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Tables for Excavations and Embankments.

DISTANCES FROM CENTER OF ROADWAY FOR CROSS-SECTIONING.
| Roapway 18 FEET WIDE. SipE Stopss 1 to 1.
_ For Sivexn Track Excavation.

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Ce f 3 x Bi in. 2: pieces 8x12in. (2% yds. edging required.) . 39¢

a ~67E69—Package of four-strand wash ~fast Rayon Floss to ‘on ate.
adap any one of the above numbers, —-we pay Sita 38¢ Ed Rayon F(pe

se ing __WE PAY POSTAGE’. ae
Stamped pieces of good wnatite varie ie
2 linen color Cotton Art Cloth in pretty but- 7m
eee | terfiy-and-flower design. (Edging not include =a

= ye | Instruction chart included.
X67E33—Stamped Pillow Top. Plain back,
a ome a in. square. (Requires 134 yds. edging) .—and ¥
we 5 lee ; : a X67E34—Scarf to match. Size about 16
Circular ae RE ) yy} ~GRequires 4 yds. edging.)..........—and we
| 43 Pa , 8 wef ee XEIES 5 Copterlece or table

a a LDP Re cas

“Ty snd Mens siirts. ADoUt ob Inches

4°

te El ‘s 65 _All-Silk Washable Radium. About 36 inches wide. For dresses, 4
slips, etc. | ) | i
Each of the above materials comes in the following COLORS: passiZg
flower, Castilian red, English violet, Pandora green, sunburn tan, Byrd blue, Spa
wine, spun gold, cactus rose, Jeanne d Arce blue, Hawaiian brown, jade green, go¥ ee
poppy, tan, Imperial blue, French beige, rose petal, marron glace, Zeppelin ghaae
claret wine, Copen blue or navy blue (all illustrated on opposite page); also fe sig

pe Pe . gee «=opink, pilot blue, orchadee, sun star, honeydew, middy blue (light navy), Silverwing
Ber aes os eee §=6erey, briar rose, Camco nile, maize, sherry brown, pink, Cocoa, coppersheen (reddish
- BR ae € [eee §=bronze), English green, chalet red (bright rust), Monticello green, white or black.

¢| “gees Order by style number for material and state color desired. |
(as OUR PRICE, Each; A yard, 94,
sewives | —and we pay postage. ¢

So aes

rif ty b. pun

| JUST FOLKS a)

= By EDGAR A. GUEST
THE PRIZES.
said an old-time champion to me, as |
he showed me many a prize,
Which he had won in his earlier days:
“Are they dazzling to your eyes?
| You think them precious to hold and
keep, but the fire I would|
throw them in he
| Could I only be the boy once more
| with his first prize yet to win.

“These are trophies of victory, andf
time was I thought them sweet.
But I’d rather be out there playing

| now and facing again defeat
Than sitting here in an idler’s chair
with my prizes round me lined,
With nothing to dread, and no+ ning
to risk, and nothing to stir my

mind.

“Oh, the game is more than its prize,
my bey, aS soon you will come
to Know,

the joy of the race is in running it,
and not in the thing to show. |

I’ve cups and medals enough to
spare, but I’d give them all to
claim

The thrill of the youngsters strug- §
gling there who haven’s yet
won a game.

“Nowe I’m settled down and watch
them go to the fields to lose or
win,

With eyes agleazn and with hearts on |
fire they’ll battle through thick |
and thin, :

And I’d rather be those who will lose |
today, and tomorrow will try |
anew, |

For they still have the joy of the |
game, while I am left with a
prize or two.” :

bonuses and stock pr

many of the Company s

were entirely eliminated
be 6.60 per cent.

A net profit of $13,07
from the redemption or s

The surplus earned dt
on the values entere¢
amounted to $42,863,5
sum substantial approp
been made to further st
of the Company.

An additional $10,000
ducted from the market
ties as a provision agai

a
a:
Tey
, wi
=
te
sae
ii
oh
f
+ 4s
o
yh righ J

y , or li,
in our
he tested

ho was found
sioner of Edu-
4 remediable eve
> costing $150,000.

arded school work along.
‘se, the burden is enormous.
ution, the Optometrical
opened offices in Neiw
free eye examinations

en to those unable to
} FKorsvth Dental IJn-

\

Avork is ‘needed every-

+ the chance to hegin
in body as well as

x "

igration Ban
o Be Relaxed
zood— i

jer in California
itrictions on im-
amoval of them,
| It recites what
{ contends that
would be the

rsons become
ot necessarily

Truths con-
3 a world by
‘When Pilate
mason to sup-

|} apparently
b which my
on. Those

(tal to Help
ied the lex-
ronger)| by
art of ithe

The Spectator

“We know ourselves so little that many think
they are about to die when they are really
in good health, and many think they are well
when, in fact, they are on the brink of death.”

That is not quite so true today as it was when
Pascal penned it. three centuries ago.

Popular education and readable books on physi-
ology have helped. The popular rules of health
are based less on superstition and more on science
than was the case a hundred ‘years ago.

Still, the body we live with from infancy to old
age is largely a stranger to Us.

Just for a test, try yourself on these 20 facts
about your body. How many do you know?

They are noted from. the first 200 pages of
Dorsey’s. popular book, “Why Behave Like Hu-
mans?”

1. One-fourth. of all. our muscles are in our
neck and face. |

2. If one-third of our skin is destroyed by
fire, acid or other accident, we die.

3. We have 32 teeth; eight on each side of
each jaw; that is, two incisors, one canine, two
bicuspids, and three molars.

4. A man 150 pounds in weight would weigh
50 pounds if he were thoroughly dried out.- Our
blood is 90) per cent water. Our bones are nearly
half, water. Conscious brains are 85 per cent
water.

5. To balance our head on our spine, we use
20 muscles. To balance our spine when walking
we use 144,

6. In walking, each leg rests: half the time.
We tire standing because neither leg gets rested.

7. With every step we take about 300 muscles
are used.

8. Our body temperature is regulated and re-
mains constant at 99 degrees.

LADY ISABEL AND THE THIRD PARTY,
| By S. E, Kiser-—-——__-———

WH Lady Isabel possessed
proud: patrician air,
Although the clothes in which she dressea

Were hardiy more than fair,

: JITHIN her gray ancestral: halls
The scene was seldom gay;
The beams that rested on the walls

Were ‘weak- em aren
ve SMU, 4) iy

HE. old. ear

A wasn’t feeling |
well,
The words he

spoke were
Bad,

‘But proudly Lady Isabel

Addressed her titled dad,

“BPE not downcast, old dear,” said she,
“The outlook’s not so worse;

Good luck’s instore for you and mg,
Despite your empty purse, °

Registered 3 2

Cy Y
ot Oki |
Office |

9, We average about one squal®y
surface and about 90 square yards
face.

10. Normally we take one breath
four heart beats. i
} di. If you stay quietly in bed you sa®
heart 20,000 beats a day.

12. A 160-pound man has about eight po’
or four quarts of blood. He can lose up to o
and-a-half quarts at a time and recover.

13. Your heart beats 40,000,000 times a year"

Tt drives the blood through the arteries.at the

average rate of 30 feet a second. When you sit
quiet it pumps about five pints of blood a min-
tte. When you run uphill it pumps seven times
as much, or 35 pints, Ncgrnan

14, The motor mechanism with which we walk
weighs about 80 pounds, . Sixty is muscle and
20 bones.

15. A man can sweat as much as 10 pints in
a day.

16. It is impossible to commit suicide by hold-
ing the breath, because as soon as conscious-
ness is lost breathing automatically begins again.

17, About 50 per cent of our body is carbon.

18. The average muscle is 25 per cent efficient.
The trained muscle is only 40 per cent efficient.

19. We have 2,000,000 tiny pores or sweat
glands. There are 500 to the square inch on
most of our body, and 2,000 to the square inch
in the palms of our hands and the soles of our
feet.

20, Just to keep the heart beating, the lungs
functioning and the body at the right tempera-
ture requires 1,700 calories a day—enough
energy to lift 200 tons a foot.

(Copyright, 1927° New York American, Inc.)

‘HAN POETRY

“MMOMORROW: Prince Gazooks arrives
To ask you for my hand;

il be the second of his wives,
The first one he has canned.

“AND he will find a:way, I know,
& To save our proud estate;
A. fortune teHer told me so,

And said, as happily he smiled:
“I’m feeling better now.”

B™. Prince Gazooks came nj

| Gal’s heart is like to big

A movie queen. from Holl.
Got to his highness °

pot Se opportunity will makes

"man, but he can't always

hold the jq

RTA NRE ee er ere ST,

barre

pany (PIN ey
girl 1s

M*
ivk b

cratic
dency J
from J
offey
ma

WY «

fo

learn.
tires.

, Le
PLidds
all rood
lerms

0 Roa

hike new;

aster,
fully

Piess SO
Prt. Touring.
little: looks and
ulpped, $895.

mPCAR IN TRADE.
rerless Motors Co.
Factory Branch,

Main 9850.

4.-pass.

like

runs

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qJopen Evenings and Sundays

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Complete Selection

Chevrolet
looks
$100

Roadster, ay
like new; priced
cash, balance 12

1925
equipped:
right.

en, evé-| months.

cond:

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AN. W,

Bs

nT,
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bal +
tar] equipped;

Roadster, 4
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wheel
condi-
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Buick 1924
ear
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months.

oo

1925 “Ford Coupe
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cash, balance easy,

1926

tip-top
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in
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Chev rolet Landeau; fully
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balance, months,

Ford Tudor
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$150 cash;
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ee] le Y] ¢
real
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a pat
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a
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D))

Se pe ay lo r J Wlotor
Used doy Dept.
[827 0 {th St. N. W.

PLOSSAL SALE OF
2D AU’ rOMOBI LIES

NOW GOING ON

irs
Ht

Co.

rer 100
CED

of
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All
TO

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FROM

pl MecReyn old

&

Ew
baker Buil iding
‘Rand 1706 14th St.
ivenings and Sundays

OU

) YOUR C AR
MED &
INTHS TO PAY
bk & HECHINGER.
"29 Vermont Crt
mand Wsth Pr

excellent

OR CO,,
Tine.

Lin shape.

B08 |
tised vars and

ures; parts, for
u ine, T6385

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{1926

PAINTED}.

1924

1923

sh, “al cal & * ° eel

22 TUDOR SEDAN
Pert oon tires. Fully equipped; will

195.

sacrifice.

“ESSEX COACH,

The motor is smooth and economical.
and looks lke new.

1926

Just out of the paint
Fully equipped. Only $425,

S850

shop

1926 Hudson 25 Anthea

1926 Ford. Roadster. elle ar idha
Page HNssex oy Ae a.

LOZG Ford | "LUdOr sis 6 xm ae eck
ii 926 Kord tN valet
1924 Ford Coupe,
1923 Ford Sedan. .
1924 Chevrolet Touring. ‘

L924 Maxwell Touring...icreces
1924 Word Touring......

**@ ee 0 6 4

*@*@ @eoeowoeeeeocheeeae

ouring (in

Po
paint shop) “ee sp teherwmeeoeane
1924 Chevrolet Poadster (in paint

shop! ; eee (
1925 Essex Coach.

1925 Hudson Coach

es @eedg

ee 8m Be

lLamiberx rt-Huds son Motors Co.

1722 L St., West of Conn. Ave.

When Used as a Deposit Will Hold Your Car.
THINKE
of the many happy days ahead and be sure
you see our wonderful’ display of ‘Used
Cars.” Large assortment. All reconditioned
standard makes,
YOUR
Chrysler Coach, 70 ..,.
deh gy pos Sedan, refinished
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24 Studebaker Coach
24 Oakland 6-54 Sedan
Nash 2638 (Advanced) Coach
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Essex Touring, better
Essex Touring, DOBRO Us bie earn eteidic 8 ied
Nash Special Coach orn seee DOV iM | are
=I
I

7
Padkard
'Asks Yow to inspect Its
Renewed Cars
We Want You to Know
What a Good Car a
Renewed Packard
Can Be
You Specify Your Own
Colors,
Your Favorite Tire,
Just How!lYou Want
Your Magtor Done, — rs
en We Prepare. thei: Buck “capsoiet’
Car to Your Order 2e Dusan Sedan 425!
Each Owner Takes a ROADS TERS
Particular Pride in

L! O24.
Some with rumble seats. Late models.}]
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hs seats. Lat els.11 924
a HAT i su Rs cath ig see 1925 Chrysler 70 Roj
et Us Show You How
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ie 8 fe Buick Roadster 1995 Chrysler 70 By
jit. £6 Brite Raud ster 11926 Nash Adv. 6,
P oy C I - OF al WV J “¢ Ths 9 rt
ackard Was] HiInecon
#1
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1985 Advanced Nash |
11925 Ford Sedan

1927 Na ah Roadster
And Ot
Fis igure What

‘SPECIAL OFFER”
HH o . Ll y 4
Buy With What

Samethi ne new to offer you! Only driven
Save | You on a

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Good Used: Car
Peerless 6-80) De

couple of hundred dollars in paying a
Chrysler 70 dhiseter,

1 22 7-—-NASH---335
Dane in 'Two- Mane Duco,
Buick Standard Coach.
26 Studebaker Big

Pully: Bquipped.
WALLACE
1927 Buick Standard
1927 Hupp 8 Sport 7

yi FOR BETTER USED CARS

108 Ls St _ Open Until 9 cat M Mi ain 16 2]
Chrysler Touring.
Nash Special

lbrysier 70
Ifhh €4
Franklin 11 Sedan.

orand new:
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Marmon Sport Sedan.

pee Jartment cl
ALL GUARANTEED

Paige rougham
Packard Tour. Sec
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$495 0 Aryeey 68 Cou

TRADE-INS

Chevrolet Touring........$75.00
Willys-Knight, Touring ...150.00
Durant Touring 50.00

octHudson Coach,
ri for akg
Coach,
Chevrolet
ie

CAR IN TRADE

2 ANE NT OR ON mem Ea SR Wea ST a en re abe THe A
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Awburn Touring aya tit fies
Nash-Elsworth Cle
Red ~-Durant Sport iit
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De Luxe Nash Sedan.

Light Six Studebaker
Dodg re “Collesiate’’
Ford Tudor seta a gla peta
Overland 6" Con pe ee ee
abi a8 meu Urine

Ali

IR

(Used Car

211925

550 1925

39811996
2]

Ge
5956/1924
250 \¢ 9296

-

2 eran

Sedan
Chevrolet Coupe
Dodge Sedan ....¢
Chevrolet Lan. Seq
Dodge Coupe ...
Chrysler 58 Coup
Maxwell Club Se
Ford Coupe ....

DIGS He Oe tS he CO Ce Or iote

~

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You Can

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Coad)

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}1926
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Chrysler
Maxwell
Dodge
Ford Coupe..
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70 Phaeton...

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ot O26 +A wr onhental Duy
DONOHOR

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+ 44 shandle 17 4
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ern it oa ec
rut thern Motor Sales | PORD ROADSTER. 1
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MOTOR €O0., _
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per

Soap 1

y : i Jewett Ae
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iStar Sp UT
and are*
ernis
4 JATH POT.

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KEITH’S RAILROAD CURVE TABLES.

Published by KEUFFEL & ESSER CO., New York.

_. Entered according to Act of Congress in the year 1883,
by W. Keuffel &.H. Esser, in the office of the Librarian of Congress,
Se in Washington, D. C.

Copyright, 1902, by Keuffel & Esser Co.

5
ws

>

HOW TO USE KEITH’S TABLES.

EXAMPLE,

Wanted a Curve with an Ext. of about 12 ft. Angle
of Intersection or I, P.=23° 20’ to the R. at Station
542 +72. ,

Ext. in Tab. IV opposite 23° 20’ = 120.87
120.87 +12=10.07. Say a 10° Curve.

Tan. in Tab. IV opp. 23° 20’ = 1183.1
1183.1 +10 =118.31.

Tab. V correction for A. 23° 20’ for a 10° Cur. =0.16
118.31 +-0.16 = 118.47 =corrected Tangent.

(If corrected Ext. is required find in same way)
Ang. 23° 20’ =23.33° +10 =2.3333 =L. C.
2° 193’ =def. for sta. 5042 | I. P.=sta. 542 +-72
4° 493/= “ +50; Tan, = 1.18.47
0-76 “ «“ jt ie eee
ce a. a eae 541 -+53.53
11° 40’= « « 5434 |b. C= 2.33.33
Bees: 86.86 |! E. C.=Sta. 543 -+86.86
~ 100—53.53 = 46.47 x3’ (def. for 1 ft. of 10° Cur.) = 139.41’ =
2 2° 193” =def. for sta. 542.
Def. for 50 ft. =2° 30’ for a 10° Curve.
Def. for 36.86 ft. =1° 502’ for a 10° Curve.

(These tables are published in Field Books of
-Keurre, & Esser Co., New York, N. Y.)

10° Curve

TABLE IV. — Tangents and Externals to a 1° Curve.

Tangent [pxterna Angle Tangent|External

Tasin I. — Minutes in Decimals of a Degree.

~

11’ | .1833 |
12 | .2000
13 . 2167
14 2333
15 - 2500
16 - 2667
17 . 2833
i8

19

20

Se St Km GO DO pat

jonh
SSH a2

Taste Il. — Inches in Decimals of a Foot.

3-32
.0078

2 3 4 9) 6 7 8 9 10 11
.1667 | .2500 | .3333 | .4167 | .5000 | .5833 | .6667 | .7500 | .8333 | .9167

| 3-16 5-16

es 8 3 8 4 %
.0104 | ad .0260 ee ae on .0625 | .0729

on f bk n
NOOR OBNORY EboNao

TABLE HI. — Radi, Ordinates and Deflections.

Deg. | Radius | a 4 . Ghee

CuHs He He G0 GO WNMDNDNN SH Ree eee

C100 OW

—>

0° 10'|34377. .036.| .145
20 |17189. .073 | .291
30 |11459. | .109] .436

8594. .145| .582
6875. 1829-427
5729. 218

4911. .205

4297. 291

3819. ~o2t

3437. 364

lice -400

2864. -436

2644. .473

2455. .509

2292. .545

2148. . 582

2022. .618

1910. .655

1809. 691

1719. 127

1637. . 764

1562. . 800

1495. . 836 3.
1432. 873 3.
1375.4 | ..909

1322. 945

1273. .982

1228. .018

1185.
1146.
1109.
1074.
1042.
1011.

—
COOMON NNO Orcer

OOO MOO ONIN N D&O OD OD

WHEONO COHWRE WOONMRO i ee ee Owemwon

eben arlaiens alent

ROAD NTN 9 O10 OBR OOO 9 O19 00 DD BNI OO ESTER STB 0 GI NINN OO 1.00 O

Becolaly -vi bplabapae ce ls ee a eeabals! > Peleg ae

P DHHS SRR eH HHH HEHE HOOOCCOOOOCOOCOCOCOCO
} DCO CO OONININIO OOOH OUCT OTE RD IB BR Go 0 Go WO OOO NNN NNNNNNNL

{Senanoannisnanounuoobnonnsousonenunue

COKReb wD

Frangene| Brera Ante
41°

1589.0 216.3
1598.0 218.7
1606.9 221.1
1615.9 223.5
1624.9 226.0
1633.9 228.4
1643.0 230.9
1652.0 233.4
1661.0 235.9
1670.0 | 238.4
1679.1 241.0
1688.1 243.5
1697.2 246.1
1706.3 248.7
1715.3 251.3
1724.4 253.9
1733.5 256.5
1742.6 259.1
1751.7 261.8
1760.8 264.5
1770.0 267.2
1779.1 269.9
1788.2 | 272.6
1797.4 275.3
1806.6 278.1
1815.7 280.8
1824.9 283.6
1834.1 286.4
1843.3 289.2
1852.5 292.0
1861.7 294.9
1870.9 297.7
1880.1 300.6
1889.4 303.5
1898.6 306.4
1907.9 309.3
1917.1 312.2
1926.4 315.2
1935.7 | 318.1
1945.0 321.1
1954.3 324.1
1963.6 327.1
1972.9 330.2
1982.2 333.2
1991.5 336.3
2000.9 339.3
2010.2 342.4
2019.6 345.5
2029.0 | 348.6
2038 . 4 351.8
2047.8 354.9
2057.2 358.1
2066.6 361.3
2076.0 | 364.5
2085. 4 367.7
2094.9 371.0
2104.3 374.2
2113.8 377.5
2123.3 380.8
2132.7 384.1

4 51°

Ibo NTO OOS

O MRNOWN ORDWNID

Om NWONMR HOORNH CONNAR ARANWO OMWAN

~~

— et — ok a Be

65

66

67

68

69

70

TABLE LV. — Tangents and Externals to a 1° Curve.

Angle [Tangent

External | Angle Tangent External | Angle |Tangent |External

8) .2 71° 4086.9 | 1308.2 81° 4893.6 | 1805.3
3 9 10’ | 4099.5 | 1315.6 10’ | 4908.0 | 1814.7
5 .6 20 AVI2Z 1) | 1822.9 20 4922.5 | 1824.1 |
8 <3 30 4124.8 | 1330.3 30 4937.0 | 1833.6 |
1 oe 40 4137.4 | 1337.7 40 4951.5 | 1848.1
4. 9 50 4150.1 | 1345.1 50 4966.1 | 1852.6 |
Pd 8 q2 4162.8 | 1352.6 82 .4980.7 | 1862.2
1 .6 10 4175.6 | 1860.1 10 4995.4 | 1871.8
4 =} 20 4188.5 | 1367.6 20 5010.0 | 1881.5
8 4 30 4201.2 | 1875.2 30 5024.8 | 1891.2 ;
3 ab 40 4214.0 | 1382.8 40 5039.5 | 1900.9 ;
7 3 50 4226.8 | 1890.4 50 5054.3 | 1910.7
1 .2 13 4239.7 | 1398.0 83 5069.2 | 1920.5
6 oe 10 4252.6 | 1405.7 10 5084.0 | 1930.4
| me: 20 4265.6 | 1413.5 20 5099.0 | 1940.¢
.6 .3 30 4278.5 | 1421.2 30 5113.9 | 1950.3 !
ay 4 40 4291.5 | 1429.0 40 5128.9 | 1960.2 \
ey 5 50 4304.6 | 1436.8 50 5143.9 | 1970.3 ;
a | 1026.6 74 4317.6 | 1444.6 84 5159.0 | 1980.4 i
.9 | 1032.8 10 4330.7 | 1452.5 10 5174.1 | 1990.5
.5 | 1039.0 20 4343.8 | 1460.4 20 5189.3 | 2000.6 .
.1 | 1045.2 30 4356.9 | 1468.4 30 5204.4 | 2010.8
.8 | 1051.4 40 4370.1 | 1476.4 40 5219.7 | 2021.1
.5 | 1057.7 50 4383.3 | 1484.4 50 5234.9 | 2031.4 \

3650.2 | 1063.9 75 4396.5 | 1492.4 85 5250.3 | 2041.7

3661.9 | 1070.2 10 4409.8 | 1500.5 10 5265.6 | 2052.1

3673.7 | 1076.6 20 4423.1 | 1508.6 20 5281.0 | 2062.5

3685.4 | 1082.9 30 4436.4 | 1516.7 30 5296.4 | 2073.0

3697.2 | 1089.3 40 4449.7 | 1524.9 40 5311.9 | 2083.5

3709.0 | 1095.7 50 4463.1 | 1533.1 50 5327.4 | 2094.1

3720.9 | 1102.2 76 4476.5 | 1541-4 86 5343.0 | 2104.7

3732.7 | 1108.6 10 4489.9 | 1549.7 10 5358.6 | 2115.3

3744.6 | 1115.1 20 4503.4 | 1558.0 20 5374.2 | 2126.0

3756.5 | 1121.7 30 4516.9 | 1566.3 30 5389.9 | 2136.7

3768.5 | 1128.2 40 4530.4 | 1574.7 40 5405.6 | 2147.5

3780.4 | 1134.8 50 4544.0 | 1583.1 50 5421.4 | 2158.4

3792.4 | 1141.4 47 4557.6 | 1591.6 87 5437.2 | 2169.2

3804.4 | 1148.0 10 4571.2 | 1600.1 10 5453.1 | 2180.2

3816.4 | 1154.7 20 4584.8 | 1608.6 20 5469.0 | 2191.1

3828.4 | 1161.3 30 4598.5 | 1617.1 30 5484.9 | 2202.2

3840.5 | 1168.1 40 4612.2 | 1625.7 AO 5500.9 | 2213.2

3852.6 | 1174.8 50 4626.0 | 1634.4 50 5517.0 | 2224.3

3864.7 | 1181.6 78 4639.8 | 1643.0 88 5533<1 | 2235.5

3876.8 | 1188.4 10 4653.6 | 1651.7 10 5549.2 | 2246.7

3889.0 | 1195.2 20 4667.4 | 1660.5 20 5565.4 | 2258.0

3901.2 | 1202.0 30 4681.3 | 1669.2 30 5581.6 | 2269.3

3913.4 | 1208.9 40 4695.2 | 1678.1 40 5597.8 | 2280.6

3925.6 | 1215.8 50 4709.2 | 1686.9 50 5614.2 | 2292.0

3937.9 | 1222.7 79 4723.2 | 1695.8 89 5630.5 | 2303.5

3950.2 | 1229.7 10 4737.2 | 1704.7 10 5646.9 | 2315.0

3962.5 | 1236.7 20 4751.2 | 1718.7 20 5663.4 | 2326.6

3974.8 | 1243.7 30 4765.3: | 2422.7 30 5679.9 | 2338.2

3987.2 | 1250.8 40 4779.4 | 1731.7 40 5696.4 | 2349.8

3999.5 | 1257.9 50 4793.6 | 1740.8 50 5713.0 | 2361.5

4011.9 | 1265.0 80 4807.7 | 1749.9 90 5729.7 | 2373.3

4024.4 | 1272.1 10 4822.0 | 1759.0 10 5746.3 | 2385.1

4036.8 | 1279.3 20 4836.2 | 1768.2 20 5763.1 | 2397.0

4049.3 | 1286.5 30 4850.5 | 1777.4 30 5779.9 | 2408.9

4061.8 | 1293.6 40 4864.8 | 1786.7 40 5796.7 | 2420.9

4074.4 | 1800.9 50 2 0 50 6 ;

4879.

1796.

5813.

.S

, WwW
bo

oO

Vv

Tas Le IV. — Tangents and Externals to a 1° Curve. = 4 ‘ i TaBLE V. Corrections for use with Table IV.

fe
#6

| oe | ree | Copyright, 1902, by Keuffel & Esser Co.
Angle |Tangent |External|| Angle |Tangent |External Angle |Tangent |External © ~~ j/ re " 2
f Meee. | For Tangents Add

a

55°| 60°| 65 | 70°

IO WO

.53| -58| .63] .63

‘ .72| .79| .84] .go

.83} .90] .Q9Q/I.06]1.14

: . .99|I.09]I.20]1.29|1.39
.70| . .92/1.04|1.29]1.42|1.54|1.66
.93|1.06]1.20|1.34]1.49|1.64|1.79|1.94

re CO Or GO Ft CO

DOWN AORHOA SNONEH

. .O1|1.22|1.53|1.84/2.15 A4
.66|1.00]1.33|1.68|2.02|2.36|2.70|/3.05|3.40|3-7
.72|1.09|1.45|1.83|2.20|2.57|2.94/3. O|4
.79|1.19|1.55|2.00|2.40|2.80 4
.86|1.30!1.74|2.18}2.62 3.06 4

4
A
9

2
4
5:37|5

.
.
a
e
.
°

7
.1O
49
88

For Externals Add
Angie 20°| 25°] 30° 35°| 40°| 45° 50°| 5
.007 |. .009|.O11I|.012}.014|.
.014].018|.023|.027|.029].032|.035}.
.022}. : .038].045]. .057|.
.036}. ; .065|.074]. .093}.
.O51}. .090}. 103}. .129}.
.072}. .131|.153). .197].
.093}- : .172|.203)}. .265}.
.1IQ}. .216|.254|. 325). ’
-I51\. , .266|.305}.. .384|.425].
.188}. .283|.332|.381].. .479].530}.
.225}. .398}.457]- .575|.636).
rp A : .483|.554|-625|.697|.711)-545]-¢ ;
SGOT. ; .568|.652|.735|.819].906}. d .17
.383}. : .678|.777]- .977|1.07|1.18]1.29}1.39
445}. ‘ .787|.903|1.02|1.13}1.25]1.38]1.50 1.62
524. ‘ .926|1.06|1.20]1.34|1.47|1.62 1.76|1.91
.603}. 1.07|1.22|1.38]1.54)1.70|1.87|2.03|2.20
.706|.985|1.06|1.25|1.43|1.62 1.80|1.99|2.18|2.38/2.58
,809|1,01|1.22|1.43/1.64|1.85|2,06|2.28|2.50 2.73|2.96
ha Sn ne an ee

WOW RA OUOORN HHWMON NWONAM UNONARO SPNOHAD SRDOWMN NWOWRU AOD

HOMO SwoOAkR NOUR SNOW WHOWONM DOWHAH ONNOEA

OWN ©

IX

TaBLE VI. Deflections for Sub Chords for Short Radius Curves. | Natural Sines

by! fy/ / / ; / / / / / ;

egree Radius | Wsubchord 10’ | 20’ | 30’ | 40’ | 50’ {de fdg.| 0’ | 10’ | 20’ | 30’ | 40’ | 50’ |Deg.
f of aS eee R ee eee ~ 0 |0000/0029|0058 0087/01 16|0145|/89940 6428/64 50/6472|6494/6517|6539| 49
Curve | sin. def. ang. 12.5 Ft. [| I5Ft. | 2uFt. | 25Ft. | for 100 ft. | 0175|0204|0233|0262/0291 |0320|8894 I |6561 |6583|6604|6626/6648/6670| 48
| IOI 0349|0378}0407|0436|0465|0494/87942|6691|6713|6734|6756/6777|6799| 47
IOr. 0523105520581 |0610|0640|0669 864 3/6820|6841 |6862|6884|6905|6926) 46
Iol. 9698|0727|0756|0785|0814|0843 |8 5944/6947 |6967 6988 |7009|7030/7050| 45
101. 0872|0901|0929|0958|0987|1016|8414.5/7071|7092|7112)7133)7153)7173) 44
101. 1045|1074|1103|1132|1161/1190|83)46/7193)7214|7234|7254|7274|7294| 43
1219|1248]1279]1305|1334|1363|82847|7314|7333|7353|7373|7392|7412| 42
1392|1421|1449}1478|1507|1536/8148/7431/7451/7470)7490|7509 7528] 41
9 |1564|1593|1622|1650|1679|1708 (8084917547 7566|7585|7604|7622]7642| 40
10 |1736|1765|1794|1822|1851|1880(79§50|7660|7679|7698|7710|7735|7753 39
LI |1908|1937|1965|1994|2022|2051|78151|7771|7790|7808|7826 7844|7862| 38
12 |2079|2108|2136|2164|2193|2221|77952|7880|7898|7916|7934|7951 7969| 37
13 |2250|2278|2306|2334|2363/2391)/76§53|7986|8004 8021/8039|8056|8073] 36
14 |24.19|2447|2476|2504|2532|2560/75954|8090/8107 8124|8141|8158)8175| 35
15 |2588|2616|2644|2672|2700/2728| 7495 5|8192|8208|/8225 8241 8258/8274] 34
16 |2756|2784|2812|2840|2868|2896|7 3956|8290|8307 [8323/8339 8355/8371] 33
17 |2924|2952|2979|3007|3035|3062|72857 [8387 |8403 8418/5434 84.50|8465] 32
18 |3090|3118/3145/3173/3201 |3228|7 1958|/8480|8496 [8511 8526|8542/8557| 31
19 132561328313311133381336513393)7085918572(8587 8601 |861618631(8646| 30

CONT Hin Bb Ww be

CURVE FORMULAS
R = T cot. } 1 Chord def. = chord?

R = 50 e

Sin. D No. chords =34
= R ex. sec } I D

T tan 3 I Tan. def. = 4 chord def.

The square of any distance, divided by twice the radius, will equal the
distance from tangent to curve, very nearly.
Table IV. contains Tangents and Externals to a 1° curve. Tan. and Ext.
to any other radius may be found nearly enough, by dividing the Tan. or
Ext. opposite the given Central Angle by the given degree of curve.
To find Deg. of Curve, having the Central Angle and Tangent: Divide
Tan. opposite the given Central Angle by the given Tangent.
To find Deg. of Curve, having the Central Angle and Tangent: Divide
Ext. opposite the given Central Angle by the given External.
To find Nat. Tan. and Nat. Ex. Sec. for any angle by Table IV.: Tan.
or Ext. of twice the given angle divided by the radius of a 1° curve will be
the Nat. Tan. or Nat. Ex. Sec.
‘To find angle for a given distance and deflection. | ;
Rule 1. Multiply the given distance by .01745 (def. for 1° for 1 ft.), and | Dez.| 60’ | 50’ | 40’ | 30
divide given deflection by the product. | eee
Rule 2. Multiply given deflection by 57.3, and divide the product by Dec.| 0’ | 10’ { 20’ {| 30’ | 40 50 :
the given distance. | 89 19848 9853/9858 9863
To find deflection for a given angle and distance. Multiply the angle | 81 |9877|9881)/9886|9890
by .01745, and the product by the distance. | 82 19903 |9907 |9911|\9914
RiGHT ANGLE TRIANGLES. Square the altitude, divide by twice the base. | ~ 83 19925/9929/9932|9936
Add quotient to base for hypotenuse. | 84 |994519948|9951/9954
Given Base 100, Alt. 10 10?+200=.5. 100+.5=100.5 hyp. 85 |9962/9964|9967/9969
Given Hyp. 100, Alt. 25 25?+200=3.125. 100—3.125 =96.875 = Base. | 86 |9976|9978|9980/9981
Error in first example, .002; in last, .045. 87 |9986/9988|9989/9990
To find Tons of Rail in one mile of track: multiply weight per yard 88 |9994|9995|9996|9997
by 11, and divide by 7. | 89

Deg.

10’ { 20’ { 30’ { 40’
0000/0029/0058/0087 |o1r16
0175/0204/0233/0262|0291
0349] 0378/0407 /0437|0466
0524/0553/0582/0612|/0641
0699/0729/0758/0787/0816
0875/0904|0934| 0963/0992
I051I/1080/ILI0| 1139|1169
1228|1257/1287/ 1317/1346
1405|1435/1465|1495|1524
1584/1614|1644| 1673/1703
1763/1793/1823/1853/1883
1944|1974|2004| 2035/2065
2126|2156/2186/2217|2247
2309/2339\2370 2401/2432
2493)2524)2555|2580)2617
2679|2711'2742/2773/2805
2867| 2899/2931 |2962/29004
3057/3089/3121/3153/3185)/3217
3249 3281)/3314/3346/3378|/3411
344313479)3508)3541/3574/3607
3640/3673(3706(3739(3772/3805
3839) 3872/3906/ 3939/3973] 4006
4040/|4074|/4108/4142|4176/4210
4245/4279/4314/ 4348/4383] 4417
4452|4487/4522/4557/4502|4628
4.663] 4699) 4734| 4770/4806| 4841
4877| 4913/4950) 4986) 5022/5059
5095/5132/5169| 5206) 5243| 5280
5317/5354/5392| 5430|5467/5505
5543/ 5581/5019] 5 658/5696/5735
5774|5812{5851{5890/5930(5969
6009/6048) 6088 | 6128/6168! 6208
6249/6289] 6330/6371|6412|6453
6494] 6536) 6577 | 6619] 6661/6703
6745|6787)| 6830! 6873/6916] 6959
7002/7046] 7089/7133/7177/7221
7205|7310/7355|7400/7445|7490
7530/7581|7627|7673| 7720) 7766
7813|7860)7907|7954) 8002/8050
8098/8146 8195/8243 8292/8342

ey ee

Deg.| 60’ | 50’ | 40’ | 30’ | 207 |
6’

10’ 20’ 30’

8441| 8401 85011 8642| 49

8744} 8796 8809} 80952] 48

9057| 9110 9217| 9271] 47

9380} 09435 9545| 9601] 46

9713} 9770 9884| 9942] 45
I.0058|I. 0117 I.0235|1.0295| 44
I.0416|1.0477 I.0599|1.0661| 43
1.0786)1.0850 I1.0977|I.1041| 42
PotL PY F2L237 I.1369|/1.1436| 41
1.I571|1.1640 I.1778/1.1847| go

I. 1988/1.2059 I.2203)1.2276/ 39
I.2423/I.2497 I.2647/1.2723| 38
1.2876/1.2054 I.31II|I.3190| 37
I.335I/1.3452 I.3597/1.3680| 36
I. 3848/1. 3934 I.4106/1.4193| 35
I.4370/1.4460 I.4041|1.4733| 34
IT.AQTQ|L. 5013]1. I.5204|/1.5301| 33
T.5497|1.5597|I. I.5798|1.5900] 32
1.6107/|/1. 6212 1.6426/1.6534| 31
1.6753/1. 6864 I. 7090|)I.7205| 30
1.7437(1.7556 1.7797|1.7917| 29
1.8165|1.82901 1.8546/1.8676|] 28
1.8940/1.9074 I.9347|1.9486| 27
1.9768|I.9912 .0204/2.0353| 26
2.0655|2.0809 .1123/2.1283]| 25
2.1609/2.1775 . 2113/2.2286| 24
2.2637\2.2817 -3183/2.3369| 23
2.3750/2.3045 -4342|2.4545| 22
2.4960|/2.5172 .5605/2.5826| 21
2.6279/2. 6511 .6985|/2.7228] 20

2.7725(2.7980 .8502|2.8770| 19
2.9319|2.9600 .0178/3.0475| 18
3.108413.1397 . 2041
3.3052/3.3402 4124
3.5261|3.5656 . 6470
3.7760/3.8208 9136
4.0611/4.1126 . 2193
4.3897|/4.4494 -5736
4.7729|4.8430 - 9804
5+ 2257/5 +3093 5.4845
50’ 40’

SSS ee
; : ~
‘
=|

30.40

8301
8603
9004
9325
9657
. 0000
-0355
0724
.1r06)
1504
.IQr8
- 2349
- 2799
.3270
- 3764
4281
. 4826
- 5399
. 6003
. 6643
7321
. 8040
. 8807
.9626
0503
-1445
. 2460
-3559
-4751
. 6051

- 7475
.9042
-0777
. 2709
-4874
W771
.O108
- 3315
. 7046

1446

Or45
0320
0495
0670
0846
1022
I198
1376
1554
1733
IQI4
2095
2278
2462
2648
2836
3026

=e

ss

~ y vemmata
aaasalaneas terpenes a dens coe ep ee

8 eS ee eee
. te er mr = ome.

ee ew oy
eo

ere te Se

I.
1 a
Be
Fs
I.
Ts
dE
i fee
Ir.
EE
IRE

bo

NO NMDSN WH DD BS HR RR SR OR OR Oe BO Oe OR Lone

ee
~<

BRARWWWWWDHIYND DH DHNHDHDDND

MPR BRWWWwWdNIY DNDN DH HH DND ARAL

aAbPDBRWWWWD bd

|__ 59”
6.1970
6.9682

( 10’ 20’ 30’ 40’
'5-7604|5.8708| 5.9758| 6.0844
6.4348|6. 5606) 6.6912! 6.8269

7.2687|7.4287
8.3450|8.5555
9. 7882/10.078
II.826/12.250
14.924/15.605
20.206/21.470
31. 242134.368
68.750

50’

40’

7.5958
8.7769
10.385
12.706
r6. 350
22.903
38.189

85.940/114. 588/171.

30’

7.7704
9.00908
Li ers Be
13.197
I7.169
24.542
42.904

885):

20’

Natural Cotangents.

7-9530
9.2553
IL.059

z|° HNWRUMUON 0 0 |
e bs

Et

Sg bes:
cSetet
ae

a emis inane leat tine

te been aor ede pee tegatana ceo

Sa a

= ‘ —— FON gy ae aT Ie eA
Sugita Te eee = ix r ree

16
17
25
26
27

9
4

47
48
59
60

i
2
7

45
47
dl
53.2
55
57
59
60

6
1
6
1
6

‘e

3

NASOAMIGSHOMAAAOR OOM
SS NANA A AN OD 09 09 09 OD

48

5)
49
DL

61.

BG
38
1 60
Calculated by Julien A. Hall, M. Am. Soc. C. E.

Sipz Stopes 114 To l.

8.6 | 58
60

58
60

1
6
5
6
1
]

hy DON 6D 1D fO
eee sae

a2

46
48
AQ
ol
o4

oO
0
9)
0
2.5
0
0
5
0

-

mere

For Sincut Track EMBANKMENT.
46.3 | 46

8 | 48
3 | 49
8 | 51

52

3

KRGOOMRMHOKRAONDMDIOMNAANYTONRAOTS H ¢
SSR NNNANNANN NAAN OD 09 09 09 OD OD SHS SH

38

49
7 | 50
52
o3
o6

2
7
7
2

Roapway 14 FEET WIDE.

MOOnMHO . a
SAHARA NNANANN

6.2
47.7 | 47
49.2
50
52
53)
56
58

0

27 || 47.5
49
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