




USB 




IISB380 




3- 


as 


-SSS3 




4ia«« 


-ue ^ 


»Br 


-s 




^ £» 


000 




IBBfil 


-888 


a&x 






t5 % 


-3 0- 


IB 


18 -to 


188 B8! 




■Jr 




-8 318 


ao 


BM 


89 1 








SIM 




« 044 


1™ 




X 


-SB 


-aaas 


Ha 


• ro 










ooo 


«* 












3S 


B- 






OL ^ 












339 


BO 




OS 


83 


81503 IKIMOir 




ffij 


500 








-M 09 


so 01333^ BI 


r 


36. «■ 


flS- 








jou^MB^sas 


SOGJ !» £80 «» 


Sr 398 


JNSA 


88^ 


a» 


(JOT-" 


M 


M 




>Mf 






-Bono 


3« 


a) MS 










-B B- 




4aiTir 








-5 888 




UflH- 


K GOU 






600 






-») 






«e 






-ft 










a aae'^ 






8000 




ea "3- 1 
















as-iBW) i-w Kio <Bu 








8a 9J 16 


Ob 


h^\^ «*«.« 


as». 


500 


JU 


m ' 




u ^1 1 ". 


w 


TBfle 






















o 


it 








« jr 






*■ 


-xm>\U 


«M0-««|«*«« 


OBSOB 


3B no- -0B|is« 58 I'M «t4 3sa 


-8 .9 


as mr 


-«- k f 


Utfl 


». r \'^J\ -M4. 


-^BmUo 


sa»« 


fTsnnl'M 




' ' or 




U4 0q 












-98 nv 








mSM 


-BB 
















' ' 



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 

«a 884 4f (K 

-i7 aaa 4ft. Bi, 

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 


«.o 1 laiu . ' 1^ ^ 


B i -C! laj, bU B55 is- 


i-ffli 


3U 400 083 333 






49iHaa 




'4 1^ 1W8 44 




imse 


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 








H ) 130 1041 11 


353 444 


1180 8)1 


[l»»4 884 00- 




tei03- 




\m la 




-5 31411041 3 


miSK. 


mee 


5SG 415 BS! 000 




ioi? r 




imixjB 


433 51 


a S 848 1B4J " 


053 048 








mas 


l»MW 


1SL4 1. 


UU4 I 




1. 191 


MS. OS 


5SG 818 066 str 




^« 








6 51 


1043 83 




1883 60 


!U6 010 883 000 






Oil F 




^m«i 


ms;,! 


1343 BB 


IS mi 


l.!82 0S 


5M I 083 333 


ao 


«31 !8 


4833 18 


15.^ » 


3400 3 






BS 048 


lasasa 


538 418 883 037 




»S3« 


4iia. ou 




43 Ml 




1345 OC 


358 jOO 


1*38 71 


5»sa4i«-ooo 




Jt-SJS. 






l!4l» 13 


r fn 








5SOB3U88- -US 


83 




iV3li33 




4fiJ 1 










5" 0.11 SB- 38 


a* 


awi a. 






U 0* 










bir eii Kte iwu 


«6 


JUSK « 


4011 (T 






J-8 8"l 




150 213 




■i- ^i we 133 


Sfl 


WS 8tt 


4948 33 








101 "S 


3S8 4B 




sa 013 088 037 


»T 


«a.t8 4u 


4046 00 




U 90 




1048 38 


350 IS 


ISSfl s 




88 


M»aa 


4041) (i 


i3iB-a 


A~3 1S3 


a-8 871 


1»BS8 


3BU839 


joaer 


iusog4 8e»iw 


89 


nuun 


4WH3S 


1330 1» 


.474 1 


jsoas 


1340 44 


080 ar 


luroB 










,^•0 . 4 «, 










338 44 Isffi 800 








ja 04 lOoo SH 


38 


WW* 




A IL 9on lur 


33 






34 






SB 


«64tt44 


> '0 4au,99i eii 


36 


!iM7M 


II 1 1 >o »wl«»' m 


S-J 


XiS4 






ts 8.101 Ofta 833 




XUI60 






.>n 0B3.9W 33 


30 


«««5> 


mi W lUS JU J4tli KJgHS tM 






40 


«6IM 


iKs mUia aoli4n:4 la'sai o^ 


13*5 M Bffl 003 1*41 0- 


^30 404 098 333 




«a3 5i 


4!J«h W 1 i '■m 4H4 ) 1 i. 




10 bb. 188 31) 




'WS3!U'1'i II 1 1 11110 


43 


^f! '^ 


44 




4B 




48 




47 




48 










a«0 B>il4««, ^ 


IJJO 3. 4^ ^ 


•Mb HU. lOflO jU OflS ^H.Wj 1 


U:. ~ .080 333 




^.eiosUas 




Bs- 300 1001 11 30.1 34 lau m 


Vte ISs'oM 33* 




SM3BS498S0O 


I^MSo 


^m\mB~m■ys^ ma, 






J663«e4988fi 


ICT 2s's4W * 


m 0-l« „|0l^ 14.11 13 ( 


^ H 14 or- 133 




Jwi as 411S8 ia 


IISS 19^114 I 


BhS 1 ' ^ 




.«SS 1 JSilO ou 


li^fliUlc oo'kk m 


MM"^'^'' 


SW 4( ^i A '■"« 1 


^ 


i ^' 


* B 1 




4^sr 


«w. 










« '^^ 



TABLE XtV.- 



[. TAK0KHT8, ETC. 



s ■« I t 3.W aat 1 



lO C 


„„, 


* 


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 

■ II 40 t«u lu , 

i8 6SU|-w a- Mu 

1^ Hog'aw 5Rb 4§n ! 
a 0" UK a -MO 



TABLE XIT.— ACTDAt TANGBMTH, KTO. 



M 


0. 


» Ca e 




* nrro 


fl Cor ■. 






1 




"t 


re 


- 


Are 








m. »s|.,50u<ii 


Haolw IS fl" 


0" 


JWOO 


^MMS 


000 00 






<»» 


<» ^S8 


a» 0° «« 


ItW ^28 






ouoaa 




JflTlSO 




asbBfLso 






^ 


JSOM 




000 








LfiO- 50 




M8 3. 




Sfi JO 


sa « 


00 00 






eOHS 


ItKJ OH. 




■asiat 






9« 


W 44 


IS 


S& OH 




00 














00- 00 




8»04. 


M 






^^. 98- 


my sa 




sa 3sa 




6-0 088 


3bjss 












s3B« ooaoo 






'* low'' 






6. m«- 


1 jiS 6M MH M 


6 , ' ne uDssa 


sa (44 WW 8" r w 




-.a -a OMOT 


« W 00 MS OH SM 


iS 50 


Sd8 IS 


OOAOO 


a, l» r ^ H A xal-w at a,ir »» 


95 !« 


d8SST( 




1 




sasaso 


ooeo 






aaa-TW 


«roo 






aSBB- 








■SB 93 








<» au4 


1X18 00 






■iS HUD 


■oeaa 






SK sa 


539 WW 






940 


>e 25 


.MO 01 


000 00 


»8 .5 58900 sa «a -s 


6- W 


sm 


Moes 


ooon 


8 ^M ms |5fti7« 




» w 


MO B 


mv 








M0.SO 


00 




HK 


UlOffl 


0* 


67 




OD 




01 ta 




0) 




84 


w 












^ W 


as 














oa 






Kdl SO 


BOailO 688 3- 


fl- wl WWSS 


H.4&> 


01 00 


o 


w ' w, ■« 


B3 


B04M flfWSft 


rsJ^w 


M eao 


m aa 


* 












*" 1 1 


» 




^ n 'aU-n osr 


^1 )« w ma. 


Ns fi« raUwrr Si 


68 .MM WW 


w 


58 1 M -L 




S4 1 ^ 1 01 1 «. 




SB 


























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 
»U) 
.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 
,112 
2.80 
318 

466 

.587 
,7()8;618 
.H2«i 
,941 



611. 
611. 
611. 
611. 
611. 
612. 
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.; 
&58.550. 
964:550.j 
070 550.( 
176,550.. 
288 561. ( 



598 

778 



299 
299 



000 
167 
833 
500 
667 
888 
000 
889;551.167 
333 
500 



495 



601 



963 299. 
148 299. 
833'299. 
.519'300. 
704|300. 
889.800. 
074,300. 
259:300. 



551.; 



551.1 



707 651. 
818 551 . 
919.552, 



444 



.800 



630.300 



025 
182 
2.88 
344 
4.50 
556 
663 



552 
552 
552 
552 
552 
553 
553 



667 
833 
000 
167 
3:38 
500 
667 
833 
000 
167 



,815 300.768 553. 
000 800.8751558. 



56» 



M. 



O 
1 
2 
3 

4 
6 
6 
7 
8 
9 

10 
11 
12 
13 
14 
16 
16 
17 
18 
19 



8.88 20 
500 21 



185:300 
870 801 
801 
.801 



556 

741 

926301 

lll!.801 

2961301 

4811301 



292 387 
:m :3:37 
708 8.87 



78(5 697.917 
918 698.12.5 
051 698.388 
184 098. 542 
816 698.7.51 ■ 
449 608.958 
.581 699,l()7\:iV 
,7lRf)W.a7rA^ 
.R.54 



619. 

619. 
062 619. 
180 619. 
297,619. 
415 620. 
.^•^6 620. 



.6.5'; 






8:37 

>.37 

.8.87. 8!)8 
3:W.011 
3:38. 12(» 
3:38.217 



667.801. 
852!301 . 
037,802. 
222:302. 
407,302. 
5931302. 
778 302. 
96.8!. 802. 
148;302. 
388 302. 

519 302. 
704 .808. 
889i308. 
074!. 80.8, 
259,803. 
414.808, 
6;30:3(X3, 
815 803. 
(H)0.808. 
1851803. 



.981 
.087 
.198 
.299 
.405 
.511 
.617 
.726 

.835 

Wii> 

048 
1.54 
260 
366 
472 
578 
685 
791 

897 
006 
115 
321 
.827 
483 
.589 
645 
7.52 
861 



620.870.803.970 
620.. 556 304.076 



553. 
553. 
554. 
554. 
554. 
554. 
554. 
554. 

.565. 
555. 
5.55. 
555. 
.5.55. 
655. 
556. 
556. 
.V)6, 
.556, 

556, 
556, 
557. 
5.57. 
.557. 
557. 
557. 
.557. 
,V)8. 
558. 



667 
838 
000 
167 
33:3 
600 
667 
833 



22 

23 
24 
26 
26 
27 
28 
29 



000 30 
167| 31 
3.881 32 
5001 33 



667 
8.88 
000 
167 
338 
500 

667 
883 
000 
167 
a83 
500 
667 
888 
0(Ki 
167i 



34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 
46 
47 
48 
49 



620.741 804 182 

620.926 304.288 

621.111 304.. 894. 559. 000; 54 

621 . 296 .804 .MW Wfi» .V?rv\ 'W* 



568.833! 60 
558.500 51 
.558.6671 52 
.558.8.88^ 53 



i^iVW .WWiV .\'ft\ "?«A .WN ^^5i -"JS?!^ '^J?* 




[. TAKOENTS, BTO. 




. OiMKi aauim.a 
.i*s:iai.atmi.Mt\iii».e 
<m.-.«liist.<io 



TABLK XIT.— ACTDAL TAKOENTB, ETC. 





,• curve. ; «~ curve. 


B" Curve. 


10»Cur»8. 


S6° 
-0 


Tan. 


A«, 


Tao 1 Arc Tan. 1 A c 


"ri^ 


Arc 


Tan 1 Arx; 


tmam 


^^ 


Ufi 481 800 UOO 381 IIS DU 000 


t^'m 


M~^ 


STm-ISTooo 


MB ina 




measisousa&jgi mj-oows 


338 931 


S»40" 


80B14S580 1B 




Eiieasa 


sasai 


us 734^800 4 1 


88! 184 TOO 417 


ASS 0-9 




305 joafiOMS 




MB on 


SI Iff- 




581 ^ao-WBa 


389 aoo 




305 358 






BW em 






381 S57 700 83a 


339 3n 




BOB 461 






SOB 8-3 


M 7S! 




s»i-8»™o*e 


389 430 


aai« 




660 831 








136 399W1 tM 


S81 »£|-0] »0 


389 sg 


IS 381 


106 671 


Ml ODD 


6 


maM 


tta5«^ 


436 sH.8ai se 


«t 034-01 4flH 






305-81 


W 167 




501)403 


asBSM 




382 18~ roi 06 








561 3S3 




wasas 


935 8B1 


ssip?s 


383 388-018™ 


889 913 


nsSBii 


weod 


561 600 


8 


SOB 08 


036 III 


ir oiiW 381 


MS4BUl-0*0SS 






806 la 


Ml 60; 






■wa sus) 


IS 1(14 8kU 619 


38^59' iULJK 




Mai 










iKia Ml 


a Hiu soa a& 


3K -TiS 


0^500 


340 8-0 


U44- 


aaaai 


BUB 001 




510 *r 




4r 4(r S03 OBr St. S6T 


oaiis 


340 388 




06 438 


fSBSIfl- 




510 4 a 


a?^ 


4!rBiD 


803 333 39^090 




340 606 




306 534 


568 388 




sioasi 


oiTsm 


43 ~4 


903 S71 38a -im 


7«3 IJT 


340 6«- 




Mb 643 


«8 6a 






W7 ~l 


«- Ml 


803 BIO 3S^ «U 


03 333 




45 1« 


BOBTSe 












8W 0<8 383 3BH 




StOBOF 


S«30 


300 858 


■mm 


IV 


511 191 


38W 


W8J3. 


804 ise 3ea ssr 70& a 




0:15 550 


B8 0B. 


563 ODD 


18 






4at3Hl) 




t41 IDt 


USB 41 




568 16- 




,„ ^t,g 


BSBRSB 


43S W4 


804 6- 383 800 04 IB 


341 286 


S%03l 


SO- IBS 


563 3»1 


30 




B39I0 








0-88! 




31 




BM 4+1 


4* «4 iMft^ >38 1M «S 14 nS 


341 4B. 


36 381 




563 66 










311 583 


BW4SI 




568 833 










Ml-TM 


eiBSe 


0-flll 


564 OOU 




&i +i( 


MO 2-1 


4.1J Ji0|«:6 & iW 4 OS SO 


341 B« 


HBSBK 




5S4 16 








439 4a rtOB iHu i»! n\yi\~m a 






o~sa 


564 am 








t^mSHUB 411M ^. 06 B» 


34a OM 


Sir SK 


WBB1 








041 111 




84 1-n 


1-40- 


308 OB- 


554 66 






Wl JfiB 


43eflai«ob iio5(M^oiM Ob(M. 


8«E0- 


93-593 


BOB 146 


504 883 








440 0'TlW 14UK 74(1 ne, Jl 










MSM< 


Ml M4 




as eat 


iwisu 


4«ritB0- '/ 


IIISIf» 


H3IS00 




SHDM 


B«"a 


440 890 


me u 


SU1»3 


BISOGfl 




)0B J 1 


Ui40s 


BiSSK 


140 SK 








441 140 










M4~l 


p«9ai 


441 804 


800 U4H dW IK Tir HI 


811 S74,B« lauiaos 11 








«*■« 




809 «B 3R6 3Wf 08 126 


348 4SG B£9 444 800 m 


566 500 




IMT. 




«1 oil 


■vn 1 w 4>w -OH ■» 


mmLJ'^.A 


566 F6- 


4<l 




i 111. ,'' 


SIB 4 


B4B !HI4Mirai.Bll (W WT WB|710 JW SM eBOIMJ SSB 810 BOO «J8 IB 1 *» 












zi^T ' '" ^^ 






51 B4S 






Ul 






SM'MO '!lill44i \ 



TABLE XIV.— ACaOAL TAHOBHTB.KTC. 



SI" 


1" Cur^e. 




• 


Onire. 4= Cune. 


B" C«r»B, 


Taa 1 Arr 


Tun 1 Are 


~T^ 


-. 1 Are 1 T..n , An; 


T.n 1 Arc 


~v 


wioB-lrSouo 


"srwlsiwft. 




loaBoueo™ sss uib go 


SUtM 


:i4uiw 






MB r,««U 83 




«5 1W0M~8 1(«»«« 


Did sue 






in' m' o' 31 


'1 Bfl'j'M B 




Ho'iooi 11 -8 uaius 84 




140 8 








1 iieoi r7-8 fltti 






Hi oil 












IU3M4 












14-^08 


•mm 


141 6- 








iwa sa"-9 5ia 




BSSBTI 


14- OU 












1447 £ 


»!3 8W 


14.33 










im 44 ~81> 04D 


14^8 93 


SM )M 








1 1 


^ 


IBft; 00,-BO 316 


IWSTft 


•mm 


I14B00 








IU40 




ISffl M -80 48- 


14a T 


^»9 














IMW ll-8U8W|14^fiS 


S4-S 








110 (w 






iBoe fl -M 1*1 NW (w 


H-*in 


1 44 011 


s, 




(J) 8J 


ID 


,; 


190 « -81 4fft I4M « 
180- -S ^1 S-HHWM 


Hi's ti>a 

0SN41O 


1 44 33 












imH^l-81 fl41 14;tl K 


bJSSt2 


1 4Bin 












IIMH 80 -ISJ -WS 1431 B- 


a* (HI 


1 4B33 












iaO» 44 8ll 4-8 14W (M 


sjsou 


1 4BS 












ijnoo-8, ao 




i««-t 


1 4B0U 


' 




1 n- 


Ul 


Biisin n-MOia 


14S! W 




148 33 


' 






" ' ;l 


1438 83 

1433 ^ 

1434 58 


8»)at3 


1148 6- 


' 




J 


lui 




a- ws 


I14S00 
1148 13 












s^ 001 


1148 U- 




1I4U Id 5 4 1X1 


B7U l>lflnjSu|l04USill»l3UU * IIW 


liWSfi 


8».aiH 


11411 no 




1141 -^6 48 8- 


W8'a--i8»10ir 






<mn 




Of 


1I4S 31 S 48 33 


ft-1 .1 «74 17 1« 






B«t«4 


l14Ub 


lu 


IJ 4 t) Mi 


1 a -H-a oil' 104 


HI \ Jill fi ' ><( n.r'iii VI 


.«8 8^ 


IIW on 1 








• ouo 










11 m 


1M)6" 








•V m 




















■sesa 












lAJOO 




i1 Ml (.1 H 




111 Jl j6 tr SH4I4H. 4 


S30 «.1 


103 33 




in Uai'i 0.1 US 




aiiwi III 88 itwiutu*! 


two BOB 


laifT 




aiMuUoo 


5«63b«lJl06 


1B.W16 78S4<«1441JB 


HSOttil 


153 00 




:i'' T'^IS t. 




^ 'iB* sa'-sB ioli*4i a 


A31 nun 


1153 33 


{' 




1 -.■<4 1 10 


^WI44i W 


Wl JA 


IIMOO 








■* 144 ft. J)l lill- 


IIMS3 








l«|lU)l.i«H 11 


11 40- 








r[h443 Ul IS. 


IIMOO 








Its 1144 1 |U.* U 






















4 ll-t Is'-WtWlStsMlS. 11? 


1158 00 


4B 


.i.^Mp^B 


tmir 


amsankii 


Niiuirx^-^i iwiMiutHMwe 


use 33 


oO 




Ms-ft. 




ifi i«w -^ -91 «a i«s BS^Ban "it 












i|ii-« 38-^1 -ntiMi ^'|R4-M 


in i» 




" 1 


J.i 


> ii 10 












^' 


y 






« 




J M 1 


f 1 


•1 ii 1 




i 


I'.d, M W tW- 






wajw 



TABLR XIT.— ACTCAI. TAII0EIIT8, BIO. 





B8 


1 c 




Cn vs. 


3 




4 Cm™ 


5 C«v^ 


















z^ 


"t^ 


Are 


T 


4 


Tan 


ire 


T^ 


Arc Tan i Arc 










ISWfl 


aata 


1068'! 


i9aa as 


=Sim 


I4G0 DO OB as4 iieo 00 


















i<m a 


7W«- 


i«wusssaui)ii0 3S 




















-94 am 


1450 89 ne tau 1160 r 








1 9a 


awB* 


1MB 01 


JHOSW 


1068 87 


imu 


■K4J-1 


i4ai i&mm uai oa 








BlttO ^ 


iSOGS 




inoaas 


iwoa; 


1986 » 


Item 


1451 1, W8 ■«« 1181 aa 








3[81 45 


iaoeaa 


iswvvaoi 1 








14&>. 08 638 483.1101 « 








31HS&] 


WIOOO 


issi gj juos 00 


1060 B5 






[4U5a(»G OlllGSOO 








183 B« 


1811 fl 


1j91 r 


jaoeas 


ions 


lB37i 


»6liOi 


14.1. 9- 636 919 IIU IS 










M13S» 


15ft. 41 


^ttoea 


10BI» 


lor -B 


i«ja4MT la 116 n 
usa s sa 353 ii«s ait 








aiasai 


taiGoo 


leea w 




HKK wi»3a aa 






10 


siaesB 


J«6fl- 


1S98 60 




lOBB 4l'l938 89 


ma- 


14W1 faT57«!iiasa9 








»I8 AS 






2f 


I0«.ri9ao44 


in 149 


1454 68 1.37 -901168 W 






13 


8189 (T 


Hi'™ 


1593 14 


isios 


1003 13 1040 O) 
lOOa 49 IMU 5> 


"W4J1 


14SG 00 S8S DOB 11S4 DO 

i4fis 4^038 *».ii(u as 










iKj j= 


t^e> 


WIS 




"9 9« 


i4Sfiaa«8S 444,11MB 








3I9> dl 








i^ !d iMi b' 


9BJ45 


nxAmt^ 1165 00 








U33 4S 








Loa4 eo ia4j j:^ 


7S6 U4 










1MB 




l^ 31 




lO&t 9"|1MJ "» 


-98 TIM 












»iow 


ISO )» 


291 M 


io«5 mIioh m 


99 069 


1467 60 639 3«U«) 00 






19 




«si a- 


J5Sa43 


4)15 to 


1065 eoiiMa a» 


-w«i 


Hi 93 689 64411166 88 








119 9i 


XK 33 






lOM D5 1944 44 


-39 013 


1458 sassoaoliU oo 








isew 


»« w 


1<)^V, 


21" L 


I06B 4i 194S 01 


99 885 






a 








JJIH3) 
















WW- 1. 


loui CI 




IM 14 1M^ 1^ 


MM 480 






























SiO.1*' 


^n 6 


lliOl (J 


-iwaiaa 


le K 91 « 


KU9-. 


i4«)4JM0a5l'll68 J3 






36 


an 36 




ISO ..4 


JB-l U 


ions 33 94 "fl 
















Ibit fl 




1068 69 94H S3 


















■■923 at 


1088 961 Ma HU 


HOI '-91 








"9 


aai to 


i»W*J 


1603 89 


2924 1 


1068 ^ «9 44 


Boaro 


I4bi 08 Ml -38 1168 67 












ieo4 4^ 




1060 7nl)960 DO 




463 so Ml eeiliiTO 00 














JB^8I 


lO-O 07,19=0 M 


itttua 


146- 9ililS 1891110 38 








win 96 


58j.) W 




9^86 


jr]4ai9si 11 


S0°994 


468 33 648 88-111 DS7 








Ll 0; 


^00 


1WK1W9 


^■" oO 


10 39 IBfil 6- 
















loOfl 6i 


■938 aa 


iff-i ia'i9f.. £ 


ua 48a 


'464 1^642 ^'il IW 


















BOS 10 


nM 58 Ma 040111 1 m 








WRSl 


asHi 00 




1980 01 


10"1 B8 IMa B) 


soasea 


465 0oB4aia8ii-soo 






37 




^sai 6 


lb08 






KM JU 












»*(>3 3t 


leoh n3 








465 83 643 0= IIT* T 






I9 


WlBflS 






•oi lO 


.0 t«19M» 


804 B14 


iiM is fl4j 9-.^ n~3 00 








a^ig w 


6S66 e 


IBilS 9X 
















516h w 








H< ^.HIU >SI>i4'iM]1 !6 








i_i » 


SI 1 1 Hsaii joo 














** 












































49 


3dM5 


oStJI b 


m,^ K^l>«fl«|l9»Si 


I 5..ln 4 








so 


3280 ea 


S88S^ 


16IB aa »ti a- lor oa isei n 


(wkh'm oaa 


Ma aaohi-o r 








assi a 


^^BM 


1B15 95 WS M 10- tr 1081 s 










C4 


i^ m 




ini M 1413, ji line 




ut "~p 




/ 






:??___ n ,1 1 ^ ^Si 


\ 



TABLR TTV.— ACTUAI, tAHOEKTS, ETC. 



an 1 Arc 

I G~i see OE 

I 9SI^ 33: 



. 1 9 C™ 




Tui Al£. 


Tui 


a™ 


OOC B.^ a4a 344 444 
aw 353 wSe B44 631 


3S«» 
SB 


5MIMW 



a iro &. 

U 48^,9- 

U 636 3- 38S4Ue»lt 

KSielB 66 4fiB BOO US:. 

B 030 ■r M* 56 9M SW 01 



^ 45£ 
354^8 
954 040 



346 66 3 S 3 
~ 3 8K 3 B 4 

7 03-3 8 5 

lECe 3 S 34CH5SE 



SVAW 963 3N B 



I 3. ssal 58 k SS d 



404 ass M ea m 






TABLK ZIV.— ACTUAL TAttOEKTS, VtO. 



«9- 


i«e 


^e. 


«« Cur^o. 




4»0 


«».. 




M 


Tan 


Are 


T.U Are 


Tan 


Are 


Tan 


Are 


Tan AT.. 


' 


1:' 

335'a 

KM90 
S«65 W 
8315 00 
1^11 

mi 1! 


SMI B 
5903 83 


IBJl 4S 

iBsaoi 
itu ^. 

ISMftj 

ISS 

]IW IS 
IBSd-V 
18.WJS 

iflaOBi 

IBJBW 


is 

xaa 1 
awooi) 
MBoaa 

«!«!» 
J985 On 

•a 1 1 


ii 

1080 18 

lose 55 
iu8-fla 

tnta OS 

1 "^ -; 

1 riJH 

loaooo 

10110 w 


16U 6 
M ^ 
US -H 

uex as 

IMS SI 

lasB 1- 
IWl " 
irss. 

IB-^ 
19~T8 

im as 

IBHBl 
lUMSoi 


810 J^ 
BIO H5I 

111 B-l 

an an 
Bliiair 

HI,!-! 

«n«i. 

HllttSt 

Bl ^1 

BiaiiK 

BIB 911 
BIT 1IM 

i'i 

BIB aas 

BIB KB 
B18 8S4 

Biy )x 

BJO lOB 


14 a 00 8IS Ml 
10 42 818-64 
I4TS 83 B48 »-8 
IITS 2a 848 I9S 
117B B Blfl 113 
11- 08 819 «J 

11-8 SKSGOSBI 
H-^ 6 BSO 511 

11-9 1 QW -3 

1140 ou sei 1 [ 

IIHO H3 tt 1 on 

Ha,OH&>, j-1 

IIB. 50 0^^49 

;::c: 

1189 -isaa iB^ 

1181 IT BM 3811 

USE 

JlSfl «BS1 4B1 

iiB woasiBs 

llH- ft, BSa a-4 
IlBB S3 BfiS AB- 
1188 ^0 6M 815 


IIBUS- 

Sr 
11 

11B4 00 
11K6S8 

iff 

iir CO 
iiB- a 

1188 33 
1188 B- 

11(0 33 
LIHBB" 

llUl « 

IIBI B" 



!« 0461198 33 OHO Olllni 



TABLE XIV.— ACTDAI. TAHQEHTS, I 



..c™. 




8- Cnrve. 


.. <»„., j ,0. Cr... 


6»' 
-5 


Tan. 1 Arc. 


T»n. 


Are. 


TM. 1 a™. 


Tan. 


Are. Tan. 


a™. 


M0.uiw3.iag 


jmTmt 




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^ 


Ut 


on 




948 


68.1'i 




v.o. 1 1 1 '■■m'^y. 




64i:»sw4:m4 


464.0W 


Ht 


819 


UK 


064 










Ml-*W9tH.iat 


164. IW 




MH 


10( 


til 


3s"mi 




Wl.B-JBWffi.OOU 
















Mi.wiw&.^n 


164!*ti) 


m 


M 


IM 


501 


-asifla 




Ml.MIIOM.MU 


4«.au6 


644 


TUK 






7so.ia; 




Mi.mm.sa 


«*™ 


MS 


000 


MX 


jTaTM.ars 




M9.SM«SS.III 






XSH 








Au.MOMW.atJU 




W 








6*11,7*7 BM8.MT 


MM 


(H3 




40; 






Mlf.UU»,gW.ftM 












IS 


6«.OB0W.iaa 


*».&» 






40; 










466. TM 


m 


4ai 


4U; 


m'40'.eii: 


JuC'ias iiM!aj.i,aii.:ii;,r,iji.iiii. 




M3:«:BHr;!r( 


4IB.H« 




667 




TjoTiu.asi 








5i«.60; 




M3.644i6Wt.06r, 


466.(166 








SlOtll.W:. 


30*. 68: 


OM.TM 


3I»!*63 


593.633 




6u.8i» eas.as) 


466. *1] 








016 741.^0 




668.680 


8IJS.6a!i 


503.000 




&M.012 


MU.eu 


466. 6;u 


947 


681 


106 


lBi:741.4B8 


36*;87; 


669.07* 


SiO.676 


BBS.IOT 


in 


5U.llffi 


ses.a^ 


166.661 


917 




108.^741.06' 


368 OOd 






T.m ™ 




6*4-871 






647 




Ua 488i741.9ra 






oe»'*44 


4«a'»i: 


946 006 


W8 H6 -U 086 


883 ■"■■'■■ ' ''' ■"'■ "■ ■- '"' i 




UBB -*! 


to OUl 


648 866 


408 7m'74s aa 




6«*.03S 


mm 


IB IB 


948 671 






5*6. lua 


IWOJTt 




648 810 


MS 984^^ 


863 HI ^B 


M6.aw 


1M160U 


4U 4HI 


949 04« 


lOB IJ4I -U SI 


363 41 1. :JB 


M6.4ati 


uwt«< 


4b IkM 


MIP«( 


409 jeoi 4.4 las 


BOa Blk 


l*U d.' jW in Wl 




5*e,iMu 


m in 


46 W 




409 69SI 4.1 363 




wo *i*r owjrjj otr 




M6.BCI6 


Ml d89 




H4U 6; 


409 680 48 M. 




1160 996^7-816(11636 


80 


Mfl.tW 


901 66 


»8in 


960 000 


409 6-fl, 48 TOO 


864 3% 


MI 111 32- BB- 1(1 00c 


30 


640.1^8 




tea xe 


960 288 


409 BIS 46 966 




Ul . SH kl 1 <>' 




&KAK 


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 


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3»C 


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4.C 


«„e. 


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760 Ml 


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1300 s 


m 0= 


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lei ft 




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"10?31 






Laos 0(1 


sa« K 




iu'<os 


168 e 




1818 J 


30 966 


1301 00 


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10*- W 


?S1 480 






BBIOOO 


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162-80 


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1824 88 


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1840 81 


'3»*ni 




watt 05 


6565 00 


181BI 


1 193 


1611 SQ 


3B« 


131100 


iSB Jl 


6,566 8 




1 486 






















W9»n.i 












1314 10 


i 0? ti^ ' 




Vma 




Tfi l\ 


1 'li Pirn's 














roBoa 


n-^Wiwfss'iaiie liwnir 


IM 41 BST 4S8 1611 W 


U^\Tl 




rv oom«i i«!i w'i'vw 






rii * 






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 




« sTWBOmooo 


isiwMSissoo 


1 <oa Q. S^H 6 




01M4J 




7IS800 80 II B 


1BO0 4 MN,Si 


IJ6T (15 *ia 


BM) 3-^lia-7 9- 


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 , 


-24 -8 






8480 




■ais 33 


IW a»j 1688 S5 


'OS 119 






its 89 




-86 4«) 






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 


^09 


*i wj" ""j 


66 6- 


1920^1 1iS3 33 1'SO 29 " 56960 BOs'lSBl fi 


68 3^ 


BS3 IS 




JO. will < IM 1 h-sil (1 1J|9«0 611|I6B> OS 


"08 S7^ 




4^1384 air i ™ 1 1 i ^ i>n)930li6WBn 


BSBil 


3.M00 


44 ?S1 il ' ' ''' -°i'^ * 








-69 808 


834 8- 




1693 1 


69 5)4 


355 00 


46 tel IJ3 




^9 84 


135.5 83 


47 9nia J II 424 






assfl- 




1695 00 


1)281 


1350 00 


49S85I586-81. ,._ [«9, ^ , -^i . , . J ,|»«. 02« 


1693 4« 


-owe 


1306 33 


no 985J 50 a783 33 


iflM as 3:191 0- [a<4 8 XI 11 9WI aaa 


imisss 




.355 6- 


HI 3853 -BBTBOO 


iB^ B- m W 1J84 3 >0I B 983 8S1 


1696 25 


991 






IBS f Ihi J.M". ii' 11 m.191. 


lano 8- 


—1 E« 


'.«• S\ 


SI 3W« J3 0-1t8 » 


19^ ! 1 1 laiiflfl 01 


•71481 


1857 B- 














-1 98, 


1^83 






~i 203 


: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, 



» 


C 






• 1 ' " • 




. 


B Cur 


"Ta 




i 


Ta 


Arc 


an. 


ji 








^^K 








;« 








•a. « 


003 i 


-^(j 


eft.S3! 


i« 










at so 


-Msa 


8« » 










ow 


5 ffi 


DHSI 








M 


■M 6 


cea 


* 












-5-B 


w 
















3w -a 


« 












Kis: 


uMia 


« 


B 


40 






J* 




m^^ 






40 39 










« 




UBJStt. 


3. A) 






T 


41 














41 




-UMS ; 








8t0 






4039 88 














KM dO ^ 








« H8 4t 






tax 9 












408. 


■«S4« Bja 


1 ^ 




0^ 


S. DrtS * 








OO' H iL| 






MT fl « 


" 


J0W&. 


ilf '"^^ 


"1 'h ' 


°»" 


A 0:. 


r"!.' 






^o.'jl 






ffl) H6 




3 


"mi 50 










V 






"" M 








WW 


44 




tw4 












J 








^OlH. SI 












4040 












41 


30 


«4a OS 


asa 


™ 1^ 


MO 4 i8 44 


u 


1^0, * Kg 




g 


4160 * 






















J 


a. M. 


































38 


40005 


Ota OuijOdO M(i^ 601 








K«1B 


oeo«UJ» 


ssl 




































































*s 10 








^ 








1 ''l^ 






so 0- BB 


7083 33 <«8- as as 


r iot ae'ea 








"" 


08B W 


*ttr Ke|8S 


S0|^B6BV3 « 











TABLB Xir.— ACTUAL TtXeWXTie, KTC 



0° Onrw. 


C«m. 




,. 0«™ 1 1« C»rv» 


o* 




Tad 1 Vro 


Taa Vc 


Tan 4"ir 


Tan Ara Un 


*" 




(mmoWb 


rriSm-(» 




446 «B8 r IS 40 m 








tea letiiiea m 






446 aw T W3 401 8B7 








te»TVi er w 


R-3 wa lono 4fi 




iHiV. 


-78 14H401 WW 


-oussi 






5«9B-B|110 rf 


BO "X j>- J51 1 -i fas 




-Mdsaio' 0-s 


-00 BOO 






8W-fll 16 -^■^ u i -i-^BSS 


40 ~1 


"-8ae4u- 19" 








eeBBei']i6H i. bm^ 






TOO 838 






r^auiish tw 






701 000 






ini40~iian sisu 




-9 0"4 40S 6-3 


-0 r 






s-oweiiw w 


44 &U 


"0 86940- OM 


Til S3» 






(To m 116J 8 




n 000 






^-l(»aJl6«^ we 


-G «r 


ID 




ITl !S8]1E 








n 444 11 u n 


uoi 






CI Bt 11 








(-1 8M 11 n «, 


0- ds» 






nsooft 




-0- 600 






e-BBTi 




B e 3ii« mi B 




-0- M 










it fine 10O4 05 

BflSlielOW JB 






401 880 


-0 883 






5-" BK 


tl? <! 


SOlbW.BB 60 


448 B «1 1 




006 










B a 664 lOM Bj 


^ tM B H OM 


448 BBi 


B *9U 










i~i IM 


ll"^ W 




V I^R ,«- 


448 9Hft 


81 4SI 




D3 133 






S-131B 


U S-5 


44fil«l 


"8106 


4WSII 


"03 600 






6-3 nWII ttl) 


44fi«l« 


-81866 


*M4II 


■TO«tt 






n SI 11 u m 


HB40« 


TBS or 




708 HI 






a-soa 


11 on 


44B(H» 


ss 


tM Ml 












449 CBl 


»««1B 












44D8]t! 


-89 698 


401 »4B 


-0(M» 






8 4 W 




-« jw) OiV -11 




HOMO 




406 098 04 600 










3 ^ 4Stl 


1006 8 




460 09" 




40- 191 W Oli 






in a^ 




&S M« 


lOuggi 


M 4ia esi o«s 


460 «ae 


86 148 


406 3IB 


U4 833 










ar^ Hse 






4wn 


■83 3SS 


406 444 


06O0O 






mm 


11-^ \a 


-B 00! 
















irseoa 






M (L 




461 MB «3 04 4ffi HM 








inau 




6 36. 






461 05 '4 IW04O5H1W 


KB BO* 






ram 




B GHU 


MIS ]< 






461 W*! ftl U-4 415 84S 


786 M- 






rem 




~fl J.lOOfl Ai 




m »» 


46 t Bl SBtt 406 061 








re 440 




B SM ooH n 


60 6fflt 


mr MO 


4r VIS 84 444 406 IM 


706 0» 






E^IS 




S80 ulim 8. 




^ us 


461 soa w6ao4flbaH 


TOO Iff 






11 " « 




bir %n 


SSt. 91 


461 4661 84 816 466 41l« 


06 833 






most 


11-7 w 


MO ab,im « 


B0-9B 


BS3 11B 


46. 6»U> 0601466 6 1 


06 HN 






jJJWj 


IIT^ 


swa-! 




Bsasas 


161 ai-w iw 406 m 




40 




llTBO. 


BOStWf 


m 1 (51 9 B^ro4o> w ii.'wi 








Il-BBS 


UO 9-S 1010 oo 


'41H44H 








11-9 81 


w )M inio a 


608 oou 4a 




rs ID 


fflf 


» a&i lOio 4» 

U BIJIOO 1 






11-^44 


iw eiwioiott 






rs-8( 


ll*B . 


W M 1011 






rBft4i 




*i 04r 1 1 4H 










aXi £;(i|l \ t 






a-BM4 


ISIS 


BNi 4»I0 1 1: 


w oa s« 41 463 !«'-«- 08tW »bi roa sai so 

^M08fo(»*4MW» r iSS 40B 0-T 708 6og ni 




trB-84 




^. fi UK <w(i 1 4 1 H in- 40P WW Ki as 




6-B«)lI»* " ■«> 1 BK11I1HH8.JISI 




MIM4II« ''I 




MM^'!« * 


«« K* K =0. 


«1035 1l«. «^t, 


MI ate IID. w. ^ 







TABLX ZIT.— ACmAl. 



71 = 


1" Curre. 


»■ Onrv*. 


3' Onrvs. 


t'Caryo. 


l.-0„... 




Tan. 


Are. 


T.n. 


Are. 


Tan. 


Arc. 


Tan. 


Are, 


Tan. 


Are. 




4W6^ 


SoOo 


SMa:^ 




im7i 


MoTS 


iwTTM 


1775.01 


n7.6a( 








KBSlfl 


7101 


K 


W44,ll 










1776.43 




i4«o!ss 






MSB.* 


710! 


33 






IS89'3I 






ms.BS 


)18!l34 


1430. S7 










00 


VMb.4l 




1363- TO 


B36a!3; 


1033! 81 


1778.35 




1431.00 










•1 


VMS.Of. 




l«M.l: 


3SM.B9 


1WM.18 


1770.87 


i18:sM 


1431.13 








7l« 


83 


9048,68 






3389.44 


1033,501577.08 










1094. 41 




00 


3047,81 






387U.00 


1033.81im,« 


3l0!l4t 


143B!oO 










87 


3047,94 




I885:a 


SSTO.R 


10-J4.13!l777.M 


ne.39( 


14S3.33 






*m.» 






aM8,fi7 




1385.80 




lOSI.WlTTB.a 


819.648 


14^.67 






iog».2s 


7 15 


<X> 


iOlS.SO 




me.sa 


B37l!s; 




81B.900 


14S>,00 




10 


«B9.SI 


711 e 


m 


■MB, 81 


snsa.ss 


laao.w 


l«7B,M 


lOSB.Oe 1779.17 


aao.168 


1Ci8,8S 








7 11 








367-01 


3S7i,7B 


10Sfi.3»,m9.5fl 


830.401 








4103. OS 


T\W 


00 


051.01 




867.41 


3873,33 


1035. 71 11780,00 










Jios.ai 


rsi 


V. 






367.91 


S373.81 


]aM,oai7so,43 












783 












10311.34:1780.83 


831 ! 161 


i43i!flr 








7I» 


t» 


MS3!« 




see!j. 




1030,85 17fll,S5 


i31.4l) 










7136 


67 


««a,6i 




869.11 




1038.971781,07 




1425!SI 




ir 


(108.33 


rw8 


83 


0S4,!1. 








1037.381783.08 


a!i!9t; 


14tS.«7 






lOS.Si 


r so 


01 






87o!a 




l037.B0'l';«3.5O 


833.169 


1436.00 




ifl 








30BS;B( 


wesiai 


1370.43 


B377!23 


101J7, 911 1783. W 


m.m 


1426. S3 




90 


« 2,11 


:"' ";' 








W7T.7S 


1038.33'l788.38 


83i!93t 


HSe.87 






4) 3.87 






1038, 5411783. IS 


1*37.00 








iil:l 


1038.88:1784.17 


Sa.178 


1437. St 








3370.44 


lOSS.lTJiTfll.JI 


833.4-30 


1437.67 






41 7.1S?iii. ' ■ rKs3S830.M 




B33.683 


1438.00 






118.42 




i039!80 1786:4: 


833.935 


1438.88 




96 








0.,., t.,,u;3. 373381. 11 


I030.W■'178S.B^ 


KM.lBl 














:Jsr3 50 1373.80'«Bl.a7 












41«i.U 


7Hfl;67 


mi.x 


3573,31 








)34!70! 


143ft! 33 






123.61 


7148.38 


mi. Si 


3574.17 






103l!08.I787!08 


834,955 


1439.07 




an 


liM.TS 


7130.00 


»63.46 


S575.0( 


18171.07 


3833 33 


1 


»5.»7 


1430.00 










!063,0l 










17S7.B3 


)3S,459 


1480.83 








71B3:3» 








3884! 44 


1033!03 


1788.33 


835.711 














577! M 


i37a!» 


3385.01 


1033.34 


iraa.75 


835,964 


1491 !oo 












578.» 






1033.65 




838.!1« 


1431.38 






1L31 06 




i08S,6l 






!Sge!n 


1083. ffr 




836.488 


1481.87 








7100,00 




tm.oi 




3336.6; 


1083. 3» 


i79o!oa 


<98.7S 


1433.00 






133.63 


7181.67 








ssar.iis 




1790.43 




1433,33 






It SI .93 




30S7.53 


ssiiffi 


378!4B 


3387.78 






1493.67 






4199.18 




3088,10 




378.87 


i3H8.33 




887!488 


1433,00 






4 37.44 


nofl.o; 




3983,33 




mis.fK 


1034.581791.67 










4 88.70 






1184,17 


lS79:7i;JM 4 




nsn'.aai 


1433 !67 






4 30.99 






3585,01 




838,945 


1484,00 






4 41. i9 




joTO.ai 






83H.49T 








4 43.48 






586! b; 








4S 


4 48.17 


71 7a! 00 


BOTliot 






^:ao7|!w!u 






4 4a. OB 




a)72.(» 


W8!s! 




i439.365 1485.31 






4 40. 8d 


7i;s:33 


3053.34 


3589,17 




>^'g.617 MSS,07 






4 47. B8 


7180.00 










49 


4 48.84 




«^:^F-^ 


18S3.09i-31l3,e9J1037,4117U5,4i 


830!n81.|436!s3 




60 




7188,33 


30r5.13'3S9l,8' 


1883 ,61 83M. 44 1037,731795,83 


830. S74' 14.16 67 






4ISK3t 


7185.00 




1383,94 33M,00 1038,05 17W.35 


830,531 1437,03 






ins. 68 


7IBU.tlr'«7ii 4;; -X'm M 1311 37|itllS .^6,10:-IS,37 17B«,6" 


830,789.1437.33 






153.94 


;iH- ■>-:-<x-r .--■•'■•^ u, ^n-r^'v: ■! irais. 50 1797.08 








iM.a 


7ilii ,■■■.: ■•■-.: ■., ... ,.■:■. 1 1.. Iitifl 001797,50 


Ij!^ 1Jm!oo 








7]^'; ■ ■.. ■■ nun. 331797. OS 














S8'i!066 1439!0D 




e/fi 


w.svrWij.ivfii;!;.; im.~; 'Mi.miaJiSi^v™!^i^»05^ 


\ 



TABLR XIV.— ACTUAI. TABOBNTB, ETC. 



lo» Gnrre. 71° 



l8i>.fiH'sS4.5CS 












too. BSD 
W9.7IB 

109. ess 






no! 887 

no. 838 



BBOUIXI 
boo! 417 

eeo.tMs 

BOO. 888 

sai.Mi 
Bei.iua 



SSI .4 



Wi.( 



!ia!ise; 



4BT.S«! 

«7!bm 

»T.788 
t57.9as 



lis. lie 

113 !U3 
«12.4S0 

tia.eia 



us. oil 

4es!i«i 
laa.ssi 

IS3.472 



BV7.BIT 

twists 



I037.(wsi«.iai 

IO«,8BWO.I»S , 



4U.(»4 718.500 



G» 7)8.333 
(»4 718. 50C 
793 718.085 
819 718.'- 
416.040 713. 



lo.arsew.srrswi.v 

■0 .454 SOT .S83\«a .-.^ j.wa . 

. BiaiBBB .Tw^^ .aaa-.OT 



TABLB XIT.— ACTDAL TAKQBDTa, BW. 





m. 


1* Oum. 


..o.,„. 


3- OiirifB 


1 


4- Onrva. 


ft* Onrra. 






Tan. 


Ara. 


Tan- 


Are 


Tan. 




Tan. 


Am. 


Tan. 


a™. 






7 
11 

ao 

:i 

u 

a* 

■9 

so 

u 
a* 

SB 
S« 

J» 

M 

4a 

M 

ss 

i 


ill 
ill 

ii 

if 


1 

i 


(HI 

at 

i 

u 

00 

n 

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n 





DS5.3! 

il 

aosslii 

!S:S 

3091. at 


is 

MM.l! 

ssos.oo 

ffi:S 

S8:S 

HlO.on 
MIO.N 

i:l 
B8U.1 


1388. tl 

11 

il 
iSI 
ill 


»0I 

£40; 
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H03 
U03 

s; 

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BIOS 
HIO 


1 
s 

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1041.23 

iii 

104S.BB 
1043.14 

SI 

[(Ms: 38 

III 


Ill 

iS 

180!. » 
1S03,U 

IBOS.S 

1X04,17 

804.se 

1805.00 
.W9.4I 

isBs:* 

1807.01 
1808. M 

S:i 
is:! 

8!il08 
813.90 

II 
11 

B17 « 

II 

810:61 

8M:4i 

il 

11 
SI 


ffi:S! 

33 33' 

aa:88i 

884.008 
834.354 
884.800 

zs 
II 

37.1 ! 
BB7:8( 
837. SS] 

11 

M,481 

m.m 

S40.4BT 
M0.74i 
41, OM 

4i:Tn 

S:ffi 

43 6» 

MSOU 

8«4llt 

11 

44 M) 

a:Sl 

846.101 
B4t.tt(l 

£:g 

MS. IK 

11 


1440.00 
441:^ 
144K:«7 

444.07 
445 CO 

44e:3» 

1448,87 

447:33 

44b:oo 
448.33 
1448,87 
t44S.O0 
I44»S8 
1449. »7 

46rt:M 
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461 :«T 

1469.00 
I48it M 
1463 87 
14*8 ■» 

14S3:B7 
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uu:«7 
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4K.B7 

l««S.f7 
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s 

I109.« 

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II 

4213.69 

«L6.a; 

si 

4X2^.95 
U84.«4 

taaa.w 

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nso.eg 

ffiSI.W 


1 

ISO 

1 
i 

7888 
7*15 

JSB8 

«% 

1 




s 

i 

J 

!' 

w 
e 

a 


U91.S 

il 

il 

100:01 

sioa.K 

«aa.8S 

SS;S 

*105.W 

iior.OT 

1107. Tl 
illO.SS 

mas 

SlIS 

ai 3.40 
14.lt 

si 


il 

8B«,1? 
M3S.O0 

ieaT;B 
»3o:e 

8631,87 
8633.3S 

saw. 17 

36%. ea 
lue.e 

3B9B.it 
16«.00 

SMI .ST 

KM. IT 
SMS. 00 
BMS.M 
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11 

isaa.BB 
1400:10 

i4oo:g« 

1101 .81 

i4ih:« 

Httl.BS 

l40a.B6 

I4<»:24 
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1407 :«! 

1407.9C 

409-Oe 
WB.fil 

40S.W 

iS 

t l.W 

4S,0S 

MIS .a 
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Willi 
Mil .81 

8416.11 

1417:^ 

9417.78 
HIB.U 

I480:« 

»»:«? 

m.k 

494 :4< 

m.n 

«4a8.ii 

243fl.<7 
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e4»T.Tf 

4«g:« 

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11 


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il 

osi.» 

OS*: 41 

loss: 38 

II 
iS;i 

\m.m 

1068. SI 

II 
El 


i 



U TANOKNTS, BTC. 



Ifl' Curve. ■>»• 



MS.41II lOiiB.m 

un.BMiiMe.w 



twitnuj'ioaa!?! 



M).40in»,8sa 



affi.SW8Ul.S7& 



SM.STTIOSO.BS 



M9 Oil l:»ll.»ii 



TOO.OTB 

Too.«ei 



U3.1<I3 ftiS.ltH 

■■».((« WW, 7" 

S.QSSMM.l 
1. 184 MM. S 
l.l«i«M.a 

i!(SMwu!o 

i.Tastce.a 

_,i,9>n «».«.. 

IKK DStnn.HM 



tld.tTOTU 



M)4.9H 
B04.4I4 
BH.CtU 



41S.367 



fioa.MYu;^.' 
floo.sso'ioss.r 



losT.miw.ooffjSOD.jii 



T(na.l0.W?.1T0'l)l)8.%31MM»lM 



aS9.098 flIO.ISH 



go mn.iflaisa.an psK.ssj » 



TABLB XIV, — ACTUAL TAKGKHTB, 9 



.3 


1 Carr 


» Oorve. 


3C„v. 


4 Catr 


fi c 


rv8 


^ 


Tan 


Arc 


Tan 


^W 


~Tii 


Arc 


Taa 1 Am 


TiT" 


iSl 




MiTBS 


lOflOW iwaliO MSVtil 








»!0M, 






Ht^S 


lOUO 4« IIMS 4» MB 450 






*Mi3a 


Tsossa 


8LJ1 iU 




1414 i: 




tOBO-M 


IB^ BBMS 1 






linsisa 


-BOB 09 


ai«i JT 




1414 8- 


£4»S0I 


1061 I< 








tme 


■nam 


WU51 


SdfljaB 
















rsoess 


«J3 1fl 
















Mi K 


TOOOO 


^113 Bl 




14n 95 


i43n(i 




IS-^ BO *10 i\ 




I 


iM 1 


-BII fl- 






1416 3a 






lt"-(KtMOir 






iEoa 


-Biii! 


«i^ oe 3&>i a 












« 






1 S 4 W 50 


141 ^ 


lis u 


lit t ^ 1 -S MoO !U3 


i4uaoa 




U.V.M 


1 1 .0 Hfl 




11 










1401 00 


11 


\f'f 1 ^ 


1104 3.4 




4^V)ll 


! 1 1 1 1 OBV 






uuow 


~!Wti li 1 1 1 » ilW 1 H 


14 -» 41 _ n^ (1 1 11 u «fi «0 


1465 -U 




IMI w 


ws« 


HIM l«^ 






£H -S 










«Ba» 


-830 (W 


181 a 




\Ul Ij 


U43 3S 


1065 03 1!M. M 


Hm B56 




IB 


4391 M 


IBI B- 


»>u»i 


M8BS 




iUUSR 




BW113 


I4B6 » 


SO 




-SS3 83 


;rtl 86 




N3:.a() 


»44 44 






l4BSe 




1 Ubb- 


-33SO0 


IIU50 


aoB so 


tie2 4a 


145 00 


IdBB Ih IHAJ I 


a.1 6^ 






IJBS 11 




LilU 




IIV, iw 








146 M 








■Jl»l 


asMii 








^iot 


141. B- 






-1)0 Kl 


1M4« 


uronn 






lOb 90 1HH,1 01 


tut 411 








~i41 S- 


n 11 








IJBBiJIMS, «|8M 0% 




















1 lU-i 






DBIIIU 










IIBM il 


" 


1" 4 


J -14a 44 


1060 5Y-« o«U a> 


14B»r 




13 S« 




1060 SbU 5oUo^ 


14 00 






-1- 1 1 


tlo0 5( 


lOrO 1 IHB on HIM> ;ai 


n-vss 






-aw 1 








10-0 401NH kItM 4t1U 






1J81 J 


i55 l)U 










10-0 81 1M.W 5 sai, 4 








-SSBO 


^141 01 


JU-hlW 




ia ■&. 


10-1 14 1>^ 1 B6 IKS, 








"85(138 




38-111 






lO-l 4 1B3J VtliS »» 






4JMU 


~taooi> 


141 &; 




)4l!ll Kl 


ma Si 


10 1 fiOIMI' JU& ^U 








-8018 


14<t VO 


3SIWB! 


ii>9« 


mm 


10- 1 |isia4i»5 HI 






IJSSK 




12144 51 


i)i8l 6 










as 




-MSUQ 


"•"■ 




14t»«{ 


*^«> 


l«-a''Ml«4) ^H58 3Ut 


141100 


40 


S'E! 


-TiBOT 


^1SS3 


H»l» 


14«»65 


^» 


IfTS OM 1fl41 B R,W »4 


14-1 13 




4-M( W 


new *) MB J9 WS4 1 








4 1 


1 Jl 14 i IIX H 1 !(*<, IK 




*o 


4*1 -3*1 t. Jiil 13a9083I4d4a 4M}VUU>14 4HUMPUt4Ba3 




4904 a !-89a la iiw aasagi w.iiaa ooiaini n lo a iMsi sasoi i~ loi « 




tWSW-^CU ISl 01 S^ M 1485 4S ^Ul fl 1(1 fl 6 1S«I JXHl 4>U I4~ M 




4*ril'-386B liaS'^SBB ll|fW%4( ~ 1^>~ IK 'l ir H %, fH li M 


f.t 


'!"" t, .'.M ^!'j' t '' ■.,,-' ,', I'Iy ■"■■!' . ' !,,-' '' V , -'*i^' '..,',"1 




is 1 

























TABUC KIT,— ACTUAL TAKGSSTS, BTO. 





« Catv* 


c 








On e 


H 






|~ 






na 


A 


~^ 


A 




^WMS «W 


B6 


"STttB 


600 






4- S08 








!HI6 ^1i> 










ran 


»W 


*4 ivr 

4^4 (HI 


■SO 9- 
















58 


25 


m 


M 


4«1BBB 


-80 WU 






-ii~ -HO a t*ii 








880 




S5. 










TIM UBId 






9- 








tj 


-iwnaa 








». 










-a- 


«. a- 




" 




39M 


K» 




w (S.>g' mm 
















■as 






110 B- 1 














-a 600 
































































-IWlteB 














n ^ 
















am Bi 


















*! 04 *L iW ^ 


Htth 






83. 












« 












«ui 




















aw 


a- iisn 


1 1 




» 




0% 


83 8»; 


SO 




£ 


Ji- 


-.„ 








4H» 


■» 06 
84 (W 


%% 




siu 


































-M 83 








& 


IW ^M 










-S4 nOl 














w 




JH « 


■34 01. 






93 










M 


S8 W 


M B* 






" 


^ w 


' 








m 












yd 










B 




u 


-JU 


Oo JU , 






J, 




» 


arw 


6.i». |63» «Utt^ 


1! 


SSSI 


«< ^j ^ ^1 " 




B^ 


^"" 


J^«.U ^ 


Bl 




















«»r 


s*t 


















6» 


2l 










ass 
























T N 


L3U 


1 .je iiB US 


u_ 


cuu tk, MS lab 1 u 




^ 


»* w 


J^'s''^ 


B8 


sais-D*s ooa-BKS. ' o 










tWfl W iH-«l 




sn 










«| 










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^ 












L 


J* im 






_^_____^^— 


— 



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«> 


IMT^ 


MMl- 


10TGUlSr«lB63^ 






uia«i 


«[ 6-|«16B S3 TW m 


i4aB-e 


1M8 ei 


lo-sw 




148a!si 








1440 8: 


MS -8 






1480.67 










£488X1 


1UH0 5I 


IKl JS8M6 


1481,00 




UA81 






msaa 


lOSOft 


1851 « 8M 8H 






13*114 






ma** 




186^ <M 808 09C 


1481 !s7 




4ai 1: 


1441 a 


Maot 




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« 


jihi» 




1454 08 




11)01 on 


1864 5e'8^ 9-) 


1491,01 


36 


i»ai» 


400 DO 




3 uoa 




iIWi 0- 


ioqi4. 


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 
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lWia,3S 






1558.67 






1169,00 




-VBw'.W ift W,Sfio lilasji 1 )i -J b 4i i\ 1 5 ..J lAiflir 'iAxsii.f 


^ 



TABLK XIV.— ACTUAL TANSBNTB, ETC, 



1 Cnrr 


Til 


A 


Ul 401 




l»18Uf 

ug DHS 

KtJSB 
65. 4&. 

65a OM 


IK 


smao 


m 


BMIS. 


111 


B54 "Ui 
6jJ »8- 


HI 
IK 


6MS80 




^oS? 


SIS 


¥i 




OS IJ- 




B^ 3. 




M BIS 




'^*'l' 





D4BS9aafl 

6IM9e» I 

oHSiiDeaa 

1 0IO96S ti 
1 1-8 963 - 

I iuenas 

1 51 AM 1 

1 otie.wt 3 

I Bo4 964 1 
0*il%4 " 

doWGa 

■ SIS B05 4 



— M Mfl ft 
B lljl e 

as-iss 2 

508 4«D BS 41 

au8 -aHS, - 

nW 8-9SS 

'ioy U3- s^ I 

H32 858S 

41i 8613 1 
fUHVI B 

jw wsw r4 



^^;.^5^e 




nu'WOftMl 












































mulss 903 


41 



ISO 43j 5 000 3 






L TANOEMTS, BTC. 



w 


1 Cnrve 1 9 Chi « 


sc. 




.c.„. 


mT 


-^1-^ 


T» 1 Arc 


Ta 1 A 


Ta 


A. 


Tau 1 ire 


4^rteraDol5 


8819 98 3900 00 


15JB 4 "000 00 




Taooo 


9»)WtM0IX 




4M1 1«T»1 91 


!3»)88 


8800 83 


151 SI 800 H 


60 51 










«WBSTB0»3S 


















46» M !WS 00 
48» 31 I*W « 


K3»0e 




1548 14, sol " 






» 


>^0-l 


1581 <x 






890^33 


15IS 60l W i. 


IIBI » 






rvSi 






«» 987808 33 


e»^)43 


mH 1 




116190 




OS 








*i4B0»T8i)O0 




■WW 00 


vtl MiSi 2 


118 1 












i«48 417811 6 J3-4S0 


w"^s 


IMHS -'603 89118 SB 


199 






158^ i- 




WO 81 ™» 33 MS,^ 49 39(* 8 




,18.90 


,853 31 


130 41 


196 8 




MBJ » TSIB on 


aa« Ifl 890- M 




1.88 18 










to 


M»t«781fie? 


iS«8 9a 


W08 33 


1»1 37 S005 46 


I188 88ig» 


1 


r<,^,588>. 






ansa 


890B17 


IMl Sl'iK6 11 


1183 97 ,9M 




m "mIisbs 8 




«ia3TI*!UW 


#M8»T 


aiooo 




164 3- ,BB5 








<e«7T»7Wifl 


esesgs 


3910 83 




1^0- SS 


181 8(>|18» 








«wuj»s3a 


ESJDS9 


sail 8 


lUt « 


■TO7-B 


I85D]I^^5 






«eoMTa«soo 


»WS3 


WSO 


1593 08 


MM 38 


185 3sll9M 


^ 9Si 3SI 1.jn 0. 


« 




mi oa 






■808 89 


IK 89 1B1« 


t 0.1 ssonwa 




46MB8TIM8 8S 


eaai -e 












8 


»M«g-8a)0< 


ij83«43 


^t^DU 


19.15 09 






50£U1^?ll58«OI 


B 




0133 11 




■Vin Vl 






»0 




1 






1 




loosss 


' 










«n' h' I 






j(r**i 








4(1 S?' 






39 1 f 














_j3euo 


B*V. M 














-848 91 


1381186 


3W3 83 














7848 83 


as40 0A 




1800 18 ■818 11 II'V ,198 




83830 




30 


48S180 


-HW )il 


n<ti ) 


WJ Ol 


1 . , ,1 , 1 


i" 


•Sb 51' 


15 01 




489 TO 1 






15-0 3. 




46U n " 


1 10 






^^"^ 


1 38v,lS71 a 




IfWiM 


! bA lis 1 3. 










leaniw' h 








l«ei OSI-BUI B 11 n.lB 




138 BOO 










SS 




30 


4903 SI TBBj 00 «17 J iOSlOBl 


J 


15-3 01 




4eiw « -sec 87 BH4 1 ins 1MB 










4«0bliJ WIH H 'tlh 1 I Jhl|P 










4eiM03 








43 


«»« " ' 


14 nils 4 5 










4'TOSi 




















11 9ooln 11 a 


4» 


170-80 


milSB, jy«m|lM«43U^ .1,-7..,"-' 


4. 




ao 




t89S 38 W4 M W41 871WB 89-81- 79 11-7 5S iro Ba 


81 iai'l5-6 s 




moai 


T885 ael«8i» s-l««a so m o wlwiw wlim S7 in 








»ni w 


7880 B- ll « on Wl 1 rtjlfios KUlll ir. 




























ST 47IB97l-f< 




»k7a> 37l~M 






'JW/TS 


«■ jj 





















—ACTUAL TANOEHTS, «TC. 



8 On ve 


T'C.r 


« 


« 


Cu 










T 




mm 


1ft). OP 


w Jt 




m 




























"^ M6 


3* K 


m'l'^jn 


6U( 


sw 


•* 



II am 4411(1 93tf| 



•feiita 3 



"81 Hil s 3 u In J m 
-85 aslis aai'o-s s 



I ME ess "OK lea e e 8 9 T4 * 



/ 1 f 



L TAKflBNTS, ETC. 























7» 1 1 Cu ve 


" Curve 




.( CQr« 


4 CurTe 


5 Cu v< 


m" T.nT*=^ 


Tan A 




Tan 


Are 


i^T 


An. 


T^L" 


An- 


4TM 18 TKM 00 


^erSsiaSr 




ivT™ 


SSTja 




iB'^nio 


aiiwi 




I 4 4 M|-91H ( 










1181 3 


19-^5 4 


945^ 


1580 34 


4 i. 99 MUa M 


















J 4 - M -WS 01) 


aes sx 






.W:I6 0I 






94 111 


IM! 00 


4 4^ 4'-»)b (i 


jMUbSasa 














1581 ai 


n 4 W U 


-aoHij 


Sim IE3BS4 




isTest 


j«a8 1: 






uie 31- 


1581 r 




"810 OU 


-.HI (wsasa 






46868 


1198] 




BHi m 


138.00 


7 1* a! B.' 








l&~81 


JM-* 






MflB-9 


i5&jn 


H 14-11 !o 




«)« Mdsse 




15*^18 














4-aj II 


Jl IW 


.^T96 3M 


SO 


n-8ffi 


aaaai 


1184 1 


19T^ 


047 441 


ms 




4 3 18|-B10 B 




ia-9S!! 


aiassB 
















I 


16-9 t» 


JU49 44 




10^ W 




i5g8a 






-i IJ HW) 


nu 


l^8ol5 


SSIODO 


1185 a* 


1980 00 


948 3S3 


1584 110 




4 (1 a l-TCI f 


J3 11180 




1580(6 


4IU0»6 




1980 4 


948 5111 


581*4 




4 4. h -'JM .M 








JMi 11 


llhSfti 


IttMH 


IWH5 
















J(M1 tt 


1118 r 












IMid 


J3j(«ai«8*i 


iiSiOiMai^ 










ir 


4 48 01 


-IKHM 


J:f-3 6Sa!lb4 




liSj 4» »JJ Tf 


llWBI 


issaof 




5850 






aaooi) 


J3-4 IHdWS 




I.18J W «I4S 3S 






1411988 


158H 00 








£1 4 DBSWu 




1383 43 JIHJ 8U 




1983 U! 






ao 


4 1 X 


»j3a 


JS-S6I)39«6 




15B3 90 2644* 


1188 08 


1983 3; 


9.10 6^0 


1688 r 




4-W8( 


JBjOU 








1188 81 




I5U811 


158- UO 




















168- as 




4 .>54 


ftwas 














iJT r 


^< 


4 ^S 


B10 01> 


Jl-S 5. W U 








1989 0< 


951995 


lUSOO 
















19&.4. 


951945 










t^nu (Mill 1 










gsjas 










.J^M J3 




158 l» VS !S 




1988 A 


954 50 


1589 00 


^8 






^1add») 




158 88,41148 8» 




1988 <. 


J.'i 88 


1589 W 






m.mwi 




I588 1sNm9« 






JJ:ta6B 








m 139 ■i 


00 


1^88 »4diO0D 








1 UOOO 


Jl 


4 Wl U 


-B51 <r 


*«» 44 tf. 5 








198 9 


U.1 tuu 


1 UOIW 








.jw umiB 




509 Jj Jill 11 






90-1 »]1 


1590 8 






lU. u 






1 DO Jl 'D 1 8 






954 198 




d* 


4_TJfMi 


IBS H- 


48H, 57M S 






iij r 


1989 1 


95! 484 














1 IH) 9. 'jO 1 


im 1 


1989 W 


J.i4 85 








UBOOO 


Jiaa » iBSfl 










9.^016 


169- 00 








.JS- BSJHBO 






























95. UOK 


16& ir 


JO -i— a» 


U(15 00 


WMU, iJW 


M 


laiW SI *i, 01, 


iiw 3 


1991 J3 


955 889 


1593 01 


40 '4 1 19 


9W li 


wi f mi 




1 






958 189 




41 1 "(Oh, 








159-1 ~ iMi. I ; 






^Ji 4X'}bB3 8 




TiTllIU 


jiwi Jl ufi'j 




10J4 _i i».rti H 






9;iU 41' 1591 UO 
















1, ihJ I5J4 a 






tf-aaj 


439^ IW1M, 


















JIi»,l ^I»S 














(Tfla; 


sawieiw* 


J3 


lf»6 14 1 ^ 1 




i^l [1 . M 


47 






23W Mm 














ABO 00 








iij 9 |JD0. 01 


11 HHI UGOII 


*0 


4 ir 14 


Tsi a" 


iKH le^ouo 


83 


159 64JM0M 




OiS 1) 1590 34 








M96 «fl'a991 




1598 0,1^111 


u9,Jm ^ 










3^ %nf 




1 IW 4jljl!Bl 6 


lllM WIllWO _ 


9 1 1 J 00 














aj 
















J/ -W- (? 




I ? A*w J« 




is 




















"'N 



TABLK XIT.— 4CTDAL TASQKNTH, ETC, 





T Carre. 




9" Carre. 




T»« 


-^i^ 


Arc. 


Tun. 


Are, 


Tan. 


a™. 


Tan. 


Are. 


Tan. 


Ato. 


m7 


7S7.K10 


isieTBT 


^sTTsi 


imft- 


BSO.BTO 


iSrwo 


5*5. an 




473.911 




787,78) 






11S8.8: 






5S2.4B3 




93! 




















5::.5.339 








700:38 








irs!T4fl 


im.'ii 




i88:iitf. 


525,r9S 


tTt 


W 




700. SOU 




n((J.4TH 


isir.Ti 


5.M 


iia»,M 


sai'.m 


)88,»S 


fett. 045 


m 




473.47: 


ffl:£ 




783. 711 






11W(,7« 










TOi 












1130, l» 


soi'.ai-! 


183.^ 


S^'.WI 




889 


473: 7H 










rfl;M7 


1130. u 


m.m 


088.058 


528,41- 




074 


473.894 


791: 18 




wa'AV 


i3i8:a 


aB,74t) 


1130,* 


sw.an 


189,187 




871 


251 


47V 0* 


791.33. 








a6.»4B 








528:t» 








791.6IKI 




739.881 










089 M3 


528,882 


879 330 




791.38 




TBO.llI 




1177. SK 


iiaiiii 


5fti:?w 


m.Vf. 


^7,03. 




474:451 






















OOO 


474.590 




































iriiHi 


M.i,3:.'a 




5a7:5in 


880 


371 




702:33 




Toiiosi 


iMoisa 


s7b:iii; 










fflC 


55( 


ira;oii 


793.600 




7111.355 


laai.l: 
















415,159 


ro2.ee 




791.511 




67H:»' 








&«:97B 




oa 


476. a9 








i*ji ;b^ 










50i,13l 


331 


111 


4^,440 


79a:ao 




7Bi:98: 


m\M 


fffsiBSE 


imlio 


mi.Mi 


m'.tbS 


5!».!M7 




208 


478.680 


793.ir 




"M.MI 


IffiS.Sf 


ST».ise 


1)33 33 




901.387 




881,481 




7«3 3S:| 




-«-.>.45i 




I17».3d7 






091.875 


Bai.sm 


H8I 30? 




7B3.50I1 




■sa.sw 


[sw:?! 


H71I.M! 


1133:8 


594:7*7 


<W,08I 


S28.7.V 




478:0ft 


793.88 




■w.iw 




B71),7«h! 


list, US 


Ml.Blie 






882.03; 












S7R9S7 




.'iHG.Oe!) 




B29:0T' 




478:381 








iksIbi 


MO.IUT 


1I34& 


IW8,»1 


m'.'(» 


6S9.S30 


88i.40; 


478. 1;S 


701:18 




TS3:sa! 


l3S3.a 


Boo.aw 


1134,70 


6K,43tt 


99< 917 


529.88 


883.593 478 670 


W4 33 








80,581 


11^.00 




903,10 




882. 778' 470. 711 












tlll8,« 




993,333 


529:391 










71)4:838 


132J:t» 


BSoiBTI 


1130.48 


im'.m 


9»3.iM3 


W9.85.1 


888,141 


473:993 


791: SS 






ISM 00 


381.171 




6!».1,19 






883.33! 




795,000 






isas.£8 


98] .371 




003,314 














7Ba.D4( 


isaa.M 


Qai,6?j 


iHo:i9 


5M,41« 


mi: 187 


.^^a,ll2; 


B3:tO- 


477:111 








laas.* 


si.m 


133.43 


KW.MIl) 


991.375 


530.4* 


«3.B81 


477,357 


™i:6oo 










138,8- 


598.81) 


094. MS 






477,701 


705. 80' 




7k!t»i 


lim'M 


OftJ^lVi 


138. to 




994.79^ 


53d:79I 


384:251 








7K..S88 


1328.117 


iMa.183 


i:l7.1. 




095. OUO 


5811.961 


984,444 


4^:981 


'■nK.oo 




TH.aao 


1«M,B4 


»a.6* 




MI7.37B 


los.aw 


381.110 


«4.l» 


»7a.IM 


708.13 




7ee.4M 


1»«T.^ 




137:b! 






531,888 




4^.362 


798,33 




7B6.M8 


laer.so 






W7:7iB 


i05:3ei 


531. 4;a 


HSb'.m 


478. «S 






~efl.9» 


887.T8 


6M.IKi 


1138 10 


IW7.»K 


ons.BSi 


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 




"/ *• 


"«*' 


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 


,*».« 






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 


IS8B-11 


;!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 


^.831 


509:49: 






sie.-.ii 


issr'a 






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 


asM.iii 




5BV.437 936. aw 




833.86- 




m.isi 


i»n)>: 






lUl^J^W 


(W7,&a 




610 :t9 


833. B33 


«a 


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 








W7.oa' 


511.431 




ao 


Kl.Sfjl 




















ȣ.aoo 














511. 73' 


831 :b6- 




Ha.44B 


[891 iiu 


rdO.J87 


iiw.w 


oaoiBBi 


io43:m 


M8!817 


Ba-:593 


611.886 


834.833 


*0 


sa.tm 


iaii.6' 


7S .Ott 


IlOd.gl 


689,748 




S68.7H 




619.08.1 


916. OW 




eu.wso 








usi.vai 


iini'.» 




«7!96l 




sa.iis- 




^..a 


lasaia 


laiij* 


iioa.a 






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 


;3;..oTaiiii4.oe 


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 












\mo( 






r.(8:S^tS7'oa 




s«.»4n 


,^yj» 






ss 


ISM.M 
lSllj.83 


™?i'^lll"!-'i'! ... ■ ■' : 'I H'wi'^ 


4S 


!!:g 


isse.ii 




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 


.167.61 


;»MS(W119;.Nfl(W3 MM 1018.13 


B7S,291S3l.6fi: 




83S:«0I 




Sisana 




575 IflO 931.85! 


M6.34B S3S.AA' 




8l>».4H^ 




T*l.iH3ni«.fl:irMi ii;siW1.'.4 




.M5.498 898.R8J 




K>!i.m 


»IH'.31I 


;3tl.iii0lrw> .-.ci.il i.i; ..- ..J .'i: ■■.a Him 






8.18.96: 














^-^ 




zu?. 


M^^?S;;;;:;:^:;.:;.; ,:,■■: :;^S^^-^^ 


■^" 



TABLR TIT.— AC 



L TAKaENTB. ETC. 



84° 


1 Curv« J OnrvB. 






B° Onrra. 




Tun Ya^ T^TArT 






TttB 


a™. 


TUD 


Arc. 




















61MBBWOU(»SO'^SS4a)UO0 


^TflBJ 


asmoi 


at»9» 


100 so 


"Mn 


iWml 




iiao ws»i a- MOW MM M 


A) Ul 




xor 




03^41 




33 




»IlL.UI»)03S3e6S] lOlMl 11 




ADi 11 


wo fi 


ilOOK 


039 -) 










i!5Si SB 4aK so 


7313; 


9801 a; 


S9! la 


i01« 


WHO* 










iisiw 68 41103 sa 


IWl BB 


isoia 


J915I 




U3S36 


B81 






3i<is 6 kws as 


SM3 38 


4J04n 


l-M V 




sn m 




0386) 


681 


17 




SIB8 OS 8410 00 


«I84 tl 


4)IWi<W 




J803 W 


awa- 




osaw 








SIflB &a H4I] 8 




4905 8S 




amsBo 


31K« 


JOS IK 


U34 IS 


esj 






5171 07\lW I S3 




4«Me7 


IIJSBI 


»a4 44 


3BSIW 


■* oa» 


034 58 








81^ M 84U Ott 


usBoae 


4»rso 




3805 00 


3S8 40 




034 S3 


IBWI 


00 


lU 


1 -1 io'mib fi »b is 


4»8 SS 


ITS* 88 


4805 58 


S98 7S 


>nMr 


103S 14 


1»B 


q 






1»B 17 


irjsaa 


liSOBU 


Mt IB 




1035 il 








ol ll|(HJ.MM V««B«10 0( 


1-36 88 


tsoea 


»4U 


9105 « 


1035-4 


ttei 








1738 «> 


9807 et 


«H9> 


«10B« 


1030 05 


108< 


34 ! 










1738 to 


sor 78 


)!95a 


eims 


I03B * 




IT 








4dlSS0 


lTi*7 41 


«0«» 


SOBOT 


(lOBSI 


103B W 


198! 












1T8- W 




-Wllrt 




iff»Ol} 


lues 






VISITS 


m» IS mu 4a 


U14 1' 


1TM4S 








1037 va 


1981 


n 




BiajB 


tlW 00 SNS » 




iTM te 


4810 01 


1S»SS: 




10^5; 








10 






4015 88 


lTai48 


iHlOBU 


imiB 


sio-« 




1«8( 


M 






SIBBSO 






1-^ M 






SlffiS 


103g IT 


ISBC 


BT 






SIM » 






1397 M 


3 08 7B 


l^« 




00 




i» 


51ft. r 






1S98S. 


S0» 17 


1038 T' 


lis: 


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laosTo 


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1089 9; 


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t:»aat 




108131 


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13B9 4( 




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116 00, 013 03 


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; 1 1 J 1 i s5 


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^15 49 0)3 M 








18 1 IbB MU,i3.1 (A «|IJ31 B 1 dB05 


JgBI 11 




11 tta' 043 64 


6K 






in |aWB UjMOS W|«oa IB USH D0|178B U 


auir 




116 35 043 «■ 


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^\ ici'stm -w via ol*ai rii-40 » 


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11 A( 1044 8~ 




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tvie a 












S-J- so 1 II 


JSS.^01 


1307 OB 


118 -5 104B.1 


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no 1 lOM OH 


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IW 8S 


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5S94 W aiSS MlffllJ B 4341 « W« 1« 






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S3M 4T B485 OOMIH WllBU EO r4S BT 


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MOT WW88 B- MiB (IB urt aah 4r M 


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IWI T 1 B inj IR 


t^:a 






5itWM'w<H'UjaiDt«>'i44 1 I -1 fin 


J1.-<I44I1 1 14 1 (IKKtUlia 


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IBM OS' 


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IBM 87, 


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laM 


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' TASU XtT.— ACnUL TAKaBMTS, WK. 



T Ourvu. »■ Ooi 






aMJMW 



Bro.t8a 1411.1 









97fl«,Tmin51.«674.W 



MWB.190I0S4.irs77 !f 
WUB.HtT JOa4.38 fi7^.;<r 
MM1IMII10DI.S8BT7 
(8 648.743 l(BI,JS5?T.t 

Ui oso.iet UKA.ai'fiTH. 

lUI»U.8lll1l)&3.41!|D:t4. 






s'leii.toBs 



86" 


1- Oarr*. 


S" Curve. 


3= CurvB. 


*• Curre. 


5» Curve. 


T»ii. 


Are, 


Tan. 


Arc. 


Tan, ] Arc, 


Tun, 


a™. 


Tan. 1 a™. 


1 
6 
« 

1 

n 

34 

au 

O 

■i 
33 
34 

B 

i 


il 
51 

■wo. a 
saw,* 

MTflBg 

msi.ot 
siSi'.tti 

11 

3«B3.8I 
!W81.8» 

5801.07 

Moa.w 
S3oa:7l 

M07.M 

iuioisj 

Mil. BO 

its 

Mil.M 
l»3S,8S 

-■Bsiin 

rsk 


UDO.m 

S 

BSlO.OO 

Mll.flJ 

KUB.DO 

III 

i 

SI 

8549,00 

as 

<590.oa 

MMM 

ssBi.sr 

MH&.OO 
Bflfl.O? 

liSTO.ua 

tlTI.BT 

isTii.e: 
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S5Ba.3s 

15*5.00 

Lwoloc 

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ww.w 

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ll 

sa 

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SKi8.S7 
MM. 14 

«eso.ia 
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38IW.B6 

dsea.ot 

S:r. 

sj; 

SBBr.fiB 
«B«.4S 

il 


4»o:b 

4251.61 

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UU.BT 
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4SSB.3S 
4109.17 

4daa.oa 

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4;tS5:B3 

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III 

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777 OS 
7TJ.B4 


2«83,Hl 
8881,44 

il 

WH.8B 

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asis.st 

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S844.44 
iSiB.OO 
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s 

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131 1:7. 
ISIB;*! 

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1318.98 
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laa.so 

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188S.M 

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mar. 91 
«i«;7J 

it 3o!di 

*30 41 

a :ii,a; 

i!l«!OH 
KIM. 60 

III 
II 

assist 
t!i3a.a7 

S187.0H 

hs7"9: 
3I38,ii; 

j[io:M 

ai4r67 
!i43.e« 

il48.«8 

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S14S.8S 

ill 

n47!ai 

n48.S3 


1050. 6E 
IWliiM 

1051 :ui 

lowiis 

I0.W6O 

1050.58 

1067:7( 

1058:91 
IKO.BO 

loiatt 

MBO.S) 

v»\.v, 

10BS.7( 

ill 

IM6.lt 

iSii 

fOfli'ei 

i(M7.IM 
a* 


700 83 

nii^oo 

1701.88 

ill 
™f 

1708 B7 
1704 00 
ITOl-W 
IT1H.B7 

170,1 111 

s's 

1708W 

iil 

mo. 00 

1710.38 

Tll!38 
711,67 
T1«.M 

iTiiln 

il 

171«.H 

i7ib:w 

I71»> 



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 

1485.83 765 



893.600 

893.758 

894.016 

894.279 

894.542 148V 

894.804!1487 

895.067 14:^7 

895.325 1488 

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 
90-2.920 
908.183 
903.446 
903.'! 08 



1436. 
1486. 
1486. 
1486. 



1488 
1488 



11765. 
89 766 
766. 



67 
94 
22 

5U 
78 
06 
88 
61 



1438.89 
1489.17 
1489.44 
1489.72 
1440.00 
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 



1444. 
1444. 
1445. 
1445. 
1445 
1445. 
1446 
1446. 
1446. 
1446. 



766 

766. 

767. 

767. 

767. 

767. 

767, 

768. 

768. 
768. 
768. 
769. 
769. 
769. 
769. 
770. 
770. 



7.52 
974 
195 
416 
637 
862 
087 
309 
580 
755 

960 
201 
422 
648 
878 
0»8 
828 
545 
766 
,991 

.216 
,441 
,667 
.888 
.109 
,884 
.559 
785 
OIU 
285 



770.460 
770.681 



770. 
771. 
771. 
771. 
771. 
772. 



908 
128 
858 
578 
808 
029 



772.254 
772.479 

772.704 
772.980 
778.165 
778.880 
773.605 
778.881 
774. (m 



44 
72 

00 
28 
56 
88 

n 

89|774 
67774 
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 
12:34 
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 
48 
67 
90 
14 
88 
62 
86 
10 

.8;) 

.57 
.81 
.05 
.29 
.52 
.76 
.00 
.24 
.48 

71 

05 
19 
48 
67 
90 
14 
88 
62 
86 



,281 
506 



1238.10 
1238.88 
1288.57 
1288 81 
1289.05 
12.S9.29 
1289.52 
1289.76 
1240.00 
1240.24 



908.971 1447.22 774.957 1240.48 
904.289 1447.50 775.186 1240.7 
904.506 1447.78 775.415 1240.95 
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 
O06.8i0 1449. 17 776.541 1242. 14 
906.0821449.44 776. 7671 1242. 8H 
906. 84511449. 72 776. 99211242 . 02 



670. 
670. 
670. 
670. 
671. 
671. 
671. 
671. 
671. 
6?2. 

672, 
672 
672, 
672 
673 
673 
673 
678, 
673. 
674. 

674. 

674. 

674. 

674. 

60. 

675 

675 

675 

676 

676. 



861 
555 
748 
945 
148 
840 
537 
780 
924 
121 

818 
515 
712 
906 
099 
296 
494 
691 
888 
086 

282 
476 
669 
860 
068 
260 
458 
655 
852 
049 



676.246 
676.448 
676.640 
676.887 
677.084 
677.282 



4 t 



6 

67t 
677 
6;8 



678 
678, 
678 
678 
679 
679 
679 
679 
679 
679 



4;.'9 
626 
828 
020 



1075.00 
1075.21 
1075.42 
1075.68 
1075.83 
1076.04 
1076.26 
1076.46 
1076.67 
1076.88 



1077. 
1077. 
1077. 
1077. 
1077. 
1078. 
1078 
1078 
1078 
1078 

1079 
1079 
1079 
1079 
1080 
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. 



9« Carre. 



Tan. 



06 
29 
50 
71 
92 
18 
38 
54 
75 
96 

.17 
.88 
.58 
.79 
.00 
21 
42 
.68 
.88 
.04 

25 

46 
67 
88 
08 
29 
50 
71 
92 
18 

38 
54 
75 
96 
17 
88 
58 
79 
00 
21 



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. 
601. 



267 
489 
,611 
783 
955 
,180 
.306 
,478 
.660 
.825 

.000 
.172 
.344 
520 
695 
870 
045 
218 
890 
565 

740 
915 
091 
268 
485 
610 
785 
960 
186 
811 

486 
658 
830 
006 
181 
856 
581 
707 
88^ 
057 



Arc. 



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 



601. 
601. 
601. 
601. 
601. 
602. 
602. 
602. 
602. 
602. 



282 
408 
588 
758 
988 
109 
284 
459 
684 
810 



959 

969 

959. 

969. 

960. 

960. 

960 

960. 

960. 

960. 

961. 

961. 

961. 

961. 

961. 

962 

962. 

962. 

962. 

962. 

962. 
96:3, 
963, 
968, 
968. 
963. 
964. 
964, 
964 
964. 



259 
444 
6:30 
816 
000 
186 
870 
556 
741 
926 

111 
296 
481 
667 
852 
037 
222 
407 
598 
778 

968 
148 
838 
519 
704 
889 
074 
259 
444 
630 



50 
ffl 
a '4 
A3 
CM. 



.217 1085.42 602 985 964.815 
.418 1085.63 603.168 965.000 542.986 868.500 
.619 1065.83 603.842 965.185 .543.147 868.667 
.816 1066.04 603.617j965.870 548.804 868 888 
.018 1086.25 603.692 965.556 543 462(869.000. „ _ 
.21011066.46 OOa.ftfttl^Jtt:^ .1\\m?» .^>Sb^ '^^^^c 
. 407 1086 .tt^W .04^W .'JRfcN^ "IJ^^c?^*^ 
. 604 1066 .88W ."il^W A\\Vj,^2^^^^ 

. 8011087 .^«yv.«^w».mY^ 



Arc. 



860.000 
860.167 
860.3.% 
860.500 
800.667 
860.888 
861.000 
861.167 
861.888 
861.600 

861.667 
861.888 
862.000 
862.167 
862.883 
862.600 
862.667 
862.888 
863.000 
863.167 



86* 



M. 



588, 
588. 
588, 
688. 
688, 
588. 
589 
689. 
589 
589. 

589, 
589, 
589. 
540. 
540, 
540 
540, 
540. 
540. 
541. 

541. 
641. 
541. 
541, 
541. 
542 
542, 
542. 
542 
542, 



.104 
262 
.419 
,574 
.729 
887 
045 
208 
.860 
,518 

,676 
.881 
986 
,148 
,801 
,<159 
,617 
,774 
982 
,090 

,248 
,406 
,568 
,721 
,879 
037 
194 
.852 
510 
.668 



868. 
863. 
868. 
868. 
864. 
864. 
864. 
864. 
864. 
864. 

865. 
865. 
865. 
865. 
865. 
865. 
866. 
866. 
866. 
866. 

866. 
866. 
867. 
867. 
867. 
867. 
867. 
867. 
868. 
868. 



883 
500 
667 
888 
000 
167 
388 
500 
667 
888 

000 
167 
833 
600 

UD4 

888 
000, 
167 
883 
600 

667 
888 
000 
167 
888 
500 
667 
888 
000 
167 



642.825 868.838 



O 

1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
1» 
13 
14 
15 
16 
17 
18 
19 

»0 
21 
22 
23 
24 
S5 
»6 
37 
2S 
29 

30 
31 
33 
33 
34 
35 
36 
37 
38 
39 

40 
41 
43 
43 
44 
45 
46 
47 
48 
49 



c^t rk 



V, — ACTUAL TANSEHTS, KTC, 



87° 


1" Onrte, 


a» Cnrv«. 


3. C»rv.. 


..c.„.. 


fi° Cane. 




Tan. 


Are. 


^ 


Are. 


Tan. 


Are. 


TttD. 


Are. 


Tb-. 1 Are, 




BwTai 


^trau.m 










I9S9.S7 


iiTsyooioSTrt 


imro 








BTin.ar 




*150!SB 










1740.. U 






I1H0.48 


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43S] OT 


I813!gi 




liwals^ 


iiwis) 1068:41 








Mll.BS 


MOS.OO 




43U.S0 






i.')eo.7i 








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lass.D-i 










1741 :39 






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11177. M 1089.68 








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3178.39 










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taB3!i4 


11178, 7G 


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817.88 


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w.astf 


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» 







— ACTTOAL TASaUNTa, KTC 



8= CoEve. 


T &.r»B. 


8* Curve. 


»° CurvB. 


10. e™. 


.,. 


Tm. Arc 


Ian. 


Are. 


Tan, 1 Arc, 


Tan. 


Arc. 


J^.J^Arc.^ 


~u: 


Mw.ineiiiM.oo 




JSTse 


SoImimTm 


604:744 


06067 


544 4aB.870.<nO 


^ 


Buft.srsiwo.aw 






B80.llD6JDfff.Tl 


ll04.BJa 


m.m 


544.589 8T0. 187 






r TiflVt 


lawioa 


B80,a87)l)87.ft; 


808.101 


967.087 


ii44.:so9ro.8js 




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i)sa.;»4 iwa.id 




DST.SSii 


844.888 


870.500 




suT.eutiliui.ii 






«8a.Ni 1088. at 




HT.40; 


MS. 048 


870.967 




DOT.iKl 


1*61.80 




i«4»:o5 


(lBl.lBa'10S8.B4 


BoaiBse 


90J.6B3 


MS.S03 


870,838 






431. HT 


■ra.677 


Ut4.» 


181.886 loea.ra 


BD5.soa 


OflT.TTB 


M6.361 


m.ooo 






fai.fti 


T-B.MOB 






606.990 


997.903 


M6.539 






mm:;^ 




rB.io; 




i8i.7S7io»g!r 


ooe.i.is 


968.148 


MB. OSS 


^l!s83 




SU8.»U 


J'^ieo 


TTt.aBi 


i^i'.m 


681.8«|,0ai.», 


600.834 


968.388 


646.SM 


871.500 


» 


9W.SH 


HM.TO 


•7s.4ai 




68a.lB11069.68 




WI.B19 


MB. 906 


871.987 





9IW.&N 


UM.OU 


-TB.TW 


I«3i48 


888,38111089.711 


60sie87 




546.159 


B71.888 




aw.TM 


IJM.W 


-T»,y46 


1845.71 


6H3.5ai|10!M Off 


(108.BBB 


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M6.310 


B72.000 






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IWS.K 


VKi.ITt'lDW.!! 


607. Ml 


189,071 


M8.4:t 


BS.167 








-au.aiB 


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Mt!.B77: 1090.42 


807. aiB 




(46.881 


872, SSS 


4 


DIU^HK 




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I1S3.177 


1099.88 


607.395 


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873 .500 




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1090. K 


607.678 


989.830 


H6'9BI 


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B9.S16 




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THl.JW. 




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1001.07 


608.981 


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i47.aa 


873.838 




gidilT: 


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7BI,BMH 




184:37: 




BB6.4M 














TBS.aja 


laisiio 


084.688 


jm'.iM 


808.831 


70:741 


947! 90 


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™a,<4; 




664,769 


109*. S9 


808. H09 




M8.06B 


873,883 












884.959 


1093.50 


898.988 




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874. 000 




si3!ij:» 


l+dfllft 


iBa.w'hi 




685,170 


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809.198 


37 :906 




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971.907 


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809.896 


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MS. 868 


8-4.837 


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913. 40T 


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875.187 




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1150:48 


886,688 


1094.17 


1110.400 


973.596 




876.883 




»I6.3«I 


HU.n 




l^fiO.TI 


889,788 


1394.38 


610.687 


073,7ffl 


Mb! 871 






BIfi.BAI 


14SB.44 


^!S51 


law.Ki 


886.989 


1091.61 


110.7« 


73.99. 


MB.Sa 


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1159,7! 


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887. ini 






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978.889 




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40 


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1)89.671 








651 913, 


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TW. 161 




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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 








MW4J 


UKMOa 


a~bdM 


(410 00 






1488 38 


iiuBiia 




1764.00 






isM 




S-*T 1. 


4410 89 




«B4a9i 


IIIS8 m 


two 40 




1704 .3S 








ai^34 




4411 e 


IBM 0~ 


wi n 


1889 18 


tmm 




1764.87 








!«!5(» 


r-8 . 


1413 110 


iMwa 


»11 B- 


1880 50 


eswiia 


nii.'ii 


1766.00 




J« 


B(wH B 


sssmr 




441B W 




20)2 w 


tBWOO 


IWOBB- 




iToo.n 








l«^3I 








^171 


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 




»» 


NM38 


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 




IWB 


,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 


*-»0 0B 


uat 1 


IBW IS 


«MS44 


isge w 


*nif» 


1110 33 


1769 B- 


so 


U8I fUl 


fM^ n 


-U 01 


(4«i™ 


oi-n - 


K 1 « iia 1 


J, nn 


1110 66 


1-0 00 
















(* 


>6nH -!< HI K 


IfflS 








1 llllIX 








1,1)1 ^H 










s^B■ u 


«3bl 6 W M 14tll* 


1*4 ,- MiMH 




IJ-UW 




)B 




HHiis ua W7 40 i4» e- 


tBUt 00 >S64 44 




177^8" 






56« I- 


awa <jg|i!T« iw hu so 


IBMflOJBSSOO 


139S 33 ai tt on IS tie 


i!-aoo 






BM-r 


HHOfl 1 "10 fll u» ■« 






7-lSB 






6BM4 
















» 01 1 








It 






^604 J- 


r 1 




45 


^ Ik 










V. J!<| 








*i ^ ^ 1 1 fl-l 










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 


.81089' 


.599261.80056 


.61314 


.78998 


.62683 


.77916 


.64038 .76810 


11 


50 .6854.S 


.81072 


.59949 


.80038' 


.61337 


.78980 


.62706 


.77897 


.64056 .76791 


10 


51 


.58567 


.81055 


.59972 


.80021. 


.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 


rS-l 


oQlim^V 


i«j* 


^ 


< 


«1C // 


8t» 


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 






.IBM 


.140!S 


.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 


.18963 G 






4.08188 


39 




0D3S 




.0U3I0 


.18a!l» B 


46048 


;ilO103 




38 


. 4T37 


■S3M 




.05143 


.18353 B 


45751 






87 


■ *l^'^ 


771 M 






.18363 6 






4:05646 


SB 




Tessa 




!02903 


.18384 e 


43DBB 




4.9BaOI 




'. 4323 


«88 




-OlfiTS 


.IMU B 


43077 




4.BUW 


64 


. 18M 


8133 


.lOflJS 


.00797 


.18414 E 


4«Ba 






39 


. 4SM 






-09730 


.18474 B 










. 49IS 


ro4so 








40430 








. 4H3 


mils 


J6T34 


:it757a 


'.ISSH 5 


395511 


:S0349 


4:91516 


80 


. 497S fl 


87787 


.16761 


,96010 


.18564 fi 


18BT7 


.S037« 


4.9oras 


ee 




eoies 










,30403 




!8 




85144 


llfiS21 




ilBBM B 










. 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 


MGsr 




;B315I 


.18775 B 




;!0S88 


4.85IOT 




. Bflia 6 


i7S39 


.17034 


.83114 


.18805 B 


I1T78 


.ISMia 


4.85013 


a 








-ffTOO 


.18836 5 


ma 


.90648 


4.84300 


20 


. EBTl 6 


!4777 


.17063 


fi-BflOfli 


.18895 S 


30090 


.30679 


4,63500 




. KKH <t 








.19SW 


saaii 










12384 






.18845 


ISWi 






7 


! 536'j B 


MttTO 












4:8147) 




. sasi B 


4WI0 


:i7183 




:]8B8» 


iB716 




4.60700 






48459 






.16010 


»880 




4.80008 






4720S 












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 


.17433 




.19227 


W107 


.S04S 


4.75919 






S85B7 






.19367 






4,7J5S4 




iisasfl B 


87S74 




s!tI99S 














S6IH 


:i7si8 




:]0317 




'.am 






jwjg B 


MMl 


.17643 


sItocot 


.19347 


16803 


.S1164 


4.734M 










580064 


.I9S7S 6 


IS058 




4.71813 






&M 
















!l583g 6 


t-as' 










^21356 






Cotan^ 


-^TiSi- 


Ci.taiiKr' 


"^^ 


CnX>B« 


*;7*5^ 


X 


«!• 




80* 


TO 




\ 


IV 


\ 



S XYI.-NATtntAL T 




i 
I 



■'■ m 



I 



I 



IB* \\ -Hi 



I 



i^fe 




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 




"^ 


.3B!W7 


•ihw^ 


:ii8.»« 


~'i^^ ~ 


Mi 


^^ ~ 


•s. 


1 
a 






!ao4a» 


2.74«S] 






404T0 a 


47005 ; 


42518 


a 






.suoa 


11.74IXM 




2:69831 




40888| 












B.TajSB 


:»B90 


2,69006 


40538 I 




42S83 
















408T3 S 


4«r8 


42619 








isosus 












42651 








.«a&» 


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 


IseftM 


9.71S1B 






40^3 f 


41B39 


42804 


a 






.30830 


3.7iac6 


iassH 


aisTSTl 




4)oae 


42929 


2 






.S6HW 


S.7106B 


.88869 


a.STlM 


40011 S 


4M3S 


43963 






If 






.S89al 


3.66038 


40015 a 


11390 


43908 








iaaKia 




.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 


'.swa 


a!oBit^ 


!so33a 


2!54953 




42418 








at 


.srass 


2.08)14 


.8«57 


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 




SI 






.SOflSS 


aisaooi 






43020 






S5 








2.59786 












w 


^87BR8 




!sUfiS3 


9.53571 


41020 3 


4033S 


43689 














3.62357 


41600 S 


40068 








»» 






Isoooo 


S.BSI49 






43738 


2 




3S 








2.519£S 












4t 


Iktbo 




!aeTS7 




41783 a 


39149 










.BTIM 


3.04875 


.39701 


S.SI503 




»2S3 








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 


.40301 


9.4S1S8 




80158 










.3S3!in 


B.flOBOa 




2.47084 


43979 £ 


35D67 


^■^ 














3.4JT1B 


43113 2 




44488 






aasse 


-f^ 


CotanK 


2.47509 


43M7 a 




°t^ 


a. 


A 


/i 


Tang C 


tnaoB 


THTIC 


J 


/ 


^ 


/ 


68' 11 


ffl 


\\' 


Wp 



I 



M- I «»• 



Ei^^iss 



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: 




otanj? 


.7a»M 


Cotoiig ll 


Tang ( 
78ia* : 


^W - 


>°K, 


Gotane 


. 


"TM^" 


«^ 


SflMII 


-Tmmo 














^0^ 








1.2U1B 


n 






.5^J8 


S74ni 


'rawT 








IiBll 


BOn 


l-SSUD 


58 






.■STSS 




.TMU 






78260 : 


27T64 


8 139 












STaw 


.TS53S 




32381 


78318 : 


37688 


B171 


lISBIflS 








iTSSJT 


JK18 


.7o5B4 




38301 


78803 : 


37611 


83M 


l.tSUS 


55 






.Tsaai 




.7Bfl2B 




33331 




3^85 




|-S3cca 








,Ts»6a 












37408 


8 316 














; 75721 




82061 


TBOM ; 


87882 


B13M 










Itsbs ] 




.TSTflT 




31684 


78551 1 






l!!3S!Il 


51 






.reioo 1 




.75813 




SlBOl 


7B098 1 


KS80 


8 461 


1.33758 










sorie 


.nSSB 




81823 


7884S 1 


!ffl53 


eiBio 


1.328^ 


49 








30033 


.76901 




31745 


78692 1 






1.3^12 


43 




IS 


.T33M 


SUMS 


.75BW 




3] 666 


78739 1 






1.3SUB 


47 






.Tsanf 




.73990 






7BT86 1 


96925 




1.2S4e7 








.;3si8 




.76042 




31607 


7W34 1 


M819 


B170S 


1.8S8U 












.78088 




31427 


78881 1 






1.3S321 










80317 


.76131 




31348 


78938 1 






1.8231l> 


43 




18 


.73407 


»1U 








7M75 1 






1.3SI76 








.rasua 




iTOfiS 






79022 1 


3IB4G 


818U8 








■JO 




iiiwa 


.7K!72 




31110 


70070 J 






lisSOBl 


« 




SI 




JS883 


.76SIB 




310BI 




2689S 


Sims 


.SI3GS 


39 




H 






.70301 








36319 


820U 




38 




M 






.76410 






79813 : 


39S44 


as»e2 


inlu 








.TTW 




.76450 




aOTSS 




30169 


aei4i 


.S174E 


H 




a 


,'am 


8MM 


.7850a 




sona 


70306 ■ 




82190 


.am 


» 




as 


.■TOIB 


SMTS 


.78548 






7V354 1 




82238 


.311U8 






nr 


.TSBl 


S5389 


.T6S91 






79101 1 


K1M3 


8338T 










.TBOa 




.76640 




30180 


7W49 : 




82330 


l!314U 


31 








iM2l 


.TBB80 




30401 




25792 




1.81301 


31 




30 


.'^SM 1 


!Ull!i 


.76783 






705U ; 


25717 


3B4M 


i.simo 


30 




M 






.76779 






79091 1 


85812 


B84S3 


.2I1B8 








. 4066 1 








30166 


7B689 : 




82581 


-81166 


28 








31896 


.76W1 




30087 








.SIOH 


27 






.4iru 


31814 








TKBl : 


2S41T 


93029 














!709S4 




59931 


78781 1 


85343 


saini 














.77010 






7Bsa9 : 








21 




-ir 




siaoB 


.TTOOT 




29776 






»i77B 




33 






.'■48S7 1 


M.18I 


.TTIOS 




BOOBO 


79931 ' 


35118 


8283$ 










.uaa 1 










79972 1 




88874 








u 




nasa 






29&U 


89(80 1 




82933 


;S0598 










HMS 


.77248 




894S3 


8006? ! 






.20G2E 


19 




42 


.T4M« 1 


MIBO 


.77SB0 




39385 




3ka» 










-kt 


.I«83 i 




.77835 




39307 


SOl^ : 






:2^ 








.74038 1 


»D9S 






39239 


802J1 I 






.20306 










asBia 


.7743(t 




39153 


9DSBS : 




B31B9 


.aOBST 


15 






.T4n9 


M835 










34523 


83218 








« 


.T47M 


MTM 






3SSBT 


S08M : 




MBM 


!2OO06 






48 




33073 






28019 








1.20024 








.T48» 


BS»-J 


.7T01S 




38S43 






10366 


1-19953 


11 






.T4BO0 I 


33511 


.77661 




38761 




a43!fl' 


83415 


1-19BS3 


iO 




51 


.T4B4fl 1 


3^90 






28887 


80518 1 














.149111 1 


aMtfl 


Ittth 




S8810 


HOBM : 






l! 19710 








.Tsoar 1 


sasoe 






38633 




21005 


33564 


1.19669 


7 






.raoea i 


39187 








90090 i 


83DS1 


B3C13 










.75188 1 


33197 


IrrsBB 




38879 


HOTsa I 


















.77941 




smti 


S0780 1 




*a71i 


U W5T 


4 








32948 


.77988 




afsss 






83761 


1. 9387 


8 






.V5aB4 I 


aaHiw 


.7S035 






§0883 : 


23637 


113811 






jm -^"z J 








iwn 


80930 1 


235BS 








/—L'-'r^J^ 


■^ / 


'.msa 

Caume 




37B94 


mji\\ 




i«i^ 


i: 9175 


r! 


f ' E. 




"TflUK I'C 


'otaiiK\ 


fisr\V 


,T..«t 



^ 



TABLE XVL-KATmUL TAHGXHT3 AKD COTANQClnS, 




TABLB TT1,_NATDRAL TAWOENT8 AMD COTANOBHTI. 




8 

1 

10 

11 

14 
15 

i 


H' 


■ 


i 
1 

Sl 
«i 

M 

35 

i 


«" 




5 

■IS 

I 




44" 


■ 


Tfliig 

.ism 
'.Been] 

s 
iS 

.arwo 

.9nB9 
.97318 


ColAns 


T«ng 


Colang 


Tiuie 


Cotatig 




(»I33 
U337a 

33072 

Bsaa 

)3893 
«772 

)>!&93 

)iir4 


M 

no 

f, 

45 
41 

■a 


ii 

.BTBiir 

s 

.98^ 

s 


j 


IKSB5 
iMUa 

oairo 

1 

)im 

116S1 

ii 


i 

i 

i 




DBOie 

s 

99639 

s 

weso 

a 

ooono 




01053 

s 

a 

s 

II 


B 

B 

1 

1 




:k.la>iE 


Tang 


' 


Jotang 


Tang 


• 


CotJUig 


Tang 


45. 


<B- 


4G- 





































ALB TTtU-HA'riT&A.L. TERS&D SDtBS AND BmCBMAL SEOAim 



m J .ams j .antts 



.ooiei' 



.wva \ ■'****\^^^X 



i-AfiLa ZVn.— NATCBAL YXBSED 8DtXS AND XTFEBKAL SXCAKTa 



.mm 
.otrrae 

.00742 , . . 



(46 \ -wmW .»« 






CULB XTO^HATOBAI TKBBBD S 



a AMD XXTB&MAL SBCAOTa 



.01M3 II .mawi i 






r™. !...«.. 



i\imi 



sa 



lABtX Zvn^ITATTraiU. TZBSXD sines AHD SXTEttHAl. BEOANTa 



\ .tlMi»\ .Wfl 

W .Q6«a\ .OK 



VABUC XVIt-R&TinUI. TERBKD SDIXS AND RXTKKKAI. BSOAKtt 



eeeoo 

■ OKIl I 

oassi I 



[ .iTTftn \ .» 
1 .DTOBlV 3i 



.«mu .OBHI R 



tUU XVH,— MATinui. TXBSID S 



I MXI9 jocmasja. SEOAim 



/ .1»3«9 / 



VHra. Ex. see. 



IBIOO 

,uiiT .iieia 

.19183 .liens 

.12150 .near 

■isiae [ awwl , 



fULS XTU-NATDBAI. TXBSSD BtRXB AKD BZTZBltAL BBOUnm 





.. 


S9* 


SO 




■■ 


• 




Vera. 


B... 


Vers. 


KiBee. 


T„ 


Ex. BBC. 


Vera. 


EX.BM. 





.11709 


.13257 




















:ia!T6 


:is5ca 


14354 


:iftH3 


Ii548n 


: 4398 


ll06S4 












. 4373 


.13137 


.15509 


.4313 


.18704 














.13441 




. 4K8 






4 




! 3397 


!l3»6 


1 4409 


.18450 




. 4313 










.3346 


.laflOT 


. 4138 


.13470 


ll50«T 














.13823 




.13485 


.15587 


114378 


.10IS6 






!l1f»l 


'. 3380 


.13637 






.15008 


.14388 








.11815 


. 3398 


.13851 




llSBll 




.11403 








.iiaas 


.1341» 


.13006 


:n5oa 


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10 4737^ I 


xm 


1 sa \ 


^ 


\^{ia> 


\ 




"568" 



YaSlI: 3tv^m.— lengths of cikculak a&c& to 9ad i. 



Peg. 



length. 




1 .0174638 

2 .0349066' 

8 .0623599; 
4 .0698132 
6 .0872665 

6 .1047196 

7 .1221730 
-8 .1896268 

9 .1670796 

10 .1746329 

11 .191 

12 .2094396, 
18 .22689281 

14 .:.'443461 

15 .2617994] 

16 .279^27 

17 .2967060! 

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 

.8901179 

.9075712 

.9250245 

.9424778 

.9599311 

.9773814 

,9948371 

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. 



.4609142 
.4783675 
.496»?06 
.6132741 
.5307274 
.5481807 
.5656340 
.5880873 
.6005406 
.6179939 

.6354472 
6629005 
.6703538 
6878070 
.7062603 
.7227186 
.7401669 
.7576202 
.7750785 
.7926268 



2. 
2. 
2. 
2. 
2. 
2. 
2. 
2. 
2. 
2. 



8(w9o01 
8274834 
8448867 
8623400 
8797938 
8972466 
9146999 
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 
.0037815 
.0040724 
.0043633 
.0046642 
.0049451 
.0052360 
.0056269 
.0058178 

.0061087 
.006:»95 
.0066904 
.0069813 
•0072722 
.0075631 
.0078540 
.0081449 
.0084358 
.0087266 

.0090175 
.0093084 
.0095993 
.0098902 
.0101811 
.0104720 
.0107629 
.0110538 
.0113446 
.0116355 

.0119264 
.0122173 
.0125082 
.0127991 
0130(100 
.OiaSROO 
.0136717 
.0189626 
.0142.535 
.0146444 

.0148863 
.0151262 
.01.'54171 
.0157080 
.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 
.0002424 

.0002473 
.0002621 
.0002670 
.0002618 
.0002666 
.0002715 
.0003763 
.0002813 
.0002880 



\ 



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D 

O 



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QQ 

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o 



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if 


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s 
4 


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1 


lb 

• 


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9 


o 

• 


5 




J2; q\^\>a\^\^ 


\* 



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.