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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.

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ALTITUDE TABLES.

187

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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
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.94
.93
.92
.91
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.99
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.96

.95
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1.0

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1. 0

.98
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.96
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.93
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.99
.98

.97
.96
.95
.94
.93

1.0

.99

.98
.97
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.94
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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

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148

A MANUAL OF TOPOGRAPHIC METHODS.

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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

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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

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LEGEND

1 I NorOuSTi I'naAc Ttaiui. Survey.

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