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KURTJENSEN GENERAL MANAGER

SALES OFFICE

19734 COATES BLVD. HASTINGS, MN 55033 MN PHONE 612-437-6337 1-800-2 MANURE (1-800-262-6873)

ACCOUNTING OFFICE

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REFERENCENUMBER

DESCRIPTION

AMOUNT

5812 & KACOOS RES BATON ROUGE LA 77625077266000888605596 5999 BATON ROUGE LA 9146 9123 LSU FACULTY CLUB 74625077266000865114539 7011 MORGAN CITY LA 9119 9124 ACADIAN INN 74668007267092473020012 7011 BATON ROUGE LA 9:18 9125 BELLEMONT HOTEL r 77622007268010407200207 i101 PAYMENT - THANK YOU 74418007274206300440003 I I

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IT'S FALL FIX-UP, PAINT-UP TIME AND VISA CAN HELP. WHEN SHOPPING FOR THOSE SPECIAL PROJECTS, TAKE ALONG YOUR VISA CARD FOR ADDED CONVENIENCE.

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WHEN YOU CHARGE UP TO A QUARTER OF A MILLION IN PROTECTION! COMMON CARRIER TRAVEL TICKET ON YOUR VISA CARD, YOU E'AC IRE EIVE UP TO $250,000 IN TRAVEL ACCIDENTAL DEATH AND VISA'S GOT YOU COVERED! PROTECTION! 'DISMEMBERMENT I I I

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240.49 AMOUNT PAST UE

240.49 AVERAGE DAILYBALANCE OL URCHASES

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159.24 AVERAGE DAILY NCEBALA OF CASH

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AVERAGE DAILYBALANCE OCURRENT RCASES

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AVERAGE DALYBALANCE

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1. NUMBER OF DAYS IN BILLINGCYCLE

VISA

32

NUMBEROFDAS IN

DIRECI INQUIRIES TO: FIRST BANKCARD CENTER P.O. BOX 3331 OMAHA, NEBRASKA 68103-0331

TO REPORT LOST OR STOLEN CARDS PHONE TOLL FREE: 800-225-4941

PHONE TOLL FREE: 800-228-7070 MAHA: 3417447) (IN NEBRASKA: 800-642-8369; IN OMAHA: 341-7447)

(IN NEBRASKA: 800-345-3341; IN OMAHA: 341-2009)

PLATINUM POINTS:

PREVIOUS 95

EARNED

USED

32

0

AVAILABLE 127

NOTICE: SEEREVERSE SIDE FOR IMPORTANT INFORMATION REGARDING YOUR RIGHTS TO DISPUTE BILLING ERRORS.

First National Bank of Omaha used a daily periodic rate to compute your finance charges which varies from month to month. The periodic rate and the corresponding Annual Percentage Rate in effect during the billing cycle is shown on the face of the statement. The periodic rate was applied to the "average daily balance of outstanding payment period" which is obtained by adding the balances (excluding finance charges) in your account at the end of each day in the billing cycle and dividing that total by the number of days in the billing cycle. The finance charge is the product of the daily periodic rate times the average daily balance times the number of days in the billing cycle.

BILLING RIGHTS SUMMARY IN CASE OF ERRORS OR QUESTIONS ABOUT YOUR BILL If you think your bill is wrong, or if you need more information about a transaction on your bill, write us on a separate sheet at: FIRST BANKCARD CENTER P.O. BOX 3331 OMAHA, NE 68103-0331 as soon as possible. We must hear from you no later than 60 days after we sent you the first bill on which the error or problem appears. You may telephone us, but doing so will not preserve your rights. In your letter, give us the following information: k Your name and account number. *AThe dollar amount of the suspected error. *ADescribe the error and explain, if you can, why you believe there is an error. If you need more information, describe the item you are unsure about. You do not have to pay any amount in question while we are investigating, but you are still obligated to pay the parts of your bill that are not in question. While we investigate your question, we cannot report you as delinquent or take any action to collect the amount you question. SPECIAL RULE FOR CREDIT CARD PURCHASES If you have a problem with the quality of goods or services that you purchased with a credit card, and you have tried in good faith to correct the problem with the merchant, you may not have to pay the remaining amount due on the goods or services. You have this protection only when the purchase price was more than $50 and the purchase was made in your home state or within 100 miles of your mailing address. (If we own or operate the merchant, or if we mailed you the advertisement for the property or services, all purchases are covered regardless of amount or location of purchase.) You may be liable for the unauthorized use of your credit card. You will not be liable for unauthorized use that occurs # after you notify us at: FIRST BANKCARD CENTER P.O. BOX 3331 OMAHA, NE 68103-0331

CALL TOLL FREE: 800-225-4941 (IN NEBRASKA, 800-345-3341; INOMAHA: 341-2009

orally or in writing of the loss, theft or possible unauthorized use. In any case, your liability will not exceed $50.

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401 Golf Course Dr.-Baxter P.O. Box 765 Brainerd, MN 56401 218-829-5117 S.

MICH Res.: 829-7317

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E

IL

t

ri

. C

N r{

:

II

wa I

4II

4g

.

w._me

r 4i

1._

3

4t_. it

.:,

11

I

);

4

I

~~~I

Ii.

:

1

,", W.

::,

::

4

y C"

.. .. _ ..

_.

Co

_

. ,

e

Y0 2 r

ii

1

-

- ---,

:

-

<4W t)

--

/ .---

--

7

..:...1..

. ... #

- .-;-.1~..~.

( :~

I

t

c"1

t;

L~4~Q

I;

-4; i

~:3"i~ --~'i;

--

I --

..

,...

I,

"till(

:/

L *(2

/0

f

~ }}

. /.:-..I

i

j

a8

"

rVLL)(i~X:

...Cc.'LA.

i

vd 1

.t

\ t

20

AL,

INDEX OF CURVE AND REDUCTION TABLES Table Table

I-SLOPE STAKE II-STADIA CORRECTION AND HORIZONTAL DISTANCES

Table II-TRIGONOMETRIC FORMULAE Table IV-NATURAL TRIGONOMETRICAL FUNCTIONS CURVE FORMULAE Table

Y-TANGENTS AND EXTERNALS TO A

10 CURVE

USEFUL RELATIONS Table

VI-INCHES TO DECIMALS OF A FOOT

Table VII-MINUTES IN DECIMALS OF A DEGREE Table VIII-MIDDLE ORDINATES OF RAILS Table

IX-SHORT RADIUS CURVES

Table

X-RODS IN FEET, 10THS AND 100THS OF FEET

Table XI-LINKS IN FEET, 1OTHS AND 100THS OF FEET

TABLE I. SLOPE STAKE

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OFANYWIDTH. SIDESLOPES 1/2 TO1.

SLOPE

STAKE SIDE

STAKE

S "

SIDE

I

ISTAKE

C.I.L.o SL.

......

' f

i

SLOPE STAKE

t

16.2

24.3 24.3

0.7

16.05

.- i=II

Distance out from Side or Shoulder Stake. 1 .3 .4 1 6 1. .61 .71 .8 1 .9 0 1 .1 I .

C

0.75 0.90 1.051 1.90 1.35 1 65 180 1.95 2.25 2.40 .55 2.70 9.85 3 8.15 8.80 345 875 3.90 4.05 4.20 435 3 465 4.80 4.95 540 5.55 5.70 5.85 4 615 6.8306.45 6.60 6 75 6.90 1.05 7.20 7.35 5 7.65 7.80 7.95 8.10 8.25 8.40 8.55 8.70 8.85 6 9 15 9.809.45 9.60 9.75 9.90 10.05 10.0 7 10 5 10.80 10.95 11.10 11.25 11.40 11.55 11 70 8 12 15 13.80 12.45 12.60 12.75 12.90 13 05 13.20 9 13.65 1880 18 95 14.10 14.25 14.40 14 55 14.70 14.85 10 35 10 15 15 15 80 1545 15.60 15.75 15.90 16.05; 16.20 11 1663 16.95 17 10 17.25 17.40 17.55 17.7017.85 1I 1815 18.30 18 45 18.60 18 75 18.90 19.05 19.20 19.85 13 1965 19.80 19.9520.10 20.25 32040120.55 20.70 14 2115 21.8021.45 2160 21.75 2220 2285 22 80 22 95 23.10 28.25 15 23.70 23.85 2265 10 2415 2430 2445 9460 24.75 2490 2505 25.20 17 25.80 2595 26.10 2695 2640 26.55 26.70 26.85 18 2715 27.30 2745 27.60 27.75 27.90 28.05 2820 28.35 2565 28.80 28.9529.10 29.25 29.40 29.55 29.70 29.85 19 20 30 15 30.30 30.45 30.60 30.75 30.90 81.05 81.20 31.85 S1 3165 31.80 81.95 8 10 32.40 32.55 32 70 22 3315 3330 33.60 85 25 33.90 34.05 34.20 4.W 34 65 35.10 35 40 35.55 35.70 8615 36.80 3645 86.6036.75 36.90 37.05 37.20 25 87.5037.65 37 80 38.40 38.55 38.70 38.85 18.10 8915 8945 39e60 39,75 39.90 40.05 40.20 40.85 4275 41 401 41.55 41.70 41.85 27 4050 4065 40 80 41.10 41.25 20 4200 42 15 42.30 42.45 42.60 4425 42.90 43.05 43.20 88485 29 4350 4365 43.80 4395 44.10 45.75 44.70 45 15 45 45 45.60 46.35 31 46.50 46.80 46 95 47.10 48 47.25 75 47.40 47.55 47.701 47.85 324800 48.15 48.30 48.60 48.90 49.05 4920 58.85 49.35 51.75 50.40 50.55 50.70 3 49.60 4965 49.80 49.95 50.10 50.25 Q.MI 34 51 00 51.15 51.30 51.45 51.60 51.90 52.05 52.20 52.85 35 52350 52.80 53.10 53.25 53.40 53.55 53.70 46.85 8.65 54.380 5445 54.60 54.75 54.90, .05 55.20 49.85 5535 55.80 56.10 56.25 56.40 56.55 56.70 38 57.00 57.15 5745 57.60 5775 57.90158.05 58.20 5835 58165 5880 58.95 59.10 5925 MM~l59.40 9 3 59.70 40 60 00 60.15 030 ,.60 45 8060 1t20 . . . o. . . . ,. . . , . . . . o 1

000 1.50 3.00 4.50 8.00 750 900 10.50 12.00 1350 15.00 1650 18 00 19 50 21.00 2250 24.00 25.50 27.00 28 60 3000 31 50 3 00

0 151 0.800.45

0.60 2.10 3.60 5.10

,

,

+

TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES STADIA REDUCTIONS FOR READING 100 orizontal Correction

Vrtical Angle

Difftence in Elevation

VerticalAngle

Horhontal Correction

Difference in Elevation

3.5 5.3 7.0 8.7 10.4

18o-30' 190 -00 190-30' 200--Oa 204-30'

10.1 10.6 11.2 11.7 12.3

30.1 30.8 31.5 32.1 32.8

21 -00' 21-30'

100-00' 100-30'

12.1 13.8 15.5 17.10 17.9

12.8 13.4 14.0 14.7 15.3

33.5 34.1 34.7 35.4 36.0

110-00/ 110-30' 120-00' 12-30' 130-00'

18.7 19.5 20.3 21.1 21.9

23°-30' 240-00' 240-30'

15.9 16.5 17.2 17.9 18.6

36.6 37.2 37.7 38.3 39.0

130-30' 14a-00' 14o-30' 150-00' 150-30'

22.7 23.4 24.2

260-0a 260 -30 27°00J

25.0

27°-30'

25.8

280-00'

19.2 19.9 20.6 21.3 22.0

39.4 39.9 40.5 41.0 42.0

160-00 160 -30 170-001 17°-30' 180-00'

26.5 27.2 28.0 28.7 29.4

280-30' 29-00' 290-30,

22.8 23.5 24.3

30°-00'

25.0

41.9 42.4 42.9 43.3

20-00' 30-00'

80-00' 8a-00,

Chains to Feet 1

........

66

132 2 .......... 3 .......... 198

4 .......... 264 5

..........

330

6 .......... 396 7 8 9 10

.......... 462 ... ...528 .......... 594 .......... 660

220-00' 220-30 23°-00,

25°-00. 250-30

;;-- ;-Feet to Chains 100 .... 1.515 200 .... 3.030 300 400 500 600 700

.... 4.545 .... 6.060 .... 7.575 .... 9.090 .... 10.606

800 .... 12.121 900 .... 13.636 1,000 .... 15.151

TABLE III. TRIGONOMETRIC FORMULAE

B

B

a C C6 b Right Triangle Oblique Triangles Solution of Right Triangles

A

For Angle A. Given

si

a

tan

o

6

Required

,cot

A,B, ,

A, a

B, b, c

B=90o-A, b = acotA,C=

A,

B, a,

B = 90-A, a

A, a

B,a, b

4,a,

b , (

, se

a

b

, cosec =

a

c

a.b

Given , Ba

b

anA=b

cotB, a =

+

= a

1+--a

S a sin A.

btan A, = B=90-A, a = sin A, b= c cos A, Solution of Oblique Triangles asin a sin Required ,b sin A C = 180o-(A -+B), = - sin 2~, A, B,

CO

sIbinB=

,C= 180-(

A+B=180-

C, tan j(A-B)= a

),

A

sin

(a

-b)tan

(A

-AB 1

C

Ssin A

4 6, a

A, B, C s= a+2 sin A= V - b(s sin jB

Sb, a

Area

=a

A. , c

Area

area

A, B, Ca Area

, area

a =

(

,=180-(A+B)

s--a)s) (s-c)

bc sin A

2 area =

2sinA

REDUCTION TO HORIZONTAL Horizontal distance = Slope distance multiplied by the cosineof the vertical angle. Thus: slope distance =319.4 ft. S I t. Horizontal distance - 319.4 x M =31. Horizontal distance also - Slope distance minus sloe distance times (i1-cosine of vertical anle). With t . same figures as in the preceding example. the followina result is obtained. Cosine 5o10' =.MS.1-.9859=.0041. Horizontal distance 319.4001=1.31. 194-.31=318.0 ft. When the rise is kown, the horizontal distance is approximately:-the slope dist ance less the square of the rise divided by twice the slope distance. Thus: rase=14 ft.. slope distance-302. ft. Horizontal distance=302 6-4 6=802.6-0.32= 30.28 ft.

TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS

~~j~

~~k~

ri

,1snIrLfk l

j

0 1. 00 343.8 .0029 1719 .0058 114.6 .0087 0116 1.0001 85.94 .0145 1,0001 68-76

00 343.8 171.9 114.6 85.94 68.75

1. 1. .99998 .99996 .99993 .99989

.1392 .1421 .1449 .1478 .1507 .1536

.1405 .1435 .1465 .1495 .1524 .1554

1.0098 1.0102 1.0107 1.0111 1.0115 1.0120

7.185 7.040 6.900 6.766 6.636 6.512

7.115 6.968 6.827 6.691 6.561 6.435

.99027 .98986 98944 .98902 .98858 .98814

.0175 1.0002 .0204 1.0002 .0233 1.0003 .0262 1.0003 .0291 1.0004 ;.0320 1.0005

57.29 49.10 42.96 38.19 34 37 31.24

.99985 99979 .99973 .99966 .99958 .99949

.1564 .1593 .1622 .1650 .1679 .1708

.1584 .1614 .1644 .1673 .1703 .1733

1.0125 1.0129 10134 1.0139 1.0144 1.0149

6.394 6.314 6.277 6.197 6.166 6.084 6.059 5.976 5.9555.871 5.855 5.769

.98769 .98723 .98676 .98629 .98580 .98531

1.0006 28.65 28.64 1.0007 2645 26.43 1 0008 24.56 24.54 1.0010 22.93 22.90 1,0011 21.49 21.47 1.012 20.23 20.21

.99939 .99929 .99917 .99905 .99892 .99878

.1736 .1765 .1794 .1822 .1851 .1880

.1763 .1793 .1823 .1853 .1883 .1914

1.0154 5.759 1,0160 5.665 1.0165 5.575 1.170 5.488 1.0176 5.403 1.0181 5.320

.0349 .0378 .0407 .0437 .0466 0495

57.30 49.11 42.98 38.20 3438 31.26

5.671 5.576 5485 5.396 5.309 5.226

,98481 .98430 .98378 .98325 .98272 .98218

5.241 5.145 5.1645.066 5.089 4.989 5016 4.915 4.945 4,843 4.877 4773

.98163 .98107 .98050 .97992 .97934 .97875

.0524 1.0014 .0553 1.0015 0582 1.0017 .0612 1.0019 .0641 14020 .0670 1.0022

19.11 18.10 17.20 1638 15.64 14.96

19.08 18.07 17.17 16.35 15.60 14.92

.99863 .99847 .99831 .99813 .99795 99776

.1908 .1937 .1965 .1994 .2022 .2051

.1944 1.0187 .1974 1.0193 1.0199 .2035 1.0205 .2065 10211 .2095 1.0217

.0699 1.0024

14.34 13.76 13.23 12.75 12.29 11.87

14.30 13.73 1320 12.71 12.25 11.83

.99756 .99736 .99714 .99692 .99668 .99644

.2079 .2108 .2136 .2164 .2193 .2221

.2126 .2156 .2186 .2217 .2247 .2278

1.0223 4.810 1.0230 4.745 1.0236 4.682 1.0243 4.620 1.0249 4.560 10256 4.502

4.705 .97815 4.638 97754 4.574 .97692 .97630 4.449 .97566 4.390 .97502

11.43 11.06 10.71 10.39 10.08 9.788

.99619 .99594 .99567 .99340 .99511 99482

.2250 .2278 2306 .2334 .2363 .2391

.2309 .2339 .2370 .2401 2432 .2462

1.0270 1.0277 1.0284 1.0291 1.0299

4.445 4.390 4.336 4.284 4.232 4.182

4.331 .97437 4.275 .97371 4.219 97304 4.165 .97237 4.1131 .97169 4.061 .97100

.0729 10027 .0758 .0787 .0816 .0846

1.0029 1.0031 1.0033 1.0036

0875 .0904 .0934 .0963 .0992 .1022

1.0038

1.0049 1.0052

11.47 11.10 10.76 10.43 10.13 9.839

.1051 .1080 .1110 .1139 .1169 .1198

1.0055 1.0058 10061 1.0065 1.0068 10072

9.567 9.309 9065 8.834 8.614 8.405

9.514 9.255 9.010 8.777 8.556 8.345

.99452 .99421 .99390 .99357 .99324 .99290

.2419 .2493 1.0306 4.133 4.011 .97030 .2447 .2524 1.0314 4.086 3962 .96959 4.039 3.914 .96887 .2555 1.0321 .2586 1.0329 3.994 3.867 96815 .2617 1.0337 3.949 3.821 .96742 2648 1.0345 3.906 3.776 .96667

.1228 .1257 .1287 .1317 .1346 .1376

1.0075 1.0079 1.0082 1.0086 1.0090 1.0094

8.206 8.016 7.834 7661 7.496 7.337

8.144 7.953 7.770 7.596 7.429 7.269

.9925. .99219 .99182 .99144 .991061 .990671

.2616 .2644 .2672 .2700 .2728 im

1.0041 1.0043 1

0046

.2679 .2711 .2742 .2773 .2805 .2836

1.0353 14361 1.0369 1.0377 1.0386 1.0394

3.864 3.822 3.782 3.742 3.703 3.665,

3.732 3.689 3.647 3.606 3.566 3.526

.96593 .96517 .96440 .96363 96285 .96206

CohE og.CioK T i nIAI0 W..~Co.C~' IcscTn A n

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Ang

S.

Tn

Can at

S

I

.

CI g

cosi

1.0403 1.0412 1.0423 1.0429 1.0438 1.0448

.96126 .96046 .95964; .95882

Si.

Tu.

s

c

C.

o

Cog.

Io

sI

.95715

1.0946 1.0961 1.0975 1.0989 1.1004 1.1019

.91355 .91236 .91116 .90996 .90875 .90753

1.0457 1.0466 1.0476 1.0485 1.0495 1.0505

.95630 .95545 .95459 .95372 .95284 .95195

1.1034 1.1049 1.1064 1.1079 1,1095 1.1110

.90631 .90507 .90383 .90259 .90133 .90007

1.0515 1.0525 1.0535 1.0545 1.0555 1.0566

.95106 95015 .94924 .94832 .94740 .94646

1.1126 1.1142 1.1158 1.1174 1.1190 1.1207

.89879 .89752 .89623 .89493 .89363 .89232

1.0576 1.0587 1.0598 1.0608 1.0619 1.0631

.94552 .94457 ,94361 .94264 .94167 .94068

1.1223 1.1240 1.1257 1.1274 1.1291 1.1308

.89101 .88968 .88835 .88701 .88566 .88431

1.0642 1 0653 1.0665 1.0676 1.0688 1.0700

.93969 .93869 .93769 ,93667 .93565 .93462

1.1326 1.1343 1.1361 1.1379 1.1397 1.1415

.88295 .88158 .88020 .87882 .87743 .87603

1.0711 1.0723 1.0736 1.0748 1.0760 1.0773

93358 93253 93148 93042 .92935 92827

1.1434 1.1452 1.1471 1.1490 1.1509 1.1528

.87462 .87321 .87178 .87036 .86892 .86748

1.0785 1.0798 1.0811 1.0824 1.0837 1.0850

.92718 92499 92388 92276 92164

1.1547 1.1566 1.1586 1.1606 1.1626 1.1646

.86603 .86457 .86310 .86163 .86015 .85866

1.0864 1.0877 1.0891 1.0904 1.0918 1.0932

92050 91936 91822 .91706 91590 91472

1.1666 1.1687 1.1707 1.1728 1.1749 1.1770

.85717 .85567 .85416 .85264 .85112 .84959

aK

.95799

92609

«

Ta

Si.csi.

tg

oa

Sa

o

Sn

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Anl

Sin. Ton.

So.

ISc Cos.

Cotg

Cod.

1.600 1.590 1.580 1.570 1.560 1.550

.84805 .84650 .84495 .84339 .84182 .84025

1.2868 1.2898 1.2929 1.2959 1.2991 1.3022

.77715 .77531 .77347 .77162 .76977 .76791

Angle

i.

Ten

CaoS

Co.

Cos.

32 10 20 30 40 50

.5299 .5324 .5348 .5373 .5398 .5422

.6249 1.1792 1.887 .6289 1.1813 1.878 .6330 1.1835 1.870 .63711.1857 1.861 .6412 1.1879 1.853 .6453 1.1901 1.844

33 10 20 30 40 50

.5446 .5471 .5495 .5519 .5544 .5568

.6494 .6536 .6577 .6619 .6661 .6703

1.1924 1.1946 1.1969 1.1992 1.2015 1.2039

1.836 1.540 1.8281.530 1.820 1.520 1.812 1.511 1.804 1.501 1.796 1.492

.83867 .83708 .83549 .83389 .83228 .83066

1.3054 1.3086 1.3118 1.3151 1.3184 1.3217

.76604 .76417 .76229 .76041 .75851 .75661

34 10 20 30 40 50

.5592 .5616 .5640 .5664 .5688 .5712

.6745 .6787 .6830 .6873 .6916 .6959

1.2062 1.2086 1.2110 1.2134 1.2158 1.2183

1.788 1.781 1.773 1.766 1.758 1.751

1.483 1.473 1.464 1.455 1.446 1.437

.82904 .82741 .82577 .82413 .82248 .82082

1.3251 1.3284 1.3318 1.3352 1.3386 1.3421

.75471 .75280 .75088 .74896 .74703 .74509

35 10 20 30 40 50

.5736 .5760 .5783 .5807 .5831 .5854

.7002 .7046 .7089 .7133 .7177 .7221

1,2208 1.2233 1.2258 1.2283 1.2309 1.2335

1.743 1.736 1.729 1.722 1.715 1.708

1.428 1.419 1.411 1.402 1.393 1.385

.81915 .81748 .81580 .81412 .81242 .81072

1.3456 1.3492 1.3527 1.3563 1.3600 1.3636

.74314 .74120 .73924 .73728 .73531 .73333

36 10 20 30 40 50

.5878 .5901 .5925 .5948 .5972 .5995

.7265 .7310 .7355 .7400 .7445 .7490

1.2361 1.2387 1.2413 1.2440 1.2466 1.2494

1.701 1.695 1.688 1.681 1.675 1.668

1.376 1.368 1.360 1.351 1.343 1.335

.80902 .80730 .80558 .80386 .80212 .80038

1.3673 1.37 11 1.3748 1.3786 1.3863

.73135 .72937 .72737 .72537 .72337 .72136

37 10 20 30 40 50

.6018 .6041 .6065 .6088 .6111 .6134

.7536 .7581 .7627 .7673 .7720 .7766

1.2521 1.2549 1.2577 1.2605 1.2633 1.2661

1.662 1.655 1.649 1.643 1.636 1.630

1.327 1.319 1.311 1.303 1.295 1.288

.79864 .79688 .79512 .79335 .79158 .78980

1.3941 1.3980 1,4020 1 4061 1,4101'

.71934 .71732 .71529 .71325 .71121 .70916

38 10 20 30 40 50

6157 .6180 .6202 .6225 6248 .6271

.7813 .7860 .7907 .7954 .8002 .8050

1.2690 1.2719 1.2748 1.2778 1.2808 1.2838

1.624 1.618 1.612 1.606 tat 1.601 1.595

1.280 1.272 1.265 1.257 1.250 1.242

.78801 .78622 .78442 .78261 .78079 .77897

1.414

.70711

Cosi . CoL it. CoseSc Tn. Sin.A

Cosin. Cog. Cose. S .

I n.a e

CURVE FORMULAE

CURVE TABLE Table of Tangent and External to a 10 Curve

A Anale of IntersectionI

To find Tangent and External for curve of any other degree, divide by degree of curve and add correction found in column of corrections. Degree of curve with a given I may be found by dividing tangent, (or external), opposite I by given tangent, (or external). The distance from a point on the tangent to the curve is very nearly the square of the tangent length divided by twice the radius. CURVE FORMULAS Radius:

R =.

50 sin % D

Length of Curve: L = 100 -also L--.0174533 X A X R Degree of Curve: D = 100

=

A L

Tangent:

T

Long Cord:

LC = 2R sin

R tan 2 A

Middle Ordinate: M = R (1External:

E

=t

tan

%A Cos

A

A)

TABLE V. TANGENTS AND EXTERNALS TO A P1 CURVE T

T

=I 0ll

E

]

T

1I

=20

E

T

IEr

I=30

+

10 20 30 40 50 20

.218 .297 .388

50.0( 58.34 66.67 75.01 83.34 91.6E

.491 .606 .733

100.01 10' 108.35 20' 116.68 30' 125.02 40, 133.36 50, 141.70

.873 1.024 1.188 1.364 1.552 1.752

150.04 158.38 166.72 175.06 183.40 191.74

1.964 2.188 2.425 2.674 2.934 3.207

200.08 30' 225.12 40' 233.47 50 241.81

3.492 3.790 4.099 4.421 4.755 5.100

250.16 258.51 266.86 275.21 283.57 291.92

5.459 5.829 6.211 6.606 7.013 7.432

30

10' 20' 30 40 50' 40

10' 208.43 20' 216.77

50

10' 20' 30' 40' 50' 60

10' 20' 30' 40' 70

10' 20' 30' 40' 50' 80

10' 20' 30' 40' 50' 90 10' 20' 30' 40' 50. 100 10' 20' 30' 40' 50'

300.28 7.863. 308.64 8.307 316.99 8.762 325.35 9.230 333.71 9.710 342.08 10.202 350.44 358.81 367.17 375.54 383.91 392.28

10.707 11.224 11.753 12.294 12.847 13.413

400.66 409.03 417.41 425.79 434.17

13.991 14.582 15.184 15.799 16.426 442.55 17.065 450.93 17.717 459.32 18.381 467.71 19.058 476.10 19.746 484.49 20.447 492.88 21.161 501.28 509.68 518.08 526.48 534.89 543.29

+

110

10 20 30 40 50

5 C.

T .03 E. .001

120

10 20' 30' 40' 50'

100 C. T .06 E .003

602.21 610.64 619.07 627.50 635.93 644.37

31.561 32.447 33.347 34.259 35.183 36.120

10' 20' 30' 40' 50'

703.51 711.97 720.44 728.90 737.37 745.85

43.029 44.066 45.116 46.178 47.253 48.341

150 10' 20 30 40 50

754.32 762.80 771.29 779.77 788.26 796.75

49.441 50.554 51.679 52.818 53.969 55.132

160

805.25 56.309.

150 C. T .19 E .017

10, 813.75 57.498 20 822.25 58.699 30' 830.76 59.914

856.30 864.82 873.35 881.88 890.41 50, 898.95

1165.7 10, 1174.4 1183.1 1191.8 40' 1200.5 20' 1209.2

30'

10 20 30' 40' 50' 째 21.887 30 C 200 22.624 10' T 23.375 20' .19 24.138 30. E 40' 24.913 25.700 50' .008 T-- Rta ZT = R tan

hl

--

79.671 81.092 82.525 83.972 85.431 86.904

1010.3 1018.9 1027.5 1036.1 1044.7 1053.3

88.389

260

250 C. T .32 E .028

T .10 E .013

15' C. T .29 E .038

1322.8 150.71

1375.6 1384.4 1393.2 1402.0 40' 1410.9 50' 1419.7

154.69 156.70 158.72 20- C. 160.76 T .39 162.81 E 164.86 166.95 .051 169.04 171.15 173.27

1428.6 1437.4 1446.3 1455.1 1464.0 50', 1472.9

175.41 177.55 179.72 250 C. T 181.89 184.08 .49 186.29

10' 20' 30' 40' 29*

10' 20' 30' 40' 50'

E = R; --e'

=

300

R exsec %

10' 20' 30' 40' 50'

E .065

1481.8 1490.7 1499.6 1508.5 1517.4 1526.3

188.51 190.74 192.99 195.25 197.53 199.82

1535.3 1544.2 1553.1 1562.1 1571.0 1580.0

202.12 300 C. T 204.44 206.77 .59 209.12 E 211.48 213.86 .078

째

30 C. T .39 E .034

89.888 91.399 92.924 94.462 96.013 E

139.11 141.01 142.93 144.85 146.79 148.75

20* C. T .26 270 E 10' .022 20' 30'

63.634 64.900 66.178 67.470 68.774 70.091

958.81 967.38 975.96 984.53 993.12 1001.7

1270.2 1279.0 1287.7 1296.5 1305.3 50' 1314.0

20' 1340.4 30' 1349.2 40' 1358.0 50' 1366.8

907.49 71.421 10' 916.03 72.764 20 924.58 74.119 30' 933.13 75.488 40' 941.69 76.869 50, 950.25 78.264

190

128.00 129.82 131.65 133.50 135.35 137.23

257 10 20' 30, 40'

5" C.

117.38 100 C. 119.12 T 120.87 122.63 .19 E 124.41 126.20 .025

1217.9 1226.6 1235.3 1244.0 1252.8 1261.5

240 50, 10' 20' 30' 40' 50'

180

25" C. T .16 E .007

1061.9 97.577 1070.6 99.155 1079.2 100.75 10878 102.35 1096.4 103.97 1105.1 105.60

10' 1331.6 152.69

40' 839.27 61.141 50 847.78 62.381 10' 20 30' 40

21*

100 C. T .13 E .011

39.006 39.993 40.992 42.004

170

째

10 5 C. 20 T .06 50 E .006 226

1113.7 107.24 10' 1122.4 108.90 20' 1131.0 110.57 30' 1139.7 112.25 40' 1148.4 113.95 50, 1157.0 115.66

669.70 678.15 686.60 695.06

20' 30 40' 50'

20" C. T .13 E .006

26.500 27.313 28.137 28.974 29.824 30.686

1310 652.81 37.070 10' 661.25 38.031

140

15째 C. T .09 E .004

551.70 560.11 568.53 576.95 585.36 593.79

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE T 31

10 20' 30' 40' 50' °

32

10' 20' 30' 40' 50'

T

216.3 218.7 221.1 223.5 226.0 228.4

1643.0 1652.0 1661.0 1670.0 1679.1 1688.1

230.9 233.4 235.9 238.4 241.0 243.5

°

1697.2 10' 1706.3 20' 1715.3 30' 1724.4 40' 1733.5 50' 1742.6

33

349

10' 20' 30' 40' 50' o

35

11=40-

E

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9

1751.7 1760.8 1770.0 1779.1 1788.2 1797.4

20' 30' 40' 50'

5° C. T .13 E .023

261.8; 264.5. 267.2 269.9 272.6 275.3 15" C.

278.1 280.8 1824.9 283.6 1834.1 286.4 1843.3 289.2 1852.5 292.0 1806.6

10' 20' 30' 40' 50' °

42

10' 20' 30' 40' 50'

246.1 LO C. 248.7 T 251.3 .26 253.9 E 256.5 259.1 .046

10' 1815.7

1

41

T .40 E .070

°

43

2257.0 2266.6 2276.2 2285.9 2295.6 30' 2305.2

440,

°

1917.1 1926.4 1935.7 1945.0 1954.3 50' 1963.6

312.2 315.2 318.1 321.1 324.1 327.1

1972.9 10' 1982.2 20' 1991.5 30' 2000.9 40' 2010.2 50' 2019.6

48" 10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

2029.0 2038.4 2047.8 2057.2 2066.6 2076.0

330.2 333.2 25" C. 336.3 T 339.3 342.4 .67 345.5 E 348.6 .117 351.8 354.9. 358.1 361.3 364.5

10' 20' 30' 40' 50'

2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

367.7 30 C. 371.0 T 374.2 .80 377.5 E 380.8 384.1 .141

50.

370

10' 20' 30' 40'

X380

390

40*

:

-

46

10' 20' 30' 40' 50'

0° C. T .53 E .093

°

47

-7

10' 20' 30' 40' 50'

---

5 C. T .17 E .037

2432.1 2441.9 2451.8 2461.7 2471.5 2481.4

428.5 10° C. 432.0 T 435.6 439.2 .34 442.8 E 446.4 .075

2551.0 2561.0 2571.0 2581.0 2591.0 2601.1

.68 E

2919.4 10' 2929.9 20' 2940.4 30' 2951.0 40', 2961.5 50' 2972.1

54*

550

10' 20' 30' 40' 50' °

56

2671.8 2681.9 2692.1 2702.3 2712.5 2722.7

592.3 596.6 600.9 605.3 609.6 614.0

3046.5 10' 3057.2

20' 3067.9 30' 3078.7 40' 3089.4 50' 3100.2 3110.9 3121.7 3132.6 3143.4 3154.2 50' 3165.1 10' 20' 30' 40'

3176.0

58.

10' 3186.9 20' 3197.8 30' 3208.8 40' 3219.7 50' 3230.7

E .189

2982.7 2993.3 3003.9 3014.5 3025.2 3035.8

570

542.2 546.3 550.4 25, C. 554.5 T 558.6 .85

°

59

10'

575.3579.5

20' 30' 40' 50'

583.8 588.0

60-

3241.7 3252.7 3263.7 3274.8 3285.8 3296.9

3308.0

10' 3319.1 20' 3330.3 30' 3341.4 40' 3352.6 .227 50 3363.8 E R xse Va E=Rexsec1I

--- - - -------~--:---

+ 5" C. T .21 E 645.2 .056

2856.7 672.7 10* C. 10' 2867.1 677.3 T 20' 2877.5 682.0 30' 2888.0 686.7 .42 E 40' 2898.4 691.4 50 2908.9 696.1 .112

534.2538.2

566.9 571.1

649.7 654.3 658.8 663.4 668.0

]=60

530

530.1

562.8

2794.5 10' 2804.9 20' 2815.2 30' 2825.6 40' 2835.9 50' 2846.3

°

.151

2611.2 2621.2 2631.3 2641.4 2651.5 2661.6

10' 20' 30' 40' 50' T=Ran~

/Z

494.8 498.7 502.5 506.4 510.3 20, C. 514.3 T 518.2 522.2 526.1

618.4 622.8 627.2 631.7 636.2 640.7

52

421.4 425.0

E

2732.9 2743.1 2753.4 2763.7 2773.9 2784.2

10' 20' 30' 40' 50'

418.0

2314.9 2324.6 2334.3 2344.1 2353.8 2363.5

2491.3 10' 2501.2 20' 2511.2 30' 2521.1 40' 2531.1 50' 2541.0

490

T = Rtan

407.6 411.1 414.5

T

°

S

450.0 453.6. 457.3 461.0 464.6 ° 468.4 15 C. ° T 45 2373.3 472.1 .51 10' 2383.1 475.8 20' 2392.8 479.6 E 30' 2402.6 483.4 .116 40' 2412.4 487.2 50' 2422.3 491.0 10' 20' 30' 40' 50'

294.9 297.7 300.6 303.5 306.4 309.3

10' 20' 30' 40' 50'

2199.4 2209.0 2218.6 2228.1 2237.7 2247.3

I

=so50

E ET

2142.2 387.4 2151.7 390.7 2161.2 394.1 2170.8 397.4 2180.3 400.8 2189.9 404.2

10' 20' 30' 40'

1861.7 1870.9 1880.1 1889.4 1898.6 1907.9

360

I

-- ~--;

700.9 705.7 710.5 715.3 720.1 725.0 15' C. T 729.9 .63 734.8 E 739.7 744.6 .168 749.6 754.6 759.6 764.6 769.7 774.7 20° C. 779.8 T 784.9 .84 E 790.1 795.2 .225 800.4

805.6 810.9 816.1 821.4 826.7 832.0 837.3 842.7

848.1 853.5 858.9 864.3 869.8 875.3

25" C. T 1.05 E .283

880.8

886.4 30 C.

908.8

T 1.27 E

914.5

.340

892.0 897.5 903.2

~-~ ~~~

-, I- -

TABLE V CONTD. TANGENTS AND EXTERNALS TO A P CURVE

1=70

I

T

E

10' 20' 30' 40' 50'

3375.0 3386.3 3397.5 3408.8 3420.1 3431.4

920.2 925.9 931.6 937.3 943.1 948.9

620 10' 20' 30' 40' 50'

3442.7 3454.1 3465.4 3476.8 3488.3 3499.7

954.8 960.6 966.5 972.4 978.3 984.3

.080

10' 20' 30' 40' 50'

3511.1 3522.6 3534.1 3545.6 3557.2 3568.7

990.2 996.2 1002.3 1008.3 1014.4 1020.5

10' C. T

640 10' 20' 30' 40' 50'

3580.3 3591.9 3603.5 3615.1 3626.8 3638.5

1026.6 1032.8 1039.0 1045.2 1051.4 1057.7

61'

63

°

65* 10' 20' 30' 40' 50'

3650.2 3661.9 3673.7 3685.4 3697.2 3709.0

'

: 5 C. T .25 E

"

I

10 20 30' 40' 50'

4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

1805.3 + 1814.7 1824.15 C. T 1833.6 1843.1 .36 1852.6 E

4162.8 4175.6 4188.5 4201.2 4214.0 4226.8

1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

.110

82* 10' 20' 30 40' 50'

4980.7 4995.4 5010.0 5024.8 5039.5 5054.3

1862.2 1871.8 1881.5 1891.2 1900.9 1910.7

4239.7 4252.6 4265.6 4278.5 4291.5 4304.6

1398.0 1405.7 1413.5 1421.2 1429.0 1436.8

10° C. 83* T 10' 20' .61 30' E 40' .220 50'

5069.2 5084.0 5099.0 5113.9 5128.9 5143.9

1920.5 10° C. 1930.4 T 1940.3 1950.3 .72 1960.2 E 1970.3 .299

4317.6 4330.7 4343.8 4356.9 4370.1 4383.3

1444.6 1452.5 1460.4 1468.4 1476.4 1484.4

10' 20' 30' 40' 50'

5159.0 5174.1 5189.3 5204.4 5219.7 5234.9

1980.4 1990.5 2000.6 2010.8 2021.1 2031,4

4396.5 4409.8 4423.1 4436.4 4449.7 4463.1

1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

s50 10' 20' 30' 40' 50'

5250.3 5265.6 5281.0 5296.4 5311.9 5327.4

2041.7 2052.1 2062.5 2073.0 2083.5 2094.1

720 10 20' 30' 40' 50' 73

10' 20' 30' 40' 50'

3792.4 3804.4 3816.4 3828.4 3840.5 3852.6

E

3864.7 10' 3876.8 20' 3889.0 30' 3901.2 40' 3913.4 50'3925.6

10' 20' 30' 40' 50' 750 10' 20' 30' 40' 50'

240 76

°

40' 4530.4 1574.7 50' 4544.0 1583.1

T

1.02

1141.4 E 1148.0 1154.7 .321 1161.3 1168.1 1174.8

77

1181.6 1188.4 1195.2 25" C. 1202.0 T 1208.9 1.28 1215.8 E

78

.403

84

°

T .91 E 332

20 C

20' 5374.2 2126.0 30' 5389.9 2136.7 40' 5405.6 2147.5 50' 5421.4 2158.4

'

T

1.22 E

4557.6 4571.2 4584.8 4598.5 4612.2 4626.0

1591.6 1600.1 1608.6 1617.1 1625.7 1634.4

10' 20' 30' 40' 50'

4639.8 4653.6 4667.4 4681.3 4695.2 4709.2

1643.0 1651.7 1660.5 1669.2 1678.1 1686.9

25" C. T 1.53 E

4723.2 1695.8

.558

.445

87' 10' 20' 30' 40' 50' 88

10' 4737.2 1704.7 20' 4751.2 1713.7

°

10' 20' 30' 40' 50'

89

5437.2 5453.1 5469.0 5484.9 5500.9 5517.0

2169.2 2180.2 2191.1 2202.2 2213.2 2224.3

5533.1 5549.2 5565.4 5581.6 5597.8 5614.2

2235.5 2246.7 2258.0 2269.3 2280.6 2292.0

5630.5 2303.5

30' 47653 1722.7

30' 5679.9 2338.2

40' 3987.2 1250.8 50' 3999.5 1257.9

40' 4779.4 1731.7 50' 4793.6 1740.8

40' 5696.4 2349.8 50' 5713.0 2361.5

80'

4011.9 1265.0 30' C.

4807.7 1749.9

°

15 C. T 1.09 E .450

20 C. T

1.45 .603

25 C. T 1.83 E

.756

10' 5646.9 2315.0 20' 5663.4 2326.6

30' 3974.8 1243.7

70"

.149

5343.0 2104.7 10' 5358.6 2115.3

86

10' 20' 30' 40' 50'

79'

10' 3950.2 1229.7 20' 3962.5 1236.7

°

15 C.

4476.5 1541.4 10' 4489.9 1549.7

20' 4503.4 1558.0 30' 4516.9 1566.3

0c

3937.9 1222.7

69'

°

10' 20' 30' 40' 50'

66* 3720.9 1102.2 10' 3732.7 1108.6

670

rI=90

T

81*

°

40' 3768.5 1128.2 50' 3780.4 1134.8

I I

+ + 5 C. T .30 E

15 C.

20' 3744.6 1115.1 30' 3756.5 1121.7

I T=80

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1

740

T .76 E

i

71*. 4086.9 104099.5 20' 4112.1 30 4124.8 40' 4137.4 50' 4150.1

.51 E .159

1063.9 1070.2 1076.6 1082.9 1089.3 1095.7

T

30' C. 9(0*

5729.7 2373.3

30' C.

10 4024.4 1272.1

T

10' 4822.0 1759.0

T

10' 5746.3 2385.1

T

204036.8 1279.3 304049.3 1286.5

1.54

20' 4836.,2 1768.2 30' 4850.5 1777.4

1.84

20' 5763.1 2397.0 30' 5779.9 2408.9

2.20

504074.4

E

40' 4864.8 1786.7

E

40' 5796.7 2420.9

E

.485

50' 4879.2 1796.0

.671

50' 5813.6 2432.9

.910

404061.8 1293.6 1300.9

T=Rtan

'

E= Rexsec

LIII,-6tC (Z19) ZOVSS NW 'SldW LS H19 "OS 0Z I VMA)NSI S3M 3DV1d NNV IS'tdl

LLZ9-LZT (zig) 1 IOISS NW 'iflVd S Hlb IV 1231:801 N 8E

l

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(612)

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I f

*

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE I 910

T

-100"

E

5830.5 2444.9

1010

10' 5847.5 2457.1 20' 30 40' 50' 92* 10' 20' 30' 40' 50'

5864.6 5881.7 5898.8 5916.0

2469.3 2481.5 2493.8 2506.1

°

5933.2 2518.5

102 10' 20' 30' 40'

6037.8 6055.4 6073.1 6090.8 6108.6 6126.4

2594.0 10 C. 2606.8 T 2619.7 2632.6 .86 2645.5 E 2658.5 .401

94 10' 20' 30' 40' 50'

6144.3 6162.2 6180.2 6198.3 6216.4 6234.6

2671.6 2684.7 2697.9 2711.2 2724.5 2737.9

95" 10' 20' 30' 40' 50'

6252.8 6271.1 6289.4 6307.9 6326.3 6344.8

2751.3 2764.8 2778.3 2792.0 2805.6 2819.4

°

°

960

°

97" 10' 20' 30' 40' 50'

98"

6400.8 6419.5 6438.4 6457.3 6476.2 6495.2 6514.3 6533.4 6552.6 6571.9

3474.4 10 C. 3491.3 T 3508.2 3525.2 .103 3542.4 E 3559.6 .536 3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 15'C.

2861.0 ° 2875.0 30' 40' 2889.0 20 C. T 2903.1 50' 1.74 ° 107 2917.3 E 2931.6 10' .809 2945.9 20' 30' 2960.3 2974.7 40' 2989.2 50'

6708.6 6728.4 6748.2 6768.1 6788.1 6808.2

100* 10' 20' 30' 40' 50'

6828.3 6848.5 6868.8 6889.2 6909.6 6930.1

3184.1 30 C. 110 3199.6 T 10' 3215.1 2.62 20' 3230.8 30' 3246.5 40' 3262.3 50' 1.22

°

I

°

3682.3 3700.2 3718.2 3736.2 3754.4 3772.6

T 1.56 E .806

=

T = R tan '

7672.9 3846.5 20 ° C. 7696.3 3865.2 T 7719.7 3884.0 2.08 7743.2 3902.9 E 7766.8 .3921.9 7790.5 3940.9 1.08 7814.3 3960.1 7838.1 3979.4. 7862.1 3998.7 7886.2 7910.4 7934.6 7959.C 7983.5 8008.0

111 . 10' 20' 30' 40' 50'

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6

1120

8494.6 8521.3 8548.1 8575.0 8602.1 8629.3

4516.6 4538.8 4561.1 4583.4 4606.0 4628.6

8656.6 8684.0 8711.5 8739.2 8767.0 8794.9

4651.3 4674.2 4697.2 4720.3 4743.6 4766.9

8822.9 8851.0 8879.3 8907.7 8936.3 8965.0

4790.4 4814.1 4837.8 4861.7 4885.7 4909.9

8993.8 9022.7 9051.7 9080.9 9110.3 9139.8

4934.1 4958.6 4983.1 5007.8 5032.6 5057.6

9169.4 9199.1 9229.0 9259.0 9289.2 9319.5

5082.7 5107.9 5133.3 5158.8 5184.5 5210.3

10' 20' 30' 40' 50'

7603.5 3791.0 106 10' 7626.6 3809.4 20' 7649.7 3827.9

10' 20' 30' 40' 50'

99*

6591.2 6610.6 6630.1 6649.6 6669.2 6688.8

T .51 E .268

7203.2 7224.7 7246.3 7268.0 40' 7289.8 50' 7311.7

108" 3003.8 ° 10' 3018.4 3033.1 25 C, 20' T 3047.9 30' 3062.8 40' 2.18 3077.7 50' E 3092.7 1.02 109" 10 3107.7 20' 3122.9 30' 3138.1 40' 3153.3 50' 3168.7

10' 20' 30' 40' 50'

3310.1 3326.1 3342.3 3358.5

5' C.

°

6363.4 2833.2

E

°

3374.9 3391.2 3407.7 3424.3 3440.9 3457.6

103" 10' 20' 30'

T

I

=110

7075.5 7096.6 7117.8 7139.0 7160.3 50' 7181.7

104" 7333.6 10' 7355.6 20' 7377.8 30' 7399.9 40' 7422.2 50' 7444.6 15° C. ° T 105 7467.0 1.30 10' 7489.6 20' 7512.2 E 30' 7534.9 .604 40' 7557.7 50' 7580.5

10' 6382.1 2847.0 20' 30' 40' 50'

E

6950.6 3278.1

20' 6992.0 30' 7012.7 40' 7033.6 50' 7054.5

2531.0 2543.5 2556.0 2568.6' 2581.3

10' 20' 30' 40' 50'

T

10' 6971.3 3294.1

5950.5 5967.9 5985.3 6002.7 6020.2

93

l

°

113

10' 20' 30' 40' 50' 114"

10 20' 30' 40' 50' 115"

10 20' 30' 40' 50'

116

°

10' 20' 30' 40' 50' °

117

10 20' 30' 40' 50' °

9349.9 5236.2 9380.5 5262.3 9411.3 5288.6 9442.2 5315.0 9473.2 5341.5 9504.4 5368.2

118

8032.7 8057.4 8082.3 8107.3 8132.3 8157.5

4018.2 ° 4037.8 4057.4 25 C. T 4077.2 4097.1 2.61 4117.0 E 4137.1 1.36 4157.3 4177.5. 4197.9 4218.4 4239.0

8182.8 8208.2 8233.7 8259.3 8285.0 8310.8

4259.7 30"C T 4280.5 4301.4 3.14 4322.4 E 4343.6 4364.8 1.63

120* 9924.0 5729.7 10' 9957.5 5758.6 20' 9991.0 5787.7 30' L0025.0 5817.0 40' L0059.0 5846.5 50' L0093.0 5876.1 .....

°

E

E= R exsec

10' 20' 30' 40' 50' 119"

10' 20' 30' 40' 50'

9535.7 9567.2 9598.9 9630.7 9662.6 9694.7

5395.1 5422.1 5449.2 5476.5 5504.0 5531.7

9727.0 9759.4 9792.0 9824.8 9857.7 9890.8

5559.4 5587.4

120.

5° C. T .62 E .360

°

10 C. T 1.25 E .721

15 C. T 1.93 E 1.09

°

20 C. T 2.52 E 1.46

25" C. T 3.16 E 1.83

5615.5 5643.8 5672.3 5700.9 °

hI

30 C. T 3.81 E 2.20

USEFUL RELATIONS Lineal feet Lineal yards Square inches Square feet Square yards Acres Cubic inches Cubic feet Links Links Feet

= miles = miles = square feet = square yards X.0002067 = acres = square yards X 4840 X.00058 = cubic feet = cubic yards X.03704 - yards X .22 = feet x .66 = links X 1.5 X.00019 X.0006 X.007 X.111

360 ° = 21600' = 1296000" ° Radius = are of 57.2957790 ° .017453292 1) = = (radius of 1 Arc Arc of 1' (radius = 1) = .000290888 Are of 1" (radius = 1) = .000004848

Curvature of Earth's surface = about 0.7 feet in 1 mile Curvature in feet = 0.667 (Dist. in miles)' Difference between are and chord length, 0.05 feet in 11% miles Probable error of a single observation = 0.6754 Error in chaining of 0.01 feet in 100 feet: Due to1. Length of tape error of 0.01 feet 2. Alignment. One end 1.4 feet out of line 3. Sag of tape at center of 0.61 feet. 4. Temperature difference of 15" 5. Difference of pull of 15 lbs. SQUARE MEASURE 144 sq. inches = 1 sq. ft. 9 sq. ft. -- 1 sq. yard 301a sq. yds. = 1 sq. rd. 40 sq. rds. = 1 rood. 4 roods =

1 acre

640 acres = 1 sq. mile. SURVEYORS' MEASURE 7.92 inches = 1 link. 25 links = 1 red. 4 rds. = 1 chain.

10 sq. chains or 16 sq. rods - 1 acre. 640 acres = 1 sq. mile. 36 sq. miles (6 miles sq.) = 1 township.

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TABLE X. RODS IN FEET, O1THS AND IOOTIIS OF FEET

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0

Feet

16.50 33.00 49.50 66.00 82.50 99.00 115.50 132.00 148.50 165.00 181.50 198.00 214.50 231.00 247.50 264.00 280.50 297.00 313.50 330.00

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Feet

346.50 363.00 379.50 396.00 412.50 429.00 445.50 462.00 478.50 495.00 511.50 528.00 544.50 561.00 577.50 594.00 610.50 627.00 643.50 660.00

41 42 43 44 45 46 47 48 49 50 51. 52 53. 54 55 56 57 58 59 60

676.50 693.00 709.50 726.00 742.50 759.00 775.50 792.00 808.50 825.00 841.50 858.00 874.50 891.00 907.50 924.00 940.50 957.00 973.50 990.00

Feet

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Feet

1006.50 1023.00 1039.50 1056.00 1072.50 1089.00 1105.50 1122.00 1138.50 1155.00 1171.50 1188.00 1204.50 1221.00 1237.50 1254.00 1270.50 1287.00 1303.50 1320.00

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 8

69

100

1336.50 1353.00 1369.50 1386.00 1402.50 1419.00 1435.50 1452.00 1468.50 1485.00 1501.50 1518.00 1534.50 1551.00 1567.50 1584.00 1600.50 1617.00 1633.50 1650.00

TABLE XI. LINKS IN FEET, O1THS AND 1OOTHS OF FEET c

Feet

.

Feet

.

Feet

.

Feet

.

Feet

.

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.66 1.32 1.98 2.64 3.30 3.96 4.62 5.28 5.94 6.60 7.26 7.92 8.58 9.24 9.90 10.56 11.22

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

11.88 12.54 13.20 13.86 14.52 15.18 15.84 16.50 17.16 17.82 18.48 19.14 19.80 20.46 21.12 21.78 22.44

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

23.10 23.76 24.42 25.08 25.74 26.40 27.06 27.72 28.38 29.04 29.730 30.36 31.03 31.68 32.34 33.00 33.66

52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

34.32 34.98 35.64 36.30 36.96 37.62 38.28 38.94 39.60 40.26 40.92 41.58 42.24 42.90 43.56 44.22 44.88

69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

45.54 46.20 46.86 47.52 48.18 48.84 49.50 50.16 50.82 5148 5~.14 52.80 53.46 5412 54.78 55.44 56.10

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

56.76 57.42 58.08 58.74 59.40 60.06 60.72 61.38 62.04 62.70 63.36 64.02 64.68 65.34 66.00 66.66 67.32

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1988 S

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WINONA, MN

JANUARY W T F

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FEBRUAiY T W T

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PH. 454-4107

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24 25 31 123

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28 27 28 29 30 MAY 4.

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SEPTEMER 1 2 26789 12 13 14 15 16 9 2 21 22 23 26 27 28 29 '77

JUNE 1 2

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