THE
KAILKOAD TAPER
THE THEORY AND APPLICATION OF A
COMPOUND TRANSITION CURVE
BASED UPON THIRTY-
FOOT CHORDS
BY
LEE PERKINS
FORMERLY ASSISTANT ENGINEER, SOUTHERN PACIFIC LINES IN
ARIZONA AND MEXICO
MEMBER AMERICAN RAILWAY ENGINEERING ASSOCIATION
FIRST EDITION
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS, INC.
LONDON: CHAPMAN & HALL, LIMITE]
1915
SV
COPYRIGHT, 1915
BY
LEE PERKINS
Stanbope ipress
F. H.GILSON COMPANY
BOSTON, U.S.A.
PREFACE
A VARIETY of transition curves are used on the different
railroads, most of them fully explained by published hand-
books. A number of years ago Mr. Wm. Hood, Chief
Engineer of the Southern Pacific, devised a compound
transition curve of unusual simplicity, and developed
several tables for this curve. For a number of years this
taper has been used on many roads with somewhat in-
complete data, usually in the form of blue prints.
This handbook has been prepared as an extension and
elaboration of Mr. Hood's earlier work, in an effort to
simplify the use of the taper, and to lessen the work of the
man in the field. With this in view, to a brief explanation
o^ the taper has been added the solution of all the usual
curve problems as applied to tapered curves. Since the
various transition curves differ only in their method of
development and their numerical values, differing not at
all in the method of inserting them between tangent and
curve, or between curves, these curve problems for
tapered curves are available for use with the tables of any
transition curve.
The transition curve herein developed is, theoretically, a
series of compound curves, each branch of the curve having
a thirty-foot chord (in the metric system a ten-meter
chord), the last branch compounding with the central
circular curve, the degree of curvature of the various
branches and ending with the main curve increasing in
direct arithmetical progression. The various tables are
to enable one to run in this series of compound curves with
iii
616268
IV PREFACE
the ease of running in a simple curve, and from a single
setting of the transit.
The primary taper tables give the various taper func-
tions for every thirty feet of taper. That all the tapers
may be available for use with all degrees and fractional
degrees of main curve, avoiding the use of inappropriate
taper lengths, additional tables have been furnished giving
the taper functions for main curves of intermediate degree,
the values having been trigonometrically interpolated.
If further interpolation be necessary it may be linear
between the values given in these tables of intermediate
values. In addition, fairly simple equations are given for
all the angular functions, frequently useful in setting
intermediate points on the taper.
The radius of main curve is assumed based on a fifty-
foot chord throughout, mainly because the roads that have
always used this taper have always used that radius.
However, this usage is in accordance with the present
tendency, obviating the necessity of using long chain
lengths in setting fifty-foot points, which are set much
more frequently than not.
All the functions of the taper for both field and drawing-
room work are given for eleven different tapers of increas-
ing taper increment, which with their forty to eight}^
lengths comprise some seven hundred tapers. Three of
these eleven, however, will be found to answer most needs
except in mountainous country.
The taper numbers used are those which have long been
employed for these curves, and are retained for the benefit of
present records, though a more logical system of number-
ing, such as the degree of curvature increment per thirty
feet of taper, might seem desirable, and is suggested for
use where this taper is hereafter adopted.
The problem of tapering old circular curves is essentially
a different one from locating new lines, and is handled
separately. The insertion of tapers between the branches
PREFACE * V
of compound curves should receive more attention than
it has generally had. A fairly simple solution of this
problem is given.
The tapers have been calculated for metric curves for
the use of the constantly increasing number of American
engineers in Mexico and South America, where this taper
is already extensively used.
Acknowledgments are due to the following, for the use
of tables reprinted from their respective books:
Professor Daniel Carhart, Logarithms of Numbers and
Trigonometric and Miscellaneous Formulas; Professor J.
C. Nagle, Logarithmic Sines and Cosines, Logarithmic
Tangents and Cotangents, Functions of a One Degree
Curve, Natural Secants and Cosecants, and Metric Con-
version Table; Mr. Walter Loring Webb, Logarithmic
Versed Sines and External Secants, Natural Sines, Cosines,
Tangents and Cotangents, and Natural Versed Sines
and External Secants; and the American Railway En-
gineering Association, for the Table of Theoretical Super-
elevation of Rails, prepared by its Committee on Track
and published in the Manual of that Association.
LEE PERKINS.
SILVER CITY, NEW MEXICO,
March, 1915.
CONTENTS
CHAPTER I
INTRODUCTION
PAGE
1. Purpose of the Taper 1
DEVELOPMENT OF THE TAPER
2. Series of Compound Curves 1
3. Central Angle, o 3
4. Co-ordinates x and y 3
5. Deflection Angles 3
6. Long Chords 3
7. t and d, giving location of B.C 6
CHAPTER II
LOCATION PROBLEMS
SIMPLE CURVES
8. Semi-Tangent, T 7
9. External, E 11
10. Tangent Offset and Distance along the Tangent to any
Point on a Curve 11
11. To Pass a Curve through a Given Point, uniting two Given
Tangents 11
12. To Pass a Curve of Given Radius through a Given Point,
and uniting with a Given Tangent 15
13. To Pass a Curve through two Given Points and uniting
with a Given Tangent 16
14. To fix upon a Tangent at the End of a Curve. 18
15. To Locate a Tangent to two Located Curves 20
16. To Relocate a Curve making the E.G. fall at a Given Point
in a Given Parallel Tangent f . 24
17. The Intersection of a Line with a Curve 26
COMPOUND CURVES
18. Partial Taper between the Branches of the Compound
Curve 27
vii
Vlll CONTENTS
PAGE
19. Taper Functions of the Partial Taper 28
20. To find the Semi-Tangents, both Radii and both Central
Angles given 31
21. To Compound a Simple Curve so the E.G. shall fall in a
Given Parallel Tangent, both Radii given 33
22. To Compound a Simple Curve so the E.G. shall fall in a
new Located Tangent, both Radii, or both Central Angles
given 34
23. To find the Second Semi-Tangent and the Central Angles,
one Semi-Tangent, the Intersection Angle and both Radii
given 36
CURVES BEYOND THE FROG
24. Taper beginning at the Heel of Frog 37
CHAPTER III
FIELD WORK
25. Selection of the Taper 40
26. Laying out a Tapered Curve 41
OBSTRUCTIONS ON THE TAPER
27. Curve run from Main Curve Produced 42
28. Curve run from a Point beyond the C.C 44
29. Taper Points set by Offset. ..', 45
30. Taper Points set from Point on Semi-Tangent 45
31. Curve Notes for the Field Book 46
CHAPTER IV
OFFICE WORK
32. Plotting a Tapered Curve 47
33. Paper Location with Tapers 47
34. Curve Compensation with Tapers 47
35. Right of Way Descriptions with Tapers 48
CHAPTER V
TAPERING OLD TRACK
36. Condition of Track 49
37. Operating Conditions 50
CONTENTS IX
METHODS OF INSERTING TAPERS
SIMPLE CURVES
PAGE
38. Shifting the Curve 50
39. Shifting the Tangents 52
40. Shifting Curve and Tangents 53
41. Increasing Degree of Curve 53
42. Increasing Degree and Shifting Curve 54
43. Maintaining Length of Line Unchanged 55
44. Increasing Degree and Shifting Curve and Tangents 57
45. Combination of Methods 57
46. Increasing Degree of Portion of Curve 59
COMPOUND CURVES
47. Similarity of Procedure 59
48. Shifting the Curves 59
49. Shifting Curves and Tangents 60
50. Shifting Lighter Branch and Increasing Degree of Sharper
Branch 60
51. Field Work with Compound Curves 61
TABLES
Radii of Curves and their Logarithms 63
Notation used in the Taper Tables 69
Important Equations abstracted from the Text 69
Taper , A = 1 71
1 ,A = 'J 74
U, A = f 78
2 , A = 1 82
21, A = 11 86
2i A = U - 90
2f, A = 2 94
3 , A = 2 97
3i, A = 3 100
3, A = 4 103
3,f A =5 105
Comparative Values of I, d, and o V 108
Maintaining Length of Line Unchanged 115
Logarithms of Numbers 117
Logarithmic Sines and Cosines 135
Logarithmic Tangents and Cotangents 150
Logarithmic Versed Sines and External Secants 165
X CONTENTS
PAGE
Functions of a One Degree Curve 210
Natural Sines, Cosines, Tangents and Cotangents 240
Natural Secants and Cosecants 263
Natural Versed Sines and External Secants 276
METRIC TABLES
Radii of Curves and their Logarithms 299
Notation used in the Taper Tables 305
Important Equations abstracted from the Text 305
Taper , A = 307
1 , A = i 310
U, A = f 313
2 , A = 1 317
2i A = H. 321
2, A = H 325
2f, A = 2 329
3 , A = 2^ 333
3J, A = 3 337
3, A = 4 340
3f , A = 5 342
Comparative Values of I, d, and o 344
Mutual Conversion of Feet and Inches into Meters and Centi-
meters 351
Trigonometric and Miscellaneous Formulas 352
Super-elevation of Rails on Curves , 355
THE RAILROAD TAPER
CHAPTER I
INTRODUCTION
PURPOSE OF THE TAPER
1. Tapered curves have gained such wide us^age that
it is needless to dwell at length on their advantages.
Where circular curves alone are used, the transition from
tangent to curve is sudden, giving a decided lurch to the
cars, unpleasant to passengers and damaging alike to
rolling stock and track. Running the super-elevation
back on the tangent does not obviate this, and it can be
remedied only by increasing the curvature gradually, in-
creasing the super-elevation of rails at the same time.
This the tapered curve accomplishes in a satisfactory
and practical manner, much as it has always been [done by
track foremen, who lined in an approximate taper by eye.
The proper use of the taper, however, insures a , uniform
curve beyond the taper, a result not easily obtained by the
trackman unaided.
DEVELOPMENT OF THE TAPER
2. The railroad taper consists, theoretically, of a series
of short curves, each of thirty-foot chord lengttj, and of
uniformly increasing curvature, compounding at:; the end
with the central main curve. The various tapirs differ
merely in the curvature increment, and, therefore, in the
length needed to lead up to the curvature of the main
curve. Fig. 1 illustrates the first one hundred and twenty
1
THK RAILROAD TAPER
DEVELOPMENT OF THE TAPER 3
feet of Taper 2, compounding with the main five-degree
curve.
3. The central angle (o) of the taper is, of course, the
summation of the central angles of its parts.
4. In Fig. 2 is shown the same curve represented by
its thirty-foot chords, showing the method of obtaining
the x and y co-ordinates of the chord-points referred to
the initial tangent and the B.C. (beginning of curve) of the
taper. The angle k is the azimuth of the various chords,
referred to the initial tangent, and the x and y co-ordinates
are the departures and latitudes of the chord-points.
These co-ordinates are given in the tables.
5. From x and y were calculated for the tables the deflec-
tion angles (/) from the initial tangent at the B.C. to the
various chord-points, by the equation
tan/ = I- (1)
y
The backsight deflection (6) from tangent at any chord-
point to the B.C. equals the central angle of the taper
up to that point minus the deflection at the B.C. to that
chord-point, and is given in the tables.
As shown in Fig. 3, the deflection from tangent at any
chord-point to any other chord-point equals the azimuth
of the long chord between the chord-points, minus the
central angle of the taper up to the first chord-point.
x" x'
This azimuth is the angle whose tangent is -77 -,-
y y
As shown in Fig. 4, the backsight deflection from tangent
at any chord-point to any other chord-point is
and is given in the tables.
6. The long chord (Ic) from the B.C. to any chord-
point, given in the tables, is
Ic = -^-,- (2)
cos/
THE RAILROAD TAPER
FlQ. 3.
FIG. 4.
FIG. 6.
(5)
THE RAILROAD TAPER
Similarly, as in Fig. 5, the long chord between any other
chord-points is
IP'-" - y y o\
cos (e' +/'-")
7. In order to make room for the taper, the simple curve
may be considered as offset from its natural position a
distance from the tangent that will be called d, the taper
beginning at a point back of this offset position of the
B.C. of the simple curve a distance along the tangent that
will be called t.
This tangent distance, t, is very nearly half the length
of the taper, its exact value, from Fig. 6, being
t = BD - IE
= y R sin o, (4)
where R is the radius of the main curve, and o the central
angle of the taper.
The value of the circular curve offset, d, from Fig. 6, is
d = DE - HI
= x R vers o. (5)
The values of t and d are given in the tables.
These two equations, 4 and 5, are the fundamental
equations of the taper, locating the center of curvature
of the main curve with reference to the tangents and the
beginning and end of curve. The equations are identical
in form for all transition curves, and similar values under
different letter designations are invariably given in their
tables. On these two distances, t and d y are based all the
solutions of curve problems in the succeeding chapters.
CHAPTER II
LOCATION PROBLEMS
8. To Find the Semi-tangents of a Tapered Curve.
Given R and / to find T.
FIG. 7.
CASE I. Tapered at both ends with the same taper.
From Fig. 7,
T = AD + AB
= t + OA tan J 7
= + (# + d) tan 1 7. (6)
7
8
THE RAILROAD TAPER
In the tables is given a value D = R + d, so the above
may be written
T = t + D tan } 7. (7)
Example. Find the semi-tangent of a 5 00' curve,
tapered with Tap. 2, total angle of curve 35 04'.
By Eqn. 7 log D 5 Tap 2 3 . 05949
log tan 17 32' 9.49960
2.55909
362.32
t = 59.99
T = 422.31
CASE II. Tapered at one end only.
It may occasionally be necessary to taper one end only
of a curve, or, considering the parallel offset tangent, to
treat the curve as tapered at one end only.
FIG. 8.
In this case the two semi-tangents will be of different
lengths, the one for the tapered end being the longer, when
I is less than 90, by an amount less than t.
From Fig. 8.
MN = MK = dcscI,
T t = t + OAtauI - MN
= t + D tan J / - d esc I, (8)
T n = R tan J I + d esc 7. (9)
LOCATION PROBLEMS 9
These equations do not change for angles greater than
90, the algebraic sign of the last term remaining un-
changed.
Example. Find the semi-tangents of a 7 00' curve,
tapered at the B.C. with Tap. 2J, no taper at the E.C. t
total angle of curve 54 22'.
By Eqn. 8 esc 54 22' 1 . 23037
d 0.95
615185
1 007333
1.0688515
2| 2.91360
Iogtan27ll / 9.71059
2.62419
420.91
+ t 54.98
475.89
1.07
B.C. to P. I. 474.82
By Eqn. 9 log R r 2.91309
log tan 27 11' 9.71059
2.62368
420.42
+ 1.07
P.I. to E.G. 421.49
CASE III. Tapered at both ends, with different tapers.
From Fig. 9,
MN = MK = d l cseI,
BM = dz esc I,
BJ = BN = MN - BM
= (di d%) esc /,
Ti = ^ + A tan J / - (di - 4)' esc 7. (10)
T 2 = t* + I> 2 tan J7 - (d z - di) esc/. (11)
These equations do not change for angles greater than
90, the algebraic sign of the last term remaining un-
changed.
10
THE RAILROAD TAPER
Example. Find the semi-tangents of a 10 00' curve,
tapered at the B.C. with Tap. 2i, and at the E.G. with
Tap. 3, total angle of curve 113 42'.
-t r -
By Eqn. 10
FIG. 9.
esc 113 42' (esc 66 18') 1.09211
4 - d, = 2.84 - 0.98 = 1.86
655266
873688
1 09211
log DIO Tap. 2i
log tan 56 51
By Eqn. 11
B.C. to P.I.
log DIO Tap. 3
log tan 56 51
2.03
2.76041
0.18500
2.94541
881.88
84.88
966.76
2.03
964.73
2.75900
0.18500
2.94400
LOCATION PROBLEMS 11
879.02
+fc 44.97
923.99
+ 2.03
P. I. to E.G. 926.02
9. Given M and J, to find the External, E.
CASE I. Tapered at both ends with the same taper.
From Fig. 7,
E = OB - R
= D sec j 7 - #, (12)
or ' E = (72 + d) sec J 7 - # - d + d
= (Jf2 + d) (sec J 7 - 1) + d
= D exsec J 7 + d. (13)
Example. Find the external of a 5 00' curve, Tap. 2,
total angle 27 12'.
By Eqn. 12 or 13, E = 33.88.
CASE II. Tapered at one end only, or at both ends, with
different tapers.
From Fig. 10,
E = VOA 2 + AB 2 -R
= VD* + (T - o 2 - R, (14)
or E = D sec tan- 1 ^^ - R, (15)
T t T t
where tan" 1 ^ is the angle whose tangent is j?
Example. Find the external to the curve given in the
example under equations 8 and 9.
By Eqn. 14 or 15, E = 102.24.
10. To Find the Tangent Offset and Tangent Distance
to any Point on the Curve.
From Fig. 11,
PD = AC + d
= RversI + d, (16)
ED = BD + t
= R sin / + t. (17)
12
THE RAILROAD TAPER
FIG. 10.
FIG. 11.
LOCATION PROBLEMS
13
Or from the Table of Functions of a 1 curve, AC is the
mid-ordinate for a central angle equal to 2 /, and BD is
half the long chord for a similar central angle.
11. Given a Point, P, referred to the JP.J., to find
the Radius of a Curve passing through F uniting the
Given Tangents.
Since the solution of this problem depends upon the
taper chosen and its value of d, and the choice of taper
depends largely upon the degree of curve, a trial solution
for an untapered curve is first made.
From Fig. 12,
FIG. 12.
OB .
sin y = sin a
R sec \ I .
-TT- sina
sin a
cosf
R = PO
sin a
sinx
PB.
(18)
(19)
14
THE RAILROAD TAPER
Since this problem occurs mainly in location, and it is
necessary merely to have the curve pass close to the
determining point without using a curve of fractional
degree, to allow room for the taper a curve of next higher
even degree is chosen, and when desirable it may be
determined as follows how close the chosen curve will pass
to the given point.
In Fig. 13, P is the point through which the curve should
pass, P r a point on the chosen curve radially opposite.
PP'=QP-R
= (OA - AD) 2 + (AB - CB) 2 - R
= V(D-PB sin 6) 2 + (D tan J / - PB cos 6) 2 - R. (20)
FIG. 13.
Example. In Fig. 13, let PB = 194.3, b = 42 24',
^4 22' r
I = 54 22'. Then o = 90 - 2 - 42 24'
= 20 25'.
By Eqn. 18, y = 23 05'
x = y -a= 2 40',
By Eqn. 19, R = 1456.8.
3 56' curve.
LOCATION PROBLEMS
15
Deciding now upon a 4 00' curve with Tap. 1, to
determine how close this curve will pass to point P:
By Eqn. 20, (D - PB sin 6) 2 =? 1698100
(D tan % I-PB cos 6) 2 = 351675
2049775
V2049775 = 1431.7
- R 1432.5
PP' = ~ - 0.8
The negative result shows that P is inside the curve
0.8 ft., which on most location is sufficiently close.
12. Find the B.C. of a Curve of Given Radius that will
pass through a Given Point referred to a Given Tangent.
\
FIG. 14.
From Fig. 14,
AB = R sin vers" 1
BP-d
D
(21)
f R times the sine of the angle whose versine is - ~ J
or R 2 = (D- BP)*
AB =
- (D- BP) 2 .
(22)
16
THE RAILROAD TAPER
Example. Given BP = 82 ft., M = 6 00', Tap. 2,
then D = 956.41, R = 955.04.
r>p 7
By Eqn. 21, vers- 1 -~ - = 22 45J',
3G9.45.
13. Given Two Points referred to a Tangent, to find
the Radius and B.C. of a Curve passing through them
and joining the Given Tangent with a Given Taper.
Since the solution of this problem depends upon the
taper chosen and its value of d, the choice of which depends
largely upon the degree of curve, a trial solution for an
untapered curve is first made.
FIG. 15.
In Fig. 15, given points P and S, referred to the tangent
by lengths DP and DS, and the angle a, to find the radius
OA and distance AD.
By geometry AD 2 = DP X DS,
AD = VDP X DS.
(23)
DB and BP may be obtained from a solution of the tri-
angle BDP.
LOCATION PROBLEMS
17
D
1 =
= AB 2 + (R - BP) 2
= AB 2 + R 2
AB 2 + BP 2
BP 2 ,
or
2BP
AB
sin 2 tan" 1 -r
(24)
(25)
A curve of next higher even degree is now chosen with
an appropriate taper, passed through S as in paragraph
12, and the distance of P from the curve determined as
follows.
FIG. 16.
From Fig. 16,
A'C = R sin vers" 1
or
- (D - CS) 2 ',
PP' = OP-R
= VOE 2 + EP 2 -R '
or
PP' =
= V(D - BP) 2 + A'B 2 - R,
D-BP
cos tan~
A'B
D-BP
-R.
(26)
(27)
(28)
(29)
18 THE RAILROAD TAPER
Example. DP = 94 ft., PS = 127 ft., angle a = 16 12'.
By Eqn. 23, AD = 144.1.
FromABDP, BP = 26.2
and DB = 90.3;
then AB = AD + DB = 234 . 4.
7?P
By Eqn. 25, tan- 1 =% = 6 23',
and # = 1060.7
5 24' curve.
Deciding now upon a 5 30' curve, Tap. 2, through S:
From A DSC, CS = 61.66
- d 1.05
CS-d= 60.61
and DC = 212.2
-DB 90.3
#C = 121.9.
By Eqn. 26, vei&- lCS ~ d = 19 38'
tt
and A'C = 350.06
-BC 121.9
A'B = 228.16.
By Eqn. 29, tan' 1 = 12 39',
and PP' = 0.14.
From the positive value of PP', P lies outside the curve
assumed. If the curve had not passed sufficiently close
to P, a slightly sharper curve would pass further out at
P', or if the curve had passed outside of P, a slightly
lighter curve would pass closer to P.
14. To Fix upon a Tangent at the End of a Curve.
In the previous problem of passing the curve through
two determining points and tangent to the back-located
tangent, it is not practical to first locate the tangent
LOCATION PROBLEMS
19
ahead and make an intersection. The curve must be
run in beyond the determining points, then a meander line
run to the next controlling point on the tangent ahead
and the tangent located as follows:
When the curve has reached a point A, Fig. 17, from
which a view may be had of the tangent desired, or of
some controlling point, B, on it, through which it is
desired to run the tangent because of properly supporting
ground, a flag may be sent to C, opposite B, (the uncer-
FIG. 17.
tainty of right angle direction will affect this very little),
and a distance therefrom equal to d of the taper. With
improvised targets of some nature, or double points and
angle between, a fairly accurate stadia shot may be
obtained, and with the angle from tangent at A to C, the
distance BL and the central angle of the rest of the curve
may readily be calculated.
From Fig. 17,
AG = 2R sin a,
OK = R cos a,
CF = VCG X AC,
OK
(30)
Rcosa
AC Rsina
20 THE RAILROAD TAPER
R
tan m =
R (3D
V(AC -2Rsma)AC
b = a + m n. (32)
Given b, AD and Z)L may be calculated by equations
9 and 8. Then
LB = CF -t
= V(AC - 2 # sin a) AC - t. (33)
Example. Assume a 5 30' curve, Tap. 2, to have been
run to point A. Distance AC by stadia is 610 ft., and
angle a is 6 10'.
By Eqn. 30, n = 64 19'.
By Eqn. 31, m = 66 01'.
By Eqn. 32, a 6 10'
+ ra 66 01'
- n 64 19'
6=7 52'.
By Eqn. 33, LB = 417.9.
15. To Connect two Located Curves by a Tangent.
In the preceding problem, if the next controlling point
had been on a curve, instead of a tangent, it would often
be necessary to locate this next curve first and then con-
nect the two curves by a tangent.
CASE I. Curves of contrary flexure.
Let AB and CD, Fig. 18, be the two located curves, to
locate tangent LM fitting the two curves with given
tapers, the curves being offset from the tangent di and d 2 ,
respectively, to provide room for the tapers.
From some point E on tangent at B, run one or more
courses, EF, to some point F on tangent at D. Calculate
the latitude and departures of N and with reference to
tangent at B as base and radius BN as meridian. The
difference of the latitudes equals OG, the difference of the
departures equals NG.
LOCATION PROBLEMS
21
Then,
NO = VOG 2 + NG 2 ,
OG
+ A + #2 +
cos c
a = 90 - e - c,
/ _ g, = a _ 6,
tt- f n/\*A
LM = ST - (t, +
= NO sine-
(34)
(35)
(36)
(37)
(38)
(39)
22
THE RAILROAD TAPER
Example. Given a 5 30' curve AB and a 4 00' curve
CD, to locate tangent connecting them, using Taper 2
on the 5 30' curve and Taper l on the 4 00' curve.
At B turn tangent to curve and set point E, and at D
turn tangent and set F. Assume BE = 100 ft., angle
/ = 9 11', EF = 384.0 ft., angle g = 6 38', FD = 100 ft.
Then a traverse from N to is as follows:
Course.
Length.
Azimuth.
Lat.
Dep.
NB .
1041.8
180 00'
-1041.8
BE..
EF..
100.0
384.0
90 00'
80 49'
+ 61.3
+ 100.0
4-379.1 -
FD
DO
100.0
1432 5
87 27'
177 27'
+ 4.4
-1431.1
+ 99.9
+ 63.7
NO
2491.5
165 03'
-2407.2
+642.7
From this traverse
NO = 2491.5,
. NG = 642.7,
GO = 2407.2,
e = 75 03'.
By Eqn. 36,
c = 6 23'.
By Eqn. 37,
a = 8 34'.
By Eqn. 38,
6 = 6 01'.
By Eqn. 39,
LM = 144.5.
By Eqn. 9,
BH = 85.08.
By Eqn. 8,
HL = 138.54.
By Eqn. 8,
MK = 133.54.
By Eqn. 9,
KD = 82.05.
If in this solution LM had been too short, or even
negative, one of the curves would have to be shifted or
sharpened, or the tapers shortened.
CASE II. Curves of similar flexure.
Determine NG and GO as in Case I.
LOCATION PROBLEMS
A FIG. 19.
Then from Fig. 19,
NO = VOG 2 + NG 2 ,
OG
i^e = m ,
cos c =
a = e + c - 90,
6=/ + <7-a,
LM = NOsmc- (ti
24
THE RAILROAD TAPER
Example. Assume the same conditions as in the
example under Case I, angle g merely being in the opposite
direction.
Then a traverse from N to is as follows:
Course.
Length.
Azimuth.
Lat.
Dep.
NB
1041 8
180 00'
-1041.8
BE
100
90 00'
+ 100
EF..
384.0
80 49'
+ 61.3
+379.1
FD
100
74 ir
+ 27 3
+ 96 2
DO
1432 5
344 IT
+ 1378 3
-390 4
NO
485.4
23 30'
+ 425.1
+184.9
From this traverse
By Eqn. 36a,
By Eqn. 37a,
By Eqn. 38a,
By Eqn. 39,
NO = 485. 4,
e = 90 - 23 30'
= 66 30'.
c = 3629'.
a = 12 59'.
6=2 50'.
LM = 156.1.
16. To Relocate a Curve so the E.C. shall fall at a
Given Point in a Given Parallel Tangent.
In Fig. 20 let ABC be the located curve, tapers omitted
for clearness, and DEF the required curve ending at F.
CG and GF are known.
By a solution of triangle KM I, KF becomes known.
The value of R 2 now depends solely upon the taper chosen
and its value of t% and d 2 , and may best be determined by
trial, using the tables of functions of a one-degree curve,
assuming at first a value of fe somewhat larger, or smaller
as the case may be, than t\. It will usually be sufficient
for the semi-tangent of the new curve approximately to
equal KF.
LOCATION PROBLEMS
25
Example. Assume curve ABC to be a 6 00' curve,
Taper 2, total angle 36 14'. CG = 7.1, GF = 42.4.
K I
FIG. 20.
From A KM I, KM = 9.7
and KI = 12.0.
By Eqn. 7, 1C = 387.88
+ KM 9.7
+ GF 42.4
KF = 440.0.
From Tables, 1 curve
TWW = 1874.7.
If the new curve were untapered,
1874.7
M
4.26.
440.0
If Taper 2 be used on the new curve, then
M
1847.7
M
\l
Apprbx. T.
4 45'
394.7
56.2
450.9
50'
387.9
57.5
445.4
55'
381.3
58.7
440.0
5 00'
374.9
60.0
434.9
26
THE RAILROAD TAPER
Assuming a 4 55' curve, Taper 2, then
by Eqn. 7, T 2 = 440.29.
In this particular case it is unnecessary to interpolate
to obtain a more exact value for the semi-tangents, 0.29 ft.
being sufficiently close. Linear interpolation between the
intermediate values given in the tables would be quite
accurate when necessary.
17. Intersection of a Line with a Curve.
In Fig. 21, given R, d, AB and angle 6, to find BP and
angle a.
tan n =
FIG. 21.
D
AB'
c = 180 - n -6,
' = n + 6' - 180,
sin n
OB .
sin e = ^ sin c
1
LOCATION PROBLEMS 27
(42)
n
= (e-c) (43)
sine
=/+</
= 90 - TO + e - c, (44)
<*'=/-</'
= 90 - n + c' - e'. (44a)
In equations 42 and 43, c' may be substituted for c with
no other changes.
Example. Given a 4 00' curve, Taper 1 J, A = 195.9
ft., 6 = 67 07'.
By Eqn. 40, n = 82 13'.
By Eqh. 41, c = 30 40'.
By Eqn. 42, e = 31 00'.
By Eqn. 43, BP = 16.34.
By Eqn. 44, a = 8 07'.
COMPOUND CURVES
18. A Taper between the Branches of a Compound
Curve is often more necessary than between curves and
tangents, as the change in curvature is often greater.
Only that portion of the complete taper required to gradu-
ally increase the curvature as desired, is used.
Example. Taper 2 from tangent to a 6 00' curve is
built up from 30 ft. of 1, 30 ft. of 2, 30 ft. of 3, 30 ft. of
4 and 30 ft. of 5 curves, but in compounding from a 2
to a 6 curve with Taper 2, the first 60 ft. is dropped off,
the deflection tables being used as if the transit were at
/ = 60, the length of taper to fit a curve of M = MI + A,
where MI is the degree of the lighter branch, and A the
curvature increment in degrees for the taper used.
28 THE RAILROAD TAPER
19. Taper Functions of the Partial Taper.
From the method of developing the taper, the length of
any taper from tangent is,
J = J(M-A). *(45)
Then the entire taper from tangent to fit the branch of
the compound curve of greater curvature is
OA
/ 2 = ^(M 2 -A), *(46)
and the length replaced by the branch of lesser curvature
is that needed to fit a curve of M = M i + A degree, or
Then the partial taper retained between the branches
of the compound has a length of
= (M 2 -M!-A). *(48)
In Fig. 22, Mi is the curve of lesser degree, M 2 the curve
of greater degree, and ABC the taper joining the two
curves, the tapers at the beginning and end of the com-
pound curve being omitted for clearness of diagram.
The two curves are offset from each other to make room
for the taper an amount KF = d r , radially to both curves,
* Equations 45, 46, 47, 48, 50, 51a, 56 and 57 are empirical
equations derived from the tables, and cannot be used with other
transition curves. When the taper functions of Mi and M 2 are
given in the tables these equations are not needed. When needed
for other transition curves, somewhat similar equations, but with
other constants, must be derived.
LOCATION PROBLEMS
29
the curve of greater curvature lying within the one of
lesser curvature.
d r = d for M = M 2 - M l (49)
to be taken from the tables.
The central angle of the partial taper is
9 (M 2 + Mi) (M 2 - Mi - A)
o,.
*(50)
or o c may be taken from the tables, being the difference
between o for / 2 and for li.
FIG. 22.
The common radial line, OF, divides this angle, o c ,
proportionally to the degrees of curve of the two branches
of the compound curve.
* See footnote, page 28.
30 THE RAILROAD TAPER
Let DA be tangent to the curve of lesser degree at the
beginning of the partial taper, and let the curve of greater
degree be backed up through angle o c , so that its tangent,
ET, shall be parallel to DA, then
t c = (Ri - R 2 - d r ) sin a, (52)
d c = R l -R*- t c cot a, (53)
or = (Ri Rz) vers a + d r cos a. (53a)
From Eqn. 4, y c = t c + # 2 sin o c . (54)
From Eqn. 5, z c = d c -+- #2 vers o c . (55)
Using the method of second differences with the tables,
the deflection to the end of the taper, from tangent at the
beginning of the partial taper, is
, (3 h + l e + 45) l c + 450 , .
fc ~ ~"
+ 2M 2 + A) (M 2 - M, - A)
fA
]
J.
Equation 56 may be used for obtaining all the deflec-
tions from tangent at A, the beginning of the partial taper,
to points on the taper, using for l c the distance of the point
beyond the beginning of the partial taper, A, li remaining
constant from equation 45.
Where MI is a multiple of A, the deflections to points
on the partial taper may be taken directly from the tables,
transit at I = li, deflection to I = li + Z c , using for l c the
distance of the point beyond the beginning of the partial
taper, A.
* See footnote, page 28.
LOCATION PROBLEMS 31
The angle of backsight to the beginning of the partial
taper, from tangent at the end of the taper, is
bs = o c -.f c . (58)
The long chord of the partial taper is, from Eqn. 2,
lc c = y c sec/ c . (59)
20. The Semi- tangents of the Compound Curve.
From Fig. 22 A = c - a, (60)
h = g + a. (61)
By Eqn. 8, SD = ti + >i tan J /i - * esc /i. (62)
By Eqn. 9, DA = Ri tan \ /i + di esc I lf (63)
By Eqn. 10
AG = t e + *D C tan \ 7 2 - (d c - eft,) esc /,. (64)
By Eqn. 11,
GH = t 2 + D 2 tan \ I 2 - (d 2 - d e ) esc 7 2 , (65)
DG = DA + AG. (66)
Solving triangle DNG gives values for DN and AfG.
Then SN = SD + DN, (67)
NH = NG + GH. (68)
Where it is desirable to obtain the semi-tangents of the
compound curve without first finding the taper functions of
the partial taper, DG may be drawn tangent to MI at F
and equations 62 to 68 become as follows:
SD = ti + Di tan i c - di esc c, (62a)
DF = #1 tan i c + di esc c, (63a)
FG = fA- tan } - (d r - A) esc g, (64a)
GH = k + D 2 tan J g - (4 - *) esc g, (65a)
DG = DF + TO, (66a)
>S^V = ^D + D^V, (67)
NH = NG + GH. (68)
Example. Given 7 = 114 24', c = 34 40', g = 7944',
Mi = 3 00', M-2. = 8 00 r . Use Taper 1 between tangent
* D c = B, + d c .
t D r = ft + dr.
32 THE RAILROAD TAPER
and 3 00' curve, Taper 2 between 3 00' and 8 00' curves,
and Taper 2J between the 8 00' curve and tangent.
Find the semi-tangents.
30
By Eqn. 48, l c = y (8 - 3 - 1)
= 120.
By Eqn. 49, and the tables,
d r = 0.79.
By Eqn. 50, o c = 9 (8 + 3) (8 - 3 - 1)
= 396',
= 6 36'.
9 X 3 (8 - 3 - 1)
By Eqn. 51a, a = - ^
= 108'
= 1 48'.
By Eqn. 52, t c = 37.47.
By Eqn. 53, d c = 1.38.
By Eqn. 54, y c = 119.80.
By Eqn. 55, x c = 6.13.
By Eqn. 57, f e = 175J' = 2 55|'.
By Eqn. 58, 6s = 3 40'.
By Eqn. 59, lc c = 119.96.
By Eqn. 60, /i = 32 52 ; .
By Eqn. 61, / 2 = 81 32'.
By Eqn. 62, SD = 637.26.
By Eqn. 63, DA = 564.59.
By Eqn. 64, AG = 656.32.
By Eqn. 65, GH = 683.74.
By Eqn. 66, DG = 1220.91.
FromADGW, NG = 727.57,
and DN =1326. 06.
By Eqn. 67, SN = 1963.32.
By Eqn. 68, NH = 1411 .31.
LOCATION PROBLEMS
33
21. Given a Located Curve, to Compound with Curve
of Given Radius so as to End on a Given Parallel Tangent,
using Three Tapers.
In Fig. 23, given located curve SAFV of radius Ri,
parallel tangent NH distant p from the original tangent
WV, Rz, di, d 2) d r , ti and fe, to find I lt 7 2 and NH.
FIG. 23.
OE = A - p - D 2 ,
OP = Ri-dr- R 2 ,
OE
COS =
OP
= Rj - R* + dj - d* - p
RI R% d r
c = I - g.
*(69)
(70)
* Where the new tangent is beyond the original tangent, requir-
ing Rz to be greater than K b p and d r in equations 69, 71 and 72
change sign. For d r see Eqn. 49.
34 THE RAILROAD TAPER
The new semi-tangents may now be determined by the
methods of the preceding problem. If the semi-tangents
of the two parts of the curve, very useful in running in the
curve, are not needed, the semi-tangents of the entire
curve may be obtained more easily as follows:
SN = (R! + di) tan J / - p esc / + *,, *(71)
NH = (Ri + di) tan J / - (Ri - Ri - d r ) sin g
'fe. *f(72)
Example. Given a located 4 30' curve, Taper 1J, in-
tersection angle 82 14', to compound onto a parallel
tangent 71 ft. beyond the original tangent, using a 2 45'
curve, Taper 1, with Taper 1 between the two curves.
ByEqn.69, C osg =
g = 24 14'.
By Eqn. 70, c = 58 00'.
By Eqn. 71, SN = 1258.99.
By Eqn. 72, NH = 1502.68.
22. Given a Located Curve, to Compound onto a new
Located Tangent, Point of Compound Approximately
Fixed, full Tapered.
In Fig. 24, AN' is the located curve, to be compounded
at about N' so as to unite with located tangent UF.
Run tangent to located curve at N', intersecting located
tangent. From Functions of a One-degree Curve deter-
mine degree of curve, M', with which to compound if
tapers were neglected. Then use such a degree of curve
that
fl 2 . ff _ * + *, (73)
and the resulting g will be very nearly g'.
* See footnote, page 33.
t Care should be taken to use a negative value for cot / when
/ is greater than 90.
LOCATION PROBLEMS 35
OE = OB + BF - FE
= R l cos]g f + N'C sin g' - (R 2 + A),
OP = Ri -R 2 -d r ,
OE
cos g = Qp
_ Ri cos g' + N'C sin g' - (ft + (fe) *,-,,
Rt-Rt- d r
Example. Given located 4 00' curve AN X , to com-
pound at about N f (N f to be about the center of the taper
between parts of the compound), so as to end on located
tangent CF. N'C = 340.5 ft., g' = 42 12', both meas-
ured on the ground.
i c u
FIG. 24.
From Functions of a 1 Curve:
T4212' = 2211.0,
R' = 5730 X ==
340.5
2211
= 882.4,
' = 629'+.
* For d r see Eqn. 49.
36 THE RAILROAD TAPER
By Eqn. 73, d 2 = 1 . 75 for 6 30' Tap. 2,
d r = 0.09.
A D 1.75 + 0.09
Approx. R 2 = 882 . 4
EB
= 881.52,
= 881.59.
406.53
Use 6 30' curve, Tap. 2.
By Eqn. 74,
COS0 =
550.79
= 42 26'.
23. Given one of the Semi-tangents of a Compound
Curve, the Intersection Angle, and both Radii, to find
the two Central Angles and the other Semi-tangent.
In Fig. 25, given SN, I, RI and R z , to find c, g, and NH.
FIG. 25.
OE = OTF + WU - UE
= (Ri + di) cos / + TN sin / - (R 2 + 4),
f)~D D _ E> J
0#
LOCATION PROBLEMS 37
(Ri + di) cos / + TN sin / - (fa + d)
Ri-R 2 - *d r
NH = LU - LN - UV + Z 2
= (#1 H- di) sin I - TN cos 7
- (fii - # 2 - *d r ) sin + fe. f(76)
Example. Given semi-tangent /V = 1963.32, MI =
3 00' Tap. 1, M 2 = 8 00' Tap. 2}, and Tap. 2 between
Mi and M 2 , / = 114 24', to find c, and N#.
212.62
By Eqn. 75, cos g = UQ2 7g >
g = 79 44'.
By Eqn. 76, NH = 1411.32.
TAPERS BEYOND THE FROG
24. When the Track Beyond the Turnout curves
back parallel to the main line, there is seldom room and
little need for a taper. When the track beyond the turn-
out curves almost immediately in the same direction as
the turnout, the taper is of much use, both as to looks and
from practical considerations.
It has been the practice on many roads to introduce a
short tangent, of twenty to thirty feet, beyond the frog,
before beginning the curve. This answers the double
purpose of giving the trackman room for an approximate
taper, and by removing the B.C. from the heel of the frog,
prevents the kink that otherwise is very likely to occur
there due to the rail joint on the outside rail. However,
this presents the very bad appearance and gives the bad
riding of the carefully avoided " broken-backed curve."
If the curve begin at the heel of the frog with a taper of
moderate length, both appearance and service are much
improved.
* For d r see Eqn. 49.
f When #2 is greater than Ri, d r becomes negative. When 7 is
greater than 90, cos / becomes negative.
38
THE RAILROAD TAPER
Considerable ease in location will often be obtained if
the curve beyond the taper may be handled as a simple
curve tangent to a parallel with the main line, instead of
with the tangent through the frog.
In Fig. 26, / is the distance from frog angle point to
actual point of frog, usually given by standard drawings.
It is
/ = \ (g + v) cot J F, (77)
where g = gauge, v = thickness of frog point, usually
one-half inch, and F = frog angle, m = length of frog
from actual point to heel.
L _ f _ *u.~ w~J
\ [p
FIG. 26.
Then
p = HE + KO - OD
= (f-+m + t)wnF+ (R + d)cosF-R, (78)
w = CH - SH - CP
= (f + m + cosF - (R + d) sinF -/. (79)
LOCATION PROBLEMS 39
From Eqn. 10,
AP = w + (R+p) tan J (F+I). - (p-d) esc (F+I). (80)
From Eqn. 11,
AN = t + (R+d) tan } (^+7) - (d-p) esc (F+7), (81)
sin/
The resulting calculations for the entire problem may
be longer than if the semi-tangent BT be calculated by
Eqn. 7, / + ra added, and triangle ACB solved. However,
p and w are very useful in a preliminary consideration of
the location of the turnout.
Example. Given a No. 9 turnout from a side track to
a branch line, with a 6 00' curve, Tap. 2J, intersection
angle 72 48', beginning at the heel of the frog, g = 4'-8i",
v = J", m = 8'-10", F = 6 22':
By Eqn. 77, / = 42.70.
By Eqn. 78, p = 10.70 + 949.72 - 955.04
= 5.38.
By Eqn. 79, w = 95.92 - 105.97 - 42.70
= -52.75.
The negative value of w means that S lies between P
andC.
By Eqn. 80, AP = - 52.75 + 794.08 - 4.88
= 736.45.
By Eqn. 81, AN = 44.99 + 790. 10 + 4.88
= 839.97.
By Eqn. 82, AB = 90.45.
CHAPTER III
FIELD WORK
SELECTION OF THE TAPER
25. The Selection of the Proper Taper for use on
each curve is an important function of the engineer. As
suggested elsewhere, the proper length of taper to use is
one on which the super-elevation of rails given the main
curve may be run off on the taper at from one-half to one
inch per rail length. This will suggest the use of Taper 1,
1J or 2, for curves that do not limit the speed of trains,
with a maximum length of about 360 ft., and thence
gradually decreasing in length as velocity and super-
elevation decrease, to a minimum of 90 ft. Although
some very short tapers are given in the tables, they are
for exceptional conditions. The Table of Comparative
Values will aid in the selection of the taper.
A table of the theoretical elevation needed to counter-
act the centrifugal forces is included with the other tables,
copied from the Proceedings of the American Railway
Engineering Association, but as the super-elevation de-
pends more upon the velocity of trains than upon the
degree of curve, and as this velocity varies with trains,
seasons and traffic, an arbitrary rule, usually a compromise,
is in force on most roads.
The beginning and end of every taper should be clearly
marked for the track foreman, so that he may know
between what points he is to give the rails a gradually
increasing super-elevation. The proper maintenance of
this gradual increase, however, is no easy task, even when
the points are well marked, and if the distance over which
40
FIELD WORK 41
it occurs be too great, and the increase in super-elevation
be too gradual, it is very likely to become and remain very
irregular, totally destroying the value of the taper.
Therefore, though theoretically a curve tapered through-
out might seem perfection, as maintained practically it
would be a very poorly riding curve. Too long a taper
is as bad as none.
The somewhat prevalent practice of fitting a circular
curve to the ground, and tangents at some undetermined
offset therefrom, then connecting the two by the neces-
sary taper to suit . the offset, has the support of a few
eminent engineers, but should be condemned as slipshod
work. It is rarely the case that more careful thought
and investigation will fail to place some other curve or
tangents in a different location, with a suitable taper
which should be chosen for totally different reasons.
The weight and velocity of trains, the weight and char-
acter of the engines and cars whose direction is to be
changed, and the amount and quickness of the change,
should alone govern the choice of taper.
If any additional cost of construction be involved in
the proper choice of taper, which is doubtful with good
choice of location, it would be justified by the resulting
lessened operating costs. Most certainly the higher
quality of locating ability required to properly place a
line to suit economic conditions is well able to solve this
lesser problem.
LAYING OUT A TAPERED CURVE
26. After the location of tangents and main curve has
been decided upon and choice of taper made, the B.C.
and E.C. should be set by measurement from the P.I.
The taper at each end should then be run from the B.C.
and E.G., the C.C. to the main curve being set preferably
by long chord from the B.C. and E.G., and then the main
curve should be run from C.C. to C.C. of tapers, or from
42 THE RAILROAD TAPER
each C.C. to the middle of the curve if it is unusually
long.
It is usual, especially for final track centers, to stake the
taper every thirty feet from B.C. and E.G., closing to the
C.C. with a short chord where the length of taper, I, is
not a multiple of 30 ft. ; but on location, and especially for
slope staking on construction, it is often desirable to
stake the station and plus fifty points, which may be done
by obtaining the deflections from Eqn. 107.
If the main curve is of moderate length, it is usual,
with the transit at the C.C., to turn the transit at the
B.C. with the backsight deflection set on the reverse side of
the vernier, thus bringing the instrument into tangent
at the C.C. with the vernier at zero, and thence run in
the main curve with foresight on the other C.C. If the
main curve is unusually long, and the other C.C. not
visible, this involves running a comparatively long curve
from a short backsight, frequently resulting in poor
closing. In this case a flag may be set at an offset from
the initial tangent equal to x of the taper, preferably
opposite the P.I., but in any event as far from the C.C.
as the curve to be run from it. With the vernier set at
the total central angle of the taper, o, and the instrument
directed at this flag, bringing it into a direction parallel
to the initial tangent, the instrument will then be tangent
to the taper at the C.C. when the vernier is brought to
zero.
PASSING OBSTRUCTIONS ON THE TAPER
27. Curve run from Main Curve Produced.
It frequently happens that either the B.C. or C.C. of
the taper is inaccessible, when it is often necessary to run
the main curve from the offset B.C. of a simple curve, or
from a point on the simple curve produced backward as
far as necessary beyond the B.C. of the simple curve, such
point being set by offset from the initial tangent.
FIELD WORK
43
In Fig. 27, point C is the B.C. of the simple curve, D
the B.C. and B the C.C. of the taper. The central angle
of the portion of the simple curve from C to B is the
central angle of the taper, o. Point A, a distance back
on the simple curve equal to CB, and about opposite the
B.C. of the taper, is a point frequently chosen from which
FIG. 27.
to run the main curve, because of the ease with which its
position may be determined. Its offset from tangent is
x of the taper, and its distance along the tangent from the
B.C. of the taper is
n = y 2 R sin o.
From Eqn. 4, R sin o = y t,
then n = 2t-y. (83)
Any other point, E, may be chosen, its offset from
tangent being,
r=d + R vers I', (84)
where I' is the central angle of the curve back of the B.C.
of the simple curve.
The distance along the tangent from the B.C. of the
taper is
s = Z- fivers/'. (85)
This is merely equivalent to suggesting that the main
curve may be run in beyond the C.C. from any point back
of the C.C. by considering it a simple curve from a parallel
tangent.
44 THE RAILROAD TAPER
28. Curve run from a Point Beyond the C.C.
When on location the C.C. is in a bad position to occupy
with the transit, a point may be set on the main curve
beyond the C.C. from a point on the semi-tangent, by
working the problem under paragraph 17 backwards.
The plus of the point to be set is assumed, and from that
angle a, Fig. 28, is known. D and A B are known. Then
tann=^, (86)
OB = , (87)
cosn
g = a - (90 - n)
= a + n - 90. (88)
Solving triangle OBP, two sides and the included angle
given,
tan (c + }(/)= |^| tan \ g, (89)
b = 180 - n - c, (90)
sine
For point P', equations 88 and 90 become
g' = 90 - (a' + n), (88a)
&' = 180 - n + c', (90a)
the other equations remaining the same.
Example. Given a 4 00' curve, Taper 1|, C.C. in a
poor location for a transit set up, the second station
beyond, 137.9 ft. from the C.C., being a particularly
good transit point. On the same ridge with this second
station is a point on the semi-tangent, PoST, 260.89 ft.
from the B.C. Determine the angle and distance from
PoST to PoC.
a = 4 X 0.6' X 137.9 + 2 36'
= 8 07'.
By Eqn. 86, n = 82 13'.
By Eqn. 87, OB = 1446.50.
By Eqn. 88,
By Eqn. 89,
By Eqn. 90,
By Eqn. 91,
FIELD WOKK
= 20'.
\- 1 g = 30 50',
c = 30 40'.
6 = 67 07'.
BP = 16.34.
45
FIG. 28.
FIG. 29.
29. Taper Points set by Offset.
When both the B.C. and the C.C. are inconvenient to
occupy with the transit, the taper points may be set by
offset from the tangent, using x and y, or they may be
set by offset from the tangent on the first half and from
the curve on the second half. In the latter case the offset
from the curve is the same as from tangent at equal
distances from B.C. and C.C.
30. Taper Points set from Point on Semi-tangent.
A few or all of the taper points are occasionally set by
measurement and angle from a point on the semi-tangent,
PoST, by a solution of the triangle in Fig. 29.
tan b =
AB =
CB-y 1
CB-y
cos b
(92)
(93)
46 . THE RAILROAD TAPER
31. Curve Notes for the Field Book.
Assuming the B.C. at Sta. 489 + 15.2, the transit
notes for a tapered curve would be as follows:
497
O +62.2 441i' 2 37*' E.G.
+32.2 4 14i'
498 +02.2 341i'
+ 72.2 3 02|'
+42.2 2 17J'
495 +12.2 l26i'
+82.2 029i' I = 195
+67.2 1323J' 13 23*' C.C. Tap. 2 o = 7 18|'
494 10 52'
+50 8 59*' TA = 41 24'
493 7 07' T = 387.16
+50 . 5 14*' Ext. = 55.64
492 3\22' R = 764.08
+50 129*' L m = 357.0
O 491 +10.2 2 37*' 4 e 41i' C.C. 7 30' R A = 26 46*'
+ 95.2 2 16*'
+65.2 139' t = 97.41
+ 35.2 107*' d = 2.71
490 +05.2 042' x = 8.93
+ 75.2 022*' lc = 194.86
+45.2 009' I = 195
+15.2 00' B.C. Tap. 2 o = 7 18|'
489
In the above, the deflections for the taper at the E.G.
are given from tangent at the C.C., calculated from the
equation
,, _
J 300
A
an empirical equation derived from the tables by the
method of second differences, in which I is the distance
from B.C. or E.G. to the point for which deflection is
wanted, and s is the distance of the transit from B.C. or
E.G. The equation gives the deflection in minutes, and
is from tangent at the transit. The deflections from
tangent at the C.C. given in the notes above are merely
to make the notes complete. Usually both tapers are
run from B.C. and E.G. towards the main curve, using
the same set of deflections.
CHAPTER IV
OFFICE WORK
32. Plotting a Tapered Curve.
In the plotting of tapered curves, it is customary, after
plotting the tangents and locating the B.C. and E.G., to
draw the simple curve in its offset position, then draw a
curve of radius twice that of the main curve extending
from B.C. and E.G. a distance equal to I, the length of
the taper, coinciding with the main curve at the C.C.
The difference between such a curve and the exact taper
is noticeable only if the drawing be on a very large scale.
33. Paper Location with Tapers.
The usual method of paper location with tapers, as
indeed frequently in location on the ground, is to offset
the simple curve from its tangents an amount equal to
d for the taper chosen. If curves predominate, they will
be located first, and with parallel curves near their prob-
able ends of radius greater by d, the tangents may be
drawn in their offset position. If tangents predominate,
they will be drawn first, with short parallel tangents near
their probable ends, and the curves drawn tangent to
these offset tangents.
After the location of the simple offset curves, and the
tangents, the tapers may be drawn or merely indicated as
desired, depending upon the scale of map used.
34. Curve Compensation with Tapers.
It is a practice on some roads to use a compensation on
the taper of half that on the main curve. An exactly
equivalent result, with a simpler and more satisfactory
grade line, is obtained if the change of grade from tangent
47
48 THE RAILROAD TAPER
to curve be made at the point opposite the offset position
of the B.C. of the simple curve, which is at the middle of
the taper, and a suitable vertical curve inserted.
This brings correct theoretical and practical results,
increasing the compensation in exact ratio with the curva-
ture, and is well suited to location in rough country, where
final consideration of the taper must be postponed until
the location of curves and tangents.
35. Right of Way Descriptions with Tapered Curves.
A suitable description of right of way when the taper
is used would be: ". . . , the center line of said rail-
road extending thence along a tangent N 1 14' W to
station 4937 -f- 48.2, a distance of 465 ft., thence along
a taper -to the right of curvature increasing one degree
every thirty feet to station 4938 + 98.2, a distance of
150 ft., thence along a 6 00' curve to the right (radius
955.04) to station 4945 + 42.8, a distance of 644.6 ft.,
thence along a taper to the right of curvature decreasing
one degree every thirty feet to station 4946 + 92.8, a
distance of 150 ft., thence along a tangent N 46 26|' E to
station 5052 + 47.1, a distance of 554.3 ft., . . . ."
CHAPTER V
TAPERING OLD TRACK
36. The Tapering of Old Track, located and con-
structed with circular curves only, calls for most careful
analysis of the conditions encountered, and generally
repays in results obtained a great deal of otherwise need-
less transit work. Although after long experience in this
particular work one may decide almost offhand upon the
taper to use and the changes to make in tangents and
curves, tjie beginner must usually make more than one
trial before arriving at the best results obtainable, which
usually combines with the most satisfactory curve for
operation the lowest cost in making the change in align-
ment. Such work is frequently complicated by bridges
on the curves or tangents near the curves, limiting the
amount track may be thrown, or by the slow, though
frequently very decided,' sliding of embankment on side
hill work, distorting the original circular curve.
It will also frequently be found that the trackman has
thrown the B.C. in towards the center of curvature,
lining in an approximate taper, and if the curve be short,
may have taken care of the additional curvature by throw-
ing the middle of the curve out. If the curve be long, it
will probably be found that a short portion beyond this
approximate taper is of unduly heavy curvature. On the
other hand, the passage of heavy engines of rigid wheel
base has frequently thrown the curve out at the B.C. and
E.C., with which is coupled unduly heavy curvature just
beyond. When allowed sufficient time, the engineer will
rerun the original simple curve to determine just where
the track is, before attempting to insert tapers. The
49
50 THE RAILROAD TAPER
resulting transit notes, with measured offsets to the track
as it is found, together with notes showing all bridges and
openings, narrow embankments and cuts, and points
where embankments and cuts may be cheaply widened
and where not, will give the engineer the data for a care-
ful office study of the conditions to be encountered.
With an understanding of the various methods suggested
below of inserting tapers, a tentative plan may be decided
upon for each curve, subject to revision when running in
the curves. Since the method involving the lowest maxi-
mum shift of track is the shifting of both curve and tan-
gents, which will then influence the next curve in each
direction, the entire series of curves and tangents must be
studied as a whole.
The insertion of tapers in old circular track will gener-
ally be accompanied by a resurfacing out of face of the
entire portion of the line involved, so that usually there
is no need to confine the shifting of track to the curves,
if the shifting of tangents also will improve results. If
the track may be ballasted at the same time the cost of
inserting tapers is practically eliminated.
37. Although, unfortunately, in the insertion of tapers
in old circular curve alignment, the physical conditions
encountered must very largely influence the choice of
taper, frequently necessitating the use oT short tapers,
the operating conditions due to amount and direction of
grade, velocity, weight and character of trains, amount
of traffic, direction of heaviest tonnage, etc., must not be
lost sight of, but must, as largely as possible, influence the
choice of taper.
METHODS OF INSERTING TAPERS IN CIRCULAR
TRACK. SIMPLE CURVES
38. Shifting the Curve. The simplest, though usually
the least desirable, method of making room for the taper
is by shifting the curve radially inward, the degree of
TAPERING OLD TRACK
51
curve remaining unchanged. The amount track will be
shifted will vary from zero at the new B.C. and E.G., to
MN, Fig. 30, at the middle of the curve (with equal tapers
at the two ends) , varying approximately with the distance
from B.C. or E.G.
MN = 00' = AB = d sec } L (95)
As this method will shorten the line somewhat, by an
amount equal to
S = 2
necessitating the cutting of rails under usual conditions,
it is to be avoided if possible except at summits, where
the rail joints are likely to be quite open, or at sags,
where the cutting of rails would be desirable to relieve
joints already too tight.
This method is limited to small values of d and 7, to
avoid throwing the inner rail onto or close to fresh em-
bankment, accentuating the tendency of the inner rail to
settle, especially on single and double track roads, where
the super-elevation must fit the speed of the fastest trains,
throwing a large part of the weight of slower trains upon
the inner rail.
52
THE RAILROAD TAPER
39. Shifting the Tangents. Where consecutive curves
are of contrary flexure, and in a lesser degree where of
similar flexure, shifting a short tangent, Fig. 31, forms a
desirable method of making room for the taper. The
tangent is shifted at its ends amounts approximately equal
to d of the tapers adopted.
b
FIG. 31.
With this method it is usual first to fit the main portion
of each curve as closely as desired by trial, not over-
looking provision for inserting a proper taper at the other
end of each curve, then connecting the two curves by a
meander line, preferably the old tangent, and proceeding as
in paragraph 15. Due to irregularities found in the track
it is not likely that these curves, fitted to the track as
found, will be exactly tangent to the old tangent, but this
is immaterial.
With this method the length of track is slightly in-
creased, but seldom enough to be objectionable.
TAPERING OLD TRACK
53
40. Shifting Curve and Tangents. This method,
Fig. 32, usually gives the most desirable rearrangement of
alignment, involving the 'lowest maximum throw of track,
and maintaining the length of line practically unchanged.
To obtain this latter result the tangents should be thrown
out about two-thirds of d of the taper opposite the old
B.C. and E.G., then run to an intersection and the curve
run in. The new curve will cross the old one on the
FIG. 32.
second half of the taper, the entire central portion of the
new curve lying inside the old curve, about one-third d
from it at the middle of the curve. These amounts will
vary with the length of the tangents and their resulting
angular shift.
41. Increasing the Degree of Curve. Where the pre-
ceding methods involve too great a throw of track with
the taper desired, the curve may be sharpened, as in Fig.
33, enough to make room for the taper.
d = (R - R') vers \ I. (97)
As the value of d depends upon both R' and the taper
chosen, which latter itself is influenced by R f , trial solu-
tions of the second half of this equation must be made
54
THE RAILROAD TAPER
until a desirable value is obtained for d. For a desirable
simplification of this point see the solution in the next
problem.
With this method of inserting tapers, track will be
thrown in toward the center of curvature throughout the
curve, the throw being a maximum about at the C.C. of
the tapers. This will be
h = (R- R') vers (} 7 - o). (98)
42. Increasing Degree and Shifting Curve. Curves
of odd minutes curvature are to be avoided as much as
possible, as, the trackman being unfamiliar with them,
they are difficult to maintain. If the curve of the pre-
ceding problem be sharpened so that (R R') vers \ I
will give a value greater than d, and the curve shifted away
from the center of curvature to bring it tangent to the
original tangents, Fig. 34, a desirable realignment is
obtained.
At the middle of the curve track will now be thrown out
an amount
or
h = [(R- R') vers } I - d] sec J 7, (99)
h= (R-D f ) exsec } 7 - d. (99a)
TAPERING OLD TRACK
55
For preliminary study, where I is not large, the factor
sec \ I may be disregarded as insignificant. The new
curve will now lie within the old throughout the tapers
and a portion of the main curve, and outside the old curve
on the middle portion of the main curve, a very desirable
rearrangement. The best balance is obtained by making
h equal about one-third d, when the maximum throw of
track at the three points of greatest divergence will be
about equal.
43. Maintaining Length of Line Unchanged. With
the proper value of h, Eqn. 99, R' may be assumed such as
to leave the length of line unchanged.
The length of line from A to B, Fig. 34, by the new
alignment is
(100)
The length of line from A to B by the old alignment is
1007
L = 2AC
M
1007
M
(101)
56 THE RAILROAD TAPER
The table on page 115 gives the values of M', I and h for
a large range of M and / with the more important tapers.
Where curves are sharper than ten-degree, tangents will
be short, and paragraphs 39 and 40 will give better results.
Where I is greater than given in the tables, paragraph 46
will usually give better results unless curves of fractional
minutes curvature are used.
When the value of M or 7 lies between those given in
the table, M' may be interpolated and then checked by
equations 100 and 101, recalculating when necessary. If
on the first trial L' L is too great, decrease M 1 '. The
irregularity of h in the table is due to using the nearest
minute for M'.
Equations 100 and 101 are based upon fifty-foot chord
measurement of both old and new curves, but any dis-
crepancy over arc measurement introduced is small and
may usually be neglected. With both curves based upon
a fifty-foot chord, increasing a 5 00' curve to a 5 15'
curve introduces a discrepancy due to arc excess of only
0.0002 ft. per hundred feet. With the old curve based
upon a hundred-foot chord and the new curve based upon
a fifty-foot chord the difference in arc excess is quite large,
especially with the higher degrees of curve, but this is
almost exactly balanced by the decreased value of AC,
equation 101, over that assumed for the table, due to the
increased value of R.
For arc measurement equations 100 and 101 become
L'(arc)=Z + ^, (lOOa)
L(arc) = 2*-2(fl-')tani/
Using these equations, if a 10 00' curve, I = 50 00',
be sharpened to a 10 17' curve, Tap. 3, as given in the
table, the new alignment would be 0.04 ft. longer than the
old. The curve would have to be sharpened to a 10 16'
curve, Tap. 3, to maintain the length unchanged.
TAPERING OLD TRACK
57
The length of line may be maintained unchanged with
many of the other problems in this chapter by arranging
by the manner of shifting curves and tangents that
approximately half the new alignment lie within and half
without the old.
44. Increasing Degree and Shifting Curve and Tan-
gents* Where / is large the smallest increase of curvature
Avoiding odd minutes will frequently give too large a value
for h of equation 99, when to avoid throwing the curve out
too much at the middle the tangents may be thrown in
at the B.C. and C.C. of the old curve, as in Fig. 35.
c + h = (R-R') vers \l - d (approx.). (102)
For the best balance of track h should about equal c.
The new tangents may be run to an intersection, new
external calculated and h checked on the ground, and if
satisfactory the curve run in.
45. Any of the preceding methods may be combined
in any one curve, by shifting the tangent at one end only
58
THE RAILROAD TAPER
FlG. 38.
TAPERING OLD TRACK 59
either the full or partial amount of d, and the curve at the
other end, or the tangents may be shifted different amounts
at the two ends of the curve, thus taking advantage of
different widths of roadbed available at different points.
On heavy grades a shorter taper may be used at the
lower end of the curve when room is limited, due to the
lower speed of ascending trains.
46. Increasing Degree of Portion of Curve. Where I
is too great to sharpen the entire curve, and the tangents
too long to be shifted advantageously, a portion only of
the curve may be sharpened to make room for the taper,
as in Fig. 36. The difference between the degree of the
old curve and the portion sharpened should preferably not
be greater than the curvature increment of the taper to
be used, and may often be less.
-r (103)
/' must of course be larger than the central angle of the
taper, or the increase in curvature to provide the offset
has been too great. I' should not be less than twice 0,
and may usually be as much as three times o.
COMPOUND CURVES
47. Any combination of the preceding problems of
this chapter may be used in inserting tapers at the ends
or between the branches of old compound curves. A few
of the possible combinations follow.
48. Shifting the Curves. In Fig. 37 the relative values
of the various d's are exaggerated, increasing the angular
change in the position of the point of compounding. How-
ever, this arrangement disturbs the branch of sharper
curvature disproportionately, which may be modified as in
Fig. 38 by shifting the branch of lighter curvature for the
entire amount of d r .
60
THE RAILROAD TAPER
49. Shifting Curves and Tangents. Where both the
curves and tangents may be shifted, as in Fig. 39, the
FIG. 39.
maximum throw of track may be much reduced. This
aids particularly with the branch of sharper curvature.
50. Shifting the Lighter Branch, and Increasing the
Curvature of the Sharper Branch. This change of align-
FIG. 40.
ment is shown in Fig. 40. With this may of course
be combined the shifting of the end of the sharper branch
to avoid curvature of odd minutes, as in paragraph 42, or
also the shifting of one or both tangents as in paragraph 44.
TAPERING OLD TRACK
FIELD WORK
61
51. The principal objection to compound curve align-
ment is the difficulty trackmen find in maintaining it to
proper curvature. It follows that in inserting tapers in
compound curves it is seldom profitable to make any
lengthy calculations based upon the theoretical location
of the curves. They will be somewhere else.
The best, method of procedure is to pick out portions of
the curves of apparently fairly uniform curvature, which
can be tested with the mid-ordinate to a hundred-foot
tape held against the rail at the ends of the tape, set up the
transit on these portions, extend them as far in each direc-
tion as they fit the track fairly well, then turn tangents and
intersect as in Fig. 41. It will usually be found that these
FIG. 41.
curves, fitted to the track, are not tangent to each other nor
to the original tangents, the offsets from which may or may
not be in a direction to facilitate the insertion of tapers.
62 THE RAILROAD TAPER
At the tangent ends, the existing offset from tangent is,
from Fig. 41,
c = AB sin a R vers a. (104)
Between the two branches of the compound curve, the
existing offset along the common radial line may be found
from Fig. 41.
A solution of right triangles OPK and O'PS will give the
sides O'P and OP and the included angle / of triangle
O'PO, from the solution of which 00' and angle g may be
obtained, from which angle n may be obtained. Then
m = b n, (105)
e = R' - R - O'O. (106)
With these data the shifting of curves and tangents
most desirable may be decided upon. 'Then to insure
perfect fitting of the curves to each other and to their
tangents, the tangents may be located in their new posi-
tions, the longer of the two branches located in its new
position by the problem in paragraph 12, and then the
shorter of the two branches located by the problem in
paragraph 22.
TABLES
63
RADII
25
, sin
,
Deg.
Radius.
Log rad.
Deg.
Radius.
Log. rad.
1
Deg.
Radius.
Log. rad.
000'
Infinite
100'
5729.60
3.75812
2 00'
2864.82
3.45710
1
343775.76
5.53627
1
5635.67
3.75095
1
2841.15
3.45349
2
171887.41
5.23524
2
5544.77
3.74388
2
2817.86
3.44992
3
114591.60
5.05915
3
5456.76
3.73693
3
2794.95
3.44637
4
85943.67
4.93421
4
5371.50
3.73010
4
2772.41
3.44286
5
68754.94
4.83730
5
5288.86
3.72336
5
2750.23
3.43937
6
57295.78
4.75812
6
5208.73
3.71673
6
2728.41
3.43591
7
49110.67
4.69118
7
5130.99
3.71020
7
2706.93
3.43248
8
42971.83
4.63318
8
5055.53
3.70377
8
2685.78
3.42907
9
37197.19
4.58203
9
4982.26
3.69743
9
2664.96
3.42569
10
34377.47
4.53627
10
4911.09
3.69118
10
2644.46
3.42234
11
31252.24
4.49488
11
4841.92
3.68502
11
2624.27
3.41901
12
28647.89
4.45709
12
4774.67
3.67895
12
2604.39
3.41571
13
26444.80
4.42234
13
4709.26
3.67295
13
2584.81
3.41243
14
24555.34
4.39016
14
4645.63
3.66704
14
2565.52
3.40918
15
22918.30
4.36018
15
4583.69
3.66121
15
2546.52
3.40595
16
21485.92
4.33215
16
4523.37
3.65546
16
2527.79
3.40274
17
20222.04
4.30583
17
4464.63
3.64979
17
2509.35
3.39956
18
19098.60
4.28100
18
4407.39
3.64418
18
2491.16
3.39640
19
18093.80
4.25753
19
4351.60
3.63865
19
2473.24
3.39327
20
17188.74
4.23524
20
4297.21
3.63319
20
2455.57
3.39015
21
16370.20
4.21405
21
4244.16
3.62779
21
2438.16
3.38706
22
15626.13
4.19385
22
4192.40
3.62246
22
2420.99
3.38399
23
14946.70
4.17555
23
4141.87
3.61720
23
2404.06
3.38095
24
14323.89
4.15606
24
4092.58
3.61200
24
2387.36
3.37792
25
13750.99
4.13833
25
4044.43
3.60686
25
2370.90
3.37491
26
13222.11
4.12130
26
3997.39
3.60177
26
2354.67
3.37193
27
12732.40
4.10491
27
3951.46
3.59676
27
2338.65
3. ,36896
28
12277.67
4.08912
28
3906.56
3.59179
28
2322.85
3.36602
29
11854.34
4.07388
29
3862.66
3.58689
29
2307.26
3.36310
30
11459.17
4.05915
30
3819.75
3.58203
30
2291.88
3.36019
31
11089.52
4.04491
31
3777.77
3.57724
31
2276.70
3.35731
32
10742.97
4.03112
32
3736.71
3.57249
32
2261 . 72
3.35444
33
10417.66
4.01777
33
3696.53
3.56779
33
2246.94
3.35159
34
10111.03
4.00480
34
3657.21
3.56315
34
2232.35
3.34876
35
9822.15
3.99221
35
3618.71
3.55855
35
2217.95
3.34595
36
9549.31
3.97997
36
3581.02
3.55401
36
2203.73
3.34316
37
9291.65
3.96809
37
3544.10
3.54951
37
2189.70
3.34038
38
9046.71
3.95649
38
3507.93
3.54505
38
2175.84
3.33763
39
8814.75
3.94521
39
3472.50
3.54064
39
2162.15
3.33489
40
8594.38
3.93421
40
3437.78
3.53628
40
2148.64
3.33216
41
8384.76
3.92341
41
3403.74
3.53196
41
2135.29
3.32946
42
8185.12
3.91303
42
3370.37
3.52768
42
2122.12
3.32677
43
7994.77
3.90281
43
3337.65
3.52344
43
2109.09
3.32410
44
7813.13
3.89282
44
3305.56
3.51924
44
2096.24
3.32144
45
7639.45
3.88306
45
3274.08
3.51509
45
2083.53
3.31880
46
7473.38
3.87352
46
3243.19
3.51097
46
2070.98
3.31618
47
7314.37
3.86418
47
3212.88
3.50689
47
2058.56
3.31357
48
7161.99
3.85503
48
3183.13
3,50285
48
2046.33
3.31098
49
7015.82
3.84608
49
3153.93
3.49885
40
2034.22
3.30840
50
6875.51
3.83730
50
3125.26
3.49489
50
2022.26
3.30584
51
6740.70
3.82870
51
3097.10
3.49096
51
2010.43
3.30329
52
6611.09
3.82027
52
3069.45
3.48706
52
1998.74
3.30076
53
6486.33
3.81200
53
3042.29
3.48320
53
1987.19
3.29824
54
6366.22
3.80388
54
3015.60
3.47937
54
1975.77
3.29574
55
6250.46
3.79591
55
2989.38
3.47558
55
1964.48
3.29325
56
6138.85
3.78809
56
2963.61
3.47182
56
1953.32
3.29077
57
6031 . 15
3.78640
57
2938.28
3.46809
57
1942.28
3.28831
58
5927.17
3.77285'
58
2913.38
3.46440
58
1931.37
3.28587
59
5826.71
3.76542
59
2888.89
3.46073
59
1920.58
3.28343
64
THE RAILROAD TAPER
RADII (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
3 00'
1909.91
3.28101
4 00'
1432.47
3.15608
5 00'
1146.01
3.05919
1
1899.36
3.27861
1
1426.52
3.15430
1
1142.20
3.05774
2
1888.93
3.27622
2
1420.63
3.15248
2
1138.42
3.05630
3
1878.61
3.27384
3
1414.78
3.15069
3
1134.66
3.05487
4
1868.40
3.27147
4
1408.99
3.14891
4
1130.93
3.05344
5
1858.30
3.26912
5
1403.24
3.14713
5
1127.20
3.05201
6
1848.31
3.26677
6
1397.53
3.14536
6
1123.54
3.05059
7
1838.42
3.26445
7
1391.88
3.14360
7
1119.88
3.04917
8
1828.65
3.26213
8
1386.26
3.14185
8
1116.24
3.04776
9
1818.97
3.25983
9
1380.70
3.14010
9
1112.63
3.04635
10
1809.40
3.25753
10
1375.17
3.13836
10
1109.04
3.04495
11
1799.93
3.25525
11
1369.70
3.13662
11
1105.48
3.04355
12
1790.56
3.25299
12
1364.26
3.13490
12
1101.94
3.04216
13
1781.27
3.25073
13
1358.87
3.13318
13
1098.42
3.04077
14
1772.09
3.24849
14
1353.53
3.13146
14
1094.92
3.03938
15
1763.01
3.24625
15
1348.21
3.12976
15
1091.44
3.03800
16
1754.01
3.24403
16
1342.95
3.12806
16
1087.99
3.03662
17
1745.11
3.24182
17
1337.72
3.12637
17
1084.56
3.03525
18
1736.30
3.23962
18
1332.54
3.12468
18
1081.15
3.03389
19
1727.57
3.23744
19
1327.39
3.12300
19
1077.76
3.03252
20
1718.93
3.23526
20
1322.29
3.12133
20
1074.39
3.03116
21
1710.38
3.23309
21
1317.22
3.11966
21
1071.05
3.02981
22
1701.92
3.23094
22
1312.19
3.11800
22
1067.72
3.02846
23
1693.53
3.22879
23
1307.21
3.11634
23
1064.42
3.02711
24
1685.23
3.22666
24
1302.26
3.11470
24
1061.13
3.02577
25
1677.01
3.22454
25
1297.34
3.11305
25
1057.87
3.02443
26
1668.87
3.22242
26
1292.47
3.11142
26
1054.62
3.02310
27
1660.81
3.22032
27
1287.63
3.10979
27
1051.40
3.02177
28
1652.83
3.21823
28
1282.82
3.10817
28
1048.19
3.02044
23
1644.92
3 21614
29
1278.05
3.10655
29
1045.01
3.01912
30
1637.09
3.21407
30
1273.32
3.10494
30
1041.84
3.01780
31
1629.33
3.21201
31
1268.62
3.10333
31
1038.69
3.01649
32
1621.64
3.20996
32
1263.96
3.10173
32
1035.57
3.01518
33
1614.03
3.20791
33
1259.33
3.10014
33
1032.46
3.01387
34
1606.49
3.20588
34
1254.73
3.09855
34
1029.37
3.01257
35
1599.02
3.20385
35
1250.17
3.09697
35
1026.29
3.01127
36
1591.62
3.20184
36
1245.64
3.09539
36
1023.24
3.00998
37
1584.28
3.19983
37
1241.15
3.09382
37
1020.20
3.00869
38
1577.01
3.19784
38
1236.68
3.09226
38
1017.19
3.00740
39
1569.81
3.19585
39
1232.25
3.09070
39
1014.19
3.00612
40
1562.68
3.19387
40
1227.85
3.08915
40
1011.20
3.00484
41
1555.61
3.19190
41
1223.48
3.08760
41
1008.24
3.00356
42
1548.60
3.18994
42
1219.14
3.08606
42
1005.29
3.00229
43
1541.66
3.18799
43
1214.84
3.08452
43
1002.36
3.00102
44
1534.78
3.18605
1 44
1210.56
3.08299
44
999.45
2.99976
45
1527.96
3.18411
45
1206.31
3.08146
45
996.55
2.99850
46
1521.19
3.18218
46
1202.10
3.07994
46
993.67
2.99724
47
1514.49
3.18027
47
1197.91
3.07842
47
990.81
2.99599
48
1507.85
3.17736
48
1193.75
3.07691
48
987.96
2.99474
49
1501.27
3.17646
49
1189.62
3.07541
49
985.13
2.99350
50
1494.74
3.17457
50
1185.51
3.07391
50
982.32
2.99225
51
1488.27
3.17268
51
1181.44
3.07241
51
979.52
2.99101
52
1481.86
3.17081
52
1177.40
3.07092
52
976.74
2.98978
53
1475.50
3.16894
53
1173.38
3.06944
53
973.97
2.98855
54
1469.19
3.16708
54
1169.39
3.06796
54
971.22
2.98732
55
1462.94
3.16523
55
1165.43
3.06649
55
968.48
2.98609
56
1456.75
3.16338
56
1161.49
3.06502
56
965.76
2.98487
57
1450.60
3.16155
57
1157.58
3.06355
57
963.06
2.98365
58
1444.50
3.15972
58
1153.70
3.06209
58
960.37
2.98244
59
1438.46
3.15790
59
1149.84 3.06064
59
957.70
2.98123
TABLES
65
RADII (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
6 00'
955.04
2.98002
7 00'
818.64
2.91309
8 00'
716.34
2.85512
952.39
2.97882
1
816.69
2.91206
1
714.85
2.85422
2
949.76
2.97762
2
814.76
2.91103
2
713.37
2.85332
3
947.15
' 2.97642
3
812.83
2.91000
3
711.90
2.85242
4
944.55
2.97522
4
810.92
2.90898
4
710.43
2.85152
5
941.96
2.97403
5
809.01
2.90795
5
708.96
2.85062
6
939.39
2.97284
6
807.11
2.90693
6
707.50
2.84973
7
936.83
2.97166
7
805.22
2.90592
7
706.05
2.84884
8
934.28
2.97048
8
803.34
2.90490
8
704.60
2.84795
9
931.75
2.96930
9
801.47
2.90389
9
703.16
2.84706
10
929.23
2.96812
10
799.61
2.90288
10
701.73
2.84617
11
926.73
2.96695
11
797.75
2.90187
11
700.30
2.84528
12
924.24
2.96578
12
795.91
2.90086
12
698.88
2.84440
13
921.76
2.96462
13
794.07
2.89986
13
697.46
2.84352
14
919.29
2.96346
14
792.24
2.89886
14
696.05
2.84264
15
916.84
2.96230
15
790.42
2.89786
15
694.64
2.84176
16
914.41
2.96114
16
788.61
2.89686
16
693.24
2.84089
17
911.98
.2.95999
17
786.80
2.89587
17
691.85
2.84t)01
18
909.57
2.95884
18
785.01
2.89487
18
690.46
2.83914
19
907.17
2.95769
19
783.22
2.89388
19
689.08
2.83827
20
904.78
2.95655
20
781.44
2.89290
20
687.70
2.83740
21
902.41
2.95540
21
779.67
2.89191
21
686.33
2.83653
22
900.05
2.95427
22
777.91
2.89093
22
684.96
2.83567
23
897.70
2.95313
23
776.15
2.88995
23
683.60
2.83480
24
895.36
2.95200
24
774.40
2.88897
24
682.25
2.83394
25
893.04
2.95087
25
772.66
2.88799
25
680.90
2.83308
26
890.72
2.94974
26
770.93
2.88702
26
679.55
2.83222
27
888.42
2.94862
27
769.21
2.88604
27
678.21
2.83136
28
886.13
2.94750
28
767.49
2.88507
28
676.88
2.83051
29
883.86
2.94638
29
765.78
2.88410
29
675.55
2.82966
30
881.59
2.94527
30
764.08
2.88314
30
674.22
2.82880
31
879.34
2.94416
31
762.39
2.88218
31
672.90
2.82795
32
877.09
2.94305
32
760.70
2.88121
32
671.59
2.82710
33
874.86
2.94194
33
759.02
2.88025
33
670.28
2.82626
34
872.64
2.94084
34
757.35
2.87930
34
668.98
2.82541
35
870.44
2.93974
35
755.69
2.87834
35
667.68
2.82457
36
868.24
2.93864
36
754.03
2.87739
36
666.39
2.88373
37
866.05
2.93754
37
752.38
2.87644
37
665.10
2 82289
38
863.88
2.93645
38
750.74
2.87549
38
663.81
2^82205
39
861.71
2.93536
39
749.10
2.87454
39
662.54
2.82121
40
859.56
2.93428
40
747.48
2.87360
40
661.26
2.82037
41
857.42
2.93319
41
745.85
2.87265
41
659.99
2.81954
42
855.28
2.93211
42
744.24
2.87171
42
658.73
2.81871
43
853.16
2.93103
43
742.63
2.87077
43
657.47
2.81788
44
851.05
2.92996
44
741.03
2.86984
44
656.22
2.81705
45
848.95
2.92888
45
739.44
2.86890
45
654.97
2.81622
46
846.86
2.92781
46
737.86
2.86797
46
653.72
2.81539
47
844.78
2.92674
47
736.28
2.86704
47
652.48
2.81457
48
842.71
2.92568
48
734.70
2.86611
48
651.25
2.81375
49
840.65
2.92461
49
733.14
2.86519
49
650.02
2.81293
50
838.60
2.92355
50
731.58
2.86426
50
648.79
2.81211
51
836.56
2.92250
51
730.03
2.86334
31
647.57
2.81129
52
834.53
2.92144
52
728.48
2.86242
52
646.35
2.81047
53
832.51
2.92039
53
726.94
2.86150
53
645.14
2.80966
54
830.50
2.91934
54
725.41
2.86058
54
643.93
2.80884
55
828.50
2.91829
55
723.88
2.85967
55
642.73
2.80803
56
826.51
2.91725
56
722.36
2.85875
56
641.53
2.80722
57
824.53
2.91620
57
720.85
2.85784
57
640.34
2.80641
58
822.55
2:91516
58
719.34
2.85693
58
639.15
2.80560
59
820.59
2.91413
59
717.84
2.85603
59
637.96
2.80480
66
THE RAILROAD TAPER
RADII (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
9 00'
636.78
2.80399
10 00'
573.14
2.75826
11 00'
521.07
2.71690
1
635.60
2.80319
1
572.19
2.75754
1
520.28
2.71624
2
634.43
2.80239
2
571.24
2.75682
2
519.50
2.71558
3
633.27
2.80159
3
570.29
2.75610
3
518.71
2.71493
4
632.10
2.80080
4
569.35
2.75538
4
517.93
2.71427
5
630.94
2.79999
5
568.41
2.75466
5
517.16
2.71362
6
629.79
2.79920
6
567.47
2.75394
6
516.38
2.71297
7
628.64
2.79840
7
566.53
2.75323
7
515.61
2.71232
8
627.49
2.79761
8
565.60
2.75251
8
514.84
2.71167
9
626.35
2.79682
9
564.67
2.75180
9
514.07
2.71102
10
625.21
2.79603
10
563.75
2.75109
10
513.30
2.71037
11
624.08
2.79524
11
562.83
2.75038
11
512.54
2.70972
12
622.95
2.79445
12
561 91
2.74967
12
511.77
2.70908
13
621.82
2.79367
13
560.99
2.74896
13
511.02
2.70843
14
620.70
2.79288
14
560.08
2.74825
14
510.26
2 70779
15
619.58
2.79210
15
559.17
2.74754
15
509.50
2.70714
16
618.47
2.79132
16
558.26
2.74684
16
508.75
2.70650
17
617.36
2.79054
17
557.36
2.74613
17
508.00
2.70586
18
616.25
2.78976
18
556.46
2.74543
18
507.25
2.70522
19
615.15
2.78898
19
555.56
2.74473
19
506.50
2.70458
20
614.05
2.78821
20
554.66
2.74403
20
505.76
2.70394
21
612.96
2.78743
21
553.77
2.74333
21
505.02
2.70330
22
611.87
2.78666
22
552.88
2.74263
22
504.28
2.70267
23
610.78
2.78589
23
551.99
2.74193
23
503.54
2.70203
24
609.70
2.78512
24
551.11
2.74124
24
502.80
2.70140
25
608.62
2.78435
25
550.23
2.74054
25
502.06
2.70076
26 607.55
2.78358
26
549.35
2.73985
26
501.33
2.70013
27 606.48
2.78281
27
548.47
2.73916
27
500.60
2.69950
28 605.41
2.78205
28
547.60
2.73847
28
499.88
2.69887
29 604.35
2.78129
29
546.73
2.73777
29
499.16
2.69824
30
603.29
2.78052
30
545.87
2.73709
30
498.43
2.69761
31
602.23
2.77976
31
545.00
2.73640
31
497.72
2.69698
32
601 . 18
2.77900
32
544.14
2.73571
32
497.00
2.69635
33
600.13
2.77824
33
543.28
2.73502
33
496.28
2.69572
34
599.08
2.77749
34
542.42
2.73434
34
495.56
2.69510
35
598.04
2.77673
35
541.57
2.73365
35
494.85
2.69447
36
597.00
2.77598
36
540.72
2.73297
36
494.14
2.69385
37
595.97
2.77523
37
539.87
2.73229
37
493.43
2.69323
38*
594.93
2.77447
38
539.03
2.73161
38
492.73
2.69261
39
593.91
2.77372
39
538.18
2.73093
39
492.02
2.69198
40
592.89
2.77297
40
537.34
2.73025
40
491.32
2.69136
41
591.87
2.77223
41
536.51
2.72957
41
490.62
2.69074
42
590.85
2.77148
42
535.67
2.72890
42
489.92
2.69013
43
589.84
2.77074
43
534.84
2.72822
43
489.22 2.68951
44
588.83
2.76997
44
534.01
2.72755
44
488.53 j 2.68889
45
587.83
2.76925
45
533.18
2.72687
45
487.84
2.68828
46
586.82
2.76851
46
532.35
2.72620
46
487.15
2.68766
47
585.82
2.76777
47
531.53
2.72553
47
486.46
2.68705
48
584.83
' 2.76703
48
530.71
2.72486
48
485.77
2.68643
49
583.84
2.76629
49
529.90
2.72419
49
485.09
2.68582
50
582.85
2.76556
50
529.08
2.72352
50
484.40
2.68521
51
581.86
2.76482
51
528.27
2.72286
51
483.72
2.68460
52
580.88
2.76409
52
527.46
2.72219
52
483.04
2.68400
53
579.90
2.76335
53
526.65
2.72152
53
482.37
2.68338
54
578.93
2.76262
54
525.85
2.72086
54
481 . 69
2.68277
55
577.95
2.76189
55
525.05
2.72020
55
481.02
2.68216
56
576.98
2.76116
56
524.25
2.71953
56
480.35
2.68156
57
576.02
2.76044
57
523.45
2.71887
57
479.68
2.68095
58
575.05
2.75971
58
522.65
2.71821
58
479.01
2.68035
59
574.10
2.75899
59
521.86
2.71755
59
478.35
2.67974
TABLES
67
RADII (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
12 00'
477.68
2.67914
13 00'
440.97
2.64441
14 00'
409.51
2.61226
1
477.02
2.67854
1
440.41
2.64386
1
409.02
2.61175
2
476.36
2.67794
2
439.85
2.64330
2
408.54
2.61123
3
475.70
2.67734
3
439.29
2.64275
3
408.05
2.61072
4
475.05
2.67674
- 4
438.73
2.64219
4
407.57
2.61020
5
474.39
2.67B14
5
438.17
2.64164
5
407.09
2.60969
6
473.74
2.67554
6
437.61
2.64109
6
406.61
2.60918
7
473.09
2.67494
7
437.05
2.64054
7
406.13
2.60867
8
472.44
2.67435
8
436.50
2.63999
8
405.66
2.60816
9
471.79
2.67375
9
435.95
2.63944
9
405.18
2.60764
10
471.15
2. .67316
10
435.40
2.63889
10
404.70
2.60713
11
470.50
2.67256
11
434.85
2.63834
11
404.22
2.60662
12
469.86
2.67197
12
434.30
2.63779
12
403.75
2.60611
13
469.22
2.67138
13
433.75
2.63724
13
403.28
2.60560
14
468.58
2.67078
14
433.21
2.63669
14 402.81
2.60510
15
467.94
2.67019
15
432.66
2.63615
15 402.33
2.60459
16
467.31
2.66960
16
432.12
2.63560
16 401.87
2.60408
17
466.68
2.66901
17
431.58
2.63506
17 i 401.40
2.60357
18
466.04
2.66843
18
431.04
2.63451
18
400.93
2.60307
19
465.41
2.66784
19
430.50
2.63397
19
400.46
2.60256
20
464.79
2.66725
20
429.96
2.63343
20
400.00
2.60206
21
464.16
2.66667
21
429.42
2.63289
21
399.53
2.60155
22
463.53
2.66608
22
428.89
2.63235
22
399.07
2.60105
23
462.91
2.66550
23
428.36
2.63181
23
398.61
2.60055
24
462.29
2.66491
24
427.82
2.63127
24
398.15
2.60005
25
461.67
2.66433
25
427.29
2.63073
25
397.69 i 2.59954
26
461.05
2.66375
26
426.76
2.63019
26
397.23
2.59904
27
460.43
2.66317
27
426.23
2.62965
27
396.77
2.59854
28
459.82
2.66259
28
425.71
2.62911
28
396.32
2.59804
29
459.20
2.66201
29
425.18
2.62858
29
395.86
2.59754
30
458.59
2.66143
30
424.66
2.62804
30
395.41
2.59704
31
457 98
2.66085
31
424.14
2.62750
31
394 95
2.5C655
32
457.37
2.66027
32
423.62
2.62697
32
394.50
2.59605
33
456.77
2.65970
33
423.09
2.62644
33
394.05
2 59555
34
456.16
2.65912
34
422.57
2.62590
34
393 . 60
2.59505
35
455.56
2.65855
35
422.06
2.62537
35
393.15
2 59456
36
454.96 | 2.65797
36
421.54
2.62484
36
3S2.70
2.59406
37
454.36
2.65740
37
421.02
2.62431
37
392.56
2.59357
38
453 . 76
2.65682
38
420.51
2.62378
38
391.81
2.59307
39
453.16
2.65625
39
420.00
2.62325
39
391.36
2.59258
40
452.57
2.65568
40
419.49
2.62272
40
390.91
2.59209
41
451.97
2.65511
41
418.98
2.62219
41
390.48
2.59160
42
451.38
2.65454
42
418.47
2.62166
42
390.04
2.59110
43
450.79
2.65397
43
417.96
2.62133
43
389.60
2.59061
44
450.20
2.65340
44
417.45
2.62061
44
389.16
2.59012
45
449.61
2.65284
45
416.95
2.62008
45
388.72
2.58963
46
449.02
2.65227
46
416.44
2.61955
46
388.28
2.58914
47
448.44
2.65170
47
415.94
2.61903
47
387.84
2.58865
48
447.86
2.65114
48
415.44
2.61851
48
387.40
2.58816
49
447.28
2.65057
49
414.94
2.61798
49
386.97
2.58767
50
446.70
2.65001
50
414.44
2.61746
50
386.53
2.58719
51
446.12
2.64945
51
413.94
2.61694
5*1
386 . 10
2.58670
52
445.54
2.64889
52
413.44
2.61642
52
385.67
2.58621
53
444.96
2.64832
53
412.95
2.61589
53
385.24
2.58573
54
444.39
2.64776
54
412.45
2.61537
54
384.81
2.58524
55
443.82
2.64720
55
411.96
2.61485
55
384 '.38
2 58476
56
443.25
2.64664
56
411.47
2.61434
56
383.95
2.58423
57
442.67
2.64608
57
410.98
2.61382
57
383.52
2 58379
58
442.11
2.64553
58
410.49
2.61330
58
383.09
2.58331
59
441.54
2.64497
59
410.00
2.61278
59
382.67
2.58282
68
THE RAILROAD TAPER
RADII (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
15 00'
382.25
2.58234
19 00'
301.91
2.47988
23 00'
249.53
2.39712
05
380.14
2.57994
05
300.59
2.47797
15
246.86
2.39245
10
378.05
2.57755
10
299.28
2.47608
30
244.24
2.38782
15
375.99
2.57518
15
297.99
2.47420
45
241.68
2.38324
20
373.95
2.57281
20
296.71
2.47233
25
371.93
2.57046
25
295.44
2.47047
24 00'
239.17
2.37871
30
369.93
2.56812
30
294.18
2.46861
15
236.71
2.37422
35
367.96
2.56580
35
292.94
2.46678
30
234.30
2.36978
40
366.00
2.56348
40
291.69
2.46492
45
231.95
2.36539
45
364.07
2.56118
45
290.46
2.46309
50
362.16
2.55890
50
289.25
2.46127
25 00'
229.64
2.36104
55
360.26
2.55662
55
288.04
2.45945
15
227.37
2.35673
30
225.15
2.35248
16 00'
358.39
2.55436
20 00'
286.84
2.45764
45
222.98
2.34827
05
356.54
2.55211
05
285.66
2.45585
10
354.70
2.54986
10
284.48
2.45405
26 00'
220.84
2.34408
15
352.88
2.54763
15
283.31
2.45226
15
218.75
2.33995
20
351.09
2.54542
20
282.15
2.45048
30
216.69
2.33584
25
349.31
2.54321
25
281.00
2.44871
45
214.68
2.33179
30
347.55
2.54101
30
279.86
2.44695
35
345.80
2.53883
35
278.73
2.44518
27 00'
212.70
2.32776
40
344.08
2.53666
40
277.61
2.44344
15
210.76
2.32379
45
342.37
2.53450
45
276.50
2.44170
30
208.85
2.31983
50
340.68
2.53234.
50
275.40
2.43996
45
206.98
2.31593
55
339.00
2.53020
55
274.30
2.43823
28 00'
205.14
2.31205
17 00'
337.34
2.52807
21 (xy
273.22
2.43651
15
203.33
2.30820
05
335.70
2.52595
05
272.14
2.43479
30
201.56
2.30440
10
334.07
2.52384
10
271.07
2.43309
45
199.81
2.30062
15
332.46
2.52174
15
270.01
2.43138
20
330.87
2.51965
20
268.96
2.42969
29 00'
198.10
2.29688
25
329.29
2.51758
25
267.91
2.42799
15
196.42
2.29318
30
327.72
2.51551
30
266.88
2.42632
30
194.76
2.28950
35
326.17
2.51344
35
265.86
2.42465
45
193.13
2.28585
40
324.64
2.51140
40
264.83
2.42298
30 00'
191.53
2.28224
45
323.12
2.50936
45
263.82
2.42131
50
321.61
2.50733
50
262.83
2.41966
55
320.12
2.50531
55
261.82
2.41800
18 OO 7
318.64
2.50330
22 00'
260.83
2.41637
05
317.17
2.50129
05
259.85
2.41472
10
315.72
2.49930
10
258.88
2.41310
15
314.28
2.49732
15
257.91
2.41147
20
312.86
2.49534
20
256.95
2.40986
25
311.44
2.49337
25
256.00
2.40824
30
310.04
2.49142
30
255.05
2.40664
35
308.66
2.48948
35
254.12
2.40504
40
307.28
2.48754
40
253.19
2.40344
45
305.92
2.48561
45
252 . 26
2.40185
50
304.57
2.48368
50
251.35
2.40027
55
303.23
2.48177
55
250.44
2.39870
TABLES 69
NOTATION
A = Curvature increment of taper per 30 ft. of taper.
M = Degree of main circular curve.
I Length of taper from the B.C. of the taper.
/ = Deflection from tangent at the B.C. of the taper.
ft /i> /2> etc. = Deflection from tangent at some point on the
taper.
6 = Deflection from tangent at the end of the taper, C.C. of
main curve, to the B.C. of the taper.
o = Central angle of the taper at each end of the curve.
d = Circular curve offset from tangent to provide room for
the taper.
t = Distance along the tangent, from opposite the offset
position of the B.C. of the simple curve to the B.C. of
the taper.
D = R + d, where R is the radius of the main circular curve.
x and y are co-ordinates of points on the taper, referred to the
tangent at the B.C. of the taper as meridian, and to a
radial line at the B.C. of the taper as base.
Ic = Long chord of the taper, from the B.C. of the Taper to
points on the taper.
5 = Distance along the taper, from the B.C. of the taper to the
transit, when an intermediate set-up is necessary.
T = Semi-tangent of the entire tapered curve, from P.I. to
B.C. or E.G.
E = External, the distance from the P.I. to a point on the
curve radially opposite.
EQUATIONS
Eqn. No.
T = t + D tan | 7. (7) Both ends, the same
taper.
T t = t + D tan 7 - d esc 7. (8) Tapered end other
end not tapered.
T n = R tan \ I + d esc 7. (9) Untapered end other
end Xapered.
T 1 = ti + Di tan \ I - (di - dj esc 7. (10) Both ends tapered
with different tapers.
T-2 = t-i + D 2 tan / - ( - dj esc 7. (11) Both ends tapered,
with different tapers.
E = D sec \ I - R. (12) Both ends the same
taper.
70 THE EAILROAD TAPER
EMPIRICAL EQUATIONS DERIVED FROM THE
TABLES
I = ~ (M - A). (45)
(1 + 15)0 + 30)
/ 300
A
(l + 28 + 45)0-iQ+450
I (I + 30)
= "loo (10S)
TABLES
71
TAPER
INTERMEDIATE VALUES
A-J
11
I
/
b
o
D
logZ)
d
t
z
y
Ic
030
30.00
0021
0021
04*
11459.18
4.05915
0.01
15.00
0.02
30.00
30.00
35
40.00
0031
003|
007
9822.17
3.99221
0.02
20.00
0.04
40.00
40.00
40
50.00
0041
005f
010
8594 41
3.93422
0.03
25.00
0.06
50.00
50.00
45
60.00
005*
008
13*
7639.49
3.88306
0.04
30.00
0.10
60.00
60.00
50
70.00
007
010*
017*
6875.56
3.83731
0.05
35.00
0.14
70.00
70.00
55
80.00
008f
0131
022
6250.53
3.79592
0.07
40.00
0.20
80.00
80.00
100
90.00
010*
016*
027
5729.70
3.75813
0.10
45.00
0.27
90.00
90.00
05
100.00
012*
020
032*
5288.99
3.72337
0.13
50.00
0.36
100 00
100.00
10
110.00
014*
024
038*
4911 25
3.69119
0.16
55.00
0.47
110.00
110.00
15
120.00
016f
0281
045
4583.89
3.66123
0.20
60.00
0.59
120.00
120.00
20
130.00
0191
032|
052
4297.45
3.63321
0.24
65.00
0.73
130.00
130.00
25
140.00
022
D37*
059*
4044.72
3.60689
0.29
70.00
0.89
140.00
140.00
30
150.00
024f
42f
107*
3820.09
3.58207
0.34
75.00
1.08
149.99
150.00
35
160.00
027f
0481
1 16
3619.11
3.55860
0.40
80.00
1.29
159.99
160.00
40
170.00
030f
0541
125
3438.25
3.53634
0.47
85.00
1.52
169.99
170.00
45
180.00
034
1 00*
134*
3274.63
3.51516
0.55
90.00
1.79
179.98
179.99
50
190.00
037*
107
144*
3125.89
3.49497
0.63
94.99
2.08
189.98
189.99
55
200.00
0411
1 13|
1 55
2990.10
3.47569
0.72
99.99
2.40
199.98
199.99
200
210.00
045
121
206
2865.64
3.45722
0.82
104.99
2.75
209.97
209.99
05
220.00
049
128*
217*
2751.16
3.43952
0.93
109.99
3.13
219.96
219.98
10
230.00
053
136*
229*
2645.51
3.42251
.05
114.99
3.55
229.95
229.98
15
240.00
0571
144|
242
2547.70
3.40615
.18
119.99
4.00
239.94
239.97
20
250.00
lOlf
1531
255
2456.89
3.39039
.32
124.98
4.49
249.93
249.97
25
260.00
106*
202
308*
2372.36
3.37518
.46
129.98
5.02
259.92
259.97
30
270.00
nil
2111
322*
2293.50
3.36050
.62
134.98
5.59
269.90
269.98
35
280.00
1161
220f
337
2219.74
3.34630
1.79
139.97
6.20
279.88
279.95
40
290.00
1211
2 301
352
2150.61
3.33256
1.97
144.97
6.86
289.86
289.94
45
300.00
1 26*
241
407*
.2085.69
3.31925
2.16
149.96
7.56
299.84
299.94
50
310.00
1 32
251*
423*
2024.62
3.30634
2.36
154.96
8.30
309.81
309.93
55
320.00
1 37|
3021
440
1967.06
3.29382
2.58
159.95
9.09
319.78
319.91
300
330.00
143*
313*
457
1912.72
3.28165
2.81
164.94
9.93
329.74
329.89
05
340.00
149*
325
5 14*
1861.35
3.26983
3.05
169.93
10.82
339.70
339.87
10
350.00
155*
337
5 32*
1812.70
3.25833
3.30
174.93
11.76
349.66
349.85
15
360.00
201|
3491
551
1766.58
3.24713
3.57
179.92
12.75
359.61
359.83
20
370.00
2081
401f
610
1722.78
3.23623
3.85
184.90
13.80
369.55
369.81
25
380.00
2 15
414*
629*
1681.16
3.22561
4.15
189.89
14.90
379.49
379.78
30
390.00
221|
427f
649*
1641.56
3.21526
4.47
194.88
16.07
389.42
389.75
35
400.00
228f
4411
710
1603.82
3.20516
4.80
199.86
17.29
399.35
399.72
40
410.00
235f
4551
731
1567.82
3.19530
5.14
204.85
18.57
409.27
409.69
45
420.00
243
509*
752*
1533.46
3.18567
5.50
209.83
19.91
419.18
419.65
50
430.00
250*
524
814*
1500.61
3.17627
5.87
214.81
21.31
429.08
429 61
55
440.00
2581
538|
837
1469.20
3.16708
6.26
219.79
22.78
438.97
439.56
400
450.00
306
554
900
1439.14
3.15810
6.67
224.77
24.31
448.85
449.51
72
THE RAILROAD TAPER
u
cS
08
US
08
02
08
dt,
OS
i rrtT FHH "
- CO "*< O <N <N O5 <M CO T-I 10 b- to T-I Tt CO
O I-H <M <M (M T-I 1-1 O 1O CO T-I iO CO O CO
o CO CO CO CO CO CO CO CO <M CQ <M T- i T-H i i O
co
rt< tO
H<!'MNrt!N,*m,-('-ji n|THn|-n|-4iFH|M n',-
T- 1 10 1^ CD c^ o 10 cq o co rf oi i i .co
tO iO 10 10 >0 "^ CO <M O TH <N 1C CO .CO
T-ir- i O O ' O
,_i r* T-I o O 'Ot-t
Ot^- O5 i I t>-
ioC^ iC^OCO
<N (N (Tq C^ (M (M 1-1 I-H 1-1 1-1 O O 'Ot-^i-H
OO 'OOT-H <M
T-I CO (M 00 I-H i i t^ T i (M
CO CO CO <M C<J I-H 10 ^ (M
OOO ' O O T-I T-H (M CO
i-i i-HOOOOO O O T-I I-H (M C^ CO
OOOOOOO O O i i i i <N <N CO CO
. n|-m|-4i
:^^fe^
OOOOOO ' O O O I-H i i (M (M CO Tt<
^ '~ H ?O O OCO O5 GO O: -^ <N co
rH rH . ^H CO iO i-( CO O CO rH ^ CO
oOOOOO O O O I-H T-H (M <N CO CO rfn
-^Oi . i i CO CO Tt< t^ Tf rfi CD (M rH <M
T-I O .T-I <M-*O<N O^ COr-H 10
o OOOO O O O T-I T-I r-t
.
OOCO .O5T-icOiOCOi-HGOGOiMOOI^O
T-I T-I O . O (M CO 10 T-I Tj< O CO T-H Th (M T=(
o OOO 'OOOOTHrH <N (N COCOTJH 10
OO ' O O O O T-I TH T-H (M <N CO -^ ''t 1 10
.
<N . ^ C^ CO t^ TfH Tfl CO (M T-H CO OO O t^ rH
O .O T- i (M CO O T-I CO O CO O CO T-H 10 Tf
O ' O O O O O T-I T-H <M <M CO CO TJ* -^ 10
' O O O O O T- i T-H rH C^ C^l CO CO -*i >O O
r
TABLES
73
12
8
OiOiOOOOt-
^cocccocococoeococoeoeococcco
TficOt^-iOOOC^OOiOO^OOit^-CO
i-H^iO"tfC'OeOC<J<N<N<N'-H'-iT-t
O O O O r- 1 1-1 <M <M CO rJH rti iO CO !> OS
i-H^fb-OCOCOOiC^iO
o oOr-ii-Hi ii i
74
THE RAILROAD TAPER
dS
08
0?,
08
OS,
68
o
08
OS
08
08
08
OS
o't,
08
-*f ^ -^ Tf * "^ CO CO <N <M T-H O ' O <N
.
(MCO'^^COO-IOCOOOO'* !LQOO
CC CO CO CO CO CO CO <N (M > i O ' O i i CO
i-- . - - - -
(N CO CO CO <N (N (M T-H ,-H O 'Or-KMCO
_
(M O CO O O5 CO <M * O . iO CO * OO OO
(M CO CO <M i i O "* - i * . ^f CO CO CO "*
<N (M (N <N (N iM I-H 1-1 O 'O^H<NCOTt<
i i <N <M i-H i i i I i i O ' O i I <N CO rf 1C
- O to "*! l-^ to O T-H . COOO t>- N OQ.Ci '
CO CO CO <M T-H iO CO . CO T- i O O O O <
o T-I T-I r_| T-l T-l O O O T-H <M CO TjH tO CO
- 00 <M Oi i i t^ h- . I-H Oi
O i i O O Tti (M . CO O
1 I T-t T-H T-l O O ' O 1 1
-.-
i O <M i i
r^ rti O
.
r- 1 oo 00 <N . t^ O O CO (X) >O Oi Oi
itOrfiCOfN . (M O Tti (N i-H ^-i T-I <M
OOOOO O'-i
.
OO .C<lr-i|^
CO CO <N i i . (M iO (N
OOOO ;OOi-i
^^H
O <M
^T-^OCO .GOfNCOOCOr-HCOt^rfcOiO
CC, ^ ^, . _ T? r-l 10 CO <N i-H T-l (M CO >0
ooo ; o o i i - i <N co * to co t^ oo
oo ; o o i i T-i c<i <N co TJ< to co oo oi
o O ; O O O 1-1 i-i <N CO "* iO CO l^ CX3 01
oooo
TABLES
75
oOOCiO^o^ooi>-coccc5^i>-i>-
C^ ^D ^^ Oi O^ Oi Oi Oi Oti Oi QO 00 t*^* ^O
'->Oo0(
CO "^ CO t^ !> CO O5 "^ T-H ^^ t^ t> ^^
l> *-O "^ CO s -! C^l ^H T j CD ^^
OOi(M^OiO
O" iOi ilMT^ii
8888888^888888
THE RAILROAD TAPER
TAPER 1. INTERMEDIATE VALUES
M
I
/
b
o
D
logZ)
d
t
z.
V
Ic
1
100
30.00
004$
004!
009
5729.62
3.75813
0.02
15.00
0.04
30.00
30.00
05
35.00
005*
006
Oil!
5288.89
3.72336
0.03
17.50
0.06
35.00
35.00
10
40.00
006!
007!
14
4911.12
3.69118
0.03
20.00
0.08
40.00
40.00
15
45.00
007!
0091
16f
4583.73
3.66122
0.04
22.50
0.10
45.00
45.00
20
50.00
008|
0111
020
4297.26
3.63319
0.05
25.00
13
50.00
50.00
25
55.00
010
13!
023!
4044.49
3.60686
0.06
27.50
0.16
55.00
55.0'J
30
60.00
OllJ
015!
027
3819.83
3.58204
0.08
30.00
0.20
60.00
60.00
35
65.00
012f
18
030!
3618.80
3.55856
0.09
32.50
0.24
65.00
65.00
40
70.00
014J
020!
035
3437.89
3.53629
0.11
35.00
0.29
70.00
70.00
45
75.00
015f
023f
039!
3274.21
3.51511
0.13
37.50
0.35
75.00
75.00
50
80.00
om
026!
044
3125.41
3.49491
0.15
40.00
0.41
80.00
80.00
55
85.00
0191
029!
048!
2989.55
3.47561
0.17
42.50
0.47
85.00
85.00
200
90.00
021
033
054
2865.02
3.45713
0.20
45.00
0.55
90.00
90.00
05
95.00
023
036!
059!
2750.45
3.43940
0.22
47.50
0.63
95.00
95.00
10
100.00
025
040
105
2644.71
3.42238
0.25
50.00
0.72
100.00
100.00
15
105.00
027
043!
10!
2546.80
3.40599
0.28
52.50
0.82
105.00
105.00
20
110.00
0291
047|
17
2455.89
3.39021
0.32
55.00
0.93
109.99
110.00
25
115.00
031!
052
23!
2371.25
3.37498
0.35
57.50
.05
114.99
115.00
30
120.00
033!
0561
30
2292.27
3.36027
0.39
60.00
.18
119 99
120.00
35
125.00
0361
100!
36!
2218.39
3.34604
0.44
62 50
.31
124.99
125.00
40
130.00
038|
1051
44
2149.12
3.33226
0.48
65.00
.46
129.99
130.00
45
135.00
0411
1101
151!
2084.06
3.31891
0.53
67.49
.62
134.98
134.99
50
140.00
044
1 15
159
2022.84
3.30596
0.58
69.99
.79
139.98
139.99
55
145.00
046!
120
206!
1965.11
3 . 29339
0.63
72.49
.97
144.98
144.99
300
150.00
049|
125!
215
1910.60
3.28117
0.69
74.99
2.16
149.97
149.99
05
155.00
052^
131
223!
1859.05
3.26929
0.75
77.49
2.36
154.97
154.99
10
160.00
055!
136!
232
1810.21
3.25773
0.81
79.99
2.57
159.97
159.99
15
165.00
058|
1421
240!
1763.89
3.24647
0.88
82.49
2.80
164.96
164.98
20
170.00
101!
1481
250
1719.88
3.23550
0.95
84.99
3.05
169.96
169.98
25
175.00
105
153!
259!
1678.03
3.22480
1.02
87.49
3.30
174.95
174.98
30
180.00
1081
200|
309
1638.19
3.21436
1.10
89.98
3.57
179.94
179.98
35
185.00
llf
207
318|
1600.20
3.20417
1.18
92.48
3.86
184.93
184.97
40
190.00
151
2 13!
329
1563.95
3.19422
1.27
94.98
4.16
189.92
189.97
45
195.00
18f
220!
339!
1529.32
3.18450
1.36
97.48
4.47
194. U
194.96
50
200.00
22!
227!
350
1496.19
3.17499
1.45
99.97
4.80
199.90
199.96
55
205.00
261
234!
400f
1464.49
3.16569
1.55
102.47
5.14
204.89
204.95
TABLES 77
TAPER 1. INTERMEDIATE VALUES (Continued) A = \
M
I
/
b
D
logZ)
d
t
z
y
Ic
400
210.00
130
242
412
1434.12
3.15659
1.65
104.97
5.50
209.88
209.95
05
215.00
134
249$
423$
1405.00
3.14768
1.76
107.47
5.87
214.87
214.95
10
220.00
138
257
435
1377.04
3.13895
1.87
109.96
6.26
219.85
219.94
15
225.00
142
3041
4461
1350.19
3.13039
1.98
112.46
6.67
224.83
224.93
20
230.00
1461
3 121
459
1324.39
3.12201
2.10
114.95
7.10
229.82
229.93
25
235.00
150*
321
511$
1299.57
3.11380
2.23
117.45
7.54
234.80
234.92
30
240.00
1 541
3291
524
1275.68
3.10574
2.36
119.94
8.01
239.77
239.91
35
245.00
1591
337*
5361
1252.66
3.09783
2.49
122.44
8.49
244.75
244.90
40
250.00
2031
3461
550
1230.48
3.09007
2.63
124.93
8.99
249.73
249.89
45
255.00
2081
3551
603$
1209.08
3.08246
2.77
127.43
9.51
254.70
254.88
50
260.00
213
404
617
1188.43
3.07497
2.92
129.92
10.05
259.67
259.87
55
265.00
2171
413
6301
1168.51
3.06763
3.08
132.41
10.60
264.64
264.85
500
270.00
222$
422*
645
1149.25
3.06041
3.24
134.91
11.18
269.61
269.84
05
275.00
227$
432
659$
1130.60
3.05331
3.40
137.40
11.78
274.57
274.82
10
280.00
232$
441$
714
1112.61
3.04634
3.57
139.89
12.40
279.53
279.81
15
285.00
237|
4501
7281
1095.19
3.03949
3.75
142.38
13.04
284.49
284.80
20
290.00
242f
5011
744
1078.33
3.03275
3.94
144.87
13.71
289.45
289.78
25
295.00
248
5 1U
759$
1062.00
3.02612
4.13
147.36
14.39
294.40
294.76
30
300.00
2531
5211
815
1046.16
3.01960
4.32
149.85
15.10
299.35
299.73
35
305.00
258f
532
8301
1030.81
3.01318
4.52
152.34
15.83
304.30
304.71
40
310.00
3041
5421
847
1015.93
3.00686
4.73
154.83
16.58
309.24
309.69
45
315.00
309f
"5531
903$
1001.49
3.00065
4.94
157.32
17.36
314.18
314.66
50
320.00
315|
604$
920
987.48
2.99453
5.16
159.81
18.16
319.12
319.63
55
325.00
3211
615$
9361
973.86
2.98850
5.38
162.30
18.98
324.06
324.61
600
330.00
327
627
954
960.65
2.98257
5.61
164.77
19.83
328.97
329.57
15
345.00
345
7011
10461
923.18
2.96529
6.34
172.22
22.53
343.73
344.47
- 30
360.00
4031
7381
1142
888.73
2.94877
7.14
179.67
25.46
358.44
359.34
45
375.00
4231
8161
1239$
856.95
2.93296
8.00
187.10
28.63
373.10
374.20
700
390.00
443$
855|
1339
827.56
2.91780
8.92
194.52
32.05
387.71
389.03
15
405.00
504$
9361
14401
800.33
2.90327
9.91
201.93
35.73
402.25
403.84
30
420.00
5261
10181
1545
775.05
2.88933
10.97
209.33
39.67
416.73
418 62
78
THE RAILROAD TAPER
08
do
0*8
dS
03
08
02
d^
C5S
o'S
08
OS
08
o't,
OS
H|N|^ Hh#H|Ni-t|NH|c>*rt|-* mfa
lO Tt* iO CO OO I-H O O CO CO <M i i ! b-
O (M CO CO (M r-i rfH ,-1 (M oo CO <M .C^l
CO CO CO O CO CO O iO T^ CO (N ^H ^H
iO iO O kO iO iO -^ CO CO (M T-H T-H
I-H ; T-H <N rt<
CO CO CO CO CO CO <N I-H r-H ;^H(NCOto
. nWHwiHlNHNH'*
<M(MCOOOOC^OOT}H . O i ( i i Q 00
O O O iO CO i i CO iO . O T-I CO O CO
<N CO CO <M <M (N I-H O ;T-H<MCOOCO
<N (M <M <M I-H T-H O ; O I-H CO ^ CO 1>
OQTt< <Ni-lO . l> TjH T-l
I -^ t -^H TJH i/5
O -Oi-HCM^uOt^CX)
.O'-HO
i-i^Hr-HtOCO . Tt< CO CO CO 1C <
T-IT-II-<OO ; o I-H <M co -^ co t^ cs
.
O -H -^ l> . CO t^ O C<J CO CO <N O CO
lOiO^C^ .COi li-Hi-HC^^i (LOCO
oooo ; o <-H <N co Tt< 10 1> oo o
ooo ; o r-i i i c<< co o co i>. oi I-H
- ' . - -- M
tX)>O(Mt^(NiOt^O5
I-H I-H (M CO O CO T-I O
OO 'OOrH (M CO -^ iOt^OOO(M
W . HIM WHMW H|MHN H|M
CO . CO t^ O i i (N i i O OO Tf O
O .I-H CO O >OTjn ^ iCOCO r^
O O O i-H 1-1 <N CO TH CO t^ O5 O (N
OOO I-H <M CO Tt< 10 COOOOii-HCO
co co co co co co co co co
COcOOiCNiOOOi i^t^
i IT IT IOQC>1CN
TABLES
79
.
*-H'^t | l>OCO
"e co ooo^H^*^'
T
[jj
o
O
O *
i Oi ^D C^ C^l CO i-~i CO GO i>- CO CD CO
^ ^ i^ T-H TT *O OO ^H ^^ tO *-O Oi t^ !>
O I^^C^T irHOOiOt)OOQO001>*i>*
tf
q
o
CD
CO
THE RAILROAD TAPER
TAPER 1|. INTERMEDIATE VALUES A = |
M
I
/
b
D
log>
d
t
X
y
Ic
130
30.00
006|
006!
013*
3819.78
3.58204
0.03
15.00
0.06
30.00
30.00
35
33.33
007!
008
015f
3618.74
3.55856
0.03
16.67
0.07
33.33
33.33
40
36.67
008|
009*
0181
3437.82
3.53628
0.04
18.33
0.09
36.67
36.67
45
40.00
009f
0111
021
3274.13
3.51509
0.05
20.00
0.11
40.00
40.00
50
43.33
OlOf
013
0231
3125.32
3.49489
0.06
21.67
0.13
43.33
43.33
55
46.67
Ollf
015
0261
2989.45
3.47559
0.07
23.33
0.16
46.67
46.67
200
50.00
013
017
030
2864.90
3.45726
0.08
25.00
0.19
50.00
50.00
05
53.33
0141
019
0331
2750.32
3.43938
0.09
26.67
0.22
53.33
53.33
10
56.67
015*
0211
0361
2644.56
3.42235
0.10
28.33
0.26
56.67
56.67
15
60.00
016!
023!
040*
2546.64
3.40597
0.12
30.00
0.30
60.00
60.00
20
63.33
0181
026
0441
2455.70
3.39018
0.13
31.67
0.34
63.33
63.33
25
66.67
019|
028*
0481
2371.05
3.37494
0.15
33.33
0.38
66.67
66.67
30
70.00
0211
0311
052*
2292.04
3.36022
0.16
35.00
0.43
70.00
70.00
33
73.33
022!
034
056|
2218.13
3.34599
0.18
36.67
0.49
73.33
73.33
40
76.67
024*
036!
1011
2148.84
3.33220
0.20
38.33
0.55
76.66
76.67
45
80.00
0261
39!
06
2083.75
3.31885
0.22
40.00
0.61
80.00
80.00
50
83.33
028
42!
1101
2022.50
3.30589
0.24
41.66
0.68
83.33
83.33
55
86.67
029f
046
115!
1964.75
3.29331
0.27
43.33
0.75
86.66
86.66
300
90.00
031*
049*
121
1910.20
3.28108
0.29
45.00
0.82
89.99
89.99
05
93.33
033*
0521
1261
1858.62
3.26919
0.32
46.66
0.90
93.33
93.33
10
96.67
035*
0561
131!
1809.75
3.25762
0.35
48.33
0.99
96.66
96.66
15
100.00
037*
100
137*
1763.39
3.24635
0.38
50.00
.09
99.99
99.99
20
103.33
039*
1 031
1431
1719.34
3.23536
0.41
51.66
.19
103.32
103.33
25
106.67
041*
1071
1491
1677.45
3.22465
0.44
53.33
.29
106.65
106.66
30
110.00
043f
llf
155*
1637.56
3.21420
0.47
54.99
.40
109.99
109.99
35
113.33
046
151
201!
1599.53
3.20399
0.51
56.66
.52
113.32
113.33
40
116.67
0481
20
2081
1563.23
3.19402
0.55
58.33
1.64
116.65
116.66
45
120.00
050*
24*
215
1528.55
3.18428
0.59
59.99
1.77
119.98
119.99
50
123.33
053
281
221!
1495.37
3.17475
0.63
61.66
1.90
123.31
123.32
55
126.67
055*
1.331
228!
1463.61
3.16543
0.67
63.33
2.04
126.64
126.65
400
130.00
058
1 38
236
1433.18
3.15630
0.71
64.99
2.19
129.97
129.99
05
133.33
100*
1 421
2431
1404.00
3.14737
0.76
66.66
2.35
133.30
133.32
10
136.67
1031
1 47*
250!
1375.98
3.13861
0.81
68.32
2.51
136.63
136.65
15
140.00
105|
1 521
258*
1349.07
3.13003
0.86
69.99
2.68
139.96
139.99
20
143.33
108*
157f
3061
1323.20
3.12163
0.91
71.65
2.86
143.29
143.32
25
146.67
111*
2021
3 141
1298.31
3.11338
0.97
73.32
3.05
146.62
146.65
TABLES 81
TAPER 1J. INTERMEDIATE VALUES (Continued) A = f
M
I
/
6
D
logD
d
t
X
y
Ic
430
150.00
114}
208}
322*
1274.35
3.10529
1.03
74.98
3.24
149.94
149.98
35
153.33
1 17}
212*
330!
1251.26
3.09735
.09
76.65
3.44
153.27
153.31
40
156.67
120J
219
339}
1229.00
3.08955
1.15
78.31
3.65
156.60
156.64
45
160.00
123|
224!
348
1207.52
3.08189
.21
79.98
3.87
159.92
159.97
50
163.33
126}
230|
356!
1186.79
3.07437
.28
81.64
4.10
163.25
163.30
55
166.67
129i
236*
405f
1166.78
3.06699
.35
83.31
4.33
166.58
166.63
500
170.00
132*
242*
415
1147.43
3.05973
.42
84.97
4.57
169.90
169.96
05
173.33
135|
248*
424}
1128.69
3.05257
.49
86.64
4.83
173.22
173.29
10
176.67
139
254|
433!
1110.61
3.04556
.57
88.30
5.09
176.55
176.62
15
180.00
142}
301}
443*
1093.09
3.03865
.65
89.96
5.36
179.87
179.95
20
183.33
145|
307|
453}
1076.12
3.03186
.73
91.63
5.64
183.19
183.28
25
186.67
149}
314
503}
1059.68
3.02517
1.81
93.29
5.93
186.51
186.60
30
190.00
152|
319!
513*
1043.74
3.01859
1.90
94.95
6.23
189.83
189.93
35
193.33
156}
3 27J
523!
1028.28
3.01211
1.99
96.62
6.54
193.15
193.25
40
196.67
200
334}
534}
1013.28
3.00573
2.08
98.28
6.86
196.47
196.59
45
200.00
203|
341}
545
998.72
2.99944
2.17
99.94
7.19
199.79
199.71
50
203.33
207*
348}
555!
984.59
2.99326
2.27
101.61
7.53
203.10
203.24
55
206.67
2 11}
355*
606!
970.85
2.98715
2.37
103.27
7.88
206.42
206.57
600
210.00
215
403
618
957.51
2.98114
2.47
104.93
8.24
209.73
209.89
15
220.00
226!
425f
652*
919.64
2.96362
2.80
109.92
9.39
219.66
219.86
30
230.00
239}
449}
728*
884.74
2.94682
3.15
114.90
10.64
229.58
229.83
45
240.00
252i
513!
806
852.48
2.93068
3.53
119.88
12.00
239.49
239.79
700
250.00
305*
539*
845
822.58
2.91518
3.94
124.85
13.47
249.38
249.75
15
260.00
319*
606
925*
794.80
2.90026
4.38
129.82
15.05
259.26
259.70
30
270.00
333f
633!
1007*
768.93
2.88589
4.85
134.79
16.76
269.12
269.64
45
280.00
348|
702*
1051
744.80
2.87204
5.36
139.76
18.58
278.95
279.57
800
290.00
404
732
1136
722.24
2.85868
5.90
144.72
20.53
288.76
289.49
15
300.00
420
802*
12 22f
701.11
2.84579
6.47
149.67
22.61
298.54
299.40
30
310.00
436}
834}
1310*
681.30
2.83334
7.08
154.62
24.83
308.29
309.29
45
320.00
453
907
1400
662.70
2.82132
7.73
159.56
27.18
318.02
319.17
900
330.00
510*
940*
1451
645.20
2.80969
8.42
164.49
29.68
327.70
329.04
15
340.00
528*
1015
15 43*
628.72
2.79846
9.14
169.42
32.32
337.34
338.88
30
350.00
546|
1050!
1637*
613.19
2.78760
9.90
174.34
35.11
346.94
348.72
45
360.00
605*
1127*
1733
598.53
2.77709
10.70
179.25
38.06
356.50
358.54
1000
370.00
625
1205
1830
584.69
2.76693
11.55
184.15
41.16
366.01
368.33
15
380.00
645|
1242!
1928*
571.61
2.75710
12.44
189.04
44.43
375.47
378.09
30
390.00
705}
13 23}
2028*
559.24
2.74760
13.37
193.92
47.85
384.87
387.82
82
THE RAILROAD TAPER
8
O
Wg
08
uS
u'S
US
US
CO l^ !>. t>- t> O O O rJH CO r- 1 i (
o -^ *o to
00 0000 00 00 OOt^ CO to -^ CO
rt|N rt|M H|N rH|M HM H
CD CO CO OS C^ Tt< CO i 1 CD O ' O5 i-i
-^ OrHOo w^ to^co ;coco
iO CO O O 10 "3 rt< CO <N '-i T-H CO
Tfl IO ^O Tfl Ttl Tj< CO <N i 1 lt CO O
H|M He* IH|N H '
O5 CO Ttn rt< T-H t^ O <M i i
^ oo toco toi^ i-3 -<N
8S8S880 1 iSSsSSS
CO CO CO <N <M i i T-H i i <M Tfi CO 00
r
- CO rJH O5 CO -<f "^ ' CO Oi OO OO i ( to
TH <N I-H O CO to ; O -H TJH <M <M C^
O5 CO CO CO to -^ i i T-H <N CO T-H O
CO "* CO T-H "tfi ; 10 O (M iO CO CO CO
THT-H^HT-HO O <M CO ^ CO 00 O
I
t^CiOOcO
OOtOCO
! i i-H O O OT-(
H|M H|M H|M H|M --'
OOO O I-H <M CO to'co OO O (M
OO O i ( C<l CO * tO l^ O5 i i CO
O O O I-H C^l CO "* CD OO O (M Tt^
o -OOrH T-I (N'* to COOOO<N O
TABLES
83
18
8
O5 OS OS
i i^t^
OiO(NO05O
i-H rH (M CO CO 1O
o
O T-H
co t^ co
O CO O O r-J
' lOfNTf
t^~ T-4 CO OS ^^ "^
lOOOiOiOOOi (
g
qnSS^^^j
i i OS 00 t^ CO i
OOrHCO^COOOOCOCOOS
OCOCOOSCO
I 1 T I T 1 T 1 C^
i i I-H i i <M C^ C^ (
888888888888
<MCOTfitocOl>.OOOSO' icNCO
84
THE RAILROAD TAPER
TAPER 2. INTERMEDIATE VALUES A = l
Af
I
/
b
D
log/)
d
t
X
y
k
200
30.00
009
009
018
2864.86
3.45710
0.04
15.00
0.08
30.00
30.00
05
32.50
010
010*
020*
2750.28
3.43938
0.05
16.25
0.09
32.50
32.50
10
35.00
OlOf
012
022!
2644.51
3.42234
0.05
17.50
0.11
35.00
35.00
15
37.50
Oil!
013*
025*
2546.58
3.40596
0.06
18.75
0.13
37.50
37.50
20
40.00
0121
015*
028
2455.64
3.39016
0.07
20.00
0.15
40.00
40.00
25
42.50
014
016|
030!
2370.98
3.37493
0.08
21.25
0.17
42.50
42.50
30
45.00
015
018!
033!
2291.97
3.36021
0.09
22.50
0.20
45.00
45.00
35
47.50
016*
020*
036!
2218.05
3.34597
0.10
23.75
0.22
47.50
47.50
40
50.00
017*
022!
i040
2148.75
3.33219
0.11
25.00
0.25
50.00
50.00
45
52.50
018*
024|
043*
2083.65
3.31882
0.12
26.25
0.28
52.50
52.50
50
55.00
019f
027
046!
2022.39
3.30586
0.13
27.50
0.32
55.00
55.00
55
57.50
021*
029
050*
1964.52
3.29326
0.14
28.75
0.35
57.50
57.50
300
60.00
022*
031*
054
1910.07
3.28105
0.16
30.00
0.39
60.00
60.00
05
62.50
024
033!
057f
1858.47
3.26916
0.17
31.25
0.43
62.50
62.50
10
65.00
025*
036*
lOlf
1809.59
3.25758
0.19
32.50
0.48
65.00
65.00
15
67.50
026f
039
105!
1763.21
3.24630
0.20
33.75
0.53
67.50
67.50
20
70.00
028J
041!
110
1719.15
3.23531
0.22
35.00
0.58
70.00
70.00
25
72.50
030
044*
114*
1677.25
3.22460
0.24
36.25
0.63
72.50
72.50
30
75.00
031*
047*
118!
1637.35
3.21414
0.26
37.50
0.69
75.00
75.00
35
77.50
033*
050
123*
1599.30
3.20393
0.28
38.75
0.75
77.50
77.50
40
80.00
034|
053*
128
1562.98
3.19395
0.30
40.00
0.81
79.99
80.00
45
82.50
036*
056*
132!
1528.28
3.18420
0.32
41.25
0.88
82.49
82.50
50
85.00
038*
059*
137!
1495.08
3.17437
0.34
42.50
0.95
84.99
85.00
55
87.50
040*
102*
142!
1463.31
3.16534
0.37
43.75
.02
87.49
87.50
400
90.00
042
104
148
1432 86
3.15620
0.39
45.00
.10
89.99
90.00
05
92.50
044
109*
153*
1403.66
3.14726
0.42
46.24
.18
92.49
92.50
10
95.00
045f
1 13
158!
1375.62
3.13850
0.45
47.49
.27
95.99
95.00
15
97.50
047f
116*
204*
1348.69
3.12991
0.48
48.74
.36
97.49
97.50
20
100.00
049f
20*
210
1322.80
3.12149
0.51
49.99
1.45
99.98
99.99
25
102.50
052
23!
215!
1297.87
3.11323
0.54
51.24
1.55
102.48
102.49
30
105.00
054
27!
221!
1273.89
3.10513
0.57
52.49
1.65
104.98
104.99
35
107.50
056*
31*
227!
1250.77
3.09718
0.60
53.74
1.76
107.48
107.49
40
110.00
058*
135!
234
1228.48
3.08937
0.63
54.99
1.87
109.98
109.99
45
112.50
100*
139!
240*
1206.98
3.08170
0.67
56.24
1.98
112.47
112.49
50
115.00
102f
144
246!
1186.22
3.07416
0.71
57.49
2.10
114.97
114.99
55
117.50
105*
148
253*
1166.18
3.06677
0.75
58.74
2.23
117.47
117.49
500
120.00
107*
152*
300
1146.80
3.05949
0.79
59.99
2.36
119.96
119.99
05
122.50
1 10
156!
306!
1128.03
3.05232
0.83
61.24
2.49
122.46
122.49
10
125.00
112*
201*
3 13!
1109.91
3.04529
0.87
62.48
2.63
124.96
124.99
TABLES 85
TAPER 2. INTERMEDIATE VALUES (Continued) A = l
u
I
/
b
D
logD
d
t
X
V
Ic
5 15
127.50
14f
206
3201
1092.35
3.03836
0.91
63.73
2.77
127.45
127.49
20
130.00
m
2101
328
1075.35
3.03155
0.96
64.98
2.92
129.95
129.98
25
132.50
20
2151
3351
1058.87
3.02484
.00
66.23
3.08
132.44
132.48
30
135.00
22*
2201
3421
1042.89
3.01823
.05
67.48
3.24
134.94
134.98
35
137.50
251
225
3501
1027.39
3.01174
.10
68.73
3.41
137.44
137.48
40
140.00
27f
2301
358
1012.35
3.00490
.15
69.98
3.58
139.93
139.98
45
142.50
30*
2351
4051
997.76
2.99903
.21
71.22
3.75
142.42
142.48
50
145.00
331
240*
4 131
983.58
2.99281
.26
72.47
3.93
144.92
144.97
55
147.50
361
245*
4211
969.80
2.98668
.32
73.72
4.12
147.41
147.47
600
150.00
39
251
430
' 956.41
2.98064
.37
74.97
4.32
149.90
149.97
15
157.50
147f
307*
4551
918.39
2.96303
.55
78.71
4.94
157.37
157.47
30
165.00
57
324f
5211
883.34
2.94613
.75
82.45
5.61
164.84
164.96
45
172.50
206*
342|
5491
850.92
2.92989
.97
86.19
6.34
172.32
172.44
700
180.00
2 16*
401*
618
820.84
2.91426
2.20
89.93
7.14
179.77
179.92
15
187.50
226|
421
6471
792.86
2.89920
2.44
93.67
8.00
187.22
187.39
30
195.00
237|
4411
7 181
766.79
2.88468
2.71
97.41
8.93
194.66
194.86
45
202.50
248*
5021
7501
742.43
2.87066
2.99
101 . 14
9.92
202.10
202.34
800
210.00
300
524
824
719.63
2.85711
3.29
104.87
10.98
209.52
209.81
15
217.50
3 m
546*
8581
698.26
2.84402
3.62
108.60
12.12
216.93
217.26
30
225.00
324
609f
9331
678.18
2.83134
3.96
112.33
13.33
224.33
224.72
45
232.50
336|
633f
10101
659.29
2.81908
4.32
116.05
14.62
231.72
232.18
900
240.00
349*
658*
1048
641.49
2.80719
4.71
119.78
15.99
239.10
239.63
15
247.50
402f
724
11261
624.69
2.79566
5.11
123.49
17.44
246.46
247.07
30
255.00
4 16*
7501
12061
608.83
2.78450
5.54
127.21
18.97
253.80
254.51
45
262.50
430*
8 17}
12471
593.82
2.77365
5.99
130.92
20.59
261.12
261.92
1000
270.00
445
845
1330
579.61
2.76314
6.47
134.63
22.30
268.42
269.36
15
277.50
459|
9 13*
14131
566.14
2.75292
6.97
138.33
24.11
275.71
276.76
30
285.00
5 15
942f
14 571
553.36
2.74301
7.49
142.03
26.00
282.96
284.16
45
292.50
530*
10 121
15 431
541.22
2.73337
8.04
145.72
27.99
290.20
291.54
1100
300.00
546*
1043*
1630
529.69
2.72402
8.62
149.41
30.08
297.40
298.92
15
307.50
602|
1115
17171
518.73
2.71494
9.23
153.09
32.26
304.58
306.28
30
315.00
619*
1147J
18061
508.29
2.70611
9.86
156.77
34.55
311.72
313.64
45
322.50
636*
12201
18561
498.36
2.69754
10.52
160.44
36.94
318.84
319.50
1200
330.00
654
1254
1948
488.88
2.68920
11.20
164.10
39.44
325.91
328.29
15
337.50
7111
1328*
20401
479.86
2.68111
11.92
167.76
42.04
332.95
335.59
30
345.00
730
14 031
21 331
471.25
2.67325
12.66
171.41
44.76
339.95
342.88
45
352.50
748*
1439|
22281
463.05
2.66563
13 44
175.05
47.59
346.90
350.15
1300
360.00
807*
1516*
2324
455.22
2.65822
14.25
178.68
. 50.51
353.81
357.40
86
THE RAILROAD TAPER
o
02
do
OS
08
8
08
ds
Win
t>- 1O 00 b- 00 rH OS <N O CO
CO O rH 1-1 O <N ^ CO (M iC O
CO O5 OS O5 O5 00 t CO iO CO CQ '
* CD t^ <N CO OO O5 >O U5 T-H ' (M <N
10 I-H c^j i-t Tt< o I-H o Ttn ;ioo
o xo CO CO CO iC >O "*! CO i i T-I TP
i-* i i CO 1C
CO CO CO CO CO <M rH -T-H
H I W|^H|N HN
10 O o co o o ; i 1 10 Tt^ 10
o <N CO <N (N -< *-i -r-
<N (N C<l rH O rH <N Tf CD 00 O
^OCO>O
(M <N i-H ^
o rH i i TH O
OOC5O
CO C^ rH CO O
O <M CO iO l> O: (N
OOO O rH CO 'f CD OO O CO
GOC4
(M <M
OO
OOOt^lM
CO 10 (N i-t <M
O rH <M CO 1C 1> O5
O -O rH rHCO ^ CO GO O <N O
O O rH oq CO iO O 00 O CO O
TABLES
87
K
J?
O 1 s I O O5
^ O^ C^ "^ QO T-H C*Q O^ '^
QOiOCOOOi iCOi ICOCO
T *OO5OOO01>-l > -OCO
COCOO(NO<NCOOOI>.i (CO
OirHOOOOOI^<NCOCOt^<N
!OOOl>.tOI>l>OcDl^O
O5 C^ ^* i^ CO *O t^- T-H CO C^l OS
o O --I <N 00 iO I> O CO JOO TfH
CO CO O5 (N iO 00 i i
THE RAILROAD TAPER
TAPER 2J. INTERMEDIATE VALUES
M
I
/
b
o
D
logD
d
t
X
y
Ic
230
30.00
oil}
111
022*
2291.93
3.36020
0.05
15.00
0.10
30.00
30.00
35
32.00
012
012!
024f
2218.01
3.34596
0.06
16.00
0.11
32.00
32.00
40
34.00
013
0141
0271
2148.70
3.33218
0.06
17.00
0.13
34.00
34.00
45
36.00
014
15J
029!
2083.60
3.31881
0.07
18.00
0.15
36.00
36.00
50
38.00
015
0171
0321
2022.34
3.30585
0.08
19.00
0.17
38.00
38.00
55
40.00
016
019
035
1964.57
3.29327
0.09
20.00
0.19
40.00
40.00
300
42.00
017
020!
0371
1910.00
3.28103
0.09
21.00
0.21
42.00
42.00
05
44.00
018}
022*
0401
1858.40
3.26914
0.10
22.00
0.23
44.00
44.00
10
46.00
019}
024*
043f
1809.51
3.25756
0.11
23.00
0.26
46.00
46.00
15
48.00
020|
0261
0461
1763.13
3.24628
0.12
24.00
0.29
48.01)
48.00
20
50.00
021|
0281
050
1719.06
3.23529
0.13
25.00
0.32
50.00
50.00
25
52.00
023
0301
0531
1677.16
3.22457
0.15
26.00
0.35
52.00
52.00
30
54.00
024}
032*
0561
1637.25
3.21411
0.16
27.00
0.38
54.00
54.00
35
56.00
025*
034f
1001
1599.19
3.20390
0.17
28.00
0.41
56.00
56.00
40
58.00
026f
037
1031
1562.86
3.19392
0.18
29.00
0.45
58.00
58.00
45
60.00
028
039*
107*
1528.16
3.18417
0.20
30.00
0.49
60.00
60.00
50
62.00
029*
041|
HI
1494.95
3.17463
0.21
31.00
0.53
62.00
62.00
55
64.00
031
0441
151
1463.17
3.16529
0.23
32.00
0.57
64.00
64.00
400
66.00
032*
046!
191
1432.71
3.15616
0.24
33.00
0.62
66.00
66.00
05
68.00
034
0491
231
1403.50
3.14721
0.26
34.00
0.67
68.00
68.00
10
70.00
035*
052
27*
1375.45
3.13844
0.28
35.00
0.72
69.99
70.00
15
72.00
037
054f
31!
1348.50
3.12985
0.29
36.00
0.77
71.99
72.00
20
74.00
038*
057!
361
1322.60
3.12143
0.31
37.00
0.83
73.99
74.00
25
76.00
040}
100*
40!
1297.67
3.11316
0.33
38.00
0.89
75.99
76.00
30
78.00
041!
103*
451
1273.67
3.10506
0.35
39.00
0.95
77.99
78.00
35
80.00
043*
106*
150
1250.54
3.09710
0.37
40.00
.01
79.99
80.00
40
82.00
045J
109*
154!
1228.25
3.08929
0.40
40.99
.08
81.99
82.00
45
84.00
047
12!
159!
1206.73
3.08161
0.42
41.99
.15
83.99
84.00
,50
86.00
048f
16
204!
1185.95
3.07407
0.44
42.99
.22
85.99
86.00
55
88.00
50*
191
209!
1165.90
3.06666
0.47
43.99
.30
87.99
88.00
500
90.00
052*
22*
2 15
1146.50
3.05937
0.49
44.99
.37
89.98
90.00
05
92.00
054*
25!
220}
1127.72
3.05220
0.52
45.99
.45
91.98
91.99
10
94.00
0561
29*
225!
1109.58
3.04516
0.54
46.99
.54
93.98
93.99
15
96.00
0581
133
231}
1092.01
3.03823
0.57
47.99
1.63
95.98
95.99
. 20
98.00
1001
136*
236!
1074.99
3.03140
0.60
48.99
1.72
97.98
97.99
25
100.00
1021
1401
2 42*
1058.50
3.02469
0.63
49.99
1.81
99.98
99.99
30
102.00
1041
144
248}
1042.50
3.01808
0.66
50.99
1.91
101.97
101.99
35
104.00
106*
147f
254}
1026.98
3.01156
0.69
51.99
2.01
103.97
103.99
40
106.00
108*
151f
300}
1011.92
3.00515
0.72
52.99
2.11
105.97
105.99
TABLES 89
TAPER 2i INTERMEDIATE VALVES (Continued) A = U
M \ I
/
b
D
log-Z)
d
t
X
V
fc
545
108.00
1 10|
1 55*
306*
997.31
2.99883
0.76
53.99
2.22
107.97
107.99
'50
110.00
1 13
159*
3 12*
983.11
2.99260
0.79
54.98
2.33
109.96
109.99
55
112.00
1 15i
203*
3 18!
969.31
2.98646
0.83
55.98
2.45
111.96
111.99
600
114.00
ii7*
207!
325*
955.90
2.98041
0.86
56.98
2.57
113.95
113.98
15
120.00
124*
220*
345
917.82
2.96276
0.98
59.98
2.95
119.94
119.98
30
126.00
1 31|
234
405!
882.70
2.94581
.11
62.97
3.36
125.93
125.97
45
132.00
139*
248
427*
850.19
2.92952
.24
65.97
3.81
131.91
131.97
700
138.00
147
302!
449!'
820.03
2.91383
.39
68.96
4.30
137.89
137.96
15
144.00
155i
318
513*
791.97
2.89871
.55
71.96
4.83
143.87
143.95
30
150.00
203|
333!
537*
765.80
2.88412
.72
74.95
5.40
149.84
149.94
45
156.00
212|
350*
602!
741.34
2.87002
.90
77.94
6.01
155.81
155.93
800
162.00
221*
407*
628!
718.43
2.85638
2.09
80.93
6.67
161.78
161.91
15
168.00
231
424!
655!
696.93
2.84319
2.29
8,3.92
7.37
167.73
167.89
30
174.00
240|
443
723!
676.73
2.83042
2.51
86.91
8.12
173.69
173.88
45
180.00
250!
501!
752*
657.71
2.81803
2.74
89.90
8.92
179.63
179.86
900
186.00
301
521*
822*
639.77
2.80602
2.99
92.88
9.77
185.57
185.84
15
192.00
3 11*
541*
852!
622.83
2.79437
3.25
95.86
10.68
191.51
191.82
30
198.00
322*
602
924*
606.81
2.78305
3.52
98.84
11.64
197.43
197.79
45
204.00
333*
623*
956!
591.64
2.77206
3.81
101.82
12.65
203.34
203.75
1000
210.00
345
645
1030
577.26
2.76137
4.12
104.80
13.71
209.25
209.70
15
216.00
356f
707*
1104*
563.61
2.75098
4.44
107.78
14.84
215.14
215.65
30
222.00
408f
730*
1139*
550.64
2.74087
4.77
110.75
16.03
221.02
221.60
45
228.00
42H
754
1215*
538.30
2.73102
5.12
113.72
17.27
226.89
227.55
1100
234.00
434
818*
1252*
526.56
2.72145
5.49
116.69
18.58
232.74
233.49
15 240.00
447
843
1330
515.38
2.71213
5.88
119.65
19.96
238.59
239.42
30
246.00
500*
908*
1408!
504.71
2.70304
6.28
122.61
21.40
244.42
245.36
45
252.00
513!
934*
1448*
494.54
2.69420
6.70
125.57
22.90
250.23
251.29
1200
258.00
527|
1001*
1528!
484.82
2.68558
7.14
128.52
24.47
256.02
257.20
15
264.00
541!
1028*
16 10*
475.54
2.67719
7.60
131.47
26.11
261.79
263.09
30
270.00
556*
1056*
1652*
466.67
2.66901
8.08
134.42
27.82
267.54
268.98
45
276.00
611
1124!
1735!
458.19
2.66105
8.58
137.36
29.61
273.27
274.87
1300
282.00
626
1153!
18 19!
450.06
2.65327
9.09
140.30
31.47
278.98
280.75
15
288.00
641*
1223*
1904!
442.29
2.64571
9.63
143.23
33.40
284.66
286.61
30
294.00
657*
1253*
1950!
434.85
2.63834
10.19
146.16
35.40
290.32
292.47
45
300.00
713*
1324^
2037*
427.71
2.63115
10.76
149.08
37.49
295.95
298.32
1400
306.00
729*
1355!
2125*
420.87
2.62415
11.36
152.00
39.65
301.55
304.15
15
312.00
746
14 27|
2213!
414.31
2.61733
11.98
154.91"
41.89
307.12
309.96
30
318.00
802!
1500*
2303*
408.04
2.61070
12.63
157.81
44.21
312.66
315.76
45
324.00
820
1523!
2353!
402.01
2.60424
13.29
160.71
46.61
318.16
321.55
1500
330.00
837*
1607*
2445
396.23
2.59795
13.98
163.60
49.09
323.63
327.33
90
THE RAILROAD TAPER
d8
d8
qg
OS.
08
08
OiOOCOOOCOiOCOOltO
CO O <N i i * O O "^ O i i
GOO5O5O500OOt^O'^(N
U5 H CN S ^ O C^
iOCOCOOXOTt<COi-i
. g^ %% %%$
^TjHT^^COlMi-l
<N C4
cocceoco(Mi-i : I-H co "3 oo
<NCO(N>OO
T ( CO t^ ^ t^ 10 i i -^ CO CO
rH T-t t I O ! T I <N -^ CO 00 T-H
O(MCOO1>O(M
COC5 -^ ^OCOCO ^ TH O
OO .OrH
O T- ( <N CO O t^ O5 (N iO
i-i (M-^ COOOOCO CO
i-H ^H ^-i (M W <M
TABLES
91
OOOiOiOil>-iO' iiOO
^D CD OS OS OS OS GO t^
COCOGO' i -^ l> O CO
OOOSOSOSGOt^iOT-HCO
CO
I"* Oi ^D ^H O5 i"H ^
QC ^^ 00 00 ^D CO OO CO Oi *^O
00 *O *O GO OS C^l TH r-H
t^-iOCOCO^fGOCOOS
iH I-H i i (M (M <M
SwScoScoScooco
1 1 1 1 T-H 1 1 T-H
92
THE RAILROAD TAPER
TAPER 2|. INTERMEDIATE VALUES
M
I
/
6
D
logZ)
d
t
X
y
k
300
30.00
013
13^
027
1909.97
3.28103
0.06
15.00
0.12
30.00
30.00
05
31.67
14^
014!
0291
1858.37
3.26913
0.07
15.83
0.13
31.67
31.67
10
33.33
151
016J
031|
1809.47
3.25755
0.07
16.67
0.15
33.33
33.33
15
35.00
0161
18i
034
1763.09
3.24627
0.08
17.50
0.17
35.00
35.00
20
36.67
0171
019
036|
1719.02
3.23528
0.09
18.33
0.18
36.67
36.67
25
38.33
0181
021
0391
1677.10
3.22456
0.09
19.17
0.20
38.33
38.33
30
40.00
0191
022|
042
1637.19
3.21410
0.10
20.00
0.22
40.00
40.00
35
41.67
0201
024^
044!
1599.13
3.20388
0.11
20.83
0.24
41.67
41.67
40
43.33
021
0261
047!
1562.80
3.19390
0.12
21.67
0.27
43.33
43.33
45
45.00
022
0281
050!
1528.09
3.18415
0.13
22.50
0.29
45.00
45.00
50
46.67
023f
030
053!
1494.88
3.17461
0.14
23.33
0.32
46.67
46.67
55
48.33
024f
032
056!
1463.09
3.16527
0.15
24.17
0.35
48.33
48.33
400
50.00
026
034
1 00
1432.63
3.15613
0.16
25.00
0.38
50.00
50.00
05
51.67
0271
036
1031
1403.41
3.14715
0.17
25.83
0.41
51.66
51.67
10
53.33
028|
0381
106!
1375.35
3.13841
0.18
26.66
0.44
53.33
53.33
15
55.00
029f
040^
101
1348.41
3.12982
0.20
27.50
0.48
55.00
55.00
20
56.67
031
042!
113!
1322.50
3.12140
0.21
28.33
0.51
56.66
56.67
25
58.33
032
044!
171
1297.56
3.11313
0.22
29.16
0.55
58.33
58.33
35
60.00
033f
047J
21
1273.56
3.10502
0.24
30.00
0.59
60.00
60.00
30
61.67
0351
049
24!
1250.42
3.09706
0.25
30.83
0.63
61.66
61.67
40
63.33
036
0521
28!
1228.12
3.08924
0.27
31.66
0.67
63.33
63.33
45
65.00
038
054f
132!
1206.59
3.08156
0.28
32.50
0.72
64.99
65.00
50
66.67
039
0571
136!
1185.81
3.07402
0.30
33.33
0.77
66.66
66.67
55
68.33
041
059!
140!
1165.74
3.06660
0.31
34.16
0.82
68.33
68.33
500
70.00
042
102
145
1146.34
3.05931
0.33
35.00
0.87
69.99
70.00
05
71.67
044
105J
1491
1127.55
3.05214
0.35
35.83
0.92
71.66
71.66
10
73.33
045|
108
153!
1109.41
3.04509
0.37
36.66
0.97
73.32
73.33
15
75.00
0471
1 11
1581
1091.83
3.03816
0.39
37.49
1.03
74.99
75.00
20
76.67
049
13
202!
1074.80
3.03133
0.41
38.33
1.09
76.66
76.66
25
78.33
050J
16!
2071
1058.30
3.02461
0.43
39.16
1.15
78.32
78.33
30
80.00
0521
19!
212
1042.29
3.01799
0.45
39.99
1.22
79.99
80.00
35
81.67
054
22f
216!
1026.76
3.01147
0.47
40.83
1.28
81.65
81.66
40
83.33
055f
26
221!
1011.69
3.00505
0.49
41.66
1.35
83.32
83.33
45
85.00
057
291
226f
997.07
2.99873
0.52
42.49
1.42
84.98
84.99
50
87.67
0591
132^
231!
982.86
2.99249
0.54
43.32
1.49
86.65
86.66
55
88.33
loll
135J
236!
969.04
2.98634
0.56
44.16
1.57
88.31
88.33
TABLES 93
TAPER 2|. INTERMEDIATE VALUES (Continued) A = l%
M
/
/
b
D
logD
i
t
X
V
Ic
600
90.00
103
139
242
955.63
2.98029
0.59
44.99
1.65
89.98
89.99
15
95.00
1 08|
1 49i
258!
917.51
2.96261
0.67
47.49
1.90
94.97
94.99
30
100.00
114f
200!
315
882.35
2.94564
0.76
49.98
2.18
99.96
99.99
45
105.00
1 21
2 11!
332!
849.80
2.92932
0.85
52.48
2.48
104.96
104.99
700
110.00
1274
2 234
351
819.59
2.91360
0.95
54.98
2.80
109.95
109.98
15
115.00
134!
236
410!
791.48
2.89844
.06
57.47
3.15
114.93
114.98
30
120.00
141!
248|
430
765.26
2.88381
.18
59.97
3.53
119.92
119.97
45
125.00
148^
302*
4 501
740.75
2.86967
.31
62.46
3.94
124.90
124.96
800
130.00
156
3 16
512
717.78
2.85599
.44
64.96
4.38
129.88
129.95
15
135.00
203!
330
534!
696.22
2.84275
.58
67.45
4.85
134.86
134.95
30
140.00
2 llf
345J
557
675.95
2.82991
.73
69.94
5.36
139.84
139.94
45
145.00
220
400|
620!
656.86
2.81747
.89
72.44
5.90
144.81
144.93
900
150.00
228|
416*
645
638.84
2.80539
2.06
74.93
6.47
149.77
149.91
15
155.00
237!
433
7 10!
621.82
2.79366
2.24
77.42
7.08
154.74
154.90
30
160.00
246!
449|
736
605.72
2.78227
2.43
79.91
7.73
159.70
159.88
45
165.00
255|
507!
802!
590.46
2.77119
2.63
82.39
8.42
164.65
164.86
1000
170.00
305
525
830
575.98
2.76041
2.84
84.88
9.14
169.60
169.84
15
175.00
314!
543
858!
562.23
2.74991
3.06
87.37
9.90
174.54
174.82
30
180.00
3 24!
6 02!
927
549.16
2.73970
3.29
89.85
10.70
179.47
179.79
45
185.00
335
6 21!
956!
536.71
2.72974
3.53
92.33
11.55
184.40
184.76
1100
190.00
345
641
1027
524.86
2.72004
3.79
94.81
12.44
189.32
189.73
15
195.00
356*
702
1058!
513.56
2.71059
4.06
97.29
13.37
194.24
194.69
30
200.00
407!
722!
1130
502.77
2.70137
4.34
99.77
14.35
199.14
199.65
45
205.00
418
744i
1202!
492.47
2.69238
4.63
102.24
15.37
204.03
204.61
1200
210.00
430
806
1236
482.62
2.68361
4.94
104.72
16.44
208.92
209.56
15
215.00
441|
828^
13 10!
473.20
2.67504
5.26
107.19
17.56
213.79
214.51
30
220.00
453f
85U
1345
464.18
2.66669
5.59
109.65
18.73
218.65
219.46
45
225.00
506
9 14!
1420!
455.54
2.65853
5.93
112.12
19.95
223.50
224.40
1300
230.00
518J
938
1457
447.26
2.65056
6.29
114.58
21.22
228.34
229.33
15
235.00
531*
1003
1534!
439.32
2.64278
6.66
117.04
22.54
233.17
234.25
30
240.00
5441
10 271
16 12
431.71
2.63519
7.05
119.50
23.91
237.98
239.17
45
245.00
557!
10 53J
16 50-1
424.40
2.62778
7.45
121.95
25.34
242.77
244.08
1400
250.00
611
11 19
1730
417.38
2.62053
7.87
124.40
26.82
247.55
248.99
15
255.00
624f
1145
1810!
410.63
2.61345
8.30
126.85
28.36
252.30
253.89
30
260.00
638!
12 12!
1851
404.15
2.60654
8.74
129.29
29.95
257.04
258.78
45
265.00
653
12 39f
1932!
397.92
2.59980
9.20
131.7$
31.60
261.77
263 67
1500
270.00
707*
1307J
2015
391.93
2.59321
9.68
134.17
33.31
266.47
268.54
30
280.00
737!
14041
2142
380.62
2.58049
10.69
139.03
36.90
275.81
278.26
1600
290.00
808
1504
23 12
370.15
2.56838
11.76
143.87
40.74
285.05
287.94
30
300.00
839|
16 05!
2445
360.45
2.55684
12.90
148.68
44.82
294.19
297.58
94
THE RAILROAD TAPER
TAPER 2|. CURVATURE INCREASING 2 00'
EVERY 30 FT. A =2
Deflections to
Transit
at
B.C.
c.c.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
2 00'
4 00'
6 00'
8 00'
10 00'
12 00'
14 00'
16 00'
18 00'
20 00'
I
30
60
90
120
150
180
210
240
270
18
045
124
215
3 18
433
600
739
930
30
018
036
121
218
327
448
621
806
1003
60
1 03
036
054
157
312
439
618
809
10 12
90
2 12
139
054
1 12
233
406
551
748
957
120
345
306
215
1 12
1 30
309
500
703
9 18
150
542
457
400
251
130
1 48
345
554
8 15
180
803
7 12
609
454
327
148
206
421
648
210
1048
951
842
721
548
403
206
224
457
240
1357
1254
1139
1012
833
642
439
224
242
270
1730
1621
1500
1327
1142
945
736
5 15
242
M
I
o
D
log>
d
t
2
y
Ic
/
400
30
036
1432.55
3.15611
0.08
15.00
0.16
30.00
30.00
600
60
148
955.35
2.98016
0.31
29.99
79
59.99
60.00
800
90
336
717.12
2.85559
0.78
44.98
2.20
89.96
89.98
1000
120
600
574.71
2.75945
1.57
59.95
4.70
119.85
119.95
1200
150
900
480.42
2.68162
2.74
74.87
8.63
149.60
149.85
1400
180
1236
413.90
2.61690
4.39
89.73
14.25
179.07
179.64
1600
210
1648
364.96
2.56225
6.57
104.50
21.87
208.08
209.24
1800
240
21 36
328.02
2.51590
9.38
119.12
31.77
236.44
238.54
2000
270
2700
299.71
2.47670
12.87
133.54
44.13
263.76
267.43
TABLES 95
TAPER 2|. INTERMEDIATE VALUES A =2
M
I
/
b
o
D
logD
d
t
X
V
Ic
1
400
30.00
018
018
036
1432.55
3.15611
0.08
15.00
0.16
30.00
30.00
05
31.25
019
019J
0381
1403.33
3.14716
0.09-
15.62
0.17
31.25
31.25
10
32.50
019|
021
040f
1375.26
3.13838
0.09
16.25
0.19
32.50
32.50
' 15
33.75
020J
022J
043
1348.31
3.12979
0.10
16.87
0.20
33.75
33.75
20
35.00
021f
023!
045}
1322.40
3.12136
0.11
17.50
0.22
35.00
35.00
25
36.25
022!
0251
048
1297.45
3.11309
0.11
18.12
0.24
36.25
36.25
30
37.50
023f
027
050!
1273.44
3.10498
0.12
18.75
0.26
37.50
37.50
35
38.75
024!
028}
0531
1250.30
3.09701
0.13
19.37
0.28
38.75
38.75
40
40.00
025f
0301
056
1227.99
3.08919
0.14
20.00
0.30
40.00
40.00
45
41.25
026f
032
058!
1206.46
3.08151
0.15
20.62
0.32
41.25
41.25
50
42.50
027f
033f
OH
1185.66
3.07396
0.15
21.25
0.34
42.50
42.50
55
43.75
029
035|
104}
1165.59
3.06655
0.16
21.87
0.37
43.75
43.75
500
45.00
030
037^-
107}
1146.18
3.05925
0.17
22.50
0.39
45.00
45.00
05
46.25
03H
0391
10*
1127.38
3.05207
0.18
23.12
0.42
46.25
46.25
10
47.50
0321
0411
Wi
1109.23
3.04502
0.19
23.75
0.44
47.50
47.50
15
48.75
033}
0431
16!
1091.64
3.03808
0.20
24.37
0.47
48.75
48.75
20
50.00
034!
0451
20
1074.60
3.03125
0.21
25.00
0.50
50.00
50.00
25
51.25
036
0471
231
1058.09
3.02452
0.22
25.62
0.54
51.25
51.25
30
52.50
037
049}
1 26}
1042.08
3.01790
0.24
26.25
0.57
52.50
52.50
35
53.75
038}
051|
130
1026.54
3.01138
0.25
26.87
0.60
53.75
53.75
40
55.00
039!
053!
1 33|
1011.46
3.00495
0.26
27.50
0.63
55.00
55.00
45
56.25
041
056
137
996.83
2.99862
0.28
28.12
0.67
56.25
56.25
50
57.50
0421
0581
140}
982.61
2.99238
0.29
28.75
0.71
57.50
57.50
55
58.75
043!
100}
1441
968.78
2.98623
0.30
29.37
0.75
58.75
58.75
600
60.00
045
103
148
955.35
2.98016
0.31
29.99
0.79
59.99
60.00
15
63.75
0491
1101
159}
917.20
2.96246
0.36
31.87
0.91
63.74
63.75
30
67.50
053!
1 18
211!
882.00
2.94547
0.41
33.74
1.05
67.49
67.50
45
71.25
0581
126
2241
849.41
2.92912
0.46
35.62
1.21
71.24
71.25
700
75.00
103
134}
237}
819.15
2.91336
0.51
37.49
1.38
74.98
75.00
15
78.75
108
1431
2511
790.99
2.89817
0.57
39.36
1.56
78.73
78.74
30
82.50
1 13
152}
305}
764.72
2.88350
0.64
41.24
1.76
82.47
82.49
45
86.25
1 18}
202
320}
740.15
2.86932
0.71
43.11
1.97
86.22
86.24
800
90.00
124
212
336
717.12
2.85559
0.78
44.98
2.20
89.96
89.98
15
93.75
129!
2221
352
695.50
2.84230
0.86
46.85
2.45
93.70
93.73
30
97.50
135f
233
408f
675.17
2.82941
0.95
48.73
2.71
97.44
97.48
45
101.25
141!
244
425!
656.01
2.81691
1.04
50.60
2.99
101.18
101.23
96
THE RAILROAD TAPER
TAPER 2|. INTERMEDIATE VALUES (Continued) A = 2
M
I
/
b
o
D
log/)
d
t
X
V
Ic
/
900
105.00
148
255}
4 43}
637.91
2.80476
1.13
52.47
3.30
104.92
104.97
15
108.75
154J
307}
'501|
620.81
2.79296
1.23
54.34
3.62
108.66
108.71
30
112.50
2.01
3 19$
520}
604.63
2.78149
.34
56.21
3.96
112.39
112.46
45
116.25
208
332
540
589.28
2.77032
.45
58.08
4.32
116.12
116.21
1000
120.00
2 15
345
600
574.71
2.75945
.57
59.95
4.70
119.85
119.9*
15
123.75
2221
3581
620}
560.86
2.74885
.69
61.82
5.11
123.58
123.69
30
127.50
229$
4 12
641}
547.69
2.73853
.82
63 68
5.54
127.31
127.43
45
131.25
2371
426
7031
535.14
2.72847
.96
65.55
6.00
131.03
131.17
1100
135.00
245
440}
725}
523.17
2.71864
2.10
67.42
6.48
134.75
134.91
15
138.75
253
4551
7481
511.75
2.70906
2.25
69.28
6.98
138.47
138.65
30
142 50
301
510}
811}
500.84
2.69970
2.41
71.15
7.51
142.18
142.39
45
146.25
309}
526
835}
490.41
2.69056
2.57
73.01
8.06
145.89
146.12
1200
150.00
3 18
542
900
480.42
2.68162
2.74
74.87
8.63
149.60
149.85
15
153.75
326|
558}
9251
470.86
2.67289
2.92
76.74
9.23
153.30
153.58
30
157.50
335}
615
950}
461.69
2.66435
3.10
78.60
9.86
157.00
157.31
45
161.25
344f
632
1016|
452.91
2.65601
3.30
80.46
10.52
160.69
161.04
1300
165.00
354
649}
1043}
444.47
2.64784
3.50
82.32
11.20
164.37
164.76
15
168.75
403}
7071
11 10|
436.37
2.63985
3.71
84.17
11.92
168.06
168.48
30
172.50
413
725}
1138}
428.59
2.63204
3.93
86.03
12.67
171.74
172.20
45
176.25
423
744
1207
421.10
2.62439
4.15
87.89
13.45
175.41
175.92
1400
180.00
433
803
1236
413.90
2.61690
4.39
89.73
14.25
179.07
179.64
15
183.75
4431
8221
1305}
406.96
2.60955
4.63
91.59
15.09
182.73
183.35
30
187.50
453}
842
1335}
400.29
2.60237
4.88
93.44
15.96
186.38
187.06
45
191.25
5041
902
14061
393.86
2.59534
5.14
95.29
16.86
190.02
190 76
1500
195.00
515
932}
1437}
387.66
2.58845
5.41
97.14
17.79
193.65
194.46
30
202.50
5371
1004}
1541!
375.90
2.57507
5.97
100.82
19.76
200.89
201.86
1600
210.00
600
1048
1648
364.96
2.56225
6.57
104.50
21.87
208.08
209.24
30
217.50
623}
1133
1756}
354.76
2.54993
7.21
108.18
24.12
215.25
216.60
1700
225.00
6 48 12 19}
1907}
345.23
2.53811
7.89
111.85
26.52
222.37
223.94
30
232.50
7 13 13 07}
2020}
336.33
2.52677
8.61
115.49
29.07
229.43
231.26
1800
240.00
7 39 1 13 57
2136
328.02
2.51590
9.38
119.12
31.77
236.44
238.54
30
247.50
805}
1448
2253}
320.22
2.50545
10.18
122.76
34.63
243.38
245.83
1900
255.00
833
1540}
24 13}
312.94
2.49546
11.03
126.38
37.64
250.26
253.07
30
262.50
901
1634}
25 35}
306 10
2.48586
11.92
129.98
40.81 257.06
260.27
2000
270.00
930
1730
2700
299.71
2.47670
12.87
133.54
44.13
263.76
267.43
TABLES
97
TAPER 3. CURVATURE INCREASING 2 30'
EVERY 30 FT. A
Deflections to
rr
1 rjinsit
at
B.C.
c.c.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
2 30'
5 00'
7 30'
10 00'
12 30'
15 00'
17 30'
20 00
' 22 30'
I
30
60
90
120
150
180
210
240
,
022*
056i
1 45
248f
407*
54H
730
933|
30
022*
045
141i
252*
4 18f
600
756*
1007*
60
1 18f
045
1 07*
226i
400
548f
752*
10 in
90
245
203f
1 07*
130
3 Hi
507*
718f
945
120
44l|
352*
248|
1 30
152*
356i
615
848|
150
707*
6 11J
500
333|
152*
215
4411
722*
180
1003f
900
741i
607*
4 18|
215
237*
526i
210
1330
1218f
10 52*
91U
715
503f
237*
300
240
1726i
1607*
1433f
1245
10 4H
822*
5481
300
M
I
o
D
logZ)
d
t
X
V
U
1
500
30
045
1146.11
3.05923
0.10
15.00
0.20
30.00
30.00
730
60
215
764.47
2.88336
0.39
29.99
0.98
59.99
60.00
1000
90
430.
574.12
2.75900
0.98
44.97
2.75
89.94
89.98
1230
120
730
460.55
2.66328
1.96
59.91
5.88
119.77
119.91
1500
150
11 15
385.68
2.58623
3.43
74.80
10.77
149.37
149.76
1730
180
1545
333.21
2.52270
5.48
89.59
17.78
178.54
179.41
2000
210
2100
295.04
2.46988
8.20
104.22
27.25
207.01
208.78
2230
240 2700
266.74
2.42609
11.69
118.63
39.49
234.42
237.72
98
THE RAILROAD TAPER
TAPER 3. INTERMEDIATE VALUES
M
I
/
6
o
D
log>
d
t
X
y
Ic
500
30.00
022*
022*
045
1146.11
3.05923
0.10
15.00
0.20
30.00
30.00
05
'31.00
023*
023!
047}
1127.30
3.05204
0.10
15.50
0.21
31.00
31.00
10
32.00
024}
025}
049*
1109.15
3.04499
0.11
16.00
0.22
32.00
32.00
15
33.00
025}
026f
052
1091.56
3.03805
0.12
16.50
0.24
33.00
33.00
20
34.00
026}
028}
054*
1074.51
3.03121
0.12
17.00
0.26
34.00
34.00
25
35.00
027
030
057
1058.00
3.02449
0.13
17.50
0.28
35.00
35.00
30
36.00
028
031*
059*
1041.98
3.01786
0.14
18.00
0.29
36.00
36.00
35
37.00
029
033
1 02
1026.44
3.01133
0.15
18.50
0.31
37.00
37.00
40
38.00
030
034*
104*
1011.35
3.00490
0.15
19.00
0.33
38.00
38.00
45
39.00
031
036}
107}
996.71
2.99857
0.16
19.50
0.35
39.00
39.00
50
40.00
032
038
1 10
982.49
2.99233
0.17
20.00
0.37
40.00
40.00
55
41.00
033i
039*
1 12!
968.66
2.98617
0.18
20.50
0.40
41.00
41.00
600
42.00
034}
041}
1 15*
955.23
2.98011
0.19
21.00
0.42
42.00
42.00
15
45.00
037*
046f
124}
917.05
2.96239
0.21
22.50
0.49
45.00
45.00
30
48.00
041
052*
133*
881.83
2.94538
0.24
24.00
0.57
48.00
48.00
45
51.00
044*
058|
143}
849.23
2.92903
0.28
25.50
0.66
51.00
51.00
700
54.00
048}
1 05}
153*
818.95
2.91326
0.31
26.99
0.76
53.99
54.00
15
57.00
052}
nil
204
790.77
2.89805
0.35
28.49
0.87
56.99
57.00
30
60.00
056}
1 18f
2 15
764.47
2.88336
0.39
29.99
0.98
59.99
60.00
45
63.00
100*
1 26
226*
739.88
2.86916
0.44
31.49
1.11
62.99
63.00
800
66.00
1 04f
133!
238*
716.82
2.85541
0.48
32.99
1.24
65.98
66.00
15
69.00
109}
141*
250|
695.17
2.84209
0.53
34.49
1.39
68.98
69.00
30
72.00
1 14
149*
303*
674.81
2.82918
0.59
35.99
1.55
71.98
71.99
45
75.00
1 18!
158
316!
655.61
2.81665
0.64
37.48
1.72
74.97
74.99
900
78.00
123f
206f
330*
637.48
2.80447
0.70
38.98
1.90
77.97
77.99
15 81.00
128f
216
344!
620.35
2.79264
0.77
40.48
2.09
80.96
80.99
30 84.00
1 34 2 25*
359*
604.13
2.78113
0.84
41.98
2.30
83.95
83.99
45 87.00
1 39* i 2 35
414*
588.74
2.76992
0.91
43.47
2.52
86.95
86.98
1000 90.00
1 45 2 45
430
574.12
2.75900
0.98
44.97
2.75
89.94
89.98
15 ! 93.00
150|
255}
446
560.23
2.74837
1.06
46.47
2.99
92.93
92.98
30 ! 96.00
156*
306
502*
547.01
2.73800
1.14
47.96
3.25
95.92
95.97
45 ', 99.00
202* 316!
519}
534.41
2.72787
1.23
49.46
3.53
98.90
98.96
1100 102.00
208f
327f
536*
522.39
2.71799
1.32
50.95
3.82
101.89
101.96
15 105.00
215
339f
554}
510.92
2.70835
1.42
52.45
4.12
104.87
104.95
30 108.00
221*
351
612*
499.95
2.69893
1.52
53.94
4.44
107.86
107.95
45 111.00
228
403}
631}
489.46
2.68972
1.62
55.44
4.78
110.84
110.94
TABLES 99
TAPERS. INTERMEDIATE VALUES (Continued} A = 2|
M
I
/
b
D
log>
d
t
X
V
Ic
1200
114.00
234!
415*
650i
479.41
2.68071
1.73
56.93
5.13
113.82
113.93
15
117.00
2 41f 4 28i
710
469.78
2.67189
1.84
58.42
5.50
116.80
116.92
30
120.00
248!
44U
730
460.55
2.66328
1.96
59.91
5.88
119.77
119.91
45
123.00
256
454*
750*
451.69
2.65484
2.08
61.41
6.29
122.75
122.90
1300
126.00
303J
508i
811*
443.18
2.64658
2.21
62.90
6.71
125.72
125.89
15 129.00
310|
522
832!
435.00
2.63849
2.34
64.39
7.15
128.69
128.88
30
132. OOj 3 18*
536
754*
427.14
2.63057
2.48
65.88
7.61
131.65
131.87
45
135.00
326|
550|
916!
419.58
2.62281
2.63
67.37
8.09
134.61
134.86
1400
138.00
334i
605i
939*
412.29
2.61520
2.78
68.86
8.58
137.57
137.84
15
141.00
342i
620*
1002!
405.26
2.60773
2.93
70.34
9.10
140.53
140.82
30
144.00
350*
636
1026*
398.50
2.60043
3.09
71.83
9.64
143.48
143.80
45
147.00
359
651*
1050*
391.98
2.59326
3.26
73.32
10.19
146.43
146.78
1500
150.00
407|
707*
11 15
385.68
2.58623
3.43
74.80
10.77
149.37
149.76
30
156. OOJ 425
740*
1205*
373.72
2.57255
3.79
77.77
11.99
155.25
155.71
1600
162.00 443i
8 14i
1257*
362.56
2.55938
4.17
80.73
13.30
161.11
161.65
30
168.00
502
849*
1351*
352.13
2.54670
4.58
83.69
14.70
166.94
167.58
1700
174.00
52H
926i
1447*
342.36
2.53448
5.02
86.64
16.19
172.75
173.50
30
180.00
54U
1003J
1545
333.20
.52270
5.48
89.58
17.78
178.54
179.41
1800
186.00
601!
1042f
1644*
324.61
.51136
5.97
92.52
19.47
184.30
185.31
30
192.00
623
11 22*
1745*
316.53
.50041
6.49
95.46
21.26
190.03
191.20
1900
198.00
644f
1203!
1848*
308.94
.48987
7.03
98.39
23.15
195.73
197.07
30
204.00
707
1246*
1953*
301.78
.47969
7.60
101.31
25.14
201.39
202.93
2000
210.00
730
1330
2100
295.04
.46988
8.20
104.22
27.25
207.01
208.78
30
216.00
753*
1415
22 08*
288.69
.46043
8.83
107.12
29.47
212.59
214.62
2100
222.00
817!
1500!
2318*
282.72
.45136
9.50
110.02
31.80
218.13
220.44
30
228.00
842*
1548
2430*
277.07
2.44259
10.19
112.90
34.25
223.62
226.23
2200
234.00
907!
1636!
2544*
271.75
2.43417
10.92
115.77
36.81
229.05
231.99
30
240.00
933!
1726J
2700
266.74
2.42609
11.69
118.63
39.49
234.42
237.72
100
THE RAILROAD TAPER
TAPER 3|. CURVATURE INCREASING 3 00'
EVERY 30 FT.
Deflections to
at
B.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
3 00'
6 00'
9 00'
12 00'
15 00'
18 00'
21 00'
24 00'
I
30
60
90
120
150
180
210
o
/
027
1 07!
206
O /
322|
457
649!
900
30
027
054
2 01!
327
5 10|
712
93H
60
1 34!
054
1 21
2 55^
448
658|
927
90
3 18
228!
121
148
349|
609
846!
120
5 37|
439
3 22!
1 48
2 15
443!
730
150
833
725!
600
4164
215
242
537!
180
1204|
1048
913|
721
5 10|
242
309
210
16 12
1446|
1303
11 OH
842
604!
309
M
l
D
log/)
d
t
X
V
lc
600
30
054
955.16
2.98008
0.12
15. OC
) 0.24
30.00
30.00
900
60
242
637.25
2.80431
0.47
29. 9^
1 1.18
59.98
60.00
1200
90
524
478.84
2.68021
1.18
44. 9f
3.30
89.91
89.97
1500
120
900
384.60
2.58501
2.35
59. 8
> 7.06
119.67
119.88
1800
150
1330
322.75
2.50887
4.11
74.71
12.91
149.10
149.65
2100
180
1854
279.78
2.44682
6.56
89.4021.29
177.91
179.17
2400
210
25 12
248.99
2.39618
9.82
103.8*
32.58
205.71
208.28
TABLES 101
TAPER 3i INTERMEDIATE VALUES' A- 3
M
I
/
b
D
logZ)
d
t
X
V
Ic
600
30.00
027
027
054
955.16
2.98008
0.12
15.00
0.24
30.00
30.00
15
32.50
029|
0311
101
916.98
2.96236
0.14
16.26
0.28
32.50
32.50
30
35.00
032|
035!
108*
881.75
2.94535
0.16
17.50
0.33
35.00
35.00
45
37.50
035*
040*
1 16
849.13
2.92897
0.18
18.75
0.39
37.50
37.50
700
40.00
038*
045*
124
818.84
2.91320
0.20
20.00
0.45
40.00
40.00
15
42.50
41|
50!
1 32*
790.65
2.89798
0.23
21.25
0.52
42.50
42.50
30
45.00
045
056*
141*
764.34
2.88329
0.26
22.49
0.59
45.00
45.00
45
47.50
048*
102
150*
739.73
2.86907
0.29
23.74
0.67
47.49
47.50
800
50.00
052
108
200
716.66
2.85531
0.32
24.99
0.76
49.99
50.00
15
52.50
055f
114|
210
694.99
2.84198
0.35
26.24
0.85
52.49
52.50
30
55.00
059|
120f
220*
674.61
2.82905
0.39
27.49
0.95
54.99
55.00
45
57.50
103|
127*
231
655.40
2.81651
0.43
28.74
1.06
57.49
57.50
900
60.00
107*
134*
242
637.25
2.80431
0.47
29.99
1.18
59.98
60.00
15
62.50
1 11|
1 411
253*
620.09
2.79245
0.51
31.24
1.31
62.48
62.50
30
65.00
1 16
149|
305*
603.85
2.78093
0.56
32.48
1.44
64.98
.64.99
45
67.50
2()|
157
317*
588.44
2.76970
0.61
33.73
1.58
67.48
67.49
1000
70.00
25
205
330
573.80
2.75876
0.66
34.98
1.73
69.97
69.99
15
72.50
29|
213|
343
559.88
2.74810
0.71
36.23
1.89
72.47
72.49
30
75.00
34*
221!
356*
546.64
2.73770
0.77
37.48
2.06
74.96
74.99
45
77.50
39*
230*
4 10
534.01
2.72755
0.83
38.73
2.24
77.45
77.49
1 1 00
80.00
44*
239*
424
521.96
2.71764
0.89
39.97
2.43
79.95
79.98
15
82.50
149f
248!
438*
510.46
2.70796
0.96
41.22
2.63
82.44
82.48
30
85.00
155
258*
453*
499.46
2.69850
1.03
42.46
2.84
84.93
84.98
45
87.50
200*
308
508*
488.94
2.68926
1.10
43.71
3.06
87.42
87.47
1200
90.00
206
318
524
478.86
2.68021
1.18
44.96
3.29
89.91
89.97
15
92.50
211!
3281
540
469.20
2.67136
1.26
46.20
3.54
92.40
92.47
30
95.00
217*
338!
556*
459.93
2.66269
1.34
47.45
3.80
94.89
94.96
45
97.50
223|
349*
613
451.03
2.65421
1.42
48.69
4.07
97.37
97.46
102 THE RAILROAD TAPER
TAPfiR 3|. INTERMEDIATE VALUES (Continued) A =
M
I
/
ft
D
log-D
d
t
X
V
Ic
1300
100.00
229*
400*
630
442.48
2.64589
1.51
49.94
4.35
99.86
99.95
15
102.50
235f
411f
647J
434.26
2.63775
1.60
51.18
4.64
102.35
102.45
30
105.00
242
423|
705*
426.36
2.62978
1.70
52.42
4.94
104.82
104.94
45
107.50
248i
435
723|
418.752.62195
1.80
53.67
5.26
107.30
107.43
1400
110.00
255
447
742
411.41
2.61427
1.90
54.91
5.59
109.78
109.92
15
112.50
301f
459*
801
404.34
2.60675
2.01
56.15
5.94
112.26
112.41
30
115.00
308|
511!
820*
397.53
2.59937
2.12
57.39
6.30
114.73
114.90
45
117.50
315|
524|
840
390.95
2.59212
2.23
58.64
6.67
117.20
117.39
1500
120.00
322|
537|
900
384.60
2.58501
2.35
59.88
7.06
119.67
119.88
30
125.00
337
604*
941*
372.53
2.57116
2.60
62.36
7.88
124.61
124.85
1600
130.00
352
632
1024
361.26
2.55782
2.87
64.84
8.76
129.54
129.82
30
135.00
407
700!
1108*
350.70
2.54494
3.15
67.31
9.70
134.45
134.79
1700
140.00
423
730|
1154
340.79
2.53249
3.45
69.78
10.70
139.34
139.75
30
145.00
440
801J
1241*
331.49
2.52047
3.77
72.25
11.77
144.22
144.70
180Q
150.00
457
833
1330
322.75
2.50887
4.11
74.71
12.91
149.10 149.65
30
155.00
514|
905!
1420*
314.51
2.49763
4.47
77.17
14.12
153.96
154.59
1900
160.00
532J
939|
1512
306.75
2.48678
4.84
79.63
15.40
158.78
159.52
30
165.00
551
1014*
1605*
299.42
2.47628
5.24
82.08
16.76
163.59
164.44
2000
170.00
610
1050
1700
292.50
2.46613
5.66
84.52
18.19
168.39
169.36
30
175.00
629J
1126!
17 56*
285.96
2.45631
6.10
86.96
19.70
173.16
174.27
2100
180.00
649J
12041
1854
279.78
2.44682
6.56
89.40
21.29
177.91
179.17
30
185.00
710
12 43 4 l
1953*
273.92
2.43762
7.04
91.83
22.96
182.62
184.06
2200
190.00
731
1323
2054
268.382.42875
7.55
94.25
24.71
187.30
188.93
30
195.00
752*
1403f
21 56*
263.132.42017 8.08
96.67
26.55
191.95
193.79
2300
200.00
814|
1445
2300
258.172.41191 8.64
99.08
28.47
196.59
198.63
2400
210.00 900
1612
25 12
248.99
2-.39618 9.82
103.88
32.58
205.71
208.28
1
TABLES
103
TAPER 3*. CURVATURE INCREASING 4 00'
EVERY 30 FT.
Deflections to
at
B.C.
C.C.
C.C.
C.C.
C.C.
C.C.
C.C.
4 00'
8 00'
12 00'
16 00'
20 00'
24 00'
28 00'
I
30
60
90
120
150
180
/
036
1 30
2 48
430
636
906
30
036
1 12
242
436
6 54
936
60
206
1 12
1 48
3 54
624
9 18
90
424
3 18
1 48
224
506
8 12
120
730
612
430
224
300
618
150
1124
954
800
542
300
336
180
1606
1424
1218
948
654
336
M
l
D
logD
d
t
X
I
lc
800
30
1 12
716.50
2.85522
0.16
15.00
0.31
30. OC
30.00
1200
60
336
478.31
2.67971
0.63
29.98
1.57
59.97
59.99
1600
90
712
359.96
2.55625
1.57
44.92
4.39
89.84
89.95
2000
120
1200
289.97
2.46235
3.13
59.78
9.40
119.42
119.79
2400
150
1800
244.63
2.38851
5.46
74.49
17.17
148. 4C
149.39
2800
180
25 12
213.85
2.33011
8.71
88.95
28.24
176.28
178.52
104 THE KAILROAD TAPER
TAPER 3. INTERMEDIATE ^VALUES A = 4
M
I
/
b
o
D
*D
d
t
X
V
Ic
800
30.00
036
036
12
716.50
2.85522
0.16
15.00
0.31
30.00
30.00
15
31.88
038!
040
181
694.82
2.84187
0.18
15.93
0.36
31.87
31.87
30
33.75
041$
044$
26
674.42
2.82893
0.20
16.87
0.41
33.74
33.75
45
35.62
0441
0491
33$
655.19
2.81637 0.22
17.81
0.46
35.62
35.62
900
37.50
0471
054
411
637.02
2.80415 0.24
18.74
0.52
37.50
37.50
15
39.38
0501
059
491
619.84
2.79228
0.26
19.68
0.58
39.37
39.37
30
41.25
053$
104
1 57$
603.58
2.78073
0.29
20.62
0.64
41.24
41.25
45
43.12
056!
1 09$
2061
588.15
2.76949 0.32
21.55
0.71 43.12
43.12
1000
45.00
100
1 15
2 15
573.49
2.75853
0.35
22.49
0.79 44.99
45.00
15
46.88
103$
1 20!
2241
559.55
2.74784
0.38
23.43
0.87 46.87
46.87
30
48.75
107
1 26|
233$
546.28
2.73742
0.41
24.36
0.95 48.74 48.75
45
50.62
110$
132f
2431
533.62
2.72723 0.44
25.30
.04 50.61
50.62
1100
52.50
141
139
2531
521.54
2.71729 0.47
26.24
.13 52.48
52.50
15
54.38
18
145$
303$
510.01
2.70758 0.51
27.17
.23 54.35 54.37
30
56.25
22
1 52
3 14
498.98
2.69808 0.55
28.11
.34 56.22 56.24
45
58.12
26
1 58!
324!
488.43
2.68880
0.59
29.04
.45
58.10
58.12
1200
60.00
130
206
336
478.31
2.67971
0.63
29.98
.57
59.97
59.99
15
61.88
1341
2131
347$
468.61
2.67081
0.67
30.91
.69
61.84
61.87
30
63.75
138|
2 20$
359
459.31
2.66211
0.72
31.85
.82 63.71 63.74
45
65.62
142!
2281
411
450.38
2.65358
0.77
32.79
.96
65.59
65.62
1300
67.50
1471
236
4231
441.79
2.64522
0.82
33.72
2.11
67.46
67.49
15
69.38
151!
244
435!
433.53
2.63702
0.87
34.65
2.26
69.33
69.36
30
71.25
1 56f
252
448$
425.58
2.62898
0.92
35.59
2.42
71.19
71.23
45
73.12
2011
300$
501!
417.92
2.62109
0.97
36.52
2.58
73.06
73.11
1400
75.00
206
309
515
410.54
2.61336
1.03
37.46
2.75
74.93
74.98
15
76.88
2 11
317!
528!
403.42
2.60576
.09
38.39
2.93
76.79
76.85
30
78.75
216
326$
542$
396.56
2.59831
.15
39.33
3.12 78.66
78.72
45
80.62
221
335!
556!
889.94
2.59100
.22
40.26
3.31 ' 80.53
80.59
1500
82.50
2 261
345
6111
383.53
2.58380
.28
41.19
3.51 82.39
82.48
30
86.25
237
404
6*41
371.35
2.56978
.42
43.06
3 93 86.12
86.21
1600
90.00
248
424
712
359.96
2.55625
.57
44.92
4.39 89.84
89.95
30
93.75
259$
444$
744
349.28
2.54317
.73
46.79
4.89 93.56
93.69
1700
97.50
3 111
506
8171
339.23
2.53049
.89
48.65
5.42 97.27
97.43
30
101.25
323 i
528
851$
329.79
2.51824
2.07
50.51
5.98 100.98
101.16
1800
105.00
336
551
927
320.90
2.50637
2.26
52.37
6.59 ;104.68
104.89
30
108.75
349
614$
1003$
312.50
2.49485
2.46
54.22
7.23 108.38 108.62
1900
112.50
4021
639
10411
304.58
2.48370
2.67
56.08
7.91 112.07
112.34
30
116.25
416
704
1120
297.07
2.47286
2.89
57.93
8.63 '115.75
116.07
2000
120.00
430
730
1200
289.97
2.46235
3.13
59.78
9.40 1119.42 119.79
30
123.75
444$
756$
1241
283.24
2.45215
3.38
61.63
10.21 123.08
123.51
2100
127.50
4591
824
13231
276.86
2.44226
3.64
63.48
11.06 126.74
127.22
30
131.25
514$
852
1406$
270.79
2.43263
3.91
65.32
11.96 130.38130.93
TABLES 105
TAPER 3|. INTERMEDIATE VALUES (Continued) A = 4
M
I
/
b
D
logZ)
d
t
X
V
Ic
2200
135.00
530
921
1451
265.02
2.42328
4.19
67.16
12.90
134.01
134.63
30
138.75
546
950
1536
259.53
2.41419
4.48
69.00
13.90
137.63
138.33
2300
142.50
602i
1021
1623i
254.33
2.40540
4.80
70.83
14.94
141.23
142.02
2400
150.00
636
1124
1800
244.63
2.38851
5.46
74.49
17.17
148.40
149.39
2500
157.50
7 llj
1230
19 4U
235.82
2.37258
6.18
78.14
19.61
155.50
156.73
2600
165.00
748
1339
2127
227.81
2.35757
6.97
81.76
22.26
162.52
164.04
2700
172.50
826^
1451
23 m
220.51
2.34343
7.81
85.37
25.14
169.45
171.31
2800
180.00
906
1606
2512
213.85
2.33011
8.71
88.95
28.24
176.29
178.52
TAPER 3f. CURVATURE INCREASING 5 00'
EVERY 30 FT. A = 5
Transit
at
Deflections to
B.C.
5 00'
C.C.
10 00'
C.C.
15 00'
C.C.
20 00'
C.C.
25 00'
C.C.
30 00'
I
30
60
90
120
150
30
60
90
120
150
045
237
530
922^
1415
045
"l30'
407
745
12 22|
/
1521
130
/
330
322|
215
"300"
707
537
545
452i
300
'345"
8 15
837
800
622i
345
215
537^
1000
M
I
D
log>
d
t
X
y
lc
/
1000
1500
2000
2500
3000
30 130
60 430
90 900
120 15 00
150 22 30
573.34
383.13
288.80
233.54
198.34
2.75841
2.58323
2.45939
2.36836
2.29741
0.20
0.78
1.96
3.90
6.81
14.99
29.97
44.88
59.66
74.21
0.39
1.96
5.49
11.73
21.89
30.00
59.96
89.75
119.09
147.50
30.00
59.99
89.92
119.67
149.04
106
THE RAILROAD TAPER
TAPER 3|. INTERMEDIATE VALUES
M
I
/
b
D
logD
d
t
X
f
Ic
1000
30.00
045
/
045
1 30
573.34
2.75841
0.20
14.99
0.39
30.00
30.00
15
31.50
0471
049
136|
559.38
2.74771
0.21
15.74
0.43
31.50
31.50
30
33.00
050}
053!
144
546.10
2.73727
0.23
16.49
0.48
33.00
33.00
45
34.50
053}
058
151}
533.43
2.72708
0.25
17.24
0.53
34.50
34.50
1100
36.00
056
102|
158f
521.34
2.71712
0.27
17.99
0.59
36.00
36.00
15
37.50
059}
107}
206*
509.79
2.70739
0.29
18.74
0.65
37.49
37.50
30
39.00
102
1 12*
214*
498.74
2.69787
0.31
19.49
0.71
38.99
39.00
45
40.50
105}
117*
222!
488.18
2.68858
0.34
20.24
0.77
40.49
40.50
1200
42.00
108*
1 221
231}
478.05
2.67947
0.37
20.99
0.84
41.99
42.00
15
43.50
1 111
1 28
2391
468.34
2.67056
0.40
21.74
0.91
43.49
43.50
30
45.00
1 15
133|
2481
459.02
2.66183
0.43
22.49
0.98
44.99
45.00
45
46.50
1 18}
139}
2571
450.07
2.65328
0.46
23.23
.06
46.49
46.50
1300
48.00
122
145}
307}
441.46
2.64489
0.49
23.98
.14
47.98
48.00
15
49.50
125*
151}
3161
433.18
2.63667
0.52
24.73
.23
49.48
49.50
30
51.00
129
157*
326*
425.21
2.62860
0.55
25.48
.32
50.98
51.00
45
52.50
132f
2 03 f
336*
417.53
2.62069
0.58
26.23
.42
52.48
52.50
1400
54.00
136|
210}
3461
410.13
2.61292
0.62
26.98
1.52
53.97
53.99
15
55.50
1 40*
2161
357}
402.99
2.60529
0.66
27.72
62
55.47
55.49
30
57.00
144}
223f
408
396.11
2.59782
0.70
28.47
.73
56.97
56.99
45
58.50
148}
230*
4181
389.46
2.59046
0.74
29.22
1.84
58.46
58.49
1500
60.00
152*
237*
430
383.03
2.58323
0.78
29.97
1.96
59.96
59.99
30
63.00
201
252
453
370.80
2.56914
0.87
31.46
2.21
62.95
62.99
TABLES 107
TAPER 3|. INTERMEDIATE VALUES - (Continued) A = 5
M
I
/
b
D
logD
d
t
X
y
Ic
1600
66.00
209|
307
1
5161
359.35
2.55552
0.96
32.96
2.48
64.44
64.99
30
69.00
218*
323
541*
348.61
2.54234
1.06
34.45
2.77
68.92
68.98
1700
72.00
227f
339*
6071
338.51
2.52957
1.17
35.94
3.09
71.90
71.97
30
75.00
237*
356i
6331
329.00
2.51720
.28
37.44
3.43
74.88
74.97
1800
78.00
247*
4 131
701i
320.04
2.50520
.40
38.92
3.79
77.86
77.96
30
81.00
257*
432
729*
311.57
2.49356
.53
40.41
4.18
80.84
80.95
1900
84.00
308
4-501
7581
303.58
2.48227
.67
41.90
4.59
83.81
83.94
30
87.00
319
510
829
295.99
2.47128
.81
43.39
5.03
86.78
86.93
2000
90.00
330
530
900
288.80
2.46060
.96
44.88
5.49
89.75
89.92
30
93.00
341*
550|
932
281.98
2.45022
2.12
46.36
5.98
92.71
92.91
2100
96.00
353
611f
10 04J
275.50
2.44012
2.28
47.85
6.50
95.67
95.89
30
99.00
405
633*
1038*
269.33
2.43028
2.45
49.33
7.05
98.62
98.87
2200
102.00
417*
6551
11 13J
263.46
2.42071
2.63
50.81
7.63
101.56
101.85
30
105.00
430
7 181
11481
257.872.41140
2.82
52.29
8.23
104.50
104.82
2300
108.00
443
742J
12251
252.55
2.40235
3.02
53.76
8.86
107.44
107.78
2400
114.00
509*
83U
13401
242.61
2.38491
3.44
56.72
10.23
113.28
113.73
2500
120.00
537*
922*
1500
233.54
2.36836
3.90
59.66
11.73
119.09
119.67
2600
126.00
606*
1016J
16221
225.24
2.35265
4.40
62.59
13.37
124.87
125.59
2700
132.00
637
11 121
17491
217.64
2.33774
4.94
65.51
15.15 130.61
131.49
2800
138.00
708*
12 10f
19 191
210.66
2.32358
5.52
68.42
17.07
136.29
137.36
2900
144.00
741
13111
20521
204.24
2.31014
6.14
71.32
19.15
141.93
143.21
3000
150.00
815
14 15
2230
198.34
2.29741
6.81
74.21
21.39
147.50
149.04
108
THE RAILROAD TAPER
*
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THE RAILROAD TAPER
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TABLES
111
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83
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112
THE RAILROAD TAPER
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883
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TABLES
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114
THE RAILROAD TAPER
5
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22 S 8^ 8 S
TABLES
ALIGNMENT REVISION
MAINTAINING LENGTH UNCHANGED
(See page 55, par. 43)
115
M
r
00'
130'
2 00'
A
1
1
1
i
Taper.
i
*
*
1
I
I
h
M'
I
h
M'
I
h
M'
I
h
M'
2 30'
5
10
15
20
25
110.00
96.00
0.04
0.14
103'
m. 60
158.00
154.00
0.01
0.23
0.35
148'
134'
132'
266!6o
224.00
218.00
214.00
QA2
0.37
0.50
0.26
2 25'
2 07'
2 04'
2 02'
110.00
94.00
92.00
0.07
0.22
0.19
2 20'
2 04'
2 02'
M
2 30'
3 00'
A
1
i
i
!
Taper.
i
i
1
H
'
I
k
M'
i
h
M'
I
h
M'
I
h
0.03
0.12
0.17
M'
10
15
20
25
30
40
50
350.00
296.00
286.00
280.00
276.00
274.00
0.84
0.71
0.87
0.75
1.05
1.25
3 10'
2 43'
2 38'
2 35'
2 33'
2 32'
132.00
125.00
123.00
0.15
0.19
0.27
2 42'
2 35'
2 33'
165.00
157.00
154.00
153.00
0.31
0.32
0.25
0.35
3 14'
3 07'
3 04'
3 03'
96.67
93.33
92.00
3 10'
3 05'
3 03'
M
4 00'
A
f
i
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Taper.
1
H
2
I
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h
M'
I h M'
I h M'
10
15
20
25
30
40
50
60
i56!66 '6.34 4 30'
139.33 0.35 4 14'
135.33 0.31 4 08'
133.33 0.24 4 05'
132.00 0.35 4 03'
110.00 0.15 4 40'
96.00 0.12 4 12'
93.00 0.10 4 06'
92.00 0.15 4 04'
91.50 0.20 4 03'
259! 66
233.00
224.00
217.00
214.00
213.00
0.81
0.76
0.69
0.51
0.75
4 49'
4 23'
4 14'
4 07'
4 04'
4 03'
116
THE RAILROAD TAPER
MAINTAINING LENGTH UNCHANGED (Continued}
M
5 00'
A
1
1
1
If
Taper.
1
|
2
21
I
I
h
M'
I
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AT
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5 30'
5 13'
5 08'
5 05'
5 03'
15
20
25
30
40
50
60
70
80
90
154.00
132.50
127.00
124.50
122.50
121.50
0.35
0.34
0.32
0.29
0.32
0.28
6 08'
5 25'
5 14'
5 09'
5 05'
5 03'
102.00
95.20
93.20
92.00
91.20
0.25
0.17
0.18
0.13
0.19
6 19'
5 26'
5 15'
5 10'
5 07'
5 05'
5 04'
223.33
190.00
182.67
176.67
174.00
172.67
172.00
0.76
0.58
0.64
0.70
0.66
0.62
0.72
6 20'
5 30'
5 19'
5 10'
5 06'
5 04'
5 03'
349.00
296.00
285.00
280.00
277.00
275.00
274.00
1.64
1.43
1.50
1.60
1.53
1.31
1.48
M
6 00'
A
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Taper.
5
2
2i
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I
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15
20
25
30
40
50
60
70
80
90
0^63
0.58
0.66
0.52
0.76
0.58
111.00
98.33
95.00
93.33
92.00
91.00
0.25
0.22
0.24
0.25
0.34
0.14
7 03'
6 25'
6 15'
6 10'
6 06'
6 03'
6^47'
6 27'
6 14'
6 08'
6 06'
6 04'
131.60
123.60
120.00
117.20
116.00
115.20
0.35
0.36
0.33
0.35
0.34
0.20
6 44'
6 24'
6 15'
6 08'
6 05'
6 03'
258.67
228.67
220.67
217.33
215.33
214.00
212.67
1.21
1.12
1.09
1.25
1.35
1.39
0.72
7 13'
6 28'
6 16'
6 11'
6 08'
6 06'
6 04'
173.50
163.50
157.00
154.00
153.00
152.00
:::: :::::
5
8 00'
A
1
H
H
- 2
Taper.
2
2J
2*
2!
/
I
h
M'
I
h
M'
I
h
M'
I
h
0.43
0.40
0.43
0.31
0.31
0.43
0.33
M'
20
25
30
40
50
60
70
80
90
112.25
101.00
97.00
93.25
92.00
91.50
91.00
9 29'
8 44'
8 28'
8 13'
8 08'
8 06'
8 04'
176.67
150.00
139.00
135.33
133.67
132.67
132.00
131.67
0.71
0.67
0.64
0.63
0.70
0.75
0.74
0.95
10 20'
9 00'
8 27'
8 16'
8 11'
8 08'
8 06'
8 05'
258 '50
232.50
224.00
219.50
217.00
215.50
!ei
.58
.57
.48
.50
.65
9 d 37'
8 45'
8 28'
8 19'
8 14'
8 11'
220.40
179.60
172.00
168.40
166.40
165.60
164.80
1.04
0.96
1.08
0.92
0.81
1.14
1.18
10 26'
8 44'
8 25'
8 16'
8 11'
8 09'
8 07'
M
10 00'
A
U
ij
2
2^
Taper.
2i
2*
2|
3
I
I
h
M'
J
h
A/'
I
h
M'
I
h
M'
25
30
40
50
60
70
80
90
258 '.00
234.80
226.40
221.60
218.80
'6!76
0.69
0.65
0.73
0.64
0.71
0.82
12 22'
10 50'
10 28'
10 19'
10 13'
10 10'
1008'
112.00
101.40
95.40
93.40
92.20
91.60
91.20
91.00
0.45
0.41
0.39
0.45
0.39
0.42
0.41
0.53
1150'
1057'
1027'
10 17'
ioir
1008'
1006'
10 05'
L99
1.90
1.95
1.86
1.90
12 bb'
iro2
10 41
10 29
10 22
2i9!6o
190.67
182.67
178.67
176.33
175.00
^36
.32
.33
.31
.30
1.46
12 27'
11 02'
10 38'
10 26'
10 19'
10 15
155.50
132.50
127.00
124.75
123.25
122.50
122. OC
LOGARITHMS OF NUMBERS 117
100
1
2
3
4
5
6
7
8
9
110
1
4
5
6
7
8
9
120
1
2
3
4
5
6
7
8
9
130
1
2
3
4
5
6
7
8
9
140
1
2
3
4
5
6
7
8
9
150
3456789
00000 00043 00087 00130 00173 00217 00260 00303 00346 00389
0432 0475 0518 0561 0604 0647 0689 0732 0775 0817
0860 0903 0945 0988 1030 1072 1115 1157 1199 1242
1284 1326 1368 1410 1452 1494 1536 1578 1620 1662
1703 1745 1787 1828 1870 1912 1953 1995 2036 2078
2119 2160 2202 2243 2284 2325 2366 2407 2449 2490
2531 2572 2612 2653 2694 2735 2776 2816 2857 2898
2938 2979 3019 3060 3100 3141 3181 3222 3262 3302
3342 3383 3423 3463 3503 3543 3583 3623 3663 3703
3743 3782 3822 3862 3902 3941 3981 4021 4060 4100
04139 04179 04218 04258 04297 04336 04376 04415, 04454 04493
4532 4571 4610 4650 4689 4727 4766 4805 4844 4883
4922 4961 4999 5038 5077 5115 5154 5192 5231 5269
5346 5385 5423 5461 5500 5538 5576 5614 5652
5690 5729 5767 5805 5843 5881 5918 5956 5994 6032
6070 6108 6145 6183 6221 6258 6296 6333 6371 6408
6446 6483 6521 6558 6595 6633 6670 6707 6744 6781
6819 6856 6893 6930 6967 7004 7041 7078 7115 7151
7188 7225 7262 7298 7335 7372 7408 7445 7482 7518
7555 7591 7628 7664 7700 7737 7773 7809 7846 7882
07918 07954 07990 08027 08063 08099 08135 08171 08207 08243
8279 8314 8350 8386 8422 8458 8493 8529 8565 8600
8636 8672 8707 8743 8778 8814 8849 8884 8920 8955
8991 9026 9061 9096 9132 9167 9202 9237 9272 9307
9342 9377 9412 9447 9482 9517 9552 9587 9621 9656
9691 9726 9760 9795 9830 9864 9899 9934 9968 10003
10037 10072 10106 10140 10175 10209 10243 10278 10312 0346
0380 0415 0449 0483 0517 0551 0585 0619 0653 0687
0721 0755 0789 0823 0857 0890 0924 0958 0992 1025
1059 1093 1126 1160 1193 1227 1261 1294 1327 1361
11394 11428 11461 11494 11528 11561 11594 11628 11661 11694
1727 1760 1793 1826 1860 1893 1926 1959 1992 2024
2057 2090 2123 2156 2189 2222 2254 2287 2320 2352
2385 2418 2450 2483 2516 2548 2581 2613 2646 2678
2710 2743 2775 2808 2840 2872 2905 2937 2969 3001
3033 3066 3098 3130 3162 3194 3226 3258 3290 3322
3354 3386 3418 3450 3481 3513 3545 3577 3609 3640
S672 3704 3735 3767 3799 3830 3862 3893 3925 3956
3988 4019 4051 4082 4114 4145 4176 4208 4239 4270
4301 4333 4364 4395 4426 4457 4489 4520 4551 4582
14613 14644 14675 14706 14737 14768 14799 14829 14860 14891
4922 4953 4983 5014 5045 5076 5106 5137 5168 5198
5229 5259 5290 5320 5351 5381 5412 5442 5473 5503
5534 5564 5594 5625 5655 5685 5715 5746 5776 5806
5836 5866 5897 5927 5957 5987 6017 6047 6077 6107
6137 6167 6197 6227 6256 6286 6316 6346 6376 6406
6435 6465 6495 6524 6554 6584 6613 6643 6673 6702
6732 6761 6791 6820 6850 6879 6909 6938 6967 6997
7026 7056 7085 7114 7143 7173 7202 7231 7260 7289
7319 7348 7377 7406 7435 7464 7493 7522 7551 7580
17609 17638 17667 17696 17725 17754 17782 17811 17840 17869
118 LOGARITHMS OF NUMBERS
N
150
1
2
3
4
5
6
7
8
9
160
1
2
3
4
5
6
7
170
1
2
3
4
5
6
7
8
9
180
1
2
3
4
5
6
7
8
190
1
2
3
4
5
6
7
8
9
200
23456789
17609 17638 17667 17696 17725 17754 17782 17811 17840 17869
7898 7926 7955 7984 8013 8041 8070 8099 8127 8156
8184 8213 8241 8270 8298 8327 8355 8384 8412 8441
8469 8498 8526 8554 8583 8611 8639 8667 8696 8724
8752 8780 8808 8837 8865 8893 8921 8949 8977 9005
9033 9061 9089 9117 9145 9173 9201 9229 9257 9285
9312 9340 9368 9396 9424 9451 9479 9507 9535 9562
9590 9618 9645 9673 9700 9728 9756 9783 9811 9838
9866 9893 9921 9948 9976 20003 20030 20058 20085 20112
20140 20167 20194 20222 20249 0276 0303 0330 0358 0385
20412 20439 20466 20493 20520 20548 20575 20602 20629 20656
0683 0710 0737 0763 0790 0817 0844 0871 0898 0925
0952 0978 1005 1032 1059 1085 1112 1139 1165 1192
1219 1245 1272 1299 1325 1352 1378 1405 1431 1458
1484 1511 1537 1564 1590 1617 1643 1669 1696 1722
1748 1775 1801 1827 1854 1880 1906 1932 1958 1985
2011 2037 2063 2089 2115 2141 2167 2194 2220 2246
2272 2298 2324 2350 2376 2401 2427 2453 2479 2505
2531 2557 2583 2608 2634 2660 2686 2712 2737 2763
2789 2814 2840 2866 2891 2917 2943 2968 2994 3019
23045 23070 23096 23121 23147 23172 23198 23223 23249 23274
3300 3325 3350 3376 3401 3426 3452 3477 3502 3528
3553 3578 3603 3629 3654 3679 3704 3729 3754 3779
3805 3830 3855 3880 3905 3930 3955 3980 4005 4030
4055 4080 4105 4130 4155 4180 4204 4229 4254 4279
4304 4329 4353 4378 4403 4428 4452 4477 4502 4527
4551 4576 4601 4625 4650 4674 4699 4724 4748 4773
4797 4822 4846 4871 4895 4920 4944 4969 4993 5018
5042 5066 5091 5115 5139 5164 5188 5212 5237 5261
5285 5310 5334 5358 5382 5406 6431 5455 5479 5503
25527 25551 25575 25600 25624 25648 25672 25696 25720 25744
5768 5792 5816 5840 5864 5888 5912 5935 5959 5983
6007 6031 6055. 6079 6102 6126 6150 6174 6198 6221
6245 6269 6293 6316 6340 6364 6387 6411 6435 6458
6482 6505 6529 6553 6576 6600 6623 6647 6670 6694
6717 6741 6764 6788 6811 6834 6858 6881 6905 6928
6951 6975 6998 7021 7045 7068 7091 7114 7138 7161
7184 7207 7231 7254 7277 7300 7323 7346 7370 7393
7416 7439 7462 7485 7508 7531 7554 7577 7600 7623
7646 7669 7692 7715 7738 7761 7784 7807 7830 7852
27875 27898 27921 27944 27967 27989 28012 28035 28058 28081
8103 8126 8149 8171 8194 8217 8240 8262 8285 8307
8330 8353 8375 8398 8421 8443 8466 8488 8511 8533
8556 8578 8601 8623 8646 8668 8691 8713 8735 8758
8780 8803 8825 8847 8870 8892 8914 8937 8959 8981
9003 9026 9048 9070 9092 9115 9137 9159 9181 9203
9226 9248 9270 9292 9314 9336 9358 9380 9403 9425
9447 9469 9491 9513 9535 9557 9579 9601 9623 9645
9667 9688 9710 9732 9754 9776 9798 9820 9842 9863
9885 9907 9929 9951 9973 999430016300383006030081
30103 30125 30146 30168 30190 30211 30233 30255 30276 30298
LOGARITHMS OF NUMBERS 119
N|0123456789
200
1
2
3
4
5
6
7
210
1
2
3
4
5
6
7
8
30103 30125 30146 30168 30190 30211 30233 30255 30276 30298
032& 0341 0363 0384 0406 0428 0449 0471 0492 0514
0535 0557 0578 0600 0621 0643 0664 068*5 0707 0728
0750 0771 0792 0814 0835 0856 0878 0899 0920 0942
0963 0984 1006 1027 1048 1069 1091 1112 1133 1154
1175 1197 1218 1239 1260 1281 1302 1323 1345 1366
1387 1408 1429 1450 1471 1492 1513 1634 1555 1576
1597 1618 1639 1660 1681 1702 1723 1744 1765 1785
1806 1827 1848 1869 1890 1911 1931 1952 1973 1994
2015 2035 2056 2077 2098 2118 2139 2160 2181 2201
32222 32243 32263 32284 32305 32325 32346 32366 32387 32408
2428 2449 2469 2490 2510 2531 2552 2572 2593 2613
2634 2654 2675 2695 2715 2736 2756 2777 2797 2818
2838 2858 2879 2899 2919 2940 2960 2980 3001 3021
3041 3062 3082 3102 3122 3143 3163 3183 3203 3224
3244 3264 3284 3304 3325 3345 3365 3385 3405 3425
3445 3465 3486 3506 3526 3546 3566 3586 3606 3626
3646 3666 3686 3706 3726 3746 3766 3786 3806 3826
3846 3866 3885 3905 3925 3945 3965 3985 4005 4025.
4044 4064 4084 4104 4124 4143 4163 4183 4203 4223
34242 34262 34282 34301 34321 34341 34361 34380 34400 34420
4439 4459 4479 4498 4518 4537 4557 4577 4596 4616
4635 4655 4674 4694 4713 4733 4753 4772 4792 4811
4830 4850 4869 4889 4908 4928 4947 4967 4986 5005
5025 5044 5064 5083 5102 5122 5141 5160 5180 5199
5218 5238 5257 5276 5295 5315 5334 5353 5372 5392
5411 5430 5449 5468 5488 5507 5526 5545 5564 5583
5603 5622 5641 5660 5679 5698 5717 5736 5755 5774
5793 5813 5832 5851 5870 5889 5908 5927 5946 5965
5984 6003 6021 6040 6059 6078 6097 6116 6135 6154
36173 36192 36211 36229 36248 36267 36286 36305 36324 36342
6361 6380 6399 6418 6436 6455 6474 6493 6511 6530
6549 6568 6586 6605 6624 6642 6661 6680 6698 6717
6736 6754 6773 6791 6810 6829 6847 6866 6884 6903
6922 6940 6959 6977 6996 7014 7033 7051 7070 7088
7107 7125 7144 7162 7181 7199 7218 7236 7254 7273
7291 7310 7328 7346 7365 7383 7401 7420 7438 7457
7475 7493 7511 7530 7548 7566 7585 7603 7621 7639
7658 7676 7694 7712 7731 7749 7767 7785 7803 7822
7840 7858 7876 7894 7912 7931 7949 7967 7985 8003
38021 38039 38057 38075 38093 38112 38130 38148 38166 38184
8202 8220 8238 8256 8274 8292 8310 8328 8346 8364
8382 8399 8417 8435 8453 8471 8489 8507 8525 8543
8561 8578 8596 8614 8632 8650 8668 8686 8703 8721
8739 8757 8775 8792 8810 8828 8846 8863 8881 8899
8917 8934 8952 8970 8987 9005 9023 9041 9058 9076
9094 9111 9129 9146 9164 9182 9199 9217 9235 9252
9270 9287 9305 9322 9340 9358 9375 9393 9410 9428
9445 9463 9480 9498 9515 9533 9550 9568 9585 9602
9620 9637 9655 9672 9690 9707 9724 9742 9759 9777
120 LOGARITHMS OF NUMBERS
N
250
1
2
3
4
5
6
7
260
1
2
3
4
5
6
7
8
9
270
1
2
3
4
5
6
7
8
9
280
1
2
3
4
5
6
7
290
1
2
3
4
6
6
7
8
300
678
39794 39811 39829 39846 39863 39881 39898 39915 39933 39950
9967 9985 40002 40019 40037 40054 40071 40088 40106 40123
4014040157 0175 0192 0209 0226 0243 0261 0278 0295
0312 0329 0346 0364 0381 0398 0415 0432 0449 0466
0483 0500 0518 0535 0552 0569 0586 0603 0620 0637
0654 0671 0688 0705 0722 0739 0756 0773 0790 0807
0824 0841 0858 0875 0892 0909 0926 0943 0960 0976
0993 1010 1027 1044 1061 1078 1095 1111 1128 1145
1162 1179 1196 1212 1229 1246 1263 1280 1296 1313
1330 1347 1363 1380 1397 1414 1430 1447 1464 1481
41497 41514 41531 41547 41564 41581 41597 41614 41631 41647
1664 1681 1697 1714 1731 1747 1764 1780 1797 1814
1830 1847 1863 1880 1896 1913 1929 1946 1963 1979
1996 2012 2029 2045 2062 2078 2095 2111 2127 2144
2160 2177 2193 2210 2226 2243 2259 2275 2292 2308
2325 2341 2357 2374 2390 2406 2423 2439 2455 2472
2488 2504 2521 2537 2553 2570 2586 2602 2619 2635
2651 2667 2684 2700 2716 2732 2749 2765 2781 2797
2813 2830 2846 2862 2878 2894 2911 2927 2943 2959
2975 2991 3008 3024 3040 3056 3072 3088 3104 3120
43136 43152 43169 43185 43201 43217 43233 43249 43265 43281
3297 3313 3329 3345 3361 3377 3393 3409 3425 3441
3457 3473 3489 3505 3521 3537 3553 3569 3584 3600
3616 3632 3648 3664 3680 3696 3712 3727 3743 3759
3775 3791 3807 3823 3838 3854 3870 3886 3902 3917
3933 3949 3965 3981 3996 4012 4028 4044 4059 4075
4091 4107 4122 4138 4154 4170 4185 4201 4217 4232
4248 4264 4279 4295 4311 4326 4342 4358 4373 4389
4404 4420 4436 4451 4467 4483 4498 4514 4529 4545
4560 4576 4592 4607 4623 4638 4654 4669 4685 4700
44716 44731 44747 44762 44778 44793 44809 44824 44840 44855
4871 4886 4902 4917 4932 4948 4963 4979 4994 5010
5025 5040 5056 5071 5086 5102 5117 5133 5148 5163
5179 5194 5209 5225 5240 5255 5271 5286 5301 5317
5332 5347 5362 5378 5393 5408 5423 5439 5454 5469
5484 5500 5515 5530 5545 5561 5576 5591 5606 5621
5637 5652 5667 5682 5697 5712 5728 5743 5758 5773
5788 5803 5818 5834 5849 5864 5879 5894 5909 5924
5939 5954 5969 5984 6000 6015 6030 6045 6060 6075
6090 6105 6120 6135 6150 6165 6180 6195 6210 6225
46240 46255 46270 46285 46300 46315 46330 46345 46359 46374
6389 6404 6419 6434 6449 6464 6479 6494 6509 6523
6538 6553 6568 6583 6598 6613 . 6627 6642 6657 6672
6687 6702 6716 6731 6746 6761 6776 6790 6805 6820
6835 6850 6864 6879 6894 6909 6923 6938 6953 6967
6982 6997 7012 7026 7041 7056 7070 7085 7100 7114
7129 7144 7159 7173 7188 7202 7217 7232 7246 7261
7276 7290 7305 7319 7334 7349 7363 7378 7392 7407
7422 7436 7451 7465 7480 7494 7509 7524 7538 7553
7567 7582 7596 7611 7625 7640 7654 7669 7683 7698
47712 47727 47741 47756 47770 47784 47799 47813 47828 47842
LOGARITHMS OF NUMBERS 121
6789
300 47712 47727 47741 47756 47770 47784 47799 47813 47828 47842
1
310
1
2
3
4
5
6
7
8
320
1
2
3
4
5
6
7
8
9
330
1
2
3
4
5
6
7
8
9
340
1
2
3
4
5
6
7
350
7857 7871 7885 7900 7914 7929 7943 7958 7972 7986
2 8001 8015 8029 8044 8058 8073 8087 8101 8116 8130
3 I 8144 8159 8173 8187 8202 8216 8230 8244 8259 8273
8287 8302 8316 8330 8344 8359 8373 8387 8401 8416
8430 8444 8458 8473 8487 8501 8515 8530 8544 8558
8572 8586 8601 8615 8629 8643 8657 8671 8686 8700
8714 8728 8742 8756 8770 8785 8799 8813 8827 8841
8855 8869 8883 8897 8911 8926 8940 8954 8968 8982
8996 9010 9024 9038 9052 9066 9080 9094 9108 9122
49136 49150 49164 49178 49192 49206 49220 49234 49248 49262
9276 9290 9304 9318 9332 9346 9360 9374 9388 9402
9415 9429 9443 9457 9471 9485 9499 9513 9527 9541
9554 9568 9582 9596 9610 9624 9638 9651 9665 9679
9693 9707 9721 9734 9748 9762 9776 9790 9803 9817
9831 9845 9859 9872 9886 9900 9914 9927 9941 9955
9969 9982 9996 50010 50024 50037 50051 50065 50079 50092
50106 50120 50133 0147 0161 0174 0188 0202 0215 0229
0243 0256 0270 0284 0297 0311 0325 0338 0352 0365
0379 0393 0406 0420 0433 0447 0461 0474 0488 0501
50515 50529 50542 50556 60569 50583 50596 50610 50623 50637
0651 0664 0678 0691 0705 0718 0732 0745 0759 0772
0786 0799 0813 0826 0840 0853 0866 0880 0893 0907
0920 0934 0947 0961 0974 0987 1001 1014 1028 1041
1055 1068 1081 1095 1108 1121 1135 1148 1162 1175
1188 1202 1215 1228 1242 1255 1268 1282 1295 1308
1322 1335 1348 1362 1375 1388 1402 1415 1428 1441
1455 1468 1481 1495 1508 1521 1534 1548 1561 1574
1587 1601 1614 1627 1640 1654 1667 1680 1693 1706
1720 1733 1746 1759 1772 1786 1799 1812 1825 1838
51851 51865 51878 51891 51904 51917 51930 51943 51957 51970
1983 1996 2009 2022 2035 2048 2061 2075 2088 2101
2114 2127 2140 2153 2166 2179 2192 2205 2218 2231
2244 2257 2270 2284 2297 2310 2323 2336 2349 2362
2375 2388 2401 2414 2427 2440 2453 2466 2479 2492
2504 2517 2530 2543 2556 2569 2582 2595 2608 2621
2634 2647 2660 2673 2686 2699 2711 2724 2737 2750
2763 2776 2789 2802 2815 2827 2840 2853 2866 2879
2892 2905 2917 2930 2943 2956 2969 2982 2994 3007
3020 3033 3046 3058 3071 3084 3097 3110 3122 3135
53148 53161 53173 53186 53199 53212 53224 53237 53250 53263
3275 3288 3301 3314 3326 3339 3352 3364 3377 3390
3403 3415 3428 3441 3453 3466 3479 3491 3504 3517
3529 3542 3555 3567 3580 3593 3605 3618 3631 3643
3656 3668 3681 3694 3706 3719 3732 3744 3757 3769
3782 3794 3807 3820 3832 3845 3857 3870 3882 3895
3908 3920 3933 3945 3958 3970 3983 3995 4008 4020
4033 4045 4058 4070 4083 4095 4108 4120 4133 4145
4158 4170 4183 4195 4208 4220 4233 4245 4258 4270
4283 4295 4307 4320 4332 4345 4357 4370 4382 4394
54407 54419 54432 54444 54456 54469 54481 54494 54506 54518
122 LOGARITHMS OF NUMBERS.
NO12345678
350
1
2
3
4
5
6
7
8
9
360
1
2
3
4
5
6
7
8
370
1
2
3
4
5
6
7
8
9
380
1
2
3
4
5
6
7
8
9
3
4
5
6
7
8
9
400
54407 64419 54432 54444 54456 54469 54481 54494 54506 54518
4531 4543 4555 4568 4580 4593 4605 4617 4630 4642
4654 4667 4679 4691 4704 4716 4728 4741 4753 4765
4777 4790 4802 4814 4827 4839 4851 4864 4876 4888
4900 4913 4925 4937 4949 4962 4974 4986 4998 5011
5023 5035 5047 5060 5072 5084 5096 5108 5121 5133
5145 5157 5169 5182 5194 5206 5218 5230 5242 5255
5267 5279 5291 5303 5315 5328 5340 5352 5364 5376
5388 6400 5413 5425 5437 5449 5461 5473 5485 6497
5509 5522 5534 5546 5558 6570 5582 5594 5606 5618
55630 55642 55654 55666 55678 55691 55703 55715 55727 55739
5751 5763 5775 6787 5799 6811 6823 5835 5847 5859
5871 5883 5895 5907 5919 5931 6943 5955 5967 5979
5991 6003 6015 6027 6038 6050 6062 6074 6086 6098
6110 6122 6134 6146 6158 6170 6182 6194 6205 6217
6229 6241 6253 6265 6277 6289 6301 6312 6324 6336
6348 6360 6372 6384 6396 6407 6419 6431 6443 6455
6467 6478 6490 6502 6514 6526 6538 6549 6561 6573
6585 6597 6608 6620 6632 6644 6656 6667 6679 6691
6703 6714 6726 6738 6750 6761 6773 6785 6797 6808
56820 56832 56844 56855 56867 56879 56891 56902 56914 56926
6937 6949 6961 6972 6984 6996 7008 7019 7031 7043
7054 7066 7078 7089 7101 7113 7124 7136 7148 7159
7171 7183 7194 7206 7217 7229 7241 7252 7264 7276
7287 7299 7310 7322 7334 7345 7357 7368 7380 7392
7403 7415 7426 7438 7449 7461 7473 7484 7496 7507
7519 7530 7542 7553 7565 7576 7588 7600 7611 7623
7634 7646 7657 7669 7680 7692 7703 7715 7726 7738
7749 7761 7772 7784 7795 7807 7818 7830 7841 7852
7864 7875 7887 7898 7910 7921 7933 7944 7955 7967
57978 57990 58001 58013 58024 58035 58047 58058 58070 58081
8092 8104 8115 8127 8138 8149 8161 8172 8184 8195
8206 8218 8229 8240 8252 8263 8274 8286 8297 8309
8320 8331 8343 8354 8365 8377 8388 8399 8410 8422
8433 8444 8456 8467 8478 8490 8501 8512 8524 8535
8546 8557 8569 8580 8591 8602 8614 8625 8636 8647
8659 8670 8681 8692 8704 8715 8726 8737 8749 8760
8771 8782 8794 8805 8816 8827 8838 8850 8861 8872
8883 8894 8906 8917 8928 8939 8950 8961 8973 8984
8995 9006 9017 9028 9040 9051 9062 9073 9084 9095
59106 59118 59129 59140 59151 59162 59173 59184 59195 59207
9218 9229 9240 9251 9262 9273 9284 9295 9306 9318
9329 9340 9351 9362 9373 9384 9395 9406 9417 9428
9439 9450 9461 9472 9483 9494 9506 9517 9528 9539
9550 9561 9572 9583 9594 9605 9616 9627 9638 9649
9660 9671 9682 9693 9704 9715 9726 9737 9748 9759
9770 9780 9791 9802 9813 9824 9835 9846 9857 9868
9879 9890 9901 9912 9923 9934 9945 9956 9966 9977
9988 9999 60010 60021 60032 60043 60054 60065 60076 60086
60097 60108 0119 0130 0141 0152 0163 0173 0184 0195
60206 60217 60228 60239 60249 60260 60271 60282 60293 60304
LOGARITHMS OF NUMBERS 123
NO12345678
400
1
2
3
4
5
9
410
1
2
3
4
5
6
7
8
9
420
1
2
3
4
5
6
7
8
9
430
1
2
3
4
5
6
7
8
9
440
1
2
3
4
5
6
7
8
9
450
60206 60217 60228 60239 60249 60260 60271 60282 60293 60304
0314 0325 0336 0347 0358 0369 0379 0390 0401 0412
0423 0433 0444 0455 0466 0477 0487 0498 0509 0520
0531 0541 0552 0563 0574 0584 0595 0606 0617 0627
0638 0649 0660 0670 0681 0692 0703 0713 0724 0735
0746 0756 0767 0778 0788 0799 0810 0821 0831 0842
0853 0863 0874 0885 0895 0906 0917 0927 0938 0949
0969 0970 0981 0991 1002 1013 1023 1034 1045 1055
1066 1077 1087 1098 1109 1119 1130 1140 1151 1162
1172 1183 1194 1204 121^ 1225 1236 1247 1257 1268
61278 61289 61300 61310 61321 61331 61342 61352 61363 61374
1384 1395 1405 1416 1426 1437 1448 1458 1469 1479
1490 1500 1511 1521 1532 1542 1553 1563 1574 1584
1595 1606 1616 1627 1637 1648 1658 1669 1679 1690
1700 1711 1721 1731 1742 1752 1763 1773 1784 1794
1805 1815 1826 1836 1847 1857 1868 1878 1888 1899
1909 1920 1930 1941 1951 1962 1972 1982 1993 2003
2014 2024 2034 2045 ' 2055 2066 2076 2086 2097 2107
2118 2128 2138 2149 2159 2170 2180 2190 2201 2211
2221 2232 2242 2252 2263 2273 2284 2294 2304 2315
62325 62335 62346 62356 62366 62377 62387 62397 62408 62418
2428 2439 2449 2459 2469 2480 2490 2500 2511 2521
2531 2542 2552 2562 2572 2583 2593 2603 2613 2624
2634 2644 2655 2665 2675 2685 2696 2706 2716 2726
2737 2747 2757 2767 2778 2788 2798 2808 2818 2829
2839 2849 2859 2870 2880 2890 2900 2910 2921 2931
2941 2951 2961 2972 2982 2992 3002 3012 3022 3033
3043 3053 3063 3073 3083 3094 3104 3114 3124 3134
3144 3155 3165 3175 3185 3195 3205 3215 3225 3236
3246 3256 3266 3276 3286 3296 3306 3317 3327 3337
63347 63357 63367 63377 63387 63397 63407 63417 63428 63438
3448 3458 3468 3478 3488 3498 3508 3518 3528 3538
3548 3558 3568 3579 3589 3599 3609 3619 3629 3639
3649 3659 3669 3679 3689 3699 3709 3719 3729 3739
3749 3759 3769 3779 3789 3799 3809 3819 3829 3839
3849 3859 3869 3879 3889 3899 3909 3919 3929 3939
3949 3959 3969 3979 3988 3998 4008 4018 4028 4038
4048 4058 4068 4078 4088 4098 4108 4118 4128 4137
4147 4157 4167 4177 4187 4197 4207 4217 4227 4237
4246 4256 4266 4276 4286 4296 4306 4316 4326 4335
64345 64355 64365 64375 64385 64395 64404 64414 64424 64434
4444 4454 4464 4473 4483 4493 4503 4513 4523 4532
4542 4552 4562 4572 4582 4591 4601 4611 4621 4631
4640 4650 4660 4670 4680 4689 4699 4709 4719 4729
4738 4748 4758 4768 4777 4787 4797 4807 4816 4826
4836 4846 4856 4865 4875 4885 4895 4904 4914 4924
4933 4943 4953 4963 4972 4982 4902 5002 5011 6021
5031 5040 5050 5060 5070 6079 5089 5099 5108 5118
5128 6137 5147 6157 5167 6176 5186 5196 5205 6215
5225 6234 5244 6254 6263 6273 5283 5292 5302 6312
65321 65331 65341 65350 65360 65369 65379 65389 65398 65408
124 LOGARITHMS OF NUMBERS
1
450
1
2
3
4
5
6
7
3
a
460
1
2
3
4
5
6
7
9
470
1
2
3
4
5
6
7
8
9
480
1
2
3
4
5
6
7
8
9
490
1
2
3
4
5
6
7
8
500
3 4: 5 6 7 8 9
65321 65331 65341 65350 65360 65369 65379 65389 65398 65408
5418 5427 5437 5447 5456 5466 5475 5485 5495 5504
5514 5523 5533 5543 5552 5562 5571 5581 5591 5600
5610 5619 5629 5639 5648 5658 5667 5677 5686 5696
5706 5715 5725 5734 5744 5753 5763 6772 5782 5792
5801 5811 5820 5830 5839 5849 5858 5868 6877 5887
5896 5906 5916 5925 5935 5944 5954 5963 5973 5982
5992 6001 6011 6020 6030 6039 6049 6058 6068 6077
6087 6096 6106 6115 6124 6134 6143 6153 6162 6172
6181 6191 6200 6210 6219 6229 6238 6247 6257 6266
66276 66285 66295 66304 66314 66323 66332 66342 66351 66361
6370 6380 6389 6398 6408 6417 6427 6436 6445 6455.
6464 6474 6483 6492 6502 6511 6521 6530 6539 6549
6558 6567 6577 6586 6596 6605 6614 6624 6633 6642
6652 6661 6671 6680 6689 6699 6708 6717 6727 6736
6745 6755 6764 6773 6783 6792 6801 6811 6820 6829
6839 6848 6857 6867 6876 6885 6894 6904 6913 6922
6932 6941 6950 6960 6969 6978 6987 6997 7006 7015
7025 7034 7043 7052 7062 7071 7080 7089 7099 7108
7117 7127 7136 7145 7154 7164 7173 7182 7191 7201
67210 67219 67228 67237 67247 67256 67265 67274 67284 67293
7302 7311 7321 733"0 7339 7348 7357 7367 7376 7385
7394 7403 7413 7422 7431 7440 7449 7459 7468 7477
7486 7495 7504 7514 7523 7532 7541 7550 7560 7569
7578 7587 7596 7605 7614 7624 7633 7642 7651 7660
7669 7679 7688 7697 7706 7715 7724 7733 7742 7752
7761 7770 7779 7788 7797 7806 7815 7825 7834 7843
7852 7861 7870 7879 7888 7897 7906 7916 7925 7934
7943 7952 7961 7970 7979 7988 7997 8006 8015 8024
8034 8043 8052 8061 8070 8079 8088 8097 8106 8115
68124 68133 68142 68151 68160 68169 68178 68187 68196 68205
8215 8224 8233 8242 8251 8260 8269 8278 8287 8296
8305 8314 8323 8332 8341 8350 8359 8368 8377 8386
8395 8404 8413 8422 8431 8440 8449 8458 8467 8476
8485 8494 8502 851.1 8520 8529 8538 8547 8556 8565
8574 8583 8592 8601 8610 8619 8628 8637 8646 8655
8664 8673 8681 8690 8699 8708 8717 8726 8735 8744
8753 8762 8771 8780 8789 8797 8806 8815 8824 8833
8842 8851 8860 8869 8878 8886 8895 8904 8913 8922
8931 8940 8949 8958 8966 8975 8984 8993 9002 9011
69020 69028 69037 69046 69055 69064 69073 69082 69090 69099
9108 9117 9126 9135 9144 9152 9161 9170 9179 9188
9197 9205 9214 9223 9232 9241 9249 9258 9267 9276
9285 9294 9302 9311 9320 9329 9338 9346 9355 9364
9373 9381 9390 9399 9408 9417 9425 9434 9443 9452
9461 9469 9478 9487 9496 9504 9513 9522 9531 9539
9548 9557 9566 9574 9583 9592 9601 9609 9618 9627
9636 9644 9653 9662 9671 9679 9688 9697 9705 9714
9723 9732 9740 9749 9758 9767 9775 9784 9793 9801
9810 9819 9827 9836 9845 9854 9862 9871 9880 9888
69897 69906 69914 69923 69932 69940 69949 69958 69966 69975
LOGARITHMS OF NUMBERS 125
3456789
500
1
2
3
4
5
6
7
8
9
510
1
2
3
4.
5
6
7
8
9
520
1
2
3
4
5
6
7
8
9
530
1
2
3
4
5
6
7
540
1
2
3
4
5
6
7
550
69897 69906 69914 69923 69932 69940 69949 69958 69966 69973
9984 9992 70001 70010 70018 70027 70036 70044 70053 70062
70070 70079 0088 0096 0105 0114 0122 0131 0140 0148
0157 0165 0174 0183 0191 0200 0209 0217 0226 0234
0243 0252 0260 0269 0278 0286 0295 0303 0312 0321
0329 0338 0346 0355 0364 0372 0381 0389 0398 0406
0415 0424 0432 0441 0449 0458 0467 0475 0484 0492
0501 0509 0518 0526 0535 0544 0552 0561 0569 0578
0586 0595 0603 0612 0621 0629 0638 0646 0655 0663
0672 0680 0689 0697 0706 0714 .0723 0731 0740 0749
70757 70766 70774 70783 70791 70800 70808 70817 70825 70834
0842 0851 0859 0868 0876 0885 0893 0902 0910 0919
0927 0935 0944 0952 0961 0969 0978 0986 0995 1003
1012 1020 1029 1037 1046 1054 1063 1071 1079 1088
1096 1105 1113 1122 1130 1139 1147 1155 1164 1172
1181 1189 1198 1206 1214 1223 1231 1240 1248 1257
1265 1273 1282 1290 1299 1307 1315 1324 1332 1341
1349 1357 1366 1374 1383 1391 1399 1408 1416 1425
1433 1441 1450 1458 1466 1475 1483 1492 1500 1508
1517 1525 1533 1542 1550 1559 1567 1575 1584 1592
71600 71609 71617 71625 71634 71642 71650 71659 71667 71675
1684 1692 1700 1709 1717 1725 1734 1742 1750 1759
1767 1775 1784 1792 1800 1809 1817 1825 1834 1842
1850 1858 1867 1875 1883 1892 1900 1908 1917 1925
1933 1941 1950 1958 1966 1975 1983 1991 1999 2008
2016 2024 2032 2041 2049 2057 2066 2074 2082 2090
2099 2107 2115 2123 2132 2140 2148 2156 2165 2173
2181 2189 2198 2206 2214 2222 2230 2239 2247 2255
22(53 2272 2280 2288 2296 2304 2313 2321 2329 2337
2346 2354 2362 2370 2378 2387 2395 2403 2411 2419
72428 72436 72444 72452 72460 72469 72477 72485 72493 72501
2609 2518 2526 2534 2542 2550 2558 2567 2575 2583
2591 2599 2607 2616 2624 2632 2640 2648 2656 2665.
2673 2681 2689 2697 2705 2713 2722 2730 2738 2746
2754 2762 2770 2779 '2787 2795 2803 2811 2819 2827
2835 2843 2852 2860 2868 2876 2884 2892 2900 2908
2916 2925 2933 2941 2949 2957 2965 2973 2981 2989
2997 3006 3014 3022 3030 3038 3046 3054 3062 3070
3078 3086 3094 3102 3111 3119 3127 3135 3143 3151
3159 3167 3175 3183 3191 3199 3207 3215 3223 3231
73239 73247 73255 73263 73272 73280 73288 732*96 73304 73312
3320 3328 3336 3344 3352 3360 3368 3376 3384 3392
3400 3408 3416 3424 3432 3440 3448 3456 3464 3472
3480 3488 3496 3504 3512 3520 3528 3536 3544 3552
3560 3568 3576 3584 3592 3600 3608 3616 3624 3632
3640 3648 3(556 3664 3672 3679 3687 3695 3703 3711
3719 3727 3735 3743 3751 3759 3767 3775 3783 3791
3799 3807 3815 3823 3830 3838 3846 3854 3862 3870
3878 3886 3894 3902 3910 3918 3926 3933 3941 3949
3957 3965 3973 3981 3989 3997 4005. 4013 4020 4028
74036 74044 74052 74060 74068 74076 74084 74092 74099 74107
126
LOGARITHMS OF NUMBERS
N
O
1
2
3
4
5
6
7
8
9 !
550
74036
74044
74052
74060
74068 74076
74084
74092
74099
74107 ;
1
4115
4123
4131
4139
4147
4155
4162
4170
4178
4186
2
4194
4202
4210
4218
4225
4233
4241
4249
4257
4265
3
4273
4280
4288
4296
4304
4312
4320
4327
4335
4343
4
4351
4359
4367
4374
4382
4390
4398
4406
4414
4421
5
4429
4437
4445
4453
4461
4468
4476
4484
4492
4500
6
4507
4515
4523
4531
4539
4547
4554
4562
4570
4578
7
4586
4593
4601
4609
4617
4624
4632
4640
4648
4656
8
4663
4671
4679
4687
4095
4702
4710
4718
4726
4733
9
4741
4749
4757
4764
4772
4780
4788
4796
4803
4811
560
74819
74827
74834
74842
74850
74858 74865
74873
74881
74889
1
4896
4904
4912
4920
4927
4935
4943
4950
4958
4966
2
4974
4981
4989
4997
5005
5012
5020
5028
5035
5043
3
5051
5059
5066
5074
5082
5089
5097
5105
5113
5120
4
5128
5136
5143
5151
5159
5166
5174
5182
5189
5197
5
5205
5213
5220
5228
5236
5243
5251
5259
5266
5274
6
5282
5289
5297
5305
5312
5320
5328
5335
5343
5351
7
5358
5366
5374
5381
5389
5397
5404
5412
5420
5427
8
5435
5442
5450
5458
5465
5473
5481
5488
5496
5504
9
5511
5519
5526
5534
5542
5549
5557
5565
5572
5580
670
75587
75595
75603
75610
75618
75626
75633
75641
75648
75656
1
5664
5671
5679
5686
5694
5702
5709
5717
5724
5732
2
5740
5747
5755
5762
5770
5778
5785
5793
5800
5808
3
5815
5823
5831
5838
5846
5853
5861
5868
5876
5884
4
5891
5899
5906
5914
5921
5929
5937
5944
5952
5959
5
5967
5974
6982
5989
5997
6005
6012
6020
6027
6035
6
6042
6050
6057
6065
6072
6080
6087
6095
6103
6110
7
6118
6125
6133
6140
6148
6155
6163
6170
6178
6185
8
6193
6200
6208
6215
6223
6230
6238
6245
6253
6260
9
6268
6275
6283
6290
6298
6305
6313
6320
6328
6335
580
76343
76350
76358
76365
76373 76380 76388
76395
76403
76410
1
6418
6425
6433
6440
6448
6455
6462
6470
6477
6485
2
6492
6500
6507
6515
6522
6530
6537
6545
6552
6559
3
6567
6574
6582
6589
6597
6604
6612
6619
6626
6634 '
4
6641
6649
6656
6664
6671
6678
6686
6693
6701
6708
5
6716
6723
6730
6738
6745
6753
6760
6768
6775
6782
6
6790
6797
6805
6812
6819
6827
6884
6842
6849
6856
7
6864
6871
6879
6886
6893
6901
6908
6916
6923
6930
8
6938
6945
6953
6960
6967
6975
6982
6989
6997
7004
9
7012
7019
7026
7034
7041
7048
7056
7063
7070
7078
590
77085
77093
77100
77107
77115
77122
77129
77137
77144
77151
1
7159
7166
7173
7181
7188
7195
7203
7210
7217
7225
2
7232
7240
7247
7254
7262
7269
7276
7283
7291
7298
3
7305
7313
7320
7327
7335
7342
7349
7357
7364
7371
4
7379
7386
7393
7401
7408
7415
7422
7430
7437
7444
5
7452
7459
7466
7474
7481
7488
7495
7503
7510
7517
6
7525
7532
7539
7546
7554
7561
7568
7576
7583
7590
7
7597
7605
7612
7619
7627
7634
7641
7648
7656
7663
8
7670
7677
7685
7692
7699
7706
7714
7721
7728
7735
9
7743
7750
7757
7764
7772
7779
7786
7793
7801
7808
600
77815
77822
77830
77837
77844
77851
77859
77866
77873
77880
LOGARITHMS OF NUMBERS 127
N
600
1
2
3
4
5
6
7
8
9
610
1
3
6
7
8
9
620
1
2
3
4
5
6
7
8
9
680
1
2
3
4
5
6
7
8
9
640
1
2
3
4
5
. 7
650
6789
77815 77822 77830 77837 77844 77851 77859 77866 77873 77880
7887 7895 7902 7909 7916 7924 7931 7938 7945 7952
7960 7967 7974 7981 7988 7996 8003 8010 8017 8025
8032 8039 8046 8053 8061 8068 8075 8082 8089 8097
8104 8111 8118 8125 8132 8140 8147 8154 8161 8168
8176 8183 8190 8197 8204 8211 8219 8226 8233 8240
8247 8254 8262 8269 8276 8283 8290 8297 8305. 8312
8319 8326 8333 8340 8347 8355 8362 8369 8376 8383
8390 8398 8405 8412 8419 8426 8433 8440 8447 8455.
8462 8469 8476 8483 8490 8497 8504 8512 8519 8526
78533 78540 78547 78554 78561 78569 78576 78583 78590 78597
8604 8611 8618 8625 8633 8640 8647 8654 8661 8668
8675 8682 8689 8696 8704 8711 8718 8725 8732 8739
8746 8753 8760 8767 8774 8781 8789 8796 8803 8810
4 I 8817 8824 8831 8838 8845 8852 8859 8866 8873 8880
5 8888 8895 8902 8909 8916 8923 8930 8937 8944 8951
8958 8965 8972 8979 8986 8993 9000 9007 9014 9021
9029 9036 9043 9050 9057 9064 9071 9078 9085 9092
9099 9106 9113 9120 9127 9134 9141 9148 9155 9162
9169 9176 9183 9190 9197 9204 9211 9218 9225 9232
79239 79246 79253 79260 79267 79274 79281 79288 79295 79302
9309 9316 9323 9330 9337 9344 9351 9358 9365 9372
9379 9386 9393 9400 9407 9414 9421 9428 9435 9442
9449 9456 9463 9470 9477 9484 9491 9498 9505 9511
9518 9525 9532 9539 9546 9553 9560 9567 9574 9581
9588 9595 9602 9609 9616 9623 9630 9637 9644 9650
9657 9664 9671 9678 9685 9692 9699 9706 9713 9720
9727 9734 9741 9748 9754 9761 9768 9775 9782 9789
9796 9803 9810 9817 9824 9831 9837 9844 9851 9858
9865 9872 9879 9886 9893 9900 9906 9913 9920 9927
79934 79941 79948 79955 79962 79969 79975 79982 79989 79996
80003 80010 80017 80024 80030 80037 80044 80051 80058 80065
0072 0079 0085 0092 0099 0106 0113 0120 0127 0134
0140 0147 0154 0161 0168 0175 0182 0188 0195 0202
0209 0216 0223 0229 0236 0243 0250 0257 0264 0271
0277 0284 0291 0298 0305 0312 0318 0325 0332 0339
0346 0353 0359 0366 0373 0380 0387 0393 0400 0407
0414 0421 0428 0434 0441 0448 0455 0462 0468 0475
0482 0489 0496 0502 0509 0516 0523 0530 0536 0543
0550 0557 0564 0570 0577 0584 0591 0598 0604 0611
80618 80625 80632 8063P 80645 80652 80659 80665 80672 80679
0686 0693 0699 0706 0713 0720 0726 0733 0740 0747
0754 0760 0767 0774 0781 0787 0794 0801 0808 0814
0821 0828 0835 0841 0848 0855 0862 0868 0875 0882
0889 0895 0902 0909 0916 0922 0929 0936 0943 0949
0956 0963 0969 0976 0983 0990 0996 1003 1010 1017
1023 1030 1037 1043 1050 1057 1064 1070 1077 1084
1090 1097 1104 1111 1117 1124 1131 1137 1144 1151
1158 1164 1171 1178 1184 1191 1198 1204 1211 1218
1224 1231 1238 1245 1251 1258 1265 1271 1278 1285
81291 81298 81305 81311 81318 81325 81331 81338 81345 81351
128 LOGARITHMS OF NUMBERS
0123456789
650
1
2
3
4
5
680
1
2
3
4
5
6
7
8
9
670
1
2
3
4
5
6
7
8
9
680
1
2
3
4
5
6
7
8
9
690
81291 81298 81305 81311 81318 81325 81331 81338 81345 81351
1358 1365 1371 1378 1385 1391 1398 1405 1411 1418
1425 1431 1438 1445 1451 1458 1465 1471 1478 1485
1491 1498 1505 1511 1518 1525 1531 1538 1544 1551
1558 1564 1571 1578 1584 1591 1598 1604 1611 1617
1624 1631 1637 1644 1651 1657 1664 1671 1677 1684
1690 1697 1704 1710 1717 1723 1730 1737 1743 1750
1757 1763 1770 1776 1783 1790 1796 1803 1809 1816
1823 1829 1836 1842 1849 1856 1862 1869 1875 1882
1889 1895 1902 1908 1915 1921 1928 1935 1941 1948
81954 81961 81968 81974 81981 81987 81994 82000 82007 82014
2020 2027 2033 2040 2046 2053 2060 2066 2073 2079
2086 2092 2099 2105 2112 2119 2125 2132 2138 2145
2151 2158 2164 2171 2178 2184 2191 2197 2204 2210
2217 2223 2230 2236 2243 2249 2256 2263 2269 2276
2282 2289 2295 2302 2308 2315 2321 2328 2334 2341
2347 2354 2360 2367 2373 2380 2387 2393 2400 2406
2413 2419 2426 2432 2439 2445 2452 2458 2465 2471
2478 2484 2491 2497 2504 2510 2517 2523 2530 2536
2543 2549 2556 2562 2569 2575 2582 2588 2595 2601
82607 82614 82620 82627 82633 82640 82646 82653 82659 82666
2672 2679 2685 2692 2698 2705 2711 2718 2724 2730
2737 2743 2750 2756 2763 2769 2776 2782 2789 2795
2802 2808 2814 2821 2827 2834 2840 2847 2853 2860
2866 2872 2879 2885 2892 2898 2905 2911 2918 2924
2930 2937 2943 2950 2956 2963 2969 2975 2982 2988
2995 3001 3008 3014 3020 3027 3033 3040 3046 3052
3059 3065 3072 3078 3085 3091 3097 3104 3110 3117
3123 3129 3136 3142 3149 3155 3161 3168 3174 3181
3187 3193 3200 3206 3213 3219 3225 3232 3238 3245
83251 83257 83264 83270 83276 83283 83289 83296 83302 83308
3315 3321 3327 3334 3340 3347 3353 3359 3366 3372
3378 3385 3391 3398 3404 3410 3417 3423 3429 3436
3442 3448 3455 3461 3467 3474 3480 3487 3493 3499
3506 3512 3518 3525 3531 3537 3544 3550 3556 3563
3569 3575 3582 3588 3594 3601 3607 3613 3620 3626
3632 3639 3645 3651 3658 3664 3670 3677 3683
3696 3702 3708 3715 3721 3727 3734 3740 3746 3753
3759 3765 3771 3778 3784 3790 3797 3803 3809 3816
3822 3828 3835 3841 3847 3853 3860 3866 3872 3879
83885 83891 83897 83904 83910 83916 83923 83929 83935 83942
3948 3954 3960 3967 3973 3979 3985 3992 3998 4004
4011 4017 4023 4029 4036 4042 4048 4055 4061 4067
4073 4080 4086 4092 4098 4105 4111 4117 4123 4130
4136 4142 4148 4155 4161 4167 4173 4180 4186 4192
4198 4205 4211 4217 4223 4230 4236 4242 4248 4255
4261 4267 4273 4280 4286 4292 4298 4305 4311 4317
4323 4330 4336 4342 4348 4354 4361 4367 4373 4379
4386 4392 4398 4404 4410 4417 4423 4429 4435 4442
4448 4454 4460 4466 4473 4479 4485 4491 4497 4504
700 84510 84516 84522 84528 84535 84541 84547 84553 84559 8456(3
LOGARITHMS OF NUMBERS 129
N
3456789
700
1
2
3
4
5
6
7
8
9
710
1
2
3
4
5
6
7
8
9
720
1
2
3
4
5
6
7
730
1
2
3
4
5
6
7
8
9
740
1
2
3
4
5
6
7
8
9
750
84510 84516 84522 84528 84535 84541 84547 84553 84559 84566
4572 4578 4584 4590 4597 4603 4609 4615 4621 4628
4634 -4640 4646 4652 4658 4665 4671 4677 4683 4689
4696 4702 4708 4714 4720 4726 4733 4739 4745 4751
4757 4763 4770 4776 4782 4788 4794 4800 4807 4813
4819 4825 4831 4837 4844 4850 4856 4862 4868 4874
4880 4887 4893 4899 4905 4911 4917 4924 4930 4936
4942 4948 4954 4960 4967 4973 4979 4985 4991 4997
5003 5009 5016 5022 5028 5034 5040 5046 5052 5058
5065 5071 5077 5083 5089 5095 5101 5107 5114 5120
85126 85132 85138 85144 85150 85156 85163 85169 85175 85181
5187 5193 5199 5205 5211 5217 5224 5230 5236 5242
5248 5254 5260 5266 5272 5278 5285 5291 5297 5303
5309 5315 5321 5327 5333 5339 5345 5352 5358 5364
5370 5376 5382 5388 5394 5400 5406 5412 5418 5425.
5431 5437 5443 5449 5455 5461 *467 5473 5479 5485
5491 5497 5503 5509 '5516 5522 6528 5534 5540 5546
5552 5558 5564 5570 5576 5582 5588 5594 5600 5606
5612 5618 5625 5631 5637 5643 5649 5655 5661 5667
5673 5679 5685 5691 5697 5703 5709 5715 5721 5727
85733 85739 85745 85751 85757 85763 85769 85775 85781 85788
5794 5800 5806 5812 5818 5824 5830 5836 5842 5848
5854 5860 5866 5872 5878 5884 5890 5896 5902 6908
5914 5920 5926 5932 5938 5944 5950 5956 5962 5968
5974 5980 5986 5992 5998 6004 6010 6016 6022 6028
6034 6040 6046 6052 6058 6064 6070 6076 6082 6088
6094 6100 6106 6112 6118 6124 6130 6136 6141 6147
6153 6159 6165 6171 6177 6183 6189 6195 6201 6207
6213 6219 6225 6231 6237 6243 6249 6255 6261 6267
6273 6279 6285 6291 6297 6303 6308 6314 6320 6326
86332 86338 86344 86350 86356 86362 86368 86374 86380 86386
6392 6398 6404 6410 6415 6421 6427 6433 6439 6445
6451 6457 6463 6469 6475 6481 6487 6493 6499 6504
6510 6516 6522 6528 6534 6540 6546 6552 6558 6564
6570 6576 6581 6587 6593 6599 6605 6611 6617 6623
6629 6635 6641 6646 6652 6658 6664 6670 6676 6682
6688 6694 6700 6705 6711 6717 6723 6729 6735 6741
6747 6753 6759 6764 6770 6776 6782 6788 6794 6800
6806 6812 6817 6823 6829 6835 6841 6847 6853 6859
6864 6870 6876 6882 6888 6894 6900 6906 6911 6917
86923 86929 86935 86941 86947 86953 86958 86964 86970 86976
6982 6988 6994 6999 7005 7011 7017 7023 7029 7035
7040 7046 7052 7058 7064 7070 7075 7081 7087 7093
7099 7105 7111 7116 7122 7128 7134 7140 7146 7151
7157 7163 7169 7175 7181 7186 7192 7198 7204 7210
7216 7221 -7227 7233 7239 7245 7251 7256 7262 7268
7274 7280 7286 7291 7297 7303 7309 7315 7320 7326
7332 7338 7344 7349 7355 7361 7367 7373 7379 7384
7390 7396 7402 7408 7413 7419 7425 7431 7437 7442
7448 7454 7460 7466 7471 7477 7483 7489 7495 7500
87506 87512 87518 87523 87529 87535 87541 87547 87552 87558
130 LOGARITHMS OF NUMBERS
NO 1234567 8 9
750
1
2
3
4
5
6
7
8
9
760
1
2
3
4
5
6
7
8
9
770
1
2
3
4
5
6
7
8
9
780
1
2
3
4
5
6
7
8
9
790
1
2
3
4
5
6
7
800
87506 87512 87518 87523 87529 87535 87541 87547 87552 87558
7564 7570 7576 7581 7587 7593 7599 7604 7610 7610
7622 7628 7633 7639 7645 7651 7656 7662 7668 7674
7679 7685 7691 7697 7703 7708 7714 7720 7726 7731
7737 7743 7749 7754 7760 7766 7772 7777 7783 7789
7795 7800 7806 7812 7818 7823 7829 7835 7841 7846
7852 7858 7864 7869 7875 7881 7887 7892 7898 7904
7910 7915 7921 7927 7933 7938 7944 7950 7955 7961
7967 7973 7978 7984 7990 7996 8001 8007 8013 8018
8024 8030 8036 8041 8047 8053 8058 8064 8070 8076
88081 88087 88093 88098 88104 88110 88116 88121 88127 88133
8138 8144 8150 8156 8161 8167 8173 8178 8184 8190
8195 8201 8207 8213 8218 8224 8230 8235 8241 8247
8252 8258 8264 8270 8275 8281 8287 8292 8298 8304
8309 8315 8321 8326 8332 8338 8343 8349 8355 8360
8366 8372 8377 8383 8389 8395 8400 8406 8412 8417
8423 8429 8434 8440 8446 8451 8457 8463 8468 8474
8480 8485 8491 8497 8502 8508 8513 8519 8525 8530
8536 8542 8547 8553 8559 8564 8570 8576 8581 8587
8593 8598 8604 8610 8615 8621 8627 8632 8638 8643
88649 88655 88660 88666 88672 88677 88683 88689 88694 88700
8705 8711 8717 8722 8728 8734 8739 8745 8750 8756
8762 8767 8773 8779 8784 8790 8795 8801 8807 8812
8818 8824 8829 8835 8840 8846 8852 8857 8863 8868
8874 8880 8885 8891 8897 8902 8908 8913 8919 8925
8930 8936 8941 8947 8953 8958 8964 8969 8975 8981
8986 8992 8997 9003 9009 9014 9020 9025 9031 9037
9042 9048 9053 9059 9064 9070 9076 9081 9087 9092
9098 9104 9109 9115 9120 9126 9131 9137 9143 9148
9154 9159 9165 9170 9176 9182 9187 9193 9198 9204
89209 89215 89221 89226 89232 89237 89243 89248 89254 89260
9265 9271 9276 9282 9287 9293 9298 9304 9310 9315
9321 9326 9332 9337 9343 9348 9354 9360 9365 9371
9376 9382 9387 9393 9398 9404 9409 9415 9421 9426
9432 9437 9443 9448 9454 9459 9465 9470 9476 9481
9487 9492 9498 9504 9509 9515 9520 9526 9531 9537
9542 9548 9553 9559 9564 9570 9575 9581 9586 9592
9597 9603 9609 9614 9620 9625 9631 9636 9642 9647
9653 9658 9664 9669 9675 9680 9686 9691 9697 9702
9708 9713 9719 9724 9730 9735 9741 9746 9752 9757
89763 89768 89774 89779 89785 89790 89796 89801 89807 89812
9818 9823 9829 9834 9840 9845 9851 9856 9862 9867
9873 9878 9883 9889 9894 9900 9905 9911 9916 9922
9927 9933 9938 9944 9949 9955 9960 9966 9971 9977
9982 9988 9993 9998 90004 90009 90015 90020 90026 90031
90037 90042 90048 90053 0059 0064 0069 0075 0080 0086
0091 0097 0102 0108 0113 0119 0124 0129 0135 0140
0146 0151 0157 0162 0168 0173 0179 0184 0189 0195
0200 0206 0211 0217 0222 0227 0233 0238 0244 0249
0255 0260 0266 0271 0276 0282 0287 0293 0298 0304
90309 90314 90320 90325 90331 90336 90342 90347 90352 90358
LOGARITHMS OF NUMBERS 131
NO 12 34 567 89
800
1
2
3
4
5
9
810
1
2
3
4
5
6
7
8
820
1
2
3
4
5
6
7
8
830
1
2
3
4
5
6
7
340
1
2
3
4
5
6
7
90309 90314 90320 90325 90331 90336 90342 90347 90352 90358
0363 0369 0374 0380 0385 0390 0396 0401 0407 0412
0417 0423 0428 0434 0439 0445 0450 0455 0461 0466
0472 0477 0482 0488 0493 0499 0504 0509 0515 0520
0526 0531 0536 0542 0547 0553 0558 0563 0569 0574
0580 0585 0590 0596 0601 0607 0612 0617 0623 0628
0634 0639 0644 0650 0655 0660 0666 0671 0677 0682
0687 0693 0698 0703 0709 0714 0720 0725 0730 0736
0741 0747 0752 0757 0763 0768 0773 0779 0784 0789
0795 0800 0806 0811 0816 0822 0827 0832 0838 0843
90849 90854 90859 90865 90870 90875 90881 90886 90891 90897
0902 0907 0913 0918 0924 0929 0934 0940 0945 0950
0956 0961 0966 0972 0977 0982 0988 0993 0998 1004
1009 1014 1020 1025 1030 1036 1041 1046 1052 1057
1062 1068 1073 1078 1084 1089 1094 1100 1105 1110
1116 1121 1126 1132 1137 1142 1148 1153 1158 1164
1169 1174 1180 1185- 1190 1196 1201 1206 1212 1217
1222 1228 1233 1238 1243 1249 1254 1259 1265 1270
1275 1281 1286 1291 1297 1302 1307 1312 1318 1323
1328 1334 1339 1344 1350 1355 1360 1365 1371 1376
91381 91387 91392 91397 91403 91408 91413 91418 91424 91429
1434 1440 1445 1450 1455 1461 1466 1471 1477 1482
1487 1492 1498 1503 1508 1514 1519 1524 1529 1535
1540 1545 1551 1556 1561 1566 1572 1577 1582 1587
1593 1598 1603 1609 1614 1619 1624 1630 1635 1640
1645 1651 1656 1661 1666 1672 1677 1682 1687 1693
1698 1703 1709 1714 1719 1724 1730 1735 1740 1745
1751 1756 1761 1766 1772 1777 1782 1787 1793 1798
1803 1808 1814 1819 1824 1829 1834 1840 1845 1850
1855 1861 1866 1871 1876 1882 1887 1892 1897 1903
91908 91913 91918 91924 91929 91934 91939 91944 91950 91955
1960 1965 1971 1976 1981 1986 1991 1997 2002 2007
2012 2018 2023 2028 2033 2038 2044 2049 2054 2059
2065 2070 2075 2080 2085 2091 2096 2101 2106 2111
2117 2122 2127 2132 2137 2143 2148 2153 2158 2163
2169 2174 2179 2184 2189 2195 2200 2205 2210 2215
2221 2226 2231 2236 2241 2247 2252 2257 2262 2267
2273 2278 2283 2288 2293 2298 2304 2309 2314 2319
2324 2330 2335 2340 2345 2350 2355 2361 2366 2371
2376 2381 2387 2392 2397 2402 2407 2412 2418 2423
92428 92433 92438 92443 92449 92454 92459 92464 92469 92474
2480 2485 2490 2495 2500 2505 2511 2516 2521 2526
2531 2536 2542 2547 2552 2557 2562 2567 2572 2578
2583 2588 2593 2598 2603 2609 2614 2619 2624 2629
2634 2639 2645 2650 2655 2660 2665 2670 2675 2681
2686 2691 2696 2701 2706 2711 2716 2722 2727 2732
2737 2742 2747 2752 2758 2763 2768 2773 2778 2783
2788 2793 2799 2804 2809 2814 2819 2824 2829 2834
2840 2845 2850 2855 2860 2865 2870 2875 2881 2886
2891 2896 2901 2906 2911 2916 2921 2927 2932 2937
850 92942 92947 92952 92957 92962 92967 92973 92978 92983 92988
LOGARITHMS OF NUMBERS
850
1
2
3
4
5
6
7
8
9
860
1
2
3
4
5
6
7
8
9
870
1
2
3
4
5
6
7
880
1
2
3
4
5
6
7
8
890
1
2
3
4
5
900
5678
92942 92947 02952 92957 92962 92967 92973 92978 92983 92988
2993 2998 3003 3008 3013 3018 3024 3029 3034 3039
3044 3049 3054 3059 3064 3069 3075 3080 3085 3090
3095 3100 3105 3110 3115 3120 3125 3131 3136 3141
3146 3151 3156 3161 3166 3171 3176 3181 3186 3192
3197 3202 3207 3212 3217 3222 3227 3232 3237 3242
3247 3252 3258 3263 3268 3273 3278 3283 3288 3293
3298 3303 3308 3313 3318 3323 3328 3334 3339 3344
3349 3354 3359 3364 3369 3374 3379 3384 3389 3394
3399 3404 3409 3414 3420 3425 3430 3435 3440 3445
93450 93455 93460 93465 93470 93475 93480 93485 93490 93495
3500 3505 3510 3515 3520 3526 3531 3536 3541 3546
3551 3556 3561 3566 3571 3576 3581 3586 3591 3596
3601 3606 3611 3616 3621 3626 . 3631 3636 3641 3646
3651 3656 3661 3666 3671 3676 3682 3687 3692 3697
3702 3707 3712 3717 3722 3727 3732 3737 3742 3747
3752 3757 3762 3767 3772 3777 3782 3787 3792 3797
3802 3807 3812 3817 3822 3827 3832 3837 3842 3847
3852 3857 3862 3867 3872 3877 3882 3887 3892 3897
3902 3907 3912 3917 3922 3927 3932 3937 3942 3947
93952 93957 93962 93967 93972 93977 93982 93987 93992 93997
4002 4007 4012 4017 4022 4027 4032 4037 4042 4047
4052 4057 4062 4067 4072 4077 4082 4086 4091 4096
4101 4106 4111 4116 4121 4126 4131 4136 4141 4146
4151 4156 4161 4166 4171 4176 4181 4186 4191 4196
4201 4206 4211 4216 4221 4226 4231 4236 4240 4245
4250 4255 4260 4265 4270 4275 4280 4285 4290 4295
4300 4305 4310 4315 4320 4325 4330 4335 4340 4345
4349 4354 4359 4364 4369 4374 4379 4384 4389 4394
4399 4404 4409 4414 4419 4424 4429 4433 4438 4443
94448 94453 94458 94463 94468 94473 94478 94483 94488 94493
4498 4503 4507 4512 4517 4522 4527 4532 4537 4542
4547 4552 4557 4562 4567 4571 4576 4581 4586 4591
4596 4601 4606 4611 4616 4621 4626 4630 4635 4640
4645 4650 4655 4660 4665 4670 4675 4680 4685 4689
4694 4699 4704 4709 4714 4719 4724 4729 4734 4738
4743 4748 4753 4758 4763 4768 4773 4778 4783 4787
4792 4797 4802 4807 4812 4817 4822 4827 4832 4836
4841 4846 4851 4856 4861 4866 4871 4876 4880 .4885
4890 4895 4900 4905 4910 4915 4919 4924 4929 4934
94939 94944 94949 94954 94959 94963 94968 94973 94978 94983
4988 4993 4998 5002 5007 5012 5017 5022 5027 5032
5036 5041 5046 5051 5056 5061 5066 5071 5075 5080
5085 5090 5095 5100 5105 5109 5114 5119 5124 5129
5134 5139 5143 5148 5153 5158 5163 5168 5173 5177
5182 5187 5192 5197 5202 5207 5211 5216 5221 5226
5231 5236 5240 5245 5250 5255 5260 5265 5270 5274
5279 5284 5289 5294 5299 5303 5308 5313 5318 5323
5328 5332 5337 5342 5347 5352 5357 5361 5366 5371
5376 5381 5386 5390 5395 5400 5405 5410 5415 5419
95424 95429 95434 95439 95444 95448 95453 95458 95463 95468
LOGARITHMS OF NUMBERS 133
0123456789
900 95424 95429 95434 95439 95444 95448 95453 95458 95463 95468
1 5472 5477 5482 5487 5492 5497 5501 5506 5511 5516
2 5521 5525 5530 5535 5540 5545 5550 5554 5559 5564
3 5569 5574 5578 5583 5588 5593 5598 5602 5607 5612
4 5617 5622 5626 5631 5636 5641 5646 5650 5655 5660
5 5665 5670 5674 5679 5684 5689 5694 5698 5703 5708
6 5713 5718 5722 5727 5732 5737 5742 5746 5751 5756
7 5761 5766 5770 5775 5780 5785 5789 5794 5799 5804
5809 5813 5818 5823 5828 5832 5837 5842 5847 5852
5856 5861 5866 5871 5875 5880 5885 5890 5895 5899
910 95904 95909 95914 95918 95923 95928 95933 95988*95942 95947
1 5952 5957 5961 5966 5971 5976 5980 5985 5990 5995
2 I 5999 6004 6009 6014 6019 6023 6028 6033 6038 6042
3 6047 6052 6057 6061 6066 6071 6076 6080 6085 6090
9
920
1
2
3
4
5
6
7
8
9
980
1
2
3
4
5
6
7
8
9
940
1
2
3
4
5
6
7
8
9
950
6095 6099 6104 6109 6114 6118 6123 6128 6133 6137
6142 6147 6152 6156 6161 6166 6171 6175 6180 6185
6190 6194 6199 6204 6209 6213 6218 6223 6227 6232
6237 6242 6246 6251 6256 6261 6265 6270 6275 6280
6284 6289 6294 6298 6303 6308 6313 6317 6322 6327
6332 6336 6341 6346 6350 6355 6360 6365 6369 6374
96379 96384 96388 96393 96398 96402 96407 96412 96417 96421
6426 6431 6435 6440 6445 6450 6454 6459 6464 6468
6473 6478 6483 6487 6492 6497 6501 6506 6511 6515
6520 6525 6530 6534 6539 6544 6548 6553 6558 6562
6567 6572 6577 6581 6586 6591 6595 6600 6605,6609
6614 6619 6624 6628 6633 6638 6642 6647 6652 6656
6661 6666 6670 6675 6680 6685 6689 6694 6699 6703
6708 6713 6717 6722 6727 6731 6736 6741 6745 6750
6755 6759 6764 6769 6774 6778 6783 6788 6792 6797
6802 6806 6811 6816 6820 6825 6830 6834 6839 6844
96848 96853 96858 96862 96867 96872 96876 96881 96886 96890
6895 6900 6904 6909 6914 6918 6923 6928 6932 6937
6942 6946 6951 6956 6960 6965 6970 6974 6979 6984
6988 6993 6997 7002 7007 7011 7016 7021 7025 7030
7035 7039 7044 7049 7053 7058 7063 7067 7072 7077
7081 7086 7090 7095 7100 7104 7109 7114 7118 7123
7128 7132 7137 7142 7146 7151 7155 7160 7165 7169
7174 7179 7183 7188 7192 7197 7202 7206 7211 7216
7220 7225 7230 7234 7239 7243 7248 7253 7257 7262
7267 7271 7276 7280 7285 7290 7294 7299 7304 7308
97313 97317 97322 97327 97331 97336 97340 97345 97350 97354 I
7359 7364 7368 7373 7377 7382 7387 7391 7396 7400 '
7405 7410 7414 7419 7424 7428 7433 7437 7442 7447
7451 7456 7460 7465 7470 7474 7479 7483 7488 7493
7497 7502 7506 7511 7516 7520 7525 7529 7534 7539
7543 7548 7552 7557 7562 7566 7571 7575 7580 7585
7589 7594 7598 7603 7607 7612 7617 7621 7626 7630
7635 7640 7644 7649 7653 7658 7663 7667 7672 7676
7681 7685 7690 7695 7699 7704 7708 7713 7717 7722
7727 7731 7736 7740 7745. 7749 7754 7759 7763 7768
97772 97777 97782 97786 97791 97795 97800 97804 97809 97813
134 LOGARITHMS OF NUMBERS
O12345678
950
1
2
3
4
5
6
7
960
970
1
2
3
4
5
6
7
980
1
2
3
4
5
6
7
8
9
990
1
2
3
4
5
f?
7
8
9
97772 97777 97782 97786 97791 97795 97800 97804 97809 97813
7818 7823 7827 7832 7836 7841 7845 7850 7855 7859
7864 7868 7873 7877 7882 7886 7891 7896 7900 7905
7909 7914 7918 7923 7928 7932 7937 7941 7946 7950
7955 7959 7964 7968 7973 7978 7982 7987 7991 7996
8000 8005 8009 8014 8019 8023 8028 8032 8037 8041
8046 8050 8055 8059 8064 8068 8073 8078 8082 8087
8091 8096 8100 8105 8109 8114 8118 8123 8127 8132
8137 8141 8146 8150 8155 8159 8164 8168 8173 8177
8182 8186-8191 8195 8200 8204 8209 8214 8218 8223
.98227 98232 98236 98241 98245 98250 98254 98259 98263 98268
8272 8277 8281 8286 8290 8295 8299 8304 8308 8313
8318 8322 8327 8331 8336 8340 8345 8349 8354 8358
8363 8367 8372 8376 8381 8385 8390 8394 8399 8403
8408 8412 8417 8421 8426 8430 8435 8439 8444 8448
8453 8457 8462 8466 8471 8475 8480 8484 8489 8493
8498 8502 8507 8511 8516 8520 8525 8529 8534 8538
8543 8547 8552 8556 8561 8565 8570 8574 8579 8583
8588 8592 8597 8601 8605 8610 8614 8619 8623 8628
8632 8637 8641 8646 8650 8655 8659 8664 8668 8673
98677 98682 98686 98691 98695 98700 98704 98709 98713 98717
8722 8726 8731 8735 8740 8744 8749 8753 8758 8762'
8767 8771 8776 8780 8784 8789 8793 8798 8802 8807
8811 8816 8820 8825 8829 8834 8838 8843 8847 8851
8856 8860 8865 8869 8874 8878 8883 8887 8892 8896
8900 8905 8909 8914 8918 8923 8927 8932 8936 8941
8945 8949 8954 8958 8963 8967 8972 8976 8981 8985
8989 8994 8998 9003 9007 9012 9016 9021 9025 9029
9034 9038 9043 9047 9052 9056 9061 9065 9069 9074
9078 9083 9087 9092 9096 9100 9105 9109 9114 9118
99123 99127 99131 99136 99140 99145 99149 99154 99158 99162
9167 9171 9176 9180 9185 9189 9193 9198 9202 9207
9211 9216 9220 9224 9229 9233 9238 9242 9247 9251
9255 9260 9264 9269 9273 9277 9282 9286 9291 9295
9300 9304 9308 9313 9317 9322 9326 9330 9335 9339
9344 9348 9352 9357 9361 9366 9370 9374 9379 9383
9388 9392 9396 9401 9405 9410 9414 9419 9423 9427
9432 9436 9441 9445 9449 9454 9458 9463 9467 9471
9476 9480 9484 9489 9493 9498 9502 9506 9511 9515
9520 9524 9528 9533 9537 9542 9546 9550 9555 . 9559
99564 99568 99572 99577 99581 99585 99590 99594 99599 99603
9607 9612 9616 9621 9625 9629 9634 9638 9642 9647
9651 9656 9660 9664 9669 9673 9677 9682 9686 9691
9699 9704 9708 9712 9717 9721 9726 9730 9734
9739 9743 9747 9752 9756 9760 9765 9769 9774 9778
9782 9787 9791 9795 9800 9804 9808 9813 9817 9822
9826 9830 9835 9839 9843 9848 9852 9856 9861 9865
9870 9874 9878 9883 9887 9891 9896 9900 9904 9909
9913 9917 9922 9926 9930 9935 9939 9944 9948 9952
9957 9961 9965 9970 9974 9978 9983 9987 9991 9996
000 00000 00004 00009 00013 00017 00022 00026 00030 00035 00039
LOGARITHMIC SINES AND COSINES
o
1
Sine Cosine
Sine
Cosine
Sine Cosine
oo
6.46373
76476
94085
7.06579
16270
24188
41797
7.46373
50512
54291
57767
60985
66784
69417
71'JOO
74248
7.76475
78594
80615
82545
84393
86166
87870
89509
91088
92612
7.94084
95508
96887
99520
8.00779
02002
03192
04350
05478
8.06578
07650
08696
09718
10717
11693
12647
13581
14495
15391
8.16268
17128
17971
18798
19610
20407
21189
21958
22713
23456
24186
10.00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
10.00000
00000
00000
00000
00000
00000
00000
9.99999
99999
99999
99999
. 99998
99998
99998
99998
99997
99997
99997
.99997
99997
99997
99997
99996
99996
99996
99996
.99995
99995
99995
99995
99995
99994
99994
27661
28324
29621
5. 30879
31495
32103
32702
33875
34450
35018
35578
36131
.36678
37217
37750
38276
39310
40320
40816
41307
.41792
42272
42746
43216
43680
44139
44594
45044
45489
45930
48485
48896
49304
49708
50108
.50504
50897
51287
51673
52055
52434
52810
53183
53552
53919
54282
.24186
24903
25609
26304 99993
99992
99992
99992
99990
99990
99987
99987
99987
9.99985
9998E
99984
99984
99983
99983
99982
8.46366 9.99982
46799
47226
47650 99981
99979
99979
9.99978
99977
99977
99977
99975
99974
99974
99974
8.54282
54642
54999
55354
55705
56054
56400
56743
57084
57421
58419
58747
59072
59395
59715
60662
8.60973
61282
61589
61894
62196
62497
62795
63385
63678
8.63968
64256
64543
64827
65110
65391
65670
65947
66497
8.60769
67575
67841
68104
68367
68627
69144
8.69400
69654
69907
70159
70409
70658
70905
71151
71395
71638
71880
9.99974
99973
99973
99972
99972
69971
99971
99970
9.99991 8.57757 9
99967
99966
99966
99964
9.99964
99963
99962
99960
99959
.99959
99958
99957
99956
99956
99955
99955
99954
9!)954
.99953
99952
99952
99951
99951
99950
99949
9.99947
99945
99942
99942
Cosine Sine
89
Cosine
Sine
Cosine
Sine
88
130
LOGARITHMIC SINES AND COSINES
t
3
4
6
Sine
Cosine
Sine
Cosine
Sine
Cosine
8.71880
9.99940
8.84358
9.99894
8.94030
9.99834
60
1
72120
99940
84539
99893
94174
99833
59
2
72359
99939
84718
99892
94317
99832
58
3
72597
!>9938
84897
99891
944(51
99831
57
4
72834
99938
85075
99891
94603
99830
56
5
. 73069
99937
85252
99890
94746
99829
55
6
73303
99936
85429
99889
94887
99828
54
7
73535
99936
85605
99888
95029
99827
53
8
73767
99935
85780
99887
95170
99825
52
9
73997
99934
85955
99886
95310
99824
51
10
8.74226
9.99934
8.86128
9.99885
8.95450
9.99823
50
11
74454
99933
86301
99884
95589
99822 49
12
74680
99932
86474
99883
95728
99821 48
13
74906
99932
86645
99882
95867
99820 47
14
75130
99931
86816
99881
9(5005
99819
46
15
75353
99930
86987
99880
96143
99817
45
16
75575
99929
87156
99879
96280
99816
44
17
75795
99929
87325
99879
96417
99815
43
18
76015
99928
87494
99878
96553
99814
42
19
76234
99927
8766 1
99877
96689
99813
41
20
8.76451
9.99926
8.87829
9.99876
8.96825
9.99812
40
21
76667
99926
87995
99875
96960
99810
39
22
76883
99925
88161
99874
97095
99809
38
23
77097
99924
88326
99873
97229
93808
37
24
77310
99923
88490
99872
97363
99807
36
25
77522
99923
88654
99871
97496
99806
35
26
77733
99922
88817
99870
97629
99804
34
27
77943
99921
88980
99869
97762
90803
33
28
78152
99920
89142
99868
97894
99802
33
29
78360
99920
89304
99867
98026
99801
31
30
8.78568
9.99919
8.89464
9.99866
8.98157
9.99800
30
31
78774
99918
89625
9981)5
98288
99798
29
32
78979
99917
89784
99864
98419
99797
28
33
79183
99917
89943
99863
98549
99796
27
34
79386
99916
P0102
99862
98679
99795
26
35
79588
99915
90260
99861
98808
99793
25
36
79789
99914
90417
99860
98937
99792
24
87
79990
99913
' 90574
99859
99066
99791
23
38
80189
99913
90730
99858
99194
99790
22
39
80388
99912
90885
99857
99322
99788
21
40
8.80585
9.99911
8.91040
9.99856
8.99450
9.99787
20
41
8078-2
99910
91195
99855
99577
99786
19
42
80978
99909
91349
99854
99704
99785
18
43
81173
99909
91502
99853
99830
99783
17
44
81367
99908
91655
99852
99956
99782
16
45
81560
99907
91807
99851
9.00082
99781
15
46
81752
99906
91959
99850
00207
99780
14
47
81944
99905
92110
99848
00332
99778
13
48
82134
99904
92261
99847
00456
99777
12
49
82324
99904
92411
99846
00581
99776
11
50
8.82513
9.99903
8.92561
9.99845
9.00704
9.99775
10
51
82701
99902
92710
99844
00828
99773
9
52
82888
99901
92859
99843
00951
99772
8
53
83075
99900
93007
99842
01074
99771
7
54
83261
9'.899
93154
99S41
01196
99769
6
55
83446
99898
93301
99840
01318
99768
5
56
83630
99898
93448
99839
01440
99767
4
57
83813
99897
93594
99838
01561
99705
3
58
83996
99896
93740
99837
01682
99764
2
59
84177
99895
93885
99836
01803
99763
1
60
84358
99894
94030
99834
01923
99761
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
86
-
85
84
LOGARITHMIC SINES AND COSINES
Sine Cosine
Sine
Cosine
Sine Cosine
9.01923
02043
02163
02283
. 02402
02520
02639
02757
02874
02992
9.03109
03226
03342
03 158
03574
!690
03805
03920
04034
04149
9.04262
04376
04490
04603
04715
04828
04940
05052
05164
05275
9.05386
05497
05607
05717
05827
05937
06046
06155
06264
06372
9.06481
06589
06804
07018
07124
07231
07337
07442
.07548
07653
07758
07863
07968
08072
08176
08280
08383
08589
9.99761
99760
99759
99757
99756
99755
99753
99752
99751
99749
9.99748
99747
99745
99744
99742
99741
99740
99737
99736
9.99734
99733
99731
99730
99728
99727
99726
99724
99723
99721
9.99720
99718
99717
99716
99714
9CC13
99711
99710
99707
9.99705
99704
99701
99699
99692
99687
99684
99678
99677
99675
08795
09101
09202
09506
09707
09807
09907
10006
10106
10205
i0304
10402
10501
9.10599
10697
10795
10990
11087
11184
11281
11377
11474
9.11570
11666
11761
11857
11952
12047
12142
12236
12331
12425
9.12519
12612
12706
12799
13078
13171
13263
13355
9.13447
13539
13630
13722
13813
18904
14085
14175
9.99675
99674
99666
99663
99661
99656
99653
99651
99650
99648
99647
99645
.99643
99637
99635
99633
99625
99615
99612
&. 99610
99595
9.99593
99589
99586
99584
14356
99581
99579
99577
99575
9.14356
14445
14535
14624
14714
14803
15069
15157
9.15245
15333
15421
15508
15683
15770
15857
15944
9.16116
16203
16289
16374
16460
16545
16631
16716
16801
17055
17139
17223
]7807
17391
17474
17558
17641
17724
.17807
17890
17973
18055
18137
18220
18302
18465
18547
9.18628
18709
18790
18871
18952
19033
19113
19193
19273
19358
Cosine Sine Cosine
..: 88
Sine Cosine
9.99575
99574
99572
99570
99568
99565
99561
9.99557
99556
99554
99552
99550
99548
99546
99545
99543
99541
9.99539
99537
99535
99533
99532
99530
89528
99526
99524
99522
9.99520
99518
99517
995 J 5
99513
99511
99509
99507
99505
9.99501
99492
99490
99486
99484
9.99482
99478
99476
99474
99472
99470
99468
99464
99462
Sine
81'
138
LOGARITHMIC SINES AND COSINES
/
9
10
11
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.19433
9.99462
9.23967
9.99335
9.28060
9.99195
60
1
19513
99460
24089
99333
28125
99192
59
2
19592
99458
24110
99331
28190
99190
58
3
19672
99456
24181
99328
28254
99187
57
4
19751
99454
24253
99326
28319
99185
56
5
19830
99452
24324
99324
28384
99183
55
6
19909
99450
24395
99322
28448
99180
54
7
19988
99448
24466
99319
28512
99177
53
8
20067
99446
24536
99317
28577
99175
52
9
20145
99444
24607
99315
28641
99172
51
10
9.20223
9.99442
9.24677
9.99313
9.28705
9.99170
50
11
20302
99440
24748
99310
28769
99167
49
12
20380
99438
24818
99308
28833
99165
48
13
20458
99436
24888
99306
28896
99162
47
14
20535
99434
24958
99304
28960
99160
46
15
20613
99432
25028
99301
29024
99157
45
16
20691
99429
25098
99299
29087
99155 '
44
17
20768
99427
25168
99297
29150
99152
43
18
20845
99425
25237
99294
29214
99150
42
19
20922
99423
25307
99-292
29277
99147
41
20
9.20999
9.99421
9.25376
9.99290
9.29340
9.99145
40
21.
21076
99419
25445
99288
29403
99142
39
22
21153
99417
25514
99285
29466
99140
38
23
21229
99415
25583
99283
29529
99137
37
24
21306
99413
25652
99281
29591
99135
36
25
21382
99411
25721
99278
29654
99132
35
23
21458
99409
25790
99276
29716
99130
34
27
21534
99407
25858
99274
29779
99127
33
28
21610
99404
25927
99271
29841
99124
32
29
21685
99402
25995
99269
29903
99122
31
30
9.21761
9.99400
9.260C3
9.99267
9.29966
9.99119
30
31
21836
99398
26131
99264
30028
99117
29
32
21912
99396
26199
99262
30090
99114
28
33
21987
99394
26267
99260
30151
99112
27
34
22062
99392
26335
99257
30213
99109
26
as
22137
99390
26403
99255
30275
99106
25
36
22211
99388
26470
99252
30336
99104
24
37
22286
99385
26538
99250
30398
99001
23
38
22361
99383
26605
99248
30459
99099
22
39
22435
99381
26672
99245
30521
99096
21
40
9.22509
9.99379
9.26739
9.99243
9.30582
9.99093
20
41
22588
99377
26806
99241
30643
99091
19
42
22657
99375
26873
99238
30704
99088
18
43
22731
99372
26940
99236
30765
99086
17
44
22805
99370
27007
99233
30826
99083
16
45
22878
99368
27073
99231
30887
99080
15
46
22952
99366
27140
99229
30947
99078
14
47
23025
99364
27206
99226
31008
99075
13
48
23098
99362
27273
99224
31068
99072
12
49
23171
99359
27339
99221
31129
99070
11
50
9.23244
9.99357
9.27405
9.99^19
9.31189
9/J9067
10
51
23317
99355
27471
99217
81250
99064
9
52
23390
99353
27537
99214
31310
99062
8
53
23462
99351
27602
99212
31370
99059
7
54
23535
99348
27668
99209
31430
99056
6
55
23607
99346
27734
99207
31490
99054
5
56
23679
99344
27799
99204
31549
99051
4
57
23752
9934?
27864
99202
31609
99048
3
58
23823
99340
27930
99200
31669
99046
2
59
23895
99337
27995
99197
31728
99043
1
60
23967
99335
28060
99195
31788
99040
1
Cosine
Sine
Cosine
Sine
Cosine
Sine
4
80
79
78
LOGARITHMIC SINES AND COSINES
12
13=
Sine Cosine
9.31788
31847
31907
31966
320:25
32084
32143
32202
32261
32319
9.32378
38437
32495
32553
32612
32786
32844
32902
9.32960
33018
' 33075
33133
33190
33248
33305
33362
33420
33477
9.33534
3359 J
33647
33704
33761
33818
33874
33931
33987
34043
9.34100
34156
34212
34324
35154
35209
Sine
Cosine
Sine
Cosine
99030
99027
99024
99022
99019
9a016
9.99013
99011
99008
9900:5
99002
99000
98991
98975
98972
98967
98964
98953
98947
98944
9.98930
. 98927
98910
34436
34491
34547
34602 98904
9.34658 9,
34713 '
34769
34824
34879
34934
34989
35014
98898
98875
98872
.35209
35263
35318
35373
35427
35481
35536
35590
35644
35698
.35752
35806
35860
35914
36022
36075
36129
36182
36449
36502
36555
36660
36713
36766
36871
36924
37028
37081
37133
37185
37237
37289
9.37341
37445
37497
37549
37600
37652
37703
37755
37806
.37858
37909
37960
38011
38062
38113
38164
38215
38266
38317
9.98872
1)8867
98864
98858
98855
98849
98346
9.98843
98840
98831
98828
988. '5
98822
98819
98816
9.98813
98810
98804
98798
98795
98789
98786
98777
98774
98771
98765
98762
98759
98756
9.98753
98750
98743
98740
98737
98734
98731
98725
9.98722
98719
98715
98712
98709
98706
98703
98700
9.38368
38418
38519
38570
38620
38721
38771
38821
39021
39071
39121
39170
39220
39270
39319
39418
39467
39517
39566
39615
39713
39762
39811
39958
40006
40055
40103
40152
40200
40249
40297
9.40346
40442
40490
40538
40586
40634
40730
40778
40873
40921
40968
41016
41063
41111
41158
41205
41252
41300
9.98690
98675
98671
98668
98665
98662
>. 38871 9.98659
98652
98649
98643
98633
98030
9.98627
98623
98614
98607
98604
98597
9.98594
98588
98584
98581
9S578
98574
98571
98565
9.98561
98558
98555
98551
98548
98545
98541
98535
98531
9.-J8528
98525
98521
98518
98515
98511
98505
98501
98494
Cosine Sine
Cosine Sine Cosine
76
Sine
140
LOGARITHMIC SINES AND COSINES
/
15
16
17
Sine
Cosine
Sine
Cosine
Sine
Cosine |
9.41300
9.98494
9.44034
9.98284
9.46594
9.98060 60
1
41347
98491
44078
98281
46635
98050
59
2
41394
98488
44122
98277
46676
98052
58
3
41441
98484
44166
98273
46717
98048
57
4
41488
98481
44210
98270
46758
9t?044
56
5
41535
98477
44253
98266
46800
98040
55
6
41 582
98474
44297
98262
46841
98036
54
7
41028
98471
44341
98259
46882
98032
53
8
41675
98467
44385
98255
46923
98029
52
9
41722
98464
41428
98251
46964
9b025
51
10
9.41768
9.98460
9.44472
9.98248
9.47005
9.98021
50
11
41815
98457
44516
9S244
47045
98017
49
12
41861
98453
44559
96240
47086
98013
48
13
41908
98450
44602
98237
47127
98009
47
14
41954
98447
44646
98233
47168
98005
4(i
15
42001
98 143
44689
98229
47209
98001
45
16
42047
98440
44733
98226
47249
97997
44
17
42093
98136
44776
98222
47290
97993
43
18
42140
ib'433
44819
98218
47330
97989
42
19
42186
98429
44862
98215
47371
97986
41
20
9.-J2232
9.98426
9.44905
9.98211
9.47411
9.97982
40
21
42278
98422
44948
98207
47452
97978
39
22
42324
98419
44992
98204
47492
97974
38
23
42370
98415
45035
98200
47533
97970
37
24
42416
98412
45077
98196
47573
97906
36
25
42461
98409
45120
98192
47613
97962
35
26
42507
98405
45163
98189
47654
97958
34
27
42553
98402
45206
98185
47094
97954
33
28
42599
98398
45249
98181
47734
97950
3.'
29
42(344
98395
45292
98177
47774
97946
31
30
9.42690
9.98391
9.45334
9.98174
9.47814
9.97942
30
31
42735
98388
45377
98170
47854
97938
29
32
42781
98384
45419
98166
47894
97934
28
33
42826
98381
45462
98162
47934
97930
27
34
42872
98377
45504
98159
47974
97926
26
35
42917
98373
45547
98155
4f'014
97922
25
36
42962
98370
45589
98151
48054
97918
24
37
43008
98366
45632
98147
48094
97914 23
38
43053
98363
45674
98144
48133
97910 | 22
39
43098
98:359
45716
98140
48173
97906 81
40
9.43143
9.98356
9.45758
9.98136
9.48213
9.97902
20
41
43188
98352
45801
98132
48252
97898
19
42
43528'*
98349
45843
98129
48292
97894
18
43
43278
98345
45885
98125
48332
97890
17
44
43323
98342
45927
98121
48371
97886
16
45
43367
98338
45969
98117
48411
97882
15
46
43412
98334
46011
98113
48450
97878
14
47
43457
98331
46053
98110
48490
97874
13
48
43502
98327
46095
98106
48529
97870
12
49
43546
98324
46136
98102
48568
97866
11
50
9.43591
9.98320
9.46178
9.98098
9.48607
9.97861
10
51
43635
98317
46220
98094
48647
97857
9
52
43680
98313
46262
98090
48686
97853
8
53
43724
98309
46303
98087
48725
97849
7
54
43769
98306
46345
98083
48764
97845
6
55
43813
98302
46386
98079
48803
97841
5
56
43857
98299
46428
98075
48842
97837
4
57
43901
98295
46469
98071
48881
97833
3
58
43946
98291
46511
98067
48920
97829
2
59
43990
98288
46552
98063
48959
97825
1
60
44034
98284
46594
98060
48998
97821
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
74
78
72
LOGARITHMIC SINES AND COSINES
141
18
19
20
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.48998
9.97821
9.51264
9.97567
9.53405
9.97299
60
1
49037
97817
51301
97563
53440
97294
59
2
490T6
97812
51338
97558
53475
97289
58
3
49115
97808
51374
97554
53509
97285
57
4
49153
97804
51411
97550
53544
97280
56
5
49192
97800
51447
97545
53578
97276
55
6
49231
97796
51484
97541
5S613
97271
54
7
49269
97792
51520
97536
53647
97266
53
8
49308
97788
51557
97532
53682
97262
52
9
49347
97784
51593
97528
53716
97257
51
10
9 49385
9.97779
9.51629
9.97523
9.53751
9.97252
50
11
49424
97775
51666
97519
53785
97248
49
12
494(52
97771
51702
97515
53819
97243
48
13
49500
97767
51738
97510
53854
97238
47
14
49539
97763
51774
97506
53888
97234
46
15
49577
97759
51811
97501
53922
97229
45
16
49615
97754
51847
97497
53957
97224
44
17
49654
97750
51883
97492
53991
97220
43
18
49692
97746
51919
97488
54025
97215
42
19
49730
97742
51955
97484
f 059
97210
41
20
9 497(58
9.97738
9.51991
9.97479
9.54093
9.97206
40
21
49806
97734
52027
97475
54127
97201
39'
22
49S14
97729
52063
97470
54161
97196
38
23
498 S-
97725
52099
97466
54195
97192
37
24
499 ->0
97721
52135
97461
54229
97187
36
25
49958
91717
52171
97457
54263
97182
35
26
49996
97713
52207
97453
54297
97178
34
27
50034
97708
52242
97448
54331
97173
33
28
500;2
97704
52278
97444
54365
97168
32
29
50110
97700
52314
97439
54399
97163
31
30
9.50118
9.97696
9.52350
9.97435
9.54433
9.97159
30
31
50le>5
97691
52385
97430
54466
97154
29
32
50223
97687
52421
97426
54500
97149
28
33
50261
97683
52456
97421
54534
97145
27
34
50298
97679
52492
97417
54567
97140
26
35
50336
97674
52527
97412
54601
97135
25
36
50374
97670
52563
97408
54635
97130
24
37
50111
97666
52598
97403
54668
97126
23
38
50449
97662
52634
97399
54702
97121
22
39
50486
97657
52669
97394
64735
97116
21
40
9.50523
9.97653
9.52705
9.97390
9.54769
9.97111
20
41
50561
97649
52740
97385
54802
97107
19
42
50598
97645
52775
97381
54836
97102
18
43
50635
97640
52811
97376
54869
97097
17
44
50673
97636
52846
97372
54903
97092
16
45
50710
97632
52881
97367
54936
97087
15
46
50747
97628
52916
97363
54969
97083
14
47
50784
97623
52951
97858
55003
97078
13
48
50821
97619
52986
97353
55036
97073
12
49
50858
97615
53021
97349
55069
97068
11
50
9.50896
9.97610
9.53056
9.97344
9 55102
9.97063
10
51
509:53
97606
53092
97340
55136
97059
9
52
50970
97602
53126
97335
55169
97054
8
53
51007
97597
53161
97331
55202
97049
7
54
51043
97593
53196
97326
55235
97044
6
55
51080
97589
53231
97322
55268
97039
5
56
51117
97584
53266
97317
55301
97035
4
57
51154
97580
53301
97312
55334
97030
3
58
51 191
97576
53336
97308
55367
97025
2
59
51227
97571
53370
97303
55400
97020
1
60
51264
97567
53405
97299
55433
97015
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
71
70
69
142
LOGARITHMIC SINES AND COSINES
/
21 22
23
/
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.55433
9.97015
9.57358
9.96717
9.59188
9.96403
60
1
55466
97010
5739
96711
59218
96397
59
2
55499
97005
57420
96706
59247
96392
58
3
55532
97001
57451
96701
59277
96387
57
4
55564
96996
57482
96696
59307
96381
56
5
55597
96991
57514
96691
59336
96376
55
6
55630
96986
57545
96686
59366
96370
54
7
556(33
96981
57576
96681
59396
96365
53
8
55695
96976
57607
96676
59425
96360
52
9
55728
96971
57638
96670
59455
96354
51
10
9.55761
9.96966
9.57669
9.96665
9.59484
9.963-19
50
11
55793
96962
57700
96C60
59514
96343
49
12
55826
96957
57731
96655
59543
96338
48
13
55858
96952
57762
96650
59573
96333
47
14
55891
96947
57793
96645
59602
96327
46
15
55923
96942
57824
96640
59632
96322
45
16
55956
96937
57855
96634
59661
96316
44
17
55988
96932
57885
96629
59690
96311
43
18
56021
96927
57916
96624
59720
96305
42
19
56053
9G922
57947
96619
59749
96300
41
20
I'. 56085
9.96917
9.57978
9.96614
9.59778
9.96294
40
' 21
561 18
96912
5800 !
96608
59808
96289
39
22
56150
90907
58039
96003
59837
96284
38
23
56182
96903
58070
96598
59866
96278
37
24
56215
96898
58101
96593
59895
96273
36
25
56*247
96893
58131
96588
59924
96267
35
26
56279
96888
58162
96582
59954
96262
34
27
56311
96883
58192
96577
59963
96256
33
28
56343
96878
58223
96572
60012
96251
32
29
56375
96873
58253
96567
60041
96245
31
30
9.56108
9.96868
9.58284
9.9G562
9.60070
9.96240
30
31
56440
96863
58314
96556
60099
96234
29
32
56472
96858
58345
96551
60128
96229
28
33
56504
96853
58375
96546
60157
962',3
27
34
56536
96848
58406
96541
60186
96218
26
a5
56568
96843
58436
06535
60215
96212
25
ae
56599
96838
58467
96530
60244
96207
24
37
56631
96833
58497
96525
60273
96201
23
38
56663
96828
58527
96520
60302
96196
22
39
56695
96823
58557
96514
60331
96190
21
40
9.56727
9.96818
9.58588
9.96509
9.60359
9.96185
20
41
56759
908 13
58618
96504
60388
96179
19
42
56790
96808
58648
96498
60417
96174
18
43
56822
96803
58678
96493
60446
96108
17
44
56854
96798
58709
96488
60474
96162
16
45
56886
96793
58739
96483
60503
V6157
15
46
56917
96788
58769
96477
60532
90151
14
47
56949
96783
58799
96472
60561
96146
13
48
56980
96778
58829
96467
60589
96140
12
49
57012
96772
58859
96461
60618
96135
11
50
9.57044
9.96767
9.58889
9.96456
9.60646
0.36189
m
51
57075
96762
58919
96451
60075
96123 9
52
57107
96757
58949
96445
60704
96118 8
53
57138
96752
58979
96440
60732
96112
7
54
57169
96747
59009
96435
60761
96107
6
55
57201
96742
59039
96129
60789
96101
K
56
57232
96737
59069
96424
60818
96095 d
57
57264
96732
59098
9641'.)
60846
96090
8
58
57295
96727
59128
96413
60875
960S4
2
59
57326
96722
59158
96408
60903
96079
1
60
57358
96717
59188
96403
60931
96073
/
Cosine
Sine
Cosine
Sine
Cosine Sine
/
68
67
66
LOGARITHMIC SINES AND COSINES
143
/
24
25
26
Sine
Cosine
Sine
Cosine
Sine
Cosine
o
9.60931
9.96073
9.62595
9.95728
9.64184
9.95366
60
60960
96067
62622
95722
64210
95360
59
2
60988
96062
62649
95716
64236
95354
58
3
61016
96056
62676
95710
64262
95348
57
4
61045
96050
62703
95704
64288
95341
56
5
61073
96045
62730
95698
64313
95335
55
6
61101
96039
62757
95692
64339
95329
54
7
61129
96034
62784
95686
64365
95323
53
8
61158
96028
62811
95680
64391
95317
52
9
61186
96022
62838
95674
64417
95310
51
10
9.61214
9.96017
9.62865
9.95668
9.64442
9.95304
50
11
61242
96011
02892
95663
64468
95298
49
12
61270
96005
62918
95657
64494
95292
48
13
61*98
96000
62915
95651
64519
95286
47
14
61326
95994
62972
95645
64545
95279
46
15
61354
95988
62999
95639"
64571
95273
45
16
61382
95982
63026
95633
64596
95267
44
17
61411
95977
63052
95627
64622
95261
43
18
61438
95971
63079
95621
64G47
95254
42
19
61466
95965
63106
95615
64673
95248
41
20
9.61494
9.95960
9.63133
9.95609
9.64698
9.95242
40
21
61522
95954
63159
95603
64724
95286
39
22
61550
95948
63186
95597
647'49
95229
38
23
61578
95942
63213
95591
64775
95223
37
24
61606
95937
63239
95585
64800
95217
36
25
61634
95931
63266
95579
64826
95211
35
26
61662
95925
63292
95573
C4851
95204
34
27
61689
95920
63319
95567
64877
95198
33
28
61717
95914
63345
95561
64902
95192
32
29
61745
95908
63372
95555
64927
95185
31
30
9.61773
9.95902
9.63398
9 95549
9.64953
9.95179
30
31
61800
95897
63425
95543
64978
95173
29
32
61828
95891
63451
95537
65003
95167 28
33
61856
95885
63478
95531
65029
95160 27
34
61883
95879
C3504
95525
65054
95154
26
35
61911
95873
63531
95519
65079
95148
25
6
61939
95868
63557
95513
65104
95141
24
37
61966
95862
63583
95507
65130
95135
23
38
61994
95856
63610
95500
65155
95129
22
39
62021
95850
63636
95494
65180
95122
21
40
9.62049
9.95844
9.63662
9.95488
9.65205
9.95116
20
41
62076
95839
63689
95482
65230
95110
19
42
62104
95833
63715
95476
65255
95103
18
43
62131
95827
63741
95470
65281
95097
17
44
62159
95821
63767
95464
65306
95090
16
45
62186
95815
63794
95458
65331
95084
15
46
62214
95810
63820
95452
65356
95078
14
47
62241
95804
63846
95446
65381
95071
13
48
62268
95798
63872
95440
65406
95065
12
49
62296
95792
63898
95434
65431
95059
. 11
50
9.62323
9.95786
9.63924
9.95427
9.65456
9.95052
10
51
62350
95780
63950
95421
65481
95046
9
52
62377
95775
63976
95415
65506
95039
8
53
62405
95769
64002
95409
65531
95033
7
54
62432
95763
64028
95403
65565
95027
6
55
62459
95757
64054
95397
65580
95020
5
56
62486
95751
64080
95391
65605
95014
4
57
62513
95745
64106
95384
65630
95007
8
58
62541
95739
64132
95378
65655
95001
2
59
62568
95733
64158
95372
65680
94995
1
60
62595
95728
64184
95366
65705
94988
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
65
64
68
144
LOGARITHMIC SINES AND COSINES
27
28
29
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.65705
9.94988
9.67161
9.94593
9.68557
9.94182
60
1
65729
94982
67186
94587
68580
94175
59
2
65754
94975
67208
94580
68603
94168
58
3
65779
94969
67232
94573
68625
94161
57
4
65804
94962
67256
94567
68648
94154
56
5
65828
94956
67280
94560
68671
94147
55
6
65853
94949
67303
94553
68694
94140
54
7
65878
94943
67327
94546
68716
94133
53
8
65902
94936
67350
94540
68739
94126
52
9
65927
94930
67374
94533
68762
94119
51
10
9.65952
9.94923
9.67398
9.94526
9.68784
9.94112
50
11
65976
94917
67421
94ol9
68807
94105
40
12
66001
94911
67445
94513
68829
94098
48
II
66025
94904
67468
94506
68852
94090
47
14
66050
94898
67492
94499
68875
94083
46
15
66075
94891
'67515
94492
68897
94076 45
16
66099
94885
67539
94485
68920
94069
44
17
66124
94878
67562
94479
68942
94062
43
18
66148
94871
6758G
94472
68965
94055
42
19
66173
94865
67609
94465
68987
94048
41
20
9.66197
9.94858
9.67633
9.94458
9.69010
9.94041
40
21
66221
94852
67656
94451
69032
94034
39
22
60246
94845
67680
94445
69055
94027
38
23
66-J70
94839
67703
94438
69077
94020
37
24
66295
94832
67726
94431
69100
94012
36
25
66319
94826
67750
94424
69122
94005
35
26
66343
94819
67773
94417
69144
93998
34
27
66368
94813
67796
94410
69167
93991
33
28
66392
94806
67820
94404
69189
93984
82
29
66416
94799
67843
94397
69212
93977
31
30
9.66441
9.94793
9.67866
9.94390
9.69284
9.93970
80
81
66465
94786
67890
94383
69256
93963
29
32
66489
94780
67913
94376
69279
93955
28
83
66513
94773
67936
94369
69301
93948
27
34
66537
94767
67959
94362
69323
08941
26
35
66562
94760
67982
94355
69345
93934
25
36
66586
94753
68006
94349
69368
93927
24
37
66610
94747
C8029
94342
69390
93920
23
38
66634
94740
68052
94335
69412
3912
22
39
66658
94734
6S075
94328
69434
93905
21
40
9.66682
9.94727
9.68098
9.94321
9.69456
9.93898
20
41
66706
94720
68121
94314
69479
93891
19
42
66731
94714
68144
94307
69501
93884
18
43
66755
94707
68167
94300
69523
93876
17
44
66779
94700
68190
94293
69545
93869
16
45
66803
94694
68213
94286
69567
93862
15
46
66827
94687
68237
94279
69589
93855
14
47
66851
94680
68260
94273
69611
93847
18
48
66875
94674
68283
94266
69638
93840
12
49
66899
94667
68305
94259
69655
93833
11
50
9.66922
9.94660
9.68328
9.94252
9.69677
9.93826
10
51
66946
94654
68351
94245
69699
93819
9
52
66970
94647
68374
94238
6.9721
93811
8
53
66994
94640
68397
94231
69743
93804
7
54
67018
94634
68420
94224
69765
93797
6
55
67042
94627
68443
94217
69787
93789
5
56
67066
94620
68466
94210
69809
93782
4
57
67090
94614
68489
94203
69831
93775
3
58
67113
94607
68512
94196
69853
93768
2
59
67137
94600
68534
94189
69875
93760
1
60
67161
94593
68557
94182
69897
93753
t
Cosine
Sine
Cosine
Sine
Cosine
Sine
,
42
61
60
LOGARITHMIC SINES AND COSINES
145
30
31
32
/
Sine
Cosine
Sine
Cosine
Sine Cosine
9.69897
9.93753
9.71184
9.93307
9.72421 9
92842
60
1
69919
93746
71205
93299
72441
92834
59
2
69941
93738
71226
93291
72461
9-2826
58
3
69963
93731
71247
93284
72482
92818
57
4
69984
93724
71268
93276
72502
9:2810
56
5
70006
93717
71289
93269
72522
92803
55
6
70028
93709
71310
93261
72542
92795
54
7
70050
93702
71331
93253
72562
9-2787
53
8
70072
93095
71352
93246
72582
92779
52
9
70093
93687
71373
93238
7~>602
92771
51
10
9.70115
9.93680
9.71393
9.932SO
9 7-2622 9.92763
50
11
70137
93673
71414
932C3
72643
92155
49
12
70159
93665
71435
93215
72663
92747
48
13
70180
93658
71456
93-207
72683
9-2739
47
14
70202
93650
71477
93200
72703
92731
46
15
70224
93643
71498
93192
72723
92723
45
16
70245
93636
71519
93184
72743
92715
44
17
70-267
93628
71539
93177
727G3
92707
43
18
70-288
93621
71560
93169
72783
92699
42
19
70310
93614
71581
93161
72803
9-2691
41
20
9.70332
9.93606
9.71602
9.93154
9.72823 9
92683
40
21
70353
93599
71622
93146
72843
92675
39
22
70375
93591
71643
93138
72863
92667
38
23
70396
93584
71664
93131
728S3
92659
37
24
70418
93577
71685
93123
72902
92651
36
25
70439
93569
71705
93115
72922
92643
35
26
70461
93562
71726
93108
72942
92635
34
27
70482
93554
71747
93100
72962
92627
33
28
70504
93547
71767
93092
72982
92619
32
29
70525
93539
71788
93084
73002
92611
31
30
9.70547
9.93532
9.71809
9.93077
9.73022 9
92603
30
31
70568
93525
71829
93069
73041
92595
29
32
70590
93517
71850
93061
73061
92587
28
33
70611
93510
71870
93053
73081
92579
27
34
70633
93502
71891
93046
73101
92571
26
35
70654
93495
71911
93038
73121
9-2563
25
36
70675
93487
71932
93030
73140
92555
24
37
70697
93480
71952
93022
73160
9-2546
23
38
70718
93472
71973
9: JO 14
73180
92538
22
39
70739
93465
71994
93007
73200
92530
21
40
9.70761
9.93457
9.72014
9.92999
9.73219 9.92522
20
41
70782
93450
72034
9-2991
73239
92514
19
42
70803
93442
72055
92983
73259
92506
18
43
70824
93435
72075
92976
73-278
92498
17
44
70846
93427
72096
92968
73298
92490
16
45
70867
93420
72116
92960
73318
92482
15
46
70888
93412
72137
92952
73337
92473
14
47
70909
93405
72157
92944
73357
92465
13
48
70931
93397
72177
92936
73377
92457
12
49
70952
93390
72198
92929
73396
92449
11
50
9.70973
9.93382
9.72218
9.92921
9.73416 9
92441
10
51
70994
93375
72238
92913
73435
92433
9
52
71015
93367
72259
92905
73455
92425
8
53
71036
93360
72279
92897
73474
92416
7
54
71058
93352
72299
92889
73494
92408
6
55
71079
93344
72320
92881
73513
92400
5
56
71100
93337
72340
92874
73533
92392
4
57
71121
93329
72360
92866
73552
92384
3
58
71142
93322
72381
92858
73572
92376
2
59
71163
93314
72401
92850
73591
92367
1
60
71184
93307
72421
92842
73611
92359
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
69
58
57
146
LOGARITHMIC SINES AND COSINES
88
84
85
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.73611
9.92359
9.74756
9.91857
9.75859
9.5)1336
60
73630
92351
74775
91849
75877
91328
59
2
73650
92343
74794
91840
75895
91319
58
3
73669
92335
74812
91832
75913
91310
57
4
73C89
92326
74831
91823
75931
91301
56
5
73708
92318
74850
91815
75949
91292
55
6
73727
92310
74868
91806
75967
91283
54
7
73747
92302
74887
91798
75985
91274
53
8
73760
92293
74906
91789
76003
91266
52
9
73785
92285
74924
91781
76021
91257
51
10
9.73805
9.92277
9.74943
9.91772
9.76039
9.91248
50
11
73824
92269
74961
91763
76057
91239
49
12
73843
92260
74980
91755
70075
91230
48
13
73863
92252
74999
91746
76093
91221
47
14
73882
92244
75017
91738
76111
91212
46
15
73901
92235
75036
91729
76129
91203
45
16
73921
92227
75054
91720
76146
91194
44
17
73940
92219
75073
91712
76164
91185
43
18
73959
92211
75091
91703
76182
91176
42
19
73978
92202
75110
91695
76200
91167
41
20
9.73997
9.92194
9.75128
9. 91 086
9.76218
9.91158
40
21
74017
92186
75147
91677
76;. ; 36
91149
39
22
74036
92177
75165
91669
76253
91141
38
23
74055
92169
75184
91660
76271
91132
37
24
74074
92161
75'.'02
91651
76289
91123
36
25
74093
92152
75221
91643
76307
91114
IB
26
74113
92144
75239
916:^4
76324
91105
34
27
74132
92136
75258
91625
76342
91096
33
28
74151
92127
75276
91617
76360
91087
32
29
74170
92119
75294
91608
76378
91078
31
30
9.74189
9.92111
9.75313
9.91599
9.76395
9.91069
30
31
74208
92102
75331
91591
76413
91060
29
32
74227
92094
75350
91582
76431
91051
28
33
74246
92086
75368
91573
76448
91042
27
34
'<4265
92077
75386
91565
76466
91033
26
35
74284
92069
75405
91556
76484
91023
25
36
74303
92060
75423
91547
76501
91014
24
3V
74322
92052
75441
91538
76519
91005
23
38
74341
92044
75459
91530
76537
90996
22
39
74360
92035
75478
91521
76554
90987
21
40
9.74379
9.92027
9.75496
9.91512
9.76572
9.90978
20
41
74398
92018
75514
91504
76590
90969
19
42
74417
92010
75533
91495
76607
90960
18
43
74436
92002
75551
91486
76625
90951
17
44
74455
91993
75569
91477
76642
90942
16
45
74474
91985
75587
91469
76660
90933
15
46
74493
91976
75605
91460
76677
90924
14
47
74512
91968
75624
91451
76695
90915
13
48
74531
91959
75642
91442
76712
90906
12
49
74549
91951
75660
91433
76730
90896
11
50
9.74568
9.91942
9.75678
9.91425
9.76747
9.90887
10
51
74587
91934
75696
91416
76765
90878
9
52
74606
91925
75714
91407
76782
90869
8
53
74625
91917
75733
91398
76800
90860
f
54
74644
91908
75751
91389
76817
90851
6
55
74662
91900
75769
91381
76835
90842
5
56
74681
91891
75787
91372
76852
90832
4
57
74700
91883
75805
91363
76870
90823
3
58
74719
91874
75823
91354
76887
90814
2
59
74737
91866
75841
91345
76904
90805
1
60
74756
91857
75859
91336
76922
90796
Cosine
Sine
Cosine
Sine
Cosine
Sine
f
56
65
64
LOGARITHMIC SINES AND COSINES
147
36
37
3
8
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.76922
9.90796
9.77946
9.90235
9.78934
9.89653
60
1
76939
90787
77963
90225
78950
89643
59
2
76957
90777
77980
90216
78967
89633
58
3
76974
90768
77997
90206
78983
896-^4
57
4
76991
90759
78013
90197
78999
89614
56
5
77009
90750
78030
90187
79015
89tt)4
55
6
77026
90741
78047
90178
79031
89594
54
7
77043
90731
78063
90168
79047
89584
53
8
77061
90722
78080
90159
79063
89574
52
9
77078
90713
78097
90149
79079
89564
51
10
9.77095
9.90704
9.78113
9.90139
9.79095
9.89554
50
11
77112
90694
78130
90130
79111
89544
49
1ST
77130
90685
78147
90120
79128
89534
48
13
77147
90676
78163
90111
79144
89524
47
14
77164
90667
78180
90101
79160
89514
46
15
77181
90657
78197
90091
79176
89504
45
16
77199
90648
78213
90082
79192
89495
44
17
77216
90639
78230
90072
79208
89485
43
18
77233
90630
78246
90063
79224
89475
42
19
77250
90620
78263
90053
79240
89465
41
20
9.77268
9.90611
9.7-280
9.90043
9.79256
9.89455
40
21
77285
90602
78296
90084
79272
89445
39
22
77302
90592
78313
90024
79288
89435
38
*3
77319
90583
78329
90014
79304
89125
37
24
77336
90574
78346
90005
79319
89415
36
25
77353
90565
78362
89995
79335
89405
35
26
77370
90555
78379
89985
79351
89395
34
27
77387
90516
78395
89976
79367
89385
33
28
77405
90537
78412
89966
79383
89375
32
29
77422
905-27
78428
89956
79399
89364
31
30
9.77439
9.90518
9.78445
9.89947
9.79415
9.89354
30
31
.77456
90509
78481
89937
79431
89344
29
32
77473
90499
78178
89927
79447
89334
28
33
77490
90190
78494
80918
79463
89324
27
31
77507
90480
78510
89908
79478
89314
26
35
77524
90471
78527
89898
79494
89301
25
36
77541
90462
78543
89888
79510
89294
24
37
77558
90452
78560
89879
79526
89284
23
38
77575
90443
78576
89869
79542
89274
22
39
77592
90434
78592
89859
79558
89264
21
40
9.77609
9.90424
9.78609
9.89849
9.79573
9.89254
20
41
77626
90415
78625
89840
79589
89244
19
42
77643
90405
78642
89830
79605
89233
18
43
77660
90396
78658
89820
78621
89223
17
44
77677
90386
78674
89810
79636
89213
16
45
77694
90377
78691
89801
79652
89203
15
46
77711
9036S
78707
89791
79668
89193
14
47
77728
90353
78723
89781
79684
89183
13
48
77744
90349
78739
89771
79699
89173
12
49
77761
90339
78756
89761
79715
89162
11
50
9.77778
9.90330
9.78772
9.89752
9.79731
9.89152
10
51
77795
90320
78788
89742
79746
89142
9
52
77812
90311
78805
89732
79762
89132
8
53
77829
90301
78821
89722
79778
89122
7
54
77846
90292
78837
89712
79793
89112
6
55
77862
90282
78853
89702
79809
89101
5
56
77879
90273
78869
89693
79825
89091
4
57
77896
90263
78886
89683
79840
89081
3
58
77913
90254
78902
89673
79856
89071
2
59
77930
90244
78918
89663
79872
89060
1
60
77946
90235
78934
89653
79887
89050
/
Cosine
Sine
Cosine
Sine
Cosine
Sine
/
68
62
t
>1
148
LOGARITHMIC SINES AND COSINES
39
40
41
Sine
Cosine
Sine
Cosine
Sine
Cosine
9.79887
9.89050
9.80807
9.88425
9.81694
9.87778
60
1
79903
89040
80822
88415
81709
87767
59
2
79918
89030
80837
88404
81723
87756
58
3
79934
890*)
80852
88394
81738
87745
t^
4
79950
89009
80867
88383
81752
87734
56
5
79965
88999
80882
88372
81767
87723
55
6
79981
88989
80897
88362
81781
87712
54
7
79996
88978
80912
88351
81796
87701
53
8
80012
88968
80927
88340
81810
87690 52
9
80027
88958
80942
88330
81825
87679 51
10
9.80043
9.88948
9.80957
9.88319
9.81839
9.87668 ' 50
11
80058
8H937
80972
88308
81854
87657 ' 49
12
80074
88927
80987
88298
81868
87646 48
13
80089
88917
81002
88287
81882
87635 47
14
80105
88906
81017
88276
81897
87624 j 46
15
80120
88896
81032
88266
81911
87613 I 45
16
80136
88886
81047
88255
81926
87601
44
17
80151
88875
81061
88244
81940
87590
43
18
80166
88865
81076
88234
81955
87579
42
19
80182
88855
81091
88223
81969
87568
41
20
9.80197
9.88844
9.81106
9.88212
9.81983
9.87557
40
21
80213
88834
81121
88201
81998
87546
39
22
80228
88824
81136
88191
82012
87535
38
23
80244
88813
81151
88180
82026
87524
37
24
80259
88803
81166
88169
82041
87513
36
25
80274
88793
81180
88158
82055
87501 85
26
80290
88782
81195
88148
82069
87490 34
27
80305
88772
81210
88137
82084
87479 33
28
80320
88761
81225
88126
82098
87468 32
28
80336
88751
81240
88115
82112
87457 31
30
9.80351
9.88741
9.81254
9.88105
9.82126
9.87446
30
31
80366
88730
81269
88094
82141
87434
29
32
80382
88720
81284
88083
82155
87423
28
33
80397
88709
81299
88072
82169
87412
27
34
80412
88699
81314
88061
82184
87401
26
35
80428
88688
81328
88051
82198
87390
25
36
80443
88678
81343
88040
82212
87378
24
37
80458
88668
81358
88029
82226
87367
23
38
80473
88657
81372
88018
82240
87356
22
39
80489
88647
81387
88007
82255
87345
21
40
9.80504
9.88636
9.81402
9.87996
9.82269
9.87334
20
41
80519
88626
81417
87985
82283
87322
19
42
80534
88615
81431
87975
82297
87311
18
43
80550
88605
81446
87964
82311
87300
17
44
80565
88594
81461
87953
82326
87288
16
45
80580
88584
81475
87942
821340
87277
15
46
80595
8*573
81490
87931
82354
87266
14
47
80610
88563
81505
87920
82368
87255
18
48
80625
88552
81519
87909
82382
87243
12
49
80641
88542
81534
87898
82396
87232
11
50
9.80656
9.88531
9.81549
9.87887
9.82410
9.87S21
10
51
80671
88521
81563
87877
82424
87209
9
52
80686
88510
81578
87866
82439
87198
8
53
80701
88499
81592
87855
824f3
87187
7
54
80716
88489
81607
87844
82467
87175
6
55
80731
88478
81622
87833
82481
87164
5
56
80746
88468
81686
87822
82495
87153
4
57
80762
88457
81651
87811
82509
87141
3
58
80777
88447
81665
87800
82523
87130
2
59
80792
88436
81680
87789
82537
87119
1
60
80807
88425
81694
87778
82551
87107
~
Cosine
Sine
Cosine
Sine
Cosine
Sine
,
50
49
48
LOGARITHMIC SINES AND COSINES
149
/
42
48
44
]
Sine
Cosine
Sine
Cosine
Sine
Cosine
o
9.82551
9.87107
9.88378
9.86413
9.84177
9.85693
60
82565
87096
83392
86401
84190
85681
59
2
82579
87085
83405
8G889
84203
85669
58
3
82593
87073
83419
86377
84216
85657
57
4
82607
87062
83432
86366
84229
85645
56
5
82621
87050
83446
86354
84242
85632
55
6
82635
87039
83459
86342
84255
85620
54
7
82649
87028
83473
86330
84269
85608
53
8
82663
87016
83486
86318
84282
85596
52
9
82677
87005
83500
86306
84295
85583
51
10
9.82691
9.86993
9.83513
9.86295
9.84308
9.85571
50
11
82705
86982
83527
86283
84321
85559
49
12
82719
86970
83540
86271
84334
85547
48
13
82733
86959
83554
86259
84347
85534
47
14
82747
86947
83567
86247
84360
85522
46
15
82rei
86936
83581
86235
84373
85510
45
16
82775
86924
83594
80888
84385
85497
44
17
82788
86913
83608
86211
84398
85485
43
18
82802
86902
83621
86200
84411
85473
42
19
82816
86890
83634
86188
84424
85460
41
20
9.82830
9.86879
9.83648
9.86176
9.84437
9.85448
40
21
82844
86867
83661
86164
84450
85436
39
22
82858
86855
83674
86152
84463
85423
38
23
82872
86844
83688
86140
84476
85411
37
24
82885
86832
83701
86128
84489
85399
36
25
82899
86821
83715
86116
84502
85386
35
26
82913
86809
83728
86104
84515
85874
34
27
82927
86798
83741
86092
84528
65361
33
28
82-941
86786
83755
86080
84540
85349
32
29
82955
86775
83768
86068
84553
85337
31
30
9.82968
9.86763
9.83781
9.86056
9.84566
9.85324
30
31
82982
86752
83795
86044
84579
85312
29
32
82996
86740
83808
86032
84592
85299
28
33
83010
86728
83821
86020
84605
85287
27
34
83023
86717
83834
86008
84618
85274
26
35
88037
86705
83848
85996
84630
85262
25
36
83051
86694
83861
85984
84643
85250
24
37
83065
86682
83874
85972
84656
85237
23
38
83078
86670
83887
859CO
84669
85225
22
39
83092
86659
83901
85948
84682
85212
21
40
9.83106
9.86647
9.83914
9.85936
9.84694
9.85200
20
41
83120
86635
83927
85924
84707
85187
19
42
83133
86624
83940
85912
84720
85175
18
43
83147
86612
83954
85900
84733
85162
17
44
83161
86600
83967
85888
84745
85150
16
45
83174
86589
83980
85876
84758
85137
15
46
83 188
86577
83993
85864
84771
85125
14
47
83202
86565
84006
85851
81784
85112
13
48
83215
86554
84020
85839
84796
85100
12
49
83229
86542
840.33
85827
84809
85087
11
50
9.83242
9.86530
9.84046
9.85815
9.84822
9.85074
10
51
83256
86518
84059
85803
84835
85062
9
52
83270
86507
84072
85791
84847
85049
8
53
83283
86495
84085
85779
84860
85037
7
54
83297
86483
84098
85766
84873
86024
6
55
83310
86472
84112
85754
84885
85012
5
56
83324
86460
84125
85742
84898
84999
4
57
83338
86448
84138
85730
84911
84986
3
58
83351
86436
84151
85718
84923
84974
2
59
83365
86425
84164
85706
84936
84961
1
60
83378
86413
84177
85693
84949
84949
Cosine
Sine
Cosine
Sine
Cosine
Sine
|
470
46
46
150
LOG. TANGENTS AND COTANGENTS
/
1
20
Tan
Cotan
Tan
Cotan
Tan
Cotan
oo
OD
8.21192
11.75808
8.54308
11.45692
60
1
6.46373
13.53627
24910
75090
54669
45331
59
2
76476
23524
25616
74384
55027
44973
58
3
94085
05915
26312
73688
55382
44618
57
4
7.06579
12.93421
26996
73004
55734
44266
56
5
16270
83730
27669
72331
56083
43917
55
6
24188
75812
28332
71668
56429
43571
54
7
30882
69118
28986
71014
56773
43227
53
8
36682
63318
29629
70371
57114
42S86
52
9
41797
58203
30263
69737
57452
42548
51
10
7.46373
12.53627
8.30888
11.69112
8.57788
11.42212
50
11
50512
49488
31505
68495
58121
41879
49
12
54291
45709
32112
67888
58451
41549
48
13
57767
42233
32711
67289
58779
41221
47
14
60986
39014
33302
66698
59105
40895
46
15
6398-2
36018
33886
66114
59428
40572
45
16
66785
33215
34461
65539
59749
40251
44
17
(19418
30582
35029
64971
60068
39932
43
18
71900
28100
35590
64410
60384
39616
42
19
74248
25752
36143
63857
60698
89302
41
20
7 76476
12.23524
8.36689
11.63311
8.61009
11.38991
40
21
78595
21405
37229
62771
61319
38681
39
22
80615
19385
37762
62238
61626
38374
38
23
82546
17454
38289
61711
61081
38069
37
24
S4394
15606
38809
61191
62234
37766
36
25
86167
13833
39323
. 60677
62535
37465 i 35
26
87871
12129
39832
60168
62834
371 C6 34
27
89510
10490
40334
59666
63131
36869
33
28
91089
08911
40880
59170
63426
36574
32
29
92613
07387
41321
58679
63718
36282
31
30
7.94086
12.05914
8.41807
11.58193
8.64009
11.35991
30
31
95510
04490
42287
57713
64298
35702
29
32
96889
03111
42762
57238
64585
35415
28
33
98225
01775
43232
56768
64870
35130
27
34
99522
00478
43696
56304
05154
34846
26
35
8.00781
11.99219
44156
55844
65435
34565
25
36
02004
97996
44611
55389
65715
34285
24
37
03194
96S06
45061
54939
65993
34007
23
38
04353
95647
45507
54493
66269
33731
22
39
05481
94519
45948
54052
66543
33457
21
40
8.06581
11.93419
8.46885
11.53615
8.66816
11.23184
20
41
07653
92347
46817
53183
67087
32913
19
42
08700
91300
47245
52755
67356
32644
18
43
09722
90278
47669
52331
67624
32376
17
44
10720
89280
48089
51911
67890
32110
16
45
11696
88304
48505
51495
68154
31846
15
46
12651
87349
48917
51083
68417
31583
14
47
13585
86415
493:25
50675
68678
31322
13
48
14500
85500
49729
50271
68938
31062
12
49
15395
84605
50130
49870
69196
30804
11
50
8.16273
11.83727
8.50527
11 .49473
8.69453
11.30547
10
51
17133
82867
50920
49080
69708
30292
9
52
17976
82024
51310
48690
69962
30038
8
53
18804
81196
51696
48304
70214
29786
7
54
19616
80384
52079
47921
70465
29535
6
55
20413
79587
52459
47541
70714
29286
5
56
21195
78805
52835
47165
70962
29038
4
57
21964
78036
53208
46792
71208
28792
3
58
22720
77280
53578
46422
71453
28547
2
59
23462
76538
53945
46055
71697
28303
1
60
24192
75808
54308
45692
71940
28060
/
Cotau
Tan
Cotan
Tan
Cotan
Tan
/
89
88
87
LOG. TANGENTS AND COTANGENTS
151
/
8
4
5
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
o
8.71940
11.28060
8.84464
11.15536
8.94195
11.05805
60
I
72181
27819
84646
15354
94340
05660
59
2
72420
27580
84826
15174
94485
05515
58
3
72659
27341
85006
14994
94630
05370
57
4
72896
27104
85185
14815
94773
05227
56
5
73132
26868
85363
14637
94917
05083
55
6
73366
26634
85540
14460
95060
04940
54
7
73600
26400
85717
14283
95202
04798
53
8
73333
2616S
85893
14107
95344
04656
52
9
74063
25937
86069
13931
95486
04514
51
10
8.74292
11.25708
8.86243
11.13757
8.95627
11.04373
50
11
74531
25479
86417
13583
95767
04238
49
12
747-18
25252
86591
13409
95908
04092
48
18
74974
25026
86763
13237
96047
03953
47
14
75199
24801
86935
13065
96187
03813
46
15
75423
24577
8710(5
12894
96325
03675
45
16
75645
24355
87277
12723
96464
03536
44
17
75867
24133
87447
12553
96602
03398
43
18
76087
23913
87616
12384
96739
03261
42
19
76306
23694
87785
12215
96877
02133
41
20
8 76535
11.23475
8.87953
11.12047
8.97013
11.02987
40
21
76743
23258
88120
11880
97150
02850
39
22
76958
23042
88287
11713
97285
02715
38
n
77173
22827
88453
11547
97421
02579
37
24
77387
22613
88618
11382
97556
02444
36
25
77600
22400
88783
11217
97691
02309
35
26'
77811
22189
88948
11053
97885
02175
34
27
78022
21978
89111
10889
97959
02041
33
28
78232
21768
89274
10726
98092
01908
32
29
78441
21559
89437
10563
98225
01775
31
30
8.78649
11.21351
8.89598
11.10402
8.98358
11.01642
30
31
78855
21145
89760
10240
98490
01510 29
32
79061
20939
89920
10080
98622
01378
28
83
79266
20734
90080
09920
98753
01247
27
34
79470
20530
90240
09760
98884
01116
26
35
79673
20327
90399
09601
99015
00985
25
36
79875
20125
90557
09443
99145
00855
24
37
80076
19924
90715
09285
99375
00735
23
38
80277
19723
90872
09128
99405
00595
22
39
80476
19524
91029
08971
99534
00466
21
40
8.80674
11.19326
8.91185
11.08815
8.99662
11.00338
20
41
80872
19128
91340
08660
99791
00209
19
42
81068
18932 -
91495
08505
99919
00081
18
43
81264
18736
91650
08350
9.00046
10.99954
17
44
81459
18541
91803
08197
00174
99826
16
45
81653
18347
91957
08043
00301
99699
15
46
81840
18154
92110
07890
00427
99573
14
47
82038
17962
92262
07738
00553
99447
18
48
82230
17770
92414
07586
00679
99331
12
49
82420
17580
92565
07435
00805
99195
11
50
8.82610
11.17390
8.92716
11.07284
9.00930
10.99070
10
51
82799
17201
92866
07134
01055
98045
9
52
82987
17013
93016
06984
01179
98821
8
53
83175
16825
93165
06835
01303
98697
7
54
83361
16639
93313
06687
01427
98573
6
55
83547
16453
93462
06538
01550
98450
5
56
83T32
16268
93609
06391
01673
98327
4
57
83916
16084
93756
06244
01796
96204
3
58
84100
15900
93903
06097
01918
96082
2
59
84282
15718
94049
05951
02040
97960
1
60
81464
15536
94195
05805
02162
97838
C
/
Cotan
Tan
Cotan
Tan
Cotan
Tan
t
86
86
84
152
LOG. TANGENTS AND COTANGENTS
/
(
7
8
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.02162
10.97838
9.08914
10.91086
9.14780
10.86220
60
02283
97717
09019
90981
14872
85128
59
2
02404
9T596
09123
90877
14963
85037
58
3
025-^5
97475
09227
90773
15054
84946
57
4
02645
97355
09330
90670
15145
84855
56
5
02766
97234
09434
90566
15236
84764
55
6
02885
97115
09537
90463
15327
84673
54
7
03005
96995
09640
90360
15417
84583
53
8
03124
96876
09742
90258
15508
84492
52
9
03242
96758
09845
90155
15598
84402
51
10
9.03361
10.96639
9.09947
10.90053
9.15688
10.84312
50
11
03479
96521
10049
89951
15777
84228
49
12
03597
96403
10150
89850
15867
84133
48
13
03714
96286
10252
89748
15956
84044
47
14
03832
96168
10353
89647
16046
83954
46
15
03948
96052
10454
89546
16)35
83865
45
16
04065
95935
10555
89445
16224
83776
44
17
04181
95819
10656
89344
16812
83688
43
18
04297
95703
10756
89244
16401
83599
42
19
04413
95587
10856
89144
16489
83511
41
20
9.04528
10.95472
9.10956
10.89044
9.16577
10.83423
40
21
04643
95357
11056
88944
16665
83335
39
22
04758
95242
11155
H8845
16753
83247
38
23
04873
95127
11254
88746
16841
83159
87
24
04987
95013
11358
88647
16928
83072
86
25
05101
94899
11452
88548
17016
82984
35
26
05214
94786
11551
88449
17103
82897
34
27
05328
94672
11649
88351
17190
82810
33
28
05441
94559
11747
88258
17277
82723
82
29
05553
94447
11845
88155
17363
82637
31
30
9.05666
10.94334
9.11943
10.88057
9.17450
10.82550
30
31
05778
94222
12040
87960
17536
82464
29
32
05890
94110
12138
87862
17622
82378
28
33
06002
93998
12235
87765
17708
82292
27
34
06118
93887
12332
8T668
17794
82206
26
35
06224
93776
12428
87572
17880
82120
25
86
06335
93665
12525
87475
17965
82035
24
37
06445
93555
12621
87379
. 18051
81949
23
38
06556
93444
12717
87283
18136
81864
22
39
06666
93334
12813
87187
18221
81779
21
40
9.06775
10.93225
9.12909
10.87091
9.18306
10.81694
20
41
06885
93115
13004
86996
18391
81609
19
42
06994
93006
13099
86901
18475
81525
18
43
07103
92897
13194
86806
18560
81440
17
44
07811
92789
13289
86711
18644
81856
16
45
07820
92680
13384
8G616
18728
81272
15
46
07428
92572
13478
86522
18812
81188
14
47
\536
92464
13573
86427
18896
81104
13
48
07643
92857
13667
86338
18979
81021
12
49
07751
92249
13761
86239
19063
80937
11
50
9.07858
10.92142
9.13854
10.86146
9.19146
10.80854
10
51
07964
92036
13948
86052
19229
80771
9
52
08071
91929
14041
85959
19312
80688
8
53
08177
91828
14134
85866
19395
80605
7
54
08288
91717
14227
85773
19478
80522
6
55
08389
91611
14320
85680
19561
80439
5
56
08495
91505
14412
85588
19643
80357
4
57
08600
91400
14504
85496
19725
80275
3
58
08705
91295
14597
85403
19807
80193
2
59
08810
91190
14688
85312
19889
80111
1
60
08914
91086
14780
85220
19971
80029
f
Cotan
Tan
Cotan
Tan
Cotan
Tan
{
83
82'
81
LOG. TANGENTS AND COTANGENTS
153
9
10
11
t
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.19971
10.80029
9.24632
10.75368
9.28865
10.71135
60
1
20053
79947
24706
75294
28933
71067
59
2
20134
79S66
24779
75221
29000
71000
58
3
20216
79784
24853
75147
29067
70933
57
4
20297
79703
24926
75074
29134
70866
56
5
20378
79622
25000
75000
29201
70799
55
6
20459
79541
25073
74927
29268
70732
54
7
20540
79460
25146
74854
29335
70665
53
8
20621
79379
25219
74781
29402
70598
52
9
20701
79299
25292
74708
29468
70532
51
10
9.20782
10.79218
9.25365
10.74685
9.29535
10.70465
50
11
20862
79138
25437
74563
29601
70399
49
12
20942
79058
25510
74490
29668
70332
48
13
21022
78978
25582
74418
29734
70266
47
14
21102
78898
25655
74345
29800
70200
46
15
21182
78818
25727
74273
29866
70134
45
16
21261
78739
25799
74201
29932
70068
44
17
21341
78659
25871
74129
29998
. 70002
43
18
21420
78580
25943
74057
30064
69936
42
19
21499
78501
26015
73985
30130
69870
41
80
9.21578
10.78422
9.26086
10.73914
9.30195
10.69805
40
21
21657
78343
26158
73842
30261
69739
39
22
21736
78264
26229
73771
30326
69674
38
23
21814
78186
26301
73699
30391
69609
37
24
21893
78107
26372
73628
30457
69543
36
25
21971
78029
26443
73557
30522
69478
35
26
22049
77951
2(5514
73486
30587
69413
34
27
22127
77873
26585
73415
30652
69348
83
28
22205
77795
26655
73345
30717
69283
32
29
22283
77717
26726
73274
30782
69218
31
30
9.22361
10.77639
9.26797
10.73203
9.30846
10.69154
30
31
22438
77562
26S67
73133
30911
69089
29
32
22516
77484
26937
73063
30975
69025
28
33
22598
77407
27008
72992
31040
68960
27
34
22670
77330
27078
72922
31104
68896
26
91
22747
77253
27148
72852
31168
68832
25
36
22821
77176
27218
72782
31233
68767
'24
37
22901
77099
27288
72712
31297
68703
23
38
22977
77023
27357
72648
31361
68639
22
39
23054
76946
27427
72573
31425
68575
21
40
9.23130
10.76870
9.27496
10.72504
9.31489
10.68511
20
41
28206
76794
27566
72434
31552
68448
19
42
23283
76717
27635
72365
31616
68384
18
43
23359
76641
27704
72296
31679
68321
17
44
23435
76565
27773
72227
31743
68257
16
45
23510
76490
27842
72158
81806
68194
15
46
23586
76414
27911
72089
31870
68130
14
47
23661
76339
27980
72020
31933
68067
13
48
23737
76263
28049
71951
31996
68004
12
49
23312
76188
28117
71883
32059
67941
11
50
9.23887
10.76113
9.28186
10.71814
9.32122
10.67878
10
51
23962
76038
28254
71746
32185
67815
9
52
24037
759(53
28323
71677
32248
67752
8
53
24112
75888
28391
71609
3231 1
67689
7
54
21186
75814
28459
71541
32873
67627
6
55
24261
75739
28527
71473
32436
67564
5
56
24335
75665
28595
71405
32498
67502
4
57
24410
75590
28662
71338
32561
67439
3
58
24481
75516
28730
71270
32623
67377
2
59
24558
75442
28798
71202
32685
67315
1
60
24632
75368
28865
71135
32747
67253
' t f
Cotan
Tan
Cotan
Tan
Cotan
Tan
80*
79
78
154
LOG. TANGENTS AND COTANGENTS
12
18
14
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
o
9.32747
10.67253
9.36336
10.63664
9.39677
10.60323
60
1
32810
67190
36394
63606
39731
602C9
59
2
32872
67128
36452
63548
39785
60215
58
3
32933
67067
36509
63491
39838
60162
57
4
32995
67005
36566
63434
89892
60108
56
5
1 33057
66943
36624
63376
39945
60055
55
6
33119
66881
36681
63319
39999
60001
54
7
83180
66820
36738
68263
40052
59948
53
8
83>42
66758
36795
63205
40106
59894
52
9
83303
66(597
36852
63148
40159
59841
51
10
9.33365
10.66635
9.36909
10.63091
9.40212
10.59788
50
11
38426
66574
36966
63034
40266
59734
49
12
38487
66513
37023
62977
40319
59681
48
13
33548
66452
37080
62920
40372
59628
47
14
33609
66391
37137
62863
40425
59575 46
15
33670
66330
37193
62807
40478
59522 45
16
33731
66269
37250
62750
40531
59469 44
17
33792
66208
37306
62G94
40584
59416
43
18
33853
66147
37363
62637
40636
593G4
42
19
33913
66087
37419
62581
40689
59311
41
20
9.33974
10.66026
9.37476
10.02524
9.40742
10.59258 40
21
34034
65966
37532
62468
40795
59205 89
22
34095
65905
37588
62412
40847
59153 i 38
23
84155
65845
37644
62356
40900
59100 ! 37
24
34215
65785
37700
62300
40952
59048 ! 36
25
34276
65724
37756
62244
41005
58995 35
26
34336
65664
87812
62188
41057
58943
34
27
34396
65604
37868
62132
41109
8891
33
28
34456
65544
37924
62076
41161
58889
32
29
34516
65484
37980
62020
41214
58786
31
30
9.34576
10.65424
9.38035
10.61965
9.41266
10.58734
30
31
34635
65365
38091
61909
41318
58682
29
32
34695
65305
38147
61853
41370
58630 1 28
33
34755
65245
38202
61798
41422
58578 I 27
34
34814
65186
38257
61743
41474
58526
26
35
34874
65126
38313
61687
41526
58474
25
36'
34933
65067
38368
61632
41578
58422
24
37
34992
65008
38423
61577
41629
58371
23
38
35051
64949
38479
61521
41681
58319
22
39
35111
64889
38534
61466
41733
58267
21
40
9.35170
10.64830
9.38589
10.61411
9.41784
10.58216
20
41
35229
64771
38644
61356
41836
58164
19
42
35288
64712
38699
61301
41887
58113
18
43
35347
64653
38754
61246
41939
58061
17
44
35405
64595
38808
61192
41990
58010
16
45
35464
64536
38863
61137
42041
57959
15
46
35523
64477
38918
61082
42093
57907
14
47
35581
64419
38972
61028
42144
57856
13
48
35640
64360
39027
60973
42195
57805
12
49
35698
64302
39082
60918
42246
57754
11
50
9.35757
10.64243
9.39136
10.60864
9.42297
10.57703
10
51
35815
64185
39190
60810
42348
57652
9
52
35873
64127
39245
60755
42390
57601
8
53
35931
64069
39299
60701
42450
57550
7
54
35989
64011
39353
60647
42501
57499
6
55
36047
63953
39407
60593
42552
57448
5
56
36105
63895
89461
60539
42603
57397
4
57
36163
63837
39515
60485
42653
57347
8
58
36221
63779
39569
60431
42704
57296
2
59
36279
63721
39623
60377
42755
57245
1
60
36336
63664
39677
60328
42805
57195
/
Cotan
Tan
Cotan
Tan
Cotan
Tan
77
76
76
LOG. TANGENTS AND COTANGENTS
155
f
15
16
17
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.42805
10.57195
9.45750
10.54250
9.48534
10.51466
60
1
42856
57144
45797
54203
48579
51421
59
2
42906
57094
45845
54155
48624
51376
58
3
42957
57043
45892
54108
48669
51331
57
4
43007
56993
45940
51060
48714
51286
56
5
43057
56943
45987
54013
48759
51241
55
6
43108
56892
46035
53965
48804
51196
54
7
43158
56842
46082
53918
48849
51151
53
8
43208
56792
46130
53870
48894
51106
52
9
43258
56742
46177
53823
48939
51061
51
10
9.43308
10.56692
9.4G224
10.53776
9.48984
10.51016
50
11
43358
56642
46271
53729
49029
50971
49
12
43408
56592
46319
53681
49073
50927
48
18
43458
56542
46366
53634
49118
50882
47
14
43508
56492
46413
53587
49163
50837
46
15
43558
56442
46460
53540
49207
50793
45
16
43607
56393
46507
53493
49252
50748
44
17
43657
56343
46554
5344G
49-^96
50704
43
18
43707
56293
46601
53399
49341
50659
42
19
43756
56244
46648
53352
49385
50615
41
20
9 43806
10.56194
9.46694
10.53306
9.49430
10.50570
40
21
43855
56145
46741
53259
49474
50526
39
22
43905
56095
46788
53212
49519
50481
38
23
43954
56046
46835
53165
49563
50437
37
24
44004
55996
46881
53119
49607
50393
S6
25
44053
55947
46928
53072
49652
50348
35
26
44102
55898
46975
53025
49696
50304
34
27
44151
55849
47021
52979
49740
50260
33
28
44201
55799
47068
52932
49784
50216
3.'
29
44250
55750
47114
52886
49828
50172
31
30
9.44299
10.55701
9.47160
10.52840
9.49872
10.50128
30
31
41348
55652
47207
52793
49916
50084
29
32
44397
55603
47253
52747
49960
50010
28
83
44446
55554
47299
52701
50004
49996
27
34
44495
55505
47346
52654
50048
49952
26
35
44544
55456
47392
52608
50092
49908
25
36
44592
55108
47438
52562
50136
49864
24
37
44641
55359
47484
52516
50180
49820
23
38
44690
55310
47E30
52470
50223
49777
22
39
44738
55262
47576
52424
50267
49733
21
40
9.44787
10.55213
9.47622
10.52378
9.50311
10.49689
20
41
44836
55164
47668
52332
50355
49645
19
42
44884
55116
47714
52286
50398
4960-3
18
43
44933
55067
47760
52240
50442
49558
17
44
44981
5.5019
47806
52194
50485
49515
16
45
45029
54971
4785:?
52148
50529
49471
15
46
45078
54922
47897
52103
50572
49428
14
47
45126
54874
47943
52057
50616
493 C 4
13
48
45174
5482(5
47989
52011
50659
49341
12
49
45222
54778
48035
51965
50703
49297
11
50
9.45271
10.54729
9.48080
10.51920
9.50746
10.49254
JO
51
45319
54681
48126
51874
50789
49211
9
52
45367
54633
48171
51829
50833
491G7
8
53
45415
54585
48217
51783
50876
49124
7
54
45463
54537
48262
51738
50919
49081
6
55
45511
54489
48307
51693
50962
49088
5
56
45559
54441
48353
51647
51005
48995
4
57
45606
54394
48398
51602
51048
48952
3
58
45654
54346
48443
51557
51092
48908
2
59
45702
54298
48489
51511
51135
48H65
60
45750
54250
48534
51466
51178
48822
/
Co tan
Tan
Cotan
Tan
Cotan
Tan
/
74
73
72
156
LOG. TANGENTS AND COTANGENTS
/
18
19
20
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.51178
10.48822
9.53697
10.46303
9.56107
10.43893
60
1
51221
48779
53738
46262
56146
43854
59
2
51264
48736
53779
46221
56185
438.5
58
3
51306
48694
53820
46180
56-J24
43776
57
4
51349
48651
53861
46139
56264
43730
56
5
51392
48608
53902
46098
56303
. 43697
55
6
51435
48565
53943
46057
56342
43658
54
7
51478
48522
53984
46016
56381
43619
53
8
51520
48480
54025
45975
56420
43580
52
9
51563
4S437
54065
45935
56459
43541
51
10
9.51606
10.48394
9.54106
10.45894
9.56498
10.43502
50
11
51648
48352
54147
4S&53
56537
43463
49
12
51691
48309
54187
45813
56576
43424
48
13
51734
48266
54228
45772
56815
43385
47
14
51770
48224
54269
45731
56654
*B46
46
15
51819
48181
54309
45691
56693
43307
45
16
51861
48139
54350
45650
56732
43268
44
17
51903
48097
54390
45610
56771
4:'2J9
43
18
51946
48054
54431
45569
56810
43190
42
19
51988
48012
54471
45529
56849
43151
41
20
9.52031
10.47969
9.54512
10.45488
9.56887
10.43118
40
21
52073
47927
54552
45448
56026
43074
39
22
52115
47885
54593
45407
5(5965
43035
38
23
52157
47843
54633
45367
57004
42996
37
24
52200
47800
54673
45327
57042
42958
30
25
52244
47758
54714
45286
57081
42919
35
26
52284
47716
54754
45246
57120
42880
34
27
52326
47674
54794
45206
57158
42842
33
28
52368
47632
54835
45165
57197
42803
82
29
52410
47590
54875
45125
57235
42765
31
30
9.52452
10.47548
9.54915
10.45085
9.57274
10.42726
30
31
52494
47506
54955
45045
57312
42688
29
32
52536
47464
54995
45005
57851
42649
28
33
52578
47422
55035
44965
57389
42611
27
34
52620
47380
55075
44925
57428
42572
26
;-;.-.
52661
47339
55115
44885
57466
42534
25
36
52703
47'.'97
55155
44845
57504"
42496
24
37
52745
47255
55195
44805
57543
42457
23
38
52787
47213
55235
44765
57581
42419
22
39
52829
47171
55275
44725
576)9
42381
21
40
9.52870
10.47130
9.55315
10.44685
9.57658
10.42342
20
41
52912
47088
65855
44645
57696
42304
19
42
52953
47047
55395
44605
57734
42266
18
43
52995
47005
55434
44566
57772
42-^28
17
44
53037
46963
55474
445-26
57810
42190
16
45
53078
4G922
55514
44486
57849
42151
15
46
53120
46880
55554
44446
57887
42113
14
47
53161
46839
55593
44407
57925
42075
13
48
53202
46798
55633
44367
579C3
42037
12
49
53244
46756
55673
44327
58001
41999
11
50
9.53285
10.46715
9.55712
10.44288
9.58039
10.41961
10
51
53327
46673
55752
44248
58077
41923
9
52
53368
46632
55791
44209
58115
41885
8
53
53409
46591
55831
44169
58153
41847
7
54
53450
46550
55870
44130
58191
41809
6
55
53492
46508
55910
44090
58229
41771
5
56
53533
46467
55949
44051
58267
41733
4
57
53574
46426
55989
44011
58304
41696
3
58
53615
46385
56028
43972
58342
41658
2
59
53656
46344
56067
43933
58380
41620
1
60
53697
46303
56107
43893
58418
41582
i
Cotan
Tan
Cotan
Tan
Cotan
Tan
/
71
70
69
LOG. TANGENTS AND COTANGENTS
157
21
22
23
/
Tan
Cotan
Tan
Cotau
Tan
Cotan
o
9.58418
10.41582
9.60641
10.39359
9.62785
10.37215
60
1
58455
41545
60677
39323
62820
37180
59
2
58493
41507
60714
39286
62855
37145
58
3
58531
41469
60750
39250
62890
37110
57
4
58569
41431
60786
39214
62926
37074
56
5
58606
41394
60823
39177
62961
37039
55
6
58644
41356
60859
39141
62996
37004
54
58681
41319
60895
39105
63031
36969
53
8
58719
41281
60931
39069
63066
36934
52
9
58757
41243
60967
39033
63101
36899
51
10
9.58794
10.41206
9.61004
10.38996
9.63135
10.36865
50
11
58832
41168
61040
38960
63170
36830
49
12
58869
41131
61076
38924
63205
36795
48
13
58907
41093
61112
38888
63240
36760
47
14
58944
41056
61148
38852
63275
36725
46
15
58981
41019
61184
38816
63310
3U690
45
16
59019
40981
61220
38780
68:345
36655
44
17
59056
40J4J
61256
38744
63379
36621
43
18
59094
40906
61292
38708
63414
36586
42
19
59131
40869
61328
38672
63449
36551
41
20
9.59168
10.40882
9.61364
10.38636
9.63484
10.36516
40
21
59205
40795
61400
38600
63519
36481
39
22
59243
40757
61430
8856*
63553
36447
38
*3
59280
40720
61472
38528
63588
36412
37
24
59317
40683
61508
3^492
63623
36377
36
25
59854
40646
61544
38456
63657
36343
35
26
59391
40609
61579
38421
03692
36308
34
27
59429
40571
61615
38385
03726
36274
33
28
59466
4(1534
61651
38349
63761
36219
32
29
59503
40497
61687
38313
63796
36204
31
30
9.59540
10.40460
9.61722
10.38278
9.63830
10.36170
30
31
59577
40423
C.1758
3S242
63865
36135
29
32
59614
40386
61794
38206
63899
36101
28
33
59651
40349
61830
38170
63934
86066
27
34
59688
40312
61865
38135
63968
36032
26
35
59725
40275
61901
38099
64003
35997
25
36
59762
40238
61936
38064
64037
35963
24
37
59799
40201
61972
:-!8028
64072
35928
23
38
59835
40165
62008
37992
64106
35894
22
39
59872
40128
62043
37-957
64140
35860
21
40
9.59909
10.40091
9.62079
10.37921
9.64175
10.35825
20
41
59946
40054
62114
37886
64209
35791
19
42
59983
40017
62150
37850
64243
35757
18
43
60019
39981
62185
37815
64278
35722
17
44
60056
39944
62221
37779
6*312
35688
16
45
60093
39907
62256
37744
64346
35654
15
46
(50130
39870
62292
37708
64381
35619
14
47
60166
39834
62327
37673
64415
35585
13
48
60203
39797
62362
37638
64449
35551
12
49
60240
39760
62398
37602
64483
35517
11
50
9.60276
10.39724
9.62433
10.37567
9.64517
10.35483
10
51
60313
39687
62468
37532
64552
35448
9
52
60349
39651
62504
37496
64586
35414
8
53
60386
39614
62539
37461
64620
35380
7
54
60422
39578
62574
37426
64654
35346
6
55
60459
39541
62609
37391
64688
35312
5
56
60495
39505
62645
37355
64722
35278
4
57
60532
39468
62680
37320
64756
35244
8
58
60568
39432
62715
37285
64790
35210
2
59
60605
39395
62750
37250
64824
35176
1
60
60641
39359
62785
87215
64858
85142
/
Cotan
Tan
Cotan
Tan
Cotan
Tan
/
68*
67
66
158
LOG. TANGENTS AND COTANGENTS
/
84
25
26
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.64858
10.35142
9.66867
10.33133
9.68818
10.31182
60
1
64892
35108
66900
33100
68850
31150
59
2
64926
35074
60933
33067
68882
31118
58
3
649GO
35040
66966
33034
68914
31086
57
4
64994
35006
66999
33001
68946
31054
56
5
65028
34972
67032
32968
68978
31022
55
6
65062
34938
67065
32935
69010
80990
54
7
65096
34904
67098
32902
69042
30958
53
8
65130
34870
67131
32869
69074
30926
52
9
65164
34836
67163
32837
69106
30894
51
10
9.65197
10.34803
9.67196
10.32804
9.69138
10.30862
50
11
65231
34769
67229
32771
69170
30830 49
12
65265
34735
67262
32738
69202
80798
48
13
65299
34701
67295
32705
69234
30766
47
14
65333
34667
67327
32673
69266
30734
46
15
65366
34634
67360
32640
69298
30702
45
16
65400
34600
67393
32607
69329
30671
44
17
65434
34566
67426
32574
69361
30639
43
18
654G7
34533
67458
32542
69393
30607
42
19
65501
34499
67491
325C9
69425
30575
41
20
9.65535
10.34465
9.67524
10.32476
9.69457
10.30543
40
21
65568
34432
67556
32444
69488
30512
39
22
65602
34398
67589
30411
69520
30480
38
23
65636
34364
67622
32378
69552
30448
37
24
656C9
34331
67654
32346
69584
30416
36
25
65703
34297
67687
32313
69615
30385
35
26
65736
34264
67719
32281
69647
30353
34
27
65770
34230
67752
32248
69679
80321
33
28
65S03
34197
67785
32215
69710
30290
32
29
65837
34163
67817
32183
69742
30258
31
30
9.65870
10.34130
9.67850
10.32150
9.69774
10.30226
30
31
65904
34096
67882
32118
t>9805
30195
29
32
65937
34063
67915
32085
69837
30163
28
33
65971
34029
67947
32053
69868
30132
27 '
34
66004
33996
67980
32020
C9900
30100
26
35
66038
33962
68012
31988
69932
30068
25
6
66071
83929
68044
31956
69963
30037
24
37
66104
a3896
68077
31923
69995
30005
23
38
66138
33862
68109
31891
70026
29974
22
39
66171
33829
68142
31858
70058
29942
21
40
9.66204
10.33796
9.68174
10.31826
9.70089
10.29911
20
41
66238
33762
68206
31794
70121
29879
19
42
66271
33729
68239
31761
70152
29848
18
43
66304
33696
68271
31729
70184
29816
17
44
66337
33663
68303
31697
70215
29785
16
45
66371
33629
68336
31664
70247
29753
15
46
66404
33596
68368
31632
70278
29722
14
47
66437
33563
68400
31600
70309
29691
13
48
66470
33530
68432
31568
70341
29659
if
49
66503
33497
68465
31535
70372
29628
11
50
9.66537
10.33463
9.68497
10.31503
9.70404
10.29596
10
51
66570
33430
68529
31471
70435
29565
9
52
66603
33397
68561
31439
70466
29534
8
53
66636
33364
68593
31407
70498
29502
7
54
66669
33331
68626
31374
70529
29471
6
55
66702
33298
68658
31342
70560
29440
5
56
66735
33265
68690
31310
70592
29408
4
57
66768
33232
68722
31278
70623
29377
3
58
66801
33199
68754
31246
70654
29346
2
59
66834
33168
68786
31214
70685
29315
1
60
66867
33133
68818
31182
70717
29283
/
Cotau
Tan
Cotan
Tan
Cotan
Tan
/
66
64
68
LOG. TANGENTS AND COTANGENTS
159
27
28
29
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
o
9.70717
10.29283
9.72567
10.27433
9.74375
10.25625
60
1
70748
29252
72598
27402
74405
25595
59
2
70779
29221
72628
27372
74435
25565
58
3
70810
29190
72659
27341
74465
25535
57
4
70841
29159
72689
27311
74494
25506
56
5
70873
29127
72720
27280
74524
25476
55
6
70904
29096
72750
27250
74554
25446
54
7
70935
29065
72780
27220
74583
25417
53
8
70906
29034
72811
27189
7461 3
25387
52
9
70997
29003
72841
27159
74643
25357
51
10
9.71028
10.28972
9.72872
10.27128
9.74673
10.25327
50
11
71059
28941
72902
27098
74702
25298
49
12
71090
28910
72932
27'068
74732
25268 48
13
71121
28879
72963
27037
74762
25238 47
! 14
71153
28847
72993
27007
74791
25209
46
I 15
71184
28816
73023
26977
7'4821
25179
45
i 16
71215
28785
73054
26946
74851
25149 44
1 17
71246
28754
73084
26916
74880
25120
43
18
71277
28723
78114
26886
74910
25090
42
19
71308
28692
73144
26856
74939
25061
41
20
9.71339
10.28661
9.73175
10.26825
9.74969
10.25031
40
21
71370
28630
73205
26795
74998
25002
39
22
71401
28599
73235
26765
75028
24972
38
-,3
71431
28569
73265
26735
75058
24942
37
24
71462
28538
73295
26705
75087
24913
36
25
71493
28507
73326
26674
75117
24883
35
26
71524
28476
7:3356
26644
75146
24854
34
27
71555
28445
73386
26614
75176
24824
33
28
71536
28.414
73416
26584
75205
24795
32
29
71617
28383
73446
26554
75235
24765
31
30
9.71648
10.28352
9.73476
10.26524
9.75264
10.24736
30
.'31
71679
28321
73507
26493
75294
24706
29
32
71709
28291
73537
26463
75323
24677
28
33
71740
28260
73567
26433
75353
24647
27
31
71771
28229
73597
26403
75382
24618
26
35
71802
28198
73627
26373
75411
21589
25
36
71833
28167
73657
26343
75441
24559
24
37
71863
28137
73687
26313
75470
24530
23
38
71894
28103
73717
26283
75500
24500
22
39
71925
28075
73747
26253
75529
24471
21
40
9.71955
10.28045
9.73777
10.26223
9.75558
10.24442
20
41
71986
28014
73807
26193
75588
24412
19
42
72017
27983
73837
26163
75617
24383
18
43
72048
279.V2
73867
26133
75647
24353
17
44
72078
27922
73897
26103
75676
24324
16
45
72109
27891
73927
26073
75705
24295
15
46
72140
27860
73957
26043
75735
242C5
14
47
72170
27830
73987
26013
75764
24236
13
48
72201
27799
74017
25983
75793
24207
12
49
72231
27769
74047
25953
75822
24178
11
i 50
9.72262
10.27738
9.74077
10.25923
9.75852
10.24148
10
51
72293
27707
74107
25893
75881
24119
9
52
72323
27677
74137
25863
75910
24090
8
53
72354
27646
74166
25834
75939
24061
7
54
72384
27616
74196
25804
75969
24031
6
55
72415
27585
74226
25774
75998
24002
5
56
72445
27555
74256
25744
76027
23973
4
57
72476
27524
74286
25714
76056
23944
3
58
72506
27494
74316
25684
76086
28914
2
59
72537
27463
74345
25655
76115
23885
1
60
72567
27433
74375
25625
76144
23856
/
Cotan
Tan
Cotan Tan
Cotan
Tan
,
62*
61
60
100
LOG. TANGENTS AND COTANGENTS
30
31
32
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.76144
10.23856
9.77877
10.22123
9.79579
10.20421
60
76173
23827
77906
22094
79607
20393
59
2
76202
23798
77935
220G5
79G35
20365
58
3
76231
23769
77963
22037
79663
20337
57
4
76261
23739
77992
22008
79691
20309
56
5
76290
23710
78020
21980
79719
20281
55
6
76319
23681
78049
21951
79747
20253
54
7
76348
23652
78077
21923
79776
20224
53
8
76377
23623
78106
21894
79804
20196
52
9
76406
23594
78135
21865
79882
20168
51
10
9.76435
10.23565
9.78163
10.21837
9.79860
10.20140
50
11
76464
23536
78192
21808
79888
20112
49
12
76493
23507
78220
21780
79916
20084
48
13
76522
23478
78249
21751
79944
20056
47
14
76551
23449
78277
21723
79972
20028
46
15
76580
23420
78306
21694
80000
20000
45
16
76609
23391
78334
21666
80028
19972
44
17
76639
23361
78363
21637
80056
19944
43
18
76668
23332
78391
21609
80084
19916
42
19
76697
23303
78419
21581
80112
19888
41
20
9.76725
10.23275
9.78448
10.21552
9.80140
10.19860
40
21
76754
23246
78476
21524
80168
19832
39
22
7678S
23217
78505
21495
80195
19805
38
23
76812
23188
78533
21467
80223
19777
37
24
76841
23159
78562
21438
80251
19749
36
25
76870
23180
78590
21410
80279
19721
35
26
76899
23101
78618
21382
80307
19693
34
27
76928
23072
78647
21353
80335
19665
33
28
76957
23043
78675
21325
8G363
19637
32
29
76986
23014
78704
21296
80391
19609
31
30
9.77015
10.22985
9.78732
10.21268
9.80419
10.19581
30
31
77044
22956
78760
21240
80447
19553
29
32
77073
22927
78789
21211
80474
19526
28
33
77101
22899
78817
21183
80502
19498
27
34
77130
22870
78845
21155
80530
19470
26
35
77159
22841
78874
21126
80558
19442
25
36
77188
22812
78902
21098
80586
19414
24
37
77217
22783
78930
21070
80614
19386
23
38
77246
22754
78959
21041
80642
19358
22
39
77274
22726
78987
21013
80669
19331
21
40
9.77303
10.22697
9.79015
10.20985
9.80697
10.19303
20
41
77332
22668
79043
20957
80725
19275
19
42
77361
22639
79072
20928
80753
19247
18
43
77390
22610
79100
20900
80781
19219
17
44
77418
22582
79128
20872
80808
19192
16
45
77447
22553
79156
20844
80836
19164
15
46
77476
22524
79185
20815
80864
19136
14
47
77505
22495
79213
20787
80892
19108
13
48
77533
22467
79241
20759
80919
19081
12
49
77562
22438
79269
20731
80947
19053
11
50
9.77591
10.22409
9.79297
10.20703
9.80975
10.19025
10
51
77619
22381
79326
20674
81003
18997
9
52
77648
22352
79354
20646
81030
18970
8
53
77677
22323
79382
20618
81058
18942
7
54
77706
22294
79410
20590
81086
18914
6
55
77734
22266
79438
20562
81113
18887
5
56
77763
22237
79466
20534
81141
18859
4
57
77791
22209
79495
20505
81169
18831
3
58
77820
22180
79523
20477
81196
18804
2
59
77849
22151
79551
20449
81224
18776
1
60
77877
22123
79579
20421
81252
18748
/
Cotan
Tan
Cotan
Tan
Cotan
Tan
,
69
68
67
LOG. TANGENTS AND COTANGENTS
161
88
84
36
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
o
9.81252
10.18748
9.82899
10.17101
9.84523
10.15477
60
1
81-279
18721
82926
17074
84550
15450
59
2
81307
18693
82953
17047
84576
15424
58
3
81335
18665
82980
17020
84603
15397
57
4
81362
18638
83008
16992
84630
15370
56
5
81390
18610
83035
16965
84657
15343
55
g
81418
18582
83062
16938
84684
15316
54
7
81445
18555
83089
16911
84711
15289
53
81473
18527
83117
16883
84738
15262
52
9
81500
18500
83144
16856
84764
15236
51
10
9.81528
10.18472
9.83171
10.16829
9.84791
10.15209
50
81556
18444
83.198
16802
84818
15182
49
12
81583
18417
83225
16775
84845
15155
48
12
81611
18389
83252
16748
84872
15128
47
14
81638
18362
83280
16720
84899
15101
46
15
81666
18334
83307
16693
84925
15075
45
16
81693
18307
83334
16666
84952
15048
44
17
81721
18279
83361
16639
84979
15021
43
18
81748
18252
83388
16612
85006
14994
42
19
81776
18224
83415
16585
85033
14967
41
20
9.81803
10.18197
9.88442
10.16558
9.85059
10.14941
40
21
81831
18169
83470
16530
85086
14914
39
22
81858
18142
83497
165015
85113
14887
38
23
81886
18114
83524
16476
85140
14860
37
\ 24
81913
18087
83551
16449
85166
14834
36
25
81941
18059
83578
16422
85193
14807
35
26
81968
18032
83605
16395
85220
14780
34
27
81996
18004
83632
16368
85247
14753
33
28
82023
17977
83659
16341
85273
14727
82
29
82051
17949
83686
16314
85300
14700
31
30
9.82078
10.17922
9.83713
10.16287
9.85327
10.14673
80
31
82106
17894
83740
16260
85354
14646
29
32
82133
1787
83768
16232
85380
14620
28
83
82161
17839
83795
16205
85407
14593
27
34
82188
17812
83822
16178
85434
14566
26
35
82215
17785
83849
16151
85460
14540
25
36
82243
17757
83876
16124
85487
14513
24
37
82270
17730
83903
16097
85514
14486
23
38
82298
17702
83930
16070
85540
14460
22
39
82325
17675
83957
16043
85567
14433
21
40
9.82352
10.17648
9.83984
10.16016
9.85594
10.14406
20
41
82880
17620
84011
15989
85620
14380
19
42
82407
17593
84038
15962
85647
14353
18
43
82435
17565
84065
15935
85674
14326
17
44
82462
17538
84092
15908
85700
14300
16
45
82489
17511
84119
15881
85727
14273
15
46
82517
17483
84146
15854
85754
14246
14
47
82544
17456
84173
15827
85780
14220
18
48
82571
17429
84200
15800
85807
14193
12
49
82599
17401
84227
15773
85834
14166
11
50
9.82626
10.17374
9.84254
10.15746
9.85860
10.14140
10
51
82653
17347
84280
15720
85887
14113
9
52
82681
17319
84307
15693
85913
14087
8
53
82708
17292
84334
15666
85940
14060
7
54
55
82735
82762
17265
17238
84361
84388
15639
15612
85967
85993
14033
14007
6
5
56
82790
17210
84415
15585
86020
13980
4
57
82817
17183
84442
15558
86046
13954
3
58
82844
17156
84469
15531
86073
13927
2
59
82871
17129
84496
15504
86100
13900
1
60
82899
17101
84523
15477
86126
13874
~ f
Cotan
Tan
Cotan
Tan
Cotan
Tan
/
56
66
64
162
LOG. TANGENTS AND COTANGENTS
/
86
87
88
/
Tan
Cotan
Tan
Cotan
Tan
Cotau
9.86126
10.13874
9.87711
10.12289
9.89281
10.10-719
60
1
86153
13847
87738
12262
89307
10693
59
2
86179
13821
87764
12236
89333
10667
58
3
86206
13794
87790
12210
89359
10641
57
4
86232
13768
87817
12183
89385
10615
56
5
86259
13741
87843
12157
89411
10589
55
6
86285
13715
87869
12131
89437
10563
54
7
86312
13668
87895
12105
89463
10537
53
8
86338
13662
87922
12078
89489
10511
52
9
863C5
13635
87948
12052
89515
10485
51
10
9.86392
10.13608
9.87974
10.12026
9.89541
10.10459
50
11
86418
13582
88000
12000
89567
10433 49
12
86445
13555
88027
11973
89593
10407 48
13
86471
13529
88053
11947
89619
10381 47
14
86498
13502
88079
11921
89645
10355
46
15
86524
13476
88105
11895
89671
10329
45
16
86551
13449
88131
11869
89697
10303
44
17
86577
13423
88158
11842
89723
10277
43
18
86603
13397
88184
11816
89749
10251
42
19
86630
13370
88210
11790
89775
10225
41
20
9.86656
10.13344
9.88236
10.11764
9.89801
10.10199
40
21
86683
13317
88262
11738
89827
10173
39
22
86709
13291
88289
11711
89853
10147
38
23
86736
13264
88315
11685
89879
10121
37
24
86762
13238
88341
11659
89905
10095
36
25
. 86789
13211
88367
11633
89931
10069
35
26
86815
13185
88893
11607
89957
10043
34
27
86842
13158
88420
11580
89983
10017
33
28
86868
13132
88446
11554
90009
09991
32
29
86894
13106
88472
11528
90035
09965
31
30
9.86921
10.13079
9.88498
10.11502
9.90061
10.09939
30
31
86947
13053
88524
11476
90086
09914
29
32
86974
13026
88550
11450
90112
09888
28
33
87000
13000
88577
11423
90138
09862
27
34
87027
12973
88603
11397
90164
09836
26
35
87053
12947
88629
11371
90190
09810
25
36
87079
12921
8H655
11345
90216
09784
24
37
87106
12894
88681
11319
90242
09758
23
38
87132
12868
88707
11293
902(58
09732
22
39
87158
12842
88733
11267
90294
09706
21
40
9.87185
10.12815
9.88759
10.11241
9.90320
10.09080
20
41
87211
12789
88786
11214
90346
09654
19
42
87238
12762
88812
11188
90371
09629
18
43
87264
12736
88838
11162
90397
09603
17
44
87290
12710
88884
11136
90423
09577
16
45
87317
12683
88890
11110
90449
09551
15
46
87343
12657
88916
11084
90475
09525
14
47
87369
12631
88942
11058
90501
09499
13
48
87396
12604
88968
11032
90527
09473
12
49
87422
12578
88994
11006
90553
09447
11
50
9.87448
10.12552
9.89020
10.10980
9.90578
10.09422
10
51
87475
13525
89046
10954
90604
OOH96
9
52
87501
12499
89073
10927
90630
09370
8
53
87527
12473
89099
10901
90656
09344
7
54
87554
12446
89125
10875
90682
09818
6
55
87580
12420
89151
10849
90708
09292
5
56
87606
12394
89177
10823
90734
09266
4
57
87633
12367
89203
10797
90759
09241
8
58
87659
12341
89229
10771
90785
09215
2
59
87685
12315
89255
10745
90811
09189
1
60
87711
12289
89281
10719
90837
09163
i
Cotan
Tan
Cotan
Tan
Cotan
Tan
/
63
52
61
LOG. TANGENTS AND COTANGENTS
163
89
40
41
/
Tan
Cotan
Tan
Cotau
Tan
Cotan
o
9.90837
10.09163
9.92381
10.07619
9.93916
10.06084
60
1
90863
09137
92407
07593
93942
06058
59
2
90889
09111
92433
07567
93967
06033
58
3
90914
09086
92458
07542
93993
06007
57
4
90940
09060
92484
07516
91018
05982
56
5
90966
09034
92510
07490
94044
05956
55
6
90992
09008
92535
07465
94069
05931
54
7
91018
08982
92561
07439
94095
05905
53
8
91043
08957
92587
07413
94120
05880
52
9
910J9
08931
92612
07388
94146
05854
51
10
9 91095
10.08905
9.92638
10.07362
9.91171
10. 05829
50
11
91121
08879
92663
07337
94197
05803
49
12
91147
08853
92689
07311
94222
05778
48
13
91172
08828
92715
07285
91248
05752
47
14
91198
08802
92740
07260
94273
05727
46
15
9J224
08776
92766
07234
94299
05701
45
16
91250
08750
92792
07208
94324
05676
44
17
91276
08724
92817
07183
94350
05650
43
18
91301
08699
92843
07157
94375
05625
42
19
91327
08673
92868
07132
94401
05599
41
20
9.91858
10.08647
9.92894
10.07106
9.94426
10.05574
40
21
91379
08621
92920
07080
94452
05548
39
22
91404
08596
92945
07055
94477
05523
38
23
91430
08570 '
92971
07029
94503
05497
37
24
91456
08544
92996
07004
94528
05472
36
25
9148.!
08518
93022
06978
94554
05446,
35
26
91507
08493
93048
06952
94579
05421
34
27
91533
08467
93073
06927
94604
05396
33
28
91559
08441
93091)
06901
94630
05370
32
29
91583
08415
93124
06876
94655
05345
31
30
9.91610
10.08390
9.93150
10.06850
9.94681
10.05319
30
31
91630
08364
93175
06825
94706
05294
29
32
91662
08338
93201
06799
94732
05268
28
33
9168S
08312
93227
06773
94757
05243
27
34
91713
08287
93252
06748
94783
05217
26
35
91739
08261
93278
06722
94808
05192
25
36
91765
08235
93303
06697
94834
05166
24
37
91791
08209
03329
06671
94859
05141
23
38
91816
08184
93354
06646
94884
05116
22
39
91842
08158
93380
06620
'J4910
05090
21
40
9.91868
10.08132
9.93406
10.06594
9.94935
10.05065
20
41
91893
08107
93431
06569
94961
05039
19
42
91919
08061
93457
06543
94986
05014
18
43
91945
08055
93482
06518
95012
04988
17
44
91971
OS029
93508
06492
95037
04963
16
45
91996
08004
93533
06467
'J5002
04938
15
46
92022
07978
93559
06441
95088
04912
14
47
92048
07952
93584
06416
95113
04887
13
48
92073
07927
93610
06390
95139
04861
12
49
92099
07901
93636
06364
95164
04836
11
50
9.92125
10.07875
9.93661
10.06339
9.95190
10.04810
10
51
92150
07850
93687
06313
95215
04785
9
52
92176
07824
93712
06288
95240'
04760
8
.',3
92202
07798
93738
06262
95266
04734
7
5"i
92227
07773
93763
06237
95291
04709
6
55
92253
07747
93789
06211
95317
04683
5
r.6
92279
07721
93814
06186
95342
04658
4
57
92304
07696
93840
06160
95368
04632
3
58
92330
07670
93865
06135
95393
04607
2
59
92356
07644
93891
06109
95418
04582
1
00
92381
07619
93916
06084
95444
04556
/
Cotan
Tan
Cotau
Tan
Cotan
Tan
,
50
49
48
164
LOG. TANGENTS AND COTANGENTS
/
42
43
44
/
Tan
Cotan
Tan
Cotan
Tan
Cotan
9.95444
10.04556
9.96966
10.03034
9.98484
10.01516
60
1
95469
04531
96991
03009
98509
01491
59
2
95495
04505
97016
02984
98534
01466
58
3
95520
04480
97042
02958
98560
01440
57
4
95545
04455
97067
02933
98585
01415
56
5
95571
04429
97092
02908
98610
01390
55
6
95596
04404
97118
02882
98635
01365
54
7
95622
04378
97143
02857
98661
01339
53
8
95647
04353
97168
02832
98686
01314
52
9
95672
04328
97193
02807
98711
01289
51
10
9.95698
10.04302
9.97219
10.02781
9.98737
10.01263
50
11
95723
04277
97244
02756
98762
01238
49
18
95748
04252
97269
02731
98787
01213
48
13
95774
04226
97295
02705
98812
01188
47
14
95799
04201
97320
02680
98838
01162
46
15
95825
04175
97345
02655
98863
01187
45
16
95850
04150
97371
02629
98888
01112
44
17
95875
04125
97396
02604
98913
01087
43
18
95901
04099
97421
02579
98939
01061
42
19
959*6
04074
97447
02553
98964
01086
41
20
9.95952
10.04048
9.97472
10.02528
9.98989
10.01011
40
21
95977
04023
97497
02503
99015
00985
39
22
96002
03998
97523
02477
99040
00960
38
23
96028
03972
97548
02452
'99065
00935
37
24
96053
03947
97573
02427
99090
00910
86
25
96078
0392-2
97598
02402
99116
00884
35
26
96104
03896
97624
02376
99141
00859
34
27
96129
03871
97649
02351
99166
00834
33
28
96155
03845
97674
02326
99191
00809
82
29
96180
03820
97700
02300
99217
00783
31
30
9.96205
10.03795
9.97725
10.02^75
9.99242
10.00758
30
31
96231
03769
97750
02250
99267
00733
29
32
96256
03744
97776
02224
99293
00707
28
33
96281
08719
97801
02199
99318
00682
27
34
96307
03693
97826
02174
99343
00657
26
35
96332
03668
97851
02149
' 99368
00632
25
36
96357
03643
97877
02123
99394
00606
24
37
96383
03617
97902
02098
99419
OC581
23
38
96408
03592
97927
02073
99444
00556
22
39
96433
03567
97953
02047
99469
00531
21
40
9.96459
10.03541
9.97978
10.02022
9.99495
10.00505
20
41
96484
03516
98003
01997
99520
00480
19
42
96510
03490
98029
01971
99545
00455
18
43
96535
03465
98054
01946
99570
00430
17
44
96560
03440
98079
01921
99596
00404
16
45
96586
03414
98104
01896
99621
00379
15
46
96611
03389
98130
01870
99646
00354
14
47
96636
03364
98155
01H45
99672
00328
13
48
96662
03338
98180
01820
99697
00303
12
49
96687
03313
98206
01794
99722
00278
11
50
9.96712
10.03288
9.98231
10.01769
9.99747
10.00253
10
51
96738
03262
98256
01744
99773
00227
9
96763
03237
98281
S 01719
99798
00202
8
58
96788
03212
98307
01693
99823
00177
B
64
96814
03186
98332
01668
99848
00152
6
65
96839
03161
98357
01643
99874
00126
5
56
96864
03136
98383
01617
99899
00101
4
57
96890
03110
98408
01592
99924
00076
3
58
96915
03085
98433
01567
99949
00051
2
59
96940
03060
98458
01542
99975
00025
1
60
96966
08034
98484
01516
10.00000
00000
f
Cotan
Tan
Cotan
Tan
Cotan
Tan
,
47
48*
46
LOG. VERSED SINES AND EXTERNAL SECANTS 165
o 1
'
Log. Vers.
D
.og. Exsec.
D
Log. Vers.
I>
Log, Exsec.
D
f
1
2
3
4
oo
2-62642
3-22848
3-58066
3-83054
60206
35218
24987
CO
2.62642
3-22848
3-58066
3-83054
60206
35218
24987
6-18271
-19707
.21119
22509
23877
1435
1412
1389
1368
6.18278
-19714
-21126
. -22516
23884
1436
1412
1390
1368
O
1
2
3
4
5
6
7
8
9
4-02436
-18272
31662
-43280
-53490
19382
15836
13389
11598
10230
4-02436"
-18272
31662
.43260
53491
19382
15836
13389
11598
10230
6-25223
-26549
.27856
29142
-30410
1346
1326
1306
1286
1268
6-25231
26557
-27864
29151
30419
1347
1326
1306
1287
1268
5
6
7
8
9
10
11
12
13
14
4-62642
-70920
78478
.85431
.91868
9151
8278
7558
6953
6437
4-62642
70921
.78478
85431
.91868
9151
8279
7557
6952
6437
6-31660
-32892
34107
35305
-36487
1250
1232
1214
1198
1182
6-31669
-32901
-34116
-35315
-36497
1250
1232
1215
1198
1182
1O
11
12
13
14
15
16
17
18
19
4-97880
5-03466
-08732
-13696
-18393
5992
5605
5266
4964
4696
4-97861
5-03466
.08732
.13697
.18393
5993
5605
5266
4964
4696
6-37653
.38803
.39938
.41059
-42165
1166
1150
1135
1121
1106
6-37663
-38814
-39949
41070
-42177
1166
1151
1135
1121
1106
15
16
17
18
19
20
21
22
23
24
5-22348
.27086
.31126
34987
-38684
4455
4238
4040
3861
3697
5-22849
.27087
-31127
.34988
.38685
4456
4238
4040
3861
3697
6-43258
-44337
.45403
46455
.47496
1093
1078
1066
1052
1040
6-43270
44349
45415
46468
47509
1093
1079
1066
1053
1040
30
21
22
23
24
25
26
27
28
29
5-42230
-45636
48915
.52073
.55121
3545
3406
3278
3158
3048
5-42231
.45638
.48916
.52075
.55123
3545
3407
3278
3159
3048
6-48524
.49539
.50544
.51536
.52518
1028
1016
1004
992
981
6-48537
-49553
50557
.51550
-52532
1028
1015
1004
993
982
25
26
27
28
29
.30
31
32
33
34
5-58068
60914
-63372
-66344
-68937
2941
2848
2757
2672
2593
5-58068
.60916
.63674
.66346
68940
2945
2848
2758
2672
2593
6-53488
. 54448
.55397
.56336
.57265
970
960
949
939
929
6-53503
. 54463
55413
.56352
57281
970
960
950
939
929
30
31
32
33
34
35
36
37
38
39
5-71455
.73902
76282
.78598
.80854
2518
2447
2379
2316
2256
5-71457
.73904
.76284
.78601
-80857
2517
2447
2380
2316
2256
6-58184
.59093
.59993
.60884
.61766
919
909
900
891
882
6-58201
.59110
.60011
.60902
.61784
919
909
900
891
882
35
36
37
38
39
40
41
42
43
44
5-83053
85198
.87291
.89335
.91332
2199
2145
2093
2044
1996
5-83056
85201
.87295
.89338
.91335
2199
2145
2093
2043
1997
6-62639
.63503
.64359
65206
.66045
872
864
855
847
839
6-62657
.63522
64378
.65226
-66065
873
864
856
848
839
40
41
42
43
44
45
46
47
48
49
5-93284
95193
.97061
5-98890
6-00680
1909
1868
1829
1790
5-93288
95197
97065
5-98894
6-00685
1952
1909
1868
1829
1791
6-66876
67700
.68515.
.69323
70124
831
823
815
808
800
6-66897
67720
.68536
.69345
-70145
831
823
816
808
800
45
46
47
48
49
50
51
52
53
54
6-02435
-04155
.05842
07496
-09120
1720
1686
1654
1623
6-02440
04160
05847
07501
.09125
1755
1720
1687
1654
1623
6-70917
71703
72482
73254
74019
793
786
779
772
765
8-70939
-71725
-72505
73277
74043
794
786
779
772
765
SO
51
52
53
54
55
56
57
58
59
6-10714
12279
.13816
15327
.16811
1565
1537
1511
1484
6-10719
12284
13822
15333
16818
1594
1565
1537
1511
1485
6- 74777
-75529
76275
77014
-77747
758
752
745
739
733
6-74802
75554
76300
77040
77773
759
752
746
739
733
55
56
57
58
5fl
60
6-18271
6.18278
1460
6 - 78474
726
6-78500
727
fifi
D
Log. Exsec
JO
Log. Vers.
JO
Log. Exsec.
D
166 LOG. VERSED SINES AND EXTERNAL SECANTS
2 3
/
Log, Vers,
r>
,og. Exsec,
J>
Log, Vers,
J>
.og, Exsec.
1>
'
o
1
2
3
4
6-78474
.79195
79909
.80618
.81322
721
714
709
703
6-78500
79221
.79937
80646
.81350
721
715
709
703
7-13687
.14168
14646
.15122
.15595
481
478
475
473
7-13746
14228
.14707
.15183
.15657
481
479
476
474
1
2
3
4
5
6
7
8
9
6-82019
82711
.83398
84079
84755
697
692
686
681
676
6-82048
.82740
.83427
84109
.84785
698
692
687
682
676
7-16066
16534
.17000
.17463
17923
475
468
466
463
460
7-16129
.16598
17064
17528
-17989
471
469
466
464
461
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
6-85425
-86091
86751
-87407
.88057
6-88703
.89344
.89980
.90612
-91239
670
665
655
650
646
641
636
631
627
6-85457
.86123
.86783
87439
.88090
6-88737
89378
90015
90647
-91275
67l
666
660
656
651
646
641
636
632
628
7-18382
.18837
.19291
.19742
.20191
7-20637
.21081
.21523
.21963
-22400
458
455
453
451
448
446
444
442
440
437
7-18448
.18905
19359
.19811
-20260
7-20707
-21152
-21595
-22035
-22473
459
456
454
452
449
447
445
442
440
438
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
6-91862
.92480
-93093
93703
.94308
622
618
613
609
605
6-91898
92516
93131
.93741
-94346
623
618
614
610
605
7-22836
.23269
.23700
.24129
-24555
435
433
431
429
426
7-22909
-23343
-23775
-24204
-24632
436
434
431
429
427
20
21
22
23
24
25
26
27
28
29
6-94909
9550G
.96099
.96688
-9727?
601
597
592
589
584
6-94948
95545
.96139
.96728
-97313
601
597
593
589
585
7-24980
.25402
.25823
26241
26658
424
422
420
418
416
7-25057
-25485
-25902
26321
-26738
425
423
421
419
417
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
6-97853
.98430
.99004
6-99573
7-00139
7-00701
.01259
.01814
-02366
.cmi4
581
577
573
569
535
562
558
555
551
548
6-97895
.98472
.99046
6-99616
7-00182
7 - 00745
01304
-01860
-02412
.02960
581
577
574
570
566
563
559
555
552
548
7-27072
27485
.27895
28304
-28711
7-29116
.29518
.29919
30319
-30716
414
412
410
409
406
405
402
40 i
399
397
7-27153
.27567
.27978
.28387
-28795
7-29205
-29604
-30006
30406
3P804
415
413
411
409
407
405
404
402
400
398
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
7-03458
.03999
-04537
-05071
-05R03
542
541
537
534
531
7-03505
.04047
.04585
.05125
-05652
545
541
538
535
531
7-31112
.31505
.31897
.32288
-3267G
395
393
392
390
388
386
7-31201
31595
.31988
32379
-32768
dUb
394
393
391
389
388
4O
41
42
43
44
45
46
47
48
49
7-06135
06655
.07177
.07695
.08211
527
52R
521
518
515
7-06185
.06706
.07228
.07747
.08263
528
525
522
519
516
7-33063
-33448
-33831
-34213
-34593
385
383
382
380
7-33156
-33542
-33926
-34309
34689
385
384
382
385
Q7Q
46
46
47
48
49
50
51
52
53
54
7-08723
.09232
.09739
.10242
10743
512
509
50R
503
500
7-08776
.09236
.09793
.10297
-107HR
513
509
507
503
501
7-34971
-35348
-35723
-36097
-36468
378
377
375
373
371
7-35069
-35446
-35822
-36196
-36569
377
376
374
373
07-1
50
51
52
53
54
55
56
57
58
59
7-11240
.11735
.12227
-12716
.13203
497
495
492
489
486
7-11297
.11792
.12285
.12775
-13262
498
495
493
490
487
7-36839
.37207
.37574
37945
-38304
370
368
367
366
364
ncn
7-36945
-37310
-37678
-38044
-38409
369
368
366
365
363
55
56
57
58
59
60
7-13687
484
7 13746
484
7.38667
362
7-38773
tJO
Log, Vers",
D
Log. Exsec.
1) '
Log. Vers,
D
Log. Exsec
D
LOG. VERSED SINES AND EXTERNAL SECANTS 167
4 5
'
Lg.Vers
D
Log.'Exs.
D
Lg.Vers.
D
Log.Exs
D
'
P.P.
o
1
2
1 3
T
6
7
9
7-38667
-39028
-39387
39745
40102
361
359
358
356
355
353
352
350
349
348
346
345
343
342
341
339
338
337
335
333
332
330
329
328
327
325
324
323
322
321
III
317
316
315
314
313
311
7-38773
-39134
-39495
-39854
-40211
7-40567
-40922
-41275
-41627
-41977
361
360
359
357
356
354
353
352
350
349
347
346
345
343
342
340
339
338
337
335
ili
it*
329
328
327
325
324
323
322
321
319
318
317
316
315
313
313
311
310
309
308
307
306
305
304
303
302
301
299
299
298
296
296
295
294
292
292
291
7-58039
-58328
-58615
-58902
59188
289
287
287
286
285
284
283
282
281
280
279
279
277
277
276
275
274
273
272
272
271
27C
269
268
267
266
266
265
264
263
2G3
261
261
260
259
258
258
257
256
255
255
254
258
252
252
251
25C
25C
24g
248
247
247
246
245
245
in
242
242
241
7-58204
-58494
-58783
59071
-59358
290
289
288
28V7
286
285
284
283
282
281
28C
28C
27S
278
277
276
275
274
274
273
272
271
270
269
269
268
267
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15
16
17
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21
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25
26
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28
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16
17
18
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7-62274
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63096
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7-62456
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63556
20
21
22
23
24
25
26
27
28
29
30
31
32
33
31
35
36
37
38
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7
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10
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8-29206
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24
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26
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8-21003
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22138
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8-29002
29129
29256
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8-29857
29987
30117
30246
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130
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129
129
129
128
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127
127
127
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126
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20
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22
23
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124
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8-30504
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30
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32
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36
37
38
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50
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8-33950
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118
118
118
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116
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115
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114
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8-34909
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114
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8-40875
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110
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8-41427
41537
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41757
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8-42569
42682
42795
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9
10
11
12
13
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10
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12
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8-35143
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8-36130
36251
36372
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8-41976
42086
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15
16
17
18
19
8-35734
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8-36734
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37095
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8-42522
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26
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Lg, Vers.
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8-53242
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96
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8-55736
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8-56226
56324
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10
11
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13
14
15
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18
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8-48811
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8-50168
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8-50688
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8-55140
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8-56714
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20
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22
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58
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B~87192
87256
87320
87384
87448
8-87512
87576
87640
87704
87768
8-87832
87895
87959
88023
8- 88150
88213
88277
88340
88404
8-88467
88530
88593
88656
.88720
8-88783
88846
8890
8897
8903
8-C9097
.89160
8922
8928
8-89411
89473
8953
8959
89660
8-8972
8978
89910
89972
8- 00034
Lg, Vers
B- 89856
.8992
90065
.90135
3.90205
90274
90344
90413
.90483
3-90552
.90622
90691
90760
.90830
3-90899
90968
.91037
91106
.91175
3-91244
91313
91382
91451
91520
3.91588
91657
91726
91794
91863
3-91932
92000
.92068
.92137
.92205
B. 92274
92342
.92410
92478
92546
92615
92683
92751
92819
92887
8.92955
.93022
.93090
93158
.93226
8-93293
.93429
.93496
93564
8-93831
Log.Exs
68
67
8.90034
90096
.90158
.90220
.90282
8.90344
.90406
90467
90529
.90591
8-90652
90714
90776
90837
91021
91083
91144
.91205
3-91876
-91937
91997
92058
92119
8-92179
-92240
-92300
92361
.92421
8-92487
.92542
92602
9266
.9272
8-9278
-9284
-9290
-9296
Z.93Q2:
8-93082
-93142
9320
9326
9332
8-9338
-9344
9350
.9356
.9361
8-93679
Lg.Vers.
6!
8-93631
.93699
.93766
.93833
93901
8-93968
94035
94102
94170
94237
-94304
94371
94438
94505
94572
8 94638
94705
94772
94839
94905
8-94972
.95039
95105
95172
^95238
8 - 95305
95371
-95437
95504
95570
95636
-95703
-95769
-95835
_95_901
95967
96033
96165
96231
Log.bxs.
P.P.
70
50
9-
10-
11.
23-
35-
40 46
58.
67
6-7
7-8
8-9
10- Q
11-1
22-3
33-5
44."
46-0 45-;
57-5 56- i
68
6-8
7-9
9-0
10-2
il-3
22-6
34-0
50 55-8
66
6-6
7-7
11-0
65
6-5
10-!
10
10. i
2021-3
30 32-0
4042-6
50J53-3
61
6-1
7-1
1010.'
2020.1
30 30-
40 40 i
50 50- i
22-021.1
33-0 32-!
44-043-:
55-0 54.:
63 62
6-2
7-3 7-2
10-5 10-3
21.020-6
31-531-0
42-041-3
52-5 51-6
60
6-0
7-0
8-C
9-0
10-0
20- C
30-029.!
40-0 39-;
50-049.:
59
5-9
19
6
60-5
70-0
80- (5
90.1
1004
200-1
300-g
400-3
500.4
P. P.
LOG. VERSED SINES AND EXTERNAL SECANTS 177
24 25
' Lg.Vers. I>
5.93679
93738
.93797
93857
93916
5-93975
94034
.94094
94153
94212
5-94271
94330
94389
. 94448
.94506
5-94505
94624
.94683
94742
.94800
5-94859
94917
94976
95034
.95093
9515!
.95210
95268
95326
-95384
8-95443
95501
95559
95617
-95675
8-95733
-95791
95849
95907
.95965
8-96023
96080
96138
96196
96253
8-96311
96368
96426
96483
^96541
8-96598
96656
96713
96770
96827
8-96885
96942
96999
.97056
97113
8-97170
Lg.Vers.
Log.Exs.
8-97606
97671
97736
97801
97865
8-97930
.97995
.98060
98125
.98190
8-98254
98319
98383
98448
98513
8-98577"
98642
98706
98770
-98835
98963
99028
9915J
9-00051
-00114
9-00178
00242
.00305
-00369
00432
00495
.0055
-0062
-00686
JD0749
.GOBI
-0087
-0093
-01002
.01065
9-01128
-01191
-01254
-01317
-01380
9.01443
Log.Exs.
64
Lg.Vers
8-98020
98077
98133
98190
-9824
9835
9841
-98470
-98527
8-98583
-98639
-98751
8-98802
-98918
-98974
.99085
8-99141
-99197
9925
99308
.99363
8-99419
99474
99529
-99585
-99640
8-99695
-99751
9991
9-0002
-0008
-0013
.0019
9-00246
-00301
-00356
-00411
.00466
9 . 00520
Lg. Vers.
Log.Exs.
01443
01505
.01568
-01631
-01694
-01756
-01819
-01882
-01944
-02007
02070
02132
02195
02257
-02319
9-02382
02444
02506
-0256S
-02631
-C269S
02755
-02817
-0288C
02942
9-03004
-03066
-03128
-03190
-03252
9-03313
-03375
-03437
03499
^03561
9.C362~2
03684
03746
03807
9-03930
0399_
04051
04115
-04176
9-04238
-0429S
-0436C
04421
-04483
9-04544
04605
04666
0472?
-0478F
04911
-0497
-0503
0509
Log.Fxs
63
61
61
61
61
61
61
61
61
60
61
~D
P.P.
63
7-1
62 61
7.
19.
29.
39.
5049-
!:
28-5
38.0
47-5
30 28.
40
5046-
P. P.
178 LOG.
VERSED SINES AND EXTERNAL SECANTS
26 27
'
Lg.Vers
D
Log. Exs
1>
Lg.Vers.
V
Log. Exs
&
'
P.P.
1
9-00520
.00575
01
9-05154
05215
61
9-03740
03792
52
5n
9-08752
-08811
59
O
1
J
00630
0068^
00739
ft
05276
05337
.05398
65
61
03845
03898
03950
53
52
08870
08929
08988
59
59
2
3
4
61 60 59
5
6
9-00794
-00848
bb
GI
9-05458
-05519
6U
61
9-04002
04055
si
9-09047
-09106
59
59
5
6
6 6-
7 7-
80
1 b-0 5
7-0 6
8
J
9
-0090
-0095
.oior
9-0106
ft
54
57
-05580
0564*5
05701
60
60
61
fin
04107
04160
04212
52
52
52
-09164
0922J
09282
58
59
59
58
7
8
9
9 9-
1010-
20 20-
3030-
9-0 8
10-0 9
20-019
5 30-029
10
9-05762
9.04264
9-09341
1O
1]
0112
05822
fin
04317
09400
59
40 40-
6 40-039
ll
01174
0122
55
05883
05943
04369
04421
52
09458
09517
58
59
12
5050.
850-049
I/
01283
06004
60
04473
09576
58
14
15
16
9-0133
0139'
54
54
9-06064
06124
bU
6Q
9-04525
04577
52
9-09634
09693
58
58
15
16
58 57
6! 5-8 5.|
17
18
ii
01445
01499
01554
it
06185
06245
06305
60
04630
04682
04734
52
52
.09752
09810
.09869
59
58
58
17
18
19
7 6-Z
8 7-7
9 8-7
B-fl
8 3
24
9-01608
01662
01715
01769
.01823
ft
54
54
9.06366
06426
06486
06546
06606
60
S8
60
60
9-04786
04837
04889
04941
04993
li
52
52
52
9-09927
09986
. 10044
10102
10161
58
58
58
58
21
22
23
24
IU
20
30
40
50
o-o
19-3
29-0
38-6
48-3
19. Q
28-5
38.0
47-3
9.01877
54
50
9-06667
ttU
fin
9-05045
51
9-10219
58
2C
.0193:
06727
05097
rf
10278
26
55 54
27
01985
j?f
06787
fin
05148
10336
08
27
6
5-5
5.4
I
02038
02092
54
-06847
-06907
60
05200
05252
52
10394
10452
58
28
29
7
8
6-4
7-3
8.3
30
31
33
34
II
9-02146
02199
02253
02307
02360
II
1
9-06967
.07027
.07087
.07146
-07206
bO
60
60
60
59
9-05303
-05355
-05407
05458
05510
51
52
51
51
51
51
51
9-10511
10569
10627
10685
10743
58
58
58
58
58
58
58
30
31
32
33
34
9
10
20
30
40
50
8-k,
9-3
18- 1
27-5
36- 1
15.8
18. 'O
27.0
38.0
43.9
9-02414
02467
9-07266
07326
-05561
05613
9-10801
10859
35
3R
37
38
39
02521
02574
02627
53
53
07386
.07445
07505
59
60
05664
05715
-05767
a
.10917
10975
11033
58
58
58
37
38
39
6
7
53
5-3
6-?
5.
6-
40
9-02681
CO
9-07565
K
05818
bl
9-11091
b8
4O
8
7-0
6-?
41
02734
ii
07324
j?s
05869
51
11149
41
9
7-9
7-
42
43
44
02787
02840
02894
fi
07684
07743
07803
60
05921
05972
06023
a
11207
11265
11323
57
58
58
42
43
44
10
20
30
8-8
L7-6
26-5
8.
17.
26-
45
46
02947
03000
53
53
07863
07922
by
59
06074
06125
51
51
9-11380
11438
b'/
58
45
4fi
40,
50'
J5-3
1:4.1
34-
43-
47
48
49
03053
03106
03159
53
53
07981
08041
08100
59
59
06176
06227
06279
51
51
51
11496
11554
11611
II
57
47
48
49
51
50
51
52
03212
03265
03318
bd
53
53
rq
08160
08219
08278
by
59
59
cq
06330
06380
06431
tt
51
9-11669
-11727
-11784
b8
57
57
50
51
52
7
8
9
5.90.Q
6-8 0-0
7-6 0-1
53
54
03371
03423
II
08338
08397
59
06482
06533
51
-11842
11899
57
53
54
10
20
8-5 0-1
17-0 0-1
55
03476
b3
08456
59
06584
51
9-11957
58
55
30
25-8 0-2
56
03529
K
.08515
08635
-12015
56
40
34-00-3
57
03582
jj2
.08574
06686
51
12072
57
57
50
42-50-4
58
59
03634
03687
53
.08634
.08693
59
06736
06787
51
12129
12187
57
58
59
eo
03740
g.Vers.
T
08752
59
06838
50
9-12244
57
60
Log. Exs.
Lg. Vers.
D
Log. Exs.
f
'
P. P.
LOG. VERSED SINES AND EXTERNAL SECANTS
28 29
179
t
Lg, Vers,
J>
Log.Exs.
J>
Lg.Vers.
I)
Log.Exs.
D
i
P. P,
1
2
3
4
5
6
7
8
9
9-06838
06888
.06939
.06990
. 07040
50
55
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
49
50
49
50
49
49
50
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
48
49
49
9-12244
-12302
12359
-12416
-12474
57
57
57
57
| 7 Z
i?
57
57
8
57
57
57
57
11
57
57
57
56
57
56
57
56
57
56
56
57
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
55
56
D
9-09823
-09872
09920
09969
10018
49
48
49
48
49
48
48
49
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
48
47
48
48
47
48
8
48
47
47
47
47
47
47
47
47
47
47
$
8
3
47
47
9-15641
15697
15752
15808
-15864
56
55
56
55
ii
56
55
55
56
55
55
55
55
55
55
55
55
55
1
2
3
4
6
7
8
9
10
20
30
40
50
6
7
8
9
10
20
30
40
50
G
7
8
9
10
20
30
40
50
6
7
8
9
10
20
30
40
50
6
7
8
9
10
20
30
40
50
1 7 7
1:1
8-6
9-6
19-1
28-7
3C 3
47-9
56
5-6
6-5
7-4
8-4
9-3
18-6
28-0
37-3
46-6
5
6 5
7 6
8 7
9 8
10 9
2018
30 27
4036
5045
51
\\
6-8
7-6
8-5
17-0
25-5
34-0
42-5
4 5
i-9
3-8
6-6
si
fci
33-0
41-2
48
4-8
5-6
6-4
7-2
8-0
16-0
24-0
32-0
40-0
5"
5
6
7
8
9
19
28
38
47
5;
5
S
7
8
9
18
27
37
46
'2
4
5<
5
5
6
7
8
16
25
33
42
4
4
6
7
8
16
24
32
40
4
4
5
6
7
7
IF
23
31
39
?
6
5
5
5
5 s
5
4
i
6
5
6
7
8
:
11
27
36
45
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:j
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ii
)
-9
y
I
'.(
56
5-6
6-6
7-5
8-5
9-4
18-8
28-2
37-6
47-1
55
5-5
6-4
7-3
8-2
9-1
18-3
27-fj
36-6
45-8
4
4
3
2
1
.0
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5O
5-0
5-8
6-6
7-5
8-3
16-6
25- Q
33-3
41-6
48
4-8
5-6
6-4
7-3
8.1
16-1
24-2
32-3
40-4
47
4-7
5-5
6-2
7-0
7-8
15-6
23-5
31-3
39-1
9-07091
07141
07192
.07242
07293
9-12531
12588
12645
12703
12760
9-10067
-10115
10164
10213
-10261
9-15920
-15975
16031
16087
-16142
5
6
7
8
9
10
11
12
13
14
9-07343
97393
07444
07494
07544
9-12817
12874
-12931
-12988
-13045
-10310
10358
10407
10455
-10504
9-16198
-16254
16309
16365
16420
10
11
12
13
14
15
16
17
10
ii.
20
21
22
23
24
25
26
27
28
29
07594
07644
07695
07745
07795
9-13102
.ISI'9
13216
13273
13330
-10552
10601
10649
10697
-10746
9-16476
16531
16587
16642
166P8
15
16
17
18
19
9-07845
07895
07945
07995
08045
9-13387
-13444
13500
13557
.13614
9-10794
10842
10890
10939
10987
9-16753
-16808
16864
16919
-16974
bb
55
55
55
55
n
11
55
55
55
55
55
55
55
55
55
55
55
55
54
55
5*
55
55
54
55
54
54
55
54
53
54
11
11
54
54
20
21
22
23
24
9-08095
08145
08195
00244
.08294
9-13671
-13727
13784
13841
13897
9-11035
11083
.11131
11179
-11227
9-17C29
-17085
-17140
-1719u
-17250
25
26
27
28
29
30
31
32
33
34
35
36
37
38
3j
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
9-08344
08394
08443
08493
08543
9-13954
14011
14067
14124
14180
9-1127b
11323
11371
11419
11467
9-17305
17361
17416
17471
-17526
30
31
32
33
34
35
36
37
S9
9-08592
08642
08691
08741
08790
9-08840
08889
08939
08988
-09087
9-14237
-14293
-14350
. 14406
-14462
9-11615
11562
-1161C
11658
-11706
9-17581
17636
17691
-177'6
.17801
9-14519
-14575
-14631
14688
14744
9-11754
1180!
11849
11897
11944
9-17856
17910
17965
18020
18075
4O
41
42
4?
^44
4^
46
47
48
49
50
51
52
53
54
55
56
57
58
59
9-09087
-09136
-09185
-09234
-09284
9-09333
-09382
-09431
-09480
-09529
9-14800
14856
14913
14969
15025
9-15081
15137
15193
15249
15305
9-11992
12039
12087
12134
12182
9-18130
-18185
18239
1829;
.18349
9-18403
18458
18513
18567
-1862?
9-12229
12277
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9-96177
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-96205
-96218
-96232
11-03616
-03780
-03944
-04108
-04273
10
11
12
13
11
15
16
17
18
Oi
20
23
24
15
16
17
18
11
20
23
24
9-95415
95429
-95443
-95457
95471
0-95333
-95473
-95613
-95753
-95894
9-96246
-96259
-96273
-96287
-96301
11-04438
-04604
-04771
-04938
-05106
9.95485
95499
95513
-95527
-95540
14
14
14
it
14
14
14
14
14
14
13
14
14
14
13
14
14
14
14
0-96035
-96176
-96318
-96461
-96603
-96314
-96328
-96342
-96355
-96369
14
13
13
14
13
14
13
14
15
15
14
13
13
15
14
13
13
14
13
13
13
13
15
13
13
if
13
15
13
13
14
13
13
13
13
15
11-05274
-05443
-05612
.05782
-05952
25
26
27
28
29
9-95554
95568
-95582
95596
.95615
0-96746
96889
97033
97177
97322
9-96383
-96397
-96410
-96424
-96438
11-06125
-06295
-06467
-06640
-06813
25
26
27
28
29
30
31
32
33
34
35
36
37
33
39
9-95624
-95638
-95652
-95666
-95680
0-97467
97612
97758
-97904
-98050
9-96451
-96465
-96479
96492
-96506
11-06987
.07161
.07336
-07512
-07688
30
31
32
33
34-
35
36
37
38
J!
40
41
42
43
44
9-95693
-95707
95721
9573B
-95749
10-98197
-98345
-98492
93640
-98789
9-96519
-96533
-96547
-96560
-96574
11-07865
-08043
-08221
-08400
-08579
1-3
1-5
3-0
4-5
B.O
7-5
6 (
7 (
8<
9<
.0
.0
.0
.0
.0'
14
i -4
1:1
2-1
2-3
4.f
7-0
9-3
1.1
1-3
2-6
4-0
5-3
6-6-
5
) 5
)-6
)-8
2-5
}-3
l-I
13
1-3
1-6
1-8
2-0
2-5
4-5
6-7
9-0
11-2
40
41
42
43
44
9-95763
-95777
-95791
-95804
-95818
14
14
13
14
14
if
14
14
11
14
14
13
14
11
V.
10-98938
-99087
-99237
-99387
-99538
9-96588
-96601
-96615
-9662S
-96642
11-08759
-08940
-09121
-09303
-09486
45
46
47
48
49
9-95835
-95846
-95860
-95874
-95888
10-99689
-99841
10-99993
11-00145
-00298
9-96656
-96669
-96683
-96697
-96715
11-09669
-09853
-10038
.10223
. 10409
45
46
47
48
49
50
51
52
53
54
9-95901
-95915
-95929
.95943
-95957
11-00451
-00605
-0075E
-00914
-01069
Ib3
154
154
155
155
155
156
156
157
157
158
D
9-96724
-96737
-96751
.9676<
-96778
11-10595
-10783
-10971
.11160
-11349
50
51
52
53
54
55
56
57
58
59
9-95976
-9598;
-95998
-96012
-96026
11-01225
-01381
-01537
01692
-01852
9-96792
-96805
-96815
-96832
-96848
11-11539
-11730
.1192?
12114
-12307
55
56
57
58
59
Q
9-96039
11-0201C
9-96859
11-12501
60
Lg, Vers
*>
Log.Exs.
Lg.Vers
D
Log.Exs,
^
'
P. P,
208 LOG. VERSED SINES AND EXTERNAL SECANTS
86 87
Lg. Vers
D
Log. Exs.
D
Lg. Vers.
D
Log. Exs.
D
>
P. P.
1
2
3
4
9-96859
96837
96887
96900
96914
13
13
13
11-12501
12696
-12891
.13087
13284
19
19
19
19
9-97665
.97679
97692
.97705
97718
13
13
13
13
11.25785
26040
26297
26554
26814
255
256
257
259
I?
2
u
6
7
8
9
25O
25-0
29-1
33-3
37-5
24O
24-0
28.0
32-0
36-0
5
6
7
8
9
9-96927
96941
96954
96968
9698T
if
11
11
13
11.13482
.13680
.13879
. 14079
14280
19
19
19<
20
20
9.97732
.97745
97758
97772
97785
lei
13
13
13
13
11.27074
.27336
.27599
27864
28131
261
262
263
265
266
b~
\
[j
10
20
30
40
50
41 -b
83-3
125-0
166-6
208-3
40-0
80.0
120-0
160-0
200-0
10
96995
11-14482
9-97798
11-28398
267
ho
230 220
11
12
13
14
97008
97022
97035
97049
13
I
14684
14887
.15092
-15297
203
20^
205
97811
.97825
.97838
.97851
13
13
13
-28668
-28938
-29211
-29485
26S
27C
272
274
11
12
13
14
6
7
8
9
23-0
26-8
30-6
34-5
22-0
25-6
29-3
33.0
15
16
17
18
19
97062
97076
97089
97103
97116
13
13
11.15502
.15709
-15917
.16125
16334
208
208
209
9-97864
-97978
97891
.97904
97917
13
13
13
13
11-29760
30037
30316
30596
30878
277
278
28C
282
15
16
17
18
19
10
20
30
40
50
38-3
76-6
115-0
153-3
191-6
36-6
73-3
110-0
146 - 6
183-3
20
21
22
23
24
97130
97143
97157
-97170
97183
13
11
1-16544
.16755
16967
.17180
17394
210
211
212
213
214
9.97931
.97944
.97957
.97970
.97984
13
13
13
11
11.31162
.31447
31734
32023
32313
2 si
287
288
29C
21
22
23
24
6
7
8
9
210
21-0
24-5
28-0
31-5
200
20-0
23-3
26-6
30-0
25
26
97197
97210
13
1.17609
.17824
2 it
9.97997
.98010
13
13
1 3
11-32606
32900
29^
25
26
10
20
35-0
70-0
33-3
68-6
27
-97224
.18041
9-1 n
.98023
13
33196
27
30
105-0
100-0
28
29
97237
97251
13
18259
18477
211
98036
.98050
13
33494
33793
29<
28
29
40
50
140-0
175-0
133-3
166-6
30
31
32
33
34
97264
97277
97291
97304
97318
13
13
13
13
13
1-18697
.18917
19138
.19361
.19581
220
i
9-98063
.98076
.98089
.98102
.98116
13
13
13
13
13
11-34095
-34398
-34704
35011
35321
301
303
305
307
309
30
31
32
33
34
6
7
8
190
19-0
22-1
25 3
4 3
0-410.3
0-40-3
O-JO-4
35
36
37
38
-32.
40
97331
97345
97358
9737T
973RR
97398
13
13
13
13
13
13
1-19809
.20034
20261
20489
-207V7
1-20947
224
225
227
227
228
230
9.n
9.98129
98142
98155
.98168
-98181
13
13
13
13
13
13
13
11-35632
35946
36261
36579"
36899
6\.i
313
315
318
320
322
35
36
37
38
39
40
Ld
20
30
40
50
31-6
63-3
95-0
126-6
158-3
0-605
1-3 1.0
2.01-5
2-6 2-0
3-32-5
9-98195
11-37221
41
97412
.21178
98208
37546
41
210
42
97425
.21410
000
.98221
13
37872
000
42
(
JO- 20
.10-0"
43
44
97438
97452
13
.21643
.21877
234
98234
.98247
13
38201
38532
331
43
44
t
1
fO-20
50-20
. 0-0
. 0-0
45
46
47
48
49
97465
97478
97492
97505
97519
13
13
13
13
13
1-22112
.22349
-22586
.22825
-23065
23f
237
239
239
9.98260
.98273
.98287
.98300
-98313
13
13
13
13
13
11-38866
.39201
39540
39880
40224
666
335
338
340
342
45
46
47
48
49
(
1(
2(
3(
4(
)0-30
)0-30
)0-60
) 1-00
) 1-50
- 0-1
0-1
- 0-1
- 5 - 2
.60.3
50
97532i
13
1.23306
241
n j o
9.98326
13
11-40569
50
50 1- D U-O U-
51
52
53
54
97545
97559
97572
97585
13
13
13
.23548
.23792
.24037
24283
243
245
246
-98339
.98352
-98365
-98378
13
13
13
40918
-41269
41622
41979
351
353
356
51
52
53
54
6
7
g
14 1
1-4 1
1-6 1
1-8 1
3 13
-3 1.3
-6 1.5
8 1-7
55
97599
13
1-24530
247
9-98392
13
11.42338
55
9
2-1 2
56
97612
24778
248
.98405
42699
3R/T
56
10
2-3 2
2 v 1
57
58
59
97625
.97639.
97652
13
13
.25028
25279
25531
251
252
98418
.98431
98444
13
13
.43064
-43431
.43802
367
370
57
58
59
20
30
40
4-6 4
7-0 6
9.3 9
5 4- 5
7 6-5
60
-97665
13
11-25785
264
9-98457
13
11.44175
616
(50
501
1-6 11
.2 10.8
'
g. Vers.
D
Log. Exs.
D
Lg, Vers.
D
Log. Exs,
D
f
P.P.
LOG. VERSED SINES AND EXTERNAL SECANTS
88 89
209
Lg.Vers
It
Log.Exs.
D
Lg.Vers.
D
Log. Exs
z>
'
P. P.
1
2
3
4
9-98457
.98470
98483
98496
98509
13
13
13
13
11-44175
.44551
44931
45313
45699
37
379
382
386
9.99235
.99248
.99261
.99274
.99287
12
13
13
11-7505
7579
.7654
.7731
.7809
74
75
76
78~
]
s
4
5
6
7
8
9
9-98522
98535
.98548
.98562
-98575
13
13
13
13
13
11.46088
.46480
46876
47275
47677
389
392
395
399
402
9-99299
9931J
-99325
.99338
.99351
12
13
11
13
11-7889
7970
-8052
8136
82223
79
80"
82
840
856
E
e
7
8
9
to
11
1'2
18
14
9-98588
.98601
-98614
.98627
-98640
13
13
13
13
13
11.48083
48493
48906
49323
.49743
4Ub
409
413
417
420
9-99363
.99376
.99389
.99402
99415
12
13
12
13
11.83095
.83986
84894
85821
.86768
872
89i
908
927
947
10
11
12
13
14
15
J6
17
18
19
9-98693
.98666
.98679
-98692
.98705
13
13
13
13
13
11-50168
.50597
51029
-51466
51906
42b
III
ft
9-99428
99440
.99453
.99466
99479
13
12
13
12
13
, s
11-87735
-88724
89735
-90769
.91829
967
989
1009
103;
1059
15
16
17
18
-li
20
21
22
23
24
9-98718
98731
.98744
.98757
.98770
13
13
13
13
13
11-52351
.52801
53255
.53713
54176
445
449
454
458
463
9-99491
99504
99517
.99530
99543
12
13
13
12
13
11-92914
94026
95167
.96338
-97541
1085
1112
1140
1171
1203
20
21
22
23
24
25
26
27
28
29
9-98783
98796
98809
-98822
.98835
13
13
13
13
13
11-54643
55116
55593
.56076
-56563
4bV
472
477
482
487
9-99555
.99568
99581
.99594
99606
12
13
12
13
12
11.98777
12.00048
01358
.02707
.04098
1236
1271
1309
1349
1391
25
26
27
28
29
30
31
32
33
34
9-98848
-98861
-98874
-98887
-98900
13
13
13
13
13
11-57056
57554
58058
58567
.59082
492
498
504
509
515
9-99619
99632
99645
99657
99670
ii
13
12
13
12-05535
.07020
.08557
.10149
11801
1436
1485
1537
1592
1652
30
31
32
33
34
3o
3fi
37
38
39
-98913
98925
.98938
.98951
-98964
13
12
13
13
13
11-59602
-60129
60662
.61202
-61747
520
527
533
i39
9-99683
99695
.99708
.99721
-99734
y
13
12
13
12-13517
.15302
1716J
19106
21139
1716
1785
1861
1943
2033
35
36
37
38
39
40
41
42
43
44
-98977
98990
99003
-99016
99C29
13
13
13
12
1.62300
.62859
.63425
.63998
.64579
5b2
559
566
573
581
9-99740
99759
99772
99784
-99797
13
12
12
13
i"o
12-23271
2551]
.27872
30367
-33013
2131
2240
2361
2495
2645
40
41
42
43
44
13 13
6 1-3 1.3
7 1.6 1.
8 1-8 1.'
9 2-0 1.9
45
46
47
48
49
99042
99055
99068
99081
-99093
13
13
13
13
12
1-65167
65762
66366
66978
-67598
ill
ft
620
9-99810
99823
.99835
99848
99861
12
13
12
13
12-35828
.38837
42068
45557
.49349
2815
3009
3231
3489
3791
45
46
47
48
49
10 2-2 2.
20 4-5 4.3
30 6-7 6-i
40 9-0 8.
50 11.2 10-8
50
51
52
53
54
-99106
-99119
-99132
99145
-99158
13
13
13
13
12
1.68227
.68865
69511
70168
70834
628
638
646
656
666
9-99873
.99886
.99899
99911
S9924
12
12
13
12
12
2-53501
58089
.63217
.69029
75736
4152
4588
5127
5812
6707
50
51
52
53
54
12
6 1-2
7 I.I
8 1.6
55
56
57
58
59
-99171
-99184
-99197
99209
99222
13
13
12
13
1-71509
.72196
72892
73600
74319
'96
9-99937
99949
.99962
99974
.99987
18
12
12
12
13
2-83667
.93371
3-05877
-23499
.53615
7931
9704
2506
7621
0116
55
56
57
58
59
91-9
10 2-1
20 4-1
30 6.2
40 8-3
50 10-4
60
99235
13
1-75050
30
o.ooooo
12
Infinity
60
'
Lg.Vers.
J>
Log.Exs,
D
Lg.Vers. |
X>
Log.Exs,
1>
7
P, P,
210
THE RAILROAD TAPER
FUNCTIONS OF A ONE-DEGREE CURVE
The Long Chords, Mid-Ordinates, Externals, and Tangent
Distances of this table are for a curve of 5730 feet radius. To
find the corresponding functions of any other curve divide the
tabular values by the degree of curve.
For metric curves having a 20-meter chord, this is a table of
the functions of a two-tenth degree curve. Multiply the values in
the table by 0.2 to obtain the functions, in meters, of a one-degree
metric curve.
1
/
L. 0. M. E. T.
L. C. M. E. T.
0.00 0.000 0.000 0.00
100.00 0.',M8 0.218 50 00
2
3.33 0.000 0.000 1.67
103.33 0.233 0.233 51.67
2
4
6.6? 001 0.001 3.33
106.66 0.2J8 0.248 53.33
4
6
10.00 0.002 0.002 5.00
310.00 0.264 0.264 55.00
6
8
13.33 0.004 0.004 6.67
113.33 0.280 280 56.67
8
10
16.67 0.006 0.006 8.33
116.66 0.297 0.297 58.33
10
12
20.00 0.009 0.009 10.00
120 00 0.314 0.314 60.00
12
14
23.33 0.012 0.012 11.67
123.33 0.332 0.332 61.67
14
16
26.67 0.015 0.015 13.33
126.66 0.350 0.350 63 33
16
18
30.00 0.019 0.019 15.00
130.00 0.3G8 0.368 65.00
18
20
33.33 0.024 0.024 16.67
133.33 0.388 0.388 66 67
20
22
36.67 0.029 0.029. 18.33
136.66 0.407 0.407 68.33
22
24
40.00 0.035 0.035 20.00
140.00 0.427 0.427 70 00
24
26
43.33 0.041 0.041 21.67
143.33 0.448 0.448 71.67
26
28
4667 0.048 0.048 23.33
146.66 0.469 0.469 73.33
28
30
50.00 0.054 0.054 25.00
15000 0.491 0.491 75.00
30
32
53 33 062 O.OC2 26.67
153.33 0.513 0.513 76.67
32
34
5667 0070 0070 28.33
156.66 0.536 0.536 78.33
34
36
6000 0.079 0.079 30.00
160.00 0.559 0.559 80.00
36
38
63.33 0.088 0.088 31.67
163.33 0.582 0.582 81.07
38
40
66.67 0.097 0.097 3333
166 66 0.606 6.606 83.33
40
42
70.00 0.107 0.107 35.00
J70.00 0.630 0.630 85.00
42
44
73.33 0.117 0.117 36. G7
173 33 0.655 0.655 86.67
44
46
76.6? 0128 0.128 38.33
176.66 0.681 0.681 88 33
46
48
80.00 0.140 0.140 40.00
180.00 0.706 0.706 90.00
48
50
83.33 0.151 0.151 41.67
18333 0.733 0.733 91.07
50
52
86 67 0.164 0.164 43.33
186.66 0.760 0.760 93.33
52
54
90 00 176 0.176 45.00
190.00 0.788 0788 95.00
54
56
9333 0.190 0.190 46.67
193.33 0.815 0.815 96.67
56
58
96.67 0.204 0.204 4833
196.66 0.844 0.844 98.33
58
60
100.00 0.218 0.218 5000
199.98 0.873 0873 100.00
60
FUNCTIONS OF A ONE-DEGREE CURVE 211
Jjo
3
9
L. C. M. E. T.
L. C. M. E. T.
/
o
199.98 0.873 0.873 100.00
299.96 1.964 a. 964 150.07
2
203.31 0.902 0.902 101.67
303.29 2.008 2.009 151 74
2
4
206.64 0.932 0.932 103.34
306.62 2.053 2.054 153.41
4
6
209.97 0.9C2 0.962 105.01
309.95 2.098 2.099 155 08
6
8
213.31 0.993 0.993 106.68
313.29 2.143 2.144 156.75
8
10
216.64 .024 1.024 108.35
316.62 2.188 2.189 158.42
10
12
219.97 .056 1.056 110.02
319.95 2.235 2.236 160.09
12
14
223.30 .088 1.088 111.69
323.28 2.282 2.283 161.76
14
16
226.64 .121 1.121 113.36
326.62 2.329 2.330 163.43
16
18
229.97 .154 1.154 115.02
329.95 2.376 2.377 165.09
18
20
233.30 .188 1.188 116.69
333.28 ?.424 2.425 166.76
20
22
236.63 .222 1.222 118.36
336.61 2.473 2.474 168.43
22
24
239.97 .256 1.256 120.03
339.95 2.523 2.523 170.10
24
26
243.30 .292 1.292 121.70
343.28 2.572 2.573 171.77
26
28
246.63 .328 1.328 123.37
346.61 2.622 2.623 17344
28
30
249.96 .364 1.364 125.03
349.94 2.672 2.G73 175.10
30
32
253.29 .399 1.399 126.70
353.27 2.724 2.725 176.72
32
34
256.62 .437 1.437 128.37
356.60 2.776 2 777 178.39
34
36
259.96 .475 1.475 130.04
359.94 2.828 2.829 180.06
36
38
263.29 .513 1.513 131.71
363.27 2.880 2.881 181.73
38
40
266.62 .552 1.552 133.38
366.60 2.933 2.934 183.40
40
42
269.96 .592 1.592 135.05
369.94 2.987 2.988 185.07
42
44
273.29 .632 1.632 136.72
373.27 3.042 3 043 186.74
44
46
276.62 .672 1.672 138.38
376.60 3.096 3 097 188.40
46
43
279.96 .712 1.712 140.05
379.94 3.151 3.152 190.07
48
50
283.29 .752 1.752 141.72
383.27 3.206 3.207 191.74
50
52
286.62 .794 1.794 143.39
386.60 3.263 3.264 193.41
52
54
289.96 .836 1.836 145.06
389.94 3.320 3.321 195.08
54
56
293.29 .878 1.878 146.73
393.27 3.377 3 378 196.75
56
58
296.62 .921 1.921 148.40
396.60 3.434 3.435 198.42
58
60
299.96 .964 1.964 150.07
399.94 3.491 3.492 2uO 09
60
4
6
L. C. M. E. T.
L. C M. E. T.
8
399.94 3.491 3.492 200.09
499.88 5.454 5.459 250.17
2
403.27 3.550 3.551 201.76
503.21 5.&27 5.o33 251.84
2
4
406.00 3.609 3.610 203.43
506.54 5.601 5.607 253.51
4
6
409.93 3.668 3.670 205.10
509.87 5.675 5681 255.18
6
8
413.26 3.727 3.730 206.77
513.20 5.749 5.755 256.85
8
10
416.59 3.787 3.790 208.44
51653 5.823 5.829 258.52
10
12
419.92 3.848 3.851 210.11
519.86 5.899 5.905 260.20
12
14
423.26 3.910 3.913 211.77
523.19 5.975 5 981 261.86
14
16
426.59 3.972 3.975 213.45
526.52 6.052 6.058 263.54
16
18
429.92 4.034 4.037 215.11
529.85 6.129 6.135 265.20
18
20
433.25 4.096 4.099 216.78
533.18 6.206 6.212 266.87
20
22
436.58 4.160 4.163 218.45
536.51 6.284 6.290 268.54
22
24
439.91 4.224 4.227 220.12
539.84 6.362 6.369 270.21
24
26
443.24 4.288 4.291 221.79
543.17 6.441 6.448 971.88
26
28
446.58 4.353 4.356 223.46
546.50 6.520 6.527 273.54
28
30
449.91 4.418 4.421 225.13
549.83 6.599 6.606 275.21
30
32
453.24 4.484 4.487 226.80
553 17 6.680 6.687 276.88
32
34
456.57 4.550 4.554 228.47
556.50 6.761 6.768 278.55
34
.36
45990 4.617 4.621 230.14
559.83 6.842 6.849 280.23
36
38
463.23 4.684 4.G88 231.81
563.16 6.923 6.931 281.90
38
40
466.56 4.751 4.755 23348
566.49 7.005 7013 283.57
40
42
469.89 4.820 4.824 235.15
569.82 7.088 7.096 285.24
42
44
473.23 4.889 4.6Q3 236.82
573.15 7 171 7.180 28691
44
46
476 56 4.958 4 962 238.48
576.48 7 255 7.264 288.59
46
48
479.89 5.027 5.031 240.15
579.81 7339 7.348 290.26
48
50
483.22 5.096 5 100 241.82
583.14 7423 7.432 291.93
50
52
486.55 5.167 5.171 243.49
586.47 7.508 7.517 293.60
52
54
489 88 5.238 5.243 245.16
589.80 7.593 7.603 295.27
54
56
493.21 5.310 5.315 24683
593.13 7.678 7 689 296 95
56
58
496 54 5.382 5.387 248.50
596.46 7.764 7 775 298.62
58
60
499.88 5 454 5.459 250.17
599.80 7.850 7 861 300.30
60
212 FUNCTIONS OF A ONE-DEGREE CURVE
6
7
/
L. C. M. E. T.
L. C. M. E. T.
/
599.80 7.850 7.861 300.30
699.60 10.69 10.71 350.44
2
603.13 7.940 7.951 301.97
702.93 10.79 10.81 352.11
2
4
606 46 8.030 8.041 303.64
706.26 10.90 10.92 353.79
4
6
609.78 8.120 8.131 305.31
709.58 11.00 11.02 355.46
6
8
613.11 8.210 8.221 306.98
712.91 11.11 11.13 357.13
8
10
616.44 8.300 8.311 308.65
716.24 11.21 11.23 35881
10
12
619.76 8.390 8.401 310.32
719.56 11.31 11.33 360.48
12
14
623.09 8.480 8.491 311.99
722.89 11.42 11.44 362.15
14
16
626.42 8.570 8.581 313.66
726.21 11.52 11.54 36383
16
13
629.74 8.660 8.671 315.33
729.53 11.63 11.65 365.50
18
20
633.07 8.750 8.761 317.00
732.86 11.73 11.75 367.17
20
22
636.40 8.844 8.856 318.67
736.19 11.84 11.86 368.85
22
24
639.72 8.939 8.951 320.34
739.51 11.95 11.97 370.52
24
26
643.05 9.033 9.046 322.01
742.84 12.06 1208 37219
26
28
646.38 9.128 9.141 323.68
746.17 12.17 12.19 373.80
28
30
649.70 9.222 9.236 325 35
749.49 12.27 12.30 375.54
30
32
653.03 9.317 9.331 327.02
752.82 12.38 12.41 377.22
32
34
656.36 9.411 9.426 328.69
756.15 12.49 12 52 378. H9
34
36
659.69 9.506 9.521 330.37
759.47 12.60 12.63 380 57
36
38
663.02 9.600 9.616 332 04
762.80 12.71 12.74 382.24
38
40
666.34 9.695 9.712 333.71
766.13 12.82 12.85 383.92
40
42
669.67 9 794 9.812 335.38
769.45 12.93 12.96 385.60
42
44
673.00 9.894 9.912 337.05
772.78 13.04 13.08 387.27
44
46
676.32 9.993 10.01 338.78
776.11 13.15 13.19 388.95
46
48
679.65 10.09 10.11 340.40
779.43 13.26 13.31 390.62
48
50
68298 10.19 10.21 342.07
782.76 13.37 13.42 392.30
50
52
686.30 10.29 10.31 343.74
786.09 13.48 13.53 393.98
52
54
68963 10.39 10.41 345.41
789.41 13.59 13.65 395.65
54
56
692.96 10.49 10.51 347.08
792.74 13-. 70 13.76 397.33
56
58
696.28 10.59 10.61 348.76
796.07 13.81 13.88 399.01
58
60
699.60 10.69 10.71 350.44
799.40 13.96 13.99 400.70
60
8
9
L. C. M. E. T.
L. C. M. E. T.
799.40 13.96 13.99 400.70
899.10 r.C6 17.71 450.95
2
802.72 14.07 14.10 402.37
902.42 17.79 17.84 452.63
2
4
806.04 14.19 14.22 40405
905.74 17.92 17.98 454.31
4
6
809.37 14.31 14.34 405.72
909.07 18.06 18.11 455.98
6
8
812.69 1443 14.46 407.39
912.39 18.19 18.25 457.66
8
10
816.01 14.55 14.58 409.06
915.71 18.32 18.38 459.34
10
12
819.34 14.66 14.70 410.74
919.04 18.46 18.52 461.02
12
14
822.66 14.78 14.82 412.41
922.36 18.59 18.65 462.70
14
16
825.98 14.90 14.94 414.08
925.68 18.72 18.79 464.37
16
18
829.31 15.02 15.06 415.75
929.01 18.86 18.92 466.05
18
20
832.63 15.14 15.18 417.43
932.33 18.99 19.06 467.73
20
22
835.95 15.26 15.30 419.10
935.65 19.12 19.19 469.41
22
24
839.28 15.38 15.43 420.77
938.98 19.26 19.33 471.08
24
26
842.60 15.51 15.55 422.45
942.30 19.40 19.47 472.76
26
28
845.92 15.63 15.68 424.12
945.62 19.54 19.61 474.43
28
30
849.25 15.75 15.80 425.79
948.95 19.68 19.75 476.10
30
32
852.57 15.88 15.93 427.47
952.27 19.82 19.89 477.78
32
34
855.89 16.00 16.05 429.15
955.59 19.96 20.03 479.46
34
36
859.22 16.12 16.18 430.82
958.92 20.10 20.17 481.14
36
38
862.54 16.25 16.30 432.50
962.24 20.24 20.31 482.83
38 '
40
865.86 16.38 16.43 434.18
965.56 20.38 20.45 484.51
40
42
869.19 16.50 16.55 435.86
968.89 20.52 20.59 486.19
42
44
872.51 16.63 16.68 437.54
972.21 20.66 20.74 487.87
44
46
875.83 16.76 16.81 439.21
975.53 20.80 20.88 489.56
46
48
879.16 16.89 16.94 440.89
978.86 20.94 21.03 491.24
48
50
882.48 17.02 17.07 442.57
982.18 21.09 21.17 492.92
50
52
885.80 17.14 17.19 444.25
985.50 21.23 21.31 494.60
52
54
889.13 17.27 17.32 445.93
988.83 21.37 21.46 496.28
54
56
892.45 17.40 17.45 447.60
992.15 21.51 21.60 497.96
56
58
895.77 17.53 17.58 449.28
995.47 21.65 21.75 499.65
58
60
899.10 17.66 17.71 450.95
998.80 21.80 21.89 501.32
60
FUNCTIONS OF A ONE-DEGREE CURVE 213
10
11
'
L C. M. E. T.
L. C. M. E. T.
/
998.8 21.80 21.89 501.32
1098.4 26.38 26.50 551.74
2
1002.1 21.94 22.03 503.00
1101.7 26.54 26.86 553.42
2
4
1005.4 22.09 82.18 504.68
1105.0 26.70 26.83 555.10
4
6
1008.8 22.24 22.33 506.36
1108 3 26.86 26.99 556.78
6
8
1012.1 22.39 22.48 508.04
1111.7 27.02 27.16 558.46
8
10
1015.4 22.54 22.63 509.72
1115.0 27.19 27.32 560.14
10
12
1018.7 22.68 22.78 511.40
1118.3 27.35 27.48 561.82
12
14
1022 32.83 22.93 513.08
1121.6 27.51 27.65 563.50
14
16
1025.4 22.98 23.08 514.76
1124.9 27.67 27.81 565.18
18
18
1028.7 23.13 23.23 516.44
1128.2 27.83 27.98 566.86
18
20
1032.0 23.28 23.38 518 12
1131 6 28.00 28.14 568.54
20
22
1035.3 23.43 23.53 519.80
11349 26.17 28.30 570.22
22
24
1038.6 23.58 23 68 521.48
1138.2 28.34 28.47 571.90
24
26
1042.0 23.73 23.84 523.16
1141.5 28.50 2864 573.58
26
28
1045.3 23.88 23.99 524.85
1144.8 28.67 28.81 575 27
28
30
1048.6 24.04 24.14 526.53
1148.1 2884 28.98 576.95
30
32
1051.9 24.19 24.30 528.21
1151.5 29.00 29.14 578.63
32
34
1055.2 24.34 24.45 529.89
1154.8 29.17 29.31 580.32
34
36
1058.6 24.49. 24.60 531.57
1158.1 29.34 29.48 582.00
36
.38
1061.9 24.64 24.76 53325
1161.4 29.50 29.05 583.69
38
40
1065.2 24.80 24.91 534.93
1164.7 29.67 29.82 585.37
40
42
1068.5 24.95 25.06 536.65
1168.0 29.84 29.99 587.05
42
44
1071.8 25.11 25.22 53829
1171 4 30.01 30.17 588.74
44
46
1075.2 25.27 25.38 539.97
1174.7 30.18 30.34 590.42
46
48
1078.5 25.43 25.54 541.65
1178.0 30.35 30.52 592.11
48
50
1081.8 25.59 25.70 54333
1181.3 30.53 3069 593.79
50
52
1085.1 25.74 25.86 545.01
1184.6 30.70 30.86 595 47
52
54
1088.4 25.90 26.02 546.69
1187.9 30.87 31.04 597.16
54
56
10U1.8 26.06 26.18 548.37
1191.3 31.04 31.21 598.84
56
58
1095.1 26.22 26.34 550 06
1104.6 31.21 31.39 600.53
58
60
1098.4 26.38 26.50 551.74
1197.9 31.39 31.56 602.22
60
12
13
L. C. M. E. T.
L. C. M. E. T.
1197.9 31.39 31.56 602.22
1297.3 36.83 37.07 652.87
I
1201.2 31.57 31.73 603.91
1300.6 3". 02 37.26 654.56
2
4
1204.5 31.74 31.91 605.60
1303.9 3". 21 37.46 656.25
4
6
1207.8 31.93 32.09 607.28
1307.2 3". 40 37.65 657.93
6
8
1211 1 32.09 32.27 608.97
1310.5 3 .59 37.85 659.62
8
10
1214.5 32.27 32.45 610.66
1313.8 3-79 38.04 661.31
10
12
1217.8 32.45 32.63 612.35
1317.2 3". 98 38.23 663. CO
12
14
1221.1 32.62 32.81 614.04
1*20.5 38.17 38.43 664.69
14
16
1224.4 32.80 32.99 615.72
1323.8 38.86 38. C2 666.37
16
18
1227.7 32.97 33.17 617.41
1327.1 38.55 38.82 668.06
18
20
1231.0 33.15 33.35 619.10
1330.4 38.75 39.01 669.75
20
ss
1231.3 33.33 33.53 6'.!0.79
1333.7 38.95 39. 2C 671.44
22
24
1237.7 33.51 33.72 622 48
1337.0 39.15 39.40 673.13
24
26
1241.0 33.69 33.90 624.16
1340.3 39.35 39.60 674.81
26
28
1244.3 33.87 34.09 6. '5. 85
1343.6 39.54 39.80 676.51
28
30
1247.6 34.06 34.27 627.55
1346.9 39.74 40.00 678.20
30
32
1250.9 34.24 34 45 629.24
1350.3 39.94 40.19 679.89
32
34
1254.2 34.42 34 64 630.93
1353.6 40.13 40.39 681.58
34
36
1257.5 34,60 34 82 632.61
1356.9 40.33 40 59 683.26
36
38
1260.8 34.78 35.01 634.30
1360.2 40.52 40.79 684.95
38
40
1264.2 34 97 35.19 635.99
1363,5 40.71 40.99 686.64
40
42
1267.5 35.16 35.37 637.68
1366.8 40.91 41.19 68833
42
44
1270.8 36.34 35.56 639.37
1370.1 41.11 41.40 690.02
44
I 46
1274.1 35.53 35.75 641.05
1373.4 41.31 41.60 691.70
46
48
1277.4 35.71 85.94 642.74
1376.7 41.51 41.81 693.39
48
50
1280.7 35.90 36.13 644.43
1380.0 41.71 42.01 695.08
50
52
1284.0 36.09 36.31 646.12
1383.4 41.91 4221 696.77
52
54
1287.4 36.27 36.50 647.81
1386.7 42.11 42.42 698.46
54
56
1290.7 36.46 30.09 619.49
1390.0 4231 42.62 700.14
56
58
1294.0 36.64 36.88 651.18
1393.3 42.51 42.83 701.83
58
60
1297.3 36.83 3r.07 652.87
1396.6 42.71 43.03 703.53
60
214 FUNCTIONS OF A ONE-DEGREE CURVE
14
16
/
L. C. M. E. T.
L. C. M. E. T.
/
1396.6 42.71 43.03 ?03.53
1495.9 49.02 49.44 754.85
2
1399.9 42.92 43.23 705.23
1499.2 49.24 49.66 756.05
2
4
1403.2 43.12 43.44 706.92
1502.5 49.46 49.89 757.74
4
6
1406.5 43.33 43.65 708.62
1505.8 49.68 50.11 759.44
6
8
1409.8 43.53 43.86 710.31
1509.1 4990 50.34 761.13
8
10
1413.1 43.74 44.07 712.01
1512.4 50.12 50.56 762.83
10
12
1416.5 43.94 44.28 713.71
1515.7 50.34 50.78 764.53
12
14
1419.8 44.15 44.49 715.40
1519.0 50.56 51.01 766.22
14
16
1423.1 44.35 44.70 717.10
1522.3 5078 51.23 767.92
16
18
1426.4 44.56 44.91 718.79
1525.6 51.00 51.46 769.61
18
20
1429.7 44.77 45.12 720.49
1528.9 51.22 51.68 771.31
20
22
1433.0 44 98 45.33 722.20
1532.2 51.44 51.90 773.01
22
24
1436.3 45.19 45.54 723.89
1535.5 51.67 52.13 774.70
24
26
1439.6 45.40 45.76 725.59
1538.8 51.89 52.36 776.40
26
28
1442.9 45.61 45.97 727.28
1542.1 52.12 52.59 778.09
28
30
1446 2 45.82 46.18 728.97
1545.4 52.34 52.82 779.79
30
32
1449.6 46.03 46.40 730.66
1548.7 52.57 53.05 781.49
32
34
1452.9 4^.24 46.61 732.35
1552.0 52.79 53.28 783.19
34
36
1456.2 46.45 46.82 734.05
1555.3 53.02 53.51 784.89
36
38
14M).5 46.66 47.04 785.74
1558.6 53.24 53.74 786.59
38
40
1462.8 46.87 47.25 737.43
1561.9 53.47 53.97 788.29
40
42
1460.1 47.08 47.46 739.12
1585.2 53.69 54.20 789.99
42
44
1469.4 47.30 47.68 740.81
1568.5 53.92 54.44 791.69
44
46
1472.7 47.51 47.90 742.51
1571.8 54.15 54.67 793.39
46
48
1476.0 47.73 48.12 744.20
1575.1 54.38 54.91 795.09
48
50
1479.3 47.94 48.34 745.89
1578.4 54.61 55.14 796.79
50
52
1482.7 48.16 48.56 747.58
1581.7 54.84 55.37 798.49
52
54
1486.0 48.37 48.78 749.27
1585.0 55.07 55.61 800.19
54
56
1489.3 48.59 49.00 750.97
1588.3 55.30 55.84 801.89
56
58
1492.6 48.80 49.22 752.66
1591.6 5553 56.08 803.59
58
60
1495.9 49.02 49.44 754.35
1594.9 55.76 56.31 805.29
60
16
17
L. C. M. E. T.
L. C. M. E. T.
/
1594.9 55.76 56.31 805.29
1693.9 62.94 63.64 856.35
2
1598.2 55.99 56.54 806.99
1697.2 63.18 63.89 858.05
2
4
1601.5 56. S3 56.78 808.64
1700.5 63.43 64.15 859.76
4
6
1604.8 56.46 57.02 810.39
1703.8 63.68 64.40 861.46
6
8
1608.1 56.70 57.26 812.09
1707.1 63.93 64.66 863.16
8
10
1611.4 56.93 57.50 813.79
1710.4 64.18 64.91 864.87
10
12
1614.7 57.17 57.74 815.49
1713.7 64.42 65.16 866.57
12
14
1618.0 57.40 57.98 817.19
1716.9 64.67 65.42 868.27
14
16
1621.3 57.64 58.22 818.89
1720.2 64.92 65.67 869.98
16
18
1624.6 57.87 58.46 820.59
1723.5 65.17 65.93 871.68
18
20
1627.9 58.11 58.70 822.29
1726.8 65.42 66.18 873.38
20
22
1631.2 58.34 58.94 823.99
1730.1 65.67 66.43 875.09
22
24
1634.5 58.58 59 19 825.69
1733.4 65.93 66.69 876.79
24
26
1637.8 58.82 59.43 82739
1736.7 66.18 66.95 878.49
26
28
1641.1 59.06 59.68 829.09
1740.0 66.44 67.21 880.20
28
30
1644.4 59.30 59 92 83079
1743.3 66.69 67.47 881.90
30
32
1647.7 59.54 60.16 832.49
1746.6 66.94 67.72 883.61
32
34
1651.0 59.78 6041 834.20
1749.9 67.20 67.98 885.32
34
36
1654.3 60.02 60.65 835.90
1753.2 67.45 68.24 887.02
36
38
1657.6 60.26 60.90 837.61
1756.5 67.71 68.50 888.73
38
40
1660.9 60.50 61.14 839.31
1759.8 67.96 68.76 890.44
40
42
1664.2 60.74 61.39 841.01
1763.1 68.21 69.03 892.15
42
44
1667.5 60.99 61.64 842.72
1766.3 68.47 69.29 893.86
44
46
1670.8 61.23 61.89 844.42
1769.6 68.73 69.56 895.56
46
48
1674.1 61.48 62.14 846.13
1772.9 68.99 69.82 897.27
48
50
1677.4 61.72 62.39 847.83
1776 2 69.25 70.09 898.98
50
52
1680.7 61.96 6-^.64 849.53
1779.5 69.50 70.36 900.69
52
54
1684.0 62.21 62.89 851 24
1782.8 69.76 70.62 902.40
54
56
1687.3 62.45 63.14 852.94
1786.1 70.02 70.89 904.10
56
58
1690.6 62.70 63 39 854.65
1789.4 70.28 71.17 905.81
58
60
1693.9 62.94 63 64 856 35
1792.7 70.54 71.42 907.52
60
FUNCTIONS OF A ONE-DEGREE CURVE 215
18
19
/
L. C. M. E. T.
L. C. M. E. T.
/
1792.7 70.54 71.42 907.52
1891.5 78.58 79.65 958.86
2
1796.0 70.80 71.69 909.23
1894.8 78.86 79.94 960.57
2
4
1799.3 71.06 71.96 910.94
1898.1 79.13 80.22 962.30
4
6
1802.6 71.33 72.23 912.65
1901.3 79.41 80.51 964.00
6
8
1805.9 71.59 72.50 914.36
1904.6 79.68 80.79 965.72
8
10
1809.2 71.85 72.77 916.07
1907.9 79.96 81.08 967.43
10
12
1812.5 72.12 73.04 917.78
1911.2 80.24 81.37 969.15
12
14
1815.7 72.38 73.31 919.49
1914.5 80.51 81.65 970.86
14
16
1819.0 72.64 73.58 921.20
1917.8 80.79 81.94 972.58
16
18
1822.3 72 91 73.85 922.91
1921.0 81.07 82.22 974.29
18
20
1825.6 73.17 74.12 924.63
1924.3 81.35 82.51 976.01
20
22
1828.9 73.43 74.39 926.34
1927.6 81.63 82.80 977.72
22
24
1832.2 73.70 74.67 928.05
1930.9 81.91 83.09 979.44
24
26
1835.5 73.97 74.94 929.76
1934.2 82.20 83.38 981.15
26
28
1838.8 74.24 75.22 931.47
1937.5 82.48 83.67 982.86
28
30
1842.1 74.51 75.49 933.18
1940.7 82.76 83.97 984.58
30
32
1845.4 74.77 75.77 934.89
1944.0 83.05 84.26 986.30
32
34
1848.7 75.04 76.04 936.60
1947.3 83.33 84.55 988.02
34
36
1852.0 75.31 76.32 938.32
1950.6 83.61 84.84 989.74
36
38
1855.3 75.58 76.59 940.03
1953.9 83.90 85.13 991.46
38
40
1858.6 75.85 76.87 941.74
1957.2 84.18 85.43 993.18
40
42
1861.9 76.12 77.14 943.45
1960.4 84.47 85.73 994.90
42
44
1865.1 76.39 77.42 945.16
1963.7 84.75 86.02 996.62
44
46
1868.4 76.67 77.70 946.88
1967.0 85.04 86.32 998.34
46
48
1871.7 76.94 77.98 948.59
1970.3 85.32 86.61 1000.0
48
50
1875.0 77.21 78.26 950.30
1973.6 85.61 86.91 1001.8
50
52
1878.3 77.49 78.53 952.01
1976.9 85.90 87.21 1003.5
52
54
1881.6 77.76 78.81 953.72
1980.1 86.19 87.50 1005.2
54
5(5
1884.9 78.03 79.09 955.44
1983.4 86.47 87.80 1006.9
56
58
1888.2 78.31 79.37 957.15
19S6.7 86.76 88.09 1008.6
58
60
1891.5 78.58 79.65 958.86
1990.0 87.05 88.39 1010.4
60
20
21
/
L. C. M. E. T.
L. C. M. E. T.
/
1990.0 87.05 88.39 1010.4
2088.5 95.95 97.58 1062.0
2
1993.3 87.34 88.69 1012.1
2091.8 96.26 97.90 1063.7
2
4
1996.6 87.63 88.99 1013.8
2095.0 96.56 98.21 1065.4
4
6
1999.8 87.92 89.29 1015.5
2098.3 96.87 98.53 1067.2
6
8
2003.1 88.21 89.59 1017.2
2101.6 97.17 98.84 1068.9
8
10
2006.4 88.50 89.89 1019.0
2104.9 97.48 99.16 1070.6
10
18
2009.7 88.79 90.19 1020.7
2108.1 97.79 99.48 1072.4
12
14
2013.0 89.08 90.49 1022.4
2111.4 98.09 99.79 1074.1
14
16
20163 89.37 90.79 1024.1
2114.7 98.40 100.1 1075.8
16
18
2019.5 89.66 91.09 1025.8
2118.0 98.70 100.4 1077.5
18
20
2022.8 89.96 91.40 1027.6
2121.2 99.00 JOO. 7 1079.3
20
22
2026.1 90.25 91.71 1029.3
2124.5 99.30 J01.1 1081.0
22
24
2029-4 90.55 92.01 1031.0
2127.8 99.60 101.4 1082.7
24
26
2032.7 90.85 92.32 1032.7
2131.0 99.90 101.7 1084.4
26
28
2036.0 91.15 92.62 1034.4
2134.3 100.2 102.0 1086.2
28
30
2039.2 91.45 92.93 1036.1
2137.6 100.5 102.3 1087.9
30
32
2042.5 91.74 93.24 1087.9
2140.9 100.8 102.7 1089.6
32
34
2045.8 92.04 93.54 1039.6
2144.1 101.1 103.0 1091.3
34
36
2049.1 92.34 93.85 1041.3
2147.4 101.4 103.3 1093.1
36
38
2052.4 92.64 94.15 1043.0
2150.7 101.7 103.6 1094.8
38
40
2055.7 92.94 94.46 1044.8
2154.0 102.1 104.0 1096.5
40
42
2058.9 98.24 94.78 1046.5
2157.2 102.4 104.3 1098.3
42
44
2062.2 93.54 95.09 1048.2
2160.5 102.7 104.6 1100.0
44
46
2065.5 93.84 95.40 1049.9
2163.8 103.0 104.9 1101.7
46
48
2068.8 94.14 85.71 1051.7
2167.1 103.3 105.3 1103.4
48
50
2072.1 94.44 96.03 1053.4
2170.3 103.6 105.6 1105.2
50
52
2075.4 94.74 96.34 1055.1
2173.6 103.9 105.9 1106.9
52
54
2078.6 95.04 96.65 1056.8
2176.9 104.2 106.3 1108.6
54
56
2081.9 95.34 96.96 1058.6
2180.1 104.5 106.6 1110.3
56
58
2085.2 95.64 97.27 1060.3
2183.4 104.8 106.9 1112.1
58
60
2088.5 95.95 97.58 1062.0
2186.7 105.2 107.2 1118.8
60
216 FUNCTIONS OF A ONE-DEGREE CURVE
22
23
L. C. M. E. T.
L. G. M. E. T.
2186.7 105.2 107.2 1113.8
2284.8 115.0 117.4 1165.8
2
2190.0 105.6 107.6 1115.5
2288.1 115.3 117.7 1167.5
2
4
2193.2 105.9 107.9 1117.3
2291.3 115.7 118.1 1169.2
4
6
2196.5 106.2 108.2 1119.0
2294.6 116.0 118.4 1171.0
6
8
2199.8 106.5 108.6 1120.7
2297.8 116.4 118.8 1172:7
8
10
2203.0 106.8 108.9 1122.4
2301.1 116.7 119.1 1174.4
10
12
2206.3 107.1 109.2 1124.2
2304.4 117.0 119.5 1176.2
12
14
2209.6 107.4 109.6 1125.9
2307.6 117.4 119.8 1177.9
14
16
22129 107.7 109.9 1127.6
2310.9 117.7 120.2 1179.7
16
18
2216.1 108.0 110.2 1129.4
2314.1 118.1 120.5- 1181.4
18
20
2219.4 108.4 110.6 1131.1
2317.4 118.4 120.9 1183.1
20
22
2222.7 108.7 110.9 1132.8
2320.7 118.7 121.2 1184.9
22
24
2225.9 109.0 111.2 1134.6
2323.9 119.1 121 6 1186.6
24
26
2229.2 109.4 111.6 1136.3
2327.2 119.4 121.9 1188.4
26
28
2232.5 109.7 111.9 1138.0
2330.4 119.8 122.3 1190.1
28
30
2235.7 110.0 112.3 1139.7
2333.7 120.1 122.6 1191.8
30
32
2239.0 110.4 112.6 1141.5
2337.0 120.4 123.0 1193.6
82
34
22423 110.7 112.9 1143.2
2340.2 120.8 123.3 1195.3
34
36
2245.6 111.0 113.3 1144.9
2343.5 121.1 123.7 1197.1
36
38
2248.8 111.4 113.6 1146.7
2346.7 121.5 124.1 1198.8
38
40
2252.1 111.7 113.9 11J8.4
2350.0 121.8 124.4 1200.5
40
42
2255.4 112.0 114.3 1150.1
2353.3 122.1 124.8 1202.3
42
44
2258.6 112.3 114.6 1151.9
2356.5 122.5 125.1 1204.0
44
46
2261.9 112.7 115.0 1153.6
2359.8 122.8 125.5 1205.8
46
48
2265.2 113.0 115.3 1155.4
2303.0 123.2 125.8 1207.5
48
50
2268.4 113.3 115.7 1157.1
2366.3 123.5 126.2 1209.2
50
52
2271.7 113.7 116.0 1158.8
2369.6 123.8 126.6 1211.0
52
54
2275.0 114.0 116.3 1160.6
2372.8 124.2 126.9 1212.7
54
56
2278.3 114.3 116.7 116-2.3
2376.1 124.5 127.3 1214.5
56
58
2281.5 114.7 117.0 1164.0
2379.3 124.9 127.6 1216.2
58
60
2284.8 115.0 117.4 11G5.8
2382.6 125.2 128.0 1218.0
60
24
25
L. 0. M. E. T.
L C. M. E. T.
23S2.6 125.2 128.0 1218.0
2480.4 135.8 139.1 1270.3
2
2385.9 125.5 128.4 1219.7
2483.6 JJ6.2 139.5 1272.0
2
4
2389.1 125.9 128.7 1221.4
2486.9 136.5 139.9 1273.8
4
6
2392.4 126.2 129.1 1223.2
2490.1 136 9 140.3 1275.5
6
8
2395.6 126.6 129.5 1224.9
2493.4 137.2 140.6 1277.3
8
10
2398.9 126.9 129.8 1226.7
2496.6 137.6 141.0 1279.0
10
12
2402.2 127.3 130.2 1228.4
2499.9 138.0 141.4 1280.8
12
14
2405.4 127.6 130.6 1230.2
2503.1 1383 141 8 1282.5
14
1
2408.7 128.0 130.9 1231.9
2506.4 138.7 142.2 1284.3
16
18
2411.9 128.3 131.3 1233.6
2509.6 139.0 142.5 1286.1
18
20
2415.2 128.7 131.7 1235.4
2512.9 139.4 142.9 1287.8
20
22
2418.5 129.0 132.0 1237.1
2516.1 139.8 143.3 1289.6
22
24
2421.7 129.4 132.4 1233.9
2519.4 140.1 143.7 1291.3
24
26
2425.0 129.7 132.8 1240.6
2522.6 140.5 144.1 1293.1
26
28
2428.2 130.1 133 1 1242.4
2525.9 140.8 144.5 1294.8
28
30
2431.5 130.4 133.5 1244.1
2529 1 141.2 144.9 1296.6
30
32
2434.8 130.8 133.9 1215.8
2532.4 141.6 145.3 1298.3
32
34
2433.0 131.1 134.2 1247.6
2535.6 142.0 145.6 1300.1
34
36
2441.3 131.5 134.6 1249.3
2538.9 142.3 146.0 1301.8
36
38
2444.5 131.8 135.0 1251.1
2542.1 142.7 146.4 1303.6
38
40
2447.8 132.2 135.4 1252.8
2545.4 143.1 146.8 1305.3
40
42
2451.1 132.6 135.7 1254.6
2548.6 143.5 147.2 1307.1
42
44
2454.3 132.9 136.1 1256.3
2551.9 143.8 147.6 1308.8
44
46
2457.6 133.3 136.5 1258.1
2555.1 144.2 148.0 1310.6
46
48
2460.S 133.6 136.9 1259.8
2558.4 144.5 148 4 1312.4
48
50
2464.1 134.0 137.2 1261.5
2561.6 144.9 148.8 1314.1
50
52
2467.4 134.4 137.6 1263.3
2564.9 145.3 149.2 1315.9
52
54
2470.6 134.7 138.0 1265.0
2568.1 145.7 149.5 1317.6
54
56
2473.9 135.1 138.4 1266.8
2571.4 146.0 149.9 1319.4
56
58
2477.1 135.4 138.7 1268.5
2574.6 146.4 150.3 1321.1
58
60
2480.4 135.8 139.1 1270.3
2577.9 146.8 150.7 1322.9
60
FUNCTIONS OF A ONE-DEGREE CURVE 217
26
27*
/
L. C. M. . E. T.
L. C. M. E. T.
/
2577.9 146.8 150.7 1322.9
2675.3 158.3 162.8 1375.6
2
2581.1 147.1 151.1 1324.6
2678.5 158.6 163.2 1377.4
2
4
2584.4 147.5 151.5 1326.4
2681.8 159.0 163.7 1379.2
4
6
2587.6 147.9 151.9 1328.1
2685.0 159.4 164.1 1380.9
6
8
2590.9 148.3 152.3 1329.9
2688.2 159.8 164.5 1882 7
8
10
2594.1 148.7 152.7 1331.6
2691.5 160.2 164.9 1384.5
10
12
2597.4 149.1 153.1 1333.4
2694.7 160.6 165.3 1386.2
12
14
2600.6 149.4 153.5 1335.2
2698.0 181.0 165.7 1388.0
14
16
2603.9 149.8 153.9 1336.9
2701.2 161.4 1661 1389.8
16
18
2607.1 150.2 154.3 1338.7
2704.4 161.8 166.5 1391.5
18
20
2610.4 150.6 154.7 1340.4
2707.7 162.2 167.0 1393.3
20
22
2613.6 151.0 155.1 1342.2
2710.9 162.6 167.4 1395.0
22
24
2616.9 151.4 155.5 1343.9
2714.1 163.0 167.8 1396.8
24
26
2620.1 151.7 155.9 1345.7
2717.4 163.4 168.2 1398.6
26
28
2623.4 152.1 156.3 1347.4
2720.6 163.8 168.6 1400.3
28
30
2626.6 152.5 156.7 1349.2
2723.8 164.2 169.1 1402.1
30
32
2629.8 152.9 157.1 1351.0
2727.1 164.6 169.5 1403.9
32
34
2633.1 153.3 157.5 1352.7
2730.3 165.0 169.9 1405.6
34
36
26363 153.7 157.9 1354.5
2733.6 165.4 170.3 1407.4
36
38
2639.6 154.0 158.3 1356.2
2736.8 165.8 170.8 1409.2
38
40
2642.8 154.4 158.7 1358.0
2740.0 166.2 171.2 1410.9
40
42
2646.1 154.8 159.1 1359.8
2743.3 166.6 171.6 1412.7
42
44
2649.3 155.2 159.5 1361.5
2746.5 167.0 172.0 1414.5
44
46
2652.6 155.6 160.0 1363.3
2749.7 1674 172.5 1416.3
46
48
2655.8 156.0 160.4 1365.1
2753.0 167.8 172.9 1418.0
48
50
2659.1 156.3 160.8 1366.8
2756.2 168.2 173.3 1419.8
50
52
2662.3 156.7 161.2 1368.6
2759.5 168.6 173.7 1421.6
52
54
2665.6 157.1 161.6 13~0.4
2762.7 169.0 174.1 1423.3
54
56
2668.8 157 5 162.0 13?2.1
2765.9 169.4 174.6 1425.1
56
58
2672.1 157.9 162.4 1373.9
2769.2 169.8 175.0 1426.9
58
60
2675.3 158.3 162.8 1375.6
2772.4 170.2 175.4 1428.6
60
28
29
L. C. M. E. T.
L. C. M. E. T.
2772.4 170.2 175.4 1428.6
2869.4 182.5 188.5 1481.9
2
2775.6 170.6 175.8 1430.4
2872.6 182.9 189.0 1483.7
2
4
2778.9 171.0 176.3 1432.2
2875.8 183 3 189.4 1485.4
4
6
2782.1 171.4 176.7 1434.0
2879.1 183.7 189.9 1487.2
6
8
2785.3 171.8 177.1 1435.7
2882.3 184.2 190.3 1489.0
8
10
2788.6 172.2 177.6 1437.5
2885.5 184.6 190.8 1490.8
10
12
2791.8 178.6 178.0 1439.3
2888.7 185.0 191.2 1492.6
12
14
2795.0 173.0 178.4 1441.1
2892.0 185.4 191.7 1494.3
14
16
2798.3 173.4 178.9 1442.8
2895.2 185.8 192.1 1496.1
16
18
2801.5 173.8 179.3 1444.6
2898.4 186.3 192.5 1497.9
18
20
2804.7 174.3 179.7 1446.4
2901.6 186.7 193.0 1499.7
20
22
2808.0 174.7 180.2 1448.2
2904.8 187.1 193.5 1501.5
22
24
2811.2 175.1 180.6 1449.9
2908.1 187.5 193.9 1503.2
24
26
2814.4 175.5 181.0 1451.7
2911.3 188.0 194.4 1505.0
26
28
2817.7 175.9 181 5 1453.5
2914.5 188.4 194.8 1506.8
28
30
2820.9 176.3 181.9 1455.2
2917.7 188.8 195.3 1S08.6
30
32
2824.1 176.7 182.3 1457.0
2921.0 189.2 195.7 1510.4
32
34
2827.4 177.1 182.8 1458.8
2924.2 189.7 196.2 1512.1
34
36
2830.6 177.5 183.2 1460.6
2927.4 190.1 196.7 1513.9
36
38
2833.8 177.9 183.6 1462.3
2930.6 190.5 197.1 1515.7
38
40
2837.1 178.4 184.1 1464.1
2933.9 190.9 197.6 1517.5
40
4-2
2840.3 178.8 184.5 1465.9
2937.1 191.4 198.0 1519.3
42
44
2843 5 179.2 185.0 1467.7
2940.3 191.9 198.5 1521.0
44
46
2846.8 179.6 185.4 1469.5
2943.5 192.4 198.9 1522.8
46
48
2850.0 1800 185.9 1471.2
2946.8 192.8 199.4 1524.6
48
50
2853.2 180.4 186.3 1473.0
2950 193.2 199.8 1526.4
50
52
2856.5 180.8 186.8 1474.8
2953.2 193.6 200.3 1528.2
52
54
2859.7 181.2 187.2 1476.6
2956.4 194.0 200.8 1530.0
54
56
2862.9 181.6 187.6 1478.3
2959.6 194.4 201.2 1531.7
56
58
2866.2 1820 188.1 14801
2962.9 194.8 201.7 1533.5
58
60
2869.4 1825 188.5 1481.9
2966.1 195.2 202.1 15353
60
218 FUNCTIONS OF A ONE-DEGREE CURVE
80
31
/
L. C. M. E. T.
L. C. M. E. T.
2966.1 195.2 202.1 1535.3
3062.6 208.4 2163 1589.0
2
2969.3 195.6 202.6 1537.1
3065.8 208.8 216.8 1590.8
2
4
2972.5 190.1 203.1 1538.9
3069.0 209.3 217.2 1592.6
4
6
2975.7 196.5 -203.5 1540.7
3072.2 209.7 217.7 1594.4
6
8
2^79 197.0 X'04.0 1542.5
3075.4 210.2 218.2 1596.2
8
10
2982.2 197.4 204.5 1544 3
3078.6 210.6 218.7 1598.0
10
12
2985.4 197.8 204.9 154G.O
3081.8 211.1 219.2 1599.8
12
14
2988.6 198.2 205.4 1547.8
3085.0 211.5 219.6 1601.6
14
16
2991.8 198.6 2059 1549.6
3088.3 212.0 220.1 1603.4
16
18
2995.0 199.1 2063 1551.4
3091.5 212.4 220.6 1605.2
18
20
2998.3 199.5 206.8 1553.2
3094.7 212.9 221.1 1607.0
20
22
3001.5 199.9 207.3 1555.0
3097.9 213.3 221 6 1608.8
22
24
3004.7 200.4 207.7 1556.8
3101.1 213.8 222.1 1610.6
24
26
3007.9 200.8 208.2 1558.6
3104.3 214.2 222.6 1612.4
26
28
3011.1 201.3 208.7 1560.4
3107.5 214.7 223.0 1614.2
28
30
3014.3 201.7 209.1 1562.2
3110.7 215.1 223.5 1616.0
30
32
3017.6 202.1 209.6 1564.0
3113.9 215.6 224.0 1617.8
32
34
3020.8 202.6 210.1 1565.7
3117.1 216.0 224.5 1619.6
34
36
3024.0 203.0 210.5 1567.5
3120.3 216.5 225.0 1621.4
36
38
3027.2 203.5 211.0 1569.3
3123.5 216.9 225.5 1623.2
38
40
3030.4 203.9 211 5 1571.1
3126.7 217.4 226.0 1625.0
40
42
3033.6 204.3 212 1572.9
3129.9 217.8 226.5 1626.8
42
44
3036.9 204.8 212.4 1574.7
3133.1 218.3 227.0 1628.6
44
46
3040.1 205.2 212.9 1576.5
3136.4 218.7 227.5 1630.5
46
48
3043.3 205.7 213.4 1578.3
3139.6 219.2 228.0 1632.3
48
50
3046.5 206.1 213.9 1580.1
3142.8 219.6 228.4 1634.1
50
52
3049.7 206.5 214.4 1581.9
3146.0 220.1 228.9 1635.9
52
54
3052.9 207 214.8 1583.7
3149.2 220.5 229.4 1637.7
54
56
3056.2 207.4 215.3 1585.5
3152.4 221.0 2- ) 9.9 1639.5
56
58
3059.4 207.9 215.8 1587.2
3155.6 221.5 230.4 1641.3
58
60
3062.6 208.4 216 3 1589.0
3158.8 2-J2.0 230.9 1643.1 60
32
33
L. C. M. E. T.
L. C. M. E. T.
o
3158.8 222.0 230.9 1G43.1
3254.9 236.0 246.1 1697 3
2
3162.0 2225 231.4 1644.9
3258 1 236.4 246.6 1699.1
2
4
3165.2 222.9 231.9 1646.7
3261.3 236.9 247.1 17009
4
6
3168.4 223.4 232.4 1648.5
3264.5 237.4 247.7 1702.7
6
8
3171.6 223.8 232.9 1650.3
3267 7 237.9 248.2 1704.5
8
10
3174.8 224.3 233.4 1652.1
3270.8 238.4 248.7 1706.4
10
12
3178.0 224 8 233.9 1653.9
3274 238 9 249.2 1708.2
12
14
3181.2 225.2 234.4 16557
3277 2 239 3 249.7 1710.0
14
16
3184.4 225.7 234.9 1657.5
32804 239.8 250.2 1711.8
16
18
3187.6 226.1 235.4 1659.3
3-J83.6 240.3 250.8 1713.6
18
20
3190.8 226.6 235.9 1661.1
3286.8 240.8 251.3 1715.5
20
22
3194.0 227.1 236.4 1662.9
3290 241.2 251.8 1717.3
22
24
3197 2 227.5 236 9 1664.7
3293.2 241 7 252.3 1719.1
24
26
3200.4 228.0 237.4 1666 5
3296.4 242.2 252.9 1720.9
26
28
3203.6 228.4 237.9 1668.3
3299.6 242.7 253.4 1722.7
28
30
3206.8 228 9 238.4 1670.1
3302.7 2432 253.9 1724.6
30
32
3210.0 229.4 239.0 1671.9
3305 9 243.6 254.4 1726.4
32
34
3213.2 229 8 239.5 1673.7
3309 1 244.1 255.0 1728.2
34
36
3216.5 230.3 240.0 1675.5
3312.3 244.6 255.5 1730.0
36
88
8219.7 230.7 240.5 1677.4
33155 245.1 256.0 1731.8
38
40
3222.9 231 2 241.0 1679.2
3318.7 245.6 256 5 1733.6
40
42
32261 231.7 241.5 1681.0
3321.9 2460 2571 1735.5
42
44
3629.3 232.2 242.0 1682.8
3325.1 246.5 257.6 1737.3
44
46
3232.5 232.6 242.5 1684.6
3328.3 247.0 258.1 1739.1
46
48
3235.7 233.1 243.0 16864
3331.5 247 5 258 6 1740.9
48
50
3238.9 233.5 243.5 1688.2
3334.6 248.0 259.2 1742.7
50
52
3242.1 234.0 244 1 1690.0
3337 8 248.4 259.7 1744.6
52
54
3245.3 234.5 244.6 1691.8
3341.0 248.9 260 2 1746.4
54
56
3248.5 2350 245.1 1693.7
3344-2 249.4 260,8 1748.2
56
58
3251.7 235.5 245.6 1695 5
3347.4 249.9 261.3 1750.0
58
60
3254.9 236.0 246.1 1697.3
3350-6 250.4 261 .B 1751.8
60
FUNCTIONS OF A ONE-DEGREE CURVE 219
34
35
/
L. O. M. E. T.
L. C. M. E. T.
3350.6 250.4 261.8 1751.8
3446.1 265.2 278.1 1806.7
2
3353.8 250.8 262.3 1753.7
3449.3 265.7 278.6 1808.5
2
4
3357.0 251.2 262.9 1755.5
3452.5 266.2 279.2 1810.3
4
6
3360.1 251.7 263.4 1757.3
3455.6 266.7 279.7 1812.2
6
8
3363.3 252.2 204.0 1759.1
3458.8 267.2 280.3 1814.0
8
10
3366.5 252.7 264.5 1761.0
3462.0 267*7 280.8 1815.8
10
12
3369.7 253.2 265.0 1762.8
3465.2 268.2 281.4 1817.7
12
14
3372.9 253.7 265.6 1764.6
3468.3 268.7 281.9 1819.5
14
16
3376.1 254.2 266.1 766.4
3471.5 269.2 282.5 1821.3
16
18
3379.2 254.7 266.7 768.3
3474.7 269.7 283.0 1823.2
18
20
3382.4 255.2 267.2 1770.1
34V7.9 270.2 283.6 1825.0
20
22
3385.6 255.7 267.7 771.9
3481.0 270.7 284.2 1826 8
22
24
3388.8 256.2 268.3 773.7
3484.2 271.2 284.7 18'28.7
24
26
339-2.0 256.7 268.8 775.6
3487.4 271.7 285.3 1830.5
26
28
3395.2 257.2 269.3 777.4
3490.6 272.2 285.9 1832.3
28
30
3398.3 257.7 269.9 779.2
3493.7 272.7 286.4 1834.2
30
32
3401.5 258.2 270.4 781.0
3496.9 273.2 287.0 1836.0
32
34
3404.7 258.7 271.0 782.9
3500.1 273. Y 287.5 1837.8
34
36
3407.9 259 2 271.5 784.7
3503.3 274.2 288.1 1839 7
36
38
3411.1 259.7 2720 1786.5
3506.5 274.7 288.7 1841.5
38
40
3414.3 260.2 272.6 1788.4
3509.6 275.2 289,2 1843.4
40
42
3417.4 260.7 273.1 1790.2
3512.8 275.7 289.8 1845.2
42
44
3420.6 261.2 273.7 1792.0
3516.0 2762 290.4 1847.1
44
46
3423.8 261.7 274.2 1793.9
3519.2 276.7 290.9 1848.9
46
48
3427.0 262.2 274.8 1795.7
35-22.3 277.2 291.5 1850.7
48
50
3430.2 262.7 275.3 1797.5
3525.5 277.7 292.0 185'2.6
50
52
3433.4 263.2 275.9 1799.3
3528.7 278.2 292.6 1854.4
52
54
3436.5 263.7 276.4 1801.2
3531.9 278.7 293.2 1856.3
54
56
3439.7 264.2 277.0 1803.0
3535.0 279.2 293.7 1858.1
56
58
3442.9 264.7 277.5 1804.8
3538.2 279.8 294.3 1859.9
58
60
3446.1 265.2 278.1 1806.7
3541.4 280.4 294.9 1861.8
60
36
37
/
L. C. M. E. T.
L. C. M. E. T.
/
3541.4 280.4 294.9 1861.8
3636.3 296.1 312.3 1917.3
2
3544.6 280 9 295.4 1863.6
3639.5 296.6 312.8 1919.1
2
4
3547.7 281.4 296.0 1865.5
3642 6 297 1 313.4 1921.0
4
6
3550.9 281.9 296.6 1867.3
3645.8 297.7 314.0 1922.8
6
8
3554.0 282.5 297.2 1869.2
3648.9 298.2 314.6 1924.7
8
10
3557.2 283.0 297.7 1871.0
3652.1 298.7 315.2 1926.5
10
12
3560.4 283.5 298.3 1872.9
3655.2 299.3 315.8 1928.4
12
14
3563.5 284.0 298.9 1874.7
3658.4 299.8 316.4 1930 2
14
16
3566.7 284.6 299.5 1876.5
3661.6 300.3 317.0 1932.1
16
18
3569.9 285.1 300.0 187'8.4
3061.7 300.9 317.5 1933.9
18
20
3573.0 285.6 300.6 1880.2
3667.9 301.4 318.1 1935.8
20
22
3576.2 286.1 301.2 1882.1
3671.0 301.9 318.7 1937.6
22
24
3579.4 286.7 301.8 1883.9
3674.2 302.5 319.3 1939.5
24
26
3582.5 2S7.2 302.3 1885.8
3677.3 303.0 319.9 1941.3
26
28
3585.7 287.7 302.9 1887.6
3680.5 303.5 320.5 1943.2
28
30
3588.8 288.2 303.5 1889.5
3683.6 304.1 321.1 1945.0
30
32
3592.0 288.8 304.1 1891.3
3686.8 304.6 321.7 1946.9
32
34
3595.2 289.3 304.6 1893.2
3690.0 305.1 322.3 1948.8
34
36
3598.3 289 8 305.2 1895.0
3693.1 305.7 322.9 1950.6
36
38
3601.5 290.3 305.8 1896.9
3696.3 306.2 323.5 1952.5
38
40
3604.7 290.9 306.4 1898.7
3699.4 306.7 324.2 1954.4
40
42
3607.8 291.4 307.0 1900.6
3702.6 307.3 324.8 1956.2
42
44
3611.0 291.9 307.5 1902.4
3705.7 307.8 325.4 1958.1
44
46
3614.1 292.4 308.1 1904.3
3708.9 308.3 326.0 1960.0
46
48
3617.3 293.0 308.7 1906.1
3712.1 308.9 3266 1961.8
48
50
3620.5 293.5 309.3 1908.0
3715 2 309.4 327 2 1963. V
50
52
3623.6 294.0 309.9 1909.8
3718.4 309.9 327.8 1965.5
52
54
3626.8 294.5 310.5 1911.7
3721 5 310.5 3-28.4 1967.4
54
56
3630.0 295.1 311.1 1913.5
3724.7 311.0 329.0 1969.3
56
58
3633.1 295.6 311.7 1915.4
3727.8 311.6 329.6 1971.1
58
60
3636.3 296.1 312.3 1917.3
3731.0 312.2 330.2 1973.0
60
220 FUNCTIONS OF A ONE-DEGREE CURVE
38
39
1
/
L. C. M. E. T.
L. C. M E. T.
3731.0 312.2 330.2 1973.0
3825.5 328-7 348.7 2029.1
2
3734.1 312.7 330.8 1974.9
3828.6 329.2 349 3 2031.0
2
4
3737.3 313.3 331.4 1976-7
3831.8 329.8 349.9 2032 9
4
6
3740.4 313.8 332.0 1978.6
3834.9 330-3 350.6 2034.7
6
8
3743.6 314.4 332.6 1980.5
3838.0 330.9 351.2 2036.6
8
10
3746.7 314.9 333.2 1982.3
3841.2 331 5 351.8 2038.5
10
12
3749.9 315.5 333.8 1984.2
3844 3 332.0 352-4 8040.4
12
14
37530 3160 334-5 1986.1
3847.4 332.6 358.1 2042 3
14
16
37562 316.6 335.1 1987.9
3850.6 333.2 353.7 2044.1
16
18
3759.3 317.1 335 7 1989.8
3853 7 333 7 354.3 2046.0
18
20
3762 5 317.7 336 3 1991.7
3856.8 334.3 354.9 2047.9
20
22
3765.6 318 2 336 9 1993-6
3860 334.9 355.6 2049.8
22
24
3768.8 318.8 337.5 1995.4
3863.1 335.4 356.2 2051.7
24
26
3771 9 319.3 338.1 1997.3
3866.2 336-0 356.9 2053.5
26
28
3775.1 319.9 338.7 1999.2
3869.4 336.6 357 5 2055.4
28
30
3778.2 3204 339.4 2001.0
3872.5 337.1 358.1 2057-3
30
32
3781.4 321.0 340.0 2002.9
3875 6 337 7 358.8 2059.2
32
34
3784 5 321.5 340-6 2004.8
3878.8 338.3 359 4 2061.1
34
36
3787.7 322.1 341.2 2006.6
3881.9 338.8 360.1 2063.0
36
38
37908 322.6 341.8 2008.5
3885.0 339 4 360.7 2064-8
38
40
3794.0 338.2 342.4 2010 4
3888.2 340.0 361.3 2066.7
40
4-2
37971 323.7 343.1 2012.3
3891.3 340.5 362.0 2068 .6
42
44
3800.3 324.3 343.7 2014.1
3894 4 341 1 362.6 2070.5
44
46
3803.4 324.8 344.3 2016
3897.6 341.7 363.3 2072.4
46
48
3806.6 325.4 344.9 2017.9
3900 7 342 2 363.9 2074 2
48
50
3809.7 325 9 345.6 2019.7
3903.8 342.8 364.5 2076 1
50
52
3812.9 3265 346.2 2021.6
3907.0 343 4 365.2 2078.0
52
54
3816.0 3270 346.8 2023.5
3910.1 343.9 365.8 2079.9
54
56
3819.2 327.6 347.4 2025 4
3913.2 344.5 3665 2081.8
56
68
3822.3 323.1 3481 2027.2
3916.4 345 1 367.1 2083.7
58
60
3825.5 328.7 348-7 2029.1
3919 5 345.6 367.7 2085-5
60
40
41
L. C. M. E. T.
L. C. M. E. T.
3919.5 345.6 367.7 2085.5
4013.4 362.9 387.4 2142.3
2
3922.6 346.1 368.4 2087 4
4016.5 G63.4 888.1 2144.2
2
4
3925.8 346 7 309 2089.3
4019.6 364.0 388.8 2146.1
4
6
3928.9 347.2 369.7 2091 2
4022.7 364.5 389.4 2148.0
6
8
3932 347.8 370.3 20H3.1
4025.9 365.1 390 1 2149.9
8
10
3935.1 348.4 371.0 2095
4029.0 365.6 390.7 2151.9
10
12
3938.3 348.9 371 6 2096 9
4032.1 366.2 391.4 2158.8
12
14
3941.4 349.5 372.3 2098.8
4035.2 366.8 392.1 2)55.7
14
16
3944 5 350.1 372.9 2100.7
4038.3 367.4 392.7 2157.6
16
18
8947.7 350.7 373.6 2102 6
4041.4 368.0 393.4 2159.5
18
20
3950.8 351.3 374.3 2104.5
4044.6 368.6 394.1 2161.4
20
2:2
3953.9 351 8 374.9 2106.3
4047.7 369.2 394.7 2163.3
22
24
3957.1 352.4 375.6 2108.2
4050.8 369.8 395.4 2165.2
24
26
3960.2 353.0 376.2 2110.1
4053.9 370.4 396.1 2167.1
26
28
3963.3 353.6 376.9 21120
4057.0 371.0 396.8 2169.0
28
30
3966.4 354.2 377.5 2113 9
4060.1 371.6 397.5 2170.9
30
32
3969.6 354.7 378.2 2115 8
4063.3 372.2 398.1 2172.8
32
34
3972.7 355.3 378.8 2117 7
4066.4 372.8 398.8 2174.7
34
36
3975.8 355.9 379.5 2119 6
4069.5 373.4 399.5 2176.6
36
38
3979.0 356.5 380 1 2121.5
4072.6 374.0 400.2 2178.5
38
40
3982.1 357.1 380.8 2123.4
4075.7 374.6 400.9 2180.4
40
4->
3985.2 357 6 381.4 2125 3
4078.8 375.2 401.5 2182.4
42
44
3988.4 358.2 382.1 2127.2
4082.0 375.8 402.2 2184.8
44
46
3991 5 358 8 382 8 2129.1
4085.1 376.4 402.9 2186.2
46
48
3994.6 359.4 383.4 2131.0
4088.2 377.0 403.6 2188.1
48
50
3997 7 360 384.1 2132.9
4091.3 377.6 404.3 2190.0
50
52
4000 9 360 5 384.8 2134.7
4094.4 378.2 404.9 2191.9
52
54
4004.0 361 1 385.4 2136.0
4097.5 378.8 405.6 2198.8
54
56
4007 1 361.7 386.1 2138.5
4100.7 379.4 406.3 2195.7
56
58
40103 362.3 3868 21404
4103.8 380.0 407.0 2197.6
58
60
4013.4 362.9 387.4 2142.3
4106.9 380.6 407.7 2199.5
60
FUNCTIONS OF A ONE-DEGREE CURVE 221
42
43
&
L. C. M. E. T.
L. C. M. E. T.
4106.9 380.6 407.7 2199.5
4200.1 398.7 428.6 2257.1
2
4110.0 381.2 408.3 2:201.4
4203.2 399.3 429.3 2259.0
2
4
4113.1 381.8 409.0 2-J03.3
4206.3 399.9 430.0 2261.0
4
6
4116.2 382.4 409.7 2205.3
4209.4 400.5 430.7 2262.9
6
8
4119.3 383.0 410.4 2207.2
4212.5 401.1 431.4 2264.8
8
10
4122.4 383.6 411.1 2209.1
4215.6 401.7 432.1 2266.7
10
12
4125.5 384.2 411.8 2211.0
4218.7 402.4 432.8 2268.7
12
14
4128.6 384.8 412.5 2212.9
4221.8 403.0 433.5 2270.6
14
16
4131.8 38r 4 413.2 2214.9
4224.9 403.6 434.2 2272.5
16
18
4134.9 38b 413.9 2216.8
4228.0 404.2 434.9 2274.5
18
20
4138.0 386 6 414.6 2218.7
4231.1 404.8 435.6 2276.4
20
22
4141.1 387.2 415.3 2220.6
4234.2 405.4 436.3 S278.3
22
24
4144.2 387.8 416.0 2222.5
4237.3 406.1 437.0 2280.2
24
26
4147.3 388.4 416.6 2224.4
4240.4 406.7 437.8 2282.2
26
28
4150.4 389.0 417.3 2226.4
4243.5 407.3 438.5 2284.1
28
30
4153.5 389.6 418.0 2228.3
4246.5 407.9 439.2 2286.0
30
32
4156.6 390,2 418.7 2230.2
4249.6 408.5 439.9 2288.0
32
34
4159.7 390.8 419.4 223'?. 1
4252.7 409.1 440.6 2289.9
34
36
4162.8 391.4 420.1 2234.0
4255.8 409.8 441.4 2291.8
36
38
4165.9 392.0 420.8 2236.0
4258.9 410.4 442.1 2293.8
38
40
4169.0 392.6 421.5 2237.9
4262.0 411.0 442.8 2295.7
40
42
4172.1 393.2 422.2 2239.8
4265.1 411.6 443.5 2297.7
42
44
4175.2 393.8 422.9 2241.7
4268.2 412.2 444.2 2299.6
44
46
4178.4 394.4 423.6 2243.6
4271.3 412.8 445.0 2301.5
46
48
4181.5 395.0 424.3 2245.6
4274.4 413.5 445.7 2303.5
48
50
4184.6 395.6 425.0 2247.5
4277.5 414.1 446.4 2305.4
50
52
4187.7 396.2 425.7 2249.4
4280.6 414.7 447.1 2307.3
52
54
4190.8 396.8 426.4 2251.3
4283.7 415.3 447.8 2309.3
54
56
4193.9 397.4 427.1 2253.3
4286.8 415.9 448.6 2311.2
56
58
4197.0 398.0 427.8 2255.2
4289.9 416.5 449.3 2313.1
58
60
4-,'00.1 398.7 428.6 2257.1
4293.0 417.2 450.0 2315.1
60
440
45
L. C. M. E. T.
L. C. M. E. T.
f
4293.0 417.2 450.0 2315.1
438"). 5 436.2 472.1 2373.4
2
4296 1 417.8 450.7 2317.0
4388.6 436.8 472.9 2375.4
2
4
4-299.2 418.4 451.5 2319.0
4391.7 437.5 473.6 2377.3
4
6
4302.2 419.1 452.2 2320.9
4394.7 438.1 474.4 2379.3
6 -
8
4305.3 419.7 452 9 2322.8
4397.8 438.8 475.1 2381.2
8
10
4308.4 420.3 453.7 2324.8
4400.9 439.4 475.9 2383.2
10
VI
4311.5 421.0 454.4 2326.7
4404.0 440.0 476.6 2385.2
12
14
4314.6 421.6 4f,5.1 2328.7
4407.0 440.7 477.4 2387.1
14
16
4317.7 422.2 455.9 2330.6
4410.1 441.3 478.1 2389.1
16
18
4320.7 422.9 456.6 2332.6
4413.2 442.0 478.9 2891.0
18
20
4323.8 423 5 457.3 2334.5
4416.3 442.6 479.6 2393.0
20
22
4326.9 424.1 458.1 2336.4
4419.3 443.2 480.4 2394.9
22
24
4330.0 424.8 458.8 2338.4
4422.4 443.9 481.1 2396.9
24
26
4333.1 425 4 459.5 2340 3
4425.5 444.5 481.9 2398.8
26
28
4336 2 426.0 460.3 2342.3
4428.6 445.2 4S2.6 2400.8
28
30
4339.2 426.7 461 2344.2
4431.6 445.8 483.4 2402.8
30
3-4
4342.3 427.3 461.7 2346.1
4434.7 446.4 484.2 2404.7
32
34
4345.4 427 9 462.5 2348.1
4437.8 447.1 484.9 2406.7
34
36
4348.5 4286 463.2 2350.0
4440.9 447.7 485.7 2408.6
36
38
4351.6 429.2 463.9 2352.0
4444.0 448.3 486.5 24106
sL
40
4354.7 429.8 464.7 2353.9
4447.0 448.9 487.2 2412.6
40
42
4357.7 430.5 485.4 2355.9
4450.1 449,5 488.0 2414.5
42
44
4360.8 431.1 466.2 2357.8
4453 2 450.2 488.7 2416.5
44
46
4363.9 431.7 466.9 2359.8
4456.3 450.8 489.5 2418.5
46
48
4367.0 432.4 467.7 2361.7
4459.3 451.5 490.3 2420.4
48
50
4370.1 433.0 468 4 2363.7
4462.4 452.1 491.0 2422.4
50
52
4373.2 433.6 469.1 2365.6
4465.5 452.7 491 8 2424.4
52
54
43762 4343 469.9 2367.6
4468.6 453 4 492.5 2426.3
54
56
43^9.3 434.9 470.6 2369.5
4471.6 454.1 493.3 2428.3
56
58
4382.4 435 b 471.4 28*1.5
4474.7 454.8 494.1 2430.2
58
60
4385.5 436.2 472.1 2373.4
4477.8 455.5 494.8 2432.2
60
222 FUNCTIONS OF A ONE-DEGREE CURVE
46
47
L. C. M. E. T.
L. C. M. E. T.
4477.8 455.5 494.8 2432.2
4569.7 475.2 518.3 2491.5
2
4480.9 456.1 495.6 2434.2
4572.7 475.9 519.0 2493.4
2
4
4483.9 456.8 496.5 2436.1
4575.8 476.5 519.8 2495.4
4
6
4487.0 457.4 497.2 2438.1
4578.8 477.2 520.6 2497.4
6
8
4490.0 458.1 497.9 2440.1
4581.9 477.8 521.4 2499.4
8
10
4493.1 458.7 498.7 2442.1
4584.9 478.5 522.2 2501.4
10
12
4496.2 459.4 499.5 2444.0
4588.0 479.2 523.0 2503.4
12
14
4499.2 460.0 500.3 2446.0
4591.0 479.8 523.8 2505.4
14
16
4502.3 460.7 501.0 2448.0
4594.1 480.5 524.6 2507.3
16
18
4505.4 461.3 501.8 2449.9
4597.1 481.1 525.4 2509.3
18
20
4508.4 462.0 502.6 2451.9
4600.2 481.7 526.2 2511.3
20
22
4511.5 462.7 503.4 2453.9
4603.2 482.3 527.0 2513.3
22
24
4514.6 463.3 504.1 24559
4606.3 483.0 527.8 2515.3
24
26
4517.6 464.0 504.9 2457.8
4609.3 483.7 528.6 2517.3
26
28
4520.7 464.6 505.7 2459.8
4612.4 484.3 529.4 2519.3
28
30
4523.7 465.3 506.5 2461.8
4615.4 485.0 530.2 2521.2
30
32
4526.8 466.0 507.3 2463. S
4618.5 485.7 531.0 2523.2
32
34
4529.9 466.6 508.0 2465.7
4621.5 486.3 531.8 2525.2
34
36
4532.9 467.3 508.8 2467.7
4624.6 487.0 532.6 2527.2
36
88
4536.0 467.9 509.6 2469.7
4627.6 487.7 533.4 2529.2
38
40
4539.1 468.6 510.4 2471.7
4630.7 488.4 534.2 2531.2
40
42
4542.1 469.3 511.1 2473.6
4633.7 489.1 535.0 2533.2
42
44
4545.2 469.9 511.9 2475.6
4636.8 489.8 535.8 2535.2
44
46
4548.2 470.6 512.7 2477.6
4639.8 490.5 536.6 2537.2
46
48
4551.3 471.2 513.5 2479.6
4642.9 491.2 537.4 2539.2
48
50
4554.4 471.9 514.3 2481.6
4645.9 491.9 53S.2 2541.2
50
52
4557.4 472.6 515.1 2483.5
4649.0 492.6 539.0 2543.1
52
54
4560.5 473.2 515.9 2485.5
4652.0 493.3 539.8 2545.1
54
56
4563.6 473.9 516.7 2487.5
4655.1 494.0 540.6 2547.1
56
58
4566.6 474.5 517.5 2489.5
4658.1 494.7 541.4 2549.1
58
60
4569.7 475.2 518.3 2491.5
4661.2 495.4 542.3 2551.1
60
48
4U
/
L. C. M. E. T.
L. C. M. E. T.
4661.2 495.4 542.3 2551.
4752.3 515.9 567.0 2611.3
2
4664.2 496.0 543.1 2553.
4755.3 516.5 567.8 2613.3
2
4
4667.3 496.7 543.9 2555.
4758.4 517.2 568.7 2615.3
4
6
4670.3 497.4 544.7 2557.
4761.4 517.9 569.5 2617.3
6
8
4673.3 498.1 545.5 2559.
4764.4 518.6 570.3 2619.3
8
10
4676.4 498.8 546.4 2561.
4767.4 519.3 571.2 2621.4
10
12
4679.4 499.4 547.2 2563.
4770.5 520.0 572.0 2623.4
12
14
4682.5 500.1 548.0 2565.
4773.5 520.7 572.8 2625.4
14
16
4685.5 500.8 548.8 2567.
4776.5 521.4 573.7 2627.4
16
18
4688.5 501.5 549.6 2569.
4779.6 522.1 574.5 2629.4
18
20
4691.6 502.2 550.5 2571.
4782.6 522.8 575.3 2631.4
20
22
4694.6 502.8 551.3 2573.
4785.6 523.5 576.2 2633.5
22
24
4697.6 503.5 552.1 2575.
4788.7 524.2 577.0 2635.5
24
26
4700.7 504.2 552.9 2577.1
4791.7 524.9 577.9 2637.5
26
28
4703.7 504.9 553.7 2579.
4794.7 525.6 578.7 2639.5
28
30
4706.7 505.6 554.6 2581.
4797.7 5','6.3 579.6 2641.5
30
32
4709.8 506.2 555.4 2583.1
4800.8 527.0 580.4 2643.5
32
34
4712.8 506.9 556.2 2585.1
4803.8 527.7 581.3 2645.6
34
36
4715.9 507.6 557.0 2587.2
4806.8 528.4 582.1 2647.6
36
38
4718.9 508.3 557.8 2589.2
4809.9 529.1 583.0 2649.6
38
40
4721.9 509.0 558.7 2591.2
4812.9 529.8 583.8 2651.6
40
42
4725.0 509.6 559.5 2593.2
4815.9 530.5 584.7 2653.7
42
44
4728.0 510.3 560.3 2595.2
4819.0 531.2 585.5 2655.7
44
46
4731.0 511.0 561.2 2597.2
4822.0 531.9 586.4 2657.7
46
48
4734.1 511.7 562.0 2599.2
4825.0 532.6 587.2 2659.7
48
50
4737.1 512.4 562.8 2601.2
4828.0 533.3 588.1 2661.8
50
52
4740.2 513.1 563.7 2603.2
4831.1 534.0 5S8.9 2663.8
52
54
4743.2 513.8 564.5 2605.2
4834.1 534.7 589.8 2665.8
54
56
4746.2 514.5 565.3 2607.2
4837.1 535.4 590.6 2667.8
56
58
4749.3 515.2 566.2 2609.3
4840.2 536.1 591.5 2669 9
58
60
4752.3 515.9 567.0 2611.3
4843.2 536.8 592.4 2671.9
60
FUNCTIONS OF A ONE-DEGREE CURVE 223
60
61
L. C. M. E. T.
L. C. M. E. T.
4843.2 536.8 592.4 2671.9
4933 6 558.2 618.5 2733.0
2
4846.2 537.5 593.2 2673 9
4936.6 558.9 619.3 2735.1
2
4
4849.2 538.2 594.1 2676.0
4939.6 559.7 620.2 2737.1
4
6
4852.2 538.9 594.9 2678.0
4942.6 560.4 621.1 2739.2
6
8
4855.2 539.6 595.8 2680.0
4945.6 561.1 622.0 2741.2
8
10
4858.3 540.3 596.7 2682.1
4948.6 561.8 622.9 2743.3
10
re
4861.3 541.0 597.5 2684.1
4951.6 562.5 623.7 2745.3
12
14
4864.3 541.7 598.4 2686.1
4954.6 563.3 624.6 2747.4
14
16
4867.3 542.4 599.3 2688.2
4957.6 584.0 625.5 2749.4
16
18
4870.3 543.1 600.1 2690.2
4960.6 564.7 626.4 2751.5
18
80
4873.3 543.9 601.0 2692.3
4963.6 565.4 627.3 2753.5
20
22
4876.3 544.6 601.9 2694.3
4966.6 566.2 628.2 2755.6
22
24
4879.4 545.3 602.7 2696.3
4969.6 566.9 629.9 2757.7
24
26
4882.4 546.0 603.6 2698.4
4972.6 567.6 630.0 2759.7
26
28
4885.4 546.7 604.5 2700.4
4975.6 568.3 630.9 2761.8
28
30
4888.4 547.4 605.3 2702.4
4978.6 569.1 631.8 2763.8
30
32
4891.4 548.1 606.2 2704.5
4981.6 569.8 632.7 2765.9
32
34
4894.4 548.8 607.0 2706.5
4984.6 570.5 633.6 2767.9
34
33
4897.4 549.5 607.9 2708.6
4987. 571.2 G34.5 2770.0
36
38
4900.4 550.2 608.8 2710.6
4990. 572.0 635.3 2772.0
38
40
4903.5 551.0 609.7 2712.6
4993. 572.7 636.2 2774.1
40
42
4906.5 551.7 610.5 2714.7
4996.7 573.4 637.1 2776.2
42
44
4909.5 552.4 611.4 2716.7
4999. 574.1 638.0 2778.2
44
46
4912.5 553.1 612.3 2718.8
5002. 574.9 638.9 2780.3
46
48
4915.5 553.8 613.2 2720.8
5005. 575.6 639.8 2782.3
48
50
4918.5 554.5 614.1 2722.8
5008. 576.3 640.7 2784.4
50
52
4921.5 555.2 614.9 2724.9
5011.7 577.0 641.6 2786.4
52
54
4924.6 555.9 615.8 2726.9
5014.7 577.8 642.5 2788.5
54
56
4927.6 556.6 616.7 2729.0
5017.7 578.5 643.4 2790.6
56
58
4930.6 557.4 617.6 2731.0
5020.7 579.2 644.3 2792.6
58
60
4933.6 558.2 618.5 2733.0
5023.7 579.9 645.2 2794.7
60
52
53
L. C. M. E. T.
L. C. M. E. T.
5023.7 579.9 645.2 2794.7
5113.5 602.0 672.7 2856.9
5026.7 580.6 646.1 2796.8
5116.5 602.8 673.7 2858.9
2
4
5029.7 581.3 647.0 2798.8
5119.4 603.5 674.6 2861.0
4
6
5032.7 582.1 647.9 2800.9
5122.4 604.3 675.5 2863.1
6
8
5035.7 582.8 648.9 2803.0
5125.4 605.0 676.4 2865.2
8
10
5038.7 583.5 649.8 2805.0
5128.4 605.8 677.4 2867.3
10
12
5041.7 584.3 650.7 2807.1
5131.3 606.5 678.3 2869.4
12
14
5044.7 585.0 651.6 2809.2
5134.3 607.3 6T9.2 2871.5
14
16
5047.7 585.7 652.5 2811.2
5137.3 608.0 680.2 2873.5
16
18
5050.7 586.5 653.4 2813.3
5140.3 608.8 681.1 2875.6
18
20
5053.6 587.2 654.3 2815.4
5143.2 609.5 682.0 2877.7
20
22
5056.6 587.9 655.2 2817.4
5146.2 610.3 683.0 2879.8
22
24
5059.6 588.7 656.2 2819.5
5149.2 611.0 683.9 2881.9
24
26
5062.6 589.4 657.1 28-'1.6
5152.1 611.8 684.9 2884.0
26
28
5065.6 590.1 658.0 2823.6
5155.1 612.5 685.8 2886.1
28
30
5068.6 590.9 658.9 2825.7
5158.1 613.3 686.7 2888.1
30
32
5071.6 591.6 659.8 2827.8
5161.1 614.0 687.7 2890.2
32
34
5074.6 592.3 660.7 2829.8
5164.0 614.8 688.6 2892.3
34
36
5077.6 593.1 661.6 2831.9
5167.0 615.5 689.6 2894.4
36
38
5080.6 593.8 662.5 2834.0
5170.0 616.3 690.5 2896.5
38
40
5083.6 594.5 663.5 2836.1
5173.0 617.0 691.5 2898.6
40
42
5086.6 595.3 664.4 2838.2
5175.9 617.8 692.4 2900.7
42
44
5089.6 596.0 665.3 2840.2
5178.9 61S.5 693.4 2902.8
44
46
5092.6 596.7 666.2 2842.3
5181.9 619.3 694.3 2904.9
46
48
5095.6 597.5 667.2 2844.4
5184.9 620.1 695.3 2907.0
48
50
5098.6 598.2 668.1 2846.5
51b7.8 620.8 696.2 2909.1
50
52
5101.6 598.9 669.0 '2848. 5
5190.8 621.5 697.1 2911.2
52
54
5104.6 599.7 669.9 2850.6
5193.8 622.3 698.1 2913.3
54
56
5107.6 600.4 670.9 2852.7
5196.7 623.0 699.0 2915.4
56
58
5110.6 601.2 671.8 2854.8
5199.7 6',>3.8 700.0 2917.5
58
60
5113.5 602.0 672.7 2856.9
S20-J.7 624.6 700.9 2919.5
60
224 FUNCTIONS OF A ONE-DEGREE CURVE
54
65
/
L.C. M. E. T.
L. C. M. E. T.
5202.7 624.6 700.9 2919.5
5291.7 647.4 7'29.9 2982.8
2
5205.7 625.4 701.9 2921.6
5294.6 648.1 730.9 2984.9
2
4
5208.6 626.1 702.8 2923.8
5297.6 648.9 731.9 2987.1
4
6
5211.6 626.9 703.8 2925.9
5300.5 649.6 732.9 2989.2
6
8
5214.6 627.6 704.8 2928.0
5303.5 650.4 733.8 2991.3
8
10
5217.5 628.4 705.7 2930.1
5306.4 651.2 734.8 2993.4
10
12
5220.5 629.2 706.7 2932.2
5309.4 652.0 735.8 2995 5
12
14
5223.5 629.9 707.7 2934.3
5312.3 652.7 736.8 2997.7
14
16
5226.4 630.7 708-6 2936.4
5315.3 653.5 737.8 2999.8
16
18
5229.4 631.4 109.6 2938.5
5318.2 654.3 733.7 3001.9
18
20
5232.4 632.2 710.5 2940.6
53-21.2 655.1 739.7 3004.0
20
22
5235.3 633.0 711.5 2942.7
5324.1 655.8 740.7 3006.2
22
24
5238.3 633.7 712.5 2944.8
5327.1 656.6 741.7 3008.3
24
26
5241.3 634.5 713.4 2946.9
53.30.0 057. 4 742.7 3010.4
26
28
5244.2 635.2 714.4 2949.0
5333.0 658.2 7'43.7 3012.5
28
30
5247.2 636.0 715.3 2951.1
5335.9 658.9 744.7 3014.7
30
32
5250.2 636.8 716.3 2953.2
5338.8 659.7 745 7 3016.8
32
34
5253.1 637.5 717.3 2955.3
5341.8 660.5 746.7 3018.9
34
36
5256.1 638.3 718.2 2957.5
5344.7 661.3 747.7 3021.1
36
38
5259.1 639.0 719.2 2959.6
5347.7 662.0 748.7 3023.2
38
40
5262.0 639.8 720.2 2961.7
5350.6 66-2.8 749.7 3025.3
40
42
5265.0 640.6 721.1 2963.8
5353.6 6636 750.7 3027.5
42
44
5268.0 641.3 722.1 2965.9
5356.5 664.4 751.7 3029.6
44
46
5270.9 642.1 723.1 2968.0
5359.5 665.1 752.6 3031.7
46
48
5-273.9 642.8 724.1 2970.1
5362.4 665.9 753.6 3033.8
48
50
5276.9 643.6 725.0 2972.2
5365.4 666.7 754.6 3036.0
50
52
5279.8 644.4 726.0 2974.4
5368.3 667.5 755.6 3038.1
52
54
5282.8 645.1 727.0 2976.5
5371.3 668.3 756.6 3040.2
54
56
5285.8 645.9 728.0 2978.6
5374.2 669.1 757.6 3042.4
56
58
5288.7 646.6 729.0 2980.7
5377.2 669.9 758.6 3044.5
58
60
5291.7 647.4 729.9 2382.8
5380.1 670.7 759.6 3046.6
60
66
57
'
L. C. M. E. T.
L.C. M. E. T.
5380.1 670.7 759.6 3046.6
5468.2 694.4 790.2 3111.1
2
5383.0 671.4 760.6 3048.8
5471.1 695.2 791.2 3113.3
2
4
5386.0 672.2 761.6 3050.9
5474.0 696.0 792.2 3115.4
4
6
5388.9 672.9 762.7 3053.1
5477.0 696.8 793.3 3117.6
6
8
5391.8 673.7 763.7 3055.2
5479.9 697.6 794.3 3119.7
8
10
5394.8 674.4 764.7 3057.4
5482.8 698.4 795.3 3121.9
10
12
5:597.7 675.2 705.7 3059.5
5485.7 699.2 796.3 3124.1
12
14
5400.7 676.0 7G6.7 3061.6
5488. 7 700.0 797.4 3126.2
14
16
5403.6 676.8 767.7 3063.8
5491.6 700.8 798.4 3128.4
16
18
5406.5 677.6 768.7 3065.9
5494.5 701.6 799.4 3130.6
18
20
5409.5 678.4 769.7 3068.1
5497.4 702.4 800.5 3132.7
20
22
5412.4 679.2 770.8 3070.2
5500.3 703.2 801.5 3134.9
2'2
24
5415.3 680.0 771.8 3072.4
5503.3 704.0 802.6 3137.0
24
26
5418.3 680.8 772.8 307'4.5
5506.2 704.8 803.6 3139.2
26
28
5421.2 681.6 773.8 3076.6
5509.1 705.6 804.7 3141.4
28
30
5424.1 682.4 774.8 3078.8
5512.0 706.4 805.7 3143.5
30
3-2
5427.1 683.2 775.8 3080.9
5515.0 707.2 806.8 3145.7
32
34
5430.0 684.0 776.8 3083.1
5517.9 708.0 807.8 3147.9
34
36
5433.0 684.8 777.8 3085.2
5520.8 708.8 808.8 3150.0
36
38
5435.9 685.6 778.9 3087.4
55:23.7 709.6 809.9 3152.2
38
40
5438.8 686.4 779.9 3089.6
55-26.7 710.4 810.9 3154.4
40
42
5441.8 687.2 780.9 3091.7
5529.6 711.2 812.0 3156.6
42
44
5444.7 688.0 781.9 3093.9
5532.5 712.0 813.0 3158.7
44
46
5447.6 688.8 783.0 3096.0
5535.4 712.8 814.1 3160.9
46
48
5450.6 689.6 784.0 3098.2
5538.4 713.6 815.1 3163.1
48
50
5453.5 690.4 785.0 3100.3
5541.3 714.4 816.2 3165.3
50
52
5456.5 691.2 786.0 3102.5
5544.2 715.2 817.2 3167.4
52
54
5459.4 692.0 787.1 3104.6
5547.1 716.0 818.3 3169.6
54
56
5462.3 69-2.8 788.1 3106.8
5550.0 716.8 819.3 3171.8
56
58
5465.3 693.6 789.1 3108.9
5553.0 717.6 820.4 3174.0
58
60
5468.2 694.4 790.2 3111.1
5555.9 718.4 821.4 3170. 1
60
FUNCTIONS OF A ONE-DEGREE CURVE 225
1
68
69
1
L. C. M. E. T.
L. C. M. E. T.
5555.9 718.4 821.4 3176.1
5643.1 742.8 853.5 3241.9
2
5558.8 719.2 822.5 3178.3
5646.0 743.6 854.6 3244.1
2
4
5561.7 720.0 823.5 3180.5
5648.9 744 4 855.7 3246.3
4
c
5564.6 720.8 824.6 3182.7
5651.8 745.3 856.8 3248.5
6
8
5567.5 721.6 825.7 3184.9
5654.7 746.1 857.9 3250.7
8
10
5570.4 722.4 826.7 3187.1
5657.6 746.9 859.0 8252.9
10
12
5573.3 723.2 827.8 3189.2
5660.5 747.7 860.0 3255.1
12
14
5576.2 724.0 828.9 3191.4
5663.4 748.6 861.1 3257.3
14
16
5579.2 724.8 829.9 3193.6
5666.3 749.4 862.2 3259.5
16 '
18
5582.1 725.6 831.0 3195.8
5669.2 750.2 863.3 3261.7
18
20
5585.0 726.5 832.1 3198.0
5672.1 751.1 864.4 3263.9
20
22
5587.9 727.3 833.1 3200.2
5675.0 751.9 865-5 3266.1
22
24
5590.8 728.1 834.2 3202.4
5677.9 752.7 866.6 3268 3
24
26
5593.7 728.9 835.3 3204.5
5680.8 753.5 867.7 3270.5
26
28
5596.6 729.7 836.3 3206.7
5683.7 754.4 868.8 3272.7
28
30
5599.5 730 5 837.4 3208.9
5686 5 755.2 869.9 3274.9
30
32
5602.4 731.3 838.4 3211.1
5689.4 756.0 871.0 3277.1
82
34
5605.3 732.1 839.5 3213.3
5692.3 756.9 872.1 3279.4
34
36
5608.2 732.9 840.6 3215.5
5695.2 757.7 873.2 3281 6
36
38
5611.1 733.7 841.6 3217.7
5698 1 758.5 874.3 3283.8
38
40
5614.0 734.6 842.7 3219.9
5701.0 7594 875.4 3286.0
40
42
5616.9 735.4 843.8 3222.1
5703.9 760.2 876.5 3288.2
42
44
5619.8 730.2 844.9 3224.3
5706.8 761 877.6 3290.5
44
4G
5622.8 737.0 846.0 3226.5
5709 7 761.9 878.7 3292.7
46
4S
5625.7 7378 847.0 3228 7
5712.6 762.7 879.8 3294.9
48
50
5628.6 738.6 848.1 32309
5715.5 763.5 880.9 3297.1
50
58
5631.5 739.4 849.2 3233.1
5718.4 764.4 882.0 3299.3
52
54
5634.4 740.2 850.3 3235.3
5721.3 765.2 883.1 3301.5
54
50
5637.3 741 851.4 3237.5
5724.2 766.0 884.2 3303.8
56
58
5040.3 741.9 85-.>.5 3239.7
5727.1 766.8 885.3 3306.0
58
60
5643.1 742.8 853.5 3241.9
5730.0 767.7 886.4 3308.2
60
60
61
L. C. M, E. T.
L. C. M. E. T.
5730.0 767.7 886.4 3308.2
5816.4 792.9 920.2 3375.2
2
5732.9 768.5 887.5 3310.4
5819.3 793.7 921.4 3377.4
2
4
5735.8 769.4 888.7 3312.7
5822.1 794.6 922.5 3379.7 .
4
6
5738.6 770.2 889.8 3314.9
5825.0 795.4 923 6 3381.9
6
8
5741.5 771.1 890.9 3317.1
5827.9 796.3 924.8 3384.2
8
10
5744 4 771.9 892.0 3319.3
5830.7 797.1 935.0 3386.4
10
12
5747.3 772.7 893.1 3321.6
5833.6 798.0 927.1 3388.7
12
14
5750.2 773.6 894.3 3323.8
5836.5 798.8 928.2 3390.9
14
16
5753.0 774.4 895.4 3326.0
5839.3 799.7 929.3 3393.2
16
18
5755.9 775.3 896.5 3328.3
5842.2 800.5 930.5 3395.4
18
20
5758.8 776.1 897.6 3330.5
5845.1 801.4 931.6 33S7.7
20
22
5761.7 776.9 898.8 3332.7
5847.9 802.2 932.8 8399.9
22
24
5764.6 777.8 899.9 3334.9
5850.8 803.1 933.9 3402.2
24
26
5767.4 778.6 901.0 3337.2
5853.7 803.9 935.1 3404.4
26
28
5770.3 779.5 902.1 3339.4
5856.5 804.8 936.3 3406.7
28
30
5773.2 780.3 903.2 3341.6
5859.4 805.6 937.. 4 3408.9
30
32
5776.1 781.1 904.4 3343.9
5862.3 806.5 938.6 3411.2
32
34
5779.0 782.0 905.5 3346.1
5865.1 807.3 939.7 3413.5
34
36
5781.8 782.8 906.6 3348.3
5868.0 808.2 940.9 3415.7
36
38
5784.7 783.7 907.7 3350.6
5870.9 809.0 942.1 3418.0
38
40
5787.6 784.5 908.8 3352.8
5873.7 809.9 943.2 3420.3
40
42
5790.5 785.3 910.0 3355.0
5876.6 810.7 944.4 3422.5
42
44
5793.4 786.2 911.1 3357.3
5879.5 811.6 945.5 3424.8
44
46
5796.2 787.0 912.3 3359.5
5882.3 812.4 946.7 3427.1
46
48
5799.1 787.9 913.4 3361.8
5885.2 813.3 947.8 3429.3
48
50
5802.0 788.7 914.5 3364.0
5888.1 814.1 949.0 3431.6
50
52
5804.9 789.5 915.7 3366.2
5890.9 815.0 950.2 3433.9
52
54
5807.8 790.4 916.8 3368.5
5893.8 815.8 951.3 3436.1
54
56
5810.6 791.2 918.0 3370.7
5896.7 816.7 952.5 3438.4
56
58
5813.5 792.1 919.1 3373.0
5899.5 817.5 953.6 3440.7
58
60
5816.4 792.9 920.2 3375.2
5902.4 818.4 954.8 3442.9
60 j
226 FUNCTIONS OF A ONE-DEGREE CURVE
62
63
/
L. C. M. E. T.
L. C. M. E. T.
/
5902.4 818.4 954.8 3442.9
5987.8 844.4 990.3 3511.3
2
5905.2 819.3 956.0 3445.2
5990.6 845.3 991.5 3513.6
2
4
5908.1 820.1 957.2 3447.5
5993.5 846.2 992.7 3515.9
4
6
5910.9 821.0 958 3 3449.7
5096.3 847.1 993.9 3518.2
6
8
5913.8 821.8 959.5 3452.0
5999.1 847.9 995.1 3520.5
8
10
5916.6 822.7 960.7 3454.3
6002 848.8 996.3 3522.8
10
12
5919.5 823.6 961.9 3456.6
6004.8 849.7 997.5 3525.1
12
14
5922.3 824.4 963.0 3458.8
6007.7 850.6 998.7 3527.4
14
16
5925.2 825.3 9G4.2 3461.1
6010.5 851.4 999.9 3529.7
16
18
5928.0 826.1 965.4 3463.4
6013.3 852.3 1001.1 3532.0
18
20
5930.9 827.0 966.6 3465.7
6016.2 853.2 1002.3 3534.3
20
22
5933.7 827.9 967.8 3107.9
6019.0 854.1 1003.5 3536.6
22
24
5936.6 828.7 968.9 3470.2
6021.8 854.9 1004.7 3538.9
24
26
5939.4 829.6 970.1 3472.5
6024.7 855.8 1005.9 3541.2
26
28
5942.3 830.4 971.3 3474.7
6027.5 856.7 1007.1 3543.5
28
30
5945.1 831.3 972.5 3477.0
6030.3 857.6 1008.4 3545.8
30
82
5947.9 832.2 973.6 3479.3
6033.2 858.4 1009.6 3548.1
32
34
5950.8 833.0 974.8 3481.6
6036.0 859.3 1010.8 3550.4
34
36
5953.6 833.9 976.0 3483.9
6038.9 860.2 1012.0 3552.7
36
U8
5956.5 834.7 977.2 3486.2
6041.7 861.1 1013.2 3555.0
38
40
5959.3 835.6 978.4 3488.5
6044.5 861.9 1014.5 3557.3
40
42
5962 2 836.5 979.6 3490.7
6047.4 862-8 1015.7 3550.6
42
44
5965.0 837.4 980.8 3493.0
6050.2 863.7 1016.9 356-J.O
44
46
5967.9 838.3 982.0 3495.3
6053.0 864.6 1018.1 3564.3
46
48
5970.7 839.1 983.2 3497.6
C055.9 865.4 1019.3 3566.6
48
50
5973.6 840.0 984.4 3499.9
6058.7 866.3 1020.6 3568.9
50
52
5976.4 840.9 985.5 3502.2
6061.6 867.2 1021.8 3571.2
52
54
5979.3 841.7 986.7 3504.5
6064.4 868.1 1023.0 3573.5
54
56
5982.1 842.6 987.9 3506.8
6067.2 868.9 1024.2 3575.8
56
58
5985.0 843.5 989.1 3509.0
6070.1 869.8 1025.4 3578.1
58
60
5987.8 844.4 990.3 3511.3
6072.9 870.7 1026.7 3580.4
60
64:
66
L. C. M. E. T.
L. C. M. E. T.
6072.9 870.7 1026.7 3580.4
6157.5 897.3 1064.0 3650.4
2
6075.7 871.5 1027.9 3582.8
6160.3 898.2 1065.2 3652.8
2
4
6078.5 872.4 1029.2 3585.1
6163.1 899.1 1066.5 3655.1
4
6
6081.4 873.3 1030.4 3587.4
6165.9 900.0 1067.7 3657.5
6
8
6084.2 874.2 1031.7 3589.7
6168.7 900.9 1069.0 3659.8
8
10
6087.0 875.1 1032.9 3592.1
6171.5 901.8 1070.2 3662.2
10
12
6089.8 875.9 1034.1 3594.4
6174.3 902.7 1071.5 3664.5
12
14
609:2.6 876.8 1035.4 3596.7
6177.1 903.6 1072.7 3666.9
14
16
6095.5 877.7 1036.6 3599.1
6179.9 904.5 1074.0 3669.2
16
18
0098.3 878.6 1037.9 3601.4
6182.7 905.4 1075.2 3671.6
18
20
6101.1 879.5 1039.1 3603.7
6185.5 906.3 1076.6 3673.9
20
22
6103.9 880.3 1040.3 3606.0
6188.3 907.2 1077.8 3676.2
22
24
6106.7 881.2 1041. G 3608.4
6191.1 908.1 1079.1 3678.6
24
26
6109.6 882.1 1042.8 3610.7
6193.9 909.0 1080.4 3680.9
26
28
6112.4 883.0 1044.1 3613.0
6196.7 909.9 1081.7 3683.3
28
30
6115.2 883.9 1045.3 3615.3
6199.5 910.8 1083.0 3685.6
30
32
6118.0 884.7 1046.5 3617.7
6202.3 911.7 1084.2 3688.0
32
34
6120.8 885.6 1047.8 3620.0
6205.1 912.6 1085.5 3690.4
34
36
6123.7 886.5 1049.0 3622.3
6208.0 913.5 1086.8 3692.7
36
38
6126.5 887.4 1050.3 3624.7
6210.8 914.4 1088.1 3695.1
38
40
6129.3 888.3 1051.5 3627.0
6213.6 915.3 1089.4 3697.4
40
42
6132.1 889.2 1052.7 3629.4
6216.4 916.2 1090.6 3699.8
42
44
6134.9 890.1 1054.0 3631.7
6219.2 917.1 1091.9 3702.2
44
46
6137.8 891.0 1055.2 3634.0
6222.0 918.0 1093.2 3704.5
46
48
6140.6 891.9 1056.5 3636.4
6224.8 918.9 1094.5 3706.9
48
50
6143.4 892.8 1057.7 3638.7
6227.6 919.8 1095.8 3709-3
50
52
6146.2 893.7 1059.0 3641.1
6230.4 920.7 1097.0 3711.6
52
54
6149.0 894.6 1060.2 3643.4
6233.2 921.6 1098.3 3714.0
54
56
6151.9 895.5 1061.5 3645.7
6236.0 922.5 1099.6 3716.3
56
58
6154.7 896.4 10(52.7 3648.1
6238.8 923.4 1100.9 3718.7
58
60
6157.5 897.3 1064.0 3650.4
6241.6 924.3 1102.2 3721.1
60
FUNCTIONS OF A ONE-DEGREE CURVE 227
66
67
L. C. M. E. T.
L. C. M. E. T.
6241.6 924.3 1102.2 3721.1
6325.2 951.8 1141.5 3792.6
2
6244.4 925.2 1103.5 3723.4
6328.0 952.7 1142.8 3795.0
2
4
6247.2 926.1 1104.8 3725.8
6330.7 953.6 1144.1 3797.4
4
6
6250.0 927.0 1106.1 3728.2
C333.5 954.5 1145.4 3799.8
6
8
6252.7 927.9 1107.4 3730.6
6336.3 955.5 1146.7 3802.2
8
10
6255 5 928.8 1108.7 3732.9
6339.0 956.4 1148.1 3804.6
10
12
6258.3 929.8 1110.0 3735.3
6341.8 957.3 1149.4 3807.0
12
14
6201.1 930.7 1111.8 3737.7
6344.6 958.2 1150.7 3809.4
14
16
6263.9 931 6 1112.6 3740.1
6347.4 959.2 1152.0 3811.8
16
18
6266.7 ( J32.5 1113.9 3742.4
6350.1 960.1 1153.3 3814.2
18
20
6269.5 933.4 1115.2 3744.8
6352.9 961.0 1154.7 3816.6
20
22
6272.3 934.3 1116.5 3747.2
6355.7 961.9 1156.0 3819.0
22
24
6275 935.3 1117.8 8749.6
6358.4 962.9 1157.4 3821.4
24
26
6277 8 936.2 1119.1 3751.9
6361.2 963.8 1158.7 3823.8
26
28
6280.6 937.1 1120.4 3754.3
6364.0 964.7 1160.1 3826.2
28
30
6283.4 938.0 1121.7 3756.7
6366.7 965.6 1161.4 3828.6
30
32
6286.2 938.9 1123.0 3759.1
6369.5 966.6 1162.8 3831.0
32
34
6289.0 939.8 1124.3 3761.5
6372.3 907.5 1164.1 3833.4
34
36
6291.8 940.8 1125.6 3763.9
6375.1 968.4 1165.5 3835.9
36
38
6294.5 941.7 1126.9 3766.3
6377.8 969.3 1166.8 3838.3
38
40
6297.3 942 6 1128.3 3768.7
6380.6 970.3 1168.2 3840.7
40
42
6300.1 943.5 1129.6 3771.0
6383.4 971.2 1169.5 3843.1
42
44
6302.9 944.4 1130.9 3773.4
6386.1 972.1 1170.9 3845.5
44
46
6305.7 945.3 1132.2 3775.8
6388.9 973.0 1172.2 3847.9
46
48
6308.5 946.3 1133.5 3778.8
6391.7 974.0 1173.6 3850.4
48
50
6311.3 947.2 1134.9 3780.6
6394.4 974.9 1174.9 3852.8
50
52
6314.1 948.1 1136.2 3783.0
6397.2 975.8 1176.3 3855.2
52
51
6316.8 949.0 1137.5 3785.4
6400.0 976.8 1177.6 3857.6
54
56
6319.6 949.9 1138.8 3787.8
6402.8 977.7 1179.0 3860.0
56
58
6322.4 950.8 1140.1 3790.2
6405.5 978.6 1180.3 3862.5
58
60
6325.2 951.8 1141.5 3792.6
6408.3 979.6 1181.6 3864.9
60
68
69
L C. M. E. T.
L. C. M. E. T.
6408.3 979.6 1181.6 3864.9
6491.1 1007.7 1222.9 3938.1
2
6411.1 980.5 1183.0 3867.3
6493.8 1008.7 1224.3 3940.6
2
4
6413.8 981.4 1184.4 3869.7
6496.6 1009.6 1225.7 3943.0
4
6
6416.6 982.4 1185.7 3872.2
6499.3 1010.6 1227.1 3945.5
6
8
6419.3 983.3 1187.1 3874.6
6502.1 1011.5 1228.5 3947.9
8
10
6422.1 984.2 1188.5 3877.0
6504.8 1012.5 1229.9 3950.4
10
12
6421.9 985.2 1189.8 3879.5
6507.5 1013.4 1231.3 3952.9
12
14
6427.6 986.1 1191.2 3881.9
6510.3 1014.4 1232.7 3955.3
14
10
6430.4 987.0 1192.6 3884.3
6513.0 1015.3 1234.1 3957.8
18
18
6433.1 988.0 1193.9 3886.8
6515.8 1016.3 1235.5 3960.2
18
20
6435.9 988.9 1195.3 3889.2
6518.5 1017.2 1236.9 3962.7
20
22
6438.7 989.8 1196.7 3891.6
6521.2 1018.2 1238.3 3965.2
22
24
6141.4 990.8 1198.0 3894.1
6524.0 1019.1 1239.7 3967.6
24
26
6444.2 991.7 1199.4 3896.5
6526.7 1020.1 1241.1 3970.1
26
28
64415. 9 992.6 1200.8 3898.9
6529.5 1021.0 1242.5 3972.5
28
30
6149.7 991.6 1202.1 3901.4
6532.2 1022.0 1243.9 3975.0
30
32
6452.5 994.5 1203.5 3903.8
6534.9 1022.9 1245.3 3977.5
32
34
6455.2 995.4 1204.9 3906.3
6537.7 1023.9 1246.7 3980.0
34
36
6458.0 996.4 1206.2 3908.7
6640.4 1024.8 1248.1 3982.4
36
38
6460.7 997.3 1207.6 3911.2
6543.2 1025.8 1249.5 3984.9
38
40
64G3.5 998.2 1209.0 3913.6
6545.9 1026.7 1250.9 3987.4
40
42
6466.3 999.2 1210.3 3916.1
6548.6 1027.7 1252.3 3989.9
42
44
6469.0 1000.1 1211.7 3918.5
6551.4 1028.6 1253.7 3992.3
44
46
6471.8 1001.0 1213.1 3921.0
6554.1 1029.6 1255.1 3994.8
46
48
6474.5 1002.0 1214.5 3923.4
6556.9 1030.5 1256.5 3997.3
48
50
6477.3 1002.9 1215.9 3925.9
6559.6 1031.5 1257.9 3999.8
50
52
6480.1 1003.8 217.3 3928.3
6562.3 1032.4 1259.3 4002.2
52
51
6482.8 1001.8 218.7 3930.8
6565.1 1033.4 1260.7 4004.7
54
56
6485.6 1005.7 220.1 3933.2
6567.8 1034.3 1262.1 4007.2
56
58
6488.3 1006.7 221.5 3935.7
6570.6 1035.3 1263.5 4009.7
58
60
6491.1 1007.7 222.9 3938.1
6573.3 1036.3 1265.0 4012.1
60
228 FUNCTIONS OF A ONE-DEGREE CURVE
70
71
L. C. M. E. T.
L. C M. E. T.
f
6573.3 1036.3 1265.0 4012.1
6654.9 1065.1 1308.4 4087.1
2
6576.0 1037.3 1266.4 4014.6
6657 .6 1066.1 1309.9 4089.7
2
4
6578.7 1038.2 1267.9 4017.1
6660.3 1067.0 1311.3 4092.2
4
6
6581.5 1039.2 1269.3 4019.6
6663.0 1068.0 1312.8 4094!7
6
8
6584.2 1040.1 1270.8 4022.1
6665.7 1068.9 1314.2 4097.2
8
10
65 C 6.9 1041.1 1272.2 4024.6
6668.4 1069.9 1315.7 4099.8
10
18
6589.6 104v!.l 1273.6 4027.1
6671.1 1070.9 1317.2 4102.3
12
14
6592.3 1043.0 1275.1 4029.6
6673.8 1071.9 1318.6 4104.8
14
16
6595.1 1044.0 1276.5 4032.1
6676.6 1072.9 1320.1 4107.3
16
18
6597.8 1044.9 1278.0 4034.6
6679.3 1073.8 1321.5 4109.8
18
20
6600.5 1045.9 1279.4 4037.1
6682.0 1074.8 1323.0 4112.4
20
22
6603.2 1046.9 1280.8 4039.6
6684,7 1075.8 13'.>4.4 4114.9
22
24
6605.9 1047.8 1282.3 4042.1
6687 4 1076.8 1325.9 4117.4
24
26
6608.7 1048.8 1283.7 404-1.6
6690.1 1077.7 1327.4 4119.9
26
28
6611.4 1049.7 1285.2 4047.1
6692.8 1078.7 1328.9 4122.4
28
30
6614.1 1050.7 1286.6 4049.6
6695.5 1079.7 1330.4 4125.0
30
32
6616.8 1051.7 1288.0 4052.1
6693.2 1080.7 1331.8 4127.5
32
34
6619.5 1052.6 1289.5 4054.6
6700.9 1081.6 1333.3 4130.1
34
36
6622.3 1053.6 1290.9 4057.1
6703.6 1082.6 1334.8 4132.6
36
38
6625.0 1054.5 1292.4 4059.6
670(3.3 1083.6 1336.3 4135.1
38
40
6627.7 1055.5 1293.8 4062.1
6709.0 1084.5 1337.8 4137.7
40
42
6630.4 1056.5 1295.3 4064.6
6711.7 1085.5 1339.2 4140.2
42
44
6633.1 1057.4 1296.7 4067.1
6714.4 1086.5 1340.7 4142.7
44
46
6635.9 1058 4 1298.2 4069.6
6717.2 1087.5 1342.2 4145. 3
46
48
6638.6 1059.3 1299.6 4072.1
6719.9 1088.4 1343.7 4147.8
48
50
6641.3 1060.3 1301.1 4074.6
6722.6 1089.4 1345.2 4150.4
50
52
6644. C 1061.3 1302.6 4077.1
6725.3 1090.4 1346.7 4152.9
52
4
6646.7 1002.2 1304.0 4079.6
6728.0 1091.3 1348.2 4155.4
51
56
6649.5 1063.2 1305.5 4082.1
6730.7 1092.3 1349.7 4158.0
56
58
6652.2 1064.1 1306.9 4084.6
6733.4 1093.3 1351.2 4160.5
58
60
6654.9 1065.1 1308.4 4087.1
6736.1 1094.3 1352.7 4163.1
60
72
73
L. C. M. E. T.
L. C. M. E. T.
'
6736.1 1094.3 1352.7 4163.1
6816.6 1123.9 1398.1 4240.0
2
6738.8 1095 2 1354.2 4165.6
6819.3 1124.8 1399.6 4242.6
2
4
6741.5 1096.2 1355.7 4168.2
6821.9 1125.8 1401.2 4245.1
4
6
6744.1 1097.2 1357.2 4170.7
68-J4.6 1126.8 1402.7 4247.7
6
8
6746.8 1098.2 1358.7 4173.3
6827.3 1127.8 1404.2 4250.3
8
10
6749.5 1099.2 1360.2 4175.8
6830.0 1128.8 1405.8 4252.9
10
12
6752 2 1100.1 1361.7 4178.4
6832.6 1129.8 1407.3 4255.5
12
14
6754.9 1101.1 1363.2 4181.0
6835.3 1130.8 1408.8 4258.1
14
16
6757.6 1102.1 1364.7 4183.5
6838.0 1131.8 1410.4 4260.7
16
18
6760.2 1103.1 1366.2 4186.1
6840.7 1132.8 1411.9 4263.2
18
20
6762.9 1104.1 1367.7 4188.6
6843.3 1133.8 1413.5 4265.8
20
22
6765.6 1105.1 1369.2 4191.2
684G.O 1134.8 1415.1 4268.4
22
24
6768.3 1106.0 1370.7 4193.7
6848.7 1135.8 1416.6 4271.0
24
26
6771.0 1107.0 1372.2 4196.3
6851.3 1136.8 1418.2 4273.6
26
28
6773.7 1108.0 1373.7 4198.8
6854.0 1137.8 1419.7 4276.2
28
30
6776.3 1109.0 1375.2 4201.4
6856.7 1138.8 1421.3 4278.8
30
32
6779.0 1109.9 1376.7 4204.0
6859.4 1139.8 1422.9 4281.4
32
34
6781.7 1110.9 1378.2 4206.5
6862.0 1140.8 1424.4 4284.0
34
36
6784.4 1111.9 1379.7 4209.1
6864.7 1141.8 1426.0 4286.6
36
38
6787.1 1112.9 1381.2 4211.7
6867.4 1142.8 1427.5 4289.2
38
40
6789.8 1113.9 1382.8 4214.3
6870.1 1143.8 1429.1 4291.8
40
42
6792.4 1114.9 1384.3 4216.8
6872.7 1144.8 1430.7 4294.4
42
44
6795.1 1115.9 1385.8 4219.4
6875.4 1145.8 1432.2 4297.0
44
46
6797.8 1116.9 1387.4 4222.0
6878.1 1146.8 1433.8 4299.6
46
48
6800.5 1117.9 1388.9 4224.5
6880.8 1147.8 1435.3 4302.2
48
50
6803.2 1118.9 1390.4 4227.1
6883.4 1148 8 1436.9 4304.8
50
52
6805.9 1119.9 1392.0 4229.7
6886.1 1149.8 1438.5 4307.4
52
54
6808.5 1120.9 1393.5 4232.3
6888.8 1150.8 1440.0 4310.0
54
56
6811.2 1121.9 1395.0 4234.8
6891.4 1151.8 1441.6 4312.6
56
68
6813.9 1122.9 1396.6 4237.4
6894.1 1152.8 1443.1 4315.2
58
60
6816.6 1123.9 1398.1 4240.0
6896.8 1153.8 1444.7 4317.8
60
FUNCTIONS OF A ONE-DEGREE CURVE 229
740
76
L. C. M. E. T.
L. C. M. E. T.
6890.8 1153.8 1444.7 4317.8
6976.4 1184.1 1492.5 4396.7
2
6899.4 1154.8 1446.2 4320.5
6979.0 1185.1 1494.1 4399.4
2
4
6902.1 1155.8 1447.8 4323.1
6981.7 1186.1 1495.7 4402.1
4
6
6904.8 1156.8 1449.4 4325.7
6984.3 1187.1 1497.3 4404.7
6
8
0907.4 1157.8 1451.0 4328.3
6986.9 1188.1 1499.0 4407.4
8
10
6910.1 1158.8 1452.6 4330.9
6989.6 1189.2 1500.6 4410.0
10
12
6912.7 1159.8 1454.1 4333.6
699-,'. 2 1190.2 1502.2 4412.7
12
14
6915.4 1160.8 1455.7 4336.2
6994.9 1191.2 1503.8 4415.3
14
16
6918.0 1161.8 1457.3 4338.8
6997.5 1192.2 1505.4 4418.0
16
18
6920.7 1162.8 1458.9 4341.4
7000.1 1193.2 1507.0 4420.7
18
20
6923.3 1163.9 1460.5 4344.0
7002.8 1194.3 1508.7 4423.3
20
22
C926.0 1164.9 1462.0 4346.7
7005.4 1195.3 1510.3 4426.0
22
24
6928.6 1165.9 1463.6 4349.3
7008.0 1196.3 1512.0 4428.6
24
26
6931.3 1166.9 1465.2 4351.9
7010.7 1197.3 1513.6 4431.3
26
28
6933.9 1167.9 1466.8 4354.5
7013.3 1198.3 1515.3 4434.0
28
30
6936.6 1168.9 1468.4 4357.1
7015.9 1199.4 1516.9 4436.6
30
32
6939.2 1169.9 1469.9 4359.8
7018.6 1200.4 1518.5 4439.3
32
34
6941.9 1170.9 1471.5 4362.4
7021.2 1201.4 1520.2 4442.0
34
3
6944.6 1171.9 1473.1 4365.1
7023.9 1-202.4 1521.8 4444.6
36
38
6947.2 1172.9 1474.7 4367.7
7026.5 1203.4 1523.5 4447.3
33
40
6949.9 1174.0 1476.4 4370.3
7029.1 3204.5 1525.1 4450.0
40
42
6952.5 1175.0 1478.0 4373.0
7031.8 1205.5 1526.7 4452. 7
42
44
6955.2 1176.0 1479.6 4375.6
7034.4 1206.5 1528.4 4455.3
44
46
6957.8 1177.0 1481.2 4378.3
7037.0 1207.5 1530.0 4458.0
46
48
0960.5 1178.0 1-182.8 4380.9
7039.7 1208.5 1531.7 4460.7
48
50
6963.1 1179.0 1484.4 4383.5
7042.3 1209.6 1533.3 4463.4
50
5:2
6965.8 1180.0 1486.0 4386.2
7045.0 1210.6 1534.9 4466.0
52
54
6968.4 1181.0 1487.7 4388.8
7047.6 1211.6 1536.6 4468.7
54
56
6971.1 1182.0 1489.3 4391.5
7050.2 1212.6 1538.2 4471.4
56
58
6973.7 1183.0 1490.9 4394.1
705-2.9 1213.6 1539.9 4474.1
58
60
6976.4 118-1.1 149:2.5 439(5.7
7055.5 1211.7 1541.5 4476.7
60
! ,
76
JJO
L. C. M. E. T.
L. C. M E. T.
7055.5 1214.7 1541.5 4476.7
7134.0 1245.6 1591.7 4557.8
2
7058.1 1215.7 1543.2 4479.4
7136.6 1246.6 1593.4 4560.5
2
4
7060.7 1216.7 1544.9 4482.1
7139.2 1247.7 1595.1 4563.3
4
6
7063.3 1217.8 1546.5 4484.8
7141.8 124S.7 1596.8 4566.0
6
8
7066.0 1218.8 1548.2 4487.5
7144.4 1249.8 1598.5 4568.7
8
10
7068.6 1219.8 1549.9 4490.2
7147.0 1250.8 1600.2 4571.5
10
12
7071.2 1220.9 1551.5 4492.9
7149.6 1251.8 1601.9 4574.2
12
14
7073.8 1221.9 1553.2 4495.6
7152.2 1252.9 1603.6 4576.9
14
16
7076.4 1222.9 1554.9 4498.3
7154.8 1253 9 1605 3 4579.7
16
18
7079.0 1224.0 1556.5 4501.0
7157.4 12550 1607.0 4582.4
18
20
7081.7 1225.0 1558.2 4503.7
7160.0 1256.0 1608.7 4585.1
20
22
7084.3 1226.0 1559.9 4506.8
7162.6 1257.0 1610.4 4587.9
22
24
7086.9 1227.1 1561.5 4509.0
7165.2 1258.1 1612.1 4590.6
24
26
7089.5 1228.1 1563.2 4511.7
7167.8 1259.1 1613.8 4593.3
26
28
7092.1 1229.1 1564 9 4514.4
7170.4 1260.2 1615.5 4596.0
28
30
7094.7 1230.2 1566.5 4517.1
7173.0 1261 2 16'17.3 4598 8
30
32
7097.4 1231.2 1568.2 4519.8
7175.6 12622 1619.0 4601.5
32
31
7100.0 1232.2 1569.9 4522.5
71782 1263.3 1620.7 4604.3
34
36
7102.6 1233.3 1571.5 4525.3
7180 8 12S4.3 1622.4 4607
36
38
7105.2 1234.3 1573.2 4528.0
7183.4 1265.4 1624.1 46098
38
40
7107.8 1235.3 1574.8 4530.7
7186.0 1266.4 1625.9 4612.5
40
42
7110.4 1236.4 1576.4 4533.4
7188 6 1267.4 1627.6 4615.3
42
44
7113.1 1237.4 1578.1 4536.1
7191.2 1268.5 1629.3 4618.0
44
46
7115.7 1238.4 1579.8 4538.8
7193.8 1269.5 1631.0 4620.8
46
48
7118.3 12395 1581.5 4541.5
7196.4 1270 6 1632.7 4623.5
48
50
7120.9 1240.5 1583.2 4544.2
7199.0 1271.6 1634 5 4626.3
50
52
7123.5 1241.5 1584.9 4547.0
7201.6 1272.7 16362 4629.0
52
54
7126.1 1242.6 1586.6 4549.7
72042 1273.7 1687.9 4631.8
54
56
7128.8 1243.6 1588.3 4552.4
7206.8 1274.8 1639.6 4634.5
56
58
7131.4 1244.6 15900 4555.1
7209.4 1275.8 1641.3 4637.3
58
6C
7134.0 1245.6 1591.7 4557.8
7212.0 1276.9 1643.1 4640.0
60
230 FUNCTIONS OF A ONE-DEGREE CURVE
78
79
L. C. M. E. T.
L. C. M. E. T.
7212.0 1276.9 1643.1 4640.0
7289.5 1308.5 1696.0 4723.4
2
7214.6 1278.0 1644.8 4642.8
7292.1 1309.5 1697.7 4726.2
2
4
7217.2 1279.0 1646.6 4645.6
7294.6 1310.6 1699.5 4729.0
4
6
7219.7 1280.1 1648.3 4648.3
7297.2 1311.7 1701.3 4731.8
6
8
7222.3 1281.1 1650.1 4651.1
7299.7 1312.7 1703.1 4734.7
8
10
7224.9 1282.2 1651.8 4653.9
7302.3 1313.8 1704.9 4737.5
10
12
7227.5 1283.2 1653.6 4656.7
7304.9 1314.9 1706.6 4740.3
12
14
7230.1 1284.3 1655.3 4659.4
7307.4 1315.9 1708.4 4743.1
14
16
7232.7 1285.3 1657.1 4662.2
7310.0 1317.0 1710.2 4745.9
16
18
7235.2 1286.4 1658.8 4665.0
7312.6 1318.1 1712.0 4748.7
18
20
7237.8 1287.4 1660.6 4667.7
7315.1 1319.1 1713.8 4751.5
20
22
7240.4 1288.5 5662.3 4670.5
7317.7 1320.2 1715.6 4751.3
22
24
7243.0 1289.5 1664.1 4673.3
7320.3 1321.3 1717.4 4757.1
24
26
7245.6 1290.6 1665.8 4676.0
7322.8 1322.3 1719.2 4760.0
26
28
7248.2 1291.6 1667.6 4678.8
7325.4 1323.4 1721.0 4762.8
28
30
7250.7 1292.7 1G69.3 4681.6
7327.9 1324.5 1722.8 4765.6
30
82
7253.3 1293.7 1671.1 4684.4
7330.5 1325.5 1724.6 4768.4
32
34
7255.9 1294.8 1672.8 4687.2
7333.1 13-J6.6 1726.4 4771.2
34
36
7258.5 1295.8 1674.6 4689.9
7335.6 1327.7 1728.2 4774.1
36
38
7261.1 1296.9 1676.3 4692.7
7338.2 1328. 7 17*0.0 4776.9
38
40
7263.7 1297.9 1678.2 4695.5
7340.8 1329.8 1731.9 4779.7
40
42
7266.2 1299.0 1679.9 4698.3
7343.3 1330.8 173S.7 4782.6
4'^
44
7268.8 1300.0 1681.7 4701.1
7345.9 1331.9 1735.5 4785.4
44
46
7271.4 1301.1 1683.5 4703.9
7348.4 1333.0 1737.3 4788.2
46
48
7274.0 1302.1 1685.3 4706.7
7351.0 1334.1 1739.1 4791.0
48
50
7276.6 1303.2 1687.1 4709.5
7353.6 1335.2 1740.9 4793.9
50
52
7279.2 1304.2 1688.8 4712.2
7356.1 1336.2 1742.7 4796.7
52
54
7281.7 1305.3 1690.6 4715.0
7358.7 1337.3 1744.5 4799.5
54
56
7284.3 1306.3 1692.4 4717.8
7361.3 1338.4 1746.3 4802.4
56
58
7286.9 1307.4 1694.2 4720.6
7363.8 1339.5 1748.1 4805. -2
58
60
7289.5 1308.5 1696.0 4723.4
7366.4 1340.6 1750.0 4808.0
60
80
81
L. C. M. E. T.
L. C. M. E. T
7366.4 1340.6 1750 4808.0
7442.7 1372.8 3805.5 4893.9
2
7368 9 1341.7 1751.8 4810.9
7445.2 1373.9 1807.3 4896.8
2
4
7371.5 1342.7 1753.7 4813.7
7447.7 1375.0 1809.2 4899.7
4
6
7374.0 1343.8 1755.5 4816.6
7450.3 1376.1 1811.1 4902.6
6
8
7376.6 1344.9 1757.4 4819.4
74M.8 1377.1 1813.0 4905.4
8
10
7379.1 1346.0 1759.2 4822.3
7455.3 1378.2 1814.9 4908.3
10
12
7381.7 1347.0 1761.0 4825.1
7457.8 1379.3 1816 8 4911.2
12
14
7384.2 1348.1 1762.9 4828.0
7460.4 1380.4 1818.6 4914.1
14
16
7386.7 1349.2 1764.7 4830. H
7462.9 1381.4 1820.5 4917.0
16
18
7389.3 1350.3 1766.6 4833.7
7465.4 1382.5 1822.4 4919.9
18
20
7391.8 1351.3 1768.4 4836.5
7467.9 1383.6 1824.2 4922.8
20
22
7394.4 1352.4 1770.2 4839.4
7470.4 1384.7 1826.1 4925.7
22
24
7396.9 1353.5 1772.1 4842.2
7473.0 1385.7 1828.0 4928.6
24
26
7399.5 1354.6 1773.9 4845.1
7475.5 1386.8 1829.9 4931.5
26
28
7402.0 1355.6 1775.8 4847.9
7478.0 1387.9 1831.8 4934.4
28
30
7404.5 1356.7 1777.6 4850.8
7480.5 1389.0 1833.7 4937.2
30
32
7407.1 1357.8 1779.4 4853.7
7483.1 1390.1 1835.6 4940.2
82
34
7409.6 1358.9 1781.3 4856.5
7485.6 1391.2 1837.5 4943.1
34
36
7412.2 1359.9 1783.1 4859.4
7488. J 1392.3 1839.4 4946.0
36
38
7414.7 1361.0 1785.0 4862.3
7490.6 1393.4 1841.3 4948.9
38
40
7417.3 1362.1 1786.8 4865.1
7493.2 1394.5 1843.2 4951.8
40
42
7419 8 1363 2 1788.6 4868.0
7495.7 1395.6 1845.1 4954.7
42
44
7422.3 1364.2 1790.5 4870.9
7498.2 1396.7 1847.0 4957.6
44
46
7424.9 1365.3 1792.4 4873.8
7500.7 1397.8 1848.9 4960.6
46
48
7427.4 1366.4 1794 3 4876.6
7503.3 1398.9 1850.8 4963.5
48
50
7430.0 1367.5 1796.2 4879.5
7505.8 1400.0 1852 7 4966.4
50
52
7432.5 1368.5 1798.0 4882.4
7508.3 1401.1 1854 6 4969.3
52
54
7435.1 1369.6 1799.9 4885 3
7510.8 1402.2 1856 5 4972.2
54
56
7437.6 1370 7 1801.8 4888.1
7513.3 1403.3 185S.4 4975.1
56
58
7440.1 1371.8 1803.7 4891.0
7515.9 1404 4 1860.3 4978.0
58
60
7442.7 1372.8 1805.5 4893.9
7518.4 1405.5 1862 3 4981. C
SO
FUNCTIONS OF A ONE-DEGREE CURVE 231
82
83
L. C. M. E. T
L. C. M. E. T.
7513.4 1405.5 1862.3 4981.0
7593.6 1438.5 1920.6 5069.4
2
7520.9 1406.6 1864.2 4983.9
7596.1 1439.6 1922.6 5072.4
2
4
7523.4 1407.7 1866.1 4986.8
7598.6 1440.7 1924.6 5075.4
4
6
7525.9 1408 8 1868.1 4989.8
7601.1 1441.8 1926.5 5078.4
6
8
7528.4 1409.9 1870.0 4992.7
7603.6 1442.9 1928.5 5081.4
8
10
7530.9 1411.0 1871 9 4995.7
7606.0 1444.0 1930.5 5084.4
10
12
7533.4 1412.1 1873 9 4998.6
7608.5 1445.1 1932.4 5087.3
12
14
7535.9 1413.2 1875.8 5001.5
7611.0 1446.2 1934.4 5090.3
14
16
7538.5 1414.3 1877.7 5004.5
7613.5 1447.3 1936.4 5093.3
16
18
7541.0 1415.4 1879.7 5007.4
7616.0 1448.4 1938.4 5096. 3
18
20
7543.5 1416.5 1881.6 5010.3
7618.5 1449.6 1940.4 5099.3
20
22
7546.0 1417.6 1883.5 5013.3
7621.0 1450.7 1942.4 5102.3
22
24
7548.5 1418.7 1885.5 5016.2
7623.5 1451.8 1944.4 5105.2
24
26
7551.0 1419.8 1887.4 5019.2
7626.0 1452.9 1946.4 5108.2
26
28
7553.5 1420.9 1889.3 5022.1
7628.5 1454.0 1948.4 5111.2
28
30
7556.0 1422.0 1891.3 5025.0
7630.9 1455.1 1950.4 5114 2
30
32
7558.5 1423.1 1893.2 5028.0
7633.4 1456.2 1952.4 5117.2
32
34
7501.0 1424.2 1895.1 5031.0
7G35.9 1457.3 1954.4 5120.2
34
36
7563.5 14-25.3 1897.1 5033.9
7638.4 1458.4 1956.4 5123.2
36
38
7566.0 1426.4 1899.0 5036.9
7640.9 1459.5 1958.4 5126.2
38
40
7568.5 1427.5 1901.0 5039.8
7643.4 1460.7 1960.4 5129.2
40
42
7571.0 1428.6 1902.9 5042.8
7645.9 1461.8 1962.4 5132.2
42
44
7573.5 1429.7 1904.9 5045.8
7648.4 1462.9 1964.4 5135.2
44
46
7576.1 1430.8 1906.9 5048.7
7650.9 1464.0 1966.4 5138.2
46
48
7578.6 H31.9 1908.8 5051.7
7653.4 1465.1 1968.4 5141.2
48
50
7581.1 1433.0 1910.8 5054.6
7655.8 1466.2 1970.4 5144.3
50
52
7583.6 1434.1 1912.8 5057.6
7658.3 1467.3 1972.4 5147.3
52
54
7586.1 1435.2 1914.7 5060.6
7660.8 1468.4 1974.4 5150.3
54
56
7588.6 1436.3 1916.7 5063.5
7663.3 14C9.5 1976.4 5153.3
56
58
7591.1 1437.4 1918.7 5066.5
7665.8 1470.6 1978.4 5156.3
58
60
7593.6 1438.5 1920.6 5069.4
7668.3 1471.8 1980.5 5159.3
60
84-
85
/
L. C. M. E. T.
L. C. M. E. 1
7668.3 1471.8 1980.5 5159.3
7742.4 1505.4 2041.8 5250.6
2
7670.8 1472.9 1982.5 5162.3
7744.8 1506.5 2043.9 5253.6
2
4
7673.2 1474.0 1984.5 5165.3
7747.3 1507.6 2046.0 5256.7
4
6
7675.7 1475.1 1986.6 5168.4
7749.7 1508.8 2048.0 5259.8
6
8
7(378.2 1476.2 1988.6 5171.4
7752.2 1509.9 2050.1 5262.9
8
10
7680.6 1477.4 1990.6 5174.4
7754.6 1511.0 2052.2 5266
10
12
7683.1 1478.5 1992.7 5177.5
7757.1 1512.2 2054.2 5269.0
12
14
7685 6 1479.6 1994.7 5180.5
77595 1513.3 2056.3 5272.1
14
16
7688.1 1480.7 1990.7 5183.5
7762.0 1514.4 2058.4 5275.2
16
18
7690.5 1481.8 1998.8 5186.6
7764 4 1515.6 2060.5 5278.3
18
20
7693.0 14&3.0 2000.8 5189.6
7766.9 1516.7 2062.6 5281.4
20
22
7695.5 1484 1 2002.8 5192.6
7769.3 1517.8 2064.7 5284.4
22
24
769r.9 1485.2 2004.9 5195.6
7771.8 1519.0 2066.8 5287.5
24
26
7700.4 1486.3 2006.9 5198.7
7774.2 1520.1 2068.9 5290.6
26
ass
770'2.9 1487.4 2008.9 5201.7
7776.7 1521.2 2071.0 5293.7
28
30
7705.3 1488 6 2011.0 5204.7
7779.1 1522.4 2073. f 5296.7
30
32
7707.8 1489.7 2013.0 5207.8
7781.5 1523.5 2075 2 5299 8
32
34
7710.3 1490.8 2015.0 5210 8
7784.0 1524.6 2077 3 5302.9
34
36
7712.8 1491.9 2017.0 5213.9
7786.4 1525.8 2079.4 5306.1
86
38
7715.2 1493.0 2019.1 5216.9
7788.9 1526.9 2081.5 5309.2
38
40
7717.7 1494.2 2021.2 5220.0
7791.3 1528.0 2083.7 5312.3
40
42
77202 1495.3 2023.2 5223.1
7793.8 1529.2 2085.8 5315.4
42
44
7722 6 1496.4 2025.3 5226.1
7796 2 1530.3 2087.9 5318.5
44
46
7725.1 1497-5 2027.4 5229.2
77987 1531.4 2090.0 5321.6
46
48
7727.6 1498.6 2029.4 5232.2
7801.1 1532.6 2092.1 5324.7
48
50
7730.0 14998 2031.5 5235.3
7803.6 1533.7 2094.2 5327.8
50
52
7732 5 1500.9 2033.6 5238.3
7806.0 1534 8 2096.3 5330 9
52
54
7735.0 1502.0 2035.6 5241 4
7808.5 1536.0 2098.4 5334.0
54
56
7737 5 1503.1 2037.7 5244 5
7810.9 1537.1 2100.6 5337.1
56
58
7739 9 1504.2 2039.8 5247.5
7813 4 1538.2 2102.7 5340.2
58
60
7742.4 15054 2041.8 5250.6
7815.8 1539.3 2104.8 5343.3
60
232 FUNCTIONS OF A ONE-DEGREE CURVE
86
87
L. C. M. E. ,T.
L. C. M. E. T.
/
7815.8 1639.3 2104.8 5343.3
7888.5 1573.6 2169.5 5437.5
2
7818.2 1540.4 2106.9 5346.4
7890.9 1574.8 2171.6 5440.7
2
4
7820.6 1541.6 2109.1 5349.5
7893.3 1575.9 2173.8 5443.9
4
6
7823.1 1542.7 2111.2 5352.7
7895.7 1577.1 2176.0 5447.1
6
8
7825.5 1543.9 2113.4 5355.8
7898.1 1578.2 2178.2 5450.3
8
10
7827.9 1545.0 2115.5 5358.9
7900.5 1579.4 2180.4 5453.4
10
12
7830.3 1546.1 2117.6 5362.0
7903.0 1580.5 2182.5 5456.6
12
14
7832.8 1547.3 2119.8 5365.2
7905.4 1581.7 2184.7 5459.8
14
16
7835.2 1548.4 2121.9 5368.3
7907.8 1582.9 2186.9 5463.0
16
18
7837.6 1549.6 2124.1 5371.4
7910.2 1584.0 2189.1 5466.2
18
20
7840.0 1550.7 2126.2 5374.6
7912.6 1585.1 2191.3 5469.4
20
22
7812.4 1551.8 2128.3 5377.7
7915.0 1586.3 2193.5 5472.5
22
24
7844.9 1553.0 2130.5 5 9 80.8
7917.4 1587.4 2195.7 5475.7
24
26
7847.3 1554.1 2132.6 5383.9
7919.8 1588.6 2197.9 5478.9
26
28
7849.7 1555.3 2134.8 5387.1
7922.2 1589.7 2200.1 5482.1
28
30
7852.1 1556.4 2136.9 5390.2
7924.6 1590.9 2202.3 5485.3
30
32
7854.6 1557.5 2139.0 5393.4
7927.1 1592.0 2204.5 5488.5
S2
34
7857.0 1558.7 2141.2 5396.5
7929.5 1593.2 2206.8 5491.7
34
36
7859.4 1559.8 2143.3 5399.7
7931.9 1594.3 2209.0 5494.9
36
38
7861.8 1561.0 2145.5 5402.8
7934.3 1595.5 2211.2 5498.1
38
40
7864.3 1562.1 2147.7 5406.0
7936.7 1596.6 2213.4 5501.3
40
42
7866.7 1563.2 2149.8 5409.1
7939.1 1597.8 2215.6 5504.5
42
44
7869.1 1564.4 2152.0 5412.3
7941.5 1598.9 2217.8 5507.7
44
46
7871.5 1565.5 2154.2 5415.4
7943.9 1600.1 2220.0 5510.9
46
48
7874.0 1566.7 2156.4 5418.6
7946.3 1601.2 2222.3 5514.1
48
50
7876.4 1567. 2158.6 5421.8
7948.7 1602.4 2224.5 5517.3
50
52
7878.8 1568.9 2160.7 5424.9
7951.2 1603.5 2226.7 5520.5
52
54
7881.2 1570.1 2162.9 5428.1
7953.6 1604.7 2228.9 5523.7
54
56
7883.6 1571.2 2165.1 5431.2
7956.0 1605.8 2231.1 5526.9
56
58
7886.1 1572.4 2167.3 5434.4
7958.4 1607.0 2233.3 5580.1
58
60
7888.5 1573.6 2169.5 5437.5
7960.8 1608.2 2235.6 5533.3
60
88
89
L. C. M. E. T.
L. C. M. E. T.
7960.8 1608.2 2235.6 5533.3
8032.4 1643.0 2303.6 5630.8
2
7963.2 1609.4 2237.8 5536.6
8034.8 1644.1 2305.9 5634.1
2
4
7965.6 1610.5 2240.1 5539.8
8037.1 1645.3 2308.2 5637.4
4
6
7968.0 1611.7 2242.3 5543.1
8039.5 1646.5 2310.5 5640.7
6
8
7970.3 1612.8 2344.6 5546.3
8041.9 1647.7 2312.8 5644.0
8
10
7972.7 1614.0 2246.8 5549.5
8044.2 1648.9 2315.1 5647.3
10
1?
7975.1 1615.2 2249.1 5552.8
8046.6 1650.0 2317.4 5650.6
12
14
7977.5 1616.3 2251.3 5556.0
8049.0 1651.2 2319.7 5653.9
14
16
7979.9 1617.5 2253.6 5559.2
8051.4 1652.4 2322.0 5657.1
16
18
7982.3 1618.6 2255.8 5562.5
8053.7 1653.6 2324.3 5660.4
18
20
7984.7 1619.8 2258.1 5565.7
8056.1 1654.8 2326.7 5663.7
20
22
7987.1 1621.0 2260.4 5568.9
8058.5 1655.9 2329.0 5667.0
22
24
7989.4 1622.1 2262.7 5572.2
8060.8 1657.1 2331.3 5670.3
24
26
7991.8 1623.3 2264.9 5575.4
8063.2 1658.3 2333.7 5673.6
26
28
7994.2 1624.4 2267.2 5578.6
8065.6 1659.5 2336.0 5676.9
28
30
7996.6 1625.6 2269.5 5581.9
8067.9 1660.7 2338.3 5680.2
30
32
7999.0 1626.8 2271.7 5585.1
8070.3 1661.8 2340.7 5683.5
32
34
8001.4 1627.9 2273.9 5588.4
8073.7 1663.0 2343.0 5686.8
34
36
8003.8 1629.1 2276.2 5591.7
8075.1 1664.2 2345.3 5690.2
36
38
8006.1 1630.2 2278.5 5594.9
8077.4 1665.4 2347.7 5693.5
38
40
8008.5 1631.4 2080.8 5598.2
8079.8 1666.6 2350.0 5696.8
40
42
8010.9 1632.6 2283.0 5601.4
8082.2 1667.7 2352.3 5700.1
42
44
8013.3 1633.7 2285.3 5604.7
8084.5 1668.8 2354.7 5703.4
44
46
8015.7 1634.9 2^87.6 5608.0
8086.9 1670.0 2357.0 5706.8
46
48
8018.1 1636.0 2289 9 5611.2
8089.3 1671.2 2359.3 5710.1
48
50
8020.5 1637.2 2292.2 5614.5
8091.6 1672.4 2361.7 5713.4
50
52
8022.9 1638.4 2294.4 5617.8
8094.0 1673.5 2364.0 5716.7
52
54
8025.2 1639.5 2296.7 5621.0
8096.4 1674.7 2366.3 5720.0
54
56
8027.6 1640.7 2299.0 5624.3
8098.8 1675.9 2368.7 5723.4
56
58
8030.0 1641.8 2301.3 5627.5
8101.1 1677.1 2371.0 5726.7
58
60
8032.4 1643.0 2303.6 5630.8
8103.5 1678.3 2373.4 5730.0
60
FUNCTIONS OF A ONE-DEGREE CURVE 233
90
91
L. C. M. E. T.
L. C. M. E. T.
/
8103.5 1678.3 2373.4 5730.0
8173.9 1713.8 2445.1 5830.9
2
8105.8 1679.5 2375.8 5733.3
8176.2 1715.0 2447.5 5834.3
2
4
8108.2 1680.6 2378.2 5736.7
8178.5 1716.2 2450.0 5837.7
4
6
8110.5 1681.8 2380.5 5740.0
8180.9 1717.4 2452.4 5841.1
6
8
8112.9 1683.0 2382.9 5743.4
8183.2 1718.6 2454.8 5844.5
8
10
8115.2 1684.2 2385.3 5746.7
8185.5 1719.7 2457.2 5847.9
10
12
8117.6 1685.4 2387.6 5750.0
8187.9 1720.9 2459.7 5851.3
12
14
8119.9 1C86.5 2390.0 5753.4
8190.2 1722.1 2462.1 5854.7
14
16
8122.3 1687.7 2392.4 5756.7
8192.5 1723.3 2464.5 5858.1
16
18
8124.6 1688.9 2394.7 5760.1
8194.8 1724.5 2467.0 5861.5
18
20
8127.0 1690.1 2397.1 5763.4
8197.2 1725.7 2469.4 5864.9
20
2-2
81 -,'9. 3 1691.3 2399.5 5766.8
8199.5 1726.9 2471.9 5868.3
22
24
8131.7 1692.5 2401.9 5770.1
8201.8 1728.1 2474.3 5871.8
24
20
8134.0 1693.6 2404.3 5773.5
8204 .2 1 729 . 3 2476 . 7 5875 . 2
26
28
8136.4 1694.8 2406.6 5776.9
8206.5 730.5 2479.2 5878.6
28
30
8138.7 1696.0 2409.0 5780.2
8208.8 731.7 2481.6 5882.0
30
32
8141.1 1697.2 2411.4 5783.6
8211.1 732.9 2484.1 5885.4
32
34
8143.4 1698. 4 2413.8 5787.0
8213.5 734.1 2486.5 5888.9
34
36
8145.8 1699.6 2416.2 5790.3
8215.8 735.3 2489.0 5892.3
36
38
8148.1 1700.7 2418.6 5793.7
8218.1 736.4 2491.5 5895.7
38
40
8150.4 1701.9 2421.0 5797.1
8220.4 737.6 2493.9 5899.2
40
4-2
8152.8 1703.1 2423.4 5800.4
8222.8 738.8 2496.4 5902.6
42
44
8155.1 1704.3 2425.8 5803.8
8225.1 740.0 2498.9 5906.0
44
46
8157.5 1705.5 2428.2 5807.2
8227.4 741.8 2501.3 5909.4
46
48
8159.8 1706.7 2430.6 5810.6
8229.7 742.4 2503.8 5912.9
48
50
8162.2 1707.9 2433.0 5814.0
8232.0 743.6 2506.3 5916.3
50
52
8164.5 1709.0 2435.4 5817.3
8234.3 744.8 2508.7 5919.8
52
54
8166.8 1710.2 2437.9 5820.7
8236.7 746.0 2511.2 5923.2
54
56
8169.2 1711.4 2440.3 5824.1
8239.0 747.2 2513.7 5926.7
56
58
8171.5 1712.6 2442.7 5827.5
8241.3 1748.4 2516.2 5930.1
58
60
8173.9 1713.8 2445.1 5830.9
8243.6 1749.6 2518.7 5933.6
60
92
93
L. C M. E. T.
L.C. M. E. T.
8243.6- 1749.6 2518.7 5933.6
8312.8 1785.7 2594.2 6088.2
0~
2
8245.9 1750.8 2521.2 5937.0
8315.1 1786.9 2596.8 6041 7
2
4
8248.2 1752.0 2523.6 5940.5
8317.4 1788.2 2599.3 6045.2
4
6
8250.6 1753.2 2526.1 5944.0
8319.7 1789.4 2601.9 6048.7
6
8
8252.9 1754.4 2528.6 5947.4
8322.0 1790,6 2604.4 6052.2
8
10
8255.2 1755.6 2531.1 5950.9
8324.3 1791.8 2(507.0 6055.8
10
12
8257.5 1756.8 2533.6 5954.4
8306.6 1793.0 2609.6 6059.3
12
14
8259.8 1758.0 2536.1 5957.8
8308.8 1794.2 2612.1 6062.8
14
16
8262.2 1759.2 2538.6 5961.3
8331.1 1795.4 2614.7 6066.4
16
18
8264.5 1760.4 2541.1 5964.8
8333.3 1796.6 2617.3 6069.9
18
20
8266.8 1761.6 2543.6 5968.2
8335.6 1797.8 2619.8 6073.4
20
82
8269.1 1762.8 2546.1 5971.7
8337.9 1799.1 2622.4 6077.0
22
24
8271.4 1764.0 2548.6 5975.2
8340.2 1800.3 2625.0 6080.5
24
26
8273.7 1765.2 2551.2 5978.7
8342.5 1801.5 2627.6 6084.1
26
28
8276.0 1766.4 2553.7 5982.2
8344.8 1802.7 2630.2 6087.6
28
30
8278.3 1767.6 2556.2 5985.6
8347.1 1803.9 2632.7 6091.2
30
32
8280.6 1768.8 2558.7 5989.1
8349.4 1805.1 2635.3 6094.7
32
34
8282.9 1770.0 2561.2 5992.6
8351.7 1806.3 2637.9 6098.3
34
36
8285.2 1771.2 2563.8 5996.1
8354.0 1807.6 2640.5 6101.8
36
38
8287.5 1772.5 2566.3 5999.6
8356.3 1808.8 2643.1 6105.4
38
40
8289.8 1773.7 2568.8 6003.1
8358.5 1810.0 2645.7 6109.0
40
42
8292.1 1774.9 2571.3 6006.6
8360.8 1811.2 2648.3 6112.5
42
44
8294.4 1776.1 2573.9 6010.1
8363.1 1812.4 2650.9 6116 1
44
46
8296.7 1777.3 2576.4 6013.6
8365.4 1813.6 2653.5 6119.7
46
48
8299.0 1778.5 2578.9 6017.1
8367.7 1814.9 2656.1 6123.2
48
50
8301.3 1779.7 2581.5 6020.6
8369.9 1816.1 2658.7 6106 8
50
52
8303.6 1780.9 2584.0 C024.1
8372.2 1817.3 2661.3 6130.4
52
51
8805.9 1782.1 2586.6 6027.6
8374.5 1818.5 2663.9 6133.9
54
56
8308.2 1783.3 2589.1 6031.1
8376.8 1819.7 2666.6 6137.5
56
58
8310.5 1784.5 2591.7 6034.6
8379.1 1820.9 2669.2 6141.1
58
60
8312.8 1785.7 2594.2 6038.2
8381.3 1822.2 2671.8 6144.7
60
234 FUNCTIONS OF A ONE-DEGREE CURVE
94
95
L. C. M. E. T.
L. C. M. E. T.
8381.3 1822.2 2671.8 6144.7
8449.2 1858.9 2751.5 6253.2
2
8383.6 1823.4 2674.4 6148.3
8451.5 1860.1 2754.2 6256.9
2
4
8385.9 1824.6 2677.0 6151.9
8453.7 1861.3 2756.9 6260.5
4
6
8388.1 1825.8 2679.7 6155.4
8456.0 1862.6 2759.6 6264.2
6
8
8390.4 1827.0 2G82.3 6159.0
8458.2 1863.8 2762.3 6267.8
8
10
8392.7 1828.3 2684.9 6162.6
8460.4 1865.0 2765.0 6271.5
10
12
8395.0 1829.5 2687.6 6166.2
8462.7 1866.3 2767.7 6275.2
12
14
8397.2 1830.7 2690.2 6169.8
8464.9 1867.5 2770.4 6278.8
14
16
8399.5 1831.3 2692.8 0173.4
8467.2 1868.7 2773.1 6282.5
16
18
8401.7 1833.1 2695.6 6177.0
8469.4 1869.9 2775.8 6286.2
18
20
8404. C 1834.4 2698.1 6180.6
8471.7 1871.2 2778.5 6289.8
20
22
8406.3 1835.6 2700.8 6184.2
8473.9 1872.4 2781.2 6293.5
22
24
8408.5 1836.8 2703.4 6187.8
8476.2 1873.6 2784.0 6297.2
24
26
8410.8 1838.0 2706.1 6191.5
8478.4 1874.9 2786.7 6300.9
26
28
8413.1 1839.3 2708.7 6195.1
8480.7 1876.1 2789.4 6304.6
28
30
8415.3 1840.5 2711.4 6198.7
8482.9 1877.3 2792.1 6308.2
30
32
8417.6 1841.7 2714.0 6202.3
8485.1 1878.6 2794.9 6311.9
32
31
8419.9 1842.9 2716.7 6205.9
8487.4 1879.8 2797.6 6315.6
34
36
8422.1 1844.2 2719.3 6209.5
8489.6 1881.0 2800.3 6319.3
36
38
8424.4 1845.4 2722.0 6213.2
8491.9 1882.3 2803.1 6323.0
38
40
8426.6 1846.6 2724.7 6216.8
8494.1 1883.5 2805.8 6326.7
40
42
8428.9 1847.8 5J727.3 6220.4
8496.3 1884.8 2808.6 6330.4
42
44
8431.2 1849.1 2730.0 6224.1
8498.6 1886.0 2811.3 6334.1
44
46
8433.4 1850.3 2732.7 6227.7
8500.8 1887.2 2814.1 6337.8
46
48
8435.7 1851.5 2735.4 6231.3
8503.0 1888.5 2816.8 6341.5
48
50
8437.9 1852.7 2738.0 6235.0
8505.3 1889.7 2819.6 6345.2
50
52
8440.8 1854.0 2740.7 6238.6
8507.5 1890.9 2822.3 6349.0
52
54
8442.4 1855.2 2743.4 6242.3
8509.8 1892.2 2825.1 6352.7
54
56
8444.7 1856.4 2746.1 6245.9
85120 1893.4 2827.8 6356.4
56
58
8447.0 1857.6 2748.8 6249.6
8514.2 1894.6 2830.6 6360.1
58
60
8449.2 1858.9 2751.5 6253.2
8516.4 1895.9 2833.4 6363.8
60
96
97
j /
L. C. M. E. T.
L. C. M. E. T.
8516 4 1895.9 2833.4 6363.8
8583.0 1933.2 2917.5 6476.6
2
8518.7 1897.1 2836.1 6367.5
8585.2 1934.4 2920.3 6480.4
2
4
85209 1898.4 2838.9 6371.3
8587.5 1935.7 2923.2 6484.2
4
6
8523.1 1899.6 2841.7 6375.0
8589.7 1936.9 2926.0 6488.0
6
8
8525 4 1900. S 2844.5 6378.7
8591.9 1938.2 2928.9 6491.8
8
10
8527.6 1902.1 2847.2 6382.5
8594 1 1939.4 2931.7 6495.6
10
12
8529 8 1903.3 2850.0 6386.2
8596.3 1940.7 2934.6 6499.4
12
14
8532.0 1904.6 2852.8 6389.9
859S.5 1941.9 2937.5 6503.2
14
16
8534.3 1905.8 2855.6 6393.7
8000.7 1943.2 2940.3 6507.1
16
18
8536.5 1907.0 2858.4 6397.4
8602.9 1944.4 2943.2 6510.9
18
20
8538.7 1908.3 2861.2 6401.2
8605.1 1945.7 2946.1 6514.7
20
22
8540 9 1909.5 2864.0 6404.9
8607.3 1946.9 2948.9 6518.5
22
24
8543.2 1910.8 2866.7 6408.7
8609.5 1948.2 2951.8 6522.3
24
26
8545.4 1912.0 2869.5 6412.4
8611.7 1949.4 2954.7 6526.2
26
28
8547 6 1913 3 2872.3 6416.2
8613.9 1950.7 2957.6 6530.0
28
30
8549.8 1914.5 2875.1 6419.9
8616.1 1952.0 2960.4 6533.8
30
32
8552 1915.7 2877.9 6423.7
8618.3 1953.2 2963.3 6537.7
32
34
8554.3 1917.0 2880.8 6427 5
8620.5 1954.5 2966.2 6541.5
34
36
8556.5 1918.2 2883.6 6431.2
8622.7 1955.7 2969.1 6545.3
36
38
8558.7 1919.5 2886.4 64350
8624.9 1957.0 2972.0 6549.2
38
40
8560.9 1920.7 2889.2 6438.8
8627.1 1958.2 2974.9 6553.0
40
42
8563.1 1922.0 2892.0 6442 5
8629.3 1959 5 2977.8 6556.9
42
44
8565.3 1923.2 2894.8 6446.3
8631.5 1960.7 2980.7 6560.7
44
46
8567 6 1924 5 2897.7 6450.1
8633.7 1962.0 2983.6 6564.6
46
48
8569.8 1925.7 2900.5 6453.9
8635.8 1963.2 2986.5 6568.4
48
50
8572.0 1927.0 2903.3 6457.6
8638.0 1964.5 2989.4 6572.3
50
52
8574.2 1928.2 2906.! 6461.4
8040.2 1965.8 2992.3 6576.2
52
54
8576.4 1929 4 2909.0 6465.2
8642.4 1967.0 2995.2 6580.0
54
56
8578.6 1930.7 2911.8 6469.0
8044.6 1968.3 2998.1 6583.9
56
58
8580.8 1931.9 2914.7 6472.8
8646 $ 1969.5 3001.1 6587.7
58
60
8583.0 1933.2 2917.5 6476.6
86490 1970.8 3004 6591.6
60
FUNCTIONS OF A ONE-DEGREE CURVE 235
98
99
L. C. M. . T.
L. C. M. E. T.
8649.0 1970.8 3004.0 6591.6
8714.3 2008.7 3092.9 6709.0
2
8651.2 1972.0 3006.9 6595.5
8716.4 2009.9 3095.9 6712.9
2
4
8653.3 1973.3 3009.8 6599.4
8718.6 2011.2 3098.9 6716.9
4
6
8655.5 1974.6 3012.8 6603.2
8720.7 2012.5 3101.9 6720.8
6
8
8657.7 1975.8 3015.7 6607.1
8722.9 2013.7 3104.9 6724.8
8
10
8659.9 1977.1 3018.6 6611.0
8725.1 2015.0 3107.9 6728.8
10
12
8662.1 1978.3 3021.6 6614.9
8727.2 2016.3 3111.0 6732.7
12
14
8664.3 1979.6 3024.5 6618.8
8729.4 2017.5 3114.0 6736.7
14
16
8666.4 1980.9 3027.5 6(122.7
8731.5 2018.8 3117.0 6740.7
16
18
8668.6 1982.1 3030.4 6C26.6
8733.7 2020.1 3120.0 6744.6
18
20
8670.8 1983.4 3033.3 6630.5
8735.9 2021.4 3123.1 6748.6
20
22
8673.0 1984.6 3036.3 6634.4
8738.0 2022.6 3126.1 6752.6
22
24
8675.2 1985.9 3039.3 6638.3
87<!0.2 2023.9 3129.1 6756.6
24
26
8677.3 1987.2 3042.2 6642.2
8742.3 2025.2 3132.2 6760.6
26
28
8679.5 1988.4 3045.2 6646.1
8744.5 2026.4 3135.2 0764.6
28
30
8681.7 1989.7 3048.1 6650.0
8746.6 2027.7 3138.3 6768.6
30
32
8683.9 1991.0 3051.1 6653.9
8748.8 2029.0 3141.3 6772.6
33
34
8686.0 1992.2 3054.1 6657.8
8750.9 2030.3 3144.4 6776.6
34
36
8688.2 1993.5 3057.0 6661.7
8753.1 2031.5 3147.4 6780.6
36
38
8690.4 1994.7 3060.0 6665.7
8755.3 2032.8 3150.5 6784.6
38
40
8692.6 1996.0 3063.0 6669.6
8757.4 2034.1 3153.5 6788.6
40
42
8694.7 1997.3 3066.0 6673.5
8759.5 2035.4 3156.6 6792.6
42
44
8696.9 1998.5 3068.9 6677.4
8761.7 2036.6 3159.7 6796.6
44
46
8699.1 1999.8 3071.9 66H1.4
8763.8 2037.9 3162.7 6800.6
46
48
8701.2 2001.1 3074.9 6685.3
8766.0 2039.2 3165.8 6804.6
48
50
8703.4 2002.3 3077.9 6689.2
8768.1 2040.5 3168.9 6808.6
50
52
8705.6 2003.6 3080.9 6693.2
8770.3 2041.7 3172.0 6812.6
52
54
8707.8 2004.9 3083.9 6697.1
8772.4 2043.0 3175.1 6816.7
54
56
8709.9 2006.1 3086.9 6701.1
8774.6 2044.3 3178.1 6820 7
56
58
8712.1 2007.4 3089.9 6705.2
8776.7 2045.6 3181.2 6824.7
58
60
8714.3 2008.7 3092.9 6709.0
8778.9 2046.8 3184.3 6828.8
60
100
101
/
L C. M. E. T.
L. C. M. E. T.
/
8778.9 2046.8 3184.3 6828.8
8842.8 2085.3 3278.3 6951.0
8781.0 2048.1 3187.4 6832.8
8844.9 2086.6 3281.5 69552
2
4
8783.1 2049.4 3190.5 6836.8
8847.0 2087.8 3284.7 6959.3
4
6
8785.3 2050.7 3193.6 6840.9
8849.2 2089.1 3287.9 6963.4
6
8
8787.4 2051.9 3196.7 6844.9
8851.3 2090.4 3291.1 6967.6
8
10
8789.6 2053.2 3199.8 6849.0
8853.4 2091.7 3294.3 6971.7
10
12
8791.7 2054.5 3202.9 6853.0
8855.5 2093.0 3297.5 6975 8
12
14
8793.9 2055.8 3506.0 6857.1
8857.6 2094.3 3300.7 6980.0
14
16
8796.0 2057.1 3209.1 6861.1
8859.8 2095.6 3303.9 6984 1
16
18
8798.9 2058.3 3212.2 6865.2
8861.9 2096.9 3307.1 6988.2
18
20
8800.3 2059.6 3215.4 6869.2
8864.0 2098.2 3310.3 6992.4
20
22
8802.4 2060.9 3218.5 6873.3
8866.1 2099.4 3313.5 6996.6
22
24
8804.5 2062.2 3321.6 6877.4
8868.2 2100.7 3316 7 7000.7
24
26
8806.7 2063.5 3224.7 6881.4
8870.3 2102.0 3319.9 7004.9
26
28
8808.8 2064.7 3227.9 6885.5
8872.4 2103.3 3323,. 1 7009.0
28
30
8810.9- 2066.0 3231 6889.6
8874.5 2104.6 3326.4 7013.2
30
32
8813.1 2067.3 3234.1 6893.7
8876.7 2105.9 3329.6 7017.3
32
34
8815.2 2068.6 3237.3 6897.8
8878.8 2107.2 3332.8 7021 5
34
36
8817.3 2069.9 3240.4 6901.8
8880.9 2108.5 3336.0 7025.7
36
38
8819.5 2071.1 3243.5 6905.9
8883.0 2109.8 3339.3 7029.9
38
40
8821.6 2072.4 3246.7 6910.0
8885.1 2111.1 3342.5 7034.0
40
42
8823.7 2073.7 3249.8 6914.1
8887.2 2112.4 3345.8 7038.2
42
44
8825.8 2075.0 3253 C 6918.2
8889.3 2113.6 3349.0 7042.4
44
46
8828.0 2076.3 3256.2 6922.3
8891.4 2114.9 3352.3 7046.6
46
48
8830.1 2077.6 3259.3 6926.4
8893.5 2116.2 3355.5 7050.8
48
50
8832.2 2078.9 3262.5 6930.5
8895.6 2117.5 3358.8 7055.0
50
52
8834.3 2080.1 3265.7 6934.6
8897.7 2118.8 3362.0 7059.2
52
54
8836.4 2081.4 3268.8 6938.7
8899.8 2120.1 3365 5 7063 4
54
56
8838 6 2082.7 ,3272.0 6942.8
8901.9 2121.4. 3368.7 7067.6
56
58
8340.7 2084.0 3275.2 6946.9
8904.0 2122.7 3372.0 7071.8
58
60
8842.8 2085.3 3278.3 6951.0
8906.1 2124.0 3375.1 7076.0
60
236 FUNCTIONS OF A ONE-DEGREE CURVE
102
103
/
L. C. M. E. T.
L. C. M. E. T.
/
8906.1 2124.0 3375.1 7076.0
8968.7 2163.0 3474.6 7203.6
2
8908.2 2125.3 3378.3 7080.2
8970.8 2164.3 3478.0 7207.9
2
4
8910.3 2126.6 .3381.6 7084.4
8972.9 2165.6 3481.4 7212.2
4
6
8912.4 2127.9 3384.9 7088.6
8974.9 2166.9 3484.7 7216 5
6
8
8914.5 2129.2 3388.2 7092.8
8977.0 2168.2 3488.1 7220.8
8
10
8916.6 2130.5 3391.5 7097.1
8979.1 2169'.5 3491.5 7225.1
10
12
8918.7 2131.8 33947 7101.3
8981.1 2170.8 3494.9 7229.5
12
14
8920.8 2133.1 :98 7105.5
8983.2 2172.1 3498.3 7233.8
14
16
8922.9 2134.4 3101.3 7109.7
8985.3 2173.4 3501.6 7238.1
16
18
8925.0 2135.7 3104.6 7114.0
8987.3 2174.7 3505.3 72424
18
20
8927.0 2137.0 3407.9 7118.2
89894 2176.1 3508.4 7246.8
20
22
8929.1 2138.3 311 1.2 7122.4
8991.5 2177.4. 3511.8 7251.1
2*.'
24
8931.2 2139.6 3H4.5 7126.7
8993.5 2178.7 3515.2 7255.4
24
26
8933.3 2140.9 3417.9 7130.9
8995.6 2180.0 3518.7 7259.8
26
28
893V 4 2142.2 3421.2 7135.2
8997.7 2181.3 3522.1 7264.1
28
30
8937.5 2143.5 3424.5 7139.4
8999.7 2182.6 3525.5 7268.5
30
32
8939.6 2144 8 3427.8 7143.7
9001.8 2183.9 3528.9 7272.8
32
34
8941.6 2146.1 3431.1 7148.0
9003.9 2185.2 3532.3 7277.2
34
36
8943.7 2147.4 3434.5 7152.2
9005.9 2186.5 3535.7 7281.5
36
38
8945.8 2148.7 3437.8 7156.5
9008.0 2187.8 3539.2 7285.9
38
40
8947.9 21500 3441.1 7160.7
9010.0 2189.1 3542.6 7290.3
40
42
8950.0 2151.3 3444.4 7165.0
9012.1 2190.5 3546.0 7294.6
42
44
8952.1 2152.6 3447.8 7169.3
9014.2 2191.8 3549.5 7299.0
44
46
8954.1 2153.9 3451.1 7173.6
9016.2 2193.1 3552.9 7303.4
46
48
8956.2 2155.2 3454.5 7177.9
9018.3 2194.4 3556.3 7307.7
48
50
8958.3 2156 5 3457.8 7182.1
9020.3 2195 7 3559.8 7312.1
50
52
8960.4 2157.8 3461.2 7186.4
9022.4 2197.0 3563.2 7316.5
52
54
8962.5 2159.1 3464.5 7190.7
9024.5 2198.3 3566.7 7320.9
54
56
8964 5 2100.4 3467.9 7195.0
9026.5 2199.6 3570.2 7325.3
56
58
S966.6 2161.7 3471.2 7199.3
9028.6 2200.9 3573.6 7329.7
58
60
8968.7 2163.0 3474.6 7203.6
9030.6 2202.3 3577.1 7334.1
60
104
105
L. C. M. E. T.
L. C. M. E. T.
9030.6 2202.3 3577.1 7334.1
9091.8 2241.8 3682.6 7467.5
2
9032 7 2203.6 3580.5 7338.5
9093.9 2243.1 3686.1 7472.0
2
4
9034.7 2204.9 3584.0 7342.9
9095.9 2244.4 3689.7 7476.5
4
6
9036.8 2206.2 3587.5 7347.3
9097.9 2245.8 3693.3 7481.0
6
8
9038.8 2207.5 3591.0 7351.7
9099.9 2247.1 3696.9 7485.5
8
10
9040.9 2208 8 3594.4 7356.1
9102.0 2248.4 3700.4 7490.0
10
12
9042.9 2210 2 3597.9 7360.5
9104.0 2249.7 3704.0 7494.5
12
14
90450 2211.5 3601.4 7364.9
9106.0 2251.1 3707.6 7499.1
14
16
9047.0 2212.8 3604.9 7369.4
9108.0 2252.4 3711.2 7503.6
16
18
9049.1 2214.1 3608.4 7373.8
9110.1 2253.7 3714.8 7508.1
18
20
9051.1 2215.4 3611.9 7378.2
9112.1 2255.0 3718.4 7512.6
20
22
9053.1 2216.7 3615.4 7382.6
9114.1 2256.4 3722.0 7517.2
22
24
9055.2 2218 3618.9 7387.1
9116.1 2257.7 3725.6 7521.7
24
26
9057.2 22194 3622.4 7391.5
9118.1 22.-9.0 3729.3 7526.3
26
28
9059.3 2220.7 3625.9 7396.0
9120.2 2260.3 3732.9 7530.8
28
30
9001.3 2222.0 3629.4 7400.4
9122.2 2261.7 3736.5 7535.3
30
32
9063.3 2223.3 3633.0 7404.8
9124.2 2263 3740.1 7539 9
32
34
9065.4 2224.6 3036.5 74093
9126.2 2264.3 3743.7 7544.4
34
] 36
9067.4 2226 3640.0 7413 8
9128 2 2265.7 3747.4 7549.0
36
38
9069.5 2227.3 3643.5 7418 2
9130.2 2267.0 3751.0 75536
38
40
9071.5 2228.6 3647.1 7422.7
9132.3 2268.3 3754.6 7558.1
40
42
9073 5 2229.9 3650.6 7427.1
9134.3 2269.6 3758.3 7562.7
42
44
90756 2231 2 3654.1 7431.6
9136.3 2271.0 3761.9 7567.3
44
46
9077 6 2232.6 3657.7 7436.1
9138.3 2272.3 3765.6 7571 8
46
48
9079.6 2233.9 3661.2 74406
9140.3 2273 6 3769.2 7576.4
48
50
9081.7 2235.2 3664.8 7445.0
9142.3 2275.0 37729 7581.0
50
52
9083.7 2236.5 3668.3 7449.5
9144.3 2276.3 3776.5 7585.6
52
54
9085.7 2237.8 3671.9 7454.0
9146 3 2277.6 3780.2 7590.2
54
56
9087.8 2239.2 3675.4 7458 5
9148.3 2278.9 3783.9 7594.8
56
58
9089.8 2240.5 3679.0 7463.0
9150.4 2280.3 3787.5 7599.4
58
60
9091 8 2241.8 3682.6 7467 5
9152 4 2281.6 3791 2 7W4
60
FUNCTIONS OF A ONE-DEGREE CURVE 237
106
107
/
L. C. M. E. T.
L. C. M. E. T.
9152.4 2-281.6 3791.2 7604.0
9212.2 2321.7 3903.1 7743.7
2
9154.4 228-2.9 3794.9 7608.6
9214.2 2323.0 3906.9 7748.4
4
9156.4 2284.3 3798.6 7613.2
9216.2 2324.4 3910.7 7753.1
4
6
9158.4 2285.6 3802.3 7617.8
9218. 2325.7 3914.5 7757.8
6
8
9160.4 2286.9 3805.9 7622.4
9220. 2327.0 3918.3 7762.5
8
10
9162.4 2288.3 3809.6 7627.0
9222. 2328.4 3922.1 7767.3
10
12
9164.4 2289.6 3813,3 7631.7
9224. 2329.7 3925.9 7772.0
12
14
9166.4 2290.9 3817.0 7636.3
9226. 2331.1 3929.7 7776.7
14
l.
9168.4 2292.3 3820.7 7610.9
9228. 233'2.4 3933.6 7781.5
16
18
9170.4 2293.6 3824.4 7645.5
9230.0 2333.7 3937.4 7786.2
18
20
9172.4 2294.9 3828.1 7650.2
9232.0 2335.1 3941.2 7791.0
20
22
9174.4 2296.3 3831.9 7654.8
9234.0 2336.4 3945.0 7795.7
22
24
9176.4 2297.6 3835.6 7659.5
9235.9 2337.8 3948.9 7800.5
24
26
9178.4 2298.9 3839.3 7664.1
9-237.9 2339.1 3952.7 7805.2
26
28
9180.4 2300.3 3843.0 7668.8
9239.9 2340.5 3956.5 7810.0
28
30
9182.4 2301.6 3846.7 7673.4
9241.9 2341.8 3960.4 7814.7
80
32
9184.4 2302.9 3850.5 7678.1
9243.8 2343.1 39642 7819.5
32
34
9186.4 2304.3 3854.2 768'.>.7
9'245.8 2344.5 3968.1 7824.3
34
36
9188.4 2305.6 3858.0 7687.4
9247.8 2345.8 3971.9 7829.1
86
38
9190.4 2306.9 3861.7 7692.1
9249.7 2347.2 3975.8 7833.8
38
40
9192.4 2308.3 3865.4 7696.7
9251.7 2348.5 3979.6 7838.6
40
42
9194.4 2309.6 3869.2 7701.4
9-253.7 2349.9 3983.5 7843.4
42
44
9196.3 2311.0 3873.0 7706.1
9255.6 2351.2 3987.4 7848.2
44
46
9198.3 2312.3 3876.7 7710.8
9257.6 2352.6 3991.3 7853.0
46
48
9200.3 2313.6 3880.5 7715.5
9259.6 2353.9 3995.1 7857.8
48
50
9202.3 2315.0 3884.2 7720.1
9261.5 2355.3 3999.0 7862.6
50
52
9204.3 2316.3 3888.0 7724.8
9263.5 2356.6 4002.9 7867.4
52
54
9206.3 2317.7 3891.8 7729.5
9265.4 2358.0 4006.8 7872.2
54
56
9208.2 2319.0 3895.6 7734.2
9267.4 2359.3 4010 7 7877.0
56
58
9210.2 2320.3 3899.3 7739.0
9269.4 2360.7 4014.6 7881.9
58
60
9212.2 2321.7 3903.1 7743.7
9-271.8 2362.0 4018.5 7886.7
60
108
109
/
L. C. M. E. T.
L. C. M. E. T.
9271.3 2362.0 4018.5 7886.7
9329.8 2402.6 4137.4 8033.2
g
9273.3 2363.3 4022.4 7891.5
9331.7 2403.9 4141.4 8038.1
2
4
9275.3 2364.7 40:26.3 7896.3
9333.6 2405.3 4145.4 8043.1
4
6
9277.2 2366.0 4030.2 7901.2
9335.6 2406.6 4149.5 8048.0
6
8
9279.2 2367.4 4034.1 7906.0
9337.5 2408.0 4153.5 8053.0
8
10
9281.1 2368.7 4038.0 7910.8
9339.4 240S.4 4157.5 8057.9
10
12
9283.1 2370.1 4042.0 7915.7
9341.4 2410.7 4161.6 8062.9
12
14
9285.0 2371.4 4045.9 7920.5
9343.3 2412.1 4165.6 8067.9
14
16
9287.0 2372.8 4049.8 7925.4
9345.2 2413.4 4169.7 8072.8
16
18
9288.9 2374.1 4053.8 7930.3
9347.2 2414.8 4173.8 8077.8
18
20
9290.9 2375.5 4057.7 7935.1
9349.1 2416.2 4177.8 8082.8
20
22
9292.8 2376.8 4061.6 7940.0
9351.0 2417.5 4181.9 8087.8
22
24
9294.8 2378.2 4065.6 7944.8
9352.9 2418.9 4186.0 8092.8
24
26
9296.7 2379.5 4069.5 7949.7
9354.9 2420.2 4190.0 8097.8
26
28
9298.7 2380.9 4073.5 7954.6
9356.8 2421.6 4193.1 > 8102.8
28
30
9300.6 2382.3 4077.5 7959.5
9358.7 2423.0 4198.2 8107.8
30
82
9302.6 2383.6 4081.4 7964.4
9360.6 2424.3 4202.3 8112.8
32
34
9304.5 2385.0 4085.4 7969.3
9362.6 2425.7 4206.4 8117.8
34
36
9306.5 2386.3 4089.4 7974.1
9364.5 2427.0 4210.5 8122.8
36
38
9308.4 2387.7 4093.4 7979.0
9366.4 2428.4 4214.6 8127.8
38
40
9310.4 2389.0 4097.3 7983.9
9368.3 2430.0 4218.7 8132.8
40
42
9312.3 2390.4 4101.3 7988.8
9370.2 2431.1 4222.8 8137.9
42
44
9314.2 2391.7 4105.3 7993.8
9372.2 2432.5 4'226.9 8142.9
44
46
9316.2 2393.1 4109.3 7998.7
9374.1 2433.9 4231.0 8147.9
46
48
9318.1 2394.4 4113.3 8003.6
9376.0 2435.2 4235.1 8153.0
48
50
9320.1 2395.8 4117.3 8008.5
9377.9 2436.6 4239.3 8158.0
50
52
9322.0 2397.2 4121.3 8013.4
9379.8 2438.0 4'243.4 8163.1
52
54
9323.9 2398.5 4125.3 8018.4
9381.7 2439.3 4247.5 8168.1
54
56
9325.9 2399.9 4129.3 8023 3
9383.7 2440.7 4251.7 8173.2
56
58
9327.8 2401.2 4133.4 8028.2
9385.6 2442.1 4255.8 8178.2
58
60
9320.8 240-2.6 4137.4 8033.2
9387.5 24434 4260.0 8183.3
60
238 FUNCTIONS OF A ONE-DEGREE CURVE
110
111
L. C. M. E. T.
L. C. M. E. T.
9387.5 2443.4 4260.0 8183.3
9444.5 2484.5 4386.4 8337.2
2
9389.4 2444.8 4264.1 8188.4
9446.4 2485.9 4390.7 8342.4
2
4 '
9391.3 2446.1 4268.3 8193.4
9448.3 2487.2 4395 8347.6
4
6
9393 2 2447.5 4272.4 8198.5
9450.1 2488.6 4399.3 8352.8
6
8
9395.1 2448.9 4276.6 8203.6
9452.0 2490.0 4403.6 8358.0
8
10
9397.0 2450.2 4280.8 8208.7
9453.9 2491.4 4407.9 8363.2
10
12
9398.9 2451.6 4284.9 8213.8
9455.8 2492.7 4412. "2 8368.5
12
14
9400.8 2453.0 4289.1 8218.9
9457.7 2494.1 4416.5 8373.7
14
16
9402.7 2454.3 4293.3 8224.0
9459.6 2495.5 4420.8 8378 9
16
18
9404.7 2455.7 4297.5 8229.1
9461.4 2496.9 4425.1 8384 1
18
20
9406.6 2457.1 4301.7 8234.2
9463.3 2498.2 4429.5 8389.4
20
22
9408.5 2458.4 4305.9 8239.3
9465.2 2499.6 4433 8 8394 6
22
24
9410.4 24598 4310.1 8244.4
9467.1 2501.0 4438.1 839.9
24
26
9412.3 2461.2 4314.3 8249.5
9469.0 2502.4 4442.5 8405.1
26
28
9414.2 2462.6 4318.5 8254.6
9470.8 2503.8 4446.8 8410.4
28
30
9416.1 2463.9 4322.7 8259.8
9472.7 2505.1 4451.2 8415.6
30
'6-2
9418.0 2465.3 4326.9 8:264.9
9474.6 2506.5 4455.5 84^0 9
32
34
9419.9 2466.7 4331.1 8270.0
9476.5 2507.9 4459.9 8426.2
34
36
9421.8 2468.0 4335.4 8275.2
9478.3 2509.3 4464.2 8431.4
36
38
9423.7 2469.4 4339.6 8280.3
9480.2 2510.6 4468.6 8436.7
38
40
9425.6 2470.8 4343.8 8285.5
9482.1 2512.0 4473.0 8442.0
40
42
9427.5 2472.1 4348.1 8290.6
9484.0 2513.4 4477.3 8447.3
42
44
9429.3 2473.5 4352.3 8295.8
9485.8 2514.8 4481.7 8452.6
44
46
9431.2 2474.9 4356.6 8300.9
9487.7 2516.2 4486.1 8457.9
46
48
9433.1 2476.3 4360.8 8306.1
9489.6 2517.5 4490.5 8463.2
48
50
9435.0 2477.6 4365.1 8311.3
9491.4 2518.9 4494.9 8468.5
50
52
9436.9 2479.0 4369.3 8316.5
9493.3 2520.3 4499.3 8473.8
52
54
9438.8 2480.4 4373.6 8321.6
9495.2 2521.7 4503.7 8479.1
54
56
9440.7 2481.7 4377.9 8326.8
9497.0 2523.1 4508.1 8484.4
56
58
9442.6 2483.1 4382.2 8332.0
9498.9 2524.5 4512.5 8489.7
58
60
9444.5 2484 5 4386,4 8337.2
9500.8 2525.8 4516.9 8495.1
60
112
113
L. C. M. E. T.
L. C. M. E T.
9500.8 2525.8 4516.9 8495.1
9556.3 2567.4 4651.6 8657.1
2
9502.6 2527.2 4521.4 8500.4
9558.2 2568.8 4656.2 8662.6
2
4
9504.5 2528.6 4525.8 8505.8
9560.0 2570.2 4660.8 8668.0
4
6
9506.4 2530.0 4530.2 8511.1
9561.8 2571.6 4665.4 8673.5
6
8
9508.2 2531.4 4534.6 8516.4
9563.7 2573.0 4669.9 8679.0
8
10
9510.1 2532.7 4539.1 8521.8
9565.5 2574.4 4674.5 8684.5
10
12
9511.9 2534.1 4543.5 8527.1
9567.4 2575.8 4679.1 8690.0
12
14
9513.8 2535.5 4548.0 8532.5
9569.2 2577.1 4683.7 8695.5
14
16
9515.7 2536.9 4552.4 8537.9
9571.0 2578.5 46883 8701.0
16
18
9517.5 2538.3 4556.9 8543.2
9572.9 2579.9 4692.9 8706.5
18
20
9519.4 2539.7 4561.3 8548.6
9574.7 2581.3 4697.5 8712.0
20
22
9521.2 2541.0 4565.8 8554.0
9576.5 2582.7 4702.1 8717.6
22
24
9523.1 2542.4 4570.3 8559.4
9578.4 2584.1 4706.8 8723.1
24
26
9524.9 2543.8 4574.8 8564.8
95802 2585.5 4711.4 8728.6
26
28
9526.8 2545.2 4579.3 8570.2
9582.0 2586.9 4716.0 8734.2
28
30
9528.6 2546.6 4583.7 8575.6
9583.8 2588.3 4720.6 8739.7
30
32
9530.5 2548.0 4588.2 8581.0
9585.7 2589.7 4725.3 8745.3
32
34
9532.3 2549.4 4592.7 8586.4
9587.5 2591.1 4729.9 8750.8
34
36
9534.2 2550.7 4597.2 8591.8
9589.3 259-2.5 4734.6 8756.4
36
38
9536.0 2552.1 4601.7 8597.2
9591.1 2593.9 4739.2 8761.9
38
40
9537.9 2553.5 4606 2 8602.6
9593.0 2595.3 4743.9 8767.5
40
42
9539.7 2554.9 4610.8 8608.0
9594.8 2596.7 4748.5 8773.1
42
44
9541.6 2556.3 4615.3 8613.5
9596.6 2598.1 4753.2 8778.6
44
46
9543.4 2557.7 4619.8 8618.9
9598.4 2599.4 4757.9 8784.2
46
48
9545.3 2559.1 4624.3 8624.3
9600.3 2600.8 4762.6 8789.8
48
50
9547.1 2560.5 4628.9 8629.8
9602.1 2602.2 4767.2 8795.4
50
52
9549.0 2561.8 4633.4 8035.2
9603.9 2603.6 4771.9 8801.0
52
54
9550.8 2563 2 4638.0 8640.7
9605.7 2605 4776.6 8806.6
54
56
9552 6 2564.6 4642.5 8646.2
9607.5 2606.4 4781.3 8812.2
56
58
<>554.5 2566.0 4647.1 8651.6
9609.4 2607.8 4786.0 8817.8
58
60
95563 2567.4 4651.6 8657.1
9611.2 2609.2 4790.7 8823.4
60
FUNCTIONS OF A ONE-DEGREE CURVE 239
i .
114
116
/
L. C. M. E. T.
L. 0. M. E. T.
9611 2 2609.2 4790.7 8823.4
9665.3 2651.3 4934.4 8994.3
2
9613.0 2610.6 4795.5 8829.1
9667.1 2652.7 4939.3 9000.1
2
4
9614.8 2612.0 4800.2 8834.7
9668.8 2654.1 4944.2 9005.9
4
6
9616.6 2613.4 4804.9 8840.3
9670.6 2655.5 4949.1 9011.6
6
8
9618.4 2614.8 4809.6 8846.0
9672.4 2656.9 4954.0 9017.4
8
10
9620.2 2616.2 4814.4 8851.6
9674.2 2658.3 4958.9 9023.2
10
12
9622.0 2617.6 4819.1 8857.2
9676.0 2659.7 4963.8 9029.0
12
14
9623.8 2619.0 4823.9 8862.9
9677.8 2661.1 4968.7 9034.8
14
16
9625.7 2620.4 4828.6 8868.5
9679.6 2662.5 4973.6 9040.7
16
18
9627.5 2621.8 4833.4 8874.2
9681.4 2663.9 4978.5 9046.5
18
20
9629.3 2623.2 4838.1 8879.9
9683.1 2665.4 4983.4 9052.3
20
22
9631.1 2624.6 4842.9 8885.5
9684.9 2666.8 4988.3 9058.1
22
24
9632.9 2626.0 4847.7 8891.2
9686.7 2668.2 4993.3 9064.0
24
26
9634,7 2627.4 4852.4 8896.9
9688.5 2669.6 4998.2 9069.8
26
28
9636.5 2628.8 4857.2 8902.6
9690.3 2671.0 5003.2 9075.7
28
30
9638.3 2630.2 4862.0 8908.3
9692.0 2672.4 5008.1 9081.5
30
32
9640.1 2631.6 4866.8 8914.0
9693.8 2673.8 5013.1 9087.4
32
34
9641.9 2633.0 4871.6 8919.7
9695.6 2675.2 5018.0 9093.2
84
36
9643.7 2634.4 4876.4 8925.4
9697.4 2676.6 5023.0 9099.1
36
38
9645.5 2635.8 4881.2 8931.1
9699.1 2678.0 5028.0 9105.0
38
40
9647.3 2637.2 4885.0 8936.8
9700.9 2679.5 5032.9 9110.8
40
42
9649.1 2638.6 4890.9 8942.6
9702.7 2680.9 5037.9 9116.7
42
44
9650.9 2640.0 4895.7 8948.3
9704.5 2682.3 5042.9 9122.6
44
46
9652.7 2641.4 4900.5 89540
9706.2 2683.7 5047 9 9128.5
46
48
9654.5 2642.9 4905.3 8959.8
9708.0 2685.1 5052.9 9134.4
48
50
9656.3 2644.3 4910.2 8965.5
9709.8 2686.5 5057.9 9140.3
50
52
9658.1 2645.7 4915.0 8971.3
9711.6 2687.9 5062.9 9146.2
5',?
54
9659.9 2647.1 4919.9 8977.0
9713.3 2689.3 5067.9 9152.1
54
56
9061.7 2648.5 4984.7 8982.8
9715.1 2690.7 5072.9 9158.1
56
58
9663.5 2649.9 4929.6 8988.5
9716.9 2692.2 5078.0 9164.0
58
60
9665.3 2651.3 4934.4 8994.3
9718.6 2693.6 5083.0 9169.9
60
116
117
L/C. M. E. T.
L. C. M. E. T.
9718.6 2693.6 5083.0 9169.9
9771.3 2736.1 5236.6 9350.5
9720.4 2695.0 5088.0 9175.9
9773.0 2737.5 5241.8 9356.6
2
4
9722.2 2696.4 5093.1 9181.8
9774.7 2788.9 5247.0 9362.7
4
6
9723.9 2697.8 5098.1 9188.8
9776.5 2740.4 5252.2 9368.9
6
8
9725.7 2699.2 5103.2 9193.7
9778.2 2741.8 5257.4 9375.0
8
10
9727.4 2700.6 5108.2 9199.7
9779.9 2743.2 5262.6 9381.1
10
12
9729.2 2702.1 5113.3 9205.6
9781.7 2744.6 5267.9 9387.3
12
14
9731.0 2703.5 5118.4 9211.6
9783.4 2746.0 5273.1 9393.4
14
16
9732.7 2704.9 5123.4 9217.6
9785.2 2747.5 5278.4 9399.5-
16
18
9734.5 2706.3 5128.5 9223.6
9;86.9 2748.9 5283.6 9405.7
18
20
9736.3 2707.7 5133.6 92296
9788.6 2750.3 5288.9 9411.9
20
22
9738.0 2709.1 5138.7 9235 5
9790.4 2751.7 5294.2 9418.0
22
24
9739.8 2710.6 5143.8 9241.5
9792.1 2753.2 5299.5 9424.2
24
26
9741.5 2712.0 5148.9 9247.6
9793.8 2754.6 5304.7 9430.4
26
28
9743.3 2713.4 5154 9">53.6
9795.6 2756.0 5310.0 9436.6
28
30
9745.0 2714.8 5159.1 9259.6
9797.3 2757.4 5315:3 9442.8
30
32
9746.8 2716.2 5164.2 9265 6
9799.0 2758.9 5320.6 9449.0
32
34
9748.5 2717.6 5169.4 9271.6
9800.7 2760.3 5325.9 9455.2
34
36
9750.3 2719.1 5174.5 9277.7
9802.5 2761.7 5331.2 9461.4
36
38
9752.0 2720.5 5179.7 9283.7
9804.2 2763.1 5336.5 9467.6
38
40
9753.8 2721.9 5184.8 9289.8
9805.9 2764.6 5341.8 9473.8
40
42
9755.6 2723.3 5190.0 9295.8
9807.7 2766.0 5347.2 9480.0
42
44
9757.3 2724.7 5195.1 9301.9
9809.4 8767. 4 5352.5 9486.3
44
46
9759.0 2726.2 5200.3 9307.9
9811.1 2768.8 5357.9 9492.5
46
48
9760.8 2727.6 5205.4 9314.0
9812.8 2770.3 5363.2 9498.7
48
60
9762.5 2729.0 5210.6 9320.1
9814.5 2771.7 5368.5 9505.0
50
52
9764.3 2730.4 5215.8 9326.1
9816.3 2773.1 5373.9 9511.2
52
54
9766.0 2731.8 5221.0 9332.2
9818.0 2774.6 5379.3 9517.5
54
56
9767.8 2733.3 5226.2 9338.3
9819.7 2776.0 53S4.7 9523.8
56
58
9769.5 2734.7 5231.4 9344.4
9821.4 2777.4 5390.0 9530.0
58
60
9771.3 2736.1 5236.6 93505
9823.1 2778.8 5395.4 9536.3
60
240 NATURAL SINES, COSINES, TANGENTS, COTAN.
1
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
r
o
1
2
3
JL_
5
6
8
g
.00000
.00029
.00058
.00087
.00116
One
One
One
One
One
00000
.00029
.00058
.00087
.00116
Infinite
3437-75
1718-87
1145-92
839-436
01745
.01774
.01803
.01832
.01862
.01891
-01920
.01949
.01978
.02007
.99985
-99984
.99984
.99983
.99983
.01746
.01775
-01804
.01833
.01862
57.2900
56-3506
55-4415
54-5613
53-7086
60
59
58
57
58
.00145
.00175
.00204
.00233
.00262
One
One
One
One
One
.00145
.00175
00204
.00233
.00262
687-549
572-957
491-106
429-718
381.971
-99982
-99982
-99981
-99980
^99980
~99979
-99979
.99978
-99977
.99977
01891
-01920
.01949
.01978
02007.
.02036
-02066
-02095
.02124
.02153
52-8821
52-0807
51-3032
50-5485
49-8157
55
54
53
52
51
10
11
12
13
!i_
15
16
17
18
19
20
21
22
23
24
.00291
.00320
.00349
.00378
.00407
One
.99999
.99999
.99999
.99999
.00291
.00320
.00349
.00378
.00407
343 . 774
312-521
286.478
264-441
245-552
.02036
.02065
-02094
.02123
.02152
49-1039
48-4121
47-7395
47-0853
46-4489
50
49
48
47
46
.00436
.00465
.00495
.00524
.00553
.99999
.99999
.99999
.99999
.99998
.00436
.00465
.00495
-00524
.00553
229.182
214.858
202.219
190-984
180-932
02181
.02211
.02240
-02269
.02298
,99976
.99976
-99975
.99974
.99974
.02182
.02211
.02240
.02269
.02298
45-8294
45-2261
44-6386
44-0661
43-5081
45
44
43
42
-i!
40
39
38
37
_36
35
34
33
32
31
.00582
.00611
.00640
.00689
.00698
.99998
.99998
.99998
.99998
.99998
00582
.00611
.00640
.00869
.00698
171-885
163-700
156-259
149-465
143-237
-02327
.02356
-02385
.02414
. 02443__
^02472
.02501
-02530
.02560
.02589
.99973
.99972
.99972
.99971
.99970
.99969
.99969
-99968
.99967
.99966
02328
.02357
.02386
.02415
.02444
42-9641
42-4335
41-9158
41-4106
40-9174
25
26
27
28
2P
00727
.00756
00785
.00814
.00844
.99997
.99997
.99997
.99997
.99996
.00727
.00756
.00785
.00815
.OC844
137-507
132.219
127-321
122.774
118-540
.02473
.02502
.02531
.02560
.02589
40-4358
39-9655
39.5059
39-0568
38-6177
30
31
32
33
34_,
35
36
37
38
39
40
41
42
43
44
.00873 i. 99996
.00902 -99993
.00931 .99998
.00960 .99995
.00989 .99995
.00873
.00902
.00931
.00960
.00989
114.589
110-892
107-426
104-171
101-107
.02618
-02647
-02676
.02705
.02734
.99966
-99965
-99964
-99963
.99963
.02619
.02648
.02677
.02706
.02735
38-1885
37.7686
37-3579
36-9560
36-5627
36-1776
35-8006
35-4313
35-0695
34-7151
30
29
28
27
26
.01018
.01047
.01076
.01105
.01134
.99995
.99995
.99994
.99994
.99994
.01018
.01047
.01076
.01105
.01135
98-2179
95-4895
92.9085
90.4633
88-1436
-02763
-02792
-02821
-02850
.02879
.99962
.99961
.99960
.99959
-99959
.02764
.02793
.02822
.02851
.02881
25
24
23
22
21
.01164
.01193
.01222-
.01251
.01280
.99993
.99993
.99993
.99992
.99992
.01164
.01193
.01222
.01251
.01280
85-9398
83-8435
81-8470
79-9434
78.1263
02908
-02938
.02967
02996
-03025
99958
-99957
.99956
.99955
.99954
.02910
.02939
.02968
.02997
.03026
34-3678
34-0273
33-6935
33-3662
33-0452
20
19
18
17
-IB
15
14
13
12
_!!
10
9
8
7
6
45
46
47
48
49
.01309
.01338
.01367
.01396
.01425
.99991
.99991
.99991
.99990
.99990
01309
.01338
.01367
.01396
01425
.01455
.01484
.01513
.01542
.01571
76-3900
74-7292
73-1390
71.6151
70.1533
03054
-03083
03112
03141
.03170
.99953
.99952
-99952
.99951
.99950
.99949
.99948
.99947
.99946
.99945
.99944
.99943
.99942
.99941
.99940
03055
.03084
-03114
-03143
.03172
32-7303
32-4213
32-1181
31-8205
31-5234
50
51
52
53
54
.01454
.01483
01513
01542
.01571
.99939
.99989
.99989
.99988
.99988
68-7501
67-4019
66.1055
64.8580
63.6567
03199
.03228
.03257
.03236
.03316
.03201
.03230
-03259
-03288
03317
31-2416
30-9599
30.6833
30-4116
30.1446
55
56
57
58
59
00
.01600
01629
01658
01687
01716
.99987
.99987
.99988
.99986
.99985
.01600
.01629
.01658
.01687
.01716
62.4992
61-3829
60.3058
59.2659
58-2612
03345
.03374
-03403
-03432
.03461
-03346
03376
03405
03434
.03463
29.8823
29-6245
,?9.3711
29.1220
28-8771
5
4
3
2
1
01745
.99985
.01746
57-2900
03490
.99939
03492
28-6363
O
Cos.
Sin.
Cot. Tan.
Cos.
Sin.
Cot.
Tan.
89
88
NATURAL SINES, COSINES, TANGENTS, COTAN. 241
2
3
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
2
3
4
.03490
.03519
.03548
.03577
.03606
-99939
99938
.99937
.99936
.99935
-03492
.03521
.03550
.03579
.03609
28-6363
28.3994
28-1664
27-9372
27-7117
-05234
.05263
-05292
-05321
.05350
.99863
.99861
.99860
.99858
99857
.05241
.05270
.05299
.05328
.05357
19-0811
18-9755
18-8711
18-7678
18.6656
6O
59
58
57
56
5
6
7
8
9
.03635
.03664
.03693
.03723
.03752
.99934
.99933
.99932
.99931
.99930
.03638
.03667
.03696
.03725
.03754
27-4899
27.2715
27-0566
26.8450
26-6367
.05379
.05408
.05437
-05466
.05495
.99855
.99854
.99852
.99851
.99849
.05387
.05416
.05445
.05474
-05503
18-5645
18-4645
18-3655
18-2677
18-1708
55
54
53
52
51
10
11
12
13
14
.03781
.03810
.03839
.03868
.03897
.99929
.99927
.99926
.99925
.99924
.03783
.03812
.03842
.03871
.03900
26-4316
26-2296
26-0307
25.8348
25-6418
-05524
.05553
.05582
.05611
.05640
.99847
.99846
.99844
.99842
.99841
.05533
.05562
.05591
.05620
.05649
18.0750
17-9802
17-8863
17-7934
17-7015
5O
49
48
47
46
15
16
17
18
19
.03926
.03955
.03984
.04013
.04042
.99923
.99922
.99921
.99919
.99918
.03929
-03958
.03987
.04016
.04046
25-4517
25-2644
25-0798
24-8978
24-7185
.05669
.05698
-05727
-05756
.05785
.99839
.99838
.99836
.99834
-99833
.05678
.05708
.05737
.05766
.05795
17-6106
17-5205
17-4314
17-3432
17-2558
45
44
43
42
41
20
21
22
23
?A
.04071
.04100
.04129
.04159
.04188
-99917
-99916
-99915
.99913
.99912
-04075
-04104
-04133
-04162
-04191
24-5418
24-3675
24-1957
24-0263
23.8593
-05814
.05844
-05873
-05902
.05931.
-99831
-99829
-99827
-99826
-99824
.05824
-05854
-05883
.05912
-05941
17-1693
17-0837
16-9990
16-9150
16-8319
4O
39
38
37
36
25
26
27
28
29
.04217
.04246
.04275
.04304
.04333
.99911
.99910
-99909
.99907
.99906
.04220
.04250
.04279
-04308
-04337
23-6945
23-5321
23-3718
23-2137
23-0577
-05960
-05989
-06018
.06047
.06076
-99822
.99821
.99819
.99817
.99815
.05970
.05999
.06029
.06058
.06087
16.7496
16-6681
16-5874
16-5075
16-4283
35
34
33
32
31
30
31
32
33
84
04362
-04391
.04420
- 04449
.04478
-99905
-99904
-99902
-99901
-99900
.04366
.04395
.04424
.04454
-04483
22-9038
22-7519
22-6020
22-4541
22-3081
.06105
.06134
.06163
.06192
-06221
.99813
-99812
-99810
-99808
-99806
.06116
-06145
-06175
.06204
-06233
16-3499
16-2722
16.1952
16.1190
16-0435
30
29
28
27
26
85
36
37
38
39
.04507
.04536
.04565
-04594
.04623
-99898
.99897
.99896
-99894
-99893
-04512
-04541
-04570
-04599
.04628
22J 640
22-0217
21-8813
21-7426
21-6056
-06250
.06279
-06308
.06337
.06366
-99804
-99803
.99801
.99799
.99797
.06262
-06291
.06321
-06350
-06379
15-9687
15-8945
15-8211
15-7483
15-6762
25
24
23
22
21
40
41
42
43
44
04653
.04682
.04711
. 04740
.04769
-99892
-99890
-99889
99888
.99886
.04658
.04687
-04716
- 04745
-04774
21-4704
21-3369
21-2049
21-0747
20-9460
-06395
06424
06453
06482
-06511
.99795
-99793
-99792
-99790
-99788
-06408
-06437
-06467
06496
-06525
15-6048
15-5340
15-4638
15-3943
15-3254
20
19
18
17
16
45
46
47
48
49
-04798
-04827
.04856
-04885
-04914
-99885
.99883
.99882
-99881
99879
-04803
.04833
04862
-04891
.04920
20-8188
20-6932
20-5691
20-4465
20-3253
-06540
.06569
06598
.06627
.06656
-99786
-99784
-99782
-99780
-9.9778
-06554
.06584
-06613
-06642
.06671
15-2571
15-1893
15-1222
15-0557
14-9898
15
14
13
12
11
50
51
52
53
54
-04943
-04972
-05001
-05030
.05059
-99878
-99876
-99875
-99873
-99872
.04949
-04978
-05007
-05037
.05066
20-2056
20-0872
19-9702
19-8546
19-7403
-06685
-06714
-06743
-06773
-06802.
.99776
-99774
.99772
.99770
.99768
-06700
-06730
.06759
-06788
.06817
14.9244
14-8596
14-7954
14.7317
14-6685
10
9
7
3
55
56
U
99
-05088
-05117
-05146
-05175
-05205
-99870
-99869
.99867
-99886
.99864
-05095
-05124
-05153
-05182
-05212
19-6273
19-5156
19-4051
19-2959
19-1879
-06831
.06860
.06889
.06918
-06947
.99766
-99764
-99762
.99760
.99758
.06847
.06876
.06905
.06934
-06963
14-6059
14-5438
14.4823
14.4212
14.3607
5
3
1
60
.05234
,99863
-05241
19-0811
.06976
-99756
-OR993
14-3007
-7~
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
*
87
86
242 NATURAL SINES, COSINES, TANGENTS, COTAN.
4
5
t
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tari.
Cot.
/
?
2
JL
.06976
.07005
.07034
.07063
.07092
99756
99754
.99752
.99750
.99748
.06993
07022
.07051
.07080
.07110
14-3007
14.2411
14.1821
14-1235
14.0655
08716
.08745
.08774
.08803
-08831
.99619
.99617
.99614
-99612
.99609
-08749
-08778
-08807
.08837
.08866
11.4301
11.3919
11.3540
11.3163
11.2789
60
59
58
57
56
6
J
J
.07121
.07150
.07179
.07208
.07237
.99746
.99744
.99742
.99740
.99738
.07139
.07168
.07197
.07227
.07256
14-0079
13-9507
13.8940
13-8378
13-7821
08860
.08889
.08918
.08947
.08976
.99607
.99604
.99602
.99599
.99596
08895
08925
-08954
-08983
-09013
11-2417
11-2048
11-1681
11-1316
11.0954
55
54
53
52
51
10
11
12
13
14
.07266
.07295
.07324
.07353
.07382
.99736
.99734
.99731
.99729
.99727
.07285
.07314
.07344
.07373
.07402
13-7267
13.6719
13-6174
13-5634
13-5098
-09005
.09034
.09063
.09092
.09121
.-99594
99591
.99588
.99586
.99583
09042
09071
-09101
.09130
09159
11.0594
11-0237
10-9882
10-9529
10-9178
50
49
48
47
4ft
15
16
17
18
19
.07411
.07440
-07469
.07498
.07527
.99725
.99723
.99721
.99719
.99716
.07431
.07461
.07480
.07519
.07548
13 4566
13-4039
13.3515
13-2996
13-2480
.09150
-09179
.09208
.09237
.09266
-99580
.99578
.99575
.99572
.99570
.09189
.09218
.09247
.09277
.09306
10-8829
10-8483
10-8139
10-7797
10.7457
45
44
43
42
41
20
21
22
23
24
.07556
.07585
.07614
.07643
.07672
.99714
.99712
.99710
.99708
.99705
.07578
.07607
.07636
.07665
.07695
13-1969
13.1461
13-0958
13-0458
12-9962
.09295
.09324
-09353
.09382
.09411
.99567
.99564
.99562
.99559
-99556
-09335
-09365
.09394
.09423
.09453
10.7119
10.6783
10-6450
10-6118
10.5789
40
39
38
37
36
25
26
27
28
29
.07701
.07730
.07759
.07788
.07817
.99703
.99701
.99699
.99696
.99694
.07724
.07753
.07782
.07812
.07841
12-9469
12-8981
12-8496
12-8014
12.7536
. 09440
.09469
.09493
.09527
-09556
.99553
.99551
.99548
.99545
.99542
.09482
.09511
.09541
.09570
.09600
10 5462
10-5136
10.4813
10-4491
10-4172
35
34
33
32
31
30
31
32
33
34
.07846
.07875
.07904
.07933
.07962
.99692
.99689
.99687
.99685
.99683
.07870
.07899
.07929
.07958
.07987
12-7062
12.6591
12-6124
12.5660
12.5199
.09585
.09614
.09642
.09671
.09700
.99540
.99537
.99534
.99531
.99528
.09629
.09658
.09688
-09717
-09746
10-3854
10-3538
10-3224
10.2913
10-2602
30
29
28
27
26
35
36
37
38
39
.07991
.08020
.08049
.08078
.08107
.99680
.99678
.99676
.99673
-99671
.08017
.08046
.08075
.08104
-08134
12-4742
12-4288
12-3838
12-3590
12-2946
.09729
.09758
-09787
.09816
-09845
.99526
.99523
-99520
.99517
.99514
.09776
-09805
-09834
.09864
.09893
10.2294
10-1988
10-1683
xO.1381
10-1080
25
24
23
22
21
40
41
42
43
44
.08136
08165
-08194
.08223
.08252
.99668
.99666
.99664
.99661
.99659
.08163
.08192
.08221
.08251
.08280
12-2505
12.2067
12-1632
12.1201
12-0772
-09874
09903
.09932
09961
.09990
-99511
-99508
-99506
.99503
-99500
.09923
.09952
-09981
.10011
.10040
10-0780
10-0483
10 0187
9-98931
9.96007
20
19
18
17
16
45
46
47
48
49
08281
.08310
.08339
.08368
.08397
.99657
.99654
.99652
.99649
.99647
.08309
.08339
.08368
.08397
.08427
12-0346
11-9923
11-9504
11-9087
11-8673
10019
10048
.10077
.10106
.10135
.99497
.99494
.99491
.99488
-99485
.10069
.10099
.10128
.10158
-10187
9-93101
9-90211
9.87338
9 84482
_O184i_
15
14
13
12
_U
50
51
52
53
54
.08428
.08455
08484
08513
08542
99644
.99642
.99639
.99637
.99635
.08456
.08485
.08514
.08544
.08573
11.8262
11.7853
11.7448
11.7045
11.6645
.10164
.10192
.10221
.10250
.10279
-99482
.99479
.99476
.99473
.99470
.10216
.10246
.10275
.10305
.10334
9-78817
9-76009
9-73217
9 70441
9.67680
10
9
8
7
6
55
56
57
58
59
08571
08600
08829
08658
08687
.99632
.99630
.99627
.99625
.99622
.08602
.08632
.08661
.08690
.08720
11-6248
11-5853
11.5461
11.5072
11.4685
10308
.10337
.10366
-10395
.10424
.99467
99464
99461
99458
99455
.10363
10393
10422
10452
10481
9-64935
9-62205
9-59490
9-56791
9-54106
5
4
3
2
1
go
08716
.99619
.08749
11-4301
.10453
99452
10510
9-51436
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot. |
Tan.
85
84
NATURAL SINES, COSINES, TANGENTS, COTAN. 243
6 7
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
1
2
3
4
10453
10482
10511
10540
10569
.99452
99449
-99446
.99443
.99440
10510
10540
10569
10599
10628
9-51436
9-48781
9-46141
9-43515
9-40904
12187
12216
12245
12274
12302
99255
99251
99248
99244
99240
.12278
12308
12338
12367
12397
8-14435
8-12481
8-10536
8-08600
8-06674
60
59
58
57
_5J
55
54
53
52
51
5O
49
48
47
46
45
44
43
42
U
5
6
7
8
9
10
11
12
13
14
10597
10626
10655
.10684
.10713
.99437
.99434
.99431
99428
.99424
10657
10687
10716
10746
10775
9-38307
9-35724
9-33155
9-30599
9-28058
12331
12360
12389
12418
12447
99237
99233
99230
99226
99222
99219
99215
99211
.99208
.99204
12426
12456
12485
12515
.12544
8-04756
8-02848
8-00948
7-99058
7.97176
7-95302
7-93438
7-91582
7-89734
7-87895
7-86064"
7-84242
7-82428
7-80622
7-78825
.10742
.10771
.10800
.10829
.10858
.99421
.99418
.99415
.99412
.99409_
.99406
.99402
.99399
.9L396
.99393
10805
10834
10883
10393
_109_22_
10952
10981
11011
11040
.11070
9-25530
9 23016
9-20516
9.18028
9.15554
9-13093
9-10646
9.08211
9-05789
9-03379
12476
12504
.12533
.12562
12591
.12574
.12603
.12633
.12662 .
.12692^
15
16
17
18
19
20
21
22
23
24
,10887
.10916
.10945
.10973
.11002
.12620
.12649
.12678
.12706
.12735
99200
.99197
.99193
-99189
-99186
.12722
.12751
.12781
.12810
.12840
.11031
.11060
.11089
11118
.11147
.99390
-99386
.99383
-99380
.99377
11099
11128
11158
11187
11217
9-00983
8-98598
8-96227
8-93867
8.91520
8-89185
8-86862
8-84551
8-82252
8-79964
-12764
-12793
12822
.12851
^12880
.99182
.99178
-99175
-99171
.99167
.12869
.12899
12929
.12958
.12988
7-77035
7-7525-4
7-73480
7-71715
7.69957
40
39
38
37
36
25
26
27
28
29
11176
.11205
11234
.11263
.11291
.99374
-93370
.99367
-99364
.99360
11246
11276
11305
11335
.11364
.12908
12937
.12968
-12995
.13024
.99163
99160
-99156
.99152
.99148
.13017
.13047
.13076
.13106
.13136
7.68208
7-66466
7-64732
7.63005
7-61287
35
34
33
32
31
30
31
32
33
34
.11320
.11349
.11378
11407
-11436
.99357
.99354
.99351
.99347
-99344_
.99341
.99337
99334
.99331
.99327
.11394
11423
.11452
.11482
.11511
8.77689
8-75425
8-73172
8-7093-1
8-68701
.13053
.13081
.13110
.13139
.13168
.99144
.99141
.99137
99133
.99129
.13165
.13195
.13224
.13254
.13284
7-59575
7-57872
7-56176
7-54487
7-52806
30
29
28
27
28
25
24
23
22
21
35
36
37
38
39
.11465
.11494
.11523
-11552
11580
.11541
.11570
.11600
.11629
.11659
8-66482
8-64275
8-62078
8-59893
8-57718
.13197
-13226
.13254
.13283
.13312
.99125
.99122
-993.18
99114
-99110
.13313
-13343
.13372
.13402
.13432
7-51132
7-49465
7-47806
7-46154
7-44509
40
41
42
43
44
45
46
47
48
49
11609
.11638
11667
-11696
.11725
.99324
-99320
.99317
.99314
.99310
.11688
.11718
.11747
-11777
-11806
8.55555
8-53402
8-51259
8.49128
8-47007
.13341
.13370
.13399
-13427
-13456
-99106
-90102
-99098
.99094
.99091
.13461
.13491
.13521
.13550
13580_
.13609
.13639
.13669
.13698
.13728
7-42871
7-41240
7.39616
7-37999
7.36389
2O
19
18
17
16
15
14
13
12
11
-11754
.11783
.11812
-11840
-11869
.99307
99303
.99300
.99297
99293
.11836
.11865
.11895
11924
.11954
'.1 1983"
,12013
.12042
12072
.12101
8-44896
8.42795
8-40705
8-38625
8-36555
-13485
.13514
.13543
.13572
.13600
99087
.99083
-99079
-99075
-99071
7-34786
7-33190
7-31600
7-30018
7-28442
50
51
52
53
54_
55
56
57
58
59
.11898
.11927
.11956
.11985
-12014
99290
.99286
99283
.99279
.99276
8.34496
8-32446
8-30406
8.28376
8-26355
.13629
.13658
.13687
13716
.13744
.99067
-99063
.99059
.99055
.99051
13758
.13787
.13817
.13846
.13876
7-26873
7-25310
7-23754
7-22204
7-20661
10
9
8
7
6
5
3
2
1
o
12043
-12071
.12100
12129
.12158
.99272
.99269
.99265
.99262
.99258
.12131
.12160
12190
12219
.12249
8 . 24345
8-22344
8-20352
8-18370
8.16398_
.13773
.13802
13831
-13860
-13889
.99047
99043
99039
99035
99031
.13906
.13935
.13965
.13995
.14024
7-19125
7-17594
7.16071
7-14553
7-13042
S2.
.12187
.99255
12278
8 14435
.13917
99027
14054
7-11537
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
8b
NATURAL SINES, COSINES, TANGENTS, COTAN.
8 9
1
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
o
2
13917
13946
13975
14004
14033
.99027
.99023
.99019
.99015
.99011
14054
14084
14113
14143
14173
7.11537
7-10038
7-08546
7-07059
7-05579
15643
15672
15701
15730
15758
98769
.98764
-98760
-98755
-98751
15838
15868
.15898
15928
.15958
6-31375
6-30189
6-29007
6-27829
6.26655
60
59
58
57
56
5
6
7
8
9
14061
14090
14119
14148
14177
.99006
.99002
.98998
.98994
.98990
14202
14232
14262
14291
14321
7-04105
7-02637
7-01174
6-99718
6-98268
15787
15816
15845
15873
15902
-98746
-98741
.98737
98732
-98728
.15988
.16017
.16047
.16077
.16107
6-25486
6-24321
6-23160
6-22003
6-20851
55
54
53
52
51
10
11
12
13
14
14205
14234
14263
14292
14320
.98986
.98982
98978
98973
98969
14351
14381
14410
14440
.14470
6-96823
6-95385
6-93952
6-92525
6-91104
15931
15959
15988
16017
16046
-98723
-98718
-98714
-98709
-98704
.16137
.16167
.16196
.16226
.16256
6-19703
6-18559
6-17419
6-16283
6-15151
5O
49
48
47
46
15
16
17
18
19
14349
.14378
.14407
.14436
-14464
98965
98961
98957
.98953
.98948
14499
.14529
.14559
.14588
.14618
6-89688
6-88278
6-86874
6-85475
6-84082
16074
16103
16132
16160
16189
-98700
-98695
-98690
.98686
.98681
.16286
.16316
.16346
-16376
.16405
6-14023
6-12899
6-11779
6-10664
6-09552
45
44
43
42
41
20
21
22
23
24
. 14493
.14522
.14551
.14580
.14608
.98944
.98940
.98936
.98931
.98927
.14648
.14678
.14707
.14737
.14767
6-82694
6-81312
6-79936
6-78564
6-77199
-16218
.16246
.16275
.16304
.16333
98676
98671
.98667
.98662
.98657
.16435
.16465
-16495
16525
.16555
6-08444
6-07340
6-06240
6-05143
6-04051
40
39
38
37
36
25
26
27
28
29
.14637
.14666
.14695
.14723
.14752
.98923
.98919
98914
.98910
.98906
.14796
.14826
.14856
.14886
.14915
6-75838
6-74483
6-73133
6-71789
6-70450
.16361
.16390
.16419
.16447
,16476
.98652
.98648
.98643
-98638
.98633
.16585
.16615
-16645
.16674
.16704
6-02962
6-01878
6-00797
5-99720
5-98646
35
34
33
32
31
30
31
32
33
34
.14781
.14810
.14838
.14867
.14896
.98902
.98897
.98893
.98889
.98884
.14945
.14975
.15005
.15034
.15064
6-69116
6-67787
6-66463
6-65144
6-63831
.16505
.16533
.16562
.16591
.16620
.98629
.98624
.98619
-98614
-98609
.16734
.16764
.16794
.16824
.16854
5-97576
5-96510
5-95448
5-94390
5-93335
30
29
28
27
26
35
36
37
38
39
.14925
.14954
.14982
.15011
.15040
98880
.98876
.98871
.98867
.98863
.15094
.15124
-15153
.15183
.15213
6-62523
6-61219
6-59921
6-58627
6-57339
-16648
.16677
.16706
16734
-16763
.98604
.98600
-98595
.98590
.98585
16884
.16914
.16944
.16974
.17004
5-92283
5-91236
5-90191
5-89151
5- ,88114
25
24
23
22
21
40
41
42
43
44
.15069
.15097
.15126
.15155
.15184
.98858
.98854
.98849
.98845
-98841
15243
.15272
15302
.15332
.15362
6.56055
6.54777
6.53503
6-52234
6-50970
.16792
.16820
,16849
.16878
.16906
.98580
.98575
.98570
.98565
.98561
-17033
17063
.17093
.17123
.17153
5-87080
5-86051
5-85024
5.84001
5.82982
20
19
18
17
16
45
46
47
48
49
.15212
.15241
.15270
.15299
.15327
98836
98832
98827
98823
.98818
.15391
.15421
.15451
.15481
.15511
6-49710
6-48456
6-47206
6-45961
6-44720
.16935
.16964
-16992
17021
17050
.98556
.98551
.98548
-98541
-98536
.17183
.17213
.17243
-17273
-17303
5.81966
5-80953
5-79944
5-78938
5-77936
15
14
13
12
11
50
51
52
53
54
.15356
.15385
.15414
15442
.15471
98814
.98809
.98805
.98800
.98796
.15540
.15570
.15600
.15630
.15660
6-43484
6-42253
6.41026
6-39804
6-38587
-17078
-17107
-17136
17164
17193
.98531
-98526
98521
98516
.98511
17333
17363
.17393
.17423
.17453
5-76937
5-75941
5-74949
5-73960
5-72974
10
9
8
7
6
55
56
57
58
59
.15500
.15529
.15557
15586
.15615
.98791
.98787
-98782
-98778
.98773
.15689
.15719
.15749
15779
.15809
6-37374
6-36165
6-34961
6-33761
6-32566
-17222
-17250
.17279
.17308
.17336
.98506
.98501
.98496
-98491
.98486
17483
.17513
.17543
17573
.17603
5-71992
5-71013
5-70037
5-69064
5-68094
5
4
3
2
_J
60
.15643
98769
.15838
6-31375
.17365
-98481
-17633
5-67128
'
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
'
81 e
NATURAL SINES, COSINES, TANGENTS, COTAN. 245
10 11
1
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
'
o
2
3
4
.17365
17393
-17422
17451
.17479
.98481
.98476
.98471
.98466
.98461
.17633
.17663
.17693
.17723
.17753
5-67128
5-66165
5-65205
5 64248
5-63295
-19081
-19109
-19138
-19167
-19195
-98163
98157
.98152
.98146
.98140
19438
-19468
-19498
-19529
19559
5-14455
5-13658
5-12862
5-12069
5-11279
60
59
58
57
56
5
6
7
8
9
.17508
.17537
.17565
.17594
17623
.98455
.98450
.98445
.98440
.98435
.17783
.17813
.17843
.17873
.17903
5-62344
5-61397
5-60452
5-59511
5-58573
-19224
-19252
-19281
-19309
-19338
.98135
-98129
98124
98118
98112
19589
19619
19649
.19680
.19710
5-10490
5-09704
5-08921
5-08139
5-07360
55
54
53
52
51
10
11
12
13
14
.17651
.17680
.17708
-17737
.17766
.98430
98425
.98420
98414
.98409
17933
.17963
.17993
.18023
.18053
5-57638
5-56706
5.55777
5-54851
5-53927
-19366
19395
19423
-19452
-19481
98107
98101
-98096
.98090
.98084
-19740
19770
.19801
19831
19861
5-06584
5-05809
5-05037
5-04267
5-03499
50
49
48
47
46
15
16
17
18
19.,
.17794
.17823
.17852
17880
.17909
.98404
.98399
.98394
.98389
.98383
.18083
.18113
.18143
.18173
18203
5-53007
5-52090
5-51176
5-50264
5-49356
19509
19538
-19566
-19595
-19623
-98079
.98073
98067
-98061
98056
.19891
.19921
.19952
-19982
-20012
5-02734
5-01971
5-01210
5-00451
4-99695
45
44
43
42
41
30
21
22
23
24
17937
.17966
.17995
.18023
.18052
.98378
.98373
.98368
.98362
.98357
.18233
18263
.18293
.18323
.18353
5-48451
5-47548
5-46648
5-45751
5-44857
-19652
.19680
.19709
-19737
-19766
.98050
.98044
.98039
.98033
.98027
-20042
-20073
,20103
-20133
20164
4.98940
4-98188
4-97438
4-96690
4.95945
40
39
38
37
36
25
26
27
28
29
.18081
.18109
.18138
.18166
18195
.98352
98347
.98341
.98336
.98331
.18384
.18414
. 18444
.18474
.18504
5-43966
5-43077
5-42192
5-41309
5 40429
.19794
-19823
-19851
.19880
.19908
.98021
.98016
-98010
-98004
-97998
.20194
.20224
20254
-20285
-20315
4-95201
4-94460
4-93721
4-92984
4-92249
35
34
33
32
31
30
31
32
33
34
.18224
.18252
.18281
.18309
.18338
98325
98320
.98315
98310
.98304
.18534
.18564
.18594
-18624
.18654
5-39552
5-38677
5-37805
5-36936
5-36070
19937
.19965
19994
.20022
-20051
-97992
-97987
-97981
-97975
-97969
-20345
-20376
- 20406
-20436
-20466
4-91516
4-90785
4-90056
4-89330
4-88605
30
29
28
27
26
35
36
37
38
9_
.18367
.18395
.18424
.18452
.18481
.98299
.98294
.98288
982a3
.98277
18634
.18714
.18745
.18775
.18805
5-35206
5-34345
5-33487
5-32631
5-31778
-20079
-20108
-20136
-20165
-20193
-97963
-97958
-97952
-97946
-97940
-20497
-20527
-20557
-20588
.20618
4-87882
4-87162
4-86444
4-85727
4 85013
25
24
23
22
21
40
41
42
43
44
.18509
.18538
18567
.18595
.18624
.98272
.98267
.98261
.98256
.98250
18835
18865
.18895
.18925
.18955
5-30928
5-30080
5-29235
5-28393
5-27553
20222
20250
-20279
20307
-20336
-97934
-97928
-97922
-97916
-97910
-20648
20679
-20709
-20739
-20770
4-84300
4-83590
4-82882
4-82175
4-81471
20
19
18
17
16
45
46
47
48
49
18652
.18681
.18710
18738
.18767
.98245
98240
.98234
98229
.98223
.18986
.19016
.19046
19076
.19106
5-26715
5-25880
5-25048
5-24218
5.23391
-20364
-20393
-20421
-20450
-20478
-97905
-97899
-97893
-97887
-97881
-20800
-20830
-20861
.20391
.20921
4-80769
4-80068
4-79370
4-78673
4-77978
15
14
13
12
_ii
50
51
52
53
54
-18795
.18824
.18852
.18881
.18910
98218
98212
98207
98201
.98196
.19136
19166
.19197
.19227
.19257
5-22566
5-21744
5-20925
5-20107
5-19293
-20507
20535
.20563
-20592
-20620
-97875
-97869
-97863
-97857
-97851
-20952
20982
.21013
.21043
.21073
4-77286
4-76595
4-75908
4-75219
4-74534
10
9
7
6
55
56
57
58
59
18938
.18967
.18995
19024
.19052
.98190
.98185
.98179
98174
98168
.19287
.19317
19347
19378
19408
5-18480
5-17671
5-16863
5-16058
5-15256
- 20649
20677
.20706
-20734
-20763
-97845
-97839
-97833
-97827
-97821
-21104
-21134
-21164
-21195
-21225
4-73851
4-73170
4-72490
4-71813
4-71137
5
4
3
!
60
.19081
.98163
.19438
5-14455
-20791
-97815
-21256
4-70463
o
T-
Cos.
Sin.
Cot.
Tan.
Co's.
Sin.
Cot.
Tan.
,
79
78
246 NATURAL SINES, COSINES, TANGENTS, COTAN.
12 13
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
'
1
2
3
4
20791
20820
20848
.20877
.20905
.97815
.97809
.97803
.97797
.97791
.21256
21286
21316
.21347
.21377 i
4-70463
4-69791
4-69121
4-68452
4-67786
22495
22523
22552
22580
22608
97437
97430
97424
97417
97411
23087
23117
23148
23179
23209
4-33148
4-32573
4-32001
4-31430
4-30860
60
59
58
57
56
5
6
7
8
9
.20933
.20962
.20990
.21019
21047
97784
.97778
97772
.97766
.97760
.21408
21438
.21469
.21499
21529
4-67121
4-66458
4-65797
4-65138
4 64480
22637
22665
22693
22722
22750
97404
-97398
.97391
97384
.97378
.23240
23271
23301
-23332
-23363
4-30291
4-29724
4-29159
4-28595
4-28032
55
54
53
52
51
10
11
12
13
14
.21076
.21104
.21132
.21161
21189
.97754
.97748
.97742
.97735
97729
21560
.21590
-21621
.21651
-21682
4-63825
4-63171
4-62518
4-61868
4-61219
22778
.22807
-22835
22863
-22892
97371
.97365
-97358
-97351
97345
23393
-23424
-23455
-23485
-23516
4-27471
4-26911
4-26352
4-25795
4-25239
50
49
48
47
46
15
16
17
18
19
.21218
.21246
.21275
.21303
-21331
.97723
.97717
97711
97705
97698
21712
.21743
.21773
.21804
.21834
4-60572
4-59927
4-59283
4-58641
4-58001
.22920
.22948
.22977
-23005
.23033
-97338
97331
.97325
-97318
.97311
-23547
-23578
-23608
-23639
.23670
4-24685
4-24132
4-23580
4-23030
4-22481
45
44
43
42
41
20
21
22
23
24
-21360
.21388
21417
21445
.21474
.97692
.97686
.97680
.97673
.97667
.21864
.21895
.21925
.21956
.21986
4-57363
4-56726
4-56091
4-55458
4-54826
.23062
.23090
.23118
.23146
.23175
-97304
-97298
-97291
-97284
-97278
-23700
-23731
-23762
-23793
-23823
4-21933
4-21387
4-20842
4-20298
4-L9756
40
39
38
37
36
25
26
27
28
29
.21502
.21530
.21559
.21587
.21616
.97661
.97655
.97648
.97642
97636
.22017
22047
.22078
.22108
.22139
4-54196
4-53568
4-52941
4-52316
4-51693
.23203
.23231
.23260
23288
-23316
-97271
-97264
.97257
-97251
.97244
-23854
-23885
-23916
.23946
23977
4-19215
4-18675
4-18137
4-17600
4-17064
35
34
33
32
31
30
31
32
33
34
.21644
.21672
21701
21729
.21758
97630
.97623
.97617
.97611
.97604
.22169
.22200
.22231
.22261
.22292
4-51071
4-50451
4-49832
4-49215
4-48600
23345
-23373
23401
-23429
-23458
-97237
-97230
.97223
97217
.97210
24008
.24039
24069
24100
24131
4-16530
4-15997
4-15465
4-14934
4-14405
30
29
28
27
26
35
38
37
38
39
.21786
21814
.21843
.21871
21899
.97598
.97592
.97585
.97579
-97573
22322
.22353
22383
.22414
.22444
4-47986
4-47374
4-46764
4-46155
4-45548
23486
-23514
.23542
23571
.23599
-97203
-97196
.97189
-97182
-97176
24162
.24193
24223
24254
-24285
4-13877
4-13350
4-12825
4-12301
4-11778
25
24
23
22
-21
40
41
42
43
44
.21928
.21956
.21985
22013
22041
.97566
-97560
.97553
.97547
.97541
.22475
.22505
22536
.22567
.22597
4-44942
4-44338
4-43735
4-43134
4-42534
23627
.23656
.23684
23712
23740
-97169
.97162
.97155
.97148
.97141
-24316
-24347
-24377
- 24408
-24439
4-11256
4-10736
4-10216
4-09699
4-09182
20
19
18
17
16
45
46
47
48
49
22070
.22098
22126
.22155
22183
.97534
.97528
.97521
.97515
.97508
.22628
.22658
.22689
22719
22750
4-41936
4-41340
4-40745
4-40152
4-39560
23769
23797
-23825
-23853
23882
.97134
.97127
97120
.97113
.97106
.24470
.24501
-24532
-24562
-24593
4-08666
4-08152
4-07639
4-07127
4-06616
15
14
13
12
11
50
51
52
53
54
22212
22240
22268
.22297
.22325
.97502
.97496
.97489
.97483
.97476
22781
22811
.22842
.22872
2290S
4-38969
4-38381
4-37793
4-37207
4-36623
-23910
23938
23966
-23995
.24023
.97100
.97093
.97086
.97079
.97072
24624
-24655
24686
24717
24747
4-06107
4-05599
4-05092
4-04586
4-04081
10
9
8
7
_6
55
56
57
58
59
.22353
.22382
22410
22438
.22467
.97470
97463
.97457
97450
.97444
22934
22964
22995
.23026
23056
4-36040
4-35459
4-34879
4-34300
4-33723
.24051
24079
24108
.24136
.24164
.97065
-97058
.97051
.97044
.97037
24778
24809
24840
24871
- 24902
4-03578
4-03076
4-02574
4-02074
4-01576
5
4
3
2
1
60
22495
97437
. 23087
4-33148
24192
97030
- 24933
4-01078
" 7
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
.
77*
76
NATURAL SINES, COSINES, TANGENTS, COTAN. 247
14 15
<
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
1
2
3
4
.24192
. 24220
. 24249
.24277
.24305
.97030
97023
.97015
-97008
.97001
24933
24964
.24995
25026
25056
4-01078
4-00582
4-00086
3-99592
3-99099
-25882
-25910
-25938
-25966
-25994
96593
-96585
96578
96570
96562
-26795
-26826
26857
-26888
26920
3-73205
3-72771
3-72338
3-71907
3-71476
o;:
5S
58
57
56
5
6
7
8
9
.24333
-24362
-24390
-24418
- 24446
96994
.96987
.96980
.96973
-96966
25087
25118
25149
25180
25211
3-98607
3-98117
3-97627
3-97139
3-96651
26022
-26050
-26079
26107
26135
96555
96547
96540
-96532
96524
26951
26982
27013
27044
27076
3-71046
3-70616
3-70188
3-69761
3-69335
55
54
53
52
51
10
11
12
13
14
. 24474
.24503
-24531
.24559
.24587
-96959
-96952
.96945
.96937
.96930
25242
25273
25304
25335
25366
3-96165
3-95680
3-95196
3-94713
3-94232
26163
.26191
26219
.26247
26275
96517
96509
96502
96494
96486
27107
27138
27169
27201
27232
3-68909
3-68485
3-68061
3-67638
3-67217
50
49
48
47
46
15
16
17
18
19
.24615
24644
-24672
.24700
.24728
.96923
.96916
-96909
.96902
.96894
.25397
25428
.25459
.25490
-25521
3-93751
3-93271
3-92793
3-92316
3-91839
-26303
26331
.26359
-26387
.26415
96479
96471
-96463
96456
-96448
27263
27294
27326
27357
27388
3-66796
3-66376
3-65957
3-65538
3-65121
45
44
43
42
41
20
21
22
23
24
24756
24784
.24813
.24841
.24869
-96887
-96880
-96873
-96866
-96858
-25552
25583
25614
25645
25676
3-91364
3-90890
3-90417
3 89945
3-89474
.28443
.26471
26500
-26528
26556
-96440
-96433
96425
-96417
96410
-27419
27451
-27482
27513
27545
3-64705
3-64289
3-63874
3-63461
3-63048
4O
39
38
37
36
25
26
27
28
29
24897
24925
24954
24982
25010
96851
-96844
-96837
-96829
-96822
25707
25738
25769
-25800
25831
3-89004
3-88536
3-88068
3-87601
3-87136
26584
26612
26640
26668
26696
96402
-96394
-96386
96379
96371
27576
27607
27638
27670
27701
3-62636
3-62224
3-61814
3-61405
3-60996
35
34
33
32
31
30
31
32
33
34
25038
25066
25094
25122
25151
96815
96807
96800
96793
96786
.25862
25893
.25924
.25955
-2598R
3-86871
3-86208
3-85745
3-85284
3-84824
26724
26752
26780
26808
26836
-96363
-96355
-96347
-96340
96332
27732
27764
27795
27826
27858
3-60588
3-60181
3-59775
3-59370
3-58966
30
29
28
27
26
35
38
37
38
39_
25179
25207
25235
25263
25291
96778
96771
96764
96756
96749
26017
26048
26079
26110
-26141
3-84364
3-83906
3-83449
3-82992
3-82537
26864
26892
26920
26948
26976
96324
96316
96308
96301
96293
27889
.27921
-27952
27983
28015
3-58562
3-58160
3-57758
3-57357
3-56957
25
24
23
22
21
40
41
42
43
44
25320
25348
25376
25404
25432
96742
96734
96727
96719
96712
26172
26203
28235
26266
26297
3-82083
3-81630
3-81177
3-80726
3-80276
27004
27032
27060
27088
27116
96285
96277
96269
96261
96253
28046
28077
28109
28140
28172
3-56557
3-56159
3-55761
3-55364
3-54968
20
19
18
17
16
45
46
47
48
49_
25460
25488
25518
25545
25573
96705
96697
96690
96682
96675
28328
26359
26390
26421
26452
3-79827
3-79378
3-78931
3-78485
3 78040
27144
27172
27200
27228
27256
96246
96238
96230
96222
S6214
28203
28234
28266
28297
28329
3-54573
3-54179
3-53785
3-53393
3-53001
15
14
13
12
11
50
51
52
53
54
25601
25629
25857
25885
25713
96667
96660
96653
96645
96638
.26483
26515
26546
26577
26608
3-77595
3-77152
3-76709
3-76268
3-75828
27284
27312
27340
27368
27396
96206
96198
96190
96182
96174
28360
28391
28423
28454
28486
3-52609
3-52219
3-51829
3-51441
3-51053
1O
9
8
7
6
55
56
57
56
59
25741
25769
25798
25826
25854
96630
96623
96615
96608
96600
.26639
.26670
-26701
26733
26764
3-75388
3-74950
3-74512
3-74075
3-73640
27424
27452
27480
27508
27536
96166
96158
96150
96142
96134
28517
28549
28580
28612
28643
3-50666
3-50279
3-49894
3-49509
3-49125
5
4
3
2
1
60
25882
-96593
26795
3-73205
27564
96126
28675
3-48741
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
'
74
74
248 NATURAL SINES, COSINES, TANGENTS, COTAN.
16 17
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
o
1
2
3
4
27564
.27592
.27620
.27648
.27676
96126
.96118
.96110
.96102
.96094
28675
28706
28738
28769
.28800
3-48741
3-48359
3-47977
3-47596
3-47216
.29237
29265
29293
.29321
-29348
95630
95622
.95613
.95605
-95596
30573
30605
30637
30669
.30700
3-27085
3-26745
3-26406
3-26067
3-25729
60
59
58
57
56
5
6
7
8
9
.27704
.27731
.27759
.27787
.27815
.96086
.96078
.96070
.96062
.96054
.28832
28864
.28895
.28927
.28958
3-46837
3-46458
3-46080
3-45703
3-45327
.29376
.29404
.29432
.29460
-29487
-95588
.95579
.95571
.95562
.95554
30732
30764
.30796
.30828
.30860
3-25392
3-25055
3-24719
3-24383
3 24049
55
54
53
52
51
10
11
12
13
14
.27843
.27871
.27899
.27927
.27955
.96046
.96037
.96029
.96021
.96013
.28990
.29021
.29053
.29084
.29116
3-44951
3-44576
3-44202
3-43829
3-43456
-29515
-29543
.29571
.29599
.29626
.95545
.95536
.95528
.95519
.95511
-30891
30923
-30955
-30987
-31019
3-23714
3-23381
3-23048
3-22715
3-22384
50
49
48
47
46
15
16
17
18
19
.27983
.28011
.28039
.28067
-2809iL
.96005
.95997
.95989
.95981
95972
.29147
.29179
.29210
.29242
.29274
3-43084
3-42713
3-42343
3-41973
3-41604
.29654
.29682
.29710
29737
-29765
.95502
.95493
.95485
95476
-95467
.31051
.31083
.31115
.31147
.31178
3-22053
3 21722
3-21392
3-21063
3-20734
45
44
43
42
41
20
21
22
23
24
.28123
.28150
.28178
.28206
.28234
.95964
.95956
.95948
.95940
.95931
.29305
.29337
.29368
.29400
.29432
3-41236
3-40869
3-40502
3-40136
3.39771
.29793
.29821
-29C49
-29876
-29904
.95459
954eO
9544i
.95433
.95424
-31210
.31243
.31274
31306
.31338
3-20406
3-20079
3-19 r /52
3-19426
3-19100
4O
39
38
37
36
25
26
27
28
29
.28262
.28290
-28318
.28346
.28374
.95923
.95915
.95907
.95898
.95890
29463
.29495
.29526
.29558
.29590
3-39406
3-39042
3-38679
3-38317
3-37955
.29932
.29960
.29987
-30015
.30043
.95415
.95407
.95398
.95389
.95380
31370
.31402
31434
.31466
.31498
3-18775
3-18451
3-18127
3-17804
3.17481
35
34
33
32
31
30
31
32
33
34
.28402
.28429
.28457
.28485
.28513
.95882
.95874
.95865
.95857
.95849
.29621
.29653
.29685
.29716
.29748
3-37594
3-37234
3-36875
3-36516
3-36158
-30071
30098
.30126
.30154
.30182
.95372
.95363
.95354
.95345
.95337
.31530
-31562
-31594
-31626
.31658
3-17159
3-16838
3-16517
3-16197
3-15877
30
29
28
27
28
35
36
37
38
39
.28541
28569
.28597
.28625
.28652
.95841
.95832
.95824
.95816
.95807
29780
.29811
.29843
.29875
.2990fi_
3-35800
3-35443
3-35087
3-34732
3-34377
.30209
.30237
.30265
.30292
.30320
.95328
.95319
-95310
-95301
.95293
.31690
.31722
.31754
.31786
.31818
3-15558
3-15240
3-14922
3-14605
3-14288
25
24
23
22
-21
40
41
42
43
44
.28680
.28708
.28736
.28764
.28792
.95799
.95791
.95782
.95774
.95766
.29938
.29970
.30001
.30033
.30065
3-34023
3-33670
3-33317
3-32965
3-32614
30348
30376
30403
.30431
.30459
-95284
-95275
-95266
-95257
-95248
.31850
.31882
.31914
.31946
.31978
3-13972
3-13656
3-13341
3-13027
3-12713
20
19
18
17
16
45
46
47
48
49
.28820
28847
28875
28903
28931
.95757
95749
.95740
.95732
.95724
.30097
.30128
.30160
.30192
.30224
3-32264
3-31914
3-31565
3-31216
3-30868
30486
.30514
.30542
.30570
.30597
-95240
-95231
-95222
-95213
-95204
32010
.32042
-32074
.32106
.32139
3-12400
3-12087
3-11775
3-11464
3-11153
15
14
13
12
11
50
51
52
53
54
28959
28987
29015
29042
29070
.95715
95707
.95698
95690
.95681
30255
30287
30319
30351
30382
3-30521
3-30174
3-29829
3-29483
3-29139
30625
30653
.30680
.30708
.30736
-95195
.95186
.95177
.95168
.95159
32171
-32203
32235
32267
32299
3-10842
3-10532
3-10223
3-09914
3-09606
1O
9
8
7
6
55
56
57
58
59
29098
29126
29154
29182
29209
.95673
95664
95656
95647
95639
30414
30446
30478
30509
30541
3-28795
3-28452
3.28109
3-27767
3-27426
-30763
-30791
30819
30846
30874
.95150
95142
.95133
.95124
.95115
32331
32363
32396
32428
32460
3-09298
3-08991
3-08685
3-08379
3-08073
5
3
2
1
go.
29237
95630
30573
3-27085
30902
95106
32492
3-07768
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
'
73
78
NATURAL SINES, COSINES, TANGENTS, COTAN. 249
18 19
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
1
2
3
4
.30902
.30929
.30957
.30985
.31012
.95106
.95097
.95088
.95079
.95070
32492
32524
32556
32588
.32621
3-07768
3-07464
3-07160
3-06857
3-06554
32557
32584
32612
32639
32667
94552
94542
94533
-94523
-94514
. 34433
34465
.34498
-34530
.34563
2-90421
2-90147
2-89873
2-89600
2-89327
6O
59
58
57
56
5
6
7
8
9
.31040
.31068
.31095
.31123
.31151
.95061
.95052
.95043
.95033
.95024
32653
.32685
.32717
.32749
.32782
3-06252
3-05950
3-05649
3-05349
3-05049
.32694
.32722
32749
.32777
.32804
-94504
.94495
94485
.94476
.94466
.34596
-34628
.34661
-34693
-34726
2-89055
2-88783
2-88511
2-88240
2-87970
55
54
53
52
51
10
11
12
13
14
.31178
.31206
.31233
.31261
.31289
.95015
.95006
.94997
.94988
.94979
.32814
.32846
.32878
.32911
.32943
3 04749
3 04450
3-04152
3-03854
3-03556
.32832
32859
32887
32914
.32942
-94457
. 94447
-94438
.94428
-94418
-34758
.34791
.34824
.34856
.34889
2-87700
2 87430
2-87161
2-86892
2-86624
5O
49
48
47
46
15
16
17
18
19
-31316
.31344
31372
.31399
.31427
.94970
.94961
.94952
.94943
.94933
.32975
.33007
.33040
.33072
.33104
3-03260
3-02963
3-02667
3-02372
3-02077
.32969
.32997
.33024
.33051
.33079
- 94409
.94399
-943SO
.94380
.94370
-34922
-34954
-34987
.35020
.35052
2-86356
2-86089
2-85822
2-85555
2-85289
45
44
43
42
41
20
21
22
23
24
.31454
.31482
.31510
.31537
-31565
.94924
.94915
.94906
.94897
.94888
-33136
-33169
-33201
.33233
.33266
3-01783
3-01489
3-01196
3-00903
3-00611
-33106
.33134
.33161
.33189
.33216
-94361
-94351
-94342
.94332
.94322
.35085
.35118
35150
.35183
-35216
2-85023
2-84758
2-84494
2-84229
2-83965
40
39
38
37
36
25
26
27
28
29
31593
31620
-31648
31675
.31703
.94878
.94869
94860
94851
.94842
-33298
-33330
.33363
.33395
.33427
3-00319
3-00028
2-99738
2-99447
2-99158
33244
-33271
33298
.33326
-33353
-94313
.94303
.94293
.94284
.94274
.35248
.35281
.35314
35346
.35379
2-83702
2-83439
2-83176
2-82914
2-82653
35
34
33
32
31
30
31
32
33
34
31730
.31758
.31786
.31813
31841
.94832
.94823
.94814
94805
.94795
33460
33492
33524
33557
33589
2-98868
2-98580
2-98292
2-98004
2-97717
.33381
.33408
33436
33463
33490
.94264
.94254
.94245
.94235
.94225
.35412
.35445
.35477
.35510
.35543
2-82391
2-82130
2-81870
2-81610
2-81350
30
29
28
27
38
35
36
37
38
39
31868
.31896
31923
.31951
.31979
.94786
.94777
.94768
.94758
.94749
33621
.33654
-33686
-33718
-33751
2-97430
2-97144
2-96858
2-96573
2.96288
-33518
33545
.33573
33600
.33627
-94215
94206
.94196
94186
.94176
-35576
-35608
35641
.35674
.35707
2-81091
2-80833
2-80574
2-80316
2 80059
25
24
23
22
21
40
41
42
43
44
.32006
32034
.32061
32089
321i6
.94740
.94730
94721
.94712
94702
.33783
33816
33848
33381
.33913
2-96004
2-95721
2-95437
2-95155
2-94872
.33655
33682
33710
33737
33764
-94167
-94157
-94147
-94137
-94127
-35740
-35772
.35805
.35838
35871
2-79802
2-79545
2-79289
2-79033
2-78778
20
19
18
17
16
45
46
47
48
49
.32144
.32171
.32199
.32227
.32254
.94693
.94684
.94674
94865
-94856
.33945
33978
.34010
34043
.34075
2-94591
2-94309
2-94028
2-93748
2-93468
33792
33819
33846
33874
33901
-94118
94108
.94098
-94088
-94078
.35904
.35937
.35969
.36002
.36035
2-78523
2-78269
2-78014
2-77761
2-77507
15
14
13
12
11
50
51
52
53
54
.32282
.32309
.32337
.32364
.32392
.94646
94637
.94627
.94618
.94609
34108
.34140
34173
.34205
.34238
2-93189
2-92910
2-92632
2-92354
2-92076
-33929
33956
33983
-34011
34038
-94068
94058
. 94049
-94039
94029
.36068
.36101
.36134
36167
.36199
2-77254
2-77002
2-76750
2-76498
2-76247
10
9
7
6
55
56
57
58
59
32419
.32447
32474
32502
-32529
94599
.94590
.94580
94571
.94561
.34270
.34303
.34335
34368
. 34400
2-91799
2-91523
2-91246
2-90971
2-90696
34065
34093
34120
34147
34175
-94019
.94009
-93999
93989
-93979
36232
.36265
.36298
.36331
.36364
2-75996
2-75746
2-75496
2-75246
2-74997
5
4
3
2
60
.32557
94552
.34433
2.90421
-34202
.93969
.38397
2-74748
Q
'
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
71
70
250 NATURAL SINES, COSINES, TANGENTS, COTAN.
20 21
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
1
2
3
4
.34202
.34229
34257
34284
.34311
93969
93959
93949
.93939
-93929
36397
.36430
36463
36496
36529
2-74748
2-74499
2-74251
2-74004
2-73756
-35837
-35864
-35891
.35918
-35945
.93358
-93348
-93337
-93327
-93316
38386
38420
-38453
.38487
.38520
2-60509
2-60283
2-60057
2-59831
2-59606
6O
59
58
57
56
5
6
7
8
9
.34339
.34366
34393
. 34421
.34448
93919
.93909
.93899
.93889
.93879
36562
36595
36628
36661
.36694
2-73509
2-73263
2-73017
2-72771
2-72526
-35973
36000
-36027
.36054
.36081
-93306
-93295
.93285
93274
93264
.38553
.38587
38620
.38654
.38687
2-59381
2-59156
2-58932
2-58708
2-58484
55
54
53
52
51
10
11
12
13
14
34475
34503
.34530
.34557
.34584
.93869
.93859
.93849
93839
.93829
-36727
-36760
.36793
.36826
.36859
2-72281
2-72036
2-71792
2-71548
2-71305
36108
.36135
36162
.36190
.36217
.93253
93243
.93232
93222
-93211
-38721
38754
.38787
38821
.38854
2-58261
2-58038
2-57815
2-57593
2-57371
50
49
48
47
4B
15
16
17
18
i?_
.34612
34639
.34666
.34694
34721
.93819
.93809
93799
.93789
.93779
36892
.36925
.36958
.36991
-37024
2-71062
2-70819
2-70577
2-70335
2-70094
.36244
-36271
-36298
.36325
.36352
-93201
-93190
-93180
-93169
-93159
.38888
.38921
.38955
.38988
39022
2-57150
2-56928
2-56707
2-56487
2-56266
45
44
43
42
41
20
21
22
23
24
-34748
.34775
.34803
.34830
.34857
-93769
93759
93748
93738
.93728
-37057
.37090
-37123
.37157
-37190
2-69853
2-69612
2-69371
2-69131
2-68892
36379
.36406
-36434
-36461
-36488
-93148
-93137
-93127
-93116
-93106
39055
39089
.39122
39156
39190
2-56046
2-55827
2-55608
2-55389
2-55170
40
39
38
37
SB
25
26
27
28
29
34884
-34912
34939
.34966
.34993
93718
93708
.93698
93688
.93677
-37223
37256
.37289
.37322
.37355
2-68653
2-68414
2.68175
2-67937
2.67700
-36515
36542
.36569
.38596
.36623
93095
-93084
.93074
93063
.93052
-39223
39257
39290
.39324
39357
2-54952
2-54734
2.54516
2.54299
2-54082
35
34
33
32
31
30
31
32
33
34
.35021
.35048
-35075
-35102
-35130
.93667
.93657
93647
.93637
93626
37388
.37422
37455
.37488
.37521
2.67462
2.67225
2-66989
2-66752
2-66516
36650
.36677
.36704
.36731
.36758
93042
93031
93020
93010
.92999
39391
-39425
-39458
-39492
-39526
2-53865
2.53648
2-53432
2-53217
2-53001
3O
29
28
27
26
35
36
37
38
39
-35157
.35184
.35211
35239
-35266
93616
93606
93596
93585
93575
37554
-37588
37621
.37654
.37687
2-66281
2-66046
2-65811
2-65576
2-65342
36785
.36812
.36839
.36867
.36894
92988
92978
92967
92956
.92945
39559
.39593
39626
39660
.39694
2-52786
2-52571
2-52357
2-52142
2-51929
25
24
23
22
21
4O
41
42
43
44
-35293
-35320
-35347
-35375
-35402
.93565
93555
93544
.93534
.93524
-37720
37754
37787
.37820
.37853
2-65109
2-64875
2-64642
2-64410
2-64177
36S21
36948
-36975
-37002
-37029
.92935
92924
-92913
-92902
-92892
-39727
.39761
39795
.39829
-39862
2-51715
2-51502
2-51289
2-51076
2-50864
20
19
18
17
16
45
46
47
48
49
-35429
35456
.35484
-35511
-35538
93514
93503
93493
.93483
93472
-37887
.37920
37953
37986
.38020
2-63945
2-63714
2-63483
2-63252
2-63021
.37056
-37083
-37110
.37137
-37164
.92881
92870
92859
92849
.92838
39896
.39930
-39963
39997
.40031
2-50652
2-50440
2-50229
2-50018
2-49807
15
14
13
12
11
50
51
52
53
54
35565
.35592
35619
.35647
35674
93462
93452
93441
-93431
93420
-38053
-38086
.38120
38153
.38186
2-62791
2-62561
2.62332
2-62103
2-61874
-37191
-37218
- 37245
37272
.37299
92827
-92816
-92805
-92794
-92784
.40065
40098
.40132
.40166
- 40200
2-49597
2-49386
2-49177
2-48967
2-48758
10
9
8
7
6
55
56
57
58
59
35701
35728
35755
35782
35810
.93410
.93400
93389
.93379
93368
-38220
.38253
38286
.38320
.38353
2.61646
2-61418
2-61190
2.60963
2-60736
.37326
.37353
37380
37407
-37434
-92773
-92762
.92751
92740
92729
40234
40267
40301
40335
40369
2-48549
2-48340
2-48132
2-47924
2.47716
5
4
3
2
1
60
35837
93358
38386
2-60509
-37461
92718
40403
2-47509
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
'
69
68
NATURAL SINES, COSINES, TANGENTS, COTAN. 251
33 33
1
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
f
1
2
3
37461
.37488
.37515
.37542
.37569
92718
.92707
92697
92686
92675
. 40403
.40436
. 40470
.40504
.40538
2-47509
2-47302
2.47095
2.46888
2-46682
39073
39100
39127
39153
.39180
92050
92039
.92028
92016
.92005
42447
42482
42516
42551
42585
2-35585
2-35395
2-35205
2-35015
2-34825
60
59
58
57
5fi
5
6
7
8
9
.37595
.37622
.37649
.37676
.37703
92664
.92653
.92642
.92631
92620
.40572
40606
.40640
.40674
.40707
2-46476
2-46270
2-46065
2-45860
2-45655
39207
39234
39280
.39287
-39314
.91994
91982
.91971
.91959
-91948
42619
42654
42688
.42722
.42757
2-34636
2-34447
2-34258
2-34069
2-33881
55
54
53
52
51
10
11
12
13
14
.37730
.37757
37784
.37811
.37838
.92609
.92598
.92587
.92576
.92565
40741
.40775
40809
40843
.40877
2-45451
2-45246
2-45043
2-44839
2.44636
-39341
-39367
-39394
-39421
- 39448
-91936
.91925
.91914
.91902
.91891
42791
.42826
42860
.42894
.42929
2-33693
2-33505
2-33317
2-33130
2-32943
50
49
48
47
46
15
16
17
18
19 ,
37865
.37892
.37919
.37946
.37973
.92554
.92543
92532
.92521
.92510
.40911
40945
.40979
.41013
.41047
2-44433
2-44230
2-44027
2-43825
2-43623
-39474
-39501
-39528
-39555
.39581
.91879
91868
91856
91845
.91833
42963
.42998
43032
43067
43101
2-32756
2-32570
2-32383
2-32197
2-32012
45
44
43
42
41
20
21
22
23
24
.37999
.38026
38053
.38080
.38107
92499
92488
.92477
92466
92455
.41081
.41115
.41149
.41183
.41217
2-43422
2-43220
2-43019
2-42819
2-42618
-39608
-39635
-39661
.39688
-39715
91822
.91810
.91799
91787
.91775
43136
43170
.43205
.43239
.43274
2-31826
2-31641
2-31456
2-31271
2-31086
40
39
38
37
3
25
26
27
28
29
.38134
.38161
.38188
-38215
.38241
.92444
.92432
.92421
.92410
92399
.41251
.41285
41319
41353
.41387
2-42418
2-42218
2-42019
2-41819
2-41620
39741
.39768
.39795
.39822
.39848
91764
91752
91741
.91729
-91718
43308
.43343
.43378
43412
.43447
2-30902
2-30718
2-30534
2-30351
2-30167
35
34
33
32
31
30
31
32
33
34
.38268
.38295
.38322
.33349
.38376
92388
.92377
92366
92355
92343
.41421
41455
41490
.41524
.41558
2 41421
2-41223
2-41025
2-40827
2-40629
39875
.39902
.39928
-39955
39982
.91706
-91694
-91683
91671
91660
.43481
.43516
.43550
43585
43620
2-29984
2-29801
2-29619
2-29437
2-29254
30
29
28
27
26
35
36
37
38
39
38403
.38430
.38456
.38483
.38510
.92332
.92321
92310
92299
.92287
.41592
41626
41660
41694
.41728
2-40432
2-40235
2-40038
2-39841
2-39645
- 40008
.40035
-40062
-40088
-40115
91648
.91636
.91625
91613
-91601
43654
.43689
.43724
.43758
.43793
2-29073
2-28891
2-28710
2-28528
2-28348
25
24
23
22
21
40
41
42
43
44
38537
38564
.38591
.38617
-38644
.92276
.92265
.92254
.92243
92231
.41763
41797
41831
.41865
.41899
2-39449
2-39253
2-39058
2-38863
2-38668
-40141
-40168
-40195
40221
40248
.91590
91578
.91566
.91555
.91543
43828
.43862
43897
43932
.43966
2-28167
2-27987
2-27806
2-27626
2 - 27447
20
19
18
17
16
45
46
47
48
49
-38671
.38698
-38725
38752
.33778
92220
92209
.92198
.92186
92175
.41933
.41968
.42002
.42036
.42070
2-38473
2-38279
2-38084
2-37891
2-37697
40275
40301
.40328
.40355
.40381
91531
91519
.91508
.91496
91484
44001
.44036
.44071
.44105
44140
2-27267
2-27088
2-26909
2-26730
2-26552
15
14
13
12
11
50
51
52
53
54
38805
.38832
.38859
38886
.38912
.92164
92152
92141
92130
.92119
.42105
.42139
.42173
.42207
42242
2-37504
2-37311
2-37118
2-36925
2-36733
. 40408
-40434
-40461
-40488
-40514
91472
91461
91449
91437
91425
44175
44210
. 44244
.44279
44314
2-26374
2-26196
2-26018
2-25840
1O
9
8
7
6
55
56
57
58
59
38939
38966
38993
.39020
.39046
.92107
.92096
92085
92073
.92062
42276
.42310
42345
42379
42413
2-36541
2-36349
2-36158
2-35967
2-35776
.40541
40567
40594
40621
40847
91414
.91402
.91390
.91378
91366
.44349
44384
44418
44453
. 44488
2-25486
2-25309
2-25132
2-24956
2-24780
5
3
2
1
60
-39073
.92050
. 42447
2-35585
40674
91355
-44523
2 24604
_o
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
f
67
66
252 NATURAL SINES, COSINES, TANGENTS, COTAN.
24* 25
t
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
o
1
2
3
40674
.40700
40727
.40753
.40780
91355
91343
.91331
.91319
9i307
44523
44558
-44593
.44627
.44662
2-24604
2-24428
2-24252
2-24077
2.23902
42262
.42288
.42315
-42341
-42367
-90631
-90618
-90606
90594
90o82
-46631
46666
46702
46737
46772
2-14451
2-14288
2-14125
2-13963
2.13801
60
59
58
57
56
5
6
7
8
9
.40806
.40833
.40860
.40886
.40913
91295
.91283
.91272
91260
.91248
44697
44732
44767
44802
44837
2-23727
?. 23553
2.23378
2-23204
2-23030
42394
-42420
-42446
42473
-42499
-90569
-90557
90545
90532
90520
.46808
.46843
46879
46914
46950
2-13639
2-13477
2-13316
2-13154
2-12993
55
54
53
52
51
10
11
12
13
14
40939
40966
40992
41019
.41045
.91236
.91224
.91212
.91200
.91188
44872
44907
44942
44977
45012
2-22857
2-22683
2.22510
2-22337
2-22164
-42525
-42552
-42578
42604
.42631
90507
90495
.90483
- 90470
-90458
46985
.47021
.47056
47092
47128
2-12832
2-12671
2-12511
2-12350
2-12190
50
49
48
47
46
15
16
17
18
19
.41072
.41098
.41125
.41151
.41178
91176
91164
91152
.91140
.91128
45047
45082
45117
45152
.45187
2.21992
2-21819
2-21647
2-21475
2-21304
.42657
.42683
.42709
42736
42762
-90446
-90433
90421
-90408
90396
.47163
.47199
.47234
.47270
-47305
2-12030
2-11871
2.11711
2-11552
2-11392
45
44
43
42
41
20
21
22
23
24
.41204
41231
41257
41284
41310
.91116
91104
.91092
.91080
91068
-45222
45257
-45292
-45327
-45362
2-21132
2-20961
2-20790
2-20619
2-20449
42788
.42815
.42841
42867
-42894
.90383
90371
-90358
-90346
-90334
-47341
.47377
.47412
.47448
-47483
2-11233
2.11075
2-10916
2-10758
2-10600
40
39
38
37
36
25
26
27
28
29
41337
41363
41390
41416
41443
-91056
-91044
-91032
.91020
91008
45397
45432
45467
45502
.45538
2-20278
2-20108
2.19938
2-19769
2.19599
.42920
42946
42972
-42999
-43025
90321
90309
90296
90284
90271
.47519
-47555
.47590
.47626
.47662
2 10442
2-10284
2-10126
2-09969
2-09811
35
34
33
32
31
30
31
32
33
34
41469
41496
41522
41549
41575
.90996
90984
90972
.90960
.90948
45573
-45608
-45643
-45678
45713
2-19430
2-19261
2-19092
2-18923
2-18755
43051
43077
-43104
-43130
-43156
90259
90246
90233
90221
.90208
.47698
.7733
.47769
.47805
47840
2-09354
2-09498
2-09341
2-09184
2-09028
30
29
28
27
26
35
36
37
38
39
41602
41628
41655
.41681
.41707
90936
-90924
-90911
90899
.90887
45748
45784
46819
45854
45889
2-18587
2-18419
2-18251
2-18084
2-17916
-43182
-43209
43235
-43261
-43287
90196
90183
90171
90158
.90146
47876
47912
47948
47984
-48019
2-08872
2-08716
2-08560
2-08405
2-08250
25
24
23
22
21
40
41
42
43
44
41734
.41760
41787
41813
41840
.90875
90863
90851
90839
-90826
45924
45960
45995
46030
46065
2-17749
2-17582
2-17416
2-17249
2-17083
-43313
-43340
43366
-43392
.43418
.90133
90120
.90108
.90095
.90082
48055
48091
48127
48163
48198
2-08094
2-07939
2-07785
2-07630
2-07476
20
19
18
17
16
45
46
47
48
49
41866
41892
41919
41945
41972
90814
90802
90790
90778
90766
46101
46136
46171
46206
46242
2-16917
2-16751
2.16585
2-16420
2-16255
- 43445
43471
43497
43523
-43549
90070
90057
90045
90032
-90019
-48234
-48270
-48306
-48342
-48378
2.07321
2-07167
2-07014
2-06860
2-06706
15
14
13
12
11
50
51
52
53
54
41998
42024
42051
42077
42104
90753
-90741
-90729
.90717
90704
46277
46312
-46348
46383
46418
2-16090
2-15925
2-15760
2-15596
2-15432
-43575
-43602
43628
43654
.43680
-90007
89994
89981
.89968
.89956
.48414
.48450
-48486
-48521
48557
2-06553
2 - 06400
2-06247
2-06094
2-05942
10
9
8
6
55
56
57
58
59
42130
42156
42183
42209
42235
.90692
.90680
.90668
.90655
.90643
46454
.46489
.46525
46560
.46595
2-15268
2-15104
2-14940
2 14777
2-14614
43706
43733
-43759
-43785
-43811
89943
-89930
-89918
89905
-89892
48593
.48629
-48665
48701
-48737
2-05790
2-05637
2-05485
2-05333
2-05182
5
3
2
1
60
.42262
90631
46631
2-14451
-43837
-89879
-48773
2-05030
_o
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
65
64
NATURAL SINES, COSINES, TANGENTS, COTAN. 253
86 37
t
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
1
2
3
4
43837
43863
.43889
.43916
.43942
89879
89867
.89854
.89841
.89828
48773
.48809
.48845
.48881
.48917
2-05030
2-04879
2-04723
2.04577
2-04426
45399
-45425
.45451
.45477
.45503
.89101
.89087
.89074
.89061
.89048
-50953
.50989
-51026
-51063
-51099
1-96261
1.96120
1-95979
1.95838
1.95698
60
59
58
57
56
5
6
7
8
9
43968
.43994
.44020
. 44046
.44072
.89816
.89803
.89790
.89777
.89764
.48953
.48989
.49026
.49062
.49098
2-04276
2-04125
2-03975
2-03825
2-03675
.45529
.45554
.45580
.45606
-45632
89035
-89021
-89008
-88995
.88981
51136
.51173
.51209
.51246
-51283
1-95557
1-95417
1-95277
1-95137
1-94997
55
54
53
52
51
10
11
12
13
14
.44098
.44124
.44151
-44177
.44203
.89752
.89739
.89726
.89713
.89700
.49134
.49170
49206
49242
.49278
2-03526
2-03376
2-03227
2-03078
2-02929
45658
.45684
.45710
.45736
.45762
-88968
.88955
.88942
-88928
.88915
-51319
-51356
-51393
.51430
51467
1-94858
1-94718
1.94579
1 . 94440
1-94301
50
49
48
47
46
15
16
17
18
19
44229
44255
.44281
.44307
.44333
.89687
.89674
.89662
.89649
-89636
.49315
.49351
.49387
.49423
.49459
2-02780
2-02631
2-02483
2-02335
2-02187
45787
.45813
.45839
.45865
.45891
-88902
-88888
-88875
.88862
.88848
.51503
-51540
-51577
.51614
-51651
1.94162
1-94023
1-93885
1.93746
1-93608
45
44
43
42
41
30
21
22
23
24
.44359
.44385
.44411
44437
.44464
.89623
.89610
.89597
-89584
.89571
.49495
.49532
.49568
.49604
.49640
2-02039
2-01891
2-01743
2-01596
2-01449
.45917
.45942
.45968
45994
.46020
.88835
-88822
88808
-88795
-88782
-51688
51724
51761
.51798
.51835
1-93470
1-93332
1.93195
1-93057
1-9?920
40
39
38
37
36
25
26
27
28
29
.44490
.44516
.44542
.44568
.44594
.89558
.89545
.89532
.89519
.89506
-49677
.49713
.49749
.49786
-49822
2-01302
2-01155
2-01008
2-00862
2-00715
.46046
.46072
46097
.46123
-46149
-88768
-88755
-88741
.88728
.88715
.51872
51909
51946
.51983
-52020
1-92782
1-92645
1-92508
1-92371
1-92235
35
34
33
32
31
30
81
32
33
34
. 44620
.44646
-44672
.44698
.44724
89493
.89480-
.89467
.89454
.89441
.49858
.49894
.49931
.49967
.50004
2-00569
2-00423
2-00277
2-00131
1.99986
.46175
.46201
.46226
.46252
46278
.88701
-88688
-88674
-88661
.88647
.52057
52094
.52131
.52168
.52205
1-92098
1-91962
1-91826
1-91690
1.91554
30
29
28
27
28
35
36
37
38
39
44750
.44776
.44802
.44828
.44854
.89428
.89415
.89402
.89389
.89376
. 50040
.50076
.50113
.50149
.50185
1-99841
1-99695
1-99550
1-99406
1-99261
.46304
.46330
46355
46381
-46407
88634
-88620
-88607
-88593
-88580
-52242
.52279
-52316
.52353
-52390
1-91418
1-91282
1.91147
1.91012
1.90876
25
24
23
22
21
40
41
42
43
44
.44880
.44906
.44932
44958
.44984
.89363
.89350
.89337
.89324
.89311
.50222
.50258
.50295
.50331
.50368
1-99116
1-98972
1-98828
1-98684
1.98540
46433
-46458
-46484
-46510
-46536
-88566
-88553
-88539
-88526
-88512
-52427
.52464
.52501
-52538
.52575
1-90741
1-90607
1-90472
1-90337
1-90203
3O
19
18
17
16
45
46
47
48
49
.45010
45036
.45062
.45088
-45114
.89298
.89285
.89272
89259
.89245
. 50404
. 50441
.50477
.50514
.50550
1-98396
1-98253
1.98110
1.97966
1-97823
-46561
-46587
.46613
-46639
.46664
-88499
-88485
-88472
-88458
. 88445
.52613
52650
-52687
.52724
.92761
1-90069
1-89935
1-89801
1-89667
1-89533
15
14
13
12
11
50
51
52
53
54
-45140
.45166
45192
.45218
.45243
.89232
.89219
-89206
.89193
-89180
.50587
-50623
50660
-50696
-50733
1-97681
1-97538
1-97395
1-97253
1-97111
.46690
.46716
.46742
.46767
.46793
.88431
88417
88404
88390
88377
52798
.52836
.52873
.52910
.52947
1-89400
1-89266
1.89133
1.89000
1-88867
10
9
8
7
6
55
56
57
58
59
.45269
.45295
.45321
-45347
45373
-89167
-89153
-89140
.89127
-89114
-50769
-50806
-50843
-50879
50916
1-96969
1-96827
1.96685
1-96544
1-96402
-46819
- 46844
-46870
-46896
-46921
88363
88349
88336
88322
88308
52985
53022
53059
53096
53134
1-88734
1-88602
1-88469
1-88337
1-88205
5
4
3
2
1
60
45399
.89101
-50953
1.96261
-46947
88295
53171
1-88073
/
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
63
63
254 NATURAL SINES, COSINES, TANGENTS, COTAN.
28 29
I
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
\
y
2
3
.46947
.46973
.46999
.47024
.47050
.88295
.88281
.88267
.88254
.88240
-53171
.53208
53246
.53283
.53320
1.88073
1-87941
1-87809
1.87677
1.87546
48481
.48506
-48532
-48557
-48583
87462
.87448
87434
87420
.87406
-55431
-55469
.55507
55545
.55583
i 80405
1.80281
1.80158
1-80034
1.79911
60
59
58
57
56
5
6
7
9
.47076
47101
.47127
.47153
.47178
.88226
88213
.88199
.88185
.88172
.53358
.53395
.53432
53470
.53507
1.87415
.1.87283
1-87152
1.87021
1-86891
-48608
48634
.48659
48684
48710
.87391
.87377
.87363
87349
.87335
.55621
-55659
.55697
-55736
-55774
1 79788
1 79665
1.79542
1.79419
1-79296
55
54
53
52
51
10
11
12
13
14
.47204
.47229
.47255
.47281
.47306
.88158
.88144
.88130
.88117
.88103
.53545
.53582
.53620
.53657
.53694
1.86760
1.86630
1.86499
1.86369
1.86239
48735
.48761
48786
.48811
48837
87321
.87306
.87292
87278
.87264
-55812
-55850
-55888
.55926
-55964
1-79174
1 7905]
1-78929
1-78807
1-78685
50
49
48
47
46
15
16
17
18
*9
47332
.47358
.47383
.47409
.47434
.88089
.88075
.88062
88048
.88034
53732
.53769
-53807
-53844
.53882
1-86109
1.85979
.85850
: -85720
-85591
.48862
.48888
.48913
.48938
-48964,
87250
.87235
87221
.87207
-87193
-56003
-56041
-56079
-56117
.56156
1-78563
1-78441
1-78319
1-78198
1-78077
45
44
43
42
,,.41
20
21
22
23
24
47460
.47486
.47511
-47537
.47562
.88020
.88006
.87993
.87979
.87965
.53920
.53957
.53995
.54032
.54070
.85462
.85333
83204
1-85075
1.84946
.48989
.49014
.49040
-49065
-49090
.87178
.87164
.87150
.87136
.87121
.56194
-56232
-56270
-56309
56347
1.77955
1-77834
1-77713
1-77592
1-77471
40
39
38
37
36
25
26
27
28
29
47588
47614
47639
.47665
.47690
.87951
.87937
87923
.87909
.87896
.54107
.54145
54183
. 54220
. 54258
1.84818
1-84689
1-84561
1.84433
1-84305
-49116
-49141
-49166
-49192
-49217
87107
87093
.87079
-87064
-87050
-56385
-56424
-56462
.56501
.56539
1-77351
1-77230
1 77110
1-76990
1-76869
35
34
33
32
31
30
31
32
33
34
.47716
.47741
.47767
-47793
.47818
.87882
.87868
.87854
.87840
.87826
54296
54333
.54371
. 54409
- 54446
1.84177
1 - 84049
1.83922
1.83794
1.83667
-49242
-49268
-49293
-49318
.49344
-87036
-87021
-87007
-86993
-86978
-56577
-56616
5'6654
.56693
.56731
1.76749
1-76629
1.76510
1-76390
1.76271
30
29
28
27
26
35
36
37
38
39
.47844
47869
.47895
.47920
.47946
.87812
.87798
.87784
.87770
-87756
- 54484
-54522
-54560
-54597
-54635
.83540
-83413
-83286
.83159
-83033
.49369
-49394
-49419
49445
.49470
-86964
-86949
-86935
-86921
.86906
56769
.56808
.56846
-56885
-56923
1-76151
1-76032
1-75913
1-75794
1-75675
25
24
23
22
-21
40
41
42
43
44
.47971
-47997
.48022
.48048
-48073
87743
.87729
87715
87701
.87687
.54673
54711
- 54748
-54786
-54824
.82906
.82780
1-82654
1-82528
1-82402
49495
49521
49546
49571
.49596
-86892
-86878
86863
86849
.86834
-56962
57000
-57039
57078
.57116
1-75556
1 75437
1-75319
1-75200
1.75082
20
19
18
17
16
45
46
47
48
49
.48099
48124
.48150
48175
.48201
.87673
.87659
.87645
.87631
.87617
.54862
. 54900
.54938
.54975
.55013
1.82276
1-82150
1-82025
1-81899
1-81774
.49622
-49647
49672
-49697
-49723
-86820
.86805
.86791
-86777
-86762
.57155
.57193
.57232
.57271
-57309
1-74964
1 . 74846
1-74728
1-74610
1 . 74492
15
14
13
12
11
50
51
52
53
54
.48226
.48252
.48277
.48303
.48328
87603
.87589
-87575
.87561
87546
.55051
.55089
.55127
.55165
. 55203
1-81649
1.81524
1.81399
1-81274
1-81150
49748
.49773
-49798
-49824
-49849
.86748
-86733
-86719
.86704
-86690
.57348
-57386
-57425
.57464
-57503
1-74375
1 . . 4257
1 - 74140
1 - 74022
1-73905
10
9
8
7
6
55
56
57
58
59
.48354
-48379
48405
.48430
.48456
87532
.87518
.87504
87490
.87476
55241
.55279
.55317
55355
.55393
1.81025
1-80901
1.80777
1.80653
1-80529
-49874
49899
-49924
49950
49975
-86675
.86661
.86646
.86632
.86617
57541
.57580
.57619
.57657
-57696
1-73788
1-73671
1.73555
1-73438
1.73321
5
4
3
2
1
90
-48481
.87462
55431
1.80405
50000
.86603
57735
1-73205
Cos.
Sin.
Cot.
Tan.
Cos,
Sin.
Cot.
Tan.
'
61
60
NATURAL SINES, COSINES, TANGENTS, COTAN. 255
30 31
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
.Cot,.
'
o
1
2
3
4
.50000
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.50050
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.86588
.86573
.88559
.86544
-57735
.57774
.57813
.57851
.57890
1.73205
1-73089
1.72973
1.72857
1.72741
.51504
51529
.51554
.51579
.51604
.85717
85702
85687
.85672
.85657
60086
60126
60165
60205
60245
1.66428
1-66318
1-66209
1-66099
i- 65990
60
59
58
57
56
5
6
7
8
9
.50126
.50151
.50176
.50201
.50227
.86530
.86515
.86501
.86486
.86471
.57929
.57968
.58007
.58046
.58085
1-72625
1.72509
1.72393
1-72278
1.72163
.51628
51653
51678
.51703
.51728
85642
85627
85612
.85597
-85582
60284
.60324
60364
60403
. 60443
1-65881
1-65772
1-65663
1 65554
1-65445
55
54
53
52
51
10
11
12
13
14
.50252
.50277
.50302
.50327
-50352
86457
.86442
.86427
.86413
.86398
.58124
.58162
.58201
.58240
-58279
1-72047
1.71932
1.71817
1.71702
1.71588
-51753
51778
-51803
51828
51852
85567
85551
.85536
-85521
.85506
60483
60522
.60562
60602
60642
1-65337
1-65228
1-65120
1.65011
1 . 64903
5O
49
48
47
48
15
16
17
18
19
.50377
50403
50428
.50453
.50478
86384
.86369
86354
.86340
.86325
.58318
.58357
.58396
-58435
.58474
1-71473
1.71358
1.71244
1-71129
1-71015
.51877
.51902
-51927
51952
.51977
.85491
.85476
-85461
-85446
85431
60681
.60721
.60761
.60801
.60841
1-64795
1-64687
1-64579
1-64471
1-64363
45
44
43
42
41
20
21
22
23
24
.50503
.50528
-50553
.50578
.50603
.86310
86295
.86281
.86266
.86251
58513
-58552
-58591
-58631
.58670
1-70901
1-70787
1-70673
1-70560
1 . 70446
52002
.52026
52051
.52076
-52101
-.85416
.85401
-85385
-85370
-85355
60881
.60921
60960
61000
61040
1-64256
1-64148
1 -64041
1-63934
1-63826
40
39
38
37
36
25
28
27
28
89
.50628
.50654
.50679
-50704
50729
.86237
86222
,86207
.86192
.86178
58709
.58748
.58787
.58826
.58865
1-70332
1-70219
1-70106
1-69992
1.69879
.52126
.52151
.52175
.52200
-52225
85340
.85325
85310
.85294
.85279
.61080
.61120
.61160
.61200
-61240
1-63719
1-63612
1-63505
1-63398
1-63292
35
34
33
32
31
30
31
32
33
34
50754
.50779
. 50804
.50829
.50854
.86163
86148
.86133
86119
.86104
.58905
.58944
.58983
.59022
.59061
1-69766
1-69653
1-69541
1-69428
1-69316
52250
52275
.52299
.52324
52349
85264
.85249
85234
85218
.85203
-61280
-61320
.61360
.61400
.61440
1-63185
1-63079
1-62972
1-62866
1-62760
30
29
28
27
26
35
36
37
38
39
50879
.50904
50929
50954
50979
.86089
-86074
.86059
86045
86030
.59101
59140
.59179
59218
.59258
1-69203
1.69091
1-68979
1.68866
1-68754
.52374
.52399
52423
52448
52473
.85188
85173
85157
.85142
-85127
61480
61520
61561
61601
.61641
1-62654
1-62548
1-62442
1-62336
1-62230
25
24
23
22
21
40
41
42
43
44
51004
51029
51054
.51079
51104
.86015
.86000
85985
-85970
.85956
.59297
.59336
.59376
.59415
.59454
1-68643
1.68531
1.68419
1-68308
1.68196
.52498
52522
52547
52572
.52597
.85112
.85096
85081
85066
-85051
61681
61721
61761
.61801
.61842
1-62125
]- 62019
1-61914
1-61808
1-61703
20
19
18
17
18
45
46
47
48
49
51129
51154
51179
51204
.51229
85941
.85926
.85911
.85896
.85881
.59494
59533
59573
.59612
.59651
1-68085
1-67974
1-67863
1.67752
1-67641
-52621
-52646
-52671
-52696
.52720
85035
85020
85005
-84989
-84974
61882
.61922
61962
.62003
62043
1-61598
1.61493
1.61388
1-61283
1-61179
15
14
13
12
11
50
51
52
53
54
.51254
51279
51304
51329
.51354
85866
.85851
85836
85821
.85806
59691
59730
59770
59809
59849
1-67530
1-67419
1-67309
1 67198
1-67088
.52745
-52770
-52794
-52319
.52844
84959
. 84943
.84928
84913
.84897
62083
62124
62164
62204
.62245
1-61074
1-60970
1 60865
1-60761
1.60657
10
9
8
7
6
55
56
57
58
59
51379
51404
.51429
51454
51479
85792
85777
.85762
.85747
85732
.59888
59928
.59967
60007
60046
1-66978
1-66867
1-66757
1-66647
1-66538
.52869
.52893
-52918
.52943
.52967
84882
84866
.84851
84836
.84820
62285
62325
62366
62406
. 62446
1.60553
1 . 60449
1-60345
1 60241
1-60137
5
4
3
2
1
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85717
60086
1-66428
52992
.84805
62487
1 - 60033
O
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
69
58
256 NATURAL SINES, COSINES, TANGENTS, COTAN.
33 33
t
Sin.
Cos
Tan.
Cot
Sin.
Cos.
Tan.
Cot.
*
o.
2
3
.52992
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.84805
84789
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. 84743
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62527
.62568
.62608
62649
-60033
.59930
.59826
59723
.59620
54464
-54488
54513
54537
-54561
.83867
.83851
83835
83819
-83804
64941
64982
65024
65065
65106
1-53986
1-53888
1-53791
1-53693
1-53595
60
59
58
57
56
6
j
9
.53115
.53140
.53164
.53189
.53214
.84728
84712
84697
84681
.84666
-62689
.62730
.62770
.62811
-62852
59517
.59414
.59311
.59208
.59105
- 54583
.54610
54635
54659
. 54683
-83788
83772
83756
83740
.83724
65148
65189
-65231
65272
65314
1-53497
1-53400
1-53302
1-53205
1.53107
55
54
53
5L
51
10
i*
13
14
.53238
.53263
.53288
.53312
.53337
84650
.84635
84619
.84604
.84588
.62892
.62933
-62973
-63014
.63055
.59002
.58900
.58797
.58695
.58593
-54708
-54732
-54756
-54781
-54805
83708
83692
83676
83660
83645
65355
-65397
-65438
-65480
-65521
1-53010
1-52913
1-52816
1-52719
1-52622
50
49
48
47
48
15
16
17
18
19..
.53361
.53386
.53411
.53435
.53460
.84573
.84557
.84542
.84526
.84511
.63095
-63136
.63177
.63217
-63258
.58490
.58388
-68286
.58184
-58083
-54829
.54854
.54878
54902
-54927
83629
83613
83597
83581
.83565
65563
-65604
65646
65688
-65729
1-52525
1-52429
1-52332
1-52235
1-52139
45
44
43
42
41
2O
21
22
23
24
-53484
.53509
.53534
.53558
.53583
.84495
84480
.84464
. 84448
.84433
-63299
-63340
- 63380
.63421
. 63462
.57981
' .57879
.57778
.57676
.57575
54951
-54975
54999
55024
.55048
.83549
.83533
83517
83501
83485
.65771
.65813
65854
.65896
.65938
1.52043
1.51946
1-51850
1-51754
1.51658
4O
39
38
37
36
25
26
27
28
29
53607
.53632
.53656
-53681
.53705
84417
. 84402
84386
.84370
.84355
63503
.63544
.63584
.63625
.63666
.57474
.57372
.57271
.57170
.57069
55072
-55097
55121
-55145
.55169
83469
83453
83437
83421
83405
.65980
.66021
.66063
.66105
-66147
1-51562
1-51466
1-51370
1-51275
1.51179
35
34
33
32
31
30
81
32
33
34
.53730
.53754
.53779
.53804
.53828
.84339
.84324
.84308
.84292
.84277
.63707
-63748
-63789
.63830
.63871
.56969
.56868
.56767
.56667
.56566
.55194
.55218
.55242
.55266
-55291
83389
83373
-83356
-83340
-83324
.66189
.66230
.66272
.66314
.66356
1-51084
1.50988
1-50893
1.50797
1.50702
30
29
28
27
26
35
36
37
38
39
.53853
.53877
.53902
.53926
.53951
84261
.84245
-84230
.84214
.84198
.63912
.63953
-63994
.64035
-64076
.56466
.56366
56265
.56165
1-56065
.55315
-55339
.55363
.55388
-55412
83308
83292
83276
83260
83244
.66398
.66440
66482
.66524
.66566
1-50607
1-50512
1.50417
1.50322
1.50228
25
24
23
22
21
40
41
42
43
44
.53975
. 54000
.54024
.54049
.54073
-84182
.84167
.84151
.84135
.84120
.64117
.64158
.64199
. 64240
-64281
1.55966
1.55866
1.55766
1.55666
1-55567
-55436
.55460
.55484
-55509
-55533
83228
.83212
33195
.83179
83163
.66608
.66650
.66692
.66734
.66776
1.50133
1.50038
1-49944
1.49849
1-49755
30
19
18
17
16
45
46
47
48
49
.54097
.54122
.54146
.54171
.54195
84104
.84038
-84072
-84057
. 84041
.64322
.64363
. 64404
. 64446
- 64487
1-55467
1.55368
1.55269
1.55170
1.55071
.55557
-55581
-55605
.55630
55654
.83147
.83131
.83115
83098
-83082
.66818
.66860
.66902
.66944
.66986
1.49661
1-49566
1.49472
1.49378
1.49284
15
14
13
12
11
50
51
59,
53
54
.54220
. 54244
.54269
.54293
.54317
84025
-84009
.83994
-83978
83962
-64528
64569
-64610
64652
-64693
1.54972
1.54873
1 . 54774
1.54675
1.54576
.55678
-55702
55726
-55750
.55775
83066
-83050
.83034
.83017
83001
.67028
.67071
.67113
.67155
.67197
1.49190
1-49097
1.49003
1.48909
1.48816
1O
9
8
7
6
55
56
57
58
59
54342
54366
54391
.54415
. 54440
83946
83930
.83915
-83899
.83883
. 64734
-64775
.64817
-64858
64899
1 . 54478
1-54379
1.54281
1.54183
1-54085
55799
-55823
-55847
.55871
-55895
82985
82969
-82953
82936
82920
.67239
.67282
.67324
.67366
.67409
1.48722
1.48629
1.48536
1-48442
1-48349
5
3
2
60
. 54464
.83867
-64941
1-53986
.55919
82904
.67451
1-48256
.O
'
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
66
NATURAL SINES, COSINES, TANGENTS, COTAN. 257
34 35
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
o
2
4
.55919
55943
.55968
.55992
.56016
-82904
82887
82871
82855
82839
67451
67493
.67536
67578
67620
1-48256
1.48163
1.48070
1-47977
1.47885
57358
57381
57405
57429
57453
-81915
81899
81882
81865
-81848
-70021
-70064
-70107
.70151
.70194
1.42815
1-42726
1-42638
1-42550
1-42462
60
59
58
57
56
5
?
1
-56040
.56064
.56088
.56112
.56136
.82822
82806
82790
.82773
.82757
67663
67705
67748
67790
67832
1-47792
1-47699
1-47607
1-47514
1-47422
-57477
-57501
-57524
-57548
-57572
-81832
-81815
81798
-81782
-81765
70238
70281
.70325
70368
70412
1-42374
1-42286
1-42198
1-42110
1-42022
55
54
53
52
51
1O
11
12
13
14
56160
.56184
.56208
.56232
56256
.82741
.82724
.82708
.82692
.82675
67875
67917
.67960
.68002
.68045
1-47330
1-47238
-47146
47053
46962
-57596
57619
57643
57667
57691
-81748
81731
81714
-81698
-81681
. 70455
.70499
70542
70586
70629
1-41934
1-41847
1-41759
1-41672
1-41584
5O
49
48
47
46
15
16
17
18
19
.56280
.56305
.56329
56353
56377
82659
.82643
.82626
.82610
-82593
.68088
.68130
68173
-68215
68258
.46870
.46778
.46686
.46595
.46503
.57715
.57738
.57762
57786
57810
81664
81647
81631
81614
81597
70673
70717
70760
70804
70848
1-41497
1-41409
1-41322
1-41235
1-41148
45
44
43
42
41
20
21
22
23
24
.56401
.56425
. 56449
.56473
.56497
82577
82561
82544
82528
82511
.68301
.68343
68386
.68429
68471
46411
-46320
-46229
.46137
1-46046
.57833
57857
57881
57904
57928
-81580
81563
81546
81530
81513
70891
70935
70979
.71023
-71066
1-41061
1-40974
1-40887
1-40800
1-40714
40
39
38
37
36
25
26
27
28
29
56521
-56545
.56569
-56593
.56617
82495
82478
82462
.82446
.82429
68514
.68557
68600
68642
68685
1-45955
1.45864
1-45773
1-45682
1-45592
-57952
57976
57999
58023
58047
-81496
81479
81462
-81445
-81428
-71110
-71154
-71198
-71242
-71285
1.40627
1 40540
1.40454
1.40367
1-40281
35
34
33
32
31
30
31
32
33
34
.56641
.56665
.56689
.56713
-56736
.82413
.82396
.82380
82363
.82347
68728
68771
68814
.68857
.68900
1-45501
1-45410
1-45320
1-45229
1-45139
-58070
58094
58118
58141
-58165
-81412
-81395
-81378
-81361
-81344
.71329
-71373
-71417
-71461
-71505
1-40195
1-40109
1-40022
1-39936
1.39850
3O
29
28
27
26
35
36
37
38
39
-56760
. 5678-ft
. 56803
56832
.568?i6_
-82330-
.82314
.82297
82281
-82264
.68942
68985
.69028
.69071
.69114
1.45049
1.44958
1-44868
1-44778
1-44688
-58189
-58212
-58236
-58260
-58283
-81327
-81310
81293
81276
81259
-71549
71593
.71637
.71681
.71725
1-39764
1-39679
1-395'S
1-39507
1-39421
25
24
23
22
21
40
41
42
43
44
56880
.56904
.56928
56952
.56976
.82248
.82231
.82214
82198
-82181
.69157
-69200
.69243
-69286
-69329
1-44598
1-44508
1-44418
1-44329
1-44239
-58307
-58330
-58354
-58378
-58401
81242
.81225
81208
81191
81174
.71769
.71813
.71857
.71901
71946
1-39336
1-39250
1.39165
1-39079
1-38994
20
19
18
17
16
45
46
47
48
49
. 57000
.57024
.57047
.57071
.57095
.82165
82148
.82132
82115
.82098
-69372
.69416
69459
.69502
69545
1.44149
1 44060
1-43970
1-43881
1-43792
58425
. 58449
58472
58496
.58519
-81157
81140
81123
81106
-81089
-71990
.72034
.72078
.72122
72167
1.38909
1.38824
1.38738
1-38653
1-38568
15
14
13
12
11
50
51
52
53
54
.57119
57143
.57167
.57191
57215
82082
82065
82048
82032
82015
-69588
69631
69675
69718
69761
1-43703
1-43614
1-43525
1-43436
1-43347
-58543
-58567
-58590
-58614
-58637
81072
81055
.81038
-81021
81004
.72211
72255
72299
72344
.72388
1-38484
1-38399
1-38314
1-38229
1-38145
10
9
8
7
6
55
56
57
58
59
57238
57262
.57286
57310
57334
81999
-81982
-81965
81949
81932
69804
69847
69891
-69934
69977
1-43258
1-43169
1-43080
1-42992
1-42903
58661
-58684
-58708
.58731
58755
80987
.80970
80953
80936
80919
. 72432
.72477
72521
.72565
72610
1-38060
1-37976
1-37891
1-37807
1-37722
5
4
3
2
60
57358
81915
.70021
1-42815
-58779
-80902
.72654
L37638
o
*
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
65
64
258 NATURAL SINES, COSINES, TANGENTS, COTAN.
36 37
Sin.
Cos.
Tan.
Cot.
Sin. 1
Cos.
Tan.
Cot.
,
2
3
58779
58802
-58826
58849
.58873
.80902
80885
80867
80850
80833
.72654
72699
.72743
.72788
72832
1.37638
1-37554
1-37470
1-37386
1-37302
60182
60205
60228
60251
60274
-79864
- 79846
-79829
.79811
79793
75355
75401
75447
-75492
-75538
1-32704
1-32624
1-32544
1-32464
1-32384
60
59
58
57
56
5
6
7
8
9
58896
58920
58943
58967
58990
80816
80799
80782
80765
80748
72877
72921
72966
73010
73055
1-37218
1.37134
1.37050
1-36967
1.36883
60298
60321
60344
-60367
-60390
79776
-79758
.79741
.79723
-79706
75584
75629
75675
-75721
-75767
1-32304
1-32224
1-32144
1-32064
1-31984
55
54
53
52
51
10
11
12
13
14
59014
59037
59061
59084
59108
80730
80713
80696
80679
80662
73100
73144
73189
73234
73278
1-36800
1.36716
1.36633
1.36549
1.36466
60414
60437
60460
60483
.60506
-79688
79671
-79653
-79635
-79618
75812
-75858
-75904
75950
-75996
1-31904
1-31825
1-31745
1-31666
1-31586
50
49
48
47
46
15
16
17
18
19
59131
59154
59178
59201
59225
80644
80627
80610
80593
80576
73323
73368
73413
73457
73502
1-36383
1.36300
1.36217
1.36134
1-36051
60529
60553
60576
60599
60622
79600
79583
-79565
-79547
-79530
76042
76088
76134
76180
76226
1-31507
1-31427
1-31348
1-31269
1-31190
45
44
43
42
41
21
22
23
24
59248
59272
59295
59318
59342
80558
80541
80524
80507
80489
73547
73592
73637
73681
73726
1.35968
1-35885
1-35802
1-35719
1-35837
60645
60668
60691
'$0714
60738
79512
.79494
.79477
79459
- 79441
76272
76318
76364
76410
76456
1-31110
1.31031
1.30952
1-30873
1 30795
40
39
38
37
36
25
26
27
28
29
.59385
59389
59412
59436
59459
80472
80455
80438
80420
80403
73771
73816
73861
73906
73951
1-35554
1-35472
1-35389
1.35307
1-35224
60761
6C784
60807
60830
60853
- 79424
79406
.79388
79371
79353
-76502
-76548
-76594
-76640
.76686
1-30716
1-30637
1-30558
1 - 30480
1 30401
35
34
33
32
31
30
31
32
33
34
59482
59506
59529
59552
59576
80386
80368
80351
80334
80318
73996
74041
74086
74131
74176
1.35142
1-35060
1.34978
1.34896
1-34814
60876
60899
60922
60945
-60968
.79335
-79318
-79300
-79282
-79264
.76733
.78779
76825
76871
76918
1-30323
1-30244
1-30166
1-30087
1-30009
30
29
28
27
26
35
36
37
38
39.
59599
59622
59646
59669
59693.
80299
-80282
-80264
80247
80230
74221
74267
74312
74357
74402
1-34732
1.34650
1-34568
1.34487
1.34405
-60991
-61015
-61038
61061
61084
79247
.79229
.79211
-79193
-79176
76964
.77010
-77057
.77103
.77149
1-29931
1.29853
1-29775
1-29696
1-29B18
25
24
23
22
21
40
41
42
43
44
.59716
.59739
.59763
.59786
.59809
.80212
80195
80178
80160
80143
74447
74492
74538
74583
.74628
1.34323
1-34242
1-34160
1-34079
1-33998
61107
61130
61153
61176
61199
-79158
-79140
-79122
-79105
-79087
.77196
77242
-77289
-77335
-77382
1-29541
1-29463
1-29385
1-29307
1-29229
20
19
18
17
Ifi
45
46
47
48
49_
59832
.59856
.59879
59902
.59926
.80125
.80108
.80091
.80073
.80056
74674
.74719
74764
74810
.74855
1-33916
1-33835
1.33754
1.33673
1-33592
-61222
61245
-61268
-61291
-61314
-79069
-79051
-79033
-79016
-78998
-77428
77475
.77521
.77568
.77615
1-29152
1-29074
1-28997
1-28919
1-28842
15
14
13
12
11
50
51
52
53
5i_
59949
59972
.59995
60019
.60042
.80038
.80021
.80003
.79986
.79968
74900
.74946
74991
75037
.75082
1-33511
1.33430
1.33349
1.33268
1-33187
-61337
-61360
.61383
6H06
61429
-78980
-78962
-78944
-78926
-78908
.77661
.77708
77754
-77801
-77848
1-28764
1-28687
1-28610
1-28533
1-28456
10
9
8
7
6
55
56
57
58
59
60065
60089
60112
60135
60158
.79951
.79934
.79916
.79899
.79881
.75128
75173
.75219
75264
.75310
1.33107
1.33026
1.32946
1-32865
1-32785
.61451
61474
61497
61520
-61543
-78891
-78873
-78855
78837
78819
.77895
-77941
77988
78035
.78082
1-28379
1-28302
1-28225
1-28148
1-28071
5
4
3
2
1
60
.60182
.79864
,75355
1-32704
-61566
78801
.78129
1-27994
.
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
63*
NATURAL SINES, COSINES, TANGENTS, COTAN. 259
38 39
1
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
'
o
1
2
3
4
61566
-61589
.61612
-61635
-61658
-78801
78783
-78765
78747
-78729
78129
78175
78222
78269
-78316
1-27994
1-27917
1-27841
1-27764
1-27688
62932
.62955
-62977
- 63000
-63022
77715
77696
77678
77660
77641
80978
81027
81075
81123
-81171
1-23490
1-23416
1-23343
1-23270
1-23196
60
59
58
57
56
5
6
7
8
9
-61681
-61704
-61726
-61749
.61772
78711
-78694
-78676
-78658
- 78640
78363
78410
78457
-78504
-78551
27611
.27535
27458
27382
27306
63045
63068
-63090
.63113
-63135
77623
77605
77586
77568
.77550
81220
81268
81316
81364
81413
1-23123
1-23050
1-22977
1-22904
1-22831
55
54
53
52
51
10
11
12
13
14
-61795
-61818
-61841
-61864
-61887
-78622
78604
78586
78568
-78550
-78598
-78645
-78692
78739
78786
27230
27153
.27077
27001
26925
-63158
-63180
-63203
-63225
.63248
.77531
.77513
.77494
.77476
.77458
.81461
.81510
-81558
-81606
.81655
1-22758
1-22685
1.22612
1-22539
1-22467
50
49
48
47
46
15
16
17
18
19
-61909
-61932
-61955
-61978
.62001
.78532
78514
-78496
- 78478
.78460
-78834
-78881
78928
-78975
.79022
.26849
26774
.26698
.26622
-26546
63271
63293
63316
-63338
.63361
. 77439
77421
. 77402
77384
.77366
.81703
.81752
-81800
-81849
.81898
1-22394
1-22321
1-22249
1.22-176
1-22104
45
44
43
42
41
20
21
22
23
24
62024
62046
.62069
-62092
62115
-78442
-78424
.78405
-78387
78369
79070
79117
-79164
79212
-79259
.26471
1-26395
1-26319
1-26244
1-26169
-63383
-63406
.63428
.63451
.63473
77347
77329
77310
.77292
. 77273
.81946
81995
-82044
-82092
82141
1.22031
1-21959
1-21886
1-21814
1-21742
40
39
38
37
36
25
26
27
28
29
-62138
-62160
.82183
. 62206
62229
78351
.78333
-78315
-78297
78279
79306
79354
79401
79449
79496
1-26093
1.26018
1-25943
1.25867
1-25792
-63496
.63518
-63540
-63563
-63585
77255
77236
77218
77199
77181
82190
82238
82287
-82336
-82385
1.21670
1.21598
1.21526
1-21454
1-21382
35
34
33
32
31
30
31
32
33
34
-62251
62274
62297
62320
-62342
78261
- 78243
-78225
-78206
-78188
79544
79591
79639
79686
79734
1-25717
1-25642
1-25567
1-25492
1.25417
-63608
-63630
-63653
-63675
63698
77162
.77144
.77125
.77107
.77088
82434
82483
-82531
-82580
-82629
1-21310
1.21238
1-21166
1-21094
1-21023
30
29
28
27
26
35
36
37
38
39
-62365
-62388
-62411
.62433
62456
78170
78152
-78134
78116
.78098
-79781
.79829
.79877
79924
-79972
1-25343
1-25268
1-25193
1-25118
1.25044
-63720
-63742
-63765
-63787
-63810
.77070
77051
.77033
77014
-76996
82678
-82727
-82776
82825
82874
1-20951
1-20879
1-20808
1-20736
1-20665
25
24
23
22
21
40
41
42
43
44
62479
.62502
-62524
-62547
.62570
.78079
78061
. 78043
78025
78007
80020
-80067
.80115
.80163
80211
1-24969
1-24895
1.24820
1.24746
1.24672
-63832
.63854
63877
.63899
-63922
-76977
-76959
-76940
-76921
76903
82923
-82972
83022
83071
-83120
1-20593
1-20522
1-20451
1-20379
1-20308
20
19
18
17
16
45
46
47
48
49
62592
62615
-62638
-62860
-62683
-77988
77970
77952
77934
77916
-80258
-80306
-80354
-80402
. 80450
1-24597
1-24523
1 24449
1.24375
1-24301
63944
63966
.63989
-64011
- 64033
76884
-76866
-76847
-76828
76810
-83169
-83218
-83268
-83317
-83366
1-20237
1-20166
1-20095
1 - 20024
1-19953
15
14
13
12
11
50
51
52
53
54
-62706
-62728
-62751
-62774
-62796
77897
-77879
77861
77843
-77824
-80498
-80546
-80594
-80642
-80690
1-24227
1-24153
1 - 24079
1 - 24005
1.23931
-64056
-64078
-64100
-64123
64145
76791
76772
76754
76735
76717
83415
-83465
-83514
-83564
-83613
1-19882
1-19811
1-19740
1-19669
1-19599
10
9
8
7
6
55
56
57
58
59
62819
-62842
.62864
.62887
-62909
-77806
-77788
-77769
77751
-77733
.80738
80786
.80834
.80882
80930
1-23858
1-23784
1-23710
1-23637
1-23563
-64167
.64190
.64212
. 64234
-64256
76698
76679
76661
76642
76623
-83662
-83712
-83761
-83811
-83860
1-19528
1-19457
1-19387
1-19316
1-19246
5
4
3
2
1
60
-62932
-77715
80978
1-23490
64279
-76604
.83910
1-19175
'
Cos.
Sin.
Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
'
61
50
260 NATURAL SINES, COSINES, TANGENTS, COTAN.
40 41
/
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
t
o
1
2
3
4
64279
64301
64323
64346
64368
76604
76586
76567
76548
76530
83910
83960
84009
84059
84108
1-19175
1-19105
1-19035
1-18964
1-18894
65606
65628
65650
65672
65694
75471
75452
75433
75414
75395
86929
86980
87031
87082
87133
1-15037
1-14969
1.14902
1.14834
1-14767
60
59
58
57
56
5
6
8
9
64390
64412
64435
64457
64479
76511
76492
76473
76455
76436
84158
84208
84258
84307
.84357
1-18824
1-18754
1-18684
1-18614
1-18544
65716
65738
65759
65781
65803
75375
75356
75337
75318
75299
87184
87236
87287
-87338
-87389
1-14699
1.14632
1-14565
1-14498
1.14430
55
54
53
52
51
10
11
12
13
14
64501
64524
64546
64568
64590
.76417
76398
.76380
76361
76342
. 84407
84457
-84507
-84556
-84606
1-18474
1-18404
1-18334
1-18264
1-18194
65825
65847
65869
65891
65913
75280
75261
-75241
-75222
75203
87441
87492
-87543
87595
87646
1-14363
1-14296
1-14229
1-14162
1-14095
50
49
48
47
46
15
16
17
18
19
64612
64635
64657
64679
64701
.76323
.76304
.76286
.76267
76248
84656
.84706
84756
.84806
84856
1.18125
1-18055
1.17986
1-17916
1-17846
-65935
- 65956
-65978
- 66000
.66022
75184
75185
75146
-75126
-75107
87698
87749
87801
-87852
.87904
1-14028
1-13961
1-13894
1-13828
1-13761
45
44
43
42
41
20
21
22
23
24
64723
64746
64768
64790
64812
76229
76210
76192
76173
76154
.84906
i/4956
85006
85057
.85107
1.17777
1-17708
1-17638
1-17569
1-17500
- 66044
-66066
-66088
-66109
-66131
-75088
-75069
-75050
-75030
75011
87955
.88007
.88059
88110
88162
1-13694
1-13627
1-13561
1-13494
1-13428
40
39
38
37
36
25
26
27
28
29
.64834
64856
.64878
64901
.64923
76135
76116
76097
76078
76059
85157
85207
85257
-85308
-85358
1-17430
1-17361
1.17292
1-17223
1.17154
-66053
66175
66197
66218
. 66240
74992
74973
74953
74934
74915
88204
88265
88317
88369
.88421
1-13361
1-13295
1-13228
1-13162
1.13096
35
34
33
32
31
30
31
32
33
34
.64945
64967
64989
65011
-65033
76041
.76022
76003
75984
75965
85408
85458
85509
.85559
85609
1-17085
1-17016
1-16947
1-16878
1-16809
-66262
66284
66306
-66327
66349
74896
74876
74857
74838
74818
.88473
.88524
.88576
.88628
-88680
1-13029
1-12963
1-12897
1-12831
1-12765
30
29
28
27
26
35
36
37
38
39
65055
65077
.65100
.65122
-65144
75946
75927
.75908
-75889
-75870
.85660
85710
85761
-85811
-85862
1-16741
1-16672
1-16603
1-16535
1-16466
-66371
-66393
-66414
66436
-66458
74799
. 74780
. 74760
. 74741
-74722
-88732
-88784
-88836
-88888
-88940
1-12699
1-12633
1-12567
1.12501
1-12435
25
24
23
22
21
40
41
42
43
44
-65166
.65188
65210
65232
-65254
-75851
-75832
-75813
-75794
-75775
-85912
-85963
86014
86064
.86115
1-16398
1.16329
1-16261
1-16192
1-16124
66480
66501
66523
66545
-66566
. 74703
. 74683
74664
- 74644
-74625
88992
89045
89097
89149
89201
1-12369
1.12303
1.12238
1.12172
1-12106
2
18
18
17
16
45
46
47
48
49
65276
-65298
-65320
-65342
-65364
.75756
75738
.75719
75700
.75680
86166
86216
.86267
86318
-86368
1-16056
1-15987
1-15919
1.15851
1-15783
-66588
-66610
-66632
-66653
-66675
- 74606
-74586
-74567
74548
74528
89253
-89306
-89358
.89410
89463
1.12041
1-11975
1.11909
1.11844
1-11778
15
14
13
12
11
50
51
52
53
54
-65386
-65408
.65430
.65452
65474
.75661
.75642
75623
-75604
75585
-86419
86470
86521
86572
-.86623
1-15715
1-15647
1-15579
1-15511
1-15443
-66697
-66718
-66740
-66762
-66783
74509
- 74489
74470
74451
-74431
89515
89567
-89620
-89672
-89725
1-11713
1-11648
1-11582
1-11517
1-11452
10
g
8
7
6
55
56
57
58
59
65496
.65518
.65540
65562
.65584
75566
75547
.75528
75509
75490
.86674
.86725
.86776
86827
86878
1-15375
1-15308
1.15240
1-15172
1-15104
-66805
-66827
-66848
.66870
66891
74412
74392
74373
74353
74334
89777
.89830
-89883
-89935
-89988
1.11387
1-11321
1-11256
1-11191
1-11126
5
4
3
2
1
6O
.65606
75471
-86929
1-15037
-66913
74314
- 90040
1-11061
1
Cos.
Sin.
j Cot.
Tan.
Cos.
Sin.
Cot.
Tan.
49
48
NATURAL SINES, COSINES, TANGENTS, COTAN. 261
42 43
*
Sin.
Cos.
Tan.
Cot.
Sin.
Cos.
Tan.
Cot.
/
2
3
4
.66913
66935
.66956
.66978
.66999
74314
74295
74276
74256
. 74237
.90040
90093
.90146
.90199
.90251
1.11061
1 10996
1.10931
1-10867
1-10802
68200
-68221
-68242
-68264
-68285
73135
-73116
-73096
-73076
-73056
93252
93306
93360
93415
93469
1-07237
1.07174
1-07112
1 07049
1-06987
6O
59
58
57
56
5
6
7
8
9
.67021
67043.
.67064
.67086
.67107
.74217
74198
74178
74159
74139
! 90304
.90357
.90410
90463
.90516
1.10737
1.10672
1.10607
1-10543
1 . 10478
68306
-68327
.68349
.68370
.68391
73036
73016
72996
72976
-72957
93524
93578
93633
-93688
93742
1.06925
1.06862
1-06800
1-06738
1 06676
55
54
53
52
51
10
11
12
13
14
.67129
.67151
.67172
.67194
67215
.74120
.74100
. 74080
.74061
. 74041
.90569
90621
.90674
90727
90781
1-10414
1.10349
1-10285
1-10220
1.10156
.68412
-68434
68455
68476
68497
-72937
-72917
-72897
-72877
-72857
-93797
-93852
93906
-93961
.94016
1-06813
1-06551
1.06489
1-06427
1 06365
5O
49
48
47
46
15
16
17
18
19
67237
.67258
67280
67301
67323
. 74022
74002
73983
.73963
73944
90834
90887
90940
90993
.91046
1.10091
1.10027
1-09963
1.09899
1.09834
68518
.68539
68561
-68582
. 68603
.72837
.72817
-72797
-72777
72757
94071
-94125
-94180
94235
.94290
1-06303
1-06241
1.06179
1-06117
1.06056
45
44
43
42
41
20
21
22
23
24
67344
67366
67387
67409
67430
.73924
. 73904
73885
73865
73846
.91099
91153
91206
91259
91313
1-09770
1-09706
1.09642
1-09578
1.09514.
68624
68645
68666
68688
68709
72737
72717
-72697
-72677
.72657
.94345
- 94400
-94455
.94510
.94565
1-05994
1-05932
1.05870
1-05809
1-05747
40
39
38
37
36
25
26
27
28
29
67452
67473
.67495
67516
.67538
.73826
.73806
.73787
.73767
73747
91366
91419
91473
91526
91580
1-09450
1.09386
1-09322
1-09258
1.09195
68730
68751
68772
68793
68814
72637
72617
72597
72577
.72557
.94620
.94676
-94731
-94786
- 94841
1-05685
1-05624
1-05562
1-05501
1-05439
35
34
33
32
31
30
31
32
33
34
.67559
67580
67602
67623
67645
.73728
-73708
.73688
.73669
.74549
91633
91687
91740
91794
91847
1-09131
1-09067
1-09003
1-08940
1-08876
68835
68857
68878
68899
68920
72537
72517
-72497
72477
.72457
-94896
-94952
-95007
-95062
-95118
1-05378
1-05317
1.05255
1-05194
1-05133
30
29
28
2?
26
35
36
37
38
39
67666
67688
67709
67730
67752
.73629
.73810
73590
73570
.73551
91901
91955
92008
92062
92116
1-08813
1-08749
1-08686
1-08622
1 -08559
68941
68962
68983
69004
69025
.72437
.72417
.72397
72377
-72357
-95173
95229
95284
-95340
-95395
1-05072
1.05010
1 - 04949
1-04888
1-04827
25
24
23
22
21
40
41
42
43
44
-67773
67795
67816
67837
-67859
.73531
.73511
.73491
.73472
.73452
92170
92224
92277
92331
92385
1-08498
1-08432
1-08369
1-08306
1 - 08243
69046
69067
-69088
-69109
.69130
72337
72317
72297
-72277
.72257
-95451
95506
.95562
.95618
-95673
1-04766
1-04705
1 04644
1-04583
1.04522
20
19
18
17
16
45
16
47
48
49
-67880
-67901
-67923
- 67944
-67965
-73432
73413
73393
73373
73353
92439
92493
92547
92601
92655
1.08179
1-08116
1-08053
1-07990
1-07927
69151
69172
69193
69214
69235
-72236
-72216
72196
72176
72156
95729
.95785
.95841
.95897
.95952
1-04461
1-04401
1 - 04340
1-04279
1.04218
15
14
13
12
11
50
51
52
53
54_
67987
-68008
-68029
68051
-68072
73333
73314
73294
-73274
73254
92709
92763
92817
.92872
.92926
1-07864
1-07801
1-07738
1-07678
1.07613
-69258
-69277
69298
.69319
-69340
72138
72116
72095
.72075
.72055
.96008
-96064
-96120
96176
-96232
1-04158
1-04097
1.04036
1-03978
1-03915
10
9
8
_J
55
56
57
58
59
68093
68115
68136
68157
.68179
.73234
73215
73195
.73175
.73155
.92980
93034
.93088
93143
93197
1-07550
1.07487
1-07425
1-07362
1-07299
-69361
69382
-69403
69424
-69445
.72035
.72015
.71995
71974
71954
-96288
96344
96400
96457
.96513
1.03855
1-03794
1-03734
1-03874
1-03613
5
1
60
. 68200
.73135
.93252
1-07237
69466
71934
.96569
1 03553
Q
1
Cos.
Sin.
Cot,
Tan.
Cos.
Sin.
Cot.
Tan.
47
46
262 NATURAL SINES, COSINES, TANGENTS, COTAN.
44 44
'
Sin.
Cos.
Tan.
Cot,
, i
/
Sin.
Cos.
Tan.
Cot.
/
1
2
J_
5
6
7
8
9
10
11
12
13
y_
15
16
17
18
12_
20
21
22
23
24_
25
26
27
28
29_
3<L
.69466
.69487
.69508
-69529
.69549
. 69570
.69591
69612
69633
.69654
.69675
.69696
69717
69737
.69758
69779
69800
.69821
.69842
.69862
-71934
.71914
71894
71873
-71853
96569
96625
96681
.96738
.96794
1-03553
1.03493
1.03433
1.03372
1.03312
60
59
58
57
56
3O
31
32
33
34
.70091
70112
70132
.70153
.70174
70195
.70215
.70236
70257
-70277
-70298
-70319
-70339
-70360
-70381
-71325
-71305
-71284
71264
-71243
71223
.71203
-71182
-71162
.71141
71121
-71100
- 71080
-71059
-71039
.98270
-98327
.98384
98441
.98499
1-01761
1-01702
1-01642
1-01583
1-01524
3O
29
28
27
26
71833
71813
.71792
71772
.71752
96850
96907
.96963
97020
97076
1-03252
1.03192
1-03132
1.03072
1-03012
55
54
53
52
51
35
36
37
38
39
40
41
42
43
44
98556
98613
-98671
98728
.98786
98843
98901
98958
-99016
-99073
1-01465
1-01406
1-01347
1-01288
1. 01229
1-01170
1-01112
1-01053
1-00994
1-00935
25
24
23
22
21
20
19
18
17
JL
15
14
13
12
11
71732
71711
.71691
71671
.71650
97133
97189
97246
97302
.97359
1 02952
1.02892
1-02832
-02772
02713
50
49
48
47
46
71630
71610
71590
71569
71549
97416
97472
.97529
97586
97643
02653
.02593
.02533
02474
02414
45
44
43
42
41
45
46
47
48
49
- 70401
- 70422
70443
- 70463
- 70484
-71019
-70998
.70978
-70957
70937
-99131
-99189
99247
.99304
.99362
1-00876
1-00818
1-00759
1-00701
1-00642
.69883
-69904
.69925
. 69946
.69966
.69987
70008
70029
. 70049
. 70070
71529
.71508
71488
71468
71447
97700
97756
97813
97870
97927
1-02355
1.02295
1.02236
1-02176
1-02117
1.02057
1.01998
1-01939
1.01879
1-01820
40
39
38
37
36
50
51
52
53
54
-70505
.70525
-70546
-70567
- 70587
70916
70896
70875
70855
. 70834
-99420
-99478
99536
-99594
-99652
1-00583
1-00525
1-00467
1.00408
1-00350
10
9
8
6
~~|
3
2
1
.71427
71407
.71386
71366
71345
. 71325
.97984
98041
.98098
.98155
98213
35
34
33
32
31
55
56
57
58
59
- 70608
70628
70649
-70670
70890
-70813
- 70793
- 70772
- 70752
-70731
-99710
-99768
-99826
-99884
-99942
1-00291
1-00233
1-00175
1-00116
1-00058
70091
.98270
1-01761
30
6O
-70711
.70711
1 . OOOOO
1-00000
Cos.
Sin.
Cot.
Tan.
*
'
Cos.
Sin.
Cot.
Tan.
45
46
NATURAL SECANTS AND COSECANTS
263
/
SECANTS.
8
1
2
3
4:
6
6
1.00000
1.00015
1.00061
1.00137
1.00244
1.00382
-1.00551
60
1
00000
00016
00062
00139
00246
00385
00554
59
2
00000
00016
00063
00140
00248
00387
00557
58
3
00000
00017
00064
00142
00250
00390
00560
57
4
00000
00017
00065
00143
00252
00392
00563
56
5
00000
00018
00066
00145
00254
00395
00566
55
6
00000
00018
00067
00147
00257
00397
00569
54
7
00000
00019
00068
00148
00259
00400
00573
53
8
00000
00020
00069
00150
00261
00403
00576
52
9
00000
00020
00070
00151
00263
00405
00579
51
10
00000
00021
00072
00153
00265
00408
00582
50
11
1.00001
1.00021
1.00073
1.00155
1.00267
1.00411
1.00585
49
12
00001
00022
00074
00156
00269
00413
0058S
48
13
00001
00023
00075
00158
00271
00416
00592
47
14
00001
00023
00076
00159
00274
00419
00595
46
15
00001
00024
00077
00161
00276
00421
00598
45
16
00001
00024
00078
00163
00278
00424
00601
44
17
00001
00025
00079
00164
00280
00427
00604
43
18
00001
00026
00081
00166
00282
00429
00608
42
19
00002
00026
00082
00168
00284
00432
00611
41
20
00002
00027
00083
00169
00287
00435
00614
40
21
1.00002
1.00028
1.00084
1.00171
1.00289
1.00438
1.00617
39
22
00002
00028
00085
00173
00291
00440
00621
38
23
00002
00029
00087
00175
00293
00443
00624
37
24
00002
00030
00088
00176
00296
00446
00627
36
25
00003
00031
00089
00178
00298
00449
00630
35
26
00003
00031
00090
00180
00300
00451
00634
34
27
00003
00032
00091
00182
00302
00454
00637
33
28
00003
00033
00093
00183
00305
00457
00640
3-2
29
00004
00034
00094
00185
00307
00460
00644
31
30
00004
00034
00095
00187
00309
00463
00647
30
31
1.00004
1.00035
1.00097
1.00189
1.00312
1.00465
1.00650
29
32
00004
00036
00098
00190
00314
00468
00654
28
33
00005
00037
00099
00192
00316
00471
00657
27
34
00005
00037
00100
00194
00318
00474
00660
26
35
00005
00038
00102
00196
00321
00477
00064
25
36
00005
00039
00103
00198
00323
00480
00667
24
37
00006
00040
00104
00200
00326
00482
00671
23
38
00006
00041
00106
00201
00328
00485
00674
22
00006
00041
00107
00203
00330
00488
00677
21
40
00007
00042
00108
00205
00333
00491
00681
20
41
1.00007
1.00043
1.00110
1.00207
1.00335
1.00494
1.00684
19
42
00007
00044
00111
00209
00337
00497
00688
18
43
00008
00045
00113
00211
00340
00500
00691
17-
44
00008
00046
00114
00213
00342
00503
00695
16
45
00009
00047
00115
00215
00345
00506
00698
15
46
00009
00048
00117
00216
00347
00509
00701
14
47
00009
00048
00118
00218
00350
00512
00705
13
48
00010
00049
00120
00220
00352
00515
00708
12
49
00010
00050
00121
00222
00854
00518
00712
11
50
00011
00051
00122
00224
00357
00521
00715
10
51
1.00011
1.00052
1.00124
1.00226
1.00359
1.00524
1.00719
9
52
00011
00053
00125
00228
00362
00527
00722
8
53
00012
00054
00127
00230
00364
00530
00726
7
54
00012
00055
00128
00232
00367
00533
00730
6
55
00013
00056
00130
00234
00369
00536
00733
5
56
00013
00057
00131
00236
00372
00539
00737
4
57
00014
00058
00133
00238
00374
00542
00740
3
58
00014
00059
00134
00240
00377
00545
00744
2
59
00015
00060
00136
00242
00379
.00548
00747
1
60
00015
00061
00137
00244
00382
00551
00751
/
89
88
87
86
86
84
83
/
COSECANTS.
264
NATURAL SECANTS AND COSECANTS
t
SECANTS.
/
i
80
9
10
11
12
13
1.00751
1.00983
1.01247
1.01543
1.01872
1.02234
1.02630
60
i
00755
00987
01251
01548
01877
02240
02637
59
2
00758
00991
01256
01553
01883
02247
02644
58
3
00762
00995
01261
01558
01889
02253
02651
57
4
00765
00999
01265
01564
01895
02259
02658
56
5
00769
01004
01270
01569
01901
02266
02665
55
6
00773
01008
01275
01574
01906
02272
02672
54
7
00776
01012
01279
01579
01912
02279
02679
53
8
00780
01016
01284
01585
01918
02285
02686
52
9
00784
01020
01289
01590
01924
02291
02693
51
10
00787
01024
01294
01595
01930
02298
02700
50
11
1.00791
1.01029
1.01298
1.01601
1.01936
1.02304
1.02707
49
12
00795
01033
01303
01606
01941
02311
02714
48
13
00799
01037
01308
01611
01947
02317
02721
47
14
00802
01041
01313
01616
01953
02323
02728
46
15
00806
01046
01318
01622
01959
02330
02735
45
16
00810
01050
01322
01627
01965
02336
02742
44
17
00813
01054
01327
01633
01971
02343
02749
43
18
00817
01059
01332
01638
01977
02349
02756
42
19
00821
01063
01337
01643
01983
02356
02763
41
JO
00825
01067
01342
01649
01989
02362
02770
40
21
1.00828
1.01071
1.01346
1.01654
1.01995
1.023G9
1.02777
39
2-1
00832
01076
01351
01659
02001
02375
02784
38
23
00836
01080
01356
01665
02007
02382
02791
37
24
00840
01084
01361
01670
02013
02388
02799
30
25
00844
01089
01366
01676
02019
02395
02806
35
26
00818
01093
01371
01681
02025
02402
02813
34
27
00851
01097
01376
01687
02031
02408
02820
33
28
00855
01102
01381
01692
02037
02415
02827
32
fe9
00859
01106
01386
01698
0-2043
02421
02834
31
80
00863
01111
01391
01703
02049
02428
02812
30
31
1.00867
1.01115
1.01395
1.01709
1.02055
1.02435
1.02849
29
32
00871
01119
01400
01714
02061
02441
02856
28
33
00875
01124
01405
01720
02067
02448
028C3
27
34
00878
01128
01410
01725
02073
02454
02870
26
35
00882
01133
01415
01731
02079
02461
02878
25
36
00886
01137
01420
01736
C2085
02468
02885
24
37
00890
01142
01425
01742
020S1
02474
02892
23
38
00894
01146
01430
01747
02097
02481
02899
22
39
00898
01151
01435
01753
02103
02488
02907
21
40
00902
01155
01440
01758
02110
02494
02914
20
41
1.00906
1.01160
1.01445
1.01764
1.02116
1.02501
1.02921
19
42
00910
01164
01450
01769
02122
02508
029-28
18
43
00914
01169
01455
01775
02128
02515
02936
17
44
00918
01173
01461
01781
02134
02521
02943
16
45
00922
01178
01466
01786
02140
02528
02950
15
46
00926
01182
01471
01792
02146
02535
02958
14
47
00930
01187
01476
01798
02153
02542
02965
13
48
00934
01191
01481
01803
02159
02548
02972
12
49
00938
01196
01486
01809
02165
02555
02980
11
50
00942
01200
01491
01815
02171
02562
02987
10
51
1.00946
1.01205
1.01496
1.01820
1.02178
1.02569
1 .02994
9
52
00950
01209
01501
01826
02184
02576
03002
8
53
00954
0121'
01506
01832
02190
02582
03009
7
54
00958
01219
01512
01837
02196
02589
03017
6
55
00962
01223
01517
01843
02203
02596
03024
5
56
00966
01228
01522
01849
02209
02603
03032
4
57
00970
01233
015.27
01854
02215
02610
03039
3
58
00975
01237
01532
01860
02221
02617
03046
2
59
00979
01242
01537
01866
02228
02624
03054
60
00983
01247
01543
01872
02234
02630
03061
f
82
81
80
79
78
7 jo
76
i
COSECANTS.
NATURAL SECANTS AND COSECANTS 265
1
SECANTS.
/
14
15
16
17
18
19
20
1.03061
1.03528
1.04030
1.045G9
1.05146
1.05762
1.06418
60
1
03069
03536
04039
04578
05156
05773
06429
59
2
03076
03544
04047
04588
051G6
05783
06440
58
3
03084
03552
04056
04597
05176
05794
06452
57
4
03091
03560
04065
04606
05186
05805
06463
56
5
03099
03568
04073
04616
05196
05815
06474
55
6
03106
03576
04082
04625
05206
05826
06486
54
7
03114
03584
04091
04635
05216
05836
06497
E3
8
03121
03592
04100
04644
05226
05847
06508
52
9
03129
03601
0)108
04653
05236
05858
06520
51
10
03137
03609
04117
04663
05246
05869
06531
50
11
1.03144
1.03617
1.04126
1.04672
1.05256
1 .05879
1.06542
49
12
03152
03625
04135
04682
0526(5
05890
06554
48
13
03159
03633
04144
04691
05276
05901
06565
47
14
03167
03642
04152
04700
05286
05911
06577
46
15
03175
03650
04161
04710
05297
05922
06588
45
16
03182
03658
04170
04719
05307
05933
06600
44
17
03190
03666
04179
04729
05317
05944
06611
4*
18
03198
03674
04188
04738
05327
05955
06622
42
19
03205
03683
04197
04748
05337
05965
06634
41
20
03213
03691
04206
04757
05347
05976
06645
40
21
1.03221
1.03699
1.04214
1.04767
1.05357
1.05987
1.06657
39
22
03228
03708
04223
04776
05367
05998
06668
38
23
03236
03716
04232
04786
05378
06009
06680
37
24
03244
03724
04241
04795
05388
06020
06691
36
25
03251
03732
04250
04805
05398
06030
06703
35
26
03259
03741
04259
04815
05408
06041
06715
34
27
08267
03749
04268
04824
05418
06052
06726
33
28
03275
03758
04277
04834
05429
06063
06738
32
29
03282
03766
04286
04843
05439
06074
06749
31
30
03290
03774
04295
04853
05449
06085
06761
30
31
1.03298
1.03783
1.04304
1.04863
1.05460
1.06096
1.06773
29
32
03306
03791
04313
04872
05470
06107
06784
28
w
03313
03799
04322
04882
05480
06118
06796
27
34
03321
03808
04331
04891
05490
06129
06807
26
35
03329
03816
04340
04901
05501
06140
06819
25
36
03337
03825
04349
04911
05511
06151
06831
24
37
03345
03833
04358
04920
05521
06162
06843
23
33
03353
03842
04367
04930
05532
06173
06854
22
39
03360
03850
04376
04940
05542
06184
06866
21
40
03368
03858
04385
04950
05552
06195
06878
20
41
1.03376
1.03867
1.04394
1.04959
1.05563
1.06206
1.06889
19
42
03384
03875
04403
04969
05573
06217
06901
18
43
03392
03884
04413
04979
05584
06228
06913
17
44
03400
03892
04422
04989
05594
06239
06925
16
45
03408
03901
04431
04998
05604
06250
06936
15
46
03416
03909
04440
05008
05615
06261
06948
14
47
03424
03918
04449
05018
05625
06272
06960
13
48
03432
03927
04458
05028
05636
06283
06972
12
.49
03439
03935
04468
05038
05646
06295
06984
11
50
03447
03944
04477
05047
05657
06306
06995
10
51
1.03455
1.03952
1 .04486
1 .05057
1.05667
1.06317
1.07007
9
52
03463
03961
04495
05067
05678
06328
07019
8
53
03471
03969
04504
05077
05688
06339
07031
7
54
03479
03978
01514
05087
05699
06350
07043
6
55
03487
03987
04523
05097
05709
06362
07055
5
56
03495
03995
04532
05107
05720
06373
07067
4
57
03503
04004
04541
05116
05730
06384
07079
3
58
03512
04013
04551
05126
05741
06395
07091
2
59
03520
04021
04560
05136
05751
06407
07103
1
60
03528
04030
04569
05146
05762
06418
07115
/
75
74
73
72
71
70
69
/
COSECANTS.
266 NATURAL SECANTS AND COSECANTS
/
SECANTS.
/
21
22
23
24
2o
26
27
1.07115
1.07853
1.08636
1.09464 1
10338
1.11260
1.12233
60
1
07126
07866
08649
09478
10353
11276
12249
59
2
07138
07879
08663
09492
10368
11292
12266
58
3
07150
07892
08676
09506
10383
11308
12283
57
4
07162
07904
08690
09520
10398
113-23
12299
56
5
07174
07917
08703
09535
10413
11339
12316
55
6
07186
07930
08717
09549
10428
11355
12333
54
7
07199
07943
08730
09563
10443
11371
12349
53
8
07211
07955
08744
09577
10458
11387
12366
52
9
07223
07968
08757
09592
10473
11403
12383
51
10
07235
07981
08771
09606
10488
11419
12400
50
y
1.07247
1 .07994
1.08784
1.09620 1
10503
1.11435
1.12416
49
12
07259
08006
08798
09635
10518
11451
12433
48
13
07271
08019
08811
09649
10533
11467
12450
47
14
07283
08032
08825
09663
10549
11483
12467
46
15
07295
08045
08839
09678
10564
11499
12484
45
16
07307
08058
08852
09692
10579
11515
12501
44
17
07320
08071
08866
09707
10594
11531
12518
43
18
07332
08084
08880
09721
10609
11547
12534
42
19
07344
08097
08893
09735
10625
11563
12551
41
20
07356
08109
08907
09750
10640
11579
12568
40
21
1.07368
1.08122
1.08921
1.09764 1
10655
1.13595
1.12585
39
22
07380
08135
08934
09779
10670
11611
12602
38
23
07393
08148
08948
09793
10686
11627
12619
37
24
07405
08161
08962
09808
10701
11643
12636
36
25
07417
08174
08975
09822
10716
11659
12653
35
26
07429
08187
08989
09837
10731
11675
1267'0
34
27
07442
08200
09003
09851
10747
11691
12687
33
28
07454
08213
09017
09866
10762
11708
12704
32
29
07466
08226
09030
09880
10777
11724
12721
31
30
07479
08239
09044
09895
10793
11740
12738
30
31
1.07491
1.08252
1.09058
1.09909 1.
10808
1.11756
1.12755
29
32
07503
08265
09072
09924
10824
11772
12772
28
33
07516
08278
09086
09939
10839
11789
12789
27
34
07528
08291
09099
09953
10854
11805
12807
26
35
07540
08305
09113
09968
10870
11821
188C4
25
36
07553
08318
09127
09982
10885
11838
12841
24
37
07565
08331
09141
09997
10901
11854
12858
23
38
07578
08344
09155
10012
10916
11870
12875
22
39
07590
08357
09169
10026
10932
11886
12892
21
40
07602
08370
09183
10041
10947
11903
12910
20
41
1.07615
1.08383
1.09197
1.10055 1.
10963
1.11919
1.12927
19
42
07627
08397
09211
10071
10978
11936
12944
18
43
07640
08410
09224
10085
10994
11952
12961
17
44
07652
08423
09238
10100
11009
11968
12979
16
45
07665
08436
09252
10115
11025
11985
12996
15
46
07677
08449
09266
10130
11041
12001
13013
14
47
07690
08463
09280
10144
11056
12018
13031
13
48
07702
08476
09294
10159
11072
12034
13048
12
49
07715
08489
09308
10174
11087
12051
13065
11
50
07727
08503
09323
10189
11103
12067
13083
10
51
1.07740
1.08516
1.09337
1.10204 1.
11119
1.12084
1.13100
9
52
07752
08529
09351
10218
11134
12100
13117
8
53
07765
08542
09365
10233
11150
12117
13135
7
54
07778
08556
09379
10248
11166
12133
13152
6
55
07790
08569
09393
10263
11181
12150
13170
5
56
07803
08582
09407
10278
11197
12166
13187
4
57
07816
08596
09421
10293
11213
12183
13205
3
58
07828
08609
09435
10308
11229
12199
13222
2
59
07841
08623
09449
10323
11244
12216
13240
1
60
07853
08636
09464
10338
11260
12233
13257
/
68
67
66
65
64
63
62
/
COSECANTS.
NATURAL SECANTS AND COSECANTS
267
SECANTS. ,
28
29
30
31
32
33
34
1 . 13257
1.14335
1.15470
1.16663
1.17918
1.19236
1.20622 60
1
13275
14354
15489
16684
17939
19259
2064:
59
2
13292
14372
15509
16704
17961
19281
20669
58
3
13310
14391
15528
16725
17982
19304
20693
57
4
13327
14409
15548
16745
18004
19327
20717
56
5
13345
14428
15567
16766
18025
19349
20740
55
6
13362
14446
15587
16786
18047
1937*
20764
54
7
13380
14465
15606
16806
18068
19394
20788
53
8
13398
14483
15626
16827
18090
19417
20812
52
9
13415
14502
15645
16848
18111
19440
20836
51
10
13433
14521
15665
16868
18133
19463
20859
50
11
1.13451
1.14539
1.15684
1.16889
1.18155
1.19485
1.20883
49
12
13468
14558
15704
16909
18176
19508
20907
48
13
13486
14576
15724
16930
18198
19531
20931
47
14
13504
14595
15743
16950
18220
19554
20955
46
15
13521
14614
15763
16971
18241
19576
20979
45
16
13539
14632
15782
16992
18263
19599
21003
44
17
13557
14651
15802
17012
18285
19622
21027
43
18
13575
14670
15822
17033
18307
19645
21051
42
19
13593
14689
15841
17054
18328
19668
21075
41
20
13610
14707
15861
17075
18350
19691
21099
40
21
1.13628
1.14726
1.15881
1.17095
1.18372
1.19713
1.21123
39
22
13646
14745
15901
17116
18394
19736
21147
38
23
13664
14764
15920
17137
18416
19759
21171
37
24
13682
14782
15940
17158
18437
19782
21195
36
25
13700
14801
15960
17178
18459
19805
21220
35
26
13718
14820
15980
17199
18481
19828
21244
34
27
13735
14839
16000
17220
18503
19851
21268
33
28
13753
14858
16019
17241
18525
19874
21292
32
29
13771
14877
16039
17262
18547
19897
21316
81
30
13789
14896
16059
17283
18569
19920
21341
30
31
1.13807
1.14914
1.16079
1.17304
1.18591
\.19944
1.21365
29
32
13825
14933
16099
17325
18613
19967
21389
28
33
13843
14952
16119
17346
18635
19990
21414
27
34
13861
14971
16139
17367
18657
20013
21438
26
35
13879
14990
16159
17388
18679
20036
21462
25
36
13897
15009
16179
17409
18701
20059
21487
24
37
18916
15028
16199
17430
18723
20083
21511
23
38
13934
15047
16219
17451
18745
20106
21535
22
39
13952
15066
16239
17472
18767
20129
21560
21
40
13970
15085
16259
17493
18790
20152
21584
20
41
1.13988
1.15105
1.16279
1.17514
1.18812
1.20176
1.21609
19
42
14006
15124
16299
17535
18834
20199
21633
18
43
14024
15143
16319
17556
18856
20222
21658
17
44
14042
15162
16339
17577
18878
20246
21682
16
45
14061
15181
16359
17598
18901
20269
21707
15
46
14079
15200
16380
17620
18923
20292
21731
14
47
14097
15219
16400
17641
18945
20316
21756
13
48
14115
15239
16420
17662
18967
20339
21781
12
49
14134
15258
16440
17683
18990
20363
21805
11
50
14152
15277
16460
17704
19012
20386
21830
10
51
1.14170
1.15296
1.16481
1.17726
1.19034
1.20410
1.21855
9
52
14188
15315
16501
17747
19057
20433
21879
8
53
14207
15335
16521
17768
19079
20457
21904
7
54
14225
15354
16541
17790
19102
20480
21929
6
55
14243
15373
16562
17811
19124
20504
21953
5
56
14262
15393
16582
17832
19146
20527
21978
4
57
14280
15412
16602
17854
19169
20551
22003
8
58
14299
15431
16623
17875
19191
20575
22028
2
59
14317
15451
16643
17896
19214
20598
22053
1
60
14335
15470
16663
17918
19236
20622
22077
61
60
59
68
67
56
65
COSECANTS.
NATURAL SECANTS AND COSECANTS
/
SECANTS.
35
36
37
38
39
40
41
1.22077
1.23607
1.25214
1.26902
1.28G76
1.30541
1.32501
60
1
22102
23633
25241
26931
28706
30573
325:35
59
2
22127
23659
25269
26960
28737
30605
32568
58
3
22152
23685
25296
26988
28767
30636
32602
57
4
22177
23711
25324
27017
28797
30668
32636
56
5
22202
23738
25351
27046
28828
30700
32669
55
6
22227
23764
25379
27075
28858
30732
32703
54
7
22252
23790
25406
27104
28889
30764
32737
53
8
22277
23816
25434
27133
28919
30796
32770
52
9
22302
23843
25462
27162
28950
30829
32804
51
10
22327
23869
25489
27191
28980
30861
32838
50
11
1.22352
1.23895
1.25517
1.27221
1.29011
1.30893
1.32872
49
12
22377
23922
25545
27250
29042
30925
32905
48
13
22402
23948
25572
27279
29072
30957
82939
47
14
22428
23975
25600
27808
29103
30989
32973
46
15
22453
24001
25628
27337
29133
31022
33007
45
16
22478
24028
25656
27366
29164
31054
33041
44
17
22503
24054
25683
27396
29195
31086
33075
43
18
22528
24081
25711
27425
29226
31119
33109
42
19
22554
24107
25739
27454
29256
31151
33143
41
20
22579
24134
25767
27483
29287
31183
33177
40
21
1.22604
1.24160
1.25795
1.27513
1.29318
1.31216
1.33211
39
22
22629
24187
25823
27542
29349
31248
33245
38
23
22G55
24213
25851
27572
29380
31281
33279
37
24
22680
24240
25879
27601
29411
31313
33314
36
25
22706
24267
25907
27630
29442
31346
33348
35
26
22731
24293
25935
27660
29473
31378
33382
34
27
22756
24320
25963
27689
29504
31411
33416
83
28
22782
24347
25991
27719
29535
31443
33451
3?
29
22807
24373
26019
27748
29566
31476
33485
31
30
22833
24400
26047
27778
29597
31509
3351 &
30
31
1.22858
1.24427
1.26075
1.27807
1.29628
1.31541
1.33554
29
32
22884
24454
26104
27837
29659
31574
33588
28
33
22909
24481
26132
27867
29690
31607
33622
27
34
22935
24508
26160
27896
29721
31640
33657
26
35
22960
24534
26188
27926
29752
31672
33691
25
36
22986
24561
26216
27956
29784
31705
33726
24
37
23012
24588
26245
27985
29815
31738
33760
23
38
23037
24615
26273
28015
29S46
31771
33795
22
39
23063
24642
26301
28045
29877
31804
33830
21
40
23089
24669
26330
28075
29909
31837
33864
20
41
1.23114
1.24696
1.26358
1.28105
1.29940
1.31870
1.33899
19
42
23140
24723
26387
28134
29971
31903
33934
18
43
23166
24750
26415
28164
30003
31936
33968
17 !
44
23192
24777
26443
28194
30034
31969
34003
16
45
23217
24804
26472
28224
30066
32002
34038
15
46
23243
24832
26500
28254
30097
32035
3407S
14
47
23269
21859
26529
28284
30129
32068
34108
13
48
23295
24886
26557
28314
30160
32101
34142
12
49
23321
24913
26586
28344
30192
32134
34177
11
50
23347
24940
26615
28374
30223
32168
34212
10
51
1.23373
1.24967
1.26643
1.28404
1.30255
1.32201
1.34247
9
52
23399
24995
26672
28434
302.S7
32234
34282
8
53
23424
25022
26701
28464
30318
32267
34317
7 i
54
23450
25049
26729
28495
30350
32301
34352
6
55
23476
23077
26758
28525
30382
32334
34387
5
56
28502
25104
26787
28555
30413
32368
34423
4
57
23529
25181
26815
28585
30445
32401
34458
3
58
23555
25159
26844
28615
30477
32434
34498
2
59
23581
25186
26873
28646
30509
32468
3452S
1
60
23607
25214
26902
28676
30541
32501
34563
,'
" t
64
68
62
61
50
49
48
/ j
COSECANTS.
J
NATURAL SECANTS AND COSECANTS
269
f
SECANTS.
/
42
43
44
45
46
47
48
1.34563
1.36733
1.39016
1.41421
1.43956
1.46628
1.49448
60
1
34599
36770
39055
41463
43999
46674
49496
59
2
34634
36807
39095
41504
44042
46719
49544
58
3
34669
36844
39134
41545
44086
46765
49593
57
4
34704
36881
39173
41586
44129
46811
49641
56
5
34740
36919
39212
41627
44173
46857
49690
55
6
34775
36956
39251
41669
44217
46903
49738
54
7
34811
36993
39291
41710
44260
46949
49787
53
8
34846
37030
39330
41752
44304
46995
49835
52
9
34882
37068
39369
41793
44347
47041
49884
51
10
34917
37105
39409
41835
44391
47087
49933
50
11
1.34953
1.37143
1.39448
1.41876
1.44435
1.47134
1.49981
49
12
34988
37180
39487
41918
44479
47180
50030
48
13
35024
37218
39527
41959
44523
47226
50079
47
14
35060
37255
39566
42001
44567
47272
50128
46
15
35095
37293
39606
42042
44610
47319
50177
45
16
35131
37330
39646
42084
44654
47365
50226
44
17
35167
37368
39685
42126
44698
47411
50275
43
18
35203
37406
39725
42168
44742
47458
50324
42
19
35238
37443
39764
42210
44787
47504
50373
41
20
35274
37481
39804
42251
44831
47551
50422
40
21
1.35310
1.37519
1.39844
1.42293
1 44875
1.47598
1.50471
39
22
35346
37556
39884
42335
44919
47644
50521
38
23
35382
37594
39924
42377
44963
47691
50570
37
24
35418
37632
39963
42419
45007
47738
50619
36
25
35454
37670
40003
42461
45052
47784
50669
35
26
35490
37708
40043
42503
45096
47831
50718
34
27
35526
37746
40083
42545
45141
47878
50767
33
28
35562
37784
40123
42587
45185
47925
50817
32
29
35598
37822
40163
42630
45209
47972
50866
31
30
35634
37860
40203
42672
45274
48019
50916
30
31
1.35670
1.37898
1.40243
1.42714
1.45319
1.48066
1.50966
29
32
35707
37936
40283
42756
45363
48113
51015
28
33
35743
37974
40324
42799
45408
48160
51065
27
34
35779
38012
40364
42841
45452
48207
51115 26
35
35815
38051
40404
42883
45497
48254
51165 ! 25
36
35852
38089
40444
42926
45542
48301
51215 24
37
35888
38127
40485
42968
45587
48349
51265
23
38
35924
38165
40525
43011
45631
48396
51314
22
39
35961
38204
40565
43053
45676
48443
51364
21
40
35997
38242
40606
43096
45721
48491
51415
20
41
1.36034
1.38280
1.40646
1.43139
1.45766
'.48538
1.51465
19
42 | 36070
38319
40687
43181
45811
48586
51515
18
43 36107
38357
40727
43224
45856
48633
51565
17
44 i 36143
38396
40768
43267
45901
48681
51615
16
45
36180
38434
40808
43310
45946
48728
51665
15
46
36217
38473
40849
43352
45992
48776
51716
14
47
36253
38512
40890
43395
46037
48824
51766
13
48
36290
38550
40930
43438
46082
48871
51817
12
49
36327
38589
40971
43481
46127
48919
51867
11
50
36363
38628
41012
43524
46178
48967
51918
10
51
1.36400
1.38666
1.41053
1.43567
1.46218
1.49015
1.51968
9
52
36437
38705
41093
43610
46263
49063
52019
8
53
36474
38744
41134
43653
46309
4911'!
52069
7
54
36511
38783
41175
43696
46354
49159
52120
6
55
36548
38822
41'.'16
43739
46400
49207
52171
5
56
36585
38860
41257
43783
46445
49255
52222
4
57
36622
38899
41298
43826
46491
49303
52273
3
58
36659
38938
41339
43869
46537
49351
52323
2
59
36696
38977
41380
43912
46582
49399
52374
1
60
36733
39016
41421
43956
46628
49448
52425
/
47
46
45
44
43
42
41
/
COSECANTS.
270
NATURAL SECANTS AND COSECANTS
/
SECANTS.
/
49
50
61
62
53
54
55
1.52425
1.55572
1.58902
1.62427
1.66164
1.70130
1.74345
60
1
52476
55626
58959
62487
66228
70198
74417
59
2
52527
55680
59016
62548
66292
70267
74490
58
3
52579
55734
59073
62609
66357
70335
74562
57
4
52630
55789
59130
62669
66421
70403
74635
56
6
52681
55843
59188
62730
66486
70472
74708
55
6
52732
55897
59245
62791
66550
70540
74781
54
7
52784
55951
59302
62852
66615
70609
74854
53
8
52835
56005
59360
62913
66679
70677
74927
52
9
52886
56060
59418
62974
66744
70746
75000
51
10
52938
56114
59475
63035
66809
70815
75073
50
11
1.52989
1.56169
1.59533
1.63096
1.66873
1.70884
1.75146
49
12
53041
56223
59590
63157
66938
70953
75219
48
13
53092
56278
59648
63218
67003
71022
75293
47
14
53144
56332
59706
63279
67068
71091
75366
46
15
53196
56387
59764
63341
67133
71160
75440
45
16
53247
56442
59822
63402
67199
71229
75513
44
17
53299
56497
59880
63464
67264
71298
75587
43
18
53351
56551
59938
63525
67329
71368
75661
42
19
53403
56606
59996
63587
67394
71437
75734
41
20
53455
56661
60054
63648
67460
71506
75808
40
21
1.53507
1.56716
1.60112
1.63710
1.67525
1.71576
1.75882
39
22
53559
56771
60171
63772
67591
71646
75956
38
23
53611
56826
60229
63834
07656
71715
76031
37
24
53663
56881
602S7
63895
67722
71785
76105
36
25
53715
56937
60346
63957
67788
71855
76179
35
26
53768
56992
60404
64019
67853
71925
76253
34
27
53820
57047
604G3
64081
67919
71995
76328
S3
28
53872
57103
60521
64144
67985
72065
76402
32
29
53924
57158
60580
64206
68051
72135
76477
31
30
53977
57213
60639
64268
68117
72205
76552
30
31
1.540-29
1.57269
1.60698
1.64330
1.68183
1.72275
1.76626
29
32
54082
5732 1
60756
64393
68250
72346
76701
28
33
54134
57380
60815
64455
68316
72416
76776
27
34
54187
57436
60874
64518
68382
72487
76851
26
35
51240
57491
60933
64580
68449
72557
76926
25
36
54292
57547
60992
64643
68515
72628
77001
24
37
54345
57603
61051
64705
68582
72698
77077
23
38
54398
57659
61111
64768
68648
72769
77152
22
39
54451
57715
61170
64831
68715
72840
77227
21
40
54504
57771
61229
64894
6878?
72911
77303
20
41
1.54557
1.57827
1.61288
1.64957
1.68848
1.72982
1.77378
19
42
54610
57883
61348
65020
68915
73053
77454
18
43
54663
57939
61407
65083
68982
73124
77530
17
44
54716
57995
61467
65146
69049
73195
77606
16
45
54769
58051
61526
65209
69116
73267
77681
15
46
54822
58108
61586
65272
69183
73338
77757
14
47
54876
58164
61646
65336
69250
73409
77833
13
48
54929
58221
61705
65399
69318
73481
77910
12
49
54982
58277
61765
65462
69385
73552
77986
11
50
55036
58333
61825
65526
69452
73624
78062
10
51
1.55089
1.58390
1.61885
1.65589
1.69520
1.73696
1.78138
9
52
55143
58447
61945
65653
69587
73768
78215
8
53
55196
58503
62005
65717
69655
73840
78291
7
54
55250
58560
62065
65780
69723
73911
78368
6
55
55803
58617
62125
65844
69790
73983
78445
5
56
55357
58674
62185
65908
69858
74056
78521
4
57
55411
58731
62246
65972
69926
74128
78598
3
58
55465
58788
62306
66036
69994
74200
78675
2
59
55518
58845
62366
66100
70062
74272
78753
1
60
55572
58902
62427
66164
70130
74345
78829
|
40
89
38
87
86
86
84
/
COSECANTS.
(
NATURAL SECANTS AND COSECANTS 271
/
SECANTS.
/
56
57
58
59
60
61
62
1.78829
1.83608
1.88708
1.94160
2.00000
2.06267
2.13005
60
1
789C6
83690
88796
94254
00101
06375
13122
59
o
78984
83773
88884
94349
00202
06483
13239
58
3
79061
83855
88972
94443
00303
06592
13356
57
4
79138
83938
89060
94537
00404
06701
13473
56
5
79216
84020
89148
94632
00505
06809
13590
55
6
79293
84103
89237
94726
00607
06918
13707
54
7
79371
84186
89325
94821
00708
07027
13825
53
8
79449
84269
89414
94916
00810
07137
13942
52
9
79527
84352
89503
95011
00912
07246
14060
51
10
79604
84435
89591
95106
01014
07356
14178
50
n
1.79682
1.84518
1.89680
1.95201
2.01116
2.07465
2.14296
49
12
79761
84601
89769
95296
01218
07575
14414
48
13 79839
84685
89858
95392
01320
07685
14533
47
14 79917
84768
89948
95487
01422
07795
14651
46
15 79995
84852
90037
95583
01525
07905
14770
45
16 80074
84935
90126
95678
01628
08015
14889
44
17 80152
85019
90216
95774
01730
08126
15008
43
18
80231
85103
90305
95870
01833
08236
15127
42
19
80309
85187
90395
95966
01936
08347
15246
41
20 80388
85271
90485
96062
02039
08458
15366
40
21
L 80467
1.85355
1.90575
1.96158
2.02143
2 08569
2.15485
39
22
80546
85439
90665
96255
02246
08680
15605
38
23 i 80625
85523
90755
96351
02349
08791
15725
37
24 80704
85608
90845
96448
02453
08903
15845
36
25
80783
85692
90935
96544
02557
09014
15965
35
26
80862
85777
91026
96641
02661
09126
16085
34
27
80942
85861
91116
96738
02765
09238
16206
33
28
81021
85946
91207
96835
02869
09350
16326
32
29
81101
86031
91297
96932
02973
09462
16447
31
30
81180
86116
91388
97029
03077
09574
16568
30
31
1.81260
1 .86201
1.91479
1.97127
2.03182
2.09686
2.16689
29
82
81340
86286
91570
97224
03286
09799
16810
28
33
81419
86371
91661
97322
03391
09911
16932
27
34
81499
86457
91752
97420
03496
10024
17053
26
35
81579
86542
91844
97517
03601
10137
17175
25
36
81659
86627
91935
97615
03706
10250
17297
24
37
81740
86713
92027
97713
03811
10363
17419
23
38
81820
86799
92118
97811
03916
10477
17541
22
39
81900
86885
92210
97910
04022
10590
17663
21
40
81981
86990
92302
98008
04128
10704
17786
20
41
1.82061
1 .87056
1.92394
1.98107
2.04233
2.10817
2.17909
19
42
82142
87142
92486
98205
04339
10931
18031
18
43
82222
87229
92578
98304
04445
11045
18154
17
44
82303
87315
92670
98403
04551
11159
18277
16
45
82384
87401
92762
98502
04658
11274
18401
15
46
82465
87488
92855
98601
04764
11388
18524
14
47
82546
87574
92947
98700
04870
11503
18648
13
48
82627
87661
93040
98799
04977
11617
18772
12
49
82709
87748
93133
98899
05084
11732
18895
11
50
82790
87834
93226
98998
05191
11847
19019
10
51
1.82871
1.87921
1.93319
1.99098
2.05298
2.11963
2.19144
9
52
82953
88008
93412
99198
05405
12078
19268
8
53
83034
88095
93505
99298
05512
12133
19393
7
54
83116
88183
93598
99398
05619
12309
19517
6
55
83198
88270
93692
99498
05727
12425
19642
5
56
83280
88357
93785
99598
05835
12540
19767
4
57
83362
88445
93879
99698
05942
12657
19892
3
58
83444
88532
93973
99799
06050
12773
20018
2
59
83526
88620
94066
99899
06158
12889
20143
1
60
83608
88708
94160
2.00000
06267
13005
20269
/
33
32
31
30
29
28
27
/
COSECANTS.
272
NATURAL SECANTS AND COSECANTS
!
,
SECANTS.
/
63
64
65
66
67
68
69
2.20269
2.28117
2.36620
2.45859 2.55930
2.66947
2.79043
60
1
20395
28-253
367C8
460-20
56106
67139
79254
59
2
20521
28390
36910
46181
56-282
67332
79460
58
3
20647
28526
37064
46342
56458
675-25
79679
57
4
20773
28663
37212
46504
56634
67718
79891
56
5
20900
28800
37361
46665
56311
67911
80104
55
6
21026
28937
37509
46827
56988
68105
80318
54
7
21153
29074
37658
46989
57165
68299
80531
53
8
21280
29211
37808
47152
57342
68494
80746
52
9
21407
29349
37957
47314
575-JO
68689
80960
51
10
21535
29487
38107
47477
57698
68884
81175
50
11
2.21662
2.29625
2.38256
2.47640 2
57876
2.69079
a. 81390
49
12
21790
29763
38406
47804
58054
69275
81605
48
13
21938
29901
38556
479G7
58333
69471
81821
47
14
22045
30040
38707
48131
58412
69667
82037
46
15
22174
30179
38857
48295
58591
69864
8-2254
45
16
22302
30318
39008
48459
58771
70061
82471
44
17
22430
30457
39159
48624
58950
70258
82688
43
18
22559
30596
39311
48789
59130
70455
82906
42
19
22688
30735
39462
48954
59311
70653
831-24
41
20
22817
30875
39614
49119
59491
70851
83342
40
21
2.22946
2 31015
2.39766
2.49284 2
59672
2.71050
2.83561
39
22
23075
31155
39918
49450
59853
71249
83780
38
23
23205
31295
40070
49616
60035
71448
83999
37
24
23334
31436
40222
49782
60-217
71647
84219
36
25
23464
31576
40375
49948
60399
71847
84439
35
26
2359 1
31717
40528
50115
60581
72047
84059
34
27
39724
31858
40681
50282
60763
72247
84S80
33
28
23855
31999
40835
50449
60946
72448
85102
32
29
23985
32140
409F8
50617
61129
72649
853-23
31
30
24116
32282
41112
50784
61313
72850
85545
30
31
2.24247
2.32424
2 41296
2.50952 2
61496
2.73052
2.85767
29
32
24378
32566
41450
51120
61680
73254
85990
28
Jffl
24509
32708
41605
51289
61864
73456
86213
27
34
24640
32850
41760
51457
62049
73659
86437
26
35
24772
32993
41914
51626
62234
73862
86661
25
36
24903
33135
42070
51795
62419
74065
86885
24
37
25035
33278
42225
51965
62604
74269
87109
23
38
25167
33422
42380
52134
62790
74473
87334
22
39
25300
33565
42536
52304
62976
74677
87560
21
40
25432
33708
42692
52474
63162
74881
87785
20
41
2.25565
2.33852
2.42848
2.52645 2
63348
2.75086
2.88011
19
42
25697
33996
43005
52815
63535
75292
88238
18
43
25830
34140
43162
52986
63722
75497
88465
17
44
25963
31284
43318
53157
63909
75703
88692
16
45
26097
34429
43476
53329
64097
75909
889-20
15
46
26230
34573
43633
53500
64-285
76116
89148
14
47
26364
34718
43790
5367-2
64473
76323
89376
13
48
26498
34863
43948
53845
64662
76530
89605
12
49
26632
35009
44106
54017
64851
76737
89834
11
50
26766
35154
44264
54190
65040
76945
90003
10
51
2.26900
2.35300
2.44423
2 54363 2.65229
2.77154
2.90-293
9
52
27035
35446
44582
54536
65419
77362
90524
8
53
27169
35593
41741
54709
65609
77571
90754
7
54
27304
35738
44900
54883
65799
77780
90986
6
55
27439
35885
45059
55057
65989
77990
91217
5
56
27574
36031
45219
55231
66180
78200
91449
4
57
27710
36178
45378
55405
66371
78410
91681
3
58
27845
36325
45539
55580
66563
78621
91914
2
59
27981
36473
45699
55755
66755
7883-2
92147
1
60
28117
36620
45859
55930
66947
79043
92380
26
25
24
28
22
21
20
/
COSECANTS.
NATURAL SECANTS AND COSECANTS
273
1
SECANTS.
/
70
71
72
73
74
75
?6
2.92380
3.07155
3.23607
3.42030 3
.62796
3.86370
4.13357
60
1
92614
07415
23897
42356
63164
86V90
13839
59
2
92849
07675
24187
42683
63533
87211
14323
58
3
93083
07936
24478
43010
63903
876:33
14809
57
4
93318
08197
24770
43337
64274
88056
15295
56
5
93554
08459
25062
43666
64645
88479
15782
55
6
93790
08721
25355
43995
65018
88904
16271
54
7
94026
08983
25648
44324
65391
89330
16761
53
8
94263
09246
25942
44655
65765
89756
17252
52
9
94500
09510
26237
44986
66 MO
90184
17744
51
10
94737
09774
26531
45317
66515
900 13
18238
50
11
2.94975
3.10038
3.26827
3.45650 3
.66892
3.9'U42
4.18733
49
12
95213
10303
27123
45983
67269
9 1473
19228
43
13
95452
10568
27420
46316
67647
91904
19725
47
14
95(591
10834
27717
46651
68025
92337
20224
46
15
95931
11101
28015
46986
68405
92770
20723
45
16
96171
11 867
28313
47321
68785
93204
21224
44
17
96411
11035
28612
47658
69167
93640
21726
43
18
96652
11903
28912
47995
69549
94076
22229
42
19
96^93
12171
29212
48333
69931
94514
22734
41
20
97135
12440
29512
48671
70315
94952
23239
40
21
2.97377
3.12709
3.29814
3.49010 3
.70700
3.95392
4.23746
39
22
97619
12979
30115
49350
71085
95832
24255
38
23
97862
13249
30418
49691
71471
96274
24764
37
24
98106
13520
30721
50032
71858
96716
25275
36
25
98349
13791
31024
50374
72246
97160
25787
35
26
98594
14063
31328
50716
72635
97604
26300
34
27
98838
14335
31633
51060
73024
98050
26814
33
28
99083
14608
31939
51404
73414
98497
27330
32
29
99329
14881
32244
51748
73806
98944
27847
31
30
99574
15155
32551
52094
74198
99393
28366
30
31
2.99821
3.15429
3.32858
3.52440 3
.74591
3.99843
4.28885
29
82
3.00067
15704
33166
52787
74984
4.00293
29406
28
33
00315
15979
33474
53134
75379
00745
29929
27
34
00562
16255
33783
53482
75775
01198
30452
26
35
00810
16531
34092
53831
76171
01652
30977
25
36
01059
16808
34403
54181
76568
02107
31503
24
3V
01308
17085
34713
54531
76966
025G3
32031
23
38
01557
17363
35025
54883
77365
03020
32560
22
39
01807
17641
35336
55235
77765
03479
33090
21
40
02057
17920
35649
55587
78166
03938
33622
20
41
3.02308
3.18199
3.35962
3.55940 3
.78568
4.04398
4.34154
19
42
02559
18479
36276
56294
78970
04860
34689
18
43
02810
18759
36590
56649
79374
05322
35224
17
44
03062
19040
36905
57005
79778
05786
&5761
16
45
03315
19322
37221
57361
80183
06251
36299
15
46
03568
19604
37537
57718
80589
06717
36839
14
47
03821
19886
37854
58076
80996
07184
37380
13
48
04075
20169
38171
58434
81404
07652
37923
12
49
04329
20453
38489
58794
81813
08121
38466
11
50
04584
20737
38808
59154
82223
08591
39012
10
51
3.04839
3.21021
3.39128
3.59514 3
.82633
4.09063
4.39558
9
52
05094
21306
39448
59876
83045
09535
40106
8
53
05350
21592
39768
60238
83457
10000
40656
7
54
05607
21878
40089
60601
83871
10484
41206
6
55
05864
22165
' 40411
60965
84285
10960
41759
5
56
06121
22452
40734
61330
84700
11437
42312
4
57
06379
22740
41057
61695
85116
11915
42867
3
58
06637
23028
41381
62061
85533
12394
43424
2
59
06896
23317
41705
62428
85951
12875
43982
1
60
07155
23607
42030
62796
86370
13357
44541
~~^~~
/
19
18
17
16
16
14
18
t
COSECANTS.
274 NATURAL SECANTS AND COSECANTS
/
SECANTS.
/
77'
78
79
80
81
82
88
4.44541
4.80973
5.24084
5.75877 6
.39245
7.18530
8.20551
60
1
45102
81633
24870
76829
40422
5:0020
22500
59
2
45664
82294
25658
77784
41602
21517
24457
58
8
46228
82956
26448
78742
42787
23019
26425
57
4
46793
83621
27241
79703
43977
24529
28402
56
5
47360
84288
28036
80667
45171
26044
30388
55
6
47928
84956
28833
81635
46369
27566
32384
54
7
48498
85627
29634
83606
47572
29095
34390
53
8
49069
86299
30436
83581
48779
30630
36405
52
9
49642
86973
31241
84558
49991
32171
38431
51
10
50216
87649
32049
85539
51208
33719
40466
50
11
4.50791
4.88327
5.32859
5.86524 6
.52429
7.35274
8.42511
49
12
51368
89007
33G7 1
87511
53655
36835
44566
48
13
51947
89689
34486
88502
54886
3S403
46632
47
14
52527
90373
35304
89497
56121
39978
48707
46
15
53109
91058
36124
90495
57361
41560
50793
45
16
53692
91746
36947
91496
58606
43148
52889
44
17
54277
92436
37772
92501
59855
44743
54996
43
18
54663
93128
38600
93509
61110
46346
571L3
42
19
55451
93821
39430
94521
62369
47955
59241
41
20
56041
94517
402U3
95536
63033
49571
61379
40
21
4.56632
4.95215
5.41099
5.9C555 6
.64902
7.51194
8.63528
39
22
57224
95914
41937
97577
66176
52825
65688
38
23
57819
96616
42778
98603
67454
54462
67859
37
24
58414
97320
43622
90633
68738
56107
70041
36
25
59012
98025
44468
6.00666
70027
57759
72234
35
26
59611
98733
45317
01703
71321
59418
74438
34
27
60211
99443
46169
02743
7-J620
61085
76653
33
28
60813
5.00155
47023
03787
73924
62759
78880
32
29
61417
00869
47881
04834
75233
64441
81118
31
30
62023
01585
48T40
05886
76547
66130
83367
30
31
4 62630
5.02303
5.49603
6.06941 6
.77866
7.67826
8.85628
29
32
63238
03024
5046S
08000
79191
69530
87901
28
33
63849
03746
51337
09062
80521
71242
90186
27
34
64461
04471
52208
10129
81856
72962
92482
26
35
65074
05197
53081
11199
83196
74689
94791
25
36
65690
05926
53958
12273
84542
76424
97111
24
37
66307
06657
54837
13350
85893
78167
99444
23
38
66925
0739C
55720
14432
87250
79918
9.01788
22
39
67545
08125
56605
15517
88612
81677
04146
21
40
68167
08863
57493
16607
89979
83443
06515
20
41
4.68791
5.09602
5.58383
6.17700 6
.91352
7.85218
9.08897
19
42
69417
10344
59277
18797;
92731
87001
11292
18
43
70044
11088
60174
19898.
94115
88792
13C99
17
44
70673
11835
61073
21004
95505
90592
16120
16
45
71303
1258?
61976
22113
96900
92400
18553
15
46
71935
13334
62881
23226
98301
94216
20999
14
47
72569
14087
63790
24343
99708
96040
23459
13
48
73205
14842
64701
25464 7
.01120
97873
25931
12
49
73843
15599
65616
20590
02538
99714
28417
11
50
74482
16359
66533
27719
03962
8.01565
30917
10
51
4.75123
5.17121
5.67454
6.28853 7
.05392
8.03423
9.33430
9
52
75T66
17886
68377
29991
06828
05291
35957
8
53
76411
18652
69304
31133
08269
07167
38497
54
77057
19421
70234
32279
09717
09052
41052
6
55
77705
20193
71166
33429
1117f
10946
43620
5
56
78355
20906
72102
34584
12630
12849
46203
4
57
79007
21742
73041
35743
14096
14760
48800
3
58
79661
22521
73983
36906
15568
16681
51411
2
59
80316
23301
74929
38073
17046
18612
54037
1
60
80973
24084
75877
39245
18530
20551
56677
/
12
11
10
9
8
7
6
/
COSECANTS.
NATURAL SECANTS AND COSECANTS 275
SECANTS.
/
84
85
86
87
88
89
o
9.56677
11.47371
14.33559
19.10732
28.65371
57.298G9
60
1
59332
51199
39547
21397
89440
58.26976
59
2
62002
55052
45586
32182
29.13917
59.27431
58
3
64687
58932
51676
43088
38812
60.31411
57
4
67387
62837
57817
541 19
64137
61.39105
56
5
70103
66769
64011
65275
89903
62.50715
55
6
72833
70728
70258
76560
30.16120
63.66460
54
7
75579
74714
76558
87976
42802
64.86572
53
8
78341
78727
82913
99524
69960
66.11304
52
9
81119
82768
89323
20.11208
97607
67.40927
51
10
83912
86837
95788
23028
31.25758
68.75736
50
11
9.86722
11.90934
15.02310
20.34989
31.54425
70.16047
49
12
89547
95060
08890
47093
83623
71.62207
48
13
92389
99214
15527
59341
32.13366
73.14583
47
14
95248
12.03397
22223
71737
43671
74.73586
46
15
98123
07610
28979
84283
74554
76.39655
45
16
10.01015
11852
35795
96982
33.06030
78.13274
44
17
03923
16125
42672
21.09838
38118
79.94968
43
18
06849
20427
49611
22852
70835
81.85315
42
19
09792
24761
56614
36027
34.04199
83.84947
41
20
12752
29125
63679
49368
38232
85.94561
40
21
10.15730
12.33521
15.70810
21.02876
34.72952
88.14924
39
22
18725
37948
78005
76555
35.08380
90.46886
38
23
21739
42408
85268
90409
44539
92.91387
37
24
24770
46900
92597
22.04440
81452
95.49471
36
25
27819
51424
99995
18653
36.19141
98.22303
35
26
30887
55982
16.07462
33050
57633
101.11185
34
27
33973
60572
14999
47635
96953
104.17574
33
28
37077
65 197
22607
62413
37.37127
107.43114
32
29
40201
69856
30287
77386
78185
110.89656
31
30
43343
74550
38041
92559
38.20155
114.59301
30
31
10.46505
12.79278
16.45869
23.07935
38.63068
118.54440
29
32
49685
84042
53772
23520
39.06957
122.77808
28
33
52886
88841
61751
39316
51855
127.32526
27
34
56106
93677
69808
553-J9
97797
132.22229
26
35
59346
98549
77944
71563
40.44820
137.51108
25
36
62605
13.03158
86159
88022
92963
143.24061
24
37
65885
08404
94456
24.04712
41.42266
149.46837
23
38
69186
13388
17.02835
21637
92772
156.26228
22
39
72507
18411
11297
38802
42.44525
163.70325
21
40
75849
23472
19843
56212
97571
171.88831
20
41
10.79212
13.28572
17.28476
24.73873
43.51961
180.93496
19
42
82596
33712
37196
91790
44.07746
190.98680
18
43
86001
38891
46005
25.09969
64980
202.22122
17
44
89428
44112
54903
28414
45.23720
214.85995
16
45
92877
49373
63893
47134
84026
229.18385
15
46
96348
54676
72975
66132
46.45963
245.55402
14
47
99841
60021
82152
85417
47.09596
264.44269
13
48
11.03356
65408
91424
26.04994
74997
286.47948
12
49
06894
70838
18.00794
24869
48.42241
312.52297
11
50
10455
76312
10262
45051
49.11406
343.77516
10
51
11.14039
13.81829
18.19830
26.65546
49.82576
381.97230
9
52
17646
87391
29501
863GO
50.55840
,429.71873
8
53
21277
92999
39274
27.07503
51.31290
491.10702
7
54
24932
98651
49153
28981
52.09027
572.95809
6
55
28610
14.04350
59139
50804
89156
687.54960
5
56
32313
10096
69233
72978
53.71790
859.43689
4
57
36040
15889
79438
95513
54.57046
1145.9157
3
58
39792
21730
89755
28.18417
55.45053
1718.8735
2
59
43569
27620
19.00185
41700
56.35946
3437.7468
1
60
47371
33559
10732
65371
57.29869
oo
i
6
4
3
2
1
/
COSECANTS.
276 NATURAL VERSED SINES AND EXTERNAL SEC.
1 2 3
<
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
/
1
2
3
4
00000
00000
00000
.00000
. 00000
.00000
.00000
.00000
.00000
.00000
00015
-00016
-00016
.00017
.00017
.00015
.00016
.00016
.00017
-00017
00061
.00062
00063
00064
-00065
.00061
.00062
.00063
.00064
-00065
00137
00139
00140
00142
00143
00137
00139
.00140
.00142
-00143
1
2
3
4
5
6
7
6
9
00000
.00000
.00000
-00000
.00000
.00000
.00000
.00000
.00000
.00000
-00018
.00018
-00019
.00020
.00020
00018
.00018
.00019
.00020
-00020
-00066
-00067
-00068
-00069
-00070
.00066
.00067
.00068
00069
-00070
00145
.00146
-00148
.00150
.00151
-00145
.00147
00148
.00150
-00151
5
6
7
8
9
10
11
12
13
14
. 00000
.00001
.00001
00001
.00001
.00000
.00001
.00001
.00001
.00001
-00021
-00021
.00022
-00023
00023
.00021
.00021
.00022
.00023
.00023
-00071
-00073
. 00074 "
.00075
-00076
.00072
.00073
-00074
00075
.00076
.00153
00154
.00156
-00158
-00159
.00153
00155
.00156
00158
00159
10
11
12
13
14
15
16
17
18
19
.00001
00001
.00001
00001
.00002
.00001
.00001
.00001
.00001
.00002
00024
.00024
00025
.00026
.00026
.00024
.00024
.00025
.00026
-00026
.00077
.00078
.00079
-00081
.00082
.00077
-00078
-00079
.00081
.00082
.00161
00162
00164
00166
.00168
00161
00163
.00164
.00166
-00168
15
18
17
18
19
20
21
22
23
24
.00002
.00002
00002
.00002
00002
.00002
.00002
-00002
.00002
-00002
-00027
00028
-00028
.00029
.00030
-00027
.00028
-00028
.00029
-00030
-00083
-00084
00085
.00087
-00088
.00083
00084
-00085
-00087
-00088
.00169
-00171
-00173
-00174
.00176
-00169
00171
00173
00175
.00176
20
21
22
23
24.
25
26
27
28
29
.00003
00003
. 00003
.00003
. 00004
. 00003
.00003
.00003
.00003
.00004
-00031
-00031
.00032
-00033
00034
OOC3 1
00031
.00032
.00033
-00034
00089
00090
-00091
.00093
.00094
-00089
00090
00091
-00093
-00094
-0017^
00179
00181
.00183
-00185
00178
.00180
00182
00183
-00185
25
26
27
28
29
30
31
32
33
34
. 00004
.00004
. 00004
.00005
-00005
.00004
. 00004
. 00004
00005
.00005
00034
00035
.00036
.00037
.00037
.00034
.00035
00036
.00037
-00037
00095
.00096
.00098
00099
00100
-OOOS5
.00097
.00098
.00099
.00100
00187
00188
00190
00192
00194
00187
00189
-00190
00192
00194
30
31
32
33
34
35
36
37
38
39
00005
.00005
.00006
.00006
.00006
.00005
.00005
.00006
00006
.00006
.00038
.00039
.00040
00041
.00041
-00038
.00039
00040
00041
.00041
00102
00103
.00104
00106
.00107
.00102
00103
00104
.00106
.00107
00196
00197
.00199
-00201
.00203
00196
-00198
-00200
00201
00203
35
36
37
38
_39
40
41
42
43
44
00007
00007
.00007
00008
00008
.00007
00007
.00007
.00008
00008
-00042
00043
00044
00045
00046
.00042
00043
- 00044
.00045
-00046
-00108
00110
00111
-00112
-00114
00108
.00110
-00111
-00113
00114
.00205
00207
00208
.00210
00212
00205
00207
00209
00211
-00213
40
41
42
43
44
45
46
47
47
49
00009
00009
.00009
.00010
00010
00009
.00009
.00009
00010
00010
00047
00048
00048
.00049
.00050
-00047
-00048
-00048
-00049
00050
-00115
OOU7
-00118
00119
.00121
00115
00117
00118
-00120
-00121
00214
00216
00218
.00220
-00222
00215
.'0216
-00218
-00220
00222
45
46
47
48
49
50
51
52
53
54
.00011
.00011
.00011
00012
.00012
.00011
00011
.00011
00012
.00012
00051
00052
00053
.00054
.00055
00051
.00052
00053
.00054
00055
-00122
00124
00125
.00127
.00128
00122
00124
.00125
00127
00128
.00224
00226
.00228
00230
00232
00224
00226
00228
00230
00232
50
51
52
53
54
55
56
57
58
59
00013
00013
00014
00014
00015
00013
.00013
-00014
.00014
.00015
00056
.00057
.00058
00059
00060
.00056
00057
00058
QUO 59
00060
00130
-00131
00133
00134
.00136
00130
00131
00133
00134
00136
00234
00236
00238
00240
.00242
-00234
00236
00238
.00240
. 00242
55
56
57
58
59
60
.00015
00015
-00061
00061
00137
-00137
00244
00244
60
NATURAL VERSED SINES AND EXTERNAL SEC. 277
4 5 6 7
t
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
o
1
2
3
4
.00244
00246
.00248
.00250
-00252
00244
00246
.00248
.00250
-00252
-00381
00383
.00386
.00388
.00391
00382
00385
.00387
-00390
-00392
00548
.00551
-00554
-00557
.00560
00551
00554
00557
00560
00563
-00745
-00749
00752
00756
.00760
.00751
00755
00758
00762
00765
]
2
3
4
5
6
7
8
9
.00254
.00256
-00258
00260
.00262
00254
00257
00259
00261
00263
.00393
-00396
.00398
00401
-00404
00395
.00397
00400
00403
00405
00563
00566
00569
00572
00576
00566
00569
00573
.00576
-00579
00763
00767
00770
-00774
-00778
00769
00773
00776
00780
.00734
5
6
7
8
9
10
11
12
13
14
00264
.00266
.00269
00271
00273
00265
.00267
.00269
00271
.00274
-00406
.00409
-00412
00114
00417
. 00408
.00411
00413
00416
00419
00579
00582
00585
00588
00591
00582
00585
00588
00592
00595
00781
00785
-00789
00792
-00796
00787
00791
00795
00799
00802
10
11
12
13
14
15
16
17
18
.19
.00275
-00277
00279
.00281
.00284
.00276
.00278
-00280
.00282
00284
-00420
00422
00425
00428
.00430
00421
00424
00427
00429
.00432
00594
00598
-00601
-00604
.00607
00598
00601
00604
-00608
.00611
-00800
- 00803
-00807
-00811
00814
-00806
00810
.00813
00817
00821
15
16
17
18
19
2O
21
22
23
24
00286
00288
-00290
-00293
-00295
00287
00289
00291
.00293
00296
.00433
00436
00438
00441
00444
-00435
-00438
00440
. 00443
.00446
-OC610
-00614
00617
00620
C0623
00614
00617
00621
00624
00627
-00818
00822
00825
00829
.00833
-00825
.00828
00832
.00836
. 00840
20
21
22
23
24
25
26
27
28
29
-00297
-00299
-00301
-00304
.00306
.00298
00300
00302
00305
00307
00447
00449
00452
00455
00458
.00449
.00451
.00454
00457
00460
00626
00630
00633
00636
00640
00630
00634
00637
00640
00644
-00837
.00840
.00844
-00848
.00852
.00844
-00848
-00851
.00855
00859
25
26
27
28
29
30
31
32
33
34
.00308
-00311
.00313
00315
00317
00309
00312
.00314
.00316
00318
00460
-00463
00466
00469
00472
00463
00465
00468
00471
-00474
00643
00646
00649
00653
.00656
00647
00650
-00654
00657
00660
-00856
00859
-00863
-00867
-00871
00863
00867
.00871
00875
00878
30
31
32
33
34
35
36
37
38
39
00320
00322
00324
.00327
.00329
00321
00323
00326
00328
.00330
. 00474
.00477
. 00480
.00483
00486
00477
00480
00482
00485
.00483
00659
00663
00666
00669
.00673
00664
00667
00671
00674
.00677
-00875
OC878
00882
.00886
.00890
.00882
00888
.00890
00894
.00898
35
36
37
38
39
40
41
42
43
44
.00332
00334
00336
-00339
-00341
00333
00335
00337
00340
00342
-00489
.00492
- 00494
-00497
-00500
-00491
.00494
00497
00500
00503
.00676
00680
00683
.00686
-00690
.00681
.00684
00688
00691
00695
00894
00898
00902
00906
00909
.00902
.00906
.00910
.00914
00918
40
41
42
43
44
45
46
47
48
49
00343
-00346
-00348
00351
00353
00345
00347
00350
00352
00354
-00503
-00506
.00509
-00512
.00515
00506
00509
00512
.00515
00518
00693
00607
-00700
00703
-00707
.00698
00701
00705
00708
.00712
00913
00917
00921
00925
00929
.00922
.00926
.00930
00934
00938
45
46
47
48
49
50
5i
52
53
54
00356
00358
00361
0036cJ
-00365
00357
00359
00362
00364
-00367
-00518
.00521
00524
00527
-00530
.00521
00524
00527
00530
00533
00710
.00714
.00717
00721
00724
00715
00719
00722
00726
00730
00933
00937
00941
00945
00949
.00942
.00946
.00950
00954
00958
50
51
52
53
54
55
56
57
58
59_
.00368
-00370
-00373
00375
.00378
00369
00372
00374
00377
00379
00533
-00536
00539
.00542
00545
00536
00539
00542
00545
00548
00728
00731
00735
00738
00742
.00733
00737
00740
00744
-00747
00953
00957
00961
.00965
00969
.00962
00968
00970
00975
.00979
55
56
57
58
59
60
00381
00382
00548
00551
00745
00751
00973
00983
60
NATURAL VERSED SINES AND EXTERNAL SEC.
8 9 10 11
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
2
3
4
00973
00977
00981
00985
00989
.00983
.00987
00991
00995
.00999
01231
01236
01240
01245
01249
01247
-01251
.01256
.01261
.01265
01519
01524
01529
01534
01540
01543
.01548
.01553
.01558
01564
01837
01843
01848
01854
01860
01872
01877
01883
.01889
01895
U
1
2
3
4
5
6
7
8
9
00994
00998
01002
01006
01010
01004
01008
01012
01016
.01020
01254
01259
01263
01268
01272
.01270
01275
.01279
01284
01289
01545
01550
01555
01560
01565
.01569
.01574
.01579
.01585
.01590
01865
01871
01876
01382
01888
.01901
.01906
01912
01918
01924
5
6
7
8
9
tf
12
13
H
01014
01018
01022
01027
01031
.01024
01029
-01033
.01037
.01041
01277
01282
01286
01291
01296
.01294
.01298
.01303
01308
01313
01570
01575
.01580
.01586
.01591
.01595
.01601
.01606
.01611
01616
01893
01899
01904
01910
01916
-01930
01936
01941
01947
01953
10
11
12
13
14
15
16
17
18
19
01035
01039
01043
01047
01052
.01046
.01050
.01054
.01059
01063
01300
01305
01310
01314
01319
.01318
01322
.01327
01332
.01337
.01596
01601
.01606
01612
.01617
.01622
.01627
.01633
.01638
.01643
01921
01927
01933
01939
-01944
01959
-01965
-01971
.01977
.01983
15
16
17
18
-12
20
21
22
23
24
01056
01060
01064
01069
01073
.01067
.01071
.01076
.01080
.01084
01324
01329
01333
01338
01343
01342
01346
01351
.01356
01361
01622
.01627
.01632
01638
.01643
01649
01651
.01659
01665
.01670
-01950
01956
01961
01967
.01973
01989
.01995
-02001
-02007
02013
30
21
22
23
24
25
26
27
28
29
.01077
.01081
.01086
.01090
.01094
.01089
.01093
.01097
01102
.01106
01348
01352
.01357
.01362
.01367
01366
.01371
-01376
01381
01386
01648
01653
01659
01664
.01669
.01676
.01681
01687
.01692
.01698
-01979
.01984
01990
01996
02002
02019
02025
02031
02037
02043
25
28
27
28
29
30
31
32
33
34
.01098
.01103
.01107
01111
.01116
.01111
.01115
.01119
.01124
.01128
.01371
.01376
.01381
-01386
01391
01391
01395
.01400
-01405
-01410
-01675
.01680
01685
-01690
-01696
.01703
.01709
.01714
.01720
.01725
02008
02013
02019
02025
02031
.02049
.02055
.02061
.02067
.02073
30
31
32
33
34
35
36
37
38
39
.01120
.01124
01129
-01133
01137
.01133
.01137
.01142
.01146
-01151
01396
01400
.01405
.01410
.01415
.01415
.01420
01425
.01430
01435
-01701
-01706
-01712
01717
-01723
.01731
.01736
.01742
01747
01753
02037
02042
.02048
02054
-02060
02079
02085
02091
.02097
-02103
35
36
37
38
-39
40
41
42
43
44
01142
01146
01151
-01155
01159
.01155
.01160
01164
01169
01173
-01420
01425
01430
01435
.01439
.01440
.01445
01450
-01455
01461
-01728
01733
-01739
-01744
-01750
01758
.01764
.01769
.01775
.01781
-02066
02072
02078
02084
02090
.02110
.02116
.02122
.02128
.02134
40
41
42
43
44
45
46
47
48
49
01164
-01168
01173
.01177
-01182
01178
01182
01187
.01191
01196
01444
.01449
.01454
01459
.01464
.01466
.01471
.01476
.01481
.01486
-01755
01760
01766
01771
01777
01786
.01792
.01793
.01803
.01809
02095
02101
02107
02113
02119
02140
02146
02153
02159
02165
45
46
47
48
49
50
51
S2
53
64
01188
01191
-01195
-01200
-01204
01200
01205
.01209
.01214
.01219
01469
01474
01479
01484
.01489
01491
01496
.01501
01506
01512
01782
01788
01793
0179U
01804
.01815
.01820
-01826
.01832
01837
02125
-02131
02137
02143
02149
02171
02178
.02184
.02190
.02196
50
51
52
53
54
55
56
57
58
59
.01209
01213
01218
01222
-01227
.01223
01228
.01233
.01237
.01242
01494
01499
.01504
.01509
-01514
.01517
.01522
01527
.01532
01537
.01810
.01815
01821
.01826
01832
01843
01849
.01854
.01860
01866
.02155
02161
02167
02173
-02179
.02203
02209
.02215
02221
.02228
55
56
57
58
59
60
01231
01247
.01519
.01543
01837
.01872
02185
.02234
60
NATURAL VERSED SINES AND EXTERNAL SEC/
13 13 14 15
t
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
o
1
2
3
.02185
02191
02197
.02203
-02210
.02234
.02240
.02247
.02253
02259
.02563
02570
02576
.02583
.02589
02630
.02637
.02644
.02651
.02658
02970
02977
02985
02992
02999
03081
.03069
.03076
03084
03091
03407
03415
03422
03430
03438
03528
.03536
03544
03552
03560
i
5
6
8
9
.02216
02222
.02228
.02234
. 02240
.02266
.02272
.02279
.02285
02291
.02596
.02602
02609
02616
02622
.02665
02672
.02679
02686
02693
03006
03013
03020
03027
03034
.03099
.03106
03114
03121
03129
03445
03453
03460
03468
.03476
03568
.03576
03584
03592
03601
5
1
8
9
10
11
12
13
14
02246
02252
02258
02265
02271
02298
02304
.02311
02317
02323
02629
02635
02642
02649
.02655
02700
02707
-02714
.02721
.02728
03041
03048
03055
03063
03070
03137
.03144
03152
03159
03167
03483
.03491
03498
.03506
.03514
03609
03617
03625
03633
03642
10
11
12
13
14
15
16
17
18
19
02277
02283
02289
02295
02302
.02330
02336
02343
.02349
.02356
.02662
02669
02675
02682
.02689
02735
02742
02749
.02756
02763
.03077
.03084
03091
03098
03106
03175
.03182
.03190
03198
03205
03521
03529
.03537
03544
03552
03650
03658
03666
03674
03683
15
16
17
18
19
20
21
22
23
24
02308
02314
02320
02327
.02333
02362
02369
02375
02382
02388
02696
02702
02709
02716
02722
.02770
.02777
.02784
.02791
.02799
.03113
03120
03127
031S4
.03142
03213
03221
03228
03236
03244
03560
03567
03575
03583
.03590
03691
.03699
03708
03716
03724
30
21
22
23
24
25
26
27
28
29
02339
02345
02352
.02358
.02364
02395
02402
02408
02415
.02421
02729
02736
02743
02749
02756
.02806
02813
.02820
02827
.02834
03149
.03156
03163
03171
03178
.03251
.03259
03267
03275
03282
.03598
-03606
03614
.03621
.03629
03732
03741
03749
03758
03766
25
26
27
23
29
30
31
32
33
34
02370
02377
02383
02389
02396
02428
.02435
02441
.02448
.02454
02763
02770
02777
02783
.02790
.02842
02849
.02856
.02863
02870
03185
03193
03200
03207
03214
03290
03298
03306
03313
03321
03637
.03645
.03653
03660
03668
03774
03783
03791
03799
03808
30
31
32
33
34
3o
36
37
38
,39
02402
02408
02415
02421
02427
02461
02468
02474
02481
.02488
02797
02804
02811
02818
02824
.02878
.02885
.02892
02899
02907
03222
03229
03236
03244
03251
03329
03337
03345
03353
03360
03676
03684
03692
03699
03707
03816
03825
03833
-03842
03850
35
36
37
38
39
40
41
42
43
44
.02434
02440
02447
02453
02459
02494
02501
02508
02515
.02521
02831
02838
02845
02852
02859
02914
02921
.02928
02936
.02943
03258
03266
03273
03281
03288
03368
03376
-03384
03392
03400
03715
03723
03731
.03739
03747
03858
.03867
03875
.03884
03892
40
41
42
43
44
45
46
47
48
49
02466
.02472
02479
.02485
02492
02528
02535
02542
.02548
02555
02866
02873
02880
02887
-02894
.02950
.02958
02965
.02972
.02980
03295
03303
03310
03318
.03325
03408
03416
.03424
03432
03439
03754
03762
03770
03778
03786
03901
03909
03918
03927
.03935
45
46
47
48
49
50
51
52
53
54
.02498
02504
02511
02517
02524
02562
02569
02576
02582
02589
.02900
02907
.02914
02921
.02928
02987
02994
03002
.03009
03017
03333
03340
03347
03355
03362
03447
03455
03463
03471
03479
03794
03802
03810
03818
03826
.03944
.03952
03961
.03969
.03978
50
51
52
53
54
55
56
57
58
59
02530
02537
02543
02550
02556
02596
02603
02610
02617
.02624
02935
.02942
02949
02956
02963
.03024
.03032
.03039
03046
03054
03370
03377
03385
03392
03400
03487
03495
03503
03512
03520
.03834
.03842
03850
03858
03866
03987
.03995
04004
04013
04021
55
56
57
58
59
60
-02563
02630
02970
.03061
03407
03528
03874
.04030
60
280 NATURAL VERSED SINES AND EXTERNAL SEC.
16 17 18 19
'
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec
t
1
2
3
4
03874
-03882
-03890
03898
-03906
.04030
.04039
.04047
04056
.04065
04370
04378
04387
04395
. 04404
04569
.04578
04588
.04597
.04606
.04894
04903
04912
.04921
04930
.05146
.05156
.05166
05176
05186
05448
.05458
05467
.05477
05486
05762
05773
05783
05794
.05805
1
2
3
4
5
6
7
8
9
-03914
-03922
.03930
.03938
.03946
.04073
.04082
04091
.04100
04108
.04412
04421
.04429
04438
-04446
04616
04625
04635
. 04644
.04653
.04939
04948
04957
04967
.04976
05196
.05206
.05216
05226
.05236
05496
05505
.05515
05524
.05534
05815
05826
05836
05847
-05858
5
6
7
8
9
10
11
12
13
14
.03954
.03963
.03971
.03979
-03987
.04117
04126
.04135
.04144
.04152
04455
.04464
-04472
.04481
. 04489
.04663
04672
.04682
.04691
. 04700
04985
.04904
.05003
.05012
05021
.05246
.05256
.05266
.05276
.05286
.05543
.05553
05562
.05572
.05582
05869
05879
05890
05901
05911
10
11
12
13
14
15
16
17
18
19
.03995
- 04003
-04011
-04019
04028
.04161
.04170
.04179
.04188
-04197
04498
04507
04515
-04524
-04533
.04710
.04719
.04729
.04738
.04748
05030
05039
05048
05057
.05067
.05297
.05307
.05317
.05327
.05337
05591
.05601
05610
05620
.05630
.05922
.05933
05944
05955
.05965
15
16
17
18
19
20
21
22
23
24
-04036
- 04044
04052
04060
.04069
-04206
.04214
.04223
.04232
.04241
-04541
-04550
-04559
-04567
.04576
.04757
.04767
.04776
04786
.04795
.05076
.05085
05094
05103
05112
.05347
-05357
.05367
.05378
.05388
.05639
05649
.05658
05668
05678
05976
-05987
05998
06009
.06020
20
21
22
23
24
25
26
27
28
29
-04077
-04085
04093
04102
.04110
.04250
04259
.04268
04277
.04286
.04585
.04593
.04602
.04611
.04620
.04805
-04815
.04824
04834
. 04843
05122
.05131
05140
05149
05158
05398
.05408
.05418
.05429
.05439
.05687
05697
05707
05716
05726
06030
06041
-06052
.06063
.06074
25
26
27
28
29
30
31
32
33
34
.04118
04126
-04135
04143
-04151
.04295
.04304
.04313
04322
.04331
.04628
-04637
-04646
04655
.04663
.04853
04863
04872
04882
.04891
05168
.05177
05186
05195
.05205
05449
.05460
.05470
.05480
.05490
05736
05746
05755
.05765
.05775
.06085
06096
.06107
06118
.06129
30
31
32
33
34
35
36
37
38
39
-04159
-04168
-04176
04184
.04193
. 04340
04349
04358
04367
04376
.04672
04681
04690
.04699
.04707
.04901
04911
04920
04930
-04940
05214
.05223
05232
05242
05251
.05501
-05511
.05521
.05532
.05542
.05785
.05794
.05804
.05814
-05824
06140
06151
.06162
.06173
06184
35
36
37
38
-39
40
41
42
43
44
.04201
.04209
-04218
-04226
-04234
.04385
.04394
.04403
.04413
.04422
.04716
04725
-04734
-04743
04752
.04950
04959
04969
04979
.04989
05260
.05270
05279
05288
.05298
.05552
.05563
.05573
.05584
.05594
.05833
.05843
05853
.05863
.05873
06195
06206
.06217
-06228
06239
40
41
42
43
44
45
46
47
48
49
- 04243
.04251
04260
.04268
.04278
.04431
. 04440
.04449
-04458
.04468
-04760
-04769
04778
-04787
04796
.04998
05008
.05018
.05028
.05038
.05307
.05316
.05326
.05335
05344
05604
.05615
.05625
.05636
-05646
.05882
-05892
05902
05912
.05922
06250
.06261
-06272
.06283
-06295
45
46
47
48
49
50
51
52
53
54
04285
.04293
04302
-04310
-04319
.04477
04486
.04495
.04504
04514
04805
04814
04323
04832
-04841
05047
.05057
.05067
.05077
.05087
.05354
05363
.05373
05382
-05391
.05657
.05667
.05678
05688
05699
-05932
-05942
.05951
.05961
.05971
-06306
-06317
-06328
06339
-06350
50
51
52
53
54
55
56
57
58
59
-04327
.04336
-04344
-04353
-043RT
04523
.04532
04541
.04551
.04560
-04850
-04858
-04867
04876
04885
.05097
05107
.05116
.05126
.05136
.05401
.05410
.05420
05429
-05439
.05709
.05720
05730
.05741
-05751
05981
05991
06001
.06011
.06021
.06362
06373
06384
06305
-06407
55
56
57
58
_59
60
-04370
.04569
04894
.05146
05448
.05762
.06031
.06418
60
NATURAL VERSED SINES AND EXTERNAL SEC. 281
20 21 33 33
/
Vers.
Ex, sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
/
1
2
3
4
.06031
-06041
.06051
06061
06071
06418
.06429
06440
-06452
06463
-06642
06652
06663
06673
.06684
07115
.07126
07138
.07150
.07162
.07282
.07293
07303
07314
07325
07853
07866
07879
07892
07904
07950
07961
07972
07984
-07995
.08636
08649
08663
-08676
08690
1
2
3
4
5
6
7
8
9
06081
.06091
06101
.06111
06121
.06474
.06486
06497
06508
.06520
06694
06705
06715
06726
06736
.07174
.07186
07199
.07211
.07223
07336
07347
07358
-07369
.07380
07917
07930
07943
07955
.07968
-08006
-08018
-08029
-08041
-08052
08703
08717
08730
-08744
08757
5
6
8
9
10
11
12
13
14
.06131
06141
06151
.06161
.06171
06531
.06542
.06554
.06565
06577
.06747
06757
-06768
06778
-06789
07235
07247
07259
07271
.07283
07391
-07402
07413
07424
07435
.07981
07994
08006
.08019
08032
-08064
-08075
-08086
-08098
08109
08771
-08784
08798
-08811
-08825
10
11
12
13
14
15
16
17
18
19
06181
06191
06201
06211
.06221
06588
.06600
.06611
.06622
.06634
06799
-06810
-06820
-06831
.06841
07295
07307
-07320
07332
.07344
07446
07457
07468
07479
-07490
08045
08058
08071
-08084
08097
08121
-08132
.08144
-08153
08167
08839
.08852
-08866
.08880
08893
15
18
17
18
19
30
21
22
23
24
.06231
.06241
.06252
06262
.06272
.06645
06657
.06668
06680
.06691
-06852
-06863
.06873
06884
.06894
07356
07368
.07380
.07393
.07405
-07501
-07512
07523
07534
07545
08109
08122
08135
08148
.08161
08178
-08190
08201
-08213
-OC225
.08907
.08921
08934
-08948
.08962
20
21
22
23
24
25
26
27
28
29
06282
06292
06302
.06312
.06323
.06703
.06715
.06726
.06738
.06749
06905
.06916
-06926
-06937
-06948
.07417
.07429
.07442
.07454
.07486
07556
07568
-07579
.07590
.07601
.08174
08087
08200
08213
08226
-08236
08248
-08259
08271
0*282
.08975
-08989
-09003
09017
.09030
25
28
27
28
29
30
31
32
33
34
06333
06343
06353
.06363
06374
06761
.06773
.06784
.06796
.06807
-06958
.06969
-06980
06990
-07001
07479
07491
07503
.07516
.07528
0761-2
07623
07634
07645
07657
.08239
.08252
08265
08278
08291
-08294
-08306
08317
08329
-08340
09044
.09058
-09072
09086
.09099
30
31
32
33
34
35
36
37
38
39
06384
06394
06404
06415
.06425
06819
.06831
06843
.06854
.06866
.07012
07022
-07033
.07044
07055
.07540
.07553
07565
.07578
.07590
.07668
-07679
-07690
07701
07713
08305
.08318
.08331
.08344
.08357
-08352
-08364
-08375
08387
08399
09113
09127
-09141
09155
09169
35
36
37
38
39
40
41
42
43
44
.06435
-06445
06456
06466
.06476
-06878
06889
06901
.06913
.06925
-07065
07076
07087
.07098
07108
-07J02
07615
07627
07b40
07652
07724
07735
07746
07757
07769
.08370
.08383
08397
08410
08423
-08410
-08422
08434
.08445
08457
-09183
09197
09211
09224
09238
4O
41
42
48
44
45
46
47
48
49
06486
.06497
06507
06517
06528
.06936
-06948
06960
.06972
06984
07119
-07130
07141
07151
07162
07665
07677
07690
07702
.07715
07780
07791
07802
07814
07825
08436
. 08449
08463
-08476
.08489
08469
08481
08492
08504
08510
.09252
09266
09280
09294
09308
45
46
47
48
49
50
51
52
53
54
06538
06548
06559
06569
.06580
06995
.07007
-07019
07031
. 07043
-07173
-07184
.07195
-07206
-07216
.07727
07740
07752
07765
.07778
07836
07848
07859
.07870
07881
.08503
.08516
.08529
.08542
08556
08528
08539
.08551
08563
.08575
09323
.09337
.09351
09365
09379
50
51
52
53
54
55
56
57
58
-SL-
.06590
06600
06611
.06621
-06632
.07055
.07067
.07079
07091
-07103
.07227
.07238
-07249
07260
07271
07790
07803
07816
07828
07841
07893
.07904
.07915
07927
-07938
08569
-08582
-08596
-08069
-08623
08586
08598
08610
.08622
08634
.09393
.09407
09421
-09435
09449
55
56
57
58
59
OG
06642
07115
07282
07853
.07950
08636
08645
09464
60
282 NATURAL VERSED SINES AND EXTERNAL SEC.
34 35 36 27
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
/
2
3
4
08645
.08657
.08669
.08681
.08693
.09464
.09478
.09492
.09506
.09520
.09369
.09382
.09394
.09406
-09418
10338
.10353
10368
10383
.10398
10121
.10133
.10146
.10159
10172
11260
.11276
11292
.11308
11323
-10899
-10913
10926
10939
10952
.12233
1224&
.12266
12283
.12299
1
2
3
4
5
6
9
.08705
.08717
.08728
.08740
.08752
-09535
.09549
.09563
09577
.09592
09431
09443
.09455
09468
.09480
10413
10428
. 10443
10458
.10473
10184
10197
10210
.10223
-10236
11339
11355
11371
11387
11403
10965
10979
-10992
-11005
11019
12316
12333
12349
.12366
.12383
5
6
7
9
1O
11
12
13
14
.08764
.08776
.08788
088CO
.08812
.09608
.09620
.09635
.09649
.09663
.09493
.09505
09517
.09530
.09542
.10488
10503
10518
10533
.10549
10248
10261
10274
10287
10300
11419
.11435
11451
11467
11483
.11032
11045
11058
11072
.11085
. 12400
12416
12433
12450
.12467
10
11
12
13
14
15
16
17
18
19
.08824
.08836
.08848
.08860
-08872
.09678
.09692
.09707
.09721
-09735
09554
.09567
.09579
.09592
.09604
10564
10579
10594
.10609
.10625
.10313
-10326
-10338
-10351
10364
-11499
11515
-11531
.11547
-11563
-11098
-11112
-11125
-11138
-11152
-12484
.12501
12518
125b4
-12551
15
16
17
18
19
20
21
22
23
24
.08884
.08896
.08908
.08920
.08932
.09750
.09764
.09779
.09793
.09808
09617
09629
.09642
.09654
.09666
.10640
10655
10670
.10686
.10701
10377
.10390
. 10403
.10416
10429
-11579
-11595
11611
11627
.11643
11165
-11178
-11192
.11205
11218
-12568
.12585
.12602
.12619
12636
20
21
22
23
24
25
28
27
28
29
.08944
.08956
.08968
-08980
-08992
.09822
.09837
.09851
.09866
.09880
.09679
09691
.09704
.09716
.09729
.10716
.10731
10747
10762
.10777
. 10442
.10455
10468
10481
10494
11659
11675
.11691
.11708
.11724
.11232
11245
11259
-11272
-11285
12653
.12670
.12687
.12704
.12721
25
26
27
28
29
30
31
32
33
34
.09004
.09016
.09028
.09040
.09052
.09895
.09909
.09924
09939
.09953
.09741
09754
.09767
.09779
.09792
.10793
10808
10824
.10839
.10854
.10507
.10520
.10533
10546
.10559
.11740
.11756
.11772
-11789
11805
-11299
11312
-11326
-11339
.11353
.12738
12755
.12772
12789
12807
3O
31
32
33
34
35
36
37
38
39
.09064
.09076
.09089
.09101
.09113
.09968
.09982
.09997
.10012
.10026
.09804
09817
09829
.09842
.09854
10870
.10885
.10901
.10916
10932
.10572
.10585
.10598
10611
.10624
.11821
.11838
11854
11870
-11886
11366
11380
-11393
-11407
.11420
12824
.12841
.12858
U875
12892
35
36
37
38
39
40
41
42
43
44
.09125
.09137
09149
.09161
.09174
.10041
.10055
.10071
.10085
.10100
09867
.09880
.09892
.09905
.09918
-10947
10963
.10978
.10994
.11009
10637
10650
.10663
10676
10689
-11903
11919
11936
.11952
-11968
-11434
-11447
11461
11474
11488
12910
.12927
.12944
.12961
.12979
4O
41
42
43
44
45
46
47
48
49
.09186
-09198
09210
.09222
09234
.10115
.10130
.10144
.10159
.10174
09930
.09943
09955
.09968
09981
-11025
.11041
.11056
.11072
.11087
.10702
.10715
.10728
10741
10755
.11985
12001
12018
12034
12051
11501
11515
-11528
-11542
-11555
12996
13013
.13031
.13048
13065
45
46
47
48
49
50
51
52
53
54
09247
-09259
09271
09283
.09296
.10189
.10204
.10218
.10233
.10248
09993
10006
-10019
10032
. 10044
.11103
11119
11134
.11150
.11166
10768
10781
10794
10807
10820
.12067
- 12084
.12100
12117
12.133
-11569
-11583
-11596
11610
-11623
-13083
-13100
-13117
13135
13152
50
51
52
53
54
55
56
57
58
59
09308
.09320
09332
09345
09357
.10263
.10278
.10293
.10308
103?3
.10057
-10070
.10082
10095
10108
.11181
.11197
.11213
.11229
.11244
10833
10847
10860
10873
10886
12150
-12166
.12183
.12199
-12216
.11637
.11651
.11664
.11678
-11692
.13170
-13187
-13205
-13222
.13240
55
56
57
58
59
60
09369
.10338
10121
.11260
10899
12233
11705
-13257
60
NATURAL VERSED SINES AND EXTERNAL SEC.
28 39 30 31
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
t
1
2
3
4
11705
11719
11733
.11746
11760
13257
.13275
.13292
.13310
13327
.12538
12552
.12566
12580
12595
14335
14354
14372
.14391
. 14409
13397
13412
-13427
13441
-13456
. 15470
.15489
.15509
.15528
.15548
14283
14298
14313
14328
14343
16663
.16684
16704
16725
16745
1
2
3
4
5
6
7
8
9
11774
11787
11801
11815
.11828
13345
13362
.13380
13398
13415
12609
12623
12637
12651
.12665
. 14428
. 14446
14465
.14483
.14502
13470
13485
13499
13514
13529
.15567
15587
-15606
-15626
.15645
14358
14373
14388
. 14403
14418
16766
16786
.16806
16827
.16848
5
6
7
8
9
10
11
12
13
14
11842
.11856
11870
11883
.11897
-13433
13451
13468
.13486
13504
12679
.12694
.12708
12722
12736
14521
14539
14558
.14576
14595
.13543
13558
13573
13587
-13602
15665
15684
.15704
.15724
.15743
14433
14449
. 14464
. 14479
. 14494
.16868
16889
16909
16930
.16950
10
11
12
13
14
15
16
17
18
19
.11911
11925
11938
.11952
11966
13521
.13539
13557
13575
.13593
.12750
12765
12779
12793
12807
14614
14632
.14651
.14670
14689
13616
-13631
.13646
13660
13675
15763
.15782
.15802
.15822
.15841
.14509
.14524
.14539
14554
14569
16971
16992
17012
17033
.17054
15
16
17
18
,19
20
21
22
23
24
.11980
.11994
.12007
.12021
.12035
13610
.13628
.13646
.13664
.13682
12822
.12836
.12850
12864
12879
.14707
.14726
.14745
14764
14782
13690
13705
13719
13734
13749
.15861
- -15881
.15901
.15920
.15940
.14584
14599
14615
. 14630
14645 .
17075
17095
.17116
17137
.17158
40
21
22
23
24
25
26
27
28
29
-12049
.12063
12077
12091
.12104
13700
.13718
.13735
.13753
.13771
12893
.12907
12921
12936
.12950
14801
.14820
14839
.14858
.14877
13763
13778
13793
13808
13822
.15960
.15980
.16000
.16019
-16039
14660
14675
-14690
.14706
.14721
.17178
.17199
.17220
17241
.17262
25
26
27
28
29
30
31
32
33
34
12118
12132
12146
12160
12174
.13789
.13807
.13825
.13843
13861
12964
12979
.12993
.13007
.13022
14896
.14914
14933
14952
14971
13837
13852
-13867
13881
13896
-16059
-16079
.16099
.16119
.16139
14736
.14751
14766
14782
.14797
17283
17304
-17325
.17346
.17367
30
31
32
33
34
35
36
37
38
39
12188
12202
12216
12230
.12244
.13879
.13897
13916
.13934
13952
.13036
.13051
.13065
.13079
. 13094
.14990
.15009
.15028
15047
.15066
13911
13926
13941
13955
.58970
.16159
16179
.16199
16219
.16239
.14812
.14827
.14843
14858
14873
-17388
17409
. 1 7430
17451
77472
35
36
37
38
39
40
41
42
43
44
12257
12271
12285
.12299
.12313
.13970
.13988
14006
. 14024
. 14042
-13108
-13122
.13137
13151
.13166
15085
15105
.15124
15143
.15162
13985
14000
-14015
14030
14044
.16259
.16279
.16299
16319
-16339
.14888
. 14904
14819
.14934
.14949
17493
17514
17535
17556
.17577
4O
41
42
43
44
45
48
47
48
49
12327
]234i
.12355
.12369
12383
14061
14079
14097
14115
.14134
13180
13195
.13209
.13223
.13238
.15181
15200
15219
15239
.15258
14059
14074
14089
14104
14119
16359
-16380
- 16400
-16420
16440
14965
.14980
-14995
-15011
-15026
17598
17620
.17641
.17662
-176S3
45
46
47
48
49
50
51
52
53
54
1239*7
12411
.12425
.12439
12454
.14152
.14170
14188
14207
.14225
.13252
.13267
.13281
13296
13310
.15277
.15296
.15315
.15335
15354
14134
14149
14164
14179
14194
.16460'
16481
.16501
16521
.16541
15041
-15057
-15072
-15087
-15103
17704
17726
17747
17768
17790
50
51
52
53
54
55
56
57
58
59
12468
12482
12496
.12510
.12524
.14243
14262
14280
.14299
14317
13325
.13339
13354
.13368
.13383
15373
.15393
.15412
15431
.15451
14208
14223
14238
-14253
.14268
.16562
.16582
.16602
16623
-16643
.15118
15134
-15149
-15164
15180
17811
.17832
.17854
.17875
17896
55
56
57
58
-59
60
.12538
14335
.13397
15470
-14283
16663
15195
17918
60
284 NATURAL VERSED SINES AND EXTERNAL SEC.
33 33 34 35
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
1
2
3
4
.15195
.15211
15226
.15241
-15257
17918
17939
17961
17982
. 18004
.16133
16149
16165
16181
16196
19236
19259
19281
19304
19327
17096
17113
17129
.17145
17161
20622
20645
20669
.20693
20717
18085
-18101
18118
18135
18152
-22077
.22102
.22127
22152
22177
O
1
3
4
5
7
8
.15272
.15288
.15303
.15319
.15334
.18025
18047
18068
18090
18111
16212
.16228
-16244
16260
16276
. 19349
19372
19394
19417
-19440
17178
.17194
17210
17227
17243
20740
.20764
20788
20812
20836
18168
18185
18202
18218
18235
- 22202
-22227
-22252
-22277
-22302
5
6
7
8
9
iO
11
12
13
14
.15350
.15365
.15381
.15396
.15412
18133
.18155
.18176
.18198
.18220
16292
16308
16324
16340
-16355
-19463
-19485
-19508
.19531
19554
17259
17276
17292
17308
17325
.20859
20883
20907
20931
.20955
18252
18269
18286
18302
18319
-22327
-22352
-22377
. 22402
22428
IO
11
12
13
14
15
16
17
18
19
.15427
.15443
.15458
15474
.15489
.18241
18263
18285
.18307
.18328
-16371
16387
16403
16419
16435
19576
.19599
.19622
19645
19668
17341
17357
17374
-17390
.17407
20979
-21003
-21027
-21051
-21075
18336
18353
18369
18386
.18403
.22453
22478
.22503
.22528
22554
15
16
17
18
19
20
21
22
23
24
15505
15520
.15536
15552
.15567
.18350
18372
.18394
18416
.18437
.16451
16467
16483
16499
16515
.19691
.19713
-19736
.19759
19782
17423
17439
17456
17472
17489
-21099
21123
-21147
21171
.21195
18420
18437
18454
18470
18487
-22579
-22604
-22629
22655
22680
20
21
22
23
24
25
26
27
28
29
15583
.15598
15614
15630
15645
.18459
.18481
.18503
18525
.18547
16531
16547
16563
16579
16595
.19805
.19828
.19851
19874
.19897
17505
-17522
17538
17554
-17571
21220
21244
21268
21292
21316
18504
18521
18538
18555
.18572
22706
22731
22756
22782
22807
25
26
27
28
29
30
31
32
33
34
.15661
.15676
.15692
15708
15723
.18569
.18591
.18613
.18635
.18657
16611
16627
16644
16660
16676
.19920
.19944
19967
19990
.20013
17587
17604
17620
17637
17653
21341
21365
21389
21414
.21438
18588
18605
18622
18639
18656
22833
22858
22884
22909
.22935
30
31
32
33
34
35
36
87
38
39
.15739
.15755
.15770
.15786
-15802
.18679
18701
18723
18745
18767
16692
16708
16724
16740
.16756
.20036
20059
-20083
-20106
.20129
17670
17686
17703
17719
.17736
21462
21487
.21511
21535
21560
18673
18690
18707
18724
.18741
.22960
.22986
23012
23037
23063
35
36
37
38
39
40
41
42
43
44
.15818
-15833
.15849
.15865
15880
.18790
18812
.18834
18856
.18878
16772
16788
16805
16821
.16837
.20152
20176
20199
20222
.20246
17752
17769
17786
17802
.17819
21584
21609
21633
21658
21682
-18758
-18775
18792
18809
18826
23089
23114
23140
23166
23192
40
41
42
43
44
45
46
47
48
49
15896
.15912
15928
15943
15959
.18901
18923
18945
18967
.18990
16853
16869
16885
16902
16918
.20269
.20292
.20316
.20339
.20363
17835
17852
17868
17885
17902
21707
21731
-21756
.21781
.21805
18843
.18860
.18877
18894
.18911
23217
23243
23269
.23295
.23321
45
46
47
48
49
50
51
52
53
54
15975
.15991
16008
16022
.18038
.19012
.19034
.19057
.19079
.19102
.16934
16950
16966
16983
.16999
20386
.20410
.20433
20457
. 20480
17918
17935
17952
17968
17985
.21830
.21855
.21879
21904
.21929
18928
18945
18962
18979
18996
.23347
.23373
-23399
23424
-23450
50
51
52
53
54
55
58
57
58
59
16054
16070
16085
16101
16117
.19124
.19146
.19169
.19191
19214
.17015
.17031
.17047
17064
17080
.20504
20527
.20551
.20575
.20598
18001
18018
18035
18051
18068
21953
.21978
22003
.22028
22053
19013
19030
19047
19064
19081
23476
23502
23529
.23555
.23581
55
56
57
58
59
60
16133
.19236
.17096
20622
18085
-22077
19098
i
23607
60
NATURAL VERSED SINES AND EXTERNAL SEC. 285
36 C
37
38 e
39
*
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
t
o
1
2
3
4
.19098
.19115
19133
.19150
.19167
23607
23633
23659
23685
23711
20136
20154
.20171
.20189
20207
.25214
25241
25269
25296
25324
21199
21217
21235
.21253
21271
26902
26931
.26960
.26988
27017
22285
22304
22322
22340
22359
28676
28706
28737
28767
28797
-5
2
4
5
6
7
9
.19184
19201
19218
.19235
19252
23738
.23764
.23790
23816
.23843
.20224
.20242
.20259
.20277
.20294
25351
25379
25406
25434
25462
21289
21307
21324
21342
.21360
27046
27075
27104
27133
27162
22377
22395
22414
22432
22450
28828
-28858
.28889
-28919
-28950
5
8
9
10
11
12
13
14
19270
19287
19304
19321
.19338
.23869
23895
23922
23948
23975
20312
.20329
20347
20365
.20382
25489
.25517
25545
25572
25600
21378
21396
21414
21432
21450
27191
27221
27250
27279
27308
22469
.22487
22506
22524
22542
28980
.29011
29042
29072
29103
1O
11
12
13
14
15
16
17
18
19
19356
19373
19390
19407
19424
.24001
.24028
24054
24081
.24107
. 20400
.20417
.20435
20453
.20470
25628
.25656
25683
25711
.25739
21468.
21486
21504
21522
.21540
27337
27366
27396
27425
.27454
.22561
.22579
22598
.22616
22634
29133
29164
29195
29226
29256
15
18
17
18
19
20
21
22
23
24
19442
.19459
.19476
19493
.19511
.24134
24160
24187
.24213
24240
.20488
20506
20523
.20541
20559
.25767
25795
25823
25851
25879
21558
21576
.21595
21613
21631
.27483
27513
27542
27572
27601
-22653
22671
22690
22708
22727
29287
29318
29349
29380
.29411
2O
21
22
23
24
25
26
27
28
29
.19528
.19545
19562
.19580
.19597
24267
.24293
24320
24347
-24373
20576
20594
.20612
20629
.20647
25907
25935
25963
25991
26019
21649
21667
21685
21703
21721
27630
-27660
27689
27719
-27748
22745
22764
22782
.22801
22819
. 29442
29473
29504
29535
29566
25
26
27
28
29
30
31
32
33
34
19614
19632
.19649
19666
19684
. 24400
24427
. 24454
24481
24508
.20665
20682
20700
.20718
20736
.26047
26075
26104
26132
26160
21739
21757
21775
.21794
21812
-27778
-27807
-27837
-27867
-27896
22838
-22856
22875
22893
22912
29597
.29628
29659
29690
29721
30
31
32
33
34
35
36
37
38
39
.19701
.19718
19736
.19753
.19770
24534
24561
24588
-24615
24642
.20753
.20771
.20789
.20807
.20824
26188
26216
26245
26273
.26301
21830
21848
21866
21884
.21902
27926
.27956
27985
28015
.28045
22930
.22949
22967
.22986
-23004
29752
29784
29815
29846
.29877
35
36
37
38
39
40
41
42
43
44
.19788
.19805
19822
19840
-19857
24669
24696
24723
24750
.24777
.20842
20860
20878
.20895
.20913
.26330
26358
26387
26415
26443
.21921
21939
21957
21975
21993
28075
28105
28134
28164
.28194
23023
23041
.23060
23079
.23097
29909
29940
29971
- 30003
30034
4O
41
42
43
44
45
46
47
48
49
.19875
.19892
.19909
.19927
19944
24804
.24832
24859
24886
24913
20931
.20949
20967
20985
.21002
26472
.26500
26529
.26557
.26586
22012
22030
22048
-22066
.22084
28224
28254
28284
28314
.28344
23116
.23134
23153
23172
.23190
30066
30097
30129
30160
30192
45
46
47
48
49
5O
51
52
53
54
19962
.19979
19997
20014
.20032
. 24940
24967
24995
25022
-25049
21020
.21038
21056
21074
.21092
.26615
26643
26672
.26701
26729
22103
22121
.22139
22157
22176
28374 '
. 28404
.28434
.28464
.28495
23209
23228
.23246
23265
23283
30223
30255
30287
30318
30350
50
51
52
53
54
55
56
57
58
59
. 20049
.20066
20084
20101
20119
25077
.25104
.25131
25159
.25186
21109
21127
21145
21163
.21181
26758
26787
.26815
26844
.26873
22194
22212
22231
22249
.22267
28525
.28555
28585
28615
.28646
23302
23321
.23339
23358
-23377
30382
30413
30445
30477
30509
55
56
57
56
59
60
.20136
.25214
21199
.26902
22285
.28676
23396
30541
60
286 NATURAL VERSED SINES AND EXTERNAL SEC.
40 41 42 43
/
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
t
o
1
2
3
4
-23396
23414
.23433
-23452
.23470
30541
.30573
.30605
.30636
.30668
.24529
.24548
24567
.24586
24605
.32501
.32535
.32568
32602
.32636
25686
.25705
25724
25744
25763
34563
.34599
.34634
.34669
.34704
26865
26884
.26904
26924
26944
36733
.36770
.36807
.36844
.36831
O
1
2
a
5
6
7
8
o
.23489
23508
23527
.23545
.23564
.30700
30732
.30764
.30796
.30829
.24625
24644
.24663
.24682
.24701
.32669
.32703
.32737
32770
.32804
25783
.25802
25822
25841
25861
.34740
.34775
.34811
34846
34882
26964
26984
.27004
27024
27043
.36919
.36956
.36993
37030
.37068
5
6
7
8
9
10
11
12
13
14
.23583
.23602
23620
23639
.23658
.30861
.30893
.30925
.30957
.30989
.24720
.24739
.24759
.24778
.24797
.32838
.32872
.32905
.32939
.32973
.25880
25900
25920
25939
25959
34917
.34953
.34988
35024
.35060
27063
27083
.27103
.27123
.27143
.37105
37143
37180
.37218
37255
1O
11
12
13
14
15
16
17
18
19
.23677
.23696
23714
23733
-23752
.31022
.31054
.31086
.31119
.31151
.24816
.24835
.24854
.24874
.24893
33007
.33041
33075
.33109
.33143
.25978
25998
26017
26037
26056
.35095
.35131
.35167
.35203
.35238
.27163
27183
27203
.27223
27243
.37293
.37330
.37368
.37406
37443
15
18
17
18
19
20
21
22
23
?A
23771
.23790
.23808
.23827
.23846
.31183
.31216
.31248
.31281
.31313
24912
.24931
.24950
.24970
.24989
.33177
.33211
.33245
.33279
.33314
.26076
26096
.26115
.26135
.26154
35274
.35310
35346
.35382
.35418
.27263
.27283
.27303
.27323
.27343
37481
.37519
.37556
.37594
.37632
20
21
22
23
24
25
26
27
28
29
.23865
-23884
.23903
-23922
-23941
.31346
.31378
.31411
.31443
.31476
.25008
.25027
.25047
.25066
.25085
.33348
.33382
.33416
.33451
.33485
.26174
.26194
.26213
.26233
.26253
.35454
.35490
.35526
35562
.35598
27363
27383
27403
27423
. 27443
.37670
.37708
.37746
.37784
37822
25
26
27
28
29
30
31
32
33
34
.23959
.23978
.23997
.24016
-24035
31509
31541
.31574
.31607
.31640
.25104
.25124
.25143
.25162
.25182
.33519
.33554
.33588
.33622
.33657
.26272
.26292
.26312
26331
.26351
.35634
35670
.35707
.35743
.35779
.27463
.27483
.27503
.27523
.27543
.37860
.37898
.37936
.37974
.38012
30
31
32
33
34
35
36
37
38
39
.24054
-24073
-24092
.24111
.24130
.31672
.31705
.31738
.31771
.31804
.25201
.25220
.25240
.25259
.25278
.33691
.33726
.33760
.33795
-33830
.26371
26390
26410
26430
26449
.35815
.35852
.35888
.35924
35961
.27563
.27583
.27603
.27623
.27643
.38051
.38089
.38127
.38165
.38204
35
36
37
38
39
40
41
42
43
44
-24149
.24168
.24187
.24206
-24225
.31837
.31870
.31903
.31936
.31969
.25297
.25317
.25336
.25356
.25375
.33864
.33899
.33934
.33968
.34003
26469
26489
.26509
.26528
.26548
.35997
.36034
.36070
.36107
.36143
27663
.27683
27703
27723
.27743
.38242
.38280
.38319
.38357
38396
40
41
42
43
44
45
46
47
48
49
. 24244
.24262
.24281
24300
-24320
.32002
.32035
.32068
.32101
.32134
.25394
25414
.25433
.25452
.25472
.34038
.34073
.34108
.34142
.34177
.26568
26588
.26607
.26627
.26647
.36180
.36217
.36253
.36290
36327
27764
.27784
.27804
27824
.27844
38434
.38473
.38512
.38550
38589
45
46
47
48
49
50
51
52
53
54
24339
.24358
.24377
.24396
244T5
.32168
.32201
.32234
.32267
.32301
.25491
.25511
25530
25549
.25569
34212
. 34247
.34282
.34317
.34352
.26667
-26686
26706
.26726
.26746
36363
.36400
.36437
.36474
36511
27864
.27884
.27905
.27925
.27945
.38628
38666
.38705
.38744
.38783
50
51
52
53
54
55
56
57
58
59
. 24434
.24453
.24472
.24491
-24510
.32334
.32368
.32401
.32434
32468
.25588
.25608
.25627
.25647
.25666
.34387
.34423
.34458
.34493
.34528
26766
.26785
.26805
.26825
.26845
.36548
36585
.36622
36669
36696
.27965
.27985
28005
.28026
.28046
.38822
.38860
38899
38938
38977
55
56
57
58
59
60
.24529
.32501
.25686
.34563
.26865
.36733
.28066
.39016
6O
NATURAL VERSED SINES AND EXTERNAL SEC. 287
44 45 46 47
1
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
1
2
3
4
28066
.28086
.28106
28127
28147
.39016
.39055
.39095
.39134
.39173
-29289
.29310
29330
29351
.29372
.41421
.41463
.41504
.41545
41586
30534
30555
.30576
30597
30618
.43956
.43999
.44042
.44086
44129
31800
.31821
31843
31864
.31885
46628
46674
46719
46765
46811
1
2
3
4
5
6
7
8
9
.28167
.28187
.28208
.28228
28248
.39212
.39251
.39291
.39330
39369
29392
.29413
29433
.29454
29475
.41627
.41669
.41710
41752
41793
.30639
.30660
30681
.30702
.30723
44173
.44217
.44260
.44304
.44347
.31907
31928
31949
31971
.31392
46857
46903
46949
.46995
-47041
5
6
7
8
9
10
11
12
13
14
.28268
28289
.28309
.28329
.28350
.39409
.39448
39487
.39527
39566
.29495
.29516
29537
29557
29578
.41835
.41876
.41918
41959
42001
.30744
.30765
.30786
.30807
.30828
.44391
44435
.44479
.44523
44567
32013
.32035
32056
-32077
-32099
47087
.47134
47180
.47226
-47272
10
11
12
13
14
15
16
17
18
19
28370
.28390
.28410
28431
28451
.39606
.39646
.39685
.39725
39764
.29599
.29619
29640
29661
29681
. 42042
.42084
.42126
42168
-42210
.30849
.30870
-30891
-30912
-30933
44610
.44654
.44698
.44742
-44787
32120
.32141
32163
-32184
32205
47319
.47365
47411
.47458
.47504
15
16
17
18
.19
20
21
22
23
24
.28471
.28492
.28512
.28532
.28553
39804
.39844
.39884
.39924
-39963
29702
.29723
29743
.29764
29785
42251
.42293
.42335
.42377
.42419
-30954
-30975
-30996
-31017
.31038
44831
.44875
.44919
.44963
45C07
-32227
32248
32270
32291
32312
47551
47598
.47644
47691
-47738
20
21
22
23
24
25
26
27
28
29
.28573
.28593
.28614
.28634
28655
. 40003
.40043
.40083
.40123
.40163
.29805
.29826
.29847
29868
-29888
.42461
.42503
.42545
.42587
.42630
.31059
31080
31101
31122
-31143
.45052
.45096
.45141
.45185
45229
32334
32355
32377
32398
32420
.47784
47831
47878
47925
-47972
25
26
27
28
29
30
31
32
33
34
.28675
.28695
.28716
.28736
-28757
.40203
.40243
.40283
.40324
40364
.29909
29930
.29951
.29971
-29992
.42672
.42714
.42756
.42799
.42841
31165
.31186
31207
31228
.31249
.45274
.45319
45363
.45408
.45452
32441
-32462
32484
32505
32527
-48019
48066
.48113
48160
-48207
30
31
32
33
34
35
36
37
38
39
.28777
28797
28818
.28838
.28859
. 40404
.40444
.40485
.40525
.40565
30013
30034
-30054
30075
-30096
42883
42926
.42968
43011
-43053
31270
-31291
-31312
.31334
.31355
45497
.45542
.45587
.45631
-45676
.32548
-32570
-32591
32613
.32634
48254
48301
.48349
48396
.48443
35
36
37
38
39
40
41
42
48
44
.28879
.28900
.28920
28941
.28961
.40606
.40646
.40687
.40727
.40768
30117
30138
.30158
.30179
30200
.43096
.43139
.43181
43224
43267
31376
31397
31418
.31439
.31461
45721
.45766
.45811
.45856
45901
32656
-32677
-32699
32720
-32742
48491
48538
48586
48633
48681
40
41
42
43
44
45
46
47
48
49
.28981
29002
29022
.29043
.29063
.40808
.40849
.40890
.40930
.40971
30221
-30242
-30263
.30283
.30304
.43310
.43352
.43395
43438
.43481
-31482
31503
31524
31545
.31567
.45946
45992
-46037
46082
-46127
-32763
-32785
32806
-32828
.32849
.48728
.48776
48824
48871
48919
45
46
47
48
49
50
51
52
53
54
29084
29104
.29125
.29145
29166
.41012
.41053
.41093
.41134
.41175
-30325
-30346
-30367
-30388
. 30409
.43524
.43567
.43610
.43653
.43696
31588
31609
31630
31651
31673
.46173
46218
46263
46309
46354
32871
32893
32914
32936
-32P57
48967
49015
.49063
.49111,
.49159
50
51
52
53
54
55
56
57
58
5fl
29187
29207
29228
29248
29269
.41216
.41257
.41298
.41339
.41380
30430
.30451
30471
-30492
-30513
.43739
.43783
.43826
-43869
.43912
31694
31715
.31736
.31758
.31779
.46400
.46445
.46491
.46537
.46582
32979
33001
33022
33044
3SOB5
.49207
49255
.49303
49351
.49399
55
56
57
58
59
60
.29289
.41421
.30534
43956
31800
.46628
33087
49448
60
288 NATURAL VERSED SINES AND EXTERNAL SEC.
48 49 50 51
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
i
2
4
33087
33109
33130
33152
33173
.49448
.49496
.49544
.49593
.49641
34394
34416
34438
34460
34482
.52425
.52476
.52527
.52579
.52630
35721
35744
35766
35788
35810
55572
55626
55680
.55734
55789
37068
37091
37113
37136
37158
58902
.58959
59016
59073
59130
O
1
2
3
4
5
6
7
8
9
33195
33217
33238
33260
33282
.49690
49738
.49787
49835
.49884
34504
34526
34548
34570
34592
52681
.52732
.52784
.52835
.52886
35833
35855
35877
35900
35922
.55843
.55897
.55951
56005
56060
37181
37204
37226
37249
37272
59188
59245
59302
59360
-59418
5
6
7
8
9
10
11
12
13
14
33303
33325
33347
33368
33390
.49933
49981
.50030
.50079
.50128
34614
34638
34658
34680
34702
52938
.52989
.53041
.53092
.53144
35944
35967
35989
36011
36034
56114
.56169
.56223
.56278
.56332
37294
37317
37340
37362
37385
59475
.59533
59590
59648
.59706
10
11
12
13
14
15
16
17
18
19
33412
33434
33455
33477
33499
.50177
.50226
50275
50324
50373
34724
34748
34768
34790
34812
53196
.53247
.53299
53351
.53403
36056
36078
36101
36123
3S146
56387
. 56442
56497
.56551
.56606
37408
37430
37453
37476
37498
.59764
59822
.59880
59938
.59996
15
16
17
18
19
20
21
22
23
24
33520
33542
33584
33586
33807
50422
50471
.50521
.50570
.50819
34834
34856
34878
34900
34923
.53455
53507
53559
.53611
.53663
3G168
36190
36213
36235
38258
56661
56716
.56771
.56826
.56881
37521
37544
37567
37589
37612
.60054
60112
60171
.60229
60287
30
21
22
23
24
25
26
27
28
29
33629
33651
33873
33694
33716
50669
.50718
.50767
.50817
.50866
34945
34967
34989
35011
35033
53715
.53768
.53820
.53872
.53924
36280
36302
36325
36347
36370
.56937
.56992
.57047
.57103
.57158
37635
37658
37680
37703
37726
.60346
.60404
60463
60521
.60580
25
28
27
28
29
30
31
32
33
34
33738
33760
33782
33803
33825
.50916
50966
51015
.51085
.51115
35055
35077
35099
35122
35144
.53977
54029
.54082
54134
.54187
36392
36415
36437
36460
36482
.57213
57269
57324
57380
.57436
37749
37771
37794
37817
.37840
60639
60698
60756
60815
60874
30
31
32
33
34
35
38
37
38
39
33847
33869
33891
33912
.33934
.51165
.51215
.51265
.51314
.51364
35166
35188
35210
35232
35254
. 54240
54292
54345
.54398
.54451
36504
36527
36549
36572
36594
57491
.57547
.57603
.57659
.57715
.37862
37885
37908
.37931
.37954
.60933
.60992
.61051
.61111
.61170
35
36
37
38
-39
40
41
42
43
44
33956
.33978
.34000
.34022
.34044
.51415
.51465
51515
.51585
.51615
35277
35299
35321
35343
35365
.54504
.54557
54610
.54663
.54716
36617
36639
36662
36684
36707
57771
.57827
.57883
.57939
57995
.37976
37999
38022
.38045
.38068
.61229
.61288
61348
.61407
.61467
40
41
42
43
44
45
46
47
48
49
.34065
-34087
.34109
34131
.34153
.51665
51716
.51768
.51817
.51867
35388
35410
35432
-35454
.35478
54769
.54822
54876
- 54929
54982
36729
36752
36775
36797
.36820
.58051
.58108
.58164
.58221
.58277
38091
38113
38136
38159
.38182
.61526
.61586
61646
.61705
.61765
45
48
47
48
49
50
51
52
53
54
34175
34197
34219
34241
34282
51918
.51968
.52019
.52069
52120
35499
-35521
35543
35565
35588
55036
.55089
55143
.55198
.55250
36842
36865
36887
36910
36932
.58333
.58390
.58447
.58503
.58560
.38205
38228
38251
38274
38298
.61825
.61885
61945
62005
62065
50
51
n
54
55
56
57
58
59_
34284
34308
34328
34350
-34372
.52171
.52222
.52273
.52323
.52374
.35610
35632
.35654
.35677
35699
.55303
.55357
.55411
.55465
.55518
.36955
36978
37000
37023
37045
.58617
.58674
58731
58788
58845
38319
38342
.38365
.38388
38411
62125
.62185
.62246
62306
.62366
55
56
57
58
59
60
34394
.52425
35721
.55572
37068
58902
38434
.62427
CO
NATURAL VERSED SINES AND EXTERNAL SEC. 289
53 53 54 55
/
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
)
1
2
3
4
38434
.38457
.38480
.38503
.38526
.62427
.62487
. 62548
.62609
. 62669
.39819
. 39842
.39865
39888
39911
.66164
.66228
.66292
66357
66421
.41221
.41245
.41269
-41292
.41316
.70130
.70198
.70267
70335
. 70403
42642
42666
-42690
-42714
42738
. 74345
74417
74490
74562
74635
1
2
3
4
5
6
7
8
9
38549
38571
38594
38617
38640
.62730
.62791
.62852
.62913
62974
39935
39958
39981
40005
40028
.66486
.66550
.66615
66679
66744
.41339
-41363
.41386
-41410
-41433
.70472
70540
.70609
70677
. 70746
-42762
-42785
42809
-42833
-42857
74708
.74781
74854
74927
.75000
5
6
7
8
9
10
11
12
13
14
38663
38686
38709
38732
38755
63035
63096
.63157
.63218
.63279
40051
40074
40098
40121
40144
.66809
66873
-66938
67003
.67068
.41457
41481
-41504
-41528
-41551
70815
70884
70953
71022
.71091
42881
-42905
42929
42953
42976
75073
75146
.75219
.75293
-75366
10
11
12
13
14
15
16
17
18
IL.
.38778
38801
38824
.38847
.38870
63341
63402
.63464
63525
63587
40168
40191
.40214
.40237
.40261
.67133
.67199
.67264
.67329
.67394
.41575
.41599
.41622
.41646
.41670
71160
71229
71298
.71368
71437
43000
-43024
43048
-43072
.43096
. 75440
.75513
.75587
.75661
75734
15
16
17
18
J9
30
21
22
23
,24
.38893
.38916
38939
.38962
.38985
63648
.63710
.63772
63834
63895
.40284
.40307
.40331
.40354
.40378
67460
.67525
67591
67656
.67722
41693
.41717
-41740
.41764
-41788
71506
.71576
71646
.71715
.71785
43120
.43144
.43168
-43192
43216
.75808
75882
.75956
.76031
76105
2O
21
22
23
24
25
26
27
28
29
.39009
.39032
.39055
.39078
39101
63957
.64019
64081
64144
.64208
.40401
.40424
40448
40471
.40494
.67788
.67853
67919
.67985
68051
.41811
.41835
.41859
.41882
.41906
.71855
.71925
71995
.72065
72135
43240
43264
-43287
-43311
-43335
76179
76253
76328
. 76402
76477
25
26
27
28
29
30
31
32
33
34
.39124
39147
.39170
.39193
.39216
.64268
.64330
.64393
.64455
64518
-40518
40541
40565
40588
.40611
.68117
.68183
.68250
.68316
.68382
.41930
.41953
.41977
42001
-42024
. 72205
. 72275
.72346
.72416
72487
43359
.43383
. 43407
43431
-43455
76552
.76626
.76701
.76776
76851
30
31
32
33
34
35
36
37
38
SSL
.39239
.39262
39286
39309
.39332
.64580
64643
.64705
.64768
.64831
.40635
.40658
40682
.40705
-40728
68449
68515
.68582
.68648
-68715
-42048
-42072
-42096
-42119
-42143
72557
.72628
. 72698
.72769
. 72840
43479
-43503
-43527
43551
.43575
76926
.77001
.77077
.77152
77227
35
36
37
38
39
40
41
42
43
,44
.39355
39378
.39401
.39424
.39447
. 64894
64957
.65020
.65083
.65146
.40752
.40775
.40799
40822
-40846
68782
.68848
68915
.68982
-69049
-42167
.42191
.42214
.42238
-42262
.72911
.72982
.73053
.73124
.73195
-43599
-43623
43647
-43671
.43695
.77303
.77378
77454
77530
77606
40
41
42
43
44
45
46
47
48
49
39471
.39494
.39517
-39540
39563
65209
.65272
.65336
.65399
.65462
.40869
.40893
.40916
-40939
.40963
.69116
.69183
.69250
.69318
.69385
.42285
.42309
.42333
.42357
.42381
.73267
.73338
.73409
.73481
.73552
43720
43744
43768
43792
43816
.77681
.77757
.77833
.77910
77986
45
46
47
48
49
50
51
52
53
54
-39586
39610
.39633
.39656
.39679
.65526
.65589
.65653
.65717
.65780
-40986
.41010
41033
.41057
.41080
. 69452
.69520
.69587
.69655
.69723
.42404
.42428
.42452
.42476
.42499
.73624
.73696
.73768
.73840
73911
43840
.43864
.43888
.43912 '
-43936
78062
.78138
.78215
.78291
.78368
50
51
52
53
54
55
56
57
58
5J
.39702
39726
.39749
.39772
-39795
. 65844
65C08
.65972
.66036
.66100
.41104
.41127
.41151
41174
.41198
.89790
.69858
.69926
.69994
.70062
42523
.42547
.42571
.42595
.42619
.73983
.74056
.74128
. 74200
.74272
-43960
-43984
-44008
.44032
.44057
. 78445
.78521
.78598
.78675
.78752
55
56
57
58
59
60
.39819
.66164
.41221
.70130
.42642
.74345
.44081
.78829
6Q
290 NATURAL VERSED SINES AND EXTERNAL SEC.
56 57 58 59
f
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
1
1
2
3
4
.44081
.44105
.44129
44153
.44177
.78829
.78906
-78984
.79061
79138
-45536
-45560
-45585
45609
-45634
.83608
83690
.83773
.83855
.83938
-47008
-47033
-47057
-47082
47107
88708
88796
88884
88972
-89060
-48496
-48521
-48546
.48571
-48596
94160
94254
.94349
- 94443
94537
1
2
3
4
5
6
7
8
9
.44201
.44225
.44250
44274
44298
79216
79293
.79371
.79449
.79527
-45658
-45683
-45707
-45731
45756
84020
84103
84186
.84269
.84352
-47131
47156
47181
-47206
-47230
89148
89237
.89325
89414
-89503
-48621
-48646
-48671
-48696
-48721
94632
94726
94821
94916
95011
5
6
7
8
9
10
11
12
13
14
.44322
.44346
.44370
-44395
-44419
79604
79682
.79761
.79839
.79917
-45780
-45805
45829
45854
.45878
84435
84518
84601
84685
.84768
-47255
-47280
47304
47329
47354
89591
89680
89769
89858
89948
-48746
-48771
-48796
-48821
-48846
-95106
-95201
-95296
95392
.95487
10
11
12
13
14
15
16
17
18
19
- 44443
-44467
44491
-44516
-44540
.79995
.80074
.80152
.80231
-80309
45903
-45927
-45951
-45976
-46000
84852
.84935
.85019
85103
-85187
47379
47403
47428
47453
-47478
-90037
-90126
-90216
.90305
-90395
48871
48896
48921
48946
-48971
95583
95678
95774
95870
95966
15
16
17
18
19
20
21
22
23
24
-44564
-44588
-44612
-44637
-44661
.80388
80467
.80546
80625
.80704
-46025
-46049
-46074
-46098
.46123
85271
85355
85439
85523
-85608
-47502
47527
-47552
-47577
-47601
-90485
90575
.90665
.90755
90845
.48996
49021
-49046
49071
.49096
96062
96158
96255
.96351
96448
20
21
22
23
24
25
26
27
28
29
-44885
-44709
-44734
-44758
-44782
.80783
80862
.80942
.81021
81101
46147
46172
-46196
-46221
-46246
.85692
85777
.85861
85946
.86031
-47626
-47651
-47676
-47701
-47725
90935
91026
91116
. 91207
91297
-49121
.49146
-49171
-49196
-49221
.96544
.96641
.96738
.96835
.96932
25
26
27
28
20
30
31
32
33
34
-44806
44831
-44855
-44879
-44903
.81180
81260
81340
81419
.81499
-46270
-46295
-46319
46344
46368
.86116
86201
86286
.86371
86457
-47750
-47775
-47800
.47825
47849
91388
.91479
91570
.91661
91752
-49246
-49271
-49296
49321
.49346
97029
.97127
.97224
.97322
97420
30
3]
32
33
34
35
36
37
38
39
44928
-44952
-44976
-45001
-45025
81579
81659
81740
.81820
81900
46393
46417
46442
.46466
46491
86542
.86627
86713
86799
-86885
47874
.47899
-47924
-47949
-47974
91844
.91935
92027
.92118
-92210
49372
.49397
49422
-49447
-49472
97517
.97615
.97713
.97811
.97910
35
36
37
38
39
40
41
42
43
44
-45049
-45073
-45098
45122
-45146
-81981
82061
.82142
82222
.82303
-46516
-46540
-46565
.46589
.46614
86970
87056
.87142
87229
-87315
-47998
-48023
-48048
-48073
-48098
.92302
92394
92486
92578
.92670
-49497
-49522
-49547
-49572
.49597
.98008
98107
.98205
.98304
.98403
40
41
42
43
44
45
46
47
48
49
-45171
-45195
-45219
-45244
.45268
.82384
.82465
-82546
82627
.82709
46639
-46663
-46688
-46712
-46737
87401
.87488
-87574
-87661
.87748
48123
48148
-48172
-48197
-48222
92762
92855
.92947
93040
93133
.49623
-49648
-49673
-49698
-49723
98502
.98601
.98700
.98799
.98899
45
46
47
48
49
SO
51
52
53
54
-45292
-45317
-45341
-45365
-45390
82790
82871
.82953
83034
.83116
-46762
-46786
-46811
-46836
.46860
.87834
87921
88008
88095
-88183
-48247
-48272
-48297
-48322
-48347
.93226
93319
.93412
93505
.93598
-49748
-49773
-49799
-49824
-49849
98998
99098
99198
99298
-99398
50
51
52
53
54
55
56
57
58
59
-45414
-45439
-45463
-45487
-45512
.83198
.83280
.83362
83444
-83526
.46885
46909
-46934
.46959
-46983
88270
.88357
88445
.88532
.88620
.48372
48396
48421
.48446
-48471
.93692
93785
93879
93973
-94066
49874
.49899
49924
49950
-49975
.99498
99598
99698
.99799
-99899
55
56
57
58
59
60
-45536
.83608
47008
.88708
48496
.94160
50000
1-00000
60
NATURAL VERSED SINES AND EXTERNAL SEC.
60 61 fc 63 63
291
'
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec
'
1
2
3
4
5UOOO
50025
.50050
-50076
50101
i. 00000
1-00101
1-00202
1-00303
1 00404
51519
-51544
-51570
-51595
.51621
1-06267
1-06375
1-06483
1-06592
1-06701
-53053
-53079
53104
.53130
.53156
1.13005
1-13122
1-13239
1.13356
1-13473
-54601
-54627
-54653
54679
547C5
1-20269
1.20395
1.20521
1-20647
1-20773
1
2
3
4
5
6
7
8
9
-50126
-50151
.50176
-50202
-50227
1-00505
1-00607
1-00708
1-00810
1.00912
-51646
-51672
-51697
-51723
-51748
1-06809
1-06918
1.07027
1.07137
1-07246
53181
-53207
-53233
53258
-53284
1-13590
1.13707
1-13825
1-13942
1.14060
54731
.54757
54782
54808
-54834
1-20900
1-21026
1-21153
1-21280
1-21407
5
6
7
8
9
10
11
12
13
14
50252
.50277
-50303
50328
.50353
1-01014
1-01116
1-01218
1-01320
1.01422
-51774
-51799
-51825
-51850
.51876
1-07356
1-07465
1-07575
1.07685
1-07795
-53310
53336
-53361
-53387
-53413
1-14178
1-14296
1-14414
1-14533
1.14651
.54860
54886
-54912
-54938
-54964
1-21535
1-21662
1-21790
1-21918
1.22045
10
11
12
13
14
15
16
17
18
19
.50378
. 50404
50429
50454
-50479
1-01525
1-01628
1-01730
1-01833
1.01936
51901
51927
.51952
51978
.52003
1-07905
1-08015
1-08126
1-08236
1-08347
53439
. 53464
-53490
-53516
.53542
1-14770
1.14889
1-150C8
1-15127
1-15246
. 54990
-55016
- 55042
.55068
.55094
1-22174
1-22302
1-22430
1-22559
1.22688
15
16
17
18
19
20
21
22
23
24
-50505
-50530
-50555
.50581
.50606
1-02039
1-02143
1.02246
1-02349
1-02453
52029
52054
-52080
52105
.52131
1-08458
1-08569
1.08680
1-08791
1.08903
-53567
-53593
-53619
53645
53670
1-15366
1-15485
1-15605
1-15725
1-15845
55120
55146
-55172
-55198
-55224
1-22817
1-22946
1-23075
1.23205
1-23334
20
21
22
23
24
25
26
27
28
29
-50631
-50656
-50682
.50707
.50732
1-02557
1.02661
1-02765
1-02869
1-02973
-52156
-52182
-52207
-52233
-52259
1-09014
1-09126
1-09238
1-09350
1-09462
53696
53722
53748
53774
53799
1-15965
1-16085
1-16206
1-16326
1-16447
-55250
-55276
-55302
.55328
-55354
1 - 23464
1-23594
1 23724
1.23855
1-23985
25
26
27
28
29
30
31
32
33
34
50758
-50783
-50808
-50834
.50859
1.03077
1-03182
1-03286
1-03391
1-03496
.52284
.52310
52335
52361
52386
1-09574
1-09686
1-09799
1-09911
1-10024
.53825
53851
53877
53903
.53928
1-16568
1-16689
1-16810
1-16932
1-17053
-55380
-55406
-55432
55458
55484
1-24116
1-24247
1-24378
1-24509
1-24640
30
31
32
33
34
35
36
37
38
39
.50884
.50910
.50935
.50960
50980
1-03601
1-03706
1-03811
1-03916
1-04022
52412
52438
52463
52489
52514
1.10137
1-10250
1-10363
1-10477
1-10590
53954
53980
54006
54032
. 54058
1.17175
1-17297
1-17419
1-17541
1 -17663
55510
55536
55563
-E5589
EE615
1-24772
1-24903
1-25035
1-25167
1 . ?53CO
35
36
37
38
. 39
40
41
42
43
44
-51011
51036
51062
-51087
51113
1-04128
1-04233
1-04339
1-04445
1-04551
52540
52566
52591
52617
52642
1-10704
1-10817
1-10931
1-11045
1-11159
.54083
-54109
54135
54161
.54187
1-17786
1-17909
1-18031
1.18154
1.18277
55641
55667
55693
55719
55745
1-25432
1-25565
1-25697
1-25830
1-25963
40
41
42
43
44
45
46
47
48
49
51138
51163
51189
51214
51239
1.04658
1-04764
1-04870
1-04977
1-05084
52668
52694
52719
52745
52771
1.11274
1.11388
1-11503
1-11617
1.11732
54213
54238
54264
54290
54316
1.18401
1-18524
1-18648
1.18772
1-18895
55771
55797
55823
55849
55876
1.26097
1-26230
1.26364
1-26498
1.26632
45
46
47
48
49
50
51
52
53
54
51265
51290
51316
51341
51366
1-05191
1-05298
1-05405
1-05512
1-05619
52796
52822
52848
52873
52899
1-11847
1-11963
1-12078
1.12193
1-12309
54342
54368
54394
54420
54446
1.19019.
1-19144
1-19268
1.19393
1.19517
55902
55928
55954
55980
56006
1-26766
1-26900
1.27035
L- 27169
L. 27304
50
51
52
53
54
55
56
57
58
59
51392
51417
51443
51468
51494
1-05727
1-05835
1-05942
1-06050
1-06158
52924
52950
52976
53001
53027
1-12425
1-12540
1-12657
1-12773
. 12889
54471
54497
54523
54549
54575
-19642
19767
19892
-20018
20143
56032
56058
56084
56111
56137
I- 27439
L. 27574
L- 27710
L- 27845
L. 27981
55
56
57
9
60
51519
1-06267
53053
1-13005
54601
20269
56163
L- 28117
60
292 NATURAL VERSED SINES AND EXTERNAL SEC.
64 65 66 67
t
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
i
o
2
3
56163
56189
56215
56241
56267
1.28117
1-28253
1-28390
1.28526
1-28663
57738
57765
57791
57817
57844
1-36620
1-36768
1.3691"
1-37064
1-37212
59326
.59353
.59379
59406
.59433
1-45859
1.46020
1.46181
1.46342
1-46504
-60927
-60954
-60980
.61007
.61034
1-55930
1-56106
1-56282
1-56458
1-56634
O
2
3
4
5
6
7
8
9
56294
56320
56346
56372
56398
1-28800
1-28937
1-29074
1-29211
1-29349
57870
57896
57923
57949
57976
1-37361
1-37509
1-37658
1-37808
1-37957
.59459
-59486
-59512
-59539
-59566
1-46665
1-46827
1-46989
1-47152
1-47314
.61061
-61088
-61114
-61141
-61168
1-56811
1.56988
1-57165
1 - 57342
1-57520
6
I
10
11
12
13
14
56425
56451
56477
56503
56529
1-29487
1-29625
1-29763
1-29901
1-30040
58002
58028
58055
58081
58108
1-38107
1-38256
1-38406
1-38556
1.38707
-59592
59619
59645
59672
59699
1-47477
1-47640
1-47804
1-47967
1.48131
-61195
.61222
61248
-61275
-61302
1-57698
1-57876
1-58054
1-58233
1-58412
1O
11
12
13
14
15
16
17
18
19
56555
56582
56608
56634
56660
1-30179
1.30318
1-30457
1-30596
1-30735
58134
58160
58187
58213
58240
1-38857
1-39008
1-39159
1-39311
1-39462
59725
59752
59779
59805
59832
1.48295
1-48459
1-48624
1.48789
1-48954
-61329
-61356
-61383
-61409
-61436
1-58591
1-58771
1-58950
1-59130
1-59311
15
16
17
18
19
20
21
22
23
24
56687
56713
56739
56765
56791
1-30875
1-31015
1-31155
1-31295
1-31436
58266
58293
58319
58345
58372
1-39614
1-39766
1-39918
1-40070
1-40222
59859
59885
59912
59938
59965
1-49119
1-49284
1-49450
1-49616
1-49782
-61463
.61490
.61517
-61544
.61570
1-59491
1-59672
1-59853
1-60035
1-60217
30
21
22
23
24
25
26
27
28
29
56818
56844
56870
56896
56923
1-31576
1-31717
1-31858
1-31999
1-32140
58398
58425
58451
58478
58504
1-40375
1-40528
1-40681
1-40835
1.40988
59992
60018
60045
60072
60098
1-49948
1-50115
1-50282
1 . 50449
1-50617
.61597
.61624
.61651
.61678
.61705
1-60399
1-60581
1-60763
1-60946
1-61129
25
26
27
28
29
30
31
32
33
34
56949
56975
57001
57028
57054
1-32282
1-32424
1-32566
1-32708
1-32850
58531
58557
58584
58610
58637
1-41142
1-41296
1.41450
1.41605
1-41760
60125
60152
60178
60205
60232
1-50784
1.50952
1-51120
1.51289
1-51457
.61732
.61759
-61785
-61812
-61839
1-61313
1-61496
1-61680
1-61864
1-62049
30
g
33
34
35
36
37
38
39
57080
57106
57133
57159
57185
1-32993
1-33135
1-33278
1-33422
1-33565
58663
58690
58716
58743
58769
1-41914
1.42070
1-42225
1.42380
1.4253CL
60259
60285
60312
60339
60365
1.51626
1.51795
1.51965
1-52134
1.52304
-61866
-61893
-61920
-61947
-61974
1-62234
l-b^419
1.62604
1.62790
1-62976
35
36
37
38
..39
40
41
42
43
44
57212
57238
57264
57291
57317
1-33708
1-33852
1-33996
1-34140
1-34284
58796
58822
58849
58875
58902
1-42692
1-42848
1.43005
1.43162
1.43318.
.60392
-60419
. 60445
. 60472
. 60499
1 . 52474
1.52645
1.52815
1.52986
1.53157
.62001
-62027
-62054
-62081
-62108
1-63162
1-63348
1-63535
1-63722
1-63909
40
41
42
43
44
45
46
47
48
49
57343
57369
57396
57422
. 57448
1 - 34429
1-34573
1-34718
1-34863
1-35009
58928
58955
58981
59008
59034
1.43476
1-43633
1.43790
1.43948
1.44106
.60526
60552
.60579
.60606
.60633
1-53329
1-53500
1-53672
1-53845
1-54017
-62135
-62162
-62189
-62216
- 62243
1-64097
1-64285
1 - 64473
1-64662
1-64851
45
46
47
48
49
50
51
52
53
54
.57475
57501
.57527
57554
57580
1.35154
1-35300
1-35446
1-35592
1-35738
-59061
-59087
-59114
-59140
.59167
1 . 44264
1.44423
1-44582
1.44741
1-44900
60659
-60686
-60713
. 60740
.60768
.54190
.54363
54536
- 54709
-54883
-62270
-62297
-62324
-62351
-62378
1-65040
1.65229
1-65419
1-65609
1-65799
50
51
52
53
54
55
56
57
58
59
57606
57633
.57659
.57685
-57712
1-35885
1-36031
1-36178
1-36325
1-36473
.59194
59220
-59247
.59273
-59300
1-45059
1.45219
1.45378
1.45539
1-45699
.60793
.60820
-60847
.60873
.60900
.55057
.55231
55405
.55580
1.55755
-62405
-62431
-62458
-62485
.62512
1-65989
1-66180
1-66371
1-66563
1.66755
55
56
57
58
59
60
57738
1.36620
.59326
1-45859
-60927
1-55930
-62539
1-66947
60
NATURAL VERSED SINES AND EXTERNAL SEC. 293
68 69 70 71
'
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
/
o
1
2
3
4
.62539
62566
.62593
.62620
62647
1-66947
1-67139
1.67332
1.67525
1-67718
-64163
64190
64218
- 64245
64272
1-79043
1-79254
1-79466
1-79679
1-79891
65798
65825
65853
-65880
.65907
1-92380
1.92614
1-92849
1-93083
1-93318
- 67443
67471
67498
67526
-67553
2-07155
2-07415
2-07675
2-07936
2-08197
1
2
3
5
6
7
8
9
62674
62701
.62728
.62755
62782
1-67911
1-68105
1-68299
1-68494
1-68689
- 64299
64326
-64353
-64381
64408
1-80104
1-80318
1-80531
1-80746
1-80960
65935
.65962
65989
-66017
- 66044
1.93554
1-93790
1-94026
1-94263
1-94500
67581
67608
67636
67663
67691
2-08459
2-08721
2-08983
2-09246
2-09510
5
6
8
9
10
11
12
13
14
62809
62836
62863
62890
62917
1.68884
1-69079
1-69275
1.69471
1.69667
64435
. 64462
. 64489
.64517
. 64544
1-81175
1-81390
1-81605
1-81821
1-82037
-66071
-66099
66126
-66154
.66181
1-94737
1-94975
1-95213
1-95452
1-95691
67718
-67746
.67773
67801
67829
2-09774
2-10038
2.10303
2-10568
2-10834
10
11
12
13
14
15
16
17
18
19
62944
62971
62998
.63025
.63052
1-69864
1-70061
1-70258
1.70455
1-70653
64571
.64598
64625
.64653
-64680
1-82254
1-82471
1-82688
1-82906
1-83124
.66208
.66236
66263
-66290
66318
1-95931
1-96171
1-96411
1-96652
1-96893
67856
67884
67911
.67939
67966
2-11101
2-11367
2-11635
2-11903
2-12171
15
16
17
18
19
20
21
22
23
24
63079
63106
63133
63161
63188
1-70851
1-71050
1-71249
1 . 71448
1.71647
-64707
. 64734
.64761
-64789
-64816
1-83342
1-83561
1-83780
1-83999
1-84219
66345
66373
- 66400
-66427
66455
1-97135
1-97377
1-97619
1-97862
1-98106
-67994
68021
-68049
68077
.68104
2-12440
2-12709
2-12979
2-13249
2-13520
20
21
22
23
24
25
26
27
28
29
63215
-63242
-63269
63296
-63323
1-71847
1 . 72047
1-72247
1 . 72448
1 . 72649
- 64843
- 64870
- 64898
- 64925
-64952
1 . 84439
1.84659
1.84880
1-85102
1-85323
-66482
66510
66537
-66564
-66592
1-98349
1-98594
1-98838
1.99083
1-99329
.68132
68159
68187
-68214
68242
2-13791
2-14063
2-14335
2-14608
2-14881
25
26
27
28
29
30
31
32
33
34
63350
-63377
. 63404
.63431
.63458
1.72850
1-73052
1-73254
1-73456
1.73659
-64979
65007
-65034
-65061
-65088
1-85545
1-85767
1-85990
1-86213
1-86437
66619
-66647
-66674
66702
-66729
1-99574
1-99821
2-00067
2-00315
2-00562
68270
-68297
.68325
68352
.68380
2-15155
2-15429
2-15704
2-15979
2-16255
30
sa
32
33
34
3!i
36
37
38
39
.63485
63512
63539
63566
.63594
1-73862
1-74065
1-74269
1-74473
1-74677
-65116
-65143
-65170
-65197
.65225
1-86661
1-86885
1-87109
1-87334
1.87560
-66756
-66784
-66811
.66839
-66866
2-00810
2-01059
2-01308
2-01557
2-01807
68408
-68435
-68463
-68490
-68518
2-16531
2-16808
2-17085
2-17363
2-17641
35
36
37
38
39
40
41
42
43
44
.63621
63648
63675
63702
63729
1-74881
1-75086
1-75292
1-75497
1-75703
-65252
-65279
65306
65334
-65361
1.87785
1.88011
1.88238
1-88465
1.88692
-66894
-66921
-66949
-66976
67003
2-02057
2-02308
2-02559
2-02810
2-03062
-68546
68573
-68601
-68628
.68656
2-17920
2-18199
2-18479
2-18759
2-19040
40
41
42
43
44
45
46
47
48
49
63756
63783
-63810
-63838
.63865
1.75909
1-76116
1-76323
1-76530
1-76737
65388
65416
65443
.65470
65497
1.88920
1-89148
1.89376
1.89605
1.89834
67031
67058
67086
67113
.67141
2-03315
2-03568
2-03821
2-04075
2-04329
.68684
-68711
.68739
-68767
-68794
2-19322
2-19604
2-19886
2-20169
2-20453
45
46
47
48
49
50
51
52
53
54
63892
-63919
63946
.63973
- 64000
1-76945
1-77154
1-77362
1.77571
1-77780
65525
65552
65579
.65607
65634
1-90063
1-90293
1.90524
1.90754
1-90986
67168
67196
67223
67251
.67278
2-04584
2-04839
2-05094
2-05350
2-05607
68822
68849
68877
68905
.68932
2-20737
2-21021
2-21306
2-21592
2-21878
50
51
52
53
54
55
56
57
58
59
-64027
-64055
- 64082
-64109
-64136
1-77990
1.78200
1-78410
1-78621
L78832
65661
-65689
65716
65743
65771
1-91217
1.91449
1-91681
1-91914
1-92147
.67306
-67333
67361
-67388
-67416
2-05864
2-06121
2-06379
2-06637
2-06896
68960
68988
.69015
. 69043
69071
2-22165
2-22452
2 - 22740
2-23028
2-23317
55
56
57
58
59
6O
.64163
1-79043
65798
1-92380
. 67443
2-07155
69098
2-23607
60
NATURAL VERSED SINES AND EXTERNAL SEC.
72 73 74 75
t
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
1
2
3
4
.69098
69126
.69154
69181
.69209
2-23607
2-23897
2-24187
2-24478
2-24770
-70763
-70791
70818
-70846
-70874
2-42030
2-42356
2-42683
2-43010
2-43337
-72436
72464
-72492
-72520
-72548
2-62796
2-63164
2-63533
2-63903
2-64274
-74118
-74146
-74174
.74202
-74231
2-86370
2-86790
2-87211
2-87633
2-88056
2
3
4
5
6
7
8
9
.69237
.69264
.69292
.69320
.69347
2-25062
2-25355
2-25648
2-25942
2-23237
70902
70930
70958
70985
71013
2-43666
2-43995
2-44324
2-44655
2.44986
-72576
-72604
-72632
-72660
.72688
2-64645
2-65018
2-65391
2-65765
2-66140
- 74259
-74287
-74315
- 74343
.74371
2-88479
2-88904
2-89330
2-89756
2-90184
5
6
7
8
9
10
11
12
13
14
-69375
.69403
.69430
.69458
-69486
2-26531
2-26827
2-27123
2-27420
2-27717
71041
71069
71097
71125
71153
2-45317
2-45650
2-45983
2.46316
2-46651
.72716
. 72744
.72772
-72800
-72828
2-66515
2-66892
2-67269
2-67647
2-68025
-74399
- 74427
. 74455
- 74484
74512
2-90613
2-91042
2-91473
2-91904
2-92337
10
11
12
13
14
15
16
17
18
19
.69514
69541
.69569
-69597
69624
2-28015
2-28313
2-28612
2-28912
2-29212
71180
71208
71236
71264
71292
2-46986
2-47321
2-47658
2-47995
2-48333
72856
72884
72912
72940
72938
2-68405
2-68785
2-69167
-69549
-69931
. 74540
-74568
-74596
-74624
-74652
2-92770
2-93204
2-93640
2-94076
2-94514
15
16
17
18
19
20
21
22
23
24
.69652
-69680
.69708
.69735
.69763
2-29512
2-29814
2-30115
2-30418
2.30721
71320
71348
71375
71403
71431
2-48671
2-49010
2-49350
2-49691
2-50032
72996
73024
73052
73080
73108
-70315
-70700
-71085
-71471
-71858
-74680
.74709
-74737
-74765
-74793
2-94952
2-95392
2-95832
2-96274
2-96716
20
21
22
23
24
25
26
27
28
29
69791
69818
-69846
-69874
-69902
2-31024
2-31328
2-31633
2-31939
2-32244
71459
71487
71515
71543
71571
2-50374
2-50716
2-51060
2-51404
2-51748
73136
73164
73192
73220
73248
- 72246
-72635
-73024
-73414
-73806
-74821
-74849
-74878
-74906
-74934
2-97160
2-97604
2-98050
2-98497
2-98944
25
26
27
28
29
30
31
32
33
34
-69929
.69957
.69985
.70013
. 70040
2-32551
2-32858
2-33166
2-33474
2-33783
71598
71626
71654
71682
71710
2-52094
2-52440
2-52787
2-53134
2-53482
73276
73304
73332
73360
73388
-74198
-74591
-74984
-75379
-75775
.74962
74990
75018
-75047
-75075
2-99393
2.99843
3-00293
3 00745
3-01198
30
31
32
33
34
35
36
37
38
31-
70068
.70096
-70124
.70151
-70179
2.34092
2-34403
2-34713
2-35025
2-35336
71738
71766
71794
71822
71850.
2-53831
2-54181
2-54531
2-54883
2-55235
73416
73444
73472
73500
73529 .
-76171
-76568
-76966
2-77365
2-77765
-75103
-75131
-75159
-75187
.75216
3-01652
3-02107
3-02563
3-03020
3-03479
35
36
37
38
39
40
41
42
43
44
.70207
-70235
. 70263
.70290
-70318
2-35649
2-35982
2-36276
2-36590
2-36905
71877
71905
71933
71961
71989
2-55587
2-55940
2-56294
2-56649
2-57005
73557
73585
73613
-73641
-73669
2-78166
2-78568
2-78970
2-79374
2-79778
-75244
-75272
-75300
-75328
.75356
3-03938
3-04398
3-04860
3-05322
3-05786
4O
41
42
43
44
45
46
47
48
49
70346
70374
. 70401
70429
. 70457
2-37221
2-37537
2-37854
2-38171
2-38489
72017
72045
72073
-72101
.72129
2-57361
2-57718
2-58076
2-58434
2-58794
-73697
73725
.73753
-73781
73809
2-80183
2-80589
2-80996
2-81404
2-81813
75385
.75413
-75441
-75469
-75497
3-06251
3-06717
3-07184
3-07652
3-08121
45
46
47
48
49
50
51
52
53
54
70485
.70513
70540
.70568
.70596
2-38808
2-39128
2-39448
2-39768
2.40089
.72157
72185
72213
.72241
72269
2-59154
2-59514
2-59876
2-60238
2-60601
73837
.73865
-73893
-73921
-73950
2-82223
2-82633
2-83045
2-83457
2-83871
-75526
-75554
75582
.75610
-75fi39
3-08591
3-09063
3-09535
3-10009
3-10484
5O
51
52
53
54
55
56
57
58
59_
.70624
70652
70679
.70707
70735
2-40411
2-40734
2-41057
2-41381
2-41705
.72296
72324
72352
.72380
. 72408
2-60965
2-61330
2-61695
2-62061
2-62428
-73978
- 74006
.74034
-74062
-74090
2-84285
2-84700
2-85116
2-85533
2-85951
-75667
75695
-75723
-75751
-75780
3-10960
3-11437
3-11915
3-12394
3-12875
55
56
57
58
59
60
70763
2-42030
72436
2-62796
74118
2-86370
.75808
3-13357
6O
NATURAL VERSED SINES AND EXTERNAL SEC. 295
76 77 78 79
'
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
'
1
2
3
4
75808
75836
75864
75892
.75921
3-13357
3-13839
3-14323
3-14809
3-15295
77505
77533
77562
77590
77618
3-44541
3-45102
3-45664
3-46228
3-46793
79209 '
79237 i
79266
79294
79323 1
3-80973
3-81633
3-82294
3-82956
3.83621
.80919
-80948
-80976
-81005
81033
4-24084
4-24870
4-25658
4-26448
4-27241
1
2
3
5
6
7
8
9
75949
75977
76005
-76034
76062
3-15782
3-16271
3-16761
3-17252
3-17744
77647
77675
77703
77732
77760
3-47360
3-47928
3-48498
3.49069
3-49642
79351
79380
79408
79437
79465
3 84288
3-84956
3-85627
3-86299
3-86973
81062
-81090
81119
81148
.81176
4-28036
4-28833
4-29634
4-30436
4-31241
5
6
7
8
9
10
11
12
13
14
.76090
76118
.76147
.76175
. 76203
3-18238
3-18733
3-19228
3-19725
3-20224
77788
77817
77845
77874
77902
3-50216
3-50791
3-51368
3-51947
3-52527
- 79493
.79522
.79550
.79579
-79607
3-87649
3-88327
3-89007
3-89689
3-90373
.81205
.81233
.81262
-81290
81319
4-32049
4-32859
4-33671
4-34486
4-35304
10
11
12
13
14
15
16
17
18
19
76231
.76260
.76288
76316
.76344
3-20723
3-21224
3-21726
3-22229
3-22734
77930
77959
.77987
78015
78044
3-53109
3-53692
3-54277
3 - 54863
3-55451
.79636
-79664
- 79693
79721
.79750
3-91058
3-91746
3-92436
3-93128
3-93821
.81348
81376
-81405
81433
.81462
4-36124
4-36947
4-37772
4-38600
4 39430
15
16
17
18
-12
20
21
22
23
24
.76373
.76401
- 76429
.76458
-76486
3-23239
3-23746
3-24255
3-24764
3-25275
.78072
.78101
.78129
.78157
78186
3-56041
3-56632
3-57224
3-57819
3-58414
.79778
79807
-79835
-79864
. 79892
3-94517
3-95215
3-95914
3-96616
3-97320
.81491
81519
.81548
81576
81605
4-40263
4-41099
4-41937
4-42778
4-43622
20
2.
2*
23
24
25
26
27
28
29
.76514
76542
.76571
76599
.76627
3-25787
3- 26300
3-26814
3-27330
3-27847
.78214
. 78242
.78271
-78299
.78328
3-59012
3-59611
3-60211
3-60813
3-61417
-79921
- 79949
-79978
-80006
-80035
3-98025
3-98733
3-99443
4-00155
4-00869
.81633
81662
81691
.81719
81748
4-44468
4-45317
4-46169
4-47023
4-47881
25
26
27
28
29
30
31
32
33
34
76655
76684
76712
76740
76769
3-28366
3-28885
3-29406
3-29929
3.30452
-78356
-78384
78413
- 78441
- 78470
3 - 62023
3-62630
3-63238
3-63849
3 - 64461
80063
-80092
.80120
80149
80177
4-01585
4-02303
4-03024
4-03746
4-04471
81776
81805
81834
81862
81891
4-48740
4-49603
4-50468
4-51337
4-52208
3O
31
32
33
-34
35
36
37
38
39
76797
76825
76854
76882
-76910
3-30977
3-31503
3-32031
3-32560
3-33090
. 78498
78526
-78555
-78583
.78612
3-65074
3-65690
3-66307
3-66925
3-67545
80206
-80234
.80263
-80291
-80320
4-05197
4-05926
4-06657
4-07390
4-08125
81919
.81948
.81977
.82005
82034
4-53081
4-53958
4-54837
4-55720
4.56605
35
38
37
38
-39.
40
41
42
43
44
76938
76967
76995
77023
77052
3-33622
3-34154
3-34689
3-35224
3-35761
. 78640
78669
-78697
78725
. 78754
3-68167
3-68791
3. 694] 7
3 - 70044
3 - 70673
-80348
-80377
-80405
- 80434
-80462
4-08863
4-09602
4-10344
4-11088
4-11835
82063
82091
82120
.82148
-82177
4-57493
4-58383
4-59277
4-60174
4-61073
40
41
42
43
44
45
46
47
48
49
77080
77108
77137
77165
77193
3-36299
3-36839
3-37380
3-37923
3-38466
.78782
.78811
.78839
.78868
78896
3-71303
3-71935
3-72569
3-73205
3-73843
-8049'
-80520
-80548
-80577
-80605
4-12583
4-13334
4-14087
4-14842
4-15599
-82206
-82234
.82263
82292
82320
4-61976
62881
63790
64701
.65616
45
48
47
48
_49
50
51
52
53
54
77222
77250
-77278
77307
77335
3-39012
3-39558
3-40106
3-40656
3-41206
-78924
-78953
-78981
79010
79038
3 - 74482
3-75123
3-75766
3-76411
3-77057
80634
.80662
.80691
.80719
. 80748
4-16359
4-17121
4-17886
4-18652
4-19421
82349
82377
.82406
.82435
..82463
-66533
-67454
-68377
-69304
-70234
50
51
52
53
54
55
56
57
58
59
77363
77392
. 77420
- 77448
77477
3-41759
3-42312
3-42867
3-43424
3-43982
.79067
79095
79123
79152
79180
3-77705
3-78355
3-79007
3-79661
3.80316
80776
.80805
-80833
-80862
80891
4-20193
4-20966
4-21742
4-22521
4-23301
.82492
.82521
.82549
82578
.82607
.71166
.72102
.73041
-73983
4-74929
55
58
57
58
-5
60
77505
8-44541
.79209
3-80973
.80919
4-24084
.82635
4-75877
6O
296 NATURAL VERSED SINES AND EXTERNAL SEC.
80 81 83 83
/
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
i
1
2
3
JL
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
.82635-
.82664
.82692
-82721
.82750
4-75877
4.76829
4-77784
4.78742
4-79703
84357
.84385
84414
. 34443
- 84471
5-39245
5-40422
5-41602
5-42787
5-43977
-86083
.86112
.86140
86169
.86188
6.18530
6-20020
6-21517
6-23019
6-24529
87813
87842
87871
87900
87929
7-20551
7-22500
7-24457
7-26425
7-28402
1
2
3
4
-82778
-82807
.82836
-82864
.82893
4-80667
4-81635
4-82606
4-83581
4-84558
. 84500
84529
84558
-84586
-84615
5-45171
5-46369
5-47572
5-48779
5-49991
86227
86256
.86284
-86313
86342
6-26044
6-27566
6-29095
6-30630
6-32171
87957
87986
88015
88044
-88073
7-30388
7-32384
7-34390
7-36405
7-38431
5
6
7
8
__1
10
11
12
13
14
-82922
-82950
82979
-83008
-83036
4-85539
4-86524
4-87511
4-88502
4-89497
. 84644
84673
84701
.84730
.84759
5-51208
5-52429
5-53655
5-54886
5-56121
86371
-86400
-86428
-86457
-86486
6-33719
6-35274
6-36835
6-38403
6-39978
-88102
-88131
.88160
-88188
-88217
7-40466
7-42511
7-44566
7-46632
7-48707
-83065
83094
83122
83151
83180
4-90495
4.91496
4-92501
4-93509
4-94521
84788
.84816
.84845
-84874
. 84903
5-57361
5-58606
5-59855
5-61110
5-62369
86515
86544
-86573
-86601
.86630
6-41560
6-43148
6 - 44743
6-46346
6-47955
-88246
-88275
-88304
-88333
-88362
7-50793
7-52889
7-54996
7-57113
7-59241
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
83208
83237
83266
83294
83323
4-95536
4-96555
4-97577
4-98603
4-99633
84931
-84960
-84989
-85018
85046
5-63633
5-64902
5-66176
5-67454
5-68738
.86659
-86688
.86717
-86746
-86774
6-49571
6-51194
6-52825
6-54462
6-56107
-88391
-88420
-88448
-88477
.88506
7-61379
7-63528
7-65688
7-67859
7-70041
20
21
22
23
24
25
26
27
28
29
83352
83380
83409
83438
83467
5-00666
5-01703
5-02743
5-03787
5-04834
85075
85104
85133
85162
85190
5-70027
5-71321
5-72620
5-73924
5-75233
-86803
-86832
-86861
-86890
-86919
6-57759
6-59418
6-61085
6-62759
6 - 64441
-88535
-88564
-88593
-88622
-88651
7-72234
7-74438
7-75653
7-78880
7-81118
83495
83524
83553
83581
83610
5-05886
5-06941
5-08000
5-09062
5-10129
85219
85248
85277
85305
85334
5-76547
5-77866
5-79191
5-80521
5-81856
-86947
-86976
-87005
-87034
-87063
6-66130
6-67826
6.69530
6-71242
6-72962
-88680
-88709
-88737
-88766
-88795
7-83367
7-85628
7-87901
7-90186
7-92482
30
31
32
33
_3J
35
36
37
38
-39
40
41
42
43
44
35
36
37
38
39
83639
83667
83696
83725
83754
5-11199
5.12273
5-13350
5-14432
5-15517
85363
85392
85420
85449
85478
5-83196
5-84542
5-85893
5.87250
5-88612
.87092
87120
.87149
.87178
-87207
6-74689
6-76424
6-78167
6-79918
6-81677
88824
88853
88882
-88911
-88940
7-94791
7-97111
7-99444
8-01788
8-04146
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
.60.
60
83782
83811
83840
83868
83897
5-16607
5-17700
5-18797
5-19898
5-21004
85507
85536
85564
85593
85622
5-89979
5-91352
5-92731
5-94115
5-95505
-87236
-87265
-87294
-87322
-87351
6-83443
6-85218
6.87001
6.88792
6.90592
-88969
.88998
-89027
-89055
-89084
8-06515
8-08897
8.11292
8-13699
8-16120
83926
83954
83983
84012
84041
5.22113
5-23226
5-24343
5.25464
5.26590
85651
85680
85708
85737
.85766
5-96900
5-98301
5-99708
6-01120
6-02538
-87380
- 87409
-87438
-87467
-87496
6-92400
6-94216
6-96040
6-97873
6-99714
-89113
-89142
89171
.89200
.89229
8-18553
8-20999
8-23459
8-25931
8-28417
45
46
47
48
49
84069
-84098
-84127
.84155
.84184
5.27719
5-28853
5-29991
5.31133
5.32279
.85795
.85823
85852
.85881
.85910
6-03962
6-05392
6-06828
6-08269
6-09717
-87524
-87553
-87582
-87611
-87640
7-01565
7-03423
7-05291
7.07167
7-09052
89258
89287
-89316
-89345
-89374
8-30917
8-33430
8-35957
8-38497
8-41052
50
51
52
53
54
55
56
57
58
59
.84213
84242
. 84270
.84299
84328
5-33429
5-34584
5-35743
5-36906
5-38073
85939
.85967
85996
.86025
.86054
6-11171
6-12630
6-14096
6-15568
6.17046
-87669
-87698
-87726
-87755
-87784
7-10946
7.12849
7-14760
7-16681
7-18612
.89403
89431
89460
89489
-89518
8-43620
8-46203
8-48800
8-51411
8.54037
84357
5-39245
.86083
6.18530
.87813
7.20551
.89547
8-56677
60
NATURAL VERSED SINES AND EXTERNAL SEC. 297
84 85 86
'
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
i
1
2
3
.89547
.89576
89605
.89634
.89663
8.56677
8.59332
8.62002
8.64687
8.67387
.91284
.91313
.91342
91371
-91400
10.47371
10-51199
10.55052
10.58932
10-82337
-93024
.93053
.93082
-93111
.93140
13-33559
13-39547
13-45586
13-51676
13-57817
1
2
3
4
5
6
7
8
9
89692
89721
89750
89779
89808
8-70103
8-72833
8-75579
8-78341
8-81119
.91429
-91458
-91487
-91516
.91545
10-66769
10-70728
10-74714
10-78727
10-82768
.93169
93198
93227
93257
93286
13-64011
13-70258
13-76558
13-82913
13-89323
5
6
7
8
9
10
11
12
13
14
.89836
89865
.89894
89923
.89952
8-83912
8-86722
8.89547
8-92389
8-95248
91574
-91603
.91632
.91661
-91690
10-88837
10-90934
10-95060
10.99214
11-03397
93315
93344
93373
. 93402
.93431
13-95788
14-02310
14-08890
14-15527
14-22223
10
11
12
13
14
15
16
17
18
19
89981
90010
90039
90068
90097
8-98123
9.01015
9-03923
9-06849
9-09792
-91719
-91748
-91777
-91806
91835
1-07610
11-11852
11-16125
11.20427
11-24761
93460
93489
93518
93547
-93576
14-28979
14-35795
14-42672
14-49611
14-56614
15
16
17
18
.19
20
21
22
23
24
90126
90155
90184
90213
90242
9.12752
9-15730
9.18725
9-21739
9-24770
91864
91893
91922
91951
91980
11-29125
11.33521
11.37948
11.42408
11.46900
93605
93634
93663
93692
93721
14-63679
14-70810
14-78005
14-85268
14-92597
20
21
22
23
24
25
26
27
28
29
90271
90300
.90329
90358
90386
9-27819
9-30887
9-33973
9.37077
9.40201
92009
.92038
92067
-92096
-92125
11.51424
11-55982
11-60572
11.65197
11.69856
93750
93779
93808
93837
93866
14-99995
15-07462
15-14999
15-22607
15-30287
25
26
27
28
29
30
31
32
33
34
90415
90444
90473
90502
90531
9-43343
9-46505
9-49685
9-52886
9-56106
.92154
92183
.92212
.92241
-92270
11-74550
n. 79278
11-84042
11-88841
11.93677
93895
93924
93953
93982
94011
15-38041
15-4b869
15-53772
15-61751
15-69808
30
31
32
33
34
35
36
37
38
39
90560
90589
90618
90647
90676
9-59346
9-62605
9-65885
9-69186
9-72507
.92299
.92328
-92357
-92386
92415
11-98549
12-03458
12-08404
12.13388
12.18411
94040
94069
94098
94127
94156
15-77944
15-86159
15-94456
16-02835
16-11297
35
36
37
38
39
40
41
42
43
44
90705
90734
90763
90792
-90821
9-75849
9-79212
9-82596
9-86001
9.89428
92444
92473
-92502
-92531
-92560
12-23472
12-28572
12-33712
12.38891
12-44112
94186
94215
94244
94273
94302
16-19843
16-28476
16.37196
16-46005
16-54903
40
41
42
43
44
45
46
47
48
49
90850
90879
90908
90937
90966
9-92877
9-96348
9-99841
10-03356
10-06894
.92589
-92618
-92647
-92676
-92705
12-49373
12-54676
12-60021
12.65408
12-70838
94331
94360
-94389
94418
- 94447
16-63893
16-72975
16-82152
16-91424
17-00794
45
46
47
48
49
50
51
52
53
54
90995
91024
.91053
.91082
.91111
10-10455
10-14039
10.17646
10-21277
10-24932
92734
-92763
.92792
.92821
-92850
12-76312
12-81829
12-87391
12-92999
12-98651
94476
94505
94534
94563
94592
17-10262
17-19830
17-29501
17-39274
17-49153
50
51
52
53
54
55
56
57
58
59
91140
91169
.91197
91226
91255
10-28610
10.32313
10-36040
10-39792
10-43569
-92879
-92908
.92937
-92966
92995
13-04350
13-10096
13.15889
13-21730
13-27620
94621
94650
94679
94708
.94737
17-59139
17-69233
17-79438
17-89755
18-00185
55
56
57
58
-59.
60
.91284
10.47371
.93024
13-33559
94766
18.10732
60
NATURAL VERSED SINES AND EXTERNAL SEC.
87 88 89
Vers.
Ex. sec.
Vers.
Ex. sec.
Vers.
Ex. sec.
>
o
2
3
.94766
94795
.94825
.94854
.94883
18-10732
18-21397
18-32182
18-43088
18-54119
.96510
.96539
.96568
96597
-96626
27-65371
27-89440
28-13917
28-38812
28-64137
98255
98284
98313
-98342
-98371
53-29869
57.26976
58-27431
59-31411
60-39105
2
3
4
5
6
7
8
9
94912
94941
.94970
.94999
.95028
18-65275
18-76560
18-87976
18-99524
19-11208
.96655
.96684
.96714
.96743
.96772
28-89903
29-16120
29-42802
29-69960
29.97607
98400
98429
.98458
.98487
.98517
61.50715
62.66460
63-86572
65-11304
66-40927
5
6
8
9
10
11
12
13
14
.95057
.95086
95115
.95144
.95173
19.23028
19-34989
19-47093
19-59341
19-71737
.96801
.96830
-96859
-96888
-96917
30-25758
30-54425
30-83623
31-13366
31-43671
98546
98575
-98604
.98633
.98662
67-75736
69-16047
70-62207
72-14583
73-73586
10
11
12
13
14
15
16
17
18
19_
-95202
95231
.95260
.95289
.95318
19-84283
19-96982
20-09838
20-22852
20-36027
-96946
-96975
.97004
.97033
.97062
31-74554
32.06030
32-38118
32-70835
33-04199
98691
98720
98749
.98778
.98807
75-39655
77-13274
78-94968
80-85315
82-84947
15
16
17
18
19
20
21
22
23
24
.95347
.95377
.95406
.95435
.95464
20-49368
20-62876
20-76555
20-90409
21 . 04440
.97092
.97121
.97150
.97179
.97208
33-38232
33-72952
34-08380
34-44539
34-81452
.98836
98866
.98895
.98924
98953
84-94561
87-14924
89-46886
91-91387
94-49471
20
21
22
23
24
25
26
27
28
29
.95493
95522
95551
.95580
.95609
21-18653
21.33050
21-47635
21-62413
21-77386
97237
.97266
.97295
.97324
97353
35-19141
35-57633
35-96953
36-37127
36-78185
.98982
.99011
.99040
-99069
-99098
97-22303
100-1119
103-1757
106-4311
109-8966
25
26
27
28
29
30
31
32
33
34
.95638
.95667
95696
.95725
95754
21-92559
22-07935
22-23520
22-39316
22-55328
.97382
.97411
.97440
.97470
.97499
37-20155
37-63068
38-06957
38-51855
38-97797
.99127
.99156
-99186
.99215
.99244
113-5930
117-5444
121-7780
126-3253
131-2223
30
31
32
33
34
35
36
37
38
39_
95783
.95812
95842
95871
95900
22.71563
22-88022
23-04712
23-21637
23-38802
.97528
.97557
.97586
-97615
.97644
39-44820
39-92963
40-42266
40-92772
41-44525
.99278
.99302
.99331
.99360
99389
136-5111
142-2406
148-4684
155-2623
162-7033
35
36
37
38
39
40
41
42
43
44
95929
95958
95987
.96016
96045
23-56212
23-73873
23-91790
24-09969
24-28414
97673
.97702
.97731
.97760
.97789
41-97571
42-51961
43-07746
43-64980
44-23720
-99418
-99447
.99476
.99505
.99535
170-8883
179-9350
189-9868
201-2212
213-8600
40
41
42
43
44
45
46
47
48
49
96074
.96103
.96132
.96161
.96190
24-47134
24-66132
24-85417
25-04994
25-24869
97819
97848
97877
.97906
.97935
44-84026
45-45963
46-09596
46-74997
47-42241
99564
.99593
.99622
.99651
.99680
228-1839
244.5540
263-4427
285-4795
311.5230
45
46
47
48
49
50
51
52
53
54
.96219
.96248
.96277
.96307
.96336
25-45051
25-65546
25-86360
26.07503
26-28981
97964
-97993
-98022
-98051
.98080
48-11406
48-82576
49-55840
50.31290
51.09027
.99709
.99738
.99767
.99796
.99825
342.7752
380-9723
428-7187
490-1070
571-9581
50
51
52
53
54
55
56
57
58
59_
.96365
.96394
.96423
.96452
.96481
26-50804
26-72978
26-95513
27-18417
27-41700
.98109
-98138
-98168
.98197
98226
51-89156
52-71790
53-57048
54-45053
55-35946
.99855
.99884
.99913
99942
99971
686-5496
858-4369
1144-916
1717-874
3436-747
55
58
57
58
59
60
.96510
27-65371
.98255
56-29869
1-00000
Infinite
60
TABLES
299
RADII METRIC
R "
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
000'
00
oo
100'
1145.930
3.05916
2 00'
572.987
2.75814
01
68754.931
4.83730
01
1127.145
3.05198
01
568.252
2.75454
02
34377.468
4.53627
02
1108.966
3.04492
02
563.595
2.75097
03
22918.310
4.36018
03
1091.364
3.03797
03
559.013
2.74742
04
17188.735
4.23524
04
1074.311
3.03113
04
554.505
2.74391
05
13750.987
4.13833
05
1057.785
3.02440
05
550.070
2.74042
06
11459.157
4.05912
06
1041.757
3.01777
06
545.705
2.73696
07
9822.134
3.99221
07
1026.209
3.01124
07
541.408
2.73352
08
8594.369
3.93421
08
1011.118
3.00480
08
537.179
2.73012
09
7639.438
3.88306
09
996.465
2.99846
09
533.015
2.72674
10
6875.496
3.83730
10
982.230
2.99221
10
528.916
2.72339
11
6250.451
3.79591
11
968.396
2.98605
11
524.879
2.72006
12
5729.582
3.75812
12
954.947
2.97998
12
520.903
2.71676
13
5288.845
3.72336
13
941.866
2.97399
13
516.985
2.71348
14
4911.070
3.69118
14
929.139
2.96808
14
513.129
2.71023
15
4583.666
3.66121
15
916.751
2.96225
15
509.328
2.70700
16
4297.187
3.63318
16
904.689
2.95650
16
505.584
2.70379
17
4044.412
3.60686
17
892.940
2.95082
17
501.894
2.70061
18
3819.723
3.58203
18
881.492
2.94522
18
498.258
2.69745
19
3618.685
3.55855
19
870.335
2.93969
19
494.674
2.69432
20
3437.752
3.53627
20
859.456
2.93422
20
491.141
2.69121
21
3274.050
3.51509
21
848.846
2.92883
21
487.658
2.68812
22 3125.230
3.49488
22
838.495
2.92350
22
484.224
2.68505
23 2989.351
3.47558
23
828.393
2.91824
23
480.838
2.68200
24
2864.795
3.45709
24
818.532
2.91304
24
477.500
2.67897
25
2750.203
3.43936
25
808.902
2.90790
25
474.207
2.67597
26
2644.427
3.42233
26
799.497
2.90282
26
470.960
2.67298
27
2546.485
3.40594
27
790.308
2.89780
27
467.756
2.67002
28
2455.540
3.39015
28
781.327
2.89283
28
464.596
2.66708
29
2370.867
3.37491
29
772.549
2.88793
29
461.479
2.66415
30
2291.838
3.36018
30
763.966
2.88307
30
458.403
2.66125
31 2217.909
3.34594
31
755.571
2.87828
31
455.367
2.65836
32 ' 2148.600
3.33216
32
747.359
2.87353
32
452.372
2.65550
33 2083.491
3.31879
33
739.323
2.86883
33
449.416
2.65265
34 ! 2022.212
3.30583
34
731.458
2.86419
34
446.498
2.64982
35 1 1964.435
3.29324
35
723.759
2.85959
35
443.618
2.64701
36 | 1909.868
3.28100
36
716.221
2.85505
36
440.775
2.64422
37 ; 1858.251
3.26910
37
708.837
2.85055
37
437.968
2.64144
38 ! 1809.350
3.25752
38
701.605
2.84609
38
435.196
2.63868
39 1762.957
3.24624
39
694.518
2.84168
39
432.460
2.63595
40
1718.883
3.23525
40
687.574
2.83732
40
429.757
2.63322
41
1676.959
3.22452
41
680.766
2.83300
41
427.088
2.63052
42
1637.032
3.21406
42
674.093
2.82872
42
424.452
2.62783
43
1598.962
3.20384
43
667.549
2.82448
43
421.849
2.62516
44
1562.623
3.19385
44
661 . 130
2.82029
44
419.277
2.62250
45
1527.899
3.18409
45
654.834
2.81613
45
416.737
2.61986
46
1494.684
3.17455
46
648.657
2.81202
46
414.227
2.61724
47
1462.883
3.16521
47
642.595
2.80794
47
411.747
2.61463
48
1432.406
3.15607
48
636.646
2.80390
48
409.296
2.61204
49
1403.174
3.14711
49
630.806
2.79990
49
406.875
2.60946
50
1375.111
3.13834
50
625.072
2.79593
50
404.482
2.60690
51
1348.148
3.12974
51
619.441
2.79200
51
402.117
2.60435
52
1322.223
3.12130
52
613.910
2.78810
52
399.780
2.60182
53
1297.276
3.11303
53
608.478
2.78424
53
397.469
2.59930
54
1273.253
3.10491
54
603.141
2.78042
54
395.186
2.59680
55
1250.103
3.09695
55
597.897
2.77663
55
392.928
2.59431
56
1227.780
3.08912
56
592.743
2.77287
56
390.696
2.59184
57
1206.241
3.08143
57
587.677
2.76914
57
388.489
2.58938
58
1185.444
3.07388
58
582.698
2.76544
58
386.307
2.58693
59
1165.352
3.06646
59
577.802
2.76178
59
384.149
2.58450
300
THE RAILROAD TAPER
RAJDII METRIC (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
3 00'
382.016
2.58208
4 00'
286.537
2.45718 i
5 00'
229.256
2.36032
[01
379.906
2.57968
01
285.348
2.45537
01
228.495
2.35888
02
377.818
2.57728
02
284.170
2.45358
02
227.739
2.35744
03
375.754
2.57490
03
283.001
2.45179
03
226.987
2.35600
04
373.713
2.57254
04
281.842
2.45001
04
226.241
2.35457
05
371.693
2.57018
05
280.692
2.44823
05
225.500
2.35315
06
369.695
2.56784
06
279.551
2.44646
06
224.764
2.35173
07
367.719
2.56552
07
278.420
3.44470
07
224.032
2.35031
08
365.763
2.56320
08
277.298
2.44295
08
223.305
2.34890
09
363.828
2.56090
09
276.185
2.44120
09
222.583
2.34749
10
361.914
2.55861
10
275.080
2.43946
10
221.865
2.34609
11
360.020
2.55633
11
273.985
2.43773
11
221.152
2.34469
12
358.145
2.55406
12
272.898
2.43600
12
220.444
2.34330
13
356.290
2.55180
13
271.820
2.43428
13
219.740
2.34191
14
354.454
2.54956
14
270.750
2.43257 1
14
219.041
2.34053
15
352.637
2.54733
15
269.689
2.43086
15
218.346
2.33915
16
350.838
2.54511
16
268.636
2.42916 j
.16
217.656
2.33777
17
349.058
2.54290
17
267.591
2.42747 1
17
216.969
2.33640
18
347.295
2.54070
18
266.555
2.42579
18
216.288
2.33503
19
345.550
2.53851
19
265.526
2.42411
19
215.610
2.33367
20
343.823
2.53633
20
264.505
2.42243
20
214.937
2.33231
21
342.113
2.53417
21
263.492
2.42077
21
214.268
2.33096
22
340.420
2.53202
22
262.487
2.41911
22
213.603
2.32961
23
338.743
2.52987
23
261.489
2.41745
23
212.942
2.32826
24
337.084
2.52774
24
260.499
2.41581
24
212.285
2.32692
25
335.440
2.52561
25
259.517
2.41417
25
211.632
2.32558
26
333.812
2.52350
26
258.542
2.41253
26
210.984
2.32425
27
332.200
2.52140
27
257.574
2.41090
27
210.339
2.32292
28
330.603
2.51931
28
256.613
2.40928
28
209.698
2.32159
29
329.022
2.51722
29
255.660
2.40766
29
209.061
2.32027
30
327.455
2.51515
30
254.713
2.40605
30
208.428
2.31896
31
325.904
2.51309
31
253.774
2.40445
31
207.799
2.31764
32
324.367
2.51104
32
252.841
2.40285
32
207.174
2.31634
33
322.845
2.50899
33
251.916
2.40126
33
206.552
2.31503
34
321.337
2.50696
34
250.997
2.39967
34
205.934
2.31373
35
319.842
2.50494
35
250.085
2.39809
35
205.320
2.31243
36
318.362
2.50292
36
249.179
2.39651
36
204.709
2.31114
37
316.896
2.50092
37
248.280
2.39494
37
204.102
2.30985
38
315.442
2.49892
38
247.387
2.39338
38
203.499
2.30856
39
314.003
2.49693
39
246.501
2.39182
39
202.899
2.30728
40
312.576
2.49496
40
245.621
2.39027
40
202.303
2.30600
41
311.162
2.49299
41
244.748
2.38872
41
201.710
2.30473
42
309.761
2.49103
42
243.880
2.38718
42
201.121
2.30346
43
308.372
2.48907
43
243.019
2.38564
43
200.535
2.30219
44
306.996
2.48713
44
242.164
2.38411
44
199.952
2.30093
45
305.632
2.48520
45
241.314
2.38258
45
199.373
2.29967
46
304.280
2.48327
46
240.471
2.38106
46
198.798
2.29841
47
302.940
2.48136
47
239.634
2.37955
47
198.225
2.29716
48
301.612
2.47945
48
238.802
2.37804
48
197.656
2.29591
49
300.295
2.47755
49
237.976
2.37653
49
197.090
2.29466
50
298.990
2.47566
50
237.156
2.37503
50
196.528
2.29342
51
297.696
2.47377
51
236.342
2.37354
51
195.968
2.29219
52
296.414
2.47190
52
235.533
2.37205
52
195.412
2.29095
53
295.142
2.47003
53
234.730
2.37057
53
194.859
2.28972
54
293.881
2.46817
54
233.932
2.36909
54
194.309
2.28849
55
292.631
2.46632
55
233.139
2.36761
55
193.762
2.28727
56
291.392
2.46448
56
232.352
2.36615
56
193.218
2.28605
57
290.163
2.46264
57
231.570
2.36468
57
192.677
2.28483
58
288.944
2.46081
58
230.794
2.36322
58
192.140
2.28362
59
287.735
2.45899
59
230.022
2.36177
59
191.605
2.28241
TABLES
RADII METRIC (Continued)
301
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
6 00'
191.073
2.28120
7 00'
163.804
2.21432
8 00'
143.356
2.15642
01
190.544
2.28000
01
163.415
2.21329
01
143.058
2.15551
02
190.018
2.27879
02
163.029
2.21226
02
142.762
2.15461
03
189.496
2.27760
03
162.644
2.21124
03
142.467
2.15371
04
188.976
2.27641
04
162.261
2.21021
04
142.173
2.15282
05
188.458
2.27521
05
161.880
2.20919
05
141.880
2.15192
06
187.944
2.27403
06
161.500
2.20817
06
141.589
2.15103
07
187.432
2.27284
07
161.122
2.20715
07
141.299
2.15014
08
186.923
2.27166
08
160.746
2.20614
08
141.010
2.14925
09
186.417
2.27049
09
160.372
2.20513
09
140.722
2.14836
10
185.914
2.26931
10
160.000
2.20412
10
140.435
2.14748
11
185.413
2.26814
11
159.629
2.20311
11
140.150
2.14659
12
184.915
2.26697
12
159.260
2.20211
12
139.865
2.14571
13
184.420
2.26581
13
158.892
2.20110
13
139.582
2.14483
14
183.927
2.26465
14
158.527
2.20010
14
139.300
2.14395
15
183.437
2.26349
15
158.163
2.19910
15
139.019
2.14307
16
182.950
2.26233
16
157.800
2.19811
16
138.739
2.14220
17
182.465
2.26118
17
157.440
2.19712
17
138.460
2.14132
18
181.983
2.26003
18
157.081
2.19612
18
138.183
2.14045
19
181.503
2.25888
19
156.724
2.19514
19
137.906
2.13958
20
181.026
2.25774
20
156.368
2.19415
20
137.631
2.13872
21
180.552
2.25660
21
156.014
2.19316
21
137.357
2.13785
22
180.079
2.25546
22
155.661
2.19218
22
137.084
2.13699
23
179.610
2.25433
23
155.310
2.19120
23
136.812
2.13612
24
179.142
2.25320
24
154.961
2.19022
24
136.541
2.13526
25
178.678
2.25207
25
154.613
2.18925
25
136.271
2.13440
26
178.215
2.25094
26
154.267
2.18827
26
136.002
2.13355
27
177.755
2.24982
27
153.923
2.18730
27
135.734
2.13269
28
177.298 2.24870
28
153.580
2.18633
28
135.468
2.13184
29
176 842 2.24759
29
153.238
2.18537
29
135.202
2.13098
30
176.389
' 2.24647
30
152.898
2.18440
30
134.937
2.13013
31
175.939
2.24536
31
152.559
2.18344
31
134.674
2.12928.
32
175.490 2.24425
32
152.222
2.18248
32
134.411
2.12843
33
175.044 i 2.24315
33
151.887
2.18152
33
134.150
2.12759
34
174.600 ; 2.24204
34
151.553
2.18056
34
133.889
2.12674
35
174.159 2.24095
35
151.220
2.17961
35
133.630
2.12590
36
173.720 2.23985
36
150.889
2.17866
36
133.371
2.12506
37
173.283 2.23876
37
150.559
2.17771
37
133.114
2.12422
38
172.848
2.23766
38
150.231
2.17676
38
132.857
2.12338
39
172.415
2.23658
39
149.904
2.17581
39
132.602
2.12255
40
171.984
2.23549
40
149.579
2.17487
40
132.347
2.12171
41
171.556
2.23441
41
149.255
2.17393
41
132.094
2.12088
42
171.130
2.23333
42
148.932
2.17299
42
131.841
2.12005
43
170.705
2.23225
43
148.611
2.17205
43
131.589
2.11922
44
170.284
2.23117
44
148.291
2.17111
44
131.339
2.11839
45
169.863
2.23010
45
147.973
2.17018
45
131.089
2.11757
46
169.446
2.22903
46
147.656
2.16925
46
130.840
2.11674
47
169.030
2.22796
47
147.340
2.16832
47
130.593
2.11592
48
168.616
2.22690
48
147.026
2.16739
48
130.346
2.11510
49
168.204
2.22584
49
146.713
2.16647
49
130.100
2.11428
50
167.794
2.22478
50
146.401
2.16554
50
129.855
2.11346
51
167.387
2.22372
51
146.091
2.16462
51
129.611
2.11264
52
166.981
2.22267
52
145.782
2.16370
52
129.368
2.11183
53
166.577
2.22162
53
145.474
2.16278
53
129.125
2.11101
54
166.175
2.22057
54
145.168
2.16187
54
128.884
2.11020
55
165.775
2.21952
55
144.862
2.16095
55
128.644
2.10939
56
165.377
2.21848
56
144.559
2.16005
56
128.404
2.10858
57
164.981
2.21743
57
144.256
2.15913
57
128.166
2.10777
58
164.587
2.21640
58
143.955
2.15823
58
127.928
2.10697
59
164.195
2.21536
59
143.655
2.15732
59
127.691
2.10616
302
THE RAILROAD TAPER
RADII METRIC (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
jog. rad.
9 00'
127.455
2.10536
10 00'
114.737
2.05970
11 00'
104.334
2.01843
01
127.220
2.10456
01
114.547
2.05898
01
104.177
2.01777
02
126.986
2.10376
02
114.357
2.05826
02
104.020
2.01712
03
126.752
2.10295
03
114.168
2.05754
03
103.864
2.01646
04
126.520
2.10216
04
113.979
2.05682
04
103.708
2.01581
05
126.288
2.10136
05
113.791
2.05611
05
103.552
2.01516
06
126.057
2.10057
06
113.604
2.05539
06
103.397
2.01451
07
125.827
2.09977
07
113.417
2.05468
07
103.243
2.01386
08
125.598
2.09898
08
113.231
2.05397
08
103.089
2.01321
09
125.370
2.09819
09
113.046
2.05326
09
102.935
2.01256
10
125.142
2.09740
10
112.861
2.05254
10
102.782
2.01192
11
124.916
2.09662
11
112.677
2.05184
11
102.629
2.01127
12
124.690
2.09583
12
112.493
2.05113
12
102.477
2.01063
13
124.465
2.09505
13
112.310
2.05042
13
102.325
2.00998
14
124.241
2.09426
14
112.128
2.04971
14
102.174
2.00934
15
124.017
2.09348
15
111.946
2.04901
15
102.023
2.00870
16
123.795
2.09270
16
111.765
2.04831
16
101.873
2.00806
17
123.573
2.09192
17
111.584
2.04760
17
101.723
2.00742
18
123.352
2.09115
18
111.404
2.04690
18
101.573
2.00678
19
123.132
2.09037
19
111.224
2.04620
19
101.424
2.00614
20
122.912
2.08959
20
111.046
2.04550
20
101.275
2.00550
21
122.694
2.08882
21
110.867
2.04480
21
101.127
2.00487
22
122.476
2.08805
22
110.689
2.04410
22
100.979
2.00423
23
122.259
2.08728
23
110.512
2.04341
23
100.832
2.00360
24
122.043
2.08651
24
110.336
2.04272
24
100.685
2.00296
25
121.827
2.08574
25
110.160
2.04202
25
100.538
2.00233
26
121.612
2.08498
26
109.984
2.04133
26
100.392
2.00170
27
121.398
2.08421
27
109.809
2.04064
27 .
100.247
2.00107
28
121.185
2.08345
28
109.635
2.03995
28
100.102
2.00044
29
120.973
2.08269
29
109.461
2.03926
29
99.957
1.99981
30
120.761
2.08193
30
109.288
2.03857
30
99.812
1.99918
31
120.550
2.08117
31
109.115
2.03788
31
99.668
1.99856
32
120.340
2.08041
32
108.943
2.03720
32
99.525
1.99793
33
120.130
2.07965
33
108.771
2.03651
33
99.382
1.99731
34
119.921
2.07890
34
108.600
2.03583
34
99.239
1.99668
35
119.713
2.07814
35
108.430
2.03515
35
99.097
1.99606
36
119.506
2.07739
36
108.260
2.03447
36
98.955
1.99544
37
119.299
2.07664
37
108.090
2.03379
37
98.813
1.99481
38
119.093
2.07589
38
107.921
2.03311
38
98.672
1.99419
39
118.888
2.07514
39
107.753
2.03243
39
98.532
1.99358
40
118.684
2.07439
40
107.585
2.03175
40
98.391
1.99296
41
118.480
2.07364
41
107.418
2.03108
41
98.251
.99234
42
118.277
2.07290
42
107.251
2.03040
42
98.112
.99172
43
118.074
2.07215
43
107.084
2.02972
43
97.973
.99111
44
117.873
2.07141
44
106.919
2.02905
44
97.834
.99049
45
117.672
2.07067
45
106.753
2.02838
45
97.696
.98988
46
117.471
2.06993
46
106.588
2.02771
46
97.558
.98926
47
117.272
2.06919
47
106.424
2.02704
47
97.420
.98865
48
117.073
2.06846
48
106.261
2.02637
48
97.283
.98804
49
116.875
2.06772
49
106.097
2.02570
49
97.147
.98743
50
116.677
2.06699
50
105.935
2.02504
50
97.010
.98682
51
116.480
2.06625
51
105.772
2.02437
51
96.874
.98621
52
116.284
2.06552
52
105.611
2.02371
52
96.739
.98560
53
116.088
2.06479
53
105.449
2.02304
53
96.604
.98500
54
115.893
2.06406
54
105.289
2.02238
54
96.469
.98439
55
115.699
2.06333
55
105.128
2.02172
55
96.334
.98378
56
115.505
2.06260
56
104.968
2.02106
56
96.200
.98318
57
115.312
2.06187
57
104.809
2.02040
57
96.067
.98257
58
115.120
2.06115
58
104.650
2.01974
58
95.933
.98197
59
114.928
2.06043
59
104.492
2.01908
59
95.800
.98137
TABLES
RADII METRIC (Continued)
303
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
12 00'
95.668
1.98077
13 00'
88.337
1.94614
14 00'
82.055
.91410
01
95.536
1.98017
01
88.224
1.94559
01
81.958
.91359
02
95.404
1.97957
02
88.112
1.94504
02
81.861
.91308
03
95.272
1.97897
03
88.000
1.94448
03
81.765
.91257
04
95.141
1.97837
04
87.888
1.94393
04
81.668
.91205
05
95.010
1.97777
05
87.776
1.94338
05
81.572
.91154
06
94.880
1.977f7
06
87.665
1.94283
06
81.476
.91103
07
94.750
1.97658
07
87.554
1.94228
07
81.380
.91052
08
94.620
1.97598
08
87.444
1.94173
08
81.285
.91001
09
94.491
.97539
09
87.333
1.94118
09
81.190
.90950
10
94.362
.97480
10
87.223
1.94063
10
81.095
.90899
11
94.233
.97420
11
87.114
1.94009
11
81.000
.90848
12
94.105
.97361
12
87.004
1.93954
12
80.905
.90798
13
93.977
.97302
13
86.895
1.93899
13
80.811
.90747
14
93.850
.97243
14
86.786
1.93845
14
80.717
.90696
15
93.723
.97185
15
86.677
1.93790
15
80.623
.90646
16
93.596
.97126
16
86.569
1.93736
16
80.529
..90595
17
93.469
.97067
17
86.461
1.93682
17
80.436
.90545
18
93.343
.97008
18
86.353
1.93628
18
80.342
.90494
19
93.217
.96950
19
86.245
1.93573
19
80.249
.90444
20
93.092
.96891
20
86.138
1.93519
20
80.156
1.90394
21
92.967
.96833
21
86.031
1.93465
21
80.064
1.90344
22
92.842
.96774
22
85.924
1.93411
22
79.971
1.90293
23
92.717
.96716
23
85.818
1.93358
23
79.879
1.90243
24
92.593
.96658
24
85.711
1.93304
24
79.787
1.90193
25
92.469
.96600
25
85.605
1.93250
25
79.696
1.90144
26
92.346
.96542
26
85.500
1.93197
26
79.604
.90093
27
92.223
.96484
27
85.394
1.93143
27
79.513
.90044
28
92.100
.96426
28
85.289
1.93089
28
79.422
.89994
29
91.977
.96368
29
85.184
1.93036
29
79.331
.89944
30
91.855
.96310
30
85.079
1.92982
30
79.240
.89894 '
31
91.733
.96253
31
84.975
1.92929
31
79.149
.89845
32
91.612
.96195
32
84.871
1.92876
32
79.059
.89795
33
91.491
.96138
33
84.767
1.92823
33
78.969
.89746
34
91.370
.96080
34
84.663
1.92769
34
78.879
.89696
35
91.249
.96023
35
84.560
1.92716
35
78.790
.89647
36
91.129
.95966
36
84.457
1.92664
36
78.700
.89597
37
91.009
.95908
37
84.354
1.92611
37
78.611
.89548
38
90.890
.95852
38
84.251
1.92558
38
78.522
.89499
39
90.770
.95794
39
84.149
1.92505
39
78.433
.89450
40
90.652
1.95738
40
84.047
1.92452
40
78.344
.89401
41
90.533
1.95681
41
83.945
1.92399
41
78.256
.89352
42
90.415
1.95624
42
83.843
1.92347
42
78.168
.89303
43
90.297
1.95567
43
83.742
.92294
43
78.080
.89254
44
90.179
1.95511
44
83.640
.92241
44
77.992
.89205
45
90.061
1.95454
45
83.540
.92189
45,
77.904
.89156
46
89.944
1.95397
46
83.439
.92137
46
77.817
.89107
47
89.828
1.95341
47
83.339
.92085
47
77.729
.89058
48
89.711
1.95285
48
83.238
.92032
48
77.642
.89010
49
89.595
1.95228
49
83 . 138
.91980
49
77.556
.88962
50
89.479
1.95172
50
83.039
.91928
50
77.469
.88913
51
89.363
1.95116
51
82.939
.91876
51
77.382
.88864
52
89.248
1.95060
52
82.840
.91824
52
77.296
.88816
53
89.133
1.95004
53
82.741
.91772
53
77.210
.88767
54
89.019
1.94948
54
82.642
.91720
54
77.124
.88719
55
88.904
1.94892
55
82.544
.91669
55
77.039
.88671
56
88.790
1.94836
56
82.446
.91617
56
76.953
.88623
57
88.676
1.94781
57
82.348
.91565
57
76.868
.88575
58
88.563
1.94725
58
82.250
1.91514
58
76.783
1.88527
59
88.450
1.94670
59
82.152
1.91462
59
76.698
1.88478
304
THE RAILROAD TAPER
RADII METRIC (Continued)
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
Deg.
Radius.
Log. rad.
15 00'
76.613
1.88430
19 00'
60.589
1.78239
23 00'
50.159
1.70035
05
76.192
1.88191
05
60.326
1.78050
15
49.626
1.69571
10
75.776
1.87953
10
60.067
.77864
30
49.106
.69113
15
75.364
1.87716
15
59.809
.77677
45
48.596
.68660
20
74.957
1.87481
20
59.554
.77491
24 00'
48.097
.68212
25
74.554
1.87247
25
59.300
.77305
15
47.609
.67769
30
74.156
1.87015
30
59.050
.77122
30
47.130
.67330
35
73.762
1.86783
35
58.801
.76938
45
46.662
.66896
40
73.372
1.86553
40
58.554
.76756
25 00'
46.202
.66466
45
72.986
1.86324
45
58.309
.76574
15
45.752
.66041
50
72.604
1.86096
50
58.067
.76393
30
45.311
.65620
55
72.227
1.85870
55
57.826
.76212
45
44.878
.65203
16 00'
71.853
1.85644
20 00'
57.588
.76033
26 00'
44.454
.64791
05
71.483
1.85420
05
57.351
.75854
15
44.038
.64383
10
71.117
1.85197
10
57.117
.75677
30
43.630
.63979
15
70.755
1.84976
15
56.884
.75499 i
45
43.230
.63579
20
70.396
1.84755
20
56.653
.75322
27 00'
42.837
.63182
25
70.041
1.84535
25
56.425
.75147
15
42.451
.62789
30
69.690
1.84317
30
56.198
.74972
30
42.072
.62399
35
69.342
1.84100
35
55.973
.74798
45
41.701
.62015
40
68.998
1.83884
40
55.749
.74624
28 00'
41.336
.61633
45
68.657
1.83668
45
55.528
.74451
15
40.977
.61254
50
68.320
1.83455
50
55.308
.74279
30
40.625
.60879
55
67.986
1.83242
55
55.090
.74107
45
40.279
.60508
17 00'
67.655
1.83030
21 00'
54.874
.73937
29 00'
39.939
.60140
05
67.327
1.82819
05
54.660
.73767
15
39.605
.59775
10
67.003
1.82609
10
54.447
.73597
30
39.277
.59414
15
66.682
1.82401
15
54.236
.73429
45
38.954
.59055
20
66.363
1.82193
20
54.026
.73260
30 00'
38.637
.58700
25
66.058
1.81986
25
53.819
.73094
30
65.736
1.81780
30
53.612
.72926
35
65.427
.81576
35
53.408
.72761
40
65.121
.81372
40
53.205
.72595
45
64.818
.81170
45
53.003
.72430
50
64.517
.80967
50
52.804
.72267
55
64.219
.80766
55
52.605
.72103
18 00'
63.924
.80566
22 00'
52.408
.71940
05
63.632
.80368
05
52.213
.71778
10
63.343
.80170
10
52.019
.71616
15
63.056
.79973
15
51.827
.71456
20
62.772
.79777
20
51.636
.71295
25
62.490
.79581
25
51.446
.71135
30
62.211
.79387
30
51.258
.70976
35
61.935
.79194
35
51.072
.70818
40
61.661
.79001
40
50.886
.70660
45
61.389
.78809
45
50.702
.70503
50
61.120
.78618
50
50.520
.70346
55
60.853
.78428
55
50.338
.70190
TABLES 305
NOTATION
A = Curvature increment of taper per 10 meters of taper.
M = Degree of main circular curve.
I = Length of taper from the B.C. of the taper.
/ = Deflection from tangent at the B.C. of the taper.
f'j /i> /2j etc. = Deflection from tangent at some point on the
taper.
b = Deflection from tangent at the end of the taper, C.C. of
main curve, to the B.C. of the taper.
o = Central angle of the taper at each end of the curve.
d = Circular curve offset from tangent to provide room for
the taper.
t = Distance along the tangent, from opposite the offset posi-
tion of the B.C. of the simple curve to the B.C. of the
taper.
D = R + d, where R is the radius of the main circular curve.
x and y are co-ordinates of points on the taper, referred to the
tangent at the B.C. of the taper as meridian, and
to a radial line at the B.C. of the taper as base.
Ic = Long chord of the taper, from the B.C. of the taper to
points on the taper,
s = Distance along the taper, from the B.C. of the taper to
the transit, when an intermediate set-up is necessary.
T = Semi-tangent of the entire tapered curve, from P.I. to
B.C. or E.G.
E = External, the distance from the P.I. to a point on the curve
radially opposite.
EQUATIONS
Eqn. No.
T = t + D tan \I. (7) Both ends the same
taper.
T t = t + D tan \ I - d esc 7. (8) Tapered end other
end not tapered.
T n = Rtan \ I + <Z csc 7. (9) Untapered end
other end tapered.
T 7 ! = ti + Di tan 7 - (di d 2 ) esc 7. (10) Both ends tapered,
with different ta-
pers.
T 2 = U + A> tan | 7 - (d* - di) esc 7. (11) Both ends tapered,
with different ta-
pers.
E = D sec % I - R. (12) Both ends the same
taper.
306 THE RAILROAD TAPER
EMPIRICAL EQUATIONS DERIVED FROM THE
METRIC TABLES
A
(45m)
(1 + 5) (Z + 10)
(107m)
(94m)
20
A
20
A
3 1 (I + 10)
(108m)
20
A
The equations under paragraph 18 as derived from the metric
taper tables become :
I = (M A). (45m)
A
In = (M 2 A). (46m)
10 M,
Zi = - -v (47m)
lc = ^ (M, - M! - A). (48m)
= 15(M 2 + Mi)(M 2 -M 1 -A) t
A
a = 15Mi(M 2r Mi-A). (51am)
20
A
2M 2 + A)(M 2 -M 1 -A)
' (56m)
+ A!- (57m)
TABLES
307
08
- O * CO 00 t"- <N i i O iO O5 00 CO <N b- CO
rH <M CO CO CO CO 0} O <* rH * i-l CO TH 10
o 10 iO iO iO iO iO IO iO T}H Tj< CO CO <> i i O
* <M to CO CO * b- iO QC t^ O 00 T ( Oi <N .CO
CO rt< iO iO iO -^ CO i i iO CO iQ (N CO lO . O
COOO>Ot^COO<M'*i ICOOC100 .C^IO
OOi IrHT-HO'OCO' l-^i 1 CO ^ . IO >O
CO ^ Tt< T^l rj< Tfl CO CO CO <M <M rH O O T-H
.
COCOGiOOCO(M(MOOOO^LO .OOCO(M
(N CO CO * CO <M i I O (M iO <M rfi . ^ ^f ^
CO CO CO CO CO CO CO C^ (N i-l rH O -OrH(N
08
i- p >- . '
(M <M CD iO O O5 CO CO t^ t^ i i . tO O rH C<1
iO O OOO-^ CO r-t rt< T-H rj< .r^cOCOCO
(M CO CO CO CO (M <N (M rH r-l O -OrH
.
*^c<j'ocot^ooocoajt^ .r-icxDOt^oo
(M CO CO CO (M rH >O CO O CO . TjH (M <N rH rH
(N CN (M <N <N <M rH rH rH O ' O rH <M CO ^
OB
rH C<J (N (M rH rH rH rH O ' O rH C^ CO ^ >O
qS
o?,,
.
IO rH C<tt^ OO CO Tf O . CO CO l>- t^ rH O O
CO "*! rf CO 05 rH IO CO . CO rH IO -^ ^ * "^
^H rH rH rH rH rH O O ' O rH rH (M CO ^ >O
08
^i00500CO<Mt^.CO .OO
r-l r-| rH rH O ^ <M . CO O
rH rH rH rH rH O O ' O rH rH (M CO ^ O O
dt
OrHOOOO 'GO rH <M COCO"* I0t^
OOOOO 'OO rH
Pi,
OOOO O O rH rH (M CO ^ "* IO CO OO
08
.
rH^HrH '. rH CO O CO O ^ CO (M CO (M <M CO
OOO 'OOrHrHI
OO O O O rH rH <M CO CO ^ O CO l^ O5
02
O ' O O O rH rH <M (M CO -^ O CO t^ OO Oi
308
THE RAILROAD TAPER
1 O O5 i
CX)OOO'
co co cc cs <N cs cs <N c< cs <M cc cq c^ <N
O O i-H i-H-i-i i-H<M<M<N(MCOCOCOCO^
TABLES
309
TAPER \ METRIC INTERMEDIATE VALUES A =
M
I
/
b
o
D
logD
d
t
X
y
Ic
45
20.000
1
009*
t
013
022|
1527.921
3.18410
0.022
10.000
0.055
20.000
20.000
50
23.333
Oil!
017*
0291
1375.141
3.13835
0.030
11.667
0.080
23.333
23.333
55
26.667
014*
0221
0361
1250.144
3.09696
0.041
13.333
0.113
26.666
26.667
1 00
30.000
017*
027*
045
1145.984
3.05918
0.054
15.000
0.153
29.999
30.000
05
33.333
020f
033*
0541
1057.855
3.02443
0.070
16.667
0.201
33.333
33.333
10
36.667
0241
040
1041
982.318
2.99225
0.088
18.332
0.259
36.665
36.666
15
40.000
028
047
1 15
916.860
2.96230
0.109
19.999
0.327
39.998
39.999
20
43.333
032}-
054*
1261
859.589
2.93429
0.133
21.666
0.407
43.331
43.332
25
46.667
036|
021
1391
809.062
2.90798
0.160
23.331
0.497
46.662
46.665
30
50.000
0411
HI
152*
764.156
2.88318
0.190
24.998
0.600
49.994
49.998
35
53.333
0461
20|
206!
723.984
2.85973
0.225
26.664
0.716
53.325
53.331
40
56.667
051*
301
221!
687.837
2.83749
0.263
28.330
0.847
56.656
56.663
45
60.000
057
40*
237*
655.139
2.81633
0.305
29.996
0.993
59.986
59.995
50
63.333
102|
151*
2541
625.423
2.79617
0.351
31.662
1.154
63.316
63.326
55
66.667
108|
203
311!
598.299
2.77692
0.402
33.327
1.332
66.644
66.658
2 00
70.000
115
215
330
573.445
2.75849
0.458
34.992
1.527
69.972
69.989
05
73.333
121*
2271
3491
550.588
2.74083
0.518
36.657
1.740
73.299
73.319
10
76.667
128*
2401
4091
529.499
2.72387
0.583
38.321
1.972
76.623
76.650
15
80.000
135*
254*
430
509.982
2.70755
0.654
39.986
2.224
79.948
79.979
20
83.333
143
3081
451!
491.872
2.69185
0.731
41.651
2.497
83.270
83.307
25
86.667
150f
323*
5141
475.020
2.67671
0.813
43.314
2.791
86.590
86.635
30
90.000
1581
3381
537*
459.303
2.66210
0.900
44.977
3.107
89.909
89.962
35
93.333
207
3541
601!
444.612
2.64798
0.994
46.639
3.446
93.224
93.288
40
96.667
2 15|
4111
626!
430.851
2.63433
.094
48.302
3.808
96.538
96.614
45
100.000
224*
428
652*
417.937
2.62111
.200
49.964
4.196
99.849
99.937
50
103.333
233*
4451
7191
405.795
2.60831
.313
51.626
4.608
103.157
103.259
55
106.667
2421
504
746!
394.361
2.59589
.433
53.285
5.047
106.461
106.581
3 00
110.000
252*
522*
8 15
383.576
2.58385
.560
54.945
5.512
109.762
109.900
05
113.333
302*
5411
8441
373.387
2.57216
.694
56.605
6.005
113.059
113 217
10
116.667
312|
601*
9141
363.750
2.56080
.836
58.262
6.526
116.351
116.534
15
120.000
323
622
945
354.622
2.54977
.985
59.920
7.077
119.639
119.848
20
123.333
334
6421
1016!
345.965
2.53903
2.142
61.576
7.658
122.922
123.160
25
126.667
345
7041
10491
337.747
2.52859
2.307
63.231
8.269
126.199
126.470
30
130.000
3561
7261
1122*
329.935
2.51843
2.480
64.885
8.911
129.470
129.775
35
133.333
407f
749
1156!
322.503
2.50853
2.661
66.539
9.586
132.734
133.078
40
136.667
4191
8 12
1231!
315.427
2.49890
2.851
68.189
10.294
135.992
136.380
45
140.000
432
835*
1307*
308.683
2.48951
3.051
69.840
11.035
139.242
139.678
50
143.000
4441
900
13441
302.249
2.48036
3.259
71.489
11.810
142.484
142.973
55
146.667
457
9241
1421!
296.107
2.47145
3.476
73.135
12.620
145.718
146.265
4 00
150.000
510
950
1500
290.240
2.46276
3.703
74.781
13.467
148.942
149.550
310
THE RAILROAD TAPER
OS
d?.
08
08
08
08
08
08
05,
ds
s
08
ds
OS
OS O O O5 O5 O5 O5 OO 1 !> 1C "* CO i 1 '
o !>. OO GO 00 OO QO l>. !> CO O ^t 1 CO rH ' i-H
. HHMnn|- HNrnlNWl-* H-di^lNnW . ^|N^|-*
* CO b 00 O T-I (M CO 1C CO t^ OO O . t^ CO
Tf O i 1 (M i 1 *ft C* t& 1C >O -* 1 CO . CO C^
o CO t t^. b !> CO CO ift TJH CO <N i i ' T-H CO
.
CO (N . O i i <M
C^Cq .COi-HO
o o CO CO CO CO iO iO TJH CO <N i i ' T-H CO O
.
i i !> CO O CO C^ 00 iO . <N CO O CO
i-H OOCOlOr-H ^H i-H .(MlO-^CO
' I ' i i (N -^ CO
CO "^ -tf ^ CO CO <M <N T-H -i-KN^COOO
CO CO CO CO <M <M T-I rH i I C<1 CO O 1> Oi
Ofl <M <M <M (M TH O ! i i <N CO iO CO OO O
o i-H C<l T-H rH i-H O ! O T-H CO Tfl CO t>- Oi
TH TH T-H T-H O ' O TH O3 ^ 1C t>- 00 O C<l
l . rH!Mrt|^ mHMNr4|- n|-r-<!NH|-4l
O .l> CO IOCO C^ TH Q OO t^ CO
CO .CO(N(NCO>O<MO^TmO
OOOO OTH<NCO"tf COOOO5THCO
. HNHlnnN r-i|TK
O CO (N .O TH <N CO iO CO t^ OO O TH
CO CO <M . CO TH O O TH CO O **< -^
o OOO 'Oi-KN CO-^>Ot>OOO(N^
OO O O TH C1 CO -^ COJ> O5 TH CO iO
TH TH TH
o O ' O O TH <N CO Tt< O CO 00 O C^l * CO
H
TABLES
311
II
OOOiOiCiOSO^OiOOt^cDCO
o
-^ <*""^ {"*> f*" 1 '^ t^- CD O5 C^ CD OS C^
> t>- ^ 00 O CO Ci >O
i Ci Oi 00 t>- CD CO O
o
T
8^SS88S*SSS J o
K, OOOO'-lT-HCO'*CDo6O'*t^i-H
rj i-ii-H i-KN
PH
w
ooo.*-** 1 !^ 881
o
o .
^^ , ,^ , , ^^ ,.. v >^, ^^^ ...^ 4. CO T-H O5 Oi '"^
o o o o o o o T-H T-H <M" co co ^' CD
O
q ;.
pj ^ CO <N C<i <M <M <N (N (M CS i (N <M CO i CQ <N
Q
b '
Sc^ScoScoScoScoScoSco
312 THE RAILROAD TAPER
TAPER 1 METRIC. INTERMEDIATE VALUES
M
I
/
6
D
logD
i
t
X
I
k
1 30
20.000
018!
0261
045
764.009
2.88310
0.043
10.000
0.109
20.000
20.000
35
21.667
021
0303
051|
723.8102.859620.051
10.833
0.133
21.666
21 667
40
23.333
023*
034;
0581
687.634:2.837360.060
11.666
0.160
23.333
23.333
45
25.000
0261
039;
105*
654.905
2.816180.071
12.499
191
24.999
25.000
50
26.667
029
044;
1 131
625.154
2.795990.082
13.333
0.225
26.665
26.666
55
28.333
032
049i
1 21*
597.991
2.776690.094
14.166
0.263
28.332
28.333
200
30.000
035
055
130
573.095
2.75823
0.108
14.999
0.305
29.998
29.999
05
31.666
038|
100!
139
550.193
2.74052
0.123
15.832
0.352
31.664
31.665
10
33.333
041*
106|
1481
529.055
2.723500.139
16.665
0.403 33.330
33.332
15
35.000
045
1 13
158
509.484
2.707130.156
17.498
0.458! 34.996, 34 998
20
36.667
048*
1 195
2081
491.316
2.691360.175
18.331
0.518! 36.661 36 665
25
38.333
052;
1 261
219
474.402
2.67615
0.195
19.164
0.583 38.327 38 331
30
40.000
056;
133!
230
458.620
2.66145
0.217
19.997
0.654 39.992; 39.997
35
41.667
100:
1411
241*
443.858
2.64725
0.240
20.829
0.730! 41.6571 41 663
40
43.333
1 04i
1 48|
2531
430.022
2.63347
0.265
21.662
0.812
43.322! 43.328
45
45.000
1081
156!
305*
417.028
2.62017
0.291
22.495
0.900
44.986
44.995
50
46.667
1 131
205
3 181
404.801
2.607240.319
23.327
0.993
46.650
46.661
55
3 00
48.333
50.000
1171
122*
213!
222*
331*
345
393.277
382.396
2.59470:0.349
2.58251 0.380
24.160
24.992
1.093
1.200
48.314
49.977
48.326
49.992
05
51.667
1271
231|
359
372.106
2.570670.413
25.824
1.313
51.640
51.657
10
53.333
132
241
4131
362.363
2.55914 0.449
26.657
1.432
53.302
53.321
15
55.000
137^
250*
428
353.123
2.54793 0.486
27.489
1.559
54.9641 54.986
20
56.667
142
300*
4431
344.348
2.537000.525
28.320
1.693
56.626
56.650
25
58.333
148
3 lOf
459
336.006
2.526350.566
29.152
1.835
58.286
58.314
30
60.000
153
32H
515
328.064
2.51596|0.609
29.984
1.984
59.946
59.978
35
61.667
15&
332
53U
320.496
2. 50582 '0.654
30.815
2.141
61.606
61 643
40
63.333
2051
343
5481
313.278
2.495930.702
31.646
2.306
63.264
63.306
45
65.000
21H
3541
605*
306.384
2.486270.752
32.477
2.480
64.922
64.969
50
66.667
2 171
406
6231
299.794
2.476820.804
33.308
2.662
66.579
66.633
55
68.333
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293.489
2.46759
0.858
34.139
2.852
68.235
68.294
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430
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287.452
2.45857
0.915
34.969
3.051
69.889
69.956
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281.666
2.449730.974
35.799
3.260
71.543
71.618
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73.333
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276.1152.44109 .035
36.629
3.477
73.195
73.278
15
75.000
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270.7882.43263 .099
37.459
3.704
74.847
74.939
20
76.667
257
5211
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265.671 2.42434
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38.288
3.941
76.497
76.600
25
78.333
304
535
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260.7522.41623
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39.117
4.187
78.145
78.259
30
80.000
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548f
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256.0202.40827
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39.946
4.444
79.792
79.918
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81.667
318^
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251.4672.40048
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40.774
4.710
81.437
81.576
40
83.333
326
6171
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247.0802.39284
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41.602
4.987
83.081
83.232
45
85.000
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242.8542.38535
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42.430
5.274
84.723
84.888
50
86.667
341
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238.7792.37800
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43.257
5.572
86.363
86.543
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88.333
349
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234.8482.37079
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44.084
5.882
88.000
88.196
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90.000
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717i
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231.0542.36372
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44.911
6.202
89.636
89.850
05
91.667
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227.3902.35677
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45.736
6.534
91.270
91.503
10
93.333
414
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12031
223.8502.34996 .985
46.562
6.877
92.901
93.154
15
95.000
422*
805*
1228
220.429 2.34327 2.083
47.387
7.232
94.529
94.805
20
96.667
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12 531
217.12212.336702.185
48.211
7.599
96.155
96.455
25
98.333
4391
8391
1319
213. 92112. 33025:2. 289
49.035
7.977
97.780
98.103
30
100.000
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8561
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210.8252.323922.397
49.858 8.369
99.399
99.751
35
101.667
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14114
207.828|2.31770 2. 508
50.681 8.772
101.016
101.401
40
103.333
507
9311
14 381 204. 925|2.31159 2.622
51.503 9.188
102 631
103.041
45
105.000
516J
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202.1132.305592.740
52.325 9.617
104.241
104.684
50
106.667
525;
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15331
199. 389 2. 29970 1 2. 861
53.145 10.059
105.849
106.326
55
108.333
536
10251
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196.7482.29391
2.986
53.965
10.513
107.452
107.969
6 00
110.000
545
1045
1630
194.188
2.28822
3.115
54.785
10.981
109.052
109.604
15
115.000
6 15
1143
1758
186.958
2.27174 ! 3.521
57.238
12.466
113.828
114.508
30
120.000
6461
1243!
1930
180.3502.256123.961
59.683
14.077
118.563
119.395
45
125.000
7181-
13 46|
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174.2992.241294.436
62.119
15.817
123.252
124.263
7 00
130.000
752^
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2245
168.751
2.227254.947
64.546
17.689
127.890
129.108
15
135.000
827i-
16001
2428
163.658
2.213945.495
66.961
19.698
132.471
133.929
30
140.000
903i
17111
2615
158.979
2.20134
6.081
69.365
21.850
136.990
138.718
TABLES
313
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Tt< 1C tO "O lO O tO lO iO CO CO CO CO CO CO t^ t^ 1> t^ 00 00 OO 00
OSCDoico^to'cdl^OsCDrHeqco COOOCD<NT^cOo6cD(M'^
TfiiOtOiO>OO>OiO>OCOCOCOCO COCOt^-lS-t-t-t^OOOOOO
t>-rHTfiOOC<liOO' 1 ^OOCOOOCOOO
OOi iCOCOC^Os>OOCO>O>O'^ti I rHiOi it^-C^iOt^t^iOC^
CO 00 OS O rH rH (N CO CO CO CO CO CO C^l O OC -<t O -* I> OS O O
rH ^ rH O 00 OS rH -* OS l> OS CO OS
rHrHrH(MCOTtlC005(M0
-a ._ .__
rHrHrHC<Jc<lC^(N'c^(N(NC^ COCOCO-^^iOiOCOcOI>
CO C^l rH C^ ^O CD 1^* CO !> CD ^ CD OO *O t^* C^J CO CD CO C^ t^ OO ^t 1
OSOSOSOSOSOSO5O5O5OSOSOSO5 OOOOOOOOOOOOOOOOOOOO
t^-O^COC^COt^CQlOCOrHOO^f COrHOSCOOCOOOOOCOI>-
rH CO lO 00 C^ 1><M 00 *
r>OCOrHCOOOI>-lO'^t
O5OSO5O5O500OOOOOC
HMH!N H|MiH|M
OS OS O O rH rH (N C^ CO CO T^ tO IO CO OO OS O rH CO T^ CO t^ OS
IO "5 iO CO CO CO l> !> 1> i> OO 00 00 OS O O rH <M <M CO rfi 10 O
O O CO CO CO cO CO CO t^ IS t^ t^ OO OO OO OO OS
TABLES
333
o iO CO CO CO ^ (M 05 10
ds
OiOCJOOOCO
do
- lo
O
^H ^ ; ,-H rti oo c^ oo *
08
lO CO l>- OO O T-H C<l
T-H (N <N T-I P CO 10
T-I CO CO O tO O CO
T-H T-H CN CN
334
THE RAILROAD TAPER
CO O O Cl
TF OS <N O
O5
TtHOOTfiOCOiOt^CQ
oc^ioooooTtico
O O O i-H TH I
Ol C^ CO ^^ ^^ GO O5 C^
CO ^~H ^^ O5 GO 00 !> 1 s "
<M' <M" c^i i-! T-i r-i r-I ^-i
* OCOOCOOCOOCO
TABLES
335
t>. CO
CO
i ( OO rt< O lO
,3 ^^^^^
S<Nc3 <M<N <N <N <N 75 (NO! CO CO CO CO 00 CO CO CO CO CO ^
O O O O O O i-H i-I rH r-l i-l i^ rH rH <N <N <>i O* <N CO CO CO
ddddbdddddd
OOI>>O'^t | CO'-HOOiOOt > -CO iO^COC^r-iOOiOOt~>-
,_, ,_, ^H ^H rH r-t T-l O O O O O O O O O O Oi OS Oi
C<i(N(N(NC^C^C^<NC^<Nci
^H i i O3 rH CO rt< rt* TH (N 1^ 00 CO <N CO CO O >O Oi (N "* ^ i i
i i <M CO CO <N -^i 00 <* <N rH <N to Oi ^ O 00 CO iO CO t^ Oi CQ
cooocoosioi it^r^^Hooo c^oit^ioc^ooocd^c^i-H
-^ Tt< CO CO CO <N (M (N T-H ^H T-H OOOOOOSOiOSOiOi
i i co co Oi <M co -H co cq oo o <N
-KNCO^OT-HCO^O^CO iC
(N<M (MiMCOCOCOCO ^^r^ ^ O O iO CO CO CO t^ t> Ir^ 00
i-< i 1 1 i I-H C^ C^ C^ (M C<l <M CQ CO CO CO CO CO CO "tf TJH -^ T^ T*<
336
THE RAILROAD TAPER
05 05 J>* C^l '^ CO 05 C^ ^^ CO *O "^ CO 05 05 CO CO 00 ^"i CO C^l t^" ^O *O
COOt^-'^OCO'-Hf^C^ Ot^-C^iOOCOOi-HOCO 00 CO 05 00 C^
|> J> CO CO CO *O *O "^ '^ CO *"^ ^2 OO CO "^ ^H 0i CO C^ 00 ^f 05 "^ 05
3^3h$$W3 ss?ig^8SS^o ^^^^^
OJC^^OOiCOOO^OOS Oit v -COOO^fi-H' i^fiHC^ OOOOOOCO
T (COi (t^-iOCOPOT^iO C s ^ T t 1 ' idO5r- lOOOOOi i Oi^COOOd
CO ^H O5 t^ t^* CO t^ t^* O5 ^^ CO CO O^ CO
<Nco^ ^^
C^
^COiO
t~--iOCOO1OO5Oi OiOC^COr i
CO -** 1 iO CO 1>- t>- 00 O CO iOt>- O <
^T-J^^T-HT-JT-H C^fMC^C^eO
GO OO *-O CO T 4 1>- CO C^ CO CO OS 00 CO CO
o' OS O5 O^ OS O5 OS OS OS GO OO OO OO OO 00 00 00 00 OO t^ I s * t>
i I 1C CO CO O CO OO CO CO t^ rt< lO OS i I lO CO I> O ^O OO -^ OS OS O
COI> O OS OS rf * O O <* iO I-H T i iO O t^ TJH <M 00 CO I> OO !> -^
to OS -^ OS O C^J OS l> >O C<| i i CN -^ 1> C^ (N ^ CN O O O T i CO CO
oJ t>^ co Tt< co CN o os 06 co ^ IN o 06 i>i to -* co c<i i-looio6b-
00 00 00 00 00 00 00 t^ t- t^ t^ t^. t^ CO CO CO CO CO CO cOcOOtoto
ocooco 1-1 ioco c3oo totoiooo
000000=000^,-,
Hf nNmHi Hf'HNH-*^lP
Sg^^2^S
to to tO lO 1C CO CO CO CO 1> l>- OO 00 OS O O i I i-< C^ CO CO T^ to O
<M -* CO 00 O <N ^ CO 00 O <N -^ CO 00 O
10 to to to co co co co co
TABLES
TAPER 3| METRIC. CURVATURE INCREASING 3 00 ;
EVERY 10 M. A = 3
Transit
at
Deflections to
B.C.
3 00'
C.C.
6 00'
C.C.
9 00'
C.C.
12 00'
C.C.
.15 00'
C.C.
18 00'
C.C.
21 00'
C.C.
24 00'
I
10
20
30
40
50
60
70
10
20
30
40
50
60
70
O /
45'
237|
530
922i
14 15
2007^
2700
045
'l 30
407|
745
1222
1800
2437^
152|
130
2 15
537|
1000
1522|
2145
330
322i
215
300
707|
12 15
18221
5 37|
545
452|
300
815
837|
800
622^
345
4 30
1007^
11221
1200
1137^
1015
752|
430
5 15
1500
15521
1545
14 37
1230
922|
5 15
345
837
1430
TAPER 3| METRIC. CURVATURE INCREASING 3 00'
EVERY 10 M. (Continued) A = 3
M
1
D
log D
d
t
X
V
lc
600
10
1 30
191 . 138
2.28135
0.065
4.998
0.131
9.999
10.000
900
20
430
127.716
2.106250.261
9.986
0.654
19.986
19.997
1200
30
900
96.320
1.983720.652
14.951
1.83029.916
29.972
V 1500
40
1500
77.912
1.89160
1.29919.868
3.910
39.697
39.889
1800
50
2230
66.186
1.82077
2.26224.703
7.129
49.166
49.680
2100
60
3130
58.471
1.766943.597
29.405
11.684
58.076
59.240
2400
70 4200
53.451
1.727965.354
33.906
17.709
66.090
68.421
|
1
338
THE RAILROAD TAPER
CO -^ CO i i OS 00 CO Tt< CO i i OS OOcOr^C^^H
rij
CO CO CO CO to CO O t^ CO OO CN CO OSr- ii lOOO^fCS
T ( T}H 1> CO CO CO OS i* ^ CO OS T ( CO CO OO CO *""< CO ^f
t>. iO CO CN i i l>-
, o irj i i t^ rJH j-*
OS O i I W CO ^ to l>- 00 O5
Or- ICO^O1>. OO O i-H C^ CO tO CO !>. OO OS O ^-H Ofl
THOOC^cOO^t 1 OOCOI>'-HOO5 COt--' itOOTt^OO
^H to iO
OOC5OOOO OOOOOO OOOOOOO
^ (M O OS t^ co TJH
os os os oo oo oo oo
"* Tt< iO iO O CO CO
OS OS O O T-H 1-1 (M
t^O5(NiOOO(McO O
CO^OT-KNr^to 1-1
(M <N CO CO CO CO CO
O CO CO CO CO l> t
i O i i C^ co cOTfitOO
1-1 T-I iM (N <M <N iM <M(NCOCOCOCO CO CO CO "tf
t^ CO CO t 1 ** CO CO t^* CO CO I>* CO CO I>* CO CO !> CO CO
COOCOCOO COCOOCOCOO COCOOCOCOOCO
COtOCOi-nO OO CO to CO T i O OOCOtOCO'-HOOO
TABLES
339
OS CO t>. i
r-t ^ CO I
^ <M O i
rH CO b- CM '
i I 00 Tt< O '
JS OS OS 00 CO Tt< O to 00 rH CM
^JOO^pCOCM OOCOOO^^
cOt^-OOOSOs rH CO <* CO 00 OS rH CN TF CO l^ OS O CM CO O OO
CO CO CO CO CO Tt< Tfi Tfi "tf rti rJH to to to iO iO iO CO CO CO CO CO
CM CO CO i I t
00 OS CO OO CO O l^ "f CO
to i"~t CO OS T-H I-H 00 ^ t^*
CO CO i4 CO C^\ !> r-n CO CO
CO t^ OO OO OS i i CN Th CO b- OS O CM CO to CO OO OS O CM CO CO
CO CO CO CO CO TjH -^ Tti "* Tt< T^ to iO to iO to to to CO CD CO CO
8ii o CD o
OS OS OS r1
COCOCOCOCO T}HTtiiOOCOI>. 1^0005001-1 (MCO^Ot^
i TfH CO ^H ^^ C*^ Ot> O^ '
i 00 CO O^ *O T-H
ii I OO i I CM OS Tf to CO
i co co oo os os co co co
t^ CO OO CO '
T i os CO -^
OO 00 OS OS OS O T-H CM CO CO
O
(M (
' OO OS O O i i <M CO
(N CQ CO CO CO CO CO
T-H CO 1 "* "^ OS CO CM GO CM l"^ CM !> CO CO !> CD !> OS CO OS 00
"53 CO *~^ '"H CM CM ^f* *O b* OS CO CM "^ CO 00 '"^ CO to GO TI "^ t^*
I i-H rH i I r-t i I T-I T-| rH CM CM CM CM CM CO CO CO
~^> "^ CO OS CO ^t^ OS OO CO CO t^* CO CO OS T-H 00 OS "^f CO (
T ( r- 1 O OS OS t^-COtO^fCOCM i ( O OS OO l^- CO tOtO^COCM
OS OS OS 00 OO OO GO 00 00 00 OO OOOOI>i>t^l> l>t^l>I
SCO ^H OO CM CM to 00 t^. CO ' _
CO rH CO rH OS CO CM IO rH OO CO tO CO OS ^ l>-
rHl>.TtlCMOS tO^f^ftOOOrH COON 1
Q . .
CO rH CO OS !> tO CO rH OS t N * CO Tf CO rH CO OS 00
sssfs cf^Il8 s^fsss fsiss
iO
t^ OO 00 OS OS O O rH CM CO Tt| tpcOi>.oqOSO rHCMcOT^t^
i CM CM CM CM CM CM
Tt< to iO to to CO CO CO l> !> 00 OO OS OS O O i ( i ( C^ CO CO iO
CO
> t^ CO i
' CO CO '
' CO CO '
CO CO CO CO ^ -t 1 "* -^ ^ rt< to to iO to iO to CO COCOcOCO
88888
340 THE RAILROAD TAPER
TAPER 3 METRIC. CURVATURE INCREASING 4 00'
EVERY 10 M. A = 4
Transit
at
Deflections to
B.C.
4 00'
C.C.
8 00'
C.C.
12 00'
C.C.
16 00'
C.C.
20 00'
C.C.
24 00'
C.C.
28 00'
I
10
20
30
40
50
60
10
20
30
40
50
60
,
100
230
200
/
440
430
300
'400
930
1620
730
740
630
400
'sod
11 30
1100
1130
1040
830
500
600
/
1510
1600
1530
1340
1030
600
100
330
720
1230
1900
2650
200
530
1020
1630
2400
300
730
1320
2030
TAPER 3 METRIC. CURVATURE INCREASING 4 00'
EVERY 10 M. (Continued) A = 4
M
l
o
D
log>
d
i
X
y
lc
800
10
200
143.443
2.15668
0.087
4.996
0.175
9.999
10.000
1200
20
600
96.016
1.98234
0.348
9.974
0.872
19.974
19.993
1600
30
1200
72.719
1.86165
0.866
14.912
2.437
29.851
29.951
2000
40
2000
59.309
1.77312
1.721
19.767
5.195
39.463
39.804
2400
50
3000
51.083
1.70828
2.986
24.477
9.432
48.526
49.434
2800
60
4200
46.067
1.66339
4.731
28.957
15.347
56.616
58.66^)
TABLES 341
TAPER 3| METRIC. INTERMEDIATE VALUES A=4
M
I
/
6
o
D
log D
d
t
X
V
Ic
1200
20.000
230
330
600
96.016
1.98234
0.348
9.974
0.872
19.974
19.993
15
20.625
237
342
619
94.095
1.97357
0.372
10.284
0.941
20.596
20.617
30
21.250
244
353*
638*
92.252
1.96498
0.397
10.594
1.013
21.217
21.241
45
21.875
251J
407
658i
90.484
1.95657
0.423
10.904
1.089
21.838
21.865
1300
22.500
258!
420
718!
88.787
1.94835
0.450
11.214
1.169
22.458
22.488
15
23.125
306i
433J
739*
87.155
1.94029
0.478
11.523
1.252
23.077
23.111
30
23.750
314
447
801
85.587
1.93241
0.508
11.833
1.339
23.696
23.734
45
24.375
322
500!
822!
84.078
1.92468
0.538
12.142
.430
24.315
24.357
1400
25.000
330
515
845
82.625
1.91711
0.570
12.450
.525
24.933
24.979
15
25.625
338i
529*
907!
81.225
1.90969
0.602
12.759
.624
25.550
25.602
30
26.250
346*
544*
931
79.876
1.90242
0.636
13.067
.727
26.167
26.224
45
26.875
355
559*
954*
78.575
1.89528
0.671
13.375
.834
26.783
26.846
1500
27.500
403!
615
1018!
77.321
1.88830
0.708
13.683
.945
27.398
27.467
30
28.750
421*
647
1108*
74.940
1.87471
0.784
14.298
2.182
28.626
28.710
1600
30.000
- 440
720
1200
72.719
1.86165
0.866
14.912
2.437
29.851
29.951
30
31.250
459
754*
1253*
70.643
1.84906
0.953
15.524
2.710
31.072
31.190
1700
32.500
518!
830
1348!
68.700
1.83696
1.045
16.135
3.002
32.288
32.427
30
33.750
539
907
1446
66.879
1.82529
1.143
16.745
3.315
33.499
33.662
1800
35.000
600
945
1545
65.170
.81405
1.246
17.353
3.648
34.704
34.895
30
36.250
621*
1024*
1646
63.567
.80323
1.356
17.959
4.002
35.904
36.126
1900
37.500
643!
1105
1748!
62.060
.79281
1.471
18.563
4.377
37.097
37.355
30
38.750
706*
1147
1853*
60.643
.78278
1.593
19.166
4.775
38.284
38.581
2000
40.000
730
1230
2000
59.309
.77312
1.721
19.767
5.195
39.463
39.804
30
41.250
754
13 14*
2108*
58.053
.76382
1.855
20.365
5.639
40.633
41.023
2100
42.500
8 18!
1400
2218!
56.870
.75488
1.996
20.961
6.106
41 . 794
42.238
30
43.750
844
1447
2331
55.755
.74628
2.143
21.554
6.598
42.945
43.449
2200
45.000
910
1535
2445
54.706
.73804
2.298
22.145
7.114
44.086
44.656
30
46.250
936*
1624*
2601
53.717
.73011
2.459
22.733
7.655
45.215
45.858
2300
47.500
1003!
1715
2718!
52.787
.72253
2.628
23.317
8.222
46.332
47.056
2400
50.000
1100
1900
3000
61.083
.70828
2.986
24.477
9.432
48.526
49.434
2500
52.500
1158!
2050
3248!
49.577
.69528
3.375
25.623
10.749
50.660
51.787
2600
55.000
1300
2245
3545
48.248
.68348
3.794
26.753
12,173
52.725
64.111
2700
57.500
1403!
2445
3848!
47.083
.67286
4.246
27.865
13.705
54.714
56.403
2800
60.000
1510
2650
4200
46.067
.66339
4.731
28.957
15.347
56.616
58.660
342
THE RAILROAD TAPER
TAPER 3f METRIC. CURVATURE INCREASING 5 00'
EVERY 10 M. A = 5
Transit
at
10
20
30
40
50
Deflections to
B.C.
5 00'
C.C.
10 00'
C.C.
15 00'
C.C.
20 00'
C.C.
25 00'
C.C.
30 00'
10
20
30
40
50
1 15
1 15
307^
230
/
550
537|
1
922|
935
1345
1422|
422^
910
15371
2345
230
652
1255
20371
'345"
922^
1640
345
"SOO"
11521
807
500
6 15
1320
1037|
615
TAPER 3| METRIC. CURVATURE INCREASING 5 00'
EVERY 10 M. (Continued] A = 5
M
I
o
D
log D
d
t
X
y
lc
1000
10
230
114.847
2.06012
0.110
4.993
0.218
9.998
10.000
1500
20
730
77.048
1.88676
0.435
9.960
1.090
19.960
19.990
2000
30
1500
58.667
1.76839
1.079
14.863
3.041
29.767
29.922
2500
40
2500
48.338
1.68429
2.136
19.638
6.465
39.164
39.694
3000
50
3730
42.331
1.62666
3.694
24.192
11.675
47.713
49.120
TABLES
343
' 1^ CO OS Tt< OO i ICO"*'
^t^ C^ ^^ "^ ^2 *O OQ ^^
i O t^ tM to CO Tf OS O 1-- T-H T-H to CO O 00 CO -* OO "* 00 CO CO
O "f C^ r-t OS b- to CS O CO CO OS Tt^ OS -^ t^. CO CO O T-I (M OS T-H
os os os os oo oo oo oo oo b- t^ -
00 >O iO 00 O CO i I T it>-tX)T^
i I O O i I Tt< OO Tf< i I O5 O5 i I
t^ CO CO O >O
iO <N CO OO t^
CO CO CO ^ CO
t^-OC^COCOC^IOt^-CO t^-OC^COT (OOt^-OO OC^TfiiOO^
Tt^ CO C^ H (O OS t > * CO ^ CO rH OS t^ TfH OS CO !> OS C^ <Q OS
OS T^H OS TT OS T^ OO CO OO CO OO CO t> C^ t"^ CO CO to Tt^ "^ CO T-H
i >O O O5 <M t^ CO O .
i IQ LO CO t^ t^ OO O5
* Tf< 001^
CO O Tt< Ttl
(N (M (NCOCOCO
COCOOO'^-
CJOOiOCOOt^
^8:
! CO
sim^ s ^~^^ ^
t^ ^ c<i o oo o "* co T-H o 06 t^
t^t-t^-tcOcOcOcOcOcotO to
a 9 S
O O O
COOMHlMT-HtO^lNr-HC
t^ OO 00 OS O O T-H C<1 CO **! tO tOCOt^OOOS
COGO <N 03 oo o OO<N<MOOO
1C -^ -^ Tfl Tfl Tfi TjH O i I Tf i I TH CO
o -^ Tt< IO O CO CO t^. !> 00 00 OS OS O O rH (M (M ^f 1C l> 00 O rH CO
O
C^l '
^ t^^O i o'cq'os CO oTrn'o OSOo'oo'osO'^rcOCq' T-H T^T^ oo"tO
O <M CO to O <N CO to T-H CO to O (M -^ O CO to CO (N T-H O tO -^ -^
CO CO CO CO ^ ** ^ ^ to tO to CO CO CO 1> 1> t^ 00 OS OT-HT-M
tO CO i>.
8 88888888 88888
8 3 8 838
344
THE RAILROAD TAPER
3"
> r 2> 00
'Oo o ^
o
O
TABLES
345
;o 82
00 5'-'
i O o CD O o
1 <N <tt CO
346
THE RAILKOAD TAPER
ar
ft'
O Ci 2
oodo
<M CO
i i Q
oo
TP
f^^lN
*o;
Kf
lOOo
CO cO
S8
a ls
QO
iis
r~^> "S O -~i^3 O P-0
CO
8
TABLES
347
:s
. CO
co
gbj,
IS co S i2
i CO fA T* <N
W
i <N O r-( H
"^f o CO ^
o "*
cq
p 10 ^ 10 co ^
ujdo
^^ fO
CO T-H
&
00
O I-H cp T-I o
l> ;H t^ (M
CO 0<Mo OCO co
1-1 P 10 "- 1 T-I
"-i 'XJ O r~^ "Q O "O ^ O f-0 '"G O
"
O * *<8 C
^ 8
348
THE RAILROAD TAPER
coo,,
c3 "^
3?
? Sis ^
' OOO 1 ' OrH
i i o oo 'i i
2 10
86
OS CO COo O
i i O ii 1 ~ '
f^^^CJ ~o'^O r^^'TSCi t-o'XJCi f^o^O j-o ^ O
8
888
TABLES
349
CO o 10 ^f O l> "^
' o o
(5 CO t ^ CO 00 *^** CD ^^ *^ ^^ C^ ^^ CO L O **^ ^^ C^ ^^
rt "*O *'O *'O **O **O
'S co^S ^"^in S^; S^Si
_ n '0 -J' L^/v' o
o ^ o . . <M o
i Oi ^ O O ^
1 <N ^ CO
1 ^ >-. O O >_
> 00 Q Q >O X
So oooo
O r "Q O
88888
350
THE RAILROAD TAPER
CO*
S
O <
8 SB* 8
is
8
S
-^,^3 r-o'XS r-0^ ^^
8 8
TABLES
351
CONVERSION OF ENGLISH INCHES INTO CENTIMETERS.
Ins.
1
2
3
4
5
6
7
8
9
Cm.
Cm.
Cm.
Cm.
Cm.
Cm.
Cm.
Cm.
Cm.
Cm.
0.000
2.540 5.080
7.620
10.16
12.70
15.24
17.78
20.32
22.86
10
25.40
27.94 30.48
33.02
35.56
38.10
40.64
43.18
45.72
48.26
20
50.80
53.34
55.88
58.42
60.96
63.50
66.04
68.58
71.12
73.66
30
76.20
78.74
81.26
83.82
86.36
88.90
91.44
93.98
96.52
99.06
40
101.60
104.14 106.68
109.22
111.76
114.30
116.84
119.38
121.92
124.46
50
127.00
129.54 132.08
134.62
137.16
139.70
142.24
144.78
147.32
149.86
60
152.40
154.94 157.48
160.02
162.56
165.10
167.64
170.18
172.72
175. 96
70
177.80
180.34 182.88
185.42
187.96
190.50
193.04
195.58
198.12
200. &6
80
203.20
205.74
208.28
210.82
213.36
215.90
218.44
220.98
223.52
226.06
90
228.60
231.14
233.68
236.22
238.76
241.30
243.84
246.38
248.92
251.46
100
254.00
256.54
259.08
261 .62
264.16
266.70
269. 24! 271. 78
274.32
276. W
CONVERSION OF CENTIMETERS INTO ENGLISH INCHES.
Cm.
1
2
3
4
5
6
.7
8
9
Ins.
Ins.
Ins
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
0.000
0.394
0.787 1.181
1.575
1.969
2.362
2.756
3.150
3.543
10
3.937
4.331
4.742J 5.118
5.512
5.906
6.299
6.693
7.087
7.480
20
7.874
8.268
8.662 9.055
9.449
9.843
10.236
10.630
11.024
11.418
30
11.811
12.205
12.599 12.992
13.386
13.780
14.173;14.567
14.961
15.356
40
15.748
16.142
16.530 16.929
17.323
17.717
18.11i;i8.504
18.898
19.292
50
19.685
20.079
20.473 20.867
21.260
21.654
22.04822.441
22.835128.229 *
60
23.622
24.016
24.410 24.804
25.197
25.591
25.98526.378
26.772
27.166
70
27.560
27.953
28.347 28.741
29.134
29.528
29.92230.316
30.709
31.103
80
31.497
31.890| 82.884' 32.678
33.071
33.46533.85934.253
34.646
35.040
90
35.434
35.8271 36.221 36.615
37.009
37.40237.79638.190
38.58338.977
100
39.370| 39.764 1 40.158 40.552
40.945
41.33941.73342.126
42.520l42.914
CONVERSION OF ENGLISH FEET INTO METERS.
Feet.
1
2
3
4
5
6
7
8
9
Met.
Met.
Met.
Met.
Met.
Met.
Met.
Met.
Met.
Met.
0.000
0.3048
0.6096
0.9144
1.2192
1.5239
1.8287
2.1335
2.4383
2.7431
10
3.0479
3.3527
8.6575
3.9623
4.2671
4.5719
4.87675.1815
5.4863
5.7911
20
6.0959
6.4006
6.7055
7.0102
7.3150
7.6198
7.92468.2294
8.5342
8.8390
30
9.1438
9.4486
9.7534
10.058
10.363
10.668
10.97211.277
11.582
11.887
40
12.192
12.496
12.801
13.106
13.411
13.716
14.02014.325
14.630
14.935
50
15.239
15.544
15.849
16.154
16.459
16.763
17.06817.373
17.678
17.983
60
18.287
18.592
18.897
19.202
19.507
19.811
20.11620.421
20.726
21.031
70
21.335
21.640
21.945
22.250
22.555
22.859
23.16423.469
23.774
24.079
80
24.383
24.688
24.993
25.298
25.602
25.907
26.21226.517
26.822
27.126
90
27.431
27.736
28.041
28.346
28.651
28.955
29.26029.565
29.870
30.174
100
30.479
30.784
31.089
31.394
31.698
32.003
32.30832.613
32.918
33.222
CONVERSION OF METERS INTO ENGLISH FEET.
Met.
1
2
3
4
5
6
7
8
9
Feet.
Feet.
Feet, i Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
0.000
3.2809
6.5618 9.8427
13.123
16.404
19.685
22.966
26.247
29.528
10
82.809
36.090
39.371 42.651
45.932
49.213
52.494
55.775
59.056
62.337
20
65.618
68.899
72.179 75.461
78.741
82.022
85.303
88.584
91.865
95.146
30
98.427
101.71
104.99 108.27
111 55
114.83
118.11
121.39
124.67
127.96
40
131.24
134.52
137.80 141.08
144.36
147.64
150.92
154.20
157.48
160.76
50
164.04
167.33
170.61 173.89
177.17
180.45
183.73
187.01
190.29
193.57
60
196.85
200.13
203.42 206.70
209.98
213.26216.54
219.82
223.10
226.38
70
229.66
232.94
236.22 239.51
242.79
246.07,249.35
252.63
255.91
259.19
80
262.47
265.75
269.03: 272.31
275.60
278.88282.16
285.44
288.72
292.00
90
295.28
298.56
301. 84 1 305.12
308.40
311.69314.97
318.25
321.53
324.81
100
328.09
331.37
334.65' 337.93
341.21
344.49347.78
351.06
354.34
.357.02
352
THE RAILROAD TAPER
TRIGONOMETRIC AND MISCELLANEOUS
FORMULAS.
SOLUTION OF RIGHT TRIANGLES.
Required.
A, (7, C
A, C, b
C, a, c
C, a, 6
Given,
a, 6
a, c
, a
A,c
Formulas.
= cot 5 = - ; 6 =
a ) (6 - a),
+ c a .
SOLUTION OF OBLIQUE TRIANGLES.
Required.
5
Given.
y4 7? /r
Formulas.
A CL b
sin A
ij
fee
f
a
tir\lf4 7?\ ^~ ton if A 4- 7?\
^4
P
.
a + o
,
, f ., ,, , , p . n j ^_ /(S ft)(.S C)
a, &, c
\ &c
^
i j /(s 6) (s c)
V 8(8 -a)
cm 1 2^8(-a)(-6)(8-c)
6c
Area
Area
Arpa
A, 6, c
>4 7? r
Area = */8 (s a) (s 6) (s c)
Area = 6c sin A
Arca _ c 2 sin ^ sin B
-A, />, C
TABLES 353
TRIGONOMETRIC AND MISCELLANEOUS
FORMULAS.
GENERAL FORMULAS.
sin A = /l cos 2 .4
sin.4
cosec A
cos A = - = vsin 2 ^. = cot A sin A,
sec A
cosA =1 2sin i 4^1 = l ver&A.
cosJ.
_vl cos 2 A ___ sin2A
cosA ~1 +
~~cotA~~ s'm2A
cot A = -1- = =
tan A sin yl
cot^l = sin 2 ^4 _ 1 +
"~
sec^l = =the reciprocal of any expression for cos A
cos A
cosec A = = the reciprocal of any expression for sin .4.
sin-4
vers^. = 1 cos.4 = 2 sin 2 1 A.
versA
354 THE BAILROAD TAPER
TRIGONOMETRIC AND MISCELLANEOUS
FORMULAS.
i j _ inn A 1 cos^i sin A
1 + secu4 sinJ. 1 +
sin .4 I cos A
sin 2 .4 = 2 sin .4 cos A,
cos 2 .4 = cos 2 ^. sin 2 .4 = 2 cos 2 J. 1.
_ll5a4-
1 tanM
2 cot A
sin (^4 7^) = sin A cosB cos A sin B.
cos (A B) = cos^l cos!? q= sin^l sinB.
1 =p tan ^1 tan B
Bin A +sinB = 2 sin (A + B) cos| (^L B>-
sin A sin B = 2 cos| (A + B) sin $ (A B).
cos A +-cosB=2coal(A + B)cos$(A B).
costf cosA = 2sm$(A + B)sin^(^4 7^).
sin 2 ^4 sin 2 B = cos 2 B cos' 2 A = sin (A -f 73) GIP (^
cos 2 -4 sin 2 7? = cos(J. + 73) cos (A B).
cos A cos 73
TABLES
TRIGONOMETRIC AND MISCELLANEOUS
FORMULAS.
MISCELLANEOUS FORMULAS.
355
Required.
Given.
F
Area of
Parallel sides = in and n
p
Trapezoid
Perp. dist. bet. them =p
2 (m
Regular Polygon
Length of side = I
Number of sides = n
T c '
Circle
Radius = r
itr' 1 [:
Ellipse
Semi-axes = a and b
Ttab
Parabola
Base = b, height = h
Ibh
Surface of
Radius of base = r
Cone
Slant height = s
Ttrs
Cylinder
Radius = r, height = h
2rtrh
Sphere
Radius = r
litr*
Zone
Height = h
2itrh
Radius of its sphere = r
Volume of
Prism or cylinder
Area of base = b
Height == h
bh
Pyramid or cone
Area of base = b
Height = h
bh
3
Frustum of
Pyramid or cone
!
Area of bases = 6 and &'
Height = h
3
Sphere \ Radius = r
farr 8
Formulas.
i. 1414J
356 MISCELLANEOUS FORMULAS
THEORETICAL SUPER-ELEVATION IN INCHES
Degree of
Curve.
Velocity in Miles per Hour.
.
$
bfl 3
Q
10
15
20
25
30
35
40
45
50
55
60
65
70
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
j
'
.
.
'
"
1
1
1
1
1
1
1
.
I
I
1
4
H
H
if
H
if
U
2
21
2l
2!
21
3
1
3
4
it
if
21
2f
2f
21
si
31
31
41
a
4|
5
51
il
2
21
21
31
3|
41
41
5f
51
61
6f
7|
81
11
If
2f
3
4|
51
51
71
7f
8|
81
If
2|
31
4
41
5f
71
j i
21
31
41
51
61
il
If
2f
4
5f
61
8
If
41
6f
81
2
4
6
8
2|
71
2|
si
31
9|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
...
i
j
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OVERDUE.
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: n 2
LJjU JLAjLLASn -
LD 21-95m-7,'37
616268
UNIVERSITY OF CALIFORNIA LIBRARY