Arthur Powell Davis.

Elevation and stadia tables. For obtaining differences of altitude for all angles and distances; horizontal distances in stadia work, etc., with all necessary corrections. Together with hydraulic tables, giving velocities for various channels and slopes online

. (page 1 of 7)
Online LibraryArthur Powell DavisElevation and stadia tables. For obtaining differences of altitude for all angles and distances; horizontal distances in stadia work, etc., with all necessary corrections. Together with hydraulic tables, giving velocities for various channels and slopes → online text (page 1 of 7)
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UC-NRLF




272 230



Illlllil MIIUIIIIIIDI
HH1I1I Ilitlllllllllll II
I 111 Illl Illlilllillllll II

!; !!!'! miiuSuMiii

|H liillii.ini I]
IllUllliU;

iinnnniiHimuuii
iBiniuiiMiniinnii




REESE LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

Deceived , igo .

Accession No. 92345 . Claxs h\-



ELEVATION AND STADIA TABLES,



FOR OBTAINING DIFFERENCES OF ALTITUDE FOR

ALL ANGLES AND DISTANCES; HORIZONTAL

DISTANCES IN STADIA WORK, ETC.. WITH

ALL NECESSARY CORRECTIONS.

TOGETHER WITH

HYDRAULIC TABLES,

GIVING VELOCITIES FOR VARIOUS CHANNELS
AND SLOPES.



BY

ARTHUR P. DAVIS,

MEM. AM. Soc. C.' E.,
Hydrographer, U. 5. Geological Survey.



FIRST EDITION.
FIRST THOUSAND.




NEW YORK:

JOHN WILEY & SONS.

LONDON: CHAPMAN & HALL, LIMITED.

1901.






Copyright, 1901,

BY

ARTHUR P. DAVIS.



ROBERT DRUMMOND, PRINTER, NEW YORK.



F.




PREFACE.



THE need of a table of Elevations for field use, suggested by
experience, led to the preparation and publication in 1893 by the
author of Table I, nearly in the form here presented, distance
being in miles, and elevations in feet. Its utility has been dem-
onstrated in the field; the first edition is exhausted, and it is here
republished in a more convenient form, and other tables added,
which it is believed will greatly increase the usefulness of the
book.

Table II carries up to 26 the difference of level in feet for one
mile.

Table III gives the curvature and refraction, h 2 = .574^2, up
to 40 miles for use in refined computations.

Table IV is for use on work of larger scale, where the dis-
tance and elevation are expressed in the same unit, as feet or
meters, and is especially adapted for stadia work. Up to 8 all
even minutes are given, and from 8 to 20 the intervals are five
minutes; the argument is the observed slant distance, and re-
duction to horizontal is given for every 30'.

Table V carries up to 40 the difference of level for a slant
distance of 100.

All these tables omit the constant corrections, c sin a, and
c cos a, where c = the focal length of the objective plus the dis-
tance from the center of the instrument to the objective and a the
vertical angle. Allowance for this may be made in preparing the
stadia rod, but is usually negligible. Table VI gives this correc-
tion prepared for use in very refined work not otherwise cor-
rected. The correction c cos a is to be added to the horizontal
distance, and that for c sin a is to be added to the difference of
elevation. All the quantities in Table VI are feet.

Table VII gives velocities direct for most practical problems
in canal construction, and the data for convenient computation
of slopes not given, for both canal and river computations, and
will be found very convenient for preliminary work.

92345






TABLE FOR OBTAINING DIFFERENCES OF
ALTITUDE FOR ANY EVEN MINUTE UP TO
15 DEGREES, AND FOR ANY DISTANCE.

(COMPUTED FROM THE FORMULA, DIFF. OF ELEVATION = 5280 X TAN. ANGLE.)

EXPLANATION OF TABLE.

The left-hand column is the minutes of the vertical angle, the
degrees being denoted by the large number at top of page. The
bold-face figures at top of column is the distance in miles. Numbers
in the body of the table denote the difference of elevation corre-
sponding to the angle on the left and the distance at top. The cor-
rection for curvature, refraction, and height of instrument is always
plus ; it therefore increases the difference of level for angles of eleva-
tion, and is subtracted from the difference of level for angles of
depression.

EXAMPLE.

Required the difference of altitude corresponding to a vertical
angle of -j- 9 l8 ' at a distance of 3.62 miles. On page 15 the
tabular number corresponding to 9 18' and

A distance of 3 miles is 2594 feet

For " " 6 " 5188 for .6 is therefore 519 "

" " 2 " 1729 for .02 " 17 "

Correction for curvature, refraction, and height of

instrument for 3.6 miles is -f- 12 ts



Total difference of altitude .... -j- 3142 feet





1


2


3


4


5


6


7


8


!! Curvature, Refraction,
and Ht. of Instrument.*


I


1.5


3-i


5


6


8


9


IT


12


14


Miles


Feet


Miles


Feet


2


3-i


6.1


9


12


15


18


22


25


28


1.6


6


10.3


65


3


4.6


9.2


14


18


23


28


3 2


37


41


2.1


7


10.4


67


4


6.1


12.3


18


25


3i


37


43


49


55


2-5


8


10.5


68


5


7-7


15-4


23


3i


38


46


54


61


69


2.8


9


10.6


69


6


9 2


18.4


28


37


46


55


65


74


83 3-T


10


10.7


70


7


10.8


21.5


32


43


54


65


75


86


97


3.4


ii


10.8


71


8


12.3


24.6


37


49


61


74


86


98


in


3.6


12


10.9


73


9


13.8


27.6


4i


55


69


83


97


in


124


3.8


13


II. O


74





15-4


30-7


46


61


77


92


108


123


138


4.1


14


n. i


75


I


16.9


33-8


5i


68


84


101


118


135


152


4-3


15


II. 2


77


2


18.4


36.9


55


74


92


in


129


147


1 66


4-5


16


H.3


78


3


20.


39-9


60


80


IOO


I2O


140


1 60


180


4-7


17


II.4


79


4


21-5


43-0


65


86


108


129


I5i


172


194


4.8


18


H-5


80


5


23.0


46.1


69


92


H5


138


161


184


207


5-o


19


ii. 6


82


6


24.6


49 ,i


74


98


123


147


172


197


221


5-2


20


11.7


83


7


26.1


52.2


78


104


131


157


183


209


235


5-4


21


n. 8


84


3


2 7 .6


55-3


83


in


138


166


194


221


249


5-5


22


11.9


86


9


2Q.2


58-4


88


117


146


175


204


233


263


5-7


23


12.0


87





30.7


6r. 4


92


123


154


184


215


246


2 7 6


5-8


24


12. 1


89


X


32-3


64.5


97


129


161


194


226 258


290


6.0


25


12.2


90


2


33-8


67.6


101


135


169


203


237 270


304


6.1


26


12.3


9i


3


35-3


70.7


1 06


141


177


212


247: 283


318


6-3


27


12.4


93


4


36.9


73-7


in


147


184


221


258 295


332


6.4


28


12.5


94


5


38.4


76.8


H5


154


192


230


269 307


346


6.5


29


12.6


96


6


39-9


79-9


120


1 60


200


240


280 319


359


6-7


30


12.7


97


7


4L5


82.9


124


166


207


249


290


332


373


6.8


31


12.8


99


8


43-0


86.0


129


172


215


258


301


344


387


6.9


32


12.9


IOO


9


44 5


89.1


134


178


223


267


312


356


401


7-0


33


13.0


IO2





46.1


92.2


I 3 8


184


230


276


323


369


415


7.2


34


13 f


103


I


47-6


95-2


143


190


238


286


333


38i


429


7-3


35


13.2


105


2


49 .2


93-3


147


197


246


295


344


393


442


7-4


36


13.3


1 06


3


50.7


101.4


152


203


253


304


355


405


456


7-5


37


13.4


108


4


52.2


104.4


157


209


261


313


366


418


470


7-6


38


13.5


109


5


53-8


107-5


161


215


269


323


376


430


484


7-8


39


13.6


in


6


55-3


110.6


166


221


276


332


387


442


498


7-9


40


13.7


112


7


56.8


II3-7


170


227


284


341


398


456


512


8.0


4i


13.8


114


8


58.4


116.7


175


233


292


350


409


467


525


8.1


42


13.9


H5


9


59-9


119.8


180


24O


300


359


419


479


539


8.2


43


14.0


117





61.4


122.9


184


246


307


369


430


492


553


8-3


44


14.1


119


I


63.0


125.9


189


252


315


378


441


504


567


8.4


45


14.2


120


2


645


129.0


194


2 5 8


323


387


452


5i6


581


8.5


46


14.3


122


3


66.0


132.1


198


264


330


396


462


528


594


8.6


47


14 4


124


4


67.6


135.2


203


270


338


405


473


54i


608


8.7


48


14-5


125


5


69.1


138.2


207


276


346


4'5


484


553


622


8.8


49


14.6


127


5


70.6


141-3


212


283


353


424


495


565


636


8.9


50


14.7


129


7


72.2


144.4


217


289


361


433


505


578


650


9.0


5i


14.8


130


3


73-7


147-5


221


295


369


442


5i6


590


664


9.1


52


14.9


132


9


75 3


150.5


226


301


376


452


527


602


677


9.2


53


15-0


134


o


76.8


153-6


230


307


384


461


538


614


691


9-3


54


I5-I


135


I


78-3


156 7


235


313


392


470


548


627


705


9-4


55


15-2


137


2


79-9


159-7


240


319


399


479


559


639


719


9-5


56


15-3


139


3


81.4


162.8


244


326


407


488


570


651


733


9.6


58


15-4


141


4


82.9


165.9


249


332


415


498


58i


664


747


9-7


59


15-5


142


5


84.5


169.0


253


338


422


507


59i


676


760


9.8


60


15.6


144


6


86.0


172.0


258


344


430


516


602


688


774


9-9


61


15-7


146


7


87-5


I75.I


263


350


438


525


613


700


788


IO.O


62


15-8


148


8


89.1


178.2


267


356


445


535


624


713


802 10.1


63


15-9


150


>9


90.6


181.3


272


363


453


544


634


725


816 > 10.2


64


16.0


151



For all distances under 1.4 miles, the
Height of Instrument is assumed 4.5



correction may be taken as + 5 feet,
feet.





i


2


3


4


5


6


7


8


9


Curvature.
Refrac. and
Ht. of Inst.


o'


92.2


184.3


276


369


461


553


645


737


829


Miles


Feet


I


93-7


187.4


281


375


468


562


656


750


843


16.1


153


2


95-2


190.5


286


381


476


571


667


762


857


16.2


155


3


96.8


193-5


290


387


484


58i


677


774


871


16.3


157


4


98.3


196.6


295


393


492


590


688


786


885


16.4


159


5


99.8


199.7


300


399


499


599


699


799


899


16.5


161


6


101.4


202.8


304


406


507


608


710


8n


912


16.6


ifc3


7


102.9


205.8


309


412


515


618


720


823


926


16.7


165


8


104.4


208.9


313


418


522


627


73i


836


940


16.8


167


9


106.0


212.


318


424


530


636


742


848


954


16.9


168


10


107 5


215.1


323


430


538


645


753


860


968


17.0


170


ii


109.1


2I8.I


327


436


545


654


763


873


982


17.1


172


12


110.6


221.2


332


442


553


664


774


885


995


17.2


174


13


112. 1


224.3


336


449


56i


673


785


897


1009


17.3


176


14


II3-7


227.3


341


455


568


682


796


909


1023


17-4


178


15


II5-2


230.4


346


461


576


691


806


922


1037


17-5


I?0


16


II6.7


233-5


350


467


584


700


817


934


1051


17.6


182


17


II8.3


236.6


355


473


59i


710


828


946


1065


17.7


184


18


II9.8


239-6


359


479


599


719


839


959


1078


17.8


186


19


121. 4


242.7


364


485


607


728


849


971


1092


17.9


188


20


122.9


245.8


369


492


614


737


860


983


1106


18.0


190


21


124.4


248.9


373


498


622


747


871


995


1120


18.1


193


22


126.0


251.9


378


504


630


756


882


1008


1134


18.2


195


23


127.5


255.0


383


5io


638


765


893


IO2O


1148


18.3


197


24


129.0


258.1


387


5i6


645


774


93


1032


1161


18.4


199


25


130.6


261.2


392


522


653


783


914


1045


H75


18.5


201


26


132.1


264.2


396


528


66 1


793


925


1057


1189


18.6


203


27


133-6


267.3


401


535


668


802


936


1069


1203


18.7


205


28


135.2


270.4


406


54i


676


8n


946


1082


1217


18.8


207


29


136.7


273-5


410


547


684


820


957


1094


1231


18.9


210


30


138.3


276.5


415


553


691


830


968


1106


1244


19.0


212


31


139.8


279.6


419


559


699


839


979


inS


1258


19.1


214


32


141.3


282.7


424


565


707


848


989


1131


1272


19.2


216


33


142.9


285.7


429


57i


714


857


IOOO


H43


1286


19-3


218


34


144.4


288.8


433


578


722


866


IOII


H55


1300


19.4


221


35


146.0


291.9


438


584


730


876


IO22


1168


I3H


19-5


223


36


147.5


295.0


442


590


737


885


1032


1180


1327


19.6


225


37


149.0


298.0


447


596


745


89 1


1043


1192


I34i


19.7


227


38


150.6


30I.I


452


602


753


903


1054


1204


1355


19.8


230


39


152.1


304.2


456


608


760


913


1065


1217


1369


19.9


232


40


153-6


307.3


461


615


768


922


1075


1229


1383


20.0


234


4i


155.2


310.3


466


621


776


93i


1086


1241


1397


20.5


2 4 6


42


156.7


3I3.4


470


627


784


940


1097


1254


1410


21.0


2 5 8


43


158.2


316.5


475


633


791


949


1108


1266


1424


21.5


270


44


159.8


319.6


479


639


799


959


1118


1278


1438


22.


282


45


161.3


322.6


484


645


807


968


1129


1291


1452


22.5


295


46


162.9


325.7


489


651


814


977


1140


1303


1466


23.0


308


47


164.4


328.8


493


658


822


986


1151


1315


1480


23-5


321


48


165.9


331-9


498


664


830


996


1162


1327


1493


24.0


335


49


167.5


334.9


502


670


837


1005


1172


1340


1507


24-5


349


50


169.0


338.0


507


676


845


1014


1183


1352


1521


25.0


363


5i


170 6


34I-I


512


682


853


1023


1194


1364


1535


25-5


378


52


172.1


344-2


5i6


688


860


1032


1205


1377


1549


26.0


393


53


173.6


347-2


521


694


868


1042


1215


1389


1563


26.5


408


54


175.2


350.3


525


701


876


1051


1226


1401


1576


27.0


423


55


176.7


353-4


530


707


883


1060


1237


1414


1590


27-5


439


56


178.2


356.5


535


713


891


1069


1248


1426


1604


28.0


455


57


179-8


359-5


539


719


899


1079


1258


1438


1618


28.5


471


58


181.3


362.6


544


725


907


1088


1269


1450


1632


29.0


487


59


182.8


365-7


549


73i


914


1097


1280


1465


1643


30.0


521





1


2


3


4


5


6


7


8


9


Curvature,
Refrac. and
Ht. of Inst.


o'


184.4


368.8


553


738


922


1106


1291


1475


1659






I


185.9


371-8


558


744


930


1116


1301


1487


1673


Miles


Feet


2


187.5


374-9


562


750


937


1125


1312


1500


1687


1.6


6


3


189.0


378.0


567


756


945


H34


1323


1512


1701


2.1


7


4


190.5


381.1


572


762


953


H43


1334


1524


1715


2-5


8


5


192.1


384.1


576


768


960


1152


1344


1537


1729


2.8


9


6


193.6


387.2


58i


774


968


1162


1355


1549


1742


3-1


10


7


195.1


390-3


585


78i


976


1171


1366


1561


1756


3-4


ii


8


196.7


393-4


590


787


983


1180


1377


1573


1770


3-6


12


9


198.2


396.4


595


793


991


1189


1388


1586


1784


38


13


10


199.8


399-5


599


799


999


"99


1398


1598


1798


4.1


14


ii


201.3


402.6


604


805


1006


1208


1409


1610


1812


4-3


15


12


202. 8


405.7


609


811


1014


1217


1420


1623


1826


4-5


16


13


204.4


408.8


613


818


IO22


1226


1431


1635


1839


4-7


17


14


205.9


411.8


618


824


1030


1235


1441


1647


1853


4.8


18


15


207.5


414 9


622


830


1037


1245


1452


1660


1867


50


19


16


209.0


418.0


627


836


1045


1254


1463


1672


1881


5-2


20


17


210.5


421.1


632


842


1053


1263


1474


1684


1895


5-4


21


18


212. 1


424.1


636


848


1060


1272


1484


1697


1909


5-5


22


19


213.6


427.2


641


854


1068


1282


1495


1709


1922


5-7


23


20


2I5.I


430.3


645


86 1


1076


1291


1506


1721


1936


5-8


24


21


216.7


433-4


650


867


1083 ( 1300


1517


1733


1950


6.0


25


22


218.2


436.4


655


873


1091


1309


1528


1746


1964


6.1


26


23


219.8


439-5


659


879


1099


1319


1538


1758


1978


6.3


27


24


221.3


442.6


664


885


1106


1328


1549


1770


1992


6.4


28


25


222.8


445-7


669


891


1114


1337


1560


1783


2006


6.5


29


26


224.4


448.7


673


897


1122


1346


1571


1795


2019


6.7


30


27


225. Q


451.8


678


904


1130


1355


1581


1807


2033


6.8


31


28


227.5


454-9


682


910


H37


1365


1592


1820


2047


6.9


32


29


229.0


458.0


687


916


"45


1374


1603


1832


2061


7.0


33


3


230.5


461.1


692


922


"53


1383


1614


1844


2075


7.2


34


31


232.1


464.1


696


928


1160


1392


1624


1857


2089


7-3


35


32


233-6


467.2


701


934


1168


1402


1635


1869


2102


7-4


36


33


235-1


470.3


705


941


1176


1411


1646


1881


2116


7-5


37


34


236.7


473-4


7ii


947


1183


1420


1657


1893


2130


7.6


38


35


238.2


476.4


715


953


1191


1429


1668


1906


2144


7-8


39


36


239-8


479-5


719


959


1199


M39


1678


1918


2158


7-9


40


37


24I-3


482.6


724


965


1207


1448


1689


1930


2172


8.0


4i


38


242.8


-+85.7


729


971


1214


1457


1700


1943


2186


8. i


42


39


244.4


488.8


733


978


1222


1466


17"


1955


2199


8.2


43


40


245-9


491.8


738


984


I23O


1476


1721


1967


2213


8-3


44


4i


247-5


494.9


742


990


1237


1485


1732


1980


2227


8.4


45


42


249.0


497-0


747


996


1245


1494


1743


1992


2241


8.5


46


43


250.5


501.1


752


IOO2


1253


1503


1754


2004


2255


8.6


47


44


252.1


504.2


756


1008


1260


1512


1765


2017


2269


8.7


48


45


253-6


507.2


761


1014


1268


1522


1775


2029


2283


8.8


49


46


255-2


5io.3


765


IO2I


1276


I53i


1786


2041


2296


8.9


50


47


256.7


513.4


770


IO27


1283


1540


1797


2054


2310


9.0


5i


48


258.2


5i6.5


775


1033


1291


1549


1808


2066


2324


9-i


52


49


259-8


519-5


779


1039


1299


1559


1818


2078


2338


9.2


53


50


261.3


522.6


784


1045


1307


1568


1829


2091


2352


9-3


54


5i


262 9


525-7


789


1051


I3H


1577


1840


2103


2366


9.4


55


52


264.4


528.8


793


1058


1322


1586


1851


2115


2380


9-5


56


53


265.9


531-9


798


1064


1330


1596


1862


2127


2393


9.6


53


54


267-5


334-9


802


IO7O


1337


1605


1872


2140


2407


9-7


59


55


269.0


538.0


807


1076


1345


1614


1883


2152


2421


9.8


60


56


270.6


54I-I


812


1082


1353


1623


1894


2164


2435


9.9


61


57


272.1


544.2


816


1088


1360


1633


1905


2177


2449


10.0


62


58


273.6


547-3


821


1095


1368


1642


1915


2189


2463


10. 1


63


59


275.2


550-3


826


IIOI


1376


1651


1926


2201


2477


IO.2


64





1


2


3


4


5


6


7


8


9


Curvature,
lefrac. and
Ht. of Inst.


o'


276.7


553-4


830


1107


1384


1660


1937


2214


2490


Miles


Feet

f


I


278.3


556.5


835


1113


1391


1670


1948


2226


2504


10.3


65


2


279.8


559-6


839


1 119


1399


1679


1959


2238


2518


10.4


67


3


281.3


562.7


844


1125


1407


1688


1969


2251


2532


10.5


68


4


282.9


565.7


849


1131


1414


1697


1980


2263


2546


10.6


69


5


284.4


568.8


853


1138


1422


1706


1991


2275


2560


10.7


70


6


286.0


571-9


858


1144


1430


1716


2 OO2


2288


2574


10.8


7i


7


287.5


575-0


862


1150


M37


1725


2OI2


2300


2587


10.9


73


8


289.0


578-1


867


1156


1445


1734


2O23


2312


2601


II.


75


9


290.6


581.2


872


1162


1453


1743


2034


2325


2615


II. 2


77


10


292.1


584-2


876


1168


1461


1753


2045


2337


2629


II.4

.


79


ii


293-7


587.3


881


ii?5


1468


1762


2056


2349


2643


II. O

r f O


82

o .


12


295.2


590-4


886


1181


1476


1771


2066


2362


2657


II. O


84


13


296.7


593-5


890


1187


1484


1780


2077


2373


2671


12.


87


14


298.3


596.6


895


"93


1491


1790


2088


2386


2685


12.2


go


15


299.8


599-6


899


1199


1499


1799


2099


2399


2698


12.4
_ _ /-


93

_ f


16


301.4


602.7


904


1205


1507


1808


2IIO


2411


2712


12.


96


17


302.9


605.8


909


1212


1515


1817


2120


2423


2726


12.8


99


18


304-4


608.9


913


1218


1522


1827


2131


2436


2740


13.0


102


19


306.0


612.0


918


1224


1530


1836


2142


2448


2754


13-2


105


20


307.5


615.0


923


1230


1538


1845


2153


2460


2768


13-4


1 08


21


309.1


618 i


927


1236


1545


1854


2163


2473


2782


13-6


III


22


310.6


621.2


932


1242


1553


1864


2174


2485


2795


13-8


114


23


312.1


624.3


936


1249


1561


1873


2185


2497


2809


I4.O


117


24


313.7


627.4


941


1255


1568


1882


2196


2510


2823


14.2


1 2O


25


3*5-2


630.5


946


1261


1576


1891


2207


2522


2837


14.4

. M y-


124


26


316.8


633.5


950


1267


1584


1901


2217


2534


2851


14.6

P M O


127


27


318.3


636.6


955


1273


1592


1910


2228


2547


2865


14.8


130


28


3I9-9


639-7


960


1279


1599


1919


224O


2559


2879


15.0


132


29


321-4


642.8


964


1286


1607


1928


2250


2571


2893


15.2


137


30


322.9


645-9


969


1292


1615


1938


226l


2584


2906


15-4

_ _,


141


31


324-5


649.0


973


1298


1622


1947


2271


2596


2920


15-6

_ _,


144


32


326 o


652.0


978


1304


1630


1956


2282


2608


2934


15.8

A *-.


148


33


327.6 655.1


983


1310


1638


1965


2293


2621


2948


10.
_


151


34


329.1 i 658.2


987


1316


1646


1975


2304


2633


2962


IO.2

fA A


J 53


35


330.6 661.3


992


1323


1653


1984


2315


2645


2976


10.4

_ y- /-


J 59


36


332.2 664.4


997


1329


1661


1993


2325


2658


2990


IO.O

*. O


163


37


333-7 667.5


IOOI


1335


1669


2002


2336


2670


3004


10.8


167


38


335.3 670.5


1006


I34i


1676


2OI2


2347


2682


3017


17.0


170


39


336.8


6736


IOIO


1347


1684


2O2I


2358


2695


3031


17.2


174


40


338-4


676.7


1015


1353


1692


2030


2369


2707


3045


17.4

, A


178

_ o _


4i



1 3 4 5 6 7

Online LibraryArthur Powell DavisElevation and stadia tables. For obtaining differences of altitude for all angles and distances; horizontal distances in stadia work, etc., with all necessary corrections. Together with hydraulic tables, giving velocities for various channels and slopes → online text (page 1 of 7)