,„,.3^So^,«aMun3U
A LIBRARY ^^
\ "^ j^^
\ Purdue UNiVERSips^
AGRICUi}tURAL EXPERlM,g1<T STATION
^eceS^my^or,..81.98.__.
CTass .^^.- >w JSooA:
^ N.
sawwi^f'nr
Digitized by the Internet Archive
in 2009 with funding from
Boston Library Consortium Member Libraries
http://www.archive.org/details/manualoftopograpOOgann
LIBRARY CATALOGUE SLIPS.
United States. Department of the interior. ( U. S. (/eologieal siirveii.)
Department of the interior \ — \ Monographs | of the | United
States geological survey | Volume XXII | [Seal of the depart-
ment] 1 Washington | government printing offlce | 1893
Second title: United States gecdogical survey | J. W. Powell
director | — | A manual | of | topographic methods | by | Henry
Gannett | chief topographer | f Vignette] |
Washington | government printing office | 1893
4°. XIV, 300 pp. 18 pi.
Gannett (Henry).
United States geological survey 1 .1. W. Powell director | — |
A manual | of | topographic methods | by | Henry Gannett | chief
topographer | [Vignette] |
Washington | government printing ofHcc | 1893
40. XIV, 300 pp. 18 pi.
[United States. De-pai-tmenl ■../' the intiTiuy. (T. .S'. tjeologieul survey).
Mono^rapli SXlI.j
United States geological survey | .1. W. Powell director | — |
A manual | of | topographic methods | by | Henry Gannett | chief
topographer | [Vigucttc] |
Washington | govcrniofut printing office | 1893
4°. XIV, 300 pp. 18 pi.
[Uniteu States. Departmnit uf the interior. iU. *. geoloyical survey.
Monograpli XXII.]
A^DVERTISE]Vd:ENT.
[Monograph XXII. ]
The puhlicatinns of thp TTnUert Stntes Geolo<;iciil Survey are issued iu aocurdauce with the statute
approved iMareh :-!, 1871t, wlii.li declaifs tliat—
"The publi<'a tioiis of the Geolof;iiMl Survey shall cousist of the auuuiil r<'i)(irt of operations, geo-
logical aud ecououiic maps iUustratiuj;- the resources and classilication of the lands, an<l re|iorts upon
general and economic f;i'olo,uy and paleontology. Tlie annual rei>ort of operations of the (ieologieal
Survey shall aecompauy the a)uiual report of the Secretary of the Interior. All sjiecial nuauoirs and
reports of said Survey shall be issne,<l in uniform quarto series if deemed necessary liy the 1 director, Init
otherwise in ordinary octavos. Three thousand copies of each shall hi> pnMished lorscieiitiHc exclL-niues
and for sale at the price of publication; and all literary and cartoniajdiic niateiials icreived in excliange
shall be the property of the United States and form a i>art of the liiuary ot tin- organization ; And the
money resulting from the sale of such publications shall be covered into the Treasury of the United
States."
The following joint resolution, referring to all government publications, was i)assed by Congress
July 7, 1882 :
"That whenever any document or report shall be ordered printed by Congress, there shall be
)u-iuted, in addition to the number iu eaih case stated, the ' usual number ' (1,900) of copies for binding
and distribution among those entitled to receive them."
Except in those cases in which au extra number of any publication has been supplied to the Sur-
vey by special resolution of Congress or has been ordered by the Secretary of the Interior, this ottice
has no copies for gratuitous distribution.
ANNUAL REPORTS.
I. First Annual Keport of the Uuited States Geological Survey, by Clarence King. 1880. 8'^. 79
pp. 1 map. — A preliuiinarv report ilescribing plan of organization and publications.
II. Second Aiiuual Kriioit of the United States Geological Survey, 1880-'81, by J. W. Powell.
1882. 8°. Iv, .58Spp, til' pi. 1 niaji.
III. Third Annual Kcpoit of tlic United States Geological Survey, 1881-'82, by J. W. Powell.
1883. 8°. xviii,5134 pp. 1)7 |d. and maps.
IV. Fourth Annual Report of the United States Geological Survey, 188L'-'88, by J. W. Powell.
1884. 8°. xxsii, 173 pp. 85 pi. and ina|is.
V. Fifth Annual Report of tlie United .States Geological Survey, 18S3-'81, by .1. W. Powell.
1885. 8°. xxxvi, 469pi). .58 pi. and nuips.
VI. Sixth Annual Report of the Uniteil States Geological Survey, 1884-'8.5, by .J. W. Powell.
1885. 8'^. xxix, 570 pp. 65 pi. and maps.
VII. Seventh Annual Report of the United States Geological Survey, 1885-'86, by J. W. Powell.
1888. 8°. XX, 656 pp. 71 pi. and maps.
VIII. Eighth Annual Report of the United States Geological- Survey, 1886-'87, by J. W. Powell
1889. 8^'. 2v. xix, 474, xii pp. 53 pi. and maps; 1 p. 1. 475-1063 pp. 54-76 pi. and maps.
IX. Ninth Annual Report of the United States Geological Survey, 1887-'88, by ,J. W. Powell.
1889. 8'^. xiii, 717 pp. 88 pi. and maps.
X. Tenth Annual Report of the United States Geological Survey, 1888-'89, by .J. W. Powell.
1890. 8°. 2v. XV, 774 pp. 98 pi. and maps; viii, 123 pp.
XI. Eleventh Annual Report of the United States Geological Survey, 1889-'9(), by ,J. W. Powell.
1891. 8--". 2v. XV, 7.57 pp. 66 pi. and maps; ix, 351 pp. .30 pi. and maps.
XII. Twelfth Annual Report of the United States Geological Survey, 1890-'91, by J. VV. Powell.
1891. 8°. 2v. xiii, 675 pp. 53 pi. and maps; xviii, .576 pp. . 146 jd. and maps.
XIII. Thirteenth Annual Report of the United States Geological Survey, 1891-'92, by .1. W.
Powell, 1893. 8°. 3 v.
II ADVKK'l'lSKMENT.
MONOGRAPHS.
I. Lake Rouneville, liy Grove Kail fiilbort. 1890. 4^^. xx, 438 pp. 51 pi. 1 map. Price $1. .50.
II. Tertiary History of the Grand ( 'anon District, with atlas, liy t'larc.nce IJ. Duttoii, Capt., U. S. A.
1882. 4^'. xiv, L'til pp. 'i'2 pi. and atlas of 21 sheets folio. Price ^ilO.OO.
III. Geology of the Comstock Lode aud the Washoe District, with atlas, liy (Jeorgc F. Keeker.
1882. 4-\ XV, 422 pp. 7 pi. and atlas of 21 sheets folio. Price $11.00.
IV. Comstock Mining aud Miners, by Eliot Lord. 1883. 4"^. xiv, 451 pp. 3 pi. Price $1.50.
V. The t'oppcr-Beari'ng Rocks of Lake Superior, by Roland Duer Irving. 1883. 4 '. xvi, llil
pp. 15 1. 29 pi. aud maps. "Price $1.85.
VI. Coutributious to tlie Knowledge of the Older Mesozoic Flora of Virginia, by William Morris
Fontaine. 1883. 4-'. xi, 144 pp. 54 1. .54 pi. Price $1.05.
VII. Silver-Lead Deposits of Eureka, Nevada, by Joseph Story Curtis. 1884. 4'. xiii, 200 pp.
16 pi. Price $1.20.
Vm. Paleontology of the Eureka District, by t'harles Do.dittle Walcott. 1884. 4'-. xiii, 298
pp. 24 1. 24 pi. Price' $1.10.
IX. Brachiopoda and LamellOiranchiata of the Raritau Clays and Grecusand Marls of New
Jersey, by Robert P. AVhittield. 1885. 4-. xx, 338 pp. 35 pi. 1 map. Price $1.15.
X. Dinocerata. A Monograph of an Extinct Order of Gigantic Mammals, by Othuiel Charles
Marsh. 1886. 4>-\ xviii, 243 pp. 56 1. .56 pi. Price $2.70.
XI. Geological History of Lalce Lahontaii, a yuateraary Lake of Northwestern Nevada, by
Israel Cook Russell. 1885. ' I'-", xiv, 288 pp. 46 pi. and maps." Price $1.75.
XII. Geology and Mining Industry of Jjeadville. Coldvado, with atlas, by Samuel Franklin Em-
mons. 1886. 4^." xxix, 770 pp. 45 pl.'aud atlas ol'3r> slnrts lolin. Price $8.40.
XIII. Geologv of the Quicksilver Dejiosits uf thi- l^nilir sl,,|ie, with atlas, by George F. Becker.
1888. 4^. xix, 486 pp. 7 pi. and atlas of 14 sheets loli... i'licc .$2.00.
XIV. Fossil Fishes and Fossil Plants of the Triassic Rocks of New Jersey and the Connecticut
Valley, by John S. Newberry. 1888. 4°.' xiv, 152 pp, 26 pi. Price $1.00.
XV. The Potomac or Younger Mesozoic Flora, by William Morris Fcmtaine. 1889. -l^. 'xiv,
377 pp. 180 pi. Text and plates bmind separately. Price $2..50.
XVI. The Paleozoic Fishes of North America, by John Strong Newberry. 1889. 4-. 340 pp.
53 pl. Price $1.00.
XVII. The Flora of the Dakota Group, a posthumous work, by Leo Lesquereux. Edited by F.
H. Knowlton. 1891. 4^. 400 pp. 66 ]d. Price $1.10.
XVIII. Gasteropoda aud Cephalopoda of the Raritan Clays and Greeusand Marls of New Jersev,
by RobertP. Whittisld. 1891. 4-\ 402 pp. 50 pi. Price $1.00.
XIX. The Penokee Iron-Bearing Series of Northern Wisconsin aud Michigan, by Kolanil D.
Irving and C. R. Van Rise. 1892. 4°. xix, 534 pp. Price $1.70.
XX. Geology of tlie Eureka District, Nevada, with an atlas, by Arnold Hague. 1892. 4'^'. xvii.
419 pp. 8 1)1. Price $5.25.
XXI. The Tertiarv Rhvnchophorous Coleoptera of the United States, by Samuel Hubbard Scud-
der. 1893. 4°. xi. 206 pp. 12 pl. Price 90 cents.
XXII. A Manual of Topographic Methods, bv Henry Gannett, chief toiiographer. 1893. 4- .
XIV. 300 pp. 18 pl. Price $1.00.
In press:
XXIII. Geology of the Green Mountains in Massachusetts, bv Raphael Pnnipellv, T. Nelson Dalei
and .T. E. Wolff.
In iireparation ;
— Mollusca and Crustacea of the Miocene Formations of New Jersey, by R. P. Whitfield.
— SauTopoda, by 0. C. Marsh.
— Stegosauria, by O. C. Marsh.
— Brontotheridte, by O. C. Marsh.
— Rejjort on the Denver Coal Basin, by S. F. Emmons.
— Report on Silver Cliff and Ten-Mile Mining Districts. Colorado, by S. F. Emmons.
— The Glacial Lake Agassiz, by Warren Upluim.
BULLETINS.
1. On Hypersthene-Andesite aud on Tricliuic Pyroxene in Augitic Rocks, by Whitman Cross,
with a Geological Sketch of Buffalo Peaks, Colorado, by S, F. Emmons. 1883. 8'^. 42 pp. 2 i)l.
Price 10 cents.
2. Gold and Silver Conversion Tables, gjvnig tlie coining values of troy ounces of fine metal, -etc.,
computed by Albert Williams, jr. 1883. 8*^. 8 p]i. Price 5 cents.
3. On the Fossil Faunas of the Upper Devonian, .along the meridian of 76° 30', from Tompkins
County, N. Y., to Bradford County, Pa., by Henry S. Williams. 1884. 8'^'. 36 pp. Price 5 cents
4. On Mesozoic Fossils, by Charles A. White. 1884. 8-. 36 pp. 9 pl. Price 5 cents.
5. A DictionaTy of Altitudes in the United States, compiled by Henry Gannett. 1884. 8°. 325
pp. Price 20 cents.
6. Elevations in the Dominion of Canada, by J. W. Spencer. 1884. 8°. 43 pp. Price 5 cents.
7. Mapoteca Geologica Americana. A Catalogue of Geological Maps of America (North and
South), 1752-1881, in geographic and chronologic order, by Jules Marcou and John Belknap Marcou.
1884. 8°. 184 pp. Price 10 cents.
ADVERTISEMENT. IH
8. On Seooudiiry Enlargemeuts of Mineral Fragments iu Certain Rcicks, by E. D. Irving and C.
E. VaiiHise. I.SSI, 's . 5li pp. ti pi. Price 10 cents.
9. A Eeport ol' W(iik ihnw in tlip Wasliiiigtim Laboratory dnring the fiscal year 18!^3-'84. F. W.
Clarke, chief chemist; T. M. Chatanl, assistaiit chemist. 1884. 8. 40 pp. Price 5 cents.
10. On the Cambrian Fauua.s of Nnrtli America. Preliminary studies, by Charles Doolittle Wal-
cott. 1884. 8°. 74 pp. 10 pi. Price 5 cents.
11. On the Quaternary and Eecent Mollusca of the Great Basin; with Descriptions of New
Forms, by E. Ellsworth Call' Introduced by a sketch of the Quaternary Lakes of the Great Basin,
by G. K. Gilbert. 1884. 8°. 66 pp. 6 pi. ' Price 5 cents.
12. A Crystallographic Study of the Thinolite of Lake Lahontan, by Edward S. Dana. 1884. 8'-'.
34 pp. ' 3 pi. Price 5 cents.
13. Boundaries of the United States and of tlie several States and Tei'ritories, with a Historical
Sketch of the Territorial Changes, by Henry Gauuett. 1885. »-. 135 pp. Price 10 cents.
14. The El«!Ctr)cal and Magnetic Properties of the Iron-Carburets, by Carl Barns and Vincent
Strouhal. 1885. 8'^. 238 pp. Price 15 cents.
15. On the Mesozoic and Cenozoic Paleontology of California, by Charles A. AAHiite. 1885. 8°.
33 pp. Price 5 cents.
16. On theHigherDevonianFanuasof Ontario County, New York, by John M. Clarke. 1885. 8°.
86 pp. 3 pi. Price 5 ceuts.
17. On the Development of Crystallization in the Igneous Eocks of Washoe, Nevada, with Notes
on the Geology of the District, by Arnold Hague and Joseph P. Iddings. 1885. 8°. 44 pp. Price 5
cents.
18. On Marine Eocene, Fresh-water Miocene, and other Fossil Mollusca of Western North America,
by Charles A. White. 1885. 8*^. 26 pp. 3 pi. Price 5 cents.
19. Notes on the Stratigraphy of California, by George F.Becker. 1885. 8^^. 28pp. Price5ceuts.
20. Contributions to the Miiieralogv of the Rocky Jlountains, by Whitman Cross and W. F. Hille-
brand. 1885. 8'-. 114 pp. 1 pi. Price" 10 cents.
21. The Lignites of the Great Siovix Eeservation. A Eeport on the Eegion between the Grand
and Moreau Rivers, Dakota, by Bailey Willis. 1885. 8'-. 16 pp. 5 pi. Price 5 cents.
22. On New Cretaceous Fossils from California, by C'harles A. White. 1885. 8-^. 25 pp. 5 pi.
Price 5 cents.
23. Observations on the .Junction between the Eastern Sandstone and the Keweenaw Series on
Keweenaw Point, Lake Superior, by R. D. Irving and T. C. Chamberlin. 1885. 8'^. 124 pp. 17 pi.
Price 15 cents.
24. List of Marine Mollusca, comprising the Quaternary fossils and recent forms from American
Localities between Cape Hatteras and Cape Roque, including the Berjnudas, by William Healey Dall.
1885. 8°. 336 pp. Price 25 cents.
25. The Present Technical Condition of the Steel Industry of the United States, by Phineas
Barnes. 1885. 8°. 85 pp. Price 10 cents.
26. Copper Smelting, by Henry M. Howe. 1885. 8^^. 107 pp. Price 10 cents.
27. Report of work done in the Division of Chemistry and Physics, mainly during the fiscal year
1884-'85. 1886. 8°. 80 pp. Price 10 cents.
28. The Gabbros and Associated Hornblende Rocks occurring iu the Neighborhood of Baltimore,
Md., by George Huntington Williams. 1886. 8^. 78 pp. 4 pi. Price 10 cents.
29. On the Fresh-water Invertebrates of the North American Jurassic, by Chiirles A. White. 1886.
8^'. 41 pp. 4 pi. Price 5 cents.
30. Second Contribution to the Studies on the Cambrian Faunas of North America, by Charles
Doolittle Walcott. 1886. 8"^. 369 pp. 33 pi. Price 25 cents.
31. Systematic Review of our Present Knowledge of Fossil Insects, including Myriapods and
Arachnids, by Samuel Hubbard Scudder. 1886. 8°. 128 pp. Price 15 cents.
32. Lists and Analyses of the Mineral Springs of the United States; a Preliminary Study, by
Albert C. Peale. 1886. 8°. 235 pp. Price 20 ^■ents.
33. Notes on the Geolo'iy of Northern California, by J. S.Di.ler. 1886. 8°. 23 pp. Price 5 cents.
34. On the relation of the Laramie Molhiscan Fauna to that of the succeeding Fresh-water Eocene
and other groups, by Charles A. AVhite. 1886. 8^. .54 pp. 5 pi. Price 10 cents.
35. Physical Properties of the Iron-Carburets, by Carl Barns and Vincent Strouhal. 1886. 8°.
62 pp. Price 10 cents.
36. SubsidenceofFineSolidParticlesiuLiquid»,bvCarlBarus. 1886. 8°. 58pp. PricelOceuts.
37. Types of the Laramie Flora, hv Lester F. Ward. 1887. 8°. 354 pp. 57 pi. Price 25 cents.
38. PeridotiteofEUiottCounty, Kentucky, by J. S.Diller. 1887. 8^. 31pp. Ipl. Price5cents.
39. The Upper Beaches and Deltas of the Glacial Lake Agassiz, by Warren Upham. 1887. 8".
84 pp. 1 pi. Price 10 cents.
40. Changes iu River Courses in Washington Territory due to Glaciation, by Bailey AVillis. 1887.
8°. 10 pj). 4 pi. Price 5 ceuts.
41. On the Fossil Faunas of the Upper Devonian— the Genesee Section, New York, by Henry S.
Williams. 1887. 8°. 121 pp. 4 pi. Price 15 cents.
42. Report of work done in the Division of Chemistry and Physics, mainly during the fiscal year
1885-'86. F.W.Clarke, chief chemist. 1887. 8". 1.52 pp. Ipl. Price 15 cents.
43. Tertiary and Cretaceous Strata of the Tuscaloosa, Tombigbee, and Alabama Rivers, l>y Eugene
A. Smifh and Lawrence C. Johnson. 1887. 8". 189 pp. 21 pi. Price 15 cents.
IV . ADVEKTISEMKNT.
U. Bihliogi-iiiUy of North Aiiiericau (ieDlogy lor 1S86, by NolsoM II. Oiirtoii. 1887. 8^'. :« pj).
Price 5 cents.
45. The Present Condition o!' Knowledge of the ( icologv iif Texns. )>y lvob.-r(- T. Hill. 1887. 8 ,
94 P11. Price 10 cents.
4ti. Nature and Origin of Deposits of Phosplialc of Liiac. l>v K. A. V. Peni'ose, jr., with an Intro-
duction by N. S. Shalcr. 1888. 8«. 143 pp. Price If. cents.
47. Analyses of Waters of tbe Yellowstone Natiinial Paik, wilh .ui Account of tlie Metlnxls of
Analysis employed, by Frank Austin Goo'ch and James Edwaril Whitlicld. 1888. S'^. 84 i)p. I'rice
10 cents.
48. On the Form and Position of the Sea Level, by Kobcrl Simpson Woodward. 1888. 8'-'. 88
pp. Price 10 cents.
49. Latitudes and Longitudes of t'ertain Points in Missouri, Kansas, and New Mexico, by Kobert
Simpson Woodward. 1889. ''8'-\ 133 pp. Price 15 cents.
50. Formulas and Tables to Facilitate the Construction and Use of Maps, by Robert Simpson
Woodward. 1889. 8'^. 124 pp. Price 15 cents.
51. On Invertebrate Fossils from the Pacific Coast, by Charles Abiathar White. 1889. 8 . 102
pp. 14 pi. Price 15 cents.
52. Subaerial Decay of Rocks and Origin of the Red Color of Certain Formations, by Israel
Cook Russell. 1889. 8°.' 65 pp. 5 pP Price 10 cents.
53. The Geology of Nantucket, by Nathaniel Southgate Shaler. 1889. 8*^. 55 pp. 10 pi. Price
10 cents.
54. On the Thernio-Electric Measurement of High Temperatures, by Carl Barns. 1889. 8°.
313 pp., incl. 1 pi. 11 pi. Price 25 cents.
55. Report of work done in the Division of Chemistry and Physics, mainly during the tiscal
year 1886-'87. Frank Wigglcsworth Clarke, chief chemist. 1889. 8". 96 pp. Price 10 cents.
56. Fossil \\'ood and^Liguite of the Potomac Formation, by Frank Hall Knowlton. 1889. 8"^.
72 pp. 7 pi. Price 10 cents.
57. A Geological Recouuoissauce in .Southwestern Kansas, by Robert Hay. 1890. ■ 8^\ 49 pp.
2 pi. Price 5 cents.
58. The Glacial Boundary in Western Peuusylvauia, Ohio, Kentucky, Indiana, and Illinois, by
George Frederick Wright, with an introduction by Thomas Chrowder Chamberlin. 1890. 8°. 112
pp. incl. 1 pi. 8 pi. Price 15 cents.
59. The Gabbros and Associated Rocks.in Delaware, by Frederick D. Chester. 1890. 8*^'. 45
pp. 1 pi. Price 10 cents.
60. Report of work done in the Division of Chemistry and Physics, mainly during the tiscal
year 1887-'88. F. W. Clarke, chief chemist. 1890. 8*^. 174 pp. Price 15 cents.
61. Contributions to the Mineralogy of the Pacific Coast, by William Harlow Melville and Wa4-
demar Lindgren. 1890. 8°. 40 pp. 3 pi. Price 5 cents.
62. The Greenstone Schist Areas of the Menominee and Marquette Regions of Michigan, a eou-
tribution to the snbjei t of dynamic metamorphism in eruptive rocks, by George Huntington Williams,
with an introduction by Roland Duer Irving. 1890. 8°. 241 pp. 16 pi. Price 30 cents.
63. A BibliogTaphy of Paleozoic Crn.stacea from 1698 to 1889, including a list of North Amer-
ican species and a systematic arrangement of genera, by Anthony W. Vogdes. 1890. 8"=. 177 pp.
Price 15 cents.
64. A Report of work done in the Division of Chemistry and Pliysics, mainly during the fiscal
year 1888-'89. F. W. Clarke, chief diemist. 1890. 8°. 60 pp. Price 10 cents.
65. Stratigraphy of the Bituminous Coal Field of Pennsylvania, Ohio, and West Virginia, l)y
Israel C. White. 1891. 8°. 212 pp. 11 pi. Price 20 cents.
66. On a Group of Volcanic Rocks from the Tewan Mountains, New Jlesico, and on the occur-
rence of Primary Qnartz in certain Basalts, by Joseph Paxson Iddings. 1890. 8°. 34 pp. Price 5
cents.
67. The relations of the Traps of the Newark System in the New Jersey Region, by Nelson
Horatio Dartou. 1890. 8-^. 82 pp. Price 10 cents.
68. Earthquakes in California in 1889, by James Edward Keeler. 1890. 8°. 25 pp. Price 5
cents.
69. A Classed and Annotated Biographv of Fossil Insects, by Samuel Howard Scudder. 1890.
8°. 101pp. Price 15 cents.
70. A Report on Astronomical Work of 1889 and 1890, by Robert Simpson Woodward. 1890. 8'-'.
79 pp. Price 10 cents.
71. Index to the Known Fossil Insects of the World, including Myriapods and Arachnids, by
Samuel Hubbard Scudder. 1891. 8°. 744 pji. Price 50 cents.
72. Altitudes between Lake Superior and the Rooky Mountains, by Warren Fpliam. 1891. 8".
229 pp. Price 20 cents.
73. The Viscosity of Solids, by Carl Barns. 1891. 8^. xii, 139 pp. 6 pi. Price 15 cents.
74. The Minerals of North Carolina, by Frederick Augustus Genth. 1891. 8°. 119 pp. Price
15 cents.
75. Record of North American Geology for 1887 to 1889, inclusive, by Nelson Horatio Darton.
1891. 8'^. 173 pp. Price 15 cents.
76. A Dictionary of Altitudes in the United States (second edition ). compiled by Henry Gannett,
chief topographer. 1891. 8^. 393 pp. Price 25 cents.
ADVERTISEMENT. V
77. The Texar. Permian and its Mesozoic types of Fossils, liy Charles A. White. 1891. .S-. 51
pp. 4 pi. Price 10 cents.
78. A report of -n'ork done in the Division of Chemistry and Physics, mainlv duriii"- the liscal
year lS89-'90. F. W. Clarke, chief chemist. 1891. 8'^. 131 pp. Price 1.5 cents. '
79. A Late Volcanic Eruption in Northern California and its peculiar lava, by J*; S. Diller.
80. Correlation papers — Devonian and Carboniferous, by Henry Shaler Williams. 1891. 8°.
279 pp. Price 20 cents.
81. Correlation papers — C.imbviau, by Charles Doolittle Walcott. 1891. 8^. 547 pp. 3 pi.
Price 25 cents.
82. Correlation papers — Cretaceous, by Charles A. White. 1891. 8^. 273 pp. 3 pi. Price 20
cents.
83. Correlation papers— Eocene, by AA'illiara Bullock Clark. 1891. S°. 173 pp. 2 pi. Price
15 cents.
84. Correlation papers— Neocene, by W. H. Dall and Q. D. Harris. _ 1892. 8^. 349 pp. 3 pi.
Price 25 cents.
85. Correlation papers^The Newark System, by l.srael Cook Russell. 1892. 8^. 344 pp. 13 pi.
Price 25 cents.
86. Correlation papers — Archean and Algonkian, by C. E. Van Hise. 1892. 8^^. .549 pp. 12 pi.
Price 25 cents.
90. A report of Tvork done in the Division of Chemistry and Phy.sics, mainly during the tisoal
year 1890-'91. F. W. Clarke, chief chemist. 1892. 8". 77 pp.' Price 10 cents.
91. Record of North American Geology for 1890, by Nelson Horatio Darton. 1891. 8'J. 88 pp.
Price 10 cents.
92. The Compressibility of Liquids, by Carl Barus. 1892. 8°. 96 pp. 29 pi. Price 10 cents.
93. Some Insects of sjn-i-ial iuterrst fioui Florissant, Colorado, and other points in the Tertiaries
of Colorado and Utah, by Sauincl Hubbard Scudder. 1892. 8^. 35 ])p. 3 pi. Price 5 cents.
94. The Slechanism of >olid Yi.scosity, by Carl Barns. 1892. 8'^\ 138 pp. Price 15 cents.
95. Earthquakes in California in 1890 and 1891, by Edward Singleton Holdeu. 1892. 8^. 31pp.
Price 5 cents.
96. The Volume Thermodynamics of Liquids, by Carl Barus. 1892. 8^. 100pp. Price 10 cents.
97. The Mesozoic Echinodermata of the United States, by W.B. Clark. 1893. 8". 207 pp. iiOpl.
Price 20 cents.
98. Flora of the Outlying Carboniferous Basins of Southwestern Missouri, by David White.
1893. 8^. 139 pp. 5 pi. Price 15 cents.
99. Record of North American Geology for 1891, by Nelson Horatio Darton. 1892. 8-. 73 pp.
Price 10 cents.
100. Bibliography and Index of the Publications of the U. S. Geological Survey, 1879-1892, by
Philip Creveling Warman. 1893. 8'^. 495 pp. Price 25 cents.
101. Insect fauna of the Rhode Island Coal Field, by Samuel Hubbard Scudder. 1893. 8-'.
27 pp. 2 pi. Price 5 cents.
103. High Temperature Work in Igneous Fn.sion and Ebullition, chictlv in relation to pressure,
by Carl Barus. 1893. 8°. 57 pp. 9 pi. Price 10 cents.
104. Glaciation of the Yellowstone Valley north of the Park, by Walter Harvey Weed. 1893. 8'^.
41 pp. 4 pi. Price 5 cents.
105. The Laramie and the overlying Livingstone Formation iu Montana, by Walter Harvey
Weed, with Report on Floia, by Frank Hall Knowlton. 1893. 8^ 68 pp. 0 ]>1. Price 10 cents.
106. The Colorado Formation and its Invertebrate Fauna, by T. \V. Stanton. 1893. 8'^. 288
pp. 45 pi. Price 20 cents.
107. The Traj) Dikes of Lake Champlain Valley and the Eastern Adirondacks, by James Furuuin
Kemp.
108. A Geological Reconnoissauce in Central Washington, by Israel Cook Russell. 1893. 8".
108 pp. 12 pi. Frice 15 cents.
109. The Eruptive and Sedimentary Rocks on Pigeon Point, Minnesota, and their contact phe-
nomena, by AVilliam Shirley Bayley. 1893. 8^. 121 pp. 16 pi. Price 15 cents.
110. The Paleozoic Section in the vicinitv of Three Forks. Moutana, bv Albert Charles Peale.
1893. 8°. 56 pp. 6 pi. Price 10 cents.
In press :
102. A Catalogue and Bibliography of North American Mesozoic Invertebrata, by C. B. Boyle.
111. Geology of the Big Stone Gap Coal Fields of VirgL.ia and Kentucky, by Marius R. Camii-
bell.
112. Earthquakes itf California in 1892. by Charles D. Perriue.
In preparation ;
— Correlation papers — Pleistocene, by T. C. Chambeiiin.
— The Moraines of the Missouri Coteau and their attendant deposits, by James Edward Todd.
— On the Structure of the Ridge between the Tacimic and the Gieen Mountain Ranges in Ver-
mont; and On the Structure of Monument Mouutaiu in Great Barriugtoii, Mass., by T. Nelson Dale.
— A Bibliography of Paleobotany, by David White.
VI ADVERTISEMENT.
STATISTICAL PAPERS.
Mineral Resource.^ of thp UuiteaState.^ [1882], by Albert Williams, , jr. 1883. 8'^. xvii,813pp.
Price .50 eeuts.
Mineral Resources ol' the Uuiteil State.s 1883 iiud 1884, liy AUiert, Williams, jr. 1885. 8^. xiv,
1011) pp. Price 60 cents. . . , ,„ , ,
Mineral R-sources of the United States, 1885. Divi.'iion of Mining- Statistics and Technology.
1886. 8°. vii, .576 pp. Price 40 cents. ' ...,,,
Mineral Resources of the United States, 1886, by Havid T. Day. 188(. 8'^. viii,813pp. Price
Mineral Resources of the United States, 1887, by David T. Day. 1888. 8". vii, 832 pp. Price
Mineral Resources of the United States, 1888, by liavid T. Day. 18R0. 8". vii, 6.52 pp. Price
^^"ilineral Resources of the United States, 1889 and 1890, by David T. Day. 1892. 8°. viii, 671 pp.
""^""Mineral'Resourceaof the United States, 1891, by David T. Day. 1893. S^'. vii, 630 pp. Price
50 cents.
The money received from the sale of these publications is deposited in the Treasury, and the
Secretary of tha't Departmeut declines tosreceive bank checks, drafts, or postage-stamps; all remit-
tances, therefore, inn.st be by POSTAL XOTK or money order, made payable to the Chief Clerk of the
IT. S. Geological Survey, or m curhkncy for the exact amount. Correspondence relating to the pub-
lications of'the Survey should be addressed
To THE Director of thv;
United States (Jeological Survey,
Washington, D. C.
Washington, D. C, Uclohei; 1893.
DEPARTMENT OF THE INTERIOR
MONOGRAPHS
United States Geological Survey
VOLUME XXII
WASHINGTON
GOVERNMENT PRINTING OFFICE
1893
1/1 12A
UNITED STATES GEOLOGICAL SURVEY
J. W. POWELL, DIRECTOR
A MANUAL
TOPOGRAPHIC METHODS
HENRY GANNEXT
CHIEF TOFOGRA.PHER
WASHINGTON
GOVERNMENT PRINTING OFFICE
1893
CONTENTS.
Page.
Letter of transmittal
Chapter I.
Introduction
Surveys under the U. S. Government : -
Exploration of the Fortieth Parallel 2
Geologic and Geographic Survey of the Territories 2
Geologic and Geographic Survey of the Rocky Mountain region - - 3
Northern Transcontineutal Survey 3
Coast and Geodetic Survey
Engineer Corps, U. S. Army *
General Land Office Surveys *
Surveys under State governments -
Massachusetts
New York ^
5
New Jersey
5
Pennsylvania
5
Railroad and other surveys
Plan of the map of the United States
Scale
Scales of topographic maps of European nations 9
9
Contour interval ■
9
Features represented
Size of sheets -
Geometric control -
Its accuracy
Its amount
Its distribution
14
Sketching
Chapter II.
15
Classification of work -
Astronomic determinations of position
17
Definitions
Astronomical transit and zenith telescope
19
Chronograph
20
Field work
YI CONTENTS.
Astronomic determinations of position — Continued. Page.
Observations for Latitude 21
Reduction of observations for latitude 23
Measurement of a division of the head of the micrometer screw 23
Measurement of a level division 26
Computation of apparent declination of stars 27
Computation of Latitude 28
Observations for time 28
Eeduction of time observations 29
Correction for error of level 29
Correction for inequality of pivots , 30
Correction for error of collimation 30
Correction for deviation in azimuth 30
Correction for diurnal aberration 31
Comparison of time 34
Observ.ations for azimuth 36
Eeduction of observations for azimuth 38
Chapter III.
Horizontal location 41
Party organization 41
Base line measurement 42
Eeduction of base line measurement 45
Eeduction to standard 45
Correction for inclination 46
Correction for temperature 46
Reduction to sea level 46
Primary triangulation 48
Selection of stations 49
Signals ; 50
Heliotropes 52
Theodolites for triangulation 54
Instructions for the measurement of horizontal angles 55
Organization of parties and prosecution of work 63
Eeduction of primary triangulation 65
Reduction to center 65
Spherical excess 65
Station adjustment 66
Figure adjustment 68
Computation of distances 72
Computation of geodetic coordinates 72
Traverse lines for primary control , . 75
Primary elevations 77
Chapter IV.
Secondary triangulation 79
The plane table 79
The alidade 82
Measurement of altitudes 84
CONTENTS. VII
Traverse work °^
Traverse plane table 86
Measurements of altitudes in c mnection with traverse work '. 89
The aneroid - --- 9^
Organization of parties and distribution of work 91
Stadia measurements.
92
The Cistern barometer 9"*
Use in field ^5
Reduction of barometric observations . - . : - 98
Utilization of the work of the public land surveys 101
Description of work 102
Chapter V.
Sketching l*'^
Origin of topographic features _ - 108
UpUffc 1"^^
Deposition from volcanic action HO
Aqueous agencies
Erosion ^^^
Weathering 1' ^
Transportation and corrasion HI
Profiles of streams and of the terrane 112
Relations between stream and terrane corrasion 113
Origin of canyons in plateau region H'i
Origin of detrital vaUeys 115
115
116
Sinks :
Piracy ----
Origin of canyons in mountain ranges 11°
Origin of water and wind gaps 116
Junctions of streams 11'^
Effect of structure on topographic forms 117
Erosion of horizontal beds of rock 118
Erosion of inclined beds of rock 1-0
Age of topographic features l-O
Conception of base level - l-l
121
Deposition from water :
121
River ridges
12^
Alluvial fans "
„ „„„„ 122
122
Glacial deposition
123
Drunvlins
123
Pitted plains
„ 123
Osars
,, . 123
Moraines
123
Glacial erosion
124
Amphitheaters '
Deposition from the atmosphere
VIII
CONTENTS.
Scale of ficldwork
Reports
Inspection
Chapter VI.
Office trork
Form of original sheets
Construction of projections .
Colors and conventions
Titles and legends
Pago.
125
125
127
128
128
129
130
130
TABLES
Page.
Table I. For computing the difference in the heights of two places from barometric
observations 1^1
II. Correction for the difference of temperature of the barometers at the two
stations ' ■'•'*
III. Correction for the difference of gravity in various latitudes 134
IV. Correction for decrease of gravity on a vertical 135
V. Correction for the height of the lower station 135
VI. Differences of altitude from angular measurements for low angles and short
distances '^^"
VII. Differences of altitude from angular measurements for unit distance and high
angles 1°-^
VIII. Corrections for curvatvire and refraction 153
IX . Differences of altitude from angular measurements applicable to scale 1 : 45000 . 154
X. Differences of altitude from angular measurements applicable to scale 1 : 30000. 156
XI. Differences of altitude from telemeter measurements 158
XII. For converting wheel revolutions into decimals of a mile 162
XIII. Constants 163
XIV. Conversion table— metres into yards 163
XV. yards into metres ■ 164
XVI. inches into metres and metres into inches 164
XVII. metres into statute and nautical miles 164
XVIII. statute and nautical miles into metres 164
XIX. Coordinates for projection of maps of large areas 165
XX. Coordinates for projection of maps, scale 1 : 250000 175
XXI. Coordinates for projection of maps, scale 1 : 125000 177
XXII. Coordinates for projection of maps, scale 1 : 62500 180
XXIII. Coordinates for proj ection of maps, scale 1 : 45000 185
XXIV. Areas of quadrilaterals on the earth's surface, one degree in latitude and in lon-
gitude 186
XXV. Areas of quadrilaterals ou the earth's surface, 30 minutes of latitude and longi-
tude 18'^
XXVI. Areas of quadrilaterals on the earth's surface, 15 minutes of latitude and longi-
tude 188
XXVII. Factors for the geodetic computation of latitudes, longitudes, and azimuths. . . 190
XXVIII. Factors for reduction of transit observations 217
XXIX. For reducing observations for latitude by Talcott's method 224
: TABLES.
Page.
Tablk XXX. For facilitating tiie reduction of observations on close circum-polar stars made
in determining the value of a revolution of the micrometer 226
XXXI. For converting sidereal time into mean time 227
XXXII. For converting mean time into sidereal time 228
XXXIII. For converting parts of the equator in arc into sidereal time 229
XXXIV. For converting sidereal time into parts of the equator in arc 230
XXXV. Logarithms of numbers 231
XXXVI Logarithms of circular functions 254
ILLUSTRATIONS
Page.
14
50
54
80
86
112
113
114
Plate I. Map of surveyed areas. Folded in pocket
II. Diagram of control
III. Baldwin base-measuring device **
IV. Signal
V. Eight-inoli theodolite and tripod
VI. Johnson plane-table— general view
VII. Traverse plane-table
VIII. Types of topography, Great plains
IX. Types of topography, Atlantic plain
X. Types of topography, Cumberland plateau
XI. Types of topography. Canyons in homogeneous rocks US
XII. Types of topography, Canyons in rocks not homogeneous 116
XIII. Types of topography. Grand canyon of Colorado river - - - 117
XIV. Types of topography. Water gaps, Pennsylvania 118
XV. Types of topography, Mississippi river ridge 121
XVI. Types of topography, Drumlins 1^2
XVII. Types of topography, Moraines .- : 1-"^
XVIII. Types of topography, Cirques 1^*
Figure 1. Astronomical transit and zenith telescope : - • 1°
2. Chronograph
3. Switchboard ^
4. Signal and instrument support
5. Heliotrope, Coast Survey = ^-'
6. Heliotrope, Steiuheil ^^
7. Eight-inch theodolite— detail ^^
8. Johnson plane-table tripod head— section 81
87
9. Douglas odometer -
10. Small telescopic aUdade -
11. Aneroid -
12. Aneroid -^ ^'^
i-in
13. Cross sections of canyons
14. Cross sections in inclined beds I-'"
LETTER OF TRANSMITTAL
Department of the Interior,
U. S. Geological Survey,
Geographic Branch,
Washington, D. C, May 17, 1892.
Sir: I have the honor to submit herewith for pubhcation a manual of
the topoga-aphic methods in use by the Geological Survey, accompanied by
a collection of constants and tables used in the reduction of astronomical
observations for position, of triang-alation, of height measurements, and
other operations connected with the making of topographic maps. It must
be understood that the methods are not fixed, but are subject to change and
development, and that this manual describes the stage of development
reached at present.
In the preparation of this work I have to acknowledge the aid of many
of my associates, notably Mr. H. M. Wilson and Mr. S. S. Gannett. To
Mr. R. S. Woodward, now connected with the U. S. Coast and Geodetic
Survey, I am indebted for the " Instructions for the Measurement of Hori-
zontal Angles " in Chapter iii. These instructions, which were di-awn up
by Mr. Woodward several years ago for the guidance of field parties en-
gaged in primary triangulation, have resulted in a great increase in accuracy
and considerable economy of time and labor. To Messrs. G. K. Gilbert
and W. J. McGee I am indebted for their kindly criticism, especially con-
cerning the chapter upon the " Origin of Topographic Features."
XIV LETTEE OF TKANSMITTAL. ^
'.I
Some of the tables liave been prepared in this office ; others have been ^
compiled from various sources, notably from appendices to reports of the ;
U. S. Coast and Geodetic Survey and "Lee's Tables and Formulae."
Very respectfully,
Henry Gannett,
Chief To;pograplier.
Hon. J. W. Powell,
Director U. S. Geological Survey.
A MANUAL OF TOPOGRAPHIC METHODS.
By Henry Gannett.
CHAPTER I.
INTRODUCTION.
The object of this manual is to present a description of the topographic
work, instruments, and methods used by the U. S. Greological Survey,
primarily for the information of the men engaged upon this work. It is
not intended as an elementary treatise upon surveying, as it presupposes a
knowledge of the application of mathematics to surveying equivalent to
that to be obtained in our professional schools. Neither is it intended as a
general treatise on topographic work, although it Tnay, to a certain extent,
supply the existing need of such a work.
The Geological Survey is engaged in making a topographic map of the
United States. Excepting for certain areas, lying mainly in the far West,
there existed, prior to the inception of this work, no maps upon a sufficiently
large scale and in suitable form for the use of the geologist. While the
primary object of the map is to meet the needs of the geologists of the
Survey, it has been thought economical to adjust the plans so that the result-
ing map may be adequate to serve all needs for which general tojjographic
maps are used.
Certain areas, especially in the far West, have been surveyed and
mapped by other organizations, notably those of the general and state gov-
ernments, upon a sufficiently large scale, and with sufficient accuracy for
the use of the Geological Survey; much material also exists in the form of
triangulation, of lines of levels, and of other partial surveys which can be
2 A MANUAL OF TOPOUEAPHIC METHODS.
put to use aud will assist to a greater or less extent iu the preparation of
the map. These maps and other material have been, or aiay be, adopted
b}^ the Geological Survey. Their extent is represented upon the accom-
panying map, PL I, as fully as possible, and they are enumerated, with a
brief description, as follows:
SURVEYS UNDER THE UNITED STATES GOVERNMENT.
The Survey of the Fortieth Parallel, from 1867 to 1872, under Mr. ■
Clarence King, embraced a zone of country 105 miles in breadth, extend-
ing from the meridian of 104° to that of 120° west of Greenwich, and
comprising an area of 87,000 square miles. The maps were made upon a
scale of 4 miles to an inch, with contours having a vertical interval of 300
feet. The work was controlled by triangulation, resting primarily upon a
base line measured by determining astronomically the latitudes of two
points, and the azimuth of the line connecting them ; and, secondarily, upon
a base line extending neai-ly from the eastern to the western limits of the
work, the coordinates of the ends of which were determined astronomically,
the latitude by zenith telescope and the longitude by telegraphic time com-
parisons. Primary triangulation was done with theodolites reading to ten
seconds. Secondary triangulation and location were executed with minute
reading instruments, and topography was sketched and afterwards trans-
fen-ed to the platted framework. Heights were measured by barometer and
the vertical arc.
The Geological and Geographical Survey of the Territories, under
Dr. F. V. Hayden, between 1873 and 1878, surveyed areas in Colorado,
New Mexico, Utah, Wyoming, Idaho, in all about 100,000 square miles.
The maps were published \ipon a scale of 4 miles to an inch, with a contour
interval of 200 feet. The base lines for the control of this work were
measured with steel tapes, under imiform tension, and with corrections for
temperature. Triangulation was carried on with ,8 -inch theodolites read-
ing to ten seconds, and was adjusted by a graphic method. Secondary
triangulation, the location of topographic details, and the measurement of
heights were effected by methods quite similar to those employed by the
Survey of the Fortieth Parallel.
PEEVIOUS MAPS. 3
The Survey of the Kocky Mountaiu Region, under Maj. J. W. Powell,
embraced an area of about 60,000 square miles, covering parts of Wyoming,
Utah, and Arizona. This work was done between 1869 and 1877. The
maps Avere drawn upon a scale of 4 miles to an inch, with contour intervals
of 250 feet. The work was controlled by triangulation from base lines
measured with wooden rods. It was carried on with a theodolite having a
10-inch circle reading by vernier to ten seconds, and was adjusted by the
method of least squares. Secondary triangulation was done with minute
reading instruments, and minor locations, together with topographic details,
were obtained by the use of the plane table. Heights were measured by
the barometer, supplemented by the vertical circle.
The Northern Transcontinental Survey, an organization instituted by
the Northern Pacific railroad company for the survey and examination of
its lands, mapped, during the years 1882 and 1883, areas in Montana, Idaho,
and Washington, aggregating about 43,000 square miles. These maps were
intended for publication upon a scale of 4 miles to an inch, with contours
haAang' vertical intervals of 200 feet. The work was based upon triangu-
lation, which was executed mainly with a theodolite having a circle 8
inches in diameter reading by vernier to ten seconds. The triangulation
was adjusted graphically. The topographic methods were quite similar to
those of the Hayden Survey.
The U. S. Coast and Geodetic Survey has covered the greater part of
the Atlantic, Gulf, and Pacific coasts with triangulation, and with a narrow
strip of topographic work. This strip is of variable width, depending
largely upon the configuration of the coast, being, as a rule, narrow where
the coast is simple, and '1>i-oad where it is complex. Altogether an area of
nearly 40,000 square miles has been surveyed, the original sheets being
upon a scale of 1:10000 or 1:20000, the contours having vertical intervals
of 20 feet. Most of this Avork is directly available as finished Avork. Upon
some of it, howcA^er,* the contours, owing to the great age of the original
maps, have been obliterated, and it becomes necessary to wesurvey this ele-
ment. In addition to its coast work, the geodetic Avork of this orgaitization
has been extended into the interior in A-arious directions, especially in New
England, and along the eastern border of the Appalachian IMountiiin system,
4 A MAIs^UAL OF TOPOGEAPHIC METHODS.
througli the states of New York, New Jersey, Pennsyh^ania, Maryland,
Yirgiuia, West Virginia, North Carohua, Tennessee, Georgia, and- Alabama.
The work of connecting the Atlantic and Pacific coasts has been carried
far toward completion, a belt having been extended westward from the
head of Chesajjeake Bay into centi-al Kansas. A base has been measured
near Colorado Springs, Colorado, and work has been extended thence east-
ward to the east boundary of the state, while from the Pacific coast triangu-
latiou has been brought eastward across California, Nevada and Utah.
Ill assisting the state sui-veys, the Coast and Geodetic Survey has,
moreover, done a considerable amount of triangulation in the states of Mas-
sachusetts, New York, New Jersey, Pennsylvania, Kentucky, Tennessee,
and Wisconsin.
The United States Lake Siu-vey has mapped the shores of the Great
lakes, caiTying triangulation around them, and connecting the head of Lake
Michigan with the foot of Lake Erie. A belt of triangulation has also been
can-ied from the neighborhood of Vincennes, Indiana, northward along the
eastern border of Illinois, connecting with the triangulation on the shore of
Lake Michigan.
The Engineer Corps, U. S. Army, has completed a number of small
pieces of topogi-aphic work in different parts of the country, and is now
engaged in mapping the com-se of the Mississippi and Missouri rivers, con-
trolling the work by geodetic methods.
The surveys of the General Land Oflice have extended over an area
of about a million and a half square miles, and plats have been prepared
representing the drainage of this entire area. The quality of this work is
of varying degrees of excellence, but from its inception in the early part
of the centurr its quality has improved greatly. Most of this Avork can be
utilized either directly or indirectly by methods to be detailed hereafter.
SURVEYS UNDER STATE GOVERNMENTS.
Massadms^ts. — Between 1830 and 1842, the state of Massachusetts
carried on what was for the time an elaborate system of triangulation,
known as the Borden Survey. By this organization numerous points, in
the aggregate several hundred, were determined within the limits of the
PEEVIOUS MAPS. 5
state. Subsequently, many of these points were redetermined by the
Coast and Greodetic Survey, by more elaborate methods, thus furnishing
what served substantially as a primary system of triangulation within which
and to which the Borden work has been adjusted. As thus adjusted, the
Borden locations are sufficiently accurate for the ordinary needs of map
work upon the scale of one mile to an inch.
New York — For several years, terminating in 1885, the state of New
York supported a survey which was devoted to the geodetic location of
points within its area. The work was of a high grade, comparing favora-
bly with that of the Coast and Greodetic and Lake Surveys.
For many years also, the same state supported what was known as the
Adirondack Survey, which was engaged mainly in a triangulation of the
Adirondack region. Of this work few results have been published.
New Jersey. — In the year 1875, the state of New Jersey instituted a
topographic survey of its area. The plan of the work contemplated a map
upon a publication scale of one mile to an inch, with contours at vertical
intervals ranging from 5 to 20 feet. Control of the work was furnished in
part by the triang-ulation of the Coast and Geodetic Survey and in part by
triangulation of its own. In July, 1884, the completion of that state was
undertaken by the U. S. Greological Survey, by which organization it was
pushed forward to a conclusion in 1887.
Pennsylvania. — In Pennsylvania considerable topographic work has
been done by the State Greological Survey. This woi'k is of a local char-
acter and confined to small areas, which have been mapped upon large
scales, and the ag'g'regate area is not large. It was carried on by traverse
by the use of stadia and level.
RAILROAD AND OTHER SURVEYS.
Besides the material above enumerated, there exist in various parts of
the country maps in great number and of varying quality. They consist of
town and county maps, mainly made by traversing roads with odometer
and compass, of railroad lines, executed in the ordinary manner by transit
and chain, the surveys of the boundaries of the states and territories, etc.
Some of this material may prove of service.
6 A MANUAL OP TOPOGRAPHIC METHODS.
In additiou to the material enumerated above, numerous astronomic
determinations of position have been made by governmental organizations
and by private parties. These positions, scattered over the interioi", will, as
far as they go, relieve the Greological Survey from carrying on this expen-
sive work.
In additiou to all this material, the railroads of the country furnish, in
their profiles, a vast bod}^ of measurements of height. These differ greatly
in value, those of certain railroads, and generally those of the great systems,
being of a high degree of accuracy, while others are worthless. The errors
in these profiles are seldom in the leveling itself, but are due to the fact
that a road is leveled in sections, the profile of each section being based
upon an arbiti'ary datum point. Mistakes often occur in joining the profiles
of the several sections, and in correcting them for diff'erences in their datum
points.
PLAN OF THE MAP OF THE UNITED STATES.
The field upon which the Geological Survey is at work is diversified.
It comprises broad plains, some of which are densely covered with forests,
while upon others trees are entirely absent. It contains high and rugged
mountains, plateaus, and low, rolling hills. In some regions its topographic
forms are upon a grand scale, while in others the entire surface is made up
of an infinity of minute detail. Some parts of the country are densely
populated, as much so as almost any region upon the surface of the globe,
while great areas in other parts of the country are almost without settle-
ment. Greologically, portions of the country are extremely complex, re-
quiring, for the elucidation of geologic problems, maps in great detail, while
other areas are simple in the extreme.
It is ob^'ious that from this diversity of conditions, both natural and
material, maps of different areas should differ in scale, and that with the
difference in natural conditions and the difference in scale there must come
differences in the methods of work employed. The system which is found
to work to advantage in the high mountain regions of the west is more or
less inapplicable to the low forested plains of the Mississippi valley and the
Atlantic plain.
PLAN OP THE MAP,
The scales which have finally been adopted for the publication of the
map are 1:62500 or very nearly 1 mile to an inch, and 1:125000, or very
nearly 2 miles to an inch.
When this work was commenced in 18H2, three different scales were
used for different parts of tlie country, depending upon the degree of com-
plexity of the topography and the geological phenomena, upon the density
of population and the importance of the region from an industrial point of
view. These scales were 1:62500, 1:125000, and 1:250000. The luaps as
fast as produced have found extended use, not only among geologists, but
in all sorts of industrial enterprises with which the surface of the ground is
concerned, and have abeady become well nigh indispensable in the pro-
jection of railroads, water works, drainage works, systems of irrigation, and
other similar industrial enterprises. Their extended use has developed a
requirement for better maps; i. e., maps upon a larger scale and in greater
detail. At one stage of its development this requirement was met by dis-
continuing all mapping upon the scale 1:250000, which it was recognized at
that time was inadequate to the requirements. Since then the standard of
the requirements has continued to rise and, consequently, the plan of the
map has been enlarged by the extension of the areas mapped upon the scale
of 1:62500, and a corresponding reduction of the areas to be mapped upon
the scale of 1:125000. Meantime, however, large areas have been mapped
upon the discarded scale, and the maps have been published and widely
distributed. Such areas will be remapped for the larger scales only as
special needs may arise.
The considerations which have determined the selection of the above
scales are as follow§: They are believed to be sufficiently large to represent
with faithfulness all the details required to picture the country and show the
proper relations of its features, and to make the map of the greatest pos-
sible service for industrial and scientific uses consistent with other require-
ments to be mentioned hereafter. These scales are sufficiently large to
present the details of nearly all geological phenomena. The map represents
the country in sufficient detail to admit of the selection upon it of general
routes for railroads and other jiublic Avorks and to show the location of
8 A MANlTxiL OF TOPOGRAPHIC METHODS.
boundary lines in such way that their position may be recognized upon the
ground. On the other hand, the scales are not so large as to prevent the
representation upon a single sheet of a considerable area, so that the rela-
tions between different regions can be seen at a glance.
A map on a larger scale than this would require a greater time for its
completion and a greater expense, and when one considers the fact that the
map upon these scales of the entire United States, even excluding Alaska,
will, at best, cost in the neighborhood of twenty million dollars and at the
present rate of progress require fifty years for its completion, one scarcely
feels inclined to increase the labor and expense without an excellent
reason for so doing. There is yet another objection to increasing the scale
beyond that absolutely necessary. To be of value, such a map must undergo
revision at frequent intervals, in order to incorporate any changes in culture
and possibly in natural features due to natm-al or artificial agencies. The
larger the scale the more frequently such revision should be made, and
hence the labor and expense of keeping a map up to date would be greatly
increased.
In this matter the experience of the ciAdlized nations of Europe, all of
which have prepared topographic maps of more or less of their areas, while
certain of them have mapped their entire areas several times, is of great
service and points immistakably in the direction of the adopted scales. The
history of these nations in this matter presents a singular degree of uni-
formity. Their first maps were upon large scales, and upon them they
attempted to represent alh details of natural and artificial topography, even
property lines, so that one set of maps would answer for all purposes. Ex-
perience of the difficulty and expense of keeping up such maps (without
coimting then- original cost) has taught them that economy consists in the
production of, not a single map, but a series of maps, each designed to serve
a special purpose ; one as a cadastral map, another as a military map, and
another, and this the most important, as a general topographic map. It
further taught that this topographic map shoukl be on a comparatively small
scale, and accordingly, as a rule, the maps of foreign countries are upon
scales approximating one mile to an inch, a scale which is sufficient to show
all topographic details of a general character, and serves all ordinary pur-
PLAN OP THE MAP. 9
poses. The following table presents the scales of the general topographic
maps of various European countries:
Scales of lopographk maps of European nations.
India 1:63360
Great Britain and Ireland 1 : 63360
Germany 1 : 100000
Austria-Hungary 1 : 75000
France 1 : 80000
Q ■+ , 1 S 1:25000
Switzerland <
I 1:50000
Holland : 1 : 25000
Spain 1 : 50000
Italy 1:100000
Swedea 1 : 100000
Russia 1 : 126000
1:20000
\ 1-A
Belgium ,
: 40000
Denmark 1 : 40000
Norway 1:100000
Portugal 1 : 100000
CONTOUE INTERVAL.
The relief of the earth's surface is now represented upon maps almost
entirely by contour lines or lines of equal elevation. Until a comparatively
recent date this element, secondary in importance only to the horizontal
element, or the plan, has been ignored.
The contour intervals which have been adopted for the map of the
United States are as follows:
For the scale of 1 : 62500, the intervals range from 5 to 50 feet; for the
scale of 1 : 125000, 10 to 100 feet, and, for the scale of 1 :250000, the interval
is 200 or 250 feet.
FEATURES REPRESENTED.
In this matter, the experience of European nations tends in the direc-
tion of reducing the number of features which should be placed upon the
map. It has been decided, in the preparation of the map of the United
States, to go even beyond the present practice of European nations in this
regard and to limit the map to the representation of all natural features
10 A MANUAL OF TOPOGEAPHIO METHODS.
wliicli are of sufficient maguitude to warrant representation upon the scale,
and to confine tlie cultural features, that is, the artificial ones, to those which
are of general or public importance, leaving out those which are jDrivate in
their nature. Under this definition the map will represent cities, towns, and
villages, roads and railroads and other means of communication (with the
exception of private roads), bridges, femes, tunnels, foixls, canals and
acequias and boundaries of civil divisions. Fences, property lines, private
roads, and other objects of a kindred nature are not represented. The
reasons for excluding priA^ate culture are apparent. They are, first, because
such features are not of sufficient general interest to pay the cost of survey-
ing or representing them; second, because they change rapidly, and, in
order to keep the maps up to date, would require constant resurveys and
republication, while if the map is not kept constantly up to date, it is mis-
leading, and, third, their number and complexity confuse the map and
render its more important features less intelligible.
SIZE OF SHEETS.
Atlas sheets are designed to be approximately of the same size, 17 5
inches in length by from 12 to 15 in breadth, depending upon the latitude,
and all those of the same scale cover equal areas, expressed in units of
latitude and longitude, that is, each sheet upon the 4-mile scale covers
one degree of latitude by one degree of longitude; each sheet upon the
2-mile scale, 30 minutes of latitude and longitude, and each sheet upon
the 1-mile scale, 15 minutes of latitude and longitude. The sheets are
thus small enough to be conveniently handled, and, if bound, form an
atlas of convenient size. From the fact that each sheet is either a full
degree or a regular integral part of a degree, its position with relation to
the adjacent sheets and to the area of the country is easy to discovei'.
GEOMETRIC CONTROL.
From the constructive point of view, a map is a sketch, corrected by
locations. The work of making locations is geometric, that of sketching is
artistic. This definition is applicable to all maps, whatever their quality or
character. However numerous the locations may be, they form no part of
CONTEOL OP THE MAPS. H
the map itself, but serve only to correct the sketch, while the sketch sup-
plies all the material of the map. The correctness of the map depends
upon four elements: first, the accuracy of location; second, the number of
locations per square inch of the map ; third, their distribution ; and, fourth,
the quality of the sketching. It is in connection with the first of these
elements that it seems desirable to define what constitutes accuracy. The
greatest accuracy attainable is not alwaj^s desirable, because it is not
economic. The highest economy is in properly subordinating means to
ends and it is not economic to execute triangulation of geodetic refinement
for the control of maps upon small scales. The quality of the work should
be such as to insure against errors of sufficient magnitude to appear upon
the scale of publication. While the tendency of errors in triangulation is
to balance one another, still they are liable to accumulate, and this liability
must be guarded against by maintaining a somewhat higher degree of
accuracy than would be required for the location of any one point. It is
not difficult to meet this first condition of accuracy of the maps The
maximum allowable error of location may be set at one-hundredth of an
inch upon the»scale of publication. This admits of an error upon the ground
not greater, on a scale of 1:62500, than 50 feet.
The second condition of correctness, that is, the number of locations
necessary for the proper control of the work, is not easily defined. The
requirements difi'er with the character of the country. A region of great
detail and of abrupt features requires more control than one of great uni-
formity and gentle slopes and of large features, so that no general rule can
be laid down. Furthermore, it depends upon the quality of the sketching ;
with indifferent sketching a greater number of locations is required in order
to bring the map up to the requisite quality.
The following table presents a summary of the amount of control
obtained during the field season of 1891 in the diff"erent fields of work in
this survey. It is presented not as a type of what should be, but to show
what has been done and also to illustrate the wide range in the amount of
control brought about by the differences in the character of the country'
and methods of work.
12
A MANUAL OF TOPOGRAPHIC METHODS.
Statistics of control , fu'W neason 1S91.
Area surveyed, square miles
Triangulation statioas
Kumber of square inches per station
Points located by triimgulation
Triangulation stations and located points .
Number of above locations per square inch
Number of miles traversed
Incbes traversed per square inch - . .'
Number of traverse stations
Traverse stations per square inch
Total number of locations per square inch.
Traverse stations per linear mile
Heights measured instrumentally
Heights measured by aneroid
Total number of measured heights
Heights per square inch
Northeast
division,
New
Enu'laud,
Vorlv
and Penn- Atlantic
sylvania. Plain.
Southeast
division,
Appalachi-
an rosion
an^
113, 600
50. 1
56.8
48, 880
56, 680
Central division.
1,276
4,034
5,310
3,450
13, 100
16, 556
56.1
66.1
9,690
9,820
26.5
As the reader will observe, the amomit of control of various sorts is
given in the above table with reference to areas in square inches upon the
map as published. It is given in these terms in order to eliminate from it
the question of scale.
No statistics of horizontal control are given for the areas surveyed in
Wisconsin, Illinois, and Kansas, because most of it is furnished by the
surveys of the General Land Office, and therefore the presentation would
be but a partial one.
There are two general methods for location of stations and of minor
points for the coiTection of the sketch, the one by angular measurements
(triangulation), the other by measurement of directions and distances,
or what is known popularly as the traverse or meander method. In ordinary
practice, work may be done by either of these two methods, or they may
be used in conjunction. The former of the two methods may be carried on
with the plane table, various forms of the theodolite, with a compass, or,
indeed, with an angle-reading instrument. The latter method may be car-
ried on with the same instruments, supplemented by various forms of odom-
eters, chain, steel tape, stadia, etc., for the measurement of distance. The
first method, whenever it can be used economically, is the most accurate,
METHODS OF CONTEOL. 13
and is, as a rule, the most rapid, and the locations are likely to be of the
greater service and distributed most uniformly. It can be used eco-
nomically where the country presents more or less relief, and where
points for location, either natural or artificial, exist in sufficient numbers
and are well distributed. These conditions are satisfied almost every-
where in the western mountain regions, where mountain peaks, summits
of hills, plateau points, buttes, etc., furnish an abundance of natural
points for stations and locations. It can be used, to a considerable
extent, though not with the same ease or economy in the Appalachian
mountains; but in this region it is necessary to supplement it extensively
by traverse lines, especially in tracing the courses of streams in the valleys.
It can be used, too, in the hill country of New England, where objects of
culture, such as churches, houses, etc., furnish an abundance of signals. On
the other hand, throughout the whole extent of the Atlantic and the Gulf
plains, where the country is level or nearly so, and is covered with forests,
the tra,verse method of surveying must be resorted to. This is a country
devoid of sharp natural objects, a country in which extended views can not
be obtained. The only economical way, therefore, of proceeding, is, start-
ing from some point located by the triaugulation, to carry a line of stations,
connected together by distance and direction measurements, until the line
checks upon a second triangulation point. For many reasons, this method
of obtaining locations is inferior to the former. It is inferior not only in
accuracy, but in the facilities which, as carried out, it affords for sketching
the country, and it should be so regarded, and should be adopted only when
it becomes necessary, or when the former method can not be appHed eco-
nomically. For convenience, traverse lines are generally run along the
roads or trails, and thus the best points for commanding views of the country
are avoided rather than sought. Being practically confined to the roads,
there is danger that the topographer neglects, in a greater or less measure,
the areas lying between them. On account of the errors incident to run-
ning a traverse it is necessary that, in this class of work, frequent locations
be made by triangulation for checking and thereby eliminating its errors.
The locations dealt with in the above table fall into one or the other
of these two classes. Locations by triangulation are of much greater value
14 A MANUAL OF TOPOGEAPHIC METHODS.
than those by traverse. As a rule, they are selected points chosen because
each controls positions in a certain area. On the other hand, traverse loca-
tions are not, as a rule, chosen for then control value, but only for inter^dsi-
bility on roads. Furthermore, the great majority of traverse stations are of
no service whatever beyond carrying the line forward, so that in estimating
the total amount of control in a certain area where the control is made up
in whole or in part of traverse lines, less weight should be given to them
than to locations by triangulation.
The third element of accuracy, the distribution of locations, is a point
concerning which it is equally difficult to speak definitely. Other things
being equal, the disti'ibution should be uniform over the area, but it will
necessarily vary with the character of the surface. The accompanying
diagram shows the amount and distribution of control in a typical piece of
work. In general, in the mountain regions, locations by angular measure-
ments are frequent and accompany the ranges or ridges, and such locations
are few in number in the valleys, being supplemented there by traverses.
The fourth of the elements of the correctness of the map depends upon
the artistic sense of the topographer, upon his ability to see things in then-
proper relation, and his facility in transferring his impressions to paper.
This is by far the most important and the most difficult to meet.
The education of the topographer, therefore, consists of two parts — the
mathematical and the artistic. The first may be acquired largely from
books, and this book knowledge must be supplemented by practice in the
field. The second, if not inherited, can be acquired only by long experi-
ence in the field, and by many can be acquired only imperfectly. In fact,
the sketching makes the map, and, therefore, the sketching upon the Oeo-
logical Survey is executed by the best topographer in the party, usually its
chief, whenever it is practicable to do so.
BUCKHANNON, W. VA,, SHEET.
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. II.
8
,^>^ (^- '^°^'
y- * '^/r-^
s
s
PI
Diagram. sliCf\Fm^ diartxitTitLon o£ control work
Statute Miles
Main and. Secotndanrr stalioxis.
inters ecti-ons firom. stalians .
Intersec'tiums £:onL ■trar-erse .
Traversed Roads or Trails
'^'
CHAPTER II.
CLASSIFICATION OF WORK.
The Avork involved in making a map usually comprises several opera-
tions, which may in practice be more or less distinct from one another.
They are enumerated as follows:
First— The location of the map upon the earth's surface, by means of
astronomic observations.
Second. — The horizontal location of points.
This is usually of thi-ee grades of accuracy, primary triangulation, or
primary traverse, in cases where triangulation is not feasible; secondary
triangulation for the location of numerous points within the primary triangu-
lation; and ordinary traverse, for the location of details.
XJiircl— The measurement of heights, which usually accompanies the
horizontal location, and which may, similariy, be divided into three classes,
in accordance with the degree of accuracy.
Fourth. — The sketching of the map.
Nearly all of the geometric work of the Survey, the work of location,
is executed by five instruments.
Theodolites, of a powerful and compact form, used in the primary
control.
Plane tables, with telescopic alidades of the best type, used for second-
ary triangulation and height measurements.
Plane tables, of crade, simple form, with ruler ahdades, used for
ti-aversing and minor triangulation.
Odometers, for measuring distance.
Aneroids, for the measurement of details of heights.
1(^ A MANUAL OF TOPOGEAPHIC METHODS.
With these instruments nine-tenths of the work is done, and these
instruments will be described in their proper places with such fullness of
detail as seems necessar)^
Other instruments, such as transits, surveyors' theodolities, compasses,
wye levels, hand and Abney levels, telemeters, chains, tapes, and mercurial
barometers, are occasionally used. Most of these instruments, which are
commonly figured and described in all works on survejang, are assumed to
be well known to the readers of this manual and will therefore receive no
special attention.
ASTRONOMIC DETERMINATIONS OF POSITION.
The object of astronomic determinations of position is to locate the
map upon the earth's surface. They are made also for the purpose of
checking and correcting positions determined by primary triangulation and
primary traverse.
With regard to the checking of the primary triangulation by astronomic
determinations, it should be understood that in the case of a single determi-
nation -the work by triangulation is far more accurate than by astronomic
determinations, even when made iinder the best of circumstances. It is,
therefore, desirable to introduce checks of this kind upon primary triangu-
lation only when the latter has been carried for a long distance, 200 or 300
miles, for instance, in the course of which it may have accumulated errors
greater than those incident to astronomic work.
The case is different with primary traverse. The great number of
courses required in this work affords an opportunity for the accumulation
of error much greater than is the case with triangulation, and consequently
it is desirable to introduce more frequent checks in this work. It may be
said that, in general, such work should be checked at every 100 miles.
As was suggested above, the best astronomic determinations are none
too good for the control of maps. Indeed, certain errors hicident to this
work, some of which as yet can not be corrected, may be of magnitude
sufficient to show upon the scale of the map. It is necessary, therefore, in
these determinations to use the best instruments and the most refined
ASTRONOMICAL DETEEMESTATIONS. 17
methods known to modern science, in order to reduce all avoidable errors
to a minimum.
Whatever determinations have been made by the U. S. Coast and
Geodetic Survey, the United States Lake Survey, or the Mississippi River
Commission, whether by astronomical work or by triangulation, these posi-
tions may be utilized for the above purposes.
DEFmiTIONS.
Sidereal time is the time indicated by the stars, a sidereal day beinp^
the time which elapses between two passages of the vernal equinox across
the meridian. Solar or apparent time is the time measured by the sun's
apparent movement or the revolution of the earth with reference to the sun,
and since the earth revolves at a differing rate in different portions of its
orbit, the solar days are not of equal length. A mean day is the average
solar day; mean time differs from solar time by an amount which varies
with the time of year, and which, under the name of " equation of time," is
given in the Nautical Almanac. Mean time differs from sidereal time by
about a day in the com'se of a year, or about four minutes in each day;
the mean day being longer than the sidereal day. To convert a given date
of mean time into sidereal time it is necessary to obtain, from the Nautical
Almanac, the sidereal time at noon immediately preceding the date in ques-
tion. Then the interval after noon, expressed in mean time, is converted
into sidereal time by table xxxii in this volume, and the result added to the
sidereal time of mean noon. Local time, whether sidereal, solar, or mean,
is the time of the locality as distinguished from the time of any other
locality. It must be distinguished from railroad time, which is the local
time only of certain meridians.
The right ascension of the sun or a star is the sidereal time which has
elapsed between the passage of the vernal equinox and the star across the
meridian. It is commonly expressed in hours, minutes, and seconds.
Declination is the angular distance of a heavenly body north or south
of the equator. It is plus when north and minus when south of the equator.
The zenith distance of a heavenly body equals its declination, minus
the latitude of the place of observation.
Latitude is determined by what is known as Talcott's method, by
MOKf XXII 2
18
A MANUAL OF TOPOGRAPHIC METHODS.
measuring the differences of zenith distance at cuhnination of two stars
which cuhninate on opposite sides of the zenith.
Longitude is determined by telegraphic comparison of local time at
two stations, the longitude of one of which is known. This involves the
determination of the errors of the clocks or chronometers used, which is
done by observation of transits of stars across the meridians of the places of
observation.
ASTRONOMICAL TRANSIT AND ZENITH TELESCOPE.
A single instrument is used for the determination both of latitude and
time. This is a combination of
the transit aiid zenith telescope.
The instruments in use upon the
Geological Survey were made by
Saegniuller and embody the latest
improvements in these combined
instruments. One of them is fig-
ured herewith. The circular base
rests upon three leveling screws.
Upon this circular base the whole
instrument can be made to re-
volve when using it as a zenith
telescope A circle is graduated
around the base, having a microm-
eter screw for slow motion, for
making settings and adjusting the
instrument in azimuth. The frame
of the instrument is cast in one
piece, and the standards are hol-
low in order to reduce the weight
of the upper part of the instrument.
The telescope has a focal distance
of 27 inches and a clear aperture
Fig. 1.— Astronomical transit and zenith telescope. pf 2.5 inchcS. ItS magnifying
power with diagonal eyepiece is 74 diameters. The length of the axis of
ASTEONOMICAL DETEEMINATIONS. 19
the telescope is 16 inches. For use as a zenith telescope, the telescope is
equipped with a vertical circle reading by vernier to 20 seconds, attached
to which is a delicate level. In the focus of the object-glass there is, besides
the ordinary reticule for use in transit work, a movable thread, which is
moved by means of a micrometer screw, by which measurements of differ-
ences of zenith distances are made. It is furnished with direct and diagonal
eyepieces, the latter of which is commonly used in astronomical work.
For use as a transit instrument, the telescope is equipped with a deli-
cate striding level for measuring the inclination of the pivots, and a revers-
ing apparatus for turning the telescope in the wyes. The reticule, as the
stationary threads in- the focus of the instrument are called, consists of five
threads for observing the transits of stars. The reticule is illuminated by
means of bull's-eye lamps, the light from which comes through the hollow
axis of the telescope and is reflected by a mirror placed at the intersection
of the telescope with its axis.
CHRONOGRAPH.
The chronograph is used for the purpose of recording the time of
transits of stars as observed with the transit instrument. It may be popu-
larly characterized as an instrument for measuring time by the yard. It
consists essentially of a drum, upon which is wound a strip of paper, and
which is kept in revolution by .a train of clockwork controlled by an escape-
ment. A pen carried upon a small car, which is moved very slowly in a
direction parallel to the axis of the cylinder, traces a spiral line upon the
paper on the drum. This pen is held in place by a magnet, which is carried
upon the car, and as long as the current from the battery passes through
the coil and thiis holds the armature the pen traces an unbroken spiral line.
If the current is suddenly broken and restored, the armature is set fi-ee for
an instant and a jog is made in the line traced. The battery commonly
used in connection with this outfit is the ordinary zinc, copper, and sulphate
of copper battery, of which four cells are usually required. The ordi-
nary dry battery can also be used and is much more convenient. With this
apparatus break-circuit chronometers are used. These difi^'er from ordinary
chronometers in the fact that they are arranged to break an electric circuit
20
A MANUAL OF TOPOGEAPHIC METHODS.
automatically at regular intervals. Those in use upon the Geological Sur-
vey break the circuit every two seconds, and the end of the minute is indi-
cated by breaking at the fifty-ninth as well as the fifty-eighth and sixtieth
seconds. When one of these chronometers is coimected with a battery and
a clu'onograph is put in the same circuit, the beginning of every even sec-
ond is recorded upon the chronograph by a jog on the paper, and the dis-
tance between the jogs in each case represents, therefore, two seconds. The
observer at the instrument is provided with a telegraph key, which may also
be put in the circuit with the clu'onometer and chronograph, and as a star
Fig. 2. — Chronograph.
near the meridian crosses a thread in the telescope he records that fact by
pressing on the key, which makes a record upon the chronograph along
with the record of the chronometer.
An illustration of the form of clu-onograph in use upon the Geological
Survey is shown upon Fig. 2.
FIELD WORK.
Since the observations for latitude and longitude, though different,
are made with the same instrument, at the same time, and by the same
party, certain parts of the work apply equally to both determinations and
may be described once for all.
ASTEONOMICAL DETEEMINATIONS. 21
lu the selection of a station, care must be taken to avoid a locality
where, for any cause, the ground is liable to be seriously jarred, as, for in-
stance, proximity to a railroad track or to a street over which heavy
wagons pass. It should have a clear view from the southern horizon through
the zenith to the northern horizon. It is desirable to locate at a convenient
distance from a telegraph station, as it is necessary to bring a wire in from
siTch station for the purjDOse of comparing chronometers. If possible, the
station should be selected upon a public reservation, in order that the per-
manence of the monument marking the spot, which is to be erected, may
be assured. But, in any event, one should avoid a locality in which such a
monument is likely to be disturbed.
The support of the instrument should consist of a brick pier sunken
fully three feet in the ground and rising above it to the requisite height.
Upon this should be placed for the immediate support of the instrument, a
block of stone well set in mortar. The cln-onograph may be set up on an
ordinary table. Over all should be erected a wall tent with a slit closed
by flaps in the roof, which can be opened when observing. The instrument
is set up upon the pier, collimated, leveled, and the verticality of the
threads tested as accurately as possible, and is then pointed upon the pole
star. This places it somoAvhere near the meridian. Then taking the time
of transit of a star which culminates close to the zenith, and comparing this
time with the right ascension of the star, a sufficiently close approximation
to the clock error is obtained for use in placing the instrument in the meri-
dian. The instrument is then turned in azimuth to point upon some close
circum-polar star approaching upper or lower culmination, mo\ang the in-
strument in azimuth with the tangent screw so as to keep the star under
the middle wire up to the instant of culmination. If this is done accurately
at the first attempt, the instrument is placed nearly in the meridian and is
ready for work, but it commonly happens that more than one trial is
required before the meridian is reached. In any case, the result should be
verified by a second star, before proceeding with the observations.
OBSERVATIONS FOR LATITUDE.
As preliminary to this work it is necessary to prepare a list of pairs of
stars, the two stars of each pair liaving such zenith distances that they will
22 A MANUAL OF TOPOGRAPHIC METHODS.
culminate at nearly equal distances from the zenith, one to the north and
the other to the soiith of it. Such a list can be prepared from the Saffbrd
•Catalogue of the Wheeler Survey. For this it is necessary to know the
approximate latitude of the station, the right ascensions and the declina-
tions of the stars. The zenith distance of a star is equal to its declination,
minus -the latitude of the place. The stars of each pair should culminate
within a few minutes of one another. They must be observed consecu-
tively, and, therefore, those stars should be selected which culminate as
nearly as possible together, leaving only a sufficient interval of time
between them for setting the instrument.
Before beginning to observe, the instrument should be closely coUimated
and di'awn into the meridian.
Upon the approach of the first star of the pair to the meridian, the
instrument shoidd be set for it, using the vertical circle for that purpose,
and setting the spirit level upon the vertical circle as nearly level as possi-
ble. Then, as the star traverses the field of the telescope, keep the movable
thread in the reticule upon it by means of the micrometer screw until it
crosses the middle vertical thread. Then read and record the micrometer
and the two ends of the level bubble. Without disturbing in the slightest
degree the setting of the telescope, turn the entire instrument 180° upon its
bed plate, when it will point north of the zenith, at the same angle that it
formerly pointed south, or vice versa, as the case ma,y be, and will be set
for the other star upon the opposite side of tl'e zenith. As this approaches
culmination, follow it with the micrometer as before, until it reaches the
middle thread; then record as before the readings of the micrometer and of
the level, whether it has changed or not.
This constitutes the observations upon a single pair of stars. For the
determination of latitude twenty such pairs of stars should be observed
each evening, if possible, and the same pairs of stars should, also assuming
it to be possible, be observed upon other evenings. The following exam-
ple, taken from observations at Rapid, South Dakota, shows a portion of
the star list and the form of record:
ASTRONOMICAL DETEEMINATIONS.
23
LATITUDE DETERMINATION.
List of Stars, for Observation icith Zenith Telescope.
[Station: Eapid, Sowth Dakota. Approximate Latitude: 44° 05'.]
Name or
number.
Saftbrd's Cat-
alogue.
Mag.
Class.
E. A.
Dec.
Zen
dist.
Setting.
7 LacertcE
10 Lacertje . . .
4.0
5.0
6.5
6.5
6.5
5.0
6.0
0.7
5.6
6.5
4.5
6.5
A A
A A
B
A
C
A
A
B
A
A
A
B
h.
22
22
22
22
22
23
23
23
23
23
24
27
34
41
47
59
08
18
42
47
52
00
49° 43'
38 29
45 37
42 42
38 42
49 26
56 34
31 56
67 12
21 03
24 32
03 35
5
1
1
12
12
23
23
19
19
38' is".
36 S.
32 N.
23 S.
23 S.
21 N.
29 If.
09 S.
07 N.
02 S
33 S.
30 N.
1 5 37 N.
^ 1 27 N.
J 5 22 S.
1 12 19 ST.
I 23 05 N".
|l9 31 S.
1676
1686
1722
Example of Record.
[Station: Rapid, South Dakota. Date; November 9, 1890. Instmment: Fautli combined transit and zenith teleacop
No. 534. Obseiver: S. S.G. Eecorder; A.F.D.]
Star name or
number.
N.or
S.
— «
Microm-
eter
reading.
Diff.
Level.
(N+S)
-(N'+S')
Remarks.
N.
S.
7 Lacertas
lOLaoerta)
N.
S.
N.
S.
S.
N.
N.
S.
N.
S.
S.
N.
Eev.
26. 256
24. 052
30. 432
20. 095
25.164
26. 703
32. 214
16. 033
26. 656
17.684
25. 345
23. 722
Sev.
—2.204
-10.337
+1. 539
-16. 181
-8. 972
+1. 623
Div.
39.9
26.5
42.0
21.9
14.1
38.1
37.5
19.9
51.0
17.0
18.0
36.0
Div.
16.7
49.7
18.7
45.0
37.6
15.0
14.1
43.1
28.0
39.6
40.9
13.2
Biv.
+56. 6
—76.2
-19.6
+60.7
—66.9
- 6.2
-51.7
+53.1
+ 1.4
+51.6
-63.0
-11.4
+79.0
—56.6
-22.4
-58.9
+49.2
- 9.7
Faint.
Distinct.
Faint
1686
1722
REDUCTION OF LATITUDE OBSERVATIONS.
Before proceeding with the reduction of latitude observations, it is nec-
essary to investigate tlie constants of the instrument, to ascertain tlie value
of a division of the latitude level, and of a division of the head of the
micrometer screw.
The value of a division of the head of the micrometer screw is measured
24 A MANUAL OP TOPOGEAPHIO METHODS.
by observing- the transits of some close circumpolar star, when near elong-a-
tion, across the movable tlu-ead, setting the thread re^oeatedly at regular
intervals in advance of the star, and taking the time of its passage, with the
reading of the micrometer. The precaution should be taken to read the
latitude level occasionally and correct for it if necessary. This correction,
which is to be applied to the observed time, is equal to one division of the
level, in seconds of time, divided by the cosine of the declination of the
star and multiplied by the level error, the average level reading being
taken as the standard.
The time from elongation of the star requires a correction in order to
reduce the curve in which tlie star apparently travels to a vertical line.
The hour angle of the star is first obtained from the equation,
cos t^ zz cot d tan q),
S being the star's declination and q> the latitude.
. The clu'onometer time of elongation, To zz a — t^ — St, a being the
right ascension of the star obtained from the JsTautical Almanac, and U the
error of the chi'onometer.
Ha^ang thus obtained the cln-onometric time of elongation, the correc-
tion in question is obtained from the observed interval of time of each ob-
servation before or after elongation, from tables in Appendix No. 14, U. S.
Coast and Greodetic Survey Report for 1880, pp. 58 and 59. A discussion
of tliis subject will be found in the appendix above referred to, and in
Chauvenet's Practical Asti-onomy, vol. ii, pp. 360 to 364.
The times of observation thus corrected for level, and distance from
elongation, are then grouped in pairs, selected as being a certain number of
revolutions of the micrometer apart, and the time intervals between the
members of each pair obtained. The mean of these, divided by the sum of
revolutions which separate the members of each pair, is yet to be corrected
for differential refraction, which is derived from the following equation:
Ref. — bl" .7 sin B sec^ Z.
R being the value of a division of the micrometer and Z the zenith distance of
the star. Four-place logarithms are sufficient for computing this correction,
as it is small. Below is given an example of record and computation of the
value of a revolution of the micrometer of combined instrument No. 534,
one of the two in possession of the Greological Survey.
TABLE OF DETEEMINATION.
25
fei=;;
oi
'if
m. s.
15 37.7
36.6
34.4
39.2
40.2
36.9
36.8
37.5
36.2
29.6
33.1
36.5
31.3
36.2
15 35.80— mean
o
"1 , ^
S i
O CO
II
. 2!
1
?
1i
ill
tbiifc
i
1
ibifc
=. '^ fc. :
1 t^ K ■
; " b ■
g 3 3 ;
i \ •
1 1 i
ll
s
£ 0.-I
'■ t-^ d d d rH
■ OOOOClOiH
rHD^ddj^dddt^g
co-*in!DOc-oo«or:;
:g3SSS3SSS5S
!cgC0'*lOt0l>Q0C0C5Or-*
|OOOOOOOOOrH.-(
i1-
■*CO
dddd ■
+-i-4-h :
• W<MMt--(iH
■ ddddd
.-lOOOOOOOOOOOOOOO i-Hy^ 1-4 CQ IM CO
ddddd dddd ddddd ddddd odd
++ ■ +1 1 1 1 1 ! 1
So
§g"
"7"
j ^ « o" CO a5
o6i-JMdcddd-*t--d
COTj<ir5lOOrH(MCOr-!0
1 +
■ j^'*coirid'*'*i>odd-^
.in^cowi-H'HOLrs^'S'CQ
S g i s
inco ,-,ccinMocoinoor-4i-HOOCiC50sc:C!CiC30Jooooi>oo»Oin'*ii«MrHomcDoa
.^^ rHOdoOOOOr^rHrHrHOOodoOOOOOOdoOOOOOOOOOO
++ +++++I 1 1 1 M . 1 1 1 M 1 1 1 1 1 1 1 1 M 1 1 1 : I+++
J!
+
o
1
■d
: 1
1 :
°
;°
o
+
•3 «^ ■
o +
Is
si
s
:S
s •
o
s
is
i
II
5
3J
3
-
;t^
S ^
o
b
s I
^
t-"
3
1 ^
3;
i
;b^
"' :
•enoiitix
•OAOI 1918
-raojotit
om omotooinomoiaomomooomoiooifloirioioomomomomo |
T-H d d d d oc cc t>^i> d d lOiri -^ -* CO co^ M r-H i-id d d d c6c«5 c^t- d diriifi**-^ coco •
Time of observa-
tion (recorded
on chronograph
sheet) .
•^8 |l ~" • "
26
A MANUAL OF TOPOGEAPHIG METHODS.
The value of a division of the level is commonly measured with a level
trier. The latitude level may, however, be easily measured by means of
the micrometer, the value of a revolution of that being obtained by the fol-
lowing method:
Point the telescope upon some well-defined terrestrial mai-k and set
the level at an extreme reading near one end of the tube. Set the movable
thread upon the object and read the micrometer and the level.
Now move the telescope and level, until the bubble is near the other
^nd of the tube. Again set the movable tlu-ead upon the object and again
read both micrometer and level. It is evident that the micrometer and the
level have measured the same angle, and that the ratio between these read-
ings equals that between h revolution of the micrometer and a level division.
An e:5ample illustrative of this is appended.
Determination of I'alue of 1 division of latitude level No. 534.
[By comparison with micrometer screw 534 ]
Microme-
ter.
Level.
Diffei
enCB.
aa.
ab.
N.
S.
Microm.
Level.
r.
8.025
8.508
d.
47.3
20.7
d.
29.2
02.7
b.
d.
48.3
a.
d.
26.55
704.9
1283.
8.509
7.984
18.9
49.8
01.0
31.0
52.5
30.45
927. 2
1599.
8.511
8.045
18.5
47.2
00.6
29.1
46.6
28.60
818.0
1333.
9.076
8.604
18.7
46.0
00.8
28.0
47.2
27.25
742.6
1286.
9.442
9. 009
23.7
48.0
06.0
30.0
43.3
24.15
583.2
1046.
10. 055
9.574
21.8
48.0
04.0
30.1
48.1
26.15
683.8
1258.
10.661
10. 212
24.0
50.7
06.1
83.0
44.9
26.80
718.2
1203.
11.771
1].252
18.3
48.3
00.7
31.9
51.9
30.60
936.4
1588.
12. 328
11.872
20.0
46.1
02.3
28.5
45. C
26.15
683.8
1192.
12. 869
12. 438
22.2
47.7
04.6
30.0
43.1
25.45
647.7
1097.
13. 468
13.080
23.0
44.5
05.3
26.9
38.8
2L55
464.4
836.
14. 146
13.702
20.1
45.4
02.4
27.8
44.4
25.35
642.6
1125.
14. 758
14. 282
Sum.
22.3
48.6
04.8
31.0
47.6
26.25
689.1
1249.
9241.9
16095.
log 16095. =4.20669.
A. C. log 9241.9 = 6.03424.
log 1 Div. Micrometer =9.87966.
IDiv. level =1".320 log. =0.12059.
LATITUDE DETERMINATION. 27
Following the determination of the constants of the instrument used,
the next step is to obtain the apparent declinations of the stars used. When-
ever possible, these should be taken from the Nautical Almanac or the
Berliner Jahrbuch. In other cases they must be computed. The positions
of stars are given in Safford's Catalogue, for the epoch 1875.0, together with
the annual precession and proper motion. The declinations there given
should be revised by the aid of more recent catalogues, particularly with
reference to stars of class C. The annual precession and proper motion
multiplied by the number of years which have elapsed and applied, together
with the effect of secular variation in precession, give the declination at the
beginning of the'year. Further corrections to bring the positions down to
the date of observation are expressed by the symbols Aa', Bh', Cc', Dd'.
Logarithms of a', b', c', d' are given in Safford's Catalogue, and A, B, C, and
D are given in the Nautical Almanac. A slight additional correction, also,
is to be made for proper motion, for the elapsed portion of the year. This
reduction is illustrated below.
LATITUDE DETERMINATION.
Example of reduction. Computation of apparent declination of star 1539.
[From Safford's Catalogue, p. 40.]
Star No. 1539
Yr.
(1890-1875) X 18. 87= +4 43. 05 = Precession for 15 years.
15X— .03= —0 00. 45 = Proper motion for 15 years.
+ 0 00. 07 = Seciilar variation in precession.
Declination, 1875.0 p^eees"sl.
45 33 29.20 , ^'J g,
Propter
tnotioc.
—.03
45 38 11. 87 = Declination 1890.
+ 9.38= Aa'
— 0. 78 = B b'
+ 6.88=C<-'
+ 10. 36=D(1'
— 0.03 = Proper motion, Jan. 1— Nov. 9, 1890.
45 38 37. 48 = Declination Nov. 9, 1890.
0. 9723
a' = + 9. 38
With all this preliminary work done, the reduction proper of latitude
observations is comparatively a simple matter. Grrouping the observations
by pairs, the mean declination of each pair is obtained, the corrections for
28
A MANUAL OF TOPOGEAPHIC METHODS.
difference of niicrometei' readings and levels are applied, witli a small cor-
rection for differential refraction, and the result is the desired latitude.
Following is an example of the reduction of six pairs of stars observed
for latitude at Rapid, South Dakota:
LATITUDE DETERMINATION.
Example of Eediiction.
[Station: Eapid, Soutli Dakota. November 9, 1890. Half Eev. Micrometer=37.900. One Div. Level-.:1.33.]
Date.
Star num-
bers.
i.
i2
Hh + ii)
Corrections.
Latitude
n.
Weight
P-
p. n.
Microm.
Level.
Eefr.
Not. 9.
JTLacertandJ
\ lOLacert. S
«
42
87.33
38
29
04.60
44 06 15.97
— 1
23.53
-6.51
—.03
44 04 45.90
.98
5.78
1539 1551
45
38
37. 4S
42
44
04.63
11 21.06
- 6
31.77
—2.06
—.11
47.12
.90
6.41
1565 1579
38
43
39.78
49
27
41.04
05 40.41
- 0
58.33
+0.46
—.03
42.51
.79
1.98
1600 1633
56
34
06.66
31
55
56.91
15 01.78
-10
13.25
-3.78
-.19
44.56
.90
4.10
1676 16S6
67
12
10.93
21
03
54.02
08 02.48
- 3
08.43
-7.44
-.07
46.54
.93
6.08
1702 1722
21
32
09.04
63
35
27.34
03 48.19
+ 1
01.51
-3.23
+.02
46. 5U
.90
5.85
5.40
30.20
November 9. "Weighted mean =44° 04' 45.59".
OBSERVATIONS FOR TIME.
With the transit mounted, leveled, and adjusted in the meridian, the
chronograph set up and rumaing and connected in a circuit with the battery,
and the chronometer and observing key connected in the same circuit the
observer is prepared to begin time observations.
The list of stars which should be used is that given in the Berliner
Jahrbuch as the list is fuller and more accurate than that in any other cat-
alogue which gives day places. Stars should be so selected north and south
of the zenith tliat the azimuth errors will balance one another as nearly as
possible, as is explained hereafter. On the approach of the selected star to
the meridian, the telescope is set by means of the vertical circle upon the
altitude of the star above the horizon, deduced from the declination and the
latitude. As the star crosses each tln'ead in the reticule, the fact is recorded
by pressing the observing key, which produces, as described above, a record
upon the chronograph sheet. In this way four time stars, as stars between
the equator and zenith are designated, and one circumpolar star, or a star so
near the pole that it is constantly in sight, should be observed. Then the
telescope should be reversed in the wyes and a similar set of stars observed.
OBSEEVATIONS FOE TIME. 29
«
Between observations upon any two stars the striding level sliotild be
placed upon the pivots of the instrument and readings taken to ascertain
the departure of the axis from a horizontal position.
In order to avoid unequal expansion of the pivots from unequal heat-
ing, both bull's-eye lamps must be lighted and placed in their stands, in
order that both pivots may be equally heated.
After the comparison of chronometers at the two stations, to be here-
after described, a similar set of stars should be observed, if possible.
EEDUCTION OP TIME OBSERVATIONS.
Certain constants of the transits should be measured before proceeding
with the reduction of time observations. The value of a division of the
striding level should be measured by means of a level trier. The equatorial
interval of time between each of the threads and the mean of all the threads
should be obtained, as it is not infrequently needed in utilizing broken or
imperfect observations. These can best be obtained from observations on
slow moving stars, but any stars may be used for the purpose. The inter-
vals as observed, are reduced to the equator by multiplying them by the
cosine of the declination of the star observed.
The object of these observations is specifically the determination of
the error of the chronometer. This error equals the right ascension of a
star minus its observed time of transit, corrected for certain instrumental
errors. These errors are as follows:
CORRECTION FOR ERROR OF LEVEL.
The level error, designated by h, is ascertained from the readings of
the striding level. The value of a division of the level in seconds of time
must have been previously ascertained by means of a level trier. The
effect of the level error is greatest at the zenith and diminishes to zero at
the horizon. The correction hi seconds of time is given by the following
equation:
Coring cos (9-f^) sec f5 — ?)B.
When the declination is north, it is to be regarded as having a plus
sign for upper and a minus sign for lower culmination. When south it is
negative.
30 A MANUAL OF TOPOGRAPHIC METHODS.
CORRECTION FOR INEQUALITY OF PIVOTS.
This correction can be made a part of the level correction.
Let p = tlie inequality of pivots.
B = iuclinatiou of axis giveu by level for clamii west.
B'= inclination of axis given bj' level for clamp east.
h = true inclination of axis for clamp west.
h'= true inclination of axis for clamp east.
,, B'-B
then p—
4
h = 'B + J) for clamp west.
h' = W — p for clamp east.
(Gliauvenet, vol. ii, p. 155.)
CORRECTION FOR ERROR OF COLLIMATION.
This correction, designated \>y c, is the departure of the mean of the
tkreads from the optical axis of the telescope. For stars at upper culmina-
tion with clamp west it is plus when the mean of the threads is east of the
axis, and minus when it is west of it. For stars at lower culmination the
reverse is the case. The value of c is one-half the difference between the
clock error indicated by stars observed before and after reversal of the
instrument, divided by the mean secant of the declinations of the stars.
This is slightly complicated with the azimuth, although the effect of that is
largely eliminated by the proper selection of stars. Consequently it is to
be obtained by approximations, in conjunction with the azimuth errors.
The correotion to be applied to each star equals c sec S zz cC, which is plus
for a star at upper culmination and minus for a star at lower culmination.
It is least for equatorial stars and increases with the secant of the declination.
CORRECTION FOR DEVIATION IN AZIMUTH.
This coiTection, designated by a, represents the error in the setting of the
instrument in the meridian. Its effect is zero at the zenith and increases toward
the horizon. Since the instrument is liable to be disturbed during the oper-
ation of reversal, it is necessary to determine the azimuth error, both before
and after reversal, separately. A comparison of the clock error, determined
from observations upon north and south stars, will furnish the data neces-
OBSERVATIONS FOE TIME. 31
saiy for the determinatiou of azimuth. Practically, it is determined by
elimination from equations involving the mean of all these stars observed
in each of the two positions of the instrument, after coiTecting- for level, and
as it is slightly complicated with coUimation it must be reached by two or
more approximations. The eiTor is essentially positive when the telescope
points east of south, and negative when west of south. The correction
applicable to any star is expressed in the following equation:
Cor. — « sin (9 — d) sec S=zaA.
It must be understood that the declination when north is positive for
upper and negative for lower culmination, and that with south declination
it is negative.
COERECTION FOE DIURNAL ABERRATION.
The right ascension of stars, as taken from the Berliner Jahrbuch, must
be corrected for diurnal aberration, which equals 0'.021 cos q) sec S. This
correction is positive for upper and negative for lower culmination.
These corrections are suunnarized in the following equation:
J t—a— (^+aA+&B+cC).
A, B, C, as seen above, are constants, depending upon the latitude of
the place of observation and the declination of the star. Tables for these
quantities will be found in an appendix to Annual Report U. S. Coast and
Geodetic Survey for 1874.
The following is an example of the form for record of observation and
reduction of time observations, taken from a campaign for the detennination
of position of Rapid, South Dakota.
32
A MANUAL OF TOPOGKAPHIC METHODS.
Time determination: Example of record.
[Kapid South Dakota, November 20, 1890. Fauth transit, No. 534. Sidereal chronometer: Bond Si, Sons, No. 187
1 divi.sion ol' level = 0" .118. Hourlyrate of chronometer = 0". 133.]
y Cephei.
*
Pegasi.
u Pisciura.
33 Piscium.
a Androm.
Cl-.m
W.
W.
W.
W.
■w.
W.
Level .;
Difference =
telescope north
TT. Sum. E.
d d d
ID.S -88.1 68.3
68.2 +87.6 19.4
- 0.5
telescope south.
W. Sum. E.
d d d
68. 0 +87. 1 19 1
20. 2 —89. 2 69. 0
— 2.1
telescope south.
TT. Sum. E.
Add
20. 0 —89. 5 69. 5
68.8 +87.2 18.4
— 2.3
telescope south, telescope south.
W. Sum. E. W. Sxtm. E.
d d d d d d
68. 2 +86. 9 18. 7 19. 8 —89. 3 69. 5
19. 9 —89. 4 69. 5 68. 3 +86. 8 18. 5
— 2. 5 — 2. 5
telescope north.
W. Sum. E.
d . d d
19. 7 —89. 5 69. 8
68.8 +87.3 18.5
-2.2
h.
23
23
6B
23
23
m. «.
34 52. 25
35 11.40
29.41
46.78
36 05.00
= 4.84
35 28.97
-.07
—.22
+.(15
35 28. 83
34 53. 13
h.
23
23
23
47 24.00
28.55
32.72
36.75
41.09
3.11
47 32.62
—.02
-.06
+.03
47 32. 57
40 55.67
h. m. s.
23 54 10. 89
14.88
19.22
23.14
27.20
5.33
23 54 19.07
—.02
—.05
+ .01
23 54 19.01
53 41.98
—37.03
h.
00
00
00
23
m. s.
00 13.33
17.96
21.94
25.95
29. 83
9.01
00 21.80
—.02
—.04
+.00
00 21.74
59 44.61
-37. 13
h. TO. ».
00 03 12.00
16.83
21.32
26.00
30.85
7.00
00 03 21.40
—.02
—.06
+ .00
00 03 21.32
00 02 44.42
rn
rv
V
Correction for level
Correction for rate
R'ednced transit
Tabular E. A
—35. 70
—36. 90
—36.90
Mean of levels = — 2^ ^ /{g _ _ pggg ^ ;, inequality of pivots . . = . 00
y Pegasi.
Br. 6.
1 Ceti.
44 Piscium.
12 Ceti.
E.
E.
E.
E.
E.
Level •!
Telescope south.
IT. Sum.. E.
19. 2 —88. 3 69. 1
68.9 +87.8 18.9
d
Telescope south.
W. Sum. E.
68.7 +87.3 18.6
19. 4 —88. 7 69. 3
d
Telescope south.
W. Sum. E.
19. 2 —88. 4 69, 2
68.5 +86.7 18.2
d
1.7
Telescope north.
IF. Sum. E.
68. 9 +87. 8 18. 9
18.9—87.9 69.0
d
0.1
h. m. s.
00 08 05.25
09.30
h. m. s.
00 10 05. 00
22.81
00 14' 20.70
24.68
28.52
32.90
37.23
4.03
ft. m. s.
00 20 17.35
20.84
24.93
29.16
33.42
5.70
ft.
00
TO.
24
25
«.
56.85
00.73
05.37
09.15
13.07
5.17
lY
1 III
13. 54 1 39. 30
II
17.65
22. 00
Sum.= 7. 74
66. 90
11 15.49
- . 9. 50
I
00 08 13.55
—.02
—.02
—.02
00 08 13.49
00 07 36.59
39.90
—.06
—.09
—.02
00 10 39.73
10 03.56
28.81
—.02
—.02
—.03
00 14 28.74
00 13 51. 75
25.14
—.02
—.02
—.04
00 20 25.06
00 19 48.17
00
00
25
24
05.03
—.02
—.02
—.05
04.94
27.91
Correction for aberration
Correction for level 6 B=
Tabular iJ. A a=
a-t=
—36. 90
—36. 17
—36. 99
—36. 89
-37. 03
Div.
Mean of levels =^ — -^^^
'-^^ X . 118 = — .027 = 6. Ineciuallty of pivots = . 00.
LOFGITUDE DETEEMINATION.
33
I++++
,1 INN
+ + ;++
4 i + i" f I
I - I : I I
+ I +++ + 1 +
^<
MON XXII 3
■Jiriir-
:ii^ <i
.^3 « + +
"Tip O »■«
II II I ". §
5"" + +
^ : a' ffl ©
Is E + +
<i< - i. :-
I I l'
I I
I "+TS
3. i (r._
5- r° I +
34
A MANUAL OF TOPOGRAPHIC METHODS.
COMPARISON OF TIME.
After time has beeii thus observed the chronometers at the two stations
shouki be compared by telegraph.
Chronometei's are compared in the foHowing manner: The chronometer
at one station being in circuit with the chronograph-and recording upon it,
the cln-onometer at tlie other station is switched into the general telegraphic
circuit, by which it is brought to the first station and switched into the
local circuit there, so that the two chronometers register upon the same
chronograph, their beats being marked side by side by the same pen.
Fig. 3.— Switcliboarcl.
After this has gone on for a minute or more the operation is reversed, the
chronometer at the first station is s\?itched into the telegraphic circuit and
made to record upon the chronograph with the clironometer at the second
station. Of course the observers are informed of the hour and minute at
which the joint record upon the several chronographs begins.
This method constitutes what is known as the automatic exchange of
signals.
The arbitrary exchange of signals is made as follows :
Each chronometer recording on its own chronograph as usual, and each
local circuit being connected with the main-line circuit, the observer at one
station breaks the circuit by means of the main-line talking-key, which
break is recorded on the chronograph sheets at both stations. The breaks
COMPARISON OF TIME. 35
are repeated at every two secouds for at least one full minute. The opera-
tion is then reversed by the observer at the second station making the
breaks which are recorded at both stations as before.
The differences of time between the chronometers at the two stations
are read from the chronograph sheets at each station and corrected for
error of the chronometers. The results from the two chronograph sheets
will differ by an amount equal to twice the time occupied in transmission
of signals. The mean of the two is therefore the approximate difference of
longitude.
This residt is yet to be corrected for personal equation, or the differ-
ence between the errors of observing of the two observers. Every observer
has the habit of recording a transit a little too early or too late, the differ-
ence between two observers not infrequently being as great as a fourth of
a second. To measure this difference, the observers usually meet, prefera-
bly at the known station, both before and after the campaign, and observe
for time each with his own instrument, or with one similar in all respects
to that used in the campaign. A comparison of the time . determinations
made by the two observers gives an approximation to the personal equation.
A better method, but one not always practicable, is for the observers,
having completed half of the observations for time and longitude, to ex-
change stations for the remainder of the work. The mean of the results
before and after exchange of stations will eliminate personal equation.
There is one error incident to this work which can not be eliminated.
This is the unequal attraction of gravity, or local attraction, or, as it is
sometimes called, station error. The neighborhood of a mountain mass
will attract the plumb line and deflect the spirit level to such an extent as
to cause serious errors in astronomical determinations of latitude and time.
The same restilt is frequently produced by a difference in density of the
underlying strata of rock, so that station errors of magnitude often appear
where they are not expected. Indeed, the station error can not be pre-
dicted Avith any certainty, either as to amount or even direction.
The only practical method of even partially ehminating this error is
to select a number of stations for astronomical location, luider conditions as
widely diverse as possible, connect them by triangulatiou, and by this
36 A MANUAL OF TOPOGEAPHIC METHODS.
means reduce all these astronomical determinations to one point, thus ob-
taining for this point a number of astronomical determinations each having
a different station error. The mean of these gives for this point a position
from which — in part, at least — station error has been eliminated, and this
mean position can be transferred back by means of the triangulation to the
several astronomical stations, thus giving each of them a position similarly
comparatively free from station eiTor.
OBSEEVATIONS FOR AZIMUTH.
The initial direction from which the directions of other lines in primary
triangulation and in primary traversing are computed is obtained by means
of astronomic observations. Such observations should be taken not only
upon the initial line, but at intervals throughout the work for its verification.
Such intervals should not exceed in the primary triangulation 100 miles, and
in primary traversing 10 to 20 miles.
Azimuth observations are made with the theodolite used in primary
triangulation or traverse. The observations consist in the measurement of
the horizontal angle between some close circumpolar star, visually Polaris,
and a terrestrial mark, generally a bull's-eye lantern set at a distance of half
a mile to a mile from the observing station. The time of observation on the
star should be noted by a chronometer or a good watch. As the star is at
a much higher angle of elevation than the lamp it is necessary not only to
level the instrument carefully but to measure the error of level and to cor-
rect for it. It is therefore essential that the value of a division of the level
bulb be known. These observations for azimuth may be made at any time
of the night, btit preferably they should be made at or near the time of
elongation of the star, as it is then moving most slowly in aziinuth, and any
eiTor in the time of observation has the least effect upon the resulting azimuth.
If such observations be taken at elongation, no record of time need be made,
and the reduction of the observations is simplified. When such observations
are made at any other time than at elongation, the time must be noted, as
it forms an element in the reduction. The error of the clock or watch used
may be obtained by comparison with railroad time, and corrected for the
difference in longitude between the station and the meridian of the railroad
time. A form of observation and record is appended.
OBSEUVATIOJSrS FOR AZIMUTH.
37
AZIMUTH OBSERVATIONS.
Exain2)le of record.
[Station: West base,
Object.
Time P. M.
Level.
3tIicrometer.
Mean
.
1
Angle.
West
end.
East
end.
A. B.
h.
11
00
18
Div.
13.9
50.5
Div.
47.]
10.2
346
101
101
345
211
327
327
211
Telesco]
' Div.
00 14. 8
32 18.1
32 19. 8
58 22.0
Teiescop
28 29.0
05 06.7
04 26.3
27 10. 7
K direct.
165 58
281 31
281 31
165 .57
'. reverse.
31 27
147 03
147 03
31 26
Div.
25.1
21.8
19.7
01.4
23.4
09.5
00.6
07.4
345
101
101
345
211
327
327
211
59
32
32
57
28
04
03
26
39.9
09.9
09.5
53.4
22.4
16,2
56.9
48.1
1
1 o
i.115
1
J
^115
Ills
|ll5
32 30.0
34 16.1
35 53. 8
37 08.8
64.4 1 57.3
+ 7.1
TT" t liatip Innrvi
11
11
09
17
20
14
50. 4 10. 3
13. 8 46. 5
64. 2 50. 8
+7.4
50. 5 10. 1
12. 9 46 6
63. 4 56. 7
+6.7
11
26
22
14. 3 1 46. 3
50.1 10.5
i
1
64. 4 I 50. 8
+7.6
AZIMUTH OBSERVATIONS.
Summary of results.
[Station : West base, Arkansas. December 27, 1888.]
Individual results.
Combined results.
2«* 10 ti^s'^sD.
1
I 38. 80
«;«;-42.35E.
J
55' t \ 41. 10 R.
46.3 3
^ 39.38
[ «:||37.65D.
J
^|*|43.90D.
I 38. 75
26; * I 33. 60 E.
J
«:;^47.05E.
V 40.10
«:^^33.15D.
)
Grand mean
294 10 39.26
38 A MANUAL OF TOPOGEAPHIG METHODS.
REDUCTION OF AZIMUTH OBSERVATIONS.
The time of observation of a star is first to be corrected for the differ-
ence in longitude, assuming that railroad time has been used, and for the
error of the watch. It is then reduced from mean to sidereal time. From
the sidereal time of observation is to be subtracted the right ascension of
Polaris, if that star is used, which is given in the Nautical Almanac, the
result being the hour angle or the sidereal time which has elapsed since it
passed the meridian of the place of observation, given in hours, minutes,
and seconds. This result is to be converted into degrees, minutes, and
seconds.
m i \ « sill t
Then tan A
1-b cos t
where a— sec 9 cot 6, y=the latitude.
h = '^
tan (J)
tan 6 (5— the declination of star.
t-z hour angle.
A zz angle between north pole and the mark.
This angle is to be con-ected for level as follows:
level corr.— — A$(w + ^t;')— (e + e')Uau.7i.
d being the value of a division of the level.
■w-}-'w', readings of west end of level bubble.
e+e', readings of east end of level bubble.
h, the angular elevation of pole star.
AZIMUTH OBSERVATIONS. ' 39
An example of reduction is as follows:
AZIMUTH OBSERVATIONS.
Example of reiluciion.
[Station: West base; December 27, 1888. Observer, S. S. G. Latitude=34 45 20.8 Longitude 92 13 31.5.]
h. VI. .s.
Tinie of observation = Tw = 11 00 18
Correction: ninetieth meridian time to 92^.215 = — 8 54
"Watch slow; ninetieth meridian time + 02 ^
local mean time *
Correction ; mean to sidereal time
Kight ascension mean sun
Tm=:10
~18
51 2B
+ 1 47
20 36
= 29
— 1
19 49
18 25
t • =28
— 24
01 24
h.
t (time) = 4
t (arc) =60
01 24
21 00
ec }1 cot 6 b =
_ tan 0
tan S
log b
logtanA 178 38 08.0 =8.3769185 0.9923296 =1—6 cost
angleto +115' 32 30.0
mark ,
Level corr. -3-8 le^el corr. = -|l j (^^.,„,)_,g_g,, | t^^ ,,
o , „ 3"] Div. ^ •"
Az. ofmai-k = 294 10 34.2 = — j~ X 7. 1 X . 694 = — 3.8
When observations for azimuth are to be made at elongation, it is nec-
essarv to know the mean time of elongation. This is computed by the
following method: the hour angle at elongation is obtained from the follow-
ing equation:
cos te =tan <p cot S.
The hour angle plus the right ascension of the star gives the sidereal
time of its western elongation, which, reduced to mean time, gives the local
mean time in question.
The azimuth of a pole star at elongation is determined by the use of
the following equation :
sin A zz sec cp cos S.
40 A MANUAL OF TOPOGRAPHIC METHODS.
The following is an example of these computations:
Example of the compntation of the azbmith at elongation^ and the local mean times of both
elo7igations of Polaris.
[Latitude = (^ —40°. Meridian of "NVasbingtou. November 28, 1891.]
• Sine Azimntli
log. sec. 40°
at elongation =
= sec. (J cos S.
= 0. 1157460
log. cos ij
88 44 05.5
1 39 05. S
= 8. 3439803
log. sine A
= 8. 4597263
Cos. hour angle at elongation, t
log. tan 40°
e. =tan <f> cot 6.
= 9.9238135
log. cot 6
88 44 05.5
88 56 17.5
= 8.3440862
log, cos te
= 8. 2678997
t« = 5 55 45. 2.
Sidereal time western elongation, Ta :=; E. A. Polaris + te.
= 1
19
35.2
= 5
56
45.2
T.= t"
15
20.4
o,=16
29
14.4
= 9
13
54.0
1
30.7
9
12
23. 3 Not. 28.
= 2
47
36.7 A.M., Nov. 28.
h.
71!. s.
a — te =
:19
23 50.0
as ^
16
20 14. 4
^
: 2
54 35.6
=
0 28.6
Sidereal time eastern elongation = 24' + a
For longitudes west of Wasliiugtou decrease times of elongation 0.66 for each degree.
CHAPTER III.
HORIZONTAL LOCATION
The primary control or geometric work is, in the ordinary case, effected
by tiiangulation. Wherever this is not practicable or not economic, resort
is had to what is known as primary traversing, but wherever the country pre-
sents sufficient relief for the purpose, triangulation is employed, as it is more
accurate and cheaper. In some parts of the country triangulation of suffi-
ciently accurate character for controlling the map has been executed by
other organizations, notably by the U. S. Coast and Geodetic Survey, and the
U. S. Lake Survey. Wherever such triangulation is available, the results
should be adopted and utilized for the control of the maps.
PARTY ORGANIZATION.
The primary triangulation is generally carried on by a special party.
It is, however, on some accounts and under certain circumstances, economi-
cal and advisable that all the work be done by one and the same party.
The disadvantage is that it divides the time and attention of the topographer,
requiring him to turn his attention from one thing to another; the advan-
tage, that it insures the selection of such points as are needed by the
topographer for carrying forward the work. If the work is done by a special
party, the points selected are more likely to be chosen on account of their
forming good figures in the triangulation, than on account of their conve-
nience and usefulness to the topographer. The secondary triangulation, the
traversing, and the sketching are usually carried on by different men, but
under a single party organization. The sketching is done by the chief of
party, the secondary triangulation and height measurement l)y his most
experienced assistant, while the traversing, with height measurement, is done
by the other assistants.
42 A MANUAL OF TOPOGEAPHIG METHODS.
BASE-LINE MEASUREMENT.
This is, ordinarily, tlie first of tlie preparatory steps toward map making.
Upon the proper selection of the site of the base line and its correct meas-
m-ement depends all the subsequent work of tri angulation. The site must
be reasonably level. It is not essential that it be absolutely so, but the
more closely it approaches a plane the less difficulty will be experienced in
making an accurate measurement. The site should afford sufficient room
for the measurement of a base from 5 to 10 miles in length. A base less
than 5 miles in length is not an economical one, inasmuch as it is less
costly to extend the base than to complicate the expansion. A greater
length than 10 miles is imnecessary, because this length permits of easy
expansion, and, if the length be greater than this, it may be difficult to con-
struct signals at the two ends of the base, which will be intervisible.
The ends of the base must be intervisible, and they must be so situated
with regard to suitable points for expansion and triangulation as to form
well proportioned figui-es. Whenever possible, the base line should form a
side or diagonal of a closed quadiilateral or pentagonal figm-e.
While it is unnecessary to devote time to obtaining the extreme of
accuracy in the measiu-ement of a base, this measurement should be so
acciu-ate that its errors can not affect the map, although multiplied many
times in the associated triangulation. All necessary precaution should be
taken to secui-e this result.
Various methods and instruments have been employed in the measure-
ment of base lines upon the Geological Survey. At first wooden rods were
employed, varnished and tipped with metal. When used in measuring,
these were supported upon trestles and contacts made between them, with
considerable refinement. The advantage of using these rods consisted in
the fact that their length is but slightly affected by temperatm-e, which is
the main source of error in base-line measurement, and being thoroughly
varnished they were not greatly affected by moistm-e.
Subsequently bars of metal were employed of the pattern known as
the Coast Survey secondary bars. These consist each of a steel rod between
two zinc tubes. As the two metals expand at different rates under changes
of temperature, their relative lengths at any temperature as compared to the
BASE LINE MEASUEEMENT. 43
i-elative lengths at a normal temperature is, theoretically, an indication of the
temperature of the bars at any time. The arrangement for indicating their
relative lengths forms a part of the apparatus, and is intended to indicate
the temperature of the bars, and thus to afford means of reducing the lengths
of the bars to a normal temperature. It has not been found, however, to
work well in practice. Besides this, there are other objections to the use of
bars of any kind, which may be summarized as follows: First, their use is
expensive. A considerable number of men are needed, and as the measure-
ment proceeds slowly it often requires from a month to six weeks to measure
and remeasure a base five miles in length. Again, since these bars are but
four meters in length, there are many contacts to be made in each mile of
measurement, and each contact affords the possibility of a trifling error.
In view of these objections and of certain positive advantages which
the change would produce, it was decided, in 1887, to drop the use of bars
in the measurement of base lines, and to adopt in their place long steel
tapes. By their use it has been found easy to attain the required degree of
accuracy in measurement, inasmu.ch as the number of contacts is reduced
to a small fraction of the number necessary in the use of bars, while the
uncertainty in regard to the temperature of the measuring apparatus is
reduced to a minimum by carrying on the measurement at night or in cloudy
weather. The expense of the measurement is greatly reduced. Fewer
men are required. The work of preparing the ground and the work of
measuring are much lessened, and the rapidity of measuring is increased
manyfold. The diminished cost makes it practicable to measiire much
longer bases, thus diminishing the number -of stations required in the
expansion. It allows, also, a measurement of base lines at shorter intervals
in the triangulation.
The tape in use has a length of 300 feet. It should be carefully com-
pared, at an observed temperature, with the standard of the U. S. Coast and
Geodetic Survey, both before and after its use in base measurement. Prefer-
ably, the site for the base line should be selected along a railway tangent,
as such a location is approximately level, and the railway ties afford an
excellent support for the tape. If such a location can not be obtained, it
should be selected so as to till the requirements above mentioned, cleared
44 A MANUAL OF TOPOGliAPHlO METHODS.
of brush and undergrowth, and, if necessary, its sharp inequalities should
be leveled. The tape should be supported by a series of low stools, whose
legs are pressed into the ground at intervals of not more than 25 feet, while
similar stools should sustain each end of the tape.
The personnel required in the measurement of a base line is, in an
ordinary case, as follows:
First. The chief of the party, who exercises a general supervision over
the work, marks the extremities of the tape and provides the necessary pre-
cautions against errors in the measurement, as hereafter stated.
Second. The rear chainman, who adjusts the rear end of the tape to the
contact marks and who carries and reads one of the thermometers.
Third.' The head chainman, who adjusts the forward end of the tape?
exerts the requisite tension upon it, and carries and reads a second ther-
mometer.
Fourth. A recorder.
The measurement of a base with the steel tape is a simple matter.
Provision must, however, be made, first, for the proper alignment of the
base ; second, for the proper tension of the tape ; and, third, for the measure-
ment of temperature.
The alignment is a simple matter, and is generally marked out upon
the gi'ound in advance of the work of measurement. In cases where a
railway tangent furnishes the site for the base line, no alignment is needed
beyond the provision for keeping the tape always at a uniform distance
from one of the rails.
For insuring a uniform tension of the tape, an ordinary spring balance
is used, which is attached to the forward end of the tape, where a tension
of twenty pounds is applied. In order to apply this uniformly, and to
insure against «lip of the tape, an apparatus de\'ised by Mr. H. L. Baldwin,
jr., of the Geological Survey, is in use.
For its use, it is necessary to obtain strips of board about five feet long
and four inches in width, in number equal to the number of lengths of tape
of which the base line consists. Numbered strips of zinc of equal nmnber,
each about eight inches long and an inch in width, are tacked to blocks of
wood, and these blocks of wood in turn nailed down upon the boards above
BASE LINE MEASUEEMENT. 45
ineiitioned, while the boards are, m case measurement is made along the
railway tangent, nailed down to the railway ties. These boards are
designed to support the devices for maintaining the tension, and the con-
tacts are marked upon the strips of zinc. Mr. Baldwin's apparatus consists
essentially of a wheel worked by a lever and held by ratchets in any
desired position. This wheel is attached to the spring balance in such a
way that by turning it the strain is put uj)on the spring balance, which is
held at the desired tension by the ratchets. A small mechanism at the rear
end of the tape is employed to hold the zero of the tape at the opposite
mark. The great length of the tape, 300 feet, allows considerable friction
or drag when the supports are frequent, and in order to insure a reasonably
uniform distribution of the strain upon the tape, it should be raised and
allowed to fall with the strain on.
The measurements should be made at night, or during cloudy days,
in order that the temperature of the air, which is that indicated by the
thermometers, and that of the tape be as nearly as possible the same. The
temperature must be carefully observed by at least two thermometers at
each tape length, in order that the best ]possible data for temperature cor-
rection may be obtained.
The base should be measured at least twice, and the two results com-
pared by sections of 1,200 feet, or four tape lengths. The ends of the
base must, if possible, be permanently marked by means of stone monu-
ments set into the ground so that their surfaces are but a few inches above
its level and the exact position of the ends should be indicated by a cross
cut in a copper bolt embedded in the head of a stone, in order that the
base may be preserved for futm-e references.
A line of levels must be run over the site or over the stools which
support the tape for the purpose of obtaining its profile and thereby the
means for deducing its horizontal length.
REDUCTION OF BASE LINE MEASUREMENT.
The first correction to be applied is that of redustion to a standard.
The correction for this is obtained by comparison with the standard of the
U. S. Coast and Geodetic Survey. The correction for the entire line is in
46 A MANUAL OF TOPOGEAPHIC METHODS.
proportion to the correction as obtained by comparison with the standard.
If the tape be longer than the standard, the correction will be positive, if
shorter, negative.
Second. The correction for inclination, the data for Avhich are obtained
by rnnning a line of levels over the base line. This line of levels gives the
rise or fall, in feet and decimals of a foot, between the points of change in
inclination. From this and the measured distance the angle of inclination
is computed from the formula, sin 0 = p ; R being the distance and h the
difference in height, both given in feet. The correction in feet to the dis-
tance is then computed by the equation, »
Corr.zr ^"f ^ 6'' R or 0.00000004231 9^ R, G being expressed in minutes.
(See Lee's Tables, p 83.)
Third. The correction for temperature. Steel expands for each degree
of temperature .0000063596 of its length. This fraction multiplied by the
average number of degrees of temperature at the time the base line was
measured above or below sixty-two degrees, which is taken as the normal
temperature, gives the proportion in which the base line is to be diminished
or extended on account of this factor. Care must be taken to obtain cor-
rectly this average temperature. It must be the mean of all the thermo-
metric readings, taken at uniform intervals of distance during the measure-
ment. If the temperature be above the normal, the correction is positive,
and vice versa.
Fourth. The reduction to sea level. The base line is measured on a
cii-cle parallel to the sea surface and raised above it, at an elevation which
is known at least approximately. This circle with radii drawn therefrom to
the center of the earth forms approximately a triangle similar to that formed
by the radii of the earth with the sea surface. The length at sea level is
derived with a sufficient approxiination to correctness by the proportion:
R: h:: K: correction.
R being the radius of the earth, h the mean height of the base line
above sea level, and K its measured length. (See Report U. S. Coast and
Geodetic Survey, 1882, Appendix 9, p. 196.)
BASE LINE MEASUREMENT.
47
The following- is an example taken from the records of measiu-ement
in 1889 near Spearville, Kansas, together \'vith the reduction of this base
for inclination, temperature, and elevation al ove sea level:
Eeeord of measurement and reduction of Spearville hase, Kansas.
[Section 1. Stations 0-10. October 16, 1889. Light rain falling.]
IXo. of Tape.
Time,
Tension.
Tliermometera.
Temperature
correction.
, Totcal length of section.
A.
B.
1
h. m.
10 13
20
26
31
37
42
47
51
55
58
Founds.
19.75
20.00
20.00
20.25
20.00
20. 125
20. 25
20.00
20. 125
20.00
50.5
50.5
50.5
50.5
50.7
51.5
51.0
50.8
50.8
50.7
50.0
50.0
50.0
50.0
50.5
50.6
50.8
50.2
50. 0
50.5
iloan temp. = 50.51
62-50.51 = 11.49
—11.49X3000.
X .000006
= -.207
1 tape length =300. 0617
10 :■ 300. 0617 = 3, 000. 617
Temperature corr — . 207
Eesult first measurement= 3, 000. 410
[Second measurement, October 17, 1889.]
No. of Tape.
Time,
p.m.
Tension.
Thermometers.
Temperature
correction.
Total length of section.
A.
?•
k. m.
12 13
21
25
29
33
36
38
41
45
50
Pounds.
20.00
20.25
20.00
19.75
20.00
20. 00
20.00
20. 12
19.75
20.13
52.3
53.3
53.8
55.0
55.0
53.8
54.0
54.5
55.1
54.5
52.4
52.9
54.0
54.8
53.2
54.0
54.0
54.0
54.4
54.1
Mean =53. 96
62 —53.96=8.04
- 8. 04 X 3000.
X. 000006
= — 145
Tape set hack from sta. 0 .85 inch.
= . 071 foot.
2
4.
Temperature corr — . 145
Eesultsecondmea3urement=3,000.40]
Correction for inclination Sjyearville base,
Correction =5HLiiL: 92 x Distance.
Approximate
distance.
Differ-
ence of
elevation.
Angle e
log e
2 log 9
log
Sinn'
2
log (list.
log
correction.
Correction.
Feet.
Feet.
, „
200
0.8
13 34
1. 1326
2. 2652
2. 6264
2. 3010
7. 1926
.0015
4,200
4.2
2 22
0. 3674
0. 7348
3.6232
6. 9844
.0010
4,000
12.0
10 08
1. 0052
2. 0104
3. 6021
8. 2389
.0173
1,000
1.0
3 23
0. 5250
1. 0501
3. 0000
6. 6765
.0005
2,000
3.0
5 04
0.7024
1.4049
3.3010
7. 3323
.0021
4,200
22.0
12 23
1. 0917
2. 1834
3.6232
8. 4330
.0271
2,800
7.0
8 27
0.9263
1. 8527
]
3.4472
7. 9263
.0084
1,000
0.0
0 00
0.0000
0. 0000
Constant. {
3. 0000
0. 0000
.0000
1,000
1.0
3 23
0. 5250
1. 0500
3.0000
6. 6764
.0005
4,200
20.0
11 16
1. 0504
2. 1008
3. 6232
8. 3504
. 0224
3,800
6.0
5 20
0. 7267
1.4535
3. 5798
7. 6597
.0046
2,000
4.0
6 45
0. 8293
1. 6dS6
3. 3010
7.5860-
.0038
5,400
31.4
19 39
1. 2934
2. 5867
3.7324
8. 9455
.0882
2,000
2.6
4 24
0. 6-137
1. 2874
3.3010
7.2148
.0016
135
0.05
1 18
0. 1072
0.2144
2. 1303
4. 9712
.0000
.1790
48
A MANUAL OF TOPOGKAPHIO METHODS.
Beductioii to sea level.
Correction
lo^ K (meti'cs) .
log A (metres).
Co log R
Spearville base : Summary by sections.
[Corrected for temperature.]
. = 4. 03956
. = 2. 87599
. 3. 19660
Stations.
First
measure.
measurl 1 I^'^—-
1
1 to 10
ID 20
20 30
30 40
40 50
50 60
60 70
70 80
80 90
90 100
100 110
110 119
119 126
3, 000. 410
.418
.431
.426
.437
.417
.369
.306
.955
.676
3, 000. 899
2, 700. 581
2, 100. 244
3,000.401
.393
.431
.446
.478
.455
.392
.350
.938
.667
3, 000. 898
2, 700. 571
2, 100. 234
First— Second.
+ .009
+.025
+.000
-.020
-.041
-.038
-.023
+.010
+.017
+.009
+.0U1
+. 010
+.010
37,806.629
37, 806. 660
-. 031=. 372
Mean of 2 raea^urement.'i = *37, 806. 645
Reduction from S. ^V. lia.se to A - 168. 235
Reduction from N. E. base to A - 2. 864
Correction for inclination — 0. 179
Reduction to sea level — 4.448
Corrected length = 37,630.919
PRIMARY TRIANGULATION.
The base line having been measured, the next step is the expansion.
This work, as well as the body of the triangulation, consists in the selection
of stations, the erection of signals, and the measurement of angles. Each
triangle proceeding from the base line outward will, when the angular meas-
urement is completed, have one side and the three angles known, from which
the other two sides can be computed by means of a simple trigonometric
fonniila.
The expansion diffei's from the body of the triangulation only in the
fact that the average length of the sides of the triangles is less. As the
expansion progresses away from the base line, the sides of successive triangles
become gradually longer, until the average length of side of the triangula-
tion is reached. Since the sides are increasing in length, and hence since any
* Con'ected for temperature.
PEIMAEY TRI ANGULATION. 49
inaccuracy in the measurement of the base is multiplied, this work must
be planned and executed with greater care than the body of the triaugula-
tion requires.
A base line measui-ed as above prescribed requires little expansion,
since from the extremities of an 8 or 10 mile base one can observe
directly on points 12 to 15 miles away, a distance as great as the average
side of a triangle. Ordinarily, from the ends of the base, the surveyor
can observe directly upon stations in his scheme of triangulation.
In the western mountain region, where the sides of triangles may be
20 to 50 miles in length, an expansion is required.
SELECTION OF STATIONS.
In the selection of triangulation stations two different sets of require-
ments must be served.
First. They iTiust be so selected as to afford what is known as strong
figures, in order to reduce to a minimum the errors which will creep into an
extended system. In order to insm-e intervisibility, they should, if possible,
be located upon hill or mountain summits, the most commanding in the
neighborhood. No triangle upon which dependence is placed for the loca-
tion of a station should have at that station an angle of less than 30° or
more than 150°.
The stations should, if practicable, be grouped into simple figures, as
quadrilaterals, or pentagons with an interior station, etc. In cases where an
area is being covered with triangulation, such groupings naturally occur,
but in certain cases the triangulation takes the form of narrow belts of fig-
ures, and then the belt may consist of simple triangles or quadrilaterals, as
more complex figures are rarely desirable.
Second. Since the sole object of this triangulation is the control of the
topographic map, the location of stations must, as far as is consistent with
accuracy, be adjusted to the needs of the topographers. This requirement
affects most seriously the distance between stations. Every atlas sheet
must contain at least two primary stations, and a third is desirable. Thus,
for controlling the sheets on the scale 1 : 62500, the stations should not be
more than 10 or 12 miles apart, and should be located with du-ect reference
MON XXII i
50 A majstual of topographic methods.
to the control of certain sheets. Again, since the primary stations must be
occupied by topographers for intersecting on numerous points, they must
be selected with reference to this requirement. They should command an
extended view, especially of points suitable for cutting in, such as hill and
mountain summits, houses^ churches, etc.
The instrument should, wherever possible, be accurately centered under
the signal. Whenever it is necessary to set up off center, the direction and
distance to the signal should be carefully measured and recorded.
While signals should be of the simplest and least expensive form which
will serve the pm-pose, their form and material must depend upon the requhe-
ments and the materials at hand. In a mountainous country, where the
summits ai'e treeless, simple cairns of stone, 7 to 10 feet in height, are em-
ployed. Where the summits are wooded, it is frequently convenient to clear
them, leaving a single tree to serve as a signal. In such cases it is advisable
to trim the tree of branches, with the exception of a tuft at the top. Where
the station is clear, but with green timber easily accessible, it is advisable
to make a tripod of small trees, each with a tuft at its top. In undulating
and hill country it is often necessary to erect scaffolds. These should be
built of sawed lumber and framed in simple fashion. If the lines are short,
a pole with a flag may be set in the top. If the lines are long, the tower
itself may serve as a signal, in which case its upper part should be clothed
in black and white cotton.
The annexed cut shows a form of framed signals adapted for use on
the treeless plains of Kansas and the rolling open hills of New England,
and elsewhere, where observing towers are not necessary. (PI rv.)
It is frequently necessary to raise the instmment to a considerable ele-
vation above the ground, in order to overlook surrounding obstacles. In
such cases the structiu-es for supporting the instrument should be combined
with the signals, and hence they may properly be described and figured
here. These observing towers should be in two parts. An interior struc-
ture, solidly built of sawed lumber, if available, for the immediate support
of the instrament, and a framework surrounding it, supporting a platform
SiaiSTALS.
51
just below the staud for the instrument, for the observer. The two should
be separate, in order that the jan-ing incident to moving about on the plat-
form be not communicated to the instrument. Such a type of obser^dng
tower is figured in Fig. 4.
Fig. 4.— Sigual and instrunioiil; suiipurt.
When sawed lumber is not obtainable, other material must be used.
In the Sierra Nevada of California, among" the sugar-pine forests, a support
52
A MANUAL OF TOrOGEAPHIC METHODS.
for the iustrumeut is not unfrequently obtained by sawing off the top of a
high tree, and setting the instrument upon the stump, 50 or 75 feet above
the ground, the tree being guyed out by wire cables to prevent swaying in
the wind. The phxtform for the observer is supported by neighboring trees,
similarly sawed off and supported for the purpose. Similar devices are
resorted to also in the forests of AVest Vu-ginia, Kentucky, and Tennessee.
In the secondary triangulation in these regions, the instrument support is,
in many cases, provided as above described, while the observer's platform,
instead of having an independent support, is attached to the same tree. This
is objectionable, but is often the best that can be done.
Fig. 5. — Coast Survey Heliotrope.
In other cases it is more economical to suppoi't the instrument upon the
ground, and to have openings made thi'ough the forest upon the station hill,
in the du-ections of the sight lines, or even to have the whole summit cleared.
It is not infrequently necessary to use more elaborate forms of signals,
especially when the point observed upon is below the horizon line, so that
the background, instead of being the sky, consists of forests or brown plains.
In such cases resort is had to heliotropes. These are simply instruments for
reflecting the sunlight to the observer at the instrument. The simplest form
is a circular mirror with a screw hinged at the back, giving a universal
motion. This is screwed into a stake or tripod over the center of the station
to be observed upon, and a ray of sunlight is thrown through a small hole
in a board nailed to a stake 10 or 15 feet away, and in the direction of the
observer at the distant station. This form has the advantage of simplicity.
HELIOTEOPES.
53
as the simplest backwoodsman can manage it; a,nd the triangulator can
firmly fix all range stakes upon one visit to the station, and be sure of seeing
the flash as he observes from each of the surrounding stations in turn.
Two other forms are m use, the Coast Survey type and the Steinheil.
See Figs. 5 and 6. The former consists of a telescope which is provided
with a screw for fastening it into any con-
venient support or upon the theodolite. Upon
the telescope is a mirror and two rings, the axis
of the rings as well as the center of support of
the mirror being parallel to the line of sight
of the telescope. The telescope being directed
upon the observing station, the mirror is so
turned as to reflect the sunlight through the
rings and necessarily to the observing station.
In many cases the use of a second mirror is
necessary, owing to the relative position of the
two stations and the sun, and such a mirror
forms a part of the outfit. This form is little
used, on account of its liability to get out of
adjustment. The Steinheil heliotrope is ac om-
pact little instrument, which can be carried in a
case like a pair of field glasses. It consists of
a small sextant mirror, the two surfaces of which
are as nearly absolutely parallel as possible.
This mirror has a small hole in the center of
the reflecting surface. Below this central hole
is a small lens in the shaft carrying the mirror, and below the lens is
some white reflecting material, as plaster of Paris. The mirror is so mounted
that it has four different motions, two about its horizontal axis and two
about its vertical axis, each of which can be separately bound or controlled
by clamps or friction movements. To use the Steinheil, it is screwed into
some wooden upright, as the side of a tree, in suc\i a position that the main
axis carrying the lens and plaster of Paris reflector shall be parallel to the
sun's rays. The observer standing behind the mii'ror receives from the rear
Fig. 6.— Steinheil Heliotrope.
54 A MANUAL OF TOPOGKAPHIO METHODS.
surface of the glass a reflection of the sun, producing an imaginary sun.
The mirror should not be moved until this imaginary sun, moving with it,
appears to rest on the object to which the flash is to be cast, as the hill on
which the triangulator is standing. As both surfaces of the mirror are par-
allel, the true reflected rays of the sun from the surface of the mirror will
also be cast on the object sighted to.
This instrument is in great favor, especially with the Western parties,
where portability is a matter of moment, first, because it is light and con-
venient to carry and use, and second, because there are no movable parts
to get out of adjustment by jarring*. This latter is a serious defect in the
Coast Sm-vey instrument, since unless frequently tested the two rings may
have moved, thus causing the reflection to be cast out of parallelism with
the line of sight of the telescope.
The use of heliotropes presupposes the employment of men to operate
them, thus increasing materially the expense of the work. Misunderstand-
ings continually arise between the heliotropers and the observer, causing
vexatious delays, and therefore their employment should be avoided when-
ever possible.
THEODOLITES FOR TRIANGULATION.
Several instruments differing widely in power and degree of accuracy
have been in use for the measurement of angles in the primary triangula-
tion. Formerly theodolites having circles 6, 7, 8, 10, and 11 inches in
diameter and reading by vernier to 10 seconds were employed, and the
results were reduced and adjusted by Least Squares. Subsequently, it
appeared desirable to employ a higher class of instruments and thus obtain
more accurate results, which would render unnecessary this tedious adjust-
ment. Pursuant to this decision the use of these vernier theodolites has
been, in the main, discontinued, and theodolites having 8-inch circles, read-
ing by micrometer microscopes, have been substituted almost universally
in the primary work.
One of these theodolites is represented in PI. v and Fig. 7.
The circle, as was above stated, has a diameter of 8 inches, and is sub-
divided to 10 minutes. The object glass is 2 inches in diameter and its
, GEOLOGICAL SURVEY
EIGHT-INCH THEODOLITE AND TRIPOD.
THEODOLITE. 55
focal distance is 16^ inches. The telescope with the eyepiece commonly
used has a -power of about 30 diameters.
The circle is read by means of two microscopes, placed opposite one
another. Within the field of the microscope is a comb stretching over the
space of 20 minutes. This comb has ten teeth, divided into two parts by
a depression, each corresponding to 2 minutes. Parts of a minute down to
2 seconds are read by means of a micrometer screw moving a pair of fine '
tkreads in the field of the microscope.
/
Fig. 7.— Eight-inch Theodolite, detail.
INSTRUCTIONS FOR THE MEASUREMENT OF HORIZONTAL ANGLES.
The following general precautions should be observed in the measure-
ment of all horizontal angles in the primary triangulation. .
The instrument should have a stable support, which may be a stone
pier, a wooden post, or a good tripod. If a portable tripod is used, its legs
should be set firmly in the ground.
The instrument should be protected from the direct rays of the sun by
means of an umbrella, or a piece of canvas like a tent fly. It should also
be shielded from winds which ma}- jar or twist either it or its support.
The foot screws of the instrument after it is leveled for work should
56 A MANUAL OF TOPOGKAPHIC METHODS.
be tight]}- clamped. Looseness of the foot screws and tripod, is a common
source of error, especially witli small instruments.
The alidade, or part of the instrument carrying the telescope and
verniers or microscopes, should move freely on the vertical axis. Clamps
should likewise move freely when loosened. Whenever either of these
moves tightly, the instrument needs cleaning, oiling, or adjusting.
The observer should always have a definite preliminary knowledge of
the objects or signals observed. The lack of it may lead to serious error
and entail cost nnich in excess of that involved in getting such knowledge.
Great care should be taken to insure correctness in the degrees and
minutes of an observed angle. The removal of an ambiguity in them is
sometimes a troublesome or expensive task.
The errors to which measured angles are subject may be divided into
two classes — viz., first, those dependent on the instrument used, or instru-
mental errors; and second, those arising from all other sources, Avhich, for
the sake of distinction, may be called extra-instrumental errors.
The best instrimients are more or less defective, and all adjustments
on which precision depends are liable to derangement. Hence the general
practice of arranging observations in such a manner that the errors due to
instrumental defects will be eliminated in the end results. The principal
errors of this kind and the methods of avoiding their effects are enumerated
below.
Measurements made with a graduated circle are subject to certain sys-
tematic errors commonly called periodic. Certain of these errors are always
eliminated in the mean (or sum) of the readings of the equidistant verniers
or microscopes, and both of the latter should be read with equal care in
precise work. Certain other errors of this class are not eliminated in the
mean of the microscope readings, and these only need consideration. Their
effect on the mean of all the measures of an angle may be rendered insig-
nificant by making the number of individual measures with the circles in
each of n equidistant positions separated by an interval equal to ^ — where
m is the number of equidistant verniers or microscopes. Thus, if w?=:2,
1 80°
the circle should be shifted after each measure by an amount equal to
INSTRUCTIONS. 57
which, for example, is 45° for « — 4 aud 30° if n=Q. The degree of ap-
proximation of this elimiuation increases rapidly with n. (For specifications
as to particular instruments see "Number of sets required and astronomical
azimuths" below.) The effect of this class of errors is always nil on an
angle equal to the angular distance between consecutive microscopes or a
multiple thereof Other things equal, therefore, we would expect the measures
of such special angles to show less range than the measures of other angles.
Besides the instrumental errors of the periodic class, there are also
accidental errors of graduation. These are in general small, however, in
the best modern circles and their effect is sufficiently eliminated by shifting
the circle in the manner explained under "Periodic errors" above.
The effect of an error of collimation on the circle reading for any
direction varies as the secant of the altitude of the object observed. The
effect on an angle between two objects varies as the difference between the
secants of their altitudes. This effect is eliminated either by reversing the
telescope in its Ys, or by transmitting it without changing the pivots in the
Ys, the same number of measures being obtained in each of the two posi-
tions of the telescope. The latter method is the better one, especially in
determining azimuth, since it eliminates at the same time errors due to
inequality of pivots and inequality in height of the Ys.
The effect of the error of inclination on the circle reading for any
direction varies as the tangent of the altitude of the object observed. If
the inclination is small, as it may always be by proper adjustment, its effect
will be negligible in most cases. But if the objects differ much in altitude,
as in azimuth work, the inclination of the axis must be carefully measured
with the striding level, so that the proper correction can be applied. The
following formula includes the corrections to the circle reading on any
object for collimation and inclination of telescope axis:
c sec /< + b tan h;
c zz collimation in seconds of arc,
b zz inclination of axis in seconds of arc,
h zr altitude of object observed.
Parallax of wires occurs when they are not in the common focal plane
of the eyepiece and objective. It is detected by moving the eye to and
fro sidewise while looking at the wires and image of the object observed.
58 A MANUAL OP TOPOGRAPHIC METHODS.
If the wires appear to move in the least, ah adjustment is necessary. The
eyepiece should always be first adjusted to give distinct vision of the cross
wires. This adjustment is entirely independent of all others and requires
only that light enough to illuminate the wires enter the telescope or micro-
scope tube. This adjustment is dependent on the eye and is in general
different for different persons. Hence maladjustment of the eyepiece can
not be corrected by moving the cross wires with reference to the objective.
Ha^ang adjusted the eyepiece, the image of the object observed may be
brought into the plane of the cross wires by means of the rack-arid-pinion
moveuient of the telescope. A few trials will make the parallax disappear.
When circles are read by micrometer microscopes it is customary to
have them. so adjusted that an even number of revolutions of the screw will
carry the wires over the image of a graduation space. If the adjustment
is not perfect, an error of run will be introduced. This may in all cases be
made small or negligible, since by means of the independent movements of
the whole microscope and the objective with respect to the circle, the image
may be given any required size. In making this adjustment some standard
space, or space whose error is known, should be used. At least once at each
station where angles are read, observations should be made for run of
micrometers. Au example of such readings is given under sample of field
notes below.
Tangent and micrometer screws should move freely, but never loosely.
In making a jjointing with the telescope the tangent screw should always
move against or push the opposing spring. Likewise, bisections with the
rhicrometer wires should be made always by making the screw pull the
micrometer frame against the opposing spring or springs.
Extra instrumental errors may be divided into four classes — namely,
errors of observation, errors from twist of tripod or other support, errors
from centering, and errors from unsteadiness of the atmosphere.
Barring blunders or mistakes, the errors of observation are in general
relatively small or unimportant. With practiced observers in angular meas-
urements, such errors are the least formidable of all the unavoidable errors,
and then' elimination in the end results is usually well nigh perfect. The
recognition of this fact is very important, for observers are prone to attribute
INSTEUCTIONS. 59
unexpected discrepancies to bad observation rather than to their much more
probable cause. After learning- how to make good observations the observer
should place the utmost confidence in them, and never yield to the tempta-
tion of changing them because they disagree with some preceding observa-
tions. Such discrepancies are in general an indication of good, rather than
poor, work.
Stations or tripods which have been unequally heated by the sun or
other source of heat usually twist more or less in azimtith. The rate of
this twist is often as great as a second of arc per minute of time, and it is
generally nearly uniform for intervals of ten to twenty minutes. The effect
of twist is to make measured angles too great or too small according as they
ai-e observed by turning the microscopes in the direction of increasing gradua-
tion or in the opposite direction. This effect is well eliminated, in g-eneral,
in the mean of two measiu-es, one made by turning the microscopes in the
direction of increasing graduation and followed immediately by turning the
microscopes in the opposite direction. Such means are called combined
measures or combined results, and all results used should be of this kind.
As the uniformity in rate of twist can not be depended on for any considera-
ble interval, the more rapidly the observations on an ang'le can be made
the better will be the elimination of the twist. The observer should not
wait more than two or three minutes after pointing on one signal before point-
ing on the next. If for any reason it should be necessary to wait longer, it
will be best to make a new reading on the first signal.
The precision of centering an instrument or signal over the reference or
geodetic point increases in importance inversely as the length of the ti'iangu-
lation lines. Thus, if it is desired to exclude errors from this source as small
as a second, one must know the position of the instrument within one-third
of an inch for lines a mile long', or within 6 inches for lines 20 miles long-.
The following easily remembered relations will serve as a guide to the re-
quired precision in any case :
1 second is equivalent to 0.3 inch at the distance of 1 mile.
1 second is equivalent to 3.0 inches at the distance of 10 miles.
1 second is equivalent to 6.0 inches at the distance of 20 miles.
1 minute is equivalent to 1.5 feet at the distance of 1 mile.
60 A MANUAL OF TOrOaKAPHlO METHODS.
The notes should always state explicitlj- where the mstrument aud
signals are and give their coordinates (preferably polar coordinates) if they
ai'e not centered.
Objects seen tlu-ough the atmosphere appear almost always unsteady,
and sometiuies this unsteadiness is so great as to render the identity of the
object doubtful. The unsteadiness is usually greatest during the middle of
the day. It generally subsides or ceases for a considerable period between
2 p. m. and sundown. There is also frequently a short interval of quietude
about sunrise, and on cloudy days many consecutive hours of steady
atmosphere may occur. For the best woi-k, observations should he made
only when the air causes small or imperceptible displacements of signals.
In applying this rule, however, the observer must use his discretion. Errors
of pointing increase rapidly with increase of unsteadiness, but it will fre-
quently happen that time may be saved by counterbalancing errors from this
source by making a greater number of observations. Thus, if signals are
fairly steady it may be economical to make double the number of observa-
tions rather than wait for better conditions.
The best results in a triangulatiou are to be obtained by measuring the
angles separately and independently. Thus, if the signals in sight around
the horizon are in order A, B, C, etc., the angles A to B, B to C, etc., are by
this method observed separately; and whenever there is sufficient time at
the observer's disposal this method should be followed.
Besides measuring single angles, it is desirable to measure independ-
ently combined angles — i. e., angles which consist of the sum of two or more
single angles. Thus, supposing O to be the observing station and A, B, and
C stations sighted on, the observer sliould measure not only the angles AOB
and BOC, but the combined angle AOC. This is necessary not only because
this angle may be used directly in the triangulation, but it will be needed in
fonning conditions for adjusting tlie angles about the observing station, or
the station adjustment, as it is called.
In order to secure the elimination of the errors mentioned above, the
following programme must be strictly adhered to:
Pointing on A and readings of both microscopes.
Pointing on B and readings of both microscopes.
INSTRUCTIONS. 61
Transit telescope and tnrn microscopes 180°.
Pointing on B and readings of both microscopes.
Pointing on A and readings of both microscopes.
1 80°
Shift circle by and proceed as before until n such sets of measures
have been obtained.
Then measure the angles B to C, C to D, etc., including the angle
necessary to close the horizon, in the same manner.
A form for record and computation of the results is given below.
When repeating instruments are used, the same programme will be fol-
lowed except that there should be five pointings instead of one on each of
A and B, the circle being read for the first pointing on A and the fifth on
B, and again for the sixth pointing on B and the tenth on A.
The impoi-tance of having the measin-es of a set follow in quick succes-
sion must be constantly borne in mind. Under ordinarily favorable condi-
tions an observer can make a pointing and read the microscopes once a
minute, and a set of five reijetitions should be made in five minutes or less.
When several stations or signals are visible and a nonrepeating instru-
ment is used, time may be saved without material loss of precision in the
angles, by observing on all the signals successively according to the follow-
ing programme, the signals being supposed in the order A, B, C, etc., as above.
Pointing on A with microscope readings.
Pointing on B with microscope readings.
Pointing on C with microscope readings.
Pointing on A with microscope readings.
Transit telescope and turn microscopes 180°.
Pointing on A with microscope readings.
Pointing on B with microscope readings.
Pointing on C with microscope readings.
Pointing on A with microscope readings.
180
Shift circle by and proceed as before until n such sets have been
obtained.
02 A MANUAL OF TOPOGRArHIC METHODS.
The angles A to B, B to C, etc., read in tlii.s way may be computed as
iu the first method, always combining the measure A to B with the immedi-
ately succeeding measure B to A to eliminate twist. There is a theoretical
objection to this process of deriving angles founded on the fact that they
are not independent, but in secondary work this objection may be ignored
as of little weight.
For the 11 -inch theodolite and for the .new 8-inch instruments made
by Fauth & Co., all of which read by micrometer microscopes, four (4) sets
of measures on as many different parts of the circle will be required ; and
for the repeating theodolite six (6) sets of measures will be requued, all
measures being made according to the programmes given above.
Under ordinary circumstances and with due care in centering, angles
measured as specified above should show an average error of closure of the
triangles not exceeding 5".
Under specially unfavorable conditions the number of sets of measures
should be increased, care being always taken to shift the circle so as to
eliminate periodic eiTors.
The practice of starting the measurement of an angle or series of
angles with the microscopes reading 0° and 180°, 90°, and 270°, etc., must
be avoided; otherwise the errors of these particular divisions will affect
many angles. In shifting the circle it is neither necessarj^ nor desirable to
1 on
have the new positions differ from the preceding one by exactly . A
difference of half a degree either way is unimportant as respects periodic
errors, and it is advantageous to have the minutes and seconds differ for the
different settings.
Field notes should be clear and full. The date, place, name and num-
ber of instrument used, and the names of observer and recorder should be
recorded at the beginning of each day's work at a station. The positions
of the instrument and signals observed should be defined either by a full
statement or reference to such in each day's notes. The time of observa-
tions should be noted at intervals to show that the instrument does not
stand too long between pointings.
ORGANIZATION^ OF PARTIES.
63
When mistakes are made in the record, the defective figures should not
be erased, but simply crossed out, and an explanation furnished in the col-
umn of remarks. Grreat care should be taken not only to avoid "cooking"
or "doctoring" notes, but to avoid suspicion thereof.
The following example of form of record is taken from the primary
triangulation executed in 1889 in western Kansas:
Record of measurement of horizontal angle.
tliviaiou of micrometer
Station.
Micr. A. Micr. B,
Mea
n reading.
Angle.
Mean.
Telescope direct.
° ' Div. ° ' Div.
93 12 11.3 273 12 09.9
129 41 11.9 309 41 13.2
129 41 16.6 309 41 12.1
93 12 10.6 273 12 09.1
Telescope reversed.
138 27 03.2 318 28 28.0
174 66 03.8 354 65 28.9
174 56 06. 2 354 55 29. 5
138 27 05.^2 318 26 27.4
Telescope reversed.
1S3 07 03.0 3 06 27.2
219 36 05.0 39 35 29.8
219 36 08. 1 39 35 29. 5
183 07 06.4 3 06 28.1
93
129
129
93
138
174
174
138
183
219
219
183
228
264
264
228
1'2 21.2
41 25. 1
41 27.7
12 19.7
27 01.2
50 01.7
56 06.7
■27 02.6
07 00.2
36 04.8
36 07.6
07 04.5
24 50.7
63 63.5
63 .57.2
24 61.4
36 29 03.9
08.0
00.5
03.1
04.6
03.1
02.8
05.8
05.9
01.8
03.9
04.3
Telescop
228 21 28. 1
e direct.
.48 24 22.6
264 53 27.4
264 64 01.1
228 24 29.3
84 53 26. 1
84 53 26.1
48 24 22.1
Newt
41 15"
=360 29' 03". !
^ Instrument over cetter of station.
ORGANIZATION OF PARTIES AND PROSECUTION OF WORK.
A party for carrying on primary triangulation usually comprises only
the chief and an assistant, with the addition of a driver and cook, in case the
party is living in camp. Frequently, however, a man is employed to super-
intend the construction of signals, and it is generally found economical to em-
ploy such a man. The chief of the party is expected to select the stations
and direct the forms of signals to be erected, and to measure angles. In a
mountainous country the selection of stations is usually a simple matter.
From the summit of a mountain the chief of a party may be able to select
stations for considerable distances ahead and to order the erection of signals,
turning over to the man employed for that purpose the business of erecting
04 A MANUAL OF TOPOGEAPHIO METHODS.
tlieni. On the other haucl, in a densely wooded region such as the Cumber-
hmd phitean, where the summits have approximately the same elevation, the
selection of stations is an extremely difficult matter, requiring- great ability
and experience and involving an immense amount of labor. In such a region
the chief of party finds it necessary to travel great distances, visit many hills,
and even has to climb to the summits of the highest trees, in order to select
iutervisible stations.
The selection of stations must be kept in advance of the reading of
angles, but it is not advisable to keep it too far ahead, on account of the
danger of the destruction of signals before angles have been read upon them.
Therefore, the chief of a part}^ finds it necessary to alternate between the
two kinds of work, selecting and preparing three or four stations, then re-
turning and measuring the angles.
"When it is necessary to use heliotropes, the party has necessarily to be
increased by one man for each heliotrope employed. The proper manage-
ment of such a party then becomes a matter calling for the exercise of much
judgment on the part of the triangulator. If it is convenient for the chief of
party to place each heliotroper before observing angles, and to show them
where to direct their instruments, men of ordinary intelligence may be em-
ployed and the work is one calling rather for time than skill. Where, how-
ever, the party is moving almost daily, the observer and heliotropers occu-
pjnng a different station nearly every day, as is possible in the dry and clear
atmosphere usually prevailing in the West, the chief of party has to arrange
a schedule for each man, showing the order in which he is to occupy the
stations and in what direction he is to flash from each. The heliotroper
must be a man having some topographic and technical skill, so that he may
find his point, set up on center and direct his flashes to the right place,
besides exercising a goodly amount of common sense judgment. A simple
code of signals being agreed upon, it then becomes an easy matter for the
triangulator to let the heliotropers know that the work is completed, when
they at once move to the next designated station.
REDUCTION OP TRIANGULATION.
65
REDUCTION OF PRIMARY TRIANGULATION.
*KBDU(!TION TO CBNTEE.
In case any station was occupied off center, the directions, as read must
first be reduced to center. In the diagram, let x be the
point occupied; y, the station, r the distance between them, A the point to
which the direction is laid and the angle at that point, and R its distance,
approximately known. Then, from the relations between the sides and the
angles of the triangle,
R : r : : sin x : sin A
r sin X
A--
- and A zz (in seconds)
R ""^" — V ^^"^Rsinl"
correction in seconds of arc.
The following example taken from the triangulation in Kansas will
serve to illustrate the form of effecting this reduction. The references are
to the diagram on page 67.
Reduction to center of station at Walton A-
[See explanation: Appendix No. 9, page 167, U. S. Coast and Geodetic Survey report for 1882.]
distance, inst. to center^ '.48 log = 9.6812
log feet to meters = 0. 5160
distance, inst. to center log meters = 9. 1652 = log r.
Direction.
xton
7°.
xtoo
73°.
X to p
105°.
X to q
185°.
X tor
273°.
X to s
306°.
9. 0859
6. 9.321
9. 1652
5.3144
9. 9806
5. 9182
9. 1652
5. 3144
9. 9849
6. 4228
9. 1652
5.3144
8. 9403
6. 2434
9. 1652
5.3144
9. 9994
6, 0070
9. 1652
5. 3144
9. 9080
6. 2514
9.1652
5.3144
Correction to direction
9. 4976
0",31
0. 3784
2". 39
0. 8873
7". 71
9. 6633
0". 46
0.48(i9
3". 06
0. 6390
4". 36
Correction to ang
, a = Jl, to 0 —0. 31 +2. 39 = +2. 08
6 = o to p — 2, 39 +7. 71 = +5. 32
a — n to p —0. 31 +7. 71 = +7.40
c—p taq —7. 71 —0. 46 = —8. 17
d! = o to r +0. 46 —3. 06 = —2. 60
e = r to s +3. 06 —4. 36 = —1. 30
ft = n to s +0. 46 —4. 36 = -3. 90
/ = s to n +4. 36 +0. 31 = +4. 67
The angles are measured on a spherical surface and the sum of the
three measured angles of each triangle should equal 180° plus the spher-
MON XXII-
66
A MANUAL OF TOPOGEAPHIC METHODS.
ical excess. The latter need be computed aud subtracted from the sum. of
the angles, however, ouly for the purpose of testing the accuracy of closure
of the triangle, as in the reduction the angles are treated as plane angles.
When the area of the triangle is large, the spherical excess in seconds (E)
should be computed by the equation:
E —
S
r^ sin 1
where S =z the area of the triangle in square miles, and r the radius of
curvature of the earth in miles. When the triangle (being within the
United States) has an area less than 500 square miles, r may be assumed
as constant, and the spherical excess may be obtained by dividing the area
in square miles by 75.5.
The next step is the adjustment of the angles about the observing sta-
tion, or the station adjustment, as it is called. Referring to the diagram,
which represents the angles read at Walton station, in Kansas, it is seen that
eight angles were measured as follows —
Obs. angle.
Station
adjust-
ment.
Correc-
tion to
center.
Angles locally
adjusted and
reduced to
center.
65
31
45
47
28.37
58.50
+.51
+.52
+2.08
+5.32
65 45 30.96
31 48 04.34
Sum ^=
97
97
33
38
26.87
28.39
97 33 35.30
97 33 35.30
—.49
+7.40
Bifference =^
—1.52
00.00
—.56
—.56
—2.60
—1.30
87
34
44
00
57.41
03.35
87 44 54.25
34 00 01.49
Sum =
121
121
44
44
60.76
59.05
121 44 55.74
121 44 55.74
+.59
—3.90
+1.71
00.00
+.02
—.49
+ .02
+ .59
44.67
+7.40
—8.17
-3.90
61
97
79
121
09
33
32
44
26,17
28.39
06.25
59.05
61 09 30.86
97 33 35.30
79 31 58.10
121 44 55.74
Sum =^
359
59
59.86
—0.14
360 00 00.00
00.00
Of these a-\-b should =: g, d-\-e should = h, and g -\- c -\- h -\- f should
= 360°. Thus are formed in this case three conditions affecting eight
unknown quantities. The method by which are found the corrections which
EBDUCTION OF TEIANGULATION.
67
fulfill these conditions is that known as the method of Least Squares. It is
umiecessaiy to explain the theory of this method, but only to show how it
is applied in the class of cases under consideration, which can best be
done by tracing a case through. There are here three equations of condi-
tions, as follows:
(1) a-\-h—[/—l".52 =0
(2) f?+e-/i+l".71 rrO
(3) ,/■ + // + c + /i - 0".14 = 0
in which the letters represent, not, as in the diagram, angles, but unknown
con-ections to the angles. The coeflicient of each of these corrections is
unity. Arrange them in tabular form, the numbers at the top referring to
the equations, thus forming what is called a table of correlates. Now mul-
tiply each coefficient by itself and every other in the same horizontal line,
and sum them. There result three normal equations, as follows :
a 1
b 1
d 1
e 1
i' -' -^
1
+3
007/
.OOz
-T
..'^3 =
= 0
2
+ 3.00)/-
.003
■fV
.71 =
= 0
a
— 1
IMw
—l.UVy +i.Mz
-0'
.14 =
= 0
68
A MANUAL OF TOPOGRAPHIC METHODS.
These three equations iuvolviug three imkiiown quantities, are then
solved by ehmination, with results as follows:
(.(;=: +.515
y — —.562
^ = +.023
These values can now be substituted in the table of correlates, columns
1, 2, 3; the algebraic sum of hues a, h, c, cl, etc., giving corrections to the
angles a, b, c, d, etc.
, ., n Corrections to
+. 51S
+.515
b
'+.515
+ .615
c
+.023 •
+.023
d
-.662
-.562
— 562
—.662
f
+.023
+.023
n
—.515
+.033
—.492
h
+.562
+ .023
+ .685
FIGURE ADJUSTMENT.
The measiu-ement of the angles having been executed by instruments
and methods much better than the needs of the map require, it is not ordi-
narily necessary to make any figure adjustment, further than an equal dis-
tribution of the error of each triangle among the tlu-ee angles.
Stillj as the necessity for a more elaborate adjustment may arise, a
description of the method of applying the least square adjustment to geo-
metric figures in triangulation is here given, with a simple example of its
apphcation.
Each geometric figure in a system of triangulation is composed of a
number of triangles. The measured angles of each triangle should equal
180° plus the spherical excess. Each triangle, therefore, furnishes an equa-
tion of condition, which is known as an angle equation. The number of
angle equations in any figure is equal to the number of closed triangles
into which it can be resolved. But since certain of these are a consequence
of the others, the number of angle conditions which it is desirable to intro-
duce is less than the number of triangles.
The number of angle equations in any figure is equal to the number
of closed lines in the figure plus one, minus the number of stations. Thus,
in" a closed quadrilateral, the number of angle equations is 6 + 1 — 4 — 3.
EEDUOTION OF TEI ANGULATION. 69
There is another class of conditions, known as side equations, which
can be best explained by reference to a figure. In the example, diagram,
suppose the figure 0, 1, 2, 3 to represent the projection of a pyramid,
of which 1, 2, 3 is the base and 0 the apex. A geometric condition of such
figm-e is that the sums of the logarithmic sines of the
angles about the base, taken in one direction, must
equal the similar sums taken in the other direction,
i. e., the product of the sines must be equal. In the
present case, log. sin 0, 1, 2 + log. sin 0, 2, 3 + log.
sin 1, 3; 0 should equal log. sin 1, 2, 0 + log. sin 2, 3, 0 + log. sin 0, 1, 3.
The number of side equations which can be formed in any figure is
equal to the number of lines in the figure, plus 3, minus twice the number
of stations in it or / + 3 — 2 n. In a quadrilateral, 6 + 3 — 8 r= 1.
The numerical term in each angle equation is the difi'erence between
the sum of the observed angles on the one hand and 180° + the spherical '
excess on the other. This is positive when the sum of the observed angles
is the greater, and vice versa. The coefficients of the unknown corrections
are in each case unity, unless weights are assigned.
The numerical term in each side equation is the difference between
the sums of the logarithmic sines, taken in the two directions. The coeffi-
cients of the unknown corrections are the differences for one second, in the
logarithmic sines of the angles.
The method of making up and solving these equations and applying
the corrections to the angles can best be shown by means of an example.
That -here given is the simplest case involving both angle and side equa-
tions, namely, the case of a quadi'ilateral. The method of forming correla-
tives and normal equations, and their solution, is similar to that employed
in station adjustment, and therefore the details are omitted.
In the equations of conditions and correlatives, the angles are desig-
nated by directions, to which the corrections are finally applied. Thus
the angle of 302 is designated as — 3/0 -|- 2/0, the sign — being given to
the left-hand and the sign + to the right-hand direction.
70
A MANUAL OF TOPOGRAPHIC METHODS.
Example of figure adjustment hy least squares,.
Observed angles.
c
3-0-1
120
39 14. 781
(«)..<
01-3
21
20 17.806
<
1-3-0
37
54 37. ISO
180
00 09. 767
ST)herica
excess
= —0.148
Closure erroi-
+ 9.619
(
0-1-2
81
52 51.222
(h)..l
1-2-0
62
22 38.500
\
2-0-1
35
44 45.861
180
00 15. 583
— 0. 189
Closure error
+15. 394
1-2-3
91
28 38.000
2-3-1
28
95 10.360
3-1-2
60
26 33. 410
180
00 21. 776
— 0. 234
Closure (
rror
+ 21.542
c
2-3-0
65
59 47. 540
{c)..{
3-0-2
84
54 28.920
\
0'2-3
29
05 59. 600
180
00 15. 9C0
— 0. 193
Closure e
rror
+ 15.767
Side equation.
[Taking 0 as the pole.]
Angle.
Log. sines of
spherical angle.
Tabular
difference
for 1".
Correc-
tions to
log. sines.
Corrected log.
sines of spherical
angles.
Spherical
excess.
Log. sines of
(<2)-
0.1.2
0.2.3
1.3.0
Sum =
1.2.0
2.3.0
0.1.3
Sum :=
From above
Difference
9.9956249.7
9. 6869340. 0
9.7884705.9
+3.0
37.9
27.0
11.0
9.4
53.7
-25.0
—127. 9
—1.2
-59.4
-77.7
-203.0
9. 9956224. 7
9. 6869212. 1
9.7884704.7
29.4710141.5
—.063
—.065
—.050
—.063
—.064
-.049
9. 9956224
9. 6869210
9. 7884703
29.4710295.6
29. 4710137
9. 9474437. 5
9. 9607184. 9
9.5628859.2
9. 9474378. 1
9. 9607107. 2
9. 5628656. 2
9. 9474378
9. 9607107
9.5628653
29. 4710481. 6
29. 4710295. 6
29. 4710141. 5
000.0
29. 4710137
0000.
00. 0000186. 0
.0= + 186.0 — 3.0 ({)+ 03.0 (;)— 37.9 (S)+ 37.9 (3)— 27.0 (5)+ 27.0 (§).
-[-11.0 (i)+ 11.0 (S)- 9.4(1)+ 9.4 (3)- 53.7 (?)+ 53.7 (J).]
Equations of condition.
.0=+ 9".619-o=+}-5 + |-J + g
.0=+15 .394— J + f — 4+ 3 — §+ J
.0 = +15 .767-| + 8-J+§-S + §
Collecting ter:
(d)
I (rf) and dividing through by 100 so as to avoid dealing with large numbers.
.0= +1.86+ .507 (5) + .030 f — .489 (?) +.379 (|) — .270 (J).
+ .176 (§) + .110(4) + .094 (g) -.637 (|).
EBDUCTION OF TEIANGULATION.
71
Tatle of correlatives.
Direc-
tion.
a.
b.
0.
d.
0/1
0/2
0/3
1/0
1/2
1/3
2/0
2/1
2/3
3/0
3/1
3/2
-1
■"'+i"'
+1
""-i"
—1
+1
"'+i"'
—1
'""-i"
+1
+.507
—.489
+ .176
+.110
—.270
-i
+1
+1
"■'lli
-1
+.030
+ .094
—1
+1
—.537
+.379
+1
Forming the normal eqaations in tbe uaual manner, Tve have :
0=+ 9.619
0=+15. 394
0=+15. 767
0=— 1.860
+6. 000
+2. 000
+2. 000
—0. 598
+2. 000
+6. 000
—2. 000
—1.076
+2.000
-2. 000
+6. 000
+0. 950
-0.598
-1. 076
+ 0.950
+1. 054
J find tlie following valnea ;
a = + 1. 900
6 = — 4. 386
c = - 5. 208
d = + 3. 059
Substituting tlie values of a, h, o, d, in the table of correlatives.
Direction.
A.
B.
C.
D.
Correction
to each
direction.
?
1
i
1
i
1
1
—1.900
+4. 386
-^.386
4-1. 551
—1.496
+0. 538
+4.037
—0.674
—2.770
—2.486
+4. 722
—2. 726
—0. 822
-4.294
+5. 496
+3.308
+0. 257
—4.049
+5.208
—5.208
+1.900
+1. 900
—4.386
+4.386
+0.336'
—0.826
—1. 900
+4.386
—4.386
—5.208
+0. 092
+0. 288
+5. 208
+5. 208
—1. 900
+1. 900
—1.643
+1. 159
—5. 208
3.0.1
0.1.3
1.3.0
0.1.2
1.2.0
2.0.1
1.2.3
2.3.1
3.1.2
2.3.0
3.0.2
0.2.3
Obsei
ved
angles.
Corrections.
Corrected spheri-
cal angles.
Sph. ex-
cess.
Plane a
agles.
120
21
37
81
62
35
91
28
60
65
84
29
39
26
54
52
22
44
28
05
26
^■9
54
05
14. 781
17. 806
37.180
51. 222
38. 500
45.861
38. 000
10. 360
33. 416
47. 540
28. 920
59. 500
—3. 308—2. 486.
—4.037+0.257
+2. 726—2. 770
^t. 037-^. 294
— t. 722—0. 674
+0.822—2.486
—4. 722—4. 049
—5. 496—2. 726
—0.257—4.294
—5.496—2.770
—3. 308—0. 822
-1-0. 674—4. 049
120
21
37
39
26
54
08.986
14. 026
37. 136
— 049
— 049
—.050
120
21
37
39
26
54
08.94
13.98
37.08
180
00
00. 148
—.148
180
00
00.00
81
62
35
44
42.891
33. 104
44.194
—.063
—.063
—.063
81
62
35
52
22
44
42.83
33.04
44.13
180
UU
00. 189
—.189
180
00
00.00
91
28
60
28
05
26
29. 229
02. 138
28. 865
—.078
—.078
—.078
91
28
60
28
05
26
29.15
02.06
28.79
180
00
00. 232
—.234
180
00
00.00
65
84
29
59
54
05
39. 274
24. 794
56. 125
—.064
—.004
j — 065
65
84
29
59
54
05
39.21
24.73
56.06
181
00
00. 193
—.193
180
00
00. OO
72
A MANUAL OF TOPOGRAPHIC METHODS.
For a full discussion of the Metliod of Least Squares and its application
to triang'ulation see "A Treatise on the Adjustment of Observations, by T.
W. Wright, B. A.," pp. 250-370. New York. D. Van Nostrand. 1884.
COMPUTATION OF DISTANCES.
In each triangle, starting with the base line, there is known at least
one side and the three angles. The remaining sides are computed by the
well-known proportion of sides to sines of opposite angles, or expressed
h sin A
mathematically, a =
sinB
In this computation distances should be
used in meters, and seven place logarithms should be employed.
The following is an example of the correction of the angles and the
computation of the sides of triangles taken from the work in Kansas:
station.
Angles locally
ad], and re-
duced to center.
i error.
Piano angles.
Log sines.
36 29 04.0
63 58 56.2
79 31 58.1
+ .5
+ .6
+ .B
36 29 04.5
63 58 66.8
79 31 58.7
0.2257704
9.9535952
9.9927124
179 59 58.3
Error=— 1.7
Log di3t. "ffewt- Walton -■ 3.57716H
Log sin Newt 9.9535952
a. c. log sin Township corner 0.2257704
Log dist. Township comer— '^^llton 3.7565267
Log dist. Newt-Walton 3.57716U
Log sin Walton 9.9927124
a. c. log sin township corner 0.2257704
Log dist. Township comer — Newt 3.7950439
COMPUTATION OF GEODETIC COORDINATES.
The next step is the computation of the latitude and longitude of the
stations and the azimuth or direction of the lines connecting them. Initially,
the latitude and longitude of some point is determined by astronomical
observations, and this point is connected with the triangulation. The
azimuth, or angle with a south line, of a line connecting this point with some
station in the triangulation is also determined by astronomical observations.
These, with the observed angles and the computed distances between the
stations, form the data from which the latitudes and longitudes of the sta-
tions and the azimuths of the lines connecting them are computed. The
EEDUCTIOISr OF TKIANGULATION. 73
difference in latitude between two adjoining- stations is obtained from the
following equation, based upon the Clarke spheroid :
-dL = K cos «' B+K^ sin^ a' C + (dL) ^D - hW" sin^ a' E, ''
in which
c?L is tlie difference in latitude.
K, the distance between the stations in meters.
a', the fore azimuth of the line connecting them, measured round clock-
wise from the south through the west.
h, the first term.
Sh, the approximate difference in latitude, being the sum of the first
twx5 terms.
B, C, D, and E, constants derived from the dimensions and figure of
the earth.
These are given for various latitudes in tables at the close of the
volume.
The difference in longitude is obtained by means of the following
formula :
,, , K sin a' A'
dM= jr~, —
cos L
in which
dM is the difference in longitude.
L', the newly determined latitude.
A', a constant, from tables near the end of the volume, and the others
as above.
The azimuths at the two ends of a line differ from one another, on
account of the converg-ence of the meridians. That first determined is known
as the fore azimuth, the other, the back azimuth. All azimuths are meas-
ured from the south jDoint around to the right.
The back azimuth is computed from the formula:
sin (L+L^
• da ^= dM
cos ^ dl^
where M is the longitude of the first station.
L, the latitude, and
L' the latitude of the second station.
74
A MANUAL OF TOPOGRAPHIC METHODS.
The constants used are those of the Clarke spheroid of 1866.
These formulae are derived and explained in Appendix No. 7, Report
U. S. Coast and Geodetic Survey for 1884.
The following are examples of the use of the formulae, taken from the
ti-i anovulation in New Mexico :
Spherical angle:
Azimuth a' :
6 .1 + 180°
Nell— Chuaca.
Nell— Zuui.
Znui— Nell.
159
120
29
54
08. 728
13. 980
38
179
34
50
54. 748
02. 124
218 24 56.872
Geodetic Cooedinates.
LONGITUDE.
35 07 25.927
log.K
4. 6236305
8. 5111933
COS ,V 9. 8930500
log (I) 3. 0278738
log. K2 9. 24726
" C 1.25696
" sin^ a' 9. 58986
log. (II) 0. 09408
log. D 2. 3679
'■ [I+II]' 6.0568
A' 108 54 40.285
Computation for longitude :
log. K 4. 6236305
" sin a' 9.7949286
"A' 8. 5092394
" sec.L' 0.0872944
rr. for diff. arc. & sine = — 15
log. (V)
Computation of azimuth :
log. E 6. 0124
" K2sin2a'8.8371
" (I) 3. 0279
log. (TV) 7. 8774
2. 776614
- 597". S76
- 9' 57". 876
Azimuth check.
(I)
(ID
1066. 286+
1.242 +
.026+
.008-
(ni)
(IV)
log. " " 3.0283792 Check:
"[I+II)= 6.0567584 Spher. angle
at
-«L
1067.546+
*
Computation of Azimuth, a, in Book , i
Splierical angle and distance = K, in Book
Station; Computed by
, page, Triangle No.
Azimntli a:
Spherical angle :
Chusca — Nell.
339
25
21
11
40. 150
38. 601
Chusca — Zuni.
4
179
33
57
18. 751
25. 650
Zuni-Cliuaca.
184
30
44. 401
PEIMAEY TEAVEESES.
75
Geodetic Coordinates.
LONGITUDE.
35 07 25. 928
log. K 4. 9280539
" B 8. 5111594
" COS a' 9.
log. (I) 3. 4378393
log. K? 9. 85610
'P C 1.26435
" siu'a' 7.79982
log. (II) 8. 92027
log. D 2. 3703
•■' [I+n]'^ 6. 8757
log. (Ill) 9.2460
log. E 6. 0214
" K^sin' a' 7.6.559
■' (I) 3.4378
log. (IV) 7.1151
(I) 2740."560+ I
(II) .083+
Computatii
T. fordiff.i
.(V)
108 50 14.518
+ 4 25. 768
108 54 40. 286
I forlongilude:
4. 9280539
8. 1.092394
0. 0872944
c&sine -129
2. 4245028
+265". 761
Computation of azimut Ii :
.(H^\
log. (TI)
2. 424503
9. 764002
2. 188514
■ 154". 350
•2' 34". 350
A zlmutti check :
— 6L +2740.818
. 176+ [I+II] 2740. 643
.001- ! log. •■ 3.4378525
[I+IIJ2 6.875705
Check :
Spher. anj
at Zuni
33 54 12. 471
33 54 12. 469
Computation of Azimuth a, in Book 67, page 4.
Spherical angle and distance = K, in Book 64, page 12, Iriangle No. 3.
Station; Computed by H. M. W.
When the hnes are not more than twenty miles in length, the equation
for latitude may be simplified without appreciable error by di'opping the
last two terms.
TRAVERSE LINES FOR PRIMARY CONTROL.
In level country, especially if it is covered with forests, it is very expen-
sive to carry on triangulation, and in some cases practically impossible to
do so. Under such circumstances the only means of obtaining an adequate
control for maps is by means of traverse lines.
A traverse line consists of a series of direction and distance measure-
ments. Each course, as the du-ection and the accompanying distance are
called, depends upon the one immediately preceding it, and a continuous
chain is thus formed. Traverse lines are largely used in the topographic
work proper for making minor locations. The primary traverse diifers
from these only in the fact that it is much more elaborately executed.
The initial point of a primary traverse must be located either by
triangulation or by astronomic determinations. The end of the line should,
76 A MANUAL OF TOPOGEAPHIC METHODS.
if possible, be a point similarlv well located. The line sliould, if practica-
ble, follow a railroad, in order to obtain the easiest possible grades, and
thus avoid errors incident to slope.
The instrument used for measuring- directions should have a circle 6 to
8 inches in diameter, and should read by vernier to 10 seconds. The the-
odolites formerly used in the primary triaugulation are generally used in
this work. A larger or more elaborate instrument is not advisable on
account of the difficulties of transporting it and frequently setting it up.
Upon short lines instruments reading to minutes may be used.
The readings should be upon signals consisting of poles, and fore and
back rodmen must be employed for carrjnng and setting them. The
angular measurements between the poles should be read by both verniers,
and it is advisable to note the compass readings at the same time, in order
to avoid gross errors. At intervals of 10 to 20 miles, depending upon the
number of courses to a mile, observations should be made for azimuth,
obsei*ving for this purpose upoii the pole star, preferably at elongation.
The measurements of distance are effected by the use of steel tapes,
and preferably by 300-feet tapes, similar to those used in measuring base
lines. Two chainmen should be employed, and in order to avoid eri'ors in
the count, it is well to count the rails, in case the woi-k is done upon rail-
road tracks.
The temperature should be noted by means of thermometers at frequent
intervals, in order that the proper corrections may be applied.
The errors incident to running primary traverses are of two classes:
errors of direction and errors of distance.
Those of direction are similar to those treated of under the head of
Instructions for the Measurement of Horizontal Angles, and need not be
specified here.
Owing to the necessity of setting up the theodolite at frequent inter-
vals, it is impracticable to observe at each station the series of angles speci-
fied in the abdve-mentioned instructions, and only a single or at the most
a double measure of the included angle, with the reading of each vernier,
is practicable for the measurement of direction. It is here provided that
observations for azimuth upon Polaris should be much more frequent than
in triangulation, and thus an absolute correction to the dii-ections is intro-
ELEVATIONS. • 77
duced mucli ofteuer. At each azimuth station the new astronomic azimuth
should be adopted in place of that carried forward, and in case the discrep-
ancy between the two is sufficiently great to involve perceptible error upon
the scale of the map, the correction should be uniformly distributed forward
from the first station.
In running these traverses all road crossings should be located, as
topographic traverses will be run over the roads and will be connected with
the primary traverses at these points. All prominent houses or natural
features of any kind in sight from the line must be located by iatersection,
as they will doubtless be used by the topographers for location.
When traversing in a country which has been surveyed by the Greneral
Land Office into townships and sections, the crossing of every township
and section line should be located, and the directions of the township lines
with reference to the line of traverse should be carefully measured in order
to establish as close a relation as possible between the traverse line which
serves as ultimate control, and the township system of surveys, which serves
as a secondary control.
Lines of traverse exceeding 100 miles in length should be reduced by
computation. The distances should be corrected for error of tape, for tem-
peratiTre, and slope, and should be reduced to sea level, in the same man-
ner as above described in treating of the reduction of base lines, in case
these corrections are of sufficient amount to affect the length appreciably
upon the map.
The courses should be corrected for convergence of meridians. Then,
commencing at the initial point, the latitude and departure of each station,
one from another, should be computed in feet. The sum of the latitudes
converted into seconds of latitude gives the difference in latitude, and the
sum of the departures converted into seconds of longitude gives the differ-
ence in longitude.
Short lines of traverse may be platted with minute reading protractors,
but in this platting the utmost care should be exercised.
PRIMARY ELEVATIONS.
The initial elevations of this work are derived from various sources.
Any trustworthy results known to be of a sufficient degree of accuracy for
78 A MANUAL OF TOPOGEAPHIC METHODS.
the 2:)urpose may be adopted. Whenever elevations have been determined
within the area to be surveyed by the United States Coast and Geodetic
Siu-vey or the United States Lake Survey, they may be accepted without
question. The work of these organizations has been sketched in the early
pai-t of this volume and is shown upon map No. 1.
Wlien these determinations are not available, initial bench marks
should, if possible, be obtained from the profiles of railroads traversing
the district. These have been adjusted and the results published in the
Dictionary of Altitudes (Bulletin No. 76, U. S. Geological Survey). In
case there are no raih'oads to furnish initial datum points, as may occur
in the sparsely settled regions of the West, or the profiles available are
regarded as untrustworthy, it may become necessary to use barometric
observations. Where a series of these, of a year or more in length is
available, the result may be regarded as sufficiently trustworthy for this
pvu-pose.
In regions where secondary triangulation is practicable the measure-
ment of heights may be taken up with the plane table directly from datum
points, as above indicated, and carried throughout the work by means of
this instrument. Otherwise it becomes necessary to do more or less level-
ing in order to extend and multiply datum points to control the less
accurate work connected with the traversing. If practicable, the wye
level should be employed.
The extent of the work of the wye level which may be required
depends mainly upon the contour interval of the map to be made. It may
be said in general, that a single line aci-oss a sheet will furnish a sufficient
number and a suitable distribution of points for the proper correction of
the subsequent work. Wherever practicable such lines should be run
along raih'oads, in order to obtain easy grades and thus lig-hten the work.
When railroads are not available, they should be run along wagon roads,
selecting, so far as they will suit the purpose, those having the easiest
grades and the straightest com-ses.
Where the control of the map is effected by means of primary ti-av-
ersing, such traverse should be accompanied by a level line, unless that of
the raih'oad which the traverse follows appears to be of sufficient accuracy.
CHAPTER IV.
SECONDARY TRIANGULATION.
The work of making secondary locations by intersection is done mainly
by plane table. The use of the theodolite for this purpose is restricted to
those cases where but little of this kind of location can be effected, and
where, therefore, it seems scarcely worth while to prepare plane-table sheets.
By means of the primary triangulation, two or three points are usually
located upon each atlas sheet. Within this primary triangulation, and
depending upon it, are then located a large number of points, either by
intersection, by traverse, or by both methods, forming a geometric frame-
work upon which the sketching of the map depends.
Location by intersection should be carried as far as practicable — that is,
all points capable of being located in this manner should be so located in
order to afford the most ample control possible for the traverse hues, by
which the intervening areas are to be filled in, it being understood that the
location by intersection is more accurate and more rapid, and consequently
in every way more economic, than location by traverse.
THE PLANE TABLE.
Much misapprehension exists, especially in this country, regarding the
character and application of this instrument. This arises, apparently, from
the fact that it is little known. For making a map the plane table is a uni-
versal instrument. It is appHcable to all kinds of country, to all methods
of work, and to all scales. For making a map it is the most simple, direct,
and economic instrument; its use renders possible the making of the map
directly from the country as copy, and renders unnecessary the making of
elaborate notes, sketches, photographs, etc., which is not only more expen-
sive, but produces inferior results.
yO A MANUAL OF TOrOGEAPHlO METHODS.
The plane table is essentially very simple, consisting' of a board upon
which is fastened a sheet of drawing paper. This board is mounted upon
a tripod, which, in the more elaborate forms of the instrument, possesses
great stiffness and stability. It should be capable of being leveled, of
being tm-ned in azimuth, and of being clamped in any position. Upon the
paper is produced directly in miniature a representation of the country.
When set up at various places within the area in process of being mapped^
the edges of the board must always be placed parallel to themselves — that
is, a certain edge of the board must always be set at the same angle with
the north and south line. This is called orienting the board.
Directions are not read off in degrees and minutes, but platted directly
upon the paper. The instrument used for this purpose is known as the
alidade, and consists of a ruler with a beveled edge, to which are attached
for i-ough work two raised sights, and for the higher class of work a tele-
scope-turning on a horizontal axis. This telescope carries also a delicate
level and a vertical arc for the measurement of angles in the vertical plane,
from which relative heights are obtained. The method of using this instru-
ment is extremely simple in principle, and becomes difficult in practice only
when a high degree of accuracy is required.
The work of making locations from intersections obtained by means of
the plane table requires that the instrument have the utmost stability con-
sistent with lightness and portability. It requires an alidade equipped with
a telescope of considerable power and good definition. In short, it requires
that the plane table be in every respect of the best modern type in order
that the highest degree of accuracy possible to represent upon the paper be
attained. Various forms of plane-table movement have been in use, includ-
ing the heavy and cumbersome but stable movement of the Coast and Geo-
detic Survey, and the light but unstable movement used by the same
organization in its less important work. At present a table is in general use
which was invented by Mr. W. D. Johnson, of this Survey, which combines
the elements of stability, lightness, and facility of operation in a remarkable
(leo-ree. (See Fig. 8.) This movement is essentially an adaptation of the
ball-and-socket principle, so made as to furnish the largest practicable
amount of bearing surface. It consists of two cups, one set inside the other.
JOHNSON PLANE TABLE AND TELESCOPIC ALIDADE,
THE PLANE-TABLE.
81
the inner surface of one and the outer surface of the other being ground so
as to fit accurately to one another. The inner cup is in two parts, or rather
consists of two rings one outside the other, the one controlling the move-
ment in level and the other that in azimuth. From each of these rings there
projects beneath the movement a screw, and upon each of these screws is a
nut by which it is clamped. There is no tangent screw for either the leveling
Johnson Plan e-IAble Head
a. Plana Table board f. VpperLepel Cup
b^ Bearing PLaze g. Ztofr'er "
<?. TripocLHeaa fi.. Jjei'sL Clamp
el. •' Z,effs t Mzimzith, CLamp
e.jiziTruztfiGzp
Fig. b.— Joliuson plane-table tripod liead. Section.
or the azimuth motion, as none is required. The movement is sustained
by a light hard-wood tripod with split legs. The board used generally
accommodates a full atlas sheet, but necessarily differs in size, owing to
the different scales of field work adopted. The largest board used for
this movement holds an atlas sheet upon a scale of 1:45000, and is 24 by 36
inches in size.
MON SXII 6
82 A MANUAL OF TOPOGRAPHIC METHODS.
The question of paper for the ^Diane-table sheets, especially in inter-
section work, is of great importance, as paper which expands and contracts
differently in different directions under varying conditions of moisture will
easily produce errors of magnitude in the work. It matters little if the
paper contracts and expands, provided it does so uniformly in all dnections,
but all paper is made with more or less fiber, and accordingly expands and
contracts more in one direction than in another. To cotmteract this, two
thicknesses of paper are used, preferably that known as Paragon paper,
moxmted with . the grain of the two sheets at right angles to one another,
and with cloth between the la5'ers. In sheets so prepared it has been found
that there is practically no distortion, even under the most severe tests.
The board is generally made of seasoned white pine, from one-half to
five-eighths of an inch thick, with cleats across the ends fastened in such a
way as to allow the body of the board to contract and expand freely, and
therefore without warping. Into the corners of this board and on the edges
at points halfway between the corners are set female screws for holding
the paper to the board. At corresponding points in the plane-table sheet
are punched holes half an inch in diameter which are lined with eyelets,
and thi'ough which pass screws with broad heads fitting into the female
screws in the boai-d. The holes in the paper, being larger than the screws,
allow the paper to expand or contract freely when the screws are loose.
When tightened, the broad heads of the screws bind the paper firmly in place.
THE ALIDADE.
The ahdade used with this plane table consists of a ruler of brass or
steel 18 inches to 2 feet in length, graduated upon a chamfered edge to suit
the scale of work, and carrying upon a column a telescope having a focal
distance of 12 to 15 inches and a power of about 15 diameters. It has a
vertical arc reading by vernier to single minutes, and a delicate level upon the
telescope. In some alidades there is an adjustment to make the zeros of the
vertical arc and the veiTuer coincide, when the telescope is horizontal, while
in others it is necessary to read the index error of the vertical arc and correct
for it, there being no such adjustment. The telescope turns in a sleeve, for
adjustment of vertical collimation.
THE PLANE-TABLE. 83
Upon the j)lane-table sheet is constructed a projection upon the scale
of the field work, and upon that are platted such of the primary points as
fall upon the sheet, each plane table sheet being made to correspond to an
atla,s sheet. These primary points are first occupied by the plane tabler.
The instrument is set over one of these stations, leveled, and clamjjed.
The ruler edge of the alidade is then laid upon the line connecting this
station with a neighboring one upon the sheet, and the table turned until
the other station is upon the vertical wire in the telescope. The instrument is
then oriented, and, after clamping in azimuth, is ready for work. Keeping
the ruler upon the occupied station on the sheet, the telescope is then turned
upon other objects which it is desirable to locate, and lines are drawn, in
turn, toward them. The instrument is then taken up fCnd moved to a second
station, where it is again set up, leveled, and oriented, as before. A sight is
then taken, and a line drawn in the direction of each point sighted from the
first station, and the intersection of each pair of sight lines is the true position
of the corresponding point upon the map. In this way, station after station
is occupied by the plane table, and numerous points are located by inter-
section. If possible, each point thus located should be intersected from at
least three stations in order to verify its location.
Any point thus located on the map may be used afterward as a station.
In case it is necessary to occupy a point toward which no line has been
drawn, or which has not been located, the simplest and best plan for effect-
ing its location is as follows :
Fasten upon the plane-table board, which necessarily has not yet been
oriented, a piece of tracing linen, or ,in default of that, a piece of tracing
paper. Assume a point upon this linen to represent the station, take sights
upon, and draw lines to all located points within the range of vision, and
then, loosening the linen from the board, move it about over the map until
these sight lines fall upon the proper points upon the map. Then prick
through the position of the station from the linen to the map underneath.
This location should then be tested by sighting from the point thus found
to the various objects to see if the sight lines fall upon the points as marked
upon the map.
84 A MANUAL OF TOPOGRAPHIC METHODS.
In case one line of sig'lit upon the required station has been obtained,
that sight Hue may be utihzed in making the location as follows by resec-
tion: Having leveled the table, place the alidade upon this sight line
already drawn, with the telescope pointing toward the object from which
the sight was taken. Then turn the table in azimuth until the telescope
falls iipon this point, and clamp it. The table is now oriented, but the posi-
tion of the present station is unknown further than that it is known to be upon
this line. Then select some station whose direction makes a wide angle
with this line, and move the alidade until the cross wire falls upon this
selected station, while the ruler at the same time is upon the representation
of the station upon the map. The ruler will then cross the sight line at
the point desired. By way of check, repeat the process with another sta-
tion or located point. For this purpose a point in suitable direction is
valuable in proportion to its proximity.
Using the instrument as described above, the topographer locates from
*them all possible points. Then visiting in turn such of them as he finds
necessaiy, pei'haps a dozen or twenty, he locates by intersection points all
over the sheet in as great number and as well distributed as possible, and
with special reference to the needs of the traverse men, who will come after
him and whose work will be located by means of his determinations. All
this work must be done with the utmost nicety and precision. The setting
of the alidade upon the station must bisect the needle hole by which it is
marked and the lines of direction must be drawn with a sharp-pointed pencil.
The necessity for precision will be recognized when it is understood
that any error introduced in the early part of the plane-table triangulation
will be not only perpetuated, but increased many times over as the work
progresses, and as soon as an error becomes appreciable it produces difficul-
ties and uncertainties in making locations, which may lead to embarrassing
delays, and ultimately require that all the work be repeated.
MEASUREMENT OF ALTITUDES.
While making horizontal locations of points with the plane table, their
heights must also be measured, relative to that of the point occupied. This
is done by means of the vertical arc of the alidade and the level upon the
TEAVBESE WOEK. 85
telescope. Pointing upon tlie object whose relative height is to be measured,
the telescope must first be brought to a horizontal position. In case the
vertical arc is movable, its zero must then be brought to the zero of the ver-
nier. In case it is not movable, the index error, with its sign, must be read.
The telescope is then raised or depressed to the point and the reading
obtained. This adjustment of the vertical arc or reading of the index error
must be done for each point, as the table cannot be leveled with sufficient
accuracy, or cannot be expected to maintain its level, so as to dispense with
it. Knowing the horizontal distance to the point and the angle of elevation
and depression, the difterence in height is obtained by the solution of a right-
angled triangle, thus:
h =:d tang a,
Ji being the difference in height, c? the distance, and a the angle of elevation
or depression. This distance is then to be corrected for curvature of the
earth and for refraction by the atmosphere. The correction for the former
is obtained with sufficient accuracy by the following empirical rule. The
curvature in feet equals two-thirds the square of the distance in miles. It is
always positive in sign, whatever may be the sign of the difference in height.
Refraction is an uncertain and variable quantity. It is usually greatest
at morning and night and least at midday. It is greater the nearer the line
of sight is to the ground. Often in desert regions it is excessive in amount.
It is usually assumed at one-seventh the curvature, and is negative.
Tables for the solution of vertical angle work are appended to this
volume. These give differences in height for all angles and distances which
should be employed, with corrections for curvature and refraction.
Differences of height should not be measured at greater distances than
10 miles, if it can be avoided. An error of 1' in the measurement of the
angle is at this distance about 15 feet, while the uncertainty of refraction
in such a length of line is necessarilj^ great.
TRAVERSE WORK.
As Stated above, under the head of primary traverses, a traverse line
consists of a series of direction and distance measurements depending upon
one another. These lines should be connected wherever possible with trian-
86 A MANUAL OF TOPOGEAPHIC METHODS.
gulation points iu order to check up accumulated errors. If it were prac-
ticable or econoroic to carry on all tlie work of location by intersection, this
would be the most accurate and on most accounts the best way to effect it,
but it is only in limited localities, such as high mountain regions, where bold
topographic forms predominate and where there is little or no culture, that
the method of intersection is practicable for locating all necessary points. It
is probable that in nine-tenths of the area of the United States it will be
found necessary to locate the details of topography, culture, and di-ainage
by means of traverse lines. In different parts of the country the relative
extent to which the two methods can be applied depends upon various
circumstances, .principally the amount of relief of the surface and the prev-
alence of forests. Thus upon the Atlantic Plain, which is densely covered
with forest, and which is very level, it is necessary to use the traverse
method exclusively, including even the primary control. Passing from this
as an extreme case, through rolling and hilly country to the high sharp
mountains of the West, the triangulation method becomes more and more
prominent while the traverse method finally becomes used but little, except
in the details of roads and other cultural features.
For executing traverse work various instruments have been in use for
measuring both distances and directions. For direction there have been
used theodolites of various forms and prismatic compasses and for distances
the stadia and the wheel.
At present all traverse work is done with plane tables, upon which the
directions and distances are platted directly. The plane table used for this
purpose is of the simplest possible form, consisting of a board about 16
inches square, into one edge of which is set a narrow box containing a com-
pass needle 3 inches in length. This table is supported by a tripod of light
construction, without leveling apparatus, the leveling of the instrument
being effected with sufficient accuracy by the tripod legs. A single screw
fastens the board to the tripod head and the adjustment in azimuth is made
by simply tm-ning the board with the hand. It is held in place by friction.
The table is adjusted in azimuth, or oriented, by means of the compass
needle — that is, it is turned until the needle rests opposite the zero marks
in the compass box, and is thus always made approximately parallel to
itself, provided the magnetic declination remains constant.
TRAVERSE PLANE TABLE AND RULER ALIDADE.
TRAVERSE WORK.
87
The alidade consists of a brass ruler, 12 inches long, with folding sights.
The edge of the ruler is graduated to facilitate platting of distances. Ordi-
nary drawing paper backed with cloth is used for plane-table sheets, and is
attached to the board by thumb tacks. *
When traversing is done along roads, as is commonly the case, dis-
tances are measured by counting the revolutions of a wheel, usually one
of the front wheels of a buggy or buckboard. For counting the revolutions,
various automatic devices have been in use. The old form of odometer
known as the pendukim was first tried and was unqualifiedly condemned.
The form now in general use was devised by Mr. E. M. Douglas of this
Survey. See Fig. 9.
^■"'Vi/viaocctf^
Fig, 9. — Douglas odometer.
For operating this a cam is placed on the hub of the wheel, which by
raising a steel spring as the wheel revolves carries the index forward one
division for each revolution. This form is the most trustworthy that has
yet been devised, but is not altogether satisfactory, and many topographers
prefer to count the revolutions of the wheel directly, using an an-angement
by which a bell is rung at each revolution.
An experience covering many thousands of miles of measiu'ement has
shown that as a working method of measuring distances on roads the wheel
is superior to the stadia, alike as to accuracy and rapidity
A traverse "man is generally assigned a tract of country within which
he is instructed to run traverses of all the public roads and of such of the
private roads as appear to be necessary in order to control the entire tract.
If practicable, he is furnished with the positions of the points located within
88 A MANUAL OF TOPOGRAPHIC METHODS.
liis ti-act properlv platted upon Lis plaue-table sheet, or, if tliese cau uot be
t\u-nished, with such descriptions of them as are necessary to enable him to
recognize them and close his lines npon them or connect with them by tri-
angnlation. He is fm-nished mth a horse and buggy or buckboard, traverse
plane table, and aneroid. He has no rodman, but is expected to sight natural
objects. Setting up his instrument at his initial station, he leA^els it roughly
by means of the tripod legs, orients it by turning the table until the com-
pass needle is on the zero mark in the compass box, then, marking a point
on the paper to represent his initial station, and placing his alidade upon it,
he points it to an object selected as his second station, and draws a line in
that direction. Driving along the road he passes the point sighted at, noting
the distance to it by the reading of the odometer, or the coimt of the revolu-
tions of the wheel, and the height as recorded by the aneroid, and passes on,
selecting some point from which he can see the point sighted at. There he
stops, sets up his table as before, orients it, and sights upon the same signal
which he sighted fi-om his initial station. He plots the distance to the signal
along the sight line from his initial station; then from the location of the sig-
nal as thus established he plots liis second station by the distance measure-
ment and the reverse of the observed direction. In this way the work pro-
gresses, a hundred stations or more being occupied in the course of the day.
In this work one should aim to make as few stations and to take as long
sights as possible consistent with accuracy. Bends of the road between
stations can be sketched with all needful accm-acy.
During the progress of the work all points off the line which are capa-
ble of being located by intersection must be located by sights taken from
stations, and special care must be taken to connect them with the points
located by the secondary triangulation, in order to afford as many checks as
possible to the accm-acy of the traverse line.
Traverse lines should close with but ti-ifling eiTor — an eighth of an inch
upon the paper in a distance of 10 or 12 miles is as great an eiTor as should
be permitted— and all errors of closm-e should be shown. No line should
be arbitrarily closed on the traverse sheet.
The traverse man should sketch or locate all country houses, should
note aU road intersections and all raih'oad crossings, specifying by simple
TRAVERSE WORK. 89
conventions the character of the crossing, whether over, under, or grade
crossing. He should similarly describe all stream crossings , distinguishing
fords, ferries, and bridges.
MEASUREMENTS OF HEIGHT IN CONNECTION WITH TEAVERSE LINES.
Height measm-ements in connection with traverse lines are effected in
one of two ways — either by vertical angles with the telescopic alidade or
by the use of the aneroid.
In regions where little or no secondary triangulation can be done, it
becomes necessary to accompany certain of the traverse lines by profiles
determined by vertical angles. Such profiles should be surveyed at inter-
vals of 4 or 6 miles where the contour interval is 20 feet, and at intervals
of 8 or 10 miles where it is 50 feet.
The alidade generally used in running these profiles is of a small com-
FiG. 10 Small Telescopic Alidade.
pact form, with low standards and short ruler. The telescope has low
power, but carries a good vertical arc and a level. The arc and vernier
are graduated to single feet with a radius of a mile, instead of degi-ees and
minutes, in order to facilitate computation. This graduation is made on the
assumption that where the angle is less than 5° the arc and the tangent do
not materially differ.
With this instrument the plan of the traverse is run precisely as above
sketched, except that a rodman is frequently employed. In running the
profile, which is done coincidently with the plan, the points sighted for
elevation may be the same as are used for the plan. If a rodman is em-
ployed, the target on the rod should be set at the height of the instrument
to simplify record and computation.
90 A MANUAL OF TOPOGEAPHIO MJOTHODS.
It must not be understood, however, that it is at all necessary that the
survey of the profile should establish the height of all the points located
by the traverse. The profile should give the elevation of all valleys and
summits, and of all road crossings. The line should be carried forward
and these points ineasured by as few and as long lines of sight as possible.
Often the roof of a house will furnish a datum point for use for a mile or
two. Indeed, in an open, settled country the line can frequently be carried
forward coutinuoiisly by using housetops as targets.
The reduction of the profile must keep pace with the field work, so
that on arriving at a check point the amount of the error may be shown at
once. If this is not more than one-fom'th or one-fifth of the contour
inten'^al, it is not considered as of material account. If, however, it reaches
half a contour interval, the work should be examined, and if the error be
not discovered the line should be resurveyed.
The heights, as determined, should be written in ink upon the plane-
table sheet in their proper places.
- THE ANEROID.
In the great majority of traverse work heights are measured with
aneroids. The aneroid consists of a vacuum box of thin coiTugated metal,
which is compressed by an increase and expanded by a decrease in the
pressm-e of the atmosphere. A ti'ain of mechanism magnifies this trifling
movement enormously and moves an index upon a graduated dial. This
dial is graduated to feet of elevation and also to inches of barometric
pressm-e.
Several sizes of aneroids are made; that having a diameter of 2 J
inches is on the whole found the most satisfactory.
Owing mainly to its extreme delicacy the aneroid is a very uncertain
instiTiment. It should be used difi'erentially only, and for small diiferences
in height and small intervals of time. Its indications should be checked
by reference to known elevations whenever opportunity is afforded during
the day, and at the beginning and ending of each day's work.
On commencing work the movable scale on the aneroid should be set
at the known height of the starting point and a note made of its reading
on the inch scale. Elevations should then be read du-ectly from the scale
THE AFEEOID.
91
of feet. The heights of all points along the line of traverse which will be
required in making the contour sketch should be read and written upon the
traverse. Every depression and elevation, road crossing, etc., should thus
be measured. There is, hoAvever, no necessity for reading the aneroid at
every station in the traverse. It will merely encumber the work with a
mass of useless data.
Upon reaching a check point, comparison should be made with the indi-
cations of the aneroid. If the difference is considerable — i e., more than a
contour interval — the error should be distributed backward along the line in
proportion to distance. If it is small, it may be neglected.
Fig. U. —Aneroid.
Fig. 12.— Works of the Aneroid.
In all this work notebooks are not required, except as a convenient form
of carrying paper upon which to make the trifling computations required.
The plane-table sheets comprise all the records necessary. The work, as
it progresses, criticises itself by its closui-es in position and elevation, and,
wherever necessary, is revised immediately.
ORGANIZATION OF PARTIES AND DISTRIBUTION OF WORK.
Secondary triangulation, traversing, measuring of heights, and sketch-
ing are commonly carried on by- one party. This consists of the chief of
party, who directs all the operations, and who does all the sketching; an
92 A MANUAL OF TOPOGEAPHIC METHODS.
assistant who carries on the secondary trianguhation, selected as possessing
special fitness for that work, and one, two, or more assistants who are
engaged in traversing, the number of these assistants depending upon the
rapidity with which the country can be sketched relative to the rate at which
the traversing progresses. If possible, the difierent items of work of such a
partv should follow one another in a certain order. The secondary trian-
gulation should be done first in order that the traverse men may be furnished
with positions and heights for locating and checking their traverse lines. The
traversing should follow, in order that all the control may be furnished to
the chief of party for his use in sketching. This order, which is followed as
closely as practicable, requires that the members of the party be scattered
over a considerable area of coimtry, and if they are living in camp it
requires that they remain away from it a considerable part of the time, or
else that a large amount of traveling be done in order to reach camp at night.
Wliere they are not living in camp, the most economical disposition is to
scatter them at various places within their fields of work. In any case, con-
stant communication must be had between the chief of party and his assist-
ants, in order that they may work in accord.
STADIA MEASUREMENT.
Under certain circumstances it is found advisable to use the stadia
method for measuring distances in place of the wheel. This is the case
where lines are to be run without reference to roads, and consequently
where the wheel cannot be employed with advantage. It has been used, too,
in southeiTL Louisiana, where peculiar methods of work imposed by the nature
of the topography have made its employment economic. The instniment used
for the stadia or telemeter method of measuring distances may be anything
cari'jnng a telescope. To the reticule of the telescope are added two or more
fixed horizontal wires placed at a certain distance apart. A rod or board
subdivided to suit the interval between the wires and painted in glaring
colors forms part of the outfit. When this rod is set up at a distance from
the telescope, that distance is ascertained from the number of subdivisions
of the rod which are included between the wires of the telescope, the value
of each division of the rod being known. Upon the Geological Survey cer-
STADIA MEASUEEMBNTS. 93
tain theodolites and telescopic alidades are equipped with stadia wires.
These wires are three in number, the intervals between them being equal.
The rods are 14 feet in length and hinged so as to close to 7 feet. The
intervals upon the rods are of one foot each. The wires in the telescope are
so spaced that when the rod is at a distance of 100 feet, the space between
the two extreme wii-es will subtend one foot on the rod. At a distance of
1,400 feet, therefore, this space will subtend the entire length of the rod,
while at a distance of 2,800 feet two adjacent wires in the telescope will
subtend the entire length of the rod. Distances less than 100 feet are esti-
mated by means of the fractional 2Dart of a foot upon the rod, which is
included between the wii'es. The distances are read off upon the rod by
the surveyor at the instrument.
In measuring distance upon slopes, correction must be made to reduce
the inclination measured to horizontal distance. Tables for this reduction
are to be found in Bulletin. Where the slope- is slight it is not regarded as
necessary to make this reduction, especially where there are frequent points
for checking and correcting the line.
The rod may be used also for measurement of the profile of a line.
For this purpose, a point should be marked upon it at the same height as
the telescope of the instrument and vertical angles taken to this point.
The work which has been can-ied on in southern Louisiana is peculiar
in the fact- that the slopes are extremely gentle, requiring, in order to show
the relief at all, a contour interval not greater than 5 feet. For the location
of contours of so small an interval, even -vertical angles are not sufficiently
accurate, and the work of measurement is effected by spirit level. The
instrument used is a theodolite of compact and simple form, to which the
name of gradienter has been applied, which is equipped with stadia wires.
The low ridges which accompany the streams of this region and which form
all the relief are located by means of lines run approximately at right angles
to the streams from their banks down to the swamps on either side. Dis-
tances are obtained by stadia and differences of elevation by using the
gradienter as 'a wye level, and the stadia rod as a level-rod.
94 A MANUAL OF TOPOGEAPHIC METHODS.
THE CISTERN BAROMETER.
lu work bavirig a large contour iuterval, 50 feet or more, the cistern
barometer is used to some extent, though not as much as formerly. Its use
is now confined to the work in the far West, where it is employed in the
determinations of heights of points in the valleys not easily reached by
vertical angles.
The barometer is an instrument for measuring the pressui-e of the
atmosphere. At the level of the sea this pressure of about 15 pounds per
square inch supports a column of mercury about 30 inches in height. As
one rises above sea level and leaves a portion of the atmosphere behind
him the pressure diminishes and the column of mercury sustained by it is
of less height.
The cistern barometer, in its most portable form, is made by H. J.
Green. It consists of a cistern into which dips the lower open end of a
glass tube 31 or 32 inches in length, the whole being inclosed in a brass
case. The cistern consists of a number of parts, including a short glass
cylinder, below which is fitted the inverted frustum of a hollow cone of
boxwood. This is succeeded by a second frustum, placed upright, from
the lower end of which depends a bag of buckskin. The bottom of the
latter is raised or lowered by means of a screw in the brass case of the
cistern. The cisteiTi is closed at the top by a boxwood ring, which is fitted
to the top of the glass cylinder. By means of an annular piece of kid,
which is securely lashed to the boxwood ring and to the barometer tube,
the cistern and the tube are connected. From the under sm-face of the
boxwood ring depends an ivory point about a quarter of an inch in length.
Upon the brass casing of the tube is a graduation into inches and twentieths,
by which, with the aid of A^erniers, the scale may be read to 0.002 of an
inch. To this brass case is attached a thei-mometer, for indicating the tem-
peratm-e of the instrument. For carriage the barometer is placed in a
wooden- case fitted to its shape, and this in turn in a case of heavy leather
fitted with a shoulder strap. It should always be carried in an inverted
position.
To read the instrument it should be hung where it can swing freely.
Then, by lowering the screw at the bottom, di-op the mercury in the cistern
THE CISTEEN BAEOMETEE. 95
until its top just touches the ivory point above mentioned. This can be
best effected by making the ivory point and its reflection from the surface
of the mercury barely touch one another. Then move the vernier until its
bottom is just tangent to the convex top of the mercury in the tube.
The vernier is read like other verniers and requires no special expla-
nation. Besides reading the height of the column of mercury in the
barometer, it is necessary to read its temperature by means of the attached
thermometer, and also the temperature of the air by means of a thermom-
eter hung in the shade.
The barometer is used differentially — that is, the difference in height
between two points is determined by the difference in the indications of two
barometers, one at each point. In order to obtain the height above sea level
of one of these points, that of the other must be known. The latter is called
the base station, and its altitude should be determined either by leveling or
by a long series of barometric observations referred to some other point
whose altitude has been established. The proper selection of a base station
or a system, of base stations for reference of work to be done in a certain
locality is a matter involving considerable judgment and a knowledge of
the peculiar errors to which the barometer is liable, as well as a knowledge
of the topography of the country and its probable influence upon the
fluctuations of barometric pressure. The base station should be near the
middle of the area. If but one base station is employed, it should be near
the middle altitude of the region. If two be used, one should be at the
altitude of the low or valley country and the other should in altitude be
near the high summits. In the Hayden survey of Colorado tln-ee base
stations were employed at once — one at Denver, at an altitude of 5,300
feet; one at Fairplay, 10,000 feet, and one near the summit of Mount
Lincoln, 14,200 feet. To these base stations were referred severally those
observations taken at points most nearly approaching them in height.
Comparisons should be made between the readings of ihe base barome-
ter and the readings of those to be used in the field. These comparisons
should be made with the barometers hung side by side and should be made
in full — i. e., by lowering the mercury from the tubes, its level in the cistern
to the ivory point, and resetting the verniers at each reading — and the
96 A MANUAL OF TOPOGEAPHIC METHODS.
attached thermometei's slioiild be read. Both barometers should be read by
the same observer. A half dozen observations made at intervals of half an
hour will answer as well as a greater number. Such comparisons should,
if practicable, be made at the beginning and the end of the season, wlien-
ever a new tube is put into either barometer, or after any repairs to either
instrument.
The discrepancies between the readings of two barometers are due to
several causes, among which are differences in setting of the scale of inches,
differences in the caliber of the tubes, causing difiPerent amounts of capillar-
ity^ and differences in the perfection of the vacuums in the tubes. Differ-
ences due to the first two are generally trifling, amounting to but a few
thousandths of an inch. If large discrepancies exist, they are usually due
to the last cause, and this should be corrected.
The cistern barometer is a very frail instrument, and although in the
mountain form it is protected from accident as thoroughly as possible, still
tubes are not infrequently broken while in the field. It is necessary, there-
fore, to provide the requisite means for making repairs, such as sealed tubes,
distilled mercury, etc. When a tube is broken, the barometer should be
opened at once, and the mercury poured out, in order to prevent it from
dissolving the screws and other brass work of the instrument.
The work of filling and replacing a tube is a delicate operation. After
taking the barometer to pieces, the new tube should be opened by breaking
off the small end, the break being made at a distance from the strictm-e equal
to that upon the old tube. It should be effected by cutting it around with
a sharp file, when a little pressure will cause it to break; then the edge of
the break should be smoothed with a file. The collar which forms the top
of the cistern should then be lashed on to the tube at the strictm-e. The
mercury to be used should be very pure, and to clear it from mechanical
impurities, it should be strained tln-ough chamois skin immediately before
use. It should then be poured into the tube through a paper funnel, and
the tube filled to within an inch of the top. Then, covering the open end
of the tube with the finger, protected by a piece of kid, invert the tube,
letting the bubble of air slowly traverse the tube up and down for the pur-
pose of collecting the minute air bubbles which may have remained in the
THE CISTERN BAEOMETER. 97
tube. Do this repeatedly, if necessary, until the mercury appears perfectly
clear of bubbles. Then fill the tube with merciu-y, ch'awing out with a straw
any bubbles that may then be near the top. Invert the tube in the case, put
on the glass ring and the upper cone of the cistern, and screw them together.
Then fill the cistern with mercury, put on the lower cone, with the bag and
the brass cover, and the work is complete. The test of a satisfactory result
is the sound made by the column of mercury as it strikes the top of the tube.
If there is a sharp metallic click the vacuum is good, but if the sound is
muffled the vacuum must be improved. It is well to warm the mercury
before pouring it into the barometer, in order to drive out any moisture in
it. This is especially ad-sdsable if the atmosphere is damp at the time.
It is by some thought advisable to boil the mercury in the tube during
the operation of filling. This is usually done over an alcohol lamp, two or
thi-ee inches of mercury being poured into the tube at a time and brought
to a boil until the tube is filled. The mercury which is to be poured into
the cistern is then also boiled. This is a very delicate and tedious operation,
and is attended with much risk to the tubes. Its utility is questionable,
inasmuch as the mercury in the barometer is exposed to the atmosphere and
soon contains as much moisture as before.
It often becomes necessary to clean the sui-face of the mercury in the
cistern. To do this, take off the lower cone of the cistern ; then, placing
the finger, protected by a piece of kid, over the open end of the tube,
invert the barometer slowly and pour out the mercury from the cistern.
Strain it tln'ough chamois skin, replace it in the cistern, and put the latter
together again.
Observations at the base stations should, whenever practicable, be
made hourly from 7 a. m. to 9 p. m., in order to insure having base obser-
vations coincident with those taken in the field. When not practicable to
do this, they should be made at 7 a. m., 2, 6, and 9 p. m. Each observation
should include the reading of the attached and detached thermometers.
Whenever the observations at a station of the U._ S. Weather Bureau are
available, they may be used as base records. In most cases, howevei, these
observations are made with barometers reading only to one-hundi-edth of
an inch, but, upon proper application, the Weather Bureau has in all cases
MON XXII 7
98 A MANUAL OF TOPOGEAPHIC METHODS.
substitiited barometers reading more minutely in order to meet the require-
ments of the work of this Sm-vey.
In field work, barometers should be read at each camp hourly during
the daytime, if practicable, or, if not, at such hours as to correspond with
the readings at the base station and with readings made by the topographer
in the course of his work, having in view the use of the camp as a sort of
secondary base station. The topographer or his assistant should read the
barometer on all stations, and at all important points the heights of which
cannot be more easily obtained by vertical angles.
Measurements of height made with cistern barometers are subject to
periodic and accidental errors. The periodic errors are probably due to
imperfections in the formulas and constants used in the reduction. Many
attempts both from theoretical and practical points of view have been made
to remedy these defects, but thus far without success. The accidental errors
are due to eiTors of obseiwation and to local differences in the pressure of
the an- at the points at which observations are made. Where the hori-
zontal distance between the two stations compared is great, such differences
may be correspondingly great, and the same is true where there is a con-
siderable difference of elevation between the two stations.
Under favorable circumstances barometric observations should give the
height within a score of feet. Where the circumstances are unfavorable — as,
for instance, where there is a great difference of elevation between the two
stations or a great horizontal distance between them — the error may be large,
reaching 100 feet, and even in extreme cases 200 feet.
REDUCTION OF BAROMETRIC OBSERVATIONS.
The pressure of the atmosphere at the sea level is approximately 15
pounds per square inch, or is equivalent to that of a column of mercury
30 inches in height. With elevation the pressin-e diminishes, but not in a
simple ratio to the altitude, as would be the case if all the strata had the
same density. The density is proportional to the pressure, and as the
pressure upon each layer is produced by the body of air above it, it follows
that each succeeding layer of air is less dense than that which underlies
THE CISTERiT BAROMETER. 99
it. The relation between altitude and atmospheric pressure, as stated by
Gilbert, is as follows:
The difl'ereuce in height of any two localities is equal to a certain constant
distance multiplied by the difference between the logarithms of the air pressures at
the two localities.
This relation gives the first and principal term in the various tables for
the reduction of barometric work. Different determinations of the constant
distance, known as the "pressure constant," have been made, and these
different pressure constants cause the principal differences in the various
tables in use.
Of the different sets of tables yielding good results, the most con-
venient for use are those known as Guyot's. They are published in the
Smithsonian Miscellaneous Collections, No. 13, and republished in this
volume tables I to V. These tables are derived from the formula of La
Place and use his coefficients. The formula, reduced to English measures,
is as follows :
Z =log. A X 60158.6 English feet <
^ ^ 900
(1+ 0.0026 cos 2 L)
, Z + 52252 h )
' +20886860+10443430 )
h rr the observed height of the barometer ■\
r — the temperature of the barometer > at the lower station;
t ^ the temperature of the air }
h' z^ the observed height of the barometer \
r' zz the temperature of the barometer > at the upper station.
t' izi the temperature of the air )
Z — the difference of level between the two barometers ;
L zz the mean latitude between the two stations;
H =: the height of the barometer at the upper station reduced to the
temperature of the barometer at the lower station ; or,
n = h' {1 + 0.00008967 (r — r')}.
Table I gives, in English feet, the value of log. H or h X 60158.6 for
every hundredth of an inch, from 12 to 31 inches in the barometer, together
100 'A MANUAL OF TOPOGKAPHIC METHODS.
witli the value of the additional thousandths, in a separate column. These
values have been diminished by a constant, which does not alter the differ-
ence required.
Table II gives the correction 2.343 feet X C'' — ^') ^i" the difference of
the temperature of the barometers at the two stations, or r — t'. As the
temperature at the upper station is generally lower, r — r' is usually posi-
tive and the correction negative. It becomes positive Avheu the temperature
of the upper barometer is higher and t — t' negative. When the heights
of the barometers have been reduced to the same temperatures, or to the
freezing point, this table will not be used.
Table IV shows the correction D' 2088686O *^ ^^ fipplied to the
approximate altitude for the decrease of gravity on a vertical acting on
the density of the mercurial column. It is always additive.
h
Table V furnishes the small con-ection ^ -,,„.-- for the decrease of
lU4:4o4:OU
gravity on a vertical acting on the density of the air ; the height of the
barometer h at the lower station representing its approximate altitude.
Like the preceding correction, it is always additive.
USE OF THE TABLES.
In Table I find first the numbers corresponding to the observed heights
of the barometer h and h'. Suppose, for instance, h zn 29.345 in. ; find in the
first column on the left the number 29.3; on the same horizontal line, in the
column headed .04, is given the number corresponding to 29.34 z: 28121.7;
in the-' last column but one on the right, we find for .005 = 4.5, or for
29.345 = 28126.2. Take Ukewise the value of h', and find the difference.
If the barometrical heights have not been previously reduced to the
same temperature or to the freezing point, apply to the difference the cor-
rection found in Table II opposite the number representing r — r'; we thus
obtain the approximate difference of level, D.
For computing the correction due to the expansion of the air according
to its temperature, or D X ( q^T ) make the sum of the tempera-
tures, subtract from that sum 64; multiply the rest into the approximate
PUBLIC LAND SUEVEYS. 101
difference D and divide the product by 900. This coiTSction is of the same
sign as (t + f — 64). By applying it, we obtain a second approximate dif-
ference of level, D'.
In Table III, with D' and the mean latitude of the stations, find the
correction for variation of gravity in latitude, and add it to D', paying due
attention to the sign.
In Table IV with D', and in Table V with D' and the height of the
barometer at the lower station, take the con-ections for the decrease of
gravity on a vertical, and add them to the approximate difference of level.
The sum thus found is the true difference of level between the two
stations, or Z; by adding the elevation of the lower station above the level
of the sea, when known, we obtain the altitude of the upper station.
UTILIZATION OF THE WORK OF THE PUBLIC LAND SURVEYS.
In all the states and territories except the original thirteen, together with
Vermont, Kentucky, Tennessee, Texas, and Alaska, the public-land sur-
veys have been carried on, and many of these states have been entii-ely
covered by these surveys.
These surveys were made for the purpose of dividing the land into
parcels suitable for sale or other disposition, and with httle reference to
map purposes. The work differs widely in quality in different parts of the
country, in some regions being very bad, in others of high quality. 6rener-
ally speaking, the later work is much the bettei*.
This work is extensively used by the Geological Survey as an aid in
the preparation of its maps. The extent to which it is utiHzed, and the
methods employed in using it, will be detailed in this chapter. Before
proceeding with this, however, it is desirable to describe the methods
by which this work has been and is carried on.
The system of subdivision is an extremely simple one. It consists, first,
in the division of the land into large blocks, the division of these blocks into
townships, approximately 6 miles on a side, and the subdivision of these
townships into sections, each containing about 1 square mile. Fm-ther
subdivision of these sections into quarter sections, or even smaller areas, has
been done by private surveyors.
102 A MANUAL OF TOPOGRAPHIC METHODS.
The. supervision of the surveys is vested in surveyors-general, one in
each state or territory in which such surveys are being carried on. The
surveys are made by contract, at certain stated prices per linear mile, and
are subject to examination by salaried officers of the Land Office.
The initial work consists in the measurement of a principal meridian
and a base line, their intersection being the initial point of the survey.
These lines are run with considerable care. The principal meridian may
be run both northward and southward from the initial point, and the
instructions require that observations be made for azimuth at intervals not
greater than 12 miles, and that the line be double chained, two sets of chain-
men being employed for that purpose. In measuring a base line, which is
to follow as closely as possible a parallel of latitude, in case the theodolite
be used-it is to be run by means of a succession of tangents to the parallel,
not exceeding 12 miles in length. At intervals of half a mile a point on the
parallel is marked by offsets from the tangent line, and at the end of 12
miles a new tangent is commenced. In case it be run by solar compass, it
must be checked by latitude observations at intervals of 12 miles. The base
line may be run either east or west from the principal meridian. At inter-
vals of 24 miles on the base line auxiliary meridians are run in the same
manner as prescribed for the principal meridian, and, at intervals of
24 miles on the meridian, correction lines are run east and west in a
similar manner. It is only recently that the interval between guide merid-
ians and coiTection lines has been reduced to 24 miles, or 4 townships.
Heretofore the intervals have differed at different times, but have in all cases
been greater. These lines are run with a solar compass or theodolite, and
never in later years with the ordinary compass, and all these lines double
chained.
By this means the country is divided into approximate squares 24 miles
on a side. Each such area is then divided into townships approximately 6
miles on a side. The east and west sides of these townships are meridians
which are run northward from the base line or from the correction line,
ha^ang a breadth upon the base or correction line of 6 miles, but decreasing
in breadth with the convergence of the meridians. The north and south
sides of the townships may be run east or west, as the case may be. The
PUBLIC LAND SYSTEM. 103
east and west township lines as at first run are simple random lines, wHch
are corrected backward in order to suit the positions of the township
corners, as determined upon the guide meridians and north and south town-
ship lines The township lines are all run with a solar compass or transit,
and double chaining is not required. The east and west sides of the sec-
tions are run in all cases northward, while the north and south sides may be
run either east or west. As in running township lines, the first east and west
and north and south lines in the northern tier of sections are merely random
lines to be corrected backward, the mile posts upon the township lines
beino- reo-arded as the final locations of the section comers. In running the
sectionlines the quarter-section corners are marked, but the lines are not run
by the Government surveyors. The accumulated errors in the subdivision
of the township are thrown into the northern and western tiers of sections.
Surveys have been started from numerous initial points, involving the
measurement of a number of principal meridians and base lines. No system
has been followed in the an-angement of principal meridians and base lines,
or in the subdivision of the country with respect to them.
In making these surveys, topography is mapped to but a limited
extent The positions of all streams are obtained at the points of crossing
of the hnes-i. e., at intervals of a mile. The same is the case with roads.
All streams of importance, however, are traversed, and, in the case of navi-
gable streams, both banks are traversed separately. The margins of all
lakes and ponds of magnitude are traversed, and the outlines of all swampy
and marshy areas are indicated. Indeed, were the work done thoroughly
everywhere, there would be obtained material for a map fairly accurate m
details of the horizontal elements. Practically, however, the degree of ful-
ness varies with the surveyor. In many cases the plats are sufficiently
full of detail for maps upon a scale of 2 miles to an inch, and m some
cases for a scale even larger. In other cases, over considerable areas, the
drainage represented is exceedingly scanty. In some townships few or no
streams are represented. In other words, for mapping purposes, the work
is by no means uniform in quality. Furthermore, no attempt has hereto-
fore been made to obtain correct positions. Most of the initial points of the
survey were assumed arbitrarilv, and their positions in latitude and longi-
104 A MANUAL OF TOPOGEAPHIC METHODS.
tude have never been determined. Another and, for mapping purposes,
important element which is wanting in this work is the relief. In some
cases aneroid observations have been taken along the lines of survey, but
they were never used for the purpose of drawing contours.
The plats are prepared in duplicate, one copy being retained at the
local land office and the other deposited in the central office at Washing-
ton. They are now being photolithographed, and a limited number
printed of each. These plats are upon a scale of 2 inches to a mile
They show the subdivisions of the townships with their areas. They show,
also the streams, roads, swamps, lakes, timber, and prairie as they existed
at the time of survey. Relief is but feebly expressed. If any attention is
paid to it, it is indicated by crude hachures.
This work is of service mainly, if not entirely, in furnishing secondary
locations. Its value for this purpose, however, differs widely. In some
regions it is not sufficiently trustworthy to be used, even when closely
controlled b}- triangulation. In forest-covered or broken country it is often
difficult to find the corners, so that it becomes necessary to supplement the
few discovered by traverses connecting one with another. This has been
the case with the sm-veys in Missouri. In open countiy, on the other hand,
where the surveys are of good quality, they furnish a complete and admi-
rable system of minor location, often obviating entkely the necessity of
making any horizontal locations, aside from the primary work necessary
to eliminate the accumulated errors of the system. In Iowa, Illinois, and
Wisconsin, traversing is done only to a limited extent and for the purpose
of locating the details of what are called "diagonal" roads — that is, roads
not upon section lines. The common practice of constructing roads upon
section lines, which, in the prairie states, has grown out of this plan of sub-
division, aids greatly in the work of survey. This system of roads is highly
developed in Kansas, where, by state law, every section line may have a
road upon it. This fact, coupled with the rectangiilar subdivision of the
sections into quai-ters, 80's, and 40's, marked by fences or hedges, and the
fact that all these subdivisions are indicated upon county maps, renders the
work in this state a simple ma-tter, while the resulting map is admirably
controlled. The same is true of Nebraska and the Dakotas, as far as settle-
PUBLIC LAND SUEVEYS. 105
■ ments have extended westward, while Wisconsin, Illinois, and Iowa present
conditions almost as favorable.
The piiblic-land surveys are corrected either by extending over
them belts of triangulation or by primary traverses. When the former is
employed, it is unnecessary to cover the area with triang-ulation. It is
sufficient to restrict it to belts of simple figures, such as triangles or quadii-
laterals, such belts being 75 to 100 miles apart.
Each triangulation station should be connected by the simplest and
most direct method with the nearest section corner of the land surveys. This
is done generally by measuring the direction and chaining the distance,
although it may be necessary to run a short traverse, or even a bit of minor
triangulation, in order to reach the section corner. In this way connection
is made with the land surveys at intervals of -10 or 16 miles along the belt of
the triangulation. These locations are of course supplemented by any other
accurate locations which may have been made in the region under survey.
When primary traverses are employed for control, connection should
be made with all section and township lines crossed, the distance along the
line to the nearest corner should be measured, and the direction of the line
relative to the courses of the traverse should be measru-ed.
In open country, where the public-land surveys are of good quality,
as above desciibed, the work of the topographic parties is reduced to the
measurement of heights, and sketching. All the roads are matters of public
record and are obtained from the county officers. The same is true of the
plats of all towns and the plans and profiles of all raih-oads. These are
obtained and placed upon outline plats of the townships, upon a scale double
that of which the maps are to be published.
Heights are measured with the vertical cu'cle and by aneroid, except in
Illinois, where, the contour interval being 10 feet, the vertical circle only is
used.
Where both are used, the vertical angle lines are run at intervals of 4
or 5 miles in one direction, while roads at intervals of a mile are run in the
other direction with aneroids, checking them upon the crossings of the
vertical angle lines. Sketching goes on coincidently with the measurement
of heights.
CHAPTER V.
SKETCHING.
This, being by far the most important part of the work of map
making, should be done by the most competent man for this work in the
party — as a rule, by its chief Besides the fact that he is presumably the
best sketcher in the party, there is another reason for requiring that he
should execute the sketching. He is held responsible for the quality of
the work, not only of the sketching, but also of the accuracy and the
sufficiency of the control. In the sketching of the map he has the best
possible opportunity for examining into the condition of the control and of
remedying any weaknesses.
Upon the completion of the secondary triangulation, the traverse
work, and the measurement of heights within an area, which may be lai-ge
or small according to convenience — but preferably should comprise a qiiarter
sheet — ^he should cause all this control to be assembled upon one sheet.
The traverse lines with all points located from them should be adjusted to
the secondary locations, and all measurements of height should be plotted
upon this skeleton, thus presenting in complete form all the control within
the area. With this sheet upon a sketching board the chief of party
should go over the ground, sketching the di'ainage, culture, and forms of
relief. The latter should be sketched in actual continuous contours, direct
from the country as copy, so that upon leaving the sketching stations the
only work remaining to complete the map will be inking and lettering. In
heavy country, however, where the contours follow one another closely, it
may often be sufficient to put in on the stations only a part of the contours —
every fifth one, for instance — in order to economize time in the field.
Stations for sketching may be selected with the utmost freedom. An exact
106
SKETCHING. 107
location is unnecessaiy. Any point on or off the road wliicli affords an
ontlook will serve. As a rule, frequent stations should be made, and one
should not attempt to sketch at great distance unless the conditions are
favorable, as they may be in a country of large, bold featui'es. It may be
necessary to travel over all the roads which haA^e been traversed and to
climb many hills in order to sketch the entire area satisfactorily. On the
other hand, in a different region the entire area may be sketched by a
limited amount of travel or from a few elevated points. In a low country
of small features much travel will be required, as these details must be
sketched from near points. In a bold country of high relief, which may
be sketched entirely from a few points, care must be exercised in the
selection of sketching stations. From a great altitude the lower details
will be dwarfed and will measurably disappear, while from low points the
relations, forms, and masses of the greater elevations cannot be properly
seen. In such a country stations at different elevations must be selected in
order to see all parts of the country to the best advantage. The extreme
summits will prove of little service as sketching stations.
Sketching- is artistic work. The power of seeing topographic forms
in their proper shapes and proportions and of transferring these impressions
to paper faithfully is of all acquirements one of the most difficult to obtain.
The difficulty is increased by the necessity of expressing form by means of
continuous contour lines at fixed intervals. This work involves a knowl-
edge of the elements of structural geology and good judgment in applying
them.
Every map, whatever its scale, is a reduction from nature and conse-
quently must be more or less generalized. It is therefore impossible that
any map can be an accui'ate, faithful picture of the country it represents.
The smaller the scale the higher must be the degree of generalization,
and the farther must the map necessarily depart from the original.
Now, it is in this matter of generalization that the judgment of the
topographer is most severely tested. He must be able to take a broad as
well as a detailed vdew of the country; he must understand the meaning
of its broad features, and then must be able to interpret details in the light
of those features. Thus, and thus only, will he be competent to ma!^-^ iust
108 A MANUAL OP TOPOGEAPHIC METHODS.
generalizations. This will enable him to decide what details should be
omitted and what ones preserved, and, where details are omitted, what to
put in their places in order to bring out the dominant features.
It is not possible to define the degree of detail which the maps should
represent. The limit commonly given — that is, the limit imposed by the
scale of the map — is not always the best. In representing country which
has little plan or system, such as moraines or sand dunes, it is well to work
in as much detail as the scale will bear. But where the country shows a
system in its sti-ucture to which the minor detail is subordinate, the omission
of some of this detail may give greater prominence to the larger features.
The amount of detail thus omitted must necessarily be left to the judgment
of the topographer, but no more should be omitted than is necessary to
give full expression to the general features of the country.
ORIGIN OF TOPOGRAPHIC FEATURES.
As an aid in the interpretation of tlie various topographic forms which
present themselves, the following brief discussion is appended.
Topographic features originate from a variety of causes and are modi-
fied by many agencies. They are formed by uplift from beneath, of great
or small extent. They are formed by deposition from volcanoes, glaciers,
water, and the atmosphere. They are formed or modified by aqueous and
ice erosion. They are modified by gravity.
These are the principal agencies in producing topographic forms as we
see them to-day. These forms are only in rare cases the work of a single
one of the above agencies ; generally two or more have taken part in pro-
ducing the present condition. Of all these, aqueous agencies are by far
the most potent. Their work is seen in nearly all topographic forms, while
in those of great age their action has been so extensive as to mask or oblit-
erate all supei-ficial traces of the action of any other agency.
The internal stresses of the earth, however produced, have resulted
in raising certain portions of the crust and depressing others. Commonly
these movements have been slow and of srreat duration. Some of them
OEIGIN OP TOPOGEAPHIC FORMS. 109
are of continental extent, producing plateaus, while others have been very
limited in extent, throwing up narrow ridges or blocks. They have
uplifted the strata at various angles, so high in some cases as to throw them
beyond the vertical, infolding the strata and even breaking them by faults.
Incidental to the uplifts are flexures and faults. The flexures may be
classed as anticlinal folds, where they are bent downward on either side,
and monoclinal flexures, where local strata first bend downward and then
by a reverse curve resume horizontality. In a fault the rock is divided by
a fracture and one part is moved up past the other.
It is through uplift that continuous mountain ranges, ridges, and
inclined plateaus have originated — not, howcA'er, in the shapes that appear
to-day, for most of them during and since their rise have been carved by
erosion out of all resemblance to the forms which uplift alone would have
given them.
The ridges and valleys of the Appalachian region are the results of
uplifts, with numerous sharp folds and faults, which raised at various angles
an alternation of hard and soft beds, from which erosion has since carved
the existing alternations of ridge and valley.
Other movements of uplift, resulting from the intrusion among the
strata of great lenses of volcanic rock, have usually resulted in the forma-
tion of elliptic mountains or groups of mountains. As these movements
have occurred at different periods in geologic history, some have been
affected more, others less, by erosion. Certain mountains of this volcanic
type present to-day an aspect little affected by erosion, while others have
been greatly modified by its agency.
Sierra la Sal, in eastern Utah, is an example of this class. Here the
stratified beds above the volcanic rock which were bent upward by the
uplift were probably broken over the top, and have been removed by
erosion until now they only sm-round the base of the group, dipping away
from it steeply, forming hogbacks.
In New Mexico there are seen numerous volcanic "necks" rising
abruptly from the plateau. These necks are intrusions of volcanic rocks,
which were forced up while molten into the stratified rocks. The latter
have since been eroded away, leaving the harder necks as isolated, prepip-
itous mountains.
110 A MANUAL OF TOPOGRAPHIC METHODS.
DEPOSITION FROM A'OLCANIC ACTION.
Deposits from volcanic action may be grouped as follows: (1) of liqviid
lava, in tlie forms a, of streams and lakes, resulting in plains, tables, and
mesas, and h, of cones with craters, with gentle slopes, (2) of scoriae and
cinders, of which have been built cones with steep slopes, either with round
tops or with craters.
Deposits of the first group consist largely of fields" of Ijasalt which have
been poured out from low vents or craters and spread in horizontal sheets,
in many cases covering great extents of territory. The Snake river plains
of Idaho furnish an example. As most of these eruptions are of recent date,
these sheets of basalt have suffered little from erosion, then- form remaining
much the same as when they were pom-ed out and spread over the land.
The surface is undulating, broken here and there by low cliffs marking the
edges of the flow, and by cracks and fissm-es here and there, especially near
the borders of the field. Owing to the frequency of the fissures, flowing
water is scarce upon these basalt fields, for the streams, sinking in the fissures,
find undergi'ouud channels, to reappear at the borders of the fields in springs.
AQUEOUS AGENCIES.
The principal agency in shaping topographic forms is aqueous erosion.
In nine-tenths of the area of the United States the work of this agency is
prominent, while over miich the larger part of the country the forms are
apparently due entirely to this action. It is so commonly seen, that the
topographer finds himself unconsciously reasoning in accordance with its
laws and attempting to apply them to forms produced by other agencies.
A country shaped by aqueous erosion is to him a " regular" country, while
one shaped by other agencies, less known, is iiTegular. The foi-mer can, to
some extent, be foreseen. In such a region, one reasons from the seen to
the unseen, while the vagaries of the latter can seldom be predicted. By
its agency the Appalachian mountains have been reduced from a compli-
cated system of mountain folds to the present comparatively low and simple
system of sandstone ridges and limestone valleys. In the Cumberland
OEIGIN OF TOPOGEAPHIC FOEMS. 1 1 1
plateau has been produced its remarkably complex drainage system. From
enormous plateaus have been carved the great ranges of Colorado, with
their peaks, canyons, and clififs. From the plateaus of the Colorado drain-
age system thousands of feet of rock have been worn away, leaving here
and there great cliffs and high plateaus to show the magnitude of its work,
while the great canyons dividing the lower plateaus, some of them a mile in
depth, though the least among its works, are the topographic wonders of
the world. From the moment the land rose above the sea, this agency of
destruction has been at work, and its labors will not cease until the land
again sinks beneath the waves.
The action of water on rocks may be divided into three parts — weather-
ing, transportation, and corrasion. The rocks of the general surface of the
land, or the terrain, are disintegrated and converted into soil by weathering.
The material thus loosened is transported by streams, and while thus being
transported it helps to corrade other material from the channels of the
streams. In weathering, the chief agents are solution by water, frost, the
mechanical beating of rain, gravity, and vegetation. Some rocks, particu-
larly limestones, are entirely dissolved by water, especially when it is charged
with carbonic acid ; others are dissolved only in part and the remaining part
is thus disintegrated. Rocks are cracked and broken by the freezing of
water in their interstices. When the foot of a cliff is undermined by erosion,
the upper portion, failing of support, breaks off in fragments by its own
weight. The roots of plants pushing their way into the interstices of rocks
pry them apart and thus aid in disintegration. In general, soft rocks disin-
tegrate more rapidly than hard rocks and soluble rocks more rapidly than
insoluble rocks. Disintegration is more rapid in a moist than in a diy climate.
The product of disintegration is soil, and this may be regarded in future
discussion as a soft bed subject to the same laws of corrasion and transpca--
tation as oth,er beds, with only such modifications as its want of cohesion
requires.
TRANSPORTATION AND CORRASION.
Rain falls upon the surface, a portion of it sinks and reappears in springs,
while another portion flows down the surface and collects in water courses,
which, joining one another, produce, finally, large streams. During a rain
112 A MxiNUAL OF TOPOGEAPHIC METHODS.
storm the entire surface is a network of water courses, from the most minute
rills to the main streams, and in studying transportation and corrasion the
action of these minute rills, which cover the entire terrain, must be considered
as fully as that of the main stream and its primary branches.
Con-asion is effected by the detritus which running water holds in
suspension. Soft rocks are corraded rapidly, hard rocks slowly. The rate
of corrasion is increased by an increase in the volume of the stream, an
increase in its velocity, an increase in the amount of detritus borne by it,
and by increased coarseness of that detritus. Hence it is that the tiny rain-
water rivulets have very feeble corrasive powers; but as they combine into
larger and larger streams, and as they wash into their channels a larger and
larger amount of detritus, and as the slope of their beds becomes greater,
their power for corrading their beds increases, and hence it is that the cor-
rading power of the main stream is greater than that of any of its branches,
and in the main stream, if the slope were uniform, the corrasive power
would be greatest near its mouth.
Suppose a stream to have initially a uniform slope from its source to
its mouth — then its volume, its velocity, and the amount of detritus borne
by it will be greatest near its mouth; and corrasion, although going on all
along its course, will be most rapid there. The slope of the stream will
therefore be reduced most rapidly in the lower part of its com-se, and thence
progressively up stream. It results from this that the normal profile of a
stream bed is a cm-ve, concave upward.
While the slope of the stream bed remains considerable and the velocity
consequently great, the stream flows in a comparatively straight channel,
and devotes its energies to deepening its bed, and thus reducing its slope.
As the slope becomes thus reduced the course of the stream changes to a
crooked, winding one, and its corrasive energies are diverted from its bottom
to the sides of its bed. It is then said to approach "baseleveL"
Swift streams commonly flow in straight- channels; sluggish streams,
in crooked channels.
While lowering its bed by corrasion the main stream lowers, necessarily,
the mouths of its immediate affluents, and these affluents are, therefore, in
addition to their own proper work, obliged to cut their lower courses down
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. Vlll.
A BIT OF THE GREAT PLAINS, COLO., AND KAN , NEAR BASE LEVEL.
Scale 125,000
ContoTxr Irrteirv-al 2 5 feet
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. IX.
A BIT OF THE ATLANTIC PLAIN, VA. NEAR BASE LEVEL.
Scale 125,000
Contour later-T-al 50 feet
ORIGm OF TOPOGRAPHIC FORMS. Ii3
to a level with the main stream. The same operation which is going on in
the main stream is going on in these affluents, but with different intensity,
owino- to their smaller volume of water and perhaps smaller amount of sedi-
ment, and to the fact noted below, that their mouths are constantly being-
lowered. Now, following up these branches as they subdivide into smaller
and smaller streams, a point is finally reached where the little rivulets, with
their feeble cutting power, are only able to keep their lower courses cut
down to the level of the stream to which they are tributary. They have
no energy to spare in working back up their own courses. At this point the
curve changes from one concave upward to one convex upward. This con-
vex curve is the curve of all the minor rain-water rivulets — in short, it is the
curve of the terrain — while the concave curve is the curve of the water
courses. The former is the curve of the upper relief of the country, the
latter is the curve of the valleys.
The relative extent of these two curves depends mainly upon the
climate and upon the range of elevation of the country, or, in other words,
upon the relative rapidity of corrasion of their beds by the perennial streams,
and the erosion of the teiTain by the rain-water rivulets. In a well- watered
reo-ion, where the range of elevation is small, and where the larger streams
are near base level, the hill forms are broad, rounded, and convex, and the
valleys are equally rounded, with concave forms. Of this type is the undu-
lating billowy surface of the Grreat Plains and the Atlantic and Gulf plains
of the Southern states.
Where the range of elevation is great, the curves both of valley and
ridge become sharper and more angular. The streams have a greater fall
and proportionally increased power, and therefore cut more rapidly; but,
on the other hand, they have more work to perform. The Cumberland
plateau, with its intricate network of streams, consists of a close alternation
of ridges and valleys, with straight slopes at very steep angles, the bottoms
of the gorges and the summits of the ridges being but slightly rounded.
Few of the streams have reached base level, except in some cases near their
mouths, and corrasion of their beds is still active. In a high mountain range
all these features become still more accented. The main streams have a
steep descent and corrade their beds rapidly. Their valleys are narrow,
MON xxii 8
114 A MANUAL OF TOPOGRAPHIC METHODS.
with steep slopes on both sides. The mouths of the secondary streams are
rapidly lowered, and thereby their work is greatly increased.
There is therefore a distinction to be observed between superficial
erosion or erosion by the petty rain-water streams on the one hand and
that by the larger streams on the other. The first forms, as a rule, convex
slopes; the last, concave slopes. Between them, however, no sharp line can
be drawn. In general, the former erodes soil only, the soft superficial bed,
while the latter, if swift, is at work chiefly on rock. The energy of the
former is widely dispersed, that of the latter is concentrated. The general
reduction of the surface is done by the former, while the latter is confined
to deepening narrow stream beds. Where the main streams are near base
level, superficial erosion goes on more rapidly than stream corrasiou, since
the slope and velocity of the streams are near a minimum. Where the
streams are still corrading rapidly, their beds are usually lowered faster
than the terrain, and the balance is more and more on the side of the
streams, the greater the range of elevation. In a mountain region, as has
just been stated, the gorges are cut far below the spurs and summits.
Hence, where stream corrasion predominates over surface erosion, the con-
cave curve predominates, and where surface erosion is more rapid than cor-
rasion by the streams, the convex curve is the ruling one.
In an arid regioia, where the rain-fall is not only scanty, but spasmodic
in character, coming mainly in sudden showers of great volume, but short
duration, the stream beds are few in number. The drainage system is
scanty and imperfectly developed. The weathering of rocks goes on slowly,
and consequently the soil bed is thin. The soft material which the
streamlets can erode is not abundant. Consequently the scanty rains do
little surface' erosion, but as they collect in large volume in the few water
courses, they deepen them at a rapid rate. Erosion of the terrain in an arid
region is therefore slow, while stream corrasion is proportionally rapid.
It is frequently the case that streams collect their waters from high
mountains, and on their way to the sea pass down through arid regions.
The action of such streams upon the arid region is the same as above
described from streams originating within this region, except that it is more
intense. Little or none of the waters of such a stream flows over the ter-
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. X.
A PORTION OF THE CUMBERLAND PLATEAU, IN W. VA.
Scale 125X100
CoiLtoiar Interval 100 feet
U. S. GEOLOGICAL SURVEY,
MONOGRAPH XXII. PL. XI.
CANYONS IN HOMOGENEOUS ROCKS.
Scale 125,000
CoiLto-ur IiiteTrv-al25 feet
ORIGIN OF TOEOGRAPHIC FORMS. 1 15
rain of the arid area, to contribute to the planing down of its surface ; but,
on the other hand, the vokime and consequently the energies of the stream
for corrasion are greatly increased by the copious contributions from the
mountain region. Therefore, in such cases corrasion by the streams reaches
a maximum, relative to erosion of the terrain.
It is tluTS that canyons in the arid region are formed. They are found
wherever, from any cause, stream corrasion is decidedly more rapid than
surface erosion.
Such canyons, when in homogeneous rocks, rarely contain vertical
cliffs. These are commonly formed in strata of differing hardness by sap-
ping and undermining, which will be explained later.
In certain parts of the arid region, notably in the Great basin, the rain-
fall is so scanty that the drainage systems are very feeble. The little rain
that falls in the valleys is at once absorbed by the thu-sty soil or the atmos-
phere, while the streams which flow down from the mountains, cutting, it
may be, deep canyons in their sides, dwindle away on reaching the valley,
depositing, as they sink, their loads of detritus. With this detritus have
been floored to a vast depth most of the valleys of the Great basin. It has
been deposited there, instead of being carried off to the sea. The Great
basin, which is in reality a large number of basins more or less independent
of one another, is without outlet simply because of its small rainfall. Were
the rainfall to increase, it would soon contain many lakes, and as the water
rose these would overfow, the higher flowing into the lower and the lower
flowing into the sea. The streams connecting them and the sea, would soon
corrade channels, cutting them down to lower and still lower levels, and
progressively draining these lakes, and thus a di'ainage system would be
established.
^nks exist in other parts of the country, but are there due to different
causes. They are common in the Appalachian region. In these sinks the
water has an undergi'ound outlet through passages in the soluble limestone
with which the valleys are floored. They are common among the terminal
moraines of the continental glacier, in Minnesota, Wisconsin, Michigan, and
New England, where they are called kettles. Here glacial material has been
deposited so recently that time has not yet been afforded for the establish-
ment of drainage systems.
116 A MANUAL OF TOrOG-KAPHIC METHODS.
Every stream tends to extend its drainage area Ly erosion at its
sources on all sides, necessarily at the expense of its neighbors. The stream
having the most rapid fall erodes the margin of its basin most rapidly.
Hence in their struggle for existence the stream having' the most rapid descent
succeeds in drawing area from others. But in so doing it diminishes its own
rate of fall, so that eventually a state of equilibrium among streams may be
reached. This extension of basins is called piracy. It is going on actively
in the Appalachian valley, Avhere numerous examples may be found.
AVhile under certain circumstances the courses of streams are mutable,
under other conditions streams maintain their courses with gi-eat pertinacity.
Of this, water gaps and canyons across mountain ranges are striking results.
Where such a canyon is found, the river flowed before the range or ridge
existed. The range may have risen across its course, in which case the
river, like a circular saw, maintained its course by corrasion, cutting the can-
yon as the mountain rose. Of this action the canyon of Green river through
the Uinta range is an example.
Or, the river, draining a surface of soft or soluble rocks, and eroding
this surface down, may have uncovered a ridge of hard rock lying- across
its course. In this case, like the other, the river maintains its course by
cutting a canyon through the ridge. The Appalachian valley presents num-
berless examples of water gaps formed as above described. Among them
maybe mentioned Delaware Water gap, through which Delaware river passes
Kittatinn}^ mountain, gaps of tiie Susquehanna and the Juniata, that of the
Potomac at Harpers Ferry, and Big Moccasin gap, while Little Moccasin
gap is in process of completion. While these are prominent and well known
cases, in certain localities, every little ridge is cut into a line of knobs by
them, so that, next to the parallelism of its ridges and valleys, the water gaps
of the Appalachian valley constitute its most prominent feature. S%ich of
these gaps as can be shown should appear on the map, and when owing to
the minuteness of these features it becomes necessary to omit them, one
should recognize the fact that the formation in this region is that of parallel
ridges and so represent the structure.
Wind gaps are abandoned water gaps, from which the stream has
been drawn away by a more powerful neighbor. These should not be
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. XII.
CANYONS AND CLIFFS IN ROCKS NOT HOMOGENOUS, N. M.
Scale 125.000
ContoiiT- liXtei-val 50 feet
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII- PL. XIII-
y'<.
A PORTION OF THE GRAND CANYON OF COLORADO RIVER, ARIZ-
Scale 20O.000
ConLour Interval 250 feet
ORIGIIf OF TOPOGRAPHIC FORMS. 117
confounded with passes, or low points in mountain rang-es, caused bj the
eating away of divides at the heads of streams.
The valley of every stream above base level slopes not only toward
the stream, but with it — i. e., toward its mouth. Every branch on entering
the valley feels the influence of this slope and turns its course in greater
or less deg'ree down tli^ valley,, entering the main stream at an acute angle.
Similarly the main stream feels the influence of the tributary and turns toward
it; hence the tributary commonly joins the main stream at the head of a bend
in the latter.
When, however, a stream has recently, by the extension of its drain-
age basin, tapped an adjacent stream, the stream so tapped may not yet
have accommodated its course to that of the principal stream, so that it still
enters it at an obtuse angle.
Again, when the stream is near base level a different condition is pre-
sented. The main stream is on a ridge of its own construction, and the
tributary often comes into the valley at a lower level than the ridge and
flows parallel with it for a distance before breaking through and joining its
waters. Loup fork of the Platte river, Nebraska, is an example of this.
The Platte flows there upon a ridge of its own creation. The Loup comes
down into its valley and flows parallel to it for many railes.
As was stated before, a stream near base level becomes crooked and
winding. It has ceased to corrade its bottom, but coiTades the sides of its
bed, especially at the heads of its bends, and deposits its load on the inside
of its bends. Its course changes frequently, now extending its bends
farther into the bank and now cutting them off. In this way it eventuallv
excavates a bi'oad alluvial bottom, which may be subject to overflow when
the stream is in flood and through which the stream Avinds in long curves,
of size roughly proportional to the magnitude of the stream.
In the preceding pages no reference has been made to the influence of
structure upon topographic forms. The alternation of hard and soft beds
of rock and the dip of these beds have decided influence upon topographic
forms, which are now to be considered. The influence of these factors upon
topography is, it must be premised, greater in the arid regions of the West
than in the moister East. The reason of this is that disintegration is much
118 A majSiual of topographic methods.
more rapid in the moister climate, and consequently that, finding an
abundance of material in the bed of soil, a larger proportion of the ener-
gies of corrasion are devoted to removing it, while proportionately less is
deA^oted to rock work. Still the effect of structure is by no means, absent
in the East.
Since disintegration and corrasion of hard or 'insoluble rocks go on
slowly, and of soft or soluble rocks rapidly, the elevated areas are conse-
quently, as a rule, composed of the former, while the depressed areas 'are
commonly of the latter class of rocks. It is the survival of the hardest.
When erosion has left a peak, a projection, spur or boss, a butte or
mesa, a neck or dike, it is commonly because the material is harder than
that adjoining. The valleys of the Appalachian region are almost without
exception cut in soluble limestone, while the ridges are mainly, and the
higher ones entirely, of sandstone.
Streams usually make their channels along lines of least resistance.
They accommodate themselves to the softness of the rocks and avoid
obstacles. The more rapid the stream, however, the less does it care for
obstacles, while gentle streams are most easily diverted.
The level surface of a plateau is generally the summit of a hard bed,
from which, it may be, softer beds have been washed away and on which
erosion has comparatively come to a standstill.
Where rocks of different hardness are subjected for the same time to
an equal intensity of corrasion, since the effect upon the softer rock is
greater than that upon the harder, it will be brought down to gentler
slopes; in other words, other things being equal, the harder the rock the
steeper the slope, the softer the rock the more gentle the slope. Now, let
this proposition be applied to the cross sections of stream beds. Suppose
two stream beds, one in soft rock, another in hard rock, both of them sab-
iected to the same climatic agencies and the same corrasive action for the
same time. In these two rocks the stream beds will be carved somewhat as
shown in Nos. 1 and 2, in Figure 13, indicating progressive stages of opera-
tion.
The simplest case for consideration and a very common one is that of
horizontal beds, alternately hard and soft, such as are represented in Fig-
U. 8. GEOLOGICAL SURVEY,
MONOGRAPH XXII. PL. XIV.
WATERGAPS, PA.
Scale es.ioo
Contour Interval 20 feet
ORIGIN OF TOPOGEAPHIC FORMS.
119
ure 13, Nos. 3 and 4 Suppose No. 3 to represent a cross section of a canyon,
the upper bed of tlie plateau being hard, succeeded by soft and hard beds
in alternation, as is seen in the Grand
canyon of the Colorado, PL xiii. The
course of the stream in forming this
canyon is shown by the light lines in
the figure. It cuts first a canyon with
steep sides in the upper hard bed,
an operation which perhaps consumes
much time. Then reaching the softer
bed below, it bu.rrows rapidly into it,
at the same time undermining the bed
above, which from its weight breaks
away, leaving cliffs. A similar opera-
tion carries it through the next hard
and soft beds. Thus a succession of
cliffs and terraces is formed. The
presence of cliffs in a canyon wall
generally indicates that the bed be-
neath the cliff is more easily eroded fig. i3— .cross sections of canyons.
than that above it. The fragments of the cliff falling upon the slope of the
soft bed below form what is known as a talus.
The above is a common case in a plateau region, since the surface bed
is usually hard. Where the surface consists of a soft bed. No. 4, Fig. 13,
represents the condition of the canyon walls. The undulating surface of
the soft bed slopes down to the cliff produced by undermining the hard bed
beneath. Otherwise the case is similar to that described above.
■ A third case is afforded by the Black canyon of the Gunnison in Col-
orado, where a hard sandstone forms the surface of the plateau, underlain
by granite. A section is represented by No. 6 in Fig. 13. The sandstone
stands at an angle of about 30°, beneath which are the walls of the granite
canyon, which are somewhat steeper, the angle of slope being perhaps 40°
to 45°. There is no undermining and consequently 4here are no vertical
cliffs.
120
A MANUAL OF TOPOGRAPHIC METHODS.
No. 2.
Fig. 14. — Cross sections i
I inclinerl "beds.
Consider next the case of a stream flowing parallel to the strike of
inclined beds, where they are alternately hard and soft. When the incli-
nation of the beds is not great, the stream, having cut down to the surface
I A of the hard' bed, as represented in
No; 1, Fig. 14, tends to travel later-
ally down the dip of the bed, under-
mining both soft and hard beds on
the lower side and extending the slope
on the upper side. When the dip is
considerable, it may carry away all
the material on the upper side, as
in No. 2, Fig. 14
In this way streams may cut broad
swaths across the terrain and remove
both hard and soft beds from great
areas of inclined plateaus.
Fine examples of streams flowing on the strike of hard inclined strata
are seen in the hogbacks of Colorado.
Next, consider the longitudinal profile of a stream which is cutting its
bed, when flowing- over a succession of- beds alternately hard and soft.
Since it cuts soft rocks more rapidly than hard ones, its profile will show
irregularities. Wliere flowing over soft beds, its current is less rapid than
over hard beds of rock. The stream adjusts its proflle to the work to be
performed.
The ultimate result of aqueous erosion upon a surface is to reduce it
to a plain of slight elevation, of gentle, easy slopes. It then approaches
base level, a condition where the entire surface resembles the condition of
a base-level stream, where vertical coiTasion is practically at an end. Abso-
lute base level is a conception merely, which many regions approach, but,
owing to the fact that as the slopes become gentler, erosion becomes feebler,
they cannot reach.
The stage of progress of an area toward base level is said to indicate
its age. In youth it may present a great elevation and high relief. Its
streams may have rapid courses with irregular profiles, broken by lakes.
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXU. PL. XV,
THE RIDGE OF MISSISSIPPI RIVER, LA.
Scale 62,5oo
Contoirr IiLt-erval 5 feet
ORIGIN OF TOPOGEAPHIC FORMS. 121
rapids, and falls. As the age of the region increases these inequalities are
cut away. The lakes are drained, the falls and rapids disajDpear. The
mountains and hills are worn down, and finally the entire surface is reduced
to a low rolling expanse. The region approaches base level. It is in its
old age. Plains represent old age among topographic featm-es.
The life of a topographic area is not to be measured in years, but in
its cycle of changes, which have little reference to time. The time required
to run through its life differs with the conditions under which and the ma-
terials upon which erosion acts. It varies with the intensity of erosive
action and with the amount of work to be done.
Sometimes a region after being reduced nearly to base level has been
again elevated. Such elevation brings again into action the erosive agen-
cies to carve and plane the terrain a second time. A region thus restored
to .youth by elevation is the mountain region of North Carolina. The
bench level of the country is an old base level, which has been raised. In
this the streams are now cutting and regulating their courses, while the
bench level, in its gentle undulations, shows the old base-level sm-face,
little affected as yet by recent erosion.
DEPOSITION FROM WATER.
When the swift current of a stream is checked, as by a reduction of
slope or by a widening of its bed, it deposits a part of its load. It is thus
that river banks, river and lake terraces, and bars at the mouth of streams .
are made. Of the building of river banks, fine examples are seen in south-
ern Louisiana. Before the stream was lined with levees the Mississippi
river overflowed its banks at every considerable rise. Loaded with detritus,
it suddenly spread over its banks to the dimensions of an inland sea; its
velocity was thereby checked and much of its load was quickly deposited,
the greater part, including the coarsest material, falling on its immediate
banks, which were thereby built up higher than the adjoining country. The
river and bayous of this region flow on the tops of ridges of their own con-
struction, the only land above the swamps. The highest ground every-
where is that on the immediate river bank, whence the slope is away from
the stream on either hand to the swamp, as shown in PL xv.
\
122 A MANUAL OF TOPOGEAPHIC METHODS.
Now, let this operation be extended farther. As a stream builds its
ridge higher it soon reaches a condition of instability and it then forsakes its
bed for an adjoining lower course. It builds this up and in turn abandons
it. So in time it builds up a di-y delta, or, as it is called, a fan, made up of
a radiating group of abandoned ridges marking its former courses.
Lake terraces are formed by the collection of material at the water's
edge. Whether brought down by gravity alone or transported by water,
its descent is checked on reaching the water and it accumulates at the
water's edge.
GLACIAL DEPOSITION,
The northern part of the United States was, in recent geologic times,
covered by a sheet of ice, a glacier of continental dirnensions. Its bound-
aries, within the United States, included New England, New York, north-
ern Pennsylvania, Ohio, Indiana and Illinois, all of Michigan, Wisconsin,
Minnesota and the Dakotas, much of Iowa, and northeastern Montana.
The glacier had a southern movement, but this advance southward was,
on the whole, neutralized by the melting of the ice on the southern bor-
der. In cold seasons, the movement of the glacier gained on the power of
the sun's heat to melt it, and it advanced southward. In warm seasons,
it retreated northward. The action of this glacier in originating and modi-
fying topographic forms was twofold. It eroded and earned away material
and it deposited material. It is the latter result that is considered here.
The material, consisting of bowlders, gravel, and sand borne by the
glacier was deposited as it melted, and consequently is most abundantly
disti-ibuted in the neighborhood of its southern boundary. Owing to the
recent character of the deposits, they have been little eroded. Lakes,
swamps and waterfalls abound in the region in question. The terminal
moraines which mark the limits of the glacier consist of an irregular mass
of material, tkrown down in the greatest confusion, with crooked winding
streams and sink holes. There is no symmetry or law in its disposition,
but it is made up of details, which bear no relation to its whole. On this
account it must be sketched piecemeal. The topographer must go all over
it, picking up each detail by itself, and necessarily the control must be
equally minute.
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII- PL. XVI,
DRUMLINS, WIS.
Scale esTkoQ
ContotLT Interval 20 feet
U. S GEOLOGICAL SURVEY
MONOGRAPH XXII- PL. XVII
A PART OF THE TERMINAL MORAINE AND PITTED PLAIN, WIS.
Scale eSTIT^o
CoTLtartrIn.tei*val 20 £ee"t
OEIGm OF TOPOGEAPHIO POEMS. 123
Within the limits of this terminal moraine, the commonest character-
istic feature of glacial deposition is the drumlin, an oval mound of drift, of
height ranging from a few feet up to several hundred feet, and from one to
several square miles in area. They ai-e extremely regular in shape and
their curves are round and smooth. In many localities they are so abun-
dant as practically to cover the surface, the intervals between them being
level and often marshy. The axes of these drumlins are commonly par-
allel, giving a curiously artificial appearance to the map. In country other-
wise level, they determine the course of the streams, forcing them to wind
around their curves. PL xvi shows a portion of the drumlin area of
southern Wisconsin, and PI. xvii a part of the terminal moraine of the
same region. Pitted plains, which are level areas dotted with little pits,
are common features of glacial action. Osars, or long winding ridges, are
not uncommon, while numerous other forms, such as kettles, etc., are fre-
quently seen, but are of less importance as topographic features.
Glaciers still exist in the Rocky mountains, the Sierra Nevada, and the
Cascade range, though they are by no means as extensive as in former
times. At the bases of many of the ranges of this region are found lateral
moraines reaching out from the mouths of mountain gorges and connected
at their ends by terminal moraines.
The lateral moraines are of regular form, stretching in narrow ridges,
in some cases parallel, in others curving away from one another from the foot
of the canyon. The terminal moraines are like that of the continental glacier,
confused masses of material heaped up in disorder and consequently diificult
to sketch in the highest degree.
GLACIAL EROSION.
Glacial erosion is very similar in its laws and action to aqueous erosion,
or rather to that part of it which is called corrasion. The principal differ-
ence between them lies in the fact that ice is much less plastic and conse-
quently does not accommodate itself so readily to the form of its channel.
It moves, too, much more slowly and in far greater volume than water.
The corrading effect of the continental glacier is shown in northern
New England, New York, Michigan, Wisconsin, and Minnesota very mark-
124 A MANUAL OF TOPOGKAPHIC METHODS.
edly. In the western part of this region it has scoured the surface, cutting
av.-av the soft rocks, and lea^^ng the hard ones in projecting knobs, as in the
^Marquette Iron range of Michigan. This work was done so recently that
the drainage systems have not yet been well developed. The streams are
tortuous and are interrupted by lakes, swamps, and rapids.
In northern New England and New York the o-lacier covered a regrion
of considerable relief, in which streams had established deep courses. Much
corrasion was done by it, but upon its retreat the streams reoccupied their
former beds.
Most of the gorges of the Rocky mountains and Sierra Nevada, which
had previously ]:>een excavated by streams, have been occupied by glaciers,
and here and there small glaciers may still be found at their heads. These
glaciers, when the}- were in their prime, occupied the gorges from side to
side, and by their erosion broadened them from the sharp almost V shape
which water corrasion had given them to a ^_^ shape, similar to that of the
bed of a stream, but manv times larger.
At the heads of the main gorge and many of its branches, where tlie
neve fields formerly iniited and were crowded together into a glacier at the
heads of the gorges, there is commonly an amphitheater with steep, even
precipitous, walls, curving around in a semicircle. In the middle of this is
sometimes a lake or pond, with a rim of rock inclosing it on the lower side.
This lake basin was scooped out by the glacial ice, as it came together
down the steep slopes of the amphitheater. Here the ice has only modified
and shaped a gorge originally carved by water. Where the little streams,
flowing toward one another down the steep mountain side, had cut many
Kttle gorges, with sharp spurs between them, the ice has pared away the
spm'S, producing an amphitheater. PL xviii illustrates the cirque in the
Rocky mountains of Colorado.
DEPOSITION FROM THE ATMOSPHERE.
The winds transport sand and deposit it in di'ifts, known as dunes,
They commonly appear as lines of hills, like hogbacks, with the gentle
slope toward the prevailing winds. Not having been shaped by erosion,
they present great inequalities of surface.
U. S. GEOLOGICAL SURVEY.
MONOGRAPH XXII. PL. XVIII.
A PORTION OF THE ELK MTS., COL., SHOWING AMPHITHEATRES.
Scale GsSoB
Contour IntervBl 100 feet
EBPORTS.
125
SCALE OF FIELD WORK.
The scale iipou which the field ^vork is executed is commonly larger
than that upon which the maps are to be published. In the northeastern
states it is set at 1:45000, the scale of publication being 1:62500. In
the southeastern States it is approximately 1 mile to an inch, the scale of
publication being for most sheets 1:125000, though certain sheets in Mary-
land and Florida hdve been published on the scale 1 : 62500. In the Missis-
sippi valley it is uniformly about double that of publication. Where the
scale of publication is 1 : 62500, the scale of field work is 2 inches to 1 mile,
and where the former is 1:125000, the latter is 1 mile to an inch. In the
western states, the scale of publication being 1 : 125000, the field sheets are
made uniformly on the scale of 1 mile to an inch.
REPORTS.
Each field party is required to make a monthly report to the chief of
division and the chief topographer upon the progress of the work in his
party during the month. In the case of topograpliic parties these reports
are made upon printed forms, of which the following is a sample :
MONTHLY REPORT OF TOPOGRAPHIC PARTY.
[To be made out in duplicate promptly at the close of each mouth, one copy to he sent to the geographer
in charge of the division and one copy to the chief topograi)her.]
Department of the Interior, U. S. Geological Survey,
189
Sir: The following report for the mouth of
topographic party under my charge :
Names and positions of all members of party, -
Instruments used,
, 189 , includes a statement of progress of the
Barnard.
Miller.
Beall.
Arrick.
Triangulation stations occupied
Points located by triangulation
Points intersected from traverse
Expended — for salaries,
Yours respectfully,
- ; all other expenses, $-
- ; total, $-
126
A MANUAL OF TOPOGRAPHIC METHODS.
Sheet. Shade surveyed area.
Upon the back of this form is a diagram representing an atlas sheet,
as above, upon which is to be indicated the area surveyed during the month.
As will be seen, this report calls for statistics concerning the control of
work, specifying secondary triangulation, traverse and the measurements of
height, together with the areas sketched.
INSPECTION. 127 1
INSPECTION.
Inspection of the work is done by the chiefs of parties and of divisions, i
and, in special cases, by persons detailed by them for this purpose. j
The accuracy and adequacy of the control are shown by the monthly J
reports and the field sheets are undergoing constant examination from the I
chiefs of party and of division. The quality of the sketching is examined i
on the ground. As far as possible this is done during the progress of the j
work, using the field sheets as soon as completed. When this is impracti- '
cable, it is done during the succeeding field season, using photographs of the
original maps.
CHAPTER VI.
OFFICE WORK.
The office work of the topograpliers consists in the reduction and trans-
fer of the work from field sheets to the original maps. The reduction is
universally effected by photography, this method having been found the
most accm'ate and economical way of effecting it.
The original sheets are to serve as the original record of work and as
manuscript for the engraver. To answer these purposes, they are made
complete in all respects as to hydrography, hypsography, and public cul-
ture. Every original sheet contains within itself all matter which is to be
engraved or placed on record, except as hereafter noted.
While it is entirely unnecessary that these sheets be fine specimens of
the draftman's skill, they are workmanlike in appearance, clear, and legible.
The original sheets are commonly drawn upon the scale upon which
they are to be published, in order that the engraving may be done directly
from the original maps rather than from photographs of them. Frequent
departures are, however, made from this rule, to meet other requirements.
The contour intervals differ widely in different parts of the country,
ranging from 6 feet up to 100 feet. Where the scale is 1 : 62500 the cona-
monest contour interval is 20 feet. In Florida and Illinois the contour
interval is reduced to 10 feet, while in the low alluvial regions of southern
Louisiana it is only 5 feet.
With a scale of 1 : 125000 the contour interval in the Apjjalachian
mountain region is 100 feet, in the Piedmont region it is 50 feet, and upon
the Atlantic plain 20 feet, while in the Dismal swamp of Virginia and North
Carolina it has been set at 5 feet. With the same scale in Missouri, Arkan-
sas, and eastern Kansas the contour interval is 50 feet, while in western
Kansas in more recent work it is 20 feet. In Texas the coni ,ar interval
128
PEOJBCTIONS. 129
rano-es from 20 to 50 feet, the later work having the smaller contour inter-
val. In the country west of the one hundredth meridian the contour
interval is frequently changed with the alternation of mountain and valley,
and intervals of 25, 50, and 100 feet are employed, the interval frequently
changing upon the same sheet. East of the one hundredth meridian the
same necessity for making frequent changes in contour interval does not
exist, and in the work throughout that region the contour interval is mii-
form upon each sheet.
The projection used is the polyconic, each sheet being projected sepa-
rately.
Upon Qriginals to be pubhshed upon a scale of 1 : 62500 the projection
interval is 5 minutes, while single minute lines may be drawn if desired.
The construction of a projection upon a scale of 1 : 62500 for a limited
area is a simple matter, but requires care and accuracy and the use of the
best di-afting instruments. The process will be described for this scale, for
which, as well as all other scales heretofore in use, tables are appended to
this volume.
First draw a line down the middle of the sheet. Lay off on this line
the length of the several projection spaces in latitude. Take from the pro-
jection table for the scale 1:62500 the length of 5 minutes of latitude and
lay it off repeatedly, thus establishing the points of intersection of parallels
at 5 minutes with the middle meridian. Through these points draw lines
across the sheet at right angles to the middle meridian, using beam com-
passes for this purpose. Lay off on these hues the dm's for 2' 30" and 7'
30" from the middle meridian, con-esponding to the latitude on each side,
and at these points erect short perpendiculars. On these lay off the dp's
corresponding to the dm's and through the points thus obtained draw and
ink the projection lines.
For other scales and areas the process is quite similar, but when a
large area such as that of the United States is to be projected, the mechan-
ical difficulties greatly increase.
Original sheets must conform in size and shape to equal parts of square
degrees— i. e., each sheet should comprise 15' of latitude by 15' of longitude,
or 30' in each dimension, according to the scale.
MON xxn 9
130 A MANUAL OF TOPOGRAPHIC METHODS.
COLORS AND CONVENTIONS.
The work upon the original sheets conforms to the system of conven-
tions and lettering adopted by the Survey. Streams must be inked in heavy
Prussian blue, lettering and culture in India ink, and contours in burnt sienna.
Indelible inks must not be used on original sheets. Every fourth, or fifth
contoin-, whatever the contour interval, should be empliasized, in order to
distinguish it from the others, and the contours so distinguished should be
freely marked in columns with the number of feet above sea level which
they indicate.
Upon the map should be located all towns of sufficient importance to
contain post-offices ; all railway stations and other settlements of any impor-
tance ; all houses, all public roads, and, in unsettled regions, the principal
trails; all railroads, canals, and acequias; all tunnels of sufficient length to
be represented ; bridges, femes, fords, and dams upon streams of sufficient
importance to be double-lined; all glaciers, marshes, sand, and sand dunes,
and all state, county, and township lines.
The convention for cities and towns must conform as closely as possible,
in extent, du-ection of streets, etc., to the actual plan of the place, and the
houses in the built portion should be blocked in.
Depression contoiu-s should, if they inclose large areas, be indicated by
numbering them freely. If the area is small, they should be hatched, the
hatchings being on the side of the line toward the depression.
The extent of forests and of flood plains will not be placed upon the
original maps, but should be colored upon photographs of them.
TITLES AND LEGENDS.
The sheets are without border or neat line, the outer projection lines
taking the place of the latter. Upon the margins the latitudes and longi-
tudes of the projection lines must be given. The titles and legends must
conform in arrangement and character to those on the printed sheets.
Wherever it is practicable to do so, care must be taken to connect the con-
tours, streams, and culture on the margins of sheets with the adjoining sheets.
All field work should, if possible, be platted and the work completed during
the office season immediately succeeding the field work, and no sheet should
be reported as completed until it is ready in all respects to be engraved.
ORIGINAL SHEET.
lOV/A
WHEATLAND SHEET
Contour Interval 20 fee
APPENDIX.
TABLES FOR COMPUTING THE DIFFERENCE IN THE HEIGHT OF TWO PLACES FROM
BAROMETRICAL OBSERVATIONS.
Table. I. — J) = G015S.5Bx log H or h. Argument: The observed height of the barometer at either station.
[Extracted from Smithsonian Miscellaneous Contributions.]
Barom-
Hundredtlis of an inch.
Thou-
Barom-
eter ifl
sandths
eter in
Eng.
of
Eng.
.OO
.01
.OS
.03
.04
.OS
.06
.07
.OS
.09
an
inch.
inc^.
Eng. ft.
Sng.ft.
Eng.ft.
Ung.fl.
Eng.ft.
Eng.ft.
Eng.ft.
Eng.ft.
Eng. ft.
Eng.ft.
Feet.
12.0
4763. 4
4785. 2
4806.9
4828. 7
4850.4
4872.1
4893. 7
4916.4
4937. 0
4938. 6
12.0
12.1
4980. 2
5001.8
5023. 4
5044.9
5066. 4
5087. 9
5109.4
5130.9
5152. 4
5173. 8
12.1
12.2
5195. 2
5216. 6
5238. 0
5259. 4
5280. 7
5302. 1
5323. 4
5344. 7
5367. 0
5387. 2
12.2
12.3
5408. 5
5429. 8
5432. 0
5472. 2
5493.4
5514. 5
5535.7
5556. 8
5578. 9
5599. 0
1
2.1
12.3
12.4
5620. 1
5641. 2
5662. 2
5683. 2
5704. 3
5725. 3
5746. 2
5767. 2
5788. 1
5809. 0
2
4.2
12.4
12.5
5829. 9
5850.8
5871. 7
5892. 6
5913. 4
5931.2
5955. 0
5975. 8
5996. 6
6017. 4
3
6.2
13.5
12.6
6038. 1
6058. 8
6079. 6
6100. 2
6120. 9
6141.6
6162. 2
6182. 8
6203. 5
6234. 0
4
8.3
12.6
12.7
6244.6
6265. 2
6285. 8
6306. 3
6326. 8
6347. 3
6367. 8
6388. 3
6408. 8
6429. 2
5
10.4
12.7
12.8
6449. 6
6470. 0
6490. 4
6510. 8
6531. 1
6551. 5
6571. 8
6592. 1
6612. 4
6632. 7
6
12.5
12.8
12.9
6652. 9
6673. 2
6693. 4
6713. 6
6733. 8
6754. 0
6774. 1
6794. 3
6814. 4
6834. 5
7
14.6
12.9
13.0
6854. 7
6874. 7
6894. 8
6914. 9
6934. 9
6955.0
6975. 0
6995. 0
7014. 9
7034.9
8
16.6
13.0
13.1
7054. 9
7074. 8
7094. 7
7114. 6
7134. 5
7154.4
7174. 3
7194. I
7213. 9
7233. 8
9
18.7
13.1
13.2
7253. 6
7273. 3
7293. 1
7312. 9
7332. 6
7352. 3
7372. 1
7391. 8
7411. 4
7431. 1
13.2
13.3
7450.8
7470. 4
7490. 0
7509. 6
7529. 2
7548. 8
7568. 4
7587. 9
7607. 4
7627. 0
13.3
13.4
7646. 5
7666. 0
7685.4
7704. 9
7724.4
7743. 8
7763. 2
7782. 6
7802.0
7821. 4
13.4
13.5
7840. 8
7860. 1
7879.4
7898. 7
7918. 0
7937. 3
7956. 6
7975. 8
7995. 1
8014. 3
13.5
13.6
8033. 6
8052.8
8071.9
8091. 1
8110.3
8129.4
8148. 6
8167.7
8)86.8
8205. 9
13.6
13.7
8225. 0
8244.0
8263. 1
8282. 1
8301.1
8320. 1
8339. 1
8358. 1
8377. 1
8396. 0
1
1.9
13.7
13.8
8415. 0
8433. 9
8452. 8
8471. 7
8490. 6
8509. 4
8528. 3
S547. 1
8565. 9
8574.8
2
3.8
13.8
13.9
8603. 6
8622. 3
8641. 1
8659. 9
8678. 6
8697.4
8716. 1
8734. 8
8753. 5
8772. 2
3
5.6
13.9
14.0
8790. 8
8809. 5
8828. 2
8846. 8
8865.4
8884. 0
8902. 6
8921.2
8939. 7
8958. 3
4
7.5
14.0
14.1
8976. 8
8995. 4
9013.9
9032. 4
9050. 8
9069. 3
9087. 8
9106. 2
9124. 6
9143. 0
5
9.4
14.1
14.2
9161. 4
9179. 8
9198. 2
9216. 6
9234 9
9253. 3
9271. 6
9289. 9
9308. 2
9326. 5
6
11.3
14.2
14.3
9344. 7
9363. 0
9381. 3
9399. 5
9417. 7
9436. 0
9454. 2
9472. 3
9490. 5
9508. 7
7
13.2
14.3
14.4
9526. 8
9545.0
9563. 1
9581. 2
9599. 3
9617. 4
9635. 5
9653. 5
9671.6
9689. 6
8
15.0
14.4
14.5
9707. 6
9725. 7
9743,7
9761. 7
9779. 6
9797. 6
9815. 6
9833. 5
9831.4
9869. 3
9
17.0
14.5
14.6
98S7. 2
9905. 1
9923. 0
9940. 9
9958. 7
9976. 5
9994.4
10012. 2
10030. 0
10047. 8
14.6
14.7
10065. 5
10083. 3
10101.1
10118. 8
10136. 6
10154. 3
10172. 0
10189, 7
10207. 4
10225. 1
14.7
14.8
10242. 7
10260. 4
10278. 0
10295. 7
10313. 3
10330. 9
10348. 5
10366. 1
10383. 6
10401. 2
1
1.7
14.8
14.9
10418. 7
10436. 3
10453.8
10471. 3
10488. 8
10506. 3
10523. 7
10541. 2
10558. 6
10576. 0
2
3.4
14.9
15.0
10593. 4
10610. 8
10628. 2
10645. 6
10662. 9
10680. 3
10697. 6
10715. 0
10732. 3
10749. 6
3
5.1
15.0
15.1
10766. 9
10784. 1
10801. 5
10818.7
10836.0
10853. 2
10870. 5
10887. 7
10904. 9
10922. 1
4
6.8
13.1
15.2
10939. 3
10956. 5
10973. 6
10990. 8
11008. 0
11025. 1
11042. 2
11059. 3
11076. 4
11093. 5
5
8.5
15.2
15.3
11110. 6
11127.7
11144. 7
1116L8
11178.8
11195. 8
11212. 8
11229. 8
11246. 8
11263. 8
6
10.2
15.3
15.4
11280. 8
11297. 8
11314. 7
11331.6
11348. 6
11365. 5
11382. 4
11399. 3
11416.2
11433.0
7
11.9
13.4
15.5
11449. 9
11466. 7
11483. 6
11500. 4
11517. 2
11534. 0
11550.8
11567. 6
11584. 4
11601.1
8
13.6
15.3
15.6
11617.9
11634. 6
11651.4
11668. 1
11684.8
11701. 5
11718.2
11734. 9
11751. 6
11768: 2
9
15.3
15.6
15.7
11784. 9
11801. 5
11818. 2
11834. 8
11851.4
11868. 0
11884. 6
11901.1
11917. 7
11934. 3
15.7
15.8
11950. 8
11967. 3
11983.8
12000. 4
12016. 9
12033. 3
12049. 8
12066. 3
12082. 7
12099. 2
15.8
15.9
12115. 6
12132.0
12148. 4
12164. 8
12181. 2
12197.6
12214. 0
12230. 4
12246. 7
12263. 1
13.9
16.0
12279. 6
12295. 9
12312. 2
12328. 5
12344. 8
12361. 1
12377.4
12393. 6
12409. 9
12426. 1
16.0
16.1
12442. 4
12458. 6
12474. 8
12491. 0
12507. 2
12523.4
12539. 6
12555. 7
12571. 9
12588. 0
16.1
16.2
12604. 2
12620. 3
12636. 4
12652. 5
12668. 6
12684. 7
12700. 8
12716. 8
12732. 9
12748. 9
1
1.6
16.2
16.3
12765. 0
12781. 0
12797. 0
12813. 0
12829. 0
12845.0
12861. 0
12876. 9
12893. 9
12908.8
2
3.1
16.3
16.4
12924. 8
12940. 7
12956. 6
12972. 5
12988.4
13004. 3
13020. 2
13036. 0
13051. 9
13067. 7
3
4.7
16.4
16.5
13083.6
13099.4
13115. 2
13131.0
13146. 8
13162. 6
13178.4
13194. 2
13210. 0
13225. 7
4
6.3
16.5
16.6
13241.5
13257. 2
13272. 9
13288. 6
13304. 3
13320. 0
13335. 7
13351.5
13367. 1
13382. 7
5
7.8
16.7
16.7
1.3398. 4
13414. 0
13429. 6
1344.5.3
13460. 8
13476.4
13492. 0
13507.6
13523. 2
13538. 7
6
9.4
16.7
16.8
13554. 3
13569. 8
13585. 4
13600. 9
13616.4
13631. 9
13647. 4
13662. 9
13678. 4
13693. 9
7
11.0
16.8
16.9
13709. 4
13724. 8
13740. 3
13755.7
13771. 1
13786. 5
13801.9
13817. 3
13832. 7
13848. 1
8
12.5
16.9
17.0
13863. 5
13878. 8
13894. 2
13909.6
13924. 9
13940. 2
13955. 6
13970. 9
13986. 2
140O1. 5
9
14.1
17.0
17.1
14016. 8
14032. 0
14047. 3
14062. 6
14077. 8
14093. 0
14108. 3
14123. f)
14138. 7
14153. 9
17.1
17.2
14169. 1
14184.3
14199.4
14214. 6
14229.8
14244. 9
14260. 1
14275. 2
14290. 3
14305. 5
17.2
17.3
14320. 6
14335. 7
14350.8
14365.8
14380. 9
14396. 0
14411.0
14426. 1
14441. 1
14456. 2
17.3
17.4
14471.2
14486.2
14501.2
14516.2
14531.2
14546. 1
14561. 1
14576. 1
14591.0
14605. 9
1
1.5
17.4
131
132
A MANUAL OF TOPOGEAPHIG METHODS.
Table.
I.— D=
60158.58 ?o<?xH
0,h. A
rgiiment
: TheoJ}
served height of b
urometer at eithei
station. —
Cont'd.
Barom-
Hundredths of an inch.
Thou-
Barom-
eter in
incE.
sandths
of
an inch.
eter in
a.
.OO
.Ol
.03
.03
.04
.05
.06
.07
.08
.09
Eng.ft.
Eng.ft.
JEng. ft.
Eng.ft.
Enq.ft.
Eng.ft.
Eng.ft.
Eng.ft.
Eng.ft.
Eng.ft.
Feet.
17.5
14620. 9
14635. 8
14C.-.U. 7
14064. 6
14080. 5
14695. 4
14710. 3
14725. 2
14740. 1
14754. 9
2
2.9
17.5
17.6
14769. 8
14784. 6
1479!). 4
11S14.:!
14829. 1
14843. 9
14858. 7
14873. 5
14888. 2
14903. 0
3
4.4
17.6
17.7
14917. 8
14932. 5
14947. :!
149lii;. 0
14976. 8
14991.5
15000. 2
1.5020. 9
13035. 6
15050, 3
4
5.8
17.7-
17.8
15065. 0
15079. 6
151194. 3
Ifiliiu. 0
15123.6
15138. 2
15152. 9
16107. 5
15122. 1
1.5196.7
5
7,3
17.8
17.9
15211. 3
15225. 9
15240. 5
15255. 0
15269. 6
15284. 2
15298. 7
15313. 3
15327. 8
15342. 4
6
8.8
17.9
18.0
15356. 8
15371. 3
15385. 8
15400. 3
15414. 8
15429. 3
15443.7
15458. 2
15472. 7
15487.1
7
10.2
18.0
18.1
15501. 5
15516. 0
15530. 4
15544. 8
15559. 2
15573. 6
15588, 0
15602. 4
15616. 8
15631. 2
8
11.7
18.1
13.2
15645. 5
15659.9
15674. 2
15688. 5
15702. 9
15717. 2
15731. 5
15745. 8
15760. 1
15774.4
9
13.1
18.2
18.3
15788. 6
15802. 9
15817, 2
15831.4
15845. 7
15359. 9
15874, 2
15888. 4
15902. 6
15916. 8
18.3
18.4
15931. 0
15945.2
15959. 4
15973. 6
15987. 8
16001. 9
16016. 1
16030.2
16044.4
16058. 5
18.4
18.5
16072. 6
16086. 8
16100. 9
16115.0
16129, 1
16143. 2
16157. 3
16171,3
16135. 4
16199. 5
18.5
18.6
16213. 5
16227. 6
16241. 6
162.55.6
16269. 7
16283. 7
16297. 7
16311,7
16325.7
16339. 6
18.6
18.7
16353. 5
16367. 5
16381. 5
16395. 4
16409. 4
16423. 3
16437. 2
16451.2
16465. 1
16479. 0
1
1.4
18.7
18.8
lb492. 9
16506. 8
16520. 7
16534. 6
16548. 5
16562. 3
16576. 2
16590. 0
16603. 9
16617. 8
2
2.7
18.8
18.9
16631. 5
16645. 4
16659. 2
16673. 0
16686. 8
16700. 6
16714.4
16728. 1
16741. 9
16755.7
3
4.1
13.9
19.0
16769. 4
16783. 2
16796. 9
16810. 6
16824. 3
16838. 1
16851.8
16865. 5
16879. 2
16892.8
4
5.4
19.0
19.1
16906. 5
16920. 2
16933. 9
16947. 5
16961. 2
16974. 9
16988. 5
17002. 1
17015. 8
17029.4
5
6.3
19.1
19.2
17043. 0
17056. 6
17070. 2
17083. S
17097. 4
17110.9
17124.5
17138. 1
17151.6
J7165.2
6
8.1
19.2
19.3
17178. 7
17192. 2
17205. 8
17219. 3
17232. 8
17246. 3
17259. 8
17273.3
17286. 8
17300. 3
7
9.5
19.3
19.4
17313.7
17327. 2
17340. 6
17354. 1
17367. 5
17380. 9
17394. 4
17407. 8
17421. 2
17434.6
" 8
10.9
19.4
19.5
17448. 0
17461. 4
17474. 8
17488. 2
17501.6
17515. 0
17523. 3
17541. 7
17555. 0
17568.4
9
12.2
19.5
19.6
17581. 7
17595. 0
17608. 3
17621. 7
17635. 0
17648. 2
17661. 5
17674. 8
17688. 1
17701.4
19.6
19.7
17714. 6
17727. 9
17741.1
17754. 4
17767. 6
17780.8
17794. 1
17807.3
17820. 5
17833. 7
19.7
19.8
17846. 9
17860. 1
17873. 3
17886. 5
17899. 6
17912. 8
17926. 0
17939. 1
17952. 2
17965.4
19.8
19.9
17978. 5
17991. 6
18004. 8
18017. 9
18031. 0
18044. 1
18057, 2
18070. 3
13083. 4
13096.4
1
1.3
19.9
20.0
18109.5
18122. 6
18135.6
18148.7
18161.7
18174. 8
18187, 8
18200. 3
13213. 8
13226. 8
2
2.6
20.0
20.1
18239. 8
18252. 8
18265. 8
18278. 8
18291. S
13304. 8
18317.7
18330.7
18343. 6
18356.6
3
3.9
20.1
20.2
18369. 5
18382. 5
18395.4
18408.3
18421.2
18434. 1
13447. 0
18459. 9
18472. 3
18435. 7
4
5.1
20.2
20.3
18498. 5
18511.4
18524. 3
18537.1
18550. 0
18502. 8
18575. 7
13.588. 5
18601.3
18614. 1
5
6.4
20.3
20.4
18626. 9
18639. 7
18652. 5
18665. 3
18678. 1
18690. 9
18703. 6
18716.4
18729. 1
18741. 9
6
7.7
20.4
20.5
18754. 6
18767. 4
18780. 1
18792. 9
18805. 6
18818. 3
18831. 0
18843. 7
13856.4
13869. 1
7
9.0
20.5
20.6
18881. S
18H94. 3
18907. 2
18919.9
18932.5
18945. 2
18957. 8
13970. 5
18983. 1
18995. 7
8
10.3
20.6
20.7
190U8. 3
19021.0
19033. 6
19046. 2
19058. 8
19071. 4
19083.9
19096. 5
19109. 1
19121. 7
9
11.6
20.7
20.8
19134. 2
19140. 8
19159. 3
19171.9
19184. 4
19196. 9
19209. 5
19222. 0
19234. 5
19247. 0
20.8
20.9
19259. 5
19272. 0
19284. 5
19297. 1
19309. 5
19322. 0
19334. 4
19346. 9
19359. 3
19371. 8
20.9
21.0
19384. 3
19396. 7
19409. 1
19421.5
19434.0
19446. 4
19458: 8
19471. 2
19483. 6
19496. 0
1
1.2
21.0
21.1
19508. 4
19520. 8
19533. 1
19545. 5
19557. 9
19570. 2 .
19589.6 19594.9
19607. 3
19619. 6
2
2.4
21.1
21.2
19632. 0
19644.3
19656. 6
19668. 9
19681. 2
19693. 5
19705. 8
19718. 0
19730. 3
19742. 6
3
3.6
21.2
21.3
19754. 9-
19767. 1
19779. 4
19791. 6
19803.9
19816. 1
19828.4
19340. 6
19852. 8
19865, 0
4
4.8
21.3
21.4
19877. 3
19889. 5
19901. 7
19913. 9
19926, 0
19938. 2
19950. 4
19962. 6
19974. 7
19986. 9
21.4
21.5
19999. 1
20011. 2
20023. 3
20035. 5
20047. 6
20059. 7
20071. 8
20033. 9
20096. 1
20108. 2
5
6.0
21.5
21.6
20120. 3
a0132. 3
20144. 4
20156. 5
20163. 6
20180. 7
20192. 7
20204. 8
20216. 9
20228. 9
6
7.2
21.6
21.7
20241. 0
20253. 0
20265 0
20277.6
20289. 1
20301. 1
20313. 1
20325. 1
20337. 1
20349. 1
7
8.4
21.7
21.8
20361. 1
20373. 0
20385. 0
20397.0
20409. 0
20420. 9
20432. 9
20444. 8
20456. 8
20468. 7
3
9.7
21.8
21.9
20480. 7
20492. 6
20504. 5
20516. 4
20523. 3
20540. 2
20552. 1
2U564. 0
20575. 9
20587. 8
9
10.9
21.9
22.0
20599. 7
20611. 5
20623. 4
20635. 3
20647. 1
20659. 0
20670. 8
20682. 7
20694. 5
20706. 3
22.0
22.1
20718.2
20732. 0
20741. 8
20753. 6
20765.4
20777. 2
20789. 0
20801. 8
20812.6
20824. 4
22.1
22.2
20836. 2
20847. 9
20859. 7
20871.4
20883. 2
20894. 9
20906. 7
20918. 4
20930. 1
20941. 9
22.2
22.3
20953. 6
20965. 3
20977. 0
20988. 7
21000. 4
21012. 1
21023. 8
21035. 4
21047. 1
21058. 8
1
1.1
22.3
22.4
21070. 5
21082. 1
21093. 8
21105. 4
21117. 1
21128.7
21140.4
21152. 0
21163. 6
21175. 3
2
2.3
22.4
22.5
21186. 9
21198. 5
21210. 1
21221. 6
21233. 2
21244. 8
21256. 4
21268. 0
21279. 5
21291. 1
3
3.4
22.5
22. G
21302. 6
21314. 2
21325. 8
21337. 3
21348. 9
21360. 4
21371. 9
21383.5
21395. 0
21406. 5
4
4.6
22.6
22.7
21418. 1
21429. 6
21441. 1
21452. 5
21464. 0
21465.5
21487.0
21498. 5
21509.9
21521.4
5
5.7
22.7
22.8
21532. 9
21544. 3
21555. 8
21567. 2
21578.7
21590. 1
21601. 6
21613. 0
21624.4
21635. 8
6
6.8
22.8
22.9
21647.3
21658. 7
21670. 1
216S1.4
21692. 8
21704.2
21715. 6
21727. 0
21738. 3
21749. 7
7
8.0
22.9
23.0
21761. 0
21772.4
21783. 7
2179.5. 1
21806. 4
21317.7
21829. 1
21840.4
21851.7
21863. 0
8
9.1
23.0
23.1
21874. 3
21885. 6
L'ls '7 n
:j!'.'(|.:, :;
21919. 6
21930. 8
21942. 1
219.53.4
21964. 7
21976.0
9
10.2
23.1
2.S.2
21987.2
21998. 5
_ . 0
22032. 3
22043. 5
22054. 7
22066, 0
22077. 2
22088. 4
23.2
23.3
22099. 6
22110. 8
22144. 5
22155.6
22166.8
22173, 0
22189. 2
22200. 4
23.3
23.4
22211. 5
22222. 7
--:■;.'
I'JJ'.'.-O
22256. 2
22267. 3
22278. 4
22289. 6
22300. 7
22311. 8
23.4
23.5
22322. 9
22334. 0
22345. 2
22356. 3
22367. 4
22378. 4
22389. 5
22400. 6
22411. 7
22422. 8
23.5
23.6
22433. 8
22444. 9
22456. 0
22467. 0
22478. 1
22439. 1
22500. 2
22511. 2
22522. 3
22533. 3
23.6
23.7
22544. 3
22555. 4
22566.4
22577.4
22588.4
22599.4
22610.4
22621.4
22632. 4
22643.4
23.7
23.8
22654.3
22665.3
22676. 3
22687. 2
22698.2
22709. 1
22720.1 1 22731.0
22742.0
22752. 9
1
1.1
23.8
23.9
22763. 8
22774. 8
22785 7
22796 6
22807 5
22818 4
22829 4
22840. 3
22851. 2
22862. 0
2
2.2
23.9
24.0
22873. 0
22883.9
22894 7
2^90 (
116 5
22927 4
22939 2
22949. 1
22960.0
22970. 8
3
3.2
24.0
24.1
22981. 7
229a2. 5
23J0i 3
14
0
lOJ h
104b 6
23057. 5
23068. 3
23079. 1
4
4.3
24,1
34.2
23089. 9
2iiao. 7
23111 4
1 >
14 8
2 1d4 5
23165. 3
23176. 1
23136, 3
6
5.4
24.2
24.3
23197. 6
23208. 3
23219 1
1 0
ol o
21-62 0
21272.7
23283. 4
23294, 2
6
6.5
24.3
21.4
23304. 9
23315. 6
23J2fa
"
- .,4 0
2J35b 3
2 u09 0
23379. 7
23390. 3
23401. 0
7
7.5
24.4
BAROMETKIC TABLES.
133
Table. I. — 0=^60158.58 x log H or li. Argtimeni: The ohiserved height of the barometer at either station-
Continued.
Barom-
Hundredth
3 of an inch.
Thou-
Barom-
eter in
Bng.
iucE.
sandths
of
an inch.
eter in
Eng.
.00
.01
.02
.03
.04
.05
.06
.07
.OS
.09
Eng.ft.
Eng.ft.
Enij./t
Eng.ft.
Eng.ft.
Eng.ft.
Eng.ft.
Eng. ft.
Eng.ft.
Eng.ft.
Feet.
24.5
23411.7
23422. 3
23433. 0
23443. 7
23464.3
23464. 9
23475. 6
23486. 2
23496. 8
23607. 4
8
8.6
24.5
24. G
23518. 1
23528. 7
23539. 3
23549. 9
23660. 5
23571. 1
23681. 7
23592. 3
23602. 9
23613. 6
9
9.7
24.6
24.7
23624. 1
23634. 6
23645. 2
23655. 8
23666. 3
23676. 9
23687.5
23698.0
33708. 6
23719. 1
24.7
24.8
23729. 7
23740. 2
33750. 7
23761.2
23771.7
23782. 3
33792. 8
23803. 3
23813.8
33824. 3
24.8
24.9
23834. 8
23845. 3
23855. 7
23866. 2
23876.7
23887. 2
33897. 7
23908. 2
23918. 6
23929. 1
1
1.0
34.9
25.0
23939. 5
23949. 9
23960. 4
23970. 8
23981. 3
23991. 7
24002. 1
24012. 5
34023. 0
24033.4
2
2.1
25.0
25.1
24043. 8
24054. 2
24064. 6
24075. 0
24085. 4
24095. 7
24106.1
24116,5
24126. 9
34137. 2
3
3.1
26.1
25.2
24147. 6
24158. 0
24168. 3
24178. 7
24189. 0
24199.4
24209. 7
24220. 1
34230. 4
24240. 8
4
4.1
25.2
25.3
24251. 1
24261. 4
24271. 8
24282. 1
24292. 4
24303. 7
24313. 0
24323. 3
24333. 6
24343. 9
5
5.1
25.3
25.4
24354. 2
24364. 5
24374. 7
24385. 0
24395. 3
24406. 5
24415. 8
24426. 1
24436. 3
24446. 6
6
6.2
26.4
25.5
24456. 8
24467. 0
24477. 3
24487. 5
24497. 8
24508. 0
24518. 2
24528. 4
24638. 7
24548. 9
7
7.2
26.5
25.6
24559. 1
24569. 3
24579. 5
24589.7
24599. 9
24610. 0
24630. 2
24630.4
24640. 6
24650.7
8
8.2
26.6
25.7
24660. 9
24671. 1
24681. 2
24691.4
24701. 6
24711. 7
34721. 8
24732. 0
• 24742, 1
24752. 3
9
9.2
26.7
25.8
24762.4
24772. 5
24782. 6
24792. 8
24802, 9
24813. 0
24833. 1
24833. 2
24843. 3
24853. 4
25.8
25.9
24863. 5
24873. 6
24883. 7
24893.7
24903. 8
24913. 9
24931. 0
24934.0
24944. 1
24964. 1
25.9
26.0
24964. 2
24974. 2
24984. 3
24994. 3
25004. 4
25014. 4
26024. 4
26034. 4
25044. 5
25064. 5
26.0
26.1
25064. 5
25074. 5
25084. 5
25094. 5
25104. 5
25114. 6
25124. 5
25134. 5
26144. 4
25154. 4
26.1
26.2
25164. 4
25174. 4
25184. 3
25194. 3
25204. 2
25214. 2
25224. 1
25334. 1
25244. 0
25254. 0
1
1.0
26.2
26.3
25263. 9
25273. 8
25283. 8
25293. 7
25303. 6
25313. 6
25323. 4
35333. 3
25343. 2
2,5353. 1
3
2.0
26.3
26.4
25363. 0
25372.9
25382.8
25392. 7
25402. 6
25412. 4
26422. 3
25432. 2
26442. 1
25451. 9
3
2.9
26.4
26.5
25461. 8
2.';471.7
25481. 5
25491.4
25501. 2
25511. 0
25620. 9
25530. 7
25540. 6
25650. 4
4
3.9
26.5
26.0
25560. 2
25570. 0
25579.8
25589. 7
25599. 5
25609. 3
25619. 1
25628. 9
25638. 7
25643. 5
5
4.9
26.6
26.7
25658. 3
25668. 1
25677.8
25687. 6
25697. 4
26707. 1
25716. 9
25726. 7
25736.4
25746. 2
6
5.9
26.7
26.8
25755. 9
25765. 6
25775. 4
25785. 1
25794. 8
25804. 6
25814. 3
26824. 0
25833. 3
25843. 5
7
6.9
26.8
26.9
25853. 2
25862. 9
25872. 6
25882. 3
25893. 0
25901. 7
25911.4
25921, 1
25930. 8
25940.5
8
7.8
26.9
27.0
25950. 2
25959. 9
25969. 6
25979. 2
25988.9
25998. 6
26008. 2
26017. 9
26027. 5
26037. 2
9
8.8
27.0
27.1
26046. 8
261156. 5
20066. 1
26075. 7
26085. 3
26095. 0
26104. 6
26114. 2
26123. 8
26133.4
27.1
27.2
26143. 0
26152.6
26162. 2
26171. 8
26181. 4
26191. 0
26200. 6
26210. 2
26219. 8
26339. 3
27.2
27.3
26238. 9
26248. 0
20258. 0
26267. 6
26277. 2
26286. 7
26296. 3
26306. 8
26315. 3
36324. 9
27.3
27.4
26334. 4
26344. 0
26353. 5
26363. 0
26372. 5
26382.1
20391. 6
26401. 1
26410. 6
26420. 1
1
0.9
27.4
27.5
26429. 6
26439. 1
26448. 6
26458. 1
26467. 6
26477. 1
26436. 5
26496. 0
26505. 5
26514, 9
2
1.9
27.5
27.6
26524. 4
26533. 9
26543.3
26552. 8
26562. 3
26571.7
26681. 2
26590. 6
26600. 0
26609. 5
3
2.3
27.6
27.7
26618. 9
26628. 4
26637. 8
26647. 2
26656. 7
26066. 1
26676. 5
26684. 9
26694. 3
26703. 7
4
3.7
27.7
27.8
26713. 1
26722. 5
26731. 9
20741. 3
26750. 7
26760. 1
26769. 6
26778. 8
26788. 2
26797. 6
5
4.7
27.8
27.9
26806. 9
26816. 3
26825. 6
26835. 0
26844. 3
26853. 7
20863.0
26872. 3
26881. 7
36891. 0
6
5.6
27.9
28.0
26900. 4
26909. 7
21919. 0
26928. 4
26937. 7
26947. 0
26956. 3
26965. 6
26975. 0'
36984. 3
7
. 6.5
28.0
28.1
26993. 6
27002. 9
27012. 2
27021.5
27030. 7
27040. 0
37049, 3
27058. 6
27067. 8
27077. 1
8
7.5
28.1
28.2
27086. 4
27095. 6
27104. 9
27114. 3
27123. 4
27132. 7
37141. 9
27151.2
27160. 4
27169, 6
9
8.4
28.2
28.3
27178. 9
27188. 1
27197. 3
27206. 6
27215. 7
27225. 0
27234. 2
27243.4
272'^2. 6
27261, 8
28.3
28.4
27271.0
27280. 2
27289. 4
27298. 6
27307. 8
27317.0
37326. 3
27335. 3
27344. 5
27353. 7
28.4
28.5
27362. 9
27372. 0
27381.2
27390. 4
27399. 5
37408. 7
37417. 3
27427. 0
27436. 1
27445. 2
28.5
28.6
27454.4
27463.5
27472. 6
27481. 8
27490. 9
37500. 0
27509. 1
27518. 2
27527.4
27536. 5
28.6
28.7
27545. 6
27554.7
27563. 8
27572. 9
27582. 0
37691. 1
27600. 2
27609. 3
27618. 3
27627. 4
1
0.9
28.7
23.8.
27636. 5
27645. 5
27654. 6
27663. 7
27672. 7
37681. 8
27690. 8
27699.9
27708. 9
27717.9
2
1.8
38.8
28.9
27727.0
27736. 0
27745. 1
27754. 1
27763. 1
27772. 2
37781. 3
27790, 2
27799. 2
27808. 3
3
2.7
28.9
29.0
27817. 2
27826. 2
27835. 2
27844. 2
27853. 2
37863. 3
37871. 2
27880. 2
37889. 1
27898. 1
4
3.6
29.0
29.1
27907.1
27916. 1
27925. 0
27934. 0
27943. 0
27951. 9
37960. 9
37969. 8
37978. 8
27937. 7
5
4.5
29.1
29.2
27996. 7
28005. 6
28014. 6
28023. 5
28032. 4
28041. 4
28050. 3
38059. 3
38068. 2
38077. 1
6
5.4
29.2
29.3 !
28086. 0
28094. 9
28103.8
28112. 8
28121. 7
28130. 6
28139. 5
28148. 4
28157. 3
28166.2
7
6.3
29.3
29.4 ,
28176. 1
28184. 0
28192. 9
28201. 7
28210. 6
28219. 5
38328. 4
38237. 3
28246. 1
38364. 9
8
7.2
29.4
29.5
28263. 8
28272. 6
28281. 5
28290. 3
28299. 2
28308. 0
28316. 9
28325. 7
28334. 5
28343. 4
9
8.1
39.5
29.6
28352. 2
28361. 0
28369.8
28378. 7
28387. 5
28396. 3
28405. 1
28413. 9
28J22.7
28431. 5
29.6
29.7
28440. 3
28449. 1
28457. 9
28466, 7
38475.4
2848J. 2
28493. 0
28501. 8
28610. 6
28519. 3
29.7
29.8
28528. 1
23536. 9
28545. 6
28554. 4
28563. 2
28571. 9
28580. 7
28589. 4
28598. 2
28606. 9
29.8
29.9
28615. 7
28624. 4
28633.2
28641. 9
28650, 6
28659. 3
28668. 1
28676. 8
28686. 5
28694. 3
1
8.6
29.9
30.0
28702.9
28711. 6
28720. 3
28729. 0
28737. 7
28746. 4
28755. 1
28763. 8
28772. 5
28781. 1
3
1.7
30.0
30.1
28789. 8
28798. 5
28807. 2
28815. 9
2S824.5
28833. 2
28841. 9
28850. 5
28859. 2
28867. 9
3
3.6
30.1
30.2
28876. 5
28885. 2
2B893. 8
28902. 5
28911. 1
38919. 8
28928. 4
38937. 0
28945. 7
28964. 3
4
3.4
30.2
30.3
28962. 9
28971. 5
28980. 1
28988. 8
28997. 4
39006. 0
29014. 0
29023. 2
39031.7
29040. 3
4.3
30.3
30.4
29048. 9
29057. 5
29066. 1
29074. 7
29083. 3
29091. 8
29100. 4
29109. 0
39117. 6
29126. 2
6
5.2
30.4
30.5
29134. 7
29143. 3
29151. 9
29160.4
29169. 0
29177. 6
29186. 1
29194. 7
29203. 2
29211.8
7
6.0
30,5
30.6
29220. 3
29228. 9
29237. 4
29245.9
29254. 4
29262. 9
29271. 5
29280. 0
39283. 5
39297. 0
8
6.9
30.6
30.7
29305. 5
29314. 0
29322. 5
29331. 1
39339. 6
29348. 1
29356. 6
29365. 1
29373. 6
29382. 0
9
7.7
30.7
30.8
29390. 5
29399. 0
29407. 5
29416. 0
29424. 4
29432. 9
29441. 4
29449. 8
29458. 3
29466. 8
30.8
30.9
29475. 2
29483. 7
29492. 1
29600. 6
29509. 0
29517. 5
29525. 9
29534. 3
29542. 8
29551. 2
30.9
134
A MAXITAL or TOPOGRAPHIC METHODS.
Taisle II. — Correct ion for r — r', or diffo-etice in the temperature of the barometers at the two stations.
This correction is neffative -when the attached thermometer at the upper station is lowest; po^tive when tlie attached
thermometer at the upper station is hip;hest.]
Cor-
Cor-
Cor-
Cor-
Cor-
Cor-
Cor-
Cor-
Cor-
F.
tion.
r.
tion.
F.
tion.
E.ft.
F.
tiOD,
E.ft.
F.
tion.
F.
tion.
F.
tion.
F,
tion.
F.
tion.
E. ft.
F.
rec-
tion,
o
E.ft.
E.ft.
E.ft.
E./t.
E.ft.
E.ft.
o
E.ft.
l.C
2.3
11.0
25.8
21. C
49.2
31.0
72.6
41.(1
96.0
51.(1
119.5
61.0
142.9
71.0
166.3
81. (.
189.7
91, t
213.2
1.5
X5
11.5
26.9
21.5
50.4
31.5
73,8
41,5
97.2
51.5
120. 6
(il.5
144.1
71.5
167. 5
81.5
190.9
91.5
214, 3
2.0
4.7
12.0
28.1
22. C
51.5
32.0
75.0
42.0
98.4
52. (1
121.8
(i2. (1
145.2
72. (1
168,7
82.0
192.1
92.0
215.5
a.i>
5.9
12.5
29.3
22.5
52.7
32,5
76.1
42.5
99.6
52. 5
123.0
62.5
146.4
72. 5
169.8
82,5
193.3
92.5
216,7
3.U
7.0
13.0
30.5
23.0
53.9
33.0
V7. 3
43.0
100.7
53.0
124.2
63.0
147.6
73.0
171.0
83.0
194.4
93.0
217.9
3.5
8.2
13.5
.31.6
23.5
55.1
33.5
78.5
43.5
101,9
53. 5
125.3
63.5
148.8
73,5
173.2
83, 5
195.6
93.5
219.0
4.0
9.4
14.0
32.8
24. C
56.2
34, 11
79.6
44,(1
103,1
54, 11
126. 5
64,(1
149,9
74,(1
173.4
84,(1
196.8
94.0
220.2
4.5
10.5
14.5
34.0
24. 5
57.4
34,5
K0.8
+4,5
104.2
54.5
127.7
64.5
151.1
74,5
174,5
84,5
197.9
94.5
231.4
5.0
11.7
lo.O
35.1
25. (i
58.6
35, 11
82. 0
45.0
105.4
55, (1
128.8
65.0
152.3
75,0
175.7
85,0
199.1
95,0
222.5
5.5
12.9
lo.5
36.3
25.5
59.7
35.5
83.2
45.^
, 106. 6
55,5
130,0
65.5
153.4
75.5
176.9
85,5
200.3
95,5
223.7
6.0
14.1
16.0
37.5
26.0
60.9
36, 0
84,3
46,0
107,8
5fi, 0
131.2
66, 0
1.54.6
76,0
|'J78. 0
86.0
201.5
96.0
224. 9
6.5
15.2
16. b
38.7
26.5
62.1
36.5
85, 5
46,5
108,9
56. 5
132,4
06,5
155.8
76.5
•179. 2
r6,5
202.6
96,5
226.1
7.0
16.4
IV. 0
39.8
27, t
63.2
37. C
86.7
47,0
110.1
57.0
133.5
6f, 0
157.0
77.0
180.4
87,0
203.8
97.0
227.2
7.5
17.6
17.5
41.0
2V.5
64.4
37, 5
87. H
47.5
111,3
57.5
134. 7
67, 5
158, 1
77.5
181.6
87,5
205.0
97.5
228.4
8.0
IS. 7
18.0
42.2
28.0
65,6
38,0
89. 0
48,0
112,4
58.0
135.9
68,0
159,3
78,0
182, 7
88.0
206.1
98.0
229.6
8.5
19.9
18.5
43.3
28.5
66,8
38,5
90.2
48,5
113.6
58. 5
137,0
68.5
160. 5
78.5
183,9
88.5
207.3
98.5
230. 7
9.0
21.1
19.0
44.5
29. (1
67.9
39.0
91.4
49.0
114,8
59,0
138.2
69,0
161.6
79.0
185,1
89.0
208.5
99.0
231.9
9.5
22.3
19.5
45.7
29. 5
69,1
39.5
92,5
49.5
116,0
59, 5
139.4
(i9, 5
162.8
79.5
186.2
89.5
209.7
99.5
233.1
iO.O
23.4
20.0
46.9
30.(1
70.3
40.0
93.7
50. 0
117,1
60.0
140.6
70. (1
164.0
80.0
187.4
90. (1
210.8
100.0
234.3
10.5
24.6
20.5
48.0
30.5
71.4
40.5
94.9
50.5
118.3
60.5
141.7
70.6
165.2
80.5
188.6
90. b
212.0
100,5
235.4
Table III. — Correction for the difference of (fravity fn various latitudes.
[ Correction ^os^t(/«e from latitude 0° to 45°; negative from 45° to 90°.]
Ap.
Latitude.
Ap-
proxi-
mate
proxi-
mate
1
diCfer- JO
ence of ana
level, l""
20' 40
6°
8°
10° 12° 14°
16° 18°
20°
22°
24°
26°
28°
30°
82°
34°
36°
38°
40°
42°
44°
45°
differ-
ence of
level.
88° 86°
84°
82°
80°
78°: 76°
1
74°
72°
70°
68°
66°
64°
62°
60°
58°
56°
64°
52°
50°
48°
46°
Eng./t. Ft.
Ft.' Ft.
^
Ft.
Ft.
Ft. ' Ft..
Ft.
Ft.
Ft.
Ft.
Fl.
Ft.
Ft.
Ft.
Ft.
Ft.
Fc.
Ft.
Ft.
Ft.
Ft.
Ft.
Eng.ft.
1,000 1 2.6
2.6 2,6
2.5
2.5
2.4; 2,4 2.3
2.2
2,1
2,0
1.9
1.7
1.6
1.5
1.3
1.1
1,0
0.8
0,6
0.5
0.3
0.1
0
1,000
2.000 5.2
5.2 5.1
5.0
4. 9 4. 7 4. 6
4.4
4.2
4,0
3.7
3.5
3.2
2,9
2,6
2,3
1.9
1.6
1,3
0.9
0.6
0.2
0
2,000
3, 000 I 7. 8
7.8 7.7
7^6
7,5
7. 3I 7. 1 6. 9
0.6
6.3
6.0
5.6
5.2
4.8
4.4
3,9
3.4
2.9
2,4
1,9
1.4
0,8
0.3
0
3,000
4,000 10,4
10,410.3
10,2
10,0
9.8' 9,5 9,2
8.8
8.4
8.0
7.5
7.0
6.4
5.8
5.2
4.6
3.9
3.2
2,5
1.8
1.1
0.4
0
4,000
5,000 13,0
13. 0 12. 9
12.7
12.5'12,211,911.5
1 1
11.0
10. 5 10. 0
9.4
8.7
8.0
7.3
6.5
5. 7: 4. 9
4.0
3.1
2.3
1.4
0.5
0
5,000
6, 000 15. 6
15, 6 15, 4
15,3
15. 0 14, 7 14. 3 13, 8
13.2
12. 6 11. 9
11.2
10,4
9.6
8.7
7.8
6.8 5,8
4.8
3,8
2,7
1.6
0.5
0
6,000
7,000 18.2
18. 2 18, 0
17. .«
17..". 17. I 16.616.1
15, 4 14, 7 13, 9
13.1
12.2
11. 2'10. 2
9.1
8.0 6.8
5.6
4.4
3.2
1.9
0.6
0
7,000
8,000 20.8
20, 7 20. 0
li'i. :i
Jii. n ]■."..-.]!). 0 18 4
17.610.815.9
15.0
13,9
12,811,6
10.4
9.1 7,8
6.4
5.0
3,6
2.2
0.7
0
8,000
9,000 23.4
23. 3 23. 2
_'J. 11
JL'..VJ-J, 1121.4 20. 7
19. .S 18. 9 17. 9
16.8
15,7
14. 4I13. 1
11.7
10.3 8.8
7.2
5.7
4.1
2.4
0.8
0
9,000
10, 000
26.0 25,9 25, 7 ■_'.'.. 4
j
2.-.. (J 24. 4 2:i. 8 23. U
22. 0 21. 0 19. 9
18.7
17.4
16. 0[14. 5
13.0
11.4' 9.7
8.0
6.3
4,6
2.7
0.9
0
10,000
11,000
28.6'28.5 28.3i28.0
27, 526. 9 26, 125, 3
24.3,23.121.9
20.6
19,1
17. 6 16, 0
14.3
12. 5 10. 7
8.8
6.9
5.0
3,0
1,0
0
11, 000
12, 000
31.2 31,130,9:30.5
30.0 29.3 28.5 27.5
26.5I25.223.9
22.4
20.9
19. 2a7. 4
15.6113.711.7
9.6
7. 5
5.4
3.3
1.1
0
12, 000
13, 000
33. 8 33. 7 33. 5,33'. 1 32. 5 31, 8,30. 9 29, 8
28.7:27.3
25.9
24. 3 22. 6
20. 8:i8. 9
16. 9il4. 8 12. 7
10.4
8,2
5.9
3.5
1.2
0
13, 000
14, 000
36. 4 36, 3 36. 0 35, 6 35, 0 34. 2 33. 3|32. 1
30.9:29.4
27.9
26. 2 24. 4
22.4
20.4
18,2
16. 0 13. 6
11.2
8.8
6.3
a8
1.3
0
14, 000
15, 000
39. 0 38. 9 38. 6,38. 1 37. 5 36. 6 35. 6 34. 4
33, 1I3L 6
1
29. 9
28. 1 26. 1
24.0
21.8
19,5
17. 1J14.6
12.1
9.4
6.8
4.1
1.4
0
15,000
16. 000
41. 641. 5 41. 2 4(1. 7 40, 0 39. 1 38. 0 36. 7
35, 3 33. 7
31.9
29.9 27.8
25.6
23.3
20,8
18. 2 15. 6
12 9
10.1
7.2
4.3
1.5
0
16, 000
17, 000 144. 2 44, 1 43. 8 43, 2 42, 541, 5 40. 4|39. 0
37. 5:35. 8
33.9
31. 8 29. 6
27.2
21.7
22.1
19. 4 16. 6
13.7
10.7
7.7
4.6
1.5
0
17, 000
18, 000 46, 8 46, 7 46, 3 45, 8 45, 0 +4, 0 42, 8,41, 3
39. 7137. 9
35.8
33. 7 31. 3
28,8
26,2
23.4
20. 5 17. 5
14.5
11.3
8.1
4.9
1.6
0
18,000
19, 000 49, 4 49. 3 48. 9 48, 3 47, 5 40. 445. 1
43.6
41.9
40.0
37.8
35. 5 33. 1
30.4
27.6
24.7
21. 7 18, 5
15,3
12.0
8.6
5,2
1.7
0
19,000
20,000 52.0,51.9 51.5 50.4 50.0
48. 9147, 5
1
45.9
44,1
42.1
39.8
37.4 34.8
32.0
29.1
26.0
22. 819. 5
16,1
12.6
9.0
5.4
1.8
0
20,000
21, 000 '54. eW. 5 54. l'53, 4'52, 5
51. 3 49. 9
48.2
46.3
44,2
41.8
39, 336, 5
33,6
30.5
27.3
23. 9 20, 5
16.9
13.2
9.5
5.7
1.9
0
21, 000
22, 000 57. 2 57. 1 56. 6 55, 9 53. 0
53.7;52.3j50.5
48.5'46,3
43.8
41. 1 38. 3
35,2
32,0
28.6
2^.121.4
17.7
13.8
9.9
6.0
2.0
0
22.000
23, 000 '59. 8 59 7 59, 2 ,58, 5 57. 5
56, 2'54. 6 52, 8
50,7'48.4
45.8
43. 0 40, 0
36.8
33,4
29,9
26.2 22.4
18.5
14.5
10.4
6.2
2.1
0
23, 000
24,000 62,4162,2 61,8 61.0:60.0
58. 6 57. 0,55. 1
52. 9j50. 5
47.8
44,9 41.8
38.4
34,9
31,2
27. 4 23. 4
19.3
15.1
10.8
0.5
2.2
0
24, 000
25, 000 ,65. 0 64. 8 64, 4,63. 6|62. 5
61,1,59.4 57,4
55, 1 52. 6
49.8
46.8 43.5
40.0
36.3
32,5
28, 5 24 3
20.1
15,7
11.3
0.8
2.3
0
25, 000
BAEOMBTEIC TABLES.
135
Table IV. — Correction, for-
Decrease of gravity
Decrease of gravity
Decrease of gravity
Approxi-
Approxi-
mate
mate
mate
difterence
difference
of level.
<»
+500
of level.
O
+500
of level.
0
+500
Eng.feet.
Feet.
Feet.
Fng. feet.
Feet.
Feet.
Eng.feet.
Feet.
Feet.
1,000
2.5
3.9
10, 000
29.8
31.5
19, 000
64.8
67.0
2, UOC
5.2
6.6
11. 000
33.3
35.1
20, 000 .
69.2
71.4
3.000
7.9
9.3
12, 000
36.9
38.7
21, 000
73.6
75.9
4, Olio
10.8
12.2
13, 000
40.6
43.5
2i, 000
78.2
80.5
5,000
13.7
15.2
14, 000
44.4
46.3
23, 000
82.9
85.2
6,000
ie.7
18.3
15. 000
48.3
50.3
24, 000
87.6
90.0
7,000
19.9
21.5
16. 000
52.3
54.3
25, 000
92.5
94.9
8,000
23.1
24.7
17. 000
56.4
58.4
9,000
26.4
28.1
18, 000
60.5
62.6
Table V. — Correction for the height of the lower station. — Positive.
Approxi-
mate
Height of the barometer
in En
jlish inches.
Height of the barometer, in En
glish inches,
at lower station.
mate
at lower station.
of level.
16
18
20
32
34
36
38
of level.
16
18
30
32
34
26
28
Eng.feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Eng.feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
1,U00
1.6
1.3
1.0
0.8
0.6
0.4
0.3
14, 000
21.9
17.8
14.1
10.8
7.7
4.9
3.3
2,000
3.1
2.5
2.0
1.5
1.1
0.7
0.3
15, 000
23.5
19.1
15.1
11.5
8.3
5.3
3.5
3,000
4.7
3.8
3.0
2.3
1.7
1.1
0.5
16, 000
25.1
20.3
16.1
12.3
8.8
5.6
2.7
4,000
6.3
5.1
4.0
3.1
2.2
1.4
0.7
17, 000
26.6
2L6
17.1
13.1
9.4
6.0
3.8
5.000
7.8
6.4
5.0
3.8
2.8
1.8
0.8
18, 000
38.2
33.9
18,1
13.8
9.9
6.3
3.0
6,000
9.1
7.6
6.0
4.6
3.3
2.1
1.0
19, 000
39.8
34.1
19.2
14.6
10.5
6.7
3.2
7,000
U.O
8.9
7.1
5.4
3.9
2.5
1.2
20, 000
31.3
35.4
20.2
15.4
11.0
7.0
3.3
8, 001)
13.5
10.2
8.1
6.2
4.4
2.8
1.3
31, 000
33.9
26.7
21.2
16.1
1L6
7.4
3.5
9,000
14.1
11.4
9.1
6.9
5.0
3.3
1.5
22, 000
34.5
28.0
22.2
16.9
12.1
7.7
3.7
10, 000
15.7
12.7
10.1
7.7
5.5
3.5
1.7
33, 000
36.0
29.2
23.2
17.7
12.7
8.1
3.8
11,000
17.2
14.0
11.1
8.5
6.1
3.9
1.8
34, OOU
37.6
30.5
34.2
18.5
13.2
8.4
4.0
12, 000
18.8
15.3
12.1
9.3
6.6
4.2
2.0
25, 000
39.1
31.8
25.2
19.2
13.8
8.8
4.1
13, 000
20.4
16.5
13.1
10.0
7.2
4.6
2.3
i
136
A MANUAL OF TOPOGEAPHIC METHODS.
t5
n
^''
s
i ^
1
o
1-
^
U -
H
s
>"
^
'3/s
.a
■9.
^
S.S
^
11
»
S
iii
•7
1
Sg'-E
1— I
5 p..!:
H5S
3 a
i
s
0
; ;.n=.a.
C»00^C..O
ooo^^co
M<n— too
mSSSc5
:?ggBS
. .eD-*03
ciNCJCJr^
rtrtrtrt
CS
: ic^cQ-
co-«cqca-i
:"3:^"
c<.-,o§3
I-i rH i-i
OOfMOiO
OOOQOC-C-
fSgSgg
s
: irtoo
oocoooo
l>lO-#CO(M
rH r-tOOO
£5S£^?2
ggggg
: ;="*"
MWMC^T-i
rHr-.^
t*
I !os-*U3
ai»r5(MCsoo
oiflcococq
^oSSSg
2*00030
SSoSS
50
; ioca^
QO-^rHOJ t-
in-*D3MrH
rtoSSS
oot-c- t-co
SoSSS
. .in-^ro Ncq<Mr^rH r-lrtrlrtrH rt rH |
§
; i^rfCO
t-cooooco
in^WNrH
oosmooS
Sflpgsg
ggggs
: :"=-*«
WWci-^r^
■-1
-*
: :«c^
0(MOt-<S>
'^COM^O
§g£Sg
gE=SSg
ssssg
■ .loi^eo
g
■ 'Ot-O
l.O,-i«t-lD
^(NW^O
C5 00C0C-C~
t-o 000
SSSgg
Cicq^r^^
S
-^OOOO-*
«M^ = §
gsgeg
SSSSK
InSio^^
. . -fj! PS cj
cici — r^rH
^^^^ •
s
• oo:Ot* t-
<M_^0§g
ggggg
SSSfelg
5?S§^1§
g
L-s cocao
WCO^CO
<M^og£
w t^wciin
gSKSS
000 t-lfiiCO
10 -#"*■* -^n
s
:CQ.H-<U5
-iOOO^M
-ioSooco
5!S3S5l
■SO-^COM
<-4 ^ r-I eH .-4
--I ^ * ' '
ce
■ cnocsco
OJi>iacoM
000"<i<00
cooiincaos
t-oocoin
sssss
SSSSra
t*
i--»-
»°--".
0 CI 00 I- l>
gg^sts
sss^^
CO— (OQO t-
.*Ti..a.coco
9
;-.--.-
-;-;-;-;-;
gSoS^g
0 JoStnS
sss^^
005 treses
S
icscQ^c;
o^co-^g
ca .-H ITS 0 10
0000 t-t-eo
cOinirairs-*
J;3iS5!g
(KOH.Tl.M
■ '#(rONr-5
^rHi-li-H
"
leooMoo
«,CO^OS
sssggs
l>-*.-H30<D
eowocoo
"*■*■* CO CO
mMcoeoM
«
■NOOi-t t-
„CQ-.SS
tr- ,-1 uO 0 ttJ
C-|>toOiO
sg5;3S
OOOt-lO-#
"t CO en- CQ so
sasss
.■*!M(M'-(
tAAtA
s
COr-.C!aot-
c- 0 0 0 in
SSSSg
55Jg^g=^
gssss
■ CQM'-ItH
r-. r-i * '
-
(MtO^CO-*
MoS»P!
ggsss
sgs^g
'JiCOiHOO
sasssi
t-COlM'-i.-i
0
lflCO(M«;cO
^gsgg
gssss
'^ CI CO CO «
^ 000 t-to
s^ssa
*
ornoioN
g'asss
sssss
conSSS
I5S88S
ssssgs
00
QO l~ 0 10 10
5;5sss
sssss
^asss
sssss
t»
0rt.n-.5J
gSL^^S^
— >QOtn(ro 0
"* CO com TO
SSSjSSs
EJS2SS.
SS3SS
«
ocsco c: t>
So^"m
gggss
§i?3i3SS
000 t-oo
S33SS
0
COfflrtSS
•rftL Its CO
sssss
SSSSS
C5-*..* ^CO
sssss
c^c<;rJ • • ■ ■ : 1
■*
ccoSgS
"<JlMCO(M(M
MCJMr-i-H
SSSSS
sssss
ooggg
«
ojSS^g
ssssss
22233
lM.-irt 0 0
gggSS
sssss
«
rtiSSSS
M Ci (O -* CO
SSSgg
00000
ggggg
00000
-
§g?§3SS
.-ic:oo t^c-
r-lC 0 00
00000
^s^gg-
00000
sgggg
1
<-o1
Ssoo©
:sr,xc:o
^«M*«
e t- X ft «
SSPSS
ei-CC»3
ALTITUDE TABLES.
187
4i
O
1
R
o
■ntoromci
■*03(MrH0i
cnooc-oco
in ^ Tti CO CO
COCOCONCN
wcawNr^
® ;
^U= 00 CO 00
■^ roiH o ci
ooc-c-a=in
in^^cQCO
»in-*-<»m
COCO(MM(M
(Mrrqcq(Mi-i
« i
corf t^cqoO
■^iMi-lOCi
oot-omin
^^COCQCO
CO in-*-* CO
cococqNN
c4wNM^
t* ;
MCO »'-( t-
2.3
2.2
2.1
1.9
1.9
00 t- CD in in
^^CO«N
* 1
; ;
WNCOOCO
COOOOCr.
Mi-tOOlOO
L- t- o in in
^cooiroN
,om^-*oi
comcJ^ei
(M* N W r-i rH
ta
Orinoco
CDUJ-JHirf
(M r-(OC35CO
^22";^
3
oorBoin
Noc-inco
C^.^ffiO0 00
t-coininrl.
«coco«cq
iriirirjcoco
COC<lSQr>«
S
"T"
t-acooon.
MOCJQOt-
CO CO in-*..*
MCONM-H
■"■*-* CO CO
oJoacqoiN
(MMi-lrH t-1
-
S2SSS
riSS^S
rHOOOOC-
Cd W^^r-^r-^
"IS^"
SS2S!^
s
lot- '-it- CO
ITS-*-* CO CO
ooom-#iM
rHOoo c-t-
""!^23
^^^;i;i
«
iri rh TlH CO CO
o t-incoiM
oosooc-eo
!!^"2!^S
(MfMNiHr-l
o
cocooicsca
ww(^it^iN
c^ OS cot- to
in r» rK CO CO
(MCa«H.Hr4
r-i r-( iH iH fH
-*-
"T~
: :
COO^MrH
OiOOt-COCC
in-*r}ico(n
(M (M iH r-l O
in r» CO CO CO
CJNNMM
rfrlrHrfrt
^
"*
r-l-* 00-*r-(
Ci (?i (N (N ci
S!^"3!^
!4Z;!^^3
sl
OCOC^POO
t-incoi-io
ffiCOt-OiA
rJlritCOIMM
r-ti-CrHOO
inriicococo
Mwcacqw
r-ljH T-l rH rH
"* i
en (Mc- CO OS
t--^(nrHCS
00C-(D lOO
r,com«(N
iHr^OoS
MNWW-I
rHrHrH -H
^!
oorftoiDcm
oot> to in-*
rHiHOOJOS
ni^-cioici
(NcdMfN tH
"
SciMWr^
-----
cococgc.^.
rlO OClOi
■*
tsojrjoc-
t-to m"*-#
CO(M(M rHr4
O O CT. O) 0>
^cicicoN
cq (M (M i-l .-I
3
raioocooi:-
oco in-* CO
COIN rHrHiH
ogSSS
©
M t-MCitO
■^caoojc-
.in^^co
Mcqr-tiHO
OOlOOiQO
rA • ■ ' '
i-
—
<d_>ri_
COrHCnOOC-
tH rH fH rS rH
--.-- =
^^^^^
r-(lOrHt-»Cl
Mr-. 0=00(0
oin^coco
<MrHi-lOOJ
gs§§ss
t=^
Tj5 CO cowed
C4 eg J rH rH
■H rHiH 1-"
S
oco
OTHOt-rH
-jcicriNCd
C-icqr^r^r^
1-1 WO OOT
iH rH rH r-i
ffiTOOTOoS
u
M rH -; rH r^
"2"2!1
iHrHrH
C=> t-'*rHQO
>o
cooioicJca
rHCSt-K)U3
CQrHrHrHrH
tHOOOIO)
g§sssg
■*
b:
t-wcoinC3
c4r-5 i-H iH-i
^2"S^
O OOS OSOO
ooooc-c-c-
»
I-*co
CO.H t-rilrH
3S""2
rtrtrtrHr.;
o§gg§
coot--it<M
oooo t-c-t-
7
loJM
inotocorf
o t-cD in-*
CO CC 0,^0
ggssss
O t-^Mg
.«5-*
oic^NWN
1-1
CO S cd eg cq
00 t-ic-^m
COMiHrHO
i-H rH ,iH r-5 r-i
g^ssss
oomcM or-
t-c-t-c-co
-
«
3o«
I3§
c9i>xeaO
OOOOrt
iHeiM-*»o
COt^oCCSO
sijsas
is;^iS
138
A MANUAL OF TOPOGEAPHIC METHODS.
i 1
SSSKS
ssss^
35!S33
!M(Mr-<00> 0000C-(OlO ift ■* ;2K M « 1
-^ _,, ^ ^Tj" CO CO CO CO CO CO COCOCOCOCO
1
O)
SSoS^
ggS55
".^.^.^^.
5!5SSg S^SSS SSSSS
s
gSlgiSS
r-tOSOOOOCO
^"^^^
3sS5§ SSSSS? SggSS
5 1
s s s ^ s
SS5'53:
SS5i3g
gSSSS SSS5SS gSSSS
S
5;§!S3?I
qJ5g^S
SSSSS3 fSS5S?SS SgSSSS 1
iS 1
CC ■^ CS CO t-
S33?J5;
sggss
gSSSiSSl SSSSS gSSSa 1
»
s§sss
gg^ss
SSSm"
SgSS?S SSSSS SS5S§
M
55!§33
gssss
sss^s
gissss §ss5?sa assss
1
>
•1
i
s
u 1
§§3^51
o =: oo t^ --D
SISSSS
sssss sssss sssaa
»H
5335S
ssssa
SSS3=3S
ggSSS SSSS8 33^SS 1
o
ssssss
sssss
SSSSS SBSSS SSSSS
3S?SSS
OOJCIXC-
SSSSS S33S=3 SSSSS
IH
COI>S>-#CC
M N-JO OS
sssss
'tSSsass S3Sg38S SSgSS
t*
^^^^^
sssss
sssss
SSSS3S ?3SE3a§ ssssa
sggss
§S6;S§
ss^ss
SSaSS SSS3S sssss
S3SgSS
SSSS3
assss
^t-JOOO ososxxoo t-t-ot-co 1
(MlMWrJW ^,H.-t.-lrt rtr-ti-liH-H
3
sssss
SS3S3S
ssaas
SSSSS 33SSS SSSS3
S 1
sssss
assss
SSSS3
oooocot-t- t-«coeo® St233^
3 !
S3a_?5?3
g3S?i§§
OOJCOOOt-
S^3S3 S3S33 33333
1-1
SSI3S3S
gasss
t-t- t- jOffl
SSSI33 33333 SSS33
e
SSSSS
ooino^
33353 33333 3^333^
e>
SSSSS
sssss
33333
CONMMfM iH rH i-i i-H 1-4 OOOOO
" 1
t-(DCDif5in
32333
3S33S S°S2g goooo
"
O -S"* CO ro
SSS3;^
3;:1S33
33g§8 ggooS °So=°
«
sa2;^s
S=l33a
S8§§S
ggggg ggsss sssss
^OOOffl
ggssg
§s§ss
SSSSS ggggg ggggg
-*
sssss
ooooo
ssggg
ggggg ggggg ggsgs
«
0000 =
ggggg
in mm ■* -*
ooooo
3SSS3 SSSSS Sgggg
01
ooooo
gssss
S§§go
ggggg ggggg ggggg
ooooo
ggggg
ggggg
OOOOO ooooo ooooo
■pi
~
^^UZ'M
i5i§i3
^ ei es <« u3
5St-XCS© i-cMM-*'© '*'^SS*
ALTITUDE TABLES.
139
»
03CqCQ-^rt
sgss»
00 00X00 t-
i>.m'*(Mi-(
^gsgs
^H^,-(^
»
!N(N(Nrtrt
fHOOOJOS
S3SBS
-*MO00t-
gsggs
M^t-I
s
««rtrt«
oogSS
gssss
gggsg
t-i>c-t-to
sggss
rtrt
5
CjNrfrtrf
ooSSS
mSwSSo
00t-C-t-E>
rt .-t o <n t-
t- t-c- toco
ggsss
rfrt
O
<N<Nrtr1 =
gssss
c^t> t^ t?-^-
sggss
gggss
r-,Wrfrtrt
'-'
:i
=^-H«00
oSSgg
ssssss
l^-l^-t- t-c-
gggss
ssssg
--"-^-^ -
■4H
id
sssss
toincaooo
00 0)00 00 c-
SDiQcOtMO
t^ t-t-t-c-
ggggg
ssggg
«
i-H^OOOi
OSOlSoOOO
sssss
iococaocj
t- t- 1- t- to
CO to coco to
sssgs
s
i-li-H OOOl
mffiSocS
OoSc~ t^t-
-*(M rHOl OO
c-i-c-<o to
to in -*) CO (N
to toco» to
sssss
s
rtOoSS
gssss
OOQO t> t-C-
CM W « 00 to
t- t>co to to
g^§5§
gg£g3
o
ooSSm
gssss
ssgse"
t-(oco toto
^COi-COOJ
to CO CO com
SKSg;S
ooosSo)
gssss
t-c-c-c-r-
ggggs
ssggs
SgSioS
?
oSSgS
t- -t (MOOD
CO 00 CO 00 t-
tOTO to toco
sgsss
ggsss
■J
■*
ggsss
SS53?2g:
mas WOOD
t-t-c-r-o
t>m-*M.-i
ggsss
ssssa
%
■*
ssggs
Qo3£^t2
c2t^?wS
ssssg
gssss
sssss
s
-*
gggss
ooc- t-^-o
f^ggSS
sssss
5SS3S
SSSg5
1
-*
ggsss
o t- in TO (M
00 t- C- t- L-
^^£oo
S»SS5
ssass
3u?§5S
fi
-*
ggssss
C~I> t-t-t-
sssss
sssss
sssss
sss?;!;
-*
00 CO 00 00 t-
C-C^ t- tr- to
SJS^gg
sssss
asssg
OiOOO to to
-*
oooo«)^>^-
^wggS
sssss
sssss
cq.-(ooioi
S55S3
©
-*
ooaot-oD-
t>t>eo sous
»SoSS
SiSSSS
ggSS5
5!§S33
»
(MOi t-irt CO
CO t-c- t-^-
t-(OOCOCO
sssss
SSSS3
OOS 00 t-o
^S33S
s§
gssss
sssss
j^fOMOOS
tH'*-*'*^
5:33^5!
«
t-C-t>C-CO
sssss
SBSSS
S3g§3
5SS3S3!
COi?l(M.-IO
i
t>t>t>COX>
ggssg
^«5lg«M
sssss
IS^^SS
Mr-HOOCl
s
'^.-laic-io
sssss;
SSSSiS
55555
^35^51
5lSgSg
•*
sssss
(Mooor-in
S5SS3!
CO CO (M .-HO
0 a)Q6QO^-
-*cococort>
u
ggggg
gS5SS
sssss
5SiS31S
(N WiHOO
sssss
f?
ssggs
sssss
f-iO00t>«S
!§:J35^
^^s^s
ss=?ssg
(H
gssss
SSSgg
oi 00 t-om
-Jl -^ -* '^ -11
^-gg^s
®g£gt;5^
sssssss
■3^.2
SSiSS
mmmmS
32S53S
sss:ss
140
A MANUAL OF TOPOGEAPHIC METHODS.
ill
^
. o
a
OOJ
-
1-C
o
OS
; : :^^
OS
III!! 1 1 oojOi
iS
; : : ; : ; ■^^^
£
■ ; : ; i \°^^^
$
; ; ; ; : oSSSS
!S
! ; 1 !o
§SS3§
; ; ; 1'^
-*
: ; loOT
gssss
. • ■ 1-4 '
SI
!; i^^
£SS§S
Si>»eBO iH(NOS-H»i
ALTITUDE TABLES.
141
a
a
a
S
s
i
cqesiwwo
nSScScS
oot-t-<oeo
§SS5Sn
^siass
SSSnS
CS
i-IO 0003
SSS5S
§:;§SSS
sssas
sssssg
c3!3Sc3c3
1
g
OOSOiXIQO"
sssss
^SSSS
aassss
WMWWN
sssss 1
■ 1
s
(NM(MM(M
sgsss
saiass
SSS?3S3
?3S;;ss
sgsss 1
1
»
sssss
sssss
S3SS5S
I3?3S?,SS
cSSSSS
sssss
g
ssssss
cj w wcg w
?5i58?3?3
SSSS^
gssss
ss3sa
1
-4*
ssssa
3c5"c5c3
SI35SS
SSS^S
35333
S3SSS 1
es
S33SS5
S3S?3SS
SnSSS
O CiCiOO
00 OO 00 00 00
t-c-t-c-c- 1
S
SSg^SS
SSSnS
SSS3S
SS323
00 t-t-t^t-
sssss 1
iH
saass
sssss
sssss
oocooot-t-
c-rr-totoo
OODWU5 1
§
W^T-O O
OOOJOSOS
OOOOOOOOC-
c-c-t-o»
oot=o«)'
.nu50U5^ 1
S
g° = SS
OJOOOOCOtO
c-c- t-t-o
<o o o o .n
^ o ,n U! w
„^^^^ 1
"
sssss
OT t-c~c~r-
^33SS
3SS3S
-*■*■*-*'*
33333 1
S
OOCOX t-l>
EiSSSS
OOWiOiO
33333
33333
33333 1
CD
L- t> t> m «s
ocgminift
S3333
33SS3
33333
33333 1
2
sssss
SS333
33333
33333
2333S
s;J;iss
«
3S3333
33333
SSS2S
3S333
■-( oooo
323S3
33333
333=1 ;j
OOOOO
ooooo
S3
3S3S2
33p;S=!
SlUSSS
33333
ssg§§
ooooo
s
'-tt-^-'OO
OOOOO
CSCSCIOSO
ooooo
ooooo
ooooo
°
woooo
sasgg
ooooo
ggggg
ooooo
ooooo
o
S§g§g
ggggg
ggggs
ggg = =
ooooo
ooooo
00
ggggg
ggggg
SS5S&
SSSS5
ggggg
ggggg 1
r>-
sssss
ooooo
§oo§o
ggggg
ggggg
ooooo
»
(o aso IT) »
oo oo o
ggggg
o o lO o ira
ooooo
ggggg
ooooo
S3333 1
«
sssss
irt in in o in
ooooo
irt in -n -* -:}<
ooooo
ooooo
ooooo
OOOOO
-^
33333
33333
ooooo
ooooo
corowffoco
ooooo
OOOOO
=,
gggSo
ggggg
ooooo
ooooo
ggggg
ooooo
«
ggggg
ggggg
ggggg
ooooo
ooooo
g3S33 1
IH
ooooo
OOOOO
ooooo
ooooo
ooooo
ooooo
Ms .2
^
osSss
S2233
Or^oOCSO
i
142
A MANUAL OF TOPOGRAPHIC METHODS.
1'
.g
S
o
eoS o SS
^JStoSS
sssss
oSS^S
s^sss
!SS33IS
s
sgsss
SSSfgSS
3SSS3
ing^^^
ft5;SSi3
!g35S3
s
as S«3iOlfi
t- » so in "*
SgggS
SS^^IS
t-eoioiOTii
^ssss
1
r-
s§gss
sssss
gggg?!
OSOOOOl>«S
SSS33
CTSCOW W i-H
1
?o
eoioiretoin
sssss
sssss
^ssss
!§33!33
^^^^51 1
1
§
irsinioioio
OOOTMM
S;5:S!S!S
^31:515139
^^5:^^ 1
1
■*
SSSISS
sssss
gg^ss
:gS!g«^
55^35!
■^-di-SI MCO
g
BSSSS
ininioic5-<*
OSCDC-t-CO
-* -* T(l -tj* T(»
-*T(I-*^'*
Sg^5i5!
ssssg 1
S
sssss
ifiioin-*"*
S5;SS!S
.^^^gg
NWi-lOO
gssss 1
i-<
SS3gS
OOOiCC t-
5iSI5!§3
^^gg^
55§§g
gSSSR 1
o
gssss
^^^^^
sss3;s
^^"^^^
O OOl OS 00
mmSmS 1
2
gSSS"
^^^^^
i3:3!tS3
gSmmcS
sssss 1
'^
gggss
gis^gg
^— ' OOOi
-i*^-* -t CO
SSSSS;
ssssss 1
t»
o oim ooc-
ss«g!5
3^^551
«om^oo
SSKSS
giSSoSS 1
03 QO O) i^ eD
-di 'S* ■* ■* -^
;3S333
^s^^^
SSSmn
ssssss 1
5
^^^^^
3353^
5:5S5g
OCO CO t>l>
SScttoS
^^comco
■*
-*
5;SSS3
53^95!
OOCIOIOO
■* '3' CO CO CO
sssss
ssgss
SISSS?3 1
■*
^!§:S3S
OJ(N.HrHO
ggggs
£gS!§g
gSSg?S5
S5SSSE3 1
5!
53SgS
.-HiHOOCi
SSKSS
sssss
Sg?SSS3
5?SSSg 1
■*
5!3ggq!
^^^nn
SSSgg
^cSmmco
SS?S(oS
sssss 1
■*
3^5! 5! 51
ss^ss
ssssss
SmSSS
ggsss
gggss 1
»
gssss
oooo t- t-eo
eo in lo ■* ■*
COCOCCTOCO
iSg5SS?3
53:;^5^gg
g§§S?i
^
5JSSSS
t- |> CO *o »ft
C-S CO TO CO 03
SS3S8
sssss
ssssp
SSSncS
S
gssss;
sssss
mSiomm
l^^c^^^
ggsss
ssssa 1
50
JS^SSS
sssss?
coTOComco
r-(00 OOl
§SSSISS
sssss 1
sg
t- tr-(0=DlO
SSSSIS?
ssssg
sgggg
ssssa
sssss |-
-*
sssss
assss
mSSSS
sssss
5SSS8
M^f^cgw
SSSSSo
sssss
S8SS"
?sgsss
a§s8s
Cq<N M(N CM
ssssgg
raSSmS
§Sg§?S2S
assss
sssss
^^^^g^
s
sssss
^OOOSOl
ssssss
sssss
ssssa
§3S5?5?5g3 1
°
i< -ti « -If To
ooooo
S22;5S
»t>.QDC50
rH
ALTITUDE TABLES.
143
i
S8g§§
00 00 OO 00 00
oooooot-c- c-t-t-tr-t-
JiE^pgg SSSSS
»
OSCiOsOCO
§8SSSS
(Momooi- oin-#eo(M
oooot-t-c^- t-Ot-C-C-
c^c^gSS S£Sw»
38
sgggs
ooSotooS
oococ-t>t- t-t-et-c-
SgSSS &Sg33
1
S
SSSSS
OCt>C-C-t> C--t-t-t-l>
ggg££ ggSSS
1
i
goggg
sssss
esoot-i^o lo-d'*!^*^
1
a
a
1
1
s
1
s
3SS8SS
ssssss
c-c-t-c-t- c-t-t-t-o
gSBgg ggggg
■*
SSBSS
sgsggg
l>OU3-*CC (NtHOmoO
g£ggS gSggg
ss
SoOWWOO
sssggE;
OW-<*iroM T-(OOJOOOO
t-l-l>I>t> t-t-ooo
£§§33 ggggg 1
s
ooSooooS
i-(0 OJI>0
00 OO C- t~ c-
t— t-t-t-C- L— OOOO
gSSoS SSSSS
s
ggsss
ociootD If;
00 t-t- t- t-
aSSE^g 8g§£S
oeoeotoeo o to o m U5
o
S3§33§
cjoo t-in -*
t-t-t-t- tr-
TO^i-tog SS&wS
sssss sssss
Socooccc-
ee t- to in D5
t>t- 1- 1- t-
?2f;egg g£sgs
ggggg ggsss
£
SSS53^?2
gE=gg§ SS§3S
COMrHOO OlOOQOt-O
K
SSg^^
t> L^ t- t- t-
.-(ocioot- oin"*Mco
t-t-ooo <»oooeo
jrarHOOO '^^^S'nS
1^-
jHOmt-O
t- L~ b- t- t-
ggg£g S^SSSS
Sg-ggg SISggS
g
St^tS^ti
SSSSig SSSSs!
oocsoot- t- o in o -*
otDioifjin inirsioirsin |
t-t-t>r- t>
SE2Eig§
oooSo ooSoS
SSSSS SSlgiSiS
S
t- c-oc-c-
t^pI^SS
5§gSg SSSSg
COOt-t-O IftU^-JCOCO
l>
t-t- t- ^>lr-
Elgggg
gg^So oooSS
OOt-OtOuS -tJ-^COf^tN
t-
I> t- 1* t> c-
gssss
sssss sssss
mmmirain loioioinin
o
t-t-r- t-c-
sssss
T#C01MWi-l OOSCOOOt-
ocDootD omininm
gssss sssss
ffl
t-c-t-t- to
SBSSS
C:)C<lM.HO oioooot-o
ifSift-*COCC (MC-l'-HOO
S
c-t- c-s^J
BSSSS
iMTHi-ipcj QOi>i>oin
igasss ssggs
(M o c: 00 1-
1> l- (D ^ to
g£SSS
358gg KKSStS
E
OOlOOgg
ssggs
^ggss E^ss;s:S
COCOMfHiH OOiClOOOO
ifiininmifa m -^ ■* ■* -*
»
ggSSig
sssss
oSSSS SSooEra
CqWr-lOO CiOlOOOOD-
iniftirainm ^jf "<r ■* -^ ■*
•*
SS^SJg^
sssgs
OJQOD^Og Ig^SSSs
5(000®
ggsss
inmmifsm moiniom
SSSSS 55SSS
gs^^ss
rH OCs 00 CO
lr-0»fti.0'* ^""SlftS
g§555 5;^§iS!g
g^ggg
SSSSB
ssssg ggsss
^^1
o
SSooo
» t- X CI o
©OOOth
S2223 2«2'2§
S< 2i
144
A MANUAL OF TOPOGEAPHIC METHODS.
o
: ;*Sg
sssss
SgSSEo
«
i :^°.".
g^s^s
gS«OOW
2 1 • ■ ■ ■ ■
'^1 ; : ; ; :
;Oggg
gss^^g
SSgSoSS
®gggg
^^gs_g
^^^^^
» 1
ffloot-eoT*t
03 OS OS OS 00
^^^^^
y-t
; ; ; ;0
gggss
ggggs
00 00 00 00 00
Si MMi
: : :*S
gggss
(N.-IOSQ0 t-
00 00 GO CO CO
M ■ : : : :
: ; i^^
£§Sgg
sssss
sssss
S M ; i :
. '©OSt^
ClCJCSOiCi
gsssss
SSSoSS
;;
: :gSS
lO -# CO .-1 O
o>oor-!0»fi
00 OO 00 00 00
3SSȤ
I I ; ■ 1
o : : : : :
:«gSg
sssss
00 c- o o -*
sssss
1
«g£gg
ggsss
sasss
ssssg
1
1
ggggs
gsgss
feSSSS
(M.-IOOSOO
OOOOOO C-C-
.«
a
O
1 : ■ ■©
ssgss
ggsss
OO 00 00 00 00
xS t-C-C-
......
k
1
: : ;Ǥ
sgssg
S^gg&S
10-* fO(M .-(
CJ OS xoo t-
X c-c-c- c-
«(-(
. . .tH
1
1
; : i°S
gg§8£g
3SS3S
oosxc-eo
xt> t-c-c-
g
: :®gS
gggSg
sssss
OOGC OOOoS
c- C-- c-c-c-
> .1-1 * '
R
i ; i M i
:«gSS
o Ci OS c; CO
sssss
00 00 00 00 t-
X t- o la la
c-c-i>c-c-
o
:§ggg
■* Cl T-H O CO
cnocicioo
ooSooSw
(M.-ICSOS00
OOOOOOt-C'
c-c- t-c-t-
1 i i : i i
"=§£§3
gsgss
M00«00«
00 00 OO t^
c-c-c-c- t-
^ . . . .
1
; ; ; ;0
§Sg^§
SgSooS
SSSooS
OOSQOCO t-
gesEsg
! . . .w
a
1 ; . .C5
sgggg
sgsss
O OS oot>o
X t> t- t- L~
i>c:-c- t-c-.
o
: ; :og
sgggs
gSSsSS
sssss
t-t-l • t-t-
c- c-c-c- 1-
• -0=!^ t~
ggggg
gssss
sssss
00 t-OO'*
t- t- t> t- r>
rt CO Ol — ! o
c-c- c-c-c-
§
• • ClCSOi
gssss
SSSbSSS
(M -J o m 00
00X00 C- t-
sssss
^g2p!g^
CS
>g£S
gggss
sssss
i-(oesoot-
oooct-t-c-
t- t-t-c-t-
Sci^gg
o
ogggg
gggss
ssssss
.-iClOOt-O
00 c- 1- t> t-
c-^-^-l^-t-
f^^ggg
i
ggggg
ggssss
sssss
oooo t-o
00 t- t- t- L-
C- t-t- t-t-
OOfflOOt-
t-C~COCOCC
1
g
gggss
oSoomS
sssss
cioot^coin
Tl'roiM'-'O
c-c-c- t-t-
ogggg
1
s
sssgg
ggass
SS2SSg
t- t- L- C- t-
SSSBS
1
■5r|
s
^o
Sooo»
§S§§2
1-H
ttr-ODCSO
ssss^
at^xeo
ALTITUDE TABLES.
145
Table VI. — Differences of aUitude to tlie nearest foot for angles from 1 minute to ^ degrees and for distances
under 1 mile — Continued.
Angle of
elevation.
Diiference.s of elevation in feet.
c ,
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
1° 01'
02
03
04
1° 05'
06
07
08
09
1° 10'
11
12
13
14
1° 15'
IG
17
IS
19
1° 20'
21
23
24
1° 25'
26
27
28
29
1° 30'
"
1.0
.98
.97
.96
.95
.94
.93
.92
.91
.90
.88
.87
.99
.98
.97
.96
.95
.93
.92
.91
.90
.89
.88
1.0
.99
.98
.96
.95
.94
.93
.92
.91
.90
.89
1.0
.98
.97
.96
.95
.94
.93
.92
.91
.90
.99
.98
.97
.96
.95
.94
.92
.91
.9Cf
1.0
.99
.98
.96
.95
.94
.93
.92
.91
1. 0
.98
.97
.96
.95
.94
.93
.92
.99
.98
.97
.96
.95
.94
.93
1.0
.99
.98
.97
.95
.94
.93
1.0
.98
.97
.96
.95
.94
.99
.98
.97
.96
.95
1.0
.99
.98
.97
.95
1.0
.98
.97
.96
.99
.98
.97
1.0
.99
.98
.99
.98
1.0
.99
i'.o'
MON XXII-
-10
146
A MANUAL OF TOPOGEAPHIC METHODS.
ALTITUDK TABLES.
147
1
a
§
1
=4-
S
s
^.^.^^^ ^^^ss g^^ss ^^s^^ ^^^^^ s^s^^
o
INWiH^O OOOaOSOO QOQOOC-t- O !0 CO iftiD WdH -* rj* M CO CO CO (M ca
-* Tli -.H -^H -^ Tt1-*MCOCO COCOCOCOCO CO CO M CO CO CO CO CO CO CO COCOCOCOCO
GO ^^^^^ mSmMTO MMMMTO OT 03 03 M M OT S CO CO CO M ffi OT M CO
S
5J§5§g mSmrom raSSSm roeoSSeo eoSmrofo mmroraS
g
^^^^^ s^^^^ ^^^^^ ^^^^^ ^^^^^ sssss
^
^s_^^^ ^^^^^■^n^^^^^ s^sss ^^^^^ ^^^^^
»0
^^^^^ ^^^^^ ^s^^^ ^^^^^ ^^^s^ ^^^^^
SI
^^^^^ ^^^^^ s^sss ss^ss sssss S8s_§is
s
i>t-eocoto lo in in -^H -Tjf ■^cococow cq w i-h .-( i-i i-(oooo osoioioooo
s
(x>(D«Mnin in^ttiTjiM co co e<nM w w ^ .-i o o o o ci o oi os oo oo oc oo
COCOCOCOCO COCOCOCOCO COmCOfOCO COCOCOCOCO COCOWNSM (MMtMcaM
o
coinmm-* ^ti* ••* eo co co (MMiMiHi-i «oooo eiosoiCico oooocoix:^
s
lO in "^ Tff Tj< COCONIMW WrHr-IWO O O OS Oi O) Oi CO O) 00 CO t- c- t- t- t-
COeOCOfOCO COCOCOCOCO COCOCOeOCO COCOlMtMiM (MCMCHMiM M(N(MW(M
■*
^SSS35S S3?3g??S SSSSS gSSSS SSSSS SSSSS
rtlCOCOC^CM (MT-(iHtH.-> OOOOJO) Ol Oj 00 00 CO t- t- t- r- C~ to (D (O dO tO
»
cocoiN(MC3 i-f-— (OOo o Os Oi OS 00 00 00 00 t— t— ir- c- 50 eo CO totommin
OTCOCOCOCO COCOCOCOCO CO(M<M(MW CJMlMfMW (MW(M<NiM (M(NC4(MN
■*
■*
■*
SSSSS SgSSS SSSSS SSSS^ SSSS8 s^s^^
^
sssss gsssss sasss §§sss sssssa aaa^s
■*
SSSgS SSSSSS SSSSS SSSSa ^S^SS S_?3SS3S3
•*
SS§g?S SgSSS SSSSS SSSSiSS ?S3^S5S3 SSSSSS
-*
^s^^^ ^^^^^ ^^^^^ ssas^ ^^^^^ ^^^^^
§
§§sSSSS SSSSS iSSSSSI S^aSS E3S3?5S?3 sss^a
Si
sssss sssss ssaas ssss^ss gg?3S3?3 sssas
«
SSSSS iSSSSS aSSS5?5 g5SS3S3S SSSSS SSSSS
«
sssss as^^s sssss sss3§3S assss sssss
s?
^SS^S SasSSS l3Sg3?3?3 I3SSSE3 s§§§§ s^^ss
■*
SS5SSS SS5S5g!?3 SS3g3SS SSSSS SSSSS 3SSSS
SI
SS3S5S3?3 SS?3SS SSSSS SSSSS SSSSS SSSS3
S3
SSS^S. S3?3SSS SSSSS SSSSS SSS2S SSSSS
S
?qcqc4?qw wwww^ wSmSS SSS22 S2SS2 wS^^^
o
148
A MANUAL OF TOPOGRAPHIC METHODS.
1
.a
a
■J
>
i
s
i
5
O
C3
sssss
sssgg
gssgg
gssss
sssss
Sgg33
1
g
sssgs
sgggg
BBSSg
gssss
ggggg
OOOJOiOO
o in ■* th Tj<
1
OD
ggggg
SSSSK
ssggg
^sssss
(MtHiHOO
OlOiCJOOOO
-* -^ Tt< -<*l tH
1
oS^fflS
gggSB
gggS3
SggSS
SSSS^
33SS5;
1
»
ggsss
ssssg
gggss
OOOClOl
5355:5;
1
s
ggggS
i-T if3 in o in
gsssg
ITS iTi in vfi irs
00 0:05 00
lO -«' -# Tjl ■*
3S55S
1
-1
OgSiOOOO
Kgggg
sssgg
gssss
SSS3S
t-t-CO tO!S
ggSBE
ggsss
SSggo
Sggg"
§^35:!5
5S§!S!5
s
giSBKS
SSSSS
ggggs
ggsss
OOOOC-t-tO
^^!g!g5;
s
ggggg
sasss
ggssg
gS§32S
Qor-t>» CO
igS!535
®
KSSSS
sssgg
ca— '.-Hoo
ClOCOQO t-
55;SSS
!S3gi3;3
l>
ggsss
ssggg
m in m ** -f.
53^55;
SSSSiS
^3:33133
s
gggss
ssssa
in in-* ^is'
00t> C-t-tO
s;gS55
S333§
l>
sssss
ggssg
OCSC5 O) 00
^^^^5
!g§3i5!3
S3S3S
sssss
gssgg
§§§5;^
5^^^^
i§S3^S
3333^ 1
t*
sssss
Sgg^S
^^^^^
CO 'O O ift -*
331553
3335:5!
s
Si^SSS
gssss
^^^^i?
!SS§53
333^3
3....
IT-
ggSog
o c: Ci 00 00
lO rj( T# -rjl ^
t- t- O '-S US
^^^^"
-^ -* Tjl -^ T}<
rHrHOO 0
c*
.-1^ ooei
§1?«S:5:
3I3J35S
■* -rP -* Tj< -^Jl
0 0 OCl Oi
s
SSg3S
51S5^S
la u'5 m -* ^
:SS39S
0 omcios
^ T1-05C0C0
o
g?§?5
!gs3i3g
""^^^
553SS
sssss
«
SSS3!;
t-eoeoiairs
■* "<ji ■* 1* ■*
:3;:S^3S
^3^5! 5!
OOOCl Oi
gssss
9
^^55^
55-33SS
g=!55!S
O OOJOJOl
■Til -* cc CO CO
gSSSKR
r-
o
S555S
s^s^s
33^5!^
51515SS
gggJSS
o?McoMeo
«£
«
Jj^^^!^
353I3S
ggggjg!
.-I O Offi O)
-fTjl -^CO CO
gssss
sssss
§
^SSig^
53:^93
N^fH .-I O
O OOiOlOO
-* coco MCO
CO t^c-c-r-
sssss
■*
9
s^igs^
5359^
5!5S§^
gsgsg
ooc-t-ixo
sgssss
»
-a. -* -tf -fj- Tjl
39^:55
SSSSS
sssss
KSSgg
SSISSS
«
3^sgg
<M«i-HrHO
OOOSOSCO
mSRmra
ggSgi?
i?S3SSg
9
^33^^
,-H^.-IO O
gg^^fg^
sssss
sssss
sssss
■3>|.2
o
|ii?;s|
5?:55^
sssss
«i>.XCSO
ALTITUDE TABLES.
149
>
■1
i
£
P
s
sssss
SSSSg
COt-OOiO
t- l> C- L- C-
C-C-D-t-t-
t-4o oosai
oot-r-CD to
toco to CD to
o
■-■ooioor-
O0 00l>l> t-
CO CI (M tH 0
t-c-e-t-t-
Sgggo
Sgggg
1-H
mSoqooooo
COt- t> t-I>
t-c-c- t-t-
OTM — 00
C' t- t- t^ t^
gggss
toco to toco
1H
3S3SS§
010)00 i>o
t- t-t-t-t-
gSfi^gg
ggggg
gggss
o
OlCOt^OlO
O C-OC-t-
SP:f3Kg
f:pi^§S
S££Sg
ggggs
iS
gssssg
00 i> O to lO
t-i>i>c-r>
T-lO©QOCO
D- t> tOtO«3
BSggg
SSSgg
■*
(M.-I00100
oocoooc- t-
t>r>c-i> t-
ggg§£
ogggg
SSSSg
iH
.-HOOlCOt-
oooot-c-t-
t- to in 'St CO
t-t-l?- t~c-
gggss
ggS3S
ggggg
IH
00 t- t-t- t-
tDiO-»#TiicO
t-c-t-t- 1-
WW rHOC»
t-t-c-t- to
gg£SS
gggSg
toeoooeo
iH
gSScSc^S
lfi»OTHcO(M
t-t- t- ^>t:-
w wo OSOJ
t^ t- t^ CD to
ggogg
ggsss
SSSgg
O
i>c>D- ^-t-
t- i> c- 1- t>
wo OOJOO
t-t-t-CDCD
ggggg
SSSSS
SSSgg
i
I^• t-t- t- t-
OOCSOOOO
t-l>tD tOCD
£§S©S
sssss
SSSgg
©
t- to CO to-*
t-c-i> t-t-
coco tM wo
t- t> t-C-t-
OOi 00 00 t-
t> CD to CD CO
gggg^
COCOCVJlM w
to CO to CO to
Sgggg
©
t^t- t~ t-c-
eOCQr-iOO
t-t- t>t-l>
ggsss
ggsss
gggss
ggggg
©
c-t-r-c-t-
(M-HOOOl
c-t*i>t- to
CD to to to CD
gssss
(M(M wo 0
gggss
us
O
sssss
i>t-c-to to
to to toco to
gssss
(M WOOOl
COCO CD too
gggss
S
t>c- t-^ t- t-
Edgggg
tOCD to CD to
SSggg
sgggg
11
^S?2S^
tr-to to toto
CD CD to CD CD
CO?^(M(M W
to CO CD CD to
gggss
00t>r-CD(O
Tl
«(M WiHO
t>C-t-l>t>
ggSBg
gggss
gggsg
ggggs
SSggg
©
1-(
c-c-c- t-to
ggggg
sssss
IN W woo
ggSSB
sgggg
g2E:!gg8
to to to to to
S3SSS
ssggg
gSSBS
ggggs
©
t- t-CD to to
to to to to to
SSSSS
woo cri 01
gSBgg
gg3S3
©
gggss
sggss
SSSiSsS
SSSSS
KBggg
sssgg
©
SSosoco
Sg3SS
SS3Sg
OOCOOOt-
tDioo mm
EgggiS
ioiSggg
©
©
SoStoto
S3SSS
ssssg
CJOOCO t>l~-
in tnmmm
gggss
ssggg 1
§
S£SSS
CD to to to to
ssgss
SSKBS
iftmiomm
coco !MiM W
irsmmioo
©
SSSgg
ssggg
sgggg
SKSSS
mlnmmS?
Smomm 1
©
sgsgss
8SOSJ0
ssggs?
KKSSS
m-^-tfcoco
lommirso
SS^^Sg 1
©
sssss
(MfMi-HO 0
CO to to to CO
SSSSK
Kggsa
;sss?sg
WW woo 1
ift 10 m m in
©
S33SS
(M wo 001
SSSKg
sssss
COCOMfMCM
inioiniriio
ssgg^ 1
°
T-( IH
SSi^l
■*-*'*■*•*
iH
©c-co©©
150
A MANUAL OF TOP0GEA.PHIC METHODS.
a
a
1
I
1
1
o
: i'.^".
sssss
SSSSoo
g^SS^
SSSSoSS
i
1
i'ggS
IlH ' ' *
g§sg§
CMi-HOCJOO
ojcnoiooco
goSoS^S
SSSSffiS
5
•*
iggss
sssgg
ggssss
SSSS^^
ssssss
^
t»
^ ' * ' ■
gssgg
^^-M
Smodotoo
«i(M.-(00
=
«
•*
^
■ ; ; ;«
oioot- to»n
ssssg
ggssss
00 QO 00 00 00
eg 5^0001
"^
:::;''
3
s
; ; i is
ojoj oicncs
gssss
ssgass
ift-^JtCOCOW
r-li-HOOsm
00 00 oot-t-
S
: : i ! 1
£
^
■*
ggggs
M « -H O OS
ojoiojoaoo
ssssss
sssss
r-iO 0105 00
oooot-c-t-
3
s
; :*o?m
sssss
OJOSOIOOOO
8SSSSS
sssss
oooiooco
00 00 t- t- L--
^
1-1
• • O500 t-
SraSSro
sssssg
sssss
COCO(Mi-HO
ooi> t^t> r-
»-»
g
-*
:«ggS
SSSSo
SSotoooo
sssss
sgssss
C-t- I> t-t-
1
o
'ggSS
gsggs
o csOi O) tr-
SffiSSoo
w^rHom
ooo [> too
^
§
%
gssgg
sggss
oooot-co
OS CO CO 00 00
ssssss
g353SgS
l>t>t> t-t-
3<;
S
ggfegg
gsgss
§g£§S
sssss
i-HOClCi 00
oooot- t>t>
r^D^Sb^t^
S
g
SSSSS
ggj^gg
ggssss
00 00 00 00 CO
0005COOO
COQOI>I>C-
l>(0 tOlO tH
C- I- [> t- t- 1
«s
SSSSS
gssss
sssss
OTOOOOOoS
QDt>l>t- t-
t-c-t> t-t- 1
1
1-1
SSSSS
gs§§s
O0»S^»
ssssg
t- I> l^ c- t-
i>r> t-c-t-
■^
ir- t-^>c-t>
§
-*
sssss
ggsss
SwSSqo
ssss?;
l?-t- t- t-t-
&
e
iH
gsggg
OTOTMOOaO
sssss
sssse
tr- t- t- t-C-
t- t- t-c-t-
•-
<
sssgs
O0iC0t>!0
igSS3S3g
ssseg
t-Ot-D-D-
l>t>l>I>D-
O
<
sggss
ssssbss
SSS5SS
.-(Oo;co t-
OOODC- t-C-
t- t> t- t-t-
s
©
ggggg
00 t-^^g
SoDTOOTOO
OOiOOOOt-
OOt-t-C't-
CD ID U3 -tjt -*
t>i> t>c-P 1
»
a>
i C0.-i00i00
1 oiOiojcooo
OOOO^OOM
SSSsSS
?i"c2t^S
SSSgg
^
5
s
gsgss
sssss
(71(M .-H O Oi
00 00 00 00 t-
t- t-t-t-D-
t-D-t-C-t-
ssggs
t»
SgggBSS
SSSoOOD
(Mi-HOO C3
00 CO 00 00 t-
tS^t^l^t^
t-ot- t- t*
D^t- t-CD to 1
"-«
°«Sqo»
sssss
OOOOOOt- t-
cooeoiom
i>c-i> t-c-
t>t^c-c*t-
Sgggg
i
ssssss
gssss
00 00 c- t-c-
05 « N t-H r-l
gggss
a
C30O0O0 00CO
SS5S5S53
ssggs
c-c-t-t- t-
COlMr-ii-tO
t-C-t- t-C-
essss
^
s
SoooOTOom
sssss
Oiooot' to
t^ C~ l> t- D-
iT] M .-H O O
sssss
1
>
s
sss^s
sssse
oiQOtxoeo
D-D-C-t-t-
(M.H0001
c-t-t-c-to
ggSSB
s
s
SSSSS3
OOOO COCOC-
t- t- c- 1- t-
F!^°§§
SSBSS
H
5^1
o
iH CI M -* O
sssss
eaD-coosb
ALTITUDE TABLES.
151
1
o.S
1
s
-*
■ -Z
1
; i iggg
1
, i*.^
1H
; ;«ggS
1
iss
t>
; ©gggg;
; .H ' ■ ■ ■
©gg
l>
; SSSSS
° ft
* ggggg
; ; I'g gsggg 1
-* 1 :^!oi3j QOi-:oin-*
eo 1 : jog^ ^^gg^
S ;®g§s ssssg
s 1 jgggS gssgg
^ 1 ^
1
a
a .
n
O
; ; :* gȣgs ssssss
<»
i ; jg ggSSS 3Sgg3
c*
o
i i»g ssssg ggsss
1
'i-(
»
iSg^ sssgg sgsss
■*
;oggs sgsss gsssg
fH
SIOJOIOJ OiOOSOSOi CIOIOJQOCO
w
Og^5;g mosSSOT SSSwoo
?0
* gg&gg SSSgg SSSSSES
1
©OS Q0lr~CDCOurS -r^tcOMiH-^ OOiOOC-t^
s
Sg g£gS3 SgSSS SSSESS
us
©moo t:toi23'S2 co m rH o o> c» oo t- to as
^ci o> oiOTOJC; OS ojoioJOToo oooooooooo
c»
sss ssssg sssss-ssass
o
®g^s g_^s^gg ^ggsss ggssss
3
. ^^^^^ s^^ss^ ^_^_^^^ ^sss^ |
■ ■© CSQOt^COin in^MMr-l OOOiOOC~ lO^lOHH-*
■ ■" a>OOJ0505 OSCJOOSOl OiCiOOMOO ODCOOOOOOO
U
■ . 0> O00OC~tDlft 'itcCCq^O OOJOOt>t- tDO^-tCO
!S 1 ■ ;
:»g ssssg ggssg gggass ggsss
ifS
• OiOi mojoiciOJ oicnojcioo oooooooooo oooooooooo
« i fl
o
i4«»-*us «0f xcs© rtMM-H-io ©i>-ao©o — ei«-*tffl ©t^QO©©
MWWMM «»»03-* M''*-*'*-* •^■*-*'*ia lOUSiOUSiS »0»«i«»i5©
152 A MANUAL OF TOPOGKAPHIC METHODS.
Table VII. — Differences of altitude from angles of elevation or depression.
. ,^.. J c + DA, + fti for angles of elevation.
Difference of altitude = \lj)k\ + ft^ for angles of depression.
D= distance
ft, = 5280 ft.
refraction.
m miles, a = angle of elevation or depression ;
•< tan a; h^ :^ correction for curvature and
A-rgument for ft, is a'; argument for A2 is ^•
0°
1°
2°
3°
40
6°
6°
JO
8°
90
10°
11°
. 12°
13°
14°
16°
hi
hi
l>j
hi
hi
hi
hi
hi
hi
hi
Feet.
h.
h.
hi
Feet.
hi
hi
hi
,
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
Feet.
0
0.0
92.2
184.4
276.7
369 2
461.9
555.0
648.3
742.0
836.3
931.0
1026. 3
1122. 3
1219. 0
1316. 5
1414.8
1
1.5
93.7
185.9
278.2
370.7
463.5
556.5
649 9
743.6
837.8
932.6
1027. 9
1123. 9
1220. 6
1318, 1
1416. 4
■2
3.1
95.2
187.4
279 8
372.3
465.0
558.0
651.4
745.2
839. 4
934.2
1029. 5
1125.5
1222. 2
1319,7; 1418, 0|
3
4.6
96.8
189.0
281.3
373.8
466.6
559.6
653. 0
746.7
841.0
935. 8
1031.1
1127.1
1223. 8
1321, 3
1419. 7
4
6.1
98.3
190.5
282.9
375.4
468.1
561.2
654.5
748.3
842.6
937.3
1032.7
1128. 7
1225. 5
1323. 0
1421.3
6
7.7
99.8
192.1
284.4
376.9
469.7
562.7
656.1
749 9
844.1
938. 9
1034. 3
1130. 3
1227. 1
1324. 6
1423. 0
6
9.2
101.4
193.6
286.0
378.5
471.2
564.3
657.7
731.4
845.7
940.5
1035, 9
1131.9
1228. 7
1326. 2
1424. 6
10.7
102.9
195.1
287. 5
380.0
472.8
565.8
659 2
753.0
847.3
942.1
1037. 5
1133. 5
1230. 3
1327. 9
1423 -9
8
12.3
104.4
196.7
289 0
381.6
474.3
567.4
660.8
754.6
848.9
943.7
1039. 1
1135. 2
1331.9
1329, 5
1427. 9
9
13.8
106.0
198.2
290.6
383.1
475.9
568.9
662.3
756.1
850.4
945.3
1040.7
1136. 8
1233. 6
1331,1
1429. 6
10
15.4
107.5
199. 8 292. 1
384.6
477.4
570.5
663.9
757.7
852.0
946.8
1042. 3
1138. 4
1235. 2
1332. 8
1431. 2
11
16.9
109.1
201.3
293. 7
386.2
479 0
572.0
665.5
759 3
853.6
948.4
1043. 8
1140. 0
1236, 8
1334,4
1432.9
12
18.4
110. 6
202.8
295.2
387.7
480.5
573.6
667.0
760.9
855.2
950.0
1045. 4
1141. 6
1238.4
1335,0 1434.5
13
20.0
112.1
204. 4
296.7
389 3
482.1
575.1
668.6
762.4
856.8
951. 0
1047.0
1143.2 1240.0
1337,7 1436.2
14
21.5
113.7
205. 91 298. 3
390.8
483.6
576.7
670.1
705.0
858.3
953.2
1048. 6
1144.8 1241.7
1339,3 1437.8
15
23.0
115.2
207. 5! 299. 8
392.4
485.2
578.2
671.7
765.6
859.9
954. 7
1050. 2
1146. 4| 1243,3
1340.9 1439 5
16
24.6
116.7
209.0; 301.3
393.9
486.7
579.8
673.3
767.1
861.5
956.3: 1051.8
1148,0; 1244.9
1342.6 1441.1
17
26.1 118.3
210. 5 302. 9
395.5
488.3
581.3
674.8
768.7
863.0
9,57,9 1053.4
1149.6. 1246,5
1344.2 1442.8
IS
27.6 119.8
212. 1 304. 4
397.0
489.8
582.9
676.4
770.3
864.6
959 5 1055.0
1151. 2| 1248.1
1345.8, 1444.4
19
29.2
121.4
213. 6 308. 0
398.6
491.3
584.4
077.9
771.8
866.2
961.1 1056.6
1152.8
1249, 8
1347.5; 1446.1
■20
30.7
122.9
215. 1, 307. 5
400.1
492.9
586.0
679 5
773.4
867.8
962.7 1058.2
1154.4
1251, 4
13491, 1447.7
21
32.3
124.4
216. 7 309. 1
401.6
494.5
587.6
681.1
775.0
869 4
964.3 1059.8
1156. 1
1253, 0
1350. 8^ 1449 4
22
33.8
126.0
218.2 310.6
403.2
496.0
5891
682.6
776.5
870.0
965, 9, 1061. 4
1157.7
1254. 6
1352.4 1451.0
23
35.3
127.5
219 8| 312.1
404.7
497.6
590.7
684.2
778.1
872.5
967.51 1063,0
1159.3
1256. 2
1354.0 1452.7
24
36.9
129.0
221. 3 313. 7
406.3
499.1
592. 2
685.7
779 7
874.1
969 0 1064.6' 1100. 9| 12.'>7. 9
1355.7, 1454.4
25
38.4
130.6
222.8
315.2
407.8
50O7
593.8
687.3
781.3
875.7
970. 6 1066. 2
1162. 5| 1259.5
1357.3 1456.0
26
39.9
132.1
224.4
316.8
409.4
502.2
595.4
688.9
782.8
877.3
972.2 1067.8
1164. 1: 1261. 1
1358.9 1457.7
27
41.5
133.6 225.9
318.3
410.9
503.8
596.9
690.4
784.4
878,8
973.8 1069 4
1165,7) 1162,7
1360.6 1459 3
28
43.0
135.2 227.4
319 9
412.5
505.3
598.5
692.0
786.0
880 4
975. 4I 1071. 0
1167. 3
1264. 4
1362.2 1461.0
29
44.5
136.7 229.0
321.4
414.0
506.9
600.0
693.6
787.5
882. 0
977, 0' 1072, 6
1168. 9
1266. 0
1363.9, 1462.6
30
46.1
138.3
230. 5
322.9
415.5
508.4
601.6
695.1
7891
883.6
978, 6. 1074. 2
1170. 6
1267. 6
1365.5! 1464.3
31
47.6
139 8
232.1
324.5
417.1
510.0
603.1
696.7
790.7
885.1
980.1' 1075.8
1172.2
1269. 3
1367,1! 1465.9
32
49.2
141.3
233.6
326.0
418.6
511.5
604.7
698.2
792.2
886.7
981. 7, 1077. 4
1173. 8
1270,9
1368.8 1467.6
33
50.7
142.9
235.1
327.6
420.2
513.0
606.2
699 8
793.8
888.3
983,3 1079,0
1175. 4
1272, 5
1370.4 1469 2
34
52.2
144.4
236.7
329.1
421.7
514.6
607.8
701.4
795.4
889 9
984,9 108O6
1177. 0
1274, 1
1372. 1
1470. 9
35
53.8
146.0
238.2
330.6
423.3
516.2
601.3
702.9
797.0
891.5
986.5 1082.2
1178. 6
1275. 7
1373. 7
1472. 5
36
55.3
147.5
239 8
332.2
424.8
517.7
610.9
704.5
798.5
893. (
988. li 1083.8
1180. 2
1277. 4
1375. 3
1474, 2
37
56.8
149.0
241.3
333.7
426.4
519.3
612.5
706.1
800.1
894.6
989.7
1085. 4
1181.8
1279, 0
1377. 0
1475. 9
38
58.4
150.6
242.8
335.3
427.9
520.8
614. 0 707. 6
801.7
896.2
991.3
1087. 0
1183.4
1280. 6
1378. 6
1477. 5
39
59.9
152.1
244.4
336.8
429 5
522.4
615.6 709.2
803.2
897.8
992.9
1088. 6
1185. 0
1282. 2
1.380. 3
1479.2
40
61.4
153.6
2J5.9
338.4
431.0
523.9
617.1 710.7
804.8
899 4
994.5
1090. 21 1186. 71 1283. 9
1381. 9
1480. 8
41
63.0
155.2 247.5
339 9
432.6
525.5
618. 7 712. 3
806.4
900.9
990,0
1091.81 1188.3! 1285.5
1383. 5
1482. 5
42
64.5
156.7 249 0
341.4
i 434.1
527.0
620.21 713.9
807.9
902.5
997.6
1093.4
1189. 9
1287. 1
1385.2
1484. 1
43
66.0
158.2 250.5
343.0
1 435.6
528.6
621.8
715.4
809.5
904.1
999 2
1095. 0
1191. 5
1288. 8
1386. 8
1485. 8
44
67.6
159 8 252.1
344.0
' 437.2
530.1
623.3
717.0
811.1
905.7
1000. 8
1096. 6
1193. 1
1290. 4
1388. 6
1487. 5
45
69.1
161.3 253.6
346.1
438.7
531.7
624.9
718.6
812.7
907.3
1002.4
1098. 2
1194. 7
1292. 0
1390. 1
1489. 1
46
70.6
162.9 255.1
347. e
440.3
533.2
626.4
720.1
814.2
908.8
1004. 0
1099, 8
1196. 3
1293. 7
1391. 8
1490. 8
47
72.2
164.4 256.'-
3491
441.8
534.8
628.0
721.7
815.8
910 4
1005. 6
1101. r
1197. 9
1295. 3
1393. 4
1492. 4
48
73.7
165.9 258.2
350.-
443.4
536.3
629 6
723.3
817,4
912,0
1007. 2
1103. 1
1199. 6
1296. 9
1395. 0
1494. 1
49
75.3
167.5 259. S
352.2
444.9
537.9
631.1
724.8
819 0
913.6
: 1008.8
1104. 7
1201. 2
1298. 5
1396. 7
1495.8
50
76. S
169.0 261.3
353. S
446.5
539.4
632.7
726.4
820.5
915.2
1010, 4
1106. 3
1202. 8
1300. 2
1398.3
1497.4
51
78.1
170.6 262. f
355.
448.0
541.0
634.2
728.0
822.1
916.'
1012, 0
1107. 9
1204. 4
1301. 8
1400, 0
1499. 1
52
79. t
172.1; 264.4
356.
449.6
542.5
635. f
729 5
823.7
918,?
1013, 6
1109, 5
1206, 0
1303,4
1401.6
1500. 7
S3
81.4
173.6 265. £
358..:
451.1
544.1
637. L
731.1
825.2
919. £
1015. 2
1111,1
1207. '
1305.0
1403, 3
1502,4
54
82. <
176.2 267..
360.
452.'
545.1
638. £
732.7
826.8
921. c
1016. i
1112.'
1209 3
1306.7
1404.9, 1504.1
55
84..
176. 7 1 269 (
361.
454.2
547.2
640. 4' 734. 2
828.4
923.1
1018.4
1114,3
1210, S
1308. 3
1406.5 1505.7
56
86.
178. 2: 270.
363.
) 455. i
548.'
642. C
735.8
830. C
924.'
1020. C
1115, £
1212, e
1309 9
1408.21 1507.4
57
87.
) . 179. 8 272.
364.
3 457.
550.:
643.
737.4
831..
926.'
1021. £
1117, £
1214, 1
1311. 6
1409,8; 1509 0
58
89.
181.3 273.6 366.
I 458.'
551.!
645.
738. a
833.
927.
1023. 1
1119.
1215, i
1313.2; 1410.51 1510.7
59
90.
3 182.9 275.2 367.
7 460.
553.4
646.
740. E
834.'
929'
1024.
1120.
1217.4
1314.8 1413,1] 1512.4
60
92.
i 184.4 276.7 369.
2 461.
555. (
648.
742. C
836.
931.
1026.
1122,
1219.
1316.5 1414.8 1514.0
ALTITUDE TABLES.
153
Table VIII. — Corrections for curvature and refraction.
D
hz
0
ll2
B
hj
D
h.
Miles.
Feet.
Miles.
Feet.
Miles.
Feet.
Miles.
Feet.
1.0
0.6
5.5
17.3
1.1
0.7
5.6
18.0
3.6
7.4
8.1
37.6
1.2
0.8
5.7
18.6
3.7
7.8
8.2
38.6
1.3
1.0
5.8
19.3
3.8
8.3
8.3
39.5
1.4
1.1
5.9
20.0
3.9
8.7
8.4
40.5
1.5
1.3
6.0
20.6
4.0
9.2
8.5
41.4
1.6
1.5
6.1
21.3
4.1
9.6
8.6
42.4
1.7
1.7
6.2
22.0
4.2
10.1
8.7
43.4
1.8
1.9
6.3
22.8
4.3
10.6
8.8
44.4
1.9
2.1
6.4
23.5
4.4
11.1
8.9
45.4
2.0
2.3
6.5
24.2
4.5
11.6
9.0
46.4
2.1
2.5
6.6
25.0
4.6
12.1
9.1
47.5
2.2
2.8
6.7
25.7
4.7
12.7
9.2
48.5
2.3
3.0
6.8
20.5 ■
4.8
13.2
9.3
49.6
2.4
3.3
6.9
27.3
4.9
13.8
9.4
50.7
2.5
3.6
7.0
28.1
5.0
14.3
9.5
51.7
2.6
3.9
7.1
28.9
5.1
14.9
9.6
52.8.
2.7
4.2
7.2
29.7
5.2
15.5
9.7
53.9
2.8
4.5
7.3
30.5
5.3
16.1
9.8
55.1
2.9
4.8
7.4
31.4
5.4
16.7
9.9
56.2
3.0
5.2
7.5
32.2
5.5
17.3
10.0
57.3
8.1
5.5
7.6
33.1
3.2
5.9
7.7
34.0
3.3
6.2
7.8
34.9
3.4
6.6
7.9
35.8
3.5
7.0
8.0
36.7
154
A MANUAL OF TOPOGEAPHIC METHODS.
Table IX. — For computlnri differences of altitude from angles o)
scale 1:45000).
[Prepared by li. S. Wooclwartl.]
_.„ - 1^.. , C + D7ii + /ia&r angles of elevation.
Difterenceof altit-:icl6= ^ _ j,;,^ ^ /^fgj angles of depression.
elev:at%on or depression (applicable to
T> — distance in scale divisions ^s inch each; a ■-
tion for curvature and refraction.
Argument, for Ai is a ; argument for ftj is D.
angle of elevation or depression; fti = 75 feet X tan a; 7i2 = correc-
fti in feet. |
D
fta
D
Ih
'
0°
1°
20
3°
4°
5"
6°
7°
Scale
livisions.
Feet.
Scale
iivisions.j
Feet.
0
.000
1.309
2.619
3.931
5.245
6.562
7.882
9.208
00
0
720
60
1
.022 1
1.331
2.641
3.952
5.266
6.583
7.905
9. 231
93
1
726
61
.043
1.353
2. 662
3.974
5.288
6.605
7.927
9.253
131
2
732
62
3
.065
1.375
2.684
3.996
5.310
6.628
7.949
9.275
161
3
738
63
1
.087
1.396
2.707
4.018
5.332
6.649
7.971
9.298
1S6
4
744
64
5
.109
1.418
2.728
4.040
5.354
6.671
7.993
9.319
208
5
750
65
6
.131
1.440
2.750
4.062
5.376
6.694
8.015
9.342
228
6
755
66
.153
1.462
2.772
4.084
•5. 398
6.715
8.037
9.364
246
7
761
67
8
.175
1.483
2.794
4.105
5.420
6.737
8.059
9.386
263
8
767
68
9
.196
1.505
2.815
4.127
5.442
6.760
8.081
9.408
279
9
772
69
10
.218
1.527
2.837
4.150
5.464
6.781
8.104
9.430
294
10
778
70
11
.240
1.549
2. 859
4.171
5.485
6.803
8.125
9.452
308
11
783
71
12
.262
1.571
2.881
4.193
5.508
6.826
8.147
9.475
322
12
789
72
13
.283
1.593
2.903
4.215
5. 530
6.847
8.170
9.496
335
13
794
73
14
.305
1.615
2.925
4.237
5.551
6.869
8.191
9.519
348
14
800
74
15
.327
1.636
2.947 •
4.258
5.573
6.892
8.214
9.541
360
15
805
75
16
.349
1.658
2.968
4.281
5.596
6.913
8.236
9.563
372
16
811
76
i;
.371
1.680
2.990
4.303
5.617
6.935
8.258
9.586
383
17
816
77
18
.393
1.702
3.012
4.324
6.639
6.958
8.280
9.607
394
18
821
78
10
.415
1.723
3.034
4.346
5.661
6.979
8.302
9.630
405
19
826
79
so
.436
1.746
3.056
4.368
5.683
7.001
8.324
9.652
416
20
832
80
21
.458
1.768
3.078
4.390
5.705
7.024
8.346
9.674
426
21
837
81
22
.480
1.789
3.100
4.412
5.727
7.045
8.368
9.697
436
22
842
82
23
.502
1.811
3.121
4.434
5.749
7.067
8. 390
9.718
446
23
847
83
24
.523
1.833
3.143
4.456
5.771
7.090
8.413
9.741
455
24
852
84
25
.545
1.855
3.165
4.477
5.793
7.111
8.434
9.763
465
25
857
85
26
.567
1.875
3.187
4.499
5.815
7.133
8.457
9.785
474
26
862
86
27
.589
1.898
3.209
4.522
5.836
7.156
8.479
9.807
483
27
867
87
28
.610
1.920
3.231
4.543
5. 859
7.177
8.501
9.829
492
28
872
88
29
.633
1.942
3.253
4.665
5.881
7.200
8.523
9.852
501
29
877
89
30
.655
1.964
3.274
4.587
5.902
7.222
8.545
9.874
509
30
882
90
31
.676
1.986
3.296
4.609
5.924
7.243
8.567
9.896
518
31
^7
91
32
.698
2.008
3.318
4.631
5.947
7.266
8.589
9.918
526
32
892
92
33
.720
2.029
3.340
4.653
5.968
7.288
8.611
9.940
534
33
897
93
34
.742
2.051
3.362
4.675
5.990
7.309
8.633
9.963
542
34
901
94
35
.763
2.073
3.384
4.696
6.013
7.332
8.656
9.985
550
35
906
95
36
.785
2.095
3.406
4.718
6.034
7.354
8.677
10. 007
558
36
911
96
37
.807
2.116
3.427
4.741
6.056
7.375
8.700
10. 029
S6G
37
916
97
38
.829
2.138
3.449
4.762
6.078
7.398
8.722
10. 051
573
38
920
98
39
.651
2.161
3.471
4.784
6.100
7.420
8.744
10. 074
581
39
925
99
40
.873
2.182
3.495
4.806
6.122
7.442
8.766
10. 096
588
40
930
100
41
.895
2.204
3.515
4.828
6.144
7.464
8.788
10. 118
595
41
934
101
42
.916
2.226
3.537
4.850
6.166
7.486
8.810
10. 141
603
42
939
102.
43
.938
2.248
3.559
4.872
6.188
7.508
8.833
10. 162
610
43
943
103
44
.960
2.269
3.580
4.894
6.210
7.530
8.854
10. 185
617
44
948
104
45
.982
2.291
3.602
4.915
6.232
7.552
8.877
10.207
624
45
953
105
46
1.003
2.313
3.624
4.938
8.254
7.574
8.899
10. 229
631
46
957
106
47
1.025
2.335
3.646
4.960
6.276
7.596
8.921
10. 252
637
47
962
107
48
1.047
2.357
3.668
4.981
6.298
7.618
8.943
10. 273
644
48
966
108
49
1.069
2.379
3.690
5.003
6.320
7.640
8.965
10. 296
651
49
971
109
50
1.091
2.401
3.712
5.025
6.342
7.662
8.987
10.318
657
50
975
110
51
1.113
2.422
3.733
5.047
6.364
7.684
9.010
10. 340
664
51
980
111
52
1.135
2.444
3.755
5.069
6.385
7.706
9.031
10. 363
670
52
984
112
53
1.156
2.466
3.776
5.091
6.408
7.729
9.054
10. 384
677
53
988
113
54
1.178
2.488
3.799
5.113
6.430
7.750
9.076
10. 407
683
54
993
114
55
1.200
2.509
3.821
5.135
6.451
7.772
9.098
10.429
690
55
997
115
56
1.222
2.532
3.843
5.157
6. 474
7.795
9.120
10. 451
696
56
1001
116
57
1.243
2.554
3.865
5.179
6.496
7.816
9.142
10. 474
702
57
1005
117
58
1.265
2.575
3.886
5.20U
6.517
7.839
9.164
10. 496
708
58
1010
118
59
1.287
2.597
3.900
5.222
6.540
7.861
9.187
10. 518
714
59
1014
119
60
1.309
2.619
3.931
5.245
6.562
7.882
9.208
10.540
720
60
1018
120
ALTITUDE TABLES.
155
Table IX. — For comjiuting differences of altitude from angles of elevation or depression (applicable to
scale i;450(90)— Continued.
h, in feet.
D
iH
D
Jh
'
8°
9°
10°
11°
12°
13°
14°
15°
Scale
divisions
Feet.
Scale
divisions
Feet.
0
10. 540
11. 878
13. 225
14. 578
15,942
17,315
18. 700
20. 096
00
0
720
60
1
10. 563
11. 901
13. 247
14. 601
16, 964
17, 338
18, 723
20. 119
93
1
726
61
2
10. 585
11. 923
13. 270
14. 623
15, 987
17, 361
18, 746
20, 143
131
2
732
62
S
10. 607
11.946
13. 292
14. 647
16, 010
17, 384
18, 769
20. 166
101
3
73S
63
4
10. 630
11. 968
13.315
14. 669
16. 033
17, 407
18, 792
20. 190
186
4
744
64
5
lO. 651
11.991
13. 337
14. 692
16, 056
17. 430
18.813
20.213
208
5
750
66
6
10. 674
12.013
13. 360
14, 714
16, 078
17. 453
18. 838
20.236
228
6
755
66
7
10. 696
12. 035
13. 382
14. 737
16, 102
17.476
18, 862
20, 260
246
7
761
67
S
10.718
12. 069
13. 405
14. 760
16,124
17,499
18, 885
20, 283
263
8
767
68
9
10. 741
12. 080
13. 427
14.782
16. 147
17. 522
18, 908
20. 307
279
9
772
69
10
10.763
12. 103
13. 450
14. 806
16, 170
17. 545
18, 931
20, 330
294
10
778
70
11
10. 786
12. 125
13. 472
14. 82S
16, 192
17, 568
18, 955
20, 353
308
11
783
71
12
10. 807
12.147
13.495
14. 851
16, 216
17, 591
18. 978
20, 377
322
12
789
72
18
10. 830,
12. 169
13. 517
14. 873
16, 238
17. 614
19, 001
20, 401
335
13
794
73
14
10. 862
12. 192
13. 540
14. 896
16, 261
17. 637
19. 024
20, 424
348
14
SOO
74
15
10. 874
12.214
13. 562
14. 918
16, 284
17, 660
19, 048
20,447
S60
15
805
75
16
10. 897
12. 237
13. 585
14. 941
16, 307
17, 683
19, 071
20, 470
372
16
811
76
17
10. 919
12. 259
13. 607
14. 964
16, 330
17, 706
19, 094
20.494
383
17
816
77
18
10. 941
12. 282
13. 630
14. 986
16, 353
17, 729
19, 117
20, 518
394
18
821
78
19
10. 963
12. 304
13. 662
15. 009
16, 375
17, 752
19, 142
20. 541
405
19
826
79
20
10. 986
12. 326
13. 676
16. 031
16, 398
17, 775
19. 164
20. 564
416
20
832
80
21
11.008
12. 349
13. 697
15. 055
16. 421
17, 798
19. 187
20, 588
426
21
837
81
22
11.030
12. 371
13. 720
15. 077
16,444
17, 821
19, 210
20, 611
436
22
842
82
23
11. 053
12. 394
13. 742
15.100
16, 467
17, 845
19, 234
20, 635
446
23
847
S3
21
11.075
12.416
13. 766
15. 123
16. 489
17, 867
19, 257
20. 659
455
24
852
84
25
11. 097
12. 439
13. 787
15, 145
16.513
17, 890
19. 280
20, 682
465
25
857
85
26
11.119
12.461
13.810
15,168
16,535
17, 914
19, 303
20, 705
474
26
86S
80
27
11. 142
12. 484
13. 833
15. 190
16, 558
17, 937
19. 327
20, 723
483
27
867
87
2S
11. 164
12.505
13.865
15. 214
16, 581
17, 959
19.350
20. 752
492
28
872
88
29
U. 186
12. 528
13. 878
15. 236
16, 604
17. 983
19,373
20, 776
501
29
877
89
30
11. 209
12. 550
13. 009
15. 259
16, 627
18, 006
19, 396
20, 799
509
30
882
90
SI
11. 231
12. .573
13. 923
15.282
16, 650
18, 029
19. 420
20, 823
518
31
887
91
32
11. 254
12. .595
13. 945
15, 304
16, 673
18, 052
19,443
20, 846
526
32
892
92
S3
11. 275
12. 618
13. 968
15, 327
16, 696
18, 075
19, 466
20, 869
534
32
897
93
34
11. 298
12. 640
13. 990
15, 349
16, 719
18. 097
19. 489
20, 893
542
34
901
94
35
11. 320
12.j60i
14. 013
16, 373
16, 741
18, 121
19, 513
20, 917
550
35
906
95
S6
11. 343
12. 683
14. o;i6
15,395
16, 765
18, 145
19,536
20, 940 .
55S
36
911
96
37
11. 366
12. 708
14. 059
15, 418
16. 787
18,167
19, 559
20. 964
566
37
916
97
ss
11.387
12. 730
14. 081
15,441
16.810
18. 190
19, 582
20, 987
573
38
920
98
39
11. 410
12. 753
14. 104
15. 463
16. 833
18, 214
19, 606
21. Oil
581
39
925
99
40
11.432
12.775
14. 126
15, 486
16.856
18, 237
19. 629
21,034
588
40
930
loo
41
11.454
12. 707
u. m
15,509
16, 870
IS, 260
19, 652
21. 0.58
595
41
934
101
42
11.476
12. 8J0
14. 1 71
15 532
16, 902
18 283
19, (176
21,082
603
42
989
102
43
11.499
12. 842
14. 194
15. ,554
16, 925
18,306
19. 699
31, 105
610
43
943
103
44
11.521
12.865
14. 216
15,577
16, 948
18,329
19,723
21, 120
017
44
948
104
45
11. 543
12. 887
14. 239
16, 600
16, 971
18, 352
19, 746
21, 152
624
45
953
105
46
11. 566
12,910
14. 262
15. 622
16. 993
18. 376
19, 769
21. 175
631
46
957
106
- 47
11. 588
12.932
14. 284
15, 646
17, 017
18, 399
19, 792
21, 199
637
47
962
107
4>l
11.611
12. 955
14.307
16, 668
17,039
18, 421
19,816
21, 223
644
48
966
108
49
11.633
12. 977
14. 329
15, 691
17. 062
18, 445
19, 839
21, 247
651
49
971
109
50
11. 6.55
13. 000
14. 352
15, 714
17. 086
18, 468
19, 862
21. 270
657
50
975
110
51
11. 677
13. 022
14. 374
15, 736
17, 108
18.491
19. 886
21. 293
664
51
980
lU
52
11.700
13. 045
14. 398
15,760
17,131
18, 514
19, 909
21. 317
670
52
984
112
53
11.722
13. 067
14. 420
15, 782
17. 154
18, 538
19, 933
21. 340
677
53
988
113
54
11. 745
13. 090
14. 443
16.805
17. 177
18, 560
19. 956
21. 364
683
54
993
114
55
11.767
13.112
14. 465
15, 828
17, 200
18, 583
19, 979
21,388
690
55
997
115
56
11.789
13. 135
14. 488
15, 850
17, 223
18, 607
20. 002
21,412
696
56
1001
116
57
lx.812
13. 157
14. 510
15, 873
17, 246
18, 630
20, 026
21, 435
702
57
1005
117
58
11.834
13. 180
14. 533
15, 896
17, 269
18,663
20, 050
21. 459
708
69
1010
118
59
11. 857
13. 202
14. 556
15, 919
17. 292
18, 676
20. 073
21,482
714
58
1014
119
60
11. 878
13. 225
14.578
16, 942
17. 315
IS. 700
20.096
21. 506
720
60
1018
120
156
A MANUAL OF TOPOGRAPHIC METHODS.
-For computing differences of altitude from angles of elevation or depreasion (applicahle to scale
of 1:30000).
[Prepared Ipy K. S. "Woodward. 1
■r^-^v e ixjx i„ C +D7i,4-/ia for ans'les of elevation.
Ditference of altitnde= J Iu,,;_|.,,.^ for „„|ies of dopressioi
opressiou.
^distance in scale divisions E>j'ineli each; (t = angle of elevation or depression ; 7i,=50feetx tan a; 7i2 = correction
for curvature and refraction.
Arguuient for Ai is a,- argument for /(•.» is D.
A, in feet.
D
ft2
D
7i2
'
0=>
1°
20
3°
4°
5°
«o
JO
Scale
divisions.
Feet.
Scale
divisions.
Feet.
0
.000
.873
1.746
2.620
3.496
4 374
5.255
6139
000
0
1080
60
1
.014
.887
1.760
2.635
3. 511
4 389
5.270
6.154
130
1
1089
61
2
.029
.902
1.775
2.649
3.525
4 403
5.284
6.109
197
2
1098
62
3
.043
.916
1.789
2.664
3.540
4 418
5.299
6. 183
243
3
1107
63
4
.058
.931
1.804
2.678
3.555
4 433
5.314
6.198
270
4
1116
64
5
.072
.945
1.819
2.693
3.569
4.447
5.328
6.213
312
5
1124
65
6
.087
.960
1.833
2.708
3.584
4 462
5.343
6. 228
342
6
1133
66
7
.102
.974
1.848
2.722
. 3. 598
4 477
5.358
6.242
309
7
1141
67
g
.116
.989
1.862
2.737
3.613
4 491
5.373
6.257
394
8
1150
68
9
.131
1.003
1.877
2.751
3.G28
4 506
5.387
6.272
418
9
1158
69
10
.145
1.018
1.891
2.706
3.642
4 521
5.402
6.287
441
10
1107
70
11
.160
1.033
1.906
2.781
3.057
4 535
5.417
6.301
463
11
1175
71
12
.174
1.047
1.921
2.795
3.072
4.550
5.431
6.316
483
12
11, S3
72
13
.189
1.0B2
1.935
2.810
3.686
4.565
5.446
6.331
503
13
1191
73
14
• .203
1.076
1.950
2.824
3.701
4 579
5.461
6.346
522
14
1199
74
13
.218
1.091
1.964
2.839
3.715
4.594
5.476
6 361
540
15
1208
75
16
.232
1.105
1.979
2.854
3.730
4. 609
5.490
6.375
558
16
1216
76
17
.247
1.120
1.993
2.868
3.745
4 623
5 505
6.390
575
17
1234
77
IS
.262
1.134
2.008
2.883
3.759
4. 638
5. £20
6 405
592
18
1231
78
19
.276
1.149
2.023
2.897
3.774
4 653
5.535
6.420
608
19
1339
79
20
.291
1.164
2.037
2.912
3.789
4.667
5.549
6 434
624
20
1247
80
21
.305
1.178
2.052
2.927
3. 803
4 682
5.564
6 449
639
21
1255
81
22
.320
1.193
2.066
2.941
3.818
4.097
5.579
6.464
654
22
1363
83
23
.334
1.207
2.081
2.956
3.832
4.711
5.593
6.479
669
23
1270
83
24
.349
1.222
2.095
2.970
3.847
4 726
5.608
6.494
683
24
1378
84
25
.363
1.236
2.110
2.985
3.862
4 741
5.623
6.508
697
25
1286
85
26
.378
1.250
2.125
2.999
3.876
4 755
5.638
6 523
711
26
1293
86
27
.392
1.265
2.139
3.014
3.891
4 770
5.652
6.538
725
27
1301
87
28
.407
1.280
2.154
3.029
3.906
4 785
5.667
6. 553
738
28
1308
88
29
.422
1.294
2.168
3.043
3.920
4 800
5.682
6.568
751
29
1315
89
30
.436
1.309
2.183
3.058
3.935
4 814
5.697
6 582
764
30
1333
90
31
.451
1.324
2.197
3.072
3.949
4 829
5.711
6.597
776
31
1330
91
33
.465
1.338
2.212
3.087
3. 964
4 844
5.726
6.612
789
32
1337
92
33
.480
1.353
2.227
3.102
3.979
4 858
5.741
6.627
801
33
1345
93
34
.494
1.367
2.241
3.116
3.993
4 873
5.755
6.642
813
34
1353
94
35
.509
1.382
2.256
3.131
4.008
4 888
5.770
6.656
825
35
1359
95
36
.523
1.396
2.270
3. 145
4. 023
4 902
5.785
6.671
837
36
1366
96
37
.538
1.411
2.285
3.160
4 037
4.917
5.800
6.686
848
37
1373
97
3S
.552
1.425
2.289
3.175
4 052
4.932
5.814
6.701
860
38
1380
98
39
.567
1.440
2.314
3.189
4.067
4 946
5.829
6 716
871
39
1387
99
40
.582
1.455
2.329
3.204
4.081
4.961
5.844
6. 730
882
40
1394
100
41
.596
1.469
2.343
3.218
4.096
4 976
5.859
6.745
893
41
1401
101
42
.611
1.4C4
2.358
3.233
4110
4.990
5.873
6.760
904
42
1408
102-
43
.625
1.498
2.372
3.248
4.125
5.005
5.888
6.775
914
43
1415
103
44
.640
1.513
2.387
3.262
4. 140
5.020
5. 903
6.790
925
44
1422
104
45
.654
1.527
2.401
3.277
4154
5.034
5.918
6.804
935
45
1429
105
46
.669
1.542
2.416
3.292
4.169
5.049
5.932
6 819
946
46
1436
106
47
.683
1.657
2.431
3.306
4184
5.064
5.947
6 834
95G
47
1442
107
48
.698
1.571
2.445
3.321
4198
5.079
5.962
6 849
966
48
1449
108
49
.712
1.586
2.460
3.335
4 213
5.093
5.977
6.864
976
49
1456
109
60
.727
1.600
2.474
3.350
4.228
5.108
5.991
6.879
980
50
1462
110
51
.742
1.615
2.489
3.365
4. 242
5.123
6.006
6.893
996
5]
1469
111
52
.756
1.629
2.503
3.379
4 257
5.137
6.021
6 908
1006
52
1476
112
53
.771
1.644
2.517
3.394
4 272
5.152
6.036
6 923
1015
53
1482
113
54
.785
1.658
2.533
3.408
4 286
5.167
6.050
6 938
1025
54
1489
114
55
.800
1. 673
2.547
3.423
4 301
5.181
6.065
6.953
1034
55
1495
115
56
.814
1.688
2.562
3.438
4.316
5.196
6.080
6 967
1043
56
1502
116
57
.829
1.702
2.576
3.452
4 330
5.211
6.095
6.982
1053
57
1508
117
58
.843
1.717
2.591
3.467
4 345
5.226
6.109
6.907
1062
58
1515
118
59
.858
1.731
2.606
^ 3. 481
4.360
5.240
6.124
7.012
1071
59
1521
119
60
.873
1.746
2.620
3.496
4 374
5.255
6.139
7.027
1080
60
1527
120
ALTITUDE TABLES.
157
-For com]}utiiig differences of altitude from aiu/les of elevation or depression (applicable to scale
of 1: 30000— Contiuued.
ft, in feet.
D
1h
D
h^
'
8°
9°
10°
11°
12°
13°
14°
15°
Scale
[livisions.
Feet.
Scale
divisions.
Feet.
0
7.027
7.919
8.816
9.719
10. 628
11.543
12. 466
13. 397
000
0
1080
60
1
7.042
7.934
8.831
9.734
10. 643
11. 558
12.482
13. 413
139
1
1089
61
2
7.056
7.949
8.846
9.749
10. 658
11. 574
12.497
13.428
197
2
1098
62
3
7.071
7.964
8.861
9.704"
10. 673
11. 589
12. 51?
13.444
242
3
1107
63
4
7.086
7.979
8.876
9.779
10. 688
11. 604
12. 528
13. 460
279
4
1116
64
o
7.101
7.994
8.891
9.794
10. 704
11. 620
12. 543
13. 475
312
g
1124
65
6
7.116
8.008
8.906
9.809
10. 719
11.635
12, 559
13. 491
342
6
1133
66
7.131
8.023
8.921
9.824
. 10. 734
11. 650
12. 574
13.506
369
7
1141
67
8
7.145
8.038
8.936
9.840
10. 749
11. 666
12. 590
13. 522
394
8
1150
68
9
7.160
8.053
8.951
9,855
10. 764
11. 681
12. 605
13. 538
418
9
1158
69
10
7.175
8.068
8.966
9. 870
10.7.SO
11.696
12. 621
13. 553
441
10
1167
70
11
7.190
8.083
8.981
9.885
10.795
11.712
12. 636
13. 569
462
11
1175
71
12
7.205
8.098
8.996
9.900
10. 810
11. 727
12, 652
13. 584
483
12
1183
72
13
7.220
8.113
9.011
9.915
10. 825
11. 742
12, 667
13. 600
503
13
1191
73
14
7.235
8.128
9.026
9. 930
10.841
11. 758
12,683
13. 616
522
14
1199
74
15
7.249
8.143
9.041
9.945
10.856
11. 773
12, 698
13. 631
540
15
1208
75
16
7.264
8.158
9.056
9.960
10.871
11.789
12. 714
13. 647
558
16
1216
76
17
7.279
8. 173
9.071
9.976
10.886
11.804
12. 729
13. 663
575
17
1224
77
18
7.294
8.188
9.086
9.991
10. 902
11. 819
12.745
13. 678
592
18
1231
78
19
7.309
8.202
9.101
10.006
10. 917
11. 835
12. 761
13. 694
608
19
1239
79
20
7.324
8.217
9.116
10.021
10. 932
11, 850
12. 776
13.709
624
20
1247
80
21
7.339
8.232
9.131
10. 036
10. 947
11, 865
12. 791
13. 725
639
21
1255
81
22
7.353
8.247
9.146
10. 051
10. 962
11.881
12. 807
13. 741
654
22
1263
82
23
7.368
8.202
9.161
10. 066
10.978
11.896
12. 822
13.756
669
23
1270
83
21
7.383
8.277
9.176
10. 082
10. 993
11.911
12. 838
13.772
683
24
1278
84
25
7.398
8.292
9.191
10.097
11. 008
11.927
12. 853
13.788
697
25
1286
85
26
7.413
8.307
9.207
10. 112
11. 023
11. 942
12. 869
13, 803
711
26
1293
86
27
7.428
8.322
9.222
10. 127
11, 039
11,958
12. 884
13. 819
725
27
1301
87
28
7.443
8.337
9.237
10.142
11. 054
11. 973
12. 900
13. 835
738
28
1308
88
29
7.457
8.352
9.252
10, 157
11. 069
11. 988
12.915
13, 860
751
29
1315
89
30
7.472
8.367
9.267
10. 172
11. 084
12. 004
12. 931
13,866
764
30
1323
90
31
7.487
8.382
9. 282
10. 18B
11. 100
12,019
12, 946
13. 882
776
31
1330
91
32
7.502
8.397
9.297
10.203
11.115
12. 034
12, 962
13, 897
789
32
1337
92
33
7.517
8.412
9.312
10.218
11. 130
12,030
12, 077
13,913
SOI
33
1345
93
3*
7.532
8.427
9.327
10.233
11. 146
12, 065
12,993
13.929
813
34
1352
94
35
7.547
8.442
9.342
10.248
11. 161
12,081
13. 008
13.944
825
35
13.59
95
36
7.562
8.457
9.3.57
10.263
11. 176
12. 096
13, 024
13. 960
837
36
1366
96
37
7.576
8.472
9.372
10.278
11. 191
12, 111
13. 039
13. 976
848
37
1373
97
38
7.591
8.487
9.387
10. 294
11.207
12. 127
13. 055
13. 991
860
38
1380
98
39
7.606
8.502
9.402
10. 309
11.222
12. 142
13,070
14.007
871
39
■ 1387
99
40
7.621
8.516
9.417
10. 324
11. 237
12. 158
13. 086
14. 023
882
40
1394
100
41
7.636
8.531
9.432
10. 339
11. 252
12. 173
13. 101
14.038
893
41
1401
101
42
7.651
8.546
9.447
10.354
11, 268
12. 188
13.117
]4.0a4
904
42
1408
102
43
7.666
8.561
9.462
10.369
11. 283
12. 204
13. 133
14. 070
914
43
1415
103
44
7.681
8.576
9.477
10. 385
11, 298
12. 219
13. 148
14. 086
925
44
1422
104
45
7.695
8.591
9.493
10.400
11.314
12. 235
13. 164
14.101
935
45
1429
105
.46
7.710
8.606
9.508
10. 415
11. 329
12.250
13. 179
14.117
946
46
1436
106
47
7.725
8.621
9.523
10.431
U.344
12. 266
13. 195
14. 133
936
47
1442
107
48
7.740
8.636
9.538
10.445
11. 359
12. 281
13.210
14148
966
48
1449
108
49
7.755
8.651
9.553
10. 460
11.375
12. 296
13.226
14. 164
976
49
1456
109
50
7.770
8.666
9.568
10. 476
11. 390
12.312
13. 241
14.180
986
50
1462
110
51
7.785
8.681
9.583
10. 491
11.405
12.327
13. 257
14. 195
996
51
1469
111
62
7.800
8.696
9.598
10.506
11.421
12, 343
13. 273
14.211
1006
52
1476
112
63
7.815
■ 8.711
9.613
10.521
11. 436
12, 358
13, 288
14. 227
1015
53
1482
113
54
7.830
8.72D
9.628
10. 536
11. 451
12.373
13, 304
14.243
1025
54
1489
114
56
7.844
8.741
9.643
10. 552
11. 467
12. 389
13. 319
14.258
1034
55
1495
115
56
7.859
8.756
9.658
10. 567
11.482
12. 404
13. 335
14. 274
1043
56
1502
116
57
7.874
8.771
9.673
10. 5S2
11. 497
12. 420
13. 350
14. 290
1053
57
1508
117
68
7. 889
8.786
9.689
10. 597
11.513
12.435
13.366
14. 306
1062
58
1515
118
59
7.904
8.801
9.704
10. 612
11. 528
12.451
13. 382
14.321
1071
59
1521
119
60
7.919
8.816
9.719
10.028
11. 543
12.406
13. 397
14.337
1080
60
1527
120
158
A MANUAL OF TOPOGEAPHIO METHODS.
Table XI. — Differences of altUude
[Prepared by
Computed from the formula A ^ D sin a cos a, in which D is the observed distance of the
D
D
D
D
D
D
D
D
D
D
D
D
D
D
"
5G0
5S0
600
620
640
660
6S0
700
720
740
760
780
800
820
0 01
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0 02
0.3
0.3
0.3
0.4
0.4.
0.4
0.4
0.4
. 0.4
0.4
0.4
0.5
0.5
0.5
0 03
0.5
0.5
0.5
0.5
0.6
0.6
O.B
0.6
0.6
0.6
0.7
0.7
0.7
0.7
U 01
0.6
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
0.9
0.9
1.0
0 05
0.8
0.8
0.9
0.9
0.9
1.0
1.0
1.0
1.0
1.1
1.1
1.1
1.2
1.2
0 06
1.0
1.0
1.1
1.1
1.1
1.2
1.2
1.2
1.3
1.3
1.3
1.4
1.4
1.4
0 07
1.1
1.2
1.2
1.3
1.3
1.3
1.4
1.4
1.5
1.5
1.6
1.6
1.6
1.7
0 08
1.3
1.4
1.4
1.4
1.5
1.5
1.6
1.6
1.7
1.7
1.8
1.8
1.9
1.9
0 09
1.5
1.5
1.6
1.6
1.7
1.7
1.8
1.8
1.9
1.9
2.0
2.0
2.1
2.1
0 10
1.6
1.7
1.7
1.8
1.9
1.9
2.0
2.0
2.1
2.2
2.2
2.3
2.3
2.4
0 11
1.8
1.9
1.9
2.0
2.0
2.1
2.2
2.2
2.3
2.4
2.4
2.5
2.6
2.6
0 12
2.0
2.0
2.1
2.2
2.2
2.3
2.4
2.4
2.5
2.6
2.7
2.7
2.8
2.9
0 13
2.1
2.2
2.3
2.3
2.4
2.5
2.6
2.6
2.7
2.8
2.9
2.9
3.0
3.1
0 14
2.3
2.4
2.4
2.5
2.6
2.7
2.8
2.8
2.9
3.0
3.1
3.2
3.3
3.3
0 IS
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.1
3.2
3.3
3.4
3.5
3.6
0 16
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.3
3.4
3.5
3.6
3.7
3.8
0 17
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
0 18
2.9
3.0
3.1
3.2
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
0 19
3.1
3.2
3.3
3.4
3.5
3.6
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
0 20
3.3
3.4
3.5
3.6
3.7
3.8
4.0
4.1
4.2
4.3
4.4
4.5
4.7
4.8
0 21
3.4
3.5
3.7
3.8
3.9
4.0
4.2
4.3
4.4
4.5
4.6
4.8
4.9
5.0
0 22
3.6
3.7
3.8
4.0
4.1
4.2
4.4
4.5
4.6
4.7
4.9
5.0
5.1
5.2
0 23
3.7
3.9
4.0
4.1
4.3
4.4
4.5
4.7
4.8
5.0
5.1
5.2
5.4
5.5
0 24
3.9
4.0
4.2
4.3
4.5
4.0
4.7
4.9
5.0
5.2
5.3
5.4
5.6
5.7
0 25
4.1
4.2
4.4
4.5
4.7
4.8
4.9
5.1
5.2
5.4
5.5
5.7
5.8
6.0
0 26
4.2
4.4
4.5
4.7
4.8
5.0
5.1
5.3
5.4
5.6
5.7
5.9
6.0
6.2
U 27
4.4
4.6
4.7
49
5.0
5.2
5.3
5.5
5.7
5.8
6.0
6.1
6.3
6.4
0 28
4.6
4.7
4.9
5.0
5.2
5.4
5.5
5.7
5.9
6.0
6.2
6.3
6.5
6.7
0 29
4.7
4.9
5.1
5.2
5.4
5.6
5.7
5.9
6.1
6.2
6.4
6.6
6.8
6.9
0 30
4.9
5.1
5.2
5.4
5.6
5.8
5.9
6.1
6.3
6.5
6.6
6.8
7.0
7.2
0 35
5.7
5.9
6.1
6.3
6.5
6.7
6.9
7.1
7.3
7.5
7.7
7.9
8.1
8.4
0 40
6.5
6.7
7.0
7.2
7.4
7.7
7.9
8.1
8.4
8.6
8.8
9.1
9.3
9.5
0 45
7.3
7.6
7.9
8.1
8.4
8.6
8.9
9.2
9.4
9.7
9.9
10.2
10.5
10.7
0 50
8.1
8.4
8.7
9.0
9.3
9.6
9.9
10.2
10.5
10.8
11.1
11.3
11.6
11.9
0 55
9.0
9.3
9.6
9.9
10.2
10.6
10.9
11.2
11.5
11.8
12.2
12.5
12.8
13.1
1 00
9.8
10.1
111.5
10.8
11.2
11.5
11.9
12.2
12.6
12.9
13.3
13.6
14.0
14.3
1 10
11.4
11.8
12.2
12.6
13.0
13.4
13.8
14.3
14.7
15.1
15.5
15.9
16.3
16.7
1 20
13.0
13.5
14.0
14.4
14.9
15.4
15.8
16.3
16.7
17.2
17.7
18.1
18.6
19.1
1 30
14.7
15.2
15.7
16.2
16.7
17.3
17.8
18.3
18.8
19.4
19.9
20.4
20.9
21.5
1 40
10.3
16.9
17.4
18.0
18.6
19.2
19.8
20.3
20.9
21.5
22.1
22.7
23.3
23.8
1 50
17.9
18.5
19.2
19.8
20.5
21.1
21.7
22.4
23.0
23.7
24.3
24.9
25.6
26.2
2 00
19.5
20.2
20.9
21.6
22.3
23.0
23.7
24.4
25.1
25.8
26.5
27.2
27.9
28.6
2 10
21.2
21.9
22.7
23.4
24.2
24.9
25.7
26.4
27.2
28.0
28.7
29.5
30.2
31.0
2 20
22.8
23.6
24.4
25.2
26.0
26.8
27.7
28.5
29.3
30.1
30.9
31.7
32.5
33.4
2 30
24.4
25.3
26.1
27.0
27.9
28.8
29.6
30.5
31.4
32.2
33.1
34.0
34.9
35.7
2 40
26.0
27.0
27.9
28.8
29.7
30.7
31.6
32.5
33.5
34.4
35.3
36.3
37.2
38.1
2 50
27.6
28.6
29.6
30.6
31.6
32.0
33.6
34.6
35.5
36.5
37.5
38.5
39.5
40.5
'8 00
29.3
30.3
31.4
32.4
33.4
34.5
35.5
36.6
37.6
38.7
39.7
40.8
41.8
42.9
1 00
39.0
40.4
41.8
43.1
44.6
45.9
47.3
48.7
50.1
51.5
52.9
54.3
55.7
57.1
5 00
48.6
50.4
52.1
53.8
55.6
57.3
59.0
60.8
62.5
64.2
66.0
67.7
69.5
71.2
D
D
D
D
D
D
D
D
»
D
D
D
D
D
560
580
000
620
640
660
6S0
700
720
740
760
780
800
820
ALTITUDE TABLES.
159
from telemeter measures.
R.S. Woodward.]
telemeter staff, a is the £
gle of elevation or depression, and h is the difference in height.
D
D
D
D
D
D
D
D
D
D
D
»
D
D
It
840
860
880
900
920
940
960
980
1,000
1,100
1,200
1,S00
1,400
1,500
2,000
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.8
0.8
0.9
1.2
0.7
0.7
0.8
0.8
0.8
0.8
0.8
0.9
0.9
1.0
1.0
1.1
1.2
1.3
1.7
1.0
1.0
1.0
1.0
1.1
1.1
1.1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
2.3
1.2
1.2
1.3
1.3
1.3
1.4
1.4
1.4
1.5
1.6
1.7
1.9
2.0
2.2
2.9
1.5
1.5
1.5
1.6
1.6
1.6
1.7
1.7
1.7
1.9
2.1
2.3
2.4
2.6
3.5
1.7
1.8
1.8
1.8
1.9
3.9
2.0
2.0
2.0
2.2
2.4
2.7
2.9
3.1
4.1
2.0
2.0
2.1
2.1
2.1
2.2
2.2
2.3
2.3
2.6
2.8
3.0
3.3
3.5
4.7
2.2
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.6
2.9
3.1
3.4
3.7
3.9
5.2
2.4
2.5
2.6
2.6
2.7
2.7
2.8
2.9
2.9
3.2
3.5
3.8
4.1
4.4
5.8
2.7
2.8
2.8
2.9
2.9
3.0
3.1
3.1
3.2
3.5
3.8
4 2
4 5
4 8
6.4
2.9
3.0
3.1
3.1
3.2
3.3
3.4
3.4
3.5
3.8
4 2
4 5
4 9
5.2
7.0
3.2
3.3
3.3
3.4
3.5
3.6
3.6
3.7
3.8
4 2
4 5
4 9
5.3
5.7
7.6
3.4
8.5
3.6
3.7
3.7
3.8
3.9
4.0
4.1
4.5
4.9
5.3
5.7
6.1
8.1
3.7
3.7
3.8
3.9
4.0
41
4.2
4.3
4 4
4 8
5.2
5.7
6.1
6.5
8.7
3.9
4 0
4.1
4.2
4.3
4 4
4 5
4.6
4 7
5.1
5.6
6.0
6.5
7.0
9.3
4.2
4 3
4.4
4 5
4.6
4 7
4 8
4 9
5.0
5.4
5.9
6.4
6.9
7.4
9.9
4.4
4.5
4.6
4 7
4 8
4 9
5.0
5.1
5.2
5.8
6.3
6.8
7.3
7.9
10.5
4 6
4 8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
6.1
6.6
7.2
7.7
8.3
11.1
4.9
5.0
5.1
5.2
5.4
5.5
5.6
5.7
5.8
6.4
7.0
7.5
8.1
8.7
11.6
5.1
5.3
5.4
5.5
5.6
5.7
5.9
6.0
6.1
6.7
7.3
7.9
8.6
9.2
12.2
5.4
5.5
5.6
5.8
5.9
6.0
6.1
6.3
6.4
7.0
7.7
8.3
9.0
9.6
12.8
5.6
5.8
5.9
6.0
6.2
6.3
6.4
6.6
6.7
7.4
8.0
8.7
9.4
10.0
13.4
5.9
6.0
6.1
6.3
6.4
6.6
6.7
6.8
7.0
7.7
8.4
9.1
9.8
10.5
14 0
6.1
U.3
6.4
6.5
6.7
6.8
7.0
7.1
7.3
8.0
8.7
9.5
10.2
10.9
14 5
6.4
6.5
6.7
6.8
7.0
7.1
7.3
7.4
7.6
8.3
9.1
9.8
10.5
11.3
15.1
6.6
6.8
6.9
7.1
7.2
7.4
7.5
7.7
7.9
8.6
9.4
10.2
11.0
11.8
15.7
6.8
7.0
7.2
7.3
7.5
7.7
7.8
8.0
8.1
9.0
9.7
10.6
11.4
12.2
16.3
7.1
7.3
7.4
7.6
7.8
7.9
8.1
8.3
8.4
9.3
10.1
11.0
11.8
12.7
16.9
7.3
7.5
7.7
7.9
8.0
8.2
8.4
8.6
8.7
9.6
10.5
11.3
12.2
13.1
17.5
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
11.2
12.2
13.2
14.3
15.3
20.4
9.8
10.0
10.2
10.5
10.6
10.9
11.2
11.4
11.6
12.8
U.O
15.1
16.3
17.4
23.3
11.0
11.3
11.5
11.8
12.0
12.3
12.6
12.8
13.1
14.4
15.7
17.0
18.3
19.6
26.2
12.2
12.5
12.8
13.1
13.4
13.7
14 0
14.2
14.5
16.0
17.4
18.9
20.3
21.8
29.1
13.4
13.8
14.1
14 4
14 7
15.0
15.4
15.7
16.0
17.6
19.2
20.8
22.4
24 0
32.0
14.7
15.0
15.4
15.7
16.1
16.4
16.8
17.1
17.5
19.2
20.9
22.7
24.4
26.2
34 9
17.1
17.5
17.9
18.3
18.7
19.1 •
19.5
20.0
20.4
22.4
24 4
26.5
28.5
30.5
40.7
19.5
20.0
20.5
20.9
21.4
21.9
22.3
22.8
23.3
25^6
27.9
30.2
32.6
34 9
40.5
22.0
22.5
23.0
23.6
24.1
24.6
25.1
25.6
26.2
28.8
31.4
34.0
36.6
39.3
52.3
24.4
25.0
25.6
26.2
26:7
27.3
27.9
28.5
29.1 .
32.0
34.9
37.8
40.7
43.6
58.1
26.9
27.5
28.1
28.8
29.4
30.1
30.7
31.3
32.0
35.2
38.4
41.6
41.8
48.0
64.0
29.3
30.0 ■
30.7
31.4
32.1
32.8
33.5
34.2
34.9
38.4
41.9
45.3
48.8
52.3
69.8
31.7
32.5
33.2
34.0
34.8
35.5
36.3
37.0
37.8
41.6
45.3
49.1
52.9
56.7
75.6
34 2
35.0
35.8
36,6
37.4
38.2
39.1
39.9
40.7
44 7
48.8
.52 9
57.0
61.0
81.4
36.6
37.5
38.4
39.2
40.1
41.0
41.8
42.7
43.6
47.9
52.3
56.7
61.0
6.5.4
87.2
39.0
40.0
40.9
41.8
42.8
43.7
44 6
45.6
46.5
51.1
55.8
60.4
65.1
69.7
93.0
41.5
42.5
43.4
44.4
45.4
46.4
47.4
48.4
49.4
54.3
59.2
64.2
69.1
74.1
98.7
43.9
44 9
46.0
47.0
48.1
49.1
50.2
51.2
52.3
57.5
62.7
67.9
73.2
78.4
104 5
58.5
59.8
61.2
62.6
64 0
65.4
66.8
68.2
69.6
76.5
83.5
90.5
97.4
104.4
139.2
72.9
74.7
76.4
78.1
79.9
81.6
83.3
85.1
86.8
95.5
104 2
112.9
121.5
130.2
173.6
D
D
D
D
D
D
D
D
D
I)
D
D
D
D
D
840
860
880
900
920
940
960
980
1,000
1,100
1,200
1,300
1,400
1,500
2,000
160
A MANCTAL OF TOPOGRAPHIC METHODS.
Computed from the formula k='D sin a (
Table XI. — Differences of altitude
[Prepared by
1 a, in ■whicli D is tlie observed distance of the
D
D
D
D
D
D
D
»
D
D
I)
D
D
D
"
100
;iio
120
130
140
150
160
170
180
190
200
220
240
260
0 01
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.1
0.1
0.1
0.1
0 02
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
- 0.1
0.2
0 03
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0 0-1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0 05
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0 06
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.5
0 07
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0 08
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0,5
0.5
0.6
0.6
0 09
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.7
0 10
0.3
0.3
0.3
0.4
0.4
0.4
0.5
0.5
0.5
0,6
0.6
0.6
0.7
0.8
0 11
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.7
0.8
0.8
0 12
0.3
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0 13
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.7
0.7
0.8
0.8
0.9
1.0
0 U
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.9
1.0
1.1
0 15
0.4
0.5
0.5
0.6
6.6
0.7
0.7
0.7
0.8
0.8
0.9
1.0
1.0
1.1
0 16
0.5
0.5
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.1
1.2
0 17
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.1
1.2
3.3
0 18
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0
1.2
1.3
1.4
0 19
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.1
1.1
1.2
1.3
1.4
0 20
0.6
0.6
0.7
0.8
0.8
0.9
0.9
1.0
1.0
1.1
1.2
1.3
1.4
1.5
0 21
0.6
0.7
0.7
0.8
0.9
0.9
1.0
l.O
1.1
1.2
1.2
1.3
1.5
1.6
0 22
0.6
0.7
0.8
0.8
0.9
1.0
1.0
1.1
1.2
1.2
1.3
1.4
1.5
1.7
0 23
0.7
0,7
0.8
0.9
0.9
1.0
1.1
1.1
1.2
1.3
1.3
1.5
1.6
1.7
0 24
0.7
0.8
0.8
0.9
1.0
1.0
1.1
1.2
1.3
1.3
1.4
1.5
1.7
1.8
0 25
0.7
0.8
0.9
0.9
1.0
1.1
1.2
1.2
1.3
1.4
1.5
1.6
1.7
1.9
0 26
0.8
0.8
0.9
1.0
1.1
1.1
1.2
1.3
1.4
1.4
1.5
1.7
1.8
2.0
0 27
0.8
0.9
0.9
1.0
1.1
1.2
1.3
1.3
1.4
1.5
1.6
1.7
1.9
2.0
0 28
0.8
0.9
1.0
1.1
1.1
1.2
1.3
1.4
1.5
1.5
1.6
1.S
2.0
2.1
0 29
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.4
1.5
1.6
1.7
1.9
2.0
2.2
0 30
0.9
1.0
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.7
1.9
2.1
2.3
0 35
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.2
2.4
2.6
0 40
1.2
1.3
1.4
1.5
1.6
1.7
1.9
2.0
2.1
2.2
2.3
2.6.
2.8
3.0
0 43
1.3
1.4
1.6
1.7
1.8
2.0
2.1
2.2
2.4
2.5
2.6
2.9
3.1
3.4
0 50
1.5
1.6
1.7
1.9
2.0
2.2
2.3
2.5
2.6
2.8
2.9
3. -2
■3.5
3.8
0 55
1.6
1.8
1.9
2.1
2.2
2.4
2.6
2.7
2.9
3.0
3.2
3.5
3.8
4.2
1 00
1.7
1.9
2.1
2.3
2.4
2.6
2.8
3.0
3.1
3.3
3.5
3.8
4.2
4.5
1 10
2.0
2.2
2.4
2.6
2.9
3.1
3.3
3.5
3.7
3.9
4.1
4.5
4.9
6.3
1 20
2.3
2.6
2.8
3.0
3.3
3.5
3.7
4.0
4.2
4.4
4.7
5.1
6.6
6.0
1 30
2.6
2.9
3.1
3.4
3.7
3.9
4.2
4.4
4.7
5.0
5.2
5.8
6.3
6.8
1 40
2.9
3.2
3.5
3.8
4.1
4.4
4.7
4.9
5.2
5.5
5.8
6.4
7.0
7.6
1 50
3.2
3.5
3.8
4.2
4.5
4.8
5.1
5.4
5.8
6.1
6.4
7.0
7.7
8.3
2 00
3.5
3.8
4.2
4.5
4.9
5.2
5.6
5.9
6.3
6.6
7.0
7.7
8.4
9.1
2 10
3.8
4.2
4.5
4.9
5.3
5.7
6.0
6.4.
6.8
7.2
7.6
8.3
9.1
9.8
2 20
4.1
4.5
4.9
5.3
5.7
6.1
6.5
6.9
7.3
7.7
8.1
8.9
9.8
10. a
2 30
4.4
4.8
5.2
5.7
6.1
6.5
7.0
7.4
7.8
8.3
8.7
9.6
10.5
11.3
2 40
4.6
6.1
5.6
6.0
6.5
7.0
7.4
7.9
8.4
8.8
9.3
10.2
11.2
12.1
2 50
4.9
5.4
5.9
6.4
6.9
7.4
7.9
8.4
8.9
9.4
9.9
10.9
11.8
12.8
300
5.2
5.7
6.3
6.8
7.3
7.8
8.4
8.9
9.4
11.9
10.5
11.5
12.5
13.6
4 00
7.0
7.7
8.4
9.0
9.7
10.4
11.1
11.8
12.5
13.2
13.9
15.3
16.7
18.1
3 00
8.7
9.6
10.4
11.3
12.2
J3.0
13.9
14.8
15.6
16.5
17.4
19.1
20.8
22.6
D
D
D
D
D
D
D
D
D
»
D
D
D
D
"
100
110
120
130
140
150
160
170
180
190
200
220
240
260
ALTITUDE TABLES.
161
from telemeter measures — Continued.
E. S. ■Woodward.]
telemeter staff, a 13 the angle of elevation or depression, and h is the difference in height.
D
D
D
D
D
D
D
D
D
D
D
D
D
D
280
300
320
840
360
380
400
420
410
460
480
500
520
540
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.5
0.5
0.6
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.8
0.9
0.9
0.9
0.6
0.6
0.7
0.7
0.7
0.8
0.8
0.9
0.9
0.9
1.0
1.0
1.1
1.1
0 7
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0
1.1
1.1
1.2
1.2
1.3
0.7
0.8
0.8
0.9
0.9
1.0
1.0
1.1
1.2
1.2
1.3
1.3
1.4
1.4
0.8
0.9
0.9
1.0
1.0
1.1
1.2
1.2
1.3
1.3
1.4
1.5
1.5
1.6
0.9
1.0
1.0
1.1
1.2
1.2
1.3
1.3
1.4
1.5
1.5
1.6
1.7
1.7
1.0
1.0
1.1
1.2
1.3
1.3
1.4
1.5
1.5
1.6
1.7
1.7
1.8
1.9
1.1
1.1
1.2
1.3
1.4
1.4
1.5
1.6
1.7
1.7
1.8
1.9
2.0
2.0
1.1
1.2
1.3
1.4
1.5
1.5
1.6
1.7
1.8
1.9
2.0
2.0
2.1
2.2
1.2
1.3
1.4
1.5
1.6
1.7
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
1.3
.1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.0
' 2.1
2.2
2.3
2.4
2.5
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
1.5
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.7
2.8
2.9
3.0
1.6
1.7
1.9
2.0
2.1
2.2
2.3
2.4
2.6
2.7
2.8
2.9
3.0
3.1
1.7
1.8
2.0
2.1
2.2
2.3
2.4
2.6
2.7
2.8
2.9
3.1
3.2
3.3
1.8
1.9
2.0
2.2
2.3
2.4
2.6
2.7
2.8
2.9
3.1
3.2
3.3
3.5
1.9
2.0
2.1
2.3
2.4
2.5
2.7
2.8
2.9
3.1
3.2
3.3
3.5
3.6
2.0
2.1
2.2
2.4
2.5
2.7
2.8
2.9
3.1
3.2
3.4
3.5
3.6
3.8
2.0
2.2
2.3
2.5
2.6
2.8
2.9
3.1
3.2
3.3
3.5
3.6
3.8
3.9
2.1
2.3
2.4
2.6
2.7
2.9
3.0
3.2
3.3
3.5
3.6
3.8
3.9
4.1
2.2
2.4
2.5
2.7
2.8
3.0
3.1
3.3
3.5
3.6
3.8
3.9
4.1
4.2
2.3
2.4
2.6
2.8
2.9
3.1
2.3
3.4
3.6
3.7
3.9
4.1
4.2
4.4
2.4
2.5
2.7
2.9
3.0
3.2
3.4
3.5
3.7
3.9
4.1
4.2
4.4
4.6
2.4
2.6
2.8
3.0
3.1
3.3
3.5
3.7
3.8
4.0
4.2
4.4
4.5
4.7
S.9
3.1
3.3
3.5
3.7
3.9
4.1
4.3
4.5
. 4.7
4.9
5.1
5.3
5.5
3.3
3.5
3.7
4.0
4.2
• 4.4
4.7
4.9
5.1
5.3'
5.6
5.8
6.0
6.3
3.7
3.9
4.2
4.5
4.7
5.0
5.2
5.5
5.8
6.0
6.3
6.5
6.8
7.1
4.1
4.4
4.7
4.9
5.2
5.5
5.8
6.1
6.4
6.7
7.0
7.3
7.6
7.9
4.5
4.8
5.1
5.4
5.8
6.1
6.4
6.7
7.0
7.4
7.7
8.0
8.3
8.6
4.9
5.2
6.6
5.9
6.3
6.6
7.0
7.3
7.7
8.0
8.4
8.7
9.1
9.4
5.7
6.1
6.5
6.9
7.3
7.7
8.1
8.6
9.0
9.4
9.8
10.2
10.6
11.0
6.5
7.0
7.4
7.9
8.4
8.8
9.3
9.8
10.2
10.7
11.2
11.6
12.1
12.6
7.3
7.9
8.4
8.9
9.4
9.9
10.5
11.0
11.5
12.0
12.6
13.1
13.6
14.1
8 1
8.7
9.3
9.9
10.5
11.0
11.6
12.2
12.8
13.4
14.0
14.5
15.1
15.7
9.0
9.6
10.2
10.9
11.5
12.2
12.8
13.4
14.1
14.7
15.4
16.0
16.6
17.3
9.8
10.5
11.2
11.9
12.6
13.3
14.0
14.6
15.3
16.0
16.7
17.4
18.1
18.8
10.6
11.3
12.1
12.8
13.6
14.4
16.1
15.9
16.6
17.4
18.1
18.9
19.6
20.4
11.4
12.2
13.0
13.8
14.6
15.5
16.3
17.1
17.9
18.7
19.5
20.3
21.2
22.0
12.2
13.1
13.9
14.8
15.7
16.6
17.4
18.3
19.2
20.0
20.9
21.8
22.7
23.5
13.0
13.9
14.8
15.8
16.7
17.7
18.6
19.5
20.5
21.4
22.3
2S.2
24.2
25.1
13.8
14.8
15.8
16.8
17.8
18.8
19.7
20.7
21.7
22.7
23.7
24.7
25.7
26.7
14.6
15.7
16.7
17.8
18.8
19.9
20.9
21.9
23.0
24.0
25.1
26.1
27.2
28.2
19.5
20.9
22.3
23.7
25.1
26.4
27.8
29.2
30.6
32.0
33.4
34.8
36.2
37.6
24.3
26.0
27.8
29.5
31.3
33.0
34.7
36.5
38.2
39.9
41.7
43.4
45.1
46.9
D
D
D
I)
D
D
D
D
D
D
D
D
D
D
280
300
320
340
360
380
400
420
440
460
480
600
620
540
-11
162
A MANUAL OF TOPOGRAPHIC METHODS.
CONSTANTS.
163
Table XIII.— Constants.
IT =3.141593
log.ir =0.4971499
180° 1
"ir^arc lo— 57°.29578=57° 17' 44" .8; log. =1.7581226
^i5?52!=_J_=3447' .74677: log.=3. 5362739
n arc 1' "
r"=ii?552^^i— =206264".80625: loe.=5. 314(251
IT Sin 1" ^
comp . log. =4 . 6855749
=log. sin 1"
Log.
Number of degrees in circumference 360=2. 5563025
Number of minutes in circumference 21,600=4.3344538
Number of seconds in circumference 1, 296, 000=6. 1126050
Lengtli of arc of 1 degree 0174,5329=8. 2418774—10
Lengtb of arc of 1 minute 00029089=6. 4637261—10
Lengtli of arc of 1 second 000004848=4. 6855749—10
Constants of generating ellipse of Clarke's spheroid.
e'= (l— *, ^ =0. 00676866
»=(1— VlIIj2)(l+<7i:ii2)-i= O.C
7. 8305030—10
7. 2299162—10
Length of the meter in inches according to various authoriiiei.
Inches.
1 meter=39. 370432, Clarke, 1866-1873.
=39. 370790, Kater, 1818.
=39.368505, Coast Survey, 1851-1858 (Hassler corrected).
=39. 38092, Hassler, 1832.
=39. 36985, L.ake Survey, 1885.
=39.377786, Theoretical ten-millionth of quadrant (Clarke).
=39. 37, By act of Congress, 1866.
The standard meter has its normal length at 32'^ E
The standard yard has its normal length at 62° F.
The value first given is the one generally adopted by scientific men in
the United States.
Values adopted in the measurement of an arc of parallel extending from Ireland to the river Ural in Russia,
as the exact relative lengths of standards used as the units of measure in the triangulations of England,
France, Belgium, Prussia, and Russia.
Standards.
Expressed in
terms of the
standard yard.
Expressed in
inches.
Expressed in
lines of the
toise.
Expressed in
millimeters.
1. 00000000
2. 13151116
1. 09362311
36.000000
76. 734402
39. 370432
405. 34622
864.00000
443.29600
914. 39180
1, 949. 03632
1, 000. 00000
CONVERSION TABLES.
Table XIV. — Meters into yards.
[Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884].
[1 meter = 1.093623 yards.]
Meters.
Yards.
Meters.
Yards.
Meters.
Yards.
Meters.
Yards.
Meters.
Yards.
100,000
109, 362. 3
90, 000
98,426.1
9,000
9, 842. 61
900
984.26
90
98. 426
9
9.843
80, 000
87,489.8
. 8,000
8, 748. 98
800
874. 90
80
87. 490
8
8.749
70, 000
76, 553. 6
7,000
7, 655. 36
700
765. 54
70
76. 554
7
7.655
60, 000
65,617.4
6,000
6, 561. 74
600
656. 17
60
65. 617
6
6.562
50, 000
54,681.2
5,000
5, 468. 12
500
546.81
50
54. 681
5
5.568
40, 000
43, 744. 9
4,000
4, 374. 49
400
437. 45
40
43.745
4
4.374
30, 000
32, 808. 7
3,000
3,280.87
300
328. 09
30
32. 809
3
3.281
20, 000
21, 872. 5
2,000
2, 187. 25
200
218.72
20
21. 872
2
2.187
10, 000
10, 936. 2
1,000
1, 093. 62
100
109. 36
10
10. 936
1
1.094
164
A MANUAL OF TOPOGEAPHIC METHODS.
Table XV. — Yards into meters.
[1 yard = 0.914392 meter.]
Tarda.
Meters.
Yards.
Meters.
Yards.
Meters.
Yards.
Meters.
Yards.
Meters.
100, 000
91,439.2
90, 000
82,295.3
9,000
8, 229. 53
900
822.95
90
82.295
9
8.230
SO, 000
73, 151. 3
8,000
7, 315. 13
800
731. 51
80
73. 151
8
7.315
70, 000
61, 007. 4
7,000
6, 400. 74
700
640.07
70
64. 007
7
6.401
60, OOO
54,863.5
6,000
5,486.35
600
548. 64
5.486
50, 000
45, 719. 6
5,000
4, 571. 96
500
457.20
50
45. 720
5
4.572
40, 000
36, 575. 7
4,000
3, 657. 57
400
365. 76
40
36. 576
4
3.658
30, 000
27,431.8
3,000
2, 743. 18
300
274. 32
3
2.743
20, 000
18,287.8
2,000
1, 828. 78
200
182. 88
20
18. 288
2
1.829
10, 000
9, 143. 9
1,000
914.39
100
91.44
10
9.144
1
0.914
Table XVI. — Meters into inches and inches into meters.
[1 meter = 39.370432 inches, log. = 1.5951702.] [1 iucli = 0.02539977 meter, log. =8.4048298.]
Meters.
Inches.
1
39.37043
. 2
78. 74086
3
118.11130
4
157. 48173
5
196. 85216
6
236. 22259
7
275. 59302
8
314. 96346
9
354. 33389
Inches.
Meters.
1
0. 025400
2
0. 050800
3
0. 076199
4
0. 101599
5
0. 126999
6
0. 152399
7
0. 177798
8
0. 203198
9
0. 228598
Table XVII. — Meters into statute and nautical miles.
Meters.
Statnte
miles.
Nautical
miles.
Meters.
Statute
miles.
Nautical
miles.
Meters.
Statnte
miles.
Nautical
miles.
Meters.
Statute
miles.
Nautical
miles.
100, 000
62. 138
53.959
90, 000
55.924
48. 563
9,000
5.592
4.856
900
0.559
0.486
90
0.056
0.049
80, 000
49. 710
43. 167
8,000
4.971
4.317
800
0.497
0.432
80
0. '50
70, 000
43.496
37. 772
7,000
4.350
3.777
700
0.435
0.378
70
0.043
0.038
60, 000
37. 283
32. 376
6,000
3.728
3.238
600
0.373
0.324
60
0.037
0.032
50, 000
31. 069
26. 980
5,000
3.107
2.698
500
0.311
0.270
50
0.031
0.027
40, 000
24.855
21. 584
4,000
2.486
2.158
400
0.249
0.216
40
0.025
0.022
30, 000
18.641
16.188
3,000
1.864
1.619
300
0.186
0.162
30
0.019
0.016
20, 000
12.428
10. 792
2,000
1.243
1.079
200
0.124
O.108
20
0.012
0.011
10, 000
6.214
5.396
1,000
0.621
0.540
100
0.062
0.054
10
0.006
0.005
Table XVIII. — Statute and nautical miles into meters.
Meters in [Meters in
Meters in
Meters in
Meters in
Meters in
Miles.
Miles.
statute
nautical
Miles.
statute
nautical
Miles.
statute
nautical
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
100
160, 933. 0
185,324.8
90
144,839.7
166. 792. 3
9
14,483.97
16, 679. 23
.9
1,448.40
1, 667. 92
.09
144.84
166. 79
80
128. 746. 4
148, 259. 8
8
12,874.64
14, 825. 98
.8
1,287.46
1, 482. 60
70
112, 653. 1
129, 727. 4
7
11, 265. 31
12, 972. 74
.7
1, 126. 53
1,297.27
.07
112. 65
129. 73
60
96, 559. 8
111, 194. 9
6
9, 655. 98
11,119.49
.6
965. 60
1, 111. 95
.06
96.56
111. 19
50
80,466.5
92,662.4
5
8,046.65
9, 266. 24
.5
804.67
926. 62
.05
40
64,373.2
74, 129. 9
4
6,437.32
7, 412. 99
.4
643. 73
741. 30
30
48, 279. 9
65, 597. 4
3
4,827.99
5, 559. 74
.3
482. 80
20
32,186.6
37, 065. 0
2
3, 218. 66
3,706.50
.2
321. 87
370. 65
.02
32.19
37.06
10
16,093.3
18,532.5
1
1,609.33
1, 853. 25
.1
160. 93
185. 32
.01
16.09
18.53
IMeters x 39.370432
Meters x 3.280869
Meters x 1.093623
Meters X 0.000621377 :
:iiiclies, or to log. of meters add 1.5951701
: feet, or to log. of meters add 0.5159889
: yards, or to log. of meters add 0.0388676
: miles, or to log. of meters add 6.7933550
PROJECTION TABLES.
165
Table XIX. — For projection of maps of large areas.
[Extracted from Appendix 'So. 6, TJ. S. Coast and Geodetic Survey Report for 1884.]
LENGTHS OF DEGREES OF THE MERIDIAN.
Latitude
Meters.*
Statute miles.
Latitude
Meters.*
Statute miles.
0
110,567.2
68. 704
45
Ill, 130. 9
69.064
1
110, 567. 6
68. 704
46
111, 150. 6
69. 066
2
110, 568. 6
68. 705
47
111, 170. 4
69. 079
3
110, 570. 3
68. 706
48
111, 190. 1
69. 091
4
110, 572. 7
68. 708
49
111, 209. 7
69. 103
5
110, 675. 8
68. 710
50
111,229.3
69. 115
6
110, 579. 5
68. 712
51
111,248.7
69. 127
7
110, 583. 9
68,715
52
111, 208. 0
69. 139
8
HO, 589. 0
68. 718
63
HI, 287. 1
69. 151
9
110, 594. 7
68. 721
54
111, 306. 0
69. 163
10
110, 601. 1
68. 725
65
111,324.8
69, 175
11
110, 608. 1
68. 730
56
111, 343. 3
69. 186
12
110, 615. 8
68. 734
57
111, 361. 5
69. 197
13
110, 624. 1
68. 739
58
HI, 379. 5
69. 209
14
110, 633. 0
68.744
59
111, 397. 2
69. 220
15
110,042.5
63. 751
60
111,414.5
69. 230
16
110, 652. 6
68. 757
61
111,431.5
69. 241
17
110, 663. 3
68. 764
62
111, 448. 2
69. 251
18
110,674.5
68. 771
63
111, 464. 4
69. 261
19
110, 686. 3
68. 778
64
111, 480. 3
69.271
20
110, 698. 7
68. 786
65
111, 495. 7
69. 281
21
110, 711. 6
68. 794
66
111,510.7
69. 290
22
HO, 725. 0
68. 802
67
111, 525. 3
69. 299
23
HO, 738. 8
68.811
68
111, 539. 3
69. 308
24
110, 753. 2
68. 820
69
111,552.9
69. 316
25
110, 768. 0
68.829-
70
111,565.9
69. 324
26
110, 783. 3 •
68. 839
71
111,578.4
69. 332
27
110,799.0
68. 848
72
111,590.4
69. 340
28
119, 815. 1
68. 858
73
HI, 601. 8
69. 347
29
110, 831. 6
68. 869
74
111,612.7
69. 354
30
110,848.5
68. 879
75
111, 622. 9
69. 360
31
110, 865. 7
68. 890
76
111, 632. 6
69. 366
32
110, 883. 2
68. 91)1
77
111, 841. 6
69. 372
33
110, 901. 1
68. 912
78
111,650.0
69. 377
34
110, 919. 2
68. 923
79
111, 657. 8
69. 382
35
110, 937. 6
68. 935
80
111, 664. 9
69. 386
36
110, 956. 2
68. 946
81
111,671.4
69. 390
37
110, 975. 1
68. 958
82
111, 677. 2
69. 394
38
110, 994. 1
68. 969
83
111, 682. 4
69. 397
39
111,013.3
68. 981
84
111, 686. 9
69. 400
40
111,032.7
68. 993
85
111, 690. 7
69. 402
41
111, 052. 2
69.006
86
111, 693. 8
69. 404
42
111, 071. 7
69. 018
87
111, 696. 2
69. 405
43
111,091.4
•69. 030
88
HI, 697. 9
69.407
44
111, 111. 1
69.043
89
111, 699. 0
69.407 .
45
111,130.9
69.054
90
111,699.3
69.407
* These quantities express tlie number of meters and statute miles contained "within an arc of which the degree of lati-
tude numed is the middle; thus, the quantity, 111032.7, opposite latitude 40°, is the number of meters between latitude 39°
30' and latitude 40° 30'.
166
A MANUAL OF TOPOGRAPHIC METHODS.
Table XIX. — For projection of maps of large areas — Continued.
[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
LENGTHS OP DEGREES OF THE PARALLEL.
Latitude.
Meters.
Statute miles.
Latitude.
Meters.
Statute miles.
0
Ill, 321
69. 172
45
78, 849
48.995
1
1,304
9.162
46
7,466
8.136
2
1,253
9.130
47
6,058
7.261
3
1,169
9.078
48
4,628
6.372
4
1,051
9.005
49
3,174
5.469
6
110, 900
68. 911
50
71, 698
44, 552
6
0,715
8.795
51
70, 200
3.621
7
0,497
8.660
52
68, 680
2.676
8
0,245
8.504
53
7,140
1.719
9
109, 959
8.326
54
5,578
0.749
10
109, 641
68. 129
55
63, 996
39. 766
U
9,289
7.910
56
2,395
8.771
12
8,904
7.670
57
60, 774
7.764
13
8,486
7.410
58
69, 135
6.745
14
8,036
7.131
59
7,478
5.716
15
107, 553
66. 830
60
55, 802
34. 674
16
7, 036
6.510
61
4,110
3.623
17
6,487
6.169
62
2,400
2.560
18
5,906
5.808
63
50, 675
1.488
19
5,294
5.427
64
48, 934
0.406
20
104, 649
65. 026
65
47, 177
29. 315
21
3,972
4.606
66
5, 407
8.215
22
3.264
4.166
67
3,622
7.106
23
2,524
3.706
68
1,823
5.988
24
1,754
3.228
69
0,012
4.862
25
100, 952
62. 729
70
38, 188
23. 729
26
100. 119
2.212
71
6,353 •
2.589
27
99, 257
1.676
72
4,606
L441
28
8,364
1.122
73
2,648
20. 287
29
7,441
0.548
74
0,781
19. 127
30
96,488
59. 956
75
28, 903
17. 960
31
5,506
9.345
76
7,017
6.788
32
4,495
8.716
77
5,123
5.611
33
3,455
8,071
78
3,220
4.428
34
2,387 ■
7.407
79
1,311
13. 242
35
91, 290
56. 725
80
19, 394
12. 051
36
90, 166
6.027
81
17, 472
10. 857
37
89, 014
5.311
' 82
15, 545
9.659
38
7,835
4.579
83
13, 612
8.458
39
6,629
3.829
84
11, 675
7.255
40
85, 396
53. 063
85
9,735
6.049
41
4,137
2.281
86
7,792
4.842
42
'2, 853
1.483
87
5,846
3.632
43
1,543
50. 669
88
3,898
2. 422 .
44
80, 208
49. 840
89
1, 949
1.211
45
78, 849
48. 995
90
"
0.000
PBOJECTION TABLES.
167
Table XIX. — For projection of maps of large areas — Continued.
[Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884.]
AECS OF THE PARALLEL IN METERS.
Latitude.
Value of 1'.
Latitude.
Value of 1'.
Latitude.
Value of 1'.
24 00
1695.9
33 00
1557. 6
42 00
1380. 9
10
3.7
10
4.7
10
77.3
20
1.5
20
1.7
20
73.7
30
1689.3
30
48.7
30
70.0
40
7.0
40
5.8
40
66.4
50
4.8
50
2.8
50
62.7
25 00
1682. 5
34 00
1539. 8
43 00
1359. 1
10
80.3
10
6.8
10
55.4
20
1678. 0
20
3.7
20
51.7
30
5.7
30
0.7
30
48.0
40
3.3
40
27.6
40
44.3
50
1.0
50
4.6
50
40.5
26 00
1668. 7
35 00
1521. 5
44 00
1336. 8
10
6.3
10
18.4
10
33.1
20
3.9
20
15.3
20
29.3
30
1.5
30
12.2
30
25.5
40
1659. 1
40
09.1.
40
21.7
50
6.7
50
05.9
50
18.0
27 00
1654. 3
36 00
1502. 8
45 00
1314. 2
10
51.8
10
1499. 6
10
10.3
20
1649.4
20
6.4
20
06.5
30
6.9
30
3.2
30
02.7
40
4.4
40
0.0
40
1298. 8
50
1.9
50
86.8
50
95.0
28 00
1639. 4
37 00
1483. 6
46 00
1291. 0
10
6.9
10
80.3
10
87.2
20 '
4.3
20
77.1
20
83.3
30
1.8
30
73.8
30
79.4
40
29.2
40
70.5
40
75.5
50
6.6
50
67.2
50
71.6
29 00
1624.0
38 00
1463. 9
47 00
1267. 6
10
21.4
10
60.6
10
63.7
20
18.8
20
57.3
20
59.7
30
6.1
30
53.9
30
55.8
40
3.5
40
50.6
• 40
51.8
50
0.8
50
47.2
50
47.8
30 00
1608. 1
39 00
1443.8
48 00
1243.8
10
5.4
"10
40.4
10
39.8
20
2.7
20
37.0
20
35.8
30
0.0
30
33.6
30
31.7
40
1597. 3
40
30.2
40
27.7
50
4.5
50
26.7
50
23.6
31 00
1591. 8
40 00
1423.3
49 00
1219. 6
10
89.0
10
19.8
10
15.5
20
6.2
20
16.3
20
11.4
30
3.4
30
12.8
30
07.3
40
0.6
40
09.3
40
03.2
50
77.8
50
05.8
50
1199.1
32 00
1574. 9
41 00
1402. 3
50 00
1195. 0
10
72.1
10
1398.8
10
90.8
20
69.2
20
95.2
20
86.7
30
6.3
30
91.6
30
82.5
40
3.4
40
88.1
40
78.4
50
0.5
50
84.5
50
74.2
168
A MANUAL OF TOPOGKAPHIC METHODS.
Table XIX, — For projections of maps of large areas — Continued.
[Extracted from Appendix No. 6, V. S. Coast and Geodetic Survey Keport for 1884.]
COORDINATES OF CUBVATUKE.
NATURAL SCALE.-VAI,TIES OF X AND Y IN METERS.
Latitude 24°.
Latitude 25°.
Latitude 26°.
Latitude 27°.
Longi-
tude.
X
T
Longi-
tude.
X
T
Longi-
tude.
X
Y
Longi-
tude.
X
Y
1 00
101, 753
361
1
00
100, 951
372
1
00
100, 118
383
1
00
99, 256
393
2 00
203, 500
1,445
2
00
201, 896
1,489
2
00
200, 231
1,532
2
00
198, 505
1,573
3 00
305,237
3,250
3
00
302, 831
3,351
3
00
300, 332
3,447
3
00
297, 742
3,539
4 00
406, 9d9
5,778
4
00
403, 749
5,957
4
00
400, 416
6,128
4
00
396, 960
6,291
5 00
508, 660
9,028
5
00
504, 645
9,307
5
00
500, 476
9,574
5
00
496, 154
9,829
6 00
610, 336
13, 001
6
00
605, 514
13,401
6
00
600, 506
13, 786
6
00
595, 316
14, 154 :
7 00
711,981
17, 695
7
00
706, 349
18, 239
7
00
700, 501
18, 763
7
00
694, 440
19, 204
8 00
313,590
23, 109
8
00
807, 146
23, 821
8
00
800,456
24, 505
8
00
793, 522
25, 159
9 00
915, 159
29, 245
9
00
907, 899
30, 146
9
00
900, 364
31, Oil
9
00
892, 554
31, 839
10 00
J, 016, 681
36, 102
10
00
1, 008, 603
37, 215
10
00
1, 000, 218
38, 282
10
00
991, 529
39, 303
11 00
1, 118, 152
43, 679
11
00
1, 109, 252
45, 026
11
00
1, 100, 015
46, 316
11
00
1, 090, 442
47, 551
12 00
1, 219, 566
51,977
00
1, 209, 841
53, 578
12
00
1, 199, 747
55, 114
12
00
1, 189, 287
56, 583
13 00
1,320,919
60, 994
13
00
I, 310, 364
62, 873
13
00
1, 299, 409
64, 675
13
00
1, 288, 1157
66, 398
14 00
1, 422, 205
70, 731
14
00
1, 410, 815
72, 909
14
00
1, 398, 994
74, 998
14
00
1, 386, 746
76, 995
15 00
1, 523, 420
81, 186
15
00
1, 511, 190
83, 685
15
00
1,498,498
86, 082
15
00
1, 485, 348
88, 374
16 00
1, 624, 558
92, 360
16
00
1, 611, 483
95, 202
16
00
1, 597, 914
97, 928
16
00
1, 583, 857
100, 534
17 00
1, 725, 614
104, 251
'17
00
1, 711, 688
107, 458
17
00
1, 697, 237
110, 534
17
00
1, 682, 267
113, 474
18 00
1, 826, 583
116, 859
18
00
1, 811, 800
120, 453
18
00
1, 796, 460
123, 899
18
00
1,780,570
127, 193
19 00
1, 927, 460
130, 184
19
00
1, 911, 813
134, 186
19
00
1, 895, 578
138, 023
19
00
1, 878, 762
141,690
20 00
2, 028, 240
144, 225
20
00
2, Oil, 722
148, 656
20
00
1, 994, 585
152, 905
20
00
1, 976, 836
156, 966
21 00
2, 128, 918
158, 981
21
00
2, 111. 522
163, 862
21
00
2,093,475
168, 544
21
00
2, 074, 786
173, 018
22 00
2, 229, 488
174, 451
22
00
2. 211, 207
179, 805
22
00
2, 192, 243
184, 939
22
00
2, 172, 606
189. 845
23 00
2, 329, 946
190, 634
23
00
2, 310, 771
196,482
23
00
2, 290, 882
202, 089
23
00
2, 270, 289
207, 447
24 00
2, 430, 287
207, 530
24
00
2,410,210
213, 894
24
00
2, 389, 387
219, 993
24
00
2, 367, 830
225, 823
25 00
2, 530, 505
225, 138
25
00
2, 609, 518
232, 038
25
00
2, 487, 753
238, 650
25
00
2, 465, 222
244, 970
26 00
2, 650, 596
243, 458
26
00
2, 608, 689
250, 914
26
00
2, 585, 973
258, 061
26
00
2, 562, 459
264, 889
27 00
2, 720, 554
262, 487
27
00
2, 707, 718
270, 521
27
00
2, 684, 042
278, 222
27
00
2, 659, 535
285, 677
28 00
2, 830, 374
282, 225
28
00
2. 806, 600
290, 859
28
00
2, 781, 953
299, 132
28
00
2, 756, 445
307, 035
29 00
2, 930, 052
302, 671
29
00
2, 905, 329
311,925
29
00
2, 879, 702
320, 788
29
00
2, 853, 181
329, 259
30 00
3, 029, 582
323, 825
30
00
3, 003, 900
333, 718
30
00
2, 977, 281
343, 197
30
00
2, 949, 739
352, 249
PEOJECTION TABLES.
169
Table XIX. — For projections of maps of large areas — Continued.
[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
COOHDINATES OF CUKVATDEE.
NATURAL SCALE.— VALUES OF X AND Y IN METERS.
Latitude 28
Latitude 29°.
Latitude 30°.
Latitude 31°.
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi.
tude.
X
Y
Longi-
tude.
X
Y
1 00
98, 363
403
1 00
97, 439
412
1
00
96, 487
421
1
00
95, 505
429
2 00
196, 719
1,612
2 00
194, 872
1,649
2
00
192, 967
1,684
2
00
191, 002
1,717
3 00
295, 062
3,627
3 00
292, 291
3,710
3
00
289, 433
3,789
3
00
286, 484
3,863
i 00
393, 385
6,447
4 00
389, 689
6,695
4
00
385, 875
6,735
4
00
381, 943
6,867
5 00
49], 682
10, 073
5 00
487, 059
10, 305
5
00
482. 288
10, 523
5
00
477, 371
10, 729
6 00
589, 945
14, 505
6 00
584, 394
14, 838
6
00
578, 665
15, 153
6
00
572, 760
15,450
7 00
688, 168
19, 741
7 00
681, 687
20, 194
7
00
674, 998
20, 623
7
00
668, 103
21, 027
8 00
786, 347
25, 782
8 00
778, 931
26, 374
8
00
771, 279
26, 934
8
00
763, 392
27,461
9 00
884, 472
32, 627
9 00
876, 120
33, 376
9
00
867, 602
34, 084
9
00
858, 619
34, 751
10 00
982, 537
40, 276
10 00
973, 246
41, 199
10
00
963, 658
43, 074
10
00
953,777
42, 897
11 00
1, 080, 637
48, 728
11 00
1, 070, 302
49, 845
11
00
1, 059, 741
50, 903
11
00
1, 048, 858
51, 898
12 00
1, 178, 464
67, 983
12 00
1, 167, 282
69, 313
12
00
1, 165, 744
60, 570
12
00
1, 143, 854
61, 753
13 00
1, 276, 312
68, 040
13 00
1, 264, 178
69, 601
13
00
1, 251, 668
71, 074
13
00
1, 238, 758
73, 462
14 00
1,374,075
78, 699
14 00
1, 360, 983
80.706
14
00
1, 347, 477
82,415
14
00
1, 333, 561
84, 024
15 00
1, 471, 745
90, 558
15 00
1,457,691
9% 631
15
00
1, 443, 193
94, 591
15
00
1, 428, 267
96, 437
16 00
1, 569, 315
103,017
16 00
1, 554, 296
105, 375
16
00
1, 638, 800
107, 603
16
00
1, 522, 837
109, 701
17 00
1, 666, 781
116, 276
17 00
1, 650, 787
118, 935
17
00
1, 634, 290
121, 449
17
00
1, 617, 294
133, 815
18 00
1, 764, 135
130, 331
18 00
1, 747, 161
133,311
18
00
1, 729, 654
136, 127
18
00
1, 711, 621
138, 777
19 00
1, 861, 371
145, 185
19 00
1, 843, 410
148, 502
19
00
1, 824, 887
151, 637
19
00
1,805,810
1.54, 586
20 00
1,958,481
160, 835
20 00
1, 939, 527
164, 506
20
00
1, 919, 983
167, 977
20
00
1,899,853
171, 241
21 00
2, 055, 460
177, 280
21 00
2,035,605
181, 324
21
00
2,014,930
185, 147
21
00
1,993,740
188, 741
22 00
2,152,302
194, 518
22 00
2, 131, 338
198, 953
22
00
2, 109, 725
203, 143
22
00
2, 087, 468
307, 086
23 00
2, 248, 998
212,550
33 00
2, 227, 020
217, 392
23
00
3, 204, 359
231, 966
23
00
3, 181, 027
336, 370
24 00
2, 345, 544
231, 374
24 00
2, 322, 539
236, 640
24
00
2, 298, 825
241, 616
24
00
3, 274, 411
246, 295
25 00
2,441,932
260, 988
25 00
2,417,893
256, 695
25
00
2, 393, 116
263, 089
25
00
2, 367, 610
267, 159
26 00
2, 538, 156
271, 391
26 00
2, 513, 074
277, 568
26
00
2, 487, 224
383, 383
26
00
2, 460, 618
288, 860
27 00
2, 634, 210
292, 582
27 00
2, 608, 075
299. 224
27
00
2,581,144
305, 498
27
00
2, 653, 427
311, 396
28 m
2, 730, 087
314, 559
28 00
2, 702, 890
321, 694
28
00
3, 674, 867
328, 432
28
00
3, 646, 029
334, 765
29 00
2, 825, 779
337, 321
29 00
2, 797, 511
344, 964
29
00
2, 768, 385
353, 183
29
00
2,738,418
358,966
30 00
2, 921, 284
360, 866
30 00
2,891,931
369, 036
30
00
2, 861, 694
376, 749
30
00
2,830,585
383, 997
170
A MANUAL OF TOPOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas — Continued.
[Extracteil from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
COORDINATES OF CURVATURE.
N-ATXJEAL SCALE.— VALUES OE X AND Y IN "METEES.
Latitude 32°.
Latitude 33°.
Latitude 34°.
Latitude 35°.
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi-
tude.
X
Y
1 00
94, 494
437
1
00
93, 454
444
1
00
92, 385
451
1
00
91, 289
457
2 00
188, 980
1,748
2
00
186, 899
1,777
2
00
184, 762
1,803
2
00
182, 568
1, 828
3 00
283, 449
3,933
3
00
280, 328
3, 997
3
00
277, 121
4,057
3
00
273, 830
4,112
4. 00
377, 894
6,991
4
00
373, 731
7,106
4
00
369, 454
7,212
4
00
365, 064
7,310
5 00
472, 307
10, 922
5
00
467, 100
11, 102
5
00
461,751
11,268
5
00
456,261
11, 421
6 00
566. 680
15, 727
6
00
560, 428
15, 986
6
00
554, 004
16, 225
6
00
547, 412
16,445
7 00
661, 004
21, 404
7
00
653,704
21,757
7
00
646, 205
22, 082
7
00
638, 509
22, 381
8 00
755, 272
27,954
8
00
746, 922
28, 414
8
00
738, 344
28, 839
8
00
729, 542
29,229
9 00
849,475
35, 375
9
00
840, 072
35, 957
9
00
830, 413
36, 494
9
00
820, 501
36, 987
10 00
943, 605
43, 667
10
00
1,933,146
44,385
10
00
922,403
45, 048
10
00
911, 379
45, 656
11 00-
1, 037, 655
52, 829
U
00
1, 026, 136
53, 697
11
00
1, 014, 305
54, 499
11
00
1, 002, 165
55, 234
.12 00
1,131,616
62, 861
12
00
1.119,033
63, 893
12
00
1, 106, 110
64, 846
12
00
1, 092, 850
65, 721
13 00
1, 225, 480
73, 761
13
00
1, 211. 829
74, 971
13
00
1, 197, 809
76, 089
13
00
1, 183, 426
77, 115
14 00
1,319,239
85, 529
14
00
1, 304, 515
86, 931
14
00
1, 289, 395
88,227
14
00
1,273,834
89, 415
15 00
1,412,885
98, 164
15
00
1,397,083
99, 771
15
00
1, 380, 858
101,258
15
00
1, 364, 214
102, 619
16 00
1,506,411
111, 664
: 16
00
1,489,526
113,491
16
00
1, 472. 190
115, 180
16
00
1,454,407
116, 728
17 00
1, 599, 808
126, 029
1 17
00
1, 581, 834
128, 089
17
00
1, 563, 381
129, 993
17
00
1, 544, 454
131, 738
18 00
1,693,067
141, 256
18
00
1, 673, 998
143, 564
18
00
1, 654, 423
145, 696
18
00
1,634,347
147, 650
19 00
1, 786, 182
157, 346
19
00
1,766,011
159, 914
19
00
1,745,308
162, 287
19
00
1,724,076
164,460
20 00
1, 879, 144
174, 296
20
00
1,857,866
177, 138
20
00
1, 836, 026
179,703
20
00
1, 813, 632
182, 168
21 00
1,971,946
192, 105
21
00
1,949,553
195, 234
21
00
1, 926, 569
198, 124
21
00
1,903,006
200, 772
22 00
2, 064, 579
210, 772
22
00
2,041,062
214, 201
! 22
00
2, 016, 929
217, 368
22
00
1, 992, 190
220, 268
23 00
2, 157. 035
230,295-
23
00
2, 132, 387 1 234, 037
23
00
2, 107, 097
237, 493
23
00
2, 081, 174
240, 657
24 00
2, 249, 305
250. 672
24
00
2,223,521 254,740
24
00
2, 197, 065
258, 497
24
00
2, 169, 949
261, 936
25 00
2, 341, 385
271,901
25
00
2, 314, 453
276, 309
!25
00
2, 286 823
280, 378
25
00
2, 258, 507
284, 102
26 00
2,433,264
293, 981
26
00
2,405,175
298, 741
26
00
2, 376, 363
303, 134
26
00
2. 346, 838
307, 154
27 00
2,524,935
316, 910
00
2. 495, 080
322, 034
27
00
2, 465, 677
326, 763
27
00
2,434,934
331, 089
28 00
2, 616, 390
340, 686
28
00
2, 585, 961
346. 187
28
00
2, 554, 756
351, 262
28
00
2, 522, 787
355, 905
29 00
2, 707, 621
. 365, 307
29
00
2, 676, 007
371, 197
29
00
2, 643, 591
376, 629
29
00
2,610,386
381, 598
30 00
2, 798, 621
390, 770
30
00
2, 765, 812
397,061
30
00
2, 732, 175
402, 863
30
00
2, 697, 724
408, 168
PEOJECTION TABLES.
171
Table XIX. — For projections of maps of large areas — Continued.
[Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884.]
COORDINATES OP CUEVATUEE.
NATUKAL SCALE
.—VALUES OF X AND T METEPS.
Latitude 36
".
Latitude 37°.
Latitude 38=.
Latitude 39°. ■
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi-
tude.
X
Y
1 00
90, 164
462
1
00
89,012
467
1
00
87, 833
472
°
1
00
86, 627
476
2 00
180, 319
1,850
2
00
178, 015
1,870
2
00
175, 656
1,888
2
00
173, 243
1,903
3 00
270,455
4,162
3
00
266, 997
4,207
3
00
263, 458
4,247
3
00
259, 839
4,281
4, OO
360, 562
7,399
4
00
355, 951
7,479
4
00
351, 230
7,549
4
00
346, 403
7,611
5 00
450, 631
11, 560
5
00
444,865
11,685
5
00
438, 962
11, 795
5
00
432, 925
11, 891
6 00
540, 653
16, 645
6
00
533, 730
16,824
6
00
526, 643
16, 983
6
00
519, 396
- 17, 121
7 00
630, 618
22, 652
7
00
622, 536
22, 896
7
00
614, 263
23, 112
7
00
605, 803
23, 300
8 00
720,517
29,583
8
00
711, 273
29, 901
8
00
701, 812
30, 183
8
00
692. 138
30,428
9 00
810,340
37,435
9
00
799,932
37,838
9
00
789, 280
38, 195
9
00
778, 388
38, 504
10 00
900. 078
46, 209
10
00
888, 503
46, 706
10
00
876, 657
47, 145
10
00
864,545
47, 527
11 00
989, 720
55,903
11
00
976, 975
56, 503
11
00
963, 933
57, 034
11
00
950, 598
57, 496
13 00
1, 079, 259
66, 515
12
00
1, 065, 34Q
67, 229
12
00
1, 051, 098
67, 860
12
00
1, 036, 536
68, 409
13 00
1, 168, 684
78, 046
13
00
1, 153, 587
78, 882
13
00
1, 138. 141
79, 622
13
00
1, 122, 349
80, 266
U 00
1, 257, 987
90, 494
14
00
1, 241, 707
91, 462
14
00
1.225,053
92,319
14
00
1, 208, 027
93, 064
15 00
1, 347, 156
103, 856
15
00
1, 329, 690
104, 967
15
00
1, 311, 823
105, 949
15
00
1, 293, 559
106,802 1
16 00
1, 436, 184
118, 133
16
00
1, 417, 526
119, 395
16
00
1, 398, 441
120, 511
16
00
1. 378, 934
121, 479 1
17 00
1, 525, 061
133, 323
17
00
1, 505, 206
134,745
17
00
1,484,899
136, 002
17
00
1, 464, 144
137,093 '
18 00
1, 613, 777
149, 423
18
00
1,592,721
151, 015
18
00
1, 571, 183
152, 421
18
00
1, 549, 177
153,642
19 00
1, 702, 324
166, 433
19
00
1, 680, 059
168, 203
19
00
1, 657, 289
169, 767
19
00
1, 634, 023
171,124
20 00
1,790,691
184, 3.50
20
00
1, 767, 211
186, 307
20
00
1, 743, 202
188, 037
20
00
1, 718, 671
189,537
21 00
1, 878, 870
203, 173
21'
00
1, 854, 169
205, 326
21
00
1, 828. 914
207, 229
21
00
1, 803, 113
208,878
22 00
1, 966, 851
222, 899
22
00
1, 940, 922
225, 258
22
00
1, 914, 415
227, 341
22
00
1, 887, 337
229, 146
23 00
2, 054, 625
243,527
23
00
2,027,462
246, 099
23
00
1, 999, 694
248,370
23
00
1, 971, 333
250,337
24 00
2, 142, 183
265, 055
24
00
2, 113, 777
267, 849
24
00
2, 084, 743
270, 315
24
00
2, 055, 091
272, 450
25 00
2, 229, 516
287, 479
25
00
2, 199, 860
290, 503
25
00
2,169,551
293, 172
25
00
2, 138, 602
295, 481
26 00
2, 316, 613
310, 798
26
00
2, 285, 699
314, 061
26
00
2, 254, 109
316, 939
26
00
2,221,854
319. 429
27 00
2.403,467
335, 009
27
00
2, 371, 287
338, 519
27
00
2, 338, 406
341, 613
27
00
2, 304, 838
344, 289
28 00
2,490,068
360. Ill
26
00
2, 456. 6l2
363, 874
28
00
2, 422, 433
367, 192
28
00
2, 387, 545
370, 059
29 00
2, 576, 407
386, 099
29
00
2, 541, 667
390, 125
29
00
2, 506, 181
393, 672
29
00
2, 469, 963
396, 736
30 00
2, 662, 475
412, 971
30
00
2, 626, 441
417, 267
30
00
2, 589, 639
421, 050
30
00
2, 552, 084
424, 317
172
A MANUAL OF TOPOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas — Continued.
[Extracted from Appendix No. 6. V. S. Coast and Geodetic Survey Report for 1884.]
COOEDINATES OP CnEVATUEE.
NATURAL SCALE.-
VALUES OF X AND T IN METERS,
Latitude 40
".
Latitude 41°.
Latitude 42°.
Latitude 43
"■
Longi-
tude.
X
T
Longi-
tude.
s
T
Longi-
tude.
X
T
Longi-
tude.
X
Y
1 00
85, 394
479
1
00
84, 136
482
1
00
82, 851
484
1
00
81, 541
485
2 00
170, 778
1,916
2
00
168, 260
1,927
2
00
165, 691
1,935
2
00
163, 071
1,941
3 00
256, 140
4,311
3
00
252, 363
4,335
3
00
248, 508
4,354
3
00
244, 578
4,367
4 00
, 341,470
7,663
4
00
336, 432
7,706
4
00
331, 292
7,739
4
00
326, 050
7,763
5 00
426, 757
11, 972
5
00
420,457
12, 039
5
00
414, 030
12, 092
5
00
407, 476
12, 129
6 00
511, 990
17, 238
6
00
504, 428
17, 335
6
00
496, 712
17,410
6
00
488, 844
17, 464
7 00
597, 158
23,400
7
00
588, 332
23, 591
7
00
679, 325
23, 693
7
00
570, 143
23,766
8 00
682, 252
30, 637
8
00
672, 159
30, 807
8
00
661, 861
30,941
8
00
651, 361
31, 036
9 00
767,260
38, 768
9
00
755,897
38, 983
9
00
744, 305
39, 152
9
00
732, 486
39, 272
10 00
852, 171
47, 852
10
00
- 839,537
48, 118
10
00
826, 648
48, 325
10
00
813, 508
48. 474
11 00
936, 975
57, 888
11
00
923, 067
58, 209
11
00
908. 879
58,459
11
00
894, 415
58, 639
12 00
1,021,661
68, 875
12
00
1,006,475
69, 256
12
00
.990,985
69, 553
12
00
975, 195
69, 766
13 00
1, 106, 218
80,611
13
00
1, 089, 752
81, 258
13
00
1, 072, 956
81, 605
13
00
1, 055, 837
81,854
14 00
1,190,636
93, 695
14
00
1, 172, 886
94, 212
14
00
1, 154, 781
94, 614
14
00
1, 136, 329
94,901
15 00
1, 274, 904
107, 525
15
00
1,255,866
108, 117
15
00
1,236,449
108, 577
15
00
1, 216, 661
108, 905
16 00
1, 359. 012
122, 300
16
00
1,338,681
122, 971
16
00
1, 317, 948
123,493
16
00
1, 296, 820
123, 864
17 00
1, 442, 949
138, 017
17
00
1, 421, 321
138, 773
17
00
1, 899, 267
139, 360
17
00
1, 376, 795
139, 777
18 00
1, 526, 704
154, 675
18
00
1, 503, 775
155, 520
18
00
1, 480, 395
156, 175
18
00
1, 456, 575
156, 640
19 00
1, 610, 267
172, 272
19
00
1, 586, 031
173, 210
19
00
1, 561, 321
173, 937
19
00
1, 536, 148
174,451
20 00
1, 693. 623
190, 805
20
00
1, 608, 079
191. 841
20
00
1, 642, 035
192, 642
20
00
1, 615, 505
193, 209
21 00
1, 776, 775
210, 272
21
00
1, 749. 909
211, 409
21
00
1, 722, 524
212, 289
21
00
1, 694, 632
212, 909
22 00
1. 8S0, 698
230, 671
2'^
00
1,831,509
231, 914
22
00
1,802,779
232. 874
22
00
1, 773, 519
233, 551
23 00
1, 942, 387
251,998
23
00
1, 912, 869
253, 352
23
00
1, 882, 788
254, 396
23
00
1, 852, 135
255,129
24 00
2, 024, 833
274, 252
24
00
1, 993, 978
275, 719
24
00
1, 962, 540
276, 850
24
00
1, 930, 528
277, 642
23 00
2, 107, 023
297. 430
25
00
2, 074, 826
299, 014
25
00
2, 042, 024
300, 234
25
00
2, 008, 628
301, 087
26 00
2. 188, 948
321, 528
26
00
2,1.55,402
323, 233
26
00
2,121 230
324, 544
26
00
2, 086, 443
325, 459
27 00
2, 270, 597
346, 543
27
00
2, 235, 695
348, 374
27
00
2, 200, 146
349, 778
27
00
2, 163, 963
350, 750
28 00
2, 351, 961
372, 473
28
00
2, 315, 695
374, 432
28
00
2, 278, 762
375, 932
28
00
2, 241, 176
376, 974
29 00
2,433,029
399, 314
29
00
2, 395, 392
401, 404
29
00
2, 357, 067
403, 002
29
00
2, 318, 071
404, 109
30 00
2,513,790
427, 063
30
00
2,474,774
429, 287
30
00
2, 435, 052
430, 985
30
00
2, 394, 639
432, 157
PEOJBCTION TABLES.
173
Table XIX.- — For projections of maps of large areas — Continued.
[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Eeport for 1884.]
COORDINATES OP CURVATURE.
NATURAL SCALE.-
-VALUES OF X AND Y TS METERS.
Latitude 44°.
Latitude 45°.
L.atitude 46°.
Latitude 47°. 1
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Longi-
tude.
X
Y
Lo
tu
1
agi-
de.
X
Y
1 00
80, 206
486
1
00
78, 847
486
1
00
77,464
486
00
76, 056
485
2 00
160, 401
1,945
2
00
157, 682
1,946
2
00
154,915
1,945
2
00
152, 100
1,942
3 00
240, 572
4,375
3
00
236, 493
4,378
3
00
232, 342
4,376
3
00
228, 119
4,368
4 00
320, 708
7,778
4
00
315, 269
7,783
4
00
309, 732
7,779
4
00
304, 101
7,765
5 00
400, 797
12, 152
5
00
393, 996
12, 160
5
00
387, 074
12, 153
5
00
380, 034
13,131
6 00
480, 82'
17,496
6
00
472, 663
17, 508
6
00
464, 354
17, 498
6
00
455, 904
17, 467
7 00
560, 786
23, 811
7
00
551, 258
23, 826
7
00
541, 562
23,813
7
00
531, 700
23, 770
8 00
640, 062
31,094
8
00
629, 769
31, 114
8
00
618,684
31, 096
8
00
607, 410
31, 040
9 00
720,445
39, 345
9
00
708, 184
39, 370
9
00
695, 708
39, 347
9
00
683, 020
39, 276
10 00
800, 122
48, 563
10
00
786,492
48, 594
10
00
772, 623
48,565
10
00
758, 520
48,477
11 00
879, 681
58, 746
11
00
864, 679
58, 782
11
00
849, 416
58, 747
11
00
833, 895
58, 640
12 00
959, 110
69, 893
12
00
942, 735
69, 936
12
00
926, 075
69, 893
12
00
909, 135
69, 765
13 OO
1, 038, 399
82, 002
13
00
1, 020, 647
82, 051
13
00
1,002,588
82, 000
13
00
984, 227
81, 849
14 00
1, 117, 535
95, 072
14
00
1,098,404
95, 127
14
00
1, 078, 943
95, 067
14
00
1,059,158
94, 890
15 00
1, 196, 507
109,100
15
00
1, 175, 994
109, 162
15
00
1, 155, 128
109, 091
15
00
1, 133, 917
108, 887
16 00
1, 275, 303
124, 084
16
00
1, 253, 404
124, 153
16
00
1, 231, 131
124, 071
16
00
1, 208, 491
123,837
17 00
1, 353, 911
140, 023
17
00
1,330,634
140, 099
17
00
1,306,940
140, 003
17
00
1, 282, 868
139, 738
18 00
1, 432, 320
156,913
18
00
1,407,640
156, 996
18
00
1, 382, 543
156, 887
18
00
1, 357, 036
156, 587
19 00
1, 510, 519
174, 753
19
00
1, 434, 443
174, 842
19
00
1,457,928
174, 718
19
00
1, 430, 984
174, 381
20 00
1, 588, 496
193, 540
20
00
1, 561, 019
193, 635
20
00
1,533,083
193, 494
20
00
1, 504, 697
193, 118
21 00
1, 666, 240
213,270
21
00
1, 637, 358
213, .371
21
00
1, 607, 997
213, 212
21
00
1, 578, 166
212, 793
22 00
1, 743, 738
233, 942
22
00
1, 713, 447
234, 048
22
00
1.682,657
233, 869
22
00
1, 651, 377
233, 405
23 00
1,820,980
255, 552
23
00
1, 789, 276
255, 663
23
00
1, 757, 052
255, 462
23
00
1, 724, 320
254, 950
24 00
1, 897, 955
278, 096
24
00
1, 864, 831
278, 211
24
00
1, 831, 170
277, 987
24
00
1, 796, 982
277, 425
25 00
1, 974, 650
301, 572
25
00
1, 940, 103
301, 690
25
•00
1, 904, 999
301, 441
25
00
1, 869, 3.51
300, 824
26 00
2, 051, 055
325, 977
26
00
2, 015, 079
326, 097
26
00
1, 978, 528
325, 820
26
00
1,941,415
325, 146
27 00
2, 127, 159
351, 306
27
00
2, 089, 749
351, 427
27
00
2, 051, 745
351, 120
27
OO
2, 013, 163
350, 386
28 00
2, 202, 950
377, 555
28
00
2, 164, 100
377, 676
28
00
2, 124, 639
377, 337
38
00
2, 084, 583
376, 539
29 00
2, 278, 417
404, 722
29
00
2, 238, 121
404, 841
29
00
2, 197, 197
404, 468
29
00
2, 155, 663
403, 602
30 00
2, 353, 550
432, 801
30
00
2, 311, 802
432, 918
30
00
2, 269, 410
432, 507
30
00
2,226,392
431, 569
174
A MAXUAL OF TOrOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas-^Continned.
[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Keport for 1884.]
COORDINATES OF CnEVATUEK.
NATURAL SCALE.- VALUES OF X AND T IN METERS.
Latitude 48°.
Latitude 49°.
Latitude 50°.
Longi-
tude.
x
y
Longi-
tude.
X
Y '
Longi-
tude.
X
Y
1 00
74, 626
484
1
00
73, 172
482
1
00
71, 696
479
2 00
149. 239
1,936
2
00
146, 331
1,928
2
00
143, 379
1,917
3 00
223, 827
4,355
3
00
219, 465
4,337
3
00
215, 037
4.313
4 00
298, 377
7.742
4
00
292,561
7,709
4
00
286, 656
7,667
5 00
372,877
12, 095
5
00
365, 606
12,044
5
00
358, 224
11, 978
6 00
447, 314
17,414
6
00
438, 588
17. 340
6
00
429, 727
17,246
7 GO
521, 677
23, 698
7
00
511,493
23, 598
7
00
501, 154
23, 469
8 00
595, 951
30, 946
8
00
584, 310
30, 815
8
00
572, 492
30,646
9 00
670, 125
39, 157
9
00
657, 026
38, 991
9
00
643, 727
38, 777
10 00
744, 186
48, 329
10
00
729, 627
48, 123
10
00
714, 847
47, 859
11 OD
. 818, 123
58, 461
11
00
802, 102
58, 212
11
00
785, 839
57, 891
12 00
891, 921
69, 552
12
00
874, 438
69, 254
12
00
856, 691
68,872
13 00
965, 570
81. 598
13
00
946, 622
81, 248
13
00
927, 389
80, 798
14 00
1,039,056
94, 598
14
00
1,018,642
94, 191
14
00
997, 922
93, 669
15 00
1,112,367
108, 551
15
00
1, 090, 485
108, 082
15
00
1, 068, 277 ■
107, 482
16 00
1, 185, 491
123, 453
16
00
1, 162, 138
122, 918
16
00
1, 138, 440
122, 234
17 00
1,258,416
139, 302
17
00
1, 233, 591
138, 697
17
00
1,208,400
137, 923
18 00
1, 331, 129
156, 096
18
00
1, 304, 829
155, 416
18
00
1, 278, 144
154, 546
19 00
1, 403, 618
173, 832
19
00
1,375,840
173, 071
19
00
1, 347, 660
172, 099
20 00
1, 475, 871
192, 506
20
00
1, 446, 613
191, 660
20
00
1, 416, 934
190, 581
21 00
1, 547, 876
212, 116
21
00
1, 517, 135
211, 180
21
00
1, 485, 956
209, 987
22 00
1, 619, 620
232, 658
22
00
1, 587, 394
231, 627
22
00
1, 554, 711
230, 314
23 00
1, 691, 091
254, 128
23
00
1, 657, 378
252,998
23
00
1, 623, 189
251, 559
24 00
1, 762, 279
276, 524
24
00
1,727,073
275, 288
24
00
1, 691, 377
273, 717
25 00
1,833,170
299, 842
25
00
1, 796, 470
298, 495
25
00
1,759,262
296, 785
26 00
1,903,752
324, 077
26
00
1, 865, 554
322, 614
26
00
1, 826, 833
320, 758
27 00
1, 974. 015
349, 225
27
00
1, 934, 315
347, 640
27
00
1,894,077
345, 633
28 00
2, 043, 945
375, 283
28
00
2, 002, 740
373, 570
28
00
1, 960, 983
371,404
29 00
2, 113, 531
402, 245
29
00
2, 070, 817
400, 399
29
00
2, 027, 538
398, 068
30 00
2, 182, 762
430, 107
30
00
2, 138, 536
428, 123
30
00
2, 093, 731
425, 619
PROJECTION TABLES.
175
Table XX. — Cooi-dinates for projection of maps. Scale ^j-ooos-
[Prepared by R. S. Woodward.]
a "
Coordinates of developed parallel for —
Inches.
'"4.36i'
8. 723
13. 083
17. 444
4.362
8. 723
13. 085
4.362
■ 8. 724
13. 087
4.363
8.726
13. 088
13. 091
17.454
4.364
8.728
13. 092
4. 365
8.730
13. 095
4.367
8.734
13.101
4.368
8.735
13. 103
3.750
3.740
3.730
3.679
3.669
3.583
3.572
3.561
.004
.004
longitude. 45' longitude. 1° longitude,
.004
.004
.004
.004
.004
7.949
7.933
7.916
7.900
7.798
7.780
7.763
7.727
7.709
7.691
7.673
7.654
7.578
7.559
7.540
7.520
7.500
7.420
7.400
7.379
7.253
7.231
7.210
7.166
7.144
7.122
.017
.017
.017
.018
.018
.018
.018
.018
Inches.
11.923
11.899
11. 874
11.850
11. 825
11. 697
11.671
11.644
11. 591
11. 563
11. 536
11.481
11. 453
11.425
11. 367
11. 338
11. 309
11.250
11. 221
11. 191
11. 130
11. 100
11.069
11. 007
10. 975
10. 943
10. 879
10. 847
10. 815
10. 749
10. 716
10. 683
.040
.040
Inches.
15. 898
15. 865
15. 832
15. 800
15.707
15. 733
15. 699
15. 665
15. 596
15. 561
15. 526
15. 454
15.418
15. 382
15. 156
15. 118
15. 079
15. 001
14. 961
14. 921
14. 840
14. 799
14. 758
14. 676
14. 633
14. 591
14. 506
14. 463
14. 420
14. 332
14. 288
14.244
4.369
8.738
13. 108
3.539
3.527
3.516
7.077
7.054
7.032
6.986
6.963
6.939
10. 616
10. 582
10. 547
10. 479
10.444
10. 409
.041
.041
.041
.041
14. 154
14. 109
14. 063
13. 972
13. 925
13. 879
176
A MANUAL OF TOPOGEAPHIC METHODS.
Table XS. — Coordiiiates for projection of maps. Scale ■
[Prepared by E. S. Woodward.]
ft
Coordinates of developed parallel for—
1
15' longitude.
30' longitude.
45' longitude.
lo longitude.
X
y
s
y
-
y
X
y
38 00
15
30
45
Inches.
17. 477
Inches.
3.458
3.446
3.434
3.422
Inches.
.005
.005
.005
.005
iTiches.
6.916
6.892
6.809
6.845
Inches.
.019
.019
.019
.019
Inches.
10. 374
10. 339
10. 303
10.267
Inches.
.042
.042
.042
.042
Inches.
13. 832
13.785
13. 737
13. 690
Inches.
.074
.074
.075
.075
4.370
8.740
13. 110
39 00
15
30
45
17. 480
3.411
3.398
3.386
3.374
.005
.005
.005
.005
6.821
6.797
6.773
6.748
.019
.019
.019
.019
10.232
10. 195
10. 159
10. 123
.042
.042
.042
.042
13.642
13. 594
13.545
13.497
.075
.075
.075
.075
4.371
8.741
13. 112
40 00
15
30
45
17.483
3.362
3.350
3.337
3. 325
.005
.005
.005
.005
6.724
6.699
6.675
6.650
.019
.019
.019
.019
10. 086
10.049
10. 012
9.975
.042
.042
.043
.043
13.448
13.399
13. 349
13. 300
.075
.075
.076
.076
4.371
8.743
13. 114
41 00
17. 486
3.312
.005
6.625
.019
9.937
.043
13. 250
.076
15
30
45
4.372
8.744
13. 117
3.300
3.287
3.275
.005
.005
.005
6.600
6.575
6.549
.019
.019
.019
9.900
9.862
9.824
.043
.043
.043
13. 200
13.149
13. 098_
.076
.076
.076
42 00
15
30
45
17.489
3.262
3.249
3.236
3.223
.005
.005
.005
.005
6.524
6.498
6.472
6.447
.019
.019
.019
.019
9.786
9.747
9.709
9.670
.043
.043
.043
.043
13.048
12. 996
12. 945
12. 893
.076
.076
.076
.076
4.373
8.746
13. 119
43 00
15
30
45
17. 492
3.210
3.197
3.184
3.170
.005
.005
.005
.005
6.421
6.394
6.368
6.342
.019
.019
.019
.019
9.631
9.592
9.552
9.513
.043
.043
.043
.043
12.842
12. 789
12. 736
12.684
.076
.076
.076
.076
4.374
8.747
13. 121
44 00
15
30
45
17.495
3.158
3.144
3.131
3.118
.005
.005
.005
.005
6.316
6.289
6.262
6.235
.019
.019
.019
.019
9.473
9.433
9.393
9.353
.043
.043
.043
.043
12.631
12.578
12.524
12.471
.077
.077
.077
.077
4.375
8.749
13. 124
45 00
15
30
45
17. 498
3.104
3.091
3.077
3.063
.005
.005
.005
.005
6.209
6.181
6.154
6.127
.019
.019
.019
.019
9.313
9.272
9.231
9.190
.043
.043
.043
.043
12.417
12.363
12. 308
12.254
.077
.077
.077
.077
4.375
8.751
13. 126
46 00
15
30
45
17. 501
3.050
3.036
3.022
3.008
.005
.005
.005
.005
6.100
6.072
6. 044
6.017
.019
.019
.019
.019
9.150
9.108
9.067
9.025
.043
.04a
.043
.043
12.200
12.144
12. 089
12. 033
.077
.077
.077
.077
4.376
8.752
13. 128
47 00
15
30
45
17. 504
2.994
2.980
2.966
2.962
.005
.005
.005
.005
5.989 *
5.961
5.933
5.904
.019
.019
.019
.019
8.983
8.941
8.899
8.857
.043
.043
.043
.043
11. 978
11.922
11.865
11.809
.076
.076
.076
.076
4.377
8.754
13. 131
f48 00
15
30
45
17.508
2.938
2.924
2.909
2.895
.005
.005
.005
.005
5.876-
5.848
5.819
5.790
.019
.019
.019
.019
8.814
8.771
8.728
8.686
.043
.043
.043
.043
11. 752
11.695
11. 638
11. 581
.076
.076
.076
.076
4.378
8.755
13. 133
^49 00
15
30
45
17. 511
2.881
2.866
2.852
2.837
.005
.005
.005
.005
5.762
5.733
5.704
5.675
.019
.019
.019
.019
8.643
8. 599
8.555
8.512
.043
.043
.043
.042
11.524
11.465
11.407
11.349
.076
.076
.076
.076
4.378
8.757
13. 135
50 00
17.514
2.823
.005
5.646
.019
8.468
.042
11.291
.076
PEOJEOTION TABLES.
177
Table XXI. — Coordinates for projection of maps. Scale ti^outt-
[Prepared by E. S. Woodward.]
Abscissas of developed parallel.
25' longi- 30' long!
tude. tude.
Ordinates of devel-
oped parallel.
Inches.
"Km
11.629
17.444
23. 259
29. 074
5.816
11. 633
17. 449
23. 265
29. 082
5.817
11. 634
17. 451
23. 268
29. 086
5.818
11. 636
17. 454
23. 272
29. 090
11. 638
17. 457
23. 276
29. 094
11. 640
17. 460
23. 280
29. 100
5.821
11.642
17. 462
23. 283
29, 104
6.822
.1. 643
17. 465
23. 287
29. 109
5.823
11. 645
17.468
23. 291
29. 113
2.642
2. 639
2.635
2.631
2,628
2. 624
2,620
2.616
2,613
2,609
2,605
2.601
2.597
2.593
2.589
2.586
2.582
2,578
2,574
2,570
2.566
2.662
2.558
2.553
2,549
2.545
2.541
2.537
2,533
2,528
2,524
2,520
2.515
2.511
2.507
2.502
2,498
2.480
2.476
2.471
2,467
2,462
2,458
2.453
2,448
2, 444
2,439
2,434
2, 425
2,420
2,415
2.410
2,406
2,401
Inches.
5.299
5,292
5.285
5,278
6,270
5.263
5.256
6.248
6,240
5.233
5,225
5.218
5,210
5.203
5.195
5.187
5.179
5.171
5.163
5.155
5.147
5.139
5.131
5.123
5.065
5,056
5.048
5. 039
5.031
5.022
4.951
4.942
4,933
4.924
4.916
4.821
4.811
4.802
Inches.
7.949
7.938
7.927
7.883
7.872
7.861
7.804
7.792
7.780
7,768
7,757
7.745
7,733
7,721
7,709
7,697
7.685
7.673
7.660
7.648
7.635
7.622
7.610
7.559
7.546
7.533
7,520
7,507
7.494
7.441
7.427
7.413
7,400
7.386
7.373
7,359
7,345
7.331
7,316
7,302
7.274
7.260
7,246
7,231
7.217
7.203
Inches.
10. 699
10, 584
10, 670
10, 555
10. 540
10, 526
10, 511
10, 496
10. 481
10, 466
10, 451
10, 436
10, 421
10, 405
10, 390
10. 37i
10, 368
10. 342
10. 327
10. 311
10. 291
10. 278
10. 262
10. 246
10. 230
10, 213
10. 197
10. 180
10. 163
10. 146
10, 130
10. 113
10, 096
10, 078
10, 061
10, 044
10. 027
10. 009
9,992
9,974
9,774
9.755
9.736
9.718
9.661
9.642
9,622
Indies.
13. 249
13, 231
13, 212
13, 194
13, 176
13. 157
13, 139
13, 120
13, 101
13, 082
13. 063
13. 045
13. 026
13. 006
12, 987
12. 967
12. 947
12. 928
12, 909
12, 889
12, 868
12, 848
12, 828
12. 808
12, 788
12, 767
12. 746
12, 725
12, 704
12. 683
12. 662
12, 641
12, 620
12. 598
12, 577
12. 556
12. 534
12. 512
12. 490
12, 467
12,445
12. 423
12. 401
12. 379
12. 356
12. 333
12. 310
12. 388
12. 265
12. 241
12. 218
12, 194
12. 171
12. 147
12. 124
12, 100
12, 076
12, 052
12, 028
12, 004
Inches.
15, 898
15, 877
15, 854
16. 833
15. 811
16. 788
15. 767
15. 744
16. 721
15. 698
15, 676
15. 664
15. 631
15. 608
15. 584
15, 560
15, 537
15. 514
15. 490
■16. 466
15,442
15, 418
15. 394
15, 369
16, 346
16, 320
15, 295
15. 270
15. 246
15. 220
15. 195
16. 169
15. 143
15. 118
15. 092
15, 066
15, 040
15, 014
14, 987
14. 960
14. 934
14, 908
14. 881
14. 854
14, 827
14. 800
14. 772
14. 745
14. 717
14. 689
14. 661
14. 633
14. 605
14. 575
14. 549
14. 620
14. 491
14. 462
14. 434
14. 405
0.001
.004
.008
-12
178 A MANUAL OF TOPOGEAPHIC METHODS.
Table XXl.— Coordinates of projection of maps. Scale t^sWd — Continued.
[Prepared by K. S. 'Wooilw.ircl.]
|1
i3
§ « i'i
'C ta a S
Abscissas of developed parallel.
Ordinates of devel-
oped parallel.
5' longi-
tude.
0' longi-
tude.
15' longi-
tude.
20' longi-
tude.
^5' longi-
tude.
30' longi-
tude.
35 00
10
20
30
40
50
36 00
10
20
30
40
50
37 "0
10
20
30
40
50
38 00
10
20
30
40
50
39 00
10
20
30
40
50
40 00
10
20
30
40
50
41 00
10
20
1 30
40
50
42 00
10
20
30
40
50
43 00
10
20
30
40
50
Inches.
Inches,
2.396
2.391
2.386
2.3S1
2.377
2.372
2.367
2.362
2.357
2.351
2.346
2. 341
2.336
2.331
2.326
2.321
2.316
2.311
2.305
2.300
2.295
2.290
2.284
2.279
2.274
2.268
2.263
2.258
2.252
2.247
2.241
2.236
2.230
2. 225
2.219
2.214
2.208
2.203
2.197
2.192
2.186
2.180
2.175
2.169
2.163
2.157
2. 152
2.146
2.140
2.135
2.129
2.123
2.117
2.111
I7iches.
4.792
4.782
4.773
4.763
4.753
4.743
4.733
4.723
4.713
4.703
4.693
4.683
4.673
4. 662
4.652
4.642
4.631
4.621
4.611
4.600
4.590
4.579
4.568
4.558
4.548
4.537
4.526
4.515
4.504
4.493
4.483
4.472
4.461
4.450
4.439
4.428
4.417
4.406
4.394
4.383
4.372
4.360
4.349
4.338
4.326
4.315
4.303
4.292
4.281
4.269
4.257
4.246
4.234
4.222
Inches.
7.188
7.174
7.159
7.144
7.130
7.115
7.099
7.085
7.070
7.055
7. 039
7.024
7.009
6.994
6.978
6.963
6.947
6.932
6.916
6.900
6.884
6.869
6.853
6.837
6.821
6.805
6.789
6.773
6.756
6.740
6.724
6.707
6.691
6.674
6.658
6.641
6.625
6.608
6.591
6.575
6.558
6.541
6.524
6.507
6.490
6.472
6.455
6.438
6.421
6.403
6.386
6.363
6.351
6.333
Inches.
9.584
9.565
9.545
9.526
9.506
9.486
9.466
9.446
9. 426
9.406
9.386
9.366
9.345
9.325
9.304
9.284
9.263
9.242
9! 200
9.179
9.158
9.137
9.116
9.095
9,073
9.052
9.030
9.008
8.987
8.965
8. 943
8.921
8.899
8.877
8.855
8.834
8.811
8.788
8.766
8.744
8.721
8.698
8.676
8.653
8.630
8.607
8.584
8.661
8.538
8.514
8.491
8.468
8.444
Inches,
11. 980
11. 956
11. 932
11. 907
11. 883
11. 858
11. 833
11. 808
11. 783
11. 757
11. 732
11. 707
11. 682
11. 656
11.630
11. 605
11. 579
11. 553
11. 527
11.501
11. 474
11. 448
11. 421
11. 395
11. 309
11. 342
11. 315
11. 288
11. 261
11. 234
11.207
11. 179
11. 152
11. 124
11. 097
11.069
11. 042
11.014
10. 985
10. 958
10. 929
10. 901
10. 873
10. 844
10. 816
10. 787
10. 759
10. 730
10. 701
10. 072
10. 643
10. 614
10. 585
10. 556
Inches.
14. 376
14. 347
14. 318
14. 288
14. 259
14. 230
14. 200
14. 170
14. 139
14. 109
14. 078
14.048
14. 018
13. 987
13. 956
13. 925
13. 894
13. 864
13.832
13. 801
13. 769
13. 737
13. 705
13. 673
13. 642
13. 610
13. 577
13. 545
13. 513
13. 480
13.448
13. 415
13. 382-
13. 349
13. 316
13. 283
13. 250
13.217
13. 183
13. 149
13. 115
13. 081
13. 048
13. 013
12. 979
12. 945
12. 910
12. 876
12. 842
12. 807
12. 772
12. 737
12. 701
12. 667
|1
0 a
34°
35°
5. 824
11. 647
17. 471
23.294
. 29.118
5
10
15
20
25
30
Inch.
0.001
.004
.009
.016
.025
.036
Inch.
0.001
.004
.009
.016
.025
.036
5,824
11. 649
17. 473
23. 297
29. 122
36=
37°
5.826
11.651
17.477
23. 302
29. 128
5
10
15
20
25
30
O.OOI
.004
.009
.016
.025
.036
0.001
.004
.009
.016
.026
.037
5.827
U. 653
17. 480
23. 306
29. 133
37° ■
38°
5
10
15
20
25
30
Inch.
0.001
.004
.009
.016
.026
.037
Inch.
0.001
.004
.009
.017
.026
.037
5.828
11. 655
17. 483
23. 310
29. 138
5.829
11. 657
17.486
23. 314
29. 143
39°
40°
6
10
15
20
25
30
0.001
.004
.009
.017
.026
.037
0.001
.004
.009
.017
.026
.038
5.830
11. 659
17. 489
23.319
29. 149
40°
41°
5.831
11. 661
17. 492
23. 323
29.154
5
10
15
20
25
30
Inch.
0.001
.004
.009
.017
.026
.038
Inch.
0.001
.004
.009
.017
.026
.038
5.832
11. 663
17. 495
23. 327
29. 159
42°
43°
5
10
16
20
25
30
0.001
.004
.010
.017
.026
.038
0.001
.004
.010
.017
.027
.038
1
PEOJECTION TABLES.
179
Table XXI. — Coordinates for projection of maps. Scale -
[Prepared by E. S. Woodwaxd.]
-Coutinued.
3
l3
i
Pi
•ggg§
■3
Abscissas of developed parallel.
Ordinatea of devel-
oped parallel.
5' longi-
tude.
10' longi-
tude.
15' longi-
tude.
20' longi-
tude.
25' longi-
tude.
30' longi-
tude.
44
46
47
48
49
60
00
10
20
30
40
50
00
10
20
3Q
40
50
00
10
20
30
40
50
00
10
20
30
40
50
00
10
20
30
40
50
00
10
20
30
40
50
00
Inches.
Inches.
2.105
2.099
2.093
2.087
2.081
2.076
2.070
2.064
2.057
2.051
2.045
2.039
2.033
2.027
2.021
2.015
2.009
2.003
1.996
1.990
1.984
1.978
1.971
1.965
1.959
1.952
1.946
1.940
1.933
1.927
1.921
1.914
1.908
1.901
1.895
1.888
1.882
Inches.
4.210
■ 4.199
4.187
4. 175
4.163
4.151
4.139
4.127
4115
4.103
4.091
4.079
4.067
4.054
4.042
4.030
4.017
4.005
3.992
3.980
3.968
3.955
3.943
3.930
3.917
3.905
8.892
3.879
3.867
3.854
3.841
3.828
3.815
3.803
3.790
3.777
3.764
Inches.
6.316
6.298
6.280
6.262
6.244
6.227
6.209
6.191
6.172
6.154
6.136
6.118
6.100
6.081
6.063
6.044
6.026
6.008
5.989
5. 970
5.951
5.933
5.914
5.895
5.876
5.857
5.838
6.819
5.800
6.781
5.762
5.743
5.723
5.704
5.684
6.665
5.646
Inches.
8.421
8.397
8.373
8.350
8.326
8.302
8.278
8.264
8.230
8.206
8.181
8.157
8.133
8.108
8.084
8.069
8.034
8.010
7.985
7.960
7.935
7.910
7.885
7.860
7.835
7.810
7.784
7.769
7.733
7.708
7.682
7.657
7.631
7.605
7.579
7.563
7.527
Inches.
10. 526
10. 496
10. 467
10. 437
10.407
10. 378
10.343
10. 317
10. 288
10. 257
10. 226
10. 197
10. 166
10. 136
10. 104
10.074
10.043
10. 013
9.981
9.951
9.919
9.888
9.857
9.826
9.794
9.762
9.730
9.699
9.667
9.635
9.603
9.571
9.539
9.507
9.174
9.442
9.409
Inches.
12. 631
12. 596
12. 560
12.524
12.489
12.453
12.417
12.381
12.345
12. 308
12. 272
12. 236
12. 199
12. 163
12. 125
12. 089
12.052
12. 015
11. 978
11. 941
11. 903
11.866
11. 828
11. 791
11. 752
11. 714
11. 677
11. 638
U.600
11. 562
11.523
11.485
11. 446
11. 408
11. 369
11.330
11.291
Mo
(3-
43"
44°
5.833
11.666
17. 498
23.331
29. 164
5
10
15
20
25
30
Inch.
0.001
.004
.010
.017
.027
.038
Inch.
0.001
-.004
.010
.017
.027
.038
5.834
11.668
17. 501
23.335
29. 169
45°
46°
5.835
11.670
17. 504
23. 339
29. 174
5
10
15
20
25
30
0.001
.004
.010
.017
.027
.038
0.001
.004
.010
.017
.027
.038
5. 836
11. 672
17. 508
23.344
29.180
470
48°
5
10
15
20
25
30
0.001
.004
.010
.017
.027
.038
0.001
.004
.010
.017
.026
.038
5.837
11.674
17.511
23.348
29. 185
5.838
11. 676
17. 514
23.352
29. 190
490
50°
5
10
15
20
25
30
0.001
.004
.010
.017
.026
.038
0.001
.004
.009
.017
.026
.038
1
180
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXH.-
-Coordinates for projection of maps. Scale ^j-suxr-
[Prepared by R. S. "Woodward.]
11
Hi
So
llli
3.1 1*
Absci
>sa3 of developed parallel.
Ordinates of devel-
oped parallel.
2J' longi-
tude.
5' loiiffi-
tude.
7J' longi-
tude.
lOMongi-
tude.
12J' lon-
gitude.
15' longi-
tude.
25 00
05
10
15
20
25
30
il
45
50
55
26 00
05
10
15
20
25
30
35
40
45
50
55
27 00
05
10
15
20
25
30
35
40
45
50
55
28 00
05
10
15
20
25
30
35
40
45
50
55
29 00
05
10
15
20
25
30
35
40
45
50
55
30 00
05
10
15
20
25
30
35
40
45
50
55
Inches.
Inches.
2. 650
2.648
2.646
2.644
2.642
2.641
2.639
2.637
2.635
2. 633
2.631
2.630
2.628
2.626
2.624
2.622
2.620
2.618
2.617
2.615
2.613
2.611
2.609
2.607
2.605
2.603
2.601
2.599
2.597
2.595
2.593
2.591
2.590
2.588
2.586
2.584
2.582
2.580
2.578
2.576
2.574
2.572
2.570
2.568
2.566
2.564
2.562
2.360
2.558
2.555
2.553
2.551
2.549
2.547
2.545
2.543
• 2.541
2.539
2.337
2.535
2.533
2.530
2.528
2.526
2.524
2.522
2.520
2.518
2.515
2.513
2.511
2.509
Inches.
5.299
5.296
5.292
5.288
5.285
5.281
5.277
5.274
5.270
5.266
5.263
5.259
5.256
5.252
5.248
5.244
5.241
5.237
5,233
5. 229
5.225
5.222
5.218
5.214
5.210
5.207
5.203
5.399
5.195
5.191
5.187
5.183
5.179
5.175
5.171
5. 167
5.163
5.159
3.155
5.151
5.147
5.143
5.139
5.135
5.131
5.127
5.123
5.119
5.115
5.111
5.107
5.103
5.098
5.094
5.090
5.086
5.082
5.078
5.073
5.069
5.065
5.061
5.057
5.052
5.048
5.044
5.039
5.035
5.031
5.026
5.022
5.018
Inches.
7.949
7.944
7.938
7.933
7.927
7.922
7.916
7.911
7.905
7.900
7.894
7.689
7.883
7.878
7.872
7.866
7.861
7.853
7.849
7.844
7.838
7.833
7.827
7.821
7.816
7.810
7.804
7.798
7.792
7.786
7.780
7.774
7.769
7.763
7.757
7.751
7.745
7.739
7.733
7.727
7.721
7.715
7.709
7.703
7.697
7.691
7.685
7.679
7.673
7.666
7.660
7.654
7.648
7.641
7.635
7.629
7.623
7.616
7.610
. 7. 604
7.598
7.591
7.583
7.578
7.572
7.565
7.359
7.552
7.546
7.540
7.533
7.527
Inches.
10. 399
10. 591
10. 584
10. 577
10. 569
10. 562
10. 553
10.548
10. 540
10. 533
10. 526
10. 518
10.511
10. 504
10. 496
10. 489
10. 481
10. 473
10. 466
10. 458
10.451
10.443
10.436
10. 428
10. 421
10.413
10. 405
10. 397
10. 389
10. 382
10. 374
10. 366
10. 358
10. 330
10. 342
10.333
10. 327
10. 319
10. 311
10. 303
10. 294
10. 286
10. 278
10. 270
10. 262
10. 234
10. 246
10. 238
10. 230
10. 222
10. 213
10. 205
10.197
10. 188
10. 180
10. 172
10.164
10. 133
10. 147
10. 138
10. 130
10. 122
10. 113
10. 104
10. 096
10. 087
10. 079
10. 070
10. 061
10. 053
10.044
10. 036
Inches.
13.248
13. 239
13.230
13. 221
13. 212
13. 203
13. 194
13.184
13. 175
13. 166
13.157
13. 148
13. 139
13. 129
13. 120
13. Ill
13. 101
13. 092
13. 082
13. 073
13.064
13.034
13. 045
13. 035
13. 026
13. 016
13. 006
12. 997
12. 987
12. 077
12. 967
12. 937
12. 948
12. 938
12. 928
12. 918
12. 908
12. 898
12. 888
12. 878
12. 868
12. 858
12. 848
12. 838
12. 828
12. 818
12. 808
12. 798
12. 788
12. 777
12. 767
12. 756
12. 746
12. 735
12. 725
12. 716
12. 704
12. 694
12. 684
12. 673
12. 663
1.2. 652
12. 641
12. 630
12. 620
12. 609
12. 598
12.587
12. 577
12. 566
12. 355
12.544
Inches.
15. 898
15. 887
13. 876
15. 865
15. 854
15. 843
15. 832
15. 821
13. 810
15. 799
15. 788
15. 777
15. 766
15. 755
13.744
15.733
13. 721
15. 710
15. 699
15. 688
15. 676
15. 665
15. 654
15. 642
15. 631
15. 620
15. 608
15. 596
15. 584
15. 572
15. 561
15. 549
15. 537
15. 325
15. 514
15. 502
15. 490
13.478
15. 466
15.454
15. 442
15. 430
15. 418
15. 403
15. 393
15. 381
15. 369
15. 357
15. 345
15. 333
15. 320
15. 308
15. 295
15. 283
15. 270
15. 258
15. 245
15. 233
15. 220
15. 208
15. 195
15. 182
15. 169
15. 157
15. 144
15. 131
15. 118
15. 105
13. 092
15. 079
15. 066
15. 053
25°
26°
5.815
11. 629
. 17. 444
23. 259
29. 074
34. 888
24
5
1?
15
Inch.
0.000
.002
.004
.007
.010
,015
Inch.
0,000
.002
.004
.007
.010
• .015
1
5.816
. 11.631
17.447
23. 262
29. 078
34.893
27°
2*
5'
74
10
12i
15"
Inch.
0.000
.002
.004
.007
.011
.015
5.816
11. 633
17.449
2.3. 265
29. 082
34.898
1
27°
.28°
f
1?
12i
15
Inch.
0.000
.002
.004
,007
.011
.013
Inch.
0.000
.002
.004
.007
.011
,016
5.817
11.634
17. 451
23. 268
29. 085
34. 903
1
29°
f
1?
If
Inch.
0.000
.002
.004
.007
.011
.016
5.818
11. 636
17. 434
23. 272
29. 090
34. 908
1
29°
30°
2*
3
1?
124
15
Inch.
0.000
.002
.004
.007
.011
.016
Inch.
0.000
.002
.004
.007
.012
.017
5.819
11. 638
17. 457
23. 276
29. 095
34.913
PEOJECTION TABLES.
181
Table XXll.—Coardinates for projection of maps. Scale -^ji^, — Continued.
[Prepared by E. S. "Woodward.]
Inches.
'"'s.'sm'
11. 640
17. 460
23. 280
29. 100
34. 919
5.821
11.645!
17.462
23. 283
29. 104
34. 925
5.822
11.643
17. 465
23. 287
29. 109
34. 930
5.823
11. 645
17.468
23. 291
29. 113
34. 936
5.824
11. 647
17. 471
23. 294
29. 118
34. 942
5.824
11.649
17. 473
23. 297
29. 122
34. 946
Abscissas of developed parallel.
Inches.
. 2. 507
2.505
2.502
2.500
2.498
2.496
2.494
2.491
2.489
2.487
2.485
2.482
2.478
2.476
2.473
2.471
2.469
2.407
2.464
2.462
2.460
2.458
2.455
2.453
2.451
2.448
2.446
2.444
2.441
2.439
2.437
2.434
2.432
2.430
2.427
2.425
2.423
2.420
2.418
2.415
2.413
2.411
2.408
2.406
2.403
2.401
2.384
2.381
2.379
2.376
2.374
2.372
2,369
2.367
2.364
2.362
2.359
2.357
2.354
2.352
2.349
2.346
2.344
2.341
Inches.
5.014
5.009
5.005
5,000
4.996
4.991
4.987
4.983
4.978
4.974
4.956
4.951
4.947
4.942
4.924
4.920
4.915
4.910
4.850
4.845
4.840
4.797
4.792
4.787
4.782
4.777
4.773
4.768
4.763
4.758
4.753
4.748
4.743
4.738
4.733
4.728
4.723
4.718
4.713
4.708
4.703
4.698
4.693
Inches.
7.520
7.514
7.507
7.5U0
7.494
7. 487
7.480
7.474
7.467
7.460
7.454
7.4A7
7.441
7.434
7.427
7.420
7.413
7.407
7.400
7.393
7. 3S6
7.379
7,372
7.366
7.331
7.324
7.317
7.303
7.296
7.289
7.282
7.275
7.267
7.260
7.253
7.246
7.239
7.231
7.224
7.217
7.210
7.203
7.195
7.188
7.181
7.174
7.166
7.159
7.151
7.144
7.137
7.129
7.122
7.115 '
7.107
7.100
7.092
7.085
7.077
7.070
7.062
7. 055
7.047
7.039
7.032
7.024
7. 017
Inches.
10. 027
10. 018
10. 009
10. 000
9.974
9.965
9.956
9.947
9. 793
9.784
9.774
9.728
9,718
9.709
9.700
9.690
9.680
9.671
9,661
9.652
9.642
9.632
9. 623
9.613
9.604
9.594
9. 584
9. 574
9.565
9.555
9.545
9.535
9. 525
9.516
9.506
9.496
9.486
9.476
9.466
9.456
9.446
9.436
9.426
9.416
9.406
9.396
9.380
9.376
9.366
9.356
Inches.
12. 534
12. 523
12. 512
12. 500
12. 489
12. 478
12. 467
12. 456
12.445
12. 434
12. 423
12. 412
12. 401
12. 390
12. 378
12. 367
12. 356
12.344
12. 333
12. 322
12. 310
12. 299
12. 287
12. 276
12. 265
12. 253
12. 241
12. 230
12. 218
12. 206
12. 195
12. 183
12. 171
12. 160
12.148
12. 136
12.124
12. 112
12. 100
12. 088
12. 076
12. 064
12. 052
12. 040
12. 028
12.016
12. 004
11. 992
11. 980
11. 908
11. 956
11. 914
11. 931
11. 919
11. 907
11. 895
11.882
II. 870
11.858
11. 845
11.833
11. 820
11. 808
11. 795
11. 783
11.770
11. 758
11. 745
11. 732
11. 720
11. 707
11.694
Inches.
15. 040
15. 027
15. 014
15. 000
14. 987
14. 974
14. 961
14. 948
14. 934
14. 921
14.908
14. 894
14. 881
14, 868
14. 854
14. 840
14. 827
14. 813
14. 800
14. 786
14. 772
14. 759
14. 745
14. 731
14. 690
14. 676
14. 662
14. 648
14. 633
14. 619
14.' 605
14. 591
14. 577
14. 563
14. 549
14. 535
14. 520
14. 506
14. 492
14. 477
14. 463
14. 448
14. 434
14. 420
14. 405
14. 391
14. 376
14. 362
14.347
14. 332
14. 318
14. 303
14. 288
14. 273
14. 259
14.244
14. 229
14. 214
14. 200
14. 183
14. 169
14, 154
14, 139
14. 124
14. 109
14. 094
14. 079
14. 064
14, 048
14, 033
Ordinates of devel-
oped parallel.
Inch.
0.000
.002
Inch.
0.000
.002
182
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXII. — Coordinates for ^projection of maps. Scale -^xm — Coutinued.
[Prepared Ijy E. S. 'Woodwartl,]
Abscissas of developed parallel.
12J' lon-
gitude.
Ordiilatea of devel-
oped parallel.
Inches.
5.826
11.651
17. 477
23. 302
29. 128
34. 954
5. 828
11.655
17. 483
23. 310
29. 138
34. 966
5.829
11. 657
17. 486
23. 314
29. 143
34. 972
5.830
11. 659
17.489
23.319
29. 149
34. 978
5.831
11. 661
17. 492
23. 323
29. 154
34.984
2. 323
2.321
2.318
2. 316
2.313
2.311
2.308
2.300
2. 298
2.295
2.292
2.290
2.287
2.284
1. 282
2.274
2.271
2.268
2.266
2.250
2.247
2.244
2.241
2.239
2.236
2.233
2.230
2.228
2.211
2.208
2.206
2.203
2.200
2.197
2.194
2.192
2.189
2.186
2.183
2.180
2.178
2.175
2.172
2.169
2.166
2.163
2.160
2.158
2.155
2.152
2.149
2. 146
2.143
Inches.
4.673
4.667
4.662
4.657
4.652
4.647
4.642
4.637
4.631
4.626
4.621
4.616
4.611
4.606
4.600
4.595
4.590
4.547
4.542
4.537
4.531
4.526
4.521
4.515
4.510
4.504
4.499
4.494
4.472
4.466
4.461
4.455
4.450
4.444
4.439
4.433
4.428
4.422
4.417
4.411
4.406
4.400
4.394
4.389
4.383
4.377
4.372
4.349
4.344
4.338
4.332
4.326
4.321
4.315
6. 963
6.955
6.947
6.939
6. 932
6.924
6.916
6.908
6.900
6.892
6.885
6.877
6.869
6.861
6.853
6.845
6.837
6.821
6.813
6.805
6.797
6.789
6.781
6.773
6.765
6.757
6.748
6.740
6.732
6.724
6.716
6.708
6.699
6.691
6.683
6.675
6.666
6.658
6.050
6.642
6.633
6.600
6.591
6.583
6.575
6.666
6.558
6.549
6.541
6.533
6.524
6.515
6.507
6.498
6.490
6.481
6.472
6.464
6.455
6.447
6.438
6.429
Inches.
9.345
9.335
9.325
9.314
9.304
9.294
9.283
9.273
9.363
9.253
9.212
9.233
9.222
9.211
9.201
9.190
9.179
9.169
9.158
9.148
9.137
9.137
9.118
9.106
9.095
9.084
9.073
9.063
9.052
9.041
9.030
9.020
9.009
8.998
8.987
Inches.
11. 683
11. 669
11. 656
11.643
11.630
11.617
11. 604
11. 591
11. 578
11.566
11. 553
11. 540
11.527
11. 514
11. 501
11. 488
■11.474
11.461
11.448
11. 435
11.422
11. 408
11. 395
11. 382
11. 369
11. 355
11. 342
11. 328
11.315
11.301
11.288
11. 374
11.261
11. 247
11.234
11.221
11. 207
11. 193
11. 180
11. 166
11. 152
11. 138
11.124
14. Ill
II. 097
11. 083
11.069
11. 056
11.042
11. 038
11.014
11.000
10. 986
10. 972
10. 958
10. 944
10. 930
10. 916
10. 902
10. 888
10. 873
10. 859
10.845
10. 830
10.816
10. 803
10. 787
10. 773
10. 759
10.744
10. 730
10. 716
14. 003
13. 987
13. 972
13,956
13.941
13.925
13.910
13. 894
13. 879
13. 863
13. 848
13. 832
13. 817
13. 801
13. 785
13. 769
13. 753
13. 737
13. 722
13. 706
13. 690
13. 674
13. 058
13. 642
13. 626
13. 610
13. 594
13. 578
13. 562
13. 545
13.529
13. 513
13. 497
13. 481
13. 465
13.448
13. 432
13. 415
13. 399
13. 382
13.360
13. 349
13. 333
13. 316
13. 300
13. 283
13. 267
13. 250
13. 233
13. 216
13. 200
13. 183
13. 166
13. 149
13. 133
13. 115
13. 099
13. 082
13. 065
13. 014
13. 996
12. 979
12. 963
12.945
12. 928
12. 910
13. 893
12. 876
12. 859
40°
Inch.
2i
0. 001
5
.002
u
.005
0
.008
2.V
.013
.019
41°
Inch.
'i>,
0.001
5
.002
7S:
.005
10
.008
12*
.013
15
.019
PEOJECTIOI^r TABLES.
183
Table XXll.— Coordinates for projection of maps. Scale ^jnr — Continued.
[Prepared by E. S. "Woodward.]
Inches.
'""5.'832'
11. 663
17. 495
23. 327
29. 159
Absci9aa.s of developed parallel.
23. 331
29. 164
34. 997
5.834
11. 668
17. 501
23. 335
29. 169
35. 003
5.835
11. 670
17. 504
23. 339
29. 174
36. 009
5.836
11. 672
17. 508
23. 344
29. ISO
35. 015
5.837
11. 674
17.511
23. 348
29. 185
35. 021
Inches.
2.140
2.137
2.134
2.132
2.129
2.126
2.123
2.120
2.117
2.114
2.111
2.108
2.096
2.093
2.090
2.087
2.084
2.C81
2.078
2.076
2.073
2. 045
2.042
2,039
2.036
1.996
1.993
1.990
1.987
1.984
1.981
1.977
1.974
1.971
1.968
1.965
1.959
1.956
1.952
1.949
1.946
1.943
1.940
1.937
1.933
1.930
1.927
1.924
4.275
4.269
4.263
4.257
4.251
4.246
4.240
4.234
4.228
4.222
4.216
4.193
4.187
4.181
4.175
4.169
4.163
4.157
4.151
4.145
4.133
4.127
4.121
4.115
4.109
4.103
4.097
4.091
4,085
4.079
4.073
4.067
4.060
4.054
4.048
4.042
4.036
4.030
4.023
4.017
4.011
4.005
3,917
3.911
3.905
Inches.
6.421
6.412
6.403
6.395
6.386
6.377
6.351
6.342
6.333
6.324
6.316
6.307
6.298
6.271
6.262
6.253
6.244
6.235
6.227
6. 218
6.209
6.200
6.191
6.181
6. 172
6.163
6.154
6.145
6.136
6.127
6.118
6.109
6.100
6.091
6.081
6.072
6.063
6.054
6.044
6.035
6.026
6.017
6.008
5.970
5.981
5 951
5.942
5.933
5.923
5.914
5.904
5.895
5.876
5-. 867
5.857
5.848
Inches.
8.561
8.550
8.503
8.491
8.479
8.468
8.456
8.444
8.432
8.326
8.314
8. 302 .
8.290
8.278
8.266
8.254
§.242
8.230
8.218
8.206
8.194
8.181
8.169
8.157
.145
7.985
7.973
7.960
7.948
7.935
7.923
7.910
7.898
7.784
7.771
7.759
7.746
7.733
7.721
7.708
7.695
Inches.
10. 701
10. 687
10. 672
10. 658
10. 643
10. 628
10. 614
10. 599
10. 585
10. 570
10. 555
10.541
10. 496
10.482
10. 467
10. 452
10.437
10. 422
10. 407
10.;
10. 348
10. 333
10. 318
10. 302
10. 287
10, 272
10. 257
10. 242
10. 227
10. 212
10. 197
10. 182
10. 166
10. 151
10. 136
10. 120
10. 105
10. 090
10. 074
10. 059
10. 043
10. 028
10. 013
9.907
9.982
9.966
9.950
9.935
9.919
9.667
9.651
9.635
9.619
Inches.
12. 842
12. 824
12. 807
12. 789
12. 772
12. 754
12. 736
12. 719
12. 701
12. 684
12. 666
12. 649
12. 631
12. 613
12. 596
12. 578
12. 560
12. 542
12.524
12. 506
12. 489
12. 471
12. 453
12. 43S
12. 417
12. 399
12. 381
12. 363
12. 345
12. 327
12. 308
12. 290
12. 272
12. 254
12. 236
12. 218
12. 200
12. 181
12. 163
12. 144
12. 126
12. 107
12. 089
12. 070
12. 052
12. 033
12.015
11. 996
II. 978
11. 959
11. 940
11. 922
11. 903
11. 884
11.865
11. 846
11. 828
11. 809
11. 790
11. 771
11. 752
11.733'
11. 714
11. 695
11. 676
11. 657
11. 638
11. 619
11. 600
11. 581
11. .562
11. 543
Ordinates of devel-
oped parallel.
184
A MANUAL OF TOrOGEAPHIC METHODS.
Table XXII. — Coordinates for projection of maps. Scale -g^jy^
[Prepared hy E. S. Woodward.]
■3.S£
Inches.
5.838
11. 676
17. 51J,
23. 352
29. 190
35. 027
Abscissas of developed parallel.
JJ' longi- 5' longi, 7^' longi- 10' longi- 12J' Ion- 15' long
tude. tilde. tude. tude. gitude. tude.
Inches.
1.921
1.917
1.9U
1.911
3.828
3.822
3.815
3.809
3.802
3.796
3.790
3.783
3.777
5.742
5.733
5.723
5.713
5.704
5.694
5.684
5.675
5.665
5.655
7.670
7.657
7.644
7.631
7.618
7.605
7.592
7.579
7.566
7.553
7.540
7.528
Inches.
9.003
9.587
9.571
9.555
9. 538
9. 522
9.506
9.490
9.474
9.458
9.442
9.426
9.409
Inches.
11. 524
11. 504
11.485
11. 466
11.446
11.427
11. 407
11. 388
11. 369
11. 349
11. 330
11. 311
Ordinates of devel-
oped parallel.
49°
"^
Inch.
^
0.001
5
.002
74
0
.005
.008
n
.013
5
.039
Table XXIII. — Coordinates for ))rojecUon of maps. Scale -^-^^jfij.
[Prepared by S. S. Gannett.]
Latitade
par.allel.
Abscissas of developed p.irallel.
Ordinates of devel-
oped parallel.
Longitude interval.
Longi-
5'
7i'
10'
15'
tude
Incb.
interval.
" o
Inches.
Inches.
Inches.
Inches.
,
39 00
6.316
9.474
12.632
18.948
5
.003
05
.309
.463
.617
.926
n
.007
07i
.305
.457
.609
.914
10
.012
10
15
.301
.294
.451
.440
.602
.587
.903
.881
15
.026
20
6.286
9.429
12.572
18. 858
Latitude
interval.
Meridi-
onal dis-
22*
25
.282
.279
.423
.418
.565
.557
.847
.836
/
Inch.
30
.271
.406
.542
.813
1
2
1.619
3.237
35
6.264
9.395
12. 527
18. 791
4
6
6
7
0.475
8.094
9.712
11. 331
37J
.260
.389
.520
.780
40
.256
.384
.512
.768
45
.J49
■.873
.497
.746
8
12. 960
50
6.2a
9.361
12.482
18. 723
9
14. 569
52i
65
.237
.234
.356
.350
.475
.467
.712
.701
10
16. 188
60
.226
.339
.452
.678
Longi-
tude in-
Inch.
40 00
05
6.226
.219
9.339
.328
12. 452
.438
18. 678
.656
'
07i
.215
.322
.429
.644
5
.003
10
.211
.316
.422
.633
n
.007
15
.203
.305
.406
.609
10
.012
20
6.196
9.293
12. 392
18. 587
15
.026
22J
.192
.288
.384
.576
Latitude
25
.188
.282
.376
.564
30
.180
.270
.361
.540
'
Inch.
35
6.173
9.259
12. 346
18. 518
1
2
3
4
1.619
3.238
4.857
6.470
8.095
37*
.169
.253
.338
.506
40
.165
.247
.330
.495
45
.157
.236
.315
.472
6
9.714
50
6.150
9.224
12.300
18.449
7
11. 333
52J
.146
.219
.292
.438
8
12. 952
55-
.142
.213
.285
.427
9
14. 571
60
.134
.201
.269
.403
10
16. 190
1
PEOJEOTION TABLES.
185
Table XXIII. — Coordinates for projection of maps. Scale 4-5^513 — Continued.
(Prepared by S. S. Gannett.]
Abscissas of developed parallel.
Longitude interval.
Ordinates of devel-
oped parallel.
Loncfi-
tnde Inch,
interval.
Meridi-
onal dis-
tance.
1.619
3.239
4.858
6.477
8.097
9.716
11.335
12. 955
14. 574
16. 193
.074
.051
■*B.961
18. 027
.015
.003
17. 979
17. 956
.944
.933
Meridi-
onal dis-
tance.
6.478
8.098
9.718
11. 337
12. 957
14. 576
16. 196
Longi-
tude in- lucli.
terval.
Meridi-
onal dis-
tance.
Inch.
1.620
3. 2.J0
186
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXIII. — Coordinates for projection of maps. Scale tsW — Continued.
[Prepared by S. S. Gannett.]
Latitude
of
Iparallel.
Abscissas of developed parallel.
Ordinates of devel-
oped parallel.
Longitude interval.
Longi-
6'
7J'
10'
15'
tude
interval.
Tncb.
0 1
Inches.
Inches.
Inches.
Inches.
,
U 00
5.848
8.771
11.695
17. 543
6
.003
05
.83!)
.759
.679
.618
7J
.007
07*
.835
.753
.670
.505
10
.012
10
15
20
.831
.823
5.815
.746
.662
.493
15
.027
8.722
11. 629
17. 444
Latitude
interval.
Meridi-
onal dis-
2^
25
.810
.806
.715 1 .621
.709 1 .613
.431
.419
30
.798
. 697 1 . 596
.394
1
2
Inch.
1.620
3.240
35
5.790
8.685 i 11.580
17. 370
3
4.861
37J
.786
.678 .571
.357
4
6.481
40
.782
.672 1 ,563
.345
5
8.101
45
.773
.660
.547
.320
6
7
8
9.721
11. 341
12. 962
50
5.765
8.647
11.530
17. 296
9
14. 582
52*
.761
.641
.523
.284
10
16. 202
55
.757
.635
.614
.271
60
.749
.623
.497
.246
Table XSIV. — Area of quadrilaterals of Earth's surface of 1^ extent in latitude and longitude.
[Prepared by E. S. AToodward.]
Middle
latitude
of <iuad-
rilateral.
Area
in square
miles.
Middle
latitude
of quad-
rilateral.
Area
in square
Middle
latitude
of quad-
rilateral.
Area
Middle
latitude
of quad-
rilateral.
Area
in square
Middle
latitude
of quad-
rilateral.
Area
in square
Middle
latitude
of quad-
rilateral.
If!
0
00
4752. 33
15
30
4583. 92
30
30
4109. 06
45
30
3354. 01
60 30
2364. 34
75
30
1205. 13
0
30
52.16
16
00
72.94
31
00
4088. 21
46
00
24.49
61 00
23.02
76
00
1164. 49
1
00
51.63
16
30
6L61
31
30
67.05
46
30
3294. 71
61 30
2291. 51
76
30
23.75
1
30
50.75
17
00
49.94
32
00
45.57
47
00
64.63
62 00
54.82
77
00
1082. 91
2
00
49.52
17
30
37.93
32
30
23.79
47
30
34.39
62 30
17.94
77
30
41.99
2
30
47.93
>
3
00
46.00
18
00
25.59
33
00
01.69
43
00
03.84
63 00
2180. 89
78
00
1000. 99
3
30
43.71
18
30
12.90
33
30
3979. 30
48
30
3173. 04
63 30
43.66
78
30
959. 90
4
00
41.07
19
00
4499. 87
34
00
56.59
49
00
41.99
64 00
06.26
79
00
18.73
4
30
38.08
19
30
86.51
34
30
33.59
49
30
10.69
64 30
2063. 68
79
30
877. 49
5
00
34.74
20
00
72.81
35
00
10.28
60
00
3079. 15
65 00
30.94
80
00
36.18
5
30
31.04
20
30
58.78
35
30
3886. 67
50
30
47.37
65 30
1993. 04
80
30
794. 79
6
00
27.00
21
00
44.41
36
00
62.76
51
00
15.34
66 00
54.97
81
00
53.34
6
30
22.61
21
30
29.71
36
30
38.56
51
30
2983. 08
66 30
16.75
31
30
11.83
7
00
17.86
22
00
14.67
37
00
14.06
52
00
50. 58
67 00
1878.37
32
00
670. 27
7
30
12.76
22
30
4399.30
37
30
3789. 26
52
30
17.85
67 30
39.34
82
30
28.64
8
00
07.32
23
00
83.60
38
00
64.18
63
00
2884. 88
68 00
1301. 16
83
00
586. 97
8
30
01.62
23
30
67.57
38
30
38.80
53
30
51.68
68 30
1762. 33
83
30
45.24
9
00
4696. 38
24
00
51.21
39
00
13.14
64
00
18.27
69 00
23.36
84
00
03. 47
9
30
88.89
24
30
34.52
39
30
3687. 18
64
30
2734. 62
69 30
1684. 24
84
30
461. 66
10
00
82.05
26
00
17.51
40
00
60.95
55
00
60.76
70 00
45.00
85
00
19.81
10
30
74.86
25
30
00.17
40
30
34.42
65
30
16.67
70 30
05.62
85
30
377. 93
11
00
67.32
26
00
4282. 50
41
00
07.62
56
00
2682. 37
71 00
1666. 10
86
00
36.02
11
30
59.43
26
30
64. 51
41
30
3580. 54
56
30
47.85
71 30
26.46
86
30
294. 08
12
00
51.20
27
00
46.20
42
00
53.17
57
00
13.13
72 00
1486. 70
87
00
52.11
12
30
42.63
27
30
27.66
42
30
25.54
57
30
2578. 19
72 30
46.81
37
30
10.12
13
00
33.71
28
00
08,61
43
00
3497. 62
58
00
43.05
73 00
06.31
38
00
168. 12
13
30
24.44
28
30
4189. 33
43
30
69.44
68
30
07.70
73 30
1366. 69
88
30
126. 10
14
00
14.82
29
00
69.74
44
00
40. 98
59
00
2472. 16
74 00
26.46
39
00
84.07
14
30
04.87
29
30
49.83
44
30
12.26
59
30
36.42
74 30
1236. 12
39
30
42.04
15
00
4594. 57
30
00
29.60
45
00
3383. 27
60
00
00.48
75 00
45.68
90
00
00.00
AREAS OF QUADEILATERALS.
187
Table XXV. — Areas of quadrilaterals of Earth's surface of 30' extent in latitude and longitude,
[Prepared by E. S. "Woodward.]
Middle
latitude
Area in
Middle
latitude
Area in
Middle
latitude
Area in
Middle
latitude
Area in
Middle
latitude
Area in
Middle
latitude
Area in
of quad-
rilateral.
square
miles.
of quad-
rilateral.
square
mUes.
of quad-
rilateral.
square
miles.
of quad-
rilateral.
square
miles.
of quad-
rilateral.
square
miles.
of quad-
rilateral.
miles.
0
30
1188. 05
30
30
1027. 27
60
30
591. 09
0
15
1188. 08
30
45
1024. 68
60
45
586. 50
1
00
1187. 92
31
00
1022. 06
61
00
582. 01
0
45
1188. 00
31
15
1019. 43
61
15
577. 45
1
30
1187. 70
3;
30
1016. 77
61
30
572. 88
1
15
1187. 82
31
45
1014. 10
61
45
568. 30
2
00
1187. 39
32
00
1011. 40
62
00
563. 71
1
45
1187. 56
32
15
1008. 69
62
15
559. 11
3
30
1186. 99
32
30
1005,96
62
30
554.49
2
2
15
45
1187. 20
1186. 76
32
45
1003. 20
62
45
549. 86
3
00
1186. 51
33
00
1000.43
63
00
545.23
3
15
1186. 24
33
15
997.64
63
15
540. 58
3
30
1185. 95
33
30
994. 83
63
30
635. 92
3
45
1185. 62
33
46
993.00
63
45
531. 25
i
00
1185. 28
34
00
989. 16
64
00
526. 57
4
15
1184. 92
34
15
986. 29
64
15
621. 88
4
30
1184. 53
34
30
983.41
64
30
517.17
4
45
1184. 13
34
45
980. 50
64
45
512. 46
5
00
1183. 70
35
00
977. 58
65
00
507. 74
5
15
1183.24
35
15
974. 64
65
16
503. 01
5
30
1182.77
35
30
971. 68
65
30
498. 26
5
45
1182. 28
35
45
968. 70
65
45
493, 51
6
00
1181. 76
36
00
965. 70
66
00
488. 75
6
15
1181. 22
36
15
962. 68
66
16
483. 97
6
30
1180. 66
36
30
959. 65
66
30
479. 19
6
45
1180. 08
36
45
956. 60
66
45
474, 40
7
00
1179. 48
37
00
953.52
67
00
469. 60
7
15
1178. 85
37
15
950. 43
67
15
464. 78
7
30
1178. 20
37
30
947.32
67
30
459. 96
7
45
1177. 53
37
46
944. 21
67
45
455. 13
8
00
1176. 84
38
00
941.05
68
00
450. 29
8
16
1176. 13
38
15
937.88
67
45
455.13
8
30
1175. 39
38
30
984.71
68
30
440.59
8
45
1174. 63
38
45
931.51
68
15
445.45
9
00
1173. 86
39
00
928.29
69
00
430.84
9
15
1173.06
39
15
935. 06
68
46
435. 72
9
30
1173. 23
39
30
921. SO
69
30
421. 06
9
45
1171. 39
39
45
918. 53
69
15
425. 96
10
00
1170.52
40
00
915. 25
70
00
411.25
10
15
1169. 63
40
15
911. 94
69
45
416.16
10
30
^ 1168. 73
40
30
908. 61
70
30
401. 41
10
45
1167. 80
40
45
905. 27
70
16
406. 34
11
00
1166. 84
41
00
901.91
71
00
391. 53
11
15
1165. 86
41
15
898. 64
70
45
396. 47
11
30
1164. 86
41
30
895. 14
71
30
381. 62
11
45
1163. 85
41
45
891. 73
71
15
386. 58
12
00
1162. 81
42
00
888. 30
72
00
371. 68
12
15
1161. 75
42
15
884.85
71
45
376, 65
12
30
1160.67
42
30
881. 39
72
30
361. 71
12
45
1159. 56
42
45
877. 91
72
15
366, 70
13
00
1158. 44
43
00
874. 41
73
00
351. 71
13
15
1157. 29
43
15
870. 90
72
45
356.71
13
30
1156. 12
43
30
867. 37
73
30
341. 68
13
45
1154. 93
43
45
863. 82
73
16
346. 69
14
00
1153.72
44
00
860. 25
74
00
331.62
14
15
1152. 48
44
15
856. 67
73
45
336. 65
14
30
1151. 23
44
30
853.07
74
30
321. 53
14
45
1149, 95
44
45
849, 46
74
16
326, 58
15
00
1148. 65
45
00
845.82
75
00
311.42
15
15
1147. 33
45
15
842. 18
74
45
316,48
15
30
1145.99
45
30
838. 51
75
30
301.28
15
45
1144. 63
45
45
834. 83
75
15
306, 36
16
00
1143. 25
46
00
831. 13
76
00
291. 12
16
15
1141. 84
46
15
827.42
75
45
296,21
16
30
1140. 41
46
30
823. 68
76
30
280. 94
16
45
1138. 96
46
45
819. 94
76
15
286,04
17
00
1137. 50
47
00
816. 18
77
00
270.73
17
15
1136. 00
47
15
812. 40
76
46
275, 84
17
30
U34.49
47
30
808. 60
77
30
260. 50
17
45
1132. 96
47
45
804. 79
77
15
265, 62
18
00
1131. 41
48
00
800. 97
78
00
250. 25
18
15
1120. 83
48
15
797. 13
77
45
255. 38
18
30
1128.24
48
30
793. 27
78
30
239. 98
18
45
1126. 62
48
45
789. 39
78
15
215.12
19
00
1124. 98
49
00
785. 50
79
00
229. 68
19
15
1123.32
49
15
781. 60
78
45
234.83
19
30
1121.64
49
30
777. 68
79
30
219. 37
19
45
1119. 93
49
45
773. 74
79
15
224.53
20
00
1118.21
50
00
769. 79
80
00
209. 05
20
15
1116. 47
50
15
765.83
79
45
214. 21
20
30
1114. 71
50
30
761. 85
80
30
198. 70
20
45
1112. 92
50
45
757.85
80
15
203. 88
21
00
1111.11
51
00
753. 84
81
00
188.34
21
15
1109, 28
51
15
749. 82
80
45
193. 52
21
30
1107.44
51
30
745.78
81
30
177. 96
21
45
1105. 57
51
45
741.72
81
15
183. 15
22
00
1103. 68
62
00
737. 65
82
00
167. 57
22
15
1101. 77
52
15
733. 67
81
45
172. 77
22
30
1099.84
52
30
729. 47
82
30
157. 16
22
45
1097. 88
52
45
725. 36
82
15
162. 37
23
00
1095. 91
53
00
721. 23
83
00
146. 74
23
15
1093. 93
53
15
717. 08
82
46
151.95
23
30
1091.90
53
30
712. 93
83
30
136. 31
23
45
1089. 87
53
45
708. 76
S3
15
141. 53
24
00
1087. 81
54
00
704. 57
84
00
125. 87
24
15
1085. 74
54
15
700. 38
83
45
131. 09
24
30
1083. 64
54
30
696. 16
84
30
115. 42
24
45
1081. 52
54
45
691. 94
84
15
120. 64
25
00
1079. 39
55
00
687. 70
85
00
104. 95
25
15
1077. 23
55
16
683.44
84
45
110. 18
25
30
1075. 05
55
30
679. 17
85
30
94.48
25
45
1072. 85
55
45
674. 89
86
15
99.72
26
00
1070. 64
56
00
670. 60
86
00
84.01
26
15
1068. 40
56
15
666. 29
85
46
89.35
26
30
1066. 14
56
30
661.97
86
30
73.52
26
45
1063. 86
56
45
657.64
86
15
78.76
27
00
1061. 56
57
00
653. 29
87
TO
63.03
27
15
1059. 24
57
15
648.93
86
45
68.37
27
30
1056. 90
57
30
644.55
87
30
52.53
27
45
1054. 54
57
45
640. 17
87
15
57.78
28
00
1052. 16
58
00
635. 77
88
00
42.03
28
15
1049. 76
58
15
631. 36
87
45
47.28
28
30
1047.34
58
30
626. 93
88
30
31.53
28
45
1044. 90
58
45
622.49
88
15
36.78
29
00
1U42. 44
59
00
618. 05
89
00
21.02
29
15
1039. 97
59
15
613. 59
88
45
26.27
29
30
1037. 47
59
30
609. 11
89
30
10.51
29
45
1034. 95
59
45
604. 62
89
15
16.76
30
00
1032. 41
60
00
600. 13
90
00
00.00
30
15
1039. 85
60
15
595. 62
89
45
5.26
188
A MANUAL OF TOPOGEAPHIG METHODS.
Table XXVI. — Areas of quadrilaterals of Earth's surface of 16' extent in latitme and longitude.
[Prepared by K. S. "Woodward.]
Middle
latitude
of quadri-
lateral.
A.rea in
Middle
latitude
Area in
MidcUe
latitude
Area in
Middle
latitude
Area in
Middle
latitude
\roa in
Middle
latitude
Area in
square
miles.
of quadri-
lateral.
square
miles.
of quadri-
lateral.
square
mues.
of quadri-
lateral.
square
miles.
of quadri-
lateral.
square
miles.
of quadri-
lateral.
square
miles.
0 07 30
297.02
8 15 00
294. 03
16 22 30
285. 28
24 30 00
270. 91
32 37 30
251. 15
40 45 00 .
226. 32
0 15 00
297.02
8 22 30
293. 94
16 30 00
285. 10
24 37 30
270. 65
32 45 00
250.80
40 52 30
225. 90
0 22 30
297. 02
8 30 00
293.85
16 37 30
284. 92
24 45 00
270. 38
32 52 30
250. 45
41 00 00
225. 48
0 30 00
297. 01
8 37 30
293. 75
16 45 00
284. 74
24 53 30
270.11
33 00 00
250. 11
41 07 30
225. 06
0 37 30
297.01
8 45 00
293. 66
16 52 30
284. 56
25 00 00 ,
269. 85
33 07 30
249. 76
41 15 00
224.64
0 45 00
297. 00
8 52 30
293. 56
17 00 00
284. 38
25 07 30
269. 58
33 15 00
249.41
41 22 30
224. 21
0 52 30
296. 99
9 00 00
293.47
17 07 30
284. 19
25 15 00
269. 31
33 22 30
249. 06
41 30 00
223. 79
1 00 00
296. 98
9 07 30
293. 37
17 15 00
284. 00
25 22 30
269. 04
33 30 00
248. 71
41 37 30
223. 36
1 07 30
290. 97
9 15 00
293. 27
17 22 30
283. 81
25 30 00
268. 76
33 37 30
248. 36
41 45 00
222. 93
1 15 00
296. 96
9 22 30
293. 16
17 30 00
283. 62
25 37 30
268. 49
33 45 00
248. 00
41 52 30
222. 50
1 22 30
296. 94
9 30 00
293. 06
17 37 30
283. 43
25 45 00
268. 21
33 52 30
247. 65
42 00 00
222. 08
1 30 00
296. 93
9 37 30
292.95
17 45 00
283. 24
25 52 30
267. 94
34 00 00
247. 29
42 07 30
221. 65
1 37 30
296. 91
9 45 00
292.85
17 52 30
2S3. 05
26 00 00
267. 66
34 07 30
246. 93
42 15 00
221. 21
1 45 00
296. 89
9 52 30
292.74
18 00 00
282. 86
26 07 30
267. 38
34 15 00
246. 57
42 22 30
220. 78
1 52 30
296.87
10 00 00
292. 63
18 07 30
282. 66
20 15 00
267. 10
34 22 30
246. 21
42 30 00
220. 35
2 00 00
296. 85
10 07 30
292. 52
18 15 00
282. 46
26 22 30
266.82
34 30 00
245. 85
42 37 30
219. 91
2 07 30
296. 82
10 15 00
292.41
18 22 30
282. 26
26 30 00
266. 54
34 37 30
245. 49
42 45 00
219. 48
2 15 00
296. 80
10 22 30
292. 30
18 30 00
282. 06
26 37 30
266. 25
34 45 00
245. 13
42 52 30
219. 04
2 22 30
296. 77
10 30 00
292. 19
18 37 30
281. 86
26 45 00
265. 97
34 -52 30
244.76
43 00 00
218. 60
2 30 00
296. 75
10 37 30
292. 07
18 45 00
281.66
26 52 30
265. 68
35 00 00
244. 40
43 07 30
218. 10
2 37 30
296. 72
10 45 00
291. 95
18 52 30
281.45
27 00 00 ' 265. 39
35 07 30
244.03
43 15 00
217. 73
2 45 00
296. 69
10 52 30
291. 83
19 00 00
281. 25
27 07 30
265. 10
35 15 00
243. 06
43 22 30
217. 28
2 52 30
296. 66
11 00 00
291. 71
19 07 30
281. 04
27 15 00
264. 81
35 22 30
243. 29
43 30 00
216.84
3 00 00
296. 63
11 07 30
291.59
19 15 00
280. 83
27 22 30
264.52
35 30 00
242. 92
43 37 30
216. 40
3 07 30
296. 60
U 15 00
291.47
19 22 30
280. 62
27 30 00
264. 23
35 37 30
242.55
43 45 00
215. 96
3 15 00
296. 56
11 22 30
291. 34
19 30 00
280. 41
27 37 30
263. 93
35 45 00
242.18
43 52 30
215. 51
3 22 30
296. 53
11 30 00
291. 22
19 37 30
280. 20
27 45 00
263. 64
35 52 30
241. 80
44 00 00
215. 06
3 30 00
296.49
11 37 30
291. 09
19 45 00
279. 99
27 52 30
263. 34
36 00 00
241.43
44 07 30
214. 61
3 37 30
296.45
11 45 00
290. 96
19 52 30
279. 77
28 00 00
263. 04
36 07 30
241. 05
44 15 00
214. 17
3 45 00
296,41
11 52 30
290. 83
20 00 00
279. 55
28 07 30
262. 74
36 15 00
240. 67
44 22 30
213. 72
3 52 30
296. 36
12 00 00
290. 70
20 07 30
279. 34
28 15 00 ' 262. 44
36 22 30
240. 29
44 30 00
213. 27
4 00 00
296. 32
12 07 30
290.57
20 15 00
279. 12
28 22 30 262. 14
36 30 00
239. 91
44 37 30
212. 82
4 07 30 296. 28
12 15 00
290.44
20 22 30
278. OQ
28 30 00 1 261. 84
36 37 30
239. 53
44 45 00
212. 37
4 15 00
296. 23
12 22 30
290. 30
20 30 00
278. 68
28 37 30
261. 53
36 45 00
239. 15
44 52 30
211.91
4 22 30
296. 18
12 30 00
290. 17
20 37 30
278. 46
28 45 00
261. 23
36 52 30
238. 77
45 00 00
211. 46
4 30 00
296. 13
12 37 30
290. 03
20 45 00
278. 23
28 52 30
260. 92
37 00 00
238. 38
45 07 30
211.00
4 37 30
296. 08
12 45 00
289. 89
20 52 30
278.00
29 00 00
260. 01
37 07 30
237. 99
45 15 00
210. 55
4 45 00
296. 03
12 52 30
289. 75
21 00 00
277. 78
29 07 30
260. 30
37 15 00
237. 61
45 22 30
210. 09
4 52 30
295. 98
13 00 00
289. 61
21 07 30
277. 55
29 15 00
259. 99
37 22 30
237. 22
45 30 00
209. 63
5 00 00
295. 93
13 07 30
289.47
21 15 00
277. 32
29 22 30
259. 68
37 30 00
236. 83
45 37 30
209. 17
5 07 30
295. 87
13 15 00
289. 33
21 22 30
277. 09
29 3i) 00
259. 37
37 37 30
236. 44
45 45 00
208. 71
5 15 00
295. 81
13 22 30
289. 18
21 30 00
276. 86
29 37 30
259. 05
37 45 00
236. 05
45 52 30
208. 25
5 22 30
295.75
13 30 00
289. 03
21 37 30
276. 63
29 45 00
258. 74
37 52 30
235. 60
46 00 00
207. 78
5 30 00
295. 69
13 37 30
288. 88
21 45 00
276. 39
29 52 30
258. 42
38 00 00
235. 26
46 07 30
207. 32
5 37 30
295. 63
13 45 00
288. 73
21 52 30
276. 16
30 00 00
258. 10
38 07 30
234. 87
46 15 00
206. 86
5 45 00
295. 57
13 52 30
288. 58
22 00 00
275. 92
30 07 30
257. 78
38 15 00
234.47'
46 22 30
206. 39
5 52 30
295. 51
14 00 00
288. 43
22 07 30
275. 68
30 15 OO
257. 46
38 22 30
234. 07
46 30 00
205. 92
6 00 00
295.44
14 07 30
288. 28
22 15 00
275.44
30 22 30
257. 14
38 30 00
233. 68
46 37 30
205. 45
6 07 30
295. 37
14 15 00
288. 12
22 22 30
275. 20
30 30 00
256. 82
38 37 30
233. 28
46 45 00
204. 99
6 15 00
295. 31
14 22 30
287.96
22 30 00
274. 96
30 37 30
256. 49
38 45 00
232. 88
46 52 30
204. 52
6 22 30
295.24
14 32 CO
287. 81
22 37 30
274. 72
30 45 00
256. 17
38 52 30
232. 48
47 00 00
204. 05
6 30 00
295. 17
14 37 30
287. 65
22 45 00
247.47
30 52 30
255. 84
39 00 00 ; 232. 07
47 07 30
203. 57
6 37 30
295. 09
14 45 00
287. 49
22 52 30
274. 22
31 00 00
255. 52
39 07 30
231. 67
47 15 00
203. 10
6 45 00
295. 02
14 52 30
287. 33
23 00 00
273. 98
31 07 30
255. 19
39 15 00
231. 27
47 22 30
202. 63
6 52 30
294. 95
15 00 00
287. 17
23 07 30
273. 73
31 15 00
254. 86
39 22 30
230. 86
47 30 00
202. 15
7 00 00
294. 87
15 07 30
287. 00
23 15 00
273.48
31 22 30
254. 53
39 30 00
230.45
47 37 30
201. 67
7 07 30
294. 79
15 15 00
286. 83
23 22 30
273. 23
31 30 00
254. 19
39 37 30
230. 04
47 45 00
201. 20
7 15 00
294. 71
15 22 30
286. 67
23 30 00
2T2. 98
31 37 30
253. 86
39 45 00
229. 03
47 52 30
200. 72
7 22 30
294. 63
15 30 00
286. 50
23 37 30
272. 72
31 45 00
253. 53
39 52 30
229. 22
48 00 00
200. 24
7 30 00
294. 55
15 37 30
286. 33
23 45 00
272.47
31 52 30
253. 19
40 00 00
228. 81
48 07 30
199. 76
7 37 30
294. 47
15 45 00
286. 16
23 52 30
272. 21
32 00 00
252. 85
40 07 30
228. 40
48 15 00
199. 28
7 45 00
294. 39
15 52 30
285. 99
24 00 00
271. 95
32 07 30
252. 51
40 15 00
227. 99
48 22 30
198.80
7 52 30
294. 30
10 00 00
285. 82
24 07 30
271.69
32 15 00
252. 17
40 22 30
227. 57
48 30 00
198. 32
8 00 00
294. 21
16 07 30
285. 64
24 15 00
271. 44
32 22 30
251. 83
40 30 00
227. 15
48 37 30
197. 83
8 07 30
294. 12
16 15 00
285. 46
24 22 30
271. 17
32 30 00
251. 49
40 37 30
226. 73
48 45 00
197. 35
AEEAS OF QUADRILATERALS.
189
Table XSVI. Areas of qitadrilaterals of Earth's surface of 15' extent in latitude and longitude — Cont'd.
[Prepared by E. S. "Woodward.]
Middle
latitude
of quadri-
lateral.
ireain
square)
milea.
Middle
latitude
of quadri-
lateral.
A.rea in
square
miles.
MidiUe
latitude
of quadri-
lateral.
Alreaiu
square
miles.
Middle
Latitude
of quadri-
lateral.
Arcaiu
square
miles.
Middle
latitudi'
of ciuadri-
latfral.
A.rea in
square
miles.
Middle
latitude
of quadri-
lateral.
Area in
square
miles.
35.38
48 52 30
196. 86
55 45 00
168. 72
62 37 30
138.04
69 30 00
105. 27
76 22 30
70.87
83 15 00
49 00 00
196. 38
55 52 30
153. 19
62 45 00
137. 47
69 37 30
104. 65
76 30 00
70.24
83 23 30
34.73
49 07 30
195. 89
56 00 00
167. 65
63 52 30
136. 89
69 45 00
104. 04
76 37 30
69.60
83 30 00
34.08
49 15 00
195. 40
56 07 30
167. 11
63 on 00
136. 31
69 52 30
103. 43
76 46 00
68.96
83 37 30
33.42
49 22 30
194. 91
56 15 00
166. 57
03 07 30
136. 73
70 00 00
102. 81
76 52 30
68.32
83 45 00
32.77
49 30 00
194. 42
56 23 30
106. 03
63 15 00
135. 15
70 07 30
102. 20
77 00 00
67.68
83 52 30
33.12
49 37 30
193. 93
56 30 00
165. 49
63 22 30
134. 66
70 15 00
101. 59
77 07 30
67.04
84 00 00
31.47
49 45 00
193. 44
56 37 30
164.95
63 30 00
133. 98
70 22 30
100. 97
77 15 00
66.41
84 07 30
30.81
49 52 30
192. 94
56 45 00
164. 41
63 37 30
133. 40
70 30 00
100. 35
77 22 30
65.77
84 15 00
30.16
50 00 00
192. 45
56 52 30
163. 87
63 45 00
132. 81
70 37 30
99.74
77 30 00
65.13
84 23 30
29.51
50 07 30
191.95
57 00 00
163. 32
63 52 30
132.33
70 45 00
99.13
77 37 30
64.49
84 30 00
28.86
50 15 00
191.46
57 07 30
162. 78
64 00 00
131. 64
70 52 30
98.50
77 45 00
63.86
84 37 30
28.20
50 22 30
190. 96
57 15 00
162. 23
64 07 30
131. 06
71 00 00
97.88
77 52 30
63.20
84 46 00
37.54
50 30 00
190. 46
57 22 30
161. 68
64 15-00
130. 47
71 07 30
97.36
78 00 00
62.56
84 52 30
36.89
60 37 30
1S9. 96
57 30 00
161. 14
64 22 30
129. 88
71 15 00
96.65
78 07 30
61.92
85 00 00
26.24
50 45 00
189. 46
57 37 30
160. 59
64 30 00
129. 29
71 22 30
96.03
78 15 00
61.28
85 07 30
25.58
50 52 30
188. nii
57 45 00
160. 04
64 37 30
128. 70
71 30 00
95.41
78 22 30
60.64
85 15 00
24.93
51 00 00
188.40
■ 57 52 30
159.49
64 45 00
128. 12
71 37 30
94.78
78 30 00
60.00
85 22 30
34.37
51 07 30
187. 96
58 00 00
158. 94
64 52 30
137. 53
71 46 00
94.16
78 37 30
59.35
85 30 00
23.62
51 15 00
187. 46
58 07 30
158. 39
65 00 00
126. 94
71 52 30
93.54
78 45 00
68.71
85 37 30
22.97
51 22 30
186. 95
58 15 00
157. 84
65 07 30
126. 34
72 00 00
92.92
78 62 30
58.06
85 45 00
22.31
51 30 00
186. 45
58 22 30
157. 29
65 16 00
125. 75
72 07 30
93.30
79 00 00
57.43
85 52 30
21.66
51 37 30
185. 94
58 30 00
156. 73
65 23 30
125. 16
72 15 00
91.68
79 07 30
56.78
86 00 00
21.00
51 45 00
185, 43
58 37 30
156. 18
65 30 00
124. 57
72 32 30
91.05
•79 15 00
56.13
86 07 30
20.35
51 52 30
184. 92
58 45 00
155. 63
65 37 30
123. 97
72 30 00
90.43
79 22 20
55.49
86 15 00
19.69
52 00 00
184. 41
58 52 30
155. 07
65 45 00
123. 38
72 37 30
89.80
79 30 00
54.84
86 22 30
19.04
52 07 30
183. 90
59 00 00
154. 51
65 52 30
123, 78
73 46 00
89.18
79 37 30
54.20
86 30 00
18.38
52 15 00
183. 39
69 07 30
153. 96
66 00 00
122. 19
72 52 30
88.55
79 45 00
63.55
86 37 30
17.73
52 22 30
182 88
59 15 00
153. 41
66 07 30
121. 59
73 00 00
87.93
79 52 30
52.91
86 45 00
17.07
52 30 00
182.37
59 22 30
152. 84
66 15 00
120. 99
73 07 30
87.30
80 00 00
52.26
86 52 30
16.41
52 37 30
181. 85
59 30 00
152. 28
66 22 30
120. 40
73 16 00
86.67
80 07 30
51.63
87 00 00
15.76
52 45 00
181. 34
59 37 30
151. 72
66 30 00
U9.80
73 22 30
86.05
80 15 00
50.97
87 07 30
16.10
52 52 30
180. S2
59 45 00
151. 16
66 37 30
119. 20
'73 30 00
85.43
80 22 30
50.32
87 15 00
14.44
53 00 00
180. 31
59 52 30
150. 60
66 45 00
118. 60
73 37 30
84.79
80 30 00
49.68
87 22 30
13.79
53 07 30
179. 79
60 00 00
150. 03
66 52 30
118. 00
73 45 00
84.16
80 37 30
49.03
87 30 00
13.13
53 15 00
179. 27
60 07 30
149. 47
67 00 00
117. 40
73 52 30
83.53
80 46 00
48.38
87 37 30
12.48
53 22 30
178. 75
60 15 00
148. 91
67 07 30
116.80
74 00 00
82.91
80 52 30
47.73
87 45 00
11.82
53 30 00
178. 23
60 23 30
148. 34
67 15 00
116.20
74 07 30
83.38
81 00 00
47.08
87 52 30
11.16
53 37 30
177.71
60 30 00
147. 77
67 22 30
115. 59
74 16 00
81.65
81 07 30
46.44
88 00 00
10.51
53 45 00
177. 19
60 37 30
147. 21
67 30 00
114. 99
74 22 30
81.01
81 15 00
45.79
88 07 30
9.85
53 52 30
176. 67
60 45 00
146. 64
67 37 30
114. 39
74 30 00
80.38
81 22 30
45.14
88 15 00
9.20
54 00 00
176. 14
60 52 30
146. 07
67 45 00
113. 78
74 37 30
79.75
81 30 00
44.49
88 22 30
8.54
54 07 30
175. 62
61 00 00
145. 50
67 52 30
113.18
74 45 00
79.12
81 37 30
43.84
88 30 00
7.88
54 15 00
175. 10
61 07 30
144.93
68 00 00
112.57
74 53 30
78.49
81 45 00
43.19
88 37 30
7.22
54 22 30
174. 57
61 15 00
144. 36
68 07 30
111. 97
75 00 00
77.86
81 53 30
42.64
88 45 00
6.57
54 30 00
174. 04
61 22 30
143. 79
68 15 00
111.36
76 07 30
77.22
82 00 00
41.89
88 53 30
5.91
54 37 30
173. 51
61 30 00
143. 22
68 22 30
110. 76
75 16 00
76.59
82 07 30
41.24
89 00 00
6.36
54 45 00
172. 99
' 61 37 30
142. 65
68 30 00
110. 15
76 22 30
75.95
82 15 00
40.59
89 07 30
4.60
54 52 30
172. 46
61 47 00
142. 08
63 37 30
109. 54
75 30 00
75.33
82 22 30
39.94
89 15 00
3.94
55 00 00
171. 93
61 52 30
141. 50
68 45 00
108. 93
75 37 30
74.69
83 30 00
39.29
89 22 30
8.28
55 07 30
171. 39
i 62 00 00
140. 93
68 52 30
108. 32
75 45 00
74.05
83 37 30
38.64
89 30 00
2.63
55 15 00
170. 86
63 07 30
140. 35
69 00 00
107. 71
75 52 30
73.42
83 45 00
37.99
89 37 30
1.97
55 22 30
170. 33
62 15 00
139. 78
69 07 30
107. 10
76 00 00
72.78
82 52 30
37.34
89 45 00
1.31
55 30 00
169. 79
1 62 22 30
139. 20
69 15 00
106. 49
76 07 30
72.14
83 00 00
36.69
89 52 30
0.66
55 37 30
169. 26
1 62 30 00
138. 62
69 22 30
105. 88
76 15 00
71.61
83 07 30
36.03
190 A MANUAL OF TOPOGEAPHIC METHODS.
TA.BLE XXVII.— fitf/ofs /or the compuiation of (jeodetic latitudes, longittides, and azimuths.
[From Appendix No. 7, Kcport U. S. Crast and Geodetic Survey, 1884.]
LATITUDE 25^.
log. A
log. B
Iditt. 1" = — 0.06 diff.l" = — 0.16
log.C
diff.l" = + 0.54
log. D log. E
diff. 1" = +0.03 diff. 1" = + 0.04
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 191
Table XXVXI. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 26°.
log. A
log. B
log. C
log. D
log. E
Latitude.
(liflF.l" = -0.06
diff. 1"— — 0.17
diff. 1"= +0.53
diff. l" = +0.03
diff. 1"= +0.04
26 00
8. 509 4439
8. 511 8283
1. 09400
2.2885
5. 8458
1
36
72
432
87
61
33
62
464
89
63
3
29
52
496
91
66
4
26
42
527
93
69
05
22
32
559
95
71
6
19
32
691
97
74
7
IG
12
633
99
77
8
12
01
655
2. 2901
79
9
09
8. 5U 8191
687
03
82
10
8. 509 4406
8.511 818!
1.09718
2. 2905
6.8485
11
02
71
750
07
88
12
8. 509 4399
61
782
09
90
la
95
51
814
11
93
14
92
40
845
13
96
15
88
30
877
15
98
16
85
20
909
17
5. 8501
17
82
10
940
19
04
18
78
00
972
20
06
19
8. 511 8089
1. 10004
22
09
20
8. 509 4372
8. 511 8079
1. 10036
2. 2924
6. 8512
21
08
69
067
26
14
22
65
59
099
28
17
23
61
48
130
30
20
24
58
38
162
32
22
25
54
28
194
34
25
26
51
18
225
36
28
27
48
08
257
38
30
28
44
8. 611 7997
288
40
33
29
41
87
820
42
36
30
8. 609 4337
8. 611 7977
1. 10351
2.2944
5. 8539
31
34
67
383
46
41
32
31
56
• 414
47
44
33
27
46
446
49
47
34
24
36
477
51
49
35
20
25
609
53
52
36
17
15
540
55
55
37
13
05
571
57
57
38
10
8. 511 7895
603
69
60
39
07
84
634
61
63
40
8. 509 4303
8. 511 7874
1. 10666
2. 2963
5. 8566
41
00
64
697
65
68
42
8. 509 4296
53
728
66
71
43
93
43
760
68
74
44
89
33
791
70
76
45
86
22
832
72
79
46
83
12
854
74
82
47
79
02
885
76
85
48
76
8. 511 7791
9J6
78
87
49
73
81
947
80
90
50
8. 609 4269
8. 511 7771
1. 10979
2.3981
5. 8593
51
05
60
1. 11010
83
95
52
62
50
041
85
98
53
5S
40
073
87
5.8601
54
66
29
103
89
04
55
52
19
134
91
06
56
48
09
166
93
09
57
46
8.511 7698
197
94
12
58
41
88
228
96
14
59
38
77
259
98
17
60
8. 509 4234
8. 511 7667
1. 11290
2.3000
5. 8630
192
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic lalituclcs, longitudes, and azimuths — Coutinued,
LATITUDE 27°.
log. A
log. B
log. C
log. D
log. E
latitude.
difl'. 1"=— 0.06
diir.l"=-0.18
diff. 1"=+0.51
diff.l"=+0.03
diff. 1"= +0.05
27 00
8. 509 4234
8.511 7667
1. 11290
2. 3000
5. 8620
1
31
57
321
02
23
2
27
46
352
04
25
3
24
36
383
06
28
4
20
25
414
07
31
5
17
15
445
09
34
6
13
05
476
11
36
7
10
8. 511 7594
507
13
39
8
06
84
538
15
42
9
03
73
569
17
44
10
8. 509 4200
8. 511 7563
1. 11600
2.3018
5. 8647
11
8. 509 4196
53
631
20
50
12
93
42
662
22
53
13
89
32
693
24
55
14
86
21
724
26
58
15
82
11
755
27
01
36
79
00
786
29
64
17
75
8. 511 7490
817
31
66
18
79
848
33
69
19
68
69
878
35
72
20
8.509 4165
8. 511 7458
1. 11909
2. 3037
5. 8675
21
61
48
940
38
77
22
58
37
971
40
80
23
54
27
1. 12002
42
83
24
51
16
032
44
86
25
47
06
063
45
88
26
44
8. 511 7395
094
47
91
27
40
85
125
49
94
28
37
74
156
51
97
29
33
64
186
63
99
30
8. 509 4130
8. 511 7353
1. 12217
2. 3054
5. 8702
31
26
43
248
66
05
32
23
32
278
58
08
33
19
22
' 309
60 .
10
34
16
11
340
61
13
35
12
01
370
63
16
36
08
8. 511 7290
401
65
19
37
05
80
482
67
22
38
01
69
462
69
24
39
8. 509 4098
58
493
70
27
40
8.509 4094
8. 511 7248
1.12523
2. 3072
5. 8730
41
91
37
554
74
33
42
87
27
584
76
35
43
84
16
615
77
38
44
80
06
646
79
41
45
77
8. 511 7195
676
81
44
46
73
84
707
83
46
47
70
74
737
84
49
48
66
63
768
86
52
49
63
53
798
88
55
50
8. 509 4059
8. 511 7142
1.12829
2. 3090
5. 8757
51
56
31
859
91
60
.52
52
21
889
93
63
53
49
10
920
95
66
54
45
00
950
96
69
55
41
8.511 7089
981
98
72
56
38
78
1. 13011
2. 3100
74
57
34
68
■ 041
02
77
58
31
57
072
03
80
59
27
46
102
05
83
60
8. 509 4024
8. 511 7036
1. 13132
2.3107
5. 8785
FACTORS FOE COMPUTATION OF GEODETIC POSITIONS. 193
Table XXVII. — Factors for ilie computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 28°.
log. A
log. B
log. C
log. D
log. E
Latitude.
diff. 1"=— 0.06
difif. l"=-0.1if
diflf. l"=+0.50
diff. l"=+0.03
diff. l"=+0.05
28 00
8. 509 4024
8. 511 7036
1. 13132
2. 3107
5. 8785
1
20
25
163
09
88
2
17
14
193
10
91
3
13
04
223
12
94
4
10
8. 511 6993
254
14
97
05
06
82
284
15
99
6
02
72 .
314
17
5. 8802
7
8.509 3999
61
345
19
05
8
95
50
375
20
08
9
92
40
405
22
11
10
8. 509 3988
8. 511 6929
1. 13435
2. 3124
5. 8813
11
85
18
465
26
16
12
81
08
496
27
19
13
78
8. 511 6897
526
29
22
14
74
86
556
31
25
15
70
75
586
32
27
16
67
65
616
34
30
17
63
54
646
36
33
18
60
43
677
37
36
19
56
33
707
39
39
20
8.509 3952
8.511 6822
1. 13737
2.3141
5.8841
21
49
11
767
42
44
22
45
00
797
44
47
23
42
8.511 6790
827 .
46
50
24
38
79
857
47
53
25
35
68
887
49
55
26
31
57
917
51
58
27
27
47
947
52
61
28
24
36
977
54
64
29
20
25
1. 14007
56
67
30
8.509 3917
8.511 6714
1. 14037
2. 3157
5.8870
31
13
04
067
69
72
32
09
8. 511 6693
097
61
75
33
06
82
127
62
78
34
02
71
157.
64
81
35
8.509 3899
61
187
66
84
36
95
50
217
67
87
37
92
39
247
69
89
38
83
28
277
70
92
39
84
17
307
72
95
40
8. 509 3881
8. 511 6607
1. 14337
2. 3174
5. 8898
41
77
8. 511 6596
366
75
5.8901
42
73
85
396
77
04 ,
43
70
74
426
79
06
44
66
63
456
80
09
45
63
52
486
82
12
46
59
42
516
83
15
47
55
31
545
85
18
48
52
20
575
87
21
49
48
09
605
88
23
50
8. 509 3845
8. 511 6498
1. 14635
2. 3190
5.8926
51
41
87
664
92
29
52
37
76
694
93
32
63
34
66
724
95
35
54
30
55
754
96
38
55
26
a
783
98
40
56
23
33
813
2. 3200
43
57
19
22
843
01
46
58
16
11
872
03
49
59
12
00
902
04
52
60
8.509 3808
8.511 6389
1. 14932
2. 3206
5.8955
MON SXII-
-13
194
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the compatation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 29°.
Latitude.
log. A
log. B
log.C
log.D
log.E
difif. 1"=— 0. 06
difl.l"=— 0.18
diff.l"=+0.49
diff. l"=+0. 03
diff.l"=+0.05
29 00
8. 509 3808
8. 511 6389
1.14932
2.3206
5.8955
1
05
78
961
08
58
01
68
991
09
60
3
8.509 3797
57
1.15021
11
63
4
94
46
050
12
66
05
90
35
080
14
69
6
86
24
109
15
72
7
83
13
139
17
75
8
79
02
168
19
78
9
76
8. 511 6291
198
20
80
10
8. 509 3772
8.511 6280
1. 15228
2.3222
5.8983
11
68
69
257
23
86
12
65
58
287
25
89
13
61
47
316
26
92
14
57
36
346
28
95
15
54
26
375
30
98
16
50
15
405
31
5. 9000
17
46
04
434
33
03
18
43
8. 511 6193
464
34
06
19
39
82
493
36
09
20
8. 509 3735
8. 511 6171
1.15522
2.3237
5.9012
21
32
60
552
39
15
22
28
49
581
40
18
23
24
38
611
42
21
24
21
27
640
43
23
25
17
16
670
45
26
26
13
05
699
47
29
27
10
8.511 6094
728
48
32
28
06
83
758
50
35
29
02
72
787
51
38
30
8. 509 3699
8. 511 6061
1.15816
2.3253
5. 9041
31
95
50
846
54
43
32
91
39
875
56
46
33
88
28
904
57
49
34
84
17
934
59
52
35
80
06
963
60
55
36
77
8. 511 5995
992
62
58
37
73
84
1. 16021
63
61
38
69
73
051
65
64
39
66
61
080
66
67
40
8. 509 3662
8. 511 5950
1. 16109
2. 3268
5. 9069
41
58
39
138
69
72
42
55
28
167
71
75
43
51
17
197
72
78
44
47
06
226
74
81
45
44
8. 511 5895
255
75
84
46
40
84
284
77
87
47
36
73
313
78
90
48
33
62
343
80
93
49
29
51
372
81
96
50
8. 509 3625
8. 511 5840
1. 16401
2. 3283
5. 9098
51
21
29
430
84
5. 9101
52
18
18
459
86
04
53
14
06
488
87
07
54
10
8. 511 5795
517
89
10
55
07
84
546
90
13
56
03
73
575
92
16
57
8. 509 3599
62
604
93
19
58
96
51
633
95
22
59
92
40
663
96
25
60
8. 509 3588
8.511 5729
1. 16692
2. 3298
5. 9127
FACTORS FOR COMPUTATIOlSr OF GEODETIC POSITIONS. 195
Table XXVIl. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 30°.
log. A
log. B
log. C
log. D
log. E
Latitude.
dlff.l" = — 0.06
diff.l"=— 0.19
diff.l"= + 0.48
diff.l" = +0.02
diff. l" = +0.05
30 00
8. 509 3588
8. 511 5729
1. 16692
2, 3298
5. 9127
1
84
18
721
99
30
2
81
06
750
2. 3301
33
3
77
8.511 5695
778
02
36
4
73
84
807
04
39
05
69
73
836
05
42
6
66
62
865
06
45
7
62
51
894
08
48
8
58
40
923
09
51
9
55
28
952
11
54
30
8. 509 3551
8.511 5617
1. 16981
2. 3312
5. 9157
11
47
06
1. 17010
14
59
12
43
8.511 5595
039
15
62
13
40
84
068
17
65
14
36
73
097
18
68
15
32
61
126
19
71
16
29
50
155
21
74
17
25
39
184
22
77
18
21
28
212
24
80
19
17
17
241
25
83
20
8. 509 3514
8.511 5505
1. 17270
2. 3327
5. 9186
21
10
8. 511 5494
299
28
89
22
06
83
328
30
92
23
02
72
357
31
95
24
8. 509 3499
61
385
32
98
25
95
49
414
34
5. 9200
26
91
38
443
35
03
27
88
27
472
37
06
28
84
16
500
38
09
29
80
04
529
39
12
30
8. 509 3476
8.511 5393
1. 17558
2.3341
5. 9215
31
72
82
587
42
18
32
69
71
615
44
21
33
65
59
644
45
24
34
61
48
673
47
27
35
57
37'
701
48
30
36
54
26
730
49
33
37
50
14
759
51
36
38
46
03
788
52
39
39
42
8. 511 5292
816
54
42
40
8. 509 3439
8. 511 5281
1. 17845
2. 3355
5.9245
41
35
69
874
56
'48
42
31
58
902
58
51
43
27
47
931
59
53
44
24
35
959
60
56
45
20
24
988
62
59
46
16
13
1. 18017
63
62
47
12
02
045
65
65
48
09
8.511 5190
074
66
68
49
05
79
102
67
71
50
8. 509 3401
8.511 5168
1. 18131
2.3368
5. 9274
51
8. 509 3397
56
160
70
77
52
94
45
188
71
80
53
90
34
217
73
83
54
86
22
245
74
86
55
.82
11
274
76
89
56
78
00
302
77
92
57
75
8.511 5088
331
78
95
58
71
77
359
80
98
59
67
66
388
81
5. 9301
60
8. 509 3363
8.511 5054
1. 18416
2.3382
5. 9304
196
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimufhs — Coutiuued.
LATITUDE 31°.
log. A
log.B
log. C
log. D
log. E
Latitude.
diff. 1"=— 0.06
diff. 1"=— 0.19
diff.l"=+0.47
diff.l"=+0.02
diff.l"=+0.05
31 00
8. 509 3363
8. 511 5054
1. 18416
2. 3382
5.9304
1
60
43
445
84
07
2
66
32
473
85
10
3
52
20
501
86
13
4
48
09
530
88
16
05
44
8. 511 4998
558
89
19
6
41
86
587
90
22
7
37
75
615
92
26
8
33
61
643
93
28
9
29
52
672
95
31
10
8. 509 3325
8. 5U 4941
1. 18700
2. 3396
5.9334
11
22
29
729
97
37
12
18
18
757
99
39
13
14
07
785
2. 3400
42
14
10
8. 511 4895
813
01
45
15
06
84
842
02
48
16
03
72
870
04
61
17
8. 509 3299
61
898
06
54
18
95
50
927
06
67
19
91
38
955
08
60
20
8.509 3287
8. 511 4827
1. 18983
2. 3409
5. 9363
21
84
15
1. 19012
10
66
22
80
04
040
12
69
23
76
8. 611 4793
068
13
72
24
81
096
14
75
25
68
70
125
16
78
26
65
58
153 .
17
81
27
61
47
181
18
84
28
57
35
209
20
87
29
53
24
238
21
90
30
8. 509 3249
8. 511 4713
1. 19266
2. 3422
5.9393
31
46
01
294
23
96
32
42
8. 511 4690
322
25
99
32
38
78
351
26
5. 9402
34
34
67
379
27
05
35
30
55
407
29
08
36
26
44
435
30
11
37
23
32
463
31
14
38
19
21
491
33
17
39
15
09
520
34
20
40
8.509 3211
8. 511 4598
1. 19548
2.3435
6. 9423
41
07
86
576
36
26
42
03
75
604
38
29
43
00
63
632
39
32
44
8. 509 3196
52
660
40
35
45
92
40
688
41
38
46
83
29
716
43
41
47
84
17
744
44
44
48
81
06
772
45
47
49
77
8. 511 4494
800
47
50
50
8. 509 3173
8. 511 4483
1. 19828
2.3448
6.9453
51
09
71
856
49
56
52
65
60
884
50
69
53
61
48
912
52
62
54
67
37
940
53
65
55
54
26
968
54
68
56
50
14
996
55
72
57
46
02
1. 20024
57
75
68
42
8.511 4391
052
58
78
59
38
79
080
59
81
60
8. 509 3134
8.5U 4368
1.20108
2.3460
5.9484
FACTORS FOE COMPUTATION" OP GEODETIC POSITIONS.
197
Table XXVll.— Factors for
; compiitaUoii of geodetic latitudes. Ion
LATITUDE 321
\id azimuths — Continued.
log. A
log.B
log.C
log.D
log.E
Latitude.
diff. 1"=— 0.06
diff. 1"=— 0.19
diff. l"=+0.46
dift'. l"=+0.02
diff. l"=+0.05
32 00
8.509 3134
8. 511 4368
1.20108
2.3460
6. 9484
1
31
56
136
62
87
27
44
164
63
90
3
23
S3
192
64
93
4
19
21
220
66
96
05
15
10
243
67
99
6
11
8.511 4298
276
68
6. 9502
7
07
87
304
69
05
8
04
75
332
70
08
9
00
63
360
71
11
10
8. 509 3096
8. 511 4252
1. 20337
2. 3473
5. 9514
11
92
40
415
74
17
12
38
29
443
76
20
13
84
17
471
76
23
14
80
05
499
78
26
15
76
8.511 4194
627
79
29
16
73
82
655
80
32
17
67
71
682
.81
36
18
65
59
610
82
38
19
61
47
638
84
41
20
8.509 3057
8. 511 4136
1. 20666
2. 3485
5. 9644
21
53
24
694
36
47
22
49
13
722
87
50
23
46
01
749
88
53
24
42
8.511 4089
777
90
66
25
38
78
805
91
60
26
34
66
833
92
63
27
30
54
860
93
06
28
26
43
888
94
69
29
22
31
916
96
72
30
8. 509 3018
8. 611 4020
1. 20944
2. 3497
5. 9575
31
15
03
971
98
78
32
11
3. 511 3996
999
99
81
33
07
35
1. 21027
2. 3500
84
34
03
73
054
02
87
35
8.509 2999
61
032
03
90
36
95
50
110
04
93
37
91
33
137
05
96
33
87
26
165
06
99
39
83
15
193
07
5. 9602
40
8. 509 2930
3. 511 3903
1. 21220
2. 3509
5. 9605
41
76
8. 511 3391
248
10
08
42
72
79
276
11
U
43
68
63
303
12
16
44
64
56
331
13
18
45
60
44
368
14
21
46
66
33
386
16
24
47
62
21
414
17
27
43
43
09
441
18
30
49
44
8. 511 3798
469
19
33
50
8. 509 2940
8. 611 3786
1. 21496
2. 3620
6.9636
51
37
74
524
21
39
52
33
63
551
23
42
53
29
61
579
24
46
54
25
39
607
25
48
55
21
27
634
26
51
56
17
16
662
27
64
57
13
04
689
28
68
68
09
8. 511 3692
717
29
61
59
06
80
744
31
64
60
8. 509 2901
8. 611 3669
1. 21772
2. 3532
6. 9667
15:18
A MAXUAL OF TOPOGEAPHIO METHODS.
Table XX^'II. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 38°,
log. A
log.B
log. C
log. D
log. E
Latitude.
diff.l"= — 0.07
di£f.l"= — 0.20
diff.l"=+0.45
AiS. l"=+0.02
diff.l"=+0.05
33 00
8.509 2901
8.511 3669
1.21772
2. 3532
5. 9667
1
8.509 2897
57
799
33
70
2
94
45
827
34
73
3
90
33
854
35
76
i
86
22
882
36
79
05
82
10
909
37
82
6
78
8. 511 3598
937
38
85
7
74
86
964
40
88
8
70
75
992
41
92
9
66
63
1.22019
42
95
10
8.509 2862
8. 511 3551
1. 22047
2. 3643
6. 9698
11
58
39
074
44
5. 9701
12
54
28
101
45
04
13
51
16
129
46
07
14
47
04
156
47
10
15
43
8.611 3492
184
49
13
16
39
80
211
50
16
17
35
69
238
51
19
18
31
57
266
52
22
19
27
45
293
53
26
20
8. 509 2823
8. 511 3433
1. 22321
2. 3554
6. 9729
21
19
21
348
65
32
22
15
10
375
56
35
23
11
8.511 3398
403
57
38 •
24
07
86
430
58
41
25
03
74
457
60
44
26
8. 509 2799
62
485
61
47
27
95
51
512
62
50
28
91
39
539
63
53
29
88
27
567
64
57
30
8. 509 2784
8. 511 3315
1. 22594
2. 3565
5.9760
31
80
03
621
66
63
82
76
8.511 3291
648
67
66
33
72
80
676
68
69
34
68
68
703
69
72
35
64
58
730
70
75
36
60
44
757
71
78
37
56
32
785
73
81
38
52
20
812
74
85
39
43
09
839
75
88
40
8. 509 2744
8. 511 3197
1.22866
2. 3576
5. 9791
41
40
85
893
77
94
42
36
73
921
78
97
43
32
61
948
79
5.9800
44
28
49
975
80
03
45
24
37
1. 23002
81
06
40
20
25
029
82
10
47
16
13
057
83
13
48
12
02
084
84
16
49
08
8.511 3090
111
85
19
50
8. 509 2704
8. 511 3078
1. 23138
2.3586
6.9822
51
01
66
165
87
26
52
8.509 2697
54
192
88
28
53
93
42
220
89
31
54
89
30
247
91
35
55
85
18
274
92
38
56
81
06
301
93
41
57
77
8. 511 2995
328
94
44
68
73
83
355
95
47
59
69
71
382
96
50
60
8. 509 2665
8. 511 2959
1.23409
2. 3597
6.9853
FAOTOES FOE COMPUTATION OF GEODETIC POSITIONS.
199
Table XXVII. — Factors for the computation of geodetic latitudes, longitades, and azimuths — Continued.
LATITUDE 340.
log. A
log.B
lug.C
log.B
log.E
Latitude
diff. 1"=— 0.07
diff.l"=_0.20
diff, 1" = + 0.45
difi'. l"=+0.02
diff. 1" = + 0.05
34 00
8. 509 2665
8. 511 2959
1. 23409
2. 3697
5. 9853
1
61
47
437
98
57
2
57
35
464
99
60
3
53
23
491
2. 3600
63
4
49
11
518
01
66
05
45
8.511 2899
546
02
69
6
41
87
572
03
72
7
37
76
699
04
76
8
33
63
626
05
79
9
30
51
653
06
82
10
8. 609 2625
8.511 2840
1. 23680
2, 3607
5. 9886
11
21
28
707
08
88
12
17
16
734
09
91
13
13
04
761
10
94
14
09
8. 511 2792
788
11
97
15
05
80
815
12
6. 9901
16
01
68
842
13
04
17
8. 609 2597
56
869
14
07
18
93
44
896
16
10
19
89
32
923
16
13
20
8. 609 2685
8. 611 2720
1. 23950
2. 3617
5. 9916
21
81
08
977
18
19
22
77
8. 511 2696
1. 24004
19
23
23
73
84
031
20
26
24
69
72
068
21
29
25
65
60
085
22
32
26
61
48
112
23
35
27
57
36
139
24
38
28
63
24
166
25
42
29
49
12
192
26
45
30
8. 509 2545
8. 611 2600
1. 24219
2. 3627
5. 9948
31
41
8. 611 2688
246
28
61
32
37
76
273
29
64
33
33
64
300
30
57
34
29
62
327
31
61
35
25
40
354
32
64
36
21
28
381
33
67
37
17
16
408
34
70
38
13
04
434
36
73
39
09
8. 511 2492
461
36
76
40
8. 509 2506
8. 511 2480
1.24488
2. 3637
5. 9980
41
0]
68
515
38
83
42
8.509 2497
56
542
39
86
43
93
44
569
40
89
44
89
32
595
41
92
45
85
20
622
42
96
46
81
08
649
43
99
47
77
8.511 2396
676
44
6. 0002
48
73
84
703
44
06
49
69
72
729
45
08
50
8.509 2465
8.511 2360
1. 24756
2. 3646
6. 0011
51
61
48
783
47
15
52
67
35
810
48
18
53
53
23
837
49
21
54
49
11
863
50
24
55
45
8. 511 2299
890
51
27
5S
41
87
917
52
31
67
37
76
944
63
34
58
33
63
970
64
37
59
29
51
997
66
40
60
8. 509 2425
2.511 2239
1. 26024
2. 3666
6. 0043
200
A MANUAL OP TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the comjyutation of geodetic latitudes, longitudes, and azimuths — Coutinued.
LATITtTDE S5°.
log. A
log.B
log.C
log.D
log.E
Latitude.
diff. 1"=— 0.07
diff. 1"=— 0.20
diff. 1"= + 0.44
difl',l"= + 0.01
diff. 1"= + 0.05
35 00
8.509 2425
8. 511 2239
1. 25024
2. 3656
6, 0043
1
21
27
050
57
47
2
17
15
077
68
50
3
13
03
104
59
53
4
09
8.5112191
131
59
56
05
05
78
157
60
59
6
01
66
184
61
63
7
8..=;09 2396
54
211
62
66
8
93
42
237
63
69
9
88
30
264
64
72
10
8.509 2384
8. 511 2118
1.25291
2.3665
6. 0075
11
80
06
317
66
79
12
76
8. 511 2094
344
67
82
13
72
82
371
68
85
14
68
70
397
69
88
15
64
57
424
70
91
16
60
45
461
70
96
17
56
33
477
71
98
18
52
21
504
72
6. 0101
19
48
09
531
73
04
20
8.509 2344
8.511 1997
1. 25557
2.3674
6. 0107
21
40
85
584
76
11
22
36
72
610
76
14
23
32
60
637
77
17
24
28
48
664
78
20
25
24
36
690
79
23
26
20
24
717
79
27
27
16
12
743
80
30
28
12
00
770
81
33
29
08
8. 611 1887
796
82
36
30
8.509 2304
8. 511 1875
1. 25823
2.3683
6. 0140
31
00
63
850
84
43
32
8. 609 2296
51
876
85
46
33
92
39
903
86
49
34
87
27
929
86
52
35
83
15
956
87
56
36
79
02
982
88
59
37
75
8.511 1790
1.26009
89
62
38
71
78
036
90
65
39
67
66
062
91
69
40
8.609 2263
8. 511 1754
1. 26088
2. 3692
6. 0172
41
59
41
115
93
75
42
65
29
141
93
78
43
51
17
168
94
81
44
47
05
194
95
85
45
43
8. 511 1693
221
96
88
46
39
80
247
97
91
47
35
68
274
98
94
48
31
56
300
99
98
49
27
44
327
99
6. 0201
50
8. 509 2222
8. 511 1632
1. 26353
2. 3700
6.0204
51
18
20
380
01
07
52
14
07
406
02
11
53
10
8.511 1596
432
03
14
54
06
83
469
04
17
55
02
71
485
05
20
56
8. 509 2198
58
512
05
24
57
94
46
538
06
27
58
90
34
665
07
30
59
86
22
591
08
33
60
8. 509 2182
8. 511 1510
1.26617
3. 3709
6. 0237
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 201
Table XXVII. — Factors for the computation of geodetic latitudes, Jongitudes, and azimuths — Continued.
LATITUDE 36°
log. A
log. B
log. C
log. D
log. E
Latitude.
dlflf.l" = -0.07
diff. 1"=— 0.20
diff. l"=+0.44
diff. J"=+0.01
diff. ] "=+0.05
36 00
8. 509 2182
8. 511 1510
1. 26617
. 2.3709
6.0237
1-
78
8.511 1497
644
10
40
2
74
85
670
10
43
3
70
73
697
11
46
4
65
61
723
12
60
05
61
48
749
13
53
6
57
36
776
14
56
7
53
24
802
14
59
8
49
12
828
15
63
9
45
8.511 1399
855
16
66
10
8. 509 2141
8. 511 1387
1. 26881
2. 3717
6.0269
11
37
75
908
18
72
12
33
63
934
19
76
13
29
50
960
19
79
14
25
38
987
20
82
15
21
26
1. 27013
21
85
16
16
14
039
22
89
17
12
01
066
23
92
18
08
8.511 1289
092
23
95
19
04
77
118
24
99
20
8. 509 2100
8. 511 1265
1. 27145
2. 3725
6. 0302
21
8. 509 2096
52
171
26
05
22
92
40
197
27
08
23
88
28
223
27
12
24
84
15
250
28
15
25
80
03
276
29
18
26
75
8.511 1191
302
30
21
27
71
79
329
31
25
28
67
66
355
31
28
29
63
54
381
32
31
30
8. 509 2059
8.511 1142
1. 27407
2. 3733
6. 0334
31
55
29
434
34
38
32
51
17
460
35
41
33
47
05
486
35
44
34
43
8. 511 1092
512
36
48
35
39
80
639
37
51
36
35
68
565
38
64
37
30
56
591
38
57
38
26
43
617
39
61
39
22
31
644
40
64
40
8. 509 2018
8. 511 1019
1. 27670
2. 3741
6. 0367
41
14
06
696
41
71
42
10
8. 511 0994
722
42
74
43
06
82
748
43
77
44
02
69
775
44
80
46
8.509 1998
57
801
45
84
46
93
45
827
45
87
47
89
32
853
46
90
48
85
20
879
47
94
49
81
08
905
48
97
50
8. 509 1977
8. 511 0895
1. 27932
2. 3748
6. 0400
51
73
83
958
49
03
52
69
71
984
50
07
53
65
58
1. 28010
51
10
54
61
46
036
51
13
55
56
34
062
52
17
56
52
21
088
63
20
57
48
09
114
54
23
58
44
8. 611 0797
141
54
27
59
40
84
167
55
30
60
8. 509 1936
8. 511 0772
1. 28193
2. 3756
6. 0433
202
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and a^iniulhn — Continued.
LATITUDE 87°.
log. A
log. B
log. C
log. D
log.E
Latitude.
dUi".l"=— 0.07
diff.l"= — 0.21
diir.l"= + 0.43
diff. 1"— + 0. 01
diff. 1"= + 0.06
37 00
8.509 1936
8. 511 0772
1.28193
2. 3756
6. 0433
1
32
60
219
56
. 37
28
47
245
57
40
3
23
35
271
58
43
i
19
22
297
69
46
05
15
10
324
69
50
6
11
8. .511 0698
350
60
53
07
85
376
61
56
8
03
73
402
62
60
9
8. 509 1899
61
428
62
63
10
8. 509 1895
8.611 0648
1.28454
2. 3763
6, 0466
11
90
36
480
64
70
12
86
23
506
65
73
13
82
11
532
65
76
14
78
8.511 0599
558
66
80
15
74
86
584
67
83
16
70
74
610
67
86
17
66
61
636
68
89
18
62
49
662
69
93
19
57
37
638
69
96
20
8.509 1853
8.511 0524
1. 28715
2. 3770
6. 0499
21
49
12
741
71
6. 0503
22
45
00
767
72
06
23
a
8.511 0487
793
72
09
24
37
75
819
73
13
25
33
62
. 845
74
16
26
28
50
871
74
19
27
24
37
897
75
23
28
20
25
923
76
26
29
16
13
949
76
29
30
8.509 1812
8. 511 0400
1. 28975
2.377/
6. 0533
31
08
8. 511 0388
1. 29001
78
36
32
04
75
027
79
39
33
00
63
053
79
43
34
8. 509 1795
51
079
80
46
35
91
38
104
81
49
36
87
26
130
81
53
37
83
13
166
82
56
38
79
01
182
83
59
39
75
8.511 0288
208
83
63
40
8. 509 1771
8.511 0276
1. 29234
2. 3784
6. 0566
41
66
64
260
85
69
42
62
51
286
86
73
43
58
39
312
86
76
44
54
26
338
87
79
45
50
14
364
87
83
46
46
01
390
88
86
47
41
8. 511 0189
416
89
89
48
37
76
442
89
93
49
33
64
468
90
96
50
8. 509 1729
8. 511 0151
1.29494
2, 3791
6. 0600
51
25
39
620
91
03
52
21
26
546
•i 92
06
53
16
14
571
93
10
54
12
02
697
93
13
55
08
8. 511 0089
623
94
16
56
04
77
649
95
20
57
00
64
675
95
23
58
8.509 1696
52
701
96
26
59
92
39
727
96
30
60
8. 509 1687
8. 511 0027
1. 29753
2. 3797
6. 0633
FAOTOES FOli COMPUTATION OF GEODETIC POSITIONS. 203
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 38°.
log. A
log. B
log. C
log. D
log. E
Latitude.
difl.l"=— 0.07
aiff.l"=— 0.21
diff.l"= + 0.43.
diff.l" = + 0.01
diff.l"= + 0.06
38 00
8.509 1687
8. 511 0027
1. 29753
2. 3797
6. 0633
1
83
14
778
98
36
2
79
02
804
98
40
3
75
8. 510 9989
830
99
43
4
71
77
856
2. 3800
47
05
67
64
882
00
50
6
62
52
908
01
53
7
58
39
934
02
57
8 ■
54
27
959
02
60
9
50
14
985
03
63
.0
8. 509 1646
8. 510 9902
1. 30011
2. 3803
6. 0667
11
42
8. 510 9889
037
04
70
12
37
77
063
05
73
13
33
64
089
05
77
14
29
52
114
06
80
16
25
39
140
07
84
16
21
27
166
07
87
17
17
14
192
08
90
18
12
02
218
08
94
19
08
8.510 9789
243
09
97
20
8.509 1604
8. 510 9777
1. 30269
2. 3810
6. 0701
21
00
64
295
10
04
22
8. 509 1596
52
321
U
07
23
92
39
347
12
11
24
87
- 27
372
12
14
25
83
14
398
13
17
26
79
01
424
13
21
27
75
8. 510 9689
450
14
24
28
71
77
476
16
28
29
66
64
501
15
31
30
8.509 1562
8. 510 9652
1.30527
2. 3816
6. 0734
31
58
39
553
16
38
32
54
27
579
17
41
33
50
14
604
17
44
34
46
01
630
18
48
35
41
8.510 9589
656
19
51
36
37
76
682
19
66
37
33
64
707
20
58
38
29
51
733
20
61
39
25
39
769
21
65
40
8. 509 1521
8. 510 9526
1. 30785
2. 3822
6. 0768
41
16
14
810
22
72
42
12
01
836
23
75
43
08
8. 510 9488
862
23
78
44
04
76
88T
24
82
45
00
63
913
24
85
46
8. 509 1495
61
939
25
89
47
91
38
965
26
92
48
87
26
990
26
95
49
83
13
1. 31016
27
99
50
8. 509 1479
8. 510 9401
1. 31042
2. 3827
6. 0802
51
75
8. 510 9388
067
28
06
52
70
76
093
28
09
53
66
63
119
29
13
54
62
50
144
30
16
55
58
38
170
30
19
56
53
25
196
31
23
57
49
13
221
31
26
58
45
00
247
32
30
59
41
8.510 9287
273
32
33
60
8. 509 1437
8. 510 9275
1. 31299
2.3833
6. 0836
•204
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for the compntaiion of geodetic latitudes, longitudes, and azimuths — Contiuvied.
LATITUDE S90.
log A
logB
log C
log I)
logE
Latitude.
difif. 1"=— 0.07
diff. 1"=— 0.21
diff. I"=+0.43
diff. 1"=+0.01
ditt. l"=+0.06
39 00
8. 509 1437
8. 510 9275
1. 31299
2. 3833
6. 0836
1
33
62
324
33
40
2
28
50
350
34
43
3
24
37
375
35
47
4
20
25
401
35
50
05
16
12
427
36
53
6
12
8. 510 9199
452
36
57
7
07
87
478
37
60
8
03
74
504
37
- 64
9
8.509 1399
62
529
38
67
10
8. 509 1395
8. 510 9149
1. 31555
2.3838
6.0871
U
91
36
581
39
74
12
86
24
606
39
77
13
82
11
632
2.3840
81
U
78
8. 510 9098
658
40
84
15
74
86
683
41
88
16
70
73
709
41
91
17
65
61
734
42
95
18
61
48
760
43
98
19
57
36
786.
43
6. 0902
20
8. 509 1353
8. 510 9023
1.31811 ■
2. 3844
6. 0905
21
49
10
837
44
08
22
44
8. 510 8998
862
45
12
23
40
85
888
45
15
2i
36
73
913
46
19
25
32
60
939
46
22
26
28
47
965
47
26
27
23
35
990
47
29
28
19
23
1.32016
48
32
29
15
09
041
48
38
30
8. 509 1311
8. 510 8897
1. 32067
2. 3849
6.0939
31
07
84
092
49
43
32
02
72
118
2.3850
46
33
8. 509 1298
59
144
50
50
34
S4
46
169
51
53
35
90
34
195
51
57
36
86
21
220
52
60
37
81
08
246
52
63
38
77
8.510 8796
271
53
67
39
73
83
297
53
70
40
8.509 1269
8.510 8771
1. 32323
2. 3854
6.0974
41
64
58
348
54
77
42
60
45
374
55
81
43
56
33
399
55
84
44
52
20
425
56
83
45
48
07
450
56
91
46
43
8. 510 8695
476
57
95
47
39
82
501
57
98
48
35
69
527
57
6. 1002
49
31
57
552
58
05
50
8. 509 1227
8.510 8644
1. 32578
2.3858
6. 1008
51
22
31
603
59
12
52
18
19
629
59
15
53
14
06
654
2.3860
19
54
10
8. 510 8593
680
60
22
55
06
81
705
61
26
56
01
68
731
61
29
57
8.509 1197
55
756
62
33
58
93
43
782
62
36
59
89
30
807
63
40
60
8.509 1184
8. 510 8517
1. 32833
2. 3863
6. 1043
FACTOES FOE COMPUTATION OF GEODETIC POSITIOE^S. 205
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and aaimutlis — Continued.
LATITUDE 40°.
log A
log B
log C
log D
log E
Latitude.
diff.l"=— 0.07
diff.l"=— 0.2'l
diff.l"=+0.42
diff.l"= + 0.01
diff. 1"= + 0.06
40 00
8. 509 1184
8.510 8517
1. 32833
2. 3863
6.1043
1
80
05
858
64
47
2
76
8. 510 8492
884
64
50
3
72
79
909
64
54
4
67
67
935
65
57
05
63
54
960
65
61
6
59
41
986
66
64
7
55
29
1. 33011
66
67
8
60
16
037
67
71
9
46
03
062
67
74
10
8. 509 1142
8. 510 8391
1. 33688
2. 3868
6. 1078
11
38
78
113
68
81
12
34
65
139
68
85
13
29
53
164
69
88
14
25
40
189
69
92
15
21
27
215
2. 3870
95
16
17
15
240
70
99
17
12
02
266
71
6. 1102
18
OS
8. 510 8289
291
71
06
19
04
77
317
72
09
20
8.509 1100
8. 510 8264
1. 33342
2. 3872
6.1113
21
8. 509 1096
51
363
72
16
22
91
38
393
73
20
23
87
26
418
73
23
24
83
13
444
74
27
25
79
00
469
74
30
26
74
8.510 8188
495
74
34
27
70
75
520
75
37
28
66
62
546
75
41
29
62
50
571
76
44
30
8.509 1057
8. 510 8137
1.33596
2. 3876
6. 1148
31
53
24
622
77
51
32
49
11
■ 647
77
55
33
45
8. 510 8099
673
77
58
34
41
86
698
78
62
35
36
73
723
78
65
36
32
61
749
79
69
37
28
48
774
79
72
38
24
35
800
79
76
39
19
23
825
2. 3880
79
40
8. 509 1015
8. 510 8010
1. 33850
2.3880
6. 1183
41
11
8.510 7997
876
81
86
42
07
84
901
81
90
43
02
72
926
81
93
44
8.509 0998
59
952
82
97
45
94
46
977
82
6. 1200
46
90
33
1. 34003
83
04
47
85
21
028
83
07
48
81
08
053
83
11
49
77
8. 510 7895
079
84
15
50
8. 509 0973
8. 510 7883
1. 34104
2.3884
6. 1218
51
68
70
129
84
22
52
64
57
155
85
25
53
60
44
180
85
29
54
56
32
206
86
32
55
52
19
231
86
36
56
47
06
256
86
39
57
43
8. 510 7793
282
87
43
58
39
81
307
87
46
59
34
68
332
87
50
60
8.509 0930
8. 510 7755
1. 34358
2. 3888
6. 1253
206
A MANUAL OP TOPOGEAPHIO METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 41°.
log. A
log.B
log.C
log.D
log.E
latitude.
difF.l"=— 0.07
diff.l" = — 0.21
diff. 1" = + 0.42
diff. 1"= + 0.01
diff. 1"= + 0.06
41 00
8. 509 0930
8.510 7755
1. 34358
2. 3888
6. 1253
1
26
42
383
88
57
2
22
30
408
89
60
3
18
17
434
89
64
4
13
04
459
89
67
05
09
8. 510 7691
484
90
71
6
05
79
510
90
75
7
00
66
535
90
78
8
8.509 0896
53
560
91
82
9
92
40
586
91
85
10
8.509 0888
8. 510 7628
1.34611
2. 3891
6. 1289
11
83
15
636
92
92
12
79
02
662
92
96
13
75
8. 510 7590
687
93
99
14
71
77
712
93
6. 1303
15
67
64
738
93
06
16
62
51
763
94
10
17
58
39
788
94
14
18
54
26
814
94
17
19
49
13
839
95
21
211
8. 509 0845
8. 510 7500
1.34864
2.3895
6. 1324
21
41
8. 510 7488
890
95
28
23
37
75
915
96
31
23
32
62
940
96
35
24
28
49
965
96
38
25
24
36
991
97
42
26
20
24
1. 35016
97
46
27
15
11
041
97
49
28
11
8.510 7398
066
98
53
29
07
85
092
98
56
30
8. 509 0803
8. 510 7373
1. 35117
2. 3898
6. 1360
31
8.509 0798
60
142
99
63 -
32
94
■ 47
168
99
67
33
90
34
193
99
70
34
86
22
218
2.3900
74
35
81
09
243
00
78
36
77
8. 510 7296
269
00
81
37
73
83 ■
294
00
85
38
69
70
319
01
88
39
64
58
345
01
92
40
». 509 0760
8.510 7245
1.35370
2. 3901
6. 1395
41
56
32
395
02
99
42
52
19
420
02
6. 1403
43
47
07
446
02
06
44
43
8. 510 7194
471
03
10
45
39
81
496
03
13
46
35
68
522
03
17
47
30
55
547
03
20
48
26
43
572
04
24
49
22
30
597
04
28
50
8. 509 0738
8. 510 7117
1. 35623
2.3904
6. 1431
51
13
04
648
05
35
52
09
8. 510 7091
673
OS
38
53
05
79
698
05
42
51
00
66
723
05
46
55
8. 509 0696
53
749
06
49
56
92
40
774
06
53
57
88
27
799
06
56
58
83
15
824
07
60
59
79
02
850
07
63
60
8. 509 0675
8. 510 6989
1.35875
2. 3907
6. 1467
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 2()7
Table XXVIT. — Factors for the compntaUon of ffcodelic latitudes, longitudes, and azimuths — Contimied.
LATITUDE 42°
log. A
log. B
Ing.C
logD.
log. E
Latitude.
diff.l"=— 0.07
:difl'. 1"=— 0.21
ditf. l"=+0.42
diff. l"=+0.00
diff. 1" =+0.06
42 00
8. 509 0675
8. 510 6989
1. 35875
2.3907
6. 1467 •
1
71
76
900
08
71
2
66
64
925
08
74
3
62
51
951
08
78
4
58
38
976
08
81
05
54
25
1. 36001
09
85
6
49
12
026
09
89
7
45
00
052
09
92
8
41
8. 510 6887
077
09
96
9
36
74
102
10
99
10
8. 509 0632
8.510 6861
1. 36127
2. 3910
6. 1503
11
28
48
152
10
07
12
24
36
178
10
10
13
19
23
203
11
14
14
15
10
228
11
17
15
11
8. 510 6797
253
11
21
16
07
84
278
12
25
17
02
72
304
12
28
18
8. 509 0598
59
329
12
32
19
94
46
354
12
35
20
8.509 6590
8.510 6733
1. 36379
2. 3913
6. 1539
21
85
20
404
13
43
22
81
07
430
13
46
23
77
8. 510 6695
455
13
50
24
72
82
480
13
54
25
68
69
505
14
57
26
64
56
530
14
61
27
60
43
556
14
64
28-
55
31
681
14
68
29
51
18
606
15
72
30
8.509 0547
8.530 6605
1.36631
2. 3915
6. 1575
31
43
8. 510 6592
056
15
79
32
38
79
682
15
83
33
34
66
707
16
86
84
30
54
732
16
90
35
25
41
757
16
93
36
21
28
782
16
97
37
17
15
808
17
6. 1601
38
13
02
833
17
04
39
08
8. 510 6490
858
17
08
40
8. 509 0504
8, 510 6477
1. 36883
2. 3917
6. 1612
41
00
64
908
17
15
42
8. 509 0496
51
934
18
19
43
91
38
959
18
22
44
87
25
984
18
26
45
83
13
1. 37009
18
30
46
78
00
034
19
33
47
74
8.510 6387
0.59
19
37
48
70
74
085
19
41
49
66
61
110
19
44
50
8. 609 0461
8.510 6348
1. 37135
2. 3919
6. 1648
51
57
36
160
20
52
52
53
23
185
20
55
53
48
10
210
20
59
54
44
8. 610 6297
235
20
63
55
40
84
261
20
66
56
36
71
286
21
70
57
31
59
311
21
73
68
27
46
336
21
77
59
23
33
361
21
81
60
8. 509 0419
8. 510 6220
1. 37386
2. 3921
6. 1084
208
A MANUAL OP TOPOGEAPHIO METHODS.
Table XXVII. — Factors for the computation of geodetic latitiides, longitudes, and azimuths — Contiuued.
LATITDDE 43°.
log. A
log.B
log.C
log.D
log.E
Latitude.
diff. 1"=— 0.07
diff. 1"«=— 0.21
diff'. 1"= + 0.42
diff. 1"= + 0.00
diff. 1"=+ 0.06
43 00
8. 509 0419
8. 510 6220
1.37386
2. 3921
6. 1684
1
14
07
412
22
88
2
10
8. 510 6195
437
22
92
3
06
82
462
22
95
i
01
69
487
22
99
05
8. 509 0397
56
512
22
6, 1703
6
93
43
537
22
06
7
89
30
663 ■
23
10
8
84
17
588
23
14
9
80
05
613
23
17
10
8. 509 0376
8. 510 G092
1. 37638
2.3923
6. 1721
11
71
79
663
23
25
12
67
66
688
24
28
13
63
53
713
24
32
14
59
40
739
24
36
15
54
28
764
24
39
16
50
15
789
24
43
17
46
02
814
24
47
18
41
8. 510 5989
839
25
50
19
37
76
864
25
54
20
8. 509 0333
8. 510 5963
1. 37889
2. 3925
6. 1758
21
29
50
915
25
61
22
24
38
940
25
65
23
20
25
965
25
69
24
16
12
990
25
72
25
12
8.510 5899
1. 38015
26
76
26
07
86
040
26
80
27
03
73
065
26
83
28
8. 509 0299
60
091
26
• 87
29
94
48
116
26
91
30
8. 509 0290
8. 510 5835
1. 38141
2. 3926
6. 1795
31
86
22
166
27
98
32
82
09
191
27
6. 1802
33
77
8.510 6796
216
27
06
34
73
83
241
27
09
35
69
71
266
27
13
36
64
58
292
27
17
37
60
45
317
27
20
38
56
32
342
27
24
39
52
19
367
28
23
40
8. 509 0247
8. 510 .5706
1. 38392
2.3928
6. 183]
41
43
8.510 5693
417
28
35
42
39
81
442
28
39
43
34
68
467
28
42
44
30
55
492
28
46
45
26
42
518
28
50
46
22
29
543
28
53
47
17
16
568
29
57
48
13
03
593
29
61
49
09
8.510 5591
618
29
65
50
8.609 0204
8. 510 5578
1. 38643
2. 3929
6. 1868
51
00
65
668
29
72
52
8. 509 0196
52
693
29
76
53
92
39
719
29
79
54
87
26
744
29
83
55
83
13
769
30
87
56
79
01
794
30
91
57
74
8.510 6488
819
30
94
58
70
75
844
30
98
59
66
02
869
30
6. 1902
60
8. 509 0162
8. 510 5449
1. 38894
2. 3930
6. 1905
FACTOES FOR OOMPUTATIOS^ OF GEODETIC POSITIONS. 209
Table XXVII. — Factors for the compulation of yeodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 44°.
log. A
log.B
log.C
log. D
log.E
Latitude.
diff. 1"=— 0.07
diff. 1"=— 0.21
difl-. l"=+0.42
diff. l"=+0.00
diff. l"=+0.06
44 00
8. 509 0162
8.510 5449
1. 38894
2. 3930
6. 1905
1
57
36
919
30
09
2
53
23
945
30
13
3
49
01
970
30
17
4
44
8. 510 5388
995
30
20
05
40
75
1. 39020
31
24
6
36
62
045
31
28
7
31
49
070
31
31
8
27
36
095
31
35
9
23
23
120
31
39
10
3. 509 0119
8. 510 5311
1. 39145
2. 3931
6. 1943
11
14
07
171
31
46
12
10
8. 510 5295
196
fl
50
13
06
82
221
31
54 •
14
02
09
246
31
58
15
8. 509 0097
56
271
31
61
16
93
43
296
31
6b
17
89
30
321
32
69
18
84
18
346
32
72
19
80
05
371
32
76
20
8. 509 0076
9. 510 5192
1. 39396
2. 3932
6. 1980
21
72
79
422
32
84
22
67
66
447
32
87
23
63
53
472
32
91
24
59
40
497
52
95
25
54
28
622
32
99
26
50
15
547
32
6. 2002
27 .
46
02
572
32
06
28
42
8. 510 5089
697
32
10
29
37
76
623
32
14
30
8. 509 0033
8. 510 5063
1.39648
2. 3932
6. 2017
31
29
50
673
32
21
32
24
37
698
H2
25
- 33
20
25
723
33
29
34
16
12
748
33
32
35
11
8.510 4999
773
33
36
36
07
86
79S
33
40
37
03
73
823
33
44
38
8. 508 9999
60
848
33
47
39
94
47
873
33
51
40
8. 508 9990
8. 510 4935
1.39898
2. 3933 .
6. 2055
41
86
22
924
33
59
42
81
09
949
33
62
43
77
8. 510 4896
974
33
66
44
73
83
999
33
70
45
69
70
1. 40024
33
74
46
64
57
049
33
77
47
60
44
074
33
81
48
56
32
099
33
85
49
51
19
124
33
89
50
8. 508 9947
8. 510 4806
1. 40149
2. 3933
6.2092
51
43
8. 510 4793
174
33
96
52
39
80
200
33
6. 2100
53
34
67
225
33
04
54
30
54
250
33
08
55
26
41
275
33
11
56
21
29
300
33
15
57
17
16
325
33
19
58
13
03
350
33
23
59
09
8. 510 4690
375
33
27
60
8. 508 9904
8. 510 4677
1. 40400
2. 3933
6. 2130
-14
210
A MANUAL OF TOPOGEAPHIO METHODS.
Table XXVII.— Fne/ors for Ihe c<>m}>ittalioii of geodetic latitudes, longitudes, and azimuths— Contimied.
LATITUDE -ISO.
log. A
!.liff.l"=-0.07
log. B
<litt'.l" = — 0.21
log. C
iliir.l" = H-0.42
log. D
dlff.l"=±0.00
log. E
cliff. 1" = +0.06
FACTORS FOR COMPUTATION OF GEODETIC POSITIONS. 211
Table XXVII.— Factors for the computation of geodetic latitudes, longitudes, and asmui^tg— Continued.
LATITUDE 46°.
log. A
log.B
log.C
log.D
log.E
Latitude
(liff. ]"=— 0.07
diff. 1"=— 0.21
diff. 1"= +0.42
difif. 1"=— 0.00
diff. 1"= +0.06
46 00
8. 508 9647
8. 510 3905
1. 41906
2. 3932
6. 2359
1
43
8. 510 3892
931
32
63
2
38
79
957
31
67
3
34
67
982
31
71
4
30
54
1. 42007
31
75
05
25
41
032
31
79
6
21
28
057
31
82
7
17
15
082
31
86
8
13
02
107
31
90
9
08
8.510 3739
132
31
94
10
8. 508 9604
8.510 3776
1.42157
2.3931
6. 2398
11
00
64
183
31
6. 2402
12
8. 508 959S
51
208
31
06
13
91
38
233 •
30
09
14
87
25
268
30
13
15
83
12
283
30
17
16
78
8. 510 3699
308
30
21
17
74
86
333
30
25
18
70
74
358
30
29
19
65
61
. 384
30
33
20
8. 508 9561
8. 510 3648
1. 42409
2. 3930
6. 2436
21
57
35
434
30
40
22
53
22
459
30
44
23
'48
09
484
29
48
24
44
8. 510 3596
509
29
52
25
40
84
534
29
56
26
35
71
559
29
60
27
31
58
584
29
64
28
27
45
610
29
67
29
23
32
635
39
71
30
8. 508 9518
8. 510 3519
1.42660
2. 3929
6. 2475
31
14
06
685
29
79
32
10
8. 510 3494
710
28
83
33
05
81
735
28
87
34
01
68
760
28
91
35
8. 508 9497
55
786
28
95
36
93
42
811
28
99
37
88
29
836
28
8, 2502
38
84
17
861
28
06
39
80
04
886
28
10
40
8. 508 9475
8. 510 3391
1. 42911
2. 3927
6. 2514
41
71
78
936
27
18
42
67
65
961
27
22
43
63
52
987
27
26
44
58
39
1. 43012
27
30
45
54
27
037
27
34
46
50
14
062
27
38
47
45
01
087
26
41
48
41
8. 510 3288
112
26
45
49
37
75
137
26
49
50
8.508 9433
8. 510 3262
1.43163
2.3926
6. 2553
51
28
49
188
26
57
52
24
37
213
26
61
53
20
24
238
26
65
54
16
11
263
25
69
55
11
8.510 3198
288
25
73
56
07
85
314
25
77
57
03
72
339
25
81
58
8.508 9398
60
364
25
84
59
94
47
389
25
88
60
8.508 9390
8. 510 3134
1. 43414
2. 3924
6. 2592
212
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for ike oompulallon of geodetic latitudes, longitudes, and azimuths— Continued.
LATITUDE 47°.
log. A
log.B
log.C
log.D
log.E
Latitude.
(liff. l"=.-0.07
<litt-. 1"=— 0.21
diB'. l"=+0.42
dift'. 1"=— 0.00
ditl'. l"=+0.07
47 00
8. 508 9390
8.510 3134
1.43414
2. 3924
6.2592
1
86
21
439
24
96
2
81
08
465
24
6. 2600
3
77
8.510 3095
490
24
04
4,
73
82
515
24
08
05
08
70
540
24
12
6
64
57
565
23
16
7
00
44
590
23
20
8
56
31
615
23
24
9
51
18
641
23
28
10
8. 508 9347
8. 510 3005
1.43666
2. 3923
6. 2632
11
43
8. 510 2993
691
23
35
12
' 38
SO ■
716
22
39
13
34
• 67
741
22
43
14
30
54
760
22
47
15
26
41
792
22
51
16
21
28
817
22
55
17
17
16
842
21
59
18
13
03
867
21
63
19
09
8. 510 2890
892
21
67
20
8, 508 9304
8. 510 2877
1.43917
2. 3921
6. 2671
21
00
64
943
21
75
22
8. 508 9296
51
968
20
79
23
91
39
993
20
83
24
87
26
1.44018
20
87
25
83
13
043
20
91
26
79
00
069
20
95
74
8. 510 2787
094
19
99
28
70
74
119.
19
6. 2702
29
66
62
144
19
00
30
8.508 9261
8. 510 2749
1.44169
2. 3919
6.2710
31
57
36
195
19
14
32
53
23
220
18
18
33
49
10
245
18
22
34
44
8. 510 2698
270
18
26
35
40
85
295
18
30
36
36
72
321
18
34
37
32
59
346
17
38
38
27
46
371
17
42
39
23
33
,396
17
a
40
8. 508 9219
8. 510 2621
1.44421
2. 3917
6. 2750
41
14
08
447
16
54
42
10
8. 510 2595
472
16
68
43
06
82
497
16
62
44
02
69
522
16
66
45
8.508 9197
57
547
16
70
46
93
44
573
15
74
47
89
31
598
15
78
48
84
18
623
15
82
49
80
05
648
15
86
50
8. 508 9176
8. 510 2493
1. 44673
2. 3914
6. 2790
51
72
80
699
14
94
52
67
67
724
14
98
53
63
54
749
14
6. 2802
54
59
41
774
13
06
55
55
28
800
13
10
50
50
16
825
13
14
57
46
03
850
13
18
58
42
8. 510 2390
875
12
22
59
38
77
900
12
26
60
8. 508 9133
8. 510 2364
1.44926
2. 3912
6. 2830
FACTORS FOE COMPUTATION OF GEODETIC POSITIONS. 213
Table XXVIl.^Factors for the computation of geodetic latitudes, lougitttdes, and azimuths — Continued.
LATITUDE 48°.
loj;. A
log. B
log. C
log. h
log. E
Lalitiule.
(liff.l" =— 0.07
cliflf.l"=— 0.21
lUff. l"=+0.42
diflU"=— 0.00
(lifif. l" = +0.07
48 00
8. 508 91B3
8. 510 2364
1. 44926
2. 3912
6. 2830
1
29
52
951
12
34
2
25
39
976
11
38
3
20
26
1.45001
11
42
i
16
13
027'
n
46
05
12
00
052
11
50
6
08
8.510 2288
077
10
54
7
03
75
102
10
58
8
8. 5118 9099
62
128
10
62
9
95
49
153
10
66
10
8. 508 9091
8. 510 2236
■ 1.45178
2. 3909
6.2870
11
86
24
203
0!)
74
12
82
11
229
09
78
13
78
8. 510 2198
254
08
82
14
74
85
279
08
86
15
69
72
304
08
90
16
65
60
330
08
94
17
61
47
355
07
98
18
57
34
380
07
6.2902
19
52
21
406
07
06
20
8. 508 9048
8. 510 2108
1.45431
2.3907
6. 2910
21
44
8.510 2096
456
06
14
22
39
83
481
06
18
23
35
70
507
06
22
?i
31
57
532
05
26
25
27
45
557
05
30
26
22
32
582
05
34
27
18
19
608
05
38
28
14
06
633
04
42
29
10
8. 510 1993
658
04
46
30
8. 508 9005
8. 510 1981
1.45683
2. 3904
6. 2950
31
01
68
709
03
54
32
8. 508 8997
55
734
03
58
33
93
42
759
03
62
34
88
30
785
02
«6
35
84
17
810
02
70
36
80
04
835
02
74
37
76
8. 510 1891
861
02
78
38
71
78
886
01
82
39
67
66
911
01
86
40
8. 508 896i
8. 510 1853
1. 45937
2. 3901
6. 2990
41
59
40
962
00
94
42
54
27
987
00
98
43
50
15
1.46012
00
6. 3002
44
46
02
038
2. 3899
06
45
41
8. 510 1789
063
99
10
46
37
76
088
99
15
47
33
64
114
98
19
48
29
51
139
98
23
49
24
38
164
98
27
50
8. 508 8920
8.510 1725
1.46190
2. 3897
6. 3031
51
16
13
215
97
35
52
12
00
240
97
39
53
08
8. 510 1687
266
96
43
54
03
74
291
96
47
55
8. 508 8899
62
316
96
51
56
95
49
342
95
55
57
90
36
367
95
59
58
86
23
392
95
63
59
82
10
418
94
67
60
8. 508 8878
8.510 1598
1.46443
2. 3894
6. 3071
214
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVU.— Factors for the comimtation of geodetic latitudes, longitudes, and azimuths— ContinneA.
LATITUDE 49°.
log. A
diff.l"=— 0.07
log.B
diff.l"=— 0.21
log. 0
fliff.l"=:+0.42
log.D
diff. 1"=— 0. 01
1. 508 8708
04
00
1.508 8695
FACTOES FOR COMPUTATION OF GEODETIC POSITIONS. 215
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 30°.
Latitude.
log. A
log. B
log. C
log. D
log. E
dift'. 1"=— 0.07
dlfif. 1"=_0.21
diff. 1"=X0.43
diff. 1"=— 0.01
diir. l"=+0.07
60 0
8. 608 8623
8. 510 0835
L 47968
2. 3871
6. 3318
1
19
22
993
70
22
2
15
09
1. 48019
70
26
3
11
8. 510 0797
044
70
30
4
06
84
070
69
34
05
02
71
096
69
39
6
8. 508 8598
.59
121
68
43
7
94
46
146
68
47
8
90
33
172
67
51
9
85
21
197
67
55
10
8. 508 8581
8. 510 0708
1.48223
2. 3866
6. 3369
11
77
8. 510 0695
248
66
63
12
73
83
274
66
68
13
68
70
299
66
72
14
64
57
325
65
76
15
60
45
350
64
80
16
56
32
376
64
84
17
52
19
401
63
88
18
47
07
427
63
93
19
43
8. 510 0594
452
62
97
20
8. 508 8539
8. 510 0581
1. 43478
2.3862 .
6. 3401
21
35
69
504
61
06
22
30
56
529
61
09
23
26
43
655
60
14
24
22
31
580
60
18
25
18
18
606
60
22
26
14
06
631
59
26
27
09
8. 510 0493
657
69
30
28
05
80
682
58
34
' 29
01
67
708
58
39
30
8. 508 8497
8. 510 0455
1.48734
2. 3857
6. 3443
31
93
42
759
67
47
32
88
29
785
56
61
33
84
17
810
66
55
34
80
04
836
65
60
35
76
8. 510 0392
861
55
64
36
71
79
887
54
68
87
07
66
913
54
72
38
63
54
938
53
76
39
59
41
964
53
81
40
8. 508 8455
8. 510 0328
1. 48989
2. 3852
6. 3485
41
50
16
1.49015
52
89
42
46
03
041
51
93
43
42
8.5W0291
066
51
97
44
38
78
092
50
6. 3502
45
34
65
117
50
06
46
29
53
143
49
10
47
26
40
169
49
14
48
21
27
194
48
18
49
17
16
220
48
23
50
8. 508 8413
8. 510 0202
1. 49246
2. 3847
6. 3527
51
08
8. 510 0190
271
47
31
52
04
77
297
46
35
63
00
64
322
46
40
54
8. 508 8396
62
348
45
44
55
92
39
374
45
48
56
87
27
399
44
52
57
83
14
425
44
56
58
79
01
451
43
61
59
75
8. 510 0089
476
43
65
60
8. 508 8371
8.510 0076
1.49502
2. 3842
6.3569
216
A MAifUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
COEEEOTIOXS TO LONGITUDE FOR DIFFERENCE IN ARC AND SINE.
Log. K
(-)
Log. difference.
Log. d M
(+)
Log. K
(-)
Log. difference.
Log.dM
(+)
Log.K
Log. difference.
Log.dM
(+)
3.876
0.000 0001
2.385
4.813
0. 000 0075
3.322
5.114
0. 000 0300
3.623
4.026
02
2. 535
4.825
080
3.334
5.120
309
3.629
4.114
03
2.623
4.834
084
3.343
5.126
318
3.635
4.177
04
2.686
4.849
089
3.358
5.132
327
3.641
4.225
05
2.734
4.860
094
3.369
5.138
336
3.647
4.265
06
2.774
4.871
098
3.380
5.144
345
3.653
4.298
07
2.807
4.882
103
3.391
5.150
354
3.659
4.327
08
2.836
4.892
108
3.401
5.156
364
3.665
4.353
09
2.862
4.903
114
3.412
5.161
373
3.670
4.376
10
2.885
4.913
119
3.422
5.167
383
3.676
4.396
11
2.905
4.922
124
3.431
5.172
392
3.681
4.415
12
2.924
4.932
130
3.441
5.178
402
3.687
4.433
. 13
2.942
4.941
136
3.450
5.183
412
3.692
4.449
14
2.958
4.950
142
3.459
5.188
422
3.697
4.464
15
2.973
4.959
147
3.463
5.193
433
3.702
4.478
16
2.987
4.968
153
'3.477
5.199
443
3.708
4.491
17
3.000
4.976
160
3.485
5.204
453
3.713
4.503
18
3.012
4.985
166
3.494
5.209
464
3.718
4.526
20
3.035
4.993
172
3.502
5.214
474
3.723
4.548
23
3.057
5.002
179
3.511
5.219
486
3.728
4.570
25
3.079
5.010
186
3.519
5.223
497
3.732
4.591
27
3.100
5. 017
192
3.526
5. 228
508
3.737
4.612
30
3.121
5.025
199
3.534
5.233
519
3.742
4.631
33
3.140
1 5.033
206
3.542
5.238
530
3.747
4.649
36
3.158
5.040
213
3.549
5.242
541
3.761
4.667
39
3.176
5.047
221
3. 556
5.247
553
3.756
4.684
.42
3.193
5.054
228
3.563
5.251
565
3.760
4.701
45
3.210
5.062
236
3.571
5.256
577
3.765
4.716
48
3.225
5.068
243
3.577
5.260
588
3.769
4.732
52
3.241
5.075
251
3.584
5.265
600
3.774
4.746
56
3.255
5. 082
259
3.591
5.269
613
3.778
4.761
59
3. 270
5.088
267
3.597
5.273
625
3.782
4.774
63
3.283
5. 095
275
3.604
5.278
637
3.787
4.788
67
3.297
5. 102
284
3.611
5.282
650
3.791
4. 801
71
3. 310
5. 108
292
3.617
5.286
663
3.795
FACTOES FOE EEDUGTION OF TEANSIT OBSEEVATIONS. 217
Table XXVIII. — Factors for reduction of transit ohservations.
[Extracted from Appendix 14, U. S. Coast and Geodetic Survey Report for 1880.]
To find A enter left-hand column -with, tlie zenith ^^distance; its intersection "with declination column gives azimuth
factor.
To find B enter ri^ht-liand column with tlie zenith distance ; its intersection with declination column gives level factor.
C is given on laat line of each section of the table.
Azimuth, factor A=sin, ^ sec. 6. Star's declination :
Inclination factor B^cos ^ sec. A.
i
0°
10°
15^
20°
22°
24°
26°
28°
30°
32°
34°
36°
38°
40° 41°
42°
430
'44°
45°
46°
47°
48°
490
50°
i
1°
.02
.02
.02
.02
.02
.02
.02
.02
.02
.02
.03
.02
.02
i
.02: .02
.02
.02
.02
.02
.02
.03
.03
.03
.03
89°
2
.04
.04
.04
.04
.04
.04
.04
.04
.04
.04
.04
.04
.04
.05
.06
.05
.05
.05
.05
.05
.05
.05
.05
.05
88
3
.05
.05
.05
.06
.06
.06
.00
.06
.06
.06
.06
.00
.07
.07
.07
.07
.07
.07
.07
.07
.08
.08
.08
.08
87
4
.07
.07
.07
.07
.08
.08
.08
.08
.08
.08
.08
.09
.09
.09
.09
.09
.10
.10
.10
.10
.10
.10
.11
.11
86
5
.09
.09
.09
.09
.09
.10
.10
.10
.10
.10
.10
.11
.11
.11
.11
.12
.12
.12
.;2
.13
.13
.13
.13
.13
85
6
.11
.11
.111
.11
.11
.11
.12
:i4
.12
.12
.13
.13
.13
.14
.14
.14
.14
.16
.15
.15
.15
.16
.16
.16
84
7
.12
.12
.131
.13
.13
.13
.11
.14
.14
.15
.15
.15
.16
.16
.16
.17
.17
.17
.18
.18
.18
.19
.19
83
8
.14
.14
.14
.15
.15
.15
.16
.16
.16
.16
.17
.17
.18
.18
.18
.19
.19
.19
.20
.20
.20
.21
.21
.22
82
9
.16
.16
.16
.17
.17
.17
.17
.18
.18
.18
.19
.19
.20
.20
.21
.21
.21
.22
.22
.22
.23
.23
.24
.24
81
lo-
.17
.18
.18
.19
.19
.19
.19
.20
.20
.21
.21
.21
.22
.23
.23
.23
.24
.24
.25
.25
.26
.26
.26
.27
SO
ll
.19
.19
.20'
.20
.21
.21
.21
.22
.22
.23
.23
.24
.24
.25
.25
.26
.26
.27
.27
.28
.28
.28
.29
.30
79
12
.21
.21
.22
.22
. 22
.23
.23
.24
.24
.25
.25
.26
.26
.27
.27
,28
.28
.29
.29
.30
.30
.31
.32
.32
78-
13
. 22
.23
.23'
.24
.24
.25
.25
.26
.26
.27
.27
.28
.29
.29
.30
.30
.31
.31
.32
.32
.33
.34
.34
.35
77
14
.2+
.25
.251
.26
.26
.27
.27
.27
.28
.29
.29
.30
.31
.32
.32
.33
.33
.34
.34
.35
..36
.36
.37
.38
76
15
.26
.26
.271
.28
.28
.28
.29
.29
.30
.31
.31
.32
.33
.34
.34
.36
.35
.36
.37
.37
.38
.39
.39
.40
76
10
.28
.28
.29,
.29
.30
.30
.31
.31
.32
.33
.33
.34
.35
.36
.37
.37
.38
.38
.39
.40
.40
.41
.42
.43
.74
17
.29
.30
.30
.31
.31
.32
.33
.33
.34
.34
.35
.36
.87
.38
.39
.39
.40
.41
.41
'.42
.43
.44
.45
.45
73
IS
.3;
.31
.32
.33
.33
.3a
.34
.35
.36
.36
.37
.38
.39
.40
.41
.42
.42
.43
.44
.44
.45
.46
.47
.48
72
19
.33
.33
.34
.35
.35
.36
.36
.37
.38
.38
.39
.40
.41
.42
.43
.44
.45
.45
.40
.47
.48
.49
.50
.51
71
20
.34
.35
.35
.36
.37
.37
.38
.39
.40
.40
.41
.42
.43
.45
.45
.46
.47
.48
.48
.49
.50
.51
.62
.53
JO
21
.36
.36
.37
.38
.39
.39
.40
.41
.41
.42' .43
.44
.45
.47
.47
.48
.49
.50
.51
.52
..52
.54
.55
.66
69
22
.37
.38
.39
.40
.40
.41
.42
.42
.43
.44' .45
.46
.48
.49
.50
.50
.61
..52
. 53
.54
.55
.56
.67
.58
68
23
.39
.40
.41
.42
.42
.43
.44
.44
.45
.46| .47
.48
.50
.51
.52
.53
.53
.51
. 5ii
.56
. 57
.58
.60
.61
67
24
.41
.41
.42
.43
.44
.45
.45
.46
.47
.48
.49
.60
.52
.53
.54
.55' .56
.67
.58
.59
.00
.61
.62
.63
66
25
.42
.43
.44
.45
.46
.46
.47
.48
.49
.60
.51
.52
.64
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.66
66
26
.44
.45
.45
.47
.47
.48
.49
.50
.51
.62
.53
.54
.56
.67
.58
.69
.60
.61
.62
.63
.64
.65
.67
.68
64
27
.45
.46
.47
.48
.49
.50
.51
.51
.62
.54
.55
.66
.58
.59
.60
.61
.62
.63
.64
.66
.67
.68
.69
.71
63
28
.47
.48
.49
.50
.51
.51
.52
.53
.54
.56
.67
.58
.60
.61
.62
.63
.64
.65
.66
.68
.69
.70
.72
.73
02
29
.48
.49
.50
.52
.52
.53
.54
.55
.56
.57
.58
.60
.61
.63
.64
.66
.66
.67
.69
.70
.71
.72
.74
.75
61
30
.50
.51
.62
.53
.64
.55
.56
.57
.68
.59
.60
.62
.63
.65
.66
.67
.68
.69
.71
.72
.73
.75
.76
.78
(iO
31
.52
.52
.53
.55
.56
.56
.67
.58
.59
.61
.62
.64
.65
.67
.68
.69
.70
.72
.73
.74
.75
.77
.78
.80
59
32
.63
.54
.56
..56
.57
.58
.69
.60
.61
.63
.64
.66
.67
.69
.70
.71
.72
.74
.75
.76
.78
.79
.81
.82
58
33
.54
.55
56
.58
.69
.60
.61
.62
.63
.64
.66
.67
.69
.71
.72
.73
.74
.76
.77
.78
.80
.81
.83
.85
57
34
.56
.57
.58
.159
.60
.61
.62
.63
.65
.66
.67
.69
.71
.73
.74
.75
.70
.78
.79
.80
.82
.84
.85
.87
66
35
.57
.58
.59
.61
.62
.63
.64
.65
.66
.68
.69
.7)
.73
.75
.76
.77
.78
.80
.81
.83
.84
.86
.87
.89
55
36
.59
.60
,61
.63
.63
.64
.65
.67
.68
.69
.71
.73
.75
.77
.78
.79
.80
.82
.83
.85
.86
.88
.90
.91
54
37
.60 .61
.62
.64
.65
.65
.67
.68
.70
.71
.73
.74
.76
.79
.80
.81
.82
.84
.85
.87
.88
.90
.92
.94
63
38
.62 .63
.64
.66
.66
.67
.69
.70
.71
.73
.74
.76
.78
.80
.82
.83
.84
.86
.87
.89
.90
.92
.94
.96
52
39
.63 .64
.65
.67
.68
.69
.70
.71
.73
.74
.76
.78
.80
.82
.83
.85
.86
.87
.89
.91
.92
.94
.96
.98
51
10
.64
.65
.66
.68
.69
.70
.72
.73
.74
.76
..77
.79
.82
.84
.85
.86
.88
.89
.91
.93
.94
.96
.98
1.00
50
41
.66
.67
.68
.70
.71
.72
.73
.74
.76
.77
.79
.81
.83
.86
.87
.88
.90
.91
.93
.94
.90
.98
1.00
1.02
49
42
.67
.68
.69
.71
.72
.73
.74
.76
.77
.79
.81
.83
.85
.87
.89
.90
.91
.93
.95
.96
.9S
1.00
1. 02
1.04
48
43
.68
.69
.71
.73
.74
.75
.76
.77
.79
.80
.82
.84
.86
.89
.90
.92
.93
.95
.96
.98
1.00
1.02
1.04
1.06
47
44
.69
.71
.72
.74
.75
.76
.77
.79
.80
.82
.84
.86
.89
.90
.92
.93
.96
.96
.98
1.00
1.02
1.04
1.06
1.08
46
45
.71
.72
.73
.75
.76
.77
.79
.80
.82
.83
.85
.87
.90
.92
.94
.95
.97
.98
1.00
1.02
1.04
1.06
1.08
1.10
46
46
.72
.73
.74'
.77
.78
.79
.80
.82
.83
.85
.87
.89
.91
.94
.95
.971 .98
1.00
1. 02
1.04
1.06
1.07
1.10
1.12
44
47
.73
.74
.76
.78
.79
.80
.81
.83
.84
.86
,88
.90
.93
.95
.97
.98,1.00
1.02
1.03
1.05
1.07
1.09
1.11
1.14
43
48
.74
.76
.77
.79
.80
.81
.83
.84
.86
.88
.90
.92
.94
.97
.98 1.00:1. 02
1.03
1. 05
1.07
1.09
1.11
1.13
1.16
42
49
.75
.77
.78
.80
.81
.83
.84
.86
.87
.89
.91
.93
.96
.99
1.001.02;!. 03
1.05
1. 07
1.09
1.11
1.13
1.15
1.17
41
60
.77
.78
.79
.82
.83
.84
.85
.87
.89
.90
.92
.95
.97
1.00
1.011.031.05
1.06
1. 08
1.10
1.12
1.14
1.17
1.19
40
51
.78
.79
.80
.83
.84
.85
.87
.88
.90
.92
.94
,96
.99
1.01
1.031.051.06
1. 08
1. 10
1.12
1.14
1.16
1.18
1.21
39
52
.79
.80
.82
.84
.85
.86
.88
.89
.91
.93
.95
.97
1.00
1.03
1.041.0611.08
1.10
1. 11
1.13
1.15
1.18
1.20
1.23
33
53
.80
.81
.83
.85
.86
.87
.89
.91
.92
.94
.96
.99
1.01
1.04
1.061.071.09
1. 11
1. 13
1.15
1.17
1.19
1. 22
1.24
37
54
.81
.82
.84
.86 .87
.89
.90
.92
.93
.95
.98
1.00
1.03
1.06
1.07 1.091.11
1. 12
1. 14
1.16
1.11
1.21
1.23
1.26
36
55
.82
.83
.85
.87, .88
.90
.91
.93
.95
.97
.99
1.01
1.01
1.0-
1. 08 1. 10 1. 12
1.14
1.16
1.18
1.20
1.22
1.25
.1.27
35
56
.83
.84
.86
.88 .89
.91
.92
.94
.06
.98
1.00
1.02
1.05
1.08
1. 10 1. 12 1. 13
1.16
1.17
1.19
1.22' 1.24
1.26
1.29
34
57
.84
.85
.87
.89 .90
.92
.93
.95
.97
.991.01
1.04
1.06
1.09
1. 11 1. 13 1. 15
1.17
1.19
1.21
1.23 1.25
1.28
1.31
33
58
.85
.86
.88
.90 .91
.93
.94
.96
.98
1. 00 1. 02
1.05
1.08
1. 11
1. 12 1. 14 1. 16
1.18
1.20
1.22
1.24 1.27
1.29
1.32
32
59
.86
.87
.89
.91 .92
.94
.95
.97
.99
1.011.03
1-.06
1. 09
1.12
1. 14 1. 15 1. 17
1.19
1.21
1.23
1. 26 1. 28
1.31
1.33
31
60
.87
.88
.90
.92 .93
.96
.96
.98
1.00
1. 02 1. 04
1.07
1.10
1.13
1.161.1711.18
1.20
1.22
1.25
1.27 1.29
1.32
1.35
SO
218
A MA]!fUAL OP TOPOGRAPHIC METHODS.
Table XXVIII. — Factors for reduction of transit oiservations — Continued.
Azimuth factor A:=sia C sec. 6. Star's declination + i. Inclination factor B=coa ^ sec. 6.
0°! 10° 15° 20° 22° ■ 24°i 26° 28° 30° 32° 34° 36° 88° 40° 41° 42° 43° 44° 45° 46° 47° ' 48° 49° 50°
.% .97 .9!) 11.01,1. 03
. 98 1. 00
.98] .991.01
.98 1.110 1.02
. 99I1. 01 1. 03
1. 02 1. 04
1.0311.05
I.O1I1.O6
1.05,1.07
.95 1 .97' .991.
.95/ .98 .9'.! 1.
.96l .9!) l.UO I.
.97 .99 L. Ill 1.
.971 l.OOjl. Olll.
.98,i.01il.02'l.
.98 1.01il.0:l|l.
.99 1.02'l.03!l.i
.OOjl. 02 1.041.
.ooii.oaii.w'i.
1.05,1.08ll.H:i. 141. 16
1.06 1.09:1.12 1.151.17
1. 07JHO 1.13,11.16 1.18
1. OS 1. 111. 14 1. 17 1. 19
1. 09 1. I3I1. 15 1.18,1.20
05 1. 07
06 1, 08
06 1. 08
07 1. 09
08 1. 0!)
1.091.
1. 10 1.
1. 10 1.
1. 11 1.
1. 12 1.
.OSl.
. 09 1.
.ooli.
. 10 1. :
.111.:
121.;
12 1. :
131.:
13 1. :
141.:
. 13 1. 16
.141. 17
. 15 1. 1.^
.15 1. 18
.161. 10;
.17:1.20'
.171.31
. 18 1. 21I
.191.22
.191.23;'
M9'I.2I 1. 23 1.25,1,
1.2011.22
1. 21 1. 23
1.22 1.24
1.23J1. 25
1.241. 26 1.28
1. 25 1.
1.26,1.
1. 27 1.
1. 27 1.
1. 28 1.
.29 1.
. 30 1.
.811.
. 31 1.
.321.
1.26
1.27
1.28
1.20
1.30
29 1. 32
30 1
31 1. 33
32 1. 34
33 1. 35
i
341.36
34 1. 37
35 1. 38
36 1. 38
37 1. 39
. 97 . 99 I. 00 1. 0;l 1. 05 1. 06 1. 08 1. HI I. 12 1. 14 1. IT 1. 20 1. 2:1 1. 27 I. 29 1. 31
.97 .9:11.01 1.04 1.11,1 l.iiT l.llil. 10 il. 1:5 1. IS 1.17 1.20 1.24 1.27 1.29 1. 31
.98 .OOU.III 1,04 1.0.'. 1.07 1.110 1. 11 1.13 1.151. IS 1.21 1.24 1.28 1.30 1.32
. 98 1. 00 1. 02 1. 04 1. 00 1. 08 1. 0;l 1. 11 1. 13 1. 16 1. IS 1. 21 1. 25 1. 281. 30 1. :f2
1.331.35 1.371.40
1.331.35 1.381.40
1.341. 36 1.381.41
1.34 1. 36 1.391.41
i 1.001. 02 1.05 1.06,1. OSl. 10 1.12 11.14 1.16 1.19 1.221.25, 1. 29'1. 30 1. 331.351. 37 1.391.42
! ■ ' I !■ : i ' i ' '':■■! ■ I I
81 ' .991.0Qtl.03' 1.051. 07|1. 08 1.101. 12 ,1. 14 1. 17 1. 19 1. 22 1. 25 1. 39 1. 31 1. 33 1. 351. 37 1.401.42
82 I .991.01;!. 03, 1. 05 1. 07il. 03 1. 10 1. 12 1. Ul- 17 1. 19 1. 23 1. 26 ,1.29 1. 31 1. 33 1. 35 1. 38 1.401.43
83 1 . 99 1. Olll. 03' 1. 06 1. 07:1. 09 1. 10 1. 12 1. 15 1. 17 1. 20,1. 23 1. 26 1. 30 1. 32 1. 34 1. 36 1, 38 1. 40 1. 43
84 I . 9911. Olll. 031:1. 06il. 07ll. 09 1. 11 1. 13 il. 15 1. 17 1. 20il, 33 1. 26 1. 30|l. 32 1. 34|1. 36 1. 38 1. 41 1. 43
85 1. 00 1. 01 1. 03 1. 06 1. 07 1. 09 1. 11 1. 13 11. 15 1. 17 1. 20 1. 33 1. 26 1. 3oll. 3211. 34 1. 36 1. 38 1. 4lll. 43
1.28 1.31
1. 29 1, 32
1.31 1.33
1.32 1.34
1. 33 1. 35
1.34 1.371
1.35 1.38
1.30! 1.
1. 37, 1. 40
1.38 1.40
1.39 1.41
1. 39 1. 42
1.40;i.43
1.41 1.44
1. 42 1. 44
1.42' 1.45
1.43; 1.46
1.43 1.46
1.44 1.4'i
1.44 1.47
1.49
1.49
1.50
1.51
1.52
1.53
1.53
1.50 1.53
1.51 1.54
1.51; 1.54
1.51' 1.54
1.52 1.55
1.53 1,55
88 1. 00 1. 01.1. 03' 1. 06 1. 08 1. 09,1. 111.13 1.15 1. 18 1. 20
89 1. 00 1. 02 1. 04' 1. 06 1. 08 1. 09: 1. 11 1. 13 1. 15 1. 18,1. 21
90 1. ODJl. 02,1. 04 1. 06,1. 08|l. 09 1. llll. 13 1. 15|l. 18,1. 21
1.231.27 1.30 1.321. 3 I 1.37 1.30 1.41 1,44 1.40 1.49' 1.52 1.55
1.241.27 1.31 I.:i2,l.:i5,l. :i71. 39, 1.411. 44,1. 47 1.49 1.52 1.56
1. 24:1. 27|il. 31,1. 32 1. 35,1. 37,1. 39 ,1. 41|1. 44 1. 47 1. 49, 1. 52; 1. 56|
r-r-T-r
FACTOES FOE REDUCTION OF TRANSIT OBSEUVATIONS. 219
Table XXVIII. — Factors for reduction of transit observations — Continued.
Azimath factor A = sin ^ sec. 6. Star's declination ± 5. Inclination factor B = cos i sec. i.
i
51°
.03
52°
.03
53°
.03
54°
.03
55°
.03
56°
.03
57°
58°
59°
.03
60°
.03
60J°
.01
61°
.04
6U°
.04
62°
.04
621°
.04
63°
.04
63i°
64°
64i°
.04
65°
.04
65J
.04
66°
.04
66i°
.04
67°
.04
i
1°
1
. 03 . 03
.04 .04
89°
2
.06
.06
.06
.06
.06
.06
.06 .07
.07
.07
.07
.07
.07
.07
.08
.08
.08' .08
.08
.08
.08
.09
.09
.09
88
3
.08
.08
.09
.09
.09
.08
. 10| . 10
.10
.10
.11
.11
.11
.11
.11
.12
.13' .13
.12
.13
.13
.13
.13
.13
87
4
.11
.11
.12
.12
.12
.12
.13
.13
.14
.14
.14
.14
.15
.15
.15
.15
.16, .16
.16
.17
.17
.17
.18
.18
86
5
.14
.14
.14
.15
.15
.16
.16
.16
.17
.17
.18
.18
.18
.19
.19
.19
.19
.30
.20
.21
.21
.31
.22
.22
85
6
.17
.17
.17
.18
.18
.19
.19
.20
.20
.21
.21
.22
.22
.22
.23
.23
.23
.24
.24
.25
.25
.26
.26
.27
84
7
.19
.20
.20
.21
.21
.22
.22
.23
.24
.24
.25
. 35
.26
.26
.26
.27
.27
.38
.28
.29
.29
.30
.31
.31
83
8
.22
.23
.23
.24
.24
.25
.26
.26
.27
.28
.28
.39
.29
.30
.30
.31
.31
.32
.32
.33
.34
.34
.35
.36
82
9
.25
.25
.26
.26
.27
.28
.29
.29
.30
.31
.32
.32
.33
.33
.34
.35
.35
.36
.36
.37
.38
.39
.39
.40
81
10
.28
.28
.29
.30
.30
.31
.32
.33
.34
.35
.35
.36
.36
.37
.38
.38
.39
.40
.40
.41
.42
.43
.43
.44
80
11
.30
.31
.32
.32
.33
.34
.35
.36
.37
.38
.39
.39
.40
.41
.41
.43
.43
.44
.44
.45
.46
.47
.48
.49
77
12
.33
..34
.35
.35
.36
.37
.38
.39
.40
.42
.42
.43
.44
.44
.45
.46
.47
.47
.48
.49
.50
.51
.53
78
13
.36
.36
.37
.38
.39
.40
.41
.42
.44
.45
.46
.46
.47
.48
.49
.50
.50
.51
.52
.53
.54
.55
!56
.58
77
14
.38
.39
.40
.41
.42
.43
.44
.46
.47
.48
.49
.50
.51
.52
.52
.53
.54
55
.56
.57
.58
.59
.61
.62
76
15
.41
.42
.43
.44
.45
.46
.48
.49
.50
.52
.53
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.64
.65
.66
75
16
.44
.45
.46
.47
.48
.49
.51
.52
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.65
.66
.68
.69
.71
74
17
.46
.47
.49
.50
.51
.52
.54
.55
.57
.58
.59
.60
.61
.62
.63
.64
.66! .67
.68
.69
.70
.72
.73
.75
73
18
.49
.50
.51
.53
.54
.55
.57
.58
.60
.62
.63
.04
.65
.66
.67
.68
.69 .70
.72
.73
.74
.76
.77
.79
72
19
.52
.53
.54
.5.'>
.57
.58
.60
.61
.63
.65
.66! .67
.68
.69
.70
.72
.73
.74
.76
.77
.78
.80
.82
.83
71
20
.54
.50
.57
.58
.60
.61
.63
.04
.66
.68
.69
.70
.72
.73
.74
.75
.77
.79
.79
.81
.83
.84
.86
.88
70
21
.57
.58
.59
.61
.62
.64
.66
.68
.70
.72
.73
.74
.75
.76
.78
.79
.80
.83
.83
.85
.86
.88
.90
.92
69
22
.60
.61
.62
.64
.65
.67
.69
.71
.73
.75
.76
.77
.78
.80
.81
.82
.84
.85
.87
.89
.90
.92
.94
.96
68
23
.62
.63
.65
.66
.68
.70
.72
.74
.76
.78
.79
.81
.83
.83
.85
.86
.88
.89
.91
.92
.94
.96
.98
1.00
67
24
.65
.66
.68
.69
.71
.73
.75
.77
.79
.81
.83
.84
.85
.87
.88
.90
.91
.93
.94
.96
.98
1.00
1.03
1.04
66
25
.67
.69
.70
.72
.74
.76
.78
.80
.83
.85
.86
.87
.89
.90
.92
.93
.95 .96
.08
1.00
1.02
1.04
1.06
1.08
65
2G
.70
.71
.73
.75
.76
.78
.80
.83
.85
.88
.89
.90
.92
.93
.95
.97
.98'l.00
1.03
1.04
1.06
1.08
1.10
1.12
64
27
.72
.74
.75
.77
.79
.81
.83
.86
.88
.91
.92
.94
.95 .97
.98
1.00
1.021.04
1.05
1.07
1.09
1.13
1.14
1.16
03
28
.75
.76
.78
.80
.82
.84
.86
.89
.91
.94
.95
.97
. 98 1. 00
1.02
1.03
1.05,1.07
1.09
1.11
1.13
1.15
1.18
1.20
62
29
.77
.79
.81
.82
.84
.87
.89
.91
.94
.97
.98
1.00
1. 02 1. 03
1.05
1.07
l.OO'l. 11
1.13
1.15
1.17
1.19
1.22
1.24
61
30
.79
.81
.83
.85
.87
.89
.92
.94
.97
1.00
1.01
1.03
1.05 1.07
1.08
1.10
1.121.141.16
1.18
1.21
1.23
1.25
1.28
60
31
.82
.84
.86
.88
.90
.93
.95
.97
1.00
1.03
1.05
1.06
1. 08,1. 10
1.11
1.13
1.151.17
1.20
1.22
1.24
1.27
1.29
1.32
59
32
.84
.80
.88
.90
.92
.95
.97
1.00
1.03
1.06
1.08
1.09
1.111.13
1.15
1.17
1.19)1.21
1.23
1.25
1.28
1.30
1.33
1.36
58
33
.87
.88
.91
.93
.95
.97
1.00
1.03
1.00
1.09
1. U
1.12
1. 14 1. 16
1.18
1.20
1. 22 1. 21
1.26
1.29
1.31
1.34
1.37
1.39
57
34
.89
.91
.93
.95
.97
1.00
1.03
1.05
1.09
1.13
1.14
1.15
1. 17 1. 19
1.21
1.23
1. 251. 27
1.30
1.32
1.35
1.37
1.40
1.43
56
35
.91
.93
.95
.98
1.00
1.03
1.05
1.08
1.11
1.15
1.16
1.18
1.201.22
1.24
1.30
1.291.31
1.33
1.36
1.38
1.41
1.44
1.47
55
36
.93
.95
.98
1.00
1.03
1.05
1.08
1.11
1.14
1.18
1.19,1.21
1.231.25
1.27
1.30
1.321.34
1.37
1.39
1.42
1.45
1.47
1.51
54
37
.96
.98
1.00
1.02
1.05
1.08
1.10
1.14
1.17
1.20
1.221.24
1.261.28
1.30
1.33
1.351.37
1.40
1.42
1.45
1.48
1.51
1.54
53
38
.98
1.00
1.02
1.05
1.07
1.10
1.13
1.16
1.20
1.33
1.251.27
1.291.31
1.33
1.36
1.38'l.40
1.43
1.46
1.48
1.51
1.54
1.58
52
39
1.00
1.02
1.05
1.07
1.10
1.12
1.15
1.19
1.22
1.26
1.281.30
1.321.34
1.36
1.39
1.411.43
1.46
1.49
1.52
1.55
1.58
1.61
51
10
1.02
1.04
1.07
1.09
1.12
1.15
1.18
1.21
1.25
1.29
1.311.33
1.351.37
1.39
1.42
1.44 1.47
1.49
1.52
1.55
1.58
1.61
1.65
50
41
1.04
1.07
1.09
1.12
1.14
1.17
1.20
1.24
1.27
1.3l!l.331.35
1.37
1.40
1.42
1.45
1.47
1.50
1.53
1;55
1.58
1.61
1.64
1.68
49
42
1.06
1.09
1.11
1.14
1.17
1.20
1.23
1.26
1.30
1. 34jl. 361. 38
1.40
1.42
1.45
1.47
1.50
1.53
1.55
1.58
1.61
1.64
1.68
1.71
48
43
1.08
1.11
1.13
1.16
1.19
1.22
1.25
1.29
1.32
1.361.391.41
1.43
1.45
1.48
1.50
1.53
1.56
1.58
1.61
1.64
1.68
1.71
1.75
47
44
1.10
1.13
1.15
1.18
1.21
1.24
1.28
1.31
1.35
1.391.41,1.43
1.46
1.48
1..50
1.53
1.56
1.581.61
1.64
1.67
1.71
1.74
1.78
46
45
1.12
1^
1.17
1.20
1.23
1.26
1.30
1.33
1.37
1.411.441.46
1.48
1.51
1.53
1.56
1.58
1.611.64
1.67
1.70
1.74
1.77
1.81
45
220
A MAXUAL OF TOPOGRAPHIC METHODS.
Table XXVIII. — Factors fur reduction- of transit ohserimtions — Continued.
Aziiniith factor A = sill sec, 5. Star's declination ± 5. Inclination factor B = cos ^ sec. 5.
i2° 53° c
i 51° 52° ! 53° 54° 55° 50= 57° 58° 59° ' 60° 60^° 61° 61^° 02° 63|o 63° 63Jo 04° 64J° 05°
46° 1. 14|1. 17 1. 19 1. 22 1.251.29
47 |1. lull. 19 1.211. 24 1.27J1.31
48 1 1. \&'y. 21 1. 23 1. 26 1 1. 30 1. 33
49 1 1. 20| 1. 23 1. 25 1. 28 1. 32 1. 35
50 1.221.24 1. 27 I.30I1.34I1. 3'
1. 36 1. 40 1. 44il. 461 1. 48 1. 51| 1. 53 1. 56 1 58|1. 611. 64 1. O'i 1. 70 1. 74 1. 77
1. 38 1. 42!! I. 40 1. 4911. 51 1. 53 1. 56 1. 58 1. 61,1. 61 1. 67 1'. 7ol 1. 73 1. 70 1. 80
1. 40 1. 44,il. 48 1. 50,1. 53 1,55 1. 58 1. 60 1. 03 1. 66 1. 69 1. 72 1. 75 1. 79 1. 82
1. 42 1, 47)1. 51 1. 53|1. 56 1. 58 11. 01 1. 63 1, 66 1. 60 1. 72 I. 75 .\. 79,1. 82 1. 86
1. 44 1. 49; 1. 53 1. 5611. 58 1. 60 1. 03 1. 66 I. 69 1. 721. 75 1. 78|!1. 8111. 85 1. 88
51 1. J; l.LM l.-".i l::- 1.:;.""' l.:i ij.4'; 1-47 l.r.l I. .".". 1. .IS 1. 00 1. 63 1. 66 1. 08 1.
52 l.•-'^ 1. J- I ::i 1 ;; I, :: I. (1 1. -t:. I 4:i 1. :>:; i.r,s i.C'i 1. 11:; 1.65 1.68 1.71 1.
5;i 1.27 1.:; ' 1 . : 1. :Vi I.:::M. I.: I. 47 1..M 1. '.' l.i'.nl. t:2 1. ns 1. 07 |l. 70 1. 73 1.
54 1.2:l l.:;U.:U l.::~ 1. 41 1 4.'> 1. 4'i 1. .) : 1. ,'.7 1. 1)2 1. 04 1. 67 1. 09 1.72 1.75 1.
55 1.30:1.33 1.36 1.30 1.4311.461.50 1.55 1.59 1.011.661.69 1.72 1.741.77 1.
1.71 1.77 l.,-<i) 1..S4 1.871.91
1.77 l.,sn l..s:: I. so 1.90 1.94
1.70 l..-<2 l.s", 1. so 1.93 1.96
l.sl l.S,-. l.S.S 1.911.951.99
1.84 1.87 1.90 1.94 1.98 2.01
63 ,1,
04 1
05 II,
35 1.381.41
36 1. 39 1. 43
381.41 1.44
39 1.421.40
41 1.441.47 I.
42 1.4.'"' 1.40 1.
4:j I. 47 1.. 'ill 1.
45 1.40 1.52 1.
40 1. 40 1. 5:;" 1.
47 1.51 1.54 1.
1. 45 I. 48
1.46; 1.50
1.48 1.52
1.49 1.53
! 1.50 1.61 1.661.081.711.74
581.63 1.681.70|l. 731. 76
60 1.65 1.701.7211.751.78
02 1.66 1.711.7411.771.80
631. 6.1' 1. 73 1. 76'1. 79 1. 81 tl. 84 1. 88 1. 911. 94 1. 97 2. 01 2. 05'2. 09 2. 13
1. 77 1. 8.1 1. 83 1. 80 1. 89 1. 93 1. 90 2. 00 2. 04
1. 79 1. 82 1. 85 1. 88 1. 91 1. 95 ll. 98 2. 02 2. 06
1. 81 1. 84 1. 87 1. 90 1. 93 1. 97 |2. 01 2. 05 2. 08
1. 83 1. 86 1. 89:1. 92 1. 95 1. 99 l2. 03'2. 07 2. 11
.6411.
.65 1.
.66 1.
18 1.73 1.781.81 1.84 LS7 l.liii l.:i:; l.'.i' - ' J
'0,1. 75 ,1.80 1. 83 1. 85 1. Ss 1. Ill 1. 'X, i. 0,-: 2. U2 2. " J
■1,1. 76 1 1. 81 1. 84]l. 87 1. 90 1. 93,1. 96 2. 00 2. OJ 2. 07
2. 11 2.15 2.19
2. 13 2. 17 2. 21
2. 14 2. 19 2. 23
Oej° 67°
1.87
1.90
1.93
2.02
2.04
2.07
2.10
2.15
2.17
2.19
2.22
2.27
. 20 2. 25 1 2. 29
. 22 2. 20 ■ 2. 31
.24 2.28 2.32
. 25 2. 30 , 2. 34
. 27 2. 31 I 2, 36
71 'l. 50 1. 54 1. 57 1. 61 1. 65 1.69 1. 74 1. 78 1. 84 1. 80 1. 92 1. 95 1. 9S| 2. 01 2. 05 2. 08 2. 12 2. 10 2, 20 i2. 24 2. 28 2. 32 2. 37
72 1 1.51 1.54 1.581.62 1.00 1.70 1.75 1.80 1.85 1.90 1.93 1.961.991
73 !l. 52 I. 55 1. .59 1. 63 1. 07 1. 71 1. 70 1. SO 1. 86 1.91 1. 94 1. 97 2. 00; 2. 04 2. 07 2. 112. 14 2. IS 2. 22 ;2. 26 2. 31 2. 35 2. 40
74 1.53 1.56 1.60 1.63 1.081.72,1.701.811.87 1.92 1. 95 1. 98 2. Oil 2.05 2.08 2. 12|2. 15 2. 19 2. 23
75 11. 53 1. 57 1. 60 1. 64 1. 63 1. 73:1. 77:1. 82 1. 88 1. 93 1. 96 1. 99 2. 02l 2. 06 2. 09 2. 13i2. 16,2. 20 2. 24||2. 29|2. 33i2. 37 i 2. 42
66 ! 1. 45,1. 48 1. 52 1. 55 1. .59 1. 03 1. 68 1. 721. 77 1. 83'l. 85' 1. 88 1. Oil 1. 951. 98 2. 01'2. 05'2. 08 2. 12 I
67 1. 46 1. 50 1. 53 1. ,57 1.60 1.651.69 1.74 1.79 1. S4 1.87 1.90 1.9:! 1. 9i; 1. 99 2. 0:i 2. 0(i 2. 10 2. 14
03 1.47 1.511 54 1. .58 1.621.06 1.70 1.75 1.8;; 1.S5 1.SS1.91 1.'.14 l.|i7 2.nl j, iin' os j. 11 j, ]3
69 1.481.521.551.59 1.63 1.071.711.701.81 1.87 1.9111.03 1.0:; 1. Oil 2. il2 J. "n 2. n:i j. ]:; -. 17
JO .1.49 1.53 1.50 1.00 1.041.68 1.73 1.771.82 1. .SS 1.91 1.94 1.07 2. OU 2. u:; 2. u7 2. 11 -. 14 2. is
2.32
«2.34
2.36
2.37
2.39
2.40
2.42
2.43
2.45
2.46
2.47
76 1.54 1.58 1.611.05 1. 69 1. 73 1.781. 83;1. SS 1.04 1.97 2.00 2.03'
77 ll. 55 1.58 1.62 1.60 1. 70 1. 74 1. 79' 1. 84:1. 89 1.051,0- 2111 2 D |
78 ;l..55 !.. 59 1.621.66 1.701. 75I1.SO 1.85 1.90 1.06 1.: . :_ -j,.j-jj -_
79 1.. 56 1.591. 631.67 1.71 1.701.80 1.S5 1.91 1.96 1.:: _ . J : _ .
8D 1.561.60 1.641.67 1.721.761.81,1.86 1.91 1.972.11 ■ J. II -" 2 'J :.:j iT-:
81 1.57|l.60'l. 64 1.68 1.72 1.77 1.81 1.80 1,02 1. 98 2. 111 j. 1:4 2. "7 2.1:12.142 ls2.:
jl.eill. 64 1.68 1.73 1.77 1.82 1.87 1.92 1.98 2. "1 l."4 2. us -. 11 -J. 151,'. IS 2.;
I. 58 I.61I1. 65 1.69 1.73 1.77 1. 82 1.87 1.93 1. 90 2. 02 2. 05 2. lis -. v^-l. Vrl. Iil2.:
1.58ll.62 1.65l.69 1. 73 1. 78 1. 83!!. 88 1. 93 1.90 2.02 2.05 2.08 2.12 2,15 2,19 2,;
1. 58 1. 62 1, 65 1, 69 11, 74 1, 78 1, 83 1, 83 1, 93 1, 99 2, 02 2, 0512, 091 2, 12,2, 16.2. 19|2. 1
1.59 1.621,601,70 1,74 1,73 )..s:;l.
1, .59 1. 62 1. 66 1.70 1. 74 1. 7;i 1 - : i
1.59 1.62 1.06 1.70 1.74 1 '
1.591.62 1.66 1,70 1, 74 ; ^
1.591.621,661,70 1,74 i T:' 1 ■, ;
n.94
, 30'2. 34'2. 39 ' 2. 43
. :n 2. 3r, 2. 40 2
.. .. ;;,;- 41) ■_.
_ _ :7 -.41 2
:, 34 2, 38 2, 43 i 2. 48
, 34(2, 39 2, 43 : 2, 48
, 3512, 39 2, 44
, 35|2, 40 2, 45
. 3612. 40 2. 45
,36 2,41,2,45
2.49
. II 2. 40 2. 50 2, 50
I I 2 40 2.51 2,50
I 2.40 2.51 2,;
112, 40 2, 51 2, 56
FACTOES FOE EEDUCTION OF TEAifSlT OBSEKVATIONS. 221
Table XXYJIl.—Faeiors for reduction of transit ohservations— Continued.
Azimuth factor A = siu i sec. S, Star's doclination ± S. Inclination factor B = cos i sec. 5.
i
67J°
.05
68°
.05
68^0
.05
69°
,05
69io
.05
70°
.05
7040
,05
70J°
.05
.05
71°
.05
...
.05
71i°
.05
711°
.05
72°
.06
72J°
.06
72i°
.06
72JO
.06
73°
.06
73i°
.06
73i°
.06
73i°
.06
740
.06
74i°
.06
i
89°
1°
2
.09
.09
.10
,10
.10
.10
,10
.10
.11
.11
.11
.11
.11
.11
.11
.12
.12
.12
.12
.12
.12
.13
.13
88
3
. 14
.14
. 14| . 15 . 15
.15
,15
.16
.16
.16
.16
.16
.17
.17
.17
.17
.18
.18
.18
.18
.19
. 19
.19
87
l
.18
.19
.19 .20 .20
.20
.21
.21
.21
.21
.22
.22
.22
.23
.23
.23
.23
.24
.24
.24
.25
.25
.26
86
5
.23
.23
.24 .24
.25
.25
.26
.26
.26
.27
.27
.27
.28
.28
.29
.29
.29
.30
.30
.31
.31
.32
.32
85
6
,27
.28
.28 .29
.30
.31
.31
.31
.32
.32
.33
.33
.33
.34
.34
.35
.35
.36
.36
.37
.37
.38
.39
84
7
.32
.33
.33! .34
.35
.36
.36
.37
.37
.37
.38
.38
.39
.39
.40
.41
.41
.42
.42
.43
.44
.44
.45
83
8
.36
.37
.38 .39
.40
.41
.41
.42
.42
.43
.43
.44
.44
.45
.46
.46
.47
.48
.48
.49
.50
.50
.51
82
g
.41
.42
.43 .44
.45
.46
.46 .47
.47
.48
.49
.49
.50
.51
.51
.52
.53
.53
.54
.55
.56
.57
.58
81
10
.45
.46
.47| .49
.50
.51
.61 .52
.53
.53
.54
.55
.55
.56
.57
.58
.59
.60
.60
.61
.02
.63
.64
80
11
.50
.51
.52' ..53
.54
.56
.56 .57
.58
.59
.59
.60
.61
.62
.63
.63
.64
.65
.66
.67
.68
.69
.70
79
12
.54
.56
.57
,58
.59
.61
.62 .62
.63
.64
.65
.63
.66
.67
.68
.69
.70
■.71
. 72
.73
.74
.75
.77
78
13
.59
.60
.61
,63
.64
.66
.67
.67
.68
.69
.70
.71
.72
.73
.74
.75
.76
.77
.78
.79
.80
.82
.83
77
14
.63
.65
.66
.68
.69
.71
.72
.72
.73
.74
.75
.76
.77
.78
.79
.80
.82
.83
.84
.85
.87
.88
.89
76
15
.68
.69
.71
.72
.74
.76
.77
.78
.78
.79
.80
.81
.83
.84
.85
.86
.87
.89
.90
.91
.93
.94
.95
75
16
.72
.74
.75
.77
.79
.81
.82
.83
.84
.85
.86
.87
.88
.89
.91
.92
.93
.94
.96
.97
.99; 1.00
1.02
74
17
.76 - 7S
. 80' . HI
.83
.85
.86' .88
.89
.90
.91
.92 .93
.95
.96
.97
.99
1.00 1.01
1.03
1.05! 1.06
1.08
73
18
.81
.83
.84| .86! .88
.90
.911 .93
.94
.95
.96
.97 .991.00 1.01
}-??o
1.04
1.06
1.07
1.09
1. 10 1. 12
1.14
72
19
.85
.87
.89' .91 .93
.95
.96i .98
.99
i.oo!i.oi
1. 03 1. 04 1. 05
1.07
1.08
1.10
1.11
1.13
1.15
1. 16i 1.18
1.20
71
20
.89
.91
.93 .95 .98
1.00
1.011.02
1.04
1.05:1.06
1.081.091.11
1.12
1.14
1.15
1.17
1.19
1.20
1.22j 1.24
1.26
70
21
.94
gii
. 98 1. 00 1. 02
1. 05
1.06:1.07
1.09
1,10 1,11 l,13 1,14'l,16
1.17
1.19
1.21
1.22
1.24
1.26
1.28 1.30
1.32
69
22
.981.00
1.021.051.07
l.OO.l.ll'l. 12
1.14
1,15 1,17 1, LSI, 20 1.2111, 23
1.25
1.26
1.28
1.30
1.32
1.34; 1.36
1.38
68
23
1.021.04
1.07 1.091.12
1, 14!l,161,17
1.19
1,2(11 21 1,2:; 1,25 1,26 1,28
1.30
1.32
1.34
1.36
1.38
1.40' 1.42
1.44
67
24
1. Oe'l. 09
1. 11 1. 14 1. Ifi
1. 19 1. 20 1, 22
1, 23 1, li.'. 1. 27 1 , i.l 1, 30 1, 32 1, 33|1, 35
1.37
1.39 1.41
1.43
1.45 1.48
1.50
66
25
l!l0|l.l3
1.1,-. 1,1s 1,21
1,241,251,27
1.28
l.i'.ii 1,31 1,:;:! 1. 3,' 1,37 1,39,1,41
1.42
1.45, 1.47
1.49
1.51
1.53
1.56
65
26
27
28
29
30
1. 15 1. 17
,1,1 ,1,1 .ir,
1, 28 1, 30' 1,31
1, Sj
1.:;,-. l.:;ii 1. :i,-< 1.411 1,421, ll'l, 46
1.48
1.51
1.52
1.54
1.57
1.59
1.61
64
l!l9l'-Jl
1. •_*-! 1. 'JT 1, :!0
1. :!;i'l, 34 1, 31
1. :;.^
l.:;:i 1, 11 1, 1:; 1. 4.' 1. 47 1, 49 1. r.l
1.53
1. 55
1.58
1.60
1.62
1.65
1.67
63
1. ■j,'^ 1, ;ii 1 . ,14
1, :;7 1, :;'.i !. 11
1, IL
1, .|.| 1. Ill 1.4^ 1. .'Hi 1. .■•2 1, Til 1. -'1'
1.58
1.00
1.63
1.65
1.68
1.70
1.73
62
1 '"^~ 1 ■"'!
1. 41; 1, l:M . r
1. 47
1 .j'l 1 .■. 1 I :■:] ) .'.', 1. ,",7 1, .''11 1 111
1.63
1.661 1.68
1.71
1.73
1.76
1.79
61
L3u'..5:;
l,:j(il,:;9 1,4:1
1,40 L4,S L.-'l
1. nil.. -.11 l..-,s 1,111) 1.112 1,114 1,110
1.69
1.71 1.73
1.76
1.79
1.81
1.84
60
31
1.35
1.38
1.40'l.44'l,47
'1.51 1,52 1,54
1,56
1, 58 1. 60 1, 62 1, 64 1, 67 1, 69|1, 71
1.74
f.iel 1.79
1.81
1.84
1.87
1.90
59
32
1.39
1.421.451.481.51
1. 55!l. 57 -I. 59
1,61
1,03 1.65' 11.67 1,691,711,74
1.7b
1.79
1.81 1.84
1.87
1.89
1.92
1.95
58
33
1.42
1.451.49 1.521.55
'1.59;l,0i:i,63
1,65
1,67,1,69
!l.721.741.761.7£
1.81
1.84
1.86 1.89
1.92
1.95; 1.98
2.01
57
34
1.46
1 . 49 1 . 53 1 . 56 1 . 60
1, 63]l, 65 1. 6S
1,70
1. 72il. 74
'l.7G1.791.811.8r
l.Sb
1.80
1.91] 1.94
1.97
2.00 2.03
2.06
56
35
1. 50|1. 53
1,56,1.601,64
|1, 681,701,72
1,74
,1.761.78
1.81|1.831. 861.8f
1.91
1.93
1.961 1.99
2.02
2.05 2.08
2.11
55
36
1.54
1.57
1, 60 1. 64 1, 68
1 1
1.721.74 1.76
1,78
1.80 1.83
11.851.881.901.9
1.95
1.98
2.01 2.04
2.07
2.10
2.13
2.16
54
37
1.57
1. 61
1, 64 1, 68 1, 72
1,761, 78 1,80
1,83
'1.851.87
1 90 1. 92 1. 95 1. 97i2. 00
2.03
2.06 2.09
2.12
2.15
2.18
2.22
53
38
1.61
1. 64
1. 681.721,76
1, 80 1, 82 1. 84
1,87
1.891.91
1.941.971.99 2.02 2.05
2.08
! 2.11 2.14
2.17
2.20
l^i
2.27
52
39
1 65
1 68
1.721,751,80
1,84 1,861,88
1,91
1.931.96
1.98 2.012.04:2.06 2.09
2.12
, 2.15 2. IE
2.22
2.25
2.28
2.32
51
50
40
1.68
1.72
1,751,791,84
1,881,901,93
1.95
1.97 2.00
2. 03 2. 05 2. 08 2. 11 2. 14
2.17
2.20 2.23
2.26
2.3C
2.83
2.37
41
1.71
1.75
1.79 1.83 1,87
l,92'l,94 1.9f
i.or
2. 01 2. 04
2. 07 2. 09!2. 12 2. 15!2.18
2.21
2.24 2.2E
2.31
2. 84
2.38
2.42
49
42
1.75
1.79
1, S3 1, 87 1, 91
1,96,1, 9H2, 01
2. 0:
2. 05 2. 118, 2. 11 2. 14'2. 16 2. 19!2. 22
2.26
2.2
2.31
2.3e
2.3£
2.43
2.46
48
43
1. 7f
1.82
1, 86 1, 90 1, 95
1,99 2,02 2,04
2. 0"
2. 09 2. 1-.
2. 15 2.182. 212. 24!2. 27
2.30
2.3
2.3'"
2.4t
2.41
2.47
2.51
47
44
1 82
1 85
1, 90 1. 94 1 98
2, 03:2, 06 2. 08
2,1
i2. 13 2. 16
2. 19 2. 22 2. 25 2. 28!2. 31
2.34
2.3
2.41
2.4E
2.4f
2.52
2.5e
46
45
1.85
1.89
1.931,97 2,02
2, 07 2. 09 2. 12,2, 1
1 1
;2.17i2.20
1
2.23 2.26 2.29,2.32 2.36
1 ! 1
2. 88
2.4
2.4>
2.4E
2.5
2.5*
2. 6C
45
222
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVIII. — Factors for reduction of transit oiservations — Continued.
Azimuth factor A = sin J sec. S, Star's declination ± 8. Inclination factor B=co3 i sec. i.
i
67S°
l.SS
68°
1.92
68io
1.96
69°
2.01
69io
2.05
70°
2.10
70J°
2.13
704°
2.15
703°
2.18
71° 71J'
71J°
71P
2.30
72°
2.33
72J°
2.36
72i°
2.39
72J°
2.42
73°
2.46
731°
2.49
73JO
2.53
73i°
2.57
74°
2.61
7^140
2.65
?
46°
2.212.24
44°
47
i.iiiii.ti:.
2. no -J. (14
2. Oil
2.14
' 111 ■' I'.i " ■ :. ■' ", ■' :;n
3.33
2.37
2.40
2.43
2.47
2.50
2.54
2.57
2.61
2.65
2.69
43
48
l-'.l-l L'. us
2. I'2 2. 07
2. 12
2. 17
2,111 J -J.' L- . -■-■ :i - :12.37
2.40
2.44
2.47
2.51
2.54
2.58
2.62
2.66
2.70
2.74
42
49
l.L'T -. "1
2. (Hi 2. ] 1
2. 11;
2.21
'■'::■■ :. ;s ■"* 41
2.44
2.48
2.51
2.55i
2.58
2.62
2.66
2.70
2.74
2.78
41
50
1. (JO 2. Ul
2. US 2. 14
2.1a
2.24
2. 27,2. 2. 2. .2, 2. .3,2..., 11,2.45
2.48
2.51
2.55
2.58
2.62
2.66
2.70
2.74
2.78
2.82
40
51
2.03
2.07
2. 12 2. 17
2.22
2.27
2.30 2.33
2.36
2.39
2.42
2.45
2.48
2.51
2.55
2.58
2.62'
2.66
2.70
2.74
2.78
2.82
2.86
39
52
2.06
2.10
2.15
2.20
2.25
2.30
2.33 2.36
2.39
2.42
2.45
2.48
2.52
2.55
2.58
2.62
2.66,
2.69
2.73
2.77
2.82
2.86
2.90
38
53
2.09
2.13
2.18
2.23
2.28
2.33
2. 36 2. 39
2.42
2.45
2.48
2.52
2.55
2.58
2. 62 2. 66
2.69
2.73
2.77
2.81
2.85
2.90
2.94
37
54
2.11
2.16
2.21
2.26
2.31
2.37
2.39 2.42
2.45
2.48
2.52
2.55
2.58
2.62
2. 65 2. 69
2.73
2.77
2.81
2.85
2.89
2.94
2.98
36
55
2.14
2.19
2.23
2.29
2.34
2.40
2.42 2.45
2.48
2.52
2.55
2.58
2.62
2.65
2.69 2.72
2.76
2. SO
2.84
2.88
2.93
2.97
3.02
35
56
:.i7-:.2i
2 ^7
2 42
2.15 2 1 =
2 51 2 55 2 5«'2 01
2 fi5'2, m
2. 72 2. 76
2.80
2.83
2.86
2.84
2.87
2.90
2.88
2.91
2.94
2.92
2.95
2.99
2.96
3.00
3.03
3.01
3.04
3.08
3.05
3.09
3.12
34
33
32
57
- '" ' -'
'- ■, _ :., - ■: 'J : - ' : ; i -^ :i I 742:78|2!82
58
59
50
I... .11 42
2.47
2w.j
^ 7, J 77 _ . .. _ . .. ..-r. „ 7.._, ; , ..77 2.8ll2.85
2.89
2.92^
2.93
2,96
2.97
3.01
3.02
3.05
3.06
3.09
3.11
3.14
3.16
3.19
31
30
liioli.Jl
-..Jl,-.obl2.0., 2.(jU2.(,i)2. ,o2. ,0
2.80
2.84 2.88
61
2. 2912. .33
2. 39 12. 44
2.50
2.56
2.59 2.62 2.65 2.69 2.72 2.76
2 79
2.83
2.8712.91
2.95
2.99
3.04
3.08
3.13
3.17
3.22
29
62
2.312.36
2.41:2.46
2.52
2.58
2.612.64 2.68 12.712.75 2.78
2 82
2.86
2.90 2.94
2.98
3.02
3.06
3.11
3.16
3.20
3.25
28
63
2.33;2.38
2.43 2.49
2.54
2.6(1
2. 64 2. 67 2. 70' 2. 74 2. 77 2. 81
2.84
2.88
2.92I2.96
3.00
3.05
3.09
3.14
3.18
3.23
3.28
27
64
2.35|2.40
2.45 2. SI
2. rt~
2. C3
2. 66 2. 69 2. 73 2. 76 2. 80i2. 83
2.87
2.91
2.9512.99
3.03
3.07
3.12
3.16
3.21
3.26
3.31
26
65
2.37 2.42
2. 47 2. 52
2.59
2.65
2.88 2.71,2.75,2.78,2.82
2.86
2.89
2.93
2. 97j3. 01
3.06
3.10
3.14
3.19
3.24
3.29
3.34
25
66
2, I'l
2 1--
2,7"2. 74 2, 77 2,1-12.84
2.88
2.92
2.96
3.00 3.04
3.08
3.13
3.17
3.22
3.27
3.31
3.37
24
67
-!_-■. -:■ . -12.86
2.90
2.94
2.98 3.02,3.06
3.10
3.15
3.20
3.24
3.29
3.34
3.39
23
68
7 7- -: _ --iL7 8Si2.92
2.96
3.0ol3.04i3.08
3.13
3.17
3.22
3.26
3.31
3.36
3.42
22
69
J . -U '^ . 4
J 7', J -ii J - 1 ll,,-7 2.90]2.94
2.98
3.0213.06 3.10
3.15
3.19
3.24
3.29
3.34
3.39
3.44
21
70
.'. 4U ■.;. 51
2. oli 2. Ui;
2. US
2. iS 2. 81 2. 8.5 2. 89,2. 92,2. 96
3.00
3.04(3.08 3.12
3.17
3.21
3.26
3.31
3.36
3.41
3.46
20
71
2.47
2.52
2.58
2.64
2.70
2.77
2.8o'2.83'2.87'2.90 2,94 2.98
3.02
3. 06^3. 103. 14
3.19
3.24
3.28
3.33
3.38
3.43
3.48
19
72
2.49
2.54
2.59
2.65
2.72
2.78
2. 8Ij2. 85j2. 88 :2. 92:2. 96'3. 00i3. 04
3. 08,3. 12,3. 16
3.21
3.25
3.30
3.35
3.40
3.45
3.50
18
73
2.50
2.55
2.61
2.67
2.73
2.80
2. 83(2. 8612. 90l 2. 94 2. 97 3. 0l|3. 05
3.09 3.14 3.18
3.22
3.27
3.32
3.37
3.42
3.47
3.52
17
74
2.51
2.57
2.62
2.68
2.74
2.81
2. 84,2. 88 2. 92; 2. 95 2. 99 3. 03,3. 07
3.ir3.]5 3.20
3.24
3.29
3.33
.3.38
3.44
3.49
3.54
16
75
2.52
2.58
2.64
,2.70
2.76
2.82
2. 86|2. 89l2. 93| 2. 97,3. 00,3. 04
3.08
3.13 3.17 3.21
3.26
3.30
3.35
3.40
3.45
3.50
3.56
15
76
J..MJ. -;-
2. i:-'2. 71
2. -1
2 -7 11 111 -M7 J nil 11. 02:3. 06
3.10
3.15,3.18:3.23
3.28
3.32
3.37
3.42
3.47
3.53
3.58
14
- -■ - - " - I'l'::. 0313.07
3.11
3. 1513.19 8. 24
3.29
3.33
3.38
3.43
3.48
3.54
3.59
13
78
. J . , - "11. 04'3.08
3.12
3.16,3.213.25
3.30
3.34
3.39
3.44
3.49
3.55
3.60
12
79
-■' i;^ ■' 7-1
J, 111 -.iMu,'K :i..i-:i (1513.09
3. 13|3. 18l3. 22
3.26
3.31
3.36
3.41
3.46
3.51
3.56
3.62
11
80
2. 57 2. 63
2! 69 2. ::,
2. 81
2^88
2. 91 2. 95 2. 99 3. 02 3. 06 3. 10
3.14
3. 19 3. 23
3.27
3.32
3.37
3.42
3.47
3.52
3.57
3.63
10
81
2. 58' 2. 64
2. 69 2. 76
2.82
2.89
2. 92 2. 9613.0013. 03 3.07:3.11
3.15
3. 20 3. 24
3.28
3.33
3.38
3.43
3.48
3.53
3.58
3.64
9
82
2.59,2.64
2.70 2.76
2.83
2.90
2. 93 2. 97 3. 00 3. 04 3. 08 3. 1213. 16
3. 20 3. 25i3. 29
3.34
3.39
3.44
2.49
3.54
3.59
3.65
8
83
2.59 2.65
2.71 2.77
2.83
2.90
2. 94 2. 97 :;. Ill 2. 0,5 3. 0913. 13'3. 17
3.21,3.2613.30
3.35
3.40
3.45
3.49
3. 55
3.60
3.66
7
84
2. 60 2. 66
2.71:2.78
2.84
2.91
2.94 2.11,-11.112 li, ml n. 09'3. 13 3. 18
3.22 3.263.31
3.35
3.40
3.45
3.50
3.55
3.61
3.66
6
85
2. 60 2. 66
2.72i2.78
2.84
2.91
2. 95 2, 98 IJ. U2 11. Ui; 3. 1013. 14:3. 18
3. 22 3. 27(3. 31
3.36
3.41
3.46
3.51
3.56
3.61
3.67
5
86
2. 61 2. l-J
2.92
2.95
2.99,3.03
.3. 06|3. 10
3. 14 3. 19
3. 23 3. 27
3.32
3.36
3.41
3.46
3.51
3.57
3.62
3.68
4
87
2.612.1'
2.92
2.95
2.99
3.03
3.07
3.11
3. 15 3. 19
3. 23 3. 28
3.32
3.37
3.42
3.47
3.52
3.57
3.62
3.68
3
88
2.61 2. i;:
2.92
2.96
2.-99
3.03
3.07
3.11
3.15 3.19
3.23 3.28
3.32
3.37
3.42
3.47
3.52
3.57
3.62
3.68
2
89
2. 6112. u:
2. 71>||2. 71)
2.80
2.92
2.96
3.00
3.03
3.07
3.11
3.15 3.19
3. 24 3. 28
3.33
3.37
3.42
3.47
3.52
3.57
3.63
3.68
1
90
2.612.67
2. 73|J2. 79
:f
2.92
2.96
3.00
3.03
3.07
3.11
3. 15 3. 19
3.24 3.28
3.33
3.37
3.42
3.47
3.52
3.57
3.63
3.68
0
FACTOES FOE EEDUCTION OF TEANSIT OBSERVATIOifS. 223
Table XXVIII. — Factors for reduction of transit observations — Continued.
Azimuthfactor A=:8inisec. 6. Star's tleclination ± S. Inclination factor B = cos ^ sec. S.
i
1^
74i°
.06
74,o
.07
75°
.07
751^
.07
7=S°
.07
75,0
76°
76,°
.07
76,°
.07
76»°
.08
77°
.08
77,°
.08
77i°
.08
77i°
.08
78°
.08
78i°
.09
78J°
78J°
, 79°
79i°
.09
79J°
.10
79J°
.10
80°
.IC
i
.07
.07
.09
. 09: • 09
'89
2
.13
.13
.13
.14
.14
.14
.14
.15
.15
.15
.16
.16
.16
.16
.17
.17
■ .18
. 18' . 16
.19
.19
.20
.2C
88
3
.20
.20
.20
.21
.21
.21
.22
.22
.22
.23
.23
.24
.24
.25
.25
.26
.26
. 271 . 27
.28
.29
.29
.31
87
4
.26
.27
.27
.27
.28
.28
.29
.29
.30
.30
.31
.32
.32
.33
.34
.34
.35
. 36: . 37
.37
.38
.39
.41
86
5
.33
.33
.34
.34
.35
.35
.36
.37
.37
.38
.39
.40
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
85
6
.39
.40
.40
.41
.42
.42
.43
.44
.45
.46
.46
.47
.49
.49
.51
.51
.52
.54
.55
.56
.57
.59
.60
84
7
.46
.46
.47
.48
.49
.50
.50
.51
.52
.53
.64
.55
.56
.57
.59
.60
.61
.62
.64
.65
.67
.69
.70
83
8
.52
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.66
.67
.68
.70
.71
.73
.75
.76
.78
.80
82
9
.58
.59
.60
.61
.62
.64
.65
.66
.67
.68
.70
.71
.72
.74
.75
.77
.78
.80
.82
.84
.86
.88
.90
81
10
.65
.66
.67
.68
.69
.71
.72
.73
.74
.76
.77
.79
.80
.82
.84
.85
.87
.89
.91
.93
.95
.98
1.00
80
11
.71
.73
.74
.75
.76
.77
.79
.80
.82
.83
.85
.86
.88
.91)
.92
.94
.96
.98
1.00
1.02
1.05
1.07
1.10
79
12
.78
.70
.80
.82
.83
.85
.86
.88
.89
.91
.92
.94
.96
.98
1.00
1.02
1.04
1.07
1.09
1.11
1.14
1.17
1.20
78
13
.84
.86
.87
.88
.90
.91
,93
.95
.96
.981.00 1.02
1.04
1.06
1.08
1.10
1.13
1.15
1.18
1.21
1.23
1.26
1.30
77
11
.91
.92
.94
.95
.97
.98
1.00
1.02
1.01
1.061.08 1,10
1.12
1.14
1.16
1.19
1.21
1.24
1.27
1.30
1.33
1.36
1.39
76
15
.97
.98
1. Oil
1.02
1.03
1.05
1.07
1.09
1.11
1.13 1.15 1,17
1,20
1.22
1.25
1.27
1.30
1,33
1.36
1.39
1.42
1.46
1,49
75
16
1.03
1.05
1.06
1.08
1.10
1.12
1.14
1, 16 1. 18'i,2o'l,2:i 1.25
1.28
1.30
1.33
1.35
1.38
1.41
1.44
1,48
1.51
1,55
1,59
74
17
1. 09
1,11
1.13
1.15
1.17
1.19
1.21
1, 2:l!l, 25 1. 28 1, 30 1. 32
1.35
1,38
1.40
1.44
1.47
1.50
1.53
1.57
1.60
1,64
1.68
73
19
1.16
1.17
1.19
1.21
1.23
1. 25 ;i. 2S 1. 3U|1, 32 1. 35 1. 37 1, 411
1.43
1.46:i.49
1.52
1.55
1.58
1.62
1.66
1.70
1.74
1.78
72
10
1.22
1.24
1.20
1.28
1.30
1.32
1. .35
1.37 1, 39|1, 42:1,45 1.47
1.51
1. 53
1.57
1.60
1.63
1.67
1.71
1.75
1.79
1.83
1.87
71
20
1.28
1.30
1.32
1.34
1.37
1.30
1.41
1. 44ll,461, 49 1,50 1.55
1.58
1.61
1.65
1.68
1,73
1.75
1.79
1.83
1.88
1.93
1.97
70
21
1.34
1.36
1.3R
1.41
1.43
1.46
1.48
1,51 1,541, 56 1.591 1.62
1.65
1.69
1,72
1.76
1.80
1.84
1.88
1.92
1.97
2.01
2.06
69
22
1.40
1.42
1.45
1.47
1.50
1.52
1. 55
1. 58 1, 60 1, 63 1. 66' 1. ■Jo
1,73
1.77
1,80
1.84
1.88
1.92
1.96
2.01
2.06
2.11
2.16
68
23
1.46
1.49
1.51
1.54
1.56
1.59
1.62
1. 04 1. 67 1. 70 1. 74[ 1. 77
1,81
1, 84il.88
1.92
1.96
2.00
2.05
2,09
2.14
2.20
2.25
67
24
1, .52
1.55
1.57
1.60
1.63
1.65
1.68
1,711, 74jl, 771. 8ll|l, 84
1,88
1. 92 1. 96
2.00
2.04
2.08
2.13
2.18
2.23
2.29
2.34
66
25
1.58
1.61
1.63
1.66
1.69
1.72
1.75 1.781,811,84 1.88 1,91
1.95
1,99 2.03
2.07
2.12
2.17
2.22
3.27
3.32
2.38
2.43
65
26
1.64
1.67
1.69
1.72
1.75
1.78
1.811.841,881,911,9.-1 1,9!)
2. 02
2, 07:2. 11
2.15
2.20
2.25
2.31
2.35
2.41
2.46
2,52
64
27
1.70
1.73
1.75
1.78
1.81
1.85
1, 88ll.911.951.98 2, (12 2, 111!
2, 10
2,14'2.18
2.23
2,28
2.33
2.38
2,43
2.49
2.55
2,61
63
28
1.70
1.78
1.81
1.84
1.87
1.91
I. 94 1. 97 2. 0i;2. 05 2, 119 2. 13
2,17
2, 21 '2, 26
2.31
2.36
2,41
2.46
2,52
2'. 58
2.64
2.70
62
29
1.81
1.84
1.87
1.90
1.94
1.97
2. 002.04 2. 08.2. 112. 15i!2. 20
2.24
2, 28 2. 33
2.38
2.43
2,48
2.54
2.60
2.66
2.73
2.79
61
30
1.87
1.90
1.93
1.96
2.00
2.03
2.07:2. 10 2. 14:2. 18 2. 22!i2. 27
3.31
2.36 2.40
2.46
2.51
2.56
3.62
2.68
2.74
2.81
2.88
60
31
1.93
1.96
1.99
2.02
2.06
2.09
2. 13 2. 17 2. 2rj J.V-J. -J'.i J. :::;
2,38
2. 43 2 48
2.53
2.58
3.64
2.70
2.76
2.83
2.89
2.97
59
32
1.98
2.01
2.05
2.08
2.12
2.15
2, 19 2, 23 2, -j: : - ' : ,1
2,45
2.50 2.55
2.60
2.66
2.72
2.78
2.84
2.91
2.98
3.05
58
33
2.04
2.07
2.10
2.14
2.18
2.21
2.25 2.29 2,:::;- - - i :
2,52
2.57i2.62
2.67
2.73
2.79
2.85
2.93
2.99
3.06
3.14
57
34
3.09
2.13
2.16
2.20
2.23
2. 27
2.312,35 2,4111' 1 ' : I ' J.:.::
2,58
2. 64'2. 69
2.75
2.80
2.87
2.93
3.00
3.07
3,14
3,23
56
35
2.15
2.18
2.22
2.25
2.29
2.33
2,37 2.412,40 J. riij, l.'i J.r.n
2,65
2. 70 2. 76
2.82
2.88
2.94
3.01
3.08
3,15 3.28
3.30
55
36
2.20
2.24
2.27
2.31
2,35
2.39
2.432.472,,52-J.,-i;2.i;l 2. CO
2, 77 2. 83
2.89
2.95
3.01
3.08
3.15
3.23 3.30
3.38
54
37
2.25
2.29
2.33
2.36
2.40
2.44
2, 49 2, 53 2. 58 2. O:.: 2, 07 2, ''J
2:7s
2. 84 2. 90
2.95
3.02'
3.08
3.15
3.23
3.30 3.38
3.47i 63
38
2.30
2.34
2.38
2.42
2. 46 2. 50
2,55 2,59 2.64,2.69
2.74i2.79
2,85
2. 90 2, 96
3,02
3.09:
3,16
3.23
3.30
3.38 3.46
3.551 52
39
2.35
2.39
2.43
2.47
2.512,56
2.60 2.65 2.70 2.75
2. 80 '2. 85
2,91
2. 97 3, 03
.3.09
3.161
3,23
3.30
3.37
3.45 3.53
3. 62 51
40
2.40
2.44
2.48
2.52
2. 57 2. 61
2.66 2.70 2.75 2.80
2. 86,, 2, 91
3.97
3.03
3,09
3.16
3.22
3.29
3.37
3.45
3.53 3.61
3. 70j 50
41
2.45
2.49
2.53
2.58
2. 62 2. 66
2.7l'2.76 2.812.86
2,92:2,97
3.03
3.09
3.16
3,22
3,29
3.36: 3.44
3.52
3.60 3.69
3.78
40
42
2.50
2.54
2.58
2.63
2. 67 2. 72
2. 77 2. 81 2. 87|2. 92 2. 97,
3.03
3.09
3.15
3,22
3,29
3.36
3.43; 3.51
3.59
3. 67 1 3. 76
3.85
48
43
2.55
2.59
2.63
2.68
2. 72 2. 77
2.82 2.87,2.922.98 3,03
3.09
3,15
3.21
3.28
3.35
3.42
3.50] 3.57
3.66
3.74 3.83
3.93
47
44
2.60
2.64
2.68
2.73
2. 77 2. 82
2.87,2.92 2.98,3.03 3.09
3.15
3.21
3.27
3.34
3.41
3.48
3.56: 3.64
3.72
3.81 3.91
4.00
46
45
2.65
2.69
2.73
2.78
2. 82 2. 87
2. 92|2. 97 3. 03 3. 08 3. 14
8.20
3.27
3.33
3.40
3.47
3.55
3.62 3.71
3.79 3.88 3.97|
4.07
45
224
A ma:n^ual of topogeaphic methods.
Table XXVIII. — Factors for reduction of transit ohservations — Continued.
Azimuth factor A=sm C sec. 5. Star's decliuation ± 6. Inclmation factor B = cos i sec. 6.
460
74J=
2. 6n
74r
75°
75io
75J=
2.S7
75r
2.92
76°
2.97
76i0 76io
3. 03 3. OS
76J°
770
77i°
3.20
77J°
3.32
77i°
3.39
78°
3.46
78i°
3.53
78J°
3.01
78i°
3.69
79°
79i°
3.86
79J°
3.95
79J°
4.04
80°
4.14
i
2.7s'2.S2
3. 14'3. 20
3.77
44°
47
^ 7
■J. 1-17
_\ |i'^
■J, 117
11. li"J
:i, 08 :i. i:
11 IP 11, 2," 11 "1
11, 118
11, 4,"
3.52' 3.59
3. 67i 3.75
3.83
3.92
4.01
4.11
4.21
43
48
11, '57
3.05
3.73
3.81
3.89
3.98
4.08
4.18
4.28
42
49
,1,03
3.71
3.79
3.87
3.96
4.05
4.14
4.24
4.35
41
50
J ;il
"'■'-''
■■!"■
.1. 11
.1,1:
■■■ ■-' ■'■ -;:"
11, 114. 1,41 : ,:;
1, -■!
1 ill
11, 08
3.76
3.84
3.93
4.02
4.11
4.20
4.30
4.41
40
51
2.91
2.95
3.00
3.05
3.10
3.16
3.21
3. 27 3. 33
3.39
3.45 11,5.
11.00
11.74
3.82
3.90
3.98
4.07
4.17
4.26
4.37
4.48
39
52
2.95
3.00
3.04
3.09
3.15
3.20
3.26
3.313.38
3.44
3. .10 11, ,-.7
11. 114
11, 71
3.79
3.87
3.95
4.04
4.13
4.22
4.32
4.43
4.54
38
63
2.99
3.04
3.09
3.14
3.19
3.24
3.30
3.36 3.42
3.48
3. 35 3. 02
11, 00
3, 77
11.84
3.92
4.01
4.09
4.19
4.28
4.3b
4.49
4.60
37
54
3.03
3.08
3.13
3.18
3.23
3.29
3.34
3.40 3.47
3.53
3. 60 3. 67
3.74
3. 81
3.89
3.97
4.00
4.15
4.24
4.34
4.44
4.55
4.66
36
55
3.07
3.11
3.16
3.22
3.27
3.33
3.39
3.45 3.51
3.57
3. 64 3. 71
3.78
3.86
8.94
4.02
4.11
4.20
4.29
4.39
4.50
4.60
4.72
35
56
3.10
3. 15
3.20
3.26
3.31
3.37
3. 43
3. 49 3. 55
3,62
3. OS 3. 70
3. Sll
3.91
3.99
4.07
4.16
4.25
4.34
4.44
4.55
4.66
4.77
•34
57
::. 11
; l:i
1. -11
1, 17
1, Til 11 81'
1, 8-
11, 0,'
4,04
4.12
4.21
4.30
4.39
4.50
4.60
4.72
4.83
33
58
1.08
4.16
4.25
4.35
4.44
4.55
4.65
4.77
4.88
32
59
> ,11 ; i 1 7
4.12
4.21
4.30
4.39
4.49
4.60
4.70
4.82
4.94
31
(iO
.:.-,!
;,-h
'■-i''
1 ,-.s
1 <i.;:i 71
I, .11
.1,
4, 17
4.25
4.34
4.44
4.54
4.64
4.75
4.87
4.99
SO
61
3.27
3.33
3.38
3.44
3.49
3.55
3.62
3. 683. 75
3. 82
3.^93.96
4.04
4.12
4.21
4.29
4.39
4.48
4.58
4.69
4.80
4.92
5.04
29
62
3.30
3.36
3.41
3.47
3.53
3.59
3.65
3. 72 3. 78
3! 85
3. 92 4. 00
4.08
4.10
4.25
4.34
4.43
4.53
4.63
4.73
4.85
4.96
5.08
28
63
3.33
3.39
3.44
3.50
3.56
3.62
3.68
3. 75 3. 82
3.89
3. 96 4. 04
4.12
4.20
4.29
4.38
4.47
4.57
4.67
4.78
4.89
5.01
5.13
27
64
3.36
3.42
3.47
3.53
3.59
3.65
3.72
3. 78,3. 85
3.92
4. 00 4. 07
4.15
4.24
4.32
4.41
4.51
4.61
4.71
4.82
4.93
5.05
5.18
26
65
3.39
3.45
3.50
3.56
3.62
3.68
2.75
3. 8113. 88
3.95
4. 03 4. 11
4.19
4.27
4.36
4.45
4.55
4.65
4.75
4.86
4.97
5.09
5.22
25
66
3, J2
:?. 47
_
■5, 50
l.fi.T
3 71
?, 7S
!. 84 3, 91
3, 99
4. 004. 14
4,22
4.31
4.40
i.49
4.58
4.68
4.79
4.90
5.01
5.14
5.26
24
67
:. 4-1
; il-
: . 1
; ^i
1 -T : 04
4, I'L'
1, 0:14, 17
t, 20
4, 1-14
4.43
4.52
4.62
4.72
4.82
4.94
5.05
5.18
5.30
23
68
1. 1 1 ■,
1- 1;; 1, 20
1, 2.^
4, 117
4.46
4.55
4.65
4.75
4.86
4.97
5.09
5.21
5.34
22
69
4, 11,
4. 1,", 1, 2,1
1.112
4,40
4.49
4.58
4.68
4.79
4.89
5.00
5.12
5.25
5.38
21
JO
J.i:
... i;
o.GJ
;.GJ
J. t;
,.j:
.. Ml
.1. Li.j 4. u;;
4. lu
4. 18 4.25
4.34
4.43
4.52
4.61
4.71
4.82
4.93
5.04
5.16
5.28
5.41
20
71
3.54
3.60
3.65
3.71
3.78
3.84
3.91
3. 98*4. 05
4.13
4. 20 4. 28
4.37
4.40
4.55
4.64
4.74
4.85
4.96
5.07
5.19
5.32
5.45
19
72
3.56
3.63
3.67
3.74
3.80
3.86
3.93
4. 00 4. 07
4.15
4. 23!4. 31
4.39
4.48
4.57
4.67
4.77
4.88
4.98
5.10
5.22
5.34
5.48
18
73
3.58
3.64
3.69
3.76
3.82
3.89
3.95
4. 02 4. 10
4.17
4.25:4.33
4.42
4.51
4.60
4.70
4.80
4.90
5.01
5.13
5.25
5.37
5.51
17
74
3.60
3.65
3.71
3.78
3.84
3.91
3.97
4. 04;4. 12
4.19
4. 2714. 36
4.44
4 53
4.62
4.72
4.82
4.93
5.04
5.15
5.27
5.40
5.53
16
75
3.61
3.67
3.73
3.79
3.86
3-92
3.99
4.06 4.14
4.21
4. 29 4. 38
4.46
4.55
4; 65
4.74
4.84
4.95
5.06
5.18
5.30
5.43
5.56
15
76
3.64
3. on
'. "-■
, 5,
.94
4. 01
4. OS 4. ir.
4, 2'_1
4. .11 '4. 40
4,4s
4. .57
4.07
4.76
4.87
4.97
5.09
5.20
5.32
5.45
5.59
14
77
3.65
3.711
-.1
'. 'Mi
4. 03
1.10 4,17
1, 11114.41
4. ,'iO
1, ,'.0
4.68
4.78
4.89
4.90
5.11
5.22
5.35
5.47
5.61
13
78
3,66
3.7:
'. 07
4. 04
4.11 4.111
4. 27
4, 11,'. 4,411
1, ,'.2
4,01
4.70
4.80
4.9]
5.01
5.13
5.24
5.37
5.50
5.63
12
79
3.67
3.7.1
1.119
4. OlJ
4.1114.21
4, 1;,^
4, 110 4.4,'.
1. ,'.4
I, OH
4.72
4.82
4.92
5.03
5.14
5.26
5.39
5.52
5.65
11
SO
3.68
3.74
i.sl
i.bl
0. 113
4.00
4.07
4.144.22
4. 3U
4. 38 4. 40
4.55
4.04
4.74
4.84
4.94
5.05
5.16
5.28
5.40
5.54
5.67
10
81
3.70
3.75
3.82
3.88
3.94
4.01
4.08
4.16 4.23
4.31
4. 39 4. 48
4. .56
4.65
4.75
4.85
4.95
5.06
5.18
5.30
5.42
5.55
5.69
9
82
3.71
3.76
3.83
^.89
3.96
4.02
4.09
4. 17 4. 24
4. 32
4. 40 4. 49
4.57
4.67
4.76
4.86
4.97
5.08
5.19
5.31
5.43
5.56
5.70
S
83
3.72
3.77
3.84
3.90
3.96
4.03
4.10
4. 18 4, i,".
4. 414. .io
4. :'.9
4. 08
4.78
4.87
4.98
5.09
5.20
5.32
5.45
5.58
5.72
7
84
3.72
3.78
3.84
3.91
3.97
4.04
4.11
4, 18 4,20
4.34
4. 42 4. 51
4.00
4.09
4.79
4.88
4.99
5.10
5.21
5.33
5.46
5.59
5.73
6
85
3.73
3.79
3.85
3.91
3.98
4.05
4.12 4. 1114 27
4. 115
4,4114.51
4.60
4.09
4.79
4.89
5.00
5.11
5.22
5.34
5.47
5.60
5.74
5
86
3.73
3.711
4. ;i.'
1, l-jli.^M L-27
4.35
4.43 4,52
4. 01
4.70
4.80
4.90
5.00
5.11
5.23
5.35
5.47
5.61
5.74
4
87
3.74
3.71.
4. 30 4. 44 4. 52
4.02
4.714.81
4.90
5.01
5.12
5.23
5.35
5.48
5.61
5.75
3
88
3.74
3,8'
4,36 4.44 4.51!
4.02
4. 71 4. 81
4.91
5.01
5.12
5.24
5.36
5.48
5.61
5.75
2
89
3.74
S.Su
1. ,m1
1 M,;
. ll'.i
1. ml
1. 1:1 -I. -Jl 4. 1.8 4.30 4.44 4.53
4.62
4. 71 4. 81
4.91
5.01
5.12
5.24
5.36
5.49
5.62
5.76
1
90
3.74
3.80
J. Sli
3! 93
3.99
4.06
4. 1314. 21 4. 28,4. 36J4. 44l4. 53 4. 62
4. 7114. 81
4.91
5.02
5.13
5.24
5.36
5.49
5.62
5.76
0
Table XXIX. — For reducing observations for latitude hy Talcotfs metliod.
[Extracted from Appendix 14. TJnited States Coast and Geodetic Survey, Eeport for 1880.]
Correction for differential refraction. — The difference of refraction for any pair of
stars ia so small that we can uegieet the variation in the state of the atmosphere at the
time of the observation from that mean state supposed in the refraction tables. The
refraction being nearly proportional to the tangent of the zenith-distance, the differ-
ence of refraction for the two stars will be given by —
r— r'=57".7 sin [z—z') sec.-s;
and since the difference of zenith-distances is measured by the micrometer, the follow-
in £; table of correction to the latitude for differential refraction has been prepared
EEDUCTION OF LATITUDE OBSEEVATIONS.
225
for the argument ^difference of zenith-distance, or J difference of micrometer-reading
on the side, and the argument "Zenith-distance" on the top. The sign of the cor-
rection is the same as that of the micrometer difference.
i diff. in
Zenith-distance
i dift-. in
zenith-
distance.
0°
lOo
20°-
25°
30°
35°
distance.
0°
10° 20°
25°
30°
35°
0
.00
.00
.00
.00
.00
.00
6.5
11
.11
K
.13
.14
.16
0.5
.01
.01
.01
.01
.01
.01
7
IX
.12
13
.14
.15
.18
1
.02
.02
.02
.02
.02
.02
7.5
13
.13
14
.15
.16
.19
1.5
.02
.03
.03
.03
.03
.03
8
13
.14
15
.16
.18
.21
2
.03
.03
.04
.04
.04
.05
8.5
14
.15
16
.17
.19
.22
2.5
.04
.04
.05
. .05
.05
.06
9
15
.16
17
.18
.20
.23
3
.05
.05
.06
.06
.07
.08
9.5
IB
.17
18
.20
.21
.24
3.5
.06
.06
.07
.07
.08
.09
10
17
.18
19
.21
.23
.26
4
.07
.07
.08
.08
.09
.10
10.5
IK
.19
W
.22
.24
.27
4.5
.08
.08
.09
.09
.10
.11
11
IK
.19
21
.23
.25
.28
5
.08
.09
.10
.10
.11
.13
11.5
1»
.20
•>v.
.24
.26
.30
5.5
.09
.10
.10
.11
.12
.14
12
2()
.21
23
.25
.27
.31
6
.10
.10
.11
.12
.13
.15
Reduction to the meridian. — First, when the line of collimation of the telescope is
off the meridian, the instrument having been revolved in azimuth and the star observed
at the hour-angle t, near the middle thread, then
2 sin^ hr cos a cos d
m= — ^ — -—. 4--= —
sm 1" sm C
and the correction to the latitude, if the two stars are observed off the meridian
= ^ (m'—m). The value of
2 sin^ ^T
t sin 1"
for every second of time up to two minutes (a star being rarely observed at a greater
distance than this from the meridian in zenith-telescope observations'! is given in the
following table :
-
Term.
-
Term.
^
Term.
-
Term.
-
Term.
Term.
1
0.00
21
0.24
41
0.91
61
2.03
s.
81
3.58
101
6.56
'2
0.00
22
0.26
42
0.96
62
2.10
82
3.67
102
5.67
3
0.00
23
0.28
43
1.01
63
2.16
83
3.76
103
6.78
4
0.01
24
0.31
44
1.06
64
2.23
84
3.85
104
5.90
5
0.01
25
0.34
45
1.10
65
2.31
85
3.94
105
6.01
6
0.02
26
0.37
46
1.15
66
2.38
86
4.03
106
6.13
7
0.02
27
0.40
47
1.20
67
2.45
87
4.12
107
6.24
8
0.03
28
0.43
48
.1.26
■ 68
2.52
88
4.22
108
6.36
9
0.04
29
0.46
49
1.31
69
2.60
89
4.32
109
6.48
10
0.05
30
0.49
50
1.36
70
2.67
90
4.42
110
6.60
11
0.06
31
0.52
51
1.42
71
2.75
91
4.52
111
6.72
12
0.08
32
0.56
52
1.48
72
2.83
92
4.62
112
6.84
13
0.09
33
0.59
53
1.53
73
2.91
93
4.72
113
6.06
14
0.11
34
0.63
54
1.59
74
2.99
94
4:82
114
7.09
15
0.12
35
0.67
65
1.65
75 »
3.07
95
4.92
115
7.21
16
0.14
36
0.71
56
1.71
76
3.15
90
5.03
116
7.34
17
0.16
37
0.75
57
1.77
77
3.23
97
5.13
117
7.46
18
0.18
38
0.80
58
1.83
78
3.32
98
5.24
118
7.60
.19
0.20
39
0.83
59
1.89
79
3.40.
99
5.34
119
7.72
20
0.22
40
0.87
60
1.96
80
3.49
100
5.45
120
7.85
MON XXII-
-15
226
A MANUAL OF TOPOGEAPHIC METHODS.
Seco7ully, when the star is observed oft' the liue of coUimatioii, the instrumeut
remaining in the plane of the meridian, then
m— — -. — zrvr- sin 0 cos o
sm 1"
2 sin^ iT_
sin 1"
i siu2(J
and the correction to the latitude is half of this quantity, whether the star be north or
south, and if the two stars forming a pair are observed off the line of collimation, two
such corrections, separately computed, must be added to the latitude. If the stars
should be south, of the equator, the essential sign of the correction is negative. The
value of m for every. 5° of declination is given in the following table:
IDs.
15.
205.
25s.
30s.
35s.
405.
45s.
50s.
55s.
60s.
6
„
„
„
„
„
„
„
„
„
S
5°
.00
.01
.02
.03
.04
.06
.08
.10
.12
.14
.17
85°
10
.01
.02
.04
.06
.08
.11
.15
.19
.23
.28
.34
80
15
.01
-.03
.05
.09
.12
.17
.22
.28
.34
.41
.49
75
20
.02
.04
.07
.11
.16
.22
.28
.36
.44
.53
.63
70
25
.02
.05
.08
.13
.19
.26
.34
.42
.52
.63
.75
65
30
.02
.05
.09
.15
.21
.29
.38
.48
.59
.71
.85
60
35
.03
.06
.10
.16
.23
.31
.41
.53
.64
.77
.92
55
40
.03
.06
.11
.17
.24
.33
.43
.54
.67
.81
.97
50
43
.03
.06
.11
.17
.25
.33
.44
.55
.68
.82
.98
45
Table XXX. — For facilitathifi the reduction of observatio7is, on close circumpolar stars^
made in determining the value of a revolution of the micrometer.
[Extmcted from Appeudix 14. TJ. S. Coast and Geodetic Surve;Vi Keport for 1880.]
Let ?=difference of time of observation and elongation of the star, and «"=num-
ber of seconds of arc in the direction of the vertical from elongation, then
cos S sin t
sin 1"
for which we can write
"z=15coS(y] *-i(L5sinl")'*=
where t is expressed in seconds of time. It is convenient to apply the term ^ (15 siu
l")^^' to the observed time of noting, additive to the observed time before, and sub-
tractive after, either elongation. The following table gives the value of i(15 sin
vyf, also of the additional term
—120 (15 sin 1")^ f when sensible, for every minute of time from elongation to QS"".
t j Term.
1
t 1 Term.
1
t
Term.
t
Term.
t
Term.
t
Term.
m
J
m.
s.
m
s.
m.
«.
m.
s.
m.
s.
6
0.0
16
0.8
26
3. .3
36
8.9
46
18.5
56
33.3
0.1
17
0.9
27
3.7
37
9.6
47
19.7
57
35.1
8
0.1
18
1.1
28
-'4.2
38
10. t
48
21.0
58
37.0
9
0.1
19
1.3
29
4.6
39
11.3
49
22.3
59
39.0
10
0.2
20
1.5
30
5.1
40
12.2
50
23.7
60
41.0
11
0.3
21
1.8
31
5.7
41
13.1
51
25.2
61
43.1
12
0.3
22
2.0
■32
6.2
42
14.1
52
26.7
62
45.2
13
0.4
23
2.3
33
6.8
43
15.1
53
28.3
63
47.4
14
0.5
24
2.6
34
7.5
44
16.2
54
29.9
64
49.7
15
0.6
25
3.0
35
8.2
45
17.3
55
31.6
65
52.1
COirV^EESION OF SIDEEAL INTO MEAN TIME.
227
Table XXXI. — For converting intervals of sidej'eal mto coi'responding intervals of mean solar time,
[Extracted from Lee'a Tables.]
Hours.
Minutes.
Seconds.
ft.
m s
m
s.
m
J
J
,
J
J
1
0 ' 09. 830
1
0.164
31
5.079
i
o.'6o3
31
0.085
2
0 19. 659
2
0.328
32
5.242
2
0.005
32
0.087
3
0 29.489
3
0.491
33
5.406
3
0.008
33
0.090
4
0 39. 318
4
0.655
34
5.570
4
0.011
34
0.093
5
0 49.148
5
0.819
35
5.734
5
0.014
35
0.096
6
0 58.977
6
0,983
36
5.89S
6
0.016
36
0.098
7
1 08. 807
7
1.147
37
6.062
7
0.019
37
0.101
8
1 18. 636
8
1.311
38
6.225
8
0.022
38
0.104
9
1 28.466
9
•1.474
39
6.389
9
0.025
39
0.106
10
1 38.296
10
1.638
40
6.553
10
0.027
40
0.109
11
1 48.125
11
1.802
41
6.717
11
0.030
41
0.112
12
1 57.955
12
1.966
42
6.881
12
0.033
42
0.115
13
2 07.784
13
2.130
43
7.044
13
0.036
43
0.118
14
2 17.614
14
2. 294
44
7.208
14
0.038
44
0.120
15
2 27.443
15
2.457
45
7.372
15
0.041
45
0.123
16
2 37. 273 ,
16
2.621
46
7.536
16
0.044
46
0.126
17
2 47.103
17
2.785
47
7.700
17
0.047
47
0.128
18
2 56.932
18
2.949
48
7.864
18
0.049
48
0.131
19
3 06. 762
19
3.113
49
8.027
19
0.052
49
0.134
20
3 16.591
20 '
3.277
50
8.191
20
0.055
50
0.137
21
3 26.421
21
3.440
51
8.355
21
0.057
51
0.140
22
3 36. 250
22
3.604
52
8.519
22
0.060
52
0.142
23
3 46.080
23
3. 768
53
8.083
23
0.063
53
0.145
24
3 55.909
24
3.932
54
8.847
24
0.066
54
0.148
25
4.096
55
9.010
25
0.068
55
0.150
26
4.259
56
9.174
26
0.071
50
0.153
27
4.423
57
9.338
27
0.074
57
0.156
28
4.587
58
9.502
28
0.076
58
0.159
29
4.751
59
9.666
29
0.079
59
0.161
30
4.915
60
9.830
30
0.082
60
0.164
228.
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXII. — For converting intervals of mean solar time into corresponding intervals of sidereal time.
[Extracted from Lee's Tables.]
Hours.
Minutes.
Seconds.
h.
m
J
m.
c.
m.
s.
».
s.
,
s.
1
0
09. 850
1
0.164
31
5'.092
i
0.' 003
3i
0.085
0
19. 713
0.329
32
5.257
2
0.005
32
0.0S8
3
0
29. 669
3
0.493
33
5.421
3
0.008
33
0.090
4
0
39.426
4
0.657
34
5.585
4
0.011
34
0.093
g
0
49.282
5
0.821
35
5.750
5
0.014
35
0.096
6
0
59. 139
6
0.986
36
5.914
6
0.016
36
0.098
7
08.995
7
1.150
37
6.078
7
0.019
37
0.101
8
18. 852
8
1.314
38
6.242
8
0.022
38
0. 104
0
28. 708
9
1.478
39
6.407
9.
0.025
39
0.106
10
38. 565
10
1.643
40
6.571
10
0.027
40
0.109
11
48.421
11
1.807
41
6.735
11
0.030
41
0.112
12
58.278
12
1.971
42
6.900
12
0.033
.42
0. 116
13
US. 134
13
■ 2. 136
43
7.064
13
0.036
43
0.118
14
2
17.991
14
2.300
44
7.228
14
0.038
44
0.120
16
2
27. 847
15
2.464
45
7.392
15
0.041
45
0.123
16
2
37. 704
16
2.628
46
7.557
16
0. 044
46
0.126
17
2
47. 560
17
2,793
47
7.721
17
0.047
47
0.129
18
2
57. 416
18
2.957
48
7.885
18
0.049
48
0.131
19
3
07. 273
19
3.121
49
8.050
19
0.052
49
0.134
20
3
17. 129
20
3.285
50
8.214
20
0.055
50
0. 137
21
3
26. 986
21
3.450
51
8.378
21
0.057
51
0.140
22
3
36. 842
22
3.614
52
8.542
22
0.060
52
0.142
23
3
46. 699
23
3.778
53
8.707
23
0.063
53
0.145
24
3
56.555
24
3.943
54
8.871
24
0.066
54
0.148
25
4.107
55
9. 035
25
0.068
5S
0.151
26
4.271
56
9.199
26
0.071
56
0.153
27
4.436
57
9.364
27
0.074
57
0.156
28
4.600
58
9.528
28
0.077
58
0.159
29
4.764
59
9.692
29
0.079
59
0.161
30
4.928
60
9.856
30
0.082
60
0.164
The quantities taken from this table mnat be added to a i
real time.
Qterval to obtain the correeponding interval in side-
CONYEESION OF AEG INTO TIME.
•229
Table XXXIII. — To comet-t parts of the equator in arc into sidereal time, or to convert terrestrial longitude
in arc into time.
[Extracted from Lee's Tables.] *
Degrees.
De
grees
De
grees
De
grees.
Degrees.
Degrees.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
1
2
3
4
5
ft. m.
0 4
0 8
0 12
0 16
0 20
61
62
63
64
65
h.
4
4
4
4
4
m.
4
8
12
16
20
121
122
123
124
125
ft.
8
8
8
8
8
4
8
12
16
20
181
182
183
181
185
ft. m.
12 4
12 8
12 12
12 16
12 20
241
242
243
244
245
ft. -m.
16 4
16 8
16 12
16 16
16 20
301
302
303
304
305
ft. m.
20 4
20 8
20 12
20 16
20 20
6
7
8
9
10
0 24
0 28
0 32
0 36
0 40
66
67
68
69
70
4
4
4
4
4
24
28
32
36
40
126
127
128
129
130
8
8
8
8
8
24
28
32
36
40
186
187
188
189
190
12 24
12 28
12 32
12 36
12 40
246
247
248
249
250
16 24
16 28
16 32
16 36
16 40
306
307
308
309
310
20 24
20 28
20 32
20 36
20 40
11
12
13
14
15
0 44
0 48
0 52
0 56
1 0
71
72
73
74
75
4
4
4
4
5
44
48
.52
56
0
131
132
133
134
135
8
8
8
8
9
44
48
52
66
0
191
192
193
194
195
12 44
12 48
12 52
12 66
13 0
261
252
253
254
255
16 44
16 48
16 52
16 56
17 0
311
312
313
314
315
20 44
20 48
20 62
20 56
21 0
16
17
. 18
19
20
1 4
1 8
1 12
1 16
1 20
76
77
78
79
80
. 5
5
5
5
5
4
8
12
16
20
136
137
138
139
140
9
9
9
9
9
4
8
12
16
20
196
197
198
199
200
13 4
13 8
13 12
13 16
13 20
256
257
258
259
260
17 4
17 8
17 12
17 16
17 20
316
317
318
319
320
21 4
21 8
21 12
21 16
21 20
21
22
23
24
25
1 24
1 28
1 32
1 36
1 40
81
82
83
84
85
5
5
5
5
5
24
28
32
36
40
141
142
143
144
145
9
9
9
9
9
24
28
32
36
40
201
202
203
204
205
13 21
13 28
13 32
13 36
13 40
261
262
263
264
265
17 24
17 28
17 32
17 36
17 40
321
323
323
324
325
21 24
21 28
21 32
21 36
21 40
26
27
28
29
30
1 4-1
1 48
1 52
1 56
2 0
86
87
88
89
90
5
5
5
5
6
44
48
52
56
0
146
147
148
149
150
9
9
9
9
10
44
48
52
56
0
206
207
208
209
210
13 44
13 48
13 52
13 56
14 0
266
267
268
269
270
17 44
17 48 ■
17 ,52
17 56
18 0
326
327
328
329
330
21 44
21 48
21 52
21 66
22 0
31
32
33
34
35
2 4
2 8
2 12
2 16
2 20
91
92
93
94
95
6
6
6
6
6
4
8
12
16
20
151
152
153
154
155
10
10
10
10
10
4
8
12
16
20
211
212
213
214
216
14 4
14 8
14 12
14 16
14 20
271
272
273
274
275
18 4
18 8
18 12
18 16
18 20
331
332
333
334
335
22 4
22 8
22 12
22 16
22 20
36
37
38
39
40
2 24
2 28
2 32
2 36
2 40
96
97
98
99
loo "
6
6
6
6
6
24
28
32
36
40
156
157
168
159
160
10
10
10
10
10
24
28
32
36
40
216
217
218
219
220
14 24
14 28
14 32
14 36
14 40
276
277
278
279
280
18 24
18 28
18 32
18 36
18 40
336
337
338
339
340
22 24
22 28
22 32
22 36
22 40
41
42
43
44
45
2 44
2 48
2 52
2 66
3 0
lOl
l02
l03
l04
l05
6
6
6
6
7
44
48
52
56
0
161
162
163
164
165
10
10
10
10
11
44
48
52
56
0
221
222
223
224
225
14 44
14 48
14 52
14 56
15 0
281
282
283
284
285
18 44
18 48
18 62
18 56
19 0
341
342
343
344
345
22 44
22 48
22 52
22 56
23 0
46
47
48
49
50
3 4
3 8
3 12
3 16
3 20
l06
107
108 .
109
no
7
7
7
7
7
4
8
12
■6
20
166
167
168
169
170
11
11
11
11
11
4
8
12
16
20
226
227
228
229
230
15 4
15 8
15 12
15 16
15 20
286
287
288
•289
290
19 4
19 8
19 12
19 16
19 20-
346
347
348
349
350
23 4
23 8
23 12
23 16
23 20
51
52
53
54
55
3 24
3 28
3 32
3 36
3 40
111
112
113
114
115
7
7
7
7
7
24
28
32
36
40
171
172
173
174
175
11
11
11
11
11
24
28
32
36
40
231
232
233
234
235
15 24
15 28
15 32
15 36
15 40
291
292
293
294
295
19 24
19 28
19 32
19 36
19 40
351
352
363
354
355
23 24
23 28
23 32
23 36
23 40
56
57
58
59
60
3 44
3 48
3 52
3 56
4 0
116
117
118
119
120
7
7
7
8
44
48
52
56
0
176
177
178
179
180
11
11
11
11
12
44
48
52
56
0
236
237
238
239
240
15 44
15 48
15 62
15 56
16 0
296
297
398
299
300
19 44
19 48
19 62
19 56
20 0
356
367
358
369
360
23 44
33 48
28 52
23 66
24 0
230
A MANUAL OF TOPOGEAPHIC METHODS.
Taule XXXIII. — To coni'ert parts of the equator in arc into sidereal time, or to eonvert teirestrial longitude
in arc into time — Continued.
[Extracted from Lee's Tables.]
1 Minutes.
Minutes.
Minutes.
Seconds.
Seconds.
Seconds.
Arc*
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
m s
,
m s.
m. s.
„
J
J
1 1
0 4
21
1 24
41
2 44
1
0.067
21
1.400
41
2.733
( 2
0 8
22
1 28
42
2 48
2
0.133
22
1.467
42
2.800
3
0 12
23
1 32
43
2 52
3
0.200
23
1.533
43
2.867
*
0 16
24
1 86
44
2 56
4
0.267
24
1.600
44
2.933
5
0 20
25
1 40
45
3 0
5
0.333
25
1.667
45
3.000
6
0 24
26
1 44
, 46 3 4
6
0.400
26
1.733
46
3.067
7
0 28
27
1 48
47 1 3 8
• 7
0.467
27
1.800
47
3.133
8
0 32
28
1 52
48 ; B 12
8
n.533
28
1.867
48
3.200
9 1 0 36
29
1 56
49 1 3 16
9
0.600
29
1.933
49
3.267
10 I 0 40
30
2 0
50 3 20
10
0.667
30
2.000
50
3.333
11
0 44
31
2 4
51 3 24
11
0.733
31
2.067
51
3.400
12
0- 48
32
2 8
52 3 28
12
0.800
32
2.133
52
3.467
13
0 52
33
2 12
53 3 32
13
0.867
33
2.200
53
3. 533
14
0 56
34
2 16
54 3 36
14
0.933
34
2.267
54
3.600 1
15
1 0
35
2 20
55 3 40
15
1.000
35
2.333
55
3.667 <
16 , 1 4
36
2 24
56 3 44
16
1.067
36
2.400
56
3. 733
17 1 1 8
37 2 28
57 3 48
17
1.133
37
2.467
57
3. 800
18 1 12
38 2 32
58 3 52 '
18
1.200
38
2.633
58
3.867
19 1 16
39 2 36
59 , 3 56
19
1.267
39
2.600
59
3.933 1
20 1 20
40 2 40
60 1 4 0
20
1.333
40
2.667
60
4.000 1
1
T.\Bi.E XXXIV. — To convert sidereal time into parts of the equator in arc, or to convert time into terrestrial
longitude in arc.
[Extracted from Lee'.^ Tables.]
Hours.
Minutes.
Seconds.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
h.
0
m
o -
m
o ,
s.
s.
, //
1
15
1
0 15
31
7 45
1
0 15
31
7 45
2
30
2
b 30
32
8 00
2
0 30
32
8 00
3
45
3
0 45
33
8 15
3
0 45
33
8 15
4
60
4
1 00
34
8 30
4
1 00
34
8 30
5
75
5
1 15
35
8 45
5
1 15
35
8 45
6
90
6
1 30
36
9 00
6
1 30
36
9 00
7
105
7
1 45
37
9 15
7
1 45
37
9 15
8
120
8
2 00
38
9 30
8
2 00
38 "
9 30
9
135
9
2 15
39
9 45
9
2 15
39
9 45
10
150
10
2 30
40
10 00
10
2 30
40
10 00
11
165
11
2 46
41
10 15
11
2 45
41
10 15
12
180
12
3 00
42
10 30
12
3 00
42
10 30
13
195
13
3 15
43
10 45
13
3 15
43
10 45
14
210
14
3 30
44
11 00
14
3 30
44
11 00
15
225
.15
3 45
45
11 15
15
3 45
45
11 15
16
240
16
4 00
46
11 30
16
4 00
46
11 30
17
255
17
4 15
47
11 45
17
4 15
47
11 45
18
270
18
4 30
48
12 00
18
4 30
48
12 00
19
285
19
4 45
49
12 15
19
4 45
49
12 15
1 20
300
20
5 00
50
12 30
20
5 00
50
12 30
21
315
21
5 15
51
12.45
21
5 15
51
12 45
22
330
22
5 30
52
13 00
22
5 30
52
13 00
23
345
23
5 45
53
13 15
23
5 45
63
13 15
24
360
24
6 00
54-
13 30
24
6 00
54
13 30
25
6 15
55
13 45
25
6 15
55
13 45
26
6 30
56
14 00
26
6 30
56
14 00
27
6 45
57
14 15
27
6 45
57
14 15
28
7 00
58
14 30
28
7 00
58
14 30
29
7 15
59
14 45
29
7 15
59
14 45
30
7 30
60
15 00,
30
7 30
60
15 00
CONVERSION OF TIME INTO AEG. 231
Table XXXIV.— To covrert sidereal lime into j)«)'(s of the equator in arc, eic,— Coutinued.
[Extracted from Lee's Tables.]
Tenths o:
seconds
Thou-
sandths
of sec-
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
Time.
Arc.
onds of
time.
s.
0.21
3.15
s.
0.41
6.15
s.
0.61
9.15
0.81
12. 15
0.061
0.015
0.30
0.22
3.30
0.42
6,30
0.62
9.30
0.82
12.30
0.002
0.03
0.45
0.23
3.45
0.43
6.45
0.63
9.45
0.83
12.45
0.60
0.24
3.60
0.44
6.60
0.64
9.60
0.84
0.004
0.05
0.75
0.25
3.75
0.45
6.75
0.65
9.75
0.85
12.75
0.005
0.075
0.90
0.26
3,90
0.40
6.90
0.66
9.90
0.86
12.90
0.006
0.090
0.07
1.05
0.27
4.U5
0.47
7.05
0.67
10.05
0.87
13.05
0.007
0.105
0.08
1.20
0.28
4.20
0.48
7.20
0.68
10.20
0.88
13.20
0.008
0,120
1.35
0.29
4.35
0.49
7.35
0.69
10.35
0.89
0.009
0.10
1.50
0.30
4.50
0.50
7.50
0.70
10.50
0.90
13.50
0,010
0,150
0.11
1.65
0.31
4.65
0.51
7.65
0.71
10.65
0.91
13.65
1.80
0.32
4.80
0.52
7.80
0.72
10. 80
0.92
13.80
0.13
1.95
0.33
4.95
0.53
7.95
0.73
10.95
0.93
13.95
2.10
0.34
5.10
0.54
8.10
0.74
11.10
0.94
0.15
2.25
0.35
5.25
0.55
8.25
0.75
11.25
0.95
14.25
0.16
2.40
0.36
5.40
0.56
8.40
0.76*
11:40
0.96
14.40
0.17
2.55
0.37
5.55
0.57
8.55
0.77
11.65
0.97
14.55
0.18
2.70
0.38
5.70
0.58
8.70
0.78
11.70
0.98
2.85
0.39
5.85
0.59
8.85
0.70
11.85
0.99
0.20
3.00
0.40
6.00
0.60
9.00
0.80
12.00
1.00
15.00
Table XXXV. — Containiiuj logarithms of nnmliers from 1 to 11,000.
[Extracted froin Gauss' Logarithmic and Trigonometric Tables.]
N.
Log.
N.
Log.
N.
Log.
N.
Log.
N.
Log.
0
_
20
1. 30 103
40
L60 206
60
1. 77 815
80
1.90 309
1
0.00 000
21
1. 32 222
41
1.61 278
61
1. 78 533
81
1. 90 849
2
0.30 103
22
1. 34 242
42
1. 62 325
62
1. 79 239
82
1. 91 381
3
0. 47 712
23
1. 36 173
43
1.63 347
63
1. 79 934
83
1. 91 908
4
0. 60 206
24
1. 38 021
44
1. 64 345
64
1.80 618
84
1.92 428
5
0. 69 897
25
1. 39 79'J
45
L65 321
65
1. 81 291
85
1. 92 942
6
0. 77 815
26
L41 497
46
1. 66 276
66
1.81 954
86
1. 93 450
7
0.84 510
27
1.43 130
47
1.67 210
67
1. 82- 607
87
8
0.90 309
28
1.44 716
48
1. 68 124
68
1. 83 251
88
1.94 448
9
0. 95 424
29
1.46 240
49
1.69 020
69
1.83 885
89
1. 94 939
10
1. 00 000
30
\. 47 712
50
1, 69 897
70
1. 84 510
90
1. 95 424
11
1.04 139
31
1.49 136
51
1. 70 757
71
1.85 126
91
1. 95 004
12
1.07 918
32
1.50 515
52
1.71 600
72
1.85 733
. 92
1.96 379
13
1.11 394
33
1, 51 851
53
1. 72 428
73
L86 332
93
1. 96 848
14
1. 14 613
34
1.53 148
54
1. 73 239
74
1.86 923
15
L17 609
35
1. 54 407
55
1. 74 036
75
L87 506
95
1. 97 772
16
1.20 412
36
1. 55 630
56
1.74 819
76
1.88 08 L
96
1. 98 227
17
1. 23 045
37
1. 56 820
57
1.75 587
77
1.88 649
18
1. 25 527
33
1. 57 978
58
1. 76 343
78
1. 89 209
98
1.99 123
1. 27 875
39
1.59 106
59
1. 77 085
79
1. 89 763
99
1. 99 564
20
1. 30 103
40
1. 60 200
60
1. 77 815
80
1. 90 309
100
2. 00 000
232
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing Jogariihms of «itw6e7's from 1 to 11,000-
[Extracted trom GauSs' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
0
00 000
30 103
47 712
60 206
69 897
77 815
84 510
90 309
95 424
1
00 000
04 139
07 918
11 394
14 613
17 609
20 412
23 045
25 527
27 875
2
30 103
32 222
34 242
36 173
38 021
39 794
41 497
43 136
44 716
46 240
3
47 712
49 136
50 515
51 851
53 148
54 407
55 630
56 820
57 978
59 106
4
60 206
61 278
62 325
63 347
64 345
65 321
60 276
67 210
68 124
69 020
5
69 897
70 757
71 600
72 428
73 239
74 036
74 819
75 587
70 343
77 085
6
77 815
78 533
79 239
79 934
80 018
81 291
81 954
82 607
83 251
83 885
84 510
85 126
85 733
86 332
.86 923
87 506
88 081
88 649
89 209
89 763
8
90 309
90 849
91 381
91 908
92 428
92 942
93 430
93 952
94 448
94 939
9
95 424
95 904
96 379
96 848
97 313
97 772
98 227
98 677
99 123
99 564
10
00 OOO
00 432
00 860
01 284
01 703
02 119
02 531
02 938
03 342
03 743
11
04 139
04 532
04 922
05 308
05 690
00 070
06 446
06 819
07 188
07 555
12
07 918
08 279
08 636
08 991
09 342
09 691
10 037
10 380
10 721
11 039
13
11 394
11 727
12 057
12 385
12 710
13 033
13 354
13 672
13 983
14 301
14
14 613
14 925
15 229
15 534
15 836
10 137
16 435
16 732
17 020
17 319
15
17 609
17 898
18 184
18 469
18 752
19 033
19 312
19 590
19 866
20 140
16
20 412
20 683
20 952
21 219
21 484
21 748
22 Oil
22 272
22 631
22 789
17
23 045
23 300
23 553
23 805
24 055
24 304
24 551
24 797
25 042
25 285
18
25 527
25 768
26 007
26 245
26 482
26 717
26 951
27 184
27 416
27 646
19
27 875
28 103
28 330
28 55(1
28 780
29 003
29 226
29 447
29 667
29 885
20
30 103
30 320
30 535
30 750
30 963
31 175
31 387
31 597
31 806
32 015
21 ■
32 222
32 428
32 634
32. 838
33 041
33 244
33 445
33 646
33 846
34 044
22
34 242
34 439
34 035
34 830
35 025
35 218
35 411
35 603
35 793
35 984
23
36 173
36 361
30 549
36 736
36 922
37 107
37 291
37 175
37 058
37 840
24
38 021
38 202
38 382
38 561
38 739
38 917
39 094
39 270
39 446
39 620
25
39 794
39 907
40 140
40 312
40 483
40 654
40 824
40 993
41 162
41 330
26
41 497
41 064
41 830
41 996
42 160
42 325
42 488
42 651
42 813
42 976
27
43 136
43 297
43 457
43 616
43 775
43 933
44 091
44 248
44 404
44 660
28
• 44 716
44 871
45 025
45 179
45 332
45 484
45 637
45 788
45 939
46 090
29
46 240
46 389
40 538
46 687
46 835
46 982
47 129
47 276
47 422
47 667
30
47 712
47 857
48 001
48 144
48 287
48 430
48 572
48 714
48 855
48 996
31
49 136
49 276
49 415
49 554
49 693
49 831
49 969
50 106
50 243
50 379
32
50 515
50 651
50 786
50 920
51 055
51 188
51 322
51 455
51 587
51 720
33
51 851
51 983
52 114
52 244
52 375
52 504
52 634
52 763
52 892
53 020
34
53 148
53 275
53 403
53 529
53 656
53 782
53 908
54 033
54 158
54 283
35
54 407
54 531
54 654
54 777
54 900
55 023
55 145
55 267
53 388
55 509
36
55 630
55 751
55 871
55 991
56 110
56 229
56 348
56 467
60 585
56 703
87
56 820
56 937
57 054
57 171
57 287
67 403
57 519
57 634
57 749
57 864
38
57 978
58 092
58 206
58 320
58 433
58 546
58 059
58 771
58 883
58 995
39
59 106
59 218
59 329
59 439
59 550
59 660
59 770
59 879
59 988
60 097
40
60 206
60 314
60 423
60 531
60 638
60 746
60 853
60 959
61 066
61 172
41
61 278
61 384
61 490
61 595
61 700
61 805
61 909
62 014
62 118
62 221
42
62 325
62 428
62 531
62 634
62 737
62 839
62 941
63 043
63 144
63 246
43
63 347
63 448
63 548
63 649
63 749
63 849
63 949
64 048
64 147
64 246.
44
64 345
64 444
64 542
64 640
64 738
64 836
64 933
65 031
65 128
65 225
45
65 321
65 418
65 514
65 610
65 706
65 801
65 896
65 992
60 087
66 181
46
66 276
66 370
66 464
66 558
66 652
66 745
66 839
66 932
67 025
67 117
47
67 210
67 302
67 394
67 486
67 578
67 069
67 701
67 852
67 943
68 034
48
68 124
68 215
68 305
68 395
68 485
68 574
68 664
68 753
68 842
68 931
49
69 020
69 108
69 197
69 285
69 373
09 461
69 548
69 636
69 723
69 810
50
69 897
69 SJ84
70 070
70 157
70 243
70 329
70 415
70 501
70 586
70 672
N".
L. 0
1
2
3
4
5,
6
7
8
9
LOGARITHMS OF NUMBEES.
233
Table XXXV. — Containing_ logarithms of numhers from 1 to 11,000 — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0
• 1
2
3
4
5
6
7
8
9
60
69 897
69 984
70 070
70 157
70 243
70 329
70 415
70 501
70 586
70 672
51
70 757
70 842
70 927
71 012
71 096
71 181
71 265
71 349
71 433
71 517
52
71 600
71 684
71 767
71 850
71 933
72 016
72 099
72 181
72 263
72 346
53
72 428
72 509
72 591
72 673
72 754
72 835
72 916
72 997
73 078
73 159
54
73 239
73 320
73 400
73 480
73 560
73 640
73 719
73 799
73 878
73 957
55
74 036
74 115
74 194
74 273
74 351
74 429
74 607
74 586
74 663
74 741
56
74 819
74 896
74 974
75 051
75 128
75 205
75 282
75 358
75 436
75 511
67
. 75 587
75 004
75 740
75 815
75 891
75 967
76 042
76 118
76 193
76 268
58
76 343
76 418
76 492
76 567
76 641
76 716
76 790
76 864
76 938
77 012
59
77 085
77 159
77 232
77 305
77 379
77 452
77 525
77 597
77 670
77 743
60
77 815
77 887
77 960
78 032
78 104
78 176
78 247
78 319
78 390
78 462
61
78 533
78 604
78 675
78 746
78 817
78 888
78 958
79 029
79 099
79 169
62
79 239
79 309
79 379
79 449
79 518
79 588
79 667
79 727
79 796
79 865
63
79 934
80 003
80 072
80 140
80 209
80 277
80 346
80 414
80 482
80 650
64
80 618
80 686
80 754
80 82X
80 889
80 956
81 023
81 090
81 158
81 224
65
81 291
81 358
81 425
81 491
81 558
81 624
81 690
81 757
81 823
81 889
66
81 954
82 020
82 086
82 151
82 217
82 282
82 347
82 413
82 478
82 543
67
82 607
82 672
82 737
82 802
82 866
82 930
82 995
83 059
83 123
83 187
68
83 251
83 315
83 378
83 442
83 506
83 569
83 632
83 696
83 759
83 833
69
83 885
83 948
84 Oil
84 073
84 136
84 198
84 261
84 323
84 386
84 448
70
84 510
84 572
84 634
84 696
84 757
84 819
84 880
84 942
85 003
85 065
71
85 126
85 187
85 248
85 309
85 370
85 431
85 491
85 552
85 612
85 673
72
85 733
85 794
85 854
85 914
85 974
86 034
86 094
86 153
86 213
86 273
73
86 332
86 392
86 451
86 510
86 570
86 629
86 688
86 747
86 806
86 864
74
86 923
86 982
87 040
87 099
87 157
87 216
87 274
87 332
87 390
87 448
75
87 506
87 564
87 622
87 679
87 737
87 795
87 852
87 910
87 967
83 024
76
8< 081
88 138
88 195
88 252
88 309
88 366
88 423
88 480
88 636
88 593
77
88 649
88 705
88 762
88 818
88 874
88 930
88 986
89 042
89 098
89 154
78
89 209
89 205
89 321
89 376
89 432
89 487
89 542
89 597
89 653
89 708
79
89 763
89 818
89 873
89 927
89 982
90 037
90 091
90 146
90 200
90 256
80
90 309
90 363
90 417
90 472
90 526
90 580
90 634
90 687
90 741
90 795
81
90 849
90 902
90 956
91 009
91 062
91 116
91 169
91 222
91 276
91 328
83
91 381
91 434
91 487
91 540
91 593
91 645
91 698
91 751
91 803
91 855
S3
91 908
91 960
92 012
92 065
92 117
92 169
92 221
92 273
92 324
93 376
84
92 428
92 480
92 531
92 583
92 634
92 686
92 737
92 788
92 840
92 891
85
92 942
92 993
93 044
93 095
93 146
93 197
93 247
93 298
93 349
93 399
86
93 450
93 500
93 551
93 601
93 651
93 702
93 752
93 802
93 852
93 902
87
93 952
94 002
94 052
94 101
94 151
94 201
94 250
94 300
94 349
94 399
88
94 448
94 498
94 547
94 596
94 645
94 694
94 743
94 792
94 841
94 890
89
94 939
94 988
95 036
95 085
95 134
95 182
95 231
95 279
95 328
95 376
90
95 424
95 472
95 521
95 569
95 617
95 665
95 713
95 761
96 809
95 856
91
95 904
95 952
95 999
96 047
96 095
96 142
96 190
96 237
■ 96 284
96 333
92
96 379
96 426
96 473
96 520
96 567
96 614
96 661
96 708
96 755
96 802
93
96 848
96 895
96 942
96 088
97 035
97 081
97 128
97 174
97 230
97 267
94
97 313
97 359
97 405
97 451
97 497
97 643
97 589
97 035
97 681
97 727
95
97 772
97 818
97 864
97 909
97 955
98 000
98 046
98 091
98 137
98 182
96
98 227
98 272
98 318
98 363
98 408
98 453
98 498
98 543
98 588
98 632
97
98 677
98 722
98 767
98 811
98 856
98 900
98 945
98 989
99 034
99 078
98
99 123
99 167
99 211
99 255
99 300
99 344
99 388
99 432
99 476
99 520
99
99 564
99 607
99 651
99 695
99 739
99 782
99 826
99 870
99 913
99 957
100
00 000
00 043
00 087
00 130
00 173
00 217
00 260
00 303
00 346
00 389
N.
L. 0
1
2
3
4
5
6
7
8
9
234
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXY. — Containing Jogariihms of numbers from 1 to 11,000 — Continued.
[Extracted from Ciauss' Logaritluuic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P
P.
100
00 000
043
087
130
173
217
260
303
346
389
101
432
475
518
561
604
647
689
732
775
817
44
43
42
102
860
903
945
988
,030
,072
,115
,157
,199
,242
1
4,4
4,3
4,2
1.13
01 284
326
368
410
452
494
536
578
620
662
2
8,8
8,6
8,4
104
703
745
787
828
870
912
953
995
,036
.078
3
13,2
12,9
12'6
105
02 119
100
202
243
284
325
366
407
449
490
4
17,6
17,2
16,8
106
531
572
612
653
694
735
776
816
857
808
5
22,0
21,5
21,0
107
938
979
,019
,060
,100
,141
.181
,222
,262
,302
6
26,4
25,8
25,2
108
03 342
383
423
463
503
543
583
623
603
703
7
30,8
30,1
29,4
109
743
782
822
802
902
941
981
,021
,060
,100
8
35,2
34,4
33,6
110
04 139
179
218
258
297
336
376
415
454
493
9
39,6
38,7
37,8
111
532
571
610
650
689
727
766
805
844
883
41
40
39
112
922
961
999
,038
,077
,115
,154
,192
,231
,269
1
4,1
4,0
3,9
113
05 308
346
385
423
461
500
538
576
614
■652
2
8,2
8,0
7,8
114
690
729
767
805
843
881
918
956
994
,032
3
12,3
12,0
11,7
115
06 070
108
145
183
221
258
296
333
371
'408
4
16,4
16,0
15,6
116
446
«3
521
558
695
633
670
707
744
781
5
20,5
20,0
19,5
117
819
856
893
930
967
,004
,041
,078
,115
,151
6
24,6
24,0
23,4
118
07 ISS
225
262
298
335
372
408
445
482
518
7
28,7
28,0
27,3
119
555
591
628
664
700
737
773
809
846
882
8
32,8
32,0
31,2
120
918
954
990
,027
,063
,099
,135
,171
,207
,243
9
36,9
36,0
35,1
121
08 279
314
350
386
422
458
493
529
565
600
88
37
36
122
636
672
707
743
778
814
849
884
920
955
1
3,8
3,7
3,6
123
991
,026
,061
,096
,132
,167
,202
,237
,272
,307
2
7,6
TA
7,2
124
09 342
377
412
447
482
517
552
587
621
656
3
11,4
11,1
10,8
125
691
728
760
795
830
864
899
934
968
,003
4
15,2
14,8
14,4
120
10 037
072
106
140
175
209
243
278
312
346
5
19,0
18,5
18,0
127
380
415
449
483
517
551
585
619
653
687
6
22,8
22,2
21,6
128
721
755
789
823
857
890
924
958
992
,025
7
26,6
25,9
25,2
129
11 059
093
126
160
193
227
261
294
327
361
8
30,4
29,6
28,8
130
394
428
461
494
528
561
594
628
661
694
9
34,2
33,3
32,4
131
727
760
793
826
860
893
926
959
992
,024
35
34
33
132
12 057
090
123
156
189
222
254
287
320
352
1
3,5
3,4
3,3
133
385
418
450
483
516
548
581
613
646
678
2
7,0
6,8
6,6
134
710
743
775
808
840
872
905
937
969
,001
3
10,5
10,2
9,9
135
13 033
066
■ 098
130
162
194
226
258
290
322"
4
14,0
13,6
13,2
136
354
386
418
450
. 481
513
545
577
609
640
5
17,5
17,0
16,5
137
672
704
735
707
799
830
862
893
925
956
6
21,0
20,4
19,8
138
988
,019
,051
,082
,114
,145
,176
,208
,239
,270
7
24,5
23,8
23,1
139
14 301
333
364
395
426
457
489
520
551
582
8
28,0
27,2
26,4
140
613
644
675
706
737
768
799
829
860
891
9
31,5
30,6
29,7
141
922
953
983
,014
,045
,076
,106
,137
,168
,198
33
31
30
142
15 229
259
290
320
351
381
412
442
473
503
1
3,2
3,1
3,0
143
534
564
594
625
655
685
715
746
776
806
2
6,4
6,2
6,0
144
836
866
897
927
957
987
,017
,047
,077
,107
3
9,6
9,3
9'0
145
16 137
167
197
227
256
286
316
346
376
406
4
12,8
12,4
12,0
146
435
465
. 495
524
554
584
613
643
673
702
5
16,0
15,5
15,0
147
732
761
791
820
850
879
909
938
967
997
6
19,2
18,6
18,0
148
17 026
056
085
114
143
173
202
231
260
289
7
22,4
21,7
21,0
149
319
348
377
406
435
464
493
522
551
580
8
25,6
24,8
24,0
150
609
638
667
696
725
754
782
811
840
869
9
28,8
27,9
27,0
N.
L. 0
1
2
3
4
5
6
7
8
9
P
P.
logaeithms of numbees.
235
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Continued.
[Extracted from Graass' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
ISO
17 609
638
667
696
725
754
782
811
840
869
151
898
926
955
984
,013
,041
,070
,099
,127
.156
29
28
152
18 184
213
241
270
298
327
355
384
412
441
1
2,9
2,8
153
469
498
526
554
583
611
639
667
696
724
2
5,8
5,6
154
752
780
808
837
865
893
921
949
977
,005
3
8,7
8,4
155
19 033
061
089
117
145
173
201
229
257
285
4
11,6
11,2
156
312
340
368
396
424
451
479
507
535
562
5
14,5
14,0
157
590
618
645
673
700
728
756
783
811
838
6
17,4
16,8
158
866
893
921
948
976
,003
,030
,058
,085
,112
7
20,3
19,6
159
20 140
167
194
232
249
276
303
330
368
385
8
23,2
22,4
160
412
439
466
493
520
548
575
602
629
656
9
26,1
25,2
161
683
710
737
763
790
817
844
871
898
925
27
2e
162
952
978-
..005
,032
,059
,085
,112
.139
,165
,192
1
2,7
2,6
163
21 219
245
272
299
325
352
378
405
431
458
2
5,4
6,2
164
4S4
511
537
564
590
617
643
669
696
722
3
8,1
7,8
165
748
775
801
827
854
880
906
932
958
985
4
10,8
10,4
166
22 on
037
063
089
115
141
167
194
220
246
5
13,5
13,0
167
272
298
324
350
376
401
427
453
479
505
6
16,2
15,6
168
531
557
583
608
634
660
686
712
737
763
7
18,9
18,2
169
789
814
840
866
891
917
943
968
994
,019
8
21,6
20,8
170
23 045
070
096
121
147
172
198
223
249
274
9
24,3
23,4
171
300
325
350
376
401
426
452
477
502
528
25 1
172
553
578
603
629
654
679
704
729
754
779
1
2,5
173
805
830
855
880
905
930
955
980
,005
,030
2
5,0
174
24 055
080
105
130
155
180
204
229
254
279
3
7,5
175
304
329
353
378
403
428
452
477
502
527
4
10,0
176
551
576
601
625
650
674
699
724
748
773
5
12,5
177
797
822
846
871
895
920
944
969
993
,018
6
15,0
178
25 042
066
091
115
139
164
188
212
237
261
7
17,5
179
285
310
331
358
382
406
431
455
479
503
8
20,0
ISO
527
551
575
600
624
648
672
696
720
744
9
22,5
181
768
792
816
840
864
888
912
935
959
983
24
2S
182
26 007
031
055
079
102
120
150
174
198
221
1
2,4
2,3
183
245
269
293
316
340
364
387
411
435
458
2
4,8
4,6
184
482
505
529
553
576
600
623
647
670
694
3
7,2
6,9
185
717
741
764
788
811
834
858
881
905
928
4
9,6
9,2
186
951
975
998
,021
,045
,068
,091
,114
,138
,161
5
12,0
11,6
187
27 184
207
231
254
277
300
323
346
370
393
6
14,4
13,8
188
416
439
462
485
508
531
554
577
600
623
7
16,8
16,1
189
646
669
692
715
738
761
784
807
830
852
8
19,2
]8,4
190
875
898
921
944
967
989
,012
,035
*058
,081
9
21,6
20,7
191
28 103
126
149
171
194
217
240
262
285
307
22
21
192
330
353
375
398
421
443
466
488
511
533
1
2,2
2,1
193
556
578
601
623
646
668
691
713
735
758
2
4,4
4,2
194
780
803
825
847
870
892
914
937
959
981
3
6,6
6,3
195
29 003
026
048
070
092
115
137
159
181
203
4
8,8
8,4
196
226
248
270
.292
314
336
358
380
403
425
5
11,0
10,5
197
447
469
491
513
535
557
579
601
623
645
6
13,2
12,6
198
667
688
710
732
754.
776
798
820
842
863
7
15,4
14,7
199
885
907
929
951
973
994
,016
,038
,060
*081
8
17,6
16,S
200
30 103
125
146
168
190
211
233
255
276
298
9
.19,8
18,9
N.
L.O
1
2
3
*
5
6
7
8
^
P.P.
236
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logariihms of numbers from 1 to 11,000-
[Estractetl from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0.
1
2
3
4
5
6
7
8
9
P.P.
200
30 103
125
146
168
190
211
233
255
276
298
201
320
341
363
384
406
428
449
471
492
514
22
21
202
535
557
578
600
621
643
664
685
707
728
1
2,2
2,1
203
750
771
792
814
835
856
878
899
920
942
2
4,4
4,2
204
963
984
,006
,027
,048
,069
,091
,112
,133
,154
3
6,6
6,3
205
31 175
197
218
239
260
281
302
323
345
366
4
8,8
8,4
206
387
408
429
450
471
492
513
534
555
576
5
11,0
10,5
207
597
618
639
660
681
703
723
744
765
785
6
13,2
12,6
208
806
827
848
869
890
911
931
952
973
994
7
15,4
14,7
209
32 015
035
. 056
077
098
118
139
160
181
201
8
17,6
16,8
210
222
243
263
284
305
325
346
366
387
408
9
19,8
18,9
2U
428
449
469
490
610
531
552
572
593
613
20 1
212
634
654
675
695
715
736
756
777
797
818
1
2,0
213
838
858
879
899
919
940
960
980
,001
,021
2
4,0
214
33 041
062
082
102
122
143
163
183
203
224
3
6,0
215
244
264
284
304
325
345
365
385
405
425
4
8,0
216
445
465
486
506
526
546
566
586
606
626
5
10,0
217
646
666
686
706
726
746
766
786
806
826
6
12,0
218
846
866
885
905
925
945
965
985
,005
,025
7
14,0
219
3i 044
061
084
104
124
143
163
183
203
223
8
16,0
220
242
262
282
301
321
341
361
380
400
420
9
18,0
221
439
459
479
498
518
%m
557
577
596
616
19 1
222
635
655
674
694
713
733
753
772
792
811
1
1,9
323
830
850
869
889
908
928
947
967
986
,005
2
3,8
224
35 025
044
064
083
102
122
141
160
180
199
3
5,7
225
218
238
257
276
295
315
334
353
372
392
4
7,6
226
411
430
449
468
488
507
526
545
564
583
5
9,5
227
603
622
641
660
679
698
717
736
755
774
6
11,4
228
793
813
832
851
870
889
908
927
946
965
7
13,3
"29
984
,003
,021
,040
,059
,078
,097
,116
,135
,154
8
15,2
230
36 173
192
211
229
248
267
286
305
324
'342
9
17,1
231
361
380
399
418
436
455
474
493
511
530
18
232
549
568
586
605
624
642
661
680
698
717
1
1,8
233
736
754
773
791
810
829
847
866
884
903
2
3,6
234
922
940
959
977
996
,014
,033
,051
,070
,088
3
5,4
235
37 107
125
144
162
181
199
218
236
254
'273
, 4
7,2
236
291
310
328
346
365
383
401
420
438
457
5
9,0
237
475
493
511
530
548
566
585
603
621
639
6
10,8
238
658
676
694
712
731
749
767
785
803
822
7
12,6
239
840
858
876
894
912
931
949
967
985
003
8
14,4
240
38 021
039
057
075
093
112
130
148
166
184
9
16,2
2a
202
220
238
256
274
292
310
328
346
364
17 1
242
382
399
417
435
453
471
489
507
525
543
1
1,7
243
561
578
596
614
632
650
668
686
703
721
2
3,4
244
739
757
775
792
810
828
846
863
881
890
3
5,1
245
917
034
952
970
987
,005
,023
,041
,058
,076
4
?»*
246
39 094
111
129
146
164
182
199
217
235
252
5
8,5
247
270
287
305
322
340
358
375
393
410
428
6
10,2
248
445
463
480
498
515
533
550
568
685
602
7
11,9
249
620
637
655
072
690
707
724
742
759
777
8
13,6
250
794
811
829
846
863
881
898
915
933
950
9
15,3 ■
K.
L. 0.
1
2
3
4
5
6
■ 7
8
9
P.P.
LOGAEITHMS OF NUMBERS.
237
Table XXXV. — Containimj logarithms of mimhers from I to 11,000 — Continued.
[Extracted from Gauss' Loo;arithmic ami Trigonometric Tablef&.J
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
250
39 794
811
829
846
863'
881
898
915
933
950
251
967
985
,002
,019
,037
,054
.071
,088
,106
,123
1
1,8
252
40140
157
175
192
209
220
243
261
278
295
2
3,6
253
312
329
346
364
381
398
415
432
449-
466
3
6,4
254
483
500
518
535
552
509
586
603
620
637
4
7,2
265
654
671
688
705
722
739
756
773
790
807
5
9,0
256
824
841
858
875
892
909
926
943
960
•976
6
10,8
257
993
,010
.027
,044
,061
,078
,095
,111
,128
,145
7
12,6
258
41 162
179
196
212
229
246
263
280
296
313
8
14,4
259
330
347
363
380
397
414
430
447
464
481
9
16,2
260
497
514
531
547
564
581
597
614
631
647
„ 1
261
664
681
697
714
731
747
764
780
797
814
1
1/7
262
83"0
847
863
880
896
913
929
946
963
979
2
3,4
263
996
,012
,029
.,045
,062
,078
,095
.,111
,127
,144
3
5,1
264
42160
177
193
210
220
243
259
275
292
308
4
6,8
265
325
341
357
374
390
406
423
439
455
472
5
8,5
266
488
504
521
537
553
570
586
602
619
635
6
10,2
267
651
667
684
700
716
732
749
765
781
797
7
11,9
268
813
830
846
862
. 878
894
911
927
943
959
8
13,6
269
975
991
,008
,024
,040
,056
,072
,088
,104
,120
9
15,3
270
43136
152
169
185
201
217
233
249
265
281
,/
271
297
313
329
345
361
.' 377
393
409
425
441
1
1,6
272
457
473
489
505
521
537
553
569
584
■ 600
2
3,2
273
616
632
048
664
680
696
712
727
743
759
2
4,8
274
775
791
807
823
838
854
870
886
902
917
4
6,4
275
933
949
965
981
996
,012
,028
.,044
,059
,075
5
8,0
276
44 091
107
122
138
154
170
186
'201
217
232
6
9,6
277
248
264
279
295
311
326
342
358
373
389
7
11,2
278
404
420
436
451
467
483
498
514
529
545
8
12,8
279
560
576
592
607
623
638
654
669
686
■ 700
9
14,4
280
716
731
747
762
778
793
809
824
840
855
,. 1
281
871
886
902
917
932
948
963
979
994
,010
1
1,5
i82
45 025
040
056
071
086
102
117
133
148
163
2
3,0
283
179
194
209
225
240
255
271
286
301
317
3
4,5
284
332
347
362
378
393
408
423
439
454
469
4
6,0
285
484
500
515
530
545
561
576
591
606
621
5
7,5
286
637
652
667
682
697
712
728
743
758
773
0
9,0
287
788
803
818
834
849
864
879
894
009
924
7
10,5
288
939
954
969
984
.,000
,016
,030
,045
,060
.,075
8
12,0
289
46 090
105
120
135
150
165
180
195
210
225
9
13,5
290
240
255
270
286
300
315
330
345
359
374
,, 1
291
389
404
419
434
449
464
479
494
509
523
1
1,4
292
538
553
668
583
598
613
627
642
657
672
2
2,8
293
687
702
716
731
746
761
776
790
805
820
3
4,2
294
■835
850
864
879
894
909
923
938
953
967
4
5,6
295
982
997
,012
.,026
..041
,056
,070
,085
,100
,114
5
7,0
296
47129
144
159
173
188
202
217
232
246
261
6
8,4
297
276
290
305
319
334
349
363
378
392
407
7
9,8
298
422
436
451
465
480
494
509
524
538
553
8
11,2
299
567
582
596
611
625
640
654
669
683
698
9
12,6
300
712
727
741
756
770
784
799
813
828
842
M".
.L. 0
1
2
3
4
5
6
7
8
9
P. P.
238
A MANUAL OF TOPOGEAPHIC METHODS.
Table XX.XV. — Containing logarithms of iiamiers from 1 to 11,000 — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
300
L. 0
47 712
1
2
3 ■
4
=
6
7
8
9
P.P.
727
741
756
770
784
799
813
828
842
301
857
871
885
900
914
929
943
958
972
986
302
48 001
015
029
044
058
073
087
101
116
130
303
144
159
173
187
202
216
230
244
259
273
15
30 1
287
302
316
330
344
359
373
387
401
416
1
1,5
305
430
444
458
473
487
501
515
530
544
558
o
3,0
306
572
■ 586
601
615
629
643
657
671
686
700
3
4,5
307
714
728
742
756
770
785
799
813
827
841
4
6,0
308
855
869
883
897
911
926
940
954
963
982
5
7,5
309
996
,010
,024
,038
,052
,066
,080
,094
,108
,122
6
9,0
310
49 136
150
164
178
192
206
220
234
248
262
7
8
10,5
12,0
311
276
290
304
318
332
346
360
374
388
402
9
13,5
312
415
429
443
457
471
485
499
513
527
541
313
554
568
582
596
610
624
638
651
665
679
314
693
707
721
734
748
762
776
790
803
817
315
831
845
859
872
886
900
914
927
941
955
11
316
969
982
996
,010
,024
,037
,051
,065
,079
,092
1
1,4
317
50 106
120
133
147
101
174
188
202.
215
229
2
2,8
318
243
256
270
284
297
311
325
338
352
365
3
4,2
319
379
393
406
420
433
447
461
474
488
501
4
5,6
320
515
529
542
556
569
583
596
610
623
637
5
6
7,0
8,4
321
651
664
678
691
705
718
732
745
759
772
7
9,8
322
786
799
813
826
840
853
866
880
893
907
8
11,2
323
920
934
947
961
974
987
,001
,014
,028
,041
9
12,6
324
51 055
068
081
095
108
121
135
148
162
175
325
188
202
215
228
242
255
268
282
295
308
326
322
335
348
362
375
388
402
415
428
441
13
327
455
468
481
495
508
521
534
548
561
574
1
1,3
328
587
601
614
627
640
654
667
680
693
706
2
2,6
329
720
733
746
759
772
786
799
812
825
838
3
3,9
330
851
865
878
891
904
917
930
943
957
970
4
5
5,2
6,5
331
983
996
,009
jm
,035
,048
4)61
,075
,088
,101
6
7,8
332
52 114
127
140
153
166
179
192
205
218
231
7
9,1
333
244
257
270
284
297
310
• 323
336
349
362
8
10,4
334
375
388
401
414
427
440
453
466
479
492
9
11,7
335
504
517
530
543
556
569
582
595
608
621
1
336
634
647
660
673
686
699
711
724
737
750
12 1
337
763
776
789
802
815
827
840
853
866
879
1
1,2
338
892
905
917
930
943
956
969
982
994
,007
2
2,4
339
53 020
033
046
058
071
084
097
110
122
135
3
3,6
340
148
161
173
186
199
212
224
237
250
263
4
5
4,8
6,0
341
275
288
301
314
326
339
352
364
377
390
6
7,2
342
403
415
428
441
453
466
479
491
504
517
7
8,4
343
529
542
555
567
580
593
605
618
631
643
8
9,6
344
656
668
681
694
706
719
732
744
757
769
. 9
10,8
345
782
794
807
820
832
845
857
870
882
895
346
908
920
933
945
958
970
983
995
,008
,020
347
54 033
045
058
070
083
095
108
120
133
145
348
158
170
183
195
208
220
233
245
238
270
349
283
295
307
820
332
345
357
370
382
394
350
407
419
432
444
456
469
481
494
506
518
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
LOGARITHMS OF NUMBEES.
239
Table XXXV". — Containing logarithms of numbers from 1 to 11,000 — Coutiuued.
[Extracted from G-ausa' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P. P.
350
51 407
419
432
444
456
469
481
494
506
518
351
531
643
656
568
580
693
605
617
630
642
352
654
667
679
691
704
716
728
741
753
765
13
353
777
790
802
814
827
839
851
864
876
888
354
900
913
926
937
949
962
974
986
998
,011
1
1,3
355
55 023
035
047
060
072
084
096
108
121
133
2
2,6
356
145
167
169
182
194
206
218
230
2J2
255
3
3,9
357
267
279
291
303
315
328
340
362
364
376
4
5,2
358
388
40O
413
■425
437
449
461
473
486
497
5
6,5
359.
509
522
534
546
558
570
582
594
606
618
6
7,8
360
630
642
654
666
678
691
703
715
727
739
7
8
9,1
10,4
361
751
763
775
787
799
811
823
836
847
859
9
11,7
362
871
883
895
907
919
931
943
955
967
979
363
991
,003
,016
,027
,038
.050
,062
,074
,086
,098
364
56 110
122
134
146
158
170
182
194
205
217
12
305
229
241
253
265
277
289
301
312
321
336
366
348
360
372
384
396
407
419
431
443
455
1
1,2
367
467
478
490
502
514
526
538
549
561
573
2
2,4
368
585
597
608
620
632
644
656
667
679
691
3
3,6
369
703
714
726
738
750
761
773
785
797
808
4
4,8
370
820
832
844
856
867
879
891
902
914
926
5
6
6,0
7,2
371
937
949
961
972
984
996
,008
,019
,031
,043
7
8,4
372
67 054
066
078
089
101
113
124
136
148
159
8
9,6
373
171
183
194
206
217
229
241
252
264
276
9
10,8
374
287
299
310
322
334
345
357
368
380
392
375
403
415
426
438
449
461
473
434
496
507
376
619
630
642
553
665
576
688
600
611
623
11
377
634
646
657
669
630
692
703
715
726
738
378
749
761
772
784
795
807
818
830
841
852
1
1,1
379
864
875
887
898
910
921
933
944
955
967
2
2,2
380
978
990
,001
,013
,024
,035
,047
,058
,070
,081
3
4
3,3
4,4
381
58 092
104
116
127
138
149
161
172
184
196
5
6,5
382
206
218
229
240
252
263
274
286
297
309
6
6,6
383
320
331
343
354
365
377
388
399
410
422
7
7,7
384
433
444
456
467
478
490
501
512
624
535
8
8,8
385
646
657
569
580
591
602
614
625
636
647
9
9,9
386
659
670
681
692
704
715
726
737
749
760
387
771
782
794
805
816
827
838
850
861
872
388
883
894
906
917
928
939
960
961
973
984
10
389
995
»ao6
,017
,028
,040
,051
,062
,073
,084
,095
390
59 106
118
129
140
151
162
173
184
195
207
1
2
1,0
2,0
391
218
229
240
251
262
273
284
295
306
318
3
3,0
392
329
340
351
362
373
384
395
406
417
428
4
4,0
393
439
450
461
472
483
494
506
517
528
539
5
5,0
394
550
661
572
683
694
6C5
616
627
638
649
6
6,0
395
660
671
682
693
704
715
726
737
748
759
7
7,0
396
770
780
701
802
813
824
835
846
857
868
8
8,0
397
879
800
901
912
923
934
946
956
966
977
9
9,0
398
988
999
,010
,021
,032
,043
,054
,065
,076
,086
399
60 097
108
119
130
141
152
163
173
184
195
400
206
217
228
239
249
260
271
282
293
304
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
240
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXY.— Containing logarithms of mimbers from 1 to i^OW— Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
3,0
4,0
5,0
6,0
7,0
8,0
9,0
LOGAEITHMS OF NUMBEES.
241
Table XXXV. — Containing logarithms of numhera from 1 to 11,000 — Continued.
[Extracted from Gauss' Logaritlimic and Triganometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
450
65 321.
331
341
350
360
369
379
389
398
408
451
418
427
437
447
456
466
475
485
495
504
452
514
523
533
543
552
562
571
581
591
600
453
610
619
629
639
648
658
667
677
686
696
454
70G
715
725
734
744
753
763
772
782
792
455
801
811
820
830
839
849
858
868
877
887
456
896
906
916
925
935
944
954
903
973
982
10
457
992
,001
*011
,020
,030
,039
,049
,058
,068
,077
1
1,0
458
66 087
096
106
115
124
134
143
153
162
172
2
2,0
459
181
191
200
. 210
219
229
238
247
257
266
3
3,0
460
276
285
295
304
314
323
332
342
351
361
4
5
4,0
5,0
461
370
380
389
398
408
417
427
436
445
455
6
6,0
462
464
474
483
492
502
511
521
530
539
549
7
7,0
463
558
507
577
586
596
605
614
624
633
642
8
8,0
464
■ 652
661
671
680
689
699
708
717
727
736
9
9,0
465
745
755
764
773
783
792
801
811
820
829
466
839
848
857
867
876
885
894
904
913
922
467
932
941
950
960
969
978
987
997
,006
,015
468
67 025
014
043
052
062
071
080
089
099
108
469
117
127
136
145
154
164
173
182
191
201
470
210
219
228
237
247
• 25G
265
274
284
293
„
471
302
311
321
330
339
348
357
367
376
385
1
0,9
472
394
403
413
422
431
440
449
459
468
477
2
1,8
473
486
495
504
514
523
532
541
550
560
569
3
2,7
474
578
687
596
605
614
624
633
642
651
660
4
3,6
475
669
679
688
697
706
715
724
733
742
752
5
4,5
476
761
770
779
788
797
806
815
825
834
843
6
5,4
477
852
861
870
879
888
897
906
916
925
934
7
6,3
478
943
952
961
970
979
988
997
,006
,015
,024
8
7,2
479
68 034
043
052
061
070
079
088
097
106
115
9
8,1
480
124
133
142
151
160
169
178
187
196
205
481
215
224
233
242
251
260
269
278
287
296
482
305
314
323
332
341
350
3')9
368
377
386
483
395
404
413
422
431
440
449
458
467
476
484
485
494
502
511
520
529
538
547
556
565
485
574
583
592-
601
010
619
628
637
646
655
S
486
664
673
681
690
699
708
717
726
735
744
1
0,8
487
753
762
771
780
789
797
806
815
824
833
2
1,0
488
842
851
860
869
878
886
895
904
913
922
3
2,4
489
931
940
949
958
966
975
984
993
,002
,011
4
3,2
490
69 020
028
037
046
055
064
078
082
090
099
5
6
4,0
4,8
5,6
491
108
117
126
135
144
152
161
170
179
188
7
492
197
205
214
223
232
241
249
258
267
276
8
6,4
493
285
294
302
311
320
329
338
346
355
364
9
7,2
494
373
381
390
399
408
417
425
434
443
452
495
461
469
478
487
496
504
513
522
531
539
496
548
557
566
574
583
592
601
609
618
627
497
636
644
653
062
671
679
°688
697
705
714
498
723
732
740
749
758
767
775
784
793
801
499
810
819
827
836
845
854
862
871
880
888
500
897
906
914
923
932
940
949
958
966
975
N.
L. 0
1
2
3
4
5
6
7
8
9
P. P.
MON XXII-
-16
242
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXV. — Containiiifj logarithms of numbers from 1 to 11,000 — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P. P.
600
69, 897
906
914
923
932
940
949
958
906
975
501
984
992
,001
,010
,018
,027
,036
,044
,053
,062
502
70, 070
079
088
096
105
114
122
131
140
148
503
157
165
174
183
191
200
209
217
226
234
504
243
252
260
269
278
286
295
303
312
321
505
329
338
346
355
364
372
381
389
398
406
506
415
424
432
441
449
458
467
475
484
492
507
501
509
518
526
535
544
552
561
569
578
9
508
586
595
603
612
621
629
638
646
655
663
1
0,9
509
672
680
689
697
706
714
723
731
740
749
2
1,8
510
757
766
774
783
791
800
808
817
825
834
3
4
2,7
3,6
511
842
851
859
868
876
885
893
902
910
919
5
4,5
512
927
935
944
952
901
969
978
980
995
,003
6
5,4
513
71,012
020
029
037
046
054
063
071
079
088
7
6,3
514
096
105
113
122
130
139
147
155
164
172
8
7,2
51-5
181
189
198
206
214
223
231
240
248
257
9
8,1
516
265
273
282
29U
299
307
315
324
332
341
517
349
357
366
374
383
391
399
408
416
425
518
433
441
450
458
466
475
483
492
500
508
519
517
525
533
542
550
559
567
575
584
592
620
600
609
617
625
634
642
650
659
667
675
521
684
692
700
709
717
725
734
742
750
759
8
522
767
775
784
792
800
809
817
825
834
842
1
0,8
523
850
858
867
875
883
892
900
908
917
926
2
1,6
524
933
941
950
958
966
975
983
991
999
,008
3
2,4
525
72, 016
024
032
041
049
957
066
074
082
090
4
3,2
526
099
107
115
123
132
140
148
156
165
173
5
4,0
527
181
189
198
206
214
222
230
239
247
255
6
4,8
528
263
272
280
288
296
304
313
321
329
337
7
5,6
529
346
354
362
370
378
387
395
403
411
419
8
6,4
530
428
436
444
452
460
469
477
485
493
601
9
7,'.
531
509
518
526
534
542
550
558
567
575
583
532
591
599
607
616
624
632
640
648
656
665
533
673
681
689
697
705
713
722
730
738
746
534
754
762
770
779
787
795
803
811
819
827
535
835
843
852
860
869
876
884
892
900
908
536
916
925
933
941
949
957
965
973
981
989
J
537
997
,006
,014
,022
,030
,038
,046
,054
,062
,070
1
0,7
538
73, 078
■ 086
094
102
111
119
127
135
143
151
2
1,4
639
159
167
175
183
191
199
207
215
223
231
3
2,1
640
239
247
255
263
272
280
288
296
304
312
4
5
2,8
3,5
541
320
328
336
344
352
360
368
376
384
392
6
4,2
542
400
408
416
424
432
440
448
456
464
472
7
4,9
543
480
488
496
504
512
520
528
536
644
552
8
5,6
544
560
568
576
584
592
600
608
616
624
632
9
6,3
545
640
648
656
664
673
679
687
695
703
711
546
719
727
735
743
751
759
767
775
783
791
547
799
807
815
823
■630
838
846
854
862
870
548
87S
886
894
902
910
918
926
933
941
949
549
957
965
973
981
989
997
*005
*013
*020
*028
650
74, 036
044
052
060
068
076
084
092
099
107
K.
L. 0
1
2
3
4
5
6
7
, 8
9
P.P.
LOGARITHMS OF IvTUMBBRS.
243
Table XXXY. — Containing logarithms of numbers from 1 to ll,00t
[Extracted from Gauss' Logarithmic and Trigonometric Tables."
N.
L. 0.
1
2
3
4
5
6
7
8
9
P.P.
550
74 036
044
052
060
068
076
084
092
099
107
551
115
123
131
139
147
155
162
170
178
186
552
194
202
210
218
225
233
241
249
257
265
553
273
280
288
296
304
312
320
327
335
343
554
351
359
367
374
382
390
398
406
414
421
555
429
437
445
453
461
468
476
484
492
500
556
507
515
523
531
539
547
554
562
570
578
557
586
593
601
609
617
624
632
640
648
656
553
663
671
679
687
695
702
710
718
726
733
559
741
749
757
764
772
780
788
796
803
811
560
819
827
834
842
850
858
865
873
881
889
561
896
904
912
920
927
935
943
950
958
966
R
562
974
981
989
997
,005
^012
,020
.028
,035
.043
1
0,8
563
75 051
059
066
074
082
089
097
105
113
120
2
1,6
564
128
136
143
151
159
166
174
■ 182
189
197
3
2,4
3,2
565
205
213
220
228
230
243
261
259
266
274
4
566
282
289
297
305
312
320
328
335
343
351
5
4,0
567
358
366
374
381
389
397
404
412
420
427
6
4,8
568
435
442
450
458
465
473
481
488
496
504
7
5,6
569
511
519
526
534
542
549
557
565
572
580
8
6,4
570
587
595
603
610
618
626
633
641
648
656
9
7,2
571
664
671
679
686
694
702
709
717
724
732
572
740
747
755
762
770
778
785
793
800
808
563
815
823
831
838
846
853
861
868
876
884
574
891
899
906
914
921
929
937
944
952
959
575
967
974
982
989
997
,005
,012
.020
.027
,035
576
76 042
050
057
065
072
080
087
095
103
110
577
118
125
133
140
148
155
163
170
178
185
578
193
200
208
215
223
230
238
245
253
260
579
268
275
283
290
298
305
313
320
328
335
580
343
350
358
365
373
380
388
395
403
410
7
1 0,7
581
418
425
433
440
448
455
462
470
477
485
582
492
500
507
515
522
530
537
545
552
559
2
1,4
683
567
574
582
589
597
604
612
619
626
634
3
2,1
584
641
649
656
664
671
678
686
693
701
708
4
2,8
585
716
723
730
738
745
753
760
768
775
782
5
3,5
586
790
797
805
812
819
827
834
842
849
856
6
4,2
587
864
871
879
886
893
901
908
916
923
930
7
4,9
588
938
945
953
960
967
975
982
989
997
,004
8
5,6
589
77 012
019
026
034
041
048
056
063
070
078
9
6,3
690
086
093
100
107
115
122
129
137
144
151
591
159
166
173
181
188
195
203
210
217
225
592
232
240
247
254
262
269
276
283
291
298
593
305
313
320
327
335
342
349
357
364
371
594
379
386
393
401
408
415
422
430
437
444
595
452
459
466
474
481
488
495
503
510
517
596
525
532
539
646
554
561
568
576
583
590
597
597
605
612
619
627
634
641
648
656
663
598
670
677
685
692
699
706
714
721
728
735
599
743
750
757
764
772
779
786
793
801
808
600
815
822
830
837
844
851
859
866
873
880
S.
L. 0.
1
2
3
4
5
6
7
8
9
P.P.
244
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Coutinned.
[Extracted from G.iuss' Log.arithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P. P.
600
77 815
822
830
837
844
851
859
866
873
880
601
887
895
902
909
916
924
931
938
945
952
602
960
967
974
981
988
^96
,003
,010
,017
,025
603
78 032
039
046
053
061
068
075
082
089
097
604
104
111
118
125
132
140
147
154
161
168
605
176
183
190
197
204
211
219
226
233
240
606
247
254
262
269
276
283
290
297
305
312
8
607
319
326
333
340
347
355
362
369
376
383
608
390
398
405
412
419
426
433
440
447
455
1
0,8
6oa
462
469
470
483
490
497
504
512
519
526
2
1,6
610
533
540
547
554
561
669
576
583
590
597
3
4
2,4
3,2
611
604
611
618
625
633
640
647
654
661
668
6
4,0
612
675
682
689
696
704
711
718
725
732
739
6
4,8
era
746
753
760
767
774
781
789
796
803
810
7
5,6
614
817
824
831
888
845
852
859
866
873
880
8
6,4
615
888
895
902
909
916
923
930
937
944
951
9
7,2
616
958
965
072
979
986
993
,000
,007
,014
,021
617
79 029
036
043
050
057
064
071
078
085
092
618
099
106
113
120
127
134
141
148
155
163
6in
169
176
183
190
197
204
211
218
225
232
620
239
246
253
260
267
274
281
288
295
302
621
309
316
323
330
337
344
351
358
360
372
7
822
379
386
393
4U0
407
414
421
428
435
442
1
0,7
623
449
456
463
470
477
484
491
498
505
511
2
l,*
624
518
525
532
539
546
553
560
567
574
581
3
2,1
625
588
595
602
609
616
623
630
637
644
650
4
2,8
626
657
664
. 671
678
685
692
699
706
713
720
5
3,5
627
727
734
741
748
754
761
768
775
782
780
6
4,2
628
796
803
810
817
824
831
837
844
851
858
7
4,9
629
865
872
879
886
893
900
906
913
920
927
8
6'6
030
934
941
948
955
962
969
976
982
989
996
9
6,3
631
80 003
010
017
024
030
037
044
051
058
065
632
072
079
085
092
099
106
113
120
127
134
633
140
147
154
161
168
175
182
188
195
202
634
209
216
223
229
236
243
250
257
264
271
6
635
277
284
291
298
305
312
318
325
332
339
636
346
353
359
366
373
380
387
393
400
407
1
0,6
637
414
421
428
434
441
448
455
462
468
475
2
1,2
638
482
489
496
502
509
516
623
530
536
543
3
1,8
639
550
557
564
570
577
584
591
698
604
611
4
2,4
640
618
625
632
638
645
652
659
665
672
679
5
6
3,0
3,6
641
686
693
699
706
713
720
726
733
740
747
7
4,2
642
754
760
767
774
781
787
794
801
808
814
8
4,8
643
821
828
835
841
848
855
862
868
875
882
9
5,4
644
889
895
902
909
916
■922
929
936
943
949
645
956
903
069
976
983
990
996
,003
,010
,017
646
81 023
030
037
043
050
057
064
070
077
084
647
090
097
104
111
117
124
131
137
144
151
648
138
164
171
178
184
191
198
204
211
218
649
224
231
238
245
251
258
265
271
278
285
650
291
298
305
311
318
325
331
338
345
351
N.
1
2
3
4
5
6
7
8
9
P. P.
LOGARITHMS OF NUMBEES.
245
Table XXXY.— Containing logarithms of niimbcrx from 1 to 11,000— Continued.
[Extracted from Gauss' Logaritlimic and Trigouometric Tables.]
8
9
315
351
411
418
4V8
485
bU
551
611
617
till
681
743
750
809
816
8Vb
883
941
948
,007
,014
073
079
138
145
204
210
269
276
334
400
341
inR
246
A MANUAL OF TOPOGEAPHIC.METHODS.
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Contmued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5 .
6
7
8
9
P. P.
•sm
84 510
516
522
528
535
541
547
553
559
566
701
572
578
584
590
597
603
609
615
621
628
702
634
640
646
052
658
665
671
677
683
689
703
696
702
708
714
720
726
733
739
745
751
704
757
763
770
776
782
788
794
800
807
813
f '
705
819
825
831
837
844
850
856
862
868
874
1
706
■ 880
887
893
899
905
911
917
924
930
936
1
0,7
707
942
948
934
960
967
973
979
985
991
997
2
1,4
708
85 003
009
016
022
028
034
040
046
052
058
3
2,1
709
065
071
077
083
089
095
101
107
114
120
4
2,8
710
126
132
138
144
150
156
163
169
175
181
5
6
3,5
4,2
711
187
193
199
205
211
217
224
230
236
242
7
4,9
712
248
254
260
266
272
278
285
291
297
303
8
5,6
713
309
315
321
327
333
339
345
352
358
364
9
6,3
714
370
376
382 .
388
394
400
406
412
418
425
715-
431
437
443
449
455
461
467
473
479
485
716
491
497
503
509
516
522
528
534
540
546
717
552
558
564
570
576
582
588
594
600
606
718
612
618
625
631
637
643
649
655
601
667
719
673
679
685
691
697
703
709
715
721
727
720
733
739
745
751
757
763
769
775
781
788
e
721
794
800
806
812
818
824
830
836
842
848
1
0,6
722
854
860
866
872
878
884
890
896
902
908
2
1,2
723
914
920
926
932
938
944
950
956
962
968
3
1,8
724
974
980
986
992
998
,004
,010
,.016
,022
,028
4
2,4
725
86 034
040
046
052
058
064
070
076
082
088
5
3,0
726
094
100
106
112
118
124
130
136
141
147
6
3,6
727
153
159
165
171
177
183
189
195
201
207
7
4,2
728
213
219
225
231
237
243
249
255
261
267
8
4,8
729
273
279
285
291
297
303
308
314
320
326
9
5,4
730
332
338
344
350
356
362
368
374
380
386
731
392
398
404
410
415
421
427
433
439
445
732
451
457
463
469
475
481
487
493
499
604
733
510
516
522
528
534
540
546
552
658
664
734
570
576
581
587
593
599
605
611
617
622
735
629
635
641
646
652
658
664
670
676
682
736
688
694
700
705
711
717
723
729
735
741
5
737
747
753
759
764
770
776
782
788
794
800
738
806
812
817
82a
829
835
841
847
853
859
1
0,5
739
864
870
876
882
888
894
900
906
911
917
2
1,0
740
923
929
935
941
947
953
958
964
970
976
3
4
1,5
2,0
741
982
988
994
999
,,005
,011
»017
,023
,029
,035
5
2,5
742
87 040
046
052
058
064
070
075
081
087
093
6
3,0
743
099
105
111
116
122
128
134
140
146
151
7
3,5
744
157
163
169
175
181
186
192
198
204
210
8
4,0
745
216
221
227
233
239
245
251
256
262
268
9
4,5
746
274
280
286
291
297
303
309
315
320
326
747
332
338
344
349
355
361
367
373
379
384
748
390
396
402
408
413
419
425
431
437
442
749
448
454
460
466
471
477
483
489
495
500
750
506
512
518
523
529
535
541
547
552
558
If.
L. 0
1
2
3
4
5
6
7
8
9
P. P.
LOGAEITHMS OF NUMBEES.
247
Table XXXV. — Containing logarithms of nunibers from 1 to llfiOO — Continued.
[Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
750
87 506
512
518
523
529
535
541
547
552
558
751
564
570
576
581
587
593
599
604
610
616
752
622
628
633
639
645
651
656
662
668
674
753
679
685
691
697
703
708
714
720
726
731
754
737
743
749
754
760
766
772
777
783
789
755
795
800
806
812
818
823
829
835
841
846
^
756
852
858
864
869
875
881
887
892
898
904
757
910
915
921
927
933
938
944
950
955
961
758
967
973
978
984
990
996
,001
,007
,013
,018
759
88 024
030
036
041
047
053
058
064
070
076
760
081
087
093
098
104
110
116
121
127
133
761
138
144
150
156
161
167
173
178
184
190
6
762
195
201
207
213
218
224
230
235
241
247
1
0,6
763
252
258
264
270
275
281
287
292
298
304
2
1,2
764
309
315
321
326
332
338
343
349
355
360
3
1,8
765
366
372
377
383
389
395
400
406
412
417
4
2,4
766
423
429
434
440
446
451
457
463
468
474
5
3,0
767
480
485
491
497
502
508
513
619
525
530
6
3,6
768
536
542
547
553
659
564
570
676
581
537
7
4,2
769
593
598
604
610
615
621
627
632
638
643
8
4,8
770
«e49
655
660
666
672
677
■ 683
689
694
700
9
6'4
771
705
711
717
722
728
734
739
745
750
756
772
762
767
773
779
784
790
795
801
807
812
773
818
824
829
835
840
846
852
857
863
868
774
874
880
885
891
897
902
908
913
919
925
775
930
936
941
947
953
958
964
969
975
981
776
986
992
997
,003
,009
,014
,020
,025
,031
,037
777
89 042
048
053
059
064
070
076
081
087
092
778
098
104
109
115
120
126
131
137
143
143
779
154
159
165
170
176
182
187
193
198
204
780
209
215
221
226
232
237
243
248
254
260
781
265
271
276
282
287'
293
298
304
310
315
5
782
321
326
332
337
343
348
354
360
365
371
1
0,5
783
376
382
387
393
398
404
409
415
421
426
2
I'O
784
432
437
443
448
454
459
465
470
476
481
3
1,5
785
487
492
498
504
509
515
520
626
531
537
4
2,0
786
542
648
553
559
564
570
575
. 581
586
592
5
2,5
787
597
603
609
614
620
625
631
638
642
647
6
3,0
788
653
658
664
669
675
680
686
691
697
702
7
3,5
789
708
713
719
724
730
735
741
746
752
757
8
4,0
790
763
768
774
779
785
790
796
801
807
812
9
4,5
791
818
823
829
834
840
845
851
856
862
867
792
873
878
883
889
894
900
905
911
916
922
793
927
933
938
944
949
955
960
966
971
977
794
982
988
993
998
,004
,009
,015
,020
«026
,031
795
90 037
042
048
053
059
064
069
075
080
086
796
091
097
102
108
113
119
124
129
135
140
797
146
151
157
162
168
173
179
184
189
195
798
200
206
211
217
222
227
233
238
244
249
799
255
260
266
271
276
282
287
293
298
304
800
309
314
320
325
331
336
342
347
352
358
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
248
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logarithms of numiers from 1 to il,000— Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0 1 1
'■•,:'.
4
_
6
'
8
9
r. P.
800
90 309
314
320
325
331
336
342
347
352
358
801
" 363
369
374
380
385
390
396
401
407
412
802
417
423
428
434
439
445
450
455
461
466
803
472
477
482
488
493
499
504
509
515
620
804
526
531
536
542
547
553
558
563
569
574
805
580
585
590
596
601
607
612
617
623
628
806
634
639
644
650
655
660
666
671
677
682
807
* 687
693
698
703
709
714
720
725
730
736
808
741
747
752
757
763
768
773
779
784
789
809
795
800
806
811
816
822
827
832
838
843
810
849
854
859
865
870
875
881
886
891
897
811
902
907
913
918
924
929
934
940
945
950
6
813
956
961
966
972
977
982
988
993
998
,004
1
0,6
813
91 009
014
020
025
030
036
041
046
052
057
2
1,2
814.
062
068
073.,-
078
084
089
094
100
105
110
3
1,8
815
116
121
126
132
137
142
148
153
158
164
4
2,4
816
169
174
180
185
190
196
201
206
212
217
5
3,0
817
222
228
233
238
243
249
254
259
265
270
6
3,6
818
275
281
286
291
297
302
307
312
318
323
7
4,2
819
328
334
339
344
350
355-
360
365
371
376
8
4,8
820
381
387
392
397
403
408
413
418
424
429
9
5,4
821
434
440
445
450
455
461
466
471
477
482
»
822
487
492
498
503
508
514
519
624
529
535
823
540
545
551
556
561
S66
572
577
582
587
824
593
598
603
609
614
619
624
030
635
640
825
645
651
656
661
666
672
677
682
687
693
826
698
703
709
714
719
724
730
735
740
745
827
751
756
761
766
772
777
782
787
793
798
828
803
808
814
819
824
829
934
840
845
850
829
855
861
866
871
876
882
887
892
897
903
sso
908
913
918
924
929
934
939
944
950
955
831
960
965
971
976
981
986
991
997
,002
,007
6
832
92 012
018
023
028
033
038
044
049
054
059
1
0,5
833
065
070
075
080
085
091
096
101
106
111
2
1,0
834
117
122
127
132
137
143
148
153
158
163
3
1,5
835
169
174
179
184
189
195
200
205
210
215
4
2,0
83<>
221
226
231
236
241
247
252
257
262
267
5
2,5
837
273
278
283
288
293
298
304
309
314
319
6
3,0
838
324
330
835
340
345
350
355
361
366
371
7
3,5
839
376
381
387
392
397
402
407
412
418
423
8
4,0
840
428
433
438
443
449
454
459
464
469
474
9
4,5
841
480
485
490
495
500
505
511
516
521
526
842
531
536
542
547
552
557
562
567
572
578
843
583
588
593
598
603
609
614
619
624
629
844
634
639
145
650
655
660
665
670
675
681
845
686
691
696
701
706
711
716
722
727
782
846
737
742
747
752
758
763
768
773
778
783
847
788
793
799
804
809
814
819
824
829
834
848
840
845
850
855
860
865
870
875
881
886
849
891
896
901
906
911
916
921
927
932
937
850
942
947
952
957
962
967
973
978
983
988
IJ".
L. 0
1
2
3
4
5
6
7
8
9
P.P..
LOGAEITHMS OF NUMBEES.
249
Table XXXV. — Containing logarithms of numbers from 1 to lljOOO — Continued.
[Extracted from Gauss' Logarithmic and. Trigonometric Tables.]
N.
L. 0
1
3
4
5
6
' ! '
9
I
.P.
850
92 942
947
952
957
962
967
973
978
983
988
851
993
998
,003
,008
,013
.018
,024
,029
,034
,039
852
93 044
049
054
059
064
069
075
080
085
090
853
095
100
105
110
115
120
125
131
136
141
854
146
151
156
161
166
171
176
181
186
192
855
197
202
207
212
217
222
227
232
237
242
856
247
252
258
263
268
273
278
283
288
293
857
298
303
308
313
318
323
328
334
339
344
6
858
349
. 354
359
364
369
374
379
384
389
394
1
0,6
859
399
404
409
414
420
425
430
435
440
445
2
1,2
8G0
450
455
460
465
470
475
480
485
490
495
3
4
1,8
2,4
861
500
505
510
515
520
526
531
536
541
546
5
3,0
862
551
556
561
566
571
576
581
586
591
596
6
3,6
863
601
606
611
616
621
626
631
636
641
646
7
4,2
864
651
656
661
666
671
676
682
687
092
697
8
4,8
865
702
707
713
717
722
727
732
737
742
747
9
5,4
866
752
757
762
767
772
777
782
787
792
797
867
802
807
812
817
822
827
832
837
842
847
868
852
857
862
867
872
877
882
887
892
897
869-
902
907
912
917
922 .
927
932
937
942
947
870
952
957
962
967
972
977
982
987
992
997
871
94 002
007
012
017
022
027
032
037
042
047
5
872
052
057
062
067
072
077
082
086
091
096
1
0,5
873
101
106
111
116
121
126
131
136
141
146
2
1,0
874
151
156
161
166
171
176
181
186
191
196
3
1,5
875
201
206
211
216
221
226
231
236
240
245
4
2,0
876
250
255
260
265
270
275
280
285
290
295
5
2,5
877
300
305
310
315
320
325
330
335
340
345
6
3,0
878
349
354
359
364
369
374
379
384
389
394
7
3,5
879
399
404
409
414
419
424
429
433
438
443
8
4,0
SSO
448
453
458
463
468
473
478
483
488
493
9
4,5
881
498
503
507
512
517
522
527
532
537
542
882
547
552
557
562
567
571
576
581
586
591
883
596
601
606
611
616
621
626
630
635
640
884
645
650
655
660
665
670
675
680
685
689
885
694
699
704
709
714
719
724
729
734
738
886
743
748
753
758
763
768
773
778
783
787
4
887
792
797
802
807
812
817
822
827
832
836
1
0,4
888
841
846
851
856
861
866
871
876
880
885
2
0,8
889
890
895
900
905
910
915
919
924
929
934
3
1,2
890
939
944
949
954
959
963
968
973
978
983
4
5
1,6
2,0
891
988
993
998
,002
,007
,012
,017
,022
,027
,032
6
2,4
892
95 036
041
046
051
056
061
066
071
075
080
7
2,8
893
085
090
095
100
105
109
114
119
124
129
8
3,2
894
134
139
143
148
153
158
163
168
173
177
9
3,6
895
182
187
192
197
202
207
211
216
221
226
896
231
236
240
245
250
255
260
265
270
274
897
279
284
289
294
299
303
308
313
318
323
898
328
332
337
342
347
352
357
361
366
371
899
376
381
386
390
395
400
405
410
415
419
900
424
429
434
439
444
448
453
458
463
468
!«-.
L. 0
1
2
3
4
3
0
7
8
9
P
.P.
250
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logaritlims of numbers from 1 to 11,000. — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
7
8
9
P.P.
900
95 424
429
434
439
-
444
448
453
458
463
468
901
472
477
482
487
492
497
501
506
511
616
902
521
525
530
635
640
545
550
554
559
564
903
669
574
578
583
588
693
598
602
607
612
904
617
622
626
631
636
641
646
650
655
660
905
665
670
674
679
684
689
694
698
703
708
906
713
718
722
727
732
737
742
746
751
756
907
761
766
770
775
780
785
789
794
799
804
91p8
809
813
818
823
828
832
837
842
847
852
909
856
861
866
871
875
880
885
890
895
899
910
904
909
914
918
923
928
933
938
942
947
911
952
957
961
966
971
976
980
985
990
995
6
912
999
»004
,009
«014
,019
,023
,028
,033
,038
,042
1
0,5 1
913
96 047
052
057
061
066
071
076
080
085
090
2
1,0 i
914
095
099
104
109
114
118
123
128
133
137
3
1,5 1
915
142
147
152
156
161
166
171
175
180
185
4
2,0
916
190
194
199
204
209
213
218
223
227
232
5
2,5
917
237
242
246
251
256
261
265
270
275
280
6
3,0
918
284
289
294
298
303
308
313
817
322
327
7
3,5
919
332
336
341
346
350
355
360
365
369
374
8
4,«
920
379
384
388
393
398
402
407
412
417
421
9
4,5
921
426
431
435
440
445
450
454
459
464
468
922
473
478
483
487
492
497
501
506
611
615
923
520
525
530
534
539
544
648
553
558
562
924
567
572
577
581
586
591
595
600
605
609
925
614
619
624
628
633
638
642
647
662
656
926
661
006
670
675
630
685
689
694
699
703
927
708
713
717
722
727
731
736
741
745
750
928
755
759
704
769
774
778
783
788
792
797
929
802
806
811
816
820
825
830
834
839
844
330
848
853
858
862
867
872
876
881
886
890
931
895
900
904
909
914
918
923
928
932
937
4
932
942
946
951
956
960
965
970
974
979
984
1
0,4
933
988
993
997
,002
,007
.011
,016
,021
,025
,030
2
0,8
934
97 035
039
044
049
053
058
063
067
072
077
3
1,2
935
081
0S6
090
095
100
104
109
114
118
123
4
1,6
936
128
132
137
142
146
151
155
160
165
169
5
2,0
937
174
179
183
188
192
197
202
206
211
216
6
2,4
938
220
225
230
234
239
243
248
253
257
262
7
2,8
939
267
271
276
280
285
290
294
299
304
308
8
3,2
910
313
317
322
327
331
336
340
345
350
354
9
3,6
941
359
364
368
373
377
382
387
391
396
400
942
405
410
414
419
424
42,S
433
437
442
447
943
451
456
460
465
470
474
479
483
488
493
944
497
502
506
511
516
520
525
529
534
539
945
543
548
552
667
662
566
571
675
580
585
946
589
594
598
603
607
612
617
621
626
630
947
635
640
644
649
663
658
663
667
672
676
948
681
685
690
693
699
704
708
713
717
722
949
727
731
736
740
745
749
754
759
763
768
950
772
777
782
786
791
795
800
804
809
813
N.
X. 0
1
2
3
4
6
6
7
8
9
P.P.
LOGARITHMS OF i^UMBEES.
251
Table XXXV. — Containing logarithms of mmibers from 1 to 11,000,-
[Estracted fi'oiu Gauss' Logarithmic aud Trigonoroetric Tables.]
0
1
2
3
7 772
777
782
786
818
823
827
832
864
868
873
877
909
914
918
923
955
959
964
968
8 000
005
009
014
046
050
055
059
091
096
100
105
137
141
146
150
182
186
191
195
227
232
236
241
272
277
281
286
318
322
327
331
363
367
372
376
408
412
417
421
453
457
462
466
498
502
507
511
543
547
552
556
588
692
597
601
632
637
641
640
677
682
686
691
722
726
731
735
767
771
776
780
811
816
820
825
856
860
865
869
900
905
909
914
945
949
954
958
989
994
998
,003
99 034
038
043
047
078
083
087
092
123
127
131
136
167
171
176
180
211
216
220
224
255
260
264
269
300
304
308
313
844
348
352
357
388
392
396
401
432
436
441
415
252
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containinfi Ingarithms of numhers from 1 to ii,00fl.— Coutinuecl.
[Extracted from Gauss' Logarithmic and Trigouometric Ta"bles-]
N.
L. 0
1
2
3
4
5
6
7
8
9
d.
louo
000 ouoo
0434
0869
1303
1737
2171
2605
3039
3472
3907
434
1001
4341
4775
5208
5642 1
6076
6510
6943
7377
7810
8244
434
1002
8677
9111
9544
9977
.0411
,0844
,1277
,1710
,2143
,2576
433
1003
001 3009
3442
3875
4308
4741
5174
5607
6039
0472
6905
433
1004
7337
7770
8202
8C35
9067
9499
9932
,0364
,0796
.1228
432
1(106
002 1601
2093
2525
2957
3389
3821
4253
4685
5116
5548
432
1006
5980
6411
6843
7275
7706
8138
8569
9001
9432
9863
431
1007
003 0295
0726
1157
1588
2019
2451
2882
3313
3744
4174
431
lOOS
4605
5U36
5467
5898
6328
6759
7190
7620
8051
8481
431
10U9
8912
9342
9773
,0203
,0633
,1063
,1493
,1924
,2354
,2784
430
1010
004 3214
3644
4074
4504
4933
'5363
5793
6223
6652
7082
430
1011
7512
7941
8371
8800
9229
9659
,0088
,0517
,0947
,1376
429
1012
005 1805
2234
2663
3092
3521
3950
4379
4808
5237
5666
429
1013
6094
6523
6952
7380
7809
8238
8666
9094
9523
9951
429
1014
006 03S0
0808
1236
1664
2092
2521
2949
3377
3805
4233
428
1015
4660
5088
5516
5944
6372
6799
7227
7655
8082
8510
428
1010
8937
9365
9792
,0219
,0647
,1074
,1501
,1928
,2355
,2782
427
1017
007 3210
3637
4064
4490
4917
5344
5771
6198
6624
7051
427
1018
7478
7904
8331
8757
9184
9610
,0037
,0463
,0889
,1316
426
1019
008 1742
2168
2594
3020
3446
3872
4298
4724
'5150
5576
426
1020
6002
6427
6853
7279
7704
8130
8556
8981
9407
9832
426
1021
009 0257
0683
1108
1533
1959
2384
2809
3234
3659
4084
425
1022
4509
4934
5359
5784
6208
6633
7058
7483
7907
8332
425
102:1
8756
9181
9605
.0030
.0454
,0878
,1303
,1727
,2151
,2575
424
1024
010 3000
3424
3848
4272
4696
5120
5544
5967
6391
6815
424
1025
7239
7662
8086
8510
8933
9357
9780
,0204
,0627
,1050
424
1026
Oil 1474
1897
2320
2743
3166
3590
4013
4436
4859
5282
423
1027
5704
6127
6550
6973
7396
7818
8241
8664
9086
9509
423
1028
9931
.0854
.,0776
,1198
,1621
,2043
,2465
.2887
,3310
,3732
422
1029
012 4154
4576
4998
5420
'5842
6264
6685
7107
7529
7951
422
1030
8372
8794
9215
9637
,0059
,0480
,0901
,1323
,1744
,2165
422
1031
013 2587
3008
3429
3850
4271
4692
5113
5534
5955
6376
421
1032
6797
7218
7639
8059
8480
8901
9321
9742
,0162
,0583
421
1033
014 1003
1424
1844
2264
2685
3105
3525
3945
4365
4785
420
1034
5205
5625
6045
6465
6885
7305
7725
8144
8564
8984
420
1035
9403
9823
,0243
„l.662
,1082
,1501
,1920
,2340
,2759
,3178
420
1036
015 3598
4017
4436
4855
5274
5693
6112
6531
6950
7369
419
1037
7788
8206
8625
9044
9462
9881
,0300
,0718
,1137
,1555
419
1038
016 1974
2392
2810
3229
3647
4065
4483
4901
5319
5737
418
1039
6155
6573
6991
7409
7827
8245
8663
9080
9498
9916
418
1040
017 0333
0751
1168
1586
2003
2421
2838
3256
3673
4090
417
1041
4507
4924
5342
5759
6176
6593
7010
7427
7844
8260
417
1042
8677
9094
9511
9927
,0344
,0761
,1177
,1594
,2010
,2427
417
1043
018 2843
3259
3676
4092
4508
4925
5341
'5757
'6173
6589
416
1044
7005
7421
7837
8253
8669
9084
9500
9916
,0332
,0747
416
1045
019 1163
1578
1994
2410
2825
3240
3656
4071
4486
4902
415
1046
5317
5732
6147
6562
6977
7392
7807
8222
8637
9052
415 1
1047
9467
9882
»0296
,0711
,1126
,1540
,1955
,2369
,2784
,3198
415
1048
020 3613
4027
4442
4856
'5270
5684
6099
6513
6927
7341
414
1049
7755
8169
8583
8997
9411
9824
,0238
,0652
,1066
,1479
414
1050
021 1893
2307
2720
3134
3547
3961
4374
4787
■5201
5614
413
N.
L. 0
1
2
3
4
»
'
7 8
9
d.
LOGAEITHMS OP NUMBEKS.
253
Table XXXV, — Containing hxjariihms of numbv.vti from 1 to J1,000. — Continued.
[Extracted from. Gauas' Logarithmic and Trigonometric Tables.]
N.
L. 0
1
2
3
4
5
6
8
9
d.
1050
021 1893
2307
2720
3134
3547
3961
4374
4787
5301
5614
413
1051
6027
6440
6854
7267
7680
8093
8506
8919
9333
9745
413
1052
022 0157
0570
0983
1396
1808
2231
2634
3046
3459
3871
413
1053
4284
4696
5109
5521
5933
6345
6758
' 7170
7583
7994
412
1054
8406
8818
9230
9643
,0054
,0466
,0878
,1289
,1701
,2113
412
1055
023 2525
2930
3348
3759
4171
4583
4994
5405
5817
6228
411
1056
6639
7050
7462
7873
8284
8095
9106
9517
9928
,0339
411
1057
024 0750
1161
1572
1982
2393
2804
3214
3025
4036
4446
411
1058
4857
5267
5678
6088
6498
6909
7319
7729
8139
8549
410
1059
8960
9370
9780
,0l90
,0600
,1010
,1419
,1829
,2239
,2649
410
1060
025 3059
3468
3878
4288
4697
5107
5516
5926
6335
6744
410
1061
7154
7563
7972
8382
8791
9300
9609
,0018
,0427
,0836
409
1062
026 1245
1654
2063
2472
2881
3289
3698
4107
4515
4924
409
1063
5333
5741
6350
6558
6967
7375
7783
8192
8600
9008
408
1064
9416
9824
,0233
,0641
,1049
,1457
,1865
,3373
,2680
,3088
408
1065
027 3496
3904
4312
4719
5127
5535
5942
6350
6757
7165
408 1
1006
7572
7979
8387
8794
9201
9609
,0016
,0423
,0830
,1237
407
1067
028 1644
2051
2458
2865
3272
3679
4086
4492
4899
5306
407
1068
5713
6119
6526
6932
73S9
7745
8152
8558
8964
9371
406
1069
9777
,0183
,0590
,0996
,1402
,1808
,2214
,2620
,3026
,3433
406
1070
029 3838
4244
4649
5055
5461
5867
6272
6678
7084
7489
406
1071
7895
8300
8706
9111
9516
9922
,0327
,0732
,1138
,1543
405
1072
030 1948
2353
2758
3163
3568
3973
4378
4783
5188
5592
405
1073
5997
6402
6807
7211
7616
8020
8425
8830
9234
9638
405
1074
031 0043
0447
0851
1256
1660
2064
2468
2872
3277
3681
404
1075
4085
4469
4893
5396
5700
6104
6508
,0Sl7
7315
7719
404
1076
8133
8526
8930
9333
9737
,0140
,0544
,1350
,1754
403
1077
032 2157
2560
2963
3367
3770
4173
4576
4979
5382
5785
403
1078
6188
6590
6993
7396
7799
8201
8604
9007
9409
9812
403
1079
033 0214
0617
1019
1422
1824
2336
2629
3031
3433
3835
402
1080
4238
4640
5042
5444
5846
62 J 8
6650
7052
7453
7855
402
1081
8257
8659
9060
9462
9864
,0265
,0667
,1068
,1470
5482
,1871
402
1082
034 2273
2674
3075
3477
3878
4279
4680
5081
5884
401
1083
6285
6686
7087
7487
7888
8289
8690
9091
9491
9893
401
1084
035 0293
0693
1094
1495
1895
2296
2696
3096
3497
3897
400
1085
4297
4698
5098
5498
5898
6298
6698
7098
7498
7898
400
1086
8298
8698
9098
9498
9898
,0297
,0697
,1097
,^496
,1896
400
1087
036 2295
2695
3094
3494
3893
4393
4692
5091
5491
5890
399
1088
6289
6688
7087
7486
7885
8284
8683
9082
9481
9880
399
1089
037 0279
0678
1076
1476
1874
2272
2671
3070
3468
3867
399
1090
4265
4663
5062
5460
5858
6357
6655
7053
7451
7849
398
1091
8248
8646
9044
9442
9839
,0237
,0635
,1033
,1431
,1829
398
1092
038 2226
2624
3022
3419
3817
4214
4612
5009
5407
5804
398
1093
6202
6599
6996
7393
7791
8188
8585
8982
9379
9776
397
1094
039 0173
0570
0067
1364
1761
2158
2554
2951
3348
3745
397
1095
4141
4538
4934
5331
5727
6124
6520
6917
7313
7709
397
1096
8106
8502
8898
9294
9690
,0086
,0482
,0878
.1274
,1670
396
1097
040 2066
2462
2858
3354
3650
4045
4441
4837
'5232
5638
396
1098
6023
6419
6814
7310
7605
8001
8396
8791
9187
9582
395
1099
9977
,0372
,0767
,1162
,1557
,1953
,2347
,3742
,3137
,3532
395
1100
N.
041 3927
L. 0
4322
4716
5111
5506
5900
6295
6690
7084
8
7479
395
1
2 3
4
5
6
9
d.
254
A MANUAL OF TOPOGRArHIC METHODS.
Tablic XXXVI. — Logarithmic sines, cosines, tangents, and cotangents.
[Extracted from Oaiiss' Logarithmic anil Tiigouomctrio Tables,]
0°
'
L. Sin.
(1.
L. Tang. 1
1
d. 0.
L. Cotg.
L. Cos.
0
1
0. 00 000
0. 00 oon
60
59
6. 46 373
0.46 373
3.53 627
6. 76 476
30103
6.76 476
30103 3.23 524
0.00 000
58
17609
6.94 085
17609 3.05 915
0. 00 000
57
4
7. 06 579
12494
9691
7. 06 579
12494
9691
2.93 421
0. 00 000
66
5
7.16 270
7. 16 270
2.83 730
0.00 000
55
6
7. 24 188
7918
7.24 188
2.75 812
0.00 000
7.30 S82
6691
7. 30 882
2.69 118
0.00 000
7.36 682
5800
7.36 682
2.63 318
0.00 000
52
11
10 ^
7.41 797
5115
4576
7.41 797
4576
2. 58 203
0. 00 000
51
7. 46 373
7. 46 373
2.53 627
0.00 000
50
4139
7. 50 512
2.49 488
0.00 000
49
7 54 291
3779
7.54 291
2.45 709
0. 00 000
48
7 57 767
3476
7. 57 767
2.42 233
0.00 000
47
14
7. 60 985
3218
2997
7. 60 986
7.63 982
2996
2.39 014
0.00 000
46
7.63 982
2.36 018
0.00 000
45
2802
7. 66 785
2. 33 215
0.00 000
44
17
7.69 417
2633
7. 69 418
2482
2. 30 582
9.99 999
43
7.71 900
2483
7. 71 900
2.28 100
9.99 999
19
20
7.74 248
2348
2227
7.74 248
. 2228
2. 25 752
9.99 999
41
7 76 475
7. 76 476
2. 23 524
9.99 999
40
2119
7.78 595
2.21 405
9.99 999
39
22
7.80 615
2021
7.80 615
2. 19 385
9.99 999
38
7.82 545
1930
7.82 546
2. 17 454
9.99 999
24
7. 84 393
1848
1773
7, 84 394
1773
2.15 606
9.99 999
36
7.86,166
7.86 167
2. 13 833
9.99 999
35
1704
7. 87 871
2.12 129
9.99 999
34
27
7.89 509
1639
7. 89 510
1639
2. 10 490
9.99 999
33
'S
7.91 088
7.91 089
2. 08 911
9.99 999
29
7.92 612
1472
7. 92 613
7. 94 086
1473
2.07 387
9.99 998
30
7.94 084
2. 05 914
9.99 998
30
7.95 508
7.95 510
2. 04 490
9.99 998
32
7.96 887
1379
7.96 889
2.03 111
9.99 998
28
33
7.98 223
1336
7.98 225
2.01 775
9.99 998
27
34
7.99 520
1259
7.99 522
1259
2. 00 478
9.99 998
8.08 781
1.99 219
9. 99 998
25
« 8. 02 0U2
8.03 192
1223
8. 02 004
1223
1.97 996
9.99 998
24
1190
8.03 194
1.96 806
9.99 997
23
38
8.04 350
1158
8. 04 353
1.95 647
9.99 997
22
39
8.05 478
1100
8. 05 481
8. 06 581
1100
1.94 519
9.99 997
40
8.06 578
1.93 419
9.99 997
20
1072
8.07 653
1.92 347
9.99 997
8.08 696
1046
8. 08 700
1.91 300
9.99 997
18
8. 09 718
1022
8.09 722
1. 90 278
9.99 997
17
44
45
8. 10 717
8.11 693
999
976
8. 10 720
976
1. 89 280
9.99 996
16
8. 11 696
1.88 304
9. 99 996
15
8. 12 651
1.87 349
9. 99 996
14
8.13 581
934
8. 13 585
934
1.86 415
9. 99 996
13
48
8.14 495
914
8. 14 500
915
1.85 300
9. 99 996
12
49
SO
8.15 391
896
877
8. 15 395
895
878
1.84 605
9. 99 996
11
8. 16 268
8. 16 273
1.83 727
9. 99 995
10
51
8.17 128
8.17 133
1.82 867
9. 99 995
9
8. 17 971
8.17 976
1, 82 024
9.99 995
53
8. 18 798
827
8. 18 804
828
1.81 196
9. 99 995
7
54
8. 19 610
797
8. 19 616
797
1.80 384
9.99 895
55
8. 20 407
8. 20 413
1. 79 587
9. 99 994
5
50
8.21 189
782
8. 21 195
1.78 805
9. 99 994
4
57
8.21 958
769
8. 21 964
1.78 036
9. 99 994
3
58
8.22 713
8. 22 720
1.77 280
9.99 994
59
8. 23 456
730
8. 23 462
8. 24 192
730
1.76 538
1. 75 808'
9.99 994
60
8. 24 186
9. 99 993
0
L. Cob.
d.
L. Cotg.
d.c.
L. Tang.
L. Sin.
'
89=
LOGAEITHMS OF CIECULAE FUNCTIONS.
255
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents. — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
1°
'
L. Sin.
d.
L. Tang.
d. 0.
L. Cotg.
L. Cos.
0
8. 24 186
717
706
695
684
673
8. 24 192
718
706
696
684
673
1. 75 808
9. 99 993
60
1
8.24 903
8. 24 910
1. 75 090
9. 99 993
59
2
8. 25 609
8.25 616
1. 74 384
9.99 993
58
3
8. 26 304
8. 26 312
1. 73 688
9. 99 993
57
4'
8. 26 988
8. 26 S96
1.73 004
9. 99 992
56
5
8.27 661
8.27 669
1.72 331
y.99 992
55
6
8. 28 324
8. 28 332
1.71 668
9.99 992
54
8. 28 977
8. 28 986
1. 71 014
9. 99 992
53
8. 29 021
8. 29 629
1.70 371
9. 99 992
52
9
8. 30 255
624
8.30 263
625
1. 69 737
9. 99 991
51
10
8.30 879
8. 30 888
1. 69 112
9. 9'J 991
50
11
8. 31 495
8. 31 505
1. 63 495
9. 99 991
49
8.32 103
8. 32 112
1. 67 S88
9. 99 990
48
13
8. 32 702
8.32 711
1. 67 289
9. 99 990
47
14
8.33 292
583
8.33 302
584
1. 66 698
9. 99 990
46
15
8. 33 875
8.33 886
1.-66 114
9.99 990
45
8. 34 450
8. 34 461
1. 65 539
9.99 989
44
17
8.35 018
568
8. 35 029
568
1. 64 971
9.99 989
43
8. 35 590
1.64 410
9. 99 989
42
19
8.36 131
8. 36 678
553
547
8. 36 143
553
546
1, 63 857
9.99 989
41
20
8. 36 689
1.63 311
9.99 988
40
8.37 217
8. 37 229
1. 62 771
9. 99 988
39
2j
8.37 750
533
8. 37 762
1. 62 238
9.99 988
38
8. 38 289
1. 61 711
9. 99 987
37
24
8.38 796
520
514
8. 38 809
520
514
1.61 191
9.99 987
36
25
8.39 310
8. 39 323
1. 60 677
9. 99 987
35
8.39 818
8. 39 832
1. 60 168
9.99 986
34
8.40 320
8. 40 334
1. 59 660
9. 99 986
33
28
8.40 816
8. 40 830
1. 59 170
9. 99 986
32
29
8.41 307
485
8.41 321
486
1.58 679
9. 99 985
31
30
8.41 792
8.41 807
1.58 193
9. 99 985
30
8.42 272
8.42 287
1. 57 713
9. 99 985
32
8.42 746
8. 42 762
475
1.57 238
9. 99 984
28
33
8.43 216
8.43 232
1. 56 768
9.99 984
27
34
8.43 680
459
8.43 696
460
1. 56 304
9. 99 984
26
8.44 156
1.65 844
9.99 983
25
36
8,44 594
8.44 611
455
1.55 389
9.99 983
24
37
8.45 044
8. 45 061
1.54 939
9. 99 983
23
8. 45 489
8. 45 507
1. 54 493
9.99 982
22
39
8.45 930
436
8. 45 948
441
437
1. 54 052
9. 99 982
21
40
8. 46 366
8. 46 385
1.53 615
9. 99 982
20
41
8.46 799
8.46 817
1.53 183
9. 99 981
19
8.47 226
8.47 245
1. 52 755
9.99 981
18
8.47 650
424
8. 47 669
1.52 331
9. 99 981
17
44
8.48 069
419
416
8.48 089
416
1.51 911
9. 99 980
16
8.48 485
8.48 505
1.51 495
9. 99 980
15
46
8.48 896
8.48 917
1.51 083
9. 99 979
14
8.49 304
8.49 325
1. 50 675
9. 99 979
13
48
8.49 708
404
8.49 729
1.50 271
9. 99 979
12
49
8. 50 108
396
8.50 130
397
1.49 870
9. 99 978
11
30
8.50 504
8.50 527
1.49 473
9. 99 978
10
51
8. 50 897
8.50 920
1.49 08U
9. 99 977
9
52
8.51 287
8.51 310
1.48 690
9.99 977
8
53
8.51 673
386
8.51 696
1.48 304
9. 99 977
7
54
8. 52 055
379
8.52 079
380
1. 47 921
9. 99 976
6
8.52 459
1.47 541
9. 99 976
5
8. 52 810
376
8. 52 835
1.47 165
9.99 975
4
57
8.53 183
373
8. 53 208
1.46 792
9. 99 975
3
58
8. 53 552
369
8.53 578
1.46 422
9. 99 974
2
59
8. 53 919
363
8. 53 945
8. 54 308
363
1.46 055
9. 99 974
1
60
8. 54 282
1.45 692
9.99 974
0
L. Cos.
d.
L. Cotg.
d. c.
L. Tang.
L. Sin.
'
880
256
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Lofiarithmic sines, cosines, tangents, and cotangents. — Coutmued.
[Erfraottd from Gauss' Logarithmic and Trigonometric Tables.]
L. Sin.
0
8. 54 282
8. 54 042
8. 54 99D
8. 55 354
8.55 705
8.56 054
8. 56 400
8. 56 743
8. 57 084
8. o7 421
10
8. 57 757
11
8. 58 089
12
8. 58 419
13
8. 58 747
14
8. 59 072
15
8. 59 395
16
8. .59 715
17
8. 60 033
18
8.6U 349
19
8. 60 662
20
8. 60 973
21
6. 61 282
22
8.61 589
23
8.61 894
24
8. 62 196
25
8. 62 497
26
8. 62 795
27
8. 63 091
28
8. 63 385
29
80
8.63 678
8. 63 968
31
8. 64 256
32
8. 64 543
33
8. 64 827
34
8.65 110
8. 66 497
8.66 769
8. 67 039
8.67 308
8. 67 575
8.67 841
8. 68 104
8. 68 367
8. 68 627
8. 68 886
8.69 144
8.69 400
8. 69 654
8.69 907
8. 70 159
8. 70 409
8. 70 658
8.70 905
8.71 151
8.71 395
8. 71 638
8.71 880
87=
LOGARITHMS OF CIRCULAR FU:srCTIO:SS.
257
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Contiuued.
[Extracted from Gauss' Logaritttraic and Trigonometric Tables.]
30
MON XXII
258
A MxVNUAL OF TOPOGEArHIG METHODS.
Table XXXVI. — Logaritltmic sines, cosines, tanncnts, and cotangents — Contiuuod.
[Bxtractea from Gauss' Losaritlimic ami Trigouometric Tables.]
4°
8. 84 358
S. 84 539
S. 8i 718
S. 81 897
8. 85^075
8.85^252
8. 85 429
8.85 605
8. 85 780
8.85 955
87 86 128
8. 86 301
8. 86 474
8.87 661
8. 87 829
8. 87 995
8. 88 161
8.88 326
8. 88 490
8. 88 654
8. 88 817
8.89 142
8.89 304
8. 89 464
8.89 625
8. 89 784
8.89 943
8.90 102
8.91 807
8. 91 959
8.92 110
8. 92 261
8. 92 411
8. 92 561
8.92 710
8.92 859
8. 93 007
8. 93 154
8. 93 3DT
8. 93 448
8. 93 594
8.93 740
8.93 885
a. 94 030
8. 84 464
8. 84 04C
8. 84 826
8. 85 006
8^85 185
"8.85 363"
8. 85 540
8.85 717
8.85 893
8.86 069
8. 86 243
8. 86 417
8. 86 591
8. 86 763
8. 87 953
8. 88 120
8. 88 287
8. 88 453
8^88_618^
" 8. 88 783
8. 88 948
8.89 111
8. 89 274
_ 8^9^432
8. 89 598
8.91 185
8.91 340
8.91 495
8.91 6.50
8.91 803
1. 15 536
1.15 354
1. 15 174
1. 14 994
L14 815
1. 14 637"
1. 14 460
1. 14 283
1.14 107
1. 13 931
1. 13 757
1. 13 583
1.13 409
1.13 237
1.13 065
1.12 894
1. 12 723
1.12 553
1.12 384
1. 12 215
1.11 880
1. 11 713
1. 11 547
1.11 382
8. 93 462
8.93 609
8.93 756
8. 93 903
8. 94 049
"8.94 195
L. Cotg. d. c.
1.11 217
1. 11 052
1. 10 889
1.10 726
1. 10 563
1. 10 402
1. 10 240
1. 10 080
1.09 920
1,09 760
1. 09 601
1.09 443
1. 09 285
1.09 128
1. 08 971
1. 08 815"
1. 08 060
1. 08 505
1. 08 350
J. 08 197
f. 08 043"
1. 07 890
1.07 738
1. 07 586
1. 07 435
9. 99 894
9. 99 893
9.99 892
9.90 891
9.99 891 I
9. 99 990"
9. 99 889
9. 99 888
9. 99 887
9. 99 880
9. 99 879
9.99 879
9. 99 878
9. 99 874
9. 99 873
9.99 872
9. 99" 871
9. 99 870
9. 99 869
9. 99 868
.99 ;
9.99 861
9.99 860
9. 99 859
9. 99 856
9. 99 855
9. 99 854
9. 99 853
9. 99 852
1. 07 284
1.07 134
1.06 835
1.06 687
1,06 538
1.06 391
1. 06 244
1. 06 097
JJ)5J)51
1, 05 805
9, 99 851
9, 99 850
9,99 848
9, 99 847
9, 99 846
9, 99 845
9, 99 844
9, 99 Si3
9. 99 842
9. 99 841
9. 99 840
9.99 839
9.99 836
9. 99 834
182
ISl
1V9
17S
3,0
3,0
3,0
3,0
6,1
6,0
6,0
5,9
9,1
9,0
9,0
8,9
12,1
12,1
11,9
11,9
15,2
15,1
14,9
14,8
18,2
18,1
17,9
17,8
21,2
21,1
20,9
20,8
24,3
24,1
23,9
23,7
27,3
27,2
26,8
26,7
17G
175
174
17S
2,9
2,9
2,9
2,9
5,9
5,8
5,8
5,8
8,8
8,8
8,7
8,6
11,7
11,7
11,6
11,5
14,7
14,6
14,5
14,4
17,6
17,5
17,4
17,3
20,5
20,4
20,3
20,2
23,5
23,3
23,2
23,1
26,4
26,2
26,1
26,0
171
170
169
168 ;
2'8
2,8
2,3
2,8
5,7
5,7
5,6
5,6
8,6
8,5
8,4
8,4
11,4
U,3
11,3
11,2
14,2
14,2
14,1
14,0
17,1
17,0
16,9
16,8
20,0
19,8
19,7
19,6
22,7
22,5
22,4
25,6
52'5
25,4
25,2
166
165
1G4
163
2,8
2,8
2,7
2,7
5,5
5,5
5,5
6,4
8,3
8,2
8,2
8,2
11,1
11,0
10,9
10,9
13,8
13,8
13,7
13,6
16,6
16,5
16,4
16,3
19,4
19,2
19,1
19,0
22,1
22,0
21,9
21,7
24,9
24,8
24,6
24,4
161
160
150
168
2,7
2,7
2,6
2,6
5,4
5,3
5,3
6,3
8,0
8,0
8,0
7,9
10,7
10,7
10,6
10,5
13,4
13,3
13,2
13,2
16,1
16,0
15^9
15,8
18,8
18,7
18,6
18,4
21,5
21,3
21,2
21,1
24,2
24,0
23,8
23,7
156
155
154
153
2,6
2,6
2,6
2,0
5,2
5,2
5,1
5,1
7,8
7,8
7,7
7,6
10,4
10,3
10,3
10,2
13,0
12,9
12,8
12,8
16,6
16,5
15,4
16,3
18,2
18,1
18'0
17,8
20,8
20,7
20,5
20,4
23,4
23,2
23,1
23,0
177
3,0
6,9
8,8
11,8
14,8
17,7
20,6
23,6
26,6
172
2,9
6,7
8,6
11,5
14,3
17,2
20,1
22,9
8,4
11,1
13,9
16,7
19,5
22,3
25,0
8,1
10,8
13,5
16,3
18,9
21,6
24,3
157
2,6
6,2
7,8
10,5
13,1
15,7
18,3
20,9
23,6
152
2,5
5,1
7,6
10,1
12,7
15,2
17,7
20,3
22,8
85°
LOGARITHMS OF CIECULAE FUNCTIONS.
259
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
91 030
94 174
94 317
94 461
94 603
94 746
94 887
95 029
95 170
95 310
95 450
95 589
95 728
97 095
97 229
97 363
97 496
97 629
97 762
97 894
98 026
98 157
98 288
98 419
98 549
98 679
98 937
99 066
99 194
99 332
99 450
99 577
99 704
00 704
00 838
00 951
01 074
01 196
01 318
01 440
01 561
01 682
01 803
8.94 195
S. 94 340
8. 94 485
8. 94 630
8. 94 773
8.94 917
8.95 060
8. 95 202
8. 95 344
8. 95 486
8.95 627
8. 95 767
8. 95 908
8.96 047
8. 90 187
8. 96 325
8. 96 464
8.96 603
8.96 739
8. 96 877
8. 97 013
8.97 150
8. 97 285
8. 97 421
8. 97 556
8.97 691
8. 97 825
8. 97 959
8. 98 092
8.98 358
8. 98 490
8. 98 622
8. 98 763
9. 00 301
9. 00 427
9.00 553
9.00 679
9. 00 805
9. 00 930
9.01 055
9.01 179
9. 01 303
9. 01 427
9.01 550
9.01 673
9. 01 796
9. 01 918
9.02 040
9.02 162
140
138
1. 05 805
1. 05 660
1.05 515
1.05 370
1. 05 227
1. 05 083
1.04 940
1.04 798
1.04 650
1. 04 514
1. 04 373
1. 04 233
1.04 092
1. 03 953
1.03 813
1.03 675
1. 03 536
1. 03 398
1. 03 261
1.03 123
1. 02 987
1.02 850
1. 02 715
1. 02 579
1. 02 444
1.02 309
1.02 175
1. 02 041
1.01 908
1. 01 775
1.01 642
1.01 510
1.0] 378
1.01 247
1. 01 116
1. 00 985-
1. 00 855
1. 00 723
1. 00 595
1. 00 466
1.00 338
1. 00 209
1.00 081
0.99 954
0 99 826
99 699
99 573
99 447
98 697
98 573
98 450
98 327
98 204
98 C82
97 960
824
9.99 823
9. 99 822
9. 99 821
0. 99 820
9. 99 819
9.99 806
9. 99 81)4
9. 99 803
9. 99 802
9.99 801
9. 99 800
9.99 798
9. 99 797
9. 99 796
9. 99 795
9.99 793
9. 99 792
9. 99 791
9. 99 790
9. 99 788
0.99 787
9. 99 786
9.99 785
9. 99 778
9. 99 777
9.99 776
9. 99 771
:1. 99 769
9.99 708
9. 99 767
9.99 765
9.99 764
9. 99 763
9. 99 761
L. Cotg. d.c. L. Tang. I L. Sin.
149
148
2,5
2,5
6,0
4,9
V,4
7,4
9,9
9,9
13,4
12,3
14,9
14,8
r/,4
17,3
19,9
19,7
22,4
22,2
T4+
US
2,4
2,4
4,8
4,8
V,3
7,2
9,6
9,5
12,0
11,9
14,4
14,3
16,8
16,7
19,2
19,1
31,6
21,4
11,2
11,1"
13,4
13,3
15,6
15,5
17,9
17,7
30,1
20,0
129
138
2,2
2,1
4,3
4,3
6,4
6,4
8,6
8,5
10,8
10,7
12,9
12,8
l.'l.O
14,9
17,2
17,1
19,4
19,2
124
123
2,1
2,0
4,i
•t,l
6,2
6,2
8,3
8,2
10,3
10,2
13,4
12,3
14„'>
14,4
16,5
16,4
18,6
18,4
4,1
6,1
8,1
10,2
12,2
14,2
16,3
18,3
146
2,4
4,9
7,3
9,7
12,2
14,6
17,0
19,5
21,9
141
2,4
4,7
7,0
9,4
11,8
14,1
16,4
18,8
21,2
136
2,3
4,5
6,8
9,1
11,3
13,6
15,9
18,1
20,4
131
2,2
8,7
10,9
13,1
15,3
17,5
19,6
126
2,1
4,2
6,3
8,4
10,5
13,6
14,7
16,8
18,9
121
10,1
12,1
14,1
16,1
18,2
84=
2(30
A MA]S^UAL OF TOPOGEAPUIC METHODS.
Taulk XXXVI. — Logarithmic sines, cosines, tangents, and cottingenls — Contiuued.
[Extractu<Uro:n Gauss' Logarithmic anil Trigouometric Tables.]
121
120
119
2,0
2,0
2,0
4,(1
4,0
4,0
(i,0
0,0
6,0
8,1
8,0
7,9
10,1
10,0
9,9
12,1
12,0
11,9
14,1
14,0
13,9
1li,l
16,0
15,9
1H,2
18,0
17,8
20,2
20,0
19,8
4o,;i
40,0
39,7
60,5
G0,0
59,5
80,7
80,0
79,3
100,8
100,0
99,2
117
110
115
2,0
1,9
1,9
a,9
3,9
3,8
5,8
6'8
5,8
V,8
7,7
7,7
9,8
9,7
9,6
11,7
11,6
11,5
13,6
13,5
13,4
lo,B
15,5
15,3
IV, (i
17,4
17,2.
19,5
19,3
19,2
39,0
38,7
38,3
i)8,b
58,0
57,5
V8,0
77,3
76,7
9V,o
96,7
95,8
lis
112
111
1
1,9
1,9
1,8
2
3,8
3,7
3,7
3
5,6
5,6
5,6
4
7,5
7,5
7,4
.■i
9,4
9,3
9,2
(i
11,3
11,2
11,1
V
13,2
13,1
13,0
8
15,1
14,9
14,8
9
17,0
16,8
16,6
10
18,8
18,7
18,5
20
37,7
.37,8
37,0
30
56,5
56,0
55,5
40
75,3
74,7
74,0
60
94,2
93,3
92,5
109
108
107
1,8
1,8
1,8
3,6
3,6
3,6
5,4
5,4
5,4
7,3.
7,2
7,1
9,1
9,0
8,9
10,9
10,8
10,7
12,7
12,6
12,5
14,5
14,4
14,3
16,4
16,2
16,0
18,2
18,0
17,8
36,3
36,0
35,7
54,5
54,0
53,5
72,7
72,0
71,3
90,8
90,0
89,2
118
2,0
15,7
17,7
19,7
39,3
114
1,9
9,5
11,4
13,3
15,2
17,1
19,0
38,0
57,0
76,0
95,0
110
1,8
3,7
5,5
7,3
9,2
11,0
12,8
14,7
16,5
18,3
36,7
55,0
73,3
91,7
106
1,8
3,5
5,3
10,6
12,4
14,1
15,9
17,7
35,3
53,0
70,7
LOGARITHMS OF OIRCULAE FUNCTIONS.
261
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued.
[Extracted froniGanss' Logarithmic aiul Trigonometric Tables.]
1. L. Tang.
I 999
9.09 101
9.09 202
9. 09 304,
9. 09 405
9. 09 506
9.09 606
9. 09 707
9.09 807
9. 09 907
0. 10 000
9. 10 106
9. 10 20.5
9. 10 304
9.10 402
9. 10 501
9.10 599
9. 10 697
9.10 795
9. 10 893
9. 10 990
9.11 087
9. 11 184
9.11 281
9. 11 377
9. 11 474
9. H 570
9. 11 666
9.11 761
9.11 857
9.11 953
S. 12 047
9. 12 142
9. 12 236
9. 12 331
9. 12 425
9. 12 519
9. 12 012
9.12 706
9. 12 799
9.12 892
9. 12 985
9.13 078
9.13 171
9. 13 263
9. 13 355
9. 13 447
9.13 539
9.13 630
9. 13 722
9. 13 813
9. 13 904
9.13 994
9. 14 085
9. 14 175
9. 14 266
9. 14 856
92
91
9. 08 914
9. 09 019
9.09 123
9.09 227
9. 09 330
n. 09 434
9. 09 537
9.09 640
9. 09 742
9.09 845
9. 09 947
9.10 049
9.10 150
9.10 253
9. 10 353
9.10 J54
9.10 5.55
9. 10 056
9. 10 756
9.10 850
9.10 956
9.11 O.iO
9.11 155
9. 11 254
9.11 353
9.11 452
9.11 551
9. 11 G49
9. 11 747
9. 11 845
9. 11 943
9. 12 040
9. 12 138
9. 12 235
9. 12 332
9. 12 428
9. 12 625
9. 12 621
9. 12 717
9. 12 813
9. 12 909
9. 13 004
9. 13 099
9.13 194
9. 13 289
9.13 384
9. 13 478
9. 13 573
9. 13 667
9. 13 761
9. 13 854
9. 13 948
9. 14 041
9. 14 134
9. 14 227
9. 14 320
9. 14 412
9. 14 504
9. 14 597
9. 14 688
9. 14 780
0.91 080
0. 90 981
0.90 877
0. 90 773
0.90 670
0.90 053
0. 89 951
0. 89 850
0. 89 748
9. 99 675
9. 99 674
9. 99 672
9. 99 670
9. 99 669
9.99 667
9. 99 666
9. 99 664
9. 99 663
9.99 661
9.99 659
9.99 658
9. 99 656
9.99 655
9.99 653
0.89 244
0.1
144
9.99 651
9. 99 650
9.99 64S
9. 99 647
9, 99 645
0.69 044
0. 88 944
0. 88 845
0. 88 746
0. 88 647
9.99 643
9. 99 642
9.99 640
9. 99 638
9.99 637
0.83 548
0. 88 449
0.88 351
0. 83 253
0. 88 155
0. 88 057 I
0.87 960
0. 87 862
0. 87 765
0. 87 068 I
0. 87 572
0. 87 475
0. 87 379
0.87 283
0. 87 187
0.87 U9l
0.86 I
0. 86 901
0.86 80G
0.86 711
0.86 016
0.86 522
0. 86 427
0. 86 333
0. 86 239
0.86 146
0.86 052
0. 85 959
0.85 866
0. 85 773
0.85 680
0.1
0. 85 496
0.85 403
0. 85 312
9. 99 635
9. 99 633
9.99 632
9. 99 630
9. 99 629
9.99 627
9. 99 625
9.99 624
9. 99 622
9. 99 620
9. 99 618 I
9. 99 617
9.99 615
9. 99 613
9.99 r '
9.99 610 1
9. 99 608
9. 99 607
9. 99 605
9. 99 603 I
9799 601 1 15
9.!
I 600
9. 99 586
9. 99 584
9. 99 582
9.99 581
9. 99 579
9. 99 577
9. 99 575
10.1
104
103
102
1,8
1,7
1,7
1,7
3,5
3,5
3,4
3,4
5,2
5,3
5,3
5,1
V,0
6,9
6,9
0,8
K,K
8,7
8,6
8,5
10,5
10,4
10,3
10,2
12,3
13,1
12,0
11,9
14,0
13,9
13,7
13,0
15,8
15,6
15,4
15,3
17,5
17,3
17,3
17,0
35,0
34,7
34,3
34,0
52,5
53,0
51,5
51,0
70,0
69,3
68,7
68,0
8V,b
86,7
85,8
85,0
101
100
99
98
1,V
1,7
1,6
1,6
3,4
3,3
3,3
3,3
5,0
5,0
5,0
4,9
6,7
6,7
6,6
6,5
8,4
8,3
8,2
8,2
10,1
10,0
9,9
9,8
11,8
11,7
11,6
11,4
13, b
13,3
13,2
13,1
15,2
15,0
14,8
14,7
16,8
16,7
16,5
16,3
3H,V
33,3
33,0
32,7
bO,b
50,0
49,5
49,0
BV,3
■66,7
66,0
65,3
84,2
83,3
83,5
81,7
97
96
95
94
1,6
1,6
1,6
1,6
3,2
3,2
3,2
3,1
4,8
4,8
. 4,8
4,7
6,5
6,4
6,3
6,3
8,1
8,0
7,9
7,8
9,7
9,6
9,5
9,4
11,3
11,2
11,1
11,0
13,9
12,8
12,7
12,5
14,6
14,4
14,2
14,1
16,2
16,0
15,8
15,7
33,3
32,0
31,7
31,3
48,b
48,0
47,5
47,0
64,7
64,0
63,3
62,7
80,8
80,0
79,2
78,3
OS
92
91
90
1,6
1,5
1,5
1,5
3,1
3,1
3,0
3,0
4,6
4,6
4,6
4,5
6,2
6,1
6,1
6,0
7,8
7,7
7,6
7,5
9,3
9,2
9,1
9,0
10,8
10,7
10,6
10,5
12,4
13,3
12,1
12,0
14,0
13,8
, 13,6
13,5
ib,b
15,3
15,2
15,0
31,0
30,7
30,3
30,0
46,5
46,0
45,5
45,0
62,0
61,3
60,7
60,0
7V,6
76,7
75,8
75,0
83=
262
A MANUAL OF TOPOaKAPHIC METHODS.
Table XXXVI. — Logarithmic shies, cosines, tangents, and cotangents — Contiuned.
[Extracted from Gauss' Logaritlimic and Trigonometvic. Tables.]
9. 14 356
9.U 445
9. 14 535
9. 14 624
9. 14 714
9. 14 8U3
9. 14 891
9. 14 980
9. 15 069
9. 15 157
9. 15 245
9. 15 333
9. 15 421
9.15 508
9. 15 596
9.16 116
9. 16 203
9. 16 289
9. 16 374
9. 16 460
9. 16 545
9. 16 631
9. 16 716
9. 16 801
9. 16 886
9. 16 970 I
9. 17 055 1
9. 17 139
9. 17 223
9. 17 307
6. 17 391
9. 17 474
9.17 ,558
9. 17 641
9. 17 973
9. 18 055
9. 18 137
9. 18 220
9. 18 302
9. 18 383 !
9. 18 465 i
9. 18 547 {
9.18 628
9.18 709
9.18 790
9.18 871
9. 18 952
9. 19 033
9.19 113
9.19 193
9. 19 273
9. 19 353
9.19 433
9. 14 780
9. 14 872
9. 14 963
9. 15 054
9.15 145
9. 15 236
9. 15 327
9.15 417
9. 15 508
9. 15 598
9. 17 965
9.18 051
9.18 136
9. 18 221
9. 18 306
9.18 391
9. 18 475
9.18 560
9. 18 644
9.18 728
9. 18 812
9. 18 896
9. 18 979
9. 19 063
9. 19 146
9.19 229
9.19 312
9.19 395
9. 19 478
9. 19 561
9.19 643
9. 19 725
9.19 807
9. 19 889
9. 19 971
0. 85 220
0.85 128
0.85 037
0.84 946
0.84 855
0.84 764
0.84 673
0.S4 583
0. 84 492
0.84 402
0.84 312
0.84 223
0. 84 133
0.84 044
0. 83 954
0. 83 865
0. 83 776
0.83 688
0.83 599
0.83 511
0.83 423
0.83 335
0. 83 247
0.83 159
0.83 072
0. 82 984
0.82 897
0.82 810
0. 82 723
0. 82 637
0.82 550
0. 82 464
0.82 378
0. 82 292
0.82 201;
0. 82 120
0.82 035
0.81 949
Q.81 864
0.81 779
0.81 694
0.81 609
0.81 525
0. 81 440
0. 81 356 I
0. 81 272 I
0. 81 188
0. 81 104
0.81 021
0. 80 937
9.99 572
9.99 570
9.99 568
9. 99 566
9.99 565
9.99 563
9.99 561
9.99 559
9.99 557
9. 90 556
9.99 554
9.99 5.52
9.99 550
9. 99 548
9. 99 546
9.99 545
9. 99 543
9.99 541
9.99 528
9.99 526
9.99 524
9.99 522
9.99 520
9. 99 518
9. 99 517
9.99 515
9.99 513
9.99 511
9.99 509
9.99 507
9.99 505
9.99 503
9.99 501
9.99 499
9.99 497
9.99 495
9.99 494
9.99 492
9.99 490
9.99 488
9. 99 486
9.99 484
9.99 482
9.99 480
9.99 478
9. 99 476
9.99 474
9. 99 472
9.99 470
9.99 468
9. 99 466
9.99 464
9. 99 462
L. Tang.
92
91
90
1,5
1,5
1,5
3,1
3,0
3,0
4,6
4,6
4,5
• 6'1
6,1
6,0
7/7
7,6
7,5
9,2
9,1
9,0
10,7
10,6
10,5
12,3
12,1
12,0
13,8
13,6
13,5
15,3
15,2
15,0
30,7
30,3
30,0
46,0
45,5
45,0
61,3
60,7
60,0
76,7
75,8
75,0
S9
88
8J
1,5
1,5
1,4
3,0
2,9
2,9
4,4
4,4
4,4
5,9
5,8
7,4
7,3
7,2
8,9
8,8
8,7
10,4
10,3
10,2
11,7
.11,6
13,4
13,2
13,0
14,8
14,7
14,5
29,3
29,0
44,0
43,5
59,3
58,7
58,0
V4,2
73,3
72,5
86
85
84
1,4
1,4
1,4
2,8
2,8
4,3
4,2
4,2
0,1
5,7
5,6
'1,'i
7,1
7,0
8,b
8,5
«8,4
10,0
9,9
9,8
ll,b
11,3
11,2
12,9
12,8
12,6
14,3
14,2
14,0
28,7
28,3
28,0
43,0
42,5
42,0
57,3
56,7
56,0
71,7
70,8
70,0
■S»
82
81
1,4
1,4
1,4
2,7
2,7
4,2
4,1
4,0
5,5
6,5
5,1
6,9
6,8
6,8
8,3
8,2
8,1
9,6
9,4
11,1
10,9
10,8
12,4
12,3
12,2
13,8
13,7
13,5
27,7
27,3
27,0
41,5
41,0
40,5
55,3
54,7
54,0
69,2
68,3
67,5
81^
LOGAEITHMS OF CIRCULAR FUNCTIONS.
263
Table XXXVI. — Loganthmic
[Extracted ftom Gai
sines, cosines, tangents, and cotangents — Continued,
iss' Logaritlunic and Trigonometric Tables.]
9.19 433
9. 19 613
9.19 592
9. 19 672
9. 19 751
9.19 830
9.19 909
9. 19 988
9. 20 067
9.20 145
9.20 223
9. 20 302
9.20 380
9.20 458
9. 20 535
9.20 768
9. 20 846
9^20 922^
9.20 999
9. 21 076
9.21 153
9.21 229
9.21 306
9.21 382
9.21 468
9.21 534
9.21 610
9^21_685^
9.21 761
9.21 836
9.21 912
9. 21 987
9. 22 002
9. 22 137
9. 22 211
9. 22 286
9.22 361
9. 22 435
9. 22 509
9, 22 583
9. 22 657
9.22 731
9.22 805
9.22 952
9.23 025
9.23 098
9.23 171
9. 23 244
9.23 317
9.23 390
9. 23 463
9.23 535
9.23 607
9.23 679
9.23 752
9.23 823
9. 23 895
9. 23 967
9. 19 971
9. 20 053
9. 20 134
9.20 216
9.20 297
9.20 378
9.20 469
9. 20 540
9. 20 021
9. 20 701
9. 22 747
9.22 824
9.22 901
9.22 977
9.23 054
9.23 130
9.23 206
9.23 283
9. 23 359
9. 23 435
9. 23 510
6.23 586
9.23 661
9.23 737
9. 23 812
9.23 887
9. 23 962
9.24 037
9.24 112
9.24 186
9. 24 261
9.24 335
9. 24 410
9. 24 484
9. 24 558
9. 24 632
0. 79 947
0. 79 866
0.79 784
0.79 703
0. 79 622
0. 79 541
0.79 460
0. 79 379
0. 79 299
0. 79 218
0.79 138
0.79 058
0. 78 978
0. 78 739
0. 78 659
0.78 580
0. 78 501
0. 78 422
0. 78 343
0.78 264
0.78 186
0.78 107
0.78 029
0. 77 951
0. 77 873
0.77 795
0.77 717
9. 99 462
9. 99 460
9.99 458
9.99 456
9. 99 454
9.99 442
9. 99 440
9.99 438
9.99 436
9. 99 434
9, 99 432
9.99 429
9. 99 427
9.99 425
9. 99 423
9.99 421
9.99 419
9. 99 417
9.99 415
9.99 413
9.99 411
9.99 409
9. 99 407
9.99 404
9. 99 402
9.99 396
9. 99 394
9. 99 392
0. 76 113
0. 76 038
0.75 963
0. 75 888
0. 75 814
0. 75 739 I
0.75 665
0.75 590
0.75 516
0.75 442
0.751
L. Tang.
9. 99 390
9. 99 388
9. 99 385
9.99 383
9. 99 381
9. 99 379
9. 99 377
9. 99 375
9. 99 372
9. 99 370
9.99 368
9.99 366
9. 99 364
9.99 363
9. 99 359
9. 99 357
9. 99 355
9. 99 353
9. 99 351
9. 99 348
9. 99 346
9.99 344
9. 99 342
9. 99 340
9. 99 337
9. 99 335
80
79
78
1,3
1,3
1,3
2,7
2,6
2,6
4,0
4,0
3,9
5,3
5,3
5,2
6,7
6,6
6,5
8,0
7,9
7,8
9,3
9,2
9,1
10,7
10,5
10,4
12,0
11,8
11,7
13,3
13,2
13,0
26,7
26,3
26,0
40,0
39,5
39,0
53,3
52,7
52,0
66,7
65,8
65,0
76
75
74
1,3
1,2
1,2
2,5
2,5
2,5
3,8
3,8
3,7
5,1
5,0
4,9
6,3
6,2
6,2
7,6
7,5
7,4
8,9
8,8
8,6
10,1
10,0
9,9
11,4
11,2
11,1
12,7
12,5
12,3
25,3
35,0
24,7
38,0
37,5
37,0
50,7
50,0
49,3
63,3
62,5
61,7
72
71
S
1,2
1,2
0,0
0,1
3,6
3,6
0,2
4,8
4,7
0,2
6,0
5,9
0,2
7,2
7,1
0,3
8,4
8,3
0,4
9,6
9,5
0,4
10,8
10,6
0,4
12,0
11,8
0,5
24,0
23,7
1,0
36,0
35,5
1,5
48,0
47,3
2,0
60,0
59,2
2,5
3
79
3
78
13,2
39,5
65,8
13,0
39,0
65,0
12,5
37,5
62,5
12,8
38,5
64,3
13,3
37,0
61,7
9,7
11,0
13,2
24,3
80°
264
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXVI. — Logaritnmic sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
10°
9. 23 967
9.24 039
9. 24 110
9.24 181
9.24 253
9. 24 324
9.24 395
9. 24 466
9.24 536
9. 24 607
9.25 098
9.25 168
9. 25 237
9.25 307
9.25 721
9. 25 790
9. 25 858
9.25 927
9. 25 995
9. 26 063
9. -6 131
9.26 199
9. 26 267
9.26 335
9. 26 403
9. 26 470
9. 26 538
9. 26 605
9. 26 672
9. 26 739
9. 26 806
9. 26 873
9. 26 940
9.27 207
9. 27 073
9.27 140
9. 27 206
9. 27 273
9. 27 339
9. 27 405
9. 27 471
9. 27 537
9. 27 602
9. 27 668
9. 27 734
9. 27 799
9. 27 864
9. 27 930
9. 27 995
9. 24 632
9. 24 706
9. 24 779
9. 24 853
9. 24 926
I. 25 000
'.25 073
9.25 365
9.25 437
9.25 510
9. 25 582
9.25 655
9.25 727
9. 25 799
9. 25 871
9. 25 943
9. 26 015
9. 26 086
9.26 158
9. 26 229
9. 26 301
9. 20 372
9.20 443
9. 26 514
9. 26 585
9.26 655
9. 26 726
9. 26 797
9. 26 867
9. 26 937
9.27 008
9. 27 078
9.27 148
9.27 218
9. 27 288
9.27 357
9. 27 427
9. 27 496
9. 27 566
9. 27 635
9.27 704
9.28 254
9.28 323
9. 28 391
9. 28 459
9. 28 527
9. 28 595
9.28 662
9. 28 730
9.28 798
9.28 865
0. 74 635
0. 74 563
0. 74 490
0.74 418
0. 74 345
0. 74 273
0. 74 201
0. 74 129
0. 74 057
0. 73 985
0.73 914
0.73 842
0. 73 771
0.73 699
0. 73 628
0. 73 657
0. 73 486
0. 73 415
0. 73 345
0 73 274
0. 73 203
0.73 133
0. 73 063
0. 72 992
0. 72 922
0. '
I 852
0.72
0.72 712
0. 72 643
0. 72 573
0. 72 504
0. 72 434
0. 72 365
0.72 296
0. 72 227
0.72T5¥
0. 72 089
0. 72 020
0.7] 951
0. 71 883
0. 71 814
0. 71 746
0. 71 677
0. 71 609
0. 71 541
L. Tang.
9.99 331
9. 99 328
9. 99 326
9. 99 324
9. 99 322
9.99 319
9.99 317
9. 99 315
9. 99 301
9. 99 299
9.99 297
9. 99 294
9. 99 292
9.99 290
9. 99 2S8
9.99 285
9.99 283
9.99 281
9.99 270
9. 99 274
9. 99 271
9.99 269
9. 99 267
9. 99 264
9. 99 202
9. 99 260
9. 99 257
9. 99 219
9. 99 217
9. 99 214
9. 99 200
9. 99 197
9. 99 195
74
73
1,2
1,2
2,5
2,4
3,7
3,6
4,9
4,9
6,2
0,1
7,4
7,3
8,6
8,5
9,9
9,7
11,1
11,0
12,3
12,2
24,7
24,3
37,0
36,5
49,3
48,7
61,7
60,8
71
1,2
70
1,2
2,4
2,3
3'6
3,5
4,7
4,7
5,9
5'8
7,1
7,0
8,3
8,2
9,5
9,3
10,6
10,5
11,8
11,7
23,7
23,3
35,5
35,0
47,3
46,7
59,2
58,3
08
67
1/1
1,1
2,3
2,2
3,4
3,4
4,5
4,5
5,7
5,6
6,8
6,7
7,9
7,8
9,1
8,9
10,2
10,0
11,3
11,2
22,7
22,3
34,0
33,5
45,3
44,7
56,7
55,8
9,0
10,8
12,0
24,0
30,0
48,0
00,0
3,4
4,6
5,8
6,9
8,0
9,2
10,4
11,5
33,0
34,5
46,0
E.7,5
66
1,1
2,2
3,3
4,4
5,5
6,6
9,9
11,0
22,0
33,0
44,0
53,0
12,3 12,2 12,0
.37,0 36,5 36,0
61,7 i 60,8 60,0
3
71
3
JO
3
69
11,8
35,5
59,2
11,7
35,0
58,3
11,5
34,5
57,5
11,3
34,0
56,7
79°
LOGAEITHMS OF CmCULAR FUNCTIONS.
265
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents-
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
11°
9.28 060
9.28 125
9. 28 190 I
9.28 254
9.28 319
9 28 705
9.28 769
9.28 833
9.28 896
9.28 960
9.29 024
9.29 087
9.29 150
9.29 214
9.29 277
9.29 340
9. 29 403
9.29 466
9.29 .529
9.29 591
9.29 054
9.29 716
9,29 779
9.29 841
9.29 903
9.29 966
9.30 028
9.30 090
9. 30 151
9. 30 213
9.30 887
9.30 947
9.31 008
9.31 068
9.31 129
9.31 i89
9.31 250
9.31 310
9.31 370
9. 31 430
i). 31 490
9.31 549
9.31 609
9.31 069
9.31 728
9:31 788
9.28 384
9.28 448 i
9.28 512
9.28 577
9.28 641 I
9.28 865
9. 28 933
9.29 000
9.29 067
9.29 134
9.29 201
9.29 268
9.29 335
9.29 402
9. 29 468
9.29 535
9.29 601
9.29 668
9.29 734
9.29 800
9. 39 932
9.29 998
9.30 064
9.30 130
9.30 195
9.30 261
9.30 326
9.30 391
9. 30 457
9.30 522
9.30 587
9.30 652
9.30 717
9.30 782
9. 30 846
9.30 911
9.30 975
9.31 040
9.31 104
9.31 168
9.31 233
9.31 297
9.31 361
9. 31 425
9.31 489^
9.31 552
9.31 616
9.31 679
9.31 743
9. 31 806
9.31 870
9.31 933
9.31 996
9.32 059
9. 32 436
9.32 498
9. 32 561
9.32 623
9.32 685
9. 32 747
L. Cotg.
L. Cotg.
0.71 135
0.71 067
0.71 000
0.70 933
0, 70 866
0.70 799
0.70 732
0.70 005
0.70 598
0. 70 532
0. 70 465
0. 70 399
0.70 332
0.70 266
0.70 200
0.70 134
0.70 068
0.70 002
0.69 936
0.69 870
0. 69^80"5~l
0. 09 739 I
0. 69 674
9.99 190
9.99 187
9.99 185
9.99 170
9.99 167
9.99 165
9.99 162
9.99 160
9.99 157
9.99 155
9.99 152
9.99 150
9. 99 147
9. 99 145
9.99 142
9.99 140
0. 69 413
0.69 348
0, 69 283
0. 69 218
0.68 767
0.68 703
0.68 639
0^68 2J)7
0. 68 194
JUi7 941_
0.67 878
0. 67 815
0. 67 7.52 I
0. 67 689
_a W 627^
0. 67 564
0. 67 502 1
0. 67 439
0.67 37
0. 07 315
9.99 112
9.99 109
9.99 106
9.99 104
9.99 101
9.99 099
9.09 096
9. 99 093
9.99 091
9.99 088
9.99 086
9.99 083
9. 99 062
9.99 059
9.99 056
9.99 054
9.99 051
9.99 048
9.99 046
9.99 043
9. 99 040
65
Gi
1/1
1,1
2,2
2,1
3,2
3,2
4,3
4,3
5,4
5,3
6,5
0,4
7,6
7,5
8,7
8,5
9,8
9,6
10,8
10,7
21,7
21,3
32,5
32,0
43,3
42,7
54,2
53,3
62
61
1,0
1,0
2,1
2,0
3,1
3,0
4,1
4,1
5,2
5,1
6,2
6,1
7,2
7,1
8,3
8,1
9,3
9,2
10,3
10,2
2C,7
20,3
31,0
30,5
41,3
40,7
51,7
50,8
59
1,0
3
0,0
2,0
0,1
3,0
0,2
3,9
0,2
4,8
0,2
5,9
a 0,3
6,9
0,4
7,9
0,4
8,8
0,4
9,8
0,5
19,7
1,0
29,5
1,5
39,3
2,0
49,2
2,5
10,7
32,0
53,3
11,0
33,0
56,0
10,5
31,5
52,5
1,0
2,1
3,2
4,2
6^3
7,4
8,4
9,4
10,5
21,0
31,5
42,0
52,5
10,0
20,0
30,0
40,0
50,0
10,8
32,5
54,2
78^
266
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXyi.—Loijayithmic
[Extractocl fnim Giii
incs, cosines, tangents, and cotangents — Continued.
as' Logarithmic and Trigouomotric Tables.]
9.31 788
9.31 847
9.31 907
9.31 9CC
9.32 202
9.32 2G1
9.32 319
9.32 437
9.32 49.5
9.32 553
9.32 S44
9.32 902
9.32 960
9.33 018
9.33 075
9.33 133
9.33 190
9.33 248
9.33 305
9.33 362
9.33 420
9.33 477
9.33 761
9.33 818
9.33 874
9.33 831
9.33 987
9.34 043
•55
9.34 100
9.34 156
9.34 212
9.34 268
9.34 324
9.34 380
9.34 436
9.34 491
9.34 547
9.34 602
9.34 058
9.34 713
9.34 769
9.34 824
9.34 879
9.34 934
9.34 989
9.35 044
9.32 933
9.32 995
9.33 057
9.33 119
9.33 180
9.33 242
9.33 303
"9.33 365
9.33 426
9.33 487
9.33 670
9.33 731
0.33 792
9.33 853
9.33 913
9.33 974
9.34 034
9.34 095
9.34 155
9Ji4 215
9.34 276
9.34 336
9.34 396
9.34 456
9.34 516
9.34 576
9.34 635
9.34 695
9.34 755
9.34 814
9.34 874
9.34 933
9.34 992
9.35 051
9.35 111
9.35 170
9.35 229
9.35 288
9.35 347
9.35 405
9.35 464"
9.35 523
9.35 581
9.35 640
9.35 698
9.35 757
9.35 815
9.35 873
9.35 931
9.35 989
L. Cotg.
L. Cotg
0. 67 253
0.67 190
0.67 128
0.67 067
0.67 005
0.66 943
0.66 881
0.66 820
0.66 758
0.66 697
0. 66 635
0.66 574
0.66 513
0.66 452
0.66 391
0.66 330
0.66 269
0.66 208
0.66 147
0. 66 q87_
0.66 026
0.65 966
0.65 905
0.65 845
0.65 785
L. Cos.
9.99 040
9. 99 038
9.99 035
9.99 032
9.99 030
9.99 027
9.99 024
9.99 022
9.99 019
9.99 016
9.99 013
9.99 Oil
9.99 008
9.99 006
9.99 002
9.98 983
9.98 980
9.98 978
9.98 975
0.65 724
0.65 664
0.65 604
0.65 544
0.65 484
0.65 424
0.65 365
0.65 305
0.65 245
0.65 ISO
0.65 126
0.65 067
0.65 008
0.64 949
0. 64 889
0. 64 830
0.64 771
0.64 712
0.64 653
0.64 595
0.64 536
0.64 477
0.64 419
0.64 360
0.64 302
0.64 243
0.64 185
0.64 127
0.64 069
0.64 Oil
0.63 953
0.63 895
0.63 837
0.03 779
0.63 721
0.63.664
9.98 953
9.98 950
9.98 947
9.98 916
9.98 913
9.98 910
C3
62
1,0
1,0
2,1
2,0
3,2
3,1
4,2
4,1
5,2
5,2
6,8
6,2
7,4
7,2
8,4
8,3
9,4
9,3
10,5
10,3
21,0
20,7
31,5
31,0
42,0
41,3
52,5
51,7
60
59
1,0
1,0
2,0
2,0
3,0
8,0
4,0
3,9
5,0
4,9
6,0
5,9
7,0
6,9
8,0
7,9
9,0
8,8
10,0
9,8
20,0
19,7
30,0
29,5
40,0
39'3
50,0
49'2
57
56
1,0
0,9
1,9
1,9
2,8
2,8
3,8
3,7
4'8
4,7
5,7
5,6
6,6
6,5
7,6
7,5
8,6
8,4
9,5
9,3
19,0
18,7
28,5
28,0
38,0
37,3
47,5
46,7
10,3
31,0
51,7
3
S 1
59
oS
9,8
29,5
49,2
9,7
29,0
48,3
1,0
2,0
3,0
4,1
5,1
6,1
7,1
8,1
9,2
10,2
20,3
30'5
40,7
50,8
3,9
4;8
5,8
6,8
7,7
8,7
9,7
19'3
29'0
38'7
48'3
0,9
1,8
2,8
3,7
4,6
5,5
6,4
7,3
8,2
9,2
18,3
27,5
36,7
45,8
10,0
30,0
50,0
9,5
28'5
47'5
77c
LOGAEITHMS OF CIECULAR FUIJGTIONS.
267
Table XXXVI — Loganthmio sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gaa33' Logaritlunio and Trigonometric Tables.]
13°
9. 35 209
9. 35 263
9. 35 318
9. 35 373
9. 35 427
9. 35 481
9.35 536
9. 35 590
9. 35 644
9. 35 698
9.35 752
9.35 806
9. 35 860
9. 35 914
9. 35 968
9. 36 022
9. 36 075
9.36 129
9.36 182
9. 36 236
9. 36 289
9. 36 342
9. 36 395
9. 36 449
9. 37 081
9. 37 133
9, 37 185
9. 37 237
9. 37 289
9. 37 341
9. 37 393
9. 37 445
9. 37 497
9. 37 549
9. 37 600
9. 37 652
9. 37 703
9. 37 755
9. 37 806
9.37 858
9. 37 909
9. 37 960
9. 38 Oil
9. 38 062
L. Tang.
9. 36 336
9. 36 394
9. 36 453
9,36 509
9. 36 566
9. 36 624
9. 36 681
9. 36 738
9. 36 795
9.36 852
9. 36 909
9. 36 966
9. 37 023
9. 37 080
9. 37 137
9. 37 193
9.37 250
9. 37 306
9. 37 363
9. 37 419
9. 37 476
9. 37 533
9. 37 588
9. 37 644
9. 37 700
9. 37 756
9.37 813
9. 37 868
9. 37 924
9. 38 918
9. 38 972
9. 39 027
9. 39 082
9. 39 136
9. 39 190
9. 39 245
9. 39 299
9. 39 353
9. 39 407
9. 39 461
9. 39 515
9. 39 569
9. 39 623
9. 39 677
L. Cotg.
0. 63 664
0. 63 606
0. 63 548
0. 63 491
0. 33 434
0.
376
0. 63 319
0. 63 262
0.63 205
0.63 148
0.63 091
0. 63 034
0. 62 977
0. 02 920
0. 62 863
0. 62 807
0.62 750
0. 62 694
0. 62 637
0. 62 581
0. 63 524
0. 63 468
0. 62 413
0. 63 356
0. 63 300
0.63 244
0.62 188
0.63 133
5. 62 076
0. 62 020
0. 61 965
0.61 909
0. 61 853
0. 61 798
0. 61 743
0. 61 687
0. 61 632
0. 61 577
0. 61 521
0. 61 466
0.61 411
0. 61 356
0. 61 301
0. 61 246
0. 61 192
0. 61 137
0. 61 082
0. 61 028
0.60 973
0. 00 918
0. 60 864
0. 60 810
0. 60 755
0. 60 701
0. 60 647
0.60 593
0. 60 539
0. 60 485
0.60 431
0. 60 377
0.60 323
9. 98 858
9.93 855
9. 98 852
9. 98 843
9. 98 840
9. 98 837
9. 98 834
9. 98 831
9. 98 828
9. 98 825
9. 98 822
9. 98 819
9. 98 816
9. 98 813
9. 98 810
9. 98 807
9. 98 804
9.98 801
9.98 798
9. 98 795
9. 98 792
9. 98 789
9. 98 786
9. 98 783
9, 98 780
9. 98 777
9. 98 774
9. 98 771
9. 98 768
9. 98 765
9. 98 763
9. 98 759
9. 98 756
9.98 753
9. 98 750
9. 98 746
9. 98 743
9. 98 740
9. 98 737
9. 98 734
9. 98 731
9. 98 728
9. 98 725
9. 98 722
9. 98 719
9. 98 715
9.98 712
9. 08 709
9. 98 706
9. 98 703
9. 98 700
S7
36
1,0
0,9
1,9
1,9
2,8
2,8
3,8
3,7
4,8
4,7
5,7
5,6
6,6
6,5
7,6
7,5
8,6
8,4
9,5
9,3
19,0
18,7
28,6
28,0
33,0
37,3
47,5
46,7
Si
53
0,9
0,9
1,8
1,8
2,7
2,6
3,6
3,5
4,5
4,4
5,4
5,3
6,3
6,2
7,2
7,1
, 8,1
8,0
9,0
8,8
18,0
17,7
27,0
26,5
36,0
35,3
45,0
44,2
51
4
3
0,8
0,1
0,0
1,7
0,1
0,1
2,6
0,2
0,2
3,4
0,3
0,2
4,2
0,3
0,2
5,1
0,4
0,3
6,0
0,5
0,4
6,8
0,5
0,4
7,6
0,6
0,4
8,5
0,7
0,5
17,0
1,3
1,0 '
35,5
2,0
1,5
34,0
2,7
2,0 1
42,5
3,3
2,5 I
3^
S6
3
53
9,3
28,0
46,7
9,2
27,5
45,8
2,8
3,7
4,6
5,5
6,4
7,3
8,2
9,2
18,3
27,5
36,7
45,8
6,9
7,8
8,7
17,3
26,0
34,7
43,3
4
4
3
53
34
58
6,9
6,8
9,7
20,6
20,2
29,0
34,4
33,8
48,3
48,1
47,2
—
9,0
27,0
45,0
76=
268
A MANUAL OJ? TOPOGEAPHIO METHODS.
Table XXXVI. — Logarithmic sines, cosinen, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.)
51
53
0,9
0,9
1,8
1,8
3,7
2,6
3,6
3,5
4,5
4,4
5,4
5,3
6,3
8,2
7,2
7,1
8,1
8,0
9,0
8,8
18,0
17,7
27,0
20,5
36,0
35,3
45,0
44,2
51
50
0,8
0,8
1,7
1/7
2,6
2,5
3,4
3,3
4,2
4,2
5,1
5,0
6,0
5,8
6,8
6,7
7,6
7,5
8,5
8,3
17,0
16,7
25,5
25,0
34,0
33,3
42,5
41,7
48
0,8
47
0,8
i
0,1
1,6
1,6
0,1
2,4
214
0,2
3,2
3,1
0,3
4,0
3,9
0,3
4,8
4,V
0,4
5,6
5,5
0,5
6,4
6,3
0,5
7,2
7,0
0,6
H,0
7,8
0,7
16,0
15,7
1,3
24,11
i;:),5
2,0
32,U
■■UrI
'■^,7
4U,ll
:jo,2
3,3
3,5
4,3
5,2
6,1
6,9
7,8
8,7
17,3
26,0
34,7
43,3
1,6
2,4
3,3
4/1
4,9
5,7
6,5
7,4
8,2
16,3
24,5
32,7
40,8
3
0,0
0,1
0,2
0,2
0,2
0,3
0,4
0,4
0,4
0,5
1,0
1,5
2,0
2,5
4
4
4
1 ^*
.53
52
6,8
6,6
6,5
20,2
19,9
19,5
33,8
33,1
32,5
! 47,2
46,4
45,5
3
3
3
54
53
52
i 9,0
! 27,0
45,0
8,8
26,5
44,2
8,7
26,0
43,3
6,4
19,1
31,9
44,6
8,5
25,5
42,5
75=
LOGARITHMS OF OlECULAK ru:NGTIO:tfS.
269
Table XXXVI. — LogarUhniie sines, cosines, tangentSj and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
15°
9. 41 300
9. 41 347
9.41 394
9.41 441
9.41 488
9.41 635
9.41 582
9.41 628
9.41 675
9.41 722
9.41 768
9.41 815
9.41 861
9.41 908
9.41 954
9.42 001
9.42 047
9.42 093
9.42 140
9.42 186
9.42 232
9.42 278
9.42 324
9.42 370
9. 42 416
9. 42 461
9.42 507
9.42 553
9.42 599
9.42 644
9.42 690
9. 42 735
9. 42 781
9. 42 826
9. 42 872
9. 42 917
9.42 962
9. 43 008
9.43 053
9. 43 098
9.43 143
9.43 188
9. 43 233
9.43 278
9.43 323
9.43 367
9.43 412
9.43 457
9.43 502
9.43 546
9.43 591
9.43 635
9.43 680
9.43 724
9.43 769
9.43 813
9.43 857
9.43 901
9.43 946
9.43 990
9. 44 034
9.43 U57
9. 43 108
9.43 1.58
9.43 208
9.43 258
9.43 308
9. 43 358
9. 43 408
9.43 458
9.43 508
9.43 658
9.43 607
9.43 657
9.43 707
9.43 756
9.44 787
9. 44 836
9. 44 884
9. 44 933
9. 44 981
9. 45 029
9.45 078
9.45 126
9. 45 174
9.45 222
9.45 271
9.45 319
9.45 367
9.45 415
9.45 463
9. 45 511
9.45 559
9.45 gu6
9.45 654
9.45 702
9.45 IW
L. Cotg.
0. 57 195
0. 57 144
0. 57 094
0. 57 043
0.56 993
0. 56 943
0. 56 892
0. 56 842
0. 56 792
0. 56 742
0. 56 692
0. 56 042
0. 56 592
0.50 542
0. 56 492
0. .56 442
0. 56 393
0. 56 343
0. 56 293
0. 56 244
0. 56 194
0.56 145
0.56 095
0. 56 040
0.55 947
0. 55 898
0.55 849
0. .55 799
0^5^750
6. 55 701
0. 55 652
0.;
603
0. 55 456
0. 55 408
0. 55 359
0. 55 310
0. 55 164
0.55 116
0. 55 067
0. 55 019
0. 54 971
0. 54 922
0. 54 874
0. 54 826
0. 54 778
0. 54 729
0.54 681
0. 54 633
0. 54 585
0. 54 537
0. 54 489
0. 54 441
0.54 394
0.54 346
0. 54 298
0. 54 250
9. 98 494
9. 9,S 491
9.98 488
9. 98 484
9. 98 481
9. 98 477
9. 98 474
9. 98 471
9.98 467
9. 98 464
9. 98 373
9. 98 370
9. 98 366
9. f 8 363
9. 98 359
9. 98 356
9. 98 352
9. 98 349
9. 98 345
9. 98 342
9.98 338
9. 98 334
9.98 331
9. 98 327
9. 98 324
9. 98 320
9.98 317
9. 98 313
9. 98 309
9. 98 306
9.98 302
9. 98 299
9.98 295
9.98 291
9.98 288 I
L. Tang. L. Sin. I d.
740
51
50
0,8
0,8
1,7
1,7
2,6
2,5
3,4
3,3
4,2
4,2
5,1
5,0
6,0
5,8
6,8
6,7
7,6
7,5
8,5
8,3
17,0
16,7
25,5
25,0
34,0
- 33,3
42,5
41,7
48
0,8
47
0,8
1,6
1,6
2,4
2,4
3,2
3,1
4,0
3,9
4,8
4,7
5,6
5,5
6,4
6,3
7,2
7,0
8,0
7,8
16,0
15,7
24,0
23,5
32j0
31,3
40,0
39,2
45
0,8
44
0,7
4
0,1
1,5
1,5
0,1
2,2
2'2
0,2
3,0
2,9
0,3
3,8
3,7
0,3
4,5
4,4
0,4
5,2
5,1
0,5
6,0
5,9
0,5
6,8
6,6
0,6
7,5
7,3
0,7
15,0
14,7
1,3
22,5
22,0
2,0
30,0
29,3
2,7
37,5
36,7
3,3
16,3
24,5
32,7
40,8
7,7
15,3
23,0
30,7
38,3
3
0,0
0,1
0,2
0,2
0,2
0,3
0,4
4
1
4
50
49
48
6,2
18,8
31,2
43;8
6,1
18,4
30,6
42,9
6,0
18,0
30,0
42,0
51
50
49
8,5
1 25,5
42,5
8,3
25,0
41,7
8,2
24,5
40,8
5,9
17,0
29,4
41,1
8,0
24,0
40,0
270
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — C'ontiuueil.
IBxtracted from Gauss' Logaritlmiic ami Trigonometric Tables.]
16°
48
47
0,8
0,8
1,6
1,6
2,4
2,4
3,2
3,1
4,0
3,9
4,8
4,7
5,6
5,5
6,4
'6,3
7,2
7,0
8,0
7,8
16,0
15,7
24,0
23,5
32,0
31,3
40,0
39,2
45
44
0,8
0,7
1,5
1,5
2,2
2,2
3,0
2,9
3,8
3,7
4,5
4,4
5,2
5,1
6,0
5,9
6,8
6,6
7,5
7,3
15,0
14,7
22,5
22,0
30,0
29,3
37,5
36,7
42
41
4
0,7
0,7
0,1
1,4
1,4
o,u
2,1
2,0
0,2
2,8
2,7
0,3
3,5
3,4
0,3
4,2
4,1
0,4
4,9
4,8
0,5
5,6
5,5
0,5
6,3
0,2
0,6
7,0
6,8
0,7
14,0
13,7
1,3
21,0
20,5
2,0
28,0
27,3
2,7
35,0
34,2
0,8
1,5
2,3
3,1
3,8
4,6
5,4
6,1
6,9
7,7
15,3
23,0
30,7
0,7
1,4
2,2
2,9
3,6
4,3
5,0
5,7
6,4
7,2
14,3
21,5
28,7
35,8
4
4
48
47
6,0
18,0
30,0
42,0
5,9
17,6
29,4
41,1
.•5
48
3
47
8,0
24,0
40,0
7,8
23,5
39,2
5,6
16,9
28,1
39,4
7,7 7,5
23,0 22,5
38,3 37,5
73°
LOGAEITHMS OF CIECULAR FUNCTIONS.
271
Table liXXYl,~~Loganthmic sinesy cosineSj tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometiic Tablea.]
17°
9. 46 670
9. 46 717
9.46 758
9.46 800
9. 46 841
9. 46 882
9. 46 923
9. 46 964
9.47 045
9. 47 086
9. 47 127
9.47 168
9. 47 209
9.47 249
9. 47 290
9. 47 330
9. 47 371
9. 47 411
9. 47 432
9. 47 492
9.47 533
_9^47_57£
9. 47 6i3
9. 47 654
9.47 694
9.47 814
9. 47 854
9. 47 894
9. 47 934
9^ 47 974
9.48 014
9. 48 054
9. 48 094
9.48 133
9. 48 173
9.48 213
9.48 252
9. 48 292
9.48 332
9. 48 371
9. 48 411
9. 43 450
9. 48 490
9.48 529
9.48 803
9. 48 842
9. 48 881
9. 48 920
9. 48 959
1.48 534
1.48 579
i. 48 624
i. 48 669
I. 48 714
I. 48 759
I. 48 804
:. 48 849
1.48 894
1.48 939
1.48 984
1.49 029
I. 49 073
1.49 118
1.49 163
'. 49 207
I. 49 252
'.49 296
.49 341
'. 49 385
'. 49 430
1. 49 474
'. 49 519
.49 563
. 49 607
9. 49 652
9. 49 696
9.49 740
9. 49 784
9. 49 828
i. 50 180
I. 50 223
1. 50 267
'. 50 311
. 50 355
. 50 398
. 50 442
. 50 485
I. 50 529
1.50 572
1. 50 616
I. 50 659
I. 50 703
I. 50 746
I. 50 789
I. 50 833
I. 50 876
I. 50 919
1. 50 962
1.51 005
'. 51 048
I. 51 092
.51 135
0.51 466
0.51 421
0. 51 376
0. 51 331
0. 51 286
9, 98 056
9. 98 052
9. 98 048
9. 98 044
0.51 241
0. 51 196
0.51 151
0. 51 106
0. 51 061
0. 51 016
0.50 971
0. 50 927
0. 50 882
_0.J0_837
0. 50 793
0. 50 748
0. 50 704
0. 50 659
0.50 615
9. 98 036
9.98 032
9.98 029
9.98 025^
9. 98 021
9. 98 017
9. 98 013 :
9. 98 009
9. 98 005
0.50 570
0. 50 526
0. 50 481
0. 50 437
0. 50 393
0. 50 348
0. 50 304
0. 50 260
0. 50 216
0. 50 172
0.50 128
0. 50 084
0.50 040
0.49 996
0.49 952
0.49 908
0.49 804
0.49 820
0.49 777
0. 49 733
0.49 689
0.49 645
0. 49 602
0. 49 558
0.49 515
0. 49 471
0. 49 428
0.49 384
0. 49 341
0. 49 297
0. 49 254
0.49 211
0.49 167
0.49 124
0. 49 081
6.49 038
0. 48 995
0.48 952
0. 48 908
0. 48 865
0. 48 822
9.98 001 I
9. 97 997 1
9. 97 993 i
9. 97 989
9. 97 986
9. 97 982
9.97 978
9. 97 974 ■
9.97
70
9. 97 966_
9. 97 962
9. 97 958
9. 97 954
9. 37 950
9.97 946
9.97 942
9. 97 938
9.97 934 !
9. 97 930
9. 97 926 '
9. 97 910
9. 97 906
9. 97 902
9. 97 898
9. 97 894
9. 97 890 I
9. 97 886
9. 97 861
9. 97 857
9. 97 8.53
9. 97 849
9. 97 845
9. 97 841
9. 97 837
9. 97 833
9. 97 829
9. 97 825
L. Tang. I L. Sin.
45
44
0,8
0,7
1,5
1,5
2,2
2,2
3,0
2,9
3,8
3,7
4,5
4,4
5,2
5,1
5,9
6,8
6,6
7,5
7,8
15,0
14,7
22,5
22,0
30,0
29,3
37,5
36,7
42
41
0,7
0,7
1,4
1,4
2,1
2,0
2,8
2,7
3,5
3,4
4,2
4,1
4,9
4,8
5,6
5,5
6,3
6,2
7,0
6,8
14,0
13,7
21,0
20,5
28,0
27,3
3b,0
34,2
39
5
4
0,6
0,1
0,1
1,3
0,2
0,1
2,0
0,2
0,2
2,6
0,3
0,3
3,2
0,4
0,3
3,9
0,5
0,4
4,6
0,6
0,5
5,2
0,7
0,5
5,8
0,8
0,6
6,5
0,8
0,7
13,0
1,7
1,3
19,5
2,5
2,0
26,0
3,3
2,7 !
32,5
4,2
3,3
5
4
43
45
4,3
5,6
12,9
16,9
21,5
28,1
30,1
39,4
38,7
-
0,7
1,4
2,2
2,9
3,6
4'3
5,0
5,7
6,4
7,2
14,3
21,5
28,7
35,8
4,0
4,7
5,3
6,0
6,7
13,3
20,0
26,7
33,3
0,0 !
0,1 I
0,2
0,2
0,2
0,3
0,4
0,4
0,4
0,5
1,0
1,5
2,0
2,5
5,5
16,5
27,5
4
3
3
4S
45
44
5,4
7,5
7,3
16,1
22,5
26,9
37,5
36,7
37,6
■
P
P.
72^
272
A MANUAL OF TOrOGKAPHIO METHODS.
Table XXXVl.^ Lof/anthmic !<'ntes, cosines, lanfjentH, and cotangents — Contiuued,
[Extraotod Iroui Gauss" Loi^iirithmic ami Trigonometric Tables.]
18°
9.48 998
9.49 037
9. 49 07(i
9.49 115
9.49 153
9. 49 192
9.49 231
9.49 269
9.49 308
9.49 347
9. 49 385
9. 49 424
9. 49 462
9. 49 500
9.49 539
9.49 577
9.49 615
9.49 654
9.49 692
9.49 7J0
9. 49 76S
9. 49 806
9.49 844
9. 49 882
9. 49 920
9.49 958
9.49 996
9.50 034
9. 50 072
9.50 110
9. 50 148
9. 50 185
9. 50 223
9.50 261
9. 50 298
9. 50 336
9. .50 374
9.50 411
9. 50 449
9.50 480
9. 50 523
9.50 561
9. 50 598
9. 50 635
9. 50 673
9.50 710
9.50 747
9.50 784
9.50 821
9.50 8.58
9. 50 890
9. 50 933
9.50 970
9.51 007
9. 51 043
9.51 080
9.51 117
9.51 154
9.51 191
9.51 227
9. 51 264
L. Tang.
9. 51 606
9,51 648
9.51 691
9.51 734
9. 51 776
9.51 819
9.51 861
9.51 903
9.51 946
9.51 988
9. 52 031
9. 52 073
9.52 115
9.52 157
9.^2 200
9.52 242
9. 52 284
9.52 326
9. 52 368
9^52 410
9. 52 452
9. 52 494
9. 52 536
9.52 578
9. 52 620
9. 52 661
9. 52 703
9. 52 745
9.52 787
9.52 829
9.53 078
9.53 120
9.53 161
9.53 202
9.53 244
9.53 492
9.53 533
9.53 574
9.53 615
9. 53 656
9. 53 697
L. Cotg.
L. Cotg.
0. 48 822
0, 48 779
0. 48 736
0.48 694
0. 48 651
0.48 008
0.48 505
0.48 ,522
0.48 480
0.48 437
0. 48 394
0. 48 352
0.48 309
0. 48 266
0.48 224
0.48 181
0.48 139
0.48 097
0.48 0.54
0.48 012
0.47 069
0.47 927
U.47 885
0.47 343
0.47 800
0. 47 716
0.47 674
0. 47 632
0. 47 590
0. 47 548
0. 47 506
0.47 464
0.47 422
0.47 380
0.47 339
0.47 297
0.47 255
0.47 213
0.47 171
0. 47 130 j
0, 47 088
0. 47 047
0. 47 005
0. 46 963
0. 46 922
0. 46 880
0. 46 839
0. 46 798
0. 46 7.56
0.46 715
0. 46 673
0. 46 632
0. 46 591
0. 46 550 !
9. 97 821
9.97 817
9.97 812
9.97 767
9.97 763
9.97 759
9.97 7.54
9.97 750
9. 97 746
9.97 742
9. 97 738
9.97 734
9.97 729
9.97 725
9^7 731
9. 97 717
9. 97 713
9.97 708
9. 97 704
9.97 700
9. 97 696
9. 97 691
9. 97 687
9.97 683
9.97 679
9.97 674
9.97 670
9.97 666
9.97 662
9. 97 657
9.97 653
9.97 649
9.97 645
9.97 640
9.97 636
9.97 632
9.97 628
9.97 623
9.97 619
9.97 615
9.97 610
9. 97 606
9 97 602
9.97 .597
9.97 593
1.97 589
0.46 508 I
0. 46 467
0. 46 426
0. 46 385
0. 46 344 I
0. 46 303 i
L. Tang. I L. Sin.
43
0,7
42
0,7
1,4
1,4
2,2
2,1
2,9
2,8
3,6
3,5
4,3
4,2
5,0
4,9
. 5,7
5,6
6,4
6,3
7,2
7,0
14,3
14,0
21,5
21,0
28,7
28,0
35,8
35,0
.S9
88
0,6
0,6
1,3
1,3
2,0
1,9
2,6
2,5
3,2
3,2
3,9
3,8
4,0
4,4
5,2
5,1
5,8
5,7
6,5
6,3
13,0
12,7
19,5
19,0
26,0
25,3
32,5
31,7
30
5
0,6
0,1
1,2
0,2
1,8
0,2
2,4
0,3
3,0
0!4
3,6
0,5
4,2
0,6
4,8
.0,7
5,4
0,8
6,0
0,8
12,0
1,7
18,0
2,5
24,0
3,3
30,0
4,2
5
.5
43
43
4,3 ;
4,2
12,9 ;
12,0
21,5 1
21,0
30,1
29,4
38,7
37,8
0,7
1,4
2,0
2,7
3,4
4,1
4,8
5,5
6,2
6,8
13,7
20,5
27,3
34,2
4,1
12,3
20,5
28,7
36,9
5,4
5,2
5,1
16,1
15,8
15,4
26'9
26,2
25,6
37,6
36,8 ;
35,9
71^
LOGAEITHMS OF CIECULAR FUifCTIONS.
273
Table XXXVI. — Logarithmic sines, cosines, iangentSj and cotangents — Contiaiued.
[Extracted from Gauss' Logaritbmic and Trigonometric Tables.]
19°
9. 51 264
9.51 301
9.51 338
9.51 374
9.51 411
9.51 447
9.51 484
9.51 520
9.51 557
9. 51 593
9.'51 629
9.51 666
9. 51 702
9.51 738
9.51 774
9.51 811
9.51 847
9.51 883
9.51 919
9.51 955
9. 52 527
9. 52 563
9. 52 598
9. 52 634
9. 52 669
9.52 705
9. 52 740
9.52 775
9. 52 811
9. 52 846
9. 58 021
9. 53 056
9.53 092
9.53 126
9.53 161
9.53 196
9. 53 231
9.53 266
9. 53 301
9.53 336
9. 53 370
9. 53 405
d. c. ! L. Cotg.
9. 53 697
9. 53 738
9.53 779
9.53 820
9.53 861
9. 53 902
9.53 943
9. 53 981
9. 54 025
9. 51 0C5
9.54 106
9.54 147
9. .54 187
9. 54 228
9.54 269
9.54 309
9. .54 350
9.54 390
9.54 431
9. 54 471
9.54 915
9.51 955
9.54 995
9. 55 035
9. 55 075
9.55 115
9.55 155
9.55 195
9. 55 235
9. 55 275
9.55 315
9.55 355
9.55 395
9. 55 434
9.-55 474
9. 55 514
9. 55 554
9.55 593
9. 55 633
9.55 673
9. 55 712
9.55 752
9.55 791
9.55 831
9.55 870
L. Cotg.
0.46 303
0.46 262
0.46 221
0.46 180
0.46 139
0.46 098
0. 46 057
0.46 016
0.45 975
0. 45 935
0.45 894
0.45 853
0.45 813
0.45 010
0. 45 569
0.45 .529
0.45 488
0.45 448
0. 45 407
0.45 367
0.45 327
0.45 286
0.45 246
0,45 206
0. 45 165
0.45 125
0.45 085
0.45 045
0.45 005
0.44 965
0.44 925
0.44 885
0.44 845
0. 44 805
0.44 765
0.44 725
0.44 685
0.44 645
0.44 6115
0.44 566
0. 44 526
0. 44 486
0. 44 446
0,44 407
0. 44 367
0.44 327
0.44 288
0.44 248
0. 44 209
0.44 169
0.44 130
0.44 090
0,44 051
0.44 Oil
0.43 972
0.43 933
0. 43 893
d. c. L. Tang.
9.97 435
9.97 430
9.97 426
9. 97 421
9. 97 417
9. 97 412
9. 97 408
9. 97 403
9. 97 399
9.97 394
9. 97 390
9.97 385
9.97 .381
9.97 376
9. 97 372
9.97 367
9.97 363
9. 97 358
9.97 353
9.97 349
9.97 340
9.97 335
9.97 331
9.97 326
9.97 322
9.97 317
9.97 312
9.97 308
9.97 303
9. 97 299
41
40
0,7
0,7
1,4
1,3
2,0
2,0
2,7
2,7
3,4
3,3
4,1
4,0
4,8
4,7
5,5
5,3
6,2
6,0
6,8
6,7
13,7
13,3
20,5
20,0
27,3
26,7
34,2
33,3
37
36
0,6
0,6
1,3
1,2
1,8
1,8
2,5
2,4
3,1
3,0
3,7
3,6
4,3
4,2
4,9
4,8
5'6
5,4
6,2
6,0
12,3
12,0
18,5
18,0
24'?
24,0
30,8
30,0
34
5
0,6
0,1
1,1
0,2
1,7
0,2
2,3
0,3
2,8
0,4
3,4
0,5
4,0
0,6
4,5
0,7
5,1
0,8
5,7
0,8
11,3
1,7
17,0
2,5
22,7
28,3
4,2
5
5
41
40
4,1
4,0
12,3
12,0
20,5
20,0
28,7
28,0
36,9
36,0
41
40
5,1
5,0
15,4
15,0
25,6
25,0
35,9
35,0
6,5
13,0
19,5
26,0
32,5
5,2
5,8
11,7
17,5
23'3
29,2
11,7
19,5
27,3
35,1
4,9
14,6
24,4
34,1
MON XXII-
-18
70=
274
A MAXUAL OF TOPOGRAPHIC METHODS.
Taiu.k WWl.—Lundrithmic shies, roslnes, taHi/euts, mid mlaiii/cnts—Contiuned.
tExtractfil from lliiuss' Logarithmic iim\ Trigouomctric Tables.]
20°
L. Sin.
rt.
L. Tang.
(I.C.
L. Cotg.
L. Cos.
a.
P.
P.
0
9. 53 405
9. 56 107
0. 43 893
9. 97 299
5
5
4
5
4
5
5
4
60
40
39
0,6
1,3
2,e
38
0,6
I
9.53 440
35
. 9. 56 146
0. 43 854
9. 97 294
59
1,3
2,0
•2,7
1,3
1,9
2,5
3,2
3,8
9.53 475
35
9. 56 185
0.43 815
9. 97 289
58
3
9. 53 509
9.56 224
0.43 776
9. 97 285
2,6.
3,2
3,9
4
9. 53 544
9. 53 578
34
9. 56 264
39
0. 43 736
9.97 276
5
6
3,3
4,0
5
9. 56 303
0. 43 697
55
6
9. 53 613
35
9.56 342
0.43 658
9. 97 271
54
7
4,7
4,6
4,4
9.53 647
34
9. 50 381
0. 43 619
9. 97 266
53
8
5,3
5,2
. 5,1
S
9.53 682
35
9.56 420
0.43 580
9. 97 262
52
9
6,0
5,8
5,7
9
9, 53 716
34
35
9. 56 459
9.56 498
39
0.43 541
5
10
20
6,7
13,3
6,5
13,0
6,3
12,7
10
e. 43 502
9. 97 252
50
11
9 53 785
34
9. 56 537
0.-43 463
9. 97 248
49
30
20,0
19,5
19,0
12
9. 53 819
34
9.56 576
0.43 424
9. 97 243
5
4
48
40
26,7
13
9.53 854
35
9. 50 615
0.43 385
9. 97 238
47
50
14
9.53 888
0. 53 922
34
34
9. 56 654
39
0. 43 346
9.97 234
46
1
37
0,6
35
0,6
34
0,0
15
9.56 693
0. 43 307
9. 97 229
45
16
9.53 957
35
9. 5B 732
0.43 268
9.97 224
4
5
5
4
44
2
1,2
1,2
1,1
17
9.53 991
34
9. 56 771
0. 43 229
9. 97 220
43
3
1,8
1,8
1,7
18
9. 54 025
34
9. 56 ,S10
0.43 190
9.97 215
42
4
2,5
2,3
2,3
19
9. 54 059
34
34
9. 56 849
38
0.43 151
■9.97 210
9. 97 206
41
5
6
8,1
3,7
2,9
3,5
2,8
3,4
20
9.56 887
0.43 113
40
9.54 127
34
9.56 926
39
0. 43 074
9. 97 201
5
4
5
39
7
f'?
*,1
4,0
22
9.54 161
34
9. .56 965
39
0.43 035
9. 97 196
38
8
4,9
4,7
23
9.54 195
34
9. 57 004
0. 42 996
9.97 192
37
24
9. 54 229
34
9.57 042
39
39
38
39
0. 42 958
9.97 187
36
20
30
40
50
12,3
18,5
24,7
30,8
11,7
17,5
23,3 .
29,2
11,3
17,0
22,7
28,3
26
28
9. .54 203
9. 54 297
9. 54 331
9. 54 365
34
34
34
34
9. 57 081
9. 57 120
9.57 158
9.57 197
0.42 919
0.42 880
0. 42 842
0. 42 803
9.97 182
9.97 178
9. 97 173
9.97 168
4
5
5
35
34
33
32
29
9. 54 399
34
34
9. 57 235
9.57 274
39
0.42 765
0.42 726
9.97 163
9. 97" 1.59
4
1
33
0,6
5
0,1
i
0,1
30
9.54 433
SO
31
9.54 466
33
9. 57 312
0. 42 688
9. 97 154
^
29
32
34
9.57 351
0. 42 649
9.97 149
4
5
5
28
33
9.54 534
34
9.57 389
0. 42 611
9. 97 145
27
34
9. 54 567
33
34
9.57 428
38
0. 42 572
9.97 140
26
5
6
7
8
9
10
20
30
2,8
3,3
3,8
4,4
5,0
5,5
11,0
16,5
0,4
0,5
0,6
0,7
0,8
0,8
1,7
2,5
0,4
0,5
0,5
0,6
0,7
1,3
2,0
35
9.54 6U1
9. 57 466
0.42 534
9.97 135
25
36
9.54 635
34
9. 57 504
0.42 496
9.97 130
4
37
0. 54 668
33
9. 57 543
0. 42 457
9.97 126
38
9.54 702
34
9. 57 581
0.42 419
9.97 121
^
22
39
9. 54 735
33
34
9.57 619
39
0.42 381
9.97 116
5
40
9. 54 769
9.57 658
0. 42 342
9.97 111
ao
41
9. 54 802
33
9.57 696
0. 42 304
40
22,0
3,3
2,7
42
9.54 836
34
9. 57 734
0. 42 266
9.97 102
18
50
27,5
4,2
3,3
33
9.57 772
0.42 228
5
5
4
5
5
44
9.54 903
34
33
9. .57 810
38
39
0.42 190
9.97 092
16
5
5
^
45
9.54 930
9.57 849
0.42 151
9.97 087
15
46
9.54 969
33
9.57 887
0.42 113
9.97 083
14
47
9. 55 003
34
9.57 925
0.42 075
9. 97 078
13
3,9
3,8
48
9.55 036
33
9. 57 963
0.42 037
9. 97 073
12
12,0
11,7
11,4
49
9.55 069
33
33
9. 58 001
9. 58 039
38
0.41 999
5
4
5
5
3
4
5
•20,0
28,0
19,5
27,3
19,0
26,6
50
9.55 102
0.41 961
9. 97 063
10
51
9.55 136
34
9. 58 077
0.41 923
9.97 059
36,0
35,1
34,2
9. 55 169
33
9.58 115
38
0.4L 885
9. 97 054
8
53
9.55 202
33
9.58 153
0.41 847
9.97 049
7
5
4
4
54
9. 55 235
33
33
9.58 191
38
0.41 809
9. 97 044
5
4
6
37.
39
3S
55
9. 55 263
9. 58 229
0.41 771
9. 97 039
5
56
9. 55 301
33
9. 58 267
38
0.41 733
9.97 035
4
0
3,7
4,9
4,8
57
9.55 334
33
9.58 304
0.41 696
9.97 030
3
11,1
14,6
14,2
58
9.55 367
33
9. 58 342
0.41 658
18,5
24,4
23,8
59
9. 55 400
33
33
9.58 380
9. 58 418
38
0.41 620
5
4
5
25,9
33,3
34,1
33,2
60
9. 55 433
0.41 582
9. 97 015
0
1. Cos.
(1.
L. Cotg.
a.c.
L. Tang.
L. Sin.
d.
'
P
.P.
69<^
LOGARITHMS OF CIEOITLAR FUNCTIONS.
275
Table XXXVI. — Lorjarithmio sines, cosines, tangents, and cotanrjents-
[Estracted from Gauss' Logaritlimic .aud Trigonometric Tables.]
21°
L. Sin.
d.
L. Tang.
d. c.
L. Cotg.
L, Cos.
0
9.55 433
9. 58 418
0. 41 582
9. 97 015
1
9. 55 466
9. 58 455
0.41 545
9. 97 010
9. 55 499
9. 58 493
0. 41 507
9. 97 005
3
9. 55 532
9. 58 531
0. 41 469
9. 97 001
4
9. .55 564
33
9. 58 569
37
0.41 431
•9. 96 996
5
9.55 597
9.58 606
0.41 394
9. 96 991
6
9. 55 630
9. .58 644
0.41 356
9. 90 980
7
9.55 663
9. 58 081
0. 41 319
9. 90 981
8
9.55 695
9.58 719
0.41 281
9. 90 976
9
9. 55 728
33
9. 58 757
37
0. 41 243
9. 96 971
10
9.55 761
9. 58 794
• 0. 41 206
9. 96 966
11
9.55 793
9. 58 832
0.41 168
9. 96 962
12
9. 55 826
9. 58 809
0.41 131
9. 96 957
13
9.55 858
9. 58 907
0.41 093
9. 96 952
14
9.55 891
32
9. 58 944
37
0.41 056
9. 90 947
15
9. 55 923
9. 58 981
0.41 019
9. 96 942
16
9. 55 956
9. 59 019
0.40 981
9. 96 937
17
9. 55 988
9. 59 056
0. 40 944
9. 96 932
18
■ 9.56 021
9. 59 094
0.40 906
9. 96 927
19
20
9. 56 053
32
9.59 131
37
0.40 869
9. 96 922
9.56 085
9. .59 168
0. 40 832
9. 90 917
21
9.56 118
9.59 205
0. 40 795
9, 90 912
22
9.56 1.50
9. .59 243
0.40 757
9. 90 907
23
9. 56 182
9.50 280
0. 40 720
9. 96 903
24
9.56 215
9.56 247
32
9. 59 317
37
0.40 683
9. 96 898
25
9. 59 354
0. 40 646
9. 96 893
26
9.56 279
9.59 391
0. 40 009
9. 90 888
27
9.56 311
9. 59 429
0. 40 571
9. 96 883
28
9.60 343
9. 59 466
0.40 534
9. 96 878
29
9.66 375
33
9. 59 503
37
0. 40 497
9.96 873
30
9. 56 -408
9.59 540
0. 40 460
9. 90 868
31
9.56 440
9. 59 577
0.40 423
9. 96 863
32
9. 56 472
9. 59 614
0. 40 386
9. 96 858
33
9. 56 504
9. 59 651
0. 40 349
9. 90 853
34
9. 56 630
32
9. 59 688
37
0,40 312
9. 96 848
35
9.56 568
9. 59 725
0. 40 275
9. 96 843
36
9.56 599
9. 59 762
0.40 238
9.96 838
37
9.56 631
9. 69 799
0.40 201
9. 90 833
38
9.56 663
9. 59 835
0. 40 165
9. 96 828
39
9.56 695
32
9. 69 872
:i7
0. 40 128
9. 96 823
10
9. 56 727
9.59 909
0. 40 091
9. 96 818
41
9. 56 759
9. 59 946
0.40 054
9. 96 813
42
9.56 790
9. 59 983
0. 40 017
9.96 808
43
9.56 822
9.60 019
0.39 981
9. 90 803
44
9. 56 854
32
9. 60 056
37
0. 39 944
9. 96 798
45
9. 56 886
9. 60 093
0. 39 907
9. 96 793
46
9.56 917
9. 60 130
0. 39 870
9. 96 788
47
9.56 949
9.60 166
0. 39 834
9. 90 783
48
9. 56 980
9.60 203
0. 39 797
9. 90 778
49
9. 57 012
32
9. 60 24U
36
0. 39 760
9. 90 772
50
9. 57 044
9. 60 276
0. 39 724
9.96 767
51
9. 57 075
9.00 313
0. 39 687
9. 96 762
52
" 9. 57 107
32
9. 60 349
0. 39 651
9.96 757
53
9. 57 138
9. 60 386
0. 39 614
9. 96 762
54
9.57 169
32
9. 60 422
37
0. 39 578
9, 96 747
55
9.57 201
9. 60 459
0.39 541
9. 96 742
56
9.57 232
31
9. 00 495
0. 39 505
9. 96 737
57
9. 57 264
9. 60 532
0. 39 468
9. 96 732
58
9. 57 295
9.60 508
0. 39 432
9. 96 727
59
9. 57 326
31
9. 60 005
30
0. 39 395
9,90 722
9, 90 717
60
9. 57 358
9. 00 041
0. 39 359
L. Cos.
d.
L. Cotg.
d. c.
L. Tang.
L. Sin.
38
0,0
37
0,0
1,3
1,2
1,9
1,8
2,5
2,5
3,2
3,1
3,8
3,7
4,4
4,3
5,1
4,9
6,7
5,0
6,3
0,2
12,7
12,3
19,0
18,5
25,3
24,7
31,7
30,8
33
33
0,6
0,5
1,1
1,1
1,0
1,0
2,8
2,7
3,3
3,2
3,8
3,7
4,4
4,3
5,0
4,8
5,5
5,3
11,0
10,7
10,5
10,0
22,0
21,3
2- ,5
20,7
0
0,1
0,1
0,2
0,2
0,3
0,2
0,4
0,3
0,5
0,4
0,6
0,5
0,7
0,6
0,8
0,7
0,9
0,8
1,0
0,8
2,0
1,7
3,0
2,5
4,0
3,3
5,0
6
»
37
38
3,1
3,8
9,2
11,4
15,4
19,0
21,6
26,6
27,8
34,2
33,9
5
4
36
88
3,6
4,8
10,8
14,2
18,0
23,8
25,2
33,2
32,4
3,0
3,6
4,2
4,8
5,4
6,0
12,0
18,0
24,0
30,0
2,1
2,6
3,1
3,6
4,1
4,6
5,2
10,3
15,6
20,7
25,8
11,1
18,5
26,9
13,9
23,1
32,4
68<:
276
A MANUAL OF TOrOGEAPHIC METHODS.
'1\UJLE XXXVI.— io.'/"»'i'/""'(- xine.f!, cosines, langciits, ami cu'tiiiflCH/.s— Coutiuiicd.
[Extractwl tVmii Gauss' Ldsaritliniii' and Triaiiuomotric Tables.]
22°
LOGAEITHMS OF CIRCULAE FUNCTIONS.
277
Table XXXVI. — Logarithmic sinesj cosines^ tangents, and cotangents — Continued.
[Extracted from Gauss' liOgarithmic and Trigonometric Tables.]
23°
L.Sm.
9.59 188
9. 59 218
9. 59 247
9. 59 277
9. 59 307
9. 59 330
9. 59 366
9. 59 396
9. 59 425
9. 59 455
9. 59 484
9. 59 614
9. 59 543
9. 59 573
9. 59 602
9. 59 632
9. 59 661
9.59 690
9. 59 720
9. 59 749
9. 59 778
9. 59 808
9. 59 837
9. 59 866
9. 59 895
9. 59 924
9. 59 954
9.59 983
9. 60 012
9. 60 041
9. 60 215
9. 60 244
9. 60 273
9. 60 302
9.60 331
9.60 359
9.60 388
9. 60 417
9. 60 446
9.60 474
9. 60 503
9. 60 532
9. CO 561
9. 60 589
9. 60 618
9. 60 646
9. 60 675
9. 60 704
9. 60 732
9. 60 761
9. 60 789
9. 60 818
9. 60 846
9.60 875
9. 60 903
9.60 931
9. 62 785
9. 62 820
9. 62 855
9. 62 890
9. 62 926
9. 62 961
9. 62 996
9.63 031
9. 63 066
9. 63 101
9. 63 135
9. 63 170
9.63 205
9. 63 240
9. 63 275
9. 63 310
9. 63 .345
9.63 379
9. 63 414
9. 63 449
9.63 484
9. 63 519
9. 63 553
9. 63 726
9.63 761
9. 63 796
9. 64 003
9. 64 037
9. 64 072
9. 64 106
9. 64 140
9. 64 175
9. 64 209
9. 64 243
9.64 278
9.64 312
9. 64 346
9. 64 381
9. 64 415
9. 64 449
9. 64 483
9. 64 517
9. 64 552
9. 64 586
9. 64 620
9.64 654
9. 64 688
9. 64 722
9. 6i 756
9. 64 790
9. 64 824
9. 64 858
L. Cotg. a. c.
L. Cotg.
0. 37 215
0.37 180
0. 37 145
0.37 110
0. 37 074
0. 37 039
0. 37 004
0. 36 969
0. 36 934
0. 36 899
0.36 865
0.30 8.30
0.36 795
0. 36 760
0. 36 725
0.36 690
0, ,36 655
0. 36 621
0. 36 586
0.30 551
0. 36 516
0. 36 481
0. 36 447
0.36 412
0. 36 377
0. 36 343
0. 36 308
0. 36 274
0. 36 239
0. 36 204
0. 36 170
0. 36 135
0. 36 101
0. 36 066
0. 36 032
0. 35 997
0.35 963
0. 35 928
0. 35 894
0. 35 860
0. 35 825
0.35 791
0. 35 757
0. 35 722
0.35 688
0.35 654
0.35 619
0. 35 585
0.35 551
0.35 517
0. 35 483
0. 35 448
0. 35 414
0. 35 380
0. 35 346
0. 35 312
0. 35 278
0. 35 244
0. 35 210
0. 35 176
0. 35 142
9. 96 403
9.96 397
9. 96 392
9. 96 387
9. 96 381
9.96 376
9. 96 370
9.96 365
9. 96 360
9. 96 354
9. 96 349
9.96 343
9.90 338
9.96 333
9.96 327^
9.96 322
9. 96 316
9.96 311
9.96 305
9. 96 284
9. 96 278
9.96 273
9.90 207
9. 96 262
9. 96 256
9. 96 251
9. 96 245
9.96 207
9. 96 201
9.96 196
9.96 190
9.96 185
9.96 179
9. 96 174
9. 96 168
9.96 162
9.96 157
9. 96 151
9 96 146
9.96 140
9.96 135
9. 90 129
9.96 123
9.96 lis
9.96 112
9.96 107
9.96 101
9. 96 095
9. 96 090
9. 96 084
9.96 079
9. 96 073
36
0,6
35
0,6
1/2
1,2
1,8
1,8
2,4
2,3
3,0
2,9
3,6
3,5
4,2
4,1
4,8
4,7
5,4
5,2
6,0
5,8
12,0
11,7
18,0
17,5
24,0
23,3
30,0
29,2
30
29
0,5
0,5
1,0
1,0
1,5
1,4
2,0
1,9
2,5
2,4
3,0
2,9
3,5
3,4
4,0
3,9
4,5
4,4
5,0
4,8
10,0
9,7
15,0
14,5
20,0
19,3
25,0
24,2
3,4
4,0
4,5
5,1
5,7
11,3
17,0
22,7
28,3
1,9
2,3
2,8
3,3
3,7
4,2
4,7
9,3
14,0
18,7
23,3
G
6
36
35
3,0
2,9
9,0
8,8
15,0
14,6
21,0
20,4
27,0
26,2
33,0
32,1
8,5
14,2
19,8
25,5
31,2
3,5
3,4
10,b
10,2
IV, b
17,0
24,5
23,8
31,0
30,6
66=
278
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXXVI. — Logarithmic sines, cosines, tatigcnts, and cotanyenis — Contimied.
[Exti-actecl from Gauss' Logaritlimic and Trigonometric Tables.)
24°
9. 60 960
9. 60 988
9. 61 QIC
9.61 045
9. 61 073
9. 61 101
9.61 129
9.61 loS
9.61 186
9.61 214
9. 01 242
9.61 270
9.61 298
9.61 326
9.61 354
9.61 382
9.61 411
9.61 438
9. 61 466
9. 61 494
9. 61 522
9.61 550
9.61 578
9.61 606
9.61 634
9.61 662
9.6] 689
9. 61 717
9. 61 745
9.61 773
9.61 800
9. 61 828
9. 61 856
9.61 883
9. 61 911
9.61 939
9.61 966
9. 61 994
9. 62 021
9. 02 049
9. 62 076
9. 62 104
9. 62 131
9. 62 159
9.62 186
9. 62 214
9. 62 241
9. 62 268
9. 62 296
9. 62 323
9. 62 350
9. 62 377
9. 62 405
9. 62 432
9. 62 459
9. 62 486
9. 62 513
9. 62 541
9. 62 568
9. 62 595
9. 64 858
9. 04 892
9. 64 026
9. 64 960
9. 64 994
9. 65 028
9. 65 062
9.65 197
9. 65 231
9. 65 265
9. 65 299
9. 65 333
9. 65 366
9. 65 400
9. 65 434
9. 63 467
9. 65 501
9. 65 535
9. 65 568
9. 65 602
9. 65 636
9. 65 669
9. 65 703
9. 65 736
9. 65 770
9. 65 803
9. 65 837
9. 65 870
9. 65 904
9. 65 937
9. 65 971
9. 66 004
9. 66 038
9. 66 071
9. 06 104
9. 66 138
9. 66 171
9. 66 204
9-. 66 238
9. 66 271
9.66 304
9. 66 337
9. 66 371
9. 66 404
9. 66 437
9. 66 470
9. 66 503
9. 66 .537
9. 66 570
9. 66 603
9. 66 636
9. 66 669
9. 66 702
9. 66 735
9. 66 768
9. 66 801
. 9. 66 834
9. 66 867
L. Cotg.
0. 35 142
0.35 108
0. 35 074
0. 35 040
0. 35 oon
0. 34 972
0. 34 938
0. 34 904
0. 34 870
0. 34 836
0. 34 803
0.34 769
0. 34 735
0. 34 701
0.34 667
0.34 634
0.34 600
0. 34 566
0. 34 533
0. 34 499
0. 34 465
0. 34 432
0. 34 398
0. 34 364
0. 34 331
0. 34 297
0. 34 264
0. 34 230
0. 34 197
0.34 163
9. 96 073
9. 96 067
9. 96 062
n. 96 056
9. 96 050
9. 96 045
9. 96 039
9. 96 034
9. 96 023
9.96 022
9. 96 017
9.96 Oil
9. 96 005
9. 96 000
9. 95 994
9. 95 988
9. 95 982
9. 95 977
9. 95 971
9. 95 965
9. 95 960 I
9. 95 954
9. 95 948
9. 95 942
9. 96 937
0. 34 130
0. 34 096
0. 34 063
0. 34 029
0.33 996
0.33 962
0.33 929
0.33 896
0.33 802
0. 33 829
9. 95 931
9. 95 925
9. 95 920
9.95 914
9.95 908
9.95 902
9.95 897
9. 95 891
9. 95 885
9. 95 879
0. 33 796
0. 33 762
0. 33 729
0. 33 696
0. 33 663
0.1
629
9. 95 873
9. 95 868
9. 95 862
9. 95 856
9. 95 850
9. 95 844
9. 95 839
9. 95 833
0.33 596
0. 33 563 I
0. 33 463
0. 33 430
0. 33 397
0. 33 364
0.33 331
0. 33 298
0. 33 265
0. 33 232
0. 33 199
0. 33 166
0. 33 133
9. 95 810
9.95 804
9. 95 798
9. 95 792
9. 95 757
9.-95 751
9. 95 745
9, 95 739
9.95 733
9. 95 728
0,6
0,6
1,1
1,1
i,v
1,6
2,3
2,2
2,8
2,8
3,4
3,3
4,0
3,8
4,b
4,4
5,1
0,0
5,V
b,6
11,3
11,0
17,0
16,b
22,7
22,0
28,3
2V,b
29
28
0,5
0,5
1,0
0,9
1,4
1,4
1,9
1,9
2'4
2,3
2,9
2,8
3,4
3,3
3,9-
3,7
4,4
4,2
4,8
4,7
9,7
9,3
14,5
14,0
19,3
18,7
24,2
23,3
G
6
34
S3
2,8
2,8
8,5
8,2
14,2
13,8
19,8
19,2
25,5
24,8
31,2
30,2
0,4
0,9
1;4:
1,8
2,2
2,7
3,2
3,6
4,0
4,5
9,0.
13,5
18,0
22,5
10,2
17,0
23,8
30,6
63"^
LOGARITHMS OF CIRCULAR FUNCTIONS.
279
Tablk XXXVI. — Logarithmic Hnes, cosi^ies, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometrii; Tables.]
950
9. 62 595
9. 62 622
9. 62 649
9. 62 676
9. 62 703
9.62 7TO
9. 62 757
9. 62 784
9.62 811
9. 62 838
9.62 865
9. 62 892
9.62 918
9.62 945
9.62 072
9. 62 999
9. 63 026
9. 63 052
9. 03 079
9. 63 106
9.03 133
9. 63 159
9.63 180
9. 63 213
9. 63 239
9. 63 266
9.63 292
9. 63 319
9.63 345
9. 63 372
9. 63 398
9. 63 425
9. 63 451
9. 63 478
9. 63 304
9. 63 .531
9. 63 557
9.63 583
9. 63 610
9. 63 636
9. 63 662
9. (i3 689
9.63 715
9. 63 741
9.63 767
9. 63 794
9.63 820
9. 63 846
9. 63 872
9. 63 898
9.63 924
9. 63 950
9. 63 976
9. 64 002
9. 64 028
9. 64 054
9. 64 080
9. 64 106
9. 64 132
9. §4 158
9. 64 184
9. 66 867
9. 66 900
9. 66 933
9. 66 966
9. 66 999
9.07 032
9.67 065
9. 67 098
9. 67 131
9. 67 163
9.67 196
9. 67 229
9. 67 262
9. 67 293
9. 67 327
9. 67 360
9. 67 393
9. 67 426
9. 67 458
9. 67 491
9. 67 524
9. 67 556
9.67 589
9.67 622
9. 67 654
9.67 687
9. 67 719
9. 67 752
9. 67 785
9.67 817
9. 67 850
9. 67 882
9. 67 915
9. 67 947
9. 67 980
9. 68 012
9. 68 044
9. 68 077
9.68 109
9. 68 142
9. 68 497
9. 68 529
9. 68 561
9. 68 593
9. 68 626
L. Cotg.
L. Cotg.
0.33 133
0.33 100
0.33 067
0.33 014
0.33 001
0. 32 968
0. 32 935
0. 32 902
0. 32 869
0. 32 837
0. 32 804
0. 32 771
0. 32 738
0. 32 705
0. 32 673
0. 32 640
0. 32 607
0. 32 574
0. 32 542
0. 32 509
0. 32 476 f
0. 32 444
0.32 411
0. 32 378
0. 32 346
0.32 313
0. 32 281
0. 32 248
0. 32 215
0.32 183
0. 32 150
0. 32 118
0. 32 085
0. 32 053
0. 32 020
0. 31 988
0.31 9.56
0.31 923
0.31 891
0.31 858
0.31 826
0. 31 794
0.31 761
0. 31 729
0.31 697
0.31 664
0.31 632
0.31 600
0.31 568
0.31 535
0. 31 503
0. 31 471
0.31 439
0.31 407
0.31 374
0.31 342
0.31 310
0. 31 278
0. 31 246
0.31 214
0. 31 182
9.95 728
9. 95 722
9.95 716
9. 95 710
9. 95 704
9795^8"
9.95 692
9. 95 686
9. 95 680
9. 95 674
9. 95 668
9. 95 663
9.95 657
9.95 65]
9. 95 645
9. 95 639
9.95 633
9.95 627'
9. 95 621
9.95 615
9. 95 603
9. 95 597
9. 95 591
9.95 585
9. 95 679
9. 95 573
9.95 567
9. 95 661
9. 95 555
9. 95 549
9. 95 543
9. 95 537
9. 95 531
9. 95 525
9. 95 519
9. 95 513
9. 95 507
9. 95 500
9. 95 494
9. 95 488
9. 95 482
9. 95 476
9. 95 470
9. 95 464
9.95 4.58
9. 95 453
9. 95 446
9. 95 440
9. 95 434
9. 95 427
9. 95 421
9.95 415
9. 95 409
9.95 403
9. 95 397
9. 95 391
9. 95 384
9. 95 378 I
9. 95 372
9. 95 366
5,0
4,8
5,0
5,3
11,0
10,7
16,b
16,0
22,0
21,3
2V,b
26,7
27
26
0,4
0,4
0,9
0,9
1,4
1,3
1,8
1,7
2,2
2,2
2,7
2,0
3,2
3,0
3,6
3,5
4-0
3,9
4,b
4'3
9,0
8,7
13,5
13,0
18,0
17,3
22,5
21,7
0,1
6
0,1
0,2
0,2
0,4
0,3
0,5
0,4
0,6
0,5
0,7
0,6
0,8
0,7
0,9
0,8
1,0
0,9
1,2
1,0
2,3
2,0
3,5
3,0
^,^
4,0
5,8
5,0
'
G
32
32
2,3
2,7
6,9
8,0
11,4
13,3
16,0
18,7
20,6
24,0
25,1
29,3
29,7
9,9
16,5
23,1
29,7
64^^
280
A MANUAL OF TOrOGEAPHIC METHODS.
Table XXXVI. — Loijariihmic shies, cosi-nes, tmufenis, and cotangents — Contin;ied.
[Extracted I'rom Gauss' Logarithmic and Trigonometric Tables.]
26°
9.64 184
9. 64 210
9. 64 236
9. 64 262
9. 64 288
9. 64 313
9.64 339
9. 64 365
9.C4 391
9. 64 417
9. 64 442 1
9. 64 468
9. 64 494 1
9. 64 519
9. 64 545
9. 64 571
9.64 596
9. 64 622
9. 64 647
9. 64 673
9. 64 698
9. 61 724
9. 64 749
9. 64 775
9. 64 800
9. 64 826
9. 64 851
9. 64 877
9. 64 902
9. 64 927
9. 64 953
9.64 978
9. 65 003
9. 65 029
9. 65 054
9.65 331
9.65 356
9. 65 381
9.65 406
9. 65 431
9.65 456
9. 65 481
9.65 506
9. 65 531
9.65 556
9. 65 580
9. 65 605
9. 65 630
9. 65 655
9.65 680
9. 65 705
9. 68 850
9.68 882
9. 68 914
9.68 946
9. 68 '978
9.69 010
9.09 042
9.69 074
9.69 106
9. 69 138
9.69 170
9.69 202
9.69 234
9.69 266
9. 69 298
9. 09 329
9. 69 361
9. 69 393
9. 69 425
9.70 089
9.70 121
9. 70 152
9.70 184
9.70 215
• 9. 70 247
9.70 278
9. 70 309
9. 70 341
9.70 372
9. 70 404
9. 70 435
9. 70 466
9. 70 498
9. 70 529
L. Cotg.
0. 31 182
0.31 150
0.31 118
0.31 086
0.31 054
0.31 022
0.30 990
0.30 958
0.30 926
0. 30 894
0.30 S62
0.30 830
0. 30 798
0.30 766
0.30 7.34
0.30 702
0.30 671
0. 30 639
0. 30 607
0. 30 575
0. 30 385
0. 30 353
0. 30 321
0. 30 290
0. 30 258
0. 30 226
0. 30 195
0.30 163
0. 30 132
0. 30 100
0. 30 (168
0. 30 037
0. 30 005
0. 29 974
0, 29 942
0.29 911
0. 29 879
0. 29 848
0. 29 816
0. 29 785
0.29 753
0. 29 722
0. 29 691
0. 29 659
0. 29 628
0. 29 596
0.29 565
0. 29 534
0. 29 502
0. 29 471
0. 29 440
0.29 408
0. 29 377
0. 29 346
0. 29 315
0. 29 283
9.95 360
9. 95 360
9.95 354
9.95 348
9.95 341
9.95 335
9.95 329
9.95 323
9.95 317
9.95 310
9.05 304
9.95 298
9. 95 292
9.95 286
9.95 279
9.95 273
9. 95 267
9. 95 261
9.95 254
9. 95 248
9.95 242
9.95 236
9. 95 229
9. 95 223
9. 95 217
9. 95 211
9. 95 204
9. 95 198
9. 95 192
9.95 185
9.95 179
9.95 173
9. 95 167
9. 95 160
9.95 154
9. 95 148
9.95 141
9.95 135
9.95 129
9.95 122
9. 95 lie
9.95 110
9. 95 103
9. 95 097
9.95 090
9. 95 084
9. 95 078
9. 95 071
9.95 065
9.95 059
9. 95 052
9.95 046
9. 95 039
9. 95 033
9.95 027
9. 95 020
9. 95 014
9. 95 007
9.05 001
9 94 995
9. 94 988
d.
«0
6
59
58
57
V
56
6
55
54
53
52
7
51
6
50
6
49
48
6
47
6
46
45
44
43
42
41
6
40
39
V
38
37
36
6
"35
34
6
33
32
31
6
SO
29
28
6
26
6
25
24
6
23
B
22
21
6
2(1
19
V
18
6
17
V
6
16
15
14
13
b
12
7
6
11
10
9
8
7
6
5
6
4
3
2
6
1
V
0
(1.
'
32
1
0,5
2
1,1
3
1,6
4
2,1
5
2,7
6
3,2
7
3,7
8
4,3
9
4,8
1»
5,3
^(1
10,7
30
16,0
40
21,3
i>0
26,7
10,3
15,5
20,7
25,8
20
25
0,4
0,4
0,9
0,8
1,3
1,2
1,7
1,7
2,2
2,1
2,6
2,5
3,0
2,9
8,5
3,3
3,9
3,8
4,3
4,2
8,7
, 8,3
13,0
12,5
17,3
16,7
21,7
20,8
0,8
1,2
1,6
2,0
2,4
2,8
3,2
3,0
4,0
8,0
12,0
16,0
20,0
_
33
31
2,3
2,2
6,9
6,0
11,4
11,1
16,0
15,5
-20,6
19'9
25,1
24,4
29,7
.28,8
2,7
8,0
13,3
18,7
24,0
63°
LOGAEITHMS OF CIECULAE FUNCTIONS.
281
Table XXXVI. — Lofiarithmic sines, cosines, tangents, and cotangents — Continued.
fExtracted from Gauss' Logaritlimic anil Trifcononietric Tables.]
27°
9. 65 705
9. 65 729
9. 65 754
9. 65 779
9. 65 804
9. 65 828
9. 65 853
9. 65 878
9. 65 902
9. 65 927
9.65 952
9. 65 976
9. 66 001
9. 66 025
9. 66 050
■ 9. 66 U75
9. 66 099
9. 66 124
9.66 148
9.66 173
9.66 197
9. 66 221
9.66 246
9. 66 270
9. 66 295
9.66 319
9. 66 343
9. 66 368
9. 66 392
9, 66 416
9. 66 441
9. 66 465
9. 66 489
9.66 513
9.66 537
9.66 562
9. 66 586
9. 66 610
9.66 634
9. 66 658
9.66 I
1 706
9. 66 S03
9. 66 827
9. 66 851
9. 66 875
9. 66 899
9. 66 922
9. 66 946
9.66 970
9. 66 994
9. 67 018
9.70 779
9.70 810
9.70 841
9. 70 873
9. 70 904
9.70 935
9. 70 966
9. 70 997
9.71 028
9.71 059
9.71 090
9.71 121
9.71 153
9.71 493
9. 71 524
9.71 555
9. 71 586
9.71 617
9.71 648
9.71 679
9. 71 709
9. 72 262
9. 72 293
9.72 323
9.72 354
9. 72 384
9. 72 415
9.72 445
9. 72 476
9. 72 506
9. 72 537
9. 72 567
L. Cotg.
L. Cotg.
0. 29 283
0. 29 252
0.29 221
0.29 190
0.29 159
0.29 127
0.29 096
0. 29 065
0. 29 034
0. 29 003
0.28 972
0. 28 941
0.28 910
0.28 879
0.28 847
0.28 816
0. 28 785
0. 28 754
0.28 723
J)^28 692
0. 28 601
0.28 630
0. 28 599
0.28 569
0. 28 538
0.28 507
0. 28 476
0. 28 445
0. 28 414
0. 28 383
0. 28 352
0. 28 321
0. 28 291
0. 28 260
0. 28 229
0.28 198
0.28 167
0. 28 137
0. 28 106
0.28 075
0. 28 045
0. 28 014
0. 27 983
0.27 952
0.27 922
0. 27 891
0. 27 860
0. 27 830
0. 27 707
0.27 677
0. 27 646
0. 27 616
0. 27 585
0. 27 555
0. 27 524
0. 27 494
9. 94 988
9. 94 982
9.94 975
9.94 969
9.94 962
9. 94 956
9.94 949
9.94 943
9. 94 936
9. 94 930
9. 94 923
9. 94 917
9. 94 911
9. 94 904
9. 94 898
9.94 891
9.94 885
9. 94 878
9. 94 871
9.94 865
9.94 858
9. 94 852
9. 94 845
9.94 839
9. 94 832
9.94 826
9. 94 819
9.94 813
9.94 806
9. 94 799
9. 94 793
9. 94 786
9. 94 780
9. 94 773
9. 94 767
9.94 760
9. 94 763
9. 94 747
9. 94 740
9.94 734
9. 94 727
9. 94 720
9. 94 714
9. 94 707
9. 94 700
9. 94 660
9. 94 654
9. 94 647
9. 94 640
9. 94 634
9. 94 627
9. 91 620
9. 94 614
9. 94 607
9. 94 600
9. 94 593
32
31
0,5
0,5
1,1
1,0
1,6
1,6
2,1
2,1
2,7
2,6
3,2
3,1
3,7
3,6
4,3
4,1
4,8
4,6
5,3
5,2
ig,7
10,3
16,0
15,5
21,3
20,7
26,7
25,8
25
24
0,4
0,4
0,8
0,8
1,2
1,2
1,7
1,6
2,1
2,0
2,5
2,4
2,9
2,8
3,3
3,2
3,8
3,6
4,2
4,0
8,3
8,0
12,5
12,0
16,7
16,0
20,8
20,0
10,0
15,0
20,0
25,0
2,3
2,7
3,1
3,4
3,8
7,7
11,5
15,3
19,2
'
G
30
31
2,1
2,6
6,4
7,8
10,7
12,9
15,0
18,1
19,3
23,2
23,6
28,4
27,9
2,5
7,5
12,5
17,5
22,5
27,5
62=
282
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXKri.— Logarithmic sines, cosines, tangents, and coinngents—ContiaueA.
[Extracted from Gauss' Logai-ithmic and Trigonometric Tables.]
S8°
SI
•0,5
30
0,5
1,0
1,0
1,0
1,5
2,1
2,0
2,6
2,5
3,1
3,0
3,6
3,5
4,1
4,0
4,6
4,5
5,2
5,0
10,3
10,0
15,5
15,0
20,7
20,0
25,8
25,0
24
2S
0,4
0,4
0,8
0,8
1,2
1,2
■ 1,6
2,0
1,9
2,4
2,3
2,8
2,7
3,2
3,1
3,6
3,4
4,0
3,8
8,0
7,7-
12,0
11,5
10,0
15,3
20,0
19,2
1,4
1,9
2,4
2,9
3,4
3;9
4,4
4,8
9,7
14,5
19,3
24,2
11,0
14,7
18,3
6
SI
31
2,2
2,6
6,6
7,8
11,1
12,9
15,5
18,1
19,9
23,2
24,4
28,4
28,8
2,5
7,5
12,5
17,5
23,5
27,5
61°
LOGARITHMS OF CIRCULAE FUNCTIONS.
283
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
39°
L. Tang.
9. 68 G71
9. 68 694
9.68 716
9. 68 739
9^68 762
9. 68 784
9. 68 807
9. 68 829
9.68 852
9.68 875
'9. 68 897"
9. 68 920
9. 68 942
9. 08 965
9.68 987
9. egliiir
9. 69 032
9. 69 055
9. 69 077
9. 69 100
9. 69 122
9. 69 345
9. 69 368
9 69 390
9. 69 412
9.69 611
9. 69 633
9. 69 655
9. 74 375
9. 74 405
9. 74 435
9. 74 465
9. 74 494
9. 74 524
9. 74 554
9. 74 583
9. 74 613
9. 74 643
9. 74 969
9. 74 998
9.75 028
9. 75 058
9.75 087
9.75 205
9. 75 235
9. 75 264
9. 75 294
9. 75 323
9. 75 353
9.75 382
9.75 411
9. 75 441
9. 75 470
9.75 500
9. 75 529
9.75 558
-9. 75 588
9.75 617
9. 75 647
9. 75 676
9.75 764
9. 75 793
9. 75 822
9. 75 852
9.75 881
9. 75 910
9. 75 939
9. 75 969
9.75 998
9. 76 027
9. 76 056
L. Cotg.
0.24 736
0. 24 706
0. 24 677
0. 24 647
0. 24 618
0. 24 589
0. 24 559
0. 24 530
0. 24 500
0. 24 471
9.93 934
9.93 927
9. 93 920
9.93 912
9. 93 905
30
0,5
29
0,5
1,0
1,0
1,5
lA
2,0
1,9
2,5
2,4
3,0
2,9
3,5
3,4
4,0
3,9 1
4,5
4,4
5,0
4,8
10,0
9,7
15,0
14,5
20,0
19,3
25,0
24,2
2*2
8
0,4
0,1 '
0,7
0,3
1,1
0,4
1,5
n,5
1,8
0,7
2,2
0,8
2,6
0,9
2,9
1,1
3,3
1,2
3,7
1,3
7,3
2,7
11,0
4,0
14,7
5,3
18,3
6,7
8
S
30
29
1,9
1,8
5,6
5,4
9,4
9,1
13,1
12,7
16,9
16,3
20,6
19,9
24,4
23,6
28,1
27,2
2,1
2,1
6,4
0,2
10//
10,4
15,0
14,5
19,3
18j6
23.6
22,8
27,'J
26,9
11,5
15,3
19,2
60=
284
A MANUAL OF TOrOGKAPHlO METHODS.
Table XXXVI. — Lognrifhmic sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
30°
9. 09 919
9. 69 941
9. 69 963
9. 69 984
9.70 OUO
9. 70 02S
9. 70 050
9. 70 072
9.70 093
9.70 115
9. 70 137
9.70 159
9.70 189
9. 70 202
9. 70 22T
9. 70 245
9. 70 267
9. 70 288
9. 70 310
9. 70 332
9. 70 353
9. 70 375
9. 70 396
9. 70 418
9.70 654
9. 70 675
9. 70 697
9. 70 718
9. 70 909
9. 70 931
9.70 952
9. 76 144
9. 76 173
9. 76 202
9. 76 231
9.76 261
9. 76 290
9.76 319
9.76 348
9. 76 377
9.76 406
9.76 435
9. 76 464
9. 76 493
9. 76 522
9. 76 551
9.77 159
9.77 188
9.77 217
9.77 240
9. 77 274
9.77 303
9. 77 332
9.77 361
9. 77 390
•9.77 418
9. 77 447
9. 77 476
9. 77 505
9. 77 533
9. 77 562
9. 77 591
9. 77 619
9.77 648
9. 77 677
9.77 706
9.77 734
9. 77 763
L. Cotg.
0. 23 856
0. 23 827
0. 23 798
0.23 769
0.23 739
9. 93 753
9. 93 746
9. 93 738
9.93 731
9.93 724
0. 23 710
0.23 681
0.23 652
0.23 623
0.23 594
0, 23 565
0.23 536
0.23 .507
0.23 478
0. 23 449
9.93 717
9. 93 709
9.93 702
9.93 695
J)^93 687
9.93 680
9.93 673
9.93 065
9.93 058
9.93 050
0. 23 420
0.23 391
0. 23 361
0.23 332
0.23 303
9.93 643
9.93 636
9.93 628
9.93 621
9. 93 614
0. 23 275
0.23 246
0. 23 217
0.23 188
0.23 159
9.93 606
9.93 599
9.93 591
9.93 584
9.93 577
0.23 130
0.23 101
0.23 072
0.23 043
0.23 014
9.93 569
9. 93 562
9.93 554
9.93 547
9.93 539
9.93 532
9.93 525
9. 93 517
9. 93 510
9.93 50£
9. 93 495
9. 93 487
9. 93 480
9.93 472
9.93 465
0. 22 097
0. 22 668
0.22 639
0.22 610
0.22 582
9.93 457
9.93 450
9. 93 442
9.93 435
9.93 427
0.22 653
0. 22 524
0. 22 495
0. 22 467
0. 22 438
9. 93 420
9.93 412
9.93 405
9. 93 397
9.93 390
0. 22 409
0.22 381
0.22 352
0. 22 323
e. 22 294
9. 93 382
9.93 375
9.93 367
9. 93 360
9. 93 352
0. 22 266
0. 22 237
0.22 209
0. 22 180
L. Tang.
9.93 344
9. 93 337
9. 93 329
9. 93 322
9. 93 314
9. 93 li07"
80
29
0,5
0,5
1,0
1,0
1,5
14
2,0
1,9
2,5
2,4
3,0
2,9
3,5
3,4
4,0
3,9
4,5
4,4
5,0
4,8
io;o
9,7
15,0
14,5
20,0
19,3
25,0
24,2
2,8
3,3
3,7
4,2'
*,7
9,3
14,0
18,7
23,3
1,0
1,4
1,8
2,1
2,4
2,8
3,2
3,5
7,0
10,5
14,0
17,5
;
J
30
29
2,1
2,1
6,4
6,2
10,7
10,4
15,0
14,5
19,3
18,6
23,6
22,8
27,9
26,9
10,0
14,0
18,0
22,0
26,0
59°
LOGAEITHMS OF GIRCULAE FUNCTIONS.
285
Taule XXXVI. — Logarithmic sineSj cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
31°
9.71 184
9.71 205
0. Tl 2a6
9. 71 247
9.71 268
9.71 289
9. 71 310
9.71 331
9. 71 352
9. 71 373
9.71 393
9. 71 414
9. 71 435
9. 71 456
9. 71 477
9. 71 498
9.71 519
9. 71 539
9. 71 560
9. 71 581
9. 71 602
9. 71 622
fl.71 643
9. 71 664
9.71 685
9. 71 705
9.71 726
9.71 747
9.71 767
9. 71 788
9. 71 809
9. 71 829
9.71 850
9.71 870
9.71 911
9.71 932
9.71 952
9,71 973
9. 72 014
9. 72 034
9.72 055
9. 72 075
9. 72 096
9. 72 238
9. 72 259
9. 72 279
9. 72 299
•8 249
'& 277
9. 78 306
9.: 8 334
9. 78 363
9. 78 391
9. 78 419
8 448
8 476
9. 78 505
9.78 533
9. 78 562
9.78 590
9.78 018
9. 78 647
9.78 675
9. 78 704
9. 78 732
9.7
760
9. 78 817
9. 78 845
9. 78 874
9. 78 902
9. 78 930
9.78 959
9. 78 987
9.79 015
9.79 043
9. 79 072
9. 79 100
9.79 128
9. 79 156
9. 79 185
9. 79 213
9. 79 241
9. 79 269
9. 79 297
9. 79 326
9. 79 354
9.79 382
9. 79 410
L. Cotg.
0.22 123
0. 22 094
0. 22 065
0, 22 037
0. 22 008
0.21 980
0. 21 951
0.21 923
0.21 894
0.21 865
0. 21 837
0,21 808
0. 21 780
0.21 751
0.21 723
U. 21 694
0. 21 666
0. 21 637
0. 21 609
0. 21 581
0.21 552
0. 21 524
0. 21 495
0. 21 467
0. 21 438
0.21 410
0.21 382
0.21 353
0. 21 325
0. 21 -296
0. 21 268
0. 21 240
0.21 211
0.21 183
0.21 155
0.21 126
0.21 098
0. 21 070
0. 21 041
0.21 013
0. 20 985
0. 20 957
0. 20 928
0.20 900
0. 20 873
0. 20 844
0. 20 815
0. 20 787
0.20 759
0. 20 731
0.20 703
0. 20 674
0. 20 646
0. 20 618
0. 20 590
0. 20 562
0. 20 534
0.20 505
0. 20 477
0. 20 449
0. 20 421
9. 93 307
9.93 299
9. 93 291
9. 93 284
9.93 276
9. 93 230
9. 93 223
9.93 215
9. 93 207
9. 93 200
9.93 192
9. 93 184
9.93 177
9.93 169
9, 93 161
9.93 154
9.93 146
9.93 138
9.93 131
9. 93 123
9. 93 115
9.93 108
9.93 100
9. 93 092
9.93 084
9. 93 077'
9. 93 069
9.93 061
9.93 053
9. 93 046
9.93 038
9.93 030
9. 93 022
9.93 014
9. 93 007
9. 92 999
9. 92 991
9. 92 983
9. 92 976
9. 93 968
9.92 960
9. 92 953
9. 92 944
9. 92 936
9. 93 929
9.92 921
9. 92 913
9. 92 905
9. 92 897
9. 92 889
9. 92 881
9. 92 874
9. 92 866
9. 92 858
9. 92 850
9. 92 842
29
1
0,5
2
1,0
3
1,4
4
1,9
5
2,4
6
2,9
7
3,4
8
3,9
9
4,4
10
4,8
20
9,7
30
14,5
40
19,3
50
24,2
1,4
1,9
2,3
2,8
3,3
3,7
4,2
4,7
9,3
14,0
18,7
23,3
10,5
10,0
14,0
13,3
17,5
16,7
S
J
0,1
0,1
0,3
0,2
0,4
0,4
0,5
0,5
»;i
0,6
0,8
0,7
0,9
0,8
1,1
0,9
1,2
1,0
1,3
1,2
2,/
2,3
4,0
3,5
b,3
4,7
6,7
5,8
S
8
30
29
1,9
1,8
5,6
5,4
9,4
9,1
13,1
12,7
16,9
16,3
20,6
19,9
24,4
23,6
28,1
27,2
]2,2
15,8
19,2
22,8
26,2
58°
286
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXVl.—Loganthmio sines, cosines, tantfents, and cotaugenis—Contmauii..
[Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
32°
29
•2S
0,5
0,5
1,1)
0,0
1,4
1,4
1,9
1,0
2,4
2,3
2,9
2,8
3,4
3,3
3,9
3,7
4,4
4,2
4,8
4,7
9,7
9,3
14,5
14,0
19,3
18,7
■24,2
23,3
21
20
0,4
0,3
0,7
0,7
1,0
1,0
1,4
1,3
1,8
1,7
2,1
2,0
2,4
2,3
2,8
2,7
3,2
3,0
3,5
3,3
7,0
6,7
10,5
10,0
14,0
13,3
17,5
16,7
8
8
29
28
1,8
1,8
.5,4
5,2
9,1
8,8
12,7
12,2
10,3
15,8
19,0
19,2
23,6
22,8
27,2
26,2
0,0
1,4
1,8
2,2
2,7
3,2
3,6
4,0
4,5
9,0
13,5
18,0
22,5
0,5
0,6
0,7
0,8
0,9
1,0
1,2
2,3
3,5
4,7
5,8
2,0
6,0
10,0
14,0
18,0
22,0
26,0
S7=
LOGARITHMS OF CIEOULAE FUNCTIONS.
287
Table XXXVI. — Logariilimic sin&s, cosives, tangents, and cotangents — Coutinued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
33^
9.73 901
9.73 921
9.73 940
9.73 959
9.73 978
9. 73 997
9. 74 017
9. 74 036
9.74 055
9. 74 074
9.74 093
9.74 113
9. 74 132
9.74 151
9.74 170
9. 74 189
a. 74 208
9.74 227
9.74 246
9.74 265
9.74 284
9.74 303
9. 74 322
9.74 341
9.74 360
9.74 379
9. 74 398
9. 74 417
9.74 436
9. 74 455
9. 74 474
9. 74 493
9.74 512
9. 74 531
9. 74 549
9. 74 568
9. 74 587
9.74 606
9. 74 625
9. 74 644
9. 74 662
9. 74 681
9. 74 700
9.74 719
9.74 737
9. 74 756
81 252
81 279
81 307
81 335
SI 362
81 39U
81 418
81 445
81 473
81 500j
81 528
81 556
81 583 !
81 611 I
81 638 i
81 666
81 693
81 721
81 748
81 776
81 941
81 968
81 996
82 023
82 051
82 078
82 106
82 133
82 161
82 188
82 21.5
82 243
82 270
82 298,
82 325
82 352
82 380
82 407
82 435
82 462
82 544
82 571
82 599
82 626
82 653
82 681
82 762
82 790
82 817
L. Cotg. a. c,
0. 18 74S
0. 18 721
0. 18 693
0. 18 665
0.18 638
0. 18 010
0. 18 582
0. 18 .555
0. 18 527
0. 18 5110
0. 18 472
0. 18 441
0. 18 417
0. 18 389
0. 18 362
0. 18 334
0.18 307
0. 18 279
0. 18 252
0.18 224
0. 18 197
0.18 169
0. 18 142
0.18 114
0.18 087
0. 18 059
0. 18 032
0. 18 004
0. 17 977
0. 17 949
0^ 17 922
0.17 894
0. 17 867
0. 17 839
0.17 812
0. 17 785
0. 17 757
0. 17 730
0.17 702
0.17 675
0. 17 648
0.17 620
0. 17 593
0.17 565
0.17 538
0. 17 511
0. 17 483
0. 17 456
0. 17 429
0. 17 401
9. 92 359
9.92 351
9.02 343
9. 92 335
_9^92 326
9. 92 3i8"
. 9.92 310
9. 92 .302
9.92 293
9.92 285
9.92 277
9.92 269
9.92 260
9. 92 252
9. 92 24!
9.92 111
9. 92 102
9. 92 094
9. 92 086
9. 92 077
9. 92 069
9. 92 060
9. 92 052
9. 92 044
9. 92 035
9. 92 027
9. 92 018
9. 92 010
9. 92 002
0. 91 993
9.91 985
9.91 976
9.91 968
9.91 959
9. 91 951
9. 91 942
9. 91 934
9.91 925
9.91 917
9. 91 908
9.91 900
9. 91 891 I
9.91 883
9.91 874
9.91 866
9. 91 857
14,0
18,7
23,3
0,4
0,9
1,4
1,8.
2,2
2,7
3,2
3,6
4,0
4,5
9,0
13,5
18,0
22,5
20
19
0'3
0,3
0,7
06
1,0
1,0
1,3
1,3
1,7
1,6
2,0
1,9
2,3
2,2
2,7
2,5
3,0
2,8
3,3
3,2
6,7
6,3
10,0
9,5
13,3
12,7
16,7
15,8
3,0
6,0
9,0
12,0
15,0
9
9
2S
27
1,6
1,5 j
4,7
4,5
7,8
7,5
10,9
10,5
14,0
13,5
17,1
16,5
20,2
19,5
23,3
- 22,5
26,4
25,5
15,2
18,6
21,9
25,3
5G''
288
A MANUAL OF TOrOGEAPHIO METHODS.
Table XXXVI. — LogarUlimic sines, cosines, tantjents, and cotangents— ContinnaA,
[Extractcil from Gauss' Logaritlimic aud Trigouometric Tables.]
34°
9. 74 756
9. 74 775
9. 74 794
9.74 812
9.74 831
9.74 850
9. 74 863
9.74 887
9.74 906
9.74 024
9. 74 943
9.74 901
9.74 9S0
9.74 999
9.75 017
9.75 036
9.75 054
9. 75 073
9.75 091
9. 75 110
9.75 V>i
9.75 147
9.75 165
9.75 184
9.75 202
9. 75 221
9.75 239
9. 75 258
9. 75 276
9.75 294
9.75 313
9.75 331
9,75 350
9.75 368
9. 75 386
9.75 405
9. 75 423
9, 75 441
9.75 459
9.75 478
9.75 496
9.75 514
9. 75 533
9.75 551
9.75 569
9.75 .587
9. 75 605
9.75 624
9.75 64 2
9.75 660
9.75 678
9.75 696
9. 75 714
9.75 733
9. 75 751
9.75 769
9.75 787
9. 75 805
9. 75 823
9.75 841
9.75 859
L. Tang. il. o,
9. 82 899
9. 82 926
9.82 953
9.82 980
9.83 008
9.83 171
9.83 198
9. 83 225
9. 83 252
9.83 280
9.83 307
9.83 334
9. 83 415
9. 83 442
9. 83 470
9. 83 497
9.83 524
9. 83 551
9. 84 119
9.84 146
9.84 173
9.84 200
9. 84 227
9. 84 254
9.84 280
9. 84 307
9. 84 334
9. 84 361
9. 84 388
9. 84 415
9. 84 442
9.84 469
9. 84 496
9. 84 523
L. Cotg. d. I
0. 17 047
0. 17 020
0.16 992
0. 16 965
0. 16 938
0. 16 911
0. 10 883
0. 16 856
0. 16 829
0.16 822
0.10 775
0. 10 748
0. 16 720
0, 16 093
0. 16 666
0. 16 639
9.91 857
9.91 849
9.91 840
9,91 832
9.91 823
9.91 815
9,91 806
9.91 798
9,91 789
9,91 781
9,91 7'
9.91 7
9.91 7:
9,91 7
9,91 7
0. 16 558
0. 16 530
0.16 503
0, 16 476
0, 16 449
0, 16 422
0. 16 395
0, 16 368
0. 16 341
0. 16 314
0. 16 287
0. 16 260
0. 16 232
0, 16 205
0. 16 178
0,16 151
0, 16 124
0.16 097
0.16 070
0. 10 043
0.10 016
0, 15 989
0, 15 902
0. 15 935
0, 15 908
0, 15 881
0. 15 854
0, 15 827
0. 15 800
0. 15 773
0. 15 746
0. 15 720
0. 15 693
0, 15 666
0. 15 639
0.15 612
0, 15 585
0. 15 5.58
0.15 531
0. 15 504
0. 15 477
9.91 729
9.91 720
9.91 712
9.91 703
9,91 695
9.91 686
9,91 677
9,91 069
9.91 660
9,91 651
9,91 643
9,91 634
9.91 625
9.91 017
9,91 608
9,91 599
9,91 .591
9.91 582
9.91 ,573
9.91 565
9,91 556
9,91 547
9.91 538
9.91 530
9.91 521
9.91 512
9,91 504
9.91 495
9.91 486
9,91 477
9.91 409
9.91 460
9. 91 451
9.91 442
9,91 433
9,91 425
9,91 416
9,91 407
9! 91 389
9,91 381
9.91 372
9.91 363
9.91 354
9,91 345
9, 91 336
28
0,5
27
0,4
0,9
0,9
1,4
1,4
1,9
1,8
2,3
2,2
2,8
2,7
3,3
3,2
3,7
3,6
4,2
4,0
4,7
4,5
9,3
9,0
14,0
13,5
18,7
18,0
23,3
22,5
1,6
4,7
7,8
10,9
14,0
17,1
20,2
23,3
26,4
0,4
0,9
1,3
1,7
2,2
2,6
3,0
3,5-
3,9
4,3
8,7
13.0
17,3
21,7
18
0,3
0,6
0,9
1,2
1,5
1,8
2,1
2,4
2,7
3,0
6,0
9,0
12,0
15,0
0,2
0,1
0,3
0,3
0,4
0,4
(1,6
0,5
0,8
0,7
0,9
0,8
1,0
0,9
1,2
1,1
1,4
1,2
1,5
1,3
3,0
2,7
4,5
4,0
6,0
5,3
12,2
15,8
19,2
22,8
26,2
8,4
11,8
15,2
18,6
21,9
25,3
55^
LOGAEITHMS OP CIRCULAE FUNCTIONS.
289
Table XXXVI. — LogarWwiie sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauas' Logarithmic and Trigonometric Tables.]
35°
9. 75 859
9. 75 877
9. 75 895
9.75 913
9. 75 931
9. 75 949
9.75 967
9. 75 985
9. 76 003
9. 76 021
9.76 039
9. 76 057
9. 76 075
9.70 093
9. 76 111
9. 76 129
9. 76 146
9.76 164
9.76 182
9. 76 200
9. 76 218
9. 76 236
9. 76 253
9. 76 271
9. 76 289
9. 76 307
9. 76 324
9. 76 342
9. 76 360
9.76 378
9. 76 395
9. 76 413
9. 76 431
9. 76 448
9. 76 466
9. 76 484
9. 76 501
9. 76 519
9. 76 537
9. 76 554
9. 76 572
9. 76 590
9. 76 607
9. 76 625
9: 76 642
9. 76 660
9. 76 677
9. 76 695
9. 76 712
9. 76 730
9. 76 747
9. 76 765
9.76 782
9.76 800
9. 76 817
9.76 835
9. 76 852
9.76 870
9.76 887
9. 76 904
9. 76 922
L. Tang. d. c.
84 523
84 550
84 576
84 603
84 630
84 657
84 684
84 711
84 738
84 764
84 791
84 818
84 845
81 872
84 899
84 935
84 952
84 979
85 006
85 033
85 140
85 166
85 193
85 220
85 247
85 273
85 300
85 487
85 514
85 540
85 567
85 594
85 620
85 647
85 674
85 700
85 727
85 754
85 780
85 807
85 834
85 860
85 887
85 913
85 940
85 967
85 993
86 020
86 046
86 073
86 100
86 126
0. 15 477
0. 15 450
0. 15 424
0. 15 397
0. 15 370
0. ]5 343
0.15 316
0. 15 289
0. 15 262
0. 15 236
0. 15 209
0. 15 182
0. 15 155
0. 15 128
0. 15 101
0. 15 075
0. 15 048
0. 15 021
0. 14 994
0. 14 967
0. 14 941
0. 14 914
0. 14 887
0. 14 860
0. 14 834
0. 14 807
0. 14 780
0. 14 753
0. 14 727
0.14 700
0. 14 673
0. 14 646
0. 14 620
0.14 593
0. 14 566
0.14 540
0.14 513
0. 14 486
0. 14 460
0. 14 433
0. 14 406
0. 14 380
0. 14 353
0. 14 326
0. 14 300
0. 14 273
0. 14 246
0. 14 220.
0. 14 193
0. 14 166
9. 91 336
9.91 328
9.91 319
9. 91 310
9. 91 301
9. 91 292
9.91 283
9.91 274
9.91 266
■9.91 257
9. 91 248
9. 91 239
9.91 230
9.91 221
9.91 212
9. 91 203
9.91 194
9.91 185
9.91 176
9.91 167
9.91 158
9.91 149
9.91 141
9.91 132
9.91 123
9.91 114
9.91 105
9.91 096
9.91 087
9.91 078
9.91 069
9.91 060
9.91 051
9. 91 042
9.91 033
9. 91 023
9.91 014
9.91 005
9. 90 996
9.90 987
9.90 978
9. 90 969
9. 90 960
9.90 951
9.90 942
0. 14 140
0. 14 113
0. 14 087
0. 14 060
0. 14 033
0. 14 007
0. 13 980
0. 13 964
0. 13 927
0. 13 900
0. 13 874
L. Cotg. d. c. L. Tang. L. Siu. d
9.90 887
9.90 878
9.90 869
9. 90 823
9. 90 814
9. 90 805
27
2«
0,4.
0,4
0,9
0,9
1,*
1,3
1,8
1,7
2,2
2,2
2,7
2,6
3,2
3,0
3,6
3,5
4,0
3,9
4,5
4,3
9,0
8,7
13,5
13,0
18,0
17,3
22,5
21,7
17
10
9
0,3
0,2
0,2
0,6
0,3
0,3
0,8
0,5
0,4
1,1
0,7
0,6
1,4
0,8
0,8
1,7
1,0
0,9
2,0
1,2
1,0
2,3
1,3
1,2
2,6
1,5
1,4
2,8
1,7
1,5
5,7
3,3
3,0
8,5
.5,0
4,5
11,3
e,7
0,0
14,2
8,3
7,5
9,0
12,0
15,0
-19
54°
290
A MANUAL OP TOPOGEAPHIC METHODS.
Table XXXVI. — Logarillimic sines, cosines, tangents, and' cotiingenis — Continued.
[Extracted from Gauss' Logaritlimic anil Trigonometric Tables.]
36°
9.76 922
9.76 939
9.76 957
9. 76 974
9. 76 991
9.77 009
9. 77 026
9. 77 043
9. 77 061
9. 77 078
9.
9.77 164
095
147
9.77 181
9.77 199
9. 77 216
9. 77 233
9. 77 250
9. 77 268
9.77 285
9.77 302
9.77 319
9. 77 336
9. 77 353
9.77 370
9.77 387
9. 77 405
9. 77 432
9. 77 456
9. 77 473
9. 77 490
9.77 507
9. 77 524
9. 77 541
9. 77 558
9. 77 575
9. 77 592
9.77 609
9.77 626
9. 77 G43
9. 77 660
9. 77 677
9. 77 694
9. 77 711
9.77 728
9. 77 744
£. 77 761
9.77 778
9.77 795
9.77 812
9.77 829
9.77 846
L. Tang. d. c
9. 86 126
9. 86 153
9.86 179
9. 86 206
9. 86 232
9. 86 269
9. 86 285
9.86 312
9. 86 338
9. 86 365
9. 86 392
9. 86 418
9. 86 445
9. 86 471
9. 86 498
9.86 656
9. 86 683
9. 86 709
9. 86 736
9. 86 815
9. 86 842
9. 86 868
9. 86 894
9. 86 921
9. 86 947
9. 86 974
9.87 000
9. 87 027
9. 87 053
9. 87 079
9.87 106
9. 87 132
9.87 158
9.87 185
9. 87 211
9. 87 238
9.87 264
9. 87 290
9.87 317
9. 87 343
9. 87 369
9. 87 396
9. 87 422
9.87 448
9. 87 475
9.87 501
9.87 527
9. 87 554
9.87 580
9.87 606
9.87 633
9.87 659
9.87 685 I
9. 87 711 I
L. Cotg. ' d.
L. Cotg.
0. 13 874
0. 13 847
0. 13 821
0. 13 794
0. 13 768
0. 13 741
0. 13 715
0. 13 688
0. 13 662
0. 13 635
0. J 3 608
0. 13 582
0. 13 555
0. 13 529
0. 13 502
0. 13 476
0. 13 449
0. 13 423
0. 13 397
0.13 370
0. 13 344
0.13 317
0. 13 291
0. 13 264
0. 13 238
0. 13 211
0. 13 185
0.13 158
0.13 132
0. 13 106
0. 13 079
0. 13 053
0. 13 026
0.13 000
0. 12 973
0. 12 947
0. 12 921
0. 12 894
0. 12 868
0. 12 842
0. 12 815
0. 12 789
0. 12 762
0. 12 736
0.12 710
0. 12 683
0. 12 657
0. 12 631
0.12 604
0.12 578
0. 12 552
0. 12 525
0. 12 499
0. 12 473
0. 12 446
0. 12 420
0. 12 394
0.12 367
0. 12 341
0. 12 315
0. 12 289
9. 90 796
9. 90 787
9. 90 777
9. 90 768
9. 90 759
9.90 750
9. 90 741
9.90 731
9. 90 722
9.90 713
9. 90 657
9.90 648
9. 90 639
9.90 630
9.90 620
9.90 611
9.90 602
9. 90 692
9. 90 565
9. 90 555
9. 90 546
9.90 424
9. 90 415
9. 90 406
9. 90 396
9. 90 311
9.90 301
9.90 292
9.90 263
9. 90 264
9. 90 244
0,9
1/4
1,8
2,2
2,7
3,2
3,6
4,0
4,5
9,0
13,5
18'0
22,5
0,4
0,9
1,3
1,7
2,2
2,6
8,7
13,0
17,3
21,7
18
17
0,3
0,3
0,6
0,6
0,9
0,8
1,2
1/1
1,5
M
1,8
1/7
2,1
2,0
2,4
2,3
2,7
2,6
3,0
2,8
6,0
5,7
9,0
8'5
12,0
11,3
15,0
14,2
0,4
0,6
0,8
0,9
1,0
1,2
1/4
1,5
3,0
4,5
4,5
4'3
V,b
7,2
l(),.'i
10,1
13,5
13,0
I6„S
15,9
19,6
18,8
22,5
21,7
2b,b
24,6
53°
LOGARITHMS OF CIECULAE FUNCTI02fS.
291
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued.
[Extraoted from Ganss' Logarithmic and Trigonometric Tables.]
37°
9. 77 946
9. 77 963
9.77 980
9.77 997
9. 78 013
9. 78 030
9. 78 047
9. 78 063
9. 78 130
9.78 147
9. 78 163
9. 78 180
9. 78 197
9. 78 213
9. 78 230
9. 78 246
9. 78 263
9. 78 280
9. 78 296
9. 78 313
9. 78 329
9. 78 346
9. 78 395
9. 78 412
9. 78 428
9. 78 445
9. 78 461
9. 78 478
9. 78 494
9. 78 510
9. 78 527
9.78 543
9. 78 560
9. 78 576
9. 78 592
9. 78 609
9. 78 625
9. 78 642
9. 78 658
9. 78 674
9. 78 691
9. 78 707
9. 78 723
9. 78 739
9. 78 756
9.78 772
9. 78 788
9. 78 805
9. 78 821
9. 78 837
L. Tang, d
87 764
87 790
87 817
87 843
87 869
87 895
87 922
; 071
88 105
88 131
88 158
88 184
88 210
88 629
88 655
88 681
89 125
89 151
89 177
89 203
89 229
89 255
89 281
L. Cotg. d. c.
0.12 289
0. 12 262
0. 12 236
0. 12 105
0. 12 078
0. 12 052
0. 12 026
0. 12 000
0. 11 973
0.11 947
0. 11 921
0. 11 895
0. 11 869
0. 11 842
0.11 816
0. 11 790
0. 11 764
0. 11 738
0. 11 711
0.11 685
0. 11 659
0.11 633
0. 11 007
0. 11 580
0. 11 554
0.11 528
0. 11 502
0. 11 476
0. 11 450
0. 11 423
0. 11 397
0. 11 371
0. 11 345
0. 11 319
0. 11 293
0. 11 267
0. 11 241
0. 11 214
0.11 188
0. 11 162
0. 11 136
0.11 110
0. 11 084
0. 11 058
0. 11 032
0.11 006
0. 10 980
0. 10 954
0. 10 927
0. 10 901
0. 10 875
0. 10 849
0. 10 823
0. 10 797
0.10 771
0. 10 745
0. 10 719
L. Tang.
90 235
90 225
90 216
90 206
90 197
90 187
90 178
90 168
90 159
90 149
90 120
90 111
90 101
89 947
89 937
89 927
89 918
89 702
89 693
89 683
89 673
0,4
0,4
0,9
0,9
1,4
1,3
1,«
1,7
2,2
2,2
2,7
2,6
3,2
3,0
3,6
3,5
4,0
3'9
4,6
4,3
9,0
8,7
13,5
13,0
18,0
17,3
22,5
21,7
17
16
0,3
0,3
0,6
0,5
0,8
0,8
1,1
1,1
l,i
1,3
I'V
1,6
2'()
1,9
2,3
2,1
2'6
2,4
2,8
2,7
5,7
5,3
K,5
8,0
11,3
10,7
14,2
13,3
10
9
0,2
0,2
0,3
0,3
0,5
0,4
0,7
0,6
0,8
0,8
1,0
0,9
1,2
1,0
1,3
1,2
1,5
1,4
1,7
1,5
3,3
3,0
5,0
4,5
6,V
6,0
8,3
7,5
1,4
1,3
4,1
3,9
6,8
6,5
9,4
9,1
12,2
11,7
14,8
14,3
17,6
16,9
20,2
19,5
22,9
22,1
2b,6
24,7
52=
292
A IMANUAL OF TOPOGKAPlilO METUODS.
Table XXXVI. — Loiiayillimic
[Extracted from Gai
/«(«, cosines, laiigents, and cotangents — Coutinued.
.s' Lojiarithmic aud Trigonometric Tables.]
38°
«50
967
9. 78 nS3
_9.7S_0!)9
9.79 015"
9. 79 031
9. 79 047
9. 79 063
9. 79 079
"977Dl)9T
9. 79 111
9. 79 128
9. 79 144
9. 79 160
9. 79 176
9. 79 192
9. 79 208
9. 79 224
9. 79 240
■9 256
9. 79 383
9^9^399
9. 79 415
9. 79 431
9. 79 447
9. 79 463
9. 79 478
9. 79 494
9. 79 510
9.79 526
9. 79 542
9.79 558
9. 79 573
9. 79 589
9. 79 605
9. 79 621
9. 79 636
9.79 652
9. 79 668
9. 79 684
9.79 699
9.79 715
9.79 731
9. 79 746
9.79 762
9. 79 778
9. 79 825
9.79 840
9. 79 856
9. 79 872
L. Tang. d. c.
9. 89 801
9.89 827
9.89 853
9.90 112
9. 90 138
9.90 164
9. 90 190
9. 90 216
9. 90 242
9. 90 268
9. 90 294
.9.90 ;
346
9. 90 449
9. 90 475
9. 90 501
9. 90 527
9. 90 553
9.90 578
9.90 604
9.90 630
9. 90 656
9.90 682
9. 90 708
9. 90 734
9.90 759
L. Cotg.
0. 10 719
0. 10 693
0. 10 667
0. 10 641
0^10_615
0. 10 589
0. 10 563
0. 10 537
O 10 511
0. 10 485
0. 10 459
0.10 4«
0. 10 407
0. 10 381
0. 10 355
0. 10 329
0. 10 303
0.10 277
0. 10 251
0. 10 225
0. 10 199
0. 10 173
0.10 147
0. 10 121
0. 10 095
0. 10 069
0.10 043
0.10 017
0. 09 99]
0. 09 965
0.09 939
0. 09 914
0.09 888
0. 09 862
0. 09 836
0. 09 810
0. 09 784
0.09 758
0. 09 732
0. 09 706
0. 09 551
0. 09 525
0. 09 499
0. 09 473
0. 09 447
0. 09 422
0. 09 396
0.09 370
0. 09 344
0.09 318
0.09 292
0.09 266
0. 09 241
0. 09 215
0.09 189
L. Cos.
9. 89 633
9.89 624
J)JS9 61£
9. 89' 004
9.89 594
9. 89 584
9. 89 574
9. 89 564
9.89 524
9. 89 514
9.89 504
9.89 495
9. 89 485
9. 89 475
J3^89 465
9. .89 455"
9. 89 445
9. 89 435
9. 89 425
9. 89 415
9.89 405
9. H9 395
9. 89 385
9. 89 375
9. 89 364
9. 89 354
9. 89 344
9. 89 334
9. 89 324
9. 89 314
9. 89 304
9. 89 294
9.89 284
9.89 274
9.89 264
9:89 254
9.89 244
9.89 233
9. 89 152
9.89 142
9.89 132
9.89 122
9. 89 091
9.89 081
9.89 071
9.89 060
P.P.
4,3
8,7
13,0
17,3
21,7
0,4
0,8
1,2
1,7
2,1
2,5
2,9
3,3
3,8
4,2
8,3
12,5
16,7
20,8
17
0,3
16
0,3
0,6
0,5
0,8
0,8
1,1
1,1
1,4
1,3
1/7
1,6
2,0
1,9
2,3
2,1
2,6
2,4
2,8
2,7
5,7
.5,3
8,5
8,0
11,3
10,7
14,2
13,3
11
10
0,2
0,2
0,4
0,3
0,6
0,5
0,7
0,7
0,9
0,8
1/1
1,0
1,3
1,2
1,5
1,3
1,6
1,5
1,8
1,7
3,7
3,3
5,5
5,0
7,3
6,7
9,2
8,3
10
10
26
25
1,3
1/2
3,9
3,8
6,5
6,2
9,1
8,8
11,7
11,2
14,3
13,8
16,9
16,2
19,5
18,8
22,1
21,2
24,7
23,8
1,2
1,5
1,8
2,0
2,2
2,5
5,0
7,5
10,0
12,5
1/4
4,3
7,2
10,1
13,0
15,9
18,8
21,7
24,6
31'
LOGAEITHMS OF CIRCULAR FUNCTIONS.
293
Table XXXVI. — Logarithmic s'mes, cosines, tangents^ and cotangents — Continued,
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
39°
9. 79 903
9.79 918
9. 79 934
9.79 950
9.79 905
9.79 981
9.79 990
9.80 012
9 80 027
9.80 043
9.80 058
9. 80 074
9. 80 C89
9.80 105
9.80 120
9.80 136
9.80 151
9. 80 160
9.80 182
9.80 197
9. 80 213
9. 80 274
9. 80 290
9.80 305
9. 80 320
9.80 428
9. 80 443
9. 80 458
9. 80 473
9. 80 489
9.80 504
9. 80 519
9. 80 534
9. 80 550
9.80 565
9.80 580
9. 80 595
9. 80 610
9. 80 625
9. 80 641
9. 80 656
9. 80 671
9. 80 686
9. 80 701
9. 80 716
90 837
90 863
90 889
90 914
90 940
90 906
90 992
91 018
91 043
91 009
91 095
91 121
91 147
91 172
91 198
91 224
91 250
91 276
91 301
91 327
91 353
91 379
91 404
91 430
91 456
91 482
91 507
91 533
91 559
91 585
91 610
91 636
91 662
91 688
91 713
91 739
91 765
91 791
91 816
91 842
91 868
91 893
91 919
91 945
91 971
91 996
92 022
92 048
92 073
92 099
92 125
92 150
92 176
92 202
92 227
92 253
92 279
92 304
92 330
92 356
92 381
0. 09 163
0.09 137
0.09 111
0. 09 086
0.08 879
0. 08 853
0. 08 828
0.08 802
0. 08 750
0. 08 724
0. 08 099
0. 08 673
0. 08 617
0. 08 621
0. 08 596
0. 08 570
0. 08 544
0. 08 518
0.1
415
0.08 390
0.08 364
0.08 338
0. 08 312
0. 08 287
0. 08 261
0. 08 235
0. 08 209
0.08 184
0.08 158
0. 08 132
0. 08 107
0. 08 081
0. 08 055
0. 08 029
0. 08 004
0. 07 978
0. 07 952
0. 07 927
0. 07 901
0. 07 875
0. 07 850
O: 07 824
0. 07 798
0.07 773
0. 07 747
0. 07 721
0. 07 696
0. 07 670
0. 07 644
0.07 619
L. Tang.
88 793
88 782
88 772
88 761
88 678
88 668
88 657
88 647
88 636
88 626
88 615
88 605
88 594
88 573
88 563
88 552
88 542
n,4
0,4
0,9
0,8
1,3
1,2
1,V
1,7
2,2
2,1
2,6
2,,')
3,0
2,9
3,!>
3,3
3'9
3,8
4,3
4,2
8,3
13,0
12,5
ri,3
16,7
21,7
20,8
1
16
0,3
2
0,5
3
0,8
4
1/1
5
1,3
6
1,6
V
1,9
H
2,1
9
2,4
10
2,7
20
5,3
30
8'0
40
10,7
50
13'3
1,2
1,J
3,6
3,4
b,9
5,7
8,3
7,9
10,6
10,2
13,0
12,5
lb,4
14,8
1V,V
17,1
20,1
19,3
22,5
21,6
24,8
23,9
50=
294
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Locjaritiimic sines, cosines, tangents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
40°
9.80 837
9. 80 852
9. 80 867
9. 80 987
9.81 002
9.81 017
9. 81 032 i
9.81 047
'9.81 061
9. 81 076 ,
9.8] 091
9. 81 106
9.81 121
9.81 136
9.81 151
9.81 166
9. SI 180
9.81 195
9. 81 210
9.81 225
9.81 240
9. 81 254
9.81 269
9. 81 284
9.81 299
9.81 314
9.81 328
9.81 343
9.81 358
9. 81 372
9. 81 387
9. 81 402
9.81 417
9.81 431
9. 81 446
9.81 461
9. 81 475
9. 81 490
9.81 505
9. 81 519
9. 81 534
9. 81 549
9.81 563
9. 81 578
9. 81 592
9.81 607
9. 81 622
9.81 636
9.81 651
9.81 665
9. 81 680
9. 81 694
9.92 381
9. 92 407
9. 92 433
9. 92 458
9. 92 484
9. 92 510
9. 92 535
9. 92 561
9. 92 587
9. 92 612
9. 92 638
9.92 663
9. 92 689
9. 92 715
9. 92 740
9. 92 766
9. 92 792
9. 92 817
9. 92 843
9. 92 868
9. 92 894
9. 92 920
9. 92 945
9. 92 971
9. 92 996
9.93 022
9. 93 048
9.93 073
9.93 099
9.93 124
9.93 150
9. 93 175
9.93 201
9. 93 227
9.93 252
9. 93 406
9. 93 431
9. 93 457
9. 93 482
9.93 508
9.93 533
9.93 559
9.93 584
9. 93 610
9.93 636
9.93 661
9. 93 687
9.93 712
9. 93 738
9.93 763
9.93 789
9. 93 814
9. 93 840
0. 07 619
0. 07 593
0.07 667
0.07 542
0.07 516
0. 07 490
0.07 465
0. 07 439
0. 07 413
0.07 388
0.U7 362
0. 07 337
0.07 311
0. 07 285
0. 07 260
0. 07 234
0.07 208
0.07 183
0. 07 157
0.07 132
O.07 106
0.07 080
0. 07 055
0.07 029
0.07 004
0. 06 978
0.06 952
0. 06 927
0.06 901
0. 06 876
0.06 850
0. 06 825
0. 06 799
0.06 773
0. 06 748
0.1
: 722
0.06 697
0.06 671
0. 06 646
0. 06 620
0. 06 594
0. 06 569
0. 06 543
0. 06 518
0. 06 492
0.06 467
0. 06 441
0. 06 416
0. 06 390
0. 06 364
0.06 339
0. 06 313
0.06 288
0. 06 262
0.1
0.06 211
0.06 186
0.06 160
0.06 135
0. 06 109
0. 06 084
d. c. L. Tang.
88 372
88 362
88 351
88 340
88 201
88 191
88 180
88 169
88 105
88 094
88 083
88 040
88 029
88 018
88 007
87 985
87 975
87 964
87 953
87 942
87 931
87 920
87 909
87 898
87 887
87 877
87 866
87 855
87 844
87 833
87 822
87 811
0,4
0,4
0,9
0,8
1,3
1,2
1/'
i:i
2,2
2,1
2,6
2,b
3,0
2,9
3,5
3,3
3,9
3,8
4,3
4,2
8,V
8,3
4,7
7,0
9,3
11,7
10
0,2
0,3
0,5
n
10 1
26
26
1,2
1,3
3,5
3,9
5,9
6,5
8,3
9,1
10,6
11,7
13,0
14,3
15,4
16,9
17,7
19,5
20,1
22,1
22,5
24,7
24,8
1,2
3,8
6,2
8,8
11,2
13,8
16,2
18,8
21,2
23,8
49=
LOGAEITHMS OF CIEOULAE FUNCTIONS.
295
Table XXXVI. — Logarithmic sines, cosines, tangents^ and cotangents — Continued.
[Extractetl from Gauss' Logarithmic and Trigonometric Tables.]
410
L. Tang.
L. Cotg.
81 694
81 709
81 723
81 738
81 752
81 767
81 781
81 796
81 810
81 825
81 9U
81 926
81 940
81 955
81 969
81 983
81 998
82 012
82 026
82 041
82 055
82 069
82 084
82 098
82 112
82 126
82 141
82 155
82 169
82 184
82 198
82 212
82 226
82 240
82 255
82 269
82 283
82 297
82 311
82 326
82 340
82 354
82 368
82 382
82 410
82 424
82 439
82 453
82 467
9. 93 916
9. 93 942
9. 93 967
9. 93 993
9.94 018
9.94 044
9. 94 069
9. 94 095
9. 94 120
9. 94 146
9. 94 171
9. 94 197
9. 94 222
9.94 248
9. 94 273
9.94 299
9.94 324
9. 94 350
9.94 375
9. 94 401
9. 94 426
9. 94 452
9. 94 477
9. 94 503
9. 94 .528
9. 94 554
9. 94 579
9. 94 604
9.94 630
9. 94 655
9. 94 681
9. 94 706
9.94 732
9. 94 757
9. 94 783
9. 95 062
9. 95 088
9.95 113
9. 95 139
9.95 164
9.95 190
9.95 215
9. 95 240
9. 95 266
9. 95 291
9. 95 317
9. 95 342
9. 95 368
9. 95 393
9. 95 418
9.95 444
0. 06 084
0. 06 058
0. 06 033
0.06 007
0. 05 982
0.05 956
0. 05 93]
0. 05 905
0. 05 880
0. 05 854
0. 05 829
0. 05 803
0.05 778
0. 05 752
0. 05 727
0. 05 701
0. 05 676
0.05 650
0. 05 625
0. 05 599
0. 05 574
0. 05 548
0. 05 523
0. 05 497
0.05 472
0.05 446
0. 05 421
0. 05 396
0. 05 370
0. 05 345
0. 05 319
0. 05 294
0. 05 268
0. 05 243
0. 05 217
0.05 192
0.05 166
0.05 141
0.05 116
0. 05 090
0. 05 065
0.05 039
0.05 014
0. 04 988
0. 04 963
0. 04 938
0. 04 912
0. 04 887
0. 04 861
0. 04 836
0.04 810
0. 04 785
0.04 760
0. 04 734
0. 04 709
0.04 683
0. 04 658
0. 04 632
0. 04 607
0.04 582
0. 04 556
87 778
87 767
87 756
87 745
87 734
87 723
87 712
87 668
87 657
87 646
87 635
87 624
87 613
87 601
87 590
87 546
87 535
87 524
87 513
87 501
87 490
87 479
87 446
87 434
87 423
87 412
87 401
87 390
87 378
87 367
87 356
87 345
87 334
87 322
87 311
87 300
87 288
9.87 277
9.87 266
9.87 255
9.87 243
9.87 232
221
9. 87 209
9.87 141
9.87 130
9.87 119
0,4
0,4
0,9
0,8
1,3
1,2
1;7
1,7
2,2
2,1
2,6
2,5
3,0
2,9
3,5
3,3
3,9
3,8
4,3
4,2
«,v
8,3
13,0
12,5
17,3
16,7
21,7
20,8
15
14
0,2
0,2
0,5
0,5
0,8
0,7
1,0
0,9
lr2
1,2
l,c
1,4
1,8
1,6
2,0
1,9
2,2
2,1
2,5
2,3
5,0
4,7
V,5
7,0
10,0
9,3
12,b
11,7
12
11
0,2
0,2
0,4
0,4
0,6
0,6
0,8
0,7
1,0
0,9
1,2
1,1
1,4
1,3
1,6
15
1,8
1,6
2,0
1,8
4,0
3,7
6,0
5,5
8,0
7,3
10,0
9,2
12
12
26
25
1,1
1,1
8,2
3,1
5,4
5,2
7,6
7,3
9,8.
9,4
11,9
11,5
14,1
13,5
16,2
15,6
18,4
17,7
20,6
19,8
22,8
21,9
24,9
23,9
1,1
3,4
5,7
7,9
10,2
12,5
14,8
17,1
19,3
21,6
23,9
48°
296
A MxiNUAL OF TOPOGKAPHIC METHODS.
Table XXXVI. — Loiiarillimic siiics, cosines, tangenis, and coteH(/e»/s— Continued.
[Extraotocl Iroin Gausa' Logarithmic and Trigonometric TivViles.)
42°
47c
LOGAEITHMS OF CIEGULAR FUNCTIONS.
297
Table XXXVI. — Logarithmic sines, cosines, tanffents, and cotangents — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables-]
430
83 378
83 392
83 405
83 419
83 432
83 441)
83 513
83 527
83 540
83 661
83 674
83 688
83 701
83 715
83 728
83 741
83 755
83 901
83 914
83 927
83 940
83 954
83 967
S3 980
83 993
84 006
84 020
84 033
84 046
84 059
84 072
84 085
84 098
84 112
84 125
84 138
84 151
84 164
84 177
9. 97 016
9. 97 042
9. 97 067
9. 97 345
9. 97 371
9. 97 396
9. 97 421
9. 97 447
9. 97 472
9.97 497
9. 97 523
9. 97 548
9.97 573
9.97 698
9. 97 624
9.97 649
9. 97 674
9.97 700
9.97 725
9. 97 750
9. 97 776
9. 97 801
9.97 826
9. 97 851
9. 97 877
9.97 902
9.97 927
9.97 953
9.98 180
9.98 206
9. 98 231
9. 98 256
9. 98 281
9. 98 307
9. 98 332
9. 98 357
L. Cotg. d. c.
0. 03 034
0. 03 009
0. 02 984
0. 02 958
0. 02 933
0. 02 908
0. 02 882
0.02 857
0. 02 832
0. 02 807
0. 02 781
0.02 756
0. 02 731
0. 02 705
0. 02 6fi0
0.02 655
0.02 629
0. 02 604*
0. 02 579
0. 02 553
0. 02 528
0. 02 503
0. 02 477
0. 02 452
0. 02 427
0. 03 402
0. 02 376
0. 02 351
0. 02 326
0.02 300
0. 02 275
0.02 250
0, 02 224
0.02 199
0. 02 174
0.02 149
0. 02 123
0. 02 098
0. 02 073
0.02 047
0.02 022
0. 01 997
0.01 971
0.01 946
0. 01 921
0.01 896
0.01 870
0.01 845
0.01 820
0.01 794
0. 01 769
0.01 744
■ 0. 01 719
0.01 693
0. 01 668
0. 01 643
0. 01 617
0.01 592
0. 01 567
0. 01 542
0.01 516
1 200
86 176
86 164
86 152
86 140
86 128
86 116
86 104
86 092
86 080
86 068
85 900
85 888
85 876
85 864
85 851
83 839
85 827
85 815
85 803
85 791
85 779
85 766
85 754
85 742
85 730
85 718
85 706
85 693
9,0
11,0
13,0
10,0.
17,0
19,0
21,0
23,0
25,0
0,4
0,4
0,9
0,8
1,3
1,2
1,Y
1,7
2,2
2,1
2,6
2,5
3,0
2,9
3,5
3,3
3,9
3,8
4,3
4,2
8,7
8,3
13,0
12,.T
l/,3
16,7
21,7
20,8
14
IS
0,2
0,2
0,5
0,4
0,7
0,6
0,9
0,9
1,2
1,1
1,4
1,3
1,6
1,5
1,9
1,7
2,1
2,0
2,3
2,2
4,V
4,3
7,0
6,,')
9,3
8,V
11,V
10,8
12
11
0,2
0,2
0,4
0,4
(1,6
0,6
0,8
0,7
1,0
0,9
1,2
i,l
1,4
1,3
1,6
l,.*)
1,8
1,6
2,0
1,8
4,0
3,V
6,0
b,5
8,0
7,3
1U,0
9,2
8,7
10,6
12,5
14,4
16,3
18,3
20,2
22,1
24,1
1,1
3,1
5,2
7,3
9,4
11,5
13,5
15,6
17,7
19,8
21,9
23,9
46°
298
A MANUAL OF TOPOGRAPHIC METHODS.
Ta^le XXXVI. — Loijarithmic sines, cosmesj tangents, and cotangents — Continued.
[Extracted, from Crauss' LogiU'itlimic and Trigonometric Tables.]
440
9. 84 177
9. 84 190
9. 84 203
9.84 216
9.84 229
9. 84 308
9. 84 321
9. 84 334
9. 84 347
9.84 360
9. 84 373
9. 84 385
9. 84 308
9. 84 411
9. 84 424
9. 84 437
9. 84 450
9. 84 463
9. 84 476
9. 84 489
9. 84 502
9.84 515
9.84 528
9. 84 540
9. 84 553
9. 84 566
9.84 579
9. 84 592
9.84 605
9. 84 618
9. 84 630
9.84 643
9. 84 656
9. 84 669
9. 84 707
9. 84 720
9. 84 733
9. 84 745
9.84 75S
9. 84 771
9. 84 784
9. 84 796
9. 84 809
9.84 822
9.84 835
9.84 847
9. 84 860
9.84 873
9. 84 885
9. 84 898
9. 84 911
9. 84 923
9.84 936
9. 84 949
9.98 509
9.98 534
9. 98 560
9. 98 585
9. 98 610
9. 98 635
9. 98 681
9.98 686
9. 98 863
9. 98 888
9.98 913
9. 98 939
9. 98 964
9. 98 989
9.99 015
9. 99 040
9.99 065
9.99 090
9.99 116
9.99 141
9.99 166
9.99 191
9.99 217
9. 99 242
9.99 267
9.99 293
9. 99 318
9.99 343
9.99 368
9.99 394
9. 99 419
9. 99 444
9. 99 460
9. 99 495
9.99 520
9. 99 545
9. 99 570
9.99 596
9. 99 621
9. 99 646
9.99 672
9. 99 697
9. 99 722
9.99 747
9.99 773
9. 99 798
9.99 823
9. 99 848
9. 99 874
9. 99 899
9.99 924
9. 99 949
9. 99 975
L. Cotg.
0. 01 516
0. 01 491
0. 01 460
0. 01 440
0.01 415
0.01 390
0. 01 365
0.01 339
0. 01 314
0. 01 289
0. 01 263
0.01 238
0.01 213
0. 01 188
0. 01 162
0.01 137
0.01 112
0. 01 087
0. 01 061
0. 01 036
0.01 Oil
0.00 985
0.00 960
0.00 935
0. 00 910
0. 00 884
0.00 859
0. 00 834
0.00 809
0. 00 783
0.00 758
0.00 733
0. GO 707
0.00 682
0. (
657
0. 00 632
0. 00 606
0. 00 581
0.00 556
0. 00 .531
0. 00 505
0. 00 480
0. 00 455
0.00 430
0. 00 404
0. 00 379
0. 00 354
0. 00 328
0.00 303
0. 00 278
0, 00 253
0. 00 227
0. 00 202
0. 00 177
0.00 152
0. 00 126
0.00 101
0. 00 076
0. 00 051
0.00 025
0. 00 000
9.85 669
9. 85 657
9.85 645^
9. 85 632
9.85 620
9. 85 608
3.85 596
9.85 583
9. 85 571
9.85 559
9. 85 547
9.85 534
9. 85 522
9. 85 510
9.85 497
9. 85 485
9. 85 473
9. 85 460
9. 85 448
9.85 436
9. 85 423
9.85 411
9.85 399
9. 85 386
9. 85 374
9.85 361
9.85 349
9.85 337
9.85 324
9. 85 312
9.85 299
9.85 287
9. 85 274
9.85 262
9.85 2.50
9. 85 237
9. 85 225
9. 85 212
9.85 200
9.85 187
9.85 175
9. 85 162
9.85 150
9.85 137
9. 85 125
9.85 112
9.85 100
9.85 087
9. 85 074
9.85 062
9. 85 049
9.85 037
9. 85 024
0,4
0,9
1,3
h^
2,2
2,6
3,0
3,5
3,9
4,3
8,7
13,0
17,3
21,7
1,7
2,1
2,5
2,9
3,3
3,8
4,2
8,3
12,5
16,7
20,8
14
13
0,2
0,2
0,5
0,4
0,7
0,6
0,9
0,9
1,2
1,1
1,4
1,3
1,6
1,5
1,9
1,7
2,1
•2,0
2,3
2,2
4,7
4,3
7,0
6,5
9,3
8,7
11,7
10,8
3,0
5,0
7,0
9,0
11,0
13,0
15,0
17,0
19,0
21,0
23,0
25,0
1,1
3,2
5,4
7,6
9,8
11,9
14,1
16,2
18,4
20,6
22,8
24,9
0,9
2,9
4,8
6,7
8,7
10,6
12,5
14,4
16,3
18,3
20,2
23,1
24,1
1,0
3,1
5,2
7,3
9,4
11,5
13,5
15,6
17,7
19,8
21,9
23,9
45=
INDEX
Acciiracy of control
Adirondack survey
Alidade
for traversing
Altitudes, measurement of, in connection with traverse
linea
"witli plane table
Amount of control
Amphitheaters
Aneroid
Apparent time
Aqueous agencies
Arid region, erosion in
Astronomic determination of position
Astronomical station, selection of
transit and zenith telescope
A zimuth, correction for deviation in
observations, example of record
example of reduction
tor
on Polaris at elongation
reduction of
summary of results
Baldwin device for stretching tape in base line meas-
urement
Barometric observations, reduction of
tables, use of
Base level
line, alignment of.
measurement
example of reduction of
instruments used in
personnel of party
reduction of
tension of tape in
selection of site
Batteries in use
Canyons, formation of
in strata, alternating hard and soft
Chronograph
Chronometer, break circuit
Cistern barometer
filling of tubes
method of use
Classification of work
Coast and Geodetic Survey, United States
Collimation, correction for error of
Colors used on original maps
Comparison of time
Contour interval
Conventions
Corrasion
Declination
Declinations, apparent, computationof
Deposition from volcanic action
water
the atmosphere
Disintegration
Distances, computation of
Diurnal aberration, correction for
Douglas odometer
Erosion
European maps, scales of
Features represented
Field work of astronomical determination
scale of
Figure adjustment
Fortieth parallel survey
Greneralization of maps
Geodetic coordinates
Geological and Geographical Survey of Territories
Geometric control
Glacial deposition
Heliotrope, Coast Survey form
Steinheil
Horizontal angles, errors incident to measurement of . .
form of record
instructions for measurement of
order of readings
location
Inequality of pivots, correction for
Inspection
Introduction
Johnson plane table
Lake survey, United States
Land OflBce plats
surveys
Latitude determination, form of record of
how determined
observations
list of stars for
reduction of
Least squares in figure adjustment
station adjustment
Legencls upon maps
Level, corrections for error of
division, measurement of
Longitude determination, example of reduction
how determined -
Massachusetts, Borden survey of
Mean time -
Method of adjusting transit in meridian -
control
Micrometer screw, measurement of division of head of
New Jersey State survey
299
300
INDEX.
Page.
New York State survey ^
Nortliern trauscontiueutnl survey 3
Odometers ^^
Offloework 128
Organization of parties *1
Pennsylvania State survey 5
Personal equation 35
Piracy H^
Plan of map of United States 6
Plane table ^
sheets 82
Primary elevations ''''
triangulation -IS
prosecution of work 63
selection of stations 49
Private surveys 5
Profiles of streams 112
Projections 129
Public land surveys, plan of 101
utilization of 101
Eailroad profiles 6
surveys 5
Eeduction to center 65
Reports 125
Eight ascension 17
Eocky Mountain region, survey of 3
Scaleof United States map 7
Secondary triangulation 79
Sidereal time 17
Signals and observing towers in triangulation 51
in triangulation 50
Sinks, origin of 115
Size of sheets 10
Sketching U-106
Solar time 17
Spherical excess 65
Stadia measurement ^ 92
Station error 35
Station adjustment 66
Support for astronomical transit 21
Surveys under United States Government 2
Talcott's method 17
Theodolites for triangulation 5i
Three-point problem 83
Time determination, example of record 32
observations for 28
reduction of 29
Titles of maps 130
Topographic features, origin of 108
forms, influence of structure upon 117
parties, distribution of work in 91
Transportation HI
Traversing 12, 13
Traverse lines for primary control 75
work 85
plane tables for 86
Triangulation 12
Uplift 108
Water gaps 116
Weathering HI
Wind gaps 116
Zenith distance 17
telescope and asti'!>uomical transit - - 18
\
\
k
y.^}^^
/.
LEGEND
1 I NorOuSTi I'naAc Ttaiui. Survey.
^^m^p I'-^.t'otttit anil Oeodetiv Sut^fty.
\Cf
\ ■*'
^
t
Vi
\^?^
•^ /
1
c^\
\
AJ/
<^
.-
•
•k \
<*
^""' '. .
'
\ ' ''
g&-:
it^i
^ ***-'-N®V-5^
^
siioinxn I'lioGUKSS OFTKLVNT.i-LVTiox Tomciui'in-
ASTRONOMIC LOC.ATKIX.
^
■y^,
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11