Fremling Field Notebooks 1989-1999

r"

4

er rare r

..

.

l -.

..

xt

.r.

t

.

+;.-

.z"

. .rat..

-

-'

t

"

.

-C:F:.:.

F"

k

tC

Fr

_':

may.

^t'x.x

}

c

r

Ys'. '"

.rC,<F

.. ,.a.

a

.. :1

"F'S-

a *'

N.

r

z. a; ?

"L.+Yir1

r2.

c

tbn2

t

k4 ?rF,

. ^r r*

r}1

s}

rr'

r

a

A

mv

r

_

r'"aFi Ju

."_

F rgtt

rr

f

t

1

" .

3'+ nra

kr

"

xf

,k'

ie :

w7 ru Hz

8r rrr

-n?

> {

jS

-3 r F"t{sC=

3

#Ti! a

...

Cfr

?

,

r

v.3z

r

-1

r

af. r-c

4

,

e

f

c

r

r7

r

t

SX

!-

x i

.1-

t

r ..

br

. r

-ri :

x

f z

fi r s

u

r

r

r

r

}

-.

r s.

{

'.

t'

,r,

,

t

}

l 'r 1.

"'-

Trtil

!":}fF

+

i r

r,

r

S

r'x

'+r *

4

-}

rfi t

Ir' r"

3 r

i. rar j r r

et

F

"

-,

s

r

'+

r"'j",

r

r'

px

"

r

is

'f

+

Frbs s 1t'

#' t +

?

a

' f t r f17z"rf, tx' . r;

..

a

s

-}

x.

9

t

4 rirc

,rr ' " Yr rrr

P-

" t',t ti"

i

ru-rti r

.lt' r

} -rs r rrs

tr hy s r .Pf}" + r r

: i

r rfi r * r ', fr ft r" r t''s+ ' it ., "fr . s {rr. v , " ,: A= £ 'flit {rPr' 1 R

'F' i k

'

fr

r

z

S. w

f

r Yc ry r t

'jt ti x

"

1. «.. c r f r i r rt , rt ... z r y ;,

t

E,

an -a '7

}-

r }

t1

t 7

c r

f t 'crne{3 r

yf

r r

I}

rrC ,.i

r

r «. rua,

t z !>y f f

?

y. s

r ' '. ~ftr} r t r rt + 7 } a ~I" r " r7' T .}4 ,r r { .}i za# r

-

s

7

rY

jr'f

-

.

d'".4

}ri'rtk z.

r

.r'

,:" r

r F

C.r°

'T ,

rrit

k

ti $

.

r

r}° 7

N

rat E s ra

,c ?I z t'r!

R',

r

'Z'i

'lt

c

i

k

, tr} r a:

r

;

Yxrte

'

Kra r{',r

ivr

nira

.

r

js

r

4

Fr

fW -t.Z1j

}

r

' ,

KL

t

"

#

'E

t.t7tr,,;. 41rr

x3

s' 1.4''rtr

4lr r

r

3

.

7ki

;y

sf

n 3 Is ix 2+r +

i

m

t..a -r.

?c U

^r,,r ;t

'x

r'

) w Ey

, L

7

'fi'r.

r

S''

:

r

}

F

" 51"; #fr

r'

'ter

r

far .r

-,.d

"

i

tI 1}£.

i

."

"+t}4

}.r

-i"""Fr

L

F

?r r''r 2c. rt

.

r Z

t

Z1 +.,.Lr

T

'?'

-eY

r f-

r

rj

y y

k. l 'XY1

!

}#t 1

n

t ti

x

n;-Y

er

f

rnr a's.'S°rr

i

rzt4rr . + .

i

.r~

1'

ni

c

.r

SJ

a ea'Fr - FrI

^S'}...,

j

£.

s.

'r

t

i

}"l

^ L}

z

2

"F!

ta. }

*:" r7

' ~

, t.

.s 4

c " lr

-,

ri

2

rfrrti

s

fe.

}

.c tt. r2a Xf7

fi ,rY y

z#

+''

'pry trr }

s

4u

}"-

r+r

i..f.:.i

L ,

4E'rg''.-yxf'.KR

t

r

t^ A4

a r

f

E

.

. S j 4"'

f '"

K13

kri xt -- Ir1 c -1-. A' y r r t Y t'

F s

f

s"F i

^r "c' -j r

s

-Y

b .. ktts '

'

Saq

Property

00 -.

1 15r

Dr. Cav,) 1 of

tH

I,;nta Address

'

Telephone W

B

MN

V1O

(l

Q?e 1

,4VC aSS x7

;o 7--ยง5 7SZ71

I~

5~-

~LS2-S3Z~-

This Book is manufactured of a High Grade 50% Rag Paper having a Water Resisting Surface, and is sewed with Nylon Waterproof Thread.

INDEX r-~

-i

1989 JAN

FEB

MAR

SMTWTFS

SMTWTFS

SMTWTFS

1234567 8 91011121314 15161718192021 22232425262728 293031

1234 5 6 7 8 91011 12131415161718 19202122232425 262728

1234 5 6 7 8 91011 12131415161718 19202122232425 262728293031

APR

MAY

JUN

1 123456 2 3 4 5 6 7 8 78910111213 9 101112131415 14151617181920 16171819202122 21222324252627 23 425 5622829 28293031 30

123 45678910 11121314151617 18192021222324 2 2627282930

AUG

JUL 1 2345678 9 101112131415 16171819202122 23242526272829

SEP

12345

12

6789101112 13141516171819 20212223242526 2728293031

3456 789 10111213141516 17181920212223 2425 227282930

OCT

NOV

DEC

12345671 891011121314 15161718192021 22232425262728 293031

1234 5 6 7 891011 12131415161718 19202122232425 2627282930

12 3456789 10111213141516 171819202122 2425262728290 31

3031

:

-

i-

k1n

)

Jcc/. 1

G ~e

"Q"4

yA i cw\a 3

~r

"

T~a~c~ -

r

L

~8~$-t-a; =---z3

--- - 9AA4Aa1 ,1~ ---

,i/

...-.. M4

~ cA~i c, 10L2 ,ca~

M Z--- -; -I I- ----

.-

11~(~ ~

: ;--- -I

it-/

^

:..4.

.#L?~ .

-

s

r'(

;4

r

7

r

Y ,

}

./V4A 1:;~~

sr.

:

PA

e5-f<

.

;y

}

..

4

-

,...

l

d

O

J

;

1

... wIt

;

_< ..

.n .

i

r

.

,

. FI

rl , ry

t~;,

-

Jc

4s

. f

r

il .f7 1

U,

a

Yis_

:7

i

J'

Iz

//Z

J....

-i< - ' \I

~c4

iP,_-

,

2'

,

.4

a

I

:;,S~

,1

"_:

3. t

/

4

-41-

I~I;

_.

5c/

fC-". r!-

(A

1~3

ci

M f

i

rf

T

~:R

V//I --I

a:I~

I-

F

(

1-

:;jP,

~<1

ii~

-

~i~U~r

1

;-k

Y

V

l

1I 1

/~

i

A':Li

4

I;

,r"

._

;I

.

- II-

If

6:.

I'

/'

'"l

ba'

i ./

ie:

1,

4,-ir

'y

,r

c:' ......

.1

"ij

.

I.

,

ib Cf~Af s/&ti v.jb

1 .j.

..

.

,; i

t9 Pr

. :Lj

I

a+

ii /{l^

L

..

,_

fl

.

A /

i

<'

_i 1

rJfJ4 1>

C2~7

,

.

.

_

.

.

..

-2-3

2

ii

2-

s

vi oi~

4

I

I.

a.

22 4

~

q

22AZD

...

2

I.a

4tLAszI # fo

(

r 3 I

1--

<41

2a

'

r

kf

< ZIIYJK ii

-

I

.

t~

(,

(

~.

.

...........

;~V

V

-i(i

'

/

f -~17r

1;/ 4,~~-a

1

r

i

~-

";

~ ;I

Je/

1,

I

14i

r

711!

r-:

L4-

Ki

1C)-i

t~' ( A

4

I1

1-i

-

/

t

ii

i

L I. I

/ .

L

.

:

I

(r

/ Lii

.i

Isyb

i

1

4 j

"i/

.. ..

_..ru"., ......_. I

.

BEE~

A .

,'

_. '

"'

"

.

~~4~Q$ n

,t

., }

~

-

'd~:

~B

-

t

." Ll I

c, r

r7

,

Fi~

~(I

j;

,/

P F",

-

_

%t

-i

WA:

22*>4i' 1

.i_.

Ti~l~

-;_.

i I.r-

A

t

t :.

8

t IaadU44I

6L

drh,

i0

6kO0

/

f

1p

/

n~l

Nov -

I,.x4 fif' 2" Gov

rsa

2'

r 4 APL j

4

2" 0a A&

_.

:,

f ;.f

> d

1~A 20,

~ ~~7

..

h1I

A

WC~dY#Qc

: ,~&~?

(tL#

4''

d , _, \A,.

,. 'I r

a/

:

re

(cvi

1/ .

4

af

L,..

}" .

N

r ';t;

ft 4,)

( rr ,-

3A9

(sti ,..,

:, .

,. ...

r t:

t

sa

r

'

13,50

1I

. _-. ; .

.

-.

.

-.-

Kari Hough Bob Weston

Box 85 Garrison, MN 56450

612-692-4477

Garrison Sports Bait and Tackle

Launch Service Pilot - Greg Erickson

Fishhouse Service Rental & Storage

Residential-Lake Homes Commercial-Business Lake Shore and Acreage Appraisals

LARRY PATER REPRESENTING

KINNEY REALTY 120 WESTMAIN STREET P.O.BOX37 CROSBY, MINNESOTA 56441

PHONE:

OFF.: 218-5468331

HOME:218-5465790

c6

t4;ja7

a2'4 -I

r

S

-

i

{

(

r cr.

*:l

II

i

I

f

- .;

A?.

~;

-- -- /-- -:

A

r

"r 1

f

'

4

ij

K

f

L

+

I

& t$

f

t

W C

IF

V

1 i,/ A-w

\.a wi f- /-. --4-~-'-~ 1

t

23

1< -

a.~ 1

i

wlti k2

~

1

i

.. ..

-

~- ~ I;: i"

Ay

~f/

"1

/ :p_

I.

1----~

.I

x~

i -

A

.

U~U~ ~ R

G,

,.

".

. _..

)~

A

7

I

{

f _s~

>

(L. n

1K. ,

it

q

r

l

;/

U'

_

K

j sr._

4.. .,;"

;??

Li

W.__a ..._._

... _..

. i

J ..

f

}::i

.I 2

/

x

r/ _ ..-

.

T

f

Tk----

1

C k

_.

! =.. .

-j +1tl

.

.W.,

Zr

._

t-----

_I .

. .

.

.. i .... ,. .....

._

1°.c. _

_

..

,.

',...

.

--- -

c~

~ ! p

N;

.f

t

' °

:

, f#

^: c

t4Z/

A

I:

B

(sr

:

rrif I

I . I

.

T

F

'4 7~ _

c .....

I

;11

2!

-fsi

:

4

1l.

..

r

'l~ -

e:

i

1

-~-

-. w

.. ,

,-

-

....

JI

'j

*

..

/ i

612

i

f

_............ a

°'

F

o .......

<7- -

I ,.

[ .

1

,

1 n.

b;~

4

/,

I-

(Ii- /

~

jv,

-

1 I~ -~

_..

--

,

I i

*.x_

i

,

l.~.~I,

&:- d. :.

.

P '.

..

~st~r

j

: r

/1B(N

5Lr

..

....

..

._.

1*i Co; ~62/

i'.

ici

rr

~--;~:~2aQ f

.

(X

4~4

i

q

4/

/1

F

K s

I

!

F

iI 1h /

"

[:

1

I

I$~

'

I

J-r1~

-

1

I

V ". Ia-~r

I 1i d

i

~

.:

f

1

C

~

~~::i

(

Yl

4

f...

f

/6

f

V-

I

1

if

Lt4i 9'O CBPIf vi l

3"x

i

I~'

I~t '

~

cY W;$r i"

ric ,.

a~~li~rr c

-~~I %.la ;lr]4 ~1 i:;< S1

/A Q . _1f " !/v

$

I.,

:

iIj/--S

-I; -

-

y

,,

A

_

~I ,

_ .

~ -

i ..

j

..

.'

.!I

i

r 'yd }.

'. M

.

..

.. _ {

, }

/

IW;_

~ ~

I>

4.

1

~&44

4i

" ..

fJ \

,

.A_

a/Y-a--i

7

__

ci4

Ita

^i

}

4

% /~,

t{/ j f ij 1; _

\.ttr

° ~Zb f

. :G

;

,..

-4 ,

i

f

I

(I

f ,

I

/

),1 ro*41 )D h

t

C1j ~a

&

2

Z2 -wa /c4J k4I;~

/lt

JIb

SD

Ieca 2.

12ea-

S4 i mf

Ii

_

4

A P.' A

ors,.

r :_{.

4nn

tit

f

f

..

x

..

..

r...

.. , r

.....~:b:L~; ;

t

C

ir

-~~ --;--I- -

_,i~ -_X

4 S t. h

i --

Fl

4

wr"

s

;

1.E

t

7 '

1

1-1

,)

"'rV 4aw

iW

C p Cyl

t

R

_r

Lf L~~t }(;4

44r

.7

-

... ,

.. ,..... ...

.(;.::-.. ,--. --:--...- --4y .---..-.-. ..:... f

w

-

S

if

r

jr

4

;

t

>2ZhC ~;)~':~l

i

I,

~

4

C

j72

7,2,L

~I SI '

,. .1

_

°

s-

eI >

.

r

._

(

A( f -~

cia

£"

7r~rt;a

61I~.3 .

i(y

-

A

CIs;rf C c .fzfr

4 1~c

4

j10

' " rdrC

7L

. 1

..

.

E.

. ...

.

,,

S iE

-"1 7 ~" j

/

i~L~j 1~

iii

Ll\

1

,7 f s

Erb}

l

r

V

:"ph

Jfr' (

r

t

rA.

/

l

/ tw

7 u

I5 U /#f ' ''

c~Jr ,r M K11 L. T2&\K

>w

.:;~Lini3gJ44:; ;

L1 II

IAi A i

r

:

Li1 ~i:;~; ~:-,-;r:-~ j JLI_

4i--.-

f f

'" 21~~

A~'~ F"

-11 ~~

f

41b

JAMES KLEIN Field Claims Representtive

NSI

b--uu'uons,

BOX 2525 BRAINERD, MN 56425

BUS: (218) 828-1099 RES: (218) 828-2069

STATE

OF

OF NATURAL DEPARTMENT DIVISION OF FORESTRY

RESOURCES

CHRIS KOBBERDAHL Forester

1601 Minnesota Drive Brainerd, MN 56401

Telephon: Office (218) 828-2565

V),

1.t5 . / i9 to

9-

',,,....

.

-LblS .4~~ - i~:"

.-

-K

Oa-C

:.:-4-

c-% A'l _

,"yv

L/

A

/., 4

L

J/..f

(. _-

..

Bi

.~.~.--~-.;-....-4---------------------

-~...... I .;

I

1...~..~.~, c---q:.... .-:;...

C J4 {~~ic

reiy ,"

r4? rr~

/

I

^7

i

LL

;

11. r

} SF

/ I)

j 4\j?

-. c(I

7 1 ~'

,

p--~~ a Ly 3 F .

1/

-J

~

I

_,F

i

la i I~ *i

_._ ,

3

i

_:

-si i~-r :;~

_..

..

t :

'!

CU

ii !,

l;

I ;

..

.. .

.

I

K1

/ 4-4

-

C~~l

1

4

<

I~i /l~i

(,I

7-77

Vi

2

nP '

;Ld

~VA(C~j

23/V

44!v a

4

&~9~2

23tV~A

i"'li

'7

,6$T

(C

JAMES KLEIN Field Claims Representative

NSI

BOX 2525 BRAINERD, MN 56425 BUS: (218) 828-1099 RES: (218) 828-2069

1C

'

cj<~

-V

KITCHEN. CASH RECEIPT

f6nk qou.,

I~

-- - ----- ----

GUEST RECEIPT

- ;------3 -- -~

Dat

--- f --

E'4-~~4~V/1 Y

L

-~ 51 ou1 r

7

GUEST RECEIPT

n tou

Of 3

na

t

870158 5ZJ

4-418; D

MBER T NO D

E:E

OLOOF.CIEK-O

CA t-

~~ ~AUTHORIZATION ~E~I :;-;

t.

5

HRG

r.,

;.

I

IL

TM,

EVCEET6U L y AT NO TI

9C

l

TIA

*r

PEA

SHUL

N

PPA

OU

IO

SHDED

4

:

INT

E01

E2A

HEEBEA

C

U

YG y

"I

H

X

r

YECHNtS DRt VISf

.i* HSE O

~;

HI AR

TOT ETREDFR

~CARD

-~'E:3~,~ 3

I~i

INV

ICE

:

~:~: ~s~~~r.: ~~: ..

,a

64SI

P

~

.iS Y R E S l:A d Ua(

i

CRDITCAR

f

HALNO E EOL O

s

OXES

TAXESc

TyO

I Y

-

AS

L

&I(Ti$:p~

EFN

MEM8ER'S

,O

::

f,. '~6

D.

2:'~;'"m

.i

8'~.z 1ri

TYPE

ENTERTAINMENT EXPENSE TOTAL NO. OF PERSONS

(HOSTS

NAME AND TITLE

DATE BUSINESS

COMPANY

OTHER BUSINESSRELATIONSHIP

1 2 3

BUSINESS REASON NATURE OF BUSINESS DISCUSSION IF

DISCUSSION IS BEFORE OR AFTER, STATEDATE& DURATION

TRAVELING EXPENSE TOTAL NO. OF PERSONS

TYPE

DATE

(BUSINESSTRAVELERS INC SELF

OTHERS

BUSINESSPURPOSE OF THIS PORTION OF TRIP

ALLOCATION

BUSINESS

PERSONAL

REIMBURSED

ALWAYS OBTAIN ITEMIZEDBILL FOR LODGINGS IF MORE THAN ONE EXPENDITURE IS INCLUDED

)

<F-,:eJr'

c: pi i~

; s,~:iFaS~~li

j ~:?.~

iej sl i ,r t~s--

Io,

L/

-

-1)

Le

{' ..

. ...

_.

" X31g i99iD

(7X-.

'

.M

tie

I

A4 a

~zcy

If

-- ; --; 1 . ;

'-7<~/

L.7 7J

PHONE: 828-1248

JOHN W. PERSON ATTORNEY AT LAW

510 LAUREL STREET P.O. Box 472

BREEN AND PERSON, LTD.

BRAINERD, MINNESOTA 56401

-

_

.U .,

71C~

....

. q

/

_

_

L7I

, i ,!,

(

IIr;;_ F: cl

~T

A;

L/ '

.; s-:; ;

.

1{

-7

!c

-

rIIi

r

.

lk

t"

2

1

~

r

-

,

t

7-

rr~ ;

/

i

a

.f-I __ .

'

..

....9J /=

....

.. jr

U

A

'

4.

)

.

If Y

r.

_...~

{

/

% *:.

A

I-

.

fI.

.

.

t

S :.

r-

;

'd

,p

..

f

;t

//_::~i

i

q e

7V... .kY

J

z,..,. 9

'.:..

-

i

C

I

IC'

,; Ini-,l

l

r "

i

-

i -

-.

,

Fe~h ~2~Y

rKI f

,~Ac

,S

I"

p

/

-

1* 4,

.~~I.*...,.. b' -"

,~

,

.," a r_.:...a

.. , :.,.

f

._..,,...

l/,,.._........,_.

. :

~/ /

. y i

. _ ,

; _ _..

-

i: i

>

I

r

..

r

t

IW

.)

r>.. LX-$

k

a1{

H

-

ljt

4 ; .. Cii+y I . ~

,"

.. _

t

°" .c~~

a."

'

.

I'I

1.: ,.

qs

yi}

b

G

x

F

W

I

aX~ ~

!C x1

{ JJ

4)

6

f11<

>'n

iJ~&U~

~i

(I

rCff~

;ACs

/

6-4

AVX

Svi V

E, ko

I

'

!

,.....

rv1& /

----

B

<:.-

..... :_:j _

_'

'/

A:

r,

V t

,-

f

_., i ,,

a

R

_.

y

.

l

..

.

-

.~ ;

/ ( yr

f _,

F

P n

.

.

*

..

A't_

l

,-

y

;~

o

._r

.-.

i~ri

.

..

.

_

..

_

_~j

i--;

.:I::1'

;

r

I

K

)

/{

iml

-i

_U

-

o

_

,

K

I ii

I

, rr---

S

-

'I"i i-~.-cai -* j.-..

i.

,i 4--

ir

:_~a ; I

; ~tc , i tc~tc~ ; .:~~~!:1~ ~

:

i; 7

i

I ~i~ i~is.l. _

1

i

8~d I

4 I"!

y

n_--

A41J4

tL

I

k I

YI

Iii

/2< g-. .

01

K ~-~-

~ ...

.

_. _

f... .... rr

f

i-

~ri; f}i

1%

/

:

LeAC

d.r

(

~54 ~~

A

&(

C~

<C

4-i

1."

~

I~

L~

2<~

.

/ L ,e

r

4:_~l:B

4"

~,~:a-

4

1

41

-~~:

.. I. ,..1.

<><~ f~

V2C r

~

4

4-i

'4

~ia14i

.;,.I.

I5 _..__"'/_ .

#4?~

.L .

K

i .. i_ .

/, lIt

,: ;-~;~ ";":...... i~-

/

-- - ----- " I

- --- -- - -t

~, c:~C

S

A,

V .s 2

4

"

.

_

/ .,y

, i

.(....

1< I

i,

Ii

(P

~-u

~I/

a

J a

I

ii

1-.

I

;

Il

5;

.

-

/

_._

1

I4 4

i _.

1

l'gi~~

IpWi

7

1 . P

I

:

I

,;

ii;i

_

i'i

-

~-Y

R

y}4

Tp

14: 44

rl

r

r

i

y4

L

_

k

/

4V

/

<

1

f1

i

,w

, r

I

.

~

A_

RG,1YL

,.

F !" /

t

Hf 4(

1. i

lA4

~4

7Thv

v

4>

/F

I

4

c.....;~~i~ P: C

jr

Zu,

-~~

I 1!1~

11

L1 L

jI

U rr

r

1

'si)

f

TT""i

C

k

iq)

-

\

i~i

7

/Lo

: tTi

~Ir 4~

I

bI

~

<~

Ak

~ :ra

rjcL

IiYt:i*f Lp 3T1~ t-

,"i

-4

1/~

r

iL-I .q

r8.

tir

4

~i

R;-t&

iF

Ci~ l:

~Lr~cz, r

i

44 a~ I3 .t'

1)

4L*:

~VA

_ AI. ;f (If>

'. 71 i .. -.

I'! ( Yo C.L~

C

z

.10

? SP~flitCH $i4LAD 1 ICE TEA

12.35

TOTALL TiAX.

--

PiID BY CASH CAND

PRINT

AflE.

SIGNATURE,

3.75

TOTAL

......... C

nR.R

................. :aI

nRaA"

NCK

THMAnK YOU FI:TC1 DINING AT tIC CORMICKS

91-07-15

2 GUESTS

NLInBER

75

r

~

;-~

+

f/ r

-

i

r

:.

i r

I

r 4

Ii

~I

s9 I,

e

f

Ili

i.

::

_

__

1

I

I

f

7~jj

k.-:.

__ :l

iz ,; i

-.

I

2

ii ,

M

; ._4

i~

_

11

... I :,

...

L~ ~X'j~2~

.

;~"..

V' _2I Q.

r{a_ ,-

-,

Ui

I

/

a: ; Ic ..

;.il j

y

Al4(

.i

I

i

.

«

'

7

!

/}11

oj

s 1rl

5vi

(

Jr/

f I

C

. ..~-4~

r4i

t

A

/

y-

/1

I ri

iI. i )Ii

i

ff

A-

ri ::

1

4

t712 ,

I

, I

i

V

~C "

h:

y

;fY

1

k

-"

t2i

J

f

:4V

1ld~

L~

f

?ZP °

;

t

r-

:'I

i ~ -~E~

/>

ji~

1... ...

2.

I

:;* t."

_.

.P

I ,.t f

.

ii

"7

''~--

6: j

n

:

d

,x

1

....

i

:i

..

Iv

Ii

i

i V

f

Vv

j _

!

.

_

_

3b.

tL

'

_.

1

_ ._ _ __

.

k_

:

,

"

Sys----

7-~ K~, ;,V~i~

I /

I J /

.,

/

..._ f

.

"

ro___.

~^

ii LAvc r

l

I f'

A,..

f~

{IIF

le t" _

tAi~i

tip

t

l P..t V/

--

-----

(

~

f

,

C

t .

y

.

t

;, ®

V$ 7

1ryLA

j'

GE

st

'

t

_e

. e

y

iLJ

-

f *-

:/

.-

,.

_..

..

..

'

_)

tt

I

"

~~>V

-

rr

x

--

Ai

/N r s/

~a~a~ac

iii Xj~~ik LA$

4xt 1

t

' s~~L~~~.LCJ~~-~~kr

Ia n., n

(

v

7-

J..;"

t"

t

{~ ~ <~

I

'4

/Q.4

^ a

zU Mn

IV y%I

Q~1

z lunches3 LI

t

VfRle

112-z

w

1/s

~

CLJYI Cec~

fi

K4 ; ,

EI .' :

,'

C A

rv,.-... i

wg",

ii

r-

,-

1-4" .. o

q

CL IL

,

1

#Lb' o-yt oto'o

aP

66'

YT1z

6 JCw 0

4/Js

"

1JI S

i ...

"1t ~l~i~

4~* /: f

I

I

4........

I';

r

........

ii

1c

x4

/7

(-

4 r"

j.

I>

f r9

4 -~-c-

Jr

r

i

_/

24

. ,

L -

VU

1~~

yYI

/

5

;iI~I~.

>-

-~b

/"

/ ~F 1

LI'

s.i"ii""~

e

F P / y'

Li

Ie

-I

Y '

I

L>:F

f42

L

<44

A

(Aa JJS;L Q ~J~&Js i

r

p

(-

I

~-:;r d

G4

> -1

U{

f

t

T<

-g 44~

y

i~(

Finest LE ECH

Fishing / 1 3 TONGA'S FEDERAL DAM LAUNCH SERVICE 218L654-3715 CATCH 'EM HERE Launch Trips 8 a.m., 2 p.m. or All Day Bait * Ice * Docking Facilities * Snacks MODERN CABINS - SPECIAL GROUP RATES Lucy & Merlyn Tonga, Federal Dam, MN 56641 Home: 5145 18th Ave., So., Mpls., MN 55417 - Ph. 612-729-5040

-I ..

_

i

iB

"

_

_. ..

-

.

ii.

4 ,. C1 j

i L

J

4 ;.

. .

r

.

M-

/ /

L.

1

_ I

/

w .

:.

;

.

._

.

i"

.

r

r

2i' e

..

'S

, i~

I .

.~

>1tL4

. ..... ;

/i

5 .. LA,

IA

- 4

1--

-i

U:i

21,.

I

sq-

7; i -.

E

41A

h~a tbkJ

~4~

rr

II -4

cjji

/i

P

z

-v-i. : 4

-r

-6

Ii

t

P

2i

-Ifi

rll: e

4n:~-

I: -"I""-" i, i~::

L1 :~r I la~ o ;.("-r i

i~ I i.~l d

i

I* " i

L

-I

k;r:.t~._ I F

Ii

/

zf

14i

a

7

.

I.

j-

iI

)

~

lar

.

3

r'7

f.

rThL4

/

s

1H

&

tk4l

4i~

;L.

C r;~

;

/~

~.~~:~e

~../C~.:.

.~:'1 A

7

:~- S I~ .-

~

kr.:2 ..

Y

Kii

x,

J

,,

j

l

l

.r9

'9

t __

7

.; \s

/ ~

i .. l.{ .

( if k~":~ l--~i i" a

i I 1^ .- w4i

Xiu

/

r-

/

I--;1;

ri

i., d-il

a1 (..

; /

i

+ i }

..

.

_

i

_

''

.Y .,

I'

'

I~~ f

/ 3.2

r1-O& r __-

1

4

2;

S~I ... _ -

,,- .. / s

(#1

_ _ t -

.

r

~

i

.

'..E'

"I

fC

I-~

* /h~1-1i,

rZ1

/

F

c

r

f

.

L

r

r

I 4 " /

4

I

/4~

9<

I

1

I

(

)

/

7<

4

a 4C

-

JA

L4.

. r 0w14 I' X4 (/

"I e gq,: 1\~~

e

t

:

7 cz

~r

3~

~

!

4 f l

r4:l

Lt-~j

*

A~i~

r,2Iil~l4 A~~~- I

£

9(

~~i~~t kc

fr f',

4: (4

/

7;

r

Minnesota Department of Natural Resources Trails & Waterways Unit

Forrest L. Boe Area Trails & Waterways Supervisor (218) 828-2690

Minnesota Department of Natural Resources 1601 Minnesota Drive Brainerd. MN 56401

rp

~iiL~ii J

Ys

:teP

7

7

i,

/

:

-

K

A

o/ lL

"

E

.r $--

pi

Ca S-

-i.; p

__

5fJi

~1 C-1 _ .?,M

e

cZ %Fi

" i:

K-

i

Jd2

j

J

i

i

:

,

L.

2

dcr4I

c4 8

~-l~xrC CA

1.

KlQ

u/ j()

.4

<1

:-,C

N'c

r

s

B

~

>1

~i I

CN;i

I

*

]

.I

.

.

/ i

(

.A::-1d.

/

j

u . .

(pii~a~' /A

f

.

f/

2:E?

s

lQ i-°-

ciq

i

-

11

t3i

.=

:j

K

..

7l

ic

r-

,

~~~

r'

Ki~1

ii

2

!-

q

i

i

i

sV"eJ;9

i-:

/

A

1/ F4AA/1 -

r. 1

Cf

A'I/

.A

V

1?6 7~d;i,

/ t

i

( 0

1

/c /-

'xi {T '

IL

A,

I

t3

i

-

DEER RIVER, MINNESOTA 56636

ON LAKE WINNIBIGOSHISH HCR 3, Box 772

RUSTIC - MODERN CABINS,

LODGE WITH GAME ROOM, BOATS, MOTORS, GAS, GROCERIES AND BAIT

SWIMMING,

FISHING, AND

SNOWMOBILING

( 218)

-2560 2A6R

JOHN AND PAM HUMPHREYS

!i

k.

~4

f'ifv :t

......... .

I

' ' 6

!

i...

*

.:

I f*

il

4.

$r i

, t;

t

a

.

/

-

{:

J

,.

r--

;

.~l ---E~:

f

I,

Si .

4

-i

I .I

' I

r: -.

:: _

.X

...4 ..

/i i~i

7~~4L~K>~

ALA a

r

1

I

J.~4Ii44b

J 4

L~-~

1

(

4

r

o

E-..

~~i~ lp

1

'4

d "

_N

9 C

b

t~r:2'

P j 1

/

4.'.

2

~4

r;;

E::

/

i;

" ' _:s 'p

~"

i~i

ii

Donald C. Lorsung City Administrator CITY OF BAXTER

P.O. Box 2626 Baxter, Minnesota 56425

(218) 829-7161 Work (218) 829-2516 Fax

I

I i2

.'s

~A _

o II

-jI i

a J, --

1

:- rl-;!1li .

,"V

p

>11: i

3

:I

n

AJr

4N~

i~4 4

'C

--

1 X9'1

ac~ i s Oct ~ Ii&

L, L4 I0

T-:r~fi

L^ r

~..i

.

''

r

(a4 2~

i.u

,.

1/

" At~, rd!~/~J

-

Y

t

-.

1

1

i71*,g

l..

}t ;

. . .

r

ip

i~

I

L~i); a dr

r-\L

,

/ ...

.

y

;,,

.

'

i~-

J0;

a~

0/~.

..

I --.

LI

r

t

~

:~

r.-

S...-~. r i~"t

:'

~

I

r

:

i

/I

si

~$I; ~~ ~+j~l

L

' 1--

/

1'

-

2. ,

4~C~4

4

/

+

-

..,._-

9.

K&G

.. )4 '

.tr

IA 42

Ldw -=

F6_

).

AI'

r

1

did

,

,

, . d

..

Al/C j 4 ((

.

.

-

:

.

. _.

..

. ; ..

4,,

_

:Z't ~J

U

Ii

,r ,L

<

1,

j

I I

I: o~ D. R~, I-

'7

~

f

~ d~i~P "I -----~Y+~rL ~-

t :9- .-...~ ...~

66

S ti LL-L

7

.V-

1}, l

J,

M

jI

YV'

ll$(LV"718 - -~,~x

I

L

I

Ii'

)~~'lr i 4i~

10I j

i

f

YA~

_e

~"

.

kkY /

:.

7

sI 1..

I

/)7:-)"

/

) '

f

1

-

ii

z!

?';~

'C

.'-2

w

'A

C-

(Jpi

I -

i

'i t L:.

/w ",

2

_.. 6'V.- k

L{J

'

,_.

t

,

.;:: _

A3

{

~

7

4K ,

t

/

fi At~

r

~

,(

43,

'i{ J1_ 'L...E

--

Y&

.

Vk2L

,J

v y .. & .

~:

1i

&I

t1

" 1 s-I

l=k .

(t

K'

kU

I-12~. ,9

1.. . .; ,.. . . .;.....~i.; .

.....1:..; i...:

~~i

L4F

-i

1

1/I Os

.

A

t At- W,. -0

;y~Lsxeo -

I

d1W

Y

2)

£

a~

IIQ

12

r4 fY~

c3cdl

ma) r

(i

/0 i;fkf

6

:%~ ~-*,

I.~I*1 EcP~ &p(A 4 IQ

o

#4 >Inw

c-w

7i\Ji

Me

%, CL~

I-~r, e~i~d~L:~FZ

494~E~--J~

40c

r, .-

e Ri

Jt/i

e&i p~e~ " ~ ecl

;se

.T

) -T)11 ouo rTup-

J rr

rr

() 42t y >14~~OI fit

5617+6 q

4

zf~l

a

9J1(frA R

J~J

~t17I.~z

2Li4e)

"115

w1

°t

L~a

i

.

1v

f

I

r,

:

-

.'

I -I

i

_j

¢~

. : . _: .;

_

INDEX OF CURVE AND REDUCTION TABLES Table

I-SLOPE STAKE

Table

II-STADIA CORRECTION AND HORIZONTAL DISTANCES

Table

III-TRIGONOMETRIC FORMULAE

Table

IV-NATURAL TRIGONOMETRICAL FUNCTIONS

CURVE FORMULAE Table

V-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 Table Table

IX-SHORT RADIUS CURVES X-RODS IN FEET, 10THS AND 100THS OF FEET XI-LINKS IN FEET,

O1THS AND 100THS OF FEET

TABLE I. SLOPE STAKE

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OF ANY WIDTH.SIDESLOPES 1V2 TO 1. SIDE ISTAKE S

SLOPE STAKE

SIDE ISTAKE It C.

L.

SLOPE STAKE 16.05

Distance out from Side or Shoulder Stake. 1.8I* 0 .4 1 .6 .8 1 .9 o 1 .1 13

00 0 15 0.80 0.45 0.60 0.75 0.90 1.05 1.20 1.35 165 180 1.95 2.10 2.25 2.40 2.55 2.70 2.85 8.00 3.15 8.80 345 3.60 3 75 3.90 4.05 4.20 4 35 4.50 4 65 4.80 4.95 5 10 52.5 540 5.55 5.70 5.85 6.00 6 15 6.80 6.45 6.60 6 75 6.90 7.05 7.20 7.35 7 50 7.65 7.80 7.95 8.10 8.25 8.40 8.55 8.70 8.85 goo 9 15 9.30 9.45 9.60 9.75 9.9010.05 10.20 10.35 10.50 10 65 10.80 10.95 11.10 11.25 11.40 11.55 11 70 11.85 12.00 12 15 19.80 12.45 12.60 12.75 12.90 13.05 13.20 13.5 1350O 13.65 18 80 13 95 14.10 14.25 14.40 14 55 14.70 14.85 15.00 15 15 15 80 15 45 15.60 15.75 15.90 16.05 16.20 16 35 16 50 16 65 16 80 16.95 17 10 17.25 17.40 17.55 17.70 17.855 18 00 18 135 18.30 18 45 18.60 18 75 18.90 19.05 19.20 19 85 19 50 19 65 19.80 19.95 20.10 20.252040 20.55 20.70 20.85 21.00 21 15 21.30 21.45 21 60 21.75 21.90 2205 2220 22 50 2265 22 60 2295 23.10 23.25 23.40 23.55 23.70 23.85 24.00 24 15 24 30 2445 4.600 24.75 2490 25 05 25.2021.85 25.50 2565 25.80 25 95 28.10 2625 2640 26.55 26.7026.85 27 45 27.30 27.60 15 27 27.00 27.75 27.90 28.05 2820 28.85 28 50 2865 28 80 28.9529.1029.25 29.40 29.5529.70 29.85 30 00 30 15 030.30 30.4530.60 30.75 30.90 81.05 31.20 31.&1 31 65 31.8031.95 32 10 3225 32.40 32.553270 82 85 31 50 33 00 33 15 33 30 33 45 33.60 33 75 33.9034.05 34.2034.35 34 50 3465 34.80 34.95 35.10 85 25 35 40 35.55 35.70 35 85 86 15 36.83036 45 36.60 36.75 36.90 37.0537.20 866.0 87.50 37.65 37 80 37.9538.10 38.2538.40 38.55 38.70 38.85 39 00 39 15 39.80 89 45 3960 39.75 39.90 40.05 40.2040.&5 4065 40 80 40.95 41.10 41.25 41 40 41.55 41.70 41.85 4050 42 00 42 15 42.3042.45 42.60 42 75 42.90 43.05 43.20 48.35 43-50 43 65 43.80 43 95 44.10 4425 4440 44.55 44.70 44 85 45 00 45 15 45.304545 45.6045.75 145.9046.0548620 46.85 46.50 46.65 46.80 46 95 47.10 47.25 47.40 47.55 47.70 47.85 48 00 48.15 48.304 4845 48.60 48 75 48.90 49.05 49 20 49.35 49.60 49 65 49.80 49.95 50.10 50.25 50.4050.55 50.70 50.85 51 00 51.15 51.30 51.45 51.60 51.75 51.90 52.0552.20 52 50 62.65 52.80 52.95 53.10 53.2553.40 53.55 53.70 5400 54.15 54.3054 45 54.6054.75 54.90 55.05 5.20 66.35 55 50 5565 55.80 55.955.10 56.2556.40 56.55 56.70 56.85 57.00 57.15 57.3057 45 57.60 57.75 57.90 58.05 58.2058 35 58 50 58.6558 80 58.95 59.1059 25 69.40 5955 59.70 59.85 60 W 60 15 60 30 60 45 60 60 60.75 6090 61.05 61 20 61.35 3835 59.85 61.35 57.00 5850 6000 000

1.50

._

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

Vertical Angle

3°-00' 4°-00' 5°-00'

7°--00' 8° -00' 9°-00

10°-00' 10°--30'

11°-00' 11°-30' 12°-00' 12°-30 13°-00'

13°--30' 14°-00' 14°--30' 15-00 15°-30'

16°-00' 16°-30' 17°-00' 17°-30' 18°-00'

r

VerticalAngle

3.5 5.3 7.0 8.7 10.4

18°-30' 19°-00' 19°-30' 20°-00' 20°-30'

10.1 10.6 11.2 11.7 12.3

30.1 30.8 31.5 32.1 32.8

12.1 13.8 15.5 17.10 17.9

210-00' 210-30, 22° -00' 22°-30' 23°-00'

12.8 13.4 14.0 14.7 15.3

33.5 34.1 34.7 35.4 36.0

18.7 19.5 20.3 21.1 21.9

23°-30' 24°-00' 24°-30' 25°-00' 25°-30'

15.9 16.5 17.2 17.9 18.6

36.6 37.2 37.7 38.3 39.0

22.7 23.4 24.2 25.0 25.8

26°-00' 26°-30' 27°-00' 270-30' 28°-00'

19.2 19.9 20.6 21.3 22.0

39.4 39.9 40.5 41.0 42.0

26.5 27.2 28.0 28.7 29.4 1

28°-30' 29000' 29°-30' 300-00'

22.8 23.5 24.3 25.0

41.9 42.4 42.9 43.3

8

I

Chains to Feet 1 2 3 4 5 6 7 8 9 10

.......... 66 .......... 132 .......... 198 .......... 264 ........ 330 .......... 396 .......... 462 .......... 528 .......... 594 .......... 660

Difference in Elevation

Horizontal Correction

Difference in Elevation

1

I I

a

Feet to Chains 100 200 300 400 500 600 700 800 900 1,000

.... .... .... .... .... ....

.... .... .... ....

1.515 3.030 4.545 6.060 7.575 9.090 10.606 12.121 13.636 15.151

TABLE III. TRIGONOMETRIC FORMULAE B c

B ca

a

A

B a

b A

a Right Triangle

For Angle

A.

Oblique Triangles Solution of Right Triangles

sin = a ,cos= c

c

, tan= a, cot = -, sec = b

a

Given

Required

a. b

A, B ,o

a, c

A, B, b

sinA

A, a

B, b,c

B = 90°-A, b = a cot A,

A, b

B, a, c

B = 90°-A, a = btan A, e =

A, c

B,

a, b

= cot B, c =

an A =

a

, cosec = a

1 ++

-- =a

2

/

cosB,b=V(c+a)(c--a) =

=

=

sin

a2

1--

a aA.

cos A. B= 90°-A, a = c sin A, b= cos A, Solution of Oblique Triangles a sin O

a sin B

Given

Required

b, C, C

b-

A, a b

B, c, C

sinB= b

A, B, c

bc

a

A, B, a

a, , (7

C

s

180-(A

csin A

B),

sin

sin A

,C= 180°-(A +B),o 0

A+B=180 - C, tan

sinA

)(A-B)=(a-b)tan- a(-A

-B!

a+b

C a sin sin A

4 b, c

A,B,

O

s

JA=

a++esin

sin iB=a+b+c , area =

a, b, a

Area

8=

A, b,c

Area

b c sin A area = b

A,B, C,a Area

area =

(

b)(-c c , = 180°-(A+B)

a)(

s(s-a)I-)

(s-

a2 sin B sin 2 sin A

REDUCTION TO HORIZONTAL Horizontal distance = Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance ° ° =319.4 ft.

Vert. angle-5 $

nl*e

a

10'.

From Table. IV. cos 5 10'= 9959.

Horizontal distance -319.4 '.995

= 318.09 ft.

Horizontal distance also - Slope distance minus slope distance times (I-cosine of vertical angle). With the same figures as in the preceding example, the following result is obtained. Cosine 50 10'= .9959. 1--.9959=.0041.

Horizontal distance 319.4X.0041=1.31. 519.4-1.31=318.09 ft. When the rise is known, the horizontal distance is approximately:-the slope distance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.. slope distance=302.6 ft. Horizontal distance=302.6-

14 -14 2 X 302.6

302.68-0.32=302.28 ft.

TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Sin

Tan.

Sec.

. Cosec.

Cotg.

Coin.

lngle

Sin.

Ton.

Sc.

Cosec.

Cotg.

Cosin.

0 .0029 .0058 .0087 .0116 .0145

0 .0029 .0058 .0087 0116 1.0001 .0145 1.0001

00 343.8 171.9 114.6 85.94 68.76

1. .99998 .99996 .99993 .99989

1.0098 1.0102 1.0107 1.0111 1.0115 1.0120

7.185 7.040 6.900 6.766 6.636 6512

7.115 6.968 6.827 6.691 6.561 6.435

.99027 .98986 .98944 .98902 .98858 .98814

.0175 .0204 .0233 .0262 .0291 .0320

.0175 .0204 .0233 .0262 .0291 .0320

1.0002 1.0002 1.0003 1.0003 1.0004 1.0005

57.30 49.11 42.98 38.20 34.38 31.26

.99985 99979 .99973 .99966 .99958 .99949

1.0125 1.0129 10134 1.0139 1.0144 1.0149

6.394 6.277 6.166 6.059 5.955 5.855

6.314 6.197 6.084 5.976 5.871 5.769

.98769 .98723 .98676 98629 .98580 .98531

.0349 .0378 .0407 .0436 .0465 .0494

.0349 .0378 .0407 .0437 .0466 0495

1.0006 1.0007

1.0012

28.65 2645 24.56 22.93 21.49 20.23

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

1.0154 1.0160 1.0165 1.0170 1.0176 1.0181

5.759 5.665 5.575 5.488 5.403 5.320

5.671 5.576 5.485 5.396 5.309 5.226

.98481 .98430 .9837e .98325 .98272 .98218

.0523 .0524 1.0014 .0552 .0553 1.0015 .0581 .0582 1.0017 .0610 .0612 1.0019 .0640 .0641 1 0020 .0669.0670 1.0022

19.11 18.10 17.20 1638 15.64 14.96

.99863 .99847 .99831 .99813 .99795 99776

1.0187 1.0193 1.0199 1.0205 10211 1.0217

5.241 5.145 .98163 5.164 5.066 .98107

1 .O008

1.0010

1.0011

5.089 5.016 4.945 4.877

4.989 4.915 4.843 4.773

.98050 .97992 .97934 .97875

.0698 .0727 .0756 .0785 .0814 .0843

.0699 .0729 .0758 .0787 .0816 .0846

1.0024 1 0027 1.0029 1.0031 1.0033 1.0036

14.34 13.76 13.23 12.75 12.29 11.87

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

1.0223 4.810 4.705 .97815 1.0230 4.745 4.638 .97754 1.0236 4.682 4.574 .97692 1.0243 4.620 4.511 .97630 1.0249 4.560 4.449 .97566 1 .0256 4.502 4.390 .97502

.0872 .0901 .0929 .0958 .0987 .1016

.0875 .0904 .0934 .0963 .0992 .1022

1.0038 1.0041 1.0043 1 0046 1.0049 1.0052

11.47 11.10 10.76 10.43 10.13 9.839

.99619 .99594 .99567 .99540 .99511 .99482

1.0263 4.445 4.331 .97437 1.0270 4.390 4.275 .97371 1.0277 4.336 4.219 .97304 1.0284 4.284 4.165 .97237 1.0291 4.232 4.113 .97169 1.0299 4.182 4.061 .97100

.1045 .1074 .1103 .1132 .1161 .1190

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

1.0055 9.567 1.0058 9.309 1.0061 9065 1.0065 8.834 1.0068 8.614 1 0072 8.405

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

1.0306 1.0314 1.0321 1.0329 1.0337 1.0345

4.133 4.086 4.039 3.994 3.949 3.906

4.011 3.962 3.914 3.867 3.821 3.776

.97030 .96959 .96887 .96815 .96742 .96667

.1219 .1248 .1276 .1305 .1334 .1363

.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

.99255 .99219 .99182 .99144 .99106 .99067

1.0353 1.0361 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

Cosin

Cotg.

Cosec.

Sec.

Cosec.

Soc.

Ton.

Sin.

Tan.

Sin. Angle

Cosin.

Cotg.

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS

Angle~Sin. Ang

Cosin.

Tan.

Cotg.

_

Sec.

Cosec.

.961261 .96046 .95964 .95882 .957991 .95715

1.0946 1.0961 1.0975 1.0989 1.1004 1.1019

2.459 2.443 2.427 2.411 2.396 2.381

3.271 3.237 3.204 3.172 3.140 3.108

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

1.1034 12.366 1.1049 2.351 1.1064 2.337 1.1079 2.323 1.1095 2.309 1.1110 2.295

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

1.0515 1.0525 1.0535 1.0545 1.0555 1.0566

3.078 3.048 3.018 2.989 2.960 2.932

.95106 .95015 .94924 .94832 .94740 .94646

1.1126 1.1142 1.1158 1.1174 1.1190 1.1207

2.281 2.268 2.254 2.241 2.228 2.215

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

1.0576 1.0587 1.0598 1.0608 1.0619 1.0631

2.904 2.877 2.850 2.824 2.798 2.773

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

1.1223 1.1240 1.1257 1.1274 1.1291 1.1308

2.203 2.190 2.178 2.166 2.154 2.142

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

1.0642 1 0653 1.0665 1.0676 1.0688 1.0700

2.747 2.723 2.699 2.675 2.651 2.628

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

1.1326 1.1343 1.1361 1.1379 1.1397 1.1415

2.130 2.119 2.107 2.096 2.085 2.073

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

1.0711 1.0723 1.0736 1.0748 1.0760 1.0773

2.605 2.583 2.560 2.539 2.517 2.496

.93358 .93253 .93148 .93042 .92935 .92827

1.1434 1.1452 1.1471 1.1490 1.1509 1.1528

2.063 2.052 2.041 2.031 2.020 2.010

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

1.0785 1.0798 1.0811 1.0824 1.0837 1.0850

2.475 2.455 2.434 2.414 2.394 2.375

.92718 .92609 .92499 .92388 .92276 .92164

1.1547 1.1566 1.1586 1.1606 1.1626 1.1646

2.000 1.990 1.980 1.970 1.961 1.951

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

1.0864 1.0877 1.0891 1.0904 1.0918 1.0932

2.356 2.337 2.318 2.300 2.282 2.264

.92050 .91936 .91822 .91706 .91590 .91472

1.1666 1.1687 1.1707 1.1728 1.1749 1.1770

1.924 1.932 1.923 1.914 1.905 1.896

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

Cosec.

Soc.

Sec.

Cotg.

Cosin.

1.0403 1.0412 1.0423 1.0429 1.0438 1.0448

3.487 3.450 3.412 3.376 3.340 3.305

1.0457 1.0466 1.0476 1.0485 1.0495 1.0505

osec.

Cosec.

Sec.

Tan.

Sin. fnle

ngle

Sin.

Cosin.

Ton.

Cotg.

11

Cotg.

i

Cosin.

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

Tan.

Sin.

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Sin.

Ton.

Sec.

Cosec.

Cotg.

1.1792 1.1813 1.1835 1.1857 1.1879 1.1901

.84805

1.1924 1.1946 1.1969 1.1992 1.2015 1.2039 1.2062

Cotg.

Agle

Sin.

Tan

Sec.

Cosec.

Cotg.

Cosin.

.84025

1.2868 1.2898 1.2929 1.2959 1.2991 1.3022

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

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

1.3054 1.3086 1.3118 1.3151 1.3184 1.3217

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

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

1.3251

1.2086 1.2110 1.2134 1.2158 1.2183

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

1.2208 1.2233 1.2258 1.2283 1.2309 1.2335

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

1.3456 1.3492 1.3527 1.3563 1.3600 1.3636

.74314

1.2361 1.2387 1.2440 1.2466 1.2494

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

1.3673 1.3711 1.3748 1.3786 1.3824 1.3863

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

1.2521 1.2549 1.2577 1.2605 1.2633 1.2661

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

1.3902 1.3941 1.3980 1.4020 1.4061 1.4101

.71934 .71732 .71529 .71325

1.2690 1.2719 1.2748 1.2778 1.2808 1.2838

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

1.414

.70711

.84650 .84495

.84339 .84182

1.2413

Cosin.

Cosin.

Cosec.

Sec.

Tan.

Sin. Angle

1.3284 1.3318 1.3352 1.3386 1.3421

Cosin.

otg.

Cosec.

.74120 .73924 .73728 .73531 .73333

.71121 .70916

Sec.

Ton.

Sin.

Angle

CURVE FORMULAE

CURVE TABLE Table of Tangent and External to a 10 Curve

A Angle of Intersection I

Q,

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 :

50 sin % D

R

Length of Curve: L

sin

=

100 D

D

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

L

Tangent:

T = R tan % A

Long Cord:

LC = 2R sin % A

Middle Ordinate: M = External :

R (1-Cos %l/ A)

E = T tan /4 A

TABLE V. TANGENTS AND EXTERNALS TO A 10 CURVE T

10' 20' 30' 40' 50'

50.0( 58.34 66.67 75.01 83.34 91.6E

.218 .297 .388 .491 .606 .733

10' 20' 30' 40' 50'

100.01 108.35 116.68 125.02 133.36 141.70

.873 1.024 1.188 1.364 1.552 1.752

10' 20' 30' 40' 50'

150.04 158.38 166.72 175.06 183.40 191.74

1.964 2.188 2.425 2.674 2.934 3.207

10' 20' 30' 40' 50'

200.08 208.43 216.77 225.12 233.47 241.81

3.492 3.790 4.099 4.421 4.755 5.100

10' 20' 30' 40' 50'

250.16 258.51 266.86 275.21 283.57 291.92

5.459 5.829 6.211 6.606 7.013 7.432

10' 20' 30' 40' 5,0'

300.28 7.863308.64 8.307 316.99 8.762 325.35 9.230 333.71 9.710 342.08 10.202

10' 20' 30' 40' 50'

350.44 358.81 367.17 375.54 383.91 392.28

10.707 11.224 11.753 12.294 12.847 13.413

10' 20' 30' 40' 50'

400.66 409.03 417.41 425.79 434.17 442.55

13.991 14.582 15.184 15.799 16.426 17.065

10' 20' 30' 40' 50'

450.93 459.32 467.71 476.10 484.49 492.88

17.717 18.381 19.058 19.746 20.447 21.161

10' 20' 30' 40' 50'

501.28 21.887 509.68 22.624 518.08 23.375 526.48 24.138 534.89 24.913 543.29 25.700

10

20

£=10*

I

30

40

50

60

70

80

90

10"

E

10°C. T .06 E .003

15' C. T .09 E .004

20' C. T .13 E .006

°

25 C. T .16 E .007

T

E

1=20*

110 10' 20' 30' 40' 50'

551.70 560.11 568.53 576.95 585.36 593.79

26.500 27.313 28.137 28.974 29.824 30.686

21 0

12, 10' 20' 30' 40' 50'

602.21 610.64 619.07 627.50 635.93 644.37

31.561 32.447 33.347 34.259 35.183 36.120

+ 5' C. T .06 E .006

13.0,

37.070 38.031 39.006 39.993 40.992 42.004

10' C. T .13 E .011

23

20' 30' 40' 50'

652.81 661.25 669.70 678.15 686.60 695.06

14* 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

1L

°

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 10' 20' 30' 40' 50'

805.25 813.75 822.25 830.76 839.27 847.78

56.309. 57.498 58.699 59.914 61.141 62.381

10' 20' 30' 40' 50'

856.30 864.82 873.35 881.88 890.41 898.95

63.634 64.900 66.178 67.470 68.774 70.091

180 10' 20' 30' 40' 50'

907.49 916.03 924.58 933.13 941.69 950.25

71.421 72.764 74.119 75.488 76.869 78.264

958.81 967.38 975.96 984.53 993.12 1001.7

79.671 81.092 82.525 83.972 85.431 86.904

15

°

17

°

19

10' 20' 30' 40' 50' °

o

C. 20 1010.3 10' 1018.9 T 20' 1027.5 .19 30' 1036.1 E 40' 1044.7 50' 1053.3 .008 I2 I= T ta T = R tan 21/z 30

1"

1

300

226 10' 20' 30' 40' 50'

1113.7 1122.4 1131.0 1139.7 1148.4 1157.0

°

1165.7 1174.4 1183.1 1191.8 1200.5 1209.2

117.38 119.12 120.87 122.63 124.41 126.20

1217.9 1226.6 1235.3 1244.0 1252.8 1261.5

128.00 129.82 131.65 133.50 135.35 137.23

10' 20' 30' 40' 50'

1270.2 1279.0 1287.7 1296.5 1305.3 1314.0

139.11 141.01 142.93 144.85 146.79 148.75

10' 20' 30' 40' 50'

1322.8 1331.6 1340.4 1349.2 1358.0 1366.8

150.71. 152.69 154.69 156.70 ° 158.72 20 C. 160.76 T .39 162.81 E 164.86 166.95 .051 169.04 171.15 173.27

10' 20' 30' 40' 50' 10' 20' 30' 40' 50' °

25

26

°

°

20 C. T .26 E .022

1061.5 1070.E 1079.2 1087 1096.4 1105.1

E

97.577 + 99.155 5' C. 100.75 T 102.35 103.97 .10 105.60 E 107.24 .013 108.90 110.57 112.25 113.95. 115.66

10' 20' 30' 40' 50'

240

15" C. T .19 E .017

T

270

1375.6 10' 1384.4 20' 1393.2 30' 1402.0 40' 1410.9 50' 1419.7

280 ° 10' 25 C. 20' T 30' 40' .32 50' E ° .028 29 10' 20' 30' 40' 50'

1428.6 1437.4 1446.3 1455.1 1464.0 1472.9

15° C. T .29 E .038

1481.8 1490.7 1499.6 1508.5 1517.4 1526.3

175.41 177.55 179.72 25'C. T 181.89 184.08 .49 186.29 E .065 188.5: 190.74 192.99 195.25. 197.53 199.82

1535.3 1544.2 1553.1 1562.1 1571.0 1580.0

202.12 30'C. T 204.44 206.77 .59 209.12 E 211.48 213.86 .078

°

88.389 30 C. 300 89.888 10' T 91.399 20' .39 92.924 30' E 94.462 40' 96.013 50' .034 xscII E I E = R exsec /11

10' C. T .19 E .025

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE I 31* 10' 20' 30' 40' 50' °

32

10' 20' 30' 40' 50' °

33

10' 20' 30' 40' 50'

T

10' 20' 30' 40' 50' °

35

10' 20' 30' 40' 50' °

36

10' 20' 30' 40' 50' °

37

10' 20' 30' 40' 50' 38" 10' 20' 30' 40' 50' °

39

10' 20' 30' 40' 50'

E

387.4 390.7 394.1 397.4 400.8 404.2

10' 20' 30' 40' 50'

2199.4 2209.0 2218.6 2228.1 2237.7 2247.3

407.6 411.1 414.5 418.0 421.4 425.0

2257.0 2266.6 2276.2 2285.9 2295.6 2305.2

428.5 10' C. 432.0 T 435.6 439.2 .34 442.8 E 446.4 .075

53

10' 20' 30' 40' 50' 44", 10' 20' 30' 40' 50'

2314.9 2324.6 2334.3 2344.1 2353.8 2363.5

450.0 453.6. 457.3 461.0 464.6 468.4

54

2373.3 2383.1 2392.8 2402.6 2412.4 2422.3

472.1 475.8 479.6 483.4 487.2 491.0

2432.1 2441.9 2451.8 2461.7 2471.5 2481.4

494.8 498.7 502.5 506.4 ° 510.3 20 C. 514.3 T .68 518.2 E 522.2 526.1 .151 530.1 534.2538.2

56

542.2 546.3 ° 550.4 25 C. 554.5 T 558.6 .85 562.8 E 566.9 .189 571.1 575.3579.5 583.8 588.0

58

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 1706.3 1715.3 1724.4 1733.5 1742.6

246.1 248.7 251.3 253.9 256.5 259.1

43"

1751.7 1760.8 1770.0 1779.1 1788.2 1797.4

261.8 264.5 267.2 269.9 272.6 275.3

1806.6 278.1 1815.7 280.8 1824.9 283.6 1834.1 286.4 1843.3 289.2 1852.5 292.0 1861.7 1870.9 1880.1 1889.4 1898.6 1907.9

5o C. T .13 E .023

15°C. T .40 E .070

10' 20' 30' 40' 50' °

42

45

10' 20' 30' 40' 50' 46"

48

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 .117 351.8 354.9358.1 361.3 364.5

2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

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

1972.9 1982.2 1991.5 2000.9 2010.2 2019.6

10' 20' 30' 40' 50' °

47

10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

2491.3 2501.2 2511.2 2521.1 2531.1 2541.0

10' 20' 30' 40' 50' °

49 10' 20' 30' 40' 50' °

50

Rtan = R TT= tan /zrt

10' 20' 30' 40' 50'

5" C. T .17 E .037

T

2732.9 2743.1 2753.4 2763.7 2773.9 2784.2

618.4 622.8 627.2 631.7 636.2 640.7

52* 2794.5 10' 2804.9 20' 2815.2 30' 2825.6 40' 2835.9 50' 2846.3

645.2 649.7 654.3 658.8 663.4 668.0

°

10' 20' 30' 40' 50'

2856.7 2867.1 2877.5 2888.0 2898.4 2908.9

°

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

°

15 C. T .51 E .116

I_E

I 51" 10' 20' 30' 40' 50'

°

55

10' 20' 30' 40' 50' °

2982.7 2993.3 3003.9 3014.5 3025.2 3035.8

1=60

672.7 677.3 682.0 686.7 691.4 696.1 700.9 705.7 710.5 715.3 720.1 725.0 15" C. T 729.9 .63 734.8 E 739.7 744.6 .168 749.6 754.6

3110.9 3121.7 3132.6 3143.4 3154.2 3165.1

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

10' 20' 30' 40' 50'

3176.0 3186.9 3197.8 3208.8 3219.7 3230.7

821.4 826.7 832.0 837.3 842.7 848.1

10' 20' 30' 40' 50'

3241.7 3252.7 3263.7 3274.8 3285.8 3296.9

853.5 858.9 864.3 869.8 875.3 880.8

3308.0 3319.1 3330.3 3341.4 3352.6 3363.8

886.4 30 C. T 892.0 897.5 1.27 903.2 E 908.8 914.5 .340

10' 20' 30' 40' 50' °

57

10' 20' 30' 40' 50'

3046.5 3057.2 3067.9 3078.7 3089.4 3100.2

°

°

°

40"

°

294.9 297.7 300.6 303.5 306.4 20 ° C. 309.3 T 312.2 .53 315.2 E 318.1 321.1 .093 324.1 327.1

1917.1 1926.4 1935.7 1945.0 1954.3 1963.6

1-50.

1T

2142.2 2151.7 2161.2 2170.8 2180.3 2189.9

I

41"

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9

°

34

=400

E

2551.0 2561.0 2571.0 2581.0 2591.0 2601.1 2611.2 2621.2 2631.3 2641.4 2651.5 2661.6

59

°

°

2671.8 2681.9 2692.1 2702.3 2712.5 2722.7

° 60 592.3 30 C. T 596.6 10' 600.9 1.02 20' 605.3 30' E 609.6 40' 614.0 .227 50' E = Rexsec 1/21 E = R exsec 1/V2I

25" C. T 1.05 E .283

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

T

E

1-700

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

5 C. T .25 E

3442.7 62* 10' 3454.1 20' 3465.4 30' 3476.8 40' 3488.3 50' 3499.7

954.8 960.6 966.5 972.4 978.3 984.3

.080

990.2 996.2 1002.3 1008.3 1014.4 1020.5

10'C. T

1026.6 1032.8 1039.0 1045.2 1051.4 1057.7

61*

°

3511.1 10' 3522.6 20' 3534.1 30' 3545.6 40' 3557.2 50' 3568.7

63

°

64

3580.3 10' 3591.9 20' 3603.5 30' 3615.1 40' 3626.8 50' 3638.5 °

65

3650.2 10' 3661.9 20' 3673.7 30' 3685.4 40' 3697.2 50' 3709.0

660 3720.9 10' 3732.7 20' 3744.6 30' 3756.5 40' 3768.5 50' 3780.4 °

67

10' 20' 30' 40' 50'

3792.4 3804.4 3816.4 3828.4 3840.5 3852.6

680 10' 20' 30' 40' 50'

3864.7 3876.8 3889.0 3901.2 3913.4 3925.6

°

69

3937.9 10' 3950.2 20' 3962.5 30' 3974.8 40' 3987.2 50' 3999.5

4011.9 70* 10' 4024.4 20' 4036.8 30' 4049.3 40' 4061.8 50' 4074.4

E

1=800

4086.9 4099.5 4112.1 4124.8 4137.4 4150.1

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1

5C. T 30 E

72*01 4162.8 1' 4175.6 20' 4188.5 30' 4201.2 40' 4214.0 50' 4226.8

1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

730

4239.7 10' 4252.6 20' 4265.6 30' 4278.5 40' 4291.5 50' 4304.6

1398.0 1405.7 1413.5 1421.2 1429.0 1436.8

740 4317.6 10' 4330.7 20' 4343.8 30' 4356.9 40' 4370.1 15 C. 50' 4383.3

1444.6 1452.5 1460.4 1468.4 1476.4 1484.4

+

1063.9 1070.2 1076.6 1082.9 1089.3 1095.7

.51 E .159

T .76 E .240

I 71

10' 20' 30' 40' 50'

750 10' 20' 30' 40' 50'

T

4396.5 4409.8 4423.1 4436.4 4449.7 4463.1

°

1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

T

10 20' 30' 40' 50'

4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

1805.3 1814.7 1824.1 1833.6 1843.1 1852.6

4980.7 4995.4 5010.0 5024.8 5039.5 5054.3

1862.2 1871.8 1881.5 1891.2 1900.9 1910.7

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

840 10' 20' 30' 40' 15oC. 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 15 C.

5250.3 5265.6 5281.0 5296.4 5311.9 5327.4

2041.7 T 2052.1 1.09 2062.5 E 2073.0 2083.5 .450 2094.1

81

.110

820 10' 20' 30' 40' 50' °

T .91 E

85° 10' 20' 30' 40' 332 50'

E

I=90

I

+ 5C. T .36 E .149

°

1102.2 76 4476.5 1108.6 10' 4489.9 1115.1 20' 4503.4 1121.7 20 C 30' 4516.9 40' 4530.4 1128.2 T 50' 4544.0 1134.8 1.02 ° 1141.4 E 77 4557.6 1148.0 10' 4571.2 1154.7 .321 20' 4584.8 1161.3 30' 4598.5 " 40' 4612.2 1168.1 1174.8 50' 4626.0

1541.4 86 5343.0 2104.7 1549.7 10' 5358.6 2115.3 1558.0 20' 5374.2 2126.0 30' 5389.9 2136.7 1566.3 20 C 40' 5405.6 2147.5 20°C. 1574.7 T T 50' 5421.4 2158.4 1583.1 1.22 1.45 ° 1591.6 E 87 5437.2 2169.2 1600.1 10' 5453.1 2180.2 .445 20' 5469.0 2191.1 .603 1608.6 1617.1 30' 5484.9 2202.2 1625.7 40' 5500.9 2213.2 1634.4 50' 5517.0 2224.3

4639.8 780 1181.6 10' 4653.6 1188.4 20' 4667.4 1195.2 25, C 30' 4681.3 T 1202.0 1208.9 1.28 40' 4695.2 1215.8 50' 4709.2 E ° 4723.2 1222.7 .403 79 1229.7 10' 4737.2 1236.7 20' 4751.2 30' 4765.3 1243.7 1250.8 40' 4779.4 1257.9 50' 4793.6

1643.0 1651.7 1660.5 1669.2 1678.1 1686.9 1695.8 1704.7 1713.7 1722!7 1731.7 1740.8

°

5533.1 88 10' 5549.2 20' 5565.4 25 C. 30' 5581.6 T 1.53 40' 5597.8 E 50' 5614.2 E ° .558 89 5630.5 10' 5646.9 20' 5663.4 30' 5679.9 40' 5696.4 50' 5713.0

2235.5 2246.7 2258.0 25° C. T 2269.3 2280.6 1.83 2292.0 E 2303.5 .756 2315.0 2326.6 2338.2 2349.8 2361.5

5729.7 5746.3 5763.1 5779.9 5796.7 5813.6

2373.3 30'C. T 2385.1 2397.0 2.20 2408.9 E 2420.9 2432.9 .910

4807.7 1749.9 30°C. 90° 1265.0 30° C. 80 T 10' 1272.1 T 10' 4822.0 1759.0 1279.3 1.54 20' 4836.2 1768.2 1.84 20' 30' 30' 4850.5 1777.4 1286.5 E 40' 40' 4864.8 1786.7 1293.6 E .671 50' 1300.9 .485 50' 4879.2 1796.0 T = R tan 1/21

E

Rexsec 1/21

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

2444.9 2457.1 2469.3 2481.5 2493.8 2506.1

5933.2 5950.5 5967.9 5985.3 6002.7 6020.2

2518.5 2531.0 2543.5 2556.0 2568.6 2581.3

6037.8 6055.4 6073.1 6090.8 6108.6 6126.4

2594.0 2606.8 2619.7 2632.6 2645.5 2658.5

103

6144.3 6162.2 6180.2 6198.3 6216.4 6234.6

2671.6 2684.7 2697.9 2711.2 2724.5 2737.9

104

6252.8 6271.1 6289.4 6307.9 6326.3 6344.8

2751.3 2764.8 2778.3 2792.0 2805.6 2819.4

105

6363.4 10' 6382.1 20' 6400.8 30' 6419.5 40' 6438.4 50' 6457.3

2833.2 2847.0 2861.0 2875.0 2889.0 2903.1

106

10' 20' 30' 40' 50' °

92 10' 20' 30' 40' 50' °

93

10' 20' 30' 40' 50' °

94

10' 20' 30' 40' 50' °

95

10' 20' 30' 40' 50' o

97

100oo I E ~-E110

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0

91

96

T

°

1010

10' 20' 30' 40' 50'

5 C. T .43 E .200

°

102

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50'

2917.3 2931.6 2945.9 2960.3 2974.7. 2989.2

980 10' 20' 30' 40' 50'

6591.2 6610.6 6630.1 6649.6 6669.2 6688.8

3003.8 3018.4 3033.1 3047.9 3062.8 3077.7

108

99° 10' 20' 30' 40' 50'

6708.6 6728.4 6748.2 6768.1 6788.1 6808.2

3092.7 3107.7 3122.9 3138.1 3153.3 3168.7

109

6828.3 6848.5 6868.8 6889.2 6909.6 6930.1

3184.1 3199.6 3215.1 3230.8 3246.5 3262.3

110

°

6476.2 6495.2 6514.3 6533.4 6552.6 6571.9

107

10' 20' 30' 40' 50'

100

o

10' 20' 30' 40' 50'

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50'

T

E

I

6950.6 6971.3 6992.0 7012.7 7033.6 7054.5

3278.1 3294.1 3310.1 3326.1 3342.3 3358.5

7075.5 7096.6 7117.8 7139.0 7160.3 7181.7

3374.9 3391.2 3407.7 3424.3 3440.9 3457.6

7203.2 7224.7 7246.3 7268.0 7289.8 7311.7

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 15o C. T 3682.3 3700.2 1.56 3718.2 E 3736.2 3754.4 .806 3772.6

7333.6 7355.6 7377.8 7399.9 7422.2 7444.6 7467.0 7489.6 7512.2 7534.9 7557.7 7580.5 7603.5 7626.6 7649.7 7672.9 7696.3 7719.7

1110

5' C. T .51 E .268

10' 20' 30' 40' 50' °

112

10' 20' 30' 40' 50' °

°

113

10' 20' 30' 40' 50' °

114

10' 20' 30' 40' 50' °

115

10' 20' 30' 40' 50' °

3791.0 3809.4 3827.9 ° 3846.5 3865.2 20 C. T 3884.0 2.08 3902.9 E ,3921.9 3940.9 1.08 3960.1 3979.4. 3998.7

116

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 4280.5 4301.4 4322.4 4343.6 4364.8

7743.2 7766.8 7790.5 7814.3 7838.1 7862.1 7886.2 7910.4 7934.6 7959.C 7983.5 8008.0

10'

20' 30' 40' 50' °

117

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

119

10' 20' 30' 40' 50'

°

T=Rtan1/z1

10' 20' 30' 40' 50'

W

T

[E

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6

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

9349.9 9380.5 9411.3 9442.2 9473.2 9504.4

5236.2 5262.3 5288.6 5315.0 5341.5 5368.2

9535.7 9567.2 9598.9 9630.7 9662.6 9694.7

5395.1 5422.1 5449.2 25' C. T 5476.5 5504.0 3.16 5531.7. E 1.83 5559.4 5587.4 5615.5 5643.8 5672.3 5700.9

=I120

" I

°

9727.0 9759.4 9792.0 9824.8 9857.7 9890.8

9924.0 10' 9957.5 20' 9991.0 30' 10025.0 40' 10059.0 50',10093.0

120

E=.Rexsecl/21

5729.7 5758.6 5787.7 5817.0 5846.5 5876.1

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

30' C. T 3.81 E 2.20

USEFUL RELATIONS Lineal feet X.00019 = miles Lineal yards X.0006 = miles Square inches X.007 = square feet Square feet X.111 = square yards Square yards x.0002067 = acres Acres x 4840 = square yards Cubic inches x.00058 = cubic feet Cubic feet x.03704 = cubic yards Links X.22 = yards Links X.66 = feet Feet X 1.5 = links 360 째 = 21600' = 1296000" Radius = arc of 57.2957790 째 Arc of 1 째 (radius = 1) = .017453292 Arc of 1' (radius = 1) = .000290888 Arc 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 째 5. Difference of pull of 15 lbs. SQUARE MEASURE 144 sq. inches = 1 sq. ft. 9 sq. ft. = 1 sq. yard 3014 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 160 sq. rods = 1 acre. 640 acres = 1 sq. mile. 36 sq. miles (6 miles sq.) = 1 township.

n

1

TABLE VI. INCHES TO DECIMALS OF A FOOT

2.

0

1

2

8

4

5

6

7

8

9

10

11

In.

0 1-32 1-16 8-32 1-8 5-32 3-16 7-82 1-4 9-32 5-16 11-32 3-8 13-32 7-16 15-32 1-2 17-32 9-16 19-82 5-8 21-32 11-16 23-32

Foot .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 0 .0026 .0859 .1693 .2526 .3359 .4193 .5026 .58591.6693 .75261.8359 .9193 1-32 .0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885 .6719.7552.8385 .9219 1-16 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911.6745 .7578 .8411 .9245 8-32 .0104 .0938 .1771 .2604 .3438 .4271 .5104.5938 .6771.7604 .8438 .9271 1-8 .0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297 5-82 .0156 .0990 .1823.2656 .3490.423 .5156 .5990.6823.7656 .8490.9323 8-16 .0182 .1016 .1849 .2682 .3516 .4349 .5182 .6016 .6849 .7682 .8516 .9349 7-82 .0208 .1042.1875.2708 .3542.4375 .5208 .6042 .5875 .7708 .8542 .9375 1-4 .0234 .1068 .1901 .2734 .3568 .4401 .5234 .6068 .6901.7734 .8568 .9401 9-32 .0260 .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7760 .8594 .9427 5-16 .0286 .1129 .1953 .2786 .3620 .4453 .5286 .6120 .6953 .7786 .8620 .9453 11-32 .0313 .1146.1979 .2813 .3646 .4479 .5313 .6146 .6979 .7813 .8646 .9479 8-8 .0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839.8672 .950 13-32 .0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 7-16 .0391 .1224 .2057 .2891 .8724 .4557 .5391 .6224 .7057 .7891 .8724 .9557 15-32 .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583 1-2 .0443 .1276 .2109 .2943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609 17-32 .0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7185 .7969 .8802 .9635 9-16 .0495 .1328 .2161 .2995 .3828 .4661 .5495 .6328 .7161 .7995 .8828 .9661 19-32 .8854 .9688 5-8 .0521.1354 .2188 .3021.3854 .4688.5521 .6354 .71881.8021 .047.1380.214 .3047 .880 .4714.554 .6380 .7214 .8047 .8880 .9714 21-32 .0573.1406 .2240 .3073 .3906 .4740 .5573 .6406.7240.8073.8906.9740 11-16 .0599 .1432 2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099.8932 .97662-32

3-4 25-32 13-16 27-32 7-8 29-32 15-16 81-2

.0625 .1458 .0651 .1484 .0677 .1510 .0703 .1536 .07291.1563 .0755 .1589 .0781 .1615 .0807 .1641 0

1

.2292 .2318 .2344 .2370 .2396 .2422 .2448 .2474

.3125 .3151 .3177 .8203 .3629 .3255 .3281 .3307

.3958 .3984 .4010 .4036 .4063 .4089 .4115 .4141

.4792 .4818 .4844 .4870 .4896 .4922 .4948 .4974

.5625 .5651 .567 .5703 .5729 .5755 .5781 .580

.6458 .6484 .6510 .6536 .6563 .6589 .6615 .6641

.7292 .7318 .7344 .7370 .7396 .7422 .7448 .7474

.8125 .8151 .8177 .8203 .8229 .8255 .8281 .8307

.8958 .8984 .9010 .9036 .9063 .9089 .9115 .9141

2

8

4

5

6

7

8

9

10

.9792 8-4 .981825-32 .9844 13-16 .9870 27-32 .9896 7-8 .992 29-32 .9948 15-16 .9974 31-8 11

TABLE VII. MINUTES IN DECIMALS OF A DEGREE 0' 30" 1 00 30 2 00 30 3 00 30 4 00 30 5 00 30 6 00 30 7 00 30 8 00 30 9 00 30 10 00

.00833 10' 30" .01667 11 00 30 .02500 .03333 12 00 30 .04167 .05000 13 00 30 .05833 .06667 14 00 30 .07500 .08333 15 00 30 .09167 .10000 16 00 30 .10833 .11667 17 00 .12500 30 .13333 18 00 .14167 30 .15000 19 00 30 .15833 .16667 20 00

.17500 20' 30" .18333 21 00 30 .19167 .20000 22 00 30 .20833 .21667 23 00 30 .22500 .2333 24 00 30 .24167 .25000 25 00 30 .25833 .26667 26 00 30 .27500 .28333 27 00 30 .29167 .30000 28 00 .30833 30 .31667 29 00 .32500 30 .33333 30 00

.34167 .35000 .35833 .36667 .37500 .38333 .39167 .40000 .40833 .41667 .42500 .43333 .44167 .45000 .45833 .46667 .47500 .48333 .49167 .500000

30' 30" 31 00 30 32 00 30 33 00 30 34 00 30 35 00 30 36 00 30 37 00 30 38 00 30 39 00 30 40 00

.50833 .51667 .52500 .53333 .54167 .55000 .55833 .56667 .57500 .58333 .59167 .60000 .60833 .61667 .62500 .63333 .64167 .65000 .65833 .66667

40' 30' 41 00 30 42 00 30 43 00 30 44 00 30 45 00 30 46 00 30 47 00 30 48 00 30 49 00 30 50 00

.67500 .68333 .69167 .70000 .70833 .71667 .72500 .73333 .74167 .75000 .75833 .76667 .77500 .78333 .79167 .80000 .80833 .81667 .82500 .83333

50' 30" 51 00 30 52 00 30 53 00 30 54 00 30 55 00 30 56 00 30 57 00 30 58 00 30 59 00 30 60 00

.84167 .85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833 .91667 .92500 .93333 .94167 .95000 .95833 .96667 .97500 .98333 .99167 1.00000

TABLE VIII. MIDDLE ORDINATES OF RAILS

Length of Rail (feet) C o I

R Feet

0-20 0-40 1-0 1-20 1-40 2-0 2-20 2-40 3-0 3-20 3-40 4-0 4-20 4-40 5 6

17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.3

7

819.

30 28 26 24 22 20 Inch Inch Inch Inch Inch Inch

C o

.08 .16 .24 .31 .39 .47 .55 .63 .71 .78 .86 .94 1.02 1.10 1.18 1.41

.07 . .20 .27 .34 .41 .48 .55 .62 .68 .75 .82 .89 .96 1.03 1.23

8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26

1.

1.44 1.24 1.05

.06 .1 .18 .23 .29 .35 .41 .47 .53 .59 .65 .71 .77 .83 .89 1.06

.05 .10 .15 .20 .25. .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .90

.04 .08 .13 .17 21 .25 .29 .33 .38 .42 .46 .50 .55 .59 .63 .76

.03 .07 .10 .13 .17 .20 .23 .27 .31 .35 .38 .42 .45 .48 .52 .62

R Feet

30 28 26 24 22 20 Inch Inch Inch Inch Inch Inch

716.8 1.88 1.64 1.42 1.20 1.01 .84 637.3 2.12 1.84 1.60 1.35 1.14 .94 573.7 2.36 2.05 1.78 1.50 1.27 1.04 521.7 2.49 2.261.9511. 39 1.15 478.3 3.83 2.47 2.15 1.81 1.54 1.26 441.7 3.05 2.66 2.30 1.96 1.66 1.36 410.33.30 2.87 2.48 2.10 1.78 1.46 383.1 3.54 3.08 2.68 2.261.91 1.57 359.3 3.76 3.28 2.832.40 2.041.67 338.3 4.00 3.48 3.02 2.572.161.78 319.6 4.21 3.67 3.18 2.70 2.281.87 302.9 4.45 3.89 3.36 2.86 2.41 1.98 287.9 4.704.09 3.55 3.002.54 2.09 262.0 5.16 4.44 3.84 3.302.802.29 240.5 5.64 4.92 4.203.593.04 2.50 222.3 6.07 5.294.58 3.883.292.70

.89 .73

TABLE IX. SHORT RADIUS CURVES Radius Feet

Chord Feet

Central Angle

Deflection Angle

Deflection for 1 Foot

35 45

10 10

16-26 12-46

8-13 6-23

49.3 38.3

50

15

17-16

8-38

34.5

60 75 100 120 150

15 15 20 20 20

14-22 11-30 11-30 9-34 7-39

7-11 5-45 5-45 4-47 3-49

28.8 23.0 17.3 14.3 11.5

190

25

7-32

3-46

9.15

200 225

25 25

7-10 6-25

3-35 3-12

8.6 7.7

240 250 275

25 25 25

5-58 5-44 5-12

2-59 2-52 2-36

7.2 6.9 6.2

288 300 350 376 400 410

50 50 50 50 50 50

9-58 9-32 8-12 7-40 7-10 7-00

4-59 4-46 4-06 3-50 3-35 3-30

6.0 5.7 4.9 4.6 4.3 4.2

To find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

TABLE X. RODS IN FEET, IOTHS AND 1OOTIIS OF FEET

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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

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

Feet

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

Feet

Feet

676.50 61 1006.50 693.00 62 1023.00 709.50 63 1039.50 726.00 64 1056.00 742.50 65 1072.50 759.00 66 1089.00 775.50 67 1105.50 792.00 68 1122.00 808.50 69 1138.50 825.00 70 1155.00 841.50 71 1171.50 858.00 72 1188.00 874.50 73 1204.50 891.00 74 1221.00 907.50 75 1237.50 924.00 76 1254.00 940.50 77 1270.50 957.00 78 1287.00 973.50 79 1303.50 990.00 80 1320.00

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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, IOTHS AND IOOTHS OF FEET

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

Feet

.

Feet

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

Feet

.

Feet

.

Feet

.z

Feet

23.10 23.76 24.42 25.08 25.74 26.40 27.06 27.72 28.38 29.04 29.70 30.36 31.02 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 51.48 52.14 52.80 53.46 54.12 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

a Q3 ~~6LAA4

-

^4

S/E

m~e

1l2

(L4)A ~s~b~-4pB:;.

.P~i

.*

1.yl.

.

V ' 1'

F

-~;s~---sP---

79"7

cFilk~ r\

t~, *

WK

~2s4

~~lit

~bP~~

w

-

-

rat

7

-

FF

-t

_

1

T

'f

I

A

l-F

r:

x

k

-

.:.

s

1

Yi

fr

Ii

a

i

s

:i4

'.

c"

i zr

«

l. f

f a

J

If.

_

'J