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Digitized by the Internet Archive
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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.
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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 |
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■*CO |
dddd ■ +-i-4-h : |
• W<MMt--(iH ■ ddddd |
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;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 |
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|
Points intersected from traverse |
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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.
143
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A MANUAL OF TOPOGEAPHIC METHODS.
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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. |
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121 |
122 |
123 |
124 |
125 |
126 |
127 |
128 |
129 |
130 |
131 |
132 |
133 |
134 |
135 |
136 |
137 |
138 |
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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' |
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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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ALTITUDE TABLES.
149
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150
A MANUAL OF TOP0GEA.PHIC METHODS.
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ALTITUDE TABLES.
151
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152 A MANUAL OF TOPOGKAPHIC METHODS.
Table VII. — Differences of altitude from angles of elevation or depression.
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. ,^.. 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 ^• |
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0° |
1° |
2° |
3° |
40 |
6° |
6° |
JO |
8° |
90 |
10° |
11° |
. 12° |
13° |
14° |
16° |
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hi |
l>j |
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hi |
hi |
hi |
hi |
hi |
hi Feet. |
h. |
h. |
hi Feet. |
hi |
hi |
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Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
Feet. |
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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 |
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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 |
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■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| |
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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 |
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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 |
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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 |
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|
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 |
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|
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 |
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|
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 |
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|
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 |
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|
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 |
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|
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 |
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|
■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 |
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|
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 |
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|
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 |
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|
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 |
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|
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 |
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|
25 |
38.4 |
130.6 |
222.8 |
315.2 |
407.8 |
50O7 |
593.8 |
687.3 |
781.3 |
875.7 |
970. 6 1066. 2 |
1162. 5| 1259.5 |
1357.3 1456.0 |
|||
|
26 |
39.9 |
132.1 |
224.4 |
316.8 |
409.4 |
502.2 |
595.4 |
688.9 |
782.8 |
877.3 |
972.2 1067.8 |
1164. 1: 1261. 1 |
1358.9 1457.7 |
|||
|
27 |
41.5 |
133.6 225.9 |
318.3 |
410.9 |
503.8 |
596.9 |
690.4 |
784.4 |
878,8 |
973.8 1069 4 |
1165,7) 1162,7 |
1360.6 1459 3 |
||||
|
28 |
43.0 |
135.2 227.4 |
319 9 |
412.5 |
505.3 |
598.5 |
692.0 |
786.0 |
880 4 |
975. 4I 1071. 0 |
1167. 3 |
1264. 4 |
1362.2 1461.0 |
|||
|
29 |
44.5 |
136.7 229.0 |
321.4 |
414.0 |
506.9 |
600.0 |
693.6 |
787.5 |
882. 0 |
977, 0' 1072, 6 |
1168. 9 |
1266. 0 |
1363.9, 1462.6 |
|||
|
30 |
46.1 |
138.3 |
230. 5 |
322.9 |
415.5 |
508.4 |
601.6 |
695.1 |
7891 |
883.6 |
978, 6. 1074. 2 |
1170. 6 |
1267. 6 |
1365.5! 1464.3 |
||
|
31 |
47.6 |
139 8 |
232.1 |
324.5 |
417.1 |
510.0 |
603.1 |
696.7 |
790.7 |
885.1 |
980.1' 1075.8 |
1172.2 |
1269. 3 |
1367,1! 1465.9 |
||
|
32 |
49.2 |
141.3 |
233.6 |
326.0 |
418.6 |
511.5 |
604.7 |
698.2 |
792.2 |
886.7 |
981. 7, 1077. 4 |
1173. 8 |
1270,9 |
1368.8 1467.6 |
||
|
33 |
50.7 |
142.9 |
235.1 |
327.6 |
420.2 |
513.0 |
606.2 |
699 8 |
793.8 |
888.3 |
983,3 1079,0 |
1175. 4 |
1272, 5 |
1370.4 1469 2 |
||
|
34 |
52.2 |
144.4 |
236.7 |
329.1 |
421.7 |
514.6 |
607.8 |
701.4 |
795.4 |
889 9 |
984,9 108O6 |
1177. 0 |
1274, 1 |
1372. 1 |
1470. 9 |
|
|
35 |
53.8 |
146.0 |
238.2 |
330.6 |
423.3 |
516.2 |
601.3 |
702.9 |
797.0 |
891.5 |
986.5 1082.2 |
1178. 6 |
1275. 7 |
1373. 7 |
1472. 5 |
|
|
36 |
55.3 |
147.5 |
239 8 |
332.2 |
424.8 |
517.7 |
610.9 |
704.5 |
798.5 |
893. ( |
988. li 1083.8 |
1180. 2 |
1277. 4 |
1375. 3 |
1474, 2 |
|
|
37 |
56.8 |
149.0 |
241.3 |
333.7 |
426.4 |
519.3 |
612.5 |
706.1 |
800.1 |
894.6 |
989.7 |
1085. 4 |
1181.8 |
1279, 0 |
1377. 0 |
1475. 9 |
|
38 |
58.4 |
150.6 |
242.8 |
335.3 |
427.9 |
520.8 |
614. 0 707. 6 |
801.7 |
896.2 |
991.3 |
1087. 0 |
1183.4 |
1280. 6 |
1378. 6 |
1477. 5 |
|
|
39 |
59.9 |
152.1 |
244.4 |
336.8 |
429 5 |
522.4 |
615.6 709.2 |
803.2 |
897.8 |
992.9 |
1088. 6 |
1185. 0 |
1282. 2 |
1.380. 3 |
1479.2 |
|
|
40 |
61.4 |
153.6 |
2J5.9 |
338.4 |
431.0 |
523.9 |
617.1 710.7 |
804.8 |
899 4 |
994.5 |
1090. 21 1186. 71 1283. 9 |
1381. 9 |
1480. 8 |
|||
|
41 |
63.0 |
155.2 247.5 |
339 9 |
432.6 |
525.5 |
618. 7 712. 3 |
806.4 |
900.9 |
990,0 |
1091.81 1188.3! 1285.5 |
1383. 5 |
1482. 5 |
||||
|
42 |
64.5 |
156.7 249 0 |
341.4 |
i 434.1 |
527.0 |
620.21 713.9 |
807.9 |
902.5 |
997.6 |
1093.4 |
1189. 9 |
1287. 1 |
1385.2 |
1484. 1 |
||
|
43 |
66.0 |
158.2 250.5 |
343.0 |
1 435.6 |
528.6 |
621.8 |
715.4 |
809.5 |
904.1 |
999 2 |
1095. 0 |
1191. 5 |
1288. 8 |
1386. 8 |
1485. 8 |
|
|
44 |
67.6 |
159 8 252.1 |
344.0 |
' 437.2 |
530.1 |
623.3 |
717.0 |
811.1 |
905.7 |
1000. 8 |
1096. 6 |
1193. 1 |
1290. 4 |
1388. 6 |
1487. 5 |
|
|
45 |
69.1 |
161.3 253.6 |
346.1 |
438.7 |
531.7 |
624.9 |
718.6 |
812.7 |
907.3 |
1002.4 |
1098. 2 |
1194. 7 |
1292. 0 |
1390. 1 |
1489. 1 |
|
|
46 |
70.6 |
162.9 255.1 |
347. e |
440.3 |
533.2 |
626.4 |
720.1 |
814.2 |
908.8 |
1004. 0 |
1099, 8 |
1196. 3 |
1293. 7 |
1391. 8 |
1490. 8 |
|
|
47 |
72.2 |
164.4 256.'- |
3491 |
441.8 |
534.8 |
628.0 |
721.7 |
815.8 |
910 4 |
1005. 6 |
1101. r |
1197. 9 |
1295. 3 |
1393. 4 |
1492. 4 |
|
|
48 |
73.7 |
165.9 258.2 |
350.- |
443.4 |
536.3 |
629 6 |
723.3 |
817,4 |
912,0 |
1007. 2 |
1103. 1 |
1199. 6 |
1296. 9 |
1395. 0 |
1494. 1 |
|
|
49 |
75.3 |
167.5 259. S |
352.2 |
444.9 |
537.9 |
631.1 |
724.8 |
819 0 |
913.6 |
: 1008.8 |
1104. 7 |
1201. 2 |
1298. 5 |
1396. 7 |
1495.8 |
|
|
50 |
76. S |
169.0 261.3 |
353. S |
446.5 |
539.4 |
632.7 |
726.4 |
820.5 |
915.2 |
1010, 4 |
1106. 3 |
1202. 8 |
1300. 2 |
1398.3 |
1497.4 |
|
|
51 |
78.1 |
170.6 262. f |
355. |
448.0 |
541.0 |
634.2 |
728.0 |
822.1 |
916.' |
1012, 0 |
1107. 9 |
1204. 4 |
1301. 8 |
1400, 0 |
1499. 1 |
|
|
52 |
79. t |
172.1; 264.4 |
356. |
449.6 |
542.5 |
635. f |
729 5 |
823.7 |
918,? |
1013, 6 |
1109, 5 |
1206, 0 |
1303,4 |
1401.6 |
1500. 7 |
|
|
S3 |
81.4 |
173.6 265. £ |
358..: |
451.1 |
544.1 |
637. L |
731.1 |
825.2 |
919. £ |
1015. 2 |
1111,1 |
1207. ' |
1305.0 |
1403, 3 |
1502,4 |
|
|
54 |
82. < |
176.2 267.. |
360. |
452.' |
545.1 |
638. £ |
732.7 |
826.8 |
921. c |
1016. i |
1112.' |
1209 3 |
1306.7 |
1404.9, 1504.1 |
||
|
55 |
84.. |
176. 7 1 269 ( |
361. |
454.2 |
547.2 |
640. 4' 734. 2 |
828.4 |
923.1 |
1018.4 |
1114,3 |
1210, S |
1308. 3 |
1406.5 1505.7 |
|||
|
56 |
86. |
178. 2: 270. |
363. |
) 455. i |
548.' |
642. C |
735.8 |
830. C |
924.' |
1020. C |
1115, £ |
1212, e |
1309 9 |
1408.21 1507.4 |
||
|
57 |
87. |
) . 179. 8 272. |
364. |
3 457. |
550.: |
643. |
737.4 |
831.. |
926.' |
1021. £ |
1117, £ |
1214, 1 |
1311. 6 |
1409,8; 1509 0 |
||
|
58 |
89. |
181.3 273.6 366. |
I 458.' |
551.! |
645. |
738. a |
833. |
927. |
1023. 1 |
1119. |
1215, i |
1313.2; 1410.51 1510.7 |
||||
|
59 |
90. |
3 182.9 275.2 367. |
7 460. |
553.4 |
646. |
740. E |
834.' |
929' |
1024. |
1120. |
1217.4 |
1314.8 1413,1] 1512.4 |
||||
|
60 |
92. |
i 184.4 276.7 369. |
2 461. |
555. ( |
648. |
742. C |
836. |
931. |
1026. |
1122, |
1219. |
1316.5 1414.8 1514.0 |
ALTITUDE TABLES.
153
Table VIII. — Corrections for curvature and refraction.
|
D |
hz |
0 |
ll2 |
B |
hj |
D |
h. |
|
Miles. |
Feet. |
Miles. |
Feet. |
Miles. |
Feet. |
Miles. |
Feet. |
|
1.0 |
0.6 |
5.5 |
17.3 |
||||
|
1.1 |
0.7 |
5.6 |
18.0 |
3.6 |
7.4 |
8.1 |
37.6 |
|
1.2 |
0.8 |
5.7 |
18.6 |
3.7 |
7.8 |
8.2 |
38.6 |
|
1.3 |
1.0 |
5.8 |
19.3 |
3.8 |
8.3 |
8.3 |
39.5 |
|
1.4 |
1.1 |
5.9 |
20.0 |
3.9 |
8.7 |
8.4 |
40.5 |
|
1.5 |
1.3 |
6.0 |
20.6 |
4.0 |
9.2 |
8.5 |
41.4 |
|
1.6 |
1.5 |
6.1 |
21.3 |
4.1 |
9.6 |
8.6 |
42.4 |
|
1.7 |
1.7 |
6.2 |
22.0 |
4.2 |
10.1 |
8.7 |
43.4 |
|
1.8 |
1.9 |
6.3 |
22.8 |
4.3 |
10.6 |
8.8 |
44.4 |
|
1.9 |
2.1 |
6.4 |
23.5 |
4.4 |
11.1 |
8.9 |
45.4 |
|
2.0 |
2.3 |
6.5 |
24.2 |
4.5 |
11.6 |
9.0 |
46.4 |
|
2.1 |
2.5 |
6.6 |
25.0 |
4.6 |
12.1 |
9.1 |
47.5 |
|
2.2 |
2.8 |
6.7 |
25.7 |
4.7 |
12.7 |
9.2 |
48.5 |
|
2.3 |
3.0 |
6.8 |
20.5 ■ |
4.8 |
13.2 |
9.3 |
49.6 |
|
2.4 |
3.3 |
6.9 |
27.3 |
4.9 |
13.8 |
9.4 |
50.7 |
|
2.5 |
3.6 |
7.0 |
28.1 |
5.0 |
14.3 |
9.5 |
51.7 |
|
2.6 |
3.9 |
7.1 |
28.9 |
5.1 |
14.9 |
9.6 |
52.8. |
|
2.7 |
4.2 |
7.2 |
29.7 |
5.2 |
15.5 |
9.7 |
53.9 |
|
2.8 |
4.5 |
7.3 |
30.5 |
5.3 |
16.1 |
9.8 |
55.1 |
|
2.9 |
4.8 |
7.4 |
31.4 |
5.4 |
16.7 |
9.9 |
56.2 |
|
3.0 |
5.2 |
7.5 |
32.2 |
5.5 |
17.3 |
10.0 |
57.3 |
|
8.1 |
5.5 |
7.6 |
33.1 |
||||
|
3.2 |
5.9 |
7.7 |
34.0 |
||||
|
3.3 |
6.2 |
7.8 |
34.9 |
||||
|
3.4 |
6.6 |
7.9 |
35.8 |
||||
|
3.5 |
7.0 |
8.0 |
36.7 |
154
A MANUAL OF TOPOGEAPHIC METHODS.
Table IX. — For computlnri differences of altitude from angles o)
scale 1:45000). [Prepared by li. S. Wooclwartl.] _.„ - 1^.. , C + D7ii + /ia&r angles of elevation.
Difterenceof altit-:icl6= ^ _ j,;,^ ^ /^fgj angles of depression.
elev:at%on or depression (applicable to
T> — distance in scale divisions ^s inch each; a ■- tion for curvature and refraction.
Argument, for Ai is a ; argument for ftj is D.
angle of elevation or depression; fti = 75 feet X tan a; 7i2 = correc-
|
fti in feet. | |
D |
fta |
D |
Ih |
||||||||
|
' |
0° |
1° |
20 |
3° |
4° |
5" |
6° |
7° |
Scale livisions. |
Feet. |
Scale iivisions.j |
Feet. |
|
0 |
.000 |
1.309 |
2.619 |
3.931 |
5.245 |
6.562 |
7.882 |
9.208 |
00 |
0 |
720 |
60 |
|
1 |
.022 1 |
1.331 |
2.641 |
3.952 |
5.266 |
6.583 |
7.905 |
9. 231 |
93 |
1 |
726 |
61 |
|
.043 |
1.353 |
2. 662 |
3.974 |
5.288 |
6.605 |
7.927 |
9.253 |
131 |
2 |
732 |
62 |
|
|
3 |
.065 |
1.375 |
2.684 |
3.996 |
5.310 |
6.628 |
7.949 |
9.275 |
161 |
3 |
738 |
63 |
|
1 |
.087 |
1.396 |
2.707 |
4.018 |
5.332 |
6.649 |
7.971 |
9.298 |
1S6 |
4 |
744 |
64 |
|
5 |
.109 |
1.418 |
2.728 |
4.040 |
5.354 |
6.671 |
7.993 |
9.319 |
208 |
5 |
750 |
65 |
|
6 |
.131 |
1.440 |
2.750 |
4.062 |
5.376 |
6.694 |
8.015 |
9.342 |
228 |
6 |
755 |
66 |
|
.153 |
1.462 |
2.772 |
4.084 |
•5. 398 |
6.715 |
8.037 |
9.364 |
246 |
7 |
761 |
67 |
|
|
8 |
.175 |
1.483 |
2.794 |
4.105 |
5.420 |
6.737 |
8.059 |
9.386 |
263 |
8 |
767 |
68 |
|
9 |
.196 |
1.505 |
2.815 |
4.127 |
5.442 |
6.760 |
8.081 |
9.408 |
279 |
9 |
772 |
69 |
|
10 |
.218 |
1.527 |
2.837 |
4.150 |
5.464 |
6.781 |
8.104 |
9.430 |
294 |
10 |
778 |
70 |
|
11 |
.240 |
1.549 |
2. 859 |
4.171 |
5.485 |
6.803 |
8.125 |
9.452 |
308 |
11 |
783 |
71 |
|
12 |
.262 |
1.571 |
2.881 |
4.193 |
5.508 |
6.826 |
8.147 |
9.475 |
322 |
12 |
789 |
72 |
|
13 |
.283 |
1.593 |
2.903 |
4.215 |
5. 530 |
6.847 |
8.170 |
9.496 |
335 |
13 |
794 |
73 |
|
14 |
.305 |
1.615 |
2.925 |
4.237 |
5.551 |
6.869 |
8.191 |
9.519 |
348 |
14 |
800 |
74 |
|
15 |
.327 |
1.636 |
2.947 • |
4.258 |
5.573 |
6.892 |
8.214 |
9.541 |
360 |
15 |
805 |
75 |
|
16 |
.349 |
1.658 |
2.968 |
4.281 |
5.596 |
6.913 |
8.236 |
9.563 |
372 |
16 |
811 |
76 |
|
i; |
.371 |
1.680 |
2.990 |
4.303 |
5.617 |
6.935 |
8.258 |
9.586 |
383 |
17 |
816 |
77 |
|
18 |
.393 |
1.702 |
3.012 |
4.324 |
6.639 |
6.958 |
8.280 |
9.607 |
394 |
18 |
821 |
78 |
|
10 |
.415 |
1.723 |
3.034 |
4.346 |
5.661 |
6.979 |
8.302 |
9.630 |
405 |
19 |
826 |
79 |
|
so |
.436 |
1.746 |
3.056 |
4.368 |
5.683 |
7.001 |
8.324 |
9.652 |
416 |
20 |
832 |
80 |
|
21 |
.458 |
1.768 |
3.078 |
4.390 |
5.705 |
7.024 |
8.346 |
9.674 |
426 |
21 |
837 |
81 |
|
22 |
.480 |
1.789 |
3.100 |
4.412 |
5.727 |
7.045 |
8.368 |
9.697 |
436 |
22 |
842 |
82 |
|
23 |
.502 |
1.811 |
3.121 |
4.434 |
5.749 |
7.067 |
8. 390 |
9.718 |
446 |
23 |
847 |
83 |
|
24 |
.523 |
1.833 |
3.143 |
4.456 |
5.771 |
7.090 |
8.413 |
9.741 |
455 |
24 |
852 |
84 |
|
25 |
.545 |
1.855 |
3.165 |
4.477 |
5.793 |
7.111 |
8.434 |
9.763 |
465 |
25 |
857 |
85 |
|
26 |
.567 |
1.875 |
3.187 |
4.499 |
5.815 |
7.133 |
8.457 |
9.785 |
474 |
26 |
862 |
86 |
|
27 |
.589 |
1.898 |
3.209 |
4.522 |
5.836 |
7.156 |
8.479 |
9.807 |
483 |
27 |
867 |
87 |
|
28 |
.610 |
1.920 |
3.231 |
4.543 |
5. 859 |
7.177 |
8.501 |
9.829 |
492 |
28 |
872 |
88 |
|
29 |
.633 |
1.942 |
3.253 |
4.665 |
5.881 |
7.200 |
8.523 |
9.852 |
501 |
29 |
877 |
89 |
|
30 |
.655 |
1.964 |
3.274 |
4.587 |
5.902 |
7.222 |
8.545 |
9.874 |
509 |
30 |
882 |
90 |
|
31 |
.676 |
1.986 |
3.296 |
4.609 |
5.924 |
7.243 |
8.567 |
9.896 |
518 |
31 |
^7 |
91 |
|
32 |
.698 |
2.008 |
3.318 |
4.631 |
5.947 |
7.266 |
8.589 |
9.918 |
526 |
32 |
892 |
92 |
|
33 |
.720 |
2.029 |
3.340 |
4.653 |
5.968 |
7.288 |
8.611 |
9.940 |
534 |
33 |
897 |
93 |
|
34 |
.742 |
2.051 |
3.362 |
4.675 |
5.990 |
7.309 |
8.633 |
9.963 |
542 |
34 |
901 |
94 |
|
35 |
.763 |
2.073 |
3.384 |
4.696 |
6.013 |
7.332 |
8.656 |
9.985 |
550 |
35 |
906 |
95 |
|
36 |
.785 |
2.095 |
3.406 |
4.718 |
6.034 |
7.354 |
8.677 |
10. 007 |
558 |
36 |
911 |
96 |
|
37 |
.807 |
2.116 |
3.427 |
4.741 |
6.056 |
7.375 |
8.700 |
10. 029 |
S6G |
37 |
916 |
97 |
|
38 |
.829 |
2.138 |
3.449 |
4.762 |
6.078 |
7.398 |
8.722 |
10. 051 |
573 |
38 |
920 |
98 |
|
39 |
.651 |
2.161 |
3.471 |
4.784 |
6.100 |
7.420 |
8.744 |
10. 074 |
581 |
39 |
925 |
99 |
|
40 |
.873 |
2.182 |
3.495 |
4.806 |
6.122 |
7.442 |
8.766 |
10. 096 |
588 |
40 |
930 |
100 |
|
41 |
.895 |
2.204 |
3.515 |
4.828 |
6.144 |
7.464 |
8.788 |
10. 118 |
595 |
41 |
934 |
101 |
|
42 |
.916 |
2.226 |
3.537 |
4.850 |
6.166 |
7.486 |
8.810 |
10. 141 |
603 |
42 |
939 |
102. |
|
43 |
.938 |
2.248 |
3.559 |
4.872 |
6.188 |
7.508 |
8.833 |
10. 162 |
610 |
43 |
943 |
103 |
|
44 |
.960 |
2.269 |
3.580 |
4.894 |
6.210 |
7.530 |
8.854 |
10. 185 |
617 |
44 |
948 |
104 |
|
45 |
.982 |
2.291 |
3.602 |
4.915 |
6.232 |
7.552 |
8.877 |
10.207 |
624 |
45 |
953 |
105 |
|
46 |
1.003 |
2.313 |
3.624 |
4.938 |
8.254 |
7.574 |
8.899 |
10. 229 |
631 |
46 |
957 |
106 |
|
47 |
1.025 |
2.335 |
3.646 |
4.960 |
6.276 |
7.596 |
8.921 |
10. 252 |
637 |
47 |
962 |
107 |
|
48 |
1.047 |
2.357 |
3.668 |
4.981 |
6.298 |
7.618 |
8.943 |
10. 273 |
644 |
48 |
966 |
108 |
|
49 |
1.069 |
2.379 |
3.690 |
5.003 |
6.320 |
7.640 |
8.965 |
10. 296 |
651 |
49 |
971 |
109 |
|
50 |
1.091 |
2.401 |
3.712 |
5.025 |
6.342 |
7.662 |
8.987 |
10.318 |
657 |
50 |
975 |
110 |
|
51 |
1.113 |
2.422 |
3.733 |
5.047 |
6.364 |
7.684 |
9.010 |
10. 340 |
664 |
51 |
980 |
111 |
|
52 |
1.135 |
2.444 |
3.755 |
5.069 |
6.385 |
7.706 |
9.031 |
10. 363 |
670 |
52 |
984 |
112 |
|
53 |
1.156 |
2.466 |
3.776 |
5.091 |
6.408 |
7.729 |
9.054 |
10. 384 |
677 |
53 |
988 |
113 |
|
54 |
1.178 |
2.488 |
3.799 |
5.113 |
6.430 |
7.750 |
9.076 |
10. 407 |
683 |
54 |
993 |
114 |
|
55 |
1.200 |
2.509 |
3.821 |
5.135 |
6.451 |
7.772 |
9.098 |
10.429 |
690 |
55 |
997 |
115 |
|
56 |
1.222 |
2.532 |
3.843 |
5.157 |
6. 474 |
7.795 |
9.120 |
10. 451 |
696 |
56 |
1001 |
116 |
|
57 |
1.243 |
2.554 |
3.865 |
5.179 |
6.496 |
7.816 |
9.142 |
10. 474 |
702 |
57 |
1005 |
117 |
|
58 |
1.265 |
2.575 |
3.886 |
5.20U |
6.517 |
7.839 |
9.164 |
10. 496 |
708 |
58 |
1010 |
118 |
|
59 |
1.287 |
2.597 |
3.900 |
5.222 |
6.540 |
7.861 |
9.187 |
10. 518 |
714 |
59 |
1014 |
119 |
|
60 |
1.309 |
2.619 |
3.931 |
5.245 |
6.562 |
7.882 |
9.208 |
10.540 |
720 |
60 |
1018 |
120 |
ALTITUDE TABLES.
155
Table IX. — For comjiuting differences of altitude from angles of elevation or depression (applicable to scale i;450(90)— Continued.
|
h, in feet. |
D |
iH |
D |
Jh |
||||||||
|
' |
8° |
9° |
10° |
11° |
12° |
13° |
14° |
15° |
Scale divisions |
Feet. |
Scale divisions |
Feet. |
|
0 |
10. 540 |
11. 878 |
13. 225 |
14. 578 |
15,942 |
17,315 |
18. 700 |
20. 096 |
00 |
0 |
720 |
60 |
|
1 |
10. 563 |
11. 901 |
13. 247 |
14. 601 |
16, 964 |
17, 338 |
18, 723 |
20. 119 |
93 |
1 |
726 |
61 |
|
2 |
10. 585 |
11. 923 |
13. 270 |
14. 623 |
15, 987 |
17, 361 |
18, 746 |
20, 143 |
131 |
2 |
732 |
62 |
|
S |
10. 607 |
11.946 |
13. 292 |
14. 647 |
16, 010 |
17, 384 |
18, 769 |
20. 166 |
101 |
3 |
73S |
63 |
|
4 |
10. 630 |
11. 968 |
13.315 |
14. 669 |
16. 033 |
17, 407 |
18, 792 |
20. 190 |
186 |
4 |
744 |
64 |
|
5 |
lO. 651 |
11.991 |
13. 337 |
14. 692 |
16, 056 |
17. 430 |
18.813 |
20.213 |
208 |
5 |
750 |
66 |
|
6 |
10. 674 |
12.013 |
13. 360 |
14, 714 |
16, 078 |
17. 453 |
18. 838 |
20.236 |
228 |
6 |
755 |
66 |
|
7 |
10. 696 |
12. 035 |
13. 382 |
14. 737 |
16, 102 |
17.476 |
18, 862 |
20, 260 |
246 |
7 |
761 |
67 |
|
S |
10.718 |
12. 069 |
13. 405 |
14. 760 |
16,124 |
17,499 |
18, 885 |
20, 283 |
263 |
8 |
767 |
68 |
|
9 |
10. 741 |
12. 080 |
13. 427 |
14.782 |
16. 147 |
17. 522 |
18, 908 |
20. 307 |
279 |
9 |
772 |
69 |
|
10 |
10.763 |
12. 103 |
13. 450 |
14. 806 |
16, 170 |
17. 545 |
18, 931 |
20, 330 |
294 |
10 |
778 |
70 |
|
11 |
10. 786 |
12. 125 |
13. 472 |
14. 82S |
16, 192 |
17, 568 |
18, 955 |
20, 353 |
308 |
11 |
783 |
71 |
|
12 |
10. 807 |
12.147 |
13.495 |
14. 851 |
16, 216 |
17, 591 |
18. 978 |
20, 377 |
322 |
12 |
789 |
72 |
|
18 |
10. 830, |
12. 169 |
13. 517 |
14. 873 |
16, 238 |
17. 614 |
19, 001 |
20, 401 |
335 |
13 |
794 |
73 |
|
14 |
10. 862 |
12. 192 |
13. 540 |
14. 896 |
16, 261 |
17. 637 |
19. 024 |
20, 424 |
348 |
14 |
SOO |
74 |
|
15 |
10. 874 |
12.214 |
13. 562 |
14. 918 |
16, 284 |
17, 660 |
19, 048 |
20,447 |
S60 |
15 |
805 |
75 |
|
16 |
10. 897 |
12. 237 |
13. 585 |
14. 941 |
16, 307 |
17, 683 |
19, 071 |
20, 470 |
372 |
16 |
811 |
76 |
|
17 |
10. 919 |
12. 259 |
13. 607 |
14. 964 |
16, 330 |
17, 706 |
19, 094 |
20.494 |
383 |
17 |
816 |
77 |
|
18 |
10. 941 |
12. 282 |
13. 630 |
14. 986 |
16, 353 |
17, 729 |
19, 117 |
20, 518 |
394 |
18 |
821 |
78 |
|
19 |
10. 963 |
12. 304 |
13. 662 |
15. 009 |
16, 375 |
17, 752 |
19, 142 |
20. 541 |
405 |
19 |
826 |
79 |
|
20 |
10. 986 |
12. 326 |
13. 676 |
16. 031 |
16, 398 |
17, 775 |
19. 164 |
20. 564 |
416 |
20 |
832 |
80 |
|
21 |
11.008 |
12. 349 |
13. 697 |
15. 055 |
16. 421 |
17, 798 |
19. 187 |
20, 588 |
426 |
21 |
837 |
81 |
|
22 |
11.030 |
12. 371 |
13. 720 |
15. 077 |
16,444 |
17, 821 |
19, 210 |
20, 611 |
436 |
22 |
842 |
82 |
|
23 |
11. 053 |
12. 394 |
13. 742 |
15.100 |
16, 467 |
17, 845 |
19, 234 |
20, 635 |
446 |
23 |
847 |
S3 |
|
21 |
11.075 |
12.416 |
13. 766 |
15. 123 |
16. 489 |
17, 867 |
19, 257 |
20. 659 |
455 |
24 |
852 |
84 |
|
25 |
11. 097 |
12. 439 |
13. 787 |
15, 145 |
16.513 |
17, 890 |
19. 280 |
20, 682 |
465 |
25 |
857 |
85 |
|
26 |
11.119 |
12.461 |
13.810 |
15,168 |
16,535 |
17, 914 |
19, 303 |
20, 705 |
474 |
26 |
86S |
80 |
|
27 |
11. 142 |
12. 484 |
13. 833 |
15. 190 |
16, 558 |
17, 937 |
19. 327 |
20, 723 |
483 |
27 |
867 |
87 |
|
2S |
11. 164 |
12.505 |
13.865 |
15. 214 |
16, 581 |
17, 959 |
19.350 |
20. 752 |
492 |
28 |
872 |
88 |
|
29 |
U. 186 |
12. 528 |
13. 878 |
15. 236 |
16, 604 |
17. 983 |
19,373 |
20, 776 |
501 |
29 |
877 |
89 |
|
30 |
11. 209 |
12. 550 |
13. 009 |
15. 259 |
16, 627 |
18, 006 |
19, 396 |
20, 799 |
509 |
30 |
882 |
90 |
|
SI |
11. 231 |
12. .573 |
13. 923 |
15.282 |
16, 650 |
18, 029 |
19. 420 |
20, 823 |
518 |
31 |
887 |
91 |
|
32 |
11. 254 |
12. .595 |
13. 945 |
15, 304 |
16, 673 |
18, 052 |
19,443 |
20, 846 |
526 |
32 |
892 |
92 |
|
S3 |
11. 275 |
12. 618 |
13. 968 |
15, 327 |
16, 696 |
18, 075 |
19, 466 |
20, 869 |
534 |
32 |
897 |
93 |
|
34 |
11. 298 |
12. 640 |
13. 990 |
15, 349 |
16, 719 |
18. 097 |
19. 489 |
20, 893 |
542 |
34 |
901 |
94 |
|
35 |
11. 320 |
12.j60i |
14. 013 |
16, 373 |
16, 741 |
18, 121 |
19, 513 |
20, 917 |
550 |
35 |
906 |
95 |
|
S6 |
11. 343 |
12. 683 |
14. o;i6 |
15,395 |
16, 765 |
18, 145 |
19,536 |
20, 940 . |
55S |
36 |
911 |
96 |
|
37 |
11. 366 |
12. 708 |
14. 059 |
15, 418 |
16. 787 |
18,167 |
19, 559 |
20. 964 |
566 |
37 |
916 |
97 |
|
ss |
11.387 |
12. 730 |
14. 081 |
15,441 |
16.810 |
18. 190 |
19, 582 |
20, 987 |
573 |
38 |
920 |
98 |
|
39 |
11. 410 |
12. 753 |
14. 104 |
15. 463 |
16. 833 |
18, 214 |
19, 606 |
21. Oil |
581 |
39 |
925 |
99 |
|
40 |
11.432 |
12.775 |
14. 126 |
15, 486 |
16.856 |
18, 237 |
19. 629 |
21,034 |
588 |
40 |
930 |
loo |
|
41 |
11.454 |
12. 707 |
u. m |
15,509 |
16, 870 |
IS, 260 |
19, 652 |
21. 0.58 |
595 |
41 |
934 |
101 |
|
42 |
11.476 |
12. 8J0 |
14. 1 71 |
15 532 |
16, 902 |
18 283 |
19, (176 |
21,082 |
603 |
42 |
989 |
102 |
|
43 |
11.499 |
12. 842 |
14. 194 |
15. ,554 |
16, 925 |
18,306 |
19. 699 |
31, 105 |
610 |
43 |
943 |
103 |
|
44 |
11.521 |
12.865 |
14. 216 |
15,577 |
16, 948 |
18,329 |
19,723 |
21, 120 |
017 |
44 |
948 |
104 |
|
45 |
11. 543 |
12. 887 |
14. 239 |
16, 600 |
16, 971 |
18, 352 |
19, 746 |
21, 152 |
624 |
45 |
953 |
105 |
|
46 |
11. 566 |
12,910 |
14. 262 |
15. 622 |
16. 993 |
18. 376 |
19, 769 |
21. 175 |
631 |
46 |
957 |
106 |
|
- 47 |
11. 588 |
12.932 |
14. 284 |
15, 646 |
17, 017 |
18, 399 |
19, 792 |
21, 199 |
637 |
47 |
962 |
107 |
|
4>l |
11.611 |
12. 955 |
14.307 |
16, 668 |
17,039 |
18, 421 |
19,816 |
21, 223 |
644 |
48 |
966 |
108 |
|
49 |
11.633 |
12. 977 |
14. 329 |
15, 691 |
17. 062 |
18, 445 |
19, 839 |
21, 247 |
651 |
49 |
971 |
109 |
|
50 |
11. 6.55 |
13. 000 |
14. 352 |
15, 714 |
17. 086 |
18, 468 |
19, 862 |
21. 270 |
657 |
50 |
975 |
110 |
|
51 |
11. 677 |
13. 022 |
14. 374 |
15, 736 |
17, 108 |
18.491 |
19. 886 |
21. 293 |
664 |
51 |
980 |
lU |
|
52 |
11.700 |
13. 045 |
14. 398 |
15,760 |
17,131 |
18, 514 |
19, 909 |
21. 317 |
670 |
52 |
984 |
112 |
|
53 |
11.722 |
13. 067 |
14. 420 |
15, 782 |
17. 154 |
18, 538 |
19, 933 |
21. 340 |
677 |
53 |
988 |
113 |
|
54 |
11. 745 |
13. 090 |
14. 443 |
16.805 |
17. 177 |
18, 560 |
19. 956 |
21. 364 |
683 |
54 |
993 |
114 |
|
55 |
11.767 |
13.112 |
14. 465 |
15, 828 |
17, 200 |
18, 583 |
19, 979 |
21,388 |
690 |
55 |
997 |
115 |
|
56 |
11.789 |
13. 135 |
14. 488 |
15, 850 |
17, 223 |
18, 607 |
20. 002 |
21,412 |
696 |
56 |
1001 |
116 |
|
57 |
lx.812 |
13. 157 |
14. 510 |
15, 873 |
17, 246 |
18, 630 |
20, 026 |
21, 435 |
702 |
57 |
1005 |
117 |
|
58 |
11.834 |
13. 180 |
14. 533 |
15, 896 |
17, 269 |
18,663 |
20, 050 |
21. 459 |
708 |
69 |
1010 |
118 |
|
59 |
11. 857 |
13. 202 |
14. 556 |
15, 919 |
17. 292 |
18, 676 |
20. 073 |
21,482 |
714 |
58 |
1014 |
119 |
|
60 |
11. 878 |
13. 225 |
14.578 |
16, 942 |
17. 315 |
IS. 700 |
20.096 |
21. 506 |
720 |
60 |
1018 |
120 |
156
A MANUAL OF TOPOGRAPHIC METHODS.
-For computing differences of altitude from angles of elevation or depreasion (applicahle to scale of 1:30000). [Prepared Ipy K. S. "Woodward. 1
■r^-^v e ixjx i„ C +D7i,4-/ia for ans'les of elevation.
Ditference of altitnde= J Iu,,;_|.,,.^ for „„|ies of dopressioi
opressiou. ^distance in scale divisions E>j'ineli each; (t = angle of elevation or depression ; 7i,=50feetx tan a; 7i2 = correction for curvature and refraction.
Arguuient for Ai is a,- argument for /(•.» is D.
|
A, in feet. |
D |
ft2 |
D |
7i2 |
||||||||
|
' |
0=> |
1° |
20 |
3° |
4° |
5° |
«o |
JO |
Scale divisions. |
Feet. |
Scale divisions. |
Feet. |
|
0 |
.000 |
.873 |
1.746 |
2.620 |
3.496 |
4 374 |
5.255 |
6139 |
000 |
0 |
1080 |
60 |
|
1 |
.014 |
.887 |
1.760 |
2.635 |
3. 511 |
4 389 |
5.270 |
6.154 |
130 |
1 |
1089 |
61 |
|
2 |
.029 |
.902 |
1.775 |
2.649 |
3.525 |
4 403 |
5.284 |
6.109 |
197 |
2 |
1098 |
62 |
|
3 |
.043 |
.916 |
1.789 |
2.664 |
3.540 |
4 418 |
5.299 |
6. 183 |
243 |
3 |
1107 |
63 |
|
4 |
.058 |
.931 |
1.804 |
2.678 |
3.555 |
4 433 |
5.314 |
6.198 |
270 |
4 |
1116 |
64 |
|
5 |
.072 |
.945 |
1.819 |
2.693 |
3.569 |
4.447 |
5.328 |
6.213 |
312 |
5 |
1124 |
65 |
|
6 |
.087 |
.960 |
1.833 |
2.708 |
3.584 |
4 462 |
5.343 |
6. 228 |
342 |
6 |
1133 |
66 |
|
7 |
.102 |
.974 |
1.848 |
2.722 |
. 3. 598 |
4 477 |
5.358 |
6.242 |
309 |
7 |
1141 |
67 |
|
g |
.116 |
.989 |
1.862 |
2.737 |
3.613 |
4 491 |
5.373 |
6.257 |
394 |
8 |
1150 |
68 |
|
9 |
.131 |
1.003 |
1.877 |
2.751 |
3.G28 |
4 506 |
5.387 |
6.272 |
418 |
9 |
1158 |
69 |
|
10 |
.145 |
1.018 |
1.891 |
2.706 |
3.642 |
4 521 |
5.402 |
6.287 |
441 |
10 |
1107 |
70 |
|
11 |
.160 |
1.033 |
1.906 |
2.781 |
3.057 |
4 535 |
5.417 |
6.301 |
463 |
11 |
1175 |
71 |
|
12 |
.174 |
1.047 |
1.921 |
2.795 |
3.072 |
4.550 |
5.431 |
6.316 |
483 |
12 |
11, S3 |
72 |
|
13 |
.189 |
1.0B2 |
1.935 |
2.810 |
3.686 |
4.565 |
5.446 |
6.331 |
503 |
13 |
1191 |
73 |
|
14 |
• .203 |
1.076 |
1.950 |
2.824 |
3.701 |
4 579 |
5.461 |
6.346 |
522 |
14 |
1199 |
74 |
|
13 |
.218 |
1.091 |
1.964 |
2.839 |
3.715 |
4.594 |
5.476 |
6 361 |
540 |
15 |
1208 |
75 |
|
16 |
.232 |
1.105 |
1.979 |
2.854 |
3.730 |
4. 609 |
5.490 |
6.375 |
558 |
16 |
1216 |
76 |
|
17 |
.247 |
1.120 |
1.993 |
2.868 |
3.745 |
4 623 |
5 505 |
6.390 |
575 |
17 |
1234 |
77 |
|
IS |
.262 |
1.134 |
2.008 |
2.883 |
3.759 |
4. 638 |
5. £20 |
6 405 |
592 |
18 |
1231 |
78 |
|
19 |
.276 |
1.149 |
2.023 |
2.897 |
3.774 |
4 653 |
5.535 |
6.420 |
608 |
19 |
1339 |
79 |
|
20 |
.291 |
1.164 |
2.037 |
2.912 |
3.789 |
4.667 |
5.549 |
6 434 |
624 |
20 |
1247 |
80 |
|
21 |
.305 |
1.178 |
2.052 |
2.927 |
3. 803 |
4 682 |
5.564 |
6 449 |
639 |
21 |
1255 |
81 |
|
22 |
.320 |
1.193 |
2.066 |
2.941 |
3.818 |
4.097 |
5.579 |
6.464 |
654 |
22 |
1363 |
83 |
|
23 |
.334 |
1.207 |
2.081 |
2.956 |
3.832 |
4.711 |
5.593 |
6.479 |
669 |
23 |
1270 |
83 |
|
24 |
.349 |
1.222 |
2.095 |
2.970 |
3.847 |
4 726 |
5.608 |
6.494 |
683 |
24 |
1378 |
84 |
|
25 |
.363 |
1.236 |
2.110 |
2.985 |
3.862 |
4 741 |
5.623 |
6.508 |
697 |
25 |
1286 |
85 |
|
26 |
.378 |
1.250 |
2.125 |
2.999 |
3.876 |
4 755 |
5.638 |
6 523 |
711 |
26 |
1293 |
86 |
|
27 |
.392 |
1.265 |
2.139 |
3.014 |
3.891 |
4 770 |
5.652 |
6.538 |
725 |
27 |
1301 |
87 |
|
28 |
.407 |
1.280 |
2.154 |
3.029 |
3.906 |
4 785 |
5.667 |
6. 553 |
738 |
28 |
1308 |
88 |
|
29 |
.422 |
1.294 |
2.168 |
3.043 |
3.920 |
4 800 |
5.682 |
6.568 |
751 |
29 |
1315 |
89 |
|
30 |
.436 |
1.309 |
2.183 |
3.058 |
3.935 |
4 814 |
5.697 |
6 582 |
764 |
30 |
1333 |
90 |
|
31 |
.451 |
1.324 |
2.197 |
3.072 |
3.949 |
4 829 |
5.711 |
6.597 |
776 |
31 |
1330 |
91 |
|
33 |
.465 |
1.338 |
2.212 |
3.087 |
3. 964 |
4 844 |
5.726 |
6.612 |
789 |
32 |
1337 |
92 |
|
33 |
.480 |
1.353 |
2.227 |
3.102 |
3.979 |
4 858 |
5.741 |
6.627 |
801 |
33 |
1345 |
93 |
|
34 |
.494 |
1.367 |
2.241 |
3.116 |
3.993 |
4 873 |
5.755 |
6.642 |
813 |
34 |
1353 |
94 |
|
35 |
.509 |
1.382 |
2.256 |
3.131 |
4.008 |
4 888 |
5.770 |
6.656 |
825 |
35 |
1359 |
95 |
|
36 |
.523 |
1.396 |
2.270 |
3. 145 |
4. 023 |
4 902 |
5.785 |
6.671 |
837 |
36 |
1366 |
96 |
|
37 |
.538 |
1.411 |
2.285 |
3.160 |
4 037 |
4.917 |
5.800 |
6.686 |
848 |
37 |
1373 |
97 |
|
3S |
.552 |
1.425 |
2.289 |
3.175 |
4 052 |
4.932 |
5.814 |
6.701 |
860 |
38 |
1380 |
98 |
|
39 |
.567 |
1.440 |
2.314 |
3.189 |
4.067 |
4 946 |
5.829 |
6 716 |
871 |
39 |
1387 |
99 |
|
40 |
.582 |
1.455 |
2.329 |
3.204 |
4.081 |
4.961 |
5.844 |
6. 730 |
882 |
40 |
1394 |
100 |
|
41 |
.596 |
1.469 |
2.343 |
3.218 |
4.096 |
4 976 |
5.859 |
6.745 |
893 |
41 |
1401 |
101 |
|
42 |
.611 |
1.4C4 |
2.358 |
3.233 |
4110 |
4.990 |
5.873 |
6.760 |
904 |
42 |
1408 |
102- |
|
43 |
.625 |
1.498 |
2.372 |
3.248 |
4.125 |
5.005 |
5.888 |
6.775 |
914 |
43 |
1415 |
103 |
|
44 |
.640 |
1.513 |
2.387 |
3.262 |
4. 140 |
5.020 |
5. 903 |
6.790 |
925 |
44 |
1422 |
104 |
|
45 |
.654 |
1.527 |
2.401 |
3.277 |
4154 |
5.034 |
5.918 |
6.804 |
935 |
45 |
1429 |
105 |
|
46 |
.669 |
1.542 |
2.416 |
3.292 |
4.169 |
5.049 |
5.932 |
6 819 |
946 |
46 |
1436 |
106 |
|
47 |
.683 |
1.657 |
2.431 |
3.306 |
4184 |
5.064 |
5.947 |
6 834 |
95G |
47 |
1442 |
107 |
|
48 |
.698 |
1.571 |
2.445 |
3.321 |
4198 |
5.079 |
5.962 |
6 849 |
966 |
48 |
1449 |
108 |
|
49 |
.712 |
1.586 |
2.460 |
3.335 |
4 213 |
5.093 |
5.977 |
6.864 |
976 |
49 |
1456 |
109 |
|
60 |
.727 |
1.600 |
2.474 |
3.350 |
4.228 |
5.108 |
5.991 |
6.879 |
980 |
50 |
1462 |
110 |
|
51 |
.742 |
1.615 |
2.489 |
3.365 |
4. 242 |
5.123 |
6.006 |
6.893 |
996 |
5] |
1469 |
111 |
|
52 |
.756 |
1.629 |
2.503 |
3.379 |
4 257 |
5.137 |
6.021 |
6 908 |
1006 |
52 |
1476 |
112 |
|
53 |
.771 |
1.644 |
2.517 |
3.394 |
4 272 |
5.152 |
6.036 |
6 923 |
1015 |
53 |
1482 |
113 |
|
54 |
.785 |
1.658 |
2.533 |
3.408 |
4 286 |
5.167 |
6.050 |
6 938 |
1025 |
54 |
1489 |
114 |
|
55 |
.800 |
1. 673 |
2.547 |
3.423 |
4 301 |
5.181 |
6.065 |
6.953 |
1034 |
55 |
1495 |
115 |
|
56 |
.814 |
1.688 |
2.562 |
3.438 |
4.316 |
5.196 |
6.080 |
6 967 |
1043 |
56 |
1502 |
116 |
|
57 |
.829 |
1.702 |
2.576 |
3.452 |
4 330 |
5.211 |
6.095 |
6.982 |
1053 |
57 |
1508 |
117 |
|
58 |
.843 |
1.717 |
2.591 |
3.467 |
4 345 |
5.226 |
6.109 |
6.907 |
1062 |
58 |
1515 |
118 |
|
59 |
.858 |
1.731 |
2.606 |
^ 3. 481 |
4.360 |
5.240 |
6.124 |
7.012 |
1071 |
59 |
1521 |
119 |
|
60 |
.873 |
1.746 |
2.620 |
3.496 |
4 374 |
5.255 |
6.139 |
7.027 |
1080 |
60 |
1527 |
120 |
ALTITUDE TABLES.
157
-For com]}utiiig differences of altitude from aiu/les of elevation or depression (applicable to scale of 1: 30000— Contiuued.
|
ft, in feet. |
D |
1h |
D |
h^ |
||||||||
|
' |
8° |
9° |
10° |
11° |
12° |
13° |
14° |
15° |
Scale [livisions. |
Feet. |
Scale divisions. |
Feet. |
|
0 |
7.027 |
7.919 |
8.816 |
9.719 |
10. 628 |
11.543 |
12. 466 |
13. 397 |
000 |
0 |
1080 |
60 |
|
1 |
7.042 |
7.934 |
8.831 |
9.734 |
10. 643 |
11. 558 |
12.482 |
13. 413 |
139 |
1 |
1089 |
61 |
|
2 |
7.056 |
7.949 |
8.846 |
9.749 |
10. 658 |
11. 574 |
12.497 |
13.428 |
197 |
2 |
1098 |
62 |
|
3 |
7.071 |
7.964 |
8.861 |
9.704" |
10. 673 |
11. 589 |
12. 51? |
13.444 |
242 |
3 |
1107 |
63 |
|
4 |
7.086 |
7.979 |
8.876 |
9.779 |
10. 688 |
11. 604 |
12. 528 |
13. 460 |
279 |
4 |
1116 |
64 |
|
o |
7.101 |
7.994 |
8.891 |
9.794 |
10. 704 |
11. 620 |
12. 543 |
13. 475 |
312 |
g |
1124 |
65 |
|
6 |
7.116 |
8.008 |
8.906 |
9.809 |
10. 719 |
11.635 |
12, 559 |
13. 491 |
342 |
6 |
1133 |
66 |
|
7.131 |
8.023 |
8.921 |
9.824 |
. 10. 734 |
11. 650 |
12. 574 |
13.506 |
369 |
7 |
1141 |
67 |
|
|
8 |
7.145 |
8.038 |
8.936 |
9.840 |
10. 749 |
11. 666 |
12. 590 |
13. 522 |
394 |
8 |
1150 |
68 |
|
9 |
7.160 |
8.053 |
8.951 |
9,855 |
10. 764 |
11. 681 |
12. 605 |
13. 538 |
418 |
9 |
1158 |
69 |
|
10 |
7.175 |
8.068 |
8.966 |
9. 870 |
10.7.SO |
11.696 |
12. 621 |
13. 553 |
441 |
10 |
1167 |
70 |
|
11 |
7.190 |
8.083 |
8.981 |
9.885 |
10.795 |
11.712 |
12. 636 |
13. 569 |
462 |
11 |
1175 |
71 |
|
12 |
7.205 |
8.098 |
8.996 |
9.900 |
10. 810 |
11. 727 |
12, 652 |
13. 584 |
483 |
12 |
1183 |
72 |
|
13 |
7.220 |
8.113 |
9.011 |
9.915 |
10. 825 |
11. 742 |
12, 667 |
13. 600 |
503 |
13 |
1191 |
73 |
|
14 |
7.235 |
8.128 |
9.026 |
9. 930 |
10.841 |
11. 758 |
12,683 |
13. 616 |
522 |
14 |
1199 |
74 |
|
15 |
7.249 |
8.143 |
9.041 |
9.945 |
10.856 |
11. 773 |
12, 698 |
13. 631 |
540 |
15 |
1208 |
75 |
|
16 |
7.264 |
8.158 |
9.056 |
9.960 |
10.871 |
11.789 |
12. 714 |
13. 647 |
558 |
16 |
1216 |
76 |
|
17 |
7.279 |
8. 173 |
9.071 |
9.976 |
10.886 |
11.804 |
12. 729 |
13. 663 |
575 |
17 |
1224 |
77 |
|
18 |
7.294 |
8.188 |
9.086 |
9.991 |
10. 902 |
11. 819 |
12.745 |
13. 678 |
592 |
18 |
1231 |
78 |
|
19 |
7.309 |
8.202 |
9.101 |
10.006 |
10. 917 |
11. 835 |
12. 761 |
13. 694 |
608 |
19 |
1239 |
79 |
|
20 |
7.324 |
8.217 |
9.116 |
10.021 |
10. 932 |
11, 850 |
12. 776 |
13.709 |
624 |
20 |
1247 |
80 |
|
21 |
7.339 |
8.232 |
9.131 |
10. 036 |
10. 947 |
11, 865 |
12. 791 |
13. 725 |
639 |
21 |
1255 |
81 |
|
22 |
7.353 |
8.247 |
9.146 |
10. 051 |
10. 962 |
11.881 |
12. 807 |
13. 741 |
654 |
22 |
1263 |
82 |
|
23 |
7.368 |
8.202 |
9.161 |
10. 066 |
10.978 |
11.896 |
12. 822 |
13.756 |
669 |
23 |
1270 |
83 |
|
21 |
7.383 |
8.277 |
9.176 |
10. 082 |
10. 993 |
11.911 |
12. 838 |
13.772 |
683 |
24 |
1278 |
84 |
|
25 |
7.398 |
8.292 |
9.191 |
10.097 |
11. 008 |
11.927 |
12. 853 |
13.788 |
697 |
25 |
1286 |
85 |
|
26 |
7.413 |
8.307 |
9.207 |
10. 112 |
11. 023 |
11. 942 |
12. 869 |
13, 803 |
711 |
26 |
1293 |
86 |
|
27 |
7.428 |
8.322 |
9.222 |
10. 127 |
11, 039 |
11,958 |
12. 884 |
13. 819 |
725 |
27 |
1301 |
87 |
|
28 |
7.443 |
8.337 |
9.237 |
10.142 |
11. 054 |
11. 973 |
12. 900 |
13. 835 |
738 |
28 |
1308 |
88 |
|
29 |
7.457 |
8.352 |
9.252 |
10, 157 |
11. 069 |
11. 988 |
12.915 |
13, 860 |
751 |
29 |
1315 |
89 |
|
30 |
7.472 |
8.367 |
9.267 |
10. 172 |
11. 084 |
12. 004 |
12. 931 |
13,866 |
764 |
30 |
1323 |
90 |
|
31 |
7.487 |
8.382 |
9. 282 |
10. 18B |
11. 100 |
12,019 |
12, 946 |
13. 882 |
776 |
31 |
1330 |
91 |
|
32 |
7.502 |
8.397 |
9.297 |
10.203 |
11.115 |
12. 034 |
12, 962 |
13, 897 |
789 |
32 |
1337 |
92 |
|
33 |
7.517 |
8.412 |
9.312 |
10.218 |
11. 130 |
12,030 |
12, 077 |
13,913 |
SOI |
33 |
1345 |
93 |
|
3* |
7.532 |
8.427 |
9.327 |
10.233 |
11. 146 |
12, 065 |
12,993 |
13.929 |
813 |
34 |
1352 |
94 |
|
35 |
7.547 |
8.442 |
9.342 |
10.248 |
11. 161 |
12,081 |
13. 008 |
13.944 |
825 |
35 |
13.59 |
95 |
|
36 |
7.562 |
8.457 |
9.3.57 |
10.263 |
11. 176 |
12. 096 |
13, 024 |
13. 960 |
837 |
36 |
1366 |
96 |
|
37 |
7.576 |
8.472 |
9.372 |
10.278 |
11. 191 |
12, 111 |
13. 039 |
13. 976 |
848 |
37 |
1373 |
97 |
|
38 |
7.591 |
8.487 |
9.387 |
10. 294 |
11.207 |
12. 127 |
13. 055 |
13. 991 |
860 |
38 |
1380 |
98 |
|
39 |
7.606 |
8.502 |
9.402 |
10. 309 |
11.222 |
12. 142 |
13,070 |
14.007 |
871 |
39 |
■ 1387 |
99 |
|
40 |
7.621 |
8.516 |
9.417 |
10. 324 |
11. 237 |
12. 158 |
13. 086 |
14. 023 |
882 |
40 |
1394 |
100 |
|
41 |
7.636 |
8.531 |
9.432 |
10. 339 |
11. 252 |
12. 173 |
13. 101 |
14.038 |
893 |
41 |
1401 |
101 |
|
42 |
7.651 |
8.546 |
9.447 |
10.354 |
11, 268 |
12. 188 |
13.117 |
]4.0a4 |
904 |
42 |
1408 |
102 |
|
43 |
7.666 |
8.561 |
9.462 |
10.369 |
11. 283 |
12. 204 |
13. 133 |
14. 070 |
914 |
43 |
1415 |
103 |
|
44 |
7.681 |
8.576 |
9.477 |
10. 385 |
11, 298 |
12. 219 |
13. 148 |
14. 086 |
925 |
44 |
1422 |
104 |
|
45 |
7.695 |
8.591 |
9.493 |
10.400 |
11.314 |
12. 235 |
13. 164 |
14.101 |
935 |
45 |
1429 |
105 |
|
.46 |
7.710 |
8.606 |
9.508 |
10. 415 |
11. 329 |
12.250 |
13. 179 |
14.117 |
946 |
46 |
1436 |
106 |
|
47 |
7.725 |
8.621 |
9.523 |
10.431 |
U.344 |
12. 266 |
13. 195 |
14. 133 |
936 |
47 |
1442 |
107 |
|
48 |
7.740 |
8.636 |
9.538 |
10.445 |
11. 359 |
12. 281 |
13.210 |
14148 |
966 |
48 |
1449 |
108 |
|
49 |
7.755 |
8.651 |
9.553 |
10. 460 |
11.375 |
12. 296 |
13.226 |
14. 164 |
976 |
49 |
1456 |
109 |
|
50 |
7.770 |
8.666 |
9.568 |
10. 476 |
11. 390 |
12.312 |
13. 241 |
14.180 |
986 |
50 |
1462 |
110 |
|
51 |
7.785 |
8.681 |
9.583 |
10. 491 |
11.405 |
12.327 |
13. 257 |
14. 195 |
996 |
51 |
1469 |
111 |
|
62 |
7.800 |
8.696 |
9.598 |
10.506 |
11.421 |
12, 343 |
13. 273 |
14.211 |
1006 |
52 |
1476 |
112 |
|
63 |
7.815 |
■ 8.711 |
9.613 |
10.521 |
11. 436 |
12, 358 |
13, 288 |
14. 227 |
1015 |
53 |
1482 |
113 |
|
54 |
7.830 |
8.72D |
9.628 |
10. 536 |
11. 451 |
12.373 |
13, 304 |
14.243 |
1025 |
54 |
1489 |
114 |
|
56 |
7.844 |
8.741 |
9.643 |
10. 552 |
11. 467 |
12. 389 |
13. 319 |
14.258 |
1034 |
55 |
1495 |
115 |
|
56 |
7.859 |
8.756 |
9.658 |
10. 567 |
11.482 |
12. 404 |
13. 335 |
14. 274 |
1043 |
56 |
1502 |
116 |
|
57 |
7.874 |
8.771 |
9.673 |
10. 5S2 |
11. 497 |
12. 420 |
13. 350 |
14. 290 |
1053 |
57 |
1508 |
117 |
|
68 |
7. 889 |
8.786 |
9.689 |
10. 597 |
11.513 |
12.435 |
13.366 |
14. 306 |
1062 |
58 |
1515 |
118 |
|
59 |
7.904 |
8.801 |
9.704 |
10. 612 |
11. 528 |
12.451 |
13. 382 |
14.321 |
1071 |
59 |
1521 |
119 |
|
60 |
7.919 |
8.816 |
9.719 |
10.028 |
11. 543 |
12.406 |
13. 397 |
14.337 |
1080 |
60 |
1527 |
120 |
158
A MANUAL OF TOPOGEAPHIO METHODS.
Table XI. — Differences of altUude
[Prepared by Computed from the formula A ^ D sin a cos a, in which D is the observed distance of the
|
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
|
|
" |
5G0 |
5S0 |
600 |
620 |
640 |
660 |
6S0 |
700 |
720 |
740 |
760 |
780 |
800 |
820 |
|
0 01 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
|
0 02 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4. |
0.4 |
0.4 |
0.4 |
. 0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
|
0 03 |
0.5 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
O.B |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.7 |
|
U 01 |
0.6 |
0.7 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.8 |
0.8 |
0.9 |
0.9 |
0.9 |
0.9 |
1.0 |
|
0 05 |
0.8 |
0.8 |
0.9 |
0.9 |
0.9 |
1.0 |
1.0 |
1.0 |
1.0 |
1.1 |
1.1 |
1.1 |
1.2 |
1.2 |
|
0 06 |
1.0 |
1.0 |
1.1 |
1.1 |
1.1 |
1.2 |
1.2 |
1.2 |
1.3 |
1.3 |
1.3 |
1.4 |
1.4 |
1.4 |
|
0 07 |
1.1 |
1.2 |
1.2 |
1.3 |
1.3 |
1.3 |
1.4 |
1.4 |
1.5 |
1.5 |
1.6 |
1.6 |
1.6 |
1.7 |
|
0 08 |
1.3 |
1.4 |
1.4 |
1.4 |
1.5 |
1.5 |
1.6 |
1.6 |
1.7 |
1.7 |
1.8 |
1.8 |
1.9 |
1.9 |
|
0 09 |
1.5 |
1.5 |
1.6 |
1.6 |
1.7 |
1.7 |
1.8 |
1.8 |
1.9 |
1.9 |
2.0 |
2.0 |
2.1 |
2.1 |
|
0 10 |
1.6 |
1.7 |
1.7 |
1.8 |
1.9 |
1.9 |
2.0 |
2.0 |
2.1 |
2.2 |
2.2 |
2.3 |
2.3 |
2.4 |
|
0 11 |
1.8 |
1.9 |
1.9 |
2.0 |
2.0 |
2.1 |
2.2 |
2.2 |
2.3 |
2.4 |
2.4 |
2.5 |
2.6 |
2.6 |
|
0 12 |
2.0 |
2.0 |
2.1 |
2.2 |
2.2 |
2.3 |
2.4 |
2.4 |
2.5 |
2.6 |
2.7 |
2.7 |
2.8 |
2.9 |
|
0 13 |
2.1 |
2.2 |
2.3 |
2.3 |
2.4 |
2.5 |
2.6 |
2.6 |
2.7 |
2.8 |
2.9 |
2.9 |
3.0 |
3.1 |
|
0 14 |
2.3 |
2.4 |
2.4 |
2.5 |
2.6 |
2.7 |
2.8 |
2.8 |
2.9 |
3.0 |
3.1 |
3.2 |
3.3 |
3.3 |
|
0 IS |
2.4 |
2.5 |
2.6 |
2.7 |
2.8 |
2.9 |
3.0 |
3.1 |
3.1 |
3.2 |
3.3 |
3.4 |
3.5 |
3.6 |
|
0 16 |
2.6 |
2.7 |
2.8 |
2.9 |
3.0 |
3.1 |
3.2 |
3.3 |
3.3 |
3.4 |
3.5 |
3.6 |
3.7 |
3.8 |
|
0 17 |
2.8 |
2.9 |
3.0 |
3.1 |
3.2 |
3.3 |
3.4 |
3.5 |
3.6 |
3.7 |
3.8 |
3.9 |
4.0 |
4.1 |
|
0 18 |
2.9 |
3.0 |
3.1 |
3.2 |
3.4 |
3.5 |
3.6 |
3.7 |
3.8 |
3.9 |
4.0 |
4.1 |
4.2 |
4.3 |
|
0 19 |
3.1 |
3.2 |
3.3 |
3.4 |
3.5 |
3.6 |
3.8 |
3.9 |
4.0 |
4.1 |
4.2 |
4.3 |
4.4 |
4.5 |
|
0 20 |
3.3 |
3.4 |
3.5 |
3.6 |
3.7 |
3.8 |
4.0 |
4.1 |
4.2 |
4.3 |
4.4 |
4.5 |
4.7 |
4.8 |
|
0 21 |
3.4 |
3.5 |
3.7 |
3.8 |
3.9 |
4.0 |
4.2 |
4.3 |
4.4 |
4.5 |
4.6 |
4.8 |
4.9 |
5.0 |
|
0 22 |
3.6 |
3.7 |
3.8 |
4.0 |
4.1 |
4.2 |
4.4 |
4.5 |
4.6 |
4.7 |
4.9 |
5.0 |
5.1 |
5.2 |
|
0 23 |
3.7 |
3.9 |
4.0 |
4.1 |
4.3 |
4.4 |
4.5 |
4.7 |
4.8 |
5.0 |
5.1 |
5.2 |
5.4 |
5.5 |
|
0 24 |
3.9 |
4.0 |
4.2 |
4.3 |
4.5 |
4.0 |
4.7 |
4.9 |
5.0 |
5.2 |
5.3 |
5.4 |
5.6 |
5.7 |
|
0 25 |
4.1 |
4.2 |
4.4 |
4.5 |
4.7 |
4.8 |
4.9 |
5.1 |
5.2 |
5.4 |
5.5 |
5.7 |
5.8 |
6.0 |
|
0 26 |
4.2 |
4.4 |
4.5 |
4.7 |
4.8 |
5.0 |
5.1 |
5.3 |
5.4 |
5.6 |
5.7 |
5.9 |
6.0 |
6.2 |
|
U 27 |
4.4 |
4.6 |
4.7 |
49 |
5.0 |
5.2 |
5.3 |
5.5 |
5.7 |
5.8 |
6.0 |
6.1 |
6.3 |
6.4 |
|
0 28 |
4.6 |
4.7 |
4.9 |
5.0 |
5.2 |
5.4 |
5.5 |
5.7 |
5.9 |
6.0 |
6.2 |
6.3 |
6.5 |
6.7 |
|
0 29 |
4.7 |
4.9 |
5.1 |
5.2 |
5.4 |
5.6 |
5.7 |
5.9 |
6.1 |
6.2 |
6.4 |
6.6 |
6.8 |
6.9 |
|
0 30 |
4.9 |
5.1 |
5.2 |
5.4 |
5.6 |
5.8 |
5.9 |
6.1 |
6.3 |
6.5 |
6.6 |
6.8 |
7.0 |
7.2 |
|
0 35 |
5.7 |
5.9 |
6.1 |
6.3 |
6.5 |
6.7 |
6.9 |
7.1 |
7.3 |
7.5 |
7.7 |
7.9 |
8.1 |
8.4 |
|
0 40 |
6.5 |
6.7 |
7.0 |
7.2 |
7.4 |
7.7 |
7.9 |
8.1 |
8.4 |
8.6 |
8.8 |
9.1 |
9.3 |
9.5 |
|
0 45 |
7.3 |
7.6 |
7.9 |
8.1 |
8.4 |
8.6 |
8.9 |
9.2 |
9.4 |
9.7 |
9.9 |
10.2 |
10.5 |
10.7 |
|
0 50 |
8.1 |
8.4 |
8.7 |
9.0 |
9.3 |
9.6 |
9.9 |
10.2 |
10.5 |
10.8 |
11.1 |
11.3 |
11.6 |
11.9 |
|
0 55 |
9.0 |
9.3 |
9.6 |
9.9 |
10.2 |
10.6 |
10.9 |
11.2 |
11.5 |
11.8 |
12.2 |
12.5 |
12.8 |
13.1 |
|
1 00 |
9.8 |
10.1 |
111.5 |
10.8 |
11.2 |
11.5 |
11.9 |
12.2 |
12.6 |
12.9 |
13.3 |
13.6 |
14.0 |
14.3 |
|
1 10 |
11.4 |
11.8 |
12.2 |
12.6 |
13.0 |
13.4 |
13.8 |
14.3 |
14.7 |
15.1 |
15.5 |
15.9 |
16.3 |
16.7 |
|
1 20 |
13.0 |
13.5 |
14.0 |
14.4 |
14.9 |
15.4 |
15.8 |
16.3 |
16.7 |
17.2 |
17.7 |
18.1 |
18.6 |
19.1 |
|
1 30 |
14.7 |
15.2 |
15.7 |
16.2 |
16.7 |
17.3 |
17.8 |
18.3 |
18.8 |
19.4 |
19.9 |
20.4 |
20.9 |
21.5 |
|
1 40 |
10.3 |
16.9 |
17.4 |
18.0 |
18.6 |
19.2 |
19.8 |
20.3 |
20.9 |
21.5 |
22.1 |
22.7 |
23.3 |
23.8 |
|
1 50 |
17.9 |
18.5 |
19.2 |
19.8 |
20.5 |
21.1 |
21.7 |
22.4 |
23.0 |
23.7 |
24.3 |
24.9 |
25.6 |
26.2 |
|
2 00 |
19.5 |
20.2 |
20.9 |
21.6 |
22.3 |
23.0 |
23.7 |
24.4 |
25.1 |
25.8 |
26.5 |
27.2 |
27.9 |
28.6 |
|
2 10 |
21.2 |
21.9 |
22.7 |
23.4 |
24.2 |
24.9 |
25.7 |
26.4 |
27.2 |
28.0 |
28.7 |
29.5 |
30.2 |
31.0 |
|
2 20 |
22.8 |
23.6 |
24.4 |
25.2 |
26.0 |
26.8 |
27.7 |
28.5 |
29.3 |
30.1 |
30.9 |
31.7 |
32.5 |
33.4 |
|
2 30 |
24.4 |
25.3 |
26.1 |
27.0 |
27.9 |
28.8 |
29.6 |
30.5 |
31.4 |
32.2 |
33.1 |
34.0 |
34.9 |
35.7 |
|
2 40 |
26.0 |
27.0 |
27.9 |
28.8 |
29.7 |
30.7 |
31.6 |
32.5 |
33.5 |
34.4 |
35.3 |
36.3 |
37.2 |
38.1 |
|
2 50 |
27.6 |
28.6 |
29.6 |
30.6 |
31.6 |
32.0 |
33.6 |
34.6 |
35.5 |
36.5 |
37.5 |
38.5 |
39.5 |
40.5 |
|
'8 00 |
29.3 |
30.3 |
31.4 |
32.4 |
33.4 |
34.5 |
35.5 |
36.6 |
37.6 |
38.7 |
39.7 |
40.8 |
41.8 |
42.9 |
|
1 00 |
39.0 |
40.4 |
41.8 |
43.1 |
44.6 |
45.9 |
47.3 |
48.7 |
50.1 |
51.5 |
52.9 |
54.3 |
55.7 |
57.1 |
|
5 00 |
48.6 |
50.4 |
52.1 |
53.8 |
55.6 |
57.3 |
59.0 |
60.8 |
62.5 |
64.2 |
66.0 |
67.7 |
69.5 |
71.2 |
|
D |
D |
D |
D |
D |
D |
D |
D |
» |
D |
D |
D |
D |
D |
|
|
560 |
580 |
000 |
620 |
640 |
660 |
6S0 |
700 |
720 |
740 |
760 |
780 |
800 |
820 |
ALTITUDE TABLES.
159
from telemeter measures.
R.S. Woodward.] telemeter staff, a is the £
gle of elevation or depression, and h is the difference in height.
|
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
» |
D |
D |
It |
|
840 |
860 |
880 |
900 |
920 |
940 |
960 |
980 |
1,000 |
1,100 |
1,200 |
1,S00 |
1,400 |
1,500 |
2,000 |
|
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.6 |
|
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.6 |
0.7 |
0.8 |
0.8 |
0.9 |
1.2 |
|
0.7 |
0.7 |
0.8 |
0.8 |
0.8 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.3 |
1.7 |
|
1.0 |
1.0 |
1.0 |
1.0 |
1.1 |
1.1 |
1.1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
2.3 |
|
1.2 |
1.2 |
1.3 |
1.3 |
1.3 |
1.4 |
1.4 |
1.4 |
1.5 |
1.6 |
1.7 |
1.9 |
2.0 |
2.2 |
2.9 |
|
1.5 |
1.5 |
1.5 |
1.6 |
1.6 |
1.6 |
1.7 |
1.7 |
1.7 |
1.9 |
2.1 |
2.3 |
2.4 |
2.6 |
3.5 |
|
1.7 |
1.8 |
1.8 |
1.8 |
1.9 |
3.9 |
2.0 |
2.0 |
2.0 |
2.2 |
2.4 |
2.7 |
2.9 |
3.1 |
4.1 |
|
2.0 |
2.0 |
2.1 |
2.1 |
2.1 |
2.2 |
2.2 |
2.3 |
2.3 |
2.6 |
2.8 |
3.0 |
3.3 |
3.5 |
4.7 |
|
2.2 |
2.3 |
2.3 |
2.4 |
2.4 |
2.5 |
2.5 |
2.6 |
2.6 |
2.9 |
3.1 |
3.4 |
3.7 |
3.9 |
5.2 |
|
2.4 |
2.5 |
2.6 |
2.6 |
2.7 |
2.7 |
2.8 |
2.9 |
2.9 |
3.2 |
3.5 |
3.8 |
4.1 |
4.4 |
5.8 |
|
2.7 |
2.8 |
2.8 |
2.9 |
2.9 |
3.0 |
3.1 |
3.1 |
3.2 |
3.5 |
3.8 |
4 2 |
4 5 |
4 8 |
6.4 |
|
2.9 |
3.0 |
3.1 |
3.1 |
3.2 |
3.3 |
3.4 |
3.4 |
3.5 |
3.8 |
4 2 |
4 5 |
4 9 |
5.2 |
7.0 |
|
3.2 |
3.3 |
3.3 |
3.4 |
3.5 |
3.6 |
3.6 |
3.7 |
3.8 |
4 2 |
4 5 |
4 9 |
5.3 |
5.7 |
7.6 |
|
3.4 |
8.5 |
3.6 |
3.7 |
3.7 |
3.8 |
3.9 |
4.0 |
4.1 |
4.5 |
4.9 |
5.3 |
5.7 |
6.1 |
8.1 |
|
3.7 |
3.7 |
3.8 |
3.9 |
4.0 |
41 |
4.2 |
4.3 |
4 4 |
4 8 |
5.2 |
5.7 |
6.1 |
6.5 |
8.7 |
|
3.9 |
4 0 |
4.1 |
4.2 |
4.3 |
4 4 |
4 5 |
4.6 |
4 7 |
5.1 |
5.6 |
6.0 |
6.5 |
7.0 |
9.3 |
|
4.2 |
4 3 |
4.4 |
4 5 |
4.6 |
4 7 |
4 8 |
4 9 |
5.0 |
5.4 |
5.9 |
6.4 |
6.9 |
7.4 |
9.9 |
|
4.4 |
4.5 |
4.6 |
4 7 |
4 8 |
4 9 |
5.0 |
5.1 |
5.2 |
5.8 |
6.3 |
6.8 |
7.3 |
7.9 |
10.5 |
|
4 6 |
4 8 |
4.9 |
5.0 |
5.1 |
5.2 |
5.3 |
5.4 |
5.5 |
6.1 |
6.6 |
7.2 |
7.7 |
8.3 |
11.1 |
|
4.9 |
5.0 |
5.1 |
5.2 |
5.4 |
5.5 |
5.6 |
5.7 |
5.8 |
6.4 |
7.0 |
7.5 |
8.1 |
8.7 |
11.6 |
|
5.1 |
5.3 |
5.4 |
5.5 |
5.6 |
5.7 |
5.9 |
6.0 |
6.1 |
6.7 |
7.3 |
7.9 |
8.6 |
9.2 |
12.2 |
|
5.4 |
5.5 |
5.6 |
5.8 |
5.9 |
6.0 |
6.1 |
6.3 |
6.4 |
7.0 |
7.7 |
8.3 |
9.0 |
9.6 |
12.8 |
|
5.6 |
5.8 |
5.9 |
6.0 |
6.2 |
6.3 |
6.4 |
6.6 |
6.7 |
7.4 |
8.0 |
8.7 |
9.4 |
10.0 |
13.4 |
|
5.9 |
6.0 |
6.1 |
6.3 |
6.4 |
6.6 |
6.7 |
6.8 |
7.0 |
7.7 |
8.4 |
9.1 |
9.8 |
10.5 |
14 0 |
|
6.1 |
U.3 |
6.4 |
6.5 |
6.7 |
6.8 |
7.0 |
7.1 |
7.3 |
8.0 |
8.7 |
9.5 |
10.2 |
10.9 |
14 5 |
|
6.4 |
6.5 |
6.7 |
6.8 |
7.0 |
7.1 |
7.3 |
7.4 |
7.6 |
8.3 |
9.1 |
9.8 |
10.5 |
11.3 |
15.1 |
|
6.6 |
6.8 |
6.9 |
7.1 |
7.2 |
7.4 |
7.5 |
7.7 |
7.9 |
8.6 |
9.4 |
10.2 |
11.0 |
11.8 |
15.7 |
|
6.8 |
7.0 |
7.2 |
7.3 |
7.5 |
7.7 |
7.8 |
8.0 |
8.1 |
9.0 |
9.7 |
10.6 |
11.4 |
12.2 |
16.3 |
|
7.1 |
7.3 |
7.4 |
7.6 |
7.8 |
7.9 |
8.1 |
8.3 |
8.4 |
9.3 |
10.1 |
11.0 |
11.8 |
12.7 |
16.9 |
|
7.3 |
7.5 |
7.7 |
7.9 |
8.0 |
8.2 |
8.4 |
8.6 |
8.7 |
9.6 |
10.5 |
11.3 |
12.2 |
13.1 |
17.5 |
|
8.6 |
8.8 |
9.0 |
9.2 |
9.4 |
9.6 |
9.8 |
10.0 |
10.2 |
11.2 |
12.2 |
13.2 |
14.3 |
15.3 |
20.4 |
|
9.8 |
10.0 |
10.2 |
10.5 |
10.6 |
10.9 |
11.2 |
11.4 |
11.6 |
12.8 |
U.O |
15.1 |
16.3 |
17.4 |
23.3 |
|
11.0 |
11.3 |
11.5 |
11.8 |
12.0 |
12.3 |
12.6 |
12.8 |
13.1 |
14.4 |
15.7 |
17.0 |
18.3 |
19.6 |
26.2 |
|
12.2 |
12.5 |
12.8 |
13.1 |
13.4 |
13.7 |
14 0 |
14.2 |
14.5 |
16.0 |
17.4 |
18.9 |
20.3 |
21.8 |
29.1 |
|
13.4 |
13.8 |
14.1 |
14 4 |
14 7 |
15.0 |
15.4 |
15.7 |
16.0 |
17.6 |
19.2 |
20.8 |
22.4 |
24 0 |
32.0 |
|
14.7 |
15.0 |
15.4 |
15.7 |
16.1 |
16.4 |
16.8 |
17.1 |
17.5 |
19.2 |
20.9 |
22.7 |
24.4 |
26.2 |
34 9 |
|
17.1 |
17.5 |
17.9 |
18.3 |
18.7 |
19.1 • |
19.5 |
20.0 |
20.4 |
22.4 |
24 4 |
26.5 |
28.5 |
30.5 |
40.7 |
|
19.5 |
20.0 |
20.5 |
20.9 |
21.4 |
21.9 |
22.3 |
22.8 |
23.3 |
25^6 |
27.9 |
30.2 |
32.6 |
34 9 |
40.5 |
|
22.0 |
22.5 |
23.0 |
23.6 |
24.1 |
24.6 |
25.1 |
25.6 |
26.2 |
28.8 |
31.4 |
34.0 |
36.6 |
39.3 |
52.3 |
|
24.4 |
25.0 |
25.6 |
26.2 |
26:7 |
27.3 |
27.9 |
28.5 |
29.1 . |
32.0 |
34.9 |
37.8 |
40.7 |
43.6 |
58.1 |
|
26.9 |
27.5 |
28.1 |
28.8 |
29.4 |
30.1 |
30.7 |
31.3 |
32.0 |
35.2 |
38.4 |
41.6 |
41.8 |
48.0 |
64.0 |
|
29.3 |
30.0 ■ |
30.7 |
31.4 |
32.1 |
32.8 |
33.5 |
34.2 |
34.9 |
38.4 |
41.9 |
45.3 |
48.8 |
52.3 |
69.8 |
|
31.7 |
32.5 |
33.2 |
34.0 |
34.8 |
35.5 |
36.3 |
37.0 |
37.8 |
41.6 |
45.3 |
49.1 |
52.9 |
56.7 |
75.6 |
|
34 2 |
35.0 |
35.8 |
36,6 |
37.4 |
38.2 |
39.1 |
39.9 |
40.7 |
44 7 |
48.8 |
.52 9 |
57.0 |
61.0 |
81.4 |
|
36.6 |
37.5 |
38.4 |
39.2 |
40.1 |
41.0 |
41.8 |
42.7 |
43.6 |
47.9 |
52.3 |
56.7 |
61.0 |
6.5.4 |
87.2 |
|
39.0 |
40.0 |
40.9 |
41.8 |
42.8 |
43.7 |
44 6 |
45.6 |
46.5 |
51.1 |
55.8 |
60.4 |
65.1 |
69.7 |
93.0 |
|
41.5 |
42.5 |
43.4 |
44.4 |
45.4 |
46.4 |
47.4 |
48.4 |
49.4 |
54.3 |
59.2 |
64.2 |
69.1 |
74.1 |
98.7 |
|
43.9 |
44 9 |
46.0 |
47.0 |
48.1 |
49.1 |
50.2 |
51.2 |
52.3 |
57.5 |
62.7 |
67.9 |
73.2 |
78.4 |
104 5 |
|
58.5 |
59.8 |
61.2 |
62.6 |
64 0 |
65.4 |
66.8 |
68.2 |
69.6 |
76.5 |
83.5 |
90.5 |
97.4 |
104.4 |
139.2 |
|
72.9 |
74.7 |
76.4 |
78.1 |
79.9 |
81.6 |
83.3 |
85.1 |
86.8 |
95.5 |
104 2 |
112.9 |
121.5 |
130.2 |
173.6 |
|
D |
D |
D |
D |
D |
D |
D |
D |
D |
I) |
D |
D |
D |
D |
D |
|
840 |
860 |
880 |
900 |
920 |
940 |
960 |
980 |
1,000 |
1,100 |
1,200 |
1,300 |
1,400 |
1,500 |
2,000 |
160
A MANCTAL OF TOPOGRAPHIC METHODS.
Computed from the formula k='D sin a (
Table XI. — Differences of altitude
[Prepared by
1 a, in ■whicli D is tlie observed distance of the
|
D |
D |
D |
D |
D |
D |
D |
» |
D |
D |
I) |
D |
D |
D |
|
|
" |
100 |
;iio |
120 |
130 |
140 |
150 |
160 |
170 |
180 |
190 |
200 |
220 |
240 |
260 |
|
0 01 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
|
0 02 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
- 0.1 |
0.2 |
|
0 03 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
|
0 0-1 |
0.1 |
0.1 |
0.1 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
|
0 05 |
0.1 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
|
0 06 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.5 |
|
0 07 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
|
0 08 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0,5 |
0.5 |
0.6 |
0.6 |
|
0 09 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.7 |
|
0 10 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0,6 |
0.6 |
0.6 |
0.7 |
0.8 |
|
0 11 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.7 |
0.8 |
0.8 |
|
0 12 |
0.3 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
|
0 13 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
1.0 |
|
0 U |
0.4 |
0.4 |
0.5 |
0.5 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
1.0 |
1.1 |
|
0 15 |
0.4 |
0.5 |
0.5 |
0.6 |
6.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
1.0 |
1.0 |
1.1 |
|
0 16 |
0.5 |
0.5 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.2 |
|
0 17 |
0.5 |
0.5 |
0.6 |
0.6 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.2 |
3.3 |
|
0 18 |
0.5 |
0.6 |
0.6 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.2 |
1.3 |
1.4 |
|
0 19 |
0.6 |
0.6 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.1 |
1.2 |
1.3 |
1.4 |
|
0 20 |
0.6 |
0.6 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
|
0 21 |
0.6 |
0.7 |
0.7 |
0.8 |
0.9 |
0.9 |
1.0 |
l.O |
1.1 |
1.2 |
1.2 |
1.3 |
1.5 |
1.6 |
|
0 22 |
0.6 |
0.7 |
0.8 |
0.8 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.2 |
1.3 |
1.4 |
1.5 |
1.7 |
|
0 23 |
0.7 |
0,7 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.1 |
1.2 |
1.3 |
1.3 |
1.5 |
1.6 |
1.7 |
|
0 24 |
0.7 |
0.8 |
0.8 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.3 |
1.3 |
1.4 |
1.5 |
1.7 |
1.8 |
|
0 25 |
0.7 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.2 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.9 |
|
0 26 |
0.8 |
0.8 |
0.9 |
1.0 |
1.1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.4 |
1.5 |
1.7 |
1.8 |
2.0 |
|
0 27 |
0.8 |
0.9 |
0.9 |
1.0 |
1.1 |
1.2 |
1.3 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.9 |
2.0 |
|
0 28 |
0.8 |
0.9 |
1.0 |
1.1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.5 |
1.6 |
1.S |
2.0 |
2.1 |
|
0 29 |
0.8 |
0.9 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.4 |
1.5 |
1.6 |
1.7 |
1.9 |
2.0 |
2.2 |
|
0 30 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.7 |
1.9 |
2.1 |
2.3 |
|
0 35 |
1.0 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.2 |
2.4 |
2.6 |
|
0 40 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.6. |
2.8 |
3.0 |
|
0 43 |
1.3 |
1.4 |
1.6 |
1.7 |
1.8 |
2.0 |
2.1 |
2.2 |
2.4 |
2.5 |
2.6 |
2.9 |
3.1 |
3.4 |
|
0 50 |
1.5 |
1.6 |
1.7 |
1.9 |
2.0 |
2.2 |
2.3 |
2.5 |
2.6 |
2.8 |
2.9 |
3. -2 |
■3.5 |
3.8 |
|
0 55 |
1.6 |
1.8 |
1.9 |
2.1 |
2.2 |
2.4 |
2.6 |
2.7 |
2.9 |
3.0 |
3.2 |
3.5 |
3.8 |
4.2 |
|
1 00 |
1.7 |
1.9 |
2.1 |
2.3 |
2.4 |
2.6 |
2.8 |
3.0 |
3.1 |
3.3 |
3.5 |
3.8 |
4.2 |
4.5 |
|
1 10 |
2.0 |
2.2 |
2.4 |
2.6 |
2.9 |
3.1 |
3.3 |
3.5 |
3.7 |
3.9 |
4.1 |
4.5 |
4.9 |
6.3 |
|
1 20 |
2.3 |
2.6 |
2.8 |
3.0 |
3.3 |
3.5 |
3.7 |
4.0 |
4.2 |
4.4 |
4.7 |
5.1 |
6.6 |
6.0 |
|
1 30 |
2.6 |
2.9 |
3.1 |
3.4 |
3.7 |
3.9 |
4.2 |
4.4 |
4.7 |
5.0 |
5.2 |
5.8 |
6.3 |
6.8 |
|
1 40 |
2.9 |
3.2 |
3.5 |
3.8 |
4.1 |
4.4 |
4.7 |
4.9 |
5.2 |
5.5 |
5.8 |
6.4 |
7.0 |
7.6 |
|
1 50 |
3.2 |
3.5 |
3.8 |
4.2 |
4.5 |
4.8 |
5.1 |
5.4 |
5.8 |
6.1 |
6.4 |
7.0 |
7.7 |
8.3 |
|
2 00 |
3.5 |
3.8 |
4.2 |
4.5 |
4.9 |
5.2 |
5.6 |
5.9 |
6.3 |
6.6 |
7.0 |
7.7 |
8.4 |
9.1 |
|
2 10 |
3.8 |
4.2 |
4.5 |
4.9 |
5.3 |
5.7 |
6.0 |
6.4. |
6.8 |
7.2 |
7.6 |
8.3 |
9.1 |
9.8 |
|
2 20 |
4.1 |
4.5 |
4.9 |
5.3 |
5.7 |
6.1 |
6.5 |
6.9 |
7.3 |
7.7 |
8.1 |
8.9 |
9.8 |
10. a |
|
2 30 |
4.4 |
4.8 |
5.2 |
5.7 |
6.1 |
6.5 |
7.0 |
7.4 |
7.8 |
8.3 |
8.7 |
9.6 |
10.5 |
11.3 |
|
2 40 |
4.6 |
6.1 |
5.6 |
6.0 |
6.5 |
7.0 |
7.4 |
7.9 |
8.4 |
8.8 |
9.3 |
10.2 |
11.2 |
12.1 |
|
2 50 |
4.9 |
5.4 |
5.9 |
6.4 |
6.9 |
7.4 |
7.9 |
8.4 |
8.9 |
9.4 |
9.9 |
10.9 |
11.8 |
12.8 |
|
300 |
5.2 |
5.7 |
6.3 |
6.8 |
7.3 |
7.8 |
8.4 |
8.9 |
9.4 |
11.9 |
10.5 |
11.5 |
12.5 |
13.6 |
|
4 00 |
7.0 |
7.7 |
8.4 |
9.0 |
9.7 |
10.4 |
11.1 |
11.8 |
12.5 |
13.2 |
13.9 |
15.3 |
16.7 |
18.1 |
|
3 00 |
8.7 |
9.6 |
10.4 |
11.3 |
12.2 |
J3.0 |
13.9 |
14.8 |
15.6 |
16.5 |
17.4 |
19.1 |
20.8 |
22.6 |
|
D |
D |
D |
D |
D |
D |
D |
D |
D |
» |
D |
D |
D |
D |
|
|
" |
100 |
110 |
120 |
130 |
140 |
150 |
160 |
170 |
180 |
190 |
200 |
220 |
240 |
260 |
ALTITUDE TABLES.
161
from telemeter measures — Continued.
E. S. ■Woodward.]
telemeter staff, a 13 the angle of elevation or depression, and h is the difference in height.
|
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
|
280 |
300 |
320 |
840 |
360 |
380 |
400 |
420 |
410 |
460 |
480 |
500 |
520 |
540 |
|
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.2 |
0.2 |
|
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
|
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
|
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.6 |
|
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
|
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.8 |
0.9 |
0.9 |
0.9 |
|
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.1 |
|
0 7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.1 |
1.2 |
1.2 |
1.3 |
|
0.7 |
0.8 |
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.2 |
1.3 |
1.3 |
1.4 |
1.4 |
|
0.8 |
0.9 |
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.2 |
1.3 |
1.3 |
1.4 |
1.5 |
1.5 |
1.6 |
|
0.9 |
1.0 |
1.0 |
1.1 |
1.2 |
1.2 |
1.3 |
1.3 |
1.4 |
1.5 |
1.5 |
1.6 |
1.7 |
1.7 |
|
1.0 |
1.0 |
1.1 |
1.2 |
1.3 |
1.3 |
1.4 |
1.5 |
1.5 |
1.6 |
1.7 |
1.7 |
1.8 |
1.9 |
|
1.1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.4 |
1.5 |
1.6 |
1.7 |
1.7 |
1.8 |
1.9 |
2.0 |
2.0 |
|
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.0 |
2.1 |
2.2 |
|
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.7 |
1.8 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
|
1.3 |
.1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.0 |
' 2.1 |
2.2 |
2.3 |
2.4 |
2.5 |
|
1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.5 |
2.6 |
2.7 |
|
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.5 |
2.6 |
2.7 |
2.8 |
|
1.5 |
1.7 |
1.8 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.5 |
2.7 |
2.8 |
2.9 |
3.0 |
|
1.6 |
1.7 |
1.9 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.6 |
2.7 |
2.8 |
2.9 |
3.0 |
3.1 |
|
1.7 |
1.8 |
2.0 |
2.1 |
2.2 |
2.3 |
2.4 |
2.6 |
2.7 |
2.8 |
2.9 |
3.1 |
3.2 |
3.3 |
|
1.8 |
1.9 |
2.0 |
2.2 |
2.3 |
2.4 |
2.6 |
2.7 |
2.8 |
2.9 |
3.1 |
3.2 |
3.3 |
3.5 |
|
1.9 |
2.0 |
2.1 |
2.3 |
2.4 |
2.5 |
2.7 |
2.8 |
2.9 |
3.1 |
3.2 |
3.3 |
3.5 |
3.6 |
|
2.0 |
2.1 |
2.2 |
2.4 |
2.5 |
2.7 |
2.8 |
2.9 |
3.1 |
3.2 |
3.4 |
3.5 |
3.6 |
3.8 |
|
2.0 |
2.2 |
2.3 |
2.5 |
2.6 |
2.8 |
2.9 |
3.1 |
3.2 |
3.3 |
3.5 |
3.6 |
3.8 |
3.9 |
|
2.1 |
2.3 |
2.4 |
2.6 |
2.7 |
2.9 |
3.0 |
3.2 |
3.3 |
3.5 |
3.6 |
3.8 |
3.9 |
4.1 |
|
2.2 |
2.4 |
2.5 |
2.7 |
2.8 |
3.0 |
3.1 |
3.3 |
3.5 |
3.6 |
3.8 |
3.9 |
4.1 |
4.2 |
|
2.3 |
2.4 |
2.6 |
2.8 |
2.9 |
3.1 |
2.3 |
3.4 |
3.6 |
3.7 |
3.9 |
4.1 |
4.2 |
4.4 |
|
2.4 |
2.5 |
2.7 |
2.9 |
3.0 |
3.2 |
3.4 |
3.5 |
3.7 |
3.9 |
4.1 |
4.2 |
4.4 |
4.6 |
|
2.4 |
2.6 |
2.8 |
3.0 |
3.1 |
3.3 |
3.5 |
3.7 |
3.8 |
4.0 |
4.2 |
4.4 |
4.5 |
4.7 |
|
S.9 |
3.1 |
3.3 |
3.5 |
3.7 |
3.9 |
4.1 |
4.3 |
4.5 |
. 4.7 |
4.9 |
5.1 |
5.3 |
5.5 |
|
3.3 |
3.5 |
3.7 |
4.0 |
4.2 |
• 4.4 |
4.7 |
4.9 |
5.1 |
5.3' |
5.6 |
5.8 |
6.0 |
6.3 |
|
3.7 |
3.9 |
4.2 |
4.5 |
4.7 |
5.0 |
5.2 |
5.5 |
5.8 |
6.0 |
6.3 |
6.5 |
6.8 |
7.1 |
|
4.1 |
4.4 |
4.7 |
4.9 |
5.2 |
5.5 |
5.8 |
6.1 |
6.4 |
6.7 |
7.0 |
7.3 |
7.6 |
7.9 |
|
4.5 |
4.8 |
5.1 |
5.4 |
5.8 |
6.1 |
6.4 |
6.7 |
7.0 |
7.4 |
7.7 |
8.0 |
8.3 |
8.6 |
|
4.9 |
5.2 |
6.6 |
5.9 |
6.3 |
6.6 |
7.0 |
7.3 |
7.7 |
8.0 |
8.4 |
8.7 |
9.1 |
9.4 |
|
5.7 |
6.1 |
6.5 |
6.9 |
7.3 |
7.7 |
8.1 |
8.6 |
9.0 |
9.4 |
9.8 |
10.2 |
10.6 |
11.0 |
|
6.5 |
7.0 |
7.4 |
7.9 |
8.4 |
8.8 |
9.3 |
9.8 |
10.2 |
10.7 |
11.2 |
11.6 |
12.1 |
12.6 |
|
7.3 |
7.9 |
8.4 |
8.9 |
9.4 |
9.9 |
10.5 |
11.0 |
11.5 |
12.0 |
12.6 |
13.1 |
13.6 |
14.1 |
|
8 1 |
8.7 |
9.3 |
9.9 |
10.5 |
11.0 |
11.6 |
12.2 |
12.8 |
13.4 |
14.0 |
14.5 |
15.1 |
15.7 |
|
9.0 |
9.6 |
10.2 |
10.9 |
11.5 |
12.2 |
12.8 |
13.4 |
14.1 |
14.7 |
15.4 |
16.0 |
16.6 |
17.3 |
|
9.8 |
10.5 |
11.2 |
11.9 |
12.6 |
13.3 |
14.0 |
14.6 |
15.3 |
16.0 |
16.7 |
17.4 |
18.1 |
18.8 |
|
10.6 |
11.3 |
12.1 |
12.8 |
13.6 |
14.4 |
16.1 |
15.9 |
16.6 |
17.4 |
18.1 |
18.9 |
19.6 |
20.4 |
|
11.4 |
12.2 |
13.0 |
13.8 |
14.6 |
15.5 |
16.3 |
17.1 |
17.9 |
18.7 |
19.5 |
20.3 |
21.2 |
22.0 |
|
12.2 |
13.1 |
13.9 |
14.8 |
15.7 |
16.6 |
17.4 |
18.3 |
19.2 |
20.0 |
20.9 |
21.8 |
22.7 |
23.5 |
|
13.0 |
13.9 |
14.8 |
15.8 |
16.7 |
17.7 |
18.6 |
19.5 |
20.5 |
21.4 |
22.3 |
2S.2 |
24.2 |
25.1 |
|
13.8 |
14.8 |
15.8 |
16.8 |
17.8 |
18.8 |
19.7 |
20.7 |
21.7 |
22.7 |
23.7 |
24.7 |
25.7 |
26.7 |
|
14.6 |
15.7 |
16.7 |
17.8 |
18.8 |
19.9 |
20.9 |
21.9 |
23.0 |
24.0 |
25.1 |
26.1 |
27.2 |
28.2 |
|
19.5 |
20.9 |
22.3 |
23.7 |
25.1 |
26.4 |
27.8 |
29.2 |
30.6 |
32.0 |
33.4 |
34.8 |
36.2 |
37.6 |
|
24.3 |
26.0 |
27.8 |
29.5 |
31.3 |
33.0 |
34.7 |
36.5 |
38.2 |
39.9 |
41.7 |
43.4 |
45.1 |
46.9 |
|
D |
D |
D |
I) |
D |
D |
D |
D |
D |
D |
D |
D |
D |
D |
|
280 |
300 |
320 |
340 |
360 |
380 |
400 |
420 |
440 |
460 |
480 |
600 |
620 |
540 |
-11
162
A MANUAL OF TOPOGRAPHIC METHODS.
CONSTANTS.
163
Table XIII.— Constants.
IT =3.141593
log.ir =0.4971499
180° 1
"ir^arc lo— 57°.29578=57° 17' 44" .8; log. =1.7581226
^i5?52!=_J_=3447' .74677: log.=3. 5362739 n arc 1' "
r"=ii?552^^i— =206264".80625: loe.=5. 314(251 IT Sin 1" ^
comp . log. =4 . 6855749 =log. sin 1" Log.
Number of degrees in circumference 360=2. 5563025
Number of minutes in circumference 21,600=4.3344538
Number of seconds in circumference 1, 296, 000=6. 1126050
Lengtli of arc of 1 degree 0174,5329=8. 2418774—10
Lengtb of arc of 1 minute 00029089=6. 4637261—10
Lengtli of arc of 1 second 000004848=4. 6855749—10
Constants of generating ellipse of Clarke's spheroid.
e'= (l— *, ^ =0. 00676866 »=(1— VlIIj2)(l+<7i:ii2)-i= O.C
7. 8305030—10 7. 2299162—10
Length of the meter in inches according to various authoriiiei.
Inches. 1 meter=39. 370432, Clarke, 1866-1873. =39. 370790, Kater, 1818.
=39.368505, Coast Survey, 1851-1858 (Hassler corrected). =39. 38092, Hassler, 1832. =39. 36985, L.ake Survey, 1885.
=39.377786, Theoretical ten-millionth of quadrant (Clarke). =39. 37, By act of Congress, 1866.
The standard meter has its normal length at 32'^ E The standard yard has its normal length at 62° F. The value first given is the one generally adopted by scientific men in the United States.
Values adopted in the measurement of an arc of parallel extending from Ireland to the river Ural in Russia, as the exact relative lengths of standards used as the units of measure in the triangulations of England, France, Belgium, Prussia, and Russia.
|
Standards. |
Expressed in terms of the standard yard. |
Expressed in inches. |
Expressed in lines of the toise. |
Expressed in millimeters. |
|
1. 00000000 2. 13151116 1. 09362311 |
36.000000 76. 734402 39. 370432 |
405. 34622 864.00000 443.29600 |
914. 39180 1, 949. 03632 1, 000. 00000 |
|
CONVERSION TABLES.
Table XIV. — Meters into yards.
[Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884].
[1 meter = 1.093623 yards.]
|
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
Yards. |
|
100,000 |
109, 362. 3 |
||||||||
|
90, 000 |
98,426.1 |
9,000 |
9, 842. 61 |
900 |
984.26 |
90 |
98. 426 |
9 |
9.843 |
|
80, 000 |
87,489.8 |
. 8,000 |
8, 748. 98 |
800 |
874. 90 |
80 |
87. 490 |
8 |
8.749 |
|
70, 000 |
76, 553. 6 |
7,000 |
7, 655. 36 |
700 |
765. 54 |
70 |
76. 554 |
7 |
7.655 |
|
60, 000 |
65,617.4 |
6,000 |
6, 561. 74 |
600 |
656. 17 |
60 |
65. 617 |
6 |
6.562 |
|
50, 000 |
54,681.2 |
5,000 |
5, 468. 12 |
500 |
546.81 |
50 |
54. 681 |
5 |
5.568 |
|
40, 000 |
43, 744. 9 |
4,000 |
4, 374. 49 |
400 |
437. 45 |
40 |
43.745 |
4 |
4.374 |
|
30, 000 |
32, 808. 7 |
3,000 |
3,280.87 |
300 |
328. 09 |
30 |
32. 809 |
3 |
3.281 |
|
20, 000 |
21, 872. 5 |
2,000 |
2, 187. 25 |
200 |
218.72 |
20 |
21. 872 |
2 |
2.187 |
|
10, 000 |
10, 936. 2 |
1,000 |
1, 093. 62 |
100 |
109. 36 |
10 |
10. 936 |
1 |
1.094 |
164
A MANUAL OF TOPOGEAPHIC METHODS.
Table XV. — Yards into meters. [1 yard = 0.914392 meter.]
|
Tarda. |
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
Yards. |
Meters. |
|
100, 000 |
91,439.2 |
||||||||
|
90, 000 |
82,295.3 |
9,000 |
8, 229. 53 |
900 |
822.95 |
90 |
82.295 |
9 |
8.230 |
|
SO, 000 |
73, 151. 3 |
8,000 |
7, 315. 13 |
800 |
731. 51 |
80 |
73. 151 |
8 |
7.315 |
|
70, 000 |
61, 007. 4 |
7,000 |
6, 400. 74 |
700 |
640.07 |
70 |
64. 007 |
7 |
6.401 |
|
60, OOO |
54,863.5 |
6,000 |
5,486.35 |
600 |
548. 64 |
5.486 |
|||
|
50, 000 |
45, 719. 6 |
5,000 |
4, 571. 96 |
500 |
457.20 |
50 |
45. 720 |
5 |
4.572 |
|
40, 000 |
36, 575. 7 |
4,000 |
3, 657. 57 |
400 |
365. 76 |
40 |
36. 576 |
4 |
3.658 |
|
30, 000 |
27,431.8 |
3,000 |
2, 743. 18 |
300 |
274. 32 |
3 |
2.743 |
||
|
20, 000 |
18,287.8 |
2,000 |
1, 828. 78 |
200 |
182. 88 |
20 |
18. 288 |
2 |
1.829 |
|
10, 000 |
9, 143. 9 |
1,000 |
914.39 |
100 |
91.44 |
10 |
9.144 |
1 |
0.914 |
Table XVI. — Meters into inches and inches into meters. [1 meter = 39.370432 inches, log. = 1.5951702.] [1 iucli = 0.02539977 meter, log. =8.4048298.]
|
Meters. |
Inches. |
|
1 |
39.37043 |
|
. 2 |
78. 74086 |
|
3 |
118.11130 |
|
4 |
157. 48173 |
|
5 |
196. 85216 |
|
6 |
236. 22259 |
|
7 |
275. 59302 |
|
8 |
314. 96346 |
|
9 |
354. 33389 |
|
Inches. |
Meters. |
|
1 |
0. 025400 |
|
2 |
0. 050800 |
|
3 |
0. 076199 |
|
4 |
0. 101599 |
|
5 |
0. 126999 |
|
6 |
0. 152399 |
|
7 |
0. 177798 |
|
8 |
0. 203198 |
|
9 |
0. 228598 |
Table XVII. — Meters into statute and nautical miles.
|
Meters. |
Statnte miles. |
Nautical miles. |
Meters. |
Statute miles. |
Nautical miles. |
Meters. |
Statnte miles. |
Nautical miles. |
Meters. |
Statute miles. |
Nautical miles. |
|
100, 000 |
62. 138 |
53.959 |
|||||||||
|
90, 000 |
55.924 |
48. 563 |
9,000 |
5.592 |
4.856 |
900 |
0.559 |
0.486 |
90 |
0.056 |
0.049 |
|
80, 000 |
49. 710 |
43. 167 |
8,000 |
4.971 |
4.317 |
800 |
0.497 |
0.432 |
80 |
0. '50 |
|
|
70, 000 |
43.496 |
37. 772 |
7,000 |
4.350 |
3.777 |
700 |
0.435 |
0.378 |
70 |
0.043 |
0.038 |
|
60, 000 |
37. 283 |
32. 376 |
6,000 |
3.728 |
3.238 |
600 |
0.373 |
0.324 |
60 |
0.037 |
0.032 |
|
50, 000 |
31. 069 |
26. 980 |
5,000 |
3.107 |
2.698 |
500 |
0.311 |
0.270 |
50 |
0.031 |
0.027 |
|
40, 000 |
24.855 |
21. 584 |
4,000 |
2.486 |
2.158 |
400 |
0.249 |
0.216 |
40 |
0.025 |
0.022 |
|
30, 000 |
18.641 |
16.188 |
3,000 |
1.864 |
1.619 |
300 |
0.186 |
0.162 |
30 |
0.019 |
0.016 |
|
20, 000 |
12.428 |
10. 792 |
2,000 |
1.243 |
1.079 |
200 |
0.124 |
O.108 |
20 |
0.012 |
0.011 |
|
10, 000 |
6.214 |
5.396 |
1,000 |
0.621 |
0.540 |
100 |
0.062 |
0.054 |
10 |
0.006 |
0.005 |
Table XVIII. — Statute and nautical miles into meters.
|
Meters in [Meters in |
Meters in |
Meters in |
Meters in |
Meters in |
|||||||
|
Miles. |
Miles. |
statute |
nautical |
Miles. |
statute |
nautical |
Miles. |
statute |
nautical |
||
|
miles. |
miles. |
miles. |
miles. |
miles. |
miles. |
miles. |
miles. |
||||
|
100 |
160, 933. 0 |
185,324.8 |
|||||||||
|
90 |
144,839.7 |
166. 792. 3 |
9 |
14,483.97 |
16, 679. 23 |
.9 |
1,448.40 |
1, 667. 92 |
.09 |
144.84 |
166. 79 |
|
80 |
128. 746. 4 |
148, 259. 8 |
8 |
12,874.64 |
14, 825. 98 |
.8 |
1,287.46 |
1, 482. 60 |
|||
|
70 |
112, 653. 1 |
129, 727. 4 |
7 |
11, 265. 31 |
12, 972. 74 |
.7 |
1, 126. 53 |
1,297.27 |
.07 |
112. 65 |
129. 73 |
|
60 |
96, 559. 8 |
111, 194. 9 |
6 |
9, 655. 98 |
11,119.49 |
.6 |
965. 60 |
1, 111. 95 |
.06 |
96.56 |
111. 19 |
|
50 |
80,466.5 |
92,662.4 |
5 |
8,046.65 |
9, 266. 24 |
.5 |
804.67 |
926. 62 |
.05 |
||
|
40 |
64,373.2 |
74, 129. 9 |
4 |
6,437.32 |
7, 412. 99 |
.4 |
643. 73 |
741. 30 |
|||
|
30 |
48, 279. 9 |
65, 597. 4 |
3 |
4,827.99 |
5, 559. 74 |
.3 |
482. 80 |
||||
|
20 |
32,186.6 |
37, 065. 0 |
2 |
3, 218. 66 |
3,706.50 |
.2 |
321. 87 |
370. 65 |
.02 |
32.19 |
37.06 |
|
10 |
16,093.3 |
18,532.5 |
1 |
1,609.33 |
1, 853. 25 |
.1 |
160. 93 |
185. 32 |
.01 |
16.09 |
18.53 |
IMeters x 39.370432 Meters x 3.280869 Meters x 1.093623 Meters X 0.000621377 :
:iiiclies, or to log. of meters add 1.5951701 : feet, or to log. of meters add 0.5159889 : yards, or to log. of meters add 0.0388676 : miles, or to log. of meters add 6.7933550
PROJECTION TABLES.
165
Table XIX. — For projection of maps of large areas. [Extracted from Appendix 'So. 6, TJ. S. Coast and Geodetic Survey Report for 1884.]
LENGTHS OF DEGREES OF THE MERIDIAN.
|
Latitude |
Meters.* |
Statute miles. |
Latitude |
Meters.* |
Statute miles. |
|
0 |
110,567.2 |
68. 704 |
45 |
Ill, 130. 9 |
69.064 |
|
1 |
110, 567. 6 |
68. 704 |
46 |
111, 150. 6 |
69. 066 |
|
2 |
110, 568. 6 |
68. 705 |
47 |
111, 170. 4 |
69. 079 |
|
3 |
110, 570. 3 |
68. 706 |
48 |
111, 190. 1 |
69. 091 |
|
4 |
110, 572. 7 |
68. 708 |
49 |
111, 209. 7 |
69. 103 |
|
5 |
110, 675. 8 |
68. 710 |
50 |
111,229.3 |
69. 115 |
|
6 |
110, 579. 5 |
68. 712 |
51 |
111,248.7 |
69. 127 |
|
7 |
110, 583. 9 |
68,715 |
52 |
111, 208. 0 |
69. 139 |
|
8 |
HO, 589. 0 |
68. 718 |
63 |
HI, 287. 1 |
69. 151 |
|
9 |
110, 594. 7 |
68. 721 |
54 |
111, 306. 0 |
69. 163 |
|
10 |
110, 601. 1 |
68. 725 |
65 |
111,324.8 |
69, 175 |
|
11 |
110, 608. 1 |
68. 730 |
56 |
111, 343. 3 |
69. 186 |
|
12 |
110, 615. 8 |
68. 734 |
57 |
111, 361. 5 |
69. 197 |
|
13 |
110, 624. 1 |
68. 739 |
58 |
HI, 379. 5 |
69. 209 |
|
14 |
110, 633. 0 |
68.744 |
59 |
111, 397. 2 |
69. 220 |
|
15 |
110,042.5 |
63. 751 |
60 |
111,414.5 |
69. 230 |
|
16 |
110, 652. 6 |
68. 757 |
61 |
111,431.5 |
69. 241 |
|
17 |
110, 663. 3 |
68. 764 |
62 |
111, 448. 2 |
69. 251 |
|
18 |
110,674.5 |
68. 771 |
63 |
111, 464. 4 |
69. 261 |
|
19 |
110, 686. 3 |
68. 778 |
64 |
111, 480. 3 |
69.271 |
|
20 |
110, 698. 7 |
68. 786 |
65 |
111, 495. 7 |
69. 281 |
|
21 |
110, 711. 6 |
68. 794 |
66 |
111,510.7 |
69. 290 |
|
22 |
HO, 725. 0 |
68. 802 |
67 |
111, 525. 3 |
69. 299 |
|
23 |
HO, 738. 8 |
68.811 |
68 |
111, 539. 3 |
69. 308 |
|
24 |
110, 753. 2 |
68. 820 |
69 |
111,552.9 |
69. 316 |
|
25 |
110, 768. 0 |
68.829- |
70 |
111,565.9 |
69. 324 |
|
26 |
110, 783. 3 • |
68. 839 |
71 |
111,578.4 |
69. 332 |
|
27 |
110,799.0 |
68. 848 |
72 |
111,590.4 |
69. 340 |
|
28 |
119, 815. 1 |
68. 858 |
73 |
HI, 601. 8 |
69. 347 |
|
29 |
110, 831. 6 |
68. 869 |
74 |
111,612.7 |
69. 354 |
|
30 |
110,848.5 |
68. 879 |
75 |
111, 622. 9 |
69. 360 |
|
31 |
110, 865. 7 |
68. 890 |
76 |
111, 632. 6 |
69. 366 |
|
32 |
110, 883. 2 |
68. 91)1 |
77 |
111, 841. 6 |
69. 372 |
|
33 |
110, 901. 1 |
68. 912 |
78 |
111,650.0 |
69. 377 |
|
34 |
110, 919. 2 |
68. 923 |
79 |
111, 657. 8 |
69. 382 |
|
35 |
110, 937. 6 |
68. 935 |
80 |
111, 664. 9 |
69. 386 |
|
36 |
110, 956. 2 |
68. 946 |
81 |
111,671.4 |
69. 390 |
|
37 |
110, 975. 1 |
68. 958 |
82 |
111, 677. 2 |
69. 394 |
|
38 |
110, 994. 1 |
68. 969 |
83 |
111, 682. 4 |
69. 397 |
|
39 |
111,013.3 |
68. 981 |
84 |
111, 686. 9 |
69. 400 |
|
40 |
111,032.7 |
68. 993 |
85 |
111, 690. 7 |
69. 402 |
|
41 |
111, 052. 2 |
69.006 |
86 |
111, 693. 8 |
69. 404 |
|
42 |
111, 071. 7 |
69. 018 |
87 |
111, 696. 2 |
69. 405 |
|
43 |
111,091.4 |
•69. 030 |
88 |
HI, 697. 9 |
69.407 |
|
44 |
111, 111. 1 |
69.043 |
89 |
111, 699. 0 |
69.407 . |
|
45 |
111,130.9 |
69.054 |
90 |
111,699.3 |
69.407 |
* These quantities express tlie number of meters and statute miles contained "within an arc of which the degree of lati- tude numed is the middle; thus, the quantity, 111032.7, opposite latitude 40°, is the number of meters between latitude 39° 30' and latitude 40° 30'.
166
A MANUAL OF TOPOGRAPHIC METHODS.
Table XIX. — For projection of maps of large areas — Continued. [Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
LENGTHS OP DEGREES OF THE PARALLEL.
|
Latitude. |
Meters. |
Statute miles. |
Latitude. |
Meters. |
Statute miles. |
|
0 |
Ill, 321 |
69. 172 |
45 |
78, 849 |
48.995 |
|
1 |
1,304 |
9.162 |
46 |
7,466 |
8.136 |
|
2 |
1,253 |
9.130 |
47 |
6,058 |
7.261 |
|
3 |
1,169 |
9.078 |
48 |
4,628 |
6.372 |
|
4 |
1,051 |
9.005 |
49 |
3,174 |
5.469 |
|
6 |
110, 900 |
68. 911 |
50 |
71, 698 |
44, 552 |
|
6 |
0,715 |
8.795 |
51 |
70, 200 |
3.621 |
|
7 |
0,497 |
8.660 |
52 |
68, 680 |
2.676 |
|
8 |
0,245 |
8.504 |
53 |
7,140 |
1.719 |
|
9 |
109, 959 |
8.326 |
54 |
5,578 |
0.749 |
|
10 |
109, 641 |
68. 129 |
55 |
63, 996 |
39. 766 |
|
U |
9,289 |
7.910 |
56 |
2,395 |
8.771 |
|
12 |
8,904 |
7.670 |
57 |
60, 774 |
7.764 |
|
13 |
8,486 |
7.410 |
58 |
69, 135 |
6.745 |
|
14 |
8,036 |
7.131 |
59 |
7,478 |
5.716 |
|
15 |
107, 553 |
66. 830 |
60 |
55, 802 |
34. 674 |
|
16 |
7, 036 |
6.510 |
61 |
4,110 |
3.623 |
|
17 |
6,487 |
6.169 |
62 |
2,400 |
2.560 |
|
18 |
5,906 |
5.808 |
63 |
50, 675 |
1.488 |
|
19 |
5,294 |
5.427 |
64 |
48, 934 |
0.406 |
|
20 |
104, 649 |
65. 026 |
65 |
47, 177 |
29. 315 |
|
21 |
3,972 |
4.606 |
66 |
5, 407 |
8.215 |
|
22 |
3.264 |
4.166 |
67 |
3,622 |
7.106 |
|
23 |
2,524 |
3.706 |
68 |
1,823 |
5.988 |
|
24 |
1,754 |
3.228 |
69 |
0,012 |
4.862 |
|
25 |
100, 952 |
62. 729 |
70 |
38, 188 |
23. 729 |
|
26 |
100. 119 |
2.212 |
71 |
6,353 • |
2.589 |
|
27 |
99, 257 |
1.676 |
72 |
4,606 |
L441 |
|
28 |
8,364 |
1.122 |
73 |
2,648 |
20. 287 |
|
29 |
7,441 |
0.548 |
74 |
0,781 |
19. 127 |
|
30 |
96,488 |
59. 956 |
75 |
28, 903 |
17. 960 |
|
31 |
5,506 |
9.345 |
76 |
7,017 |
6.788 |
|
32 |
4,495 |
8.716 |
77 |
5,123 |
5.611 |
|
33 |
3,455 |
8,071 |
78 |
3,220 |
4.428 |
|
34 |
2,387 ■ |
7.407 |
79 |
1,311 |
13. 242 |
|
35 |
91, 290 |
56. 725 |
80 |
19, 394 |
12. 051 |
|
36 |
90, 166 |
6.027 |
81 |
17, 472 |
10. 857 |
|
37 |
89, 014 |
5.311 |
' 82 |
15, 545 |
9.659 |
|
38 |
7,835 |
4.579 |
83 |
13, 612 |
8.458 |
|
39 |
6,629 |
3.829 |
84 |
11, 675 |
7.255 |
|
40 |
85, 396 |
53. 063 |
85 |
9,735 |
6.049 |
|
41 |
4,137 |
2.281 |
86 |
7,792 |
4.842 |
|
42 |
'2, 853 |
1.483 |
87 |
5,846 |
3.632 |
|
43 |
1,543 |
50. 669 |
88 |
3,898 |
2. 422 . |
|
44 |
80, 208 |
49. 840 |
89 |
1, 949 |
1.211 |
|
45 |
78, 849 |
48. 995 |
90 |
" |
0.000 |
PBOJECTION TABLES.
167
Table XIX. — For projection of maps of large areas — Continued. [Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884.]
AECS OF THE PARALLEL IN METERS.
|
Latitude. |
Value of 1'. |
Latitude. |
Value of 1'. |
Latitude. |
Value of 1'. |
|
24 00 |
1695.9 |
33 00 |
1557. 6 |
42 00 |
1380. 9 |
|
10 |
3.7 |
10 |
4.7 |
10 |
77.3 |
|
20 |
1.5 |
20 |
1.7 |
20 |
73.7 |
|
30 |
1689.3 |
30 |
48.7 |
30 |
70.0 |
|
40 |
7.0 |
40 |
5.8 |
40 |
66.4 |
|
50 |
4.8 |
50 |
2.8 |
50 |
62.7 |
|
25 00 |
1682. 5 |
34 00 |
1539. 8 |
43 00 |
1359. 1 |
|
10 |
80.3 |
10 |
6.8 |
10 |
55.4 |
|
20 |
1678. 0 |
20 |
3.7 |
20 |
51.7 |
|
30 |
5.7 |
30 |
0.7 |
30 |
48.0 |
|
40 |
3.3 |
40 |
27.6 |
40 |
44.3 |
|
50 |
1.0 |
50 |
4.6 |
50 |
40.5 |
|
26 00 |
1668. 7 |
35 00 |
1521. 5 |
44 00 |
1336. 8 |
|
10 |
6.3 |
10 |
18.4 |
10 |
33.1 |
|
20 |
3.9 |
20 |
15.3 |
20 |
29.3 |
|
30 |
1.5 |
30 |
12.2 |
30 |
25.5 |
|
40 |
1659. 1 |
40 |
09.1. |
40 |
21.7 |
|
50 |
6.7 |
50 |
05.9 |
50 |
18.0 |
|
27 00 |
1654. 3 |
36 00 |
1502. 8 |
45 00 |
1314. 2 |
|
10 |
51.8 |
10 |
1499. 6 |
10 |
10.3 |
|
20 |
1649.4 |
20 |
6.4 |
20 |
06.5 |
|
30 |
6.9 |
30 |
3.2 |
30 |
02.7 |
|
40 |
4.4 |
40 |
0.0 |
40 |
1298. 8 |
|
50 |
1.9 |
50 |
86.8 |
50 |
95.0 |
|
28 00 |
1639. 4 |
37 00 |
1483. 6 |
46 00 |
1291. 0 |
|
10 |
6.9 |
10 |
80.3 |
10 |
87.2 |
|
20 ' |
4.3 |
20 |
77.1 |
20 |
83.3 |
|
30 |
1.8 |
30 |
73.8 |
30 |
79.4 |
|
40 |
29.2 |
40 |
70.5 |
40 |
75.5 |
|
50 |
6.6 |
50 |
67.2 |
50 |
71.6 |
|
29 00 |
1624.0 |
38 00 |
1463. 9 |
47 00 |
1267. 6 |
|
10 |
21.4 |
10 |
60.6 |
10 |
63.7 |
|
20 |
18.8 |
20 |
57.3 |
20 |
59.7 |
|
30 |
6.1 |
30 |
53.9 |
30 |
55.8 |
|
40 |
3.5 |
40 |
50.6 |
• 40 |
51.8 |
|
50 |
0.8 |
50 |
47.2 |
50 |
47.8 |
|
30 00 |
1608. 1 |
39 00 |
1443.8 |
48 00 |
1243.8 |
|
10 |
5.4 |
"10 |
40.4 |
10 |
39.8 |
|
20 |
2.7 |
20 |
37.0 |
20 |
35.8 |
|
30 |
0.0 |
30 |
33.6 |
30 |
31.7 |
|
40 |
1597. 3 |
40 |
30.2 |
40 |
27.7 |
|
50 |
4.5 |
50 |
26.7 |
50 |
23.6 |
|
31 00 |
1591. 8 |
40 00 |
1423.3 |
49 00 |
1219. 6 |
|
10 |
89.0 |
10 |
19.8 |
10 |
15.5 |
|
20 |
6.2 |
20 |
16.3 |
20 |
11.4 |
|
30 |
3.4 |
30 |
12.8 |
30 |
07.3 |
|
40 |
0.6 |
40 |
09.3 |
40 |
03.2 |
|
50 |
77.8 |
50 |
05.8 |
50 |
1199.1 |
|
32 00 |
1574. 9 |
41 00 |
1402. 3 |
50 00 |
1195. 0 |
|
10 |
72.1 |
10 |
1398.8 |
10 |
90.8 |
|
20 |
69.2 |
20 |
95.2 |
20 |
86.7 |
|
30 |
6.3 |
30 |
91.6 |
30 |
82.5 |
|
40 |
3.4 |
40 |
88.1 |
40 |
78.4 |
|
50 |
0.5 |
50 |
84.5 |
50 |
74.2 |
168
A MANUAL OF TOPOGKAPHIC METHODS.
Table XIX, — For projections of maps of large areas — Continued. [Extracted from Appendix No. 6, V. S. Coast and Geodetic Survey Keport for 1884.]
COORDINATES OF CUBVATUKE.
|
NATURAL SCALE.-VAI,TIES OF X AND Y IN METERS. |
||||||||||||||
|
Latitude 24°. |
Latitude 25°. |
Latitude 26°. |
Latitude 27°. |
|||||||||||
|
Longi- tude. |
X |
T |
Longi- tude. |
X |
T |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
|||
|
1 00 |
101, 753 |
361 |
1 |
00 |
100, 951 |
372 |
1 |
00 |
100, 118 |
383 |
1 |
00 |
99, 256 |
393 |
|
2 00 |
203, 500 |
1,445 |
2 |
00 |
201, 896 |
1,489 |
2 |
00 |
200, 231 |
1,532 |
2 |
00 |
198, 505 |
1,573 |
|
3 00 |
305,237 |
3,250 |
3 |
00 |
302, 831 |
3,351 |
3 |
00 |
300, 332 |
3,447 |
3 |
00 |
297, 742 |
3,539 |
|
4 00 |
406, 9d9 |
5,778 |
4 |
00 |
403, 749 |
5,957 |
4 |
00 |
400, 416 |
6,128 |
4 |
00 |
396, 960 |
6,291 |
|
5 00 |
508, 660 |
9,028 |
5 |
00 |
504, 645 |
9,307 |
5 |
00 |
500, 476 |
9,574 |
5 |
00 |
496, 154 |
9,829 |
|
6 00 |
610, 336 |
13, 001 |
6 |
00 |
605, 514 |
13,401 |
6 |
00 |
600, 506 |
13, 786 |
6 |
00 |
595, 316 |
14, 154 : |
|
7 00 |
711,981 |
17, 695 |
7 |
00 |
706, 349 |
18, 239 |
7 |
00 |
700, 501 |
18, 763 |
7 |
00 |
694, 440 |
19, 204 |
|
8 00 |
313,590 |
23, 109 |
8 |
00 |
807, 146 |
23, 821 |
8 |
00 |
800,456 |
24, 505 |
8 |
00 |
793, 522 |
25, 159 |
|
9 00 |
915, 159 |
29, 245 |
9 |
00 |
907, 899 |
30, 146 |
9 |
00 |
900, 364 |
31, Oil |
9 |
00 |
892, 554 |
31, 839 |
|
10 00 |
J, 016, 681 |
36, 102 |
10 |
00 |
1, 008, 603 |
37, 215 |
10 |
00 |
1, 000, 218 |
38, 282 |
10 |
00 |
991, 529 |
39, 303 |
|
11 00 |
1, 118, 152 |
43, 679 |
11 |
00 |
1, 109, 252 |
45, 026 |
11 |
00 |
1, 100, 015 |
46, 316 |
11 |
00 |
1, 090, 442 |
47, 551 |
|
12 00 |
1, 219, 566 |
51,977 |
00 |
1, 209, 841 |
53, 578 |
12 |
00 |
1, 199, 747 |
55, 114 |
12 |
00 |
1, 189, 287 |
56, 583 |
|
|
13 00 |
1,320,919 |
60, 994 |
13 |
00 |
I, 310, 364 |
62, 873 |
13 |
00 |
1, 299, 409 |
64, 675 |
13 |
00 |
1, 288, 1157 |
66, 398 |
|
14 00 |
1, 422, 205 |
70, 731 |
14 |
00 |
1, 410, 815 |
72, 909 |
14 |
00 |
1, 398, 994 |
74, 998 |
14 |
00 |
1, 386, 746 |
76, 995 |
|
15 00 |
1, 523, 420 |
81, 186 |
15 |
00 |
1, 511, 190 |
83, 685 |
15 |
00 |
1,498,498 |
86, 082 |
15 |
00 |
1, 485, 348 |
88, 374 |
|
16 00 |
1, 624, 558 |
92, 360 |
16 |
00 |
1, 611, 483 |
95, 202 |
16 |
00 |
1, 597, 914 |
97, 928 |
16 |
00 |
1, 583, 857 |
100, 534 |
|
17 00 |
1, 725, 614 |
104, 251 |
'17 |
00 |
1, 711, 688 |
107, 458 |
17 |
00 |
1, 697, 237 |
110, 534 |
17 |
00 |
1, 682, 267 |
113, 474 |
|
18 00 |
1, 826, 583 |
116, 859 |
18 |
00 |
1, 811, 800 |
120, 453 |
18 |
00 |
1, 796, 460 |
123, 899 |
18 |
00 |
1,780,570 |
127, 193 |
|
19 00 |
1, 927, 460 |
130, 184 |
19 |
00 |
1, 911, 813 |
134, 186 |
19 |
00 |
1, 895, 578 |
138, 023 |
19 |
00 |
1, 878, 762 |
141,690 |
|
20 00 |
2, 028, 240 |
144, 225 |
20 |
00 |
2, Oil, 722 |
148, 656 |
20 |
00 |
1, 994, 585 |
152, 905 |
20 |
00 |
1, 976, 836 |
156, 966 |
|
21 00 |
2, 128, 918 |
158, 981 |
21 |
00 |
2, 111. 522 |
163, 862 |
21 |
00 |
2,093,475 |
168, 544 |
21 |
00 |
2, 074, 786 |
173, 018 |
|
22 00 |
2, 229, 488 |
174, 451 |
22 |
00 |
2. 211, 207 |
179, 805 |
22 |
00 |
2, 192, 243 |
184, 939 |
22 |
00 |
2, 172, 606 |
189. 845 |
|
23 00 |
2, 329, 946 |
190, 634 |
23 |
00 |
2, 310, 771 |
196,482 |
23 |
00 |
2, 290, 882 |
202, 089 |
23 |
00 |
2, 270, 289 |
207, 447 |
|
24 00 |
2, 430, 287 |
207, 530 |
24 |
00 |
2,410,210 |
213, 894 |
24 |
00 |
2, 389, 387 |
219, 993 |
24 |
00 |
2, 367, 830 |
225, 823 |
|
25 00 |
2, 530, 505 |
225, 138 |
25 |
00 |
2, 609, 518 |
232, 038 |
25 |
00 |
2, 487, 753 |
238, 650 |
25 |
00 |
2, 465, 222 |
244, 970 |
|
26 00 |
2, 650, 596 |
243, 458 |
26 |
00 |
2, 608, 689 |
250, 914 |
26 |
00 |
2, 585, 973 |
258, 061 |
26 |
00 |
2, 562, 459 |
264, 889 |
|
27 00 |
2, 720, 554 |
262, 487 |
27 |
00 |
2, 707, 718 |
270, 521 |
27 |
00 |
2, 684, 042 |
278, 222 |
27 |
00 |
2, 659, 535 |
285, 677 |
|
28 00 |
2, 830, 374 |
282, 225 |
28 |
00 |
2. 806, 600 |
290, 859 |
28 |
00 |
2, 781, 953 |
299, 132 |
28 |
00 |
2, 756, 445 |
307, 035 |
|
29 00 |
2, 930, 052 |
302, 671 |
29 |
00 |
2, 905, 329 |
311,925 |
29 |
00 |
2, 879, 702 |
320, 788 |
29 |
00 |
2, 853, 181 |
329, 259 |
|
30 00 |
3, 029, 582 |
323, 825 |
30 |
00 |
3, 003, 900 |
333, 718 |
30 |
00 |
2, 977, 281 |
343, 197 |
30 |
00 |
2, 949, 739 |
352, 249 |
PEOJECTION TABLES.
169
Table XIX. — For projections of maps of large areas — Continued. [Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
COOHDINATES OF CUKVATDEE.
|
NATURAL SCALE.— VALUES OF X AND Y IN METERS. |
|||||||||||||
|
Latitude 28 |
Latitude 29°. |
Latitude 30°. |
Latitude 31°. |
||||||||||
|
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi. tude. |
X |
Y |
Longi- tude. |
X |
Y |
||
|
1 00 |
98, 363 |
403 |
1 00 |
97, 439 |
412 |
1 |
00 |
96, 487 |
421 |
1 |
00 |
95, 505 |
429 |
|
2 00 |
196, 719 |
1,612 |
2 00 |
194, 872 |
1,649 |
2 |
00 |
192, 967 |
1,684 |
2 |
00 |
191, 002 |
1,717 |
|
3 00 |
295, 062 |
3,627 |
3 00 |
292, 291 |
3,710 |
3 |
00 |
289, 433 |
3,789 |
3 |
00 |
286, 484 |
3,863 |
|
i 00 |
393, 385 |
6,447 |
4 00 |
389, 689 |
6,695 |
4 |
00 |
385, 875 |
6,735 |
4 |
00 |
381, 943 |
6,867 |
|
5 00 |
49], 682 |
10, 073 |
5 00 |
487, 059 |
10, 305 |
5 |
00 |
482. 288 |
10, 523 |
5 |
00 |
477, 371 |
10, 729 |
|
6 00 |
589, 945 |
14, 505 |
6 00 |
584, 394 |
14, 838 |
6 |
00 |
578, 665 |
15, 153 |
6 |
00 |
572, 760 |
15,450 |
|
7 00 |
688, 168 |
19, 741 |
7 00 |
681, 687 |
20, 194 |
7 |
00 |
674, 998 |
20, 623 |
7 |
00 |
668, 103 |
21, 027 |
|
8 00 |
786, 347 |
25, 782 |
8 00 |
778, 931 |
26, 374 |
8 |
00 |
771, 279 |
26, 934 |
8 |
00 |
763, 392 |
27,461 |
|
9 00 |
884, 472 |
32, 627 |
9 00 |
876, 120 |
33, 376 |
9 |
00 |
867, 602 |
34, 084 |
9 |
00 |
858, 619 |
34, 751 |
|
10 00 |
982, 537 |
40, 276 |
10 00 |
973, 246 |
41, 199 |
10 |
00 |
963, 658 |
43, 074 |
10 |
00 |
953,777 |
42, 897 |
|
11 00 |
1, 080, 637 |
48, 728 |
11 00 |
1, 070, 302 |
49, 845 |
11 |
00 |
1, 059, 741 |
50, 903 |
11 |
00 |
1, 048, 858 |
51, 898 |
|
12 00 |
1, 178, 464 |
67, 983 |
12 00 |
1, 167, 282 |
69, 313 |
12 |
00 |
1, 165, 744 |
60, 570 |
12 |
00 |
1, 143, 854 |
61, 753 |
|
13 00 |
1, 276, 312 |
68, 040 |
13 00 |
1, 264, 178 |
69, 601 |
13 |
00 |
1, 251, 668 |
71, 074 |
13 |
00 |
1, 238, 758 |
73, 462 |
|
14 00 |
1,374,075 |
78, 699 |
14 00 |
1, 360, 983 |
80.706 |
14 |
00 |
1, 347, 477 |
82,415 |
14 |
00 |
1, 333, 561 |
84, 024 |
|
15 00 |
1, 471, 745 |
90, 558 |
15 00 |
1,457,691 |
9% 631 |
15 |
00 |
1, 443, 193 |
94, 591 |
15 |
00 |
1, 428, 267 |
96, 437 |
|
16 00 |
1, 569, 315 |
103,017 |
16 00 |
1, 554, 296 |
105, 375 |
16 |
00 |
1, 638, 800 |
107, 603 |
16 |
00 |
1, 522, 837 |
109, 701 |
|
17 00 |
1, 666, 781 |
116, 276 |
17 00 |
1, 650, 787 |
118, 935 |
17 |
00 |
1, 634, 290 |
121, 449 |
17 |
00 |
1, 617, 294 |
133, 815 |
|
18 00 |
1, 764, 135 |
130, 331 |
18 00 |
1, 747, 161 |
133,311 |
18 |
00 |
1, 729, 654 |
136, 127 |
18 |
00 |
1, 711, 621 |
138, 777 |
|
19 00 |
1, 861, 371 |
145, 185 |
19 00 |
1, 843, 410 |
148, 502 |
19 |
00 |
1, 824, 887 |
151, 637 |
19 |
00 |
1,805,810 |
1.54, 586 |
|
20 00 |
1,958,481 |
160, 835 |
20 00 |
1, 939, 527 |
164, 506 |
20 |
00 |
1, 919, 983 |
167, 977 |
20 |
00 |
1,899,853 |
171, 241 |
|
21 00 |
2, 055, 460 |
177, 280 |
21 00 |
2,035,605 |
181, 324 |
21 |
00 |
2,014,930 |
185, 147 |
21 |
00 |
1,993,740 |
188, 741 |
|
22 00 |
2,152,302 |
194, 518 |
22 00 |
2, 131, 338 |
198, 953 |
22 |
00 |
2, 109, 725 |
203, 143 |
22 |
00 |
2, 087, 468 |
307, 086 |
|
23 00 |
2, 248, 998 |
212,550 |
33 00 |
2, 227, 020 |
217, 392 |
23 |
00 |
3, 204, 359 |
231, 966 |
23 |
00 |
3, 181, 027 |
336, 370 |
|
24 00 |
2, 345, 544 |
231, 374 |
24 00 |
2, 322, 539 |
236, 640 |
24 |
00 |
2, 298, 825 |
241, 616 |
24 |
00 |
3, 274, 411 |
246, 295 |
|
25 00 |
2,441,932 |
260, 988 |
25 00 |
2,417,893 |
256, 695 |
25 |
00 |
2, 393, 116 |
263, 089 |
25 |
00 |
2, 367, 610 |
267, 159 |
|
26 00 |
2, 538, 156 |
271, 391 |
26 00 |
2, 513, 074 |
277, 568 |
26 |
00 |
2, 487, 224 |
383, 383 |
26 |
00 |
2, 460, 618 |
288, 860 |
|
27 00 |
2, 634, 210 |
292, 582 |
27 00 |
2, 608, 075 |
299. 224 |
27 |
00 |
2,581,144 |
305, 498 |
27 |
00 |
2, 653, 427 |
311, 396 |
|
28 m |
2, 730, 087 |
314, 559 |
28 00 |
2, 702, 890 |
321, 694 |
28 |
00 |
3, 674, 867 |
328, 432 |
28 |
00 |
3, 646, 029 |
334, 765 |
|
29 00 |
2, 825, 779 |
337, 321 |
29 00 |
2, 797, 511 |
344, 964 |
29 |
00 |
2, 768, 385 |
353, 183 |
29 |
00 |
2,738,418 |
358,966 |
|
30 00 |
2, 921, 284 |
360, 866 |
30 00 |
2,891,931 |
369, 036 |
30 |
00 |
2, 861, 694 |
376, 749 |
30 |
00 |
2,830,585 |
383, 997 |
170
A MANUAL OF TOPOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas — Continued. [Extracteil from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]
COORDINATES OF CURVATURE.
|
N-ATXJEAL SCALE.— VALUES OE X AND Y IN "METEES. |
||||||||||||||
|
Latitude 32°. |
Latitude 33°. |
Latitude 34°. |
Latitude 35°. |
|||||||||||
|
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
|||
|
1 00 |
94, 494 |
437 |
1 |
00 |
93, 454 |
444 |
1 |
00 |
92, 385 |
451 |
1 |
00 |
91, 289 |
457 |
|
2 00 |
188, 980 |
1,748 |
2 |
00 |
186, 899 |
1,777 |
2 |
00 |
184, 762 |
1,803 |
2 |
00 |
182, 568 |
1, 828 |
|
3 00 |
283, 449 |
3,933 |
3 |
00 |
280, 328 |
3, 997 |
3 |
00 |
277, 121 |
4,057 |
3 |
00 |
273, 830 |
4,112 |
|
4. 00 |
377, 894 |
6,991 |
4 |
00 |
373, 731 |
7,106 |
4 |
00 |
369, 454 |
7,212 |
4 |
00 |
365, 064 |
7,310 |
|
5 00 |
472, 307 |
10, 922 |
5 |
00 |
467, 100 |
11, 102 |
5 |
00 |
461,751 |
11,268 |
5 |
00 |
456,261 |
11, 421 |
|
6 00 |
566. 680 |
15, 727 |
6 |
00 |
560, 428 |
15, 986 |
6 |
00 |
554, 004 |
16, 225 |
6 |
00 |
547, 412 |
16,445 |
|
7 00 |
661, 004 |
21, 404 |
7 |
00 |
653,704 |
21,757 |
7 |
00 |
646, 205 |
22, 082 |
7 |
00 |
638, 509 |
22, 381 |
|
8 00 |
755, 272 |
27,954 |
8 |
00 |
746, 922 |
28, 414 |
8 |
00 |
738, 344 |
28, 839 |
8 |
00 |
729, 542 |
29,229 |
|
9 00 |
849,475 |
35, 375 |
9 |
00 |
840, 072 |
35, 957 |
9 |
00 |
830, 413 |
36, 494 |
9 |
00 |
820, 501 |
36, 987 |
|
10 00 |
943, 605 |
43, 667 |
10 |
00 |
1,933,146 |
44,385 |
10 |
00 |
922,403 |
45, 048 |
10 |
00 |
911, 379 |
45, 656 |
|
11 00- |
1, 037, 655 |
52, 829 |
U |
00 |
1, 026, 136 |
53, 697 |
11 |
00 |
1, 014, 305 |
54, 499 |
11 |
00 |
1, 002, 165 |
55, 234 |
|
.12 00 |
1,131,616 |
62, 861 |
12 |
00 |
1.119,033 |
63, 893 |
12 |
00 |
1, 106, 110 |
64, 846 |
12 |
00 |
1, 092, 850 |
65, 721 |
|
13 00 |
1, 225, 480 |
73, 761 |
13 |
00 |
1, 211. 829 |
74, 971 |
13 |
00 |
1, 197, 809 |
76, 089 |
13 |
00 |
1, 183, 426 |
77, 115 |
|
14 00 |
1,319,239 |
85, 529 |
14 |
00 |
1, 304, 515 |
86, 931 |
14 |
00 |
1, 289, 395 |
88,227 |
14 |
00 |
1,273,834 |
89, 415 |
|
15 00 |
1,412,885 |
98, 164 |
15 |
00 |
1,397,083 |
99, 771 |
15 |
00 |
1, 380, 858 |
101,258 |
15 |
00 |
1, 364, 214 |
102, 619 |
|
16 00 |
1,506,411 |
111, 664 |
: 16 |
00 |
1,489,526 |
113,491 |
16 |
00 |
1, 472. 190 |
115, 180 |
16 |
00 |
1,454,407 |
116, 728 |
|
17 00 |
1, 599, 808 |
126, 029 |
1 17 |
00 |
1, 581, 834 |
128, 089 |
17 |
00 |
1, 563, 381 |
129, 993 |
17 |
00 |
1, 544, 454 |
131, 738 |
|
18 00 |
1,693,067 |
141, 256 |
18 |
00 |
1, 673, 998 |
143, 564 |
18 |
00 |
1, 654, 423 |
145, 696 |
18 |
00 |
1,634,347 |
147, 650 |
|
19 00 |
1, 786, 182 |
157, 346 |
19 |
00 |
1,766,011 |
159, 914 |
19 |
00 |
1,745,308 |
162, 287 |
19 |
00 |
1,724,076 |
164,460 |
|
20 00 |
1, 879, 144 |
174, 296 |
20 |
00 |
1,857,866 |
177, 138 |
20 |
00 |
1, 836, 026 |
179,703 |
20 |
00 |
1, 813, 632 |
182, 168 |
|
21 00 |
1,971,946 |
192, 105 |
21 |
00 |
1,949,553 |
195, 234 |
21 |
00 |
1, 926, 569 |
198, 124 |
21 |
00 |
1,903,006 |
200, 772 |
|
22 00 |
2, 064, 579 |
210, 772 |
22 |
00 |
2,041,062 |
214, 201 |
! 22 |
00 |
2, 016, 929 |
217, 368 |
22 |
00 |
1, 992, 190 |
220, 268 |
|
23 00 |
2, 157. 035 |
230,295- |
23 |
00 |
2, 132, 387 1 234, 037 |
23 |
00 |
2, 107, 097 |
237, 493 |
23 |
00 |
2, 081, 174 |
240, 657 |
|
|
24 00 |
2, 249, 305 |
250. 672 |
24 |
00 |
2,223,521 254,740 |
24 |
00 |
2, 197, 065 |
258, 497 |
24 |
00 |
2, 169, 949 |
261, 936 |
|
|
25 00 |
2, 341, 385 |
271,901 |
25 |
00 |
2, 314, 453 |
276, 309 |
!25 |
00 |
2, 286 823 |
280, 378 |
25 |
00 |
2, 258, 507 |
284, 102 |
|
26 00 |
2,433,264 |
293, 981 |
26 |
00 |
2,405,175 |
298, 741 |
26 |
00 |
2, 376, 363 |
303, 134 |
26 |
00 |
2. 346, 838 |
307, 154 |
|
27 00 |
2,524,935 |
316, 910 |
00 |
2. 495, 080 |
322, 034 |
27 |
00 |
2, 465, 677 |
326, 763 |
27 |
00 |
2,434,934 |
331, 089 |
|
|
28 00 |
2, 616, 390 |
340, 686 |
28 |
00 |
2, 585, 961 |
346. 187 |
28 |
00 |
2, 554, 756 |
351, 262 |
28 |
00 |
2, 522, 787 |
355, 905 |
|
29 00 |
2, 707, 621 |
. 365, 307 |
29 |
00 |
2, 676, 007 |
371, 197 |
29 |
00 |
2, 643, 591 |
376, 629 |
29 |
00 |
2,610,386 |
381, 598 |
|
30 00 |
2, 798, 621 |
390, 770 |
30 |
00 |
2, 765, 812 |
397,061 |
30 |
00 |
2, 732, 175 |
402, 863 |
30 |
00 |
2, 697, 724 |
408, 168 |
PEOJECTION TABLES.
171
Table XIX. — For projections of maps of large areas — Continued. [Extracted from Appendix No. 6, TJ. S. Coast and Geodetic Survey Eeport for 1884.]
COORDINATES OP CUEVATUEE.
|
NATUKAL SCALE |
.—VALUES OF X AND T METEPS. |
|||||||||||||
|
Latitude 36 |
". |
Latitude 37°. |
Latitude 38=. |
Latitude 39°. ■ |
||||||||||
|
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
|||
|
1 00 |
90, 164 |
462 |
1 |
00 |
89,012 |
467 |
1 |
00 |
87, 833 |
472 |
° 1 |
00 |
86, 627 |
476 |
|
2 00 |
180, 319 |
1,850 |
2 |
00 |
178, 015 |
1,870 |
2 |
00 |
175, 656 |
1,888 |
2 |
00 |
173, 243 |
1,903 |
|
3 00 |
270,455 |
4,162 |
3 |
00 |
266, 997 |
4,207 |
3 |
00 |
263, 458 |
4,247 |
3 |
00 |
259, 839 |
4,281 |
|
4, OO |
360, 562 |
7,399 |
4 |
00 |
355, 951 |
7,479 |
4 |
00 |
351, 230 |
7,549 |
4 |
00 |
346, 403 |
7,611 |
|
5 00 |
450, 631 |
11, 560 |
5 |
00 |
444,865 |
11,685 |
5 |
00 |
438, 962 |
11, 795 |
5 |
00 |
432, 925 |
11, 891 |
|
6 00 |
540, 653 |
16, 645 |
6 |
00 |
533, 730 |
16,824 |
6 |
00 |
526, 643 |
16, 983 |
6 |
00 |
519, 396 |
- 17, 121 |
|
7 00 |
630, 618 |
22, 652 |
7 |
00 |
622, 536 |
22, 896 |
7 |
00 |
614, 263 |
23, 112 |
7 |
00 |
605, 803 |
23, 300 |
|
8 00 |
720,517 |
29,583 |
8 |
00 |
711, 273 |
29, 901 |
8 |
00 |
701, 812 |
30, 183 |
8 |
00 |
692. 138 |
30,428 |
|
9 00 |
810,340 |
37,435 |
9 |
00 |
799,932 |
37,838 |
9 |
00 |
789, 280 |
38, 195 |
9 |
00 |
778, 388 |
38, 504 |
|
10 00 |
900. 078 |
46, 209 |
10 |
00 |
888, 503 |
46, 706 |
10 |
00 |
876, 657 |
47, 145 |
10 |
00 |
864,545 |
47, 527 |
|
11 00 |
989, 720 |
55,903 |
11 |
00 |
976, 975 |
56, 503 |
11 |
00 |
963, 933 |
57, 034 |
11 |
00 |
950, 598 |
57, 496 |
|
13 00 |
1, 079, 259 |
66, 515 |
12 |
00 |
1, 065, 34Q |
67, 229 |
12 |
00 |
1, 051, 098 |
67, 860 |
12 |
00 |
1, 036, 536 |
68, 409 |
|
13 00 |
1, 168, 684 |
78, 046 |
13 |
00 |
1, 153, 587 |
78, 882 |
13 |
00 |
1, 138. 141 |
79, 622 |
13 |
00 |
1, 122, 349 |
80, 266 |
|
U 00 |
1, 257, 987 |
90, 494 |
14 |
00 |
1, 241, 707 |
91, 462 |
14 |
00 |
1.225,053 |
92,319 |
14 |
00 |
1, 208, 027 |
93, 064 |
|
15 00 |
1, 347, 156 |
103, 856 |
15 |
00 |
1, 329, 690 |
104, 967 |
15 |
00 |
1, 311, 823 |
105, 949 |
15 |
00 |
1, 293, 559 |
106,802 1 |
|
16 00 |
1, 436, 184 |
118, 133 |
16 |
00 |
1, 417, 526 |
119, 395 |
16 |
00 |
1, 398, 441 |
120, 511 |
16 |
00 |
1. 378, 934 |
121, 479 1 |
|
17 00 |
1, 525, 061 |
133, 323 |
17 |
00 |
1, 505, 206 |
134,745 |
17 |
00 |
1,484,899 |
136, 002 |
17 |
00 |
1, 464, 144 |
137,093 ' |
|
18 00 |
1, 613, 777 |
149, 423 |
18 |
00 |
1,592,721 |
151, 015 |
18 |
00 |
1, 571, 183 |
152, 421 |
18 |
00 |
1, 549, 177 |
153,642 |
|
19 00 |
1, 702, 324 |
166, 433 |
19 |
00 |
1, 680, 059 |
168, 203 |
19 |
00 |
1, 657, 289 |
169, 767 |
19 |
00 |
1, 634, 023 |
171,124 |
|
20 00 |
1,790,691 |
184, 3.50 |
20 |
00 |
1, 767, 211 |
186, 307 |
20 |
00 |
1, 743, 202 |
188, 037 |
20 |
00 |
1, 718, 671 |
189,537 |
|
21 00 |
1, 878, 870 |
203, 173 |
21' |
00 |
1, 854, 169 |
205, 326 |
21 |
00 |
1, 828. 914 |
207, 229 |
21 |
00 |
1, 803, 113 |
208,878 |
|
22 00 |
1, 966, 851 |
222, 899 |
22 |
00 |
1, 940, 922 |
225, 258 |
22 |
00 |
1, 914, 415 |
227, 341 |
22 |
00 |
1, 887, 337 |
229, 146 |
|
23 00 |
2, 054, 625 |
243,527 |
23 |
00 |
2,027,462 |
246, 099 |
23 |
00 |
1, 999, 694 |
248,370 |
23 |
00 |
1, 971, 333 |
250,337 |
|
24 00 |
2, 142, 183 |
265, 055 |
24 |
00 |
2, 113, 777 |
267, 849 |
24 |
00 |
2, 084, 743 |
270, 315 |
24 |
00 |
2, 055, 091 |
272, 450 |
|
25 00 |
2, 229, 516 |
287, 479 |
25 |
00 |
2, 199, 860 |
290, 503 |
25 |
00 |
2,169,551 |
293, 172 |
25 |
00 |
2, 138, 602 |
295, 481 |
|
26 00 |
2, 316, 613 |
310, 798 |
26 |
00 |
2, 285, 699 |
314, 061 |
26 |
00 |
2, 254, 109 |
316, 939 |
26 |
00 |
2,221,854 |
319. 429 |
|
27 00 |
2.403,467 |
335, 009 |
27 |
00 |
2, 371, 287 |
338, 519 |
27 |
00 |
2, 338, 406 |
341, 613 |
27 |
00 |
2, 304, 838 |
344, 289 |
|
28 00 |
2,490,068 |
360. Ill |
26 |
00 |
2, 456. 6l2 |
363, 874 |
28 |
00 |
2, 422, 433 |
367, 192 |
28 |
00 |
2, 387, 545 |
370, 059 |
|
29 00 |
2, 576, 407 |
386, 099 |
29 |
00 |
2, 541, 667 |
390, 125 |
29 |
00 |
2, 506, 181 |
393, 672 |
29 |
00 |
2, 469, 963 |
396, 736 |
|
30 00 |
2, 662, 475 |
412, 971 |
30 |
00 |
2, 626, 441 |
417, 267 |
30 |
00 |
2, 589, 639 |
421, 050 |
30 |
00 |
2, 552, 084 |
424, 317 |
172
A MANUAL OF TOPOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas — Continued. [Extracted from Appendix No. 6. V. S. Coast and Geodetic Survey Report for 1884.]
COOEDINATES OP CnEVATUEE.
|
NATURAL SCALE.- |
VALUES OF X AND T IN METERS, |
|||||||||||||
|
Latitude 40 |
". |
Latitude 41°. |
Latitude 42°. |
Latitude 43 |
"■ |
|||||||||
|
Longi- tude. |
X |
T |
Longi- tude. |
s |
T |
Longi- tude. |
X |
T |
Longi- tude. |
X |
Y |
|||
|
1 00 |
85, 394 |
479 |
1 |
00 |
84, 136 |
482 |
1 |
00 |
82, 851 |
484 |
1 |
00 |
81, 541 |
485 |
|
2 00 |
170, 778 |
1,916 |
2 |
00 |
168, 260 |
1,927 |
2 |
00 |
165, 691 |
1,935 |
2 |
00 |
163, 071 |
1,941 |
|
3 00 |
256, 140 |
4,311 |
3 |
00 |
252, 363 |
4,335 |
3 |
00 |
248, 508 |
4,354 |
3 |
00 |
244, 578 |
4,367 |
|
4 00 |
, 341,470 |
7,663 |
4 |
00 |
336, 432 |
7,706 |
4 |
00 |
331, 292 |
7,739 |
4 |
00 |
326, 050 |
7,763 |
|
5 00 |
426, 757 |
11, 972 |
5 |
00 |
420,457 |
12, 039 |
5 |
00 |
414, 030 |
12, 092 |
5 |
00 |
407, 476 |
12, 129 |
|
6 00 |
511, 990 |
17, 238 |
6 |
00 |
504, 428 |
17, 335 |
6 |
00 |
496, 712 |
17,410 |
6 |
00 |
488, 844 |
17, 464 |
|
7 00 |
597, 158 |
23,400 |
7 |
00 |
588, 332 |
23, 591 |
7 |
00 |
679, 325 |
23, 693 |
7 |
00 |
570, 143 |
23,766 |
|
8 00 |
682, 252 |
30, 637 |
8 |
00 |
672, 159 |
30, 807 |
8 |
00 |
661, 861 |
30,941 |
8 |
00 |
651, 361 |
31, 036 |
|
9 00 |
767,260 |
38, 768 |
9 |
00 |
755,897 |
38, 983 |
9 |
00 |
744, 305 |
39, 152 |
9 |
00 |
732, 486 |
39, 272 |
|
10 00 |
852, 171 |
47, 852 |
10 |
00 |
- 839,537 |
48, 118 |
10 |
00 |
826, 648 |
48, 325 |
10 |
00 |
813, 508 |
48. 474 |
|
11 00 |
936, 975 |
57, 888 |
11 |
00 |
923, 067 |
58, 209 |
11 |
00 |
908. 879 |
58,459 |
11 |
00 |
894, 415 |
58, 639 |
|
12 00 |
1,021,661 |
68, 875 |
12 |
00 |
1,006,475 |
69, 256 |
12 |
00 |
.990,985 |
69, 553 |
12 |
00 |
975, 195 |
69, 766 |
|
13 00 |
1, 106, 218 |
80,611 |
13 |
00 |
1, 089, 752 |
81, 258 |
13 |
00 |
1, 072, 956 |
81, 605 |
13 |
00 |
1, 055, 837 |
81,854 |
|
14 00 |
1,190,636 |
93, 695 |
14 |
00 |
1, 172, 886 |
94, 212 |
14 |
00 |
1, 154, 781 |
94, 614 |
14 |
00 |
1, 136, 329 |
94,901 |
|
15 00 |
1, 274, 904 |
107, 525 |
15 |
00 |
1,255,866 |
108, 117 |
15 |
00 |
1,236,449 |
108, 577 |
15 |
00 |
1, 216, 661 |
108, 905 |
|
16 00 |
1, 359. 012 |
122, 300 |
16 |
00 |
1,338,681 |
122, 971 |
16 |
00 |
1, 317, 948 |
123,493 |
16 |
00 |
1, 296, 820 |
123, 864 |
|
17 00 |
1, 442, 949 |
138, 017 |
17 |
00 |
1, 421, 321 |
138, 773 |
17 |
00 |
1, 899, 267 |
139, 360 |
17 |
00 |
1, 376, 795 |
139, 777 |
|
18 00 |
1, 526, 704 |
154, 675 |
18 |
00 |
1, 503, 775 |
155, 520 |
18 |
00 |
1, 480, 395 |
156, 175 |
18 |
00 |
1, 456, 575 |
156, 640 |
|
19 00 |
1, 610, 267 |
172, 272 |
19 |
00 |
1, 586, 031 |
173, 210 |
19 |
00 |
1, 561, 321 |
173, 937 |
19 |
00 |
1, 536, 148 |
174,451 |
|
20 00 |
1, 693. 623 |
190, 805 |
20 |
00 |
1, 608, 079 |
191. 841 |
20 |
00 |
1, 642, 035 |
192, 642 |
20 |
00 |
1, 615, 505 |
193, 209 |
|
21 00 |
1, 776, 775 |
210, 272 |
21 |
00 |
1, 749. 909 |
211, 409 |
21 |
00 |
1, 722, 524 |
212, 289 |
21 |
00 |
1, 694, 632 |
212, 909 |
|
22 00 |
1. 8S0, 698 |
230, 671 |
2'^ |
00 |
1,831,509 |
231, 914 |
22 |
00 |
1,802,779 |
232. 874 |
22 |
00 |
1, 773, 519 |
233, 551 |
|
23 00 |
1, 942, 387 |
251,998 |
23 |
00 |
1, 912, 869 |
253, 352 |
23 |
00 |
1, 882, 788 |
254, 396 |
23 |
00 |
1, 852, 135 |
255,129 |
|
24 00 |
2, 024, 833 |
274, 252 |
24 |
00 |
1, 993, 978 |
275, 719 |
24 |
00 |
1, 962, 540 |
276, 850 |
24 |
00 |
1, 930, 528 |
277, 642 |
|
23 00 |
2, 107, 023 |
297. 430 |
25 |
00 |
2, 074, 826 |
299, 014 |
25 |
00 |
2, 042, 024 |
300, 234 |
25 |
00 |
2, 008, 628 |
301, 087 |
|
26 00 |
2. 188, 948 |
321, 528 |
26 |
00 |
2,1.55,402 |
323, 233 |
26 |
00 |
2,121 230 |
324, 544 |
26 |
00 |
2, 086, 443 |
325, 459 |
|
27 00 |
2, 270, 597 |
346, 543 |
27 |
00 |
2, 235, 695 |
348, 374 |
27 |
00 |
2, 200, 146 |
349, 778 |
27 |
00 |
2, 163, 963 |
350, 750 |
|
28 00 |
2, 351, 961 |
372, 473 |
28 |
00 |
2, 315, 695 |
374, 432 |
28 |
00 |
2, 278, 762 |
375, 932 |
28 |
00 |
2, 241, 176 |
376, 974 |
|
29 00 |
2,433,029 |
399, 314 |
29 |
00 |
2, 395, 392 |
401, 404 |
29 |
00 |
2, 357, 067 |
403, 002 |
29 |
00 |
2, 318, 071 |
404, 109 |
|
30 00 |
2,513,790 |
427, 063 |
30 |
00 |
2,474,774 |
429, 287 |
30 |
00 |
2, 435, 052 |
430, 985 |
30 |
00 |
2, 394, 639 |
432, 157 |
PEOJBCTION TABLES.
173
Table XIX.- — For projections of maps of large areas — Continued. [Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Eeport for 1884.]
COORDINATES OP CURVATURE.
|
NATURAL SCALE.- |
-VALUES OF X AND Y TS METERS. |
|||||||||||||
|
Latitude 44°. |
Latitude 45°. |
L.atitude 46°. |
Latitude 47°. 1 |
|||||||||||
|
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Longi- tude. |
X |
Y |
Lo tu 1 |
agi- de. |
X |
Y |
||
|
1 00 |
80, 206 |
486 |
1 |
00 |
78, 847 |
486 |
1 |
00 |
77,464 |
486 |
00 |
76, 056 |
485 |
|
|
2 00 |
160, 401 |
1,945 |
2 |
00 |
157, 682 |
1,946 |
2 |
00 |
154,915 |
1,945 |
2 |
00 |
152, 100 |
1,942 |
|
3 00 |
240, 572 |
4,375 |
3 |
00 |
236, 493 |
4,378 |
3 |
00 |
232, 342 |
4,376 |
3 |
00 |
228, 119 |
4,368 |
|
4 00 |
320, 708 |
7,778 |
4 |
00 |
315, 269 |
7,783 |
4 |
00 |
309, 732 |
7,779 |
4 |
00 |
304, 101 |
7,765 |
|
5 00 |
400, 797 |
12, 152 |
5 |
00 |
393, 996 |
12, 160 |
5 |
00 |
387, 074 |
12, 153 |
5 |
00 |
380, 034 |
13,131 |
|
6 00 |
480, 82' |
17,496 |
6 |
00 |
472, 663 |
17, 508 |
6 |
00 |
464, 354 |
17, 498 |
6 |
00 |
455, 904 |
17, 467 |
|
7 00 |
560, 786 |
23, 811 |
7 |
00 |
551, 258 |
23, 826 |
7 |
00 |
541, 562 |
23,813 |
7 |
00 |
531, 700 |
23, 770 |
|
8 00 |
640, 062 |
31,094 |
8 |
00 |
629, 769 |
31, 114 |
8 |
00 |
618,684 |
31, 096 |
8 |
00 |
607, 410 |
31, 040 |
|
9 00 |
720,445 |
39, 345 |
9 |
00 |
708, 184 |
39, 370 |
9 |
00 |
695, 708 |
39, 347 |
9 |
00 |
683, 020 |
39, 276 |
|
10 00 |
800, 122 |
48, 563 |
10 |
00 |
786,492 |
48, 594 |
10 |
00 |
772, 623 |
48,565 |
10 |
00 |
758, 520 |
48,477 |
|
11 00 |
879, 681 |
58, 746 |
11 |
00 |
864, 679 |
58, 782 |
11 |
00 |
849, 416 |
58, 747 |
11 |
00 |
833, 895 |
58, 640 |
|
12 00 |
959, 110 |
69, 893 |
12 |
00 |
942, 735 |
69, 936 |
12 |
00 |
926, 075 |
69, 893 |
12 |
00 |
909, 135 |
69, 765 |
|
13 OO |
1, 038, 399 |
82, 002 |
13 |
00 |
1, 020, 647 |
82, 051 |
13 |
00 |
1,002,588 |
82, 000 |
13 |
00 |
984, 227 |
81, 849 |
|
14 00 |
1, 117, 535 |
95, 072 |
14 |
00 |
1,098,404 |
95, 127 |
14 |
00 |
1, 078, 943 |
95, 067 |
14 |
00 |
1,059,158 |
94, 890 |
|
15 00 |
1, 196, 507 |
109,100 |
15 |
00 |
1, 175, 994 |
109, 162 |
15 |
00 |
1, 155, 128 |
109, 091 |
15 |
00 |
1, 133, 917 |
108, 887 |
|
16 00 |
1, 275, 303 |
124, 084 |
16 |
00 |
1, 253, 404 |
124, 153 |
16 |
00 |
1, 231, 131 |
124, 071 |
16 |
00 |
1, 208, 491 |
123,837 |
|
17 00 |
1, 353, 911 |
140, 023 |
17 |
00 |
1,330,634 |
140, 099 |
17 |
00 |
1,306,940 |
140, 003 |
17 |
00 |
1, 282, 868 |
139, 738 |
|
18 00 |
1, 432, 320 |
156,913 |
18 |
00 |
1,407,640 |
156, 996 |
18 |
00 |
1, 382, 543 |
156, 887 |
18 |
00 |
1, 357, 036 |
156, 587 |
|
19 00 |
1, 510, 519 |
174, 753 |
19 |
00 |
1, 434, 443 |
174, 842 |
19 |
00 |
1,457,928 |
174, 718 |
19 |
00 |
1, 430, 984 |
174, 381 |
|
20 00 |
1, 588, 496 |
193, 540 |
20 |
00 |
1, 561, 019 |
193, 635 |
20 |
00 |
1,533,083 |
193, 494 |
20 |
00 |
1, 504, 697 |
193, 118 |
|
21 00 |
1, 666, 240 |
213,270 |
21 |
00 |
1, 637, 358 |
213, .371 |
21 |
00 |
1, 607, 997 |
213, 212 |
21 |
00 |
1, 578, 166 |
212, 793 |
|
22 00 |
1, 743, 738 |
233, 942 |
22 |
00 |
1, 713, 447 |
234, 048 |
22 |
00 |
1.682,657 |
233, 869 |
22 |
00 |
1, 651, 377 |
233, 405 |
|
23 00 |
1,820,980 |
255, 552 |
23 |
00 |
1, 789, 276 |
255, 663 |
23 |
00 |
1, 757, 052 |
255, 462 |
23 |
00 |
1, 724, 320 |
254, 950 |
|
24 00 |
1, 897, 955 |
278, 096 |
24 |
00 |
1, 864, 831 |
278, 211 |
24 |
00 |
1, 831, 170 |
277, 987 |
24 |
00 |
1, 796, 982 |
277, 425 |
|
25 00 |
1, 974, 650 |
301, 572 |
25 |
00 |
1, 940, 103 |
301, 690 |
25 |
•00 |
1, 904, 999 |
301, 441 |
25 |
00 |
1, 869, 3.51 |
300, 824 |
|
26 00 |
2, 051, 055 |
325, 977 |
26 |
00 |
2, 015, 079 |
326, 097 |
26 |
00 |
1, 978, 528 |
325, 820 |
26 |
00 |
1,941,415 |
325, 146 |
|
27 00 |
2, 127, 159 |
351, 306 |
27 |
00 |
2, 089, 749 |
351, 427 |
27 |
00 |
2, 051, 745 |
351, 120 |
27 |
OO |
2, 013, 163 |
350, 386 |
|
28 00 |
2, 202, 950 |
377, 555 |
28 |
00 |
2, 164, 100 |
377, 676 |
28 |
00 |
2, 124, 639 |
377, 337 |
38 |
00 |
2, 084, 583 |
376, 539 |
|
29 00 |
2, 278, 417 |
404, 722 |
29 |
00 |
2, 238, 121 |
404, 841 |
29 |
00 |
2, 197, 197 |
404, 468 |
29 |
00 |
2, 155, 663 |
403, 602 |
|
30 00 |
2, 353, 550 |
432, 801 |
30 |
00 |
2, 311, 802 |
432, 918 |
30 |
00 |
2, 269, 410 |
432, 507 |
30 |
00 |
2,226,392 |
431, 569 |
174
A MAXUAL OF TOrOGEAPHIC METHODS.
Table XIX. — For projections of maps of large areas-^Continned.
[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Keport for 1884.]
COORDINATES OF CnEVATUEK.
|
NATURAL SCALE.- VALUES OF X AND T IN METERS. |
||||||||||
|
Latitude 48°. |
Latitude 49°. |
Latitude 50°. |
||||||||
|
Longi- tude. |
x |
y |
Longi- tude. |
X |
Y ' |
Longi- tude. |
X |
Y |
||
|
1 00 |
74, 626 |
484 |
1 |
00 |
73, 172 |
482 |
1 |
00 |
71, 696 |
479 |
|
2 00 |
149. 239 |
1,936 |
2 |
00 |
146, 331 |
1,928 |
2 |
00 |
143, 379 |
1,917 |
|
3 00 |
223, 827 |
4,355 |
3 |
00 |
219, 465 |
4,337 |
3 |
00 |
215, 037 |
4.313 |
|
4 00 |
298, 377 |
7.742 |
4 |
00 |
292,561 |
7,709 |
4 |
00 |
286, 656 |
7,667 |
|
5 00 |
372,877 |
12, 095 |
5 |
00 |
365, 606 |
12,044 |
5 |
00 |
358, 224 |
11, 978 |
|
6 00 |
447, 314 |
17,414 |
6 |
00 |
438, 588 |
17. 340 |
6 |
00 |
429, 727 |
17,246 |
|
7 GO |
521, 677 |
23, 698 |
7 |
00 |
511,493 |
23, 598 |
7 |
00 |
501, 154 |
23, 469 |
|
8 00 |
595, 951 |
30, 946 |
8 |
00 |
584, 310 |
30, 815 |
8 |
00 |
572, 492 |
30,646 |
|
9 00 |
670, 125 |
39, 157 |
9 |
00 |
657, 026 |
38, 991 |
9 |
00 |
643, 727 |
38, 777 |
|
10 00 |
744, 186 |
48, 329 |
10 |
00 |
729, 627 |
48, 123 |
10 |
00 |
714, 847 |
47, 859 |
|
11 OD |
. 818, 123 |
58, 461 |
11 |
00 |
802, 102 |
58, 212 |
11 |
00 |
785, 839 |
57, 891 |
|
12 00 |
891, 921 |
69, 552 |
12 |
00 |
874, 438 |
69, 254 |
12 |
00 |
856, 691 |
68,872 |
|
13 00 |
965, 570 |
81. 598 |
13 |
00 |
946, 622 |
81, 248 |
13 |
00 |
927, 389 |
80, 798 |
|
14 00 |
1,039,056 |
94, 598 |
14 |
00 |
1,018,642 |
94, 191 |
14 |
00 |
997, 922 |
93, 669 |
|
15 00 |
1,112,367 |
108, 551 |
15 |
00 |
1, 090, 485 |
108, 082 |
15 |
00 |
1, 068, 277 ■ |
107, 482 |
|
16 00 |
1, 185, 491 |
123, 453 |
16 |
00 |
1, 162, 138 |
122, 918 |
16 |
00 |
1, 138, 440 |
122, 234 |
|
17 00 |
1,258,416 |
139, 302 |
17 |
00 |
1, 233, 591 |
138, 697 |
17 |
00 |
1,208,400 |
137, 923 |
|
18 00 |
1, 331, 129 |
156, 096 |
18 |
00 |
1, 304, 829 |
155, 416 |
18 |
00 |
1, 278, 144 |
154, 546 |
|
19 00 |
1, 403, 618 |
173, 832 |
19 |
00 |
1,375,840 |
173, 071 |
19 |
00 |
1, 347, 660 |
172, 099 |
|
20 00 |
1, 475, 871 |
192, 506 |
20 |
00 |
1, 446, 613 |
191, 660 |
20 |
00 |
1, 416, 934 |
190, 581 |
|
21 00 |
1, 547, 876 |
212, 116 |
21 |
00 |
1, 517, 135 |
211, 180 |
21 |
00 |
1, 485, 956 |
209, 987 |
|
22 00 |
1, 619, 620 |
232, 658 |
22 |
00 |
1, 587, 394 |
231, 627 |
22 |
00 |
1, 554, 711 |
230, 314 |
|
23 00 |
1, 691, 091 |
254, 128 |
23 |
00 |
1, 657, 378 |
252,998 |
23 |
00 |
1, 623, 189 |
251, 559 |
|
24 00 |
1, 762, 279 |
276, 524 |
24 |
00 |
1,727,073 |
275, 288 |
24 |
00 |
1, 691, 377 |
273, 717 |
|
25 00 |
1,833,170 |
299, 842 |
25 |
00 |
1, 796, 470 |
298, 495 |
25 |
00 |
1,759,262 |
296, 785 |
|
26 00 |
1,903,752 |
324, 077 |
26 |
00 |
1, 865, 554 |
322, 614 |
26 |
00 |
1, 826, 833 |
320, 758 |
|
27 00 |
1, 974. 015 |
349, 225 |
27 |
00 |
1, 934, 315 |
347, 640 |
27 |
00 |
1,894,077 |
345, 633 |
|
28 00 |
2, 043, 945 |
375, 283 |
28 |
00 |
2, 002, 740 |
373, 570 |
28 |
00 |
1, 960, 983 |
371,404 |
|
29 00 |
2, 113, 531 |
402, 245 |
29 |
00 |
2, 070, 817 |
400, 399 |
29 |
00 |
2, 027, 538 |
398, 068 |
|
30 00 |
2, 182, 762 |
430, 107 |
30 |
00 |
2, 138, 536 |
428, 123 |
30 |
00 |
2, 093, 731 |
425, 619 |
PROJECTION TABLES.
175
Table XX. — Cooi-dinates for projection of maps. Scale ^j-ooos- [Prepared by R. S. Woodward.]
a "
Coordinates of developed parallel for —
Inches.
'"4.36i' 8. 723 13. 083
17. 444 4.362 8. 723
13. 085
4.362 ■ 8. 724 13. 087
4.363 8.726 13. 088
13. 091 17.454 4.364 8.728 13. 092
4. 365 8.730 13. 095
4.367 8.734 13.101
4.368 8.735 13. 103
3.750 3.740 3.730
3.679 3.669
3.583 3.572 3.561
.004 .004
longitude. 45' longitude. 1° longitude,
.004 .004 .004
.004 .004
7.949 7.933 7.916 7.900
7.798 7.780 7.763
7.727 7.709 7.691
7.673 7.654
7.578 7.559 7.540
7.520 7.500
7.420 7.400 7.379
7.253 7.231 7.210
7.166 7.144 7.122
.017 .017 .017
.018 .018
.018 .018 .018
Inches. 11.923 11.899 11. 874 11.850
11. 825
11. 697 11.671 11.644
11. 591 11. 563 11. 536
11.481 11. 453 11.425
11. 367 11. 338 11. 309
11.250 11. 221 11. 191
11. 130 11. 100 11.069
11. 007 10. 975 10. 943
10. 879 10. 847 10. 815
10. 749 10. 716 10. 683
.040 .040
Inches. 15. 898 15. 865 15. 832 15. 800
15.707 15. 733 15. 699 15. 665
15. 596 15. 561 15. 526
15. 454 15.418 15. 382
15. 156 15. 118 15. 079
15. 001 14. 961 14. 921
14. 840 14. 799 14. 758
14. 676 14. 633 14. 591
14. 506 14. 463 14. 420
14. 332 14. 288 14.244
4.369 8.738 13. 108
3.539 3.527 3.516
7.077 7.054 7.032
6.986 6.963 6.939
10. 616 10. 582 10. 547
10. 479 10.444 10. 409
.041 .041 .041
.041
14. 154 14. 109 14. 063
13. 972 13. 925 13. 879
176
A MANUAL OF TOPOGEAPHIC METHODS.
Table XS. — Coordiiiates for projection of maps. Scale ■ [Prepared by E. S. Woodward.]
|
ft |
Coordinates of developed parallel for— |
||||||||
|
1 |
15' longitude. |
30' longitude. |
45' longitude. |
lo longitude. |
|||||
|
X |
y |
s |
y |
- |
y |
X |
y |
||
|
38 00 15 30 45 |
Inches. 17. 477 |
Inches. 3.458 3.446 3.434 3.422 |
Inches. .005 .005 .005 .005 |
iTiches. 6.916 6.892 6.809 6.845 |
Inches. .019 .019 .019 .019 |
Inches. 10. 374 10. 339 10. 303 10.267 |
Inches. .042 .042 .042 .042 |
Inches. 13. 832 13.785 13. 737 13. 690 |
Inches. .074 .074 .075 .075 |
|
4.370 8.740 13. 110 |
|||||||||
|
39 00 15 30 45 |
17. 480 |
3.411 3.398 3.386 3.374 |
.005 .005 .005 .005 |
6.821 6.797 6.773 6.748 |
.019 .019 .019 .019 |
10.232 10. 195 10. 159 10. 123 |
.042 .042 .042 .042 |
13.642 13. 594 13.545 13.497 |
.075 .075 .075 .075 |
|
4.371 8.741 13. 112 |
|||||||||
|
40 00 15 30 45 |
17.483 |
3.362 3.350 3.337 3. 325 |
.005 .005 .005 .005 |
6.724 6.699 6.675 6.650 |
.019 .019 .019 .019 |
10. 086 10.049 10. 012 9.975 |
.042 .042 .043 .043 |
13.448 13.399 13. 349 13. 300 |
.075 .075 .076 .076 |
|
4.371 8.743 13. 114 |
|||||||||
|
41 00 |
17. 486 |
3.312 |
.005 |
6.625 |
.019 |
9.937 |
.043 |
13. 250 |
.076 |
|
15 30 45 |
4.372 8.744 13. 117 |
3.300 3.287 3.275 |
.005 .005 .005 |
6.600 6.575 6.549 |
.019 .019 .019 |
9.900 9.862 9.824 |
.043 .043 .043 |
13. 200 13.149 13. 098_ |
.076 .076 .076 |
|
42 00 15 30 45 |
17.489 |
3.262 3.249 3.236 3.223 |
.005 .005 .005 .005 |
6.524 6.498 6.472 6.447 |
.019 .019 .019 .019 |
9.786 9.747 9.709 9.670 |
.043 .043 .043 .043 |
13.048 12. 996 12. 945 12. 893 |
.076 .076 .076 .076 |
|
4.373 8.746 13. 119 |
|||||||||
|
43 00 15 30 45 |
17. 492 |
3.210 3.197 3.184 3.170 |
.005 .005 .005 .005 |
6.421 6.394 6.368 6.342 |
.019 .019 .019 .019 |
9.631 9.592 9.552 9.513 |
.043 .043 .043 .043 |
12.842 12. 789 12. 736 12.684 |
.076 .076 .076 .076 |
|
4.374 8.747 13. 121 |
|||||||||
|
44 00 15 30 45 |
17.495 |
3.158 3.144 3.131 3.118 |
.005 .005 .005 .005 |
6.316 6.289 6.262 6.235 |
.019 .019 .019 .019 |
9.473 9.433 9.393 9.353 |
.043 .043 .043 .043 |
12.631 12.578 12.524 12.471 |
.077 .077 .077 .077 |
|
4.375 8.749 13. 124 |
|||||||||
|
45 00 15 30 45 |
17. 498 |
3.104 3.091 3.077 3.063 |
.005 .005 .005 .005 |
6.209 6.181 6.154 6.127 |
.019 .019 .019 .019 |
9.313 9.272 9.231 9.190 |
.043 .043 .043 .043 |
12.417 12.363 12. 308 12.254 |
.077 .077 .077 .077 |
|
4.375 8.751 13. 126 |
|||||||||
|
46 00 15 30 45 |
17. 501 |
3.050 3.036 3.022 3.008 |
.005 .005 .005 .005 |
6.100 6.072 6. 044 6.017 |
.019 .019 .019 .019 |
9.150 9.108 9.067 9.025 |
.043 .04a .043 .043 |
12.200 12.144 12. 089 12. 033 |
.077 .077 .077 .077 |
|
4.376 8.752 13. 128 |
|||||||||
|
47 00 15 30 45 |
17. 504 |
2.994 2.980 2.966 2.962 |
.005 .005 .005 .005 |
5.989 * 5.961 5.933 5.904 |
.019 .019 .019 .019 |
8.983 8.941 8.899 8.857 |
.043 .043 .043 .043 |
11. 978 11.922 11.865 11.809 |
.076 .076 .076 .076 |
|
4.377 8.754 13. 131 |
|||||||||
|
f48 00 15 30 45 |
17.508 |
2.938 2.924 2.909 2.895 |
.005 .005 .005 .005 |
5.876- 5.848 5.819 5.790 |
.019 .019 .019 .019 |
8.814 8.771 8.728 8.686 |
.043 .043 .043 .043 |
11. 752 11.695 11. 638 11. 581 |
.076 .076 .076 .076 |
|
4.378 8.755 13. 133 |
|||||||||
|
^49 00 15 30 45 |
17. 511 |
2.881 2.866 2.852 2.837 |
.005 .005 .005 .005 |
5.762 5.733 5.704 5.675 |
.019 .019 .019 .019 |
8.643 8. 599 8.555 8.512 |
.043 .043 .043 .042 |
11.524 11.465 11.407 11.349 |
.076 .076 .076 .076 |
|
4.378 8.757 13. 135 |
|||||||||
|
50 00 |
17.514 |
2.823 |
.005 |
5.646 |
.019 |
8.468 |
.042 |
11.291 |
.076 |
PEOJEOTION TABLES.
177
Table XXI. — Coordinates for projection of maps. Scale ti^outt- [Prepared by E. S. Woodward.]
Abscissas of developed parallel.
25' longi- 30' long! tude. tude.
Ordinates of devel- oped parallel.
Inches.
"Km
11.629 17.444 23. 259 29. 074
5.816 11. 633 17. 449 23. 265 29. 082
5.817 11. 634 17. 451 23. 268 29. 086
5.818 11. 636 17. 454 23. 272 29. 090
11. 638 17. 457 23. 276 29. 094
11. 640 17. 460 23. 280 29. 100
5.821 11.642 17. 462 23. 283 29, 104
6.822 .1. 643 17. 465 23. 287 29. 109
5.823 11. 645 17.468 23. 291 29. 113
2.642 2. 639 2.635 2.631
2,628 2. 624 2,620 2.616 2,613 2,609
2,605 2.601 2.597 2.593 2.589 2.586
2.582 2,578 2,574 2,570 2.566 2.662
2.558 2.553 2,549 2.545 2.541 2.537
2,533 2,528 2,524 2,520 2.515 2.511
2.507 2.502 2,498
2.480 2.476 2.471 2,467 2,462 2,458
2.453 2,448 2, 444 2,439 2,434
2, 425 2,420 2,415 2.410 2,406 2,401
Inches. 5.299 5,292 5.285 5,278 6,270 5.263
5.256 6.248 6,240 5.233 5,225 5.218
5,210 5.203 5.195 5.187 5.179 5.171
5.163 5.155 5.147 5.139 5.131 5.123
5.065 5,056 5.048 5. 039 5.031 5.022
4.951 4.942 4,933 4.924 4.916
4.821 4.811 4.802
Inches. 7.949 7.938 7.927
7.883 7.872 7.861
7.804 7.792 7.780 7,768 7,757
7.745 7,733 7,721 7,709 7,697 7.685
7.673 7.660 7.648 7.635 7.622 7.610
7.559 7.546 7.533
7,520 7,507 7.494
7.441 7.427 7.413 7,400 7.386 7.373
7,359 7,345 7.331 7,316 7,302
7.274 7.260 7,246 7,231 7.217 7.203
Inches. 10. 699 10, 584 10, 670 10, 555 10. 540 10, 526
10, 511 10, 496 10. 481 10, 466 10, 451 10, 436
10, 421 10, 405 10, 390 10. 37i 10, 368 10. 342
10. 327 10. 311 10. 291 10. 278 10. 262 10. 246
10. 230 10, 213 10. 197 10. 180 10. 163 10. 146
10, 130 10. 113 10, 096 10, 078 10, 061 10, 044
10. 027 10. 009 9,992 9,974
9,774 9.755 9.736 9.718
9.661 9.642 9,622
Indies. 13. 249 13, 231 13, 212 13, 194 13, 176 13. 157
13, 139 13, 120 13, 101 13, 082 13. 063 13. 045
13. 026 13. 006 12, 987 12. 967 12. 947 12. 928
12, 909 12, 889 12, 868 12, 848 12, 828 12. 808
12, 788 12, 767 12. 746 12, 725 12, 704 12. 683
12. 662 12, 641 12, 620 12. 598 12, 577 12. 556
12. 534 12. 512 12. 490 12, 467 12,445 12. 423
12. 401 12. 379 12. 356 12. 333 12. 310 12. 388
12. 265 12. 241 12. 218 12, 194 12. 171 12. 147
12. 124 12, 100 12, 076 12, 052 12, 028 12, 004
Inches. 15, 898 15, 877
15, 854
16. 833
15. 811
16. 788
15. 767 15. 744
16. 721 15. 698 15, 676 15. 664
15. 631 15. 608 15. 584 15, 560 15, 537 15. 514
15. 490 ■16. 466 15,442 15, 418 15. 394
15, 369
16, 346 16, 320 15, 295 15. 270 15. 246 15. 220
15. 195 16. 169 15. 143 15. 118 15. 092 15, 066
15, 040 15, 014 14, 987 14. 960 14. 934 14, 908
14. 881 14. 854 14, 827 14. 800 14. 772 14. 745
14. 717 14. 689 14. 661 14. 633 14. 605 14. 575
14. 549 14. 620 14. 491 14. 462 14. 434 14. 405
0.001 .004 .008
-12
178 A MANUAL OF TOPOGEAPHIC METHODS.
Table XXl.— Coordinates of projection of maps. Scale t^sWd — Continued. [Prepared by K. S. 'Wooilw.ircl.]
|
|1 i3 |
§ « i'i 'C ta a S |
Abscissas of developed parallel. |
Ordinates of devel- oped parallel. |
|||||||
|
5' longi- tude. |
0' longi- tude. |
15' longi- tude. |
20' longi- tude. |
^5' longi- tude. |
30' longi- tude. |
|||||
|
35 00 10 20 30 40 50 36 00 10 20 30 40 50 37 "0 10 20 30 40 50 38 00 10 20 30 40 50 39 00 10 20 30 40 50 40 00 10 20 30 40 50 41 00 10 20 1 30 40 50 42 00 10 20 30 40 50 43 00 10 20 30 40 50 |
Inches. |
Inches, 2.396 2.391 2.386 2.3S1 2.377 2.372 2.367 2.362 2.357 2.351 2.346 2. 341 2.336 2.331 2.326 2.321 2.316 2.311 2.305 2.300 2.295 2.290 2.284 2.279 2.274 2.268 2.263 2.258 2.252 2.247 2.241 2.236 2.230 2. 225 2.219 2.214 2.208 2.203 2.197 2.192 2.186 2.180 2.175 2.169 2.163 2.157 2. 152 2.146 2.140 2.135 2.129 2.123 2.117 2.111 |
I7iches. 4.792 4.782 4.773 4.763 4.753 4.743 4.733 4.723 4.713 4.703 4.693 4.683 4.673 4. 662 4.652 4.642 4.631 4.621 4.611 4.600 4.590 4.579 4.568 4.558 4.548 4.537 4.526 4.515 4.504 4.493 4.483 4.472 4.461 4.450 4.439 4.428 4.417 4.406 4.394 4.383 4.372 4.360 4.349 4.338 4.326 4.315 4.303 4.292 4.281 4.269 4.257 4.246 4.234 4.222 |
Inches. 7.188 7.174 7.159 7.144 7.130 7.115 7.099 7.085 7.070 7.055 7. 039 7.024 7.009 6.994 6.978 6.963 6.947 6.932 6.916 6.900 6.884 6.869 6.853 6.837 6.821 6.805 6.789 6.773 6.756 6.740 6.724 6.707 6.691 6.674 6.658 6.641 6.625 6.608 6.591 6.575 6.558 6.541 6.524 6.507 6.490 6.472 6.455 6.438 6.421 6.403 6.386 6.363 6.351 6.333 |
Inches. 9.584 9.565 9.545 9.526 9.506 9.486 9.466 9.446 9. 426 9.406 9.386 9.366 9.345 9.325 9.304 9.284 9.263 9.242 9! 200 9.179 9.158 9.137 9.116 9.095 9,073 9.052 9.030 9.008 8.987 8.965 8. 943 8.921 8.899 8.877 8.855 8.834 8.811 8.788 8.766 8.744 8.721 8.698 8.676 8.653 8.630 8.607 8.584 8.661 8.538 8.514 8.491 8.468 8.444 |
Inches, 11. 980 11. 956 11. 932 11. 907 11. 883 11. 858 11. 833 11. 808 11. 783 11. 757 11. 732 11. 707 11. 682 11. 656 11.630 11. 605 11. 579 11. 553 11. 527 11.501 11. 474 11. 448 11. 421 11. 395 11. 309 11. 342 11. 315 11. 288 11. 261 11. 234 11.207 11. 179 11. 152 11. 124 11. 097 11.069 11. 042 11.014 10. 985 10. 958 10. 929 10. 901 10. 873 10. 844 10. 816 10. 787 10. 759 10. 730 10. 701 10. 072 10. 643 10. 614 10. 585 10. 556 |
Inches. 14. 376 14. 347 14. 318 14. 288 14. 259 14. 230 14. 200 14. 170 14. 139 14. 109 14. 078 14.048 14. 018 13. 987 13. 956 13. 925 13. 894 13. 864 13.832 13. 801 13. 769 13. 737 13. 705 13. 673 13. 642 13. 610 13. 577 13. 545 13. 513 13. 480 13.448 13. 415 13. 382- 13. 349 13. 316 13. 283 13. 250 13.217 13. 183 13. 149 13. 115 13. 081 13. 048 13. 013 12. 979 12. 945 12. 910 12. 876 12. 842 12. 807 12. 772 12. 737 12. 701 12. 667 |
|1 0 a |
34° |
35° |
|
5. 824 11. 647 17. 471 23.294 . 29.118 |
||||||||||
|
5 10 15 20 25 30 |
Inch. 0.001 .004 .009 .016 .025 .036 |
Inch. 0.001 .004 .009 .016 .025 .036 |
||||||||
|
5,824 11. 649 17. 473 23. 297 29. 122 |
||||||||||
|
36= |
37° |
|||||||||
|
5.826 11.651 17.477 23. 302 29. 128 |
||||||||||
|
5 10 15 20 25 30 |
O.OOI .004 .009 .016 .025 .036 |
0.001 .004 .009 .016 .026 .037 |
||||||||
|
5.827 U. 653 17. 480 23. 306 29. 133 |
||||||||||
|
37° ■ |
38° |
|||||||||
|
5 10 15 20 25 30 |
Inch. 0.001 .004 .009 .016 .026 .037 |
Inch. 0.001 .004 .009 .017 .026 .037 |
||||||||
|
5.828 11. 655 17. 483 23. 310 29. 138 |
||||||||||
|
5.829 11. 657 17.486 23. 314 29. 143 |
||||||||||
|
39° |
40° |
|||||||||
|
6 10 15 20 25 30 |
0.001 .004 .009 .017 .026 .037 |
0.001 .004 .009 .017 .026 .038 |
||||||||
|
5.830 11. 659 17. 489 23.319 29. 149 |
||||||||||
|
40° |
41° |
|||||||||
|
5.831 11. 661 17. 492 23. 323 29.154 |
||||||||||
|
5 10 15 20 25 30 |
Inch. 0.001 .004 .009 .017 .026 .038 |
Inch. 0.001 .004 .009 .017 .026 .038 |
||||||||
|
5.832 11. 663 17. 495 23. 327 29. 159 |
||||||||||
|
42° |
43° |
|||||||||
|
5 10 16 20 25 30 |
0.001 .004 .010 .017 .026 .038 |
0.001 .004 .010 .017 .027 .038 |
||||||||
|
1 |
PEOJECTION TABLES.
179
Table XXI. — Coordinates for projection of maps. Scale - [Prepared by E. S. Woodwaxd.]
-Coutinued.
|
3 l3 |
i Pi |
•ggg§ ■3 |
Abscissas of developed parallel. |
Ordinatea of devel- oped parallel. |
|||||||
|
5' longi- tude. |
10' longi- tude. |
15' longi- tude. |
20' longi- tude. |
25' longi- tude. |
30' longi- tude. |
||||||
|
44 46 47 48 49 60 |
00 10 20 30 40 50 00 10 20 3Q 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 10 20 30 40 50 00 |
Inches. |
Inches. 2.105 2.099 2.093 2.087 2.081 2.076 2.070 2.064 2.057 2.051 2.045 2.039 2.033 2.027 2.021 2.015 2.009 2.003 1.996 1.990 1.984 1.978 1.971 1.965 1.959 1.952 1.946 1.940 1.933 1.927 1.921 1.914 1.908 1.901 1.895 1.888 1.882 |
Inches. 4.210 ■ 4.199 4.187 4. 175 4.163 4.151 4.139 4.127 4115 4.103 4.091 4.079 4.067 4.054 4.042 4.030 4.017 4.005 3.992 3.980 3.968 3.955 3.943 3.930 3.917 3.905 8.892 3.879 3.867 3.854 3.841 3.828 3.815 3.803 3.790 3.777 3.764 |
Inches. 6.316 6.298 6.280 6.262 6.244 6.227 6.209 6.191 6.172 6.154 6.136 6.118 6.100 6.081 6.063 6.044 6.026 6.008 5.989 5. 970 5.951 5.933 5.914 5.895 5.876 5.857 5.838 6.819 5.800 6.781 5.762 5.743 5.723 5.704 5.684 6.665 5.646 |
Inches. 8.421 8.397 8.373 8.350 8.326 8.302 8.278 8.264 8.230 8.206 8.181 8.157 8.133 8.108 8.084 8.069 8.034 8.010 7.985 7.960 7.935 7.910 7.885 7.860 7.835 7.810 7.784 7.769 7.733 7.708 7.682 7.657 7.631 7.605 7.579 7.563 7.527 |
Inches. 10. 526 10. 496 10. 467 10. 437 10.407 10. 378 10.343 10. 317 10. 288 10. 257 10. 226 10. 197 10. 166 10. 136 10. 104 10.074 10.043 10. 013 9.981 9.951 9.919 9.888 9.857 9.826 9.794 9.762 9.730 9.699 9.667 9.635 9.603 9.571 9.539 9.507 9.174 9.442 9.409 |
Inches. 12. 631 12. 596 12. 560 12.524 12.489 12.453 12.417 12.381 12.345 12. 308 12. 272 12. 236 12. 199 12. 163 12. 125 12. 089 12.052 12. 015 11. 978 11. 941 11. 903 11.866 11. 828 11. 791 11. 752 11. 714 11. 677 11. 638 U.600 11. 562 11.523 11.485 11. 446 11. 408 11. 369 11.330 11.291 |
Mo (3- |
43" |
44° |
|
5.833 11.666 17. 498 23.331 29. 164 |
|||||||||||
|
5 10 15 20 25 30 |
Inch. 0.001 .004 .010 .017 .027 .038 |
Inch. 0.001 -.004 .010 .017 .027 .038 |
|||||||||
|
5.834 11.668 17. 501 23.335 29. 169 |
|||||||||||
|
45° |
46° |
||||||||||
|
5.835 11.670 17. 504 23. 339 29. 174 |
|||||||||||
|
5 10 15 20 25 30 |
0.001 .004 .010 .017 .027 .038 |
0.001 .004 .010 .017 .027 .038 |
|||||||||
|
5. 836 11. 672 17. 508 23.344 29.180 |
|||||||||||
|
470 |
48° |
||||||||||
|
5 10 15 20 25 30 |
0.001 .004 .010 .017 .027 .038 |
0.001 .004 .010 .017 .026 .038 |
|||||||||
|
5.837 11.674 17.511 23.348 29. 185 |
|||||||||||
|
5.838 11. 676 17. 514 23.352 29. 190 |
490 |
50° |
|||||||||
|
5 10 15 20 25 30 |
0.001 .004 .010 .017 .026 .038 |
0.001 .004 .009 .017 .026 .038 |
|||||||||
|
1 |
180
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXH.-
-Coordinates for projection of maps. Scale ^j-suxr- [Prepared by R. S. "Woodward.]
|
11 Hi |
So llli 3.1 1* |
Absci |
>sa3 of developed parallel. |
Ordinates of devel- oped parallel. |
||||||
|
2J' longi- tude. |
5' loiiffi- tude. |
7J' longi- tude. |
lOMongi- tude. |
12J' lon- gitude. |
15' longi- tude. |
|||||
|
25 00 05 10 15 20 25 30 il 45 50 55 26 00 05 10 15 20 25 30 35 40 45 50 55 27 00 05 10 15 20 25 30 35 40 45 50 55 28 00 05 10 15 20 25 30 35 40 45 50 55 29 00 05 10 15 20 25 30 35 40 45 50 55 30 00 05 10 15 20 25 30 35 40 45 50 55 |
Inches. |
Inches. 2. 650 2.648 2.646 2.644 2.642 2.641 2.639 2.637 2.635 2. 633 2.631 2.630 2.628 2.626 2.624 2.622 2.620 2.618 2.617 2.615 2.613 2.611 2.609 2.607 2.605 2.603 2.601 2.599 2.597 2.595 2.593 2.591 2.590 2.588 2.586 2.584 2.582 2.580 2.578 2.576 2.574 2.572 2.570 2.568 2.566 2.564 2.562 2.360 2.558 2.555 2.553 2.551 2.549 2.547 2.545 2.543 • 2.541 2.539 2.337 2.535 2.533 2.530 2.528 2.526 2.524 2.522 2.520 2.518 2.515 2.513 2.511 2.509 |
Inches. 5.299 5.296 5.292 5.288 5.285 5.281 5.277 5.274 5.270 5.266 5.263 5.259 5.256 5.252 5.248 5.244 5.241 5.237 5,233 5. 229 5.225 5.222 5.218 5.214 5.210 5.207 5.203 5.399 5.195 5.191 5.187 5.183 5.179 5.175 5.171 5. 167 5.163 5.159 3.155 5.151 5.147 5.143 5.139 5.135 5.131 5.127 5.123 5.119 5.115 5.111 5.107 5.103 5.098 5.094 5.090 5.086 5.082 5.078 5.073 5.069 5.065 5.061 5.057 5.052 5.048 5.044 5.039 5.035 5.031 5.026 5.022 5.018 |
Inches. 7.949 7.944 7.938 7.933 7.927 7.922 7.916 7.911 7.905 7.900 7.894 7.689 7.883 7.878 7.872 7.866 7.861 7.853 7.849 7.844 7.838 7.833 7.827 7.821 7.816 7.810 7.804 7.798 7.792 7.786 7.780 7.774 7.769 7.763 7.757 7.751 7.745 7.739 7.733 7.727 7.721 7.715 7.709 7.703 7.697 7.691 7.685 7.679 7.673 7.666 7.660 7.654 7.648 7.641 7.635 7.629 7.623 7.616 7.610 . 7. 604 7.598 7.591 7.583 7.578 7.572 7.565 7.359 7.552 7.546 7.540 7.533 7.527 |
Inches. 10. 399 10. 591 10. 584 10. 577 10. 569 10. 562 10. 553 10.548 10. 540 10. 533 10. 526 10. 518 10.511 10. 504 10. 496 10. 489 10. 481 10. 473 10. 466 10. 458 10.451 10.443 10.436 10. 428 10. 421 10.413 10. 405 10. 397 10. 389 10. 382 10. 374 10. 366 10. 358 10. 330 10. 342 10.333 10. 327 10. 319 10. 311 10. 303 10. 294 10. 286 10. 278 10. 270 10. 262 10. 234 10. 246 10. 238 10. 230 10. 222 10. 213 10. 205 10.197 10. 188 10. 180 10. 172 10.164 10. 133 10. 147 10. 138 10. 130 10. 122 10. 113 10. 104 10. 096 10. 087 10. 079 10. 070 10. 061 10. 053 10.044 10. 036 |
Inches. 13.248 13. 239 13.230 13. 221 13. 212 13. 203 13. 194 13.184 13. 175 13. 166 13.157 13. 148 13. 139 13. 129 13. 120 13. Ill 13. 101 13. 092 13. 082 13. 073 13.064 13.034 13. 045 13. 035 13. 026 13. 016 13. 006 12. 997 12. 987 12. 077 12. 967 12. 937 12. 948 12. 938 12. 928 12. 918 12. 908 12. 898 12. 888 12. 878 12. 868 12. 858 12. 848 12. 838 12. 828 12. 818 12. 808 12. 798 12. 788 12. 777 12. 767 12. 756 12. 746 12. 735 12. 725 12. 716 12. 704 12. 694 12. 684 12. 673 12. 663 1.2. 652 12. 641 12. 630 12. 620 12. 609 12. 598 12.587 12. 577 12. 566 12. 355 12.544 |
Inches. 15. 898 15. 887 13. 876 15. 865 15. 854 15. 843 15. 832 15. 821 13. 810 15. 799 15. 788 15. 777 15. 766 15. 755 13.744 15.733 13. 721 15. 710 15. 699 15. 688 15. 676 15. 665 15. 654 15. 642 15. 631 15. 620 15. 608 15. 596 15. 584 15. 572 15. 561 15. 549 15. 537 15. 325 15. 514 15. 502 15. 490 13.478 15. 466 15.454 15. 442 15. 430 15. 418 15. 403 15. 393 15. 381 15. 369 15. 357 15. 345 15. 333 15. 320 15. 308 15. 295 15. 283 15. 270 15. 258 15. 245 15. 233 15. 220 15. 208 15. 195 15. 182 15. 169 15. 157 15. 144 15. 131 15. 118 15. 105 13. 092 15. 079 15. 066 15. 053 |
25° |
26° |
|
|
5.815 11. 629 . 17. 444 23. 259 29. 074 34. 888 |
||||||||||
|
24 5 1? 15 |
Inch. 0.000 .002 .004 .007 .010 ,015 |
Inch. 0,000 .002 .004 .007 .010 • .015 |
||||||||
|
1 |
||||||||||
|
5.816 . 11.631 17.447 23. 262 29. 078 34.893 |
||||||||||
|
27° |
||||||||||
|
2* 5' 74 10 12i 15" |
Inch. 0.000 .002 .004 .007 .011 .015 |
|||||||||
|
5.816 11. 633 17.449 2.3. 265 29. 082 34.898 |
1 |
|||||||||
|
27° |
.28° |
|||||||||
|
f 1? 12i 15 |
Inch. 0.000 .002 .004 ,007 .011 .013 |
Inch. 0.000 .002 .004 .007 .011 ,016 |
||||||||
|
5.817 11.634 17. 451 23. 268 29. 085 34. 903 |
||||||||||
|
1 |
||||||||||
|
29° |
||||||||||
|
f 1? If |
Inch. 0.000 .002 .004 .007 .011 .016 |
|||||||||
|
5.818 11. 636 17. 434 23. 272 29. 090 34. 908 |
||||||||||
|
1 |
||||||||||
|
29° |
30° |
|||||||||
|
2* 3 1? 124 15 |
Inch. 0.000 .002 .004 .007 .011 .016 |
Inch. 0.000 .002 .004 .007 .012 .017 |
||||||||
|
5.819 11. 638 17. 457 23. 276 29. 095 34.913 |
||||||||||
PEOJECTION TABLES.
181
Table XXll.—Coardinates for projection of maps. Scale -^ji^, — Continued. [Prepared by E. S. "Woodward.]
Inches.
'"'s.'sm'
11. 640 17. 460 23. 280 29. 100 34. 919
5.821 11.645! 17.462 23. 283 29. 104 34. 925
5.822 11.643 17. 465 23. 287 29. 109 34. 930
5.823 11. 645 17.468 23. 291 29. 113 34. 936
5.824 11. 647 17. 471 23. 294 29. 118 34. 942
5.824 11.649 17. 473 23. 297 29. 122 34. 946
Abscissas of developed parallel.
Inches.
. 2. 507 2.505 2.502 2.500 2.498 2.496 2.494 2.491 2.489 2.487 2.485 2.482
2.478 2.476 2.473 2.471 2.469 2.407 2.464 2.462 2.460 2.458 2.455
2.453 2.451 2.448 2.446 2.444 2.441 2.439 2.437 2.434 2.432 2.430 2.427
2.425 2.423 2.420 2.418 2.415 2.413 2.411 2.408 2.406 2.403 2.401
2.384 2.381 2.379 2.376 2.374 2.372 2,369
2.367 2.364 2.362 2.359 2.357 2.354 2.352 2.349 2.346 2.344 2.341
Inches. 5.014 5.009 5.005 5,000 4.996 4.991 4.987 4.983 4.978 4.974
4.956 4.951 4.947 4.942
4.924 4.920 4.915 4.910
4.850 4.845 4.840
4.797
4.792 4.787 4.782 4.777 4.773 4.768 4.763 4.758 4.753 4.748 4.743 4.738
4.733 4.728 4.723 4.718 4.713 4.708 4.703 4.698 4.693
Inches. 7.520 7.514 7.507 7.5U0 7.494 7. 487 7.480 7.474 7.467 7.460 7.454 7.4A7
7.441 7.434 7.427 7.420 7.413 7.407 7.400 7.393 7. 3S6 7.379 7,372 7.366
7.331 7.324 7.317
|
7.303 |
|
7.296 |
|
7.289 |
|
7.282 |
|
7.275 |
|
7.267 |
|
7.260 |
|
7.253 |
|
7.246 |
|
7.239 |
|
7.231 |
|
7.224 |
|
7.217 |
|
7.210 |
|
7.203 |
|
7.195 |
|
7.188 |
|
7.181 |
|
7.174 |
|
7.166 |
|
7.159 |
|
7.151 |
|
7.144 |
|
7.137 |
|
7.129 |
|
7.122 |
|
7.115 ' |
|
7.107 |
|
7.100 |
|
7.092 |
|
7.085 |
|
7.077 |
|
7.070 |
|
7.062 |
|
7. 055 |
|
7.047 |
|
7.039 |
|
7.032 |
|
7.024 |
|
7. 017 |
Inches. 10. 027 10. 018 10. 009 10. 000
9.974 9.965 9.956 9.947
9. 793 9.784 9.774
9.728 9,718 9.709
9.700 9.690 9.680 9.671 9,661 9.652 9.642 9.632 9. 623 9.613 9.604 9.594
9. 584 9. 574 9.565 9.555 9.545 9.535 9. 525 9.516 9.506 9.496 9.486 9.476
9.466 9.456 9.446 9.436 9.426 9.416 9.406 9.396 9.380 9.376 9.366 9.356
Inches. 12. 534 12. 523 12. 512 12. 500 12. 489 12. 478 12. 467 12. 456 12.445 12. 434 12. 423 12. 412
12. 401 12. 390 12. 378 12. 367 12. 356 12.344 12. 333 12. 322 12. 310 12. 299 12. 287 12. 276
12. 265 12. 253 12. 241 12. 230 12. 218 12. 206 12. 195 12. 183 12. 171 12. 160 12.148 12. 136
12.124 12. 112 12. 100 12. 088 12. 076 12. 064 12. 052 12. 040 12. 028 12.016 12. 004 11. 992
11. 980 11. 908 11. 956 11. 914 11. 931 11. 919 11. 907 11. 895 11.882 II. 870 11.858 11. 845
11.833 11. 820 11. 808 11. 795 11. 783 11.770 11. 758 11. 745 11. 732 11. 720 11. 707 11.694
Inches. 15. 040 15. 027 15. 014 15. 000 14. 987 14. 974 14. 961 14. 948 14. 934 14. 921 14.908 14. 894
14. 881 14, 868 14. 854 14. 840 14. 827 14. 813 14. 800 14. 786 14. 772 14. 759 14. 745 14. 731
14. 690 14. 676 14. 662 14. 648 14. 633 14. 619 14.' 605 14. 591 14. 577 14. 563
14. 549 14. 535 14. 520 14. 506 14. 492 14. 477 14. 463 14. 448 14. 434 14. 420 14. 405 14. 391
14. 376 14. 362 14.347 14. 332 14. 318 14. 303 14. 288 14. 273 14. 259 14.244 14. 229 14. 214
14. 200 14. 183 14. 169 14, 154 14, 139 14. 124 14. 109 14. 094 14. 079 14. 064 14, 048 14, 033
Ordinates of devel- oped parallel.
Inch. 0.000 .002
Inch. 0.000 .002
182
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXII. — Coordinates for ^projection of maps. Scale -^xm — Coutinued. [Prepared Ijy E. S. 'Woodwartl,]
Abscissas of developed parallel.
12J' lon- gitude.
Ordiilatea of devel- oped parallel.
Inches.
5.826 11.651 17. 477 23. 302 29. 128 34. 954
5. 828 11.655 17. 483 23. 310 29. 138 34. 966
5.829 11. 657 17. 486 23. 314 29. 143 34. 972
5.830 11. 659 17.489 23.319 29. 149 34. 978
5.831 11. 661 17. 492 23. 323 29. 154 34.984
2. 323 2.321 2.318 2. 316 2.313 2.311 2.308
2.300 2. 298 2.295 2.292 2.290 2.287 2.284
1. 282
2.274 2.271 2.268 2.266
2.250 2.247 2.244
2.241 2.239 2.236 2.233 2.230 2.228
2.211
2.208 2.206 2.203 2.200 2.197 2.194 2.192 2.189 2.186 2.183 2.180 2.178
2.175 2.172 2.169 2.166 2.163 2.160 2.158 2.155 2.152 2.149 2. 146 2.143
Inches. 4.673 4.667 4.662 4.657 4.652 4.647 4.642 4.637 4.631 4.626 4.621 4.616
4.611 4.606 4.600 4.595 4.590
4.547 4.542 4.537 4.531 4.526 4.521 4.515 4.510 4.504 4.499 4.494
4.472 4.466 4.461 4.455 4.450 4.444 4.439 4.433 4.428 4.422
4.417 4.411 4.406 4.400 4.394 4.389 4.383 4.377 4.372
4.349 4.344 4.338 4.332 4.326 4.321 4.315
6. 963 6.955 6.947 6.939 6. 932 6.924
6.916
6.908 6.900 6.892 6.885 6.877 6.869 6.861 6.853 6.845 6.837
6.821 6.813 6.805 6.797 6.789 6.781 6.773 6.765 6.757 6.748 6.740 6.732
6.724 6.716 6.708 6.699 6.691 6.683 6.675 6.666 6.658 6.050 6.642 6.633
6.600 6.591 6.583 6.575 6.666 6.558 6.549 6.541 6.533
6.524 6.515 6.507 6.498 6.490 6.481 6.472 6.464 6.455 6.447 6.438 6.429
Inches. 9.345 9.335 9.325 9.314 9.304 9.294 9.283 9.273 9.363 9.253 9.212 9.233
9.222 9.211 9.201 9.190 9.179 9.169 9.158 9.148 9.137 9.137 9.118 9.106
9.095 9.084 9.073 9.063 9.052 9.041 9.030 9.020 9.009 8.998 8.987
Inches. 11. 683 11. 669 11. 656 11.643 11.630 11.617 11. 604 11. 591 11. 578 11.566 11. 553 11. 540
11.527 11. 514 11. 501 11. 488 ■11.474 11.461 11.448 11. 435 11.422 11. 408 11. 395 11. 382
11. 369 11. 355 11. 342 11. 328 11.315 11.301 11.288 11. 374 11.261 11. 247 11.234 11.221
11. 207 11. 193 11. 180 11. 166 11. 152 11. 138 11.124 14. Ill II. 097 11. 083 11.069 11. 056
11.042 11. 038 11.014 11.000 10. 986 10. 972 10. 958 10. 944 10. 930 10. 916 10. 902 10. 888
10. 873 10. 859 10.845 10. 830 10.816 10. 803 10. 787 10. 773 10. 759 10.744 10. 730 10. 716
14. 003 13. 987 13. 972 13,956 13.941 13.925 13.910 13. 894 13. 879 13. 863 13. 848
13. 832 13. 817 13. 801 13. 785 13. 769 13. 753 13. 737 13. 722 13. 706 13. 690 13. 674 13. 058
13. 642 13. 626 13. 610 13. 594 13. 578 13. 562 13. 545 13.529 13. 513 13. 497 13. 481 13. 465
13.448 13. 432 13. 415 13. 399 13. 382 13.360 13. 349 13. 333 13. 316 13. 300 13. 283 13. 267
13. 250 13. 233 13. 216 13. 200 13. 183 13. 166 13. 149 13. 133 13. 115 13. 099 13. 082 13. 065
13. 014 13. 996 12. 979 12. 963 12.945 12. 928
12. 910
13. 893 12. 876 12. 859
|
40° |
|
|
Inch. |
|
|
2i |
0. 001 |
|
5 |
.002 |
|
u |
.005 |
|
0 |
.008 |
|
2.V |
.013 |
|
.019 |
|
41° |
|
|
Inch. |
|
|
'i>, |
0.001 |
|
5 |
.002 |
|
7S: |
.005 |
|
10 |
.008 |
|
12* |
.013 |
|
15 |
.019 |
PEOJECTIOI^r TABLES.
183
Table XXll.— Coordinates for projection of maps. Scale ^jnr — Continued. [Prepared by E. S. "Woodward.]
Inches.
'""5.'832' 11. 663 17. 495 23. 327 29. 159
Absci9aa.s of developed parallel.
23. 331 29. 164 34. 997
5.834 11. 668 17. 501 23. 335 29. 169 35. 003
5.835 11. 670 17. 504 23. 339 29. 174 36. 009
5.836 11. 672 17. 508 23. 344 29. ISO 35. 015
5.837 11. 674 17.511 23. 348 29. 185 35. 021
Inches. 2.140 2.137 2.134 2.132 2.129 2.126 2.123 2.120 2.117 2.114 2.111 2.108
2.096 2.093 2.090 2.087 2.084 2.C81 2.078 2.076 2.073
2. 045 2.042 2,039 2.036
1.996 1.993 1.990 1.987 1.984 1.981 1.977 1.974 1.971 1.968 1.965
1.959 1.956 1.952 1.949 1.946 1.943 1.940 1.937 1.933 1.930 1.927 1.924
4.275 4.269 4.263 4.257 4.251 4.246 4.240 4.234 4.228 4.222 4.216
4.193 4.187 4.181 4.175 4.169 4.163 4.157 4.151 4.145
4.133 4.127 4.121 4.115 4.109 4.103 4.097 4.091 4,085 4.079 4.073
4.067 4.060 4.054 4.048 4.042 4.036 4.030 4.023 4.017 4.011 4.005
3,917 3.911 3.905
Inches. 6.421 6.412 6.403 6.395 6.386 6.377
6.351 6.342 6.333 6.324
6.316 6.307 6.298
6.271 6.262 6.253 6.244 6.235 6.227 6. 218
6.209 6.200 6.191 6.181 6. 172 6.163 6.154 6.145 6.136 6.127 6.118 6.109
6.100 6.091 6.081 6.072 6.063 6.054 6.044 6.035 6.026 6.017 6.008
5.970 5.981 5 951 5.942 5.933 5.923 5.914 5.904 5.895
5.876 5-. 867 5.857 5.848
Inches. 8.561 8.550
8.503 8.491 8.479 8.468 8.456 8.444 8.432
8.326 8.314 8. 302 . 8.290
8.278 8.266 8.254 §.242 8.230 8.218 8.206 8.194 8.181 8.169 8.157
.145
7.985 7.973 7.960 7.948 7.935 7.923 7.910 7.898
7.784 7.771 7.759 7.746 7.733 7.721 7.708 7.695
Inches. 10. 701 10. 687 10. 672 10. 658 10. 643 10. 628 10. 614 10. 599 10. 585 10. 570 10. 555 10.541
10. 496 10.482 10. 467 10. 452 10.437 10. 422 10. 407
10.;
10. 348 10. 333 10. 318 10. 302 10. 287 10, 272 10. 257 10. 242 10. 227 10. 212 10. 197 10. 182
10. 166 10. 151 10. 136 10. 120 10. 105 10. 090 10. 074 10. 059 10. 043 10. 028 10. 013 9.907
9.982 9.966 9.950 9.935 9.919
9.667 9.651 9.635 9.619
Inches. 12. 842 12. 824 12. 807 12. 789 12. 772 12. 754 12. 736 12. 719 12. 701 12. 684 12. 666 12. 649
12. 631 12. 613 12. 596 12. 578 12. 560 12. 542 12.524 12. 506 12. 489 12. 471 12. 453 12. 43S
12. 417 12. 399 12. 381 12. 363 12. 345 12. 327 12. 308 12. 290 12. 272 12. 254 12. 236 12. 218
12. 200 12. 181 12. 163 12. 144 12. 126 12. 107 12. 089 12. 070 12. 052 12. 033 12.015 11. 996
II. 978 11. 959 11. 940 11. 922 11. 903 11. 884 11.865 11. 846 11. 828 11. 809 11. 790 11. 771
11. 752 11.733' 11. 714 11. 695 11. 676 11. 657 11. 638 11. 619 11. 600 11. 581 11. .562 11. 543
Ordinates of devel- oped parallel.
184
A MANUAL OF TOrOGEAPHIC METHODS.
Table XXII. — Coordinates for projection of maps. Scale -g^jy^ [Prepared hy E. S. Woodward.]
■3.S£
Inches.
5.838 11. 676 17. 51J, 23. 352 29. 190 35. 027
Abscissas of developed parallel.
JJ' longi- 5' longi, 7^' longi- 10' longi- 12J' Ion- 15' long tude. tilde. tude. tude. gitude. tude.
Inches. 1.921 1.917 1.9U 1.911
3.828 3.822 3.815 3.809 3.802 3.796 3.790 3.783 3.777
5.742 5.733 5.723 5.713 5.704 5.694 5.684 5.675 5.665 5.655
7.670 7.657 7.644 7.631 7.618 7.605 7.592 7.579 7.566 7.553 7.540
7.528
Inches. 9.003 9.587 9.571 9.555 9. 538 9. 522 9.506 9.490 9.474 9.458 9.442 9.426
9.409
Inches. 11. 524 11. 504 11.485 11. 466 11.446 11.427 11. 407 11. 388 11. 369 11. 349 11. 330 11. 311
Ordinates of devel- oped parallel.
|
49° |
|
|
"^ |
|
|
Inch. |
|
|
^ |
0.001 |
|
5 |
.002 |
|
74 0 |
.005 .008 |
|
n |
.013 |
|
5 |
.039 |
Table XXIII. — Coordinates for ))rojecUon of maps. Scale -^-^^jfij. [Prepared by S. S. Gannett.]
|
Latitade par.allel. |
Abscissas of developed p.irallel. |
Ordinates of devel- oped parallel. |
||||
|
Longitude interval. |
||||||
|
Longi- |
||||||
|
5' |
7i' |
10' |
15' |
tude |
Incb. |
|
|
interval. |
||||||
|
" o |
Inches. |
Inches. |
Inches. |
Inches. |
, |
|
|
39 00 |
6.316 |
9.474 |
12.632 |
18.948 |
5 |
.003 |
|
05 |
.309 |
.463 |
.617 |
.926 |
n |
.007 |
|
07i |
.305 |
.457 |
.609 |
.914 |
10 |
.012 |
|
10 15 |
.301 .294 |
.451 .440 |
.602 .587 |
.903 .881 |
15 |
.026 |
|
20 |
6.286 |
9.429 |
12.572 |
18. 858 |
Latitude interval. |
Meridi- onal dis- |
|
22* 25 |
.282 .279 |
.423 .418 |
.565 .557 |
.847 .836 |
||
|
/ |
Inch. |
|||||
|
30 |
.271 |
.406 |
.542 |
.813 |
1 2 |
1.619 3.237 |
|
35 |
6.264 |
9.395 |
12. 527 |
18. 791 |
4 6 6 7 |
0.475 8.094 9.712 11. 331 |
|
37J |
.260 |
.389 |
.520 |
.780 |
||
|
40 |
.256 |
.384 |
.512 |
.768 |
||
|
45 |
.J49 |
■.873 |
.497 |
.746 |
||
|
8 |
12. 960 |
|||||
|
50 |
6.2a |
9.361 |
12.482 |
18. 723 |
9 |
14. 569 |
|
52i 65 |
.237 .234 |
.356 .350 |
.475 .467 |
.712 .701 |
10 |
16. 188 |
|
60 |
.226 |
.339 |
.452 |
.678 |
Longi- tude in- |
Inch. |
|
40 00 05 |
6.226 .219 |
9.339 .328 |
12. 452 .438 |
18. 678 .656 |
||
|
' |
||||||
|
07i |
.215 |
.322 |
.429 |
.644 |
5 |
.003 |
|
10 |
.211 |
.316 |
.422 |
.633 |
n |
.007 |
|
15 |
.203 |
.305 |
.406 |
.609 |
10 |
.012 |
|
20 |
6.196 |
9.293 |
12. 392 |
18. 587 |
15 |
.026 |
|
22J |
.192 |
.288 |
.384 |
.576 |
Latitude |
|
|
25 |
.188 |
.282 |
.376 |
.564 |
||
|
30 |
.180 |
.270 |
.361 |
.540 |
||
|
' |
Inch. |
|||||
|
35 |
6.173 |
9.259 |
12. 346 |
18. 518 |
1 2 3 4 |
1.619 3.238 4.857 6.470 8.095 |
|
37* |
.169 |
.253 |
.338 |
.506 |
||
|
40 |
.165 |
.247 |
.330 |
.495 |
||
|
45 |
.157 |
.236 |
.315 |
.472 |
||
|
6 |
9.714 |
|||||
|
50 |
6.150 |
9.224 |
12.300 |
18.449 |
7 |
11. 333 |
|
52J |
.146 |
.219 |
.292 |
.438 |
8 |
12. 952 |
|
55- |
.142 |
.213 |
.285 |
.427 |
9 |
14. 571 |
|
60 |
.134 |
.201 |
.269 |
.403 |
10 |
16. 190 |
|
1 |
PEOJEOTION TABLES.
185
Table XXIII. — Coordinates for projection of maps. Scale 4-5^513 — Continued. (Prepared by S. S. Gannett.]
Abscissas of developed parallel.
Longitude interval.
Ordinates of devel- oped parallel.
Loncfi- tnde Inch,
interval.
Meridi- onal dis- tance.
1.619 3.239 4.858 6.477 8.097 9.716 11.335 12. 955 14. 574 16. 193
.074 .051
■*B.961
18. 027 .015 .003
17. 979
17. 956 .944 .933
Meridi- onal dis- tance.
6.478 8.098 9.718
11. 337
12. 957 14. 576 16. 196
Longi- tude in- lucli. terval.
Meridi- onal dis- tance.
Inch. 1.620 3. 2.J0
186
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXIII. — Coordinates for projection of maps. Scale tsW — Continued. [Prepared by S. S. Gannett.]
|
Latitude of Iparallel. |
Abscissas of developed parallel. |
Ordinates of devel- oped parallel. |
||||
|
Longitude interval. |
||||||
|
Longi- |
||||||
|
6' |
7J' |
10' |
15' |
tude interval. |
Tncb. |
|
|
0 1 |
Inches. |
Inches. |
Inches. |
Inches. |
, |
|
|
U 00 |
5.848 |
8.771 |
11.695 |
17. 543 |
6 |
.003 |
|
05 |
.83!) |
.759 |
.679 |
.618 |
7J |
.007 |
|
07* |
.835 |
.753 |
.670 |
.505 |
10 |
.012 |
|
10 15 20 |
.831 .823 5.815 |
.746 |
.662 |
.493 |
15 |
.027 |
|
8.722 |
11. 629 |
17. 444 |
Latitude interval. |
Meridi- onal dis- |
||
|
2^ 25 |
.810 .806 |
.715 1 .621 .709 1 .613 |
.431 .419 |
|||
|
30 |
.798 |
. 697 1 . 596 |
.394 |
1 2 |
Inch. 1.620 3.240 |
|
|
35 |
5.790 |
8.685 i 11.580 |
17. 370 |
3 |
4.861 |
|
|
37J |
.786 |
.678 .571 |
.357 |
4 |
6.481 |
|
|
40 |
.782 |
.672 1 ,563 |
.345 |
5 |
8.101 |
|
|
45 |
.773 |
.660 |
.547 |
.320 |
6 7 8 |
9.721 11. 341 12. 962 |
|
50 |
5.765 |
8.647 |
11.530 |
17. 296 |
9 |
14. 582 |
|
52* |
.761 |
.641 |
.523 |
.284 |
10 |
16. 202 |
|
55 |
.757 |
.635 |
.614 |
.271 |
||
|
60 |
.749 |
.623 |
.497 |
.246 |
Table XSIV. — Area of quadrilaterals of Earth's surface of 1^ extent in latitude and longitude. [Prepared by E. S. AToodward.]
|
Middle latitude of <iuad- rilateral. |
Area in square miles. |
Middle latitude of quad- rilateral. |
Area in square |
Middle latitude of quad- rilateral. |
Area |
Middle latitude of quad- rilateral. |
Area in square |
Middle latitude of quad- rilateral. |
Area in square |
Middle latitude of quad- rilateral. |
If! |
|||||
|
0 |
00 |
4752. 33 |
15 |
30 |
4583. 92 |
30 |
30 |
4109. 06 |
45 |
30 |
3354. 01 |
60 30 |
2364. 34 |
75 |
30 |
1205. 13 |
|
0 |
30 |
52.16 |
16 |
00 |
72.94 |
31 |
00 |
4088. 21 |
46 |
00 |
24.49 |
61 00 |
23.02 |
76 |
00 |
1164. 49 |
|
1 |
00 |
51.63 |
16 |
30 |
6L61 |
31 |
30 |
67.05 |
46 |
30 |
3294. 71 |
61 30 |
2291. 51 |
76 |
30 |
23.75 |
|
1 |
30 |
50.75 |
17 |
00 |
49.94 |
32 |
00 |
45.57 |
47 |
00 |
64.63 |
62 00 |
54.82 |
77 |
00 |
1082. 91 |
|
2 |
00 |
49.52 |
17 |
30 |
37.93 |
32 |
30 |
23.79 |
47 |
30 |
34.39 |
62 30 |
17.94 |
77 |
30 |
41.99 |
|
2 |
30 |
47.93 |
> |
|||||||||||||
|
3 |
00 |
46.00 |
18 |
00 |
25.59 |
33 |
00 |
01.69 |
43 |
00 |
03.84 |
63 00 |
2180. 89 |
78 |
00 |
1000. 99 |
|
3 |
30 |
43.71 |
18 |
30 |
12.90 |
33 |
30 |
3979. 30 |
48 |
30 |
3173. 04 |
63 30 |
43.66 |
78 |
30 |
959. 90 |
|
4 |
00 |
41.07 |
19 |
00 |
4499. 87 |
34 |
00 |
56.59 |
49 |
00 |
41.99 |
64 00 |
06.26 |
79 |
00 |
18.73 |
|
4 |
30 |
38.08 |
19 |
30 |
86.51 |
34 |
30 |
33.59 |
49 |
30 |
10.69 |
64 30 |
2063. 68 |
79 |
30 |
877. 49 |
|
5 |
00 |
34.74 |
20 |
00 |
72.81 |
35 |
00 |
10.28 |
60 |
00 |
3079. 15 |
65 00 |
30.94 |
80 |
00 |
36.18 |
|
5 |
30 |
31.04 |
20 |
30 |
58.78 |
35 |
30 |
3886. 67 |
50 |
30 |
47.37 |
65 30 |
1993. 04 |
80 |
30 |
794. 79 |
|
6 |
00 |
27.00 |
21 |
00 |
44.41 |
36 |
00 |
62.76 |
51 |
00 |
15.34 |
66 00 |
54.97 |
81 |
00 |
53.34 |
|
6 |
30 |
22.61 |
21 |
30 |
29.71 |
36 |
30 |
38.56 |
51 |
30 |
2983. 08 |
66 30 |
16.75 |
31 |
30 |
11.83 |
|
7 |
00 |
17.86 |
22 |
00 |
14.67 |
37 |
00 |
14.06 |
52 |
00 |
50. 58 |
67 00 |
1878.37 |
32 |
00 |
670. 27 |
|
7 |
30 |
12.76 |
22 |
30 |
4399.30 |
37 |
30 |
3789. 26 |
52 |
30 |
17.85 |
67 30 |
39.34 |
82 |
30 |
28.64 |
|
8 |
00 |
07.32 |
23 |
00 |
83.60 |
38 |
00 |
64.18 |
63 |
00 |
2884. 88 |
68 00 |
1301. 16 |
83 |
00 |
586. 97 |
|
8 |
30 |
01.62 |
23 |
30 |
67.57 |
38 |
30 |
38.80 |
53 |
30 |
51.68 |
68 30 |
1762. 33 |
83 |
30 |
45.24 |
|
9 |
00 |
4696. 38 |
24 |
00 |
51.21 |
39 |
00 |
13.14 |
64 |
00 |
18.27 |
69 00 |
23.36 |
84 |
00 |
03. 47 |
|
9 |
30 |
88.89 |
24 |
30 |
34.52 |
39 |
30 |
3687. 18 |
64 |
30 |
2734. 62 |
69 30 |
1684. 24 |
84 |
30 |
461. 66 |
|
10 |
00 |
82.05 |
26 |
00 |
17.51 |
40 |
00 |
60.95 |
55 |
00 |
60.76 |
70 00 |
45.00 |
85 |
00 |
19.81 |
|
10 |
30 |
74.86 |
25 |
30 |
00.17 |
40 |
30 |
34.42 |
65 |
30 |
16.67 |
70 30 |
05.62 |
85 |
30 |
377. 93 |
|
11 |
00 |
67.32 |
26 |
00 |
4282. 50 |
41 |
00 |
07.62 |
56 |
00 |
2682. 37 |
71 00 |
1666. 10 |
86 |
00 |
36.02 |
|
11 |
30 |
59.43 |
26 |
30 |
64. 51 |
41 |
30 |
3580. 54 |
56 |
30 |
47.85 |
71 30 |
26.46 |
86 |
30 |
294. 08 |
|
12 |
00 |
51.20 |
27 |
00 |
46.20 |
42 |
00 |
53.17 |
57 |
00 |
13.13 |
72 00 |
1486. 70 |
87 |
00 |
52.11 |
|
12 |
30 |
42.63 |
27 |
30 |
27.66 |
42 |
30 |
25.54 |
57 |
30 |
2578. 19 |
72 30 |
46.81 |
37 |
30 |
10.12 |
|
13 |
00 |
33.71 |
28 |
00 |
08,61 |
43 |
00 |
3497. 62 |
58 |
00 |
43.05 |
73 00 |
06.31 |
38 |
00 |
168. 12 |
|
13 |
30 |
24.44 |
28 |
30 |
4189. 33 |
43 |
30 |
69.44 |
68 |
30 |
07.70 |
73 30 |
1366. 69 |
88 |
30 |
126. 10 |
|
14 |
00 |
14.82 |
29 |
00 |
69.74 |
44 |
00 |
40. 98 |
59 |
00 |
2472. 16 |
74 00 |
26.46 |
39 |
00 |
84.07 |
|
14 |
30 |
04.87 |
29 |
30 |
49.83 |
44 |
30 |
12.26 |
59 |
30 |
36.42 |
74 30 |
1236. 12 |
39 |
30 |
42.04 |
|
15 |
00 |
4594. 57 |
30 |
00 |
29.60 |
45 |
00 |
3383. 27 |
60 |
00 |
00.48 |
75 00 |
45.68 |
90 |
00 |
00.00 |
AREAS OF QUADEILATERALS.
187
Table XXV. — Areas of quadrilaterals of Earth's surface of 30' extent in latitude and longitude, [Prepared by E. S. "Woodward.]
|
Middle latitude |
Area in |
Middle latitude |
Area in |
Middle latitude |
Area in |
Middle latitude |
Area in |
Middle latitude |
Area in |
Middle latitude |
Area in |
||||||
|
of quad- rilateral. |
square miles. |
of quad- rilateral. |
square mUes. |
of quad- rilateral. |
square miles. |
of quad- rilateral. |
square miles. |
of quad- rilateral. |
square miles. |
of quad- rilateral. |
miles. |
||||||
|
0 |
30 |
1188. 05 |
30 |
30 |
1027. 27 |
60 |
30 |
591. 09 |
0 |
15 |
1188. 08 |
30 |
45 |
1024. 68 |
60 |
45 |
586. 50 |
|
1 |
00 |
1187. 92 |
31 |
00 |
1022. 06 |
61 |
00 |
582. 01 |
0 |
45 |
1188. 00 |
31 |
15 |
1019. 43 |
61 |
15 |
577. 45 |
|
1 |
30 |
1187. 70 |
3; |
30 |
1016. 77 |
61 |
30 |
572. 88 |
1 |
15 |
1187. 82 |
31 |
45 |
1014. 10 |
61 |
45 |
568. 30 |
|
2 |
00 |
1187. 39 |
32 |
00 |
1011. 40 |
62 |
00 |
563. 71 |
1 |
45 |
1187. 56 |
32 |
15 |
1008. 69 |
62 |
15 |
559. 11 |
|
3 |
30 |
1186. 99 |
32 |
30 |
1005,96 |
62 |
30 |
554.49 |
2 2 |
15 45 |
1187. 20 1186. 76 |
32 |
45 |
1003. 20 |
62 |
45 |
549. 86 |
|
3 |
00 |
1186. 51 |
33 |
00 |
1000.43 |
63 |
00 |
545.23 |
3 |
15 |
1186. 24 |
33 |
15 |
997.64 |
63 |
15 |
540. 58 |
|
3 |
30 |
1185. 95 |
33 |
30 |
994. 83 |
63 |
30 |
635. 92 |
3 |
45 |
1185. 62 |
33 |
46 |
993.00 |
63 |
45 |
531. 25 |
|
i |
00 |
1185. 28 |
34 |
00 |
989. 16 |
64 |
00 |
526. 57 |
4 |
15 |
1184. 92 |
34 |
15 |
986. 29 |
64 |
15 |
621. 88 |
|
4 |
30 |
1184. 53 |
34 |
30 |
983.41 |
64 |
30 |
517.17 |
4 |
45 |
1184. 13 |
34 |
45 |
980. 50 |
64 |
45 |
512. 46 |
|
5 |
00 |
1183. 70 |
35 |
00 |
977. 58 |
65 |
00 |
507. 74 |
5 |
15 |
1183.24 |
35 |
15 |
974. 64 |
65 |
16 |
503. 01 |
|
5 |
30 |
1182.77 |
35 |
30 |
971. 68 |
65 |
30 |
498. 26 |
5 |
45 |
1182. 28 |
35 |
45 |
968. 70 |
65 |
45 |
493, 51 |
|
6 |
00 |
1181. 76 |
36 |
00 |
965. 70 |
66 |
00 |
488. 75 |
6 |
15 |
1181. 22 |
36 |
15 |
962. 68 |
66 |
16 |
483. 97 |
|
6 |
30 |
1180. 66 |
36 |
30 |
959. 65 |
66 |
30 |
479. 19 |
6 |
45 |
1180. 08 |
36 |
45 |
956. 60 |
66 |
45 |
474, 40 |
|
7 |
00 |
1179. 48 |
37 |
00 |
953.52 |
67 |
00 |
469. 60 |
7 |
15 |
1178. 85 |
37 |
15 |
950. 43 |
67 |
15 |
464. 78 |
|
7 |
30 |
1178. 20 |
37 |
30 |
947.32 |
67 |
30 |
459. 96 |
7 |
45 |
1177. 53 |
37 |
46 |
944. 21 |
67 |
45 |
455. 13 |
|
8 |
00 |
1176. 84 |
38 |
00 |
941.05 |
68 |
00 |
450. 29 |
8 |
16 |
1176. 13 |
38 |
15 |
937.88 |
67 |
45 |
455.13 |
|
8 |
30 |
1175. 39 |
38 |
30 |
984.71 |
68 |
30 |
440.59 |
8 |
45 |
1174. 63 |
38 |
45 |
931.51 |
68 |
15 |
445.45 |
|
9 |
00 |
1173. 86 |
39 |
00 |
928.29 |
69 |
00 |
430.84 |
9 |
15 |
1173.06 |
39 |
15 |
935. 06 |
68 |
46 |
435. 72 |
|
9 |
30 |
1173. 23 |
39 |
30 |
921. SO |
69 |
30 |
421. 06 |
9 |
45 |
1171. 39 |
39 |
45 |
918. 53 |
69 |
15 |
425. 96 |
|
10 |
00 |
1170.52 |
40 |
00 |
915. 25 |
70 |
00 |
411.25 |
10 |
15 |
1169. 63 |
40 |
15 |
911. 94 |
69 |
45 |
416.16 |
|
10 |
30 |
^ 1168. 73 |
40 |
30 |
908. 61 |
70 |
30 |
401. 41 |
10 |
45 |
1167. 80 |
40 |
45 |
905. 27 |
70 |
16 |
406. 34 |
|
11 |
00 |
1166. 84 |
41 |
00 |
901.91 |
71 |
00 |
391. 53 |
11 |
15 |
1165. 86 |
41 |
15 |
898. 64 |
70 |
45 |
396. 47 |
|
11 |
30 |
1164. 86 |
41 |
30 |
895. 14 |
71 |
30 |
381. 62 |
11 |
45 |
1163. 85 |
41 |
45 |
891. 73 |
71 |
15 |
386. 58 |
|
12 |
00 |
1162. 81 |
42 |
00 |
888. 30 |
72 |
00 |
371. 68 |
12 |
15 |
1161. 75 |
42 |
15 |
884.85 |
71 |
45 |
376, 65 |
|
12 |
30 |
1160.67 |
42 |
30 |
881. 39 |
72 |
30 |
361. 71 |
12 |
45 |
1159. 56 |
42 |
45 |
877. 91 |
72 |
15 |
366, 70 |
|
13 |
00 |
1158. 44 |
43 |
00 |
874. 41 |
73 |
00 |
351. 71 |
13 |
15 |
1157. 29 |
43 |
15 |
870. 90 |
72 |
45 |
356.71 |
|
13 |
30 |
1156. 12 |
43 |
30 |
867. 37 |
73 |
30 |
341. 68 |
13 |
45 |
1154. 93 |
43 |
45 |
863. 82 |
73 |
16 |
346. 69 |
|
14 |
00 |
1153.72 |
44 |
00 |
860. 25 |
74 |
00 |
331.62 |
14 |
15 |
1152. 48 |
44 |
15 |
856. 67 |
73 |
45 |
336. 65 |
|
14 |
30 |
1151. 23 |
44 |
30 |
853.07 |
74 |
30 |
321. 53 |
14 |
45 |
1149, 95 |
44 |
45 |
849, 46 |
74 |
16 |
326, 58 |
|
15 |
00 |
1148. 65 |
45 |
00 |
845.82 |
75 |
00 |
311.42 |
15 |
15 |
1147. 33 |
45 |
15 |
842. 18 |
74 |
45 |
316,48 |
|
15 |
30 |
1145.99 |
45 |
30 |
838. 51 |
75 |
30 |
301.28 |
15 |
45 |
1144. 63 |
45 |
45 |
834. 83 |
75 |
15 |
306, 36 |
|
16 |
00 |
1143. 25 |
46 |
00 |
831. 13 |
76 |
00 |
291. 12 |
16 |
15 |
1141. 84 |
46 |
15 |
827.42 |
75 |
45 |
296,21 |
|
16 |
30 |
1140. 41 |
46 |
30 |
823. 68 |
76 |
30 |
280. 94 |
16 |
45 |
1138. 96 |
46 |
45 |
819. 94 |
76 |
15 |
286,04 |
|
17 |
00 |
1137. 50 |
47 |
00 |
816. 18 |
77 |
00 |
270.73 |
17 |
15 |
1136. 00 |
47 |
15 |
812. 40 |
76 |
46 |
275, 84 |
|
17 |
30 |
U34.49 |
47 |
30 |
808. 60 |
77 |
30 |
260. 50 |
17 |
45 |
1132. 96 |
47 |
45 |
804. 79 |
77 |
15 |
265, 62 |
|
18 |
00 |
1131. 41 |
48 |
00 |
800. 97 |
78 |
00 |
250. 25 |
18 |
15 |
1120. 83 |
48 |
15 |
797. 13 |
77 |
45 |
255. 38 |
|
18 |
30 |
1128.24 |
48 |
30 |
793. 27 |
78 |
30 |
239. 98 |
18 |
45 |
1126. 62 |
48 |
45 |
789. 39 |
78 |
15 |
215.12 |
|
19 |
00 |
1124. 98 |
49 |
00 |
785. 50 |
79 |
00 |
229. 68 |
19 |
15 |
1123.32 |
49 |
15 |
781. 60 |
78 |
45 |
234.83 |
|
19 |
30 |
1121.64 |
49 |
30 |
777. 68 |
79 |
30 |
219. 37 |
19 |
45 |
1119. 93 |
49 |
45 |
773. 74 |
79 |
15 |
224.53 |
|
20 |
00 |
1118.21 |
50 |
00 |
769. 79 |
80 |
00 |
209. 05 |
20 |
15 |
1116. 47 |
50 |
15 |
765.83 |
79 |
45 |
214. 21 |
|
20 |
30 |
1114. 71 |
50 |
30 |
761. 85 |
80 |
30 |
198. 70 |
20 |
45 |
1112. 92 |
50 |
45 |
757.85 |
80 |
15 |
203. 88 |
|
21 |
00 |
1111.11 |
51 |
00 |
753. 84 |
81 |
00 |
188.34 |
21 |
15 |
1109, 28 |
51 |
15 |
749. 82 |
80 |
45 |
193. 52 |
|
21 |
30 |
1107.44 |
51 |
30 |
745.78 |
81 |
30 |
177. 96 |
21 |
45 |
1105. 57 |
51 |
45 |
741.72 |
81 |
15 |
183. 15 |
|
22 |
00 |
1103. 68 |
62 |
00 |
737. 65 |
82 |
00 |
167. 57 |
22 |
15 |
1101. 77 |
52 |
15 |
733. 67 |
81 |
45 |
172. 77 |
|
22 |
30 |
1099.84 |
52 |
30 |
729. 47 |
82 |
30 |
157. 16 |
22 |
45 |
1097. 88 |
52 |
45 |
725. 36 |
82 |
15 |
162. 37 |
|
23 |
00 |
1095. 91 |
53 |
00 |
721. 23 |
83 |
00 |
146. 74 |
23 |
15 |
1093. 93 |
53 |
15 |
717. 08 |
82 |
46 |
151.95 |
|
23 |
30 |
1091.90 |
53 |
30 |
712. 93 |
83 |
30 |
136. 31 |
23 |
45 |
1089. 87 |
53 |
45 |
708. 76 |
S3 |
15 |
141. 53 |
|
24 |
00 |
1087. 81 |
54 |
00 |
704. 57 |
84 |
00 |
125. 87 |
24 |
15 |
1085. 74 |
54 |
15 |
700. 38 |
83 |
45 |
131. 09 |
|
24 |
30 |
1083. 64 |
54 |
30 |
696. 16 |
84 |
30 |
115. 42 |
24 |
45 |
1081. 52 |
54 |
45 |
691. 94 |
84 |
15 |
120. 64 |
|
25 |
00 |
1079. 39 |
55 |
00 |
687. 70 |
85 |
00 |
104. 95 |
25 |
15 |
1077. 23 |
55 |
16 |
683.44 |
84 |
45 |
110. 18 |
|
25 |
30 |
1075. 05 |
55 |
30 |
679. 17 |
85 |
30 |
94.48 |
25 |
45 |
1072. 85 |
55 |
45 |
674. 89 |
86 |
15 |
99.72 |
|
26 |
00 |
1070. 64 |
56 |
00 |
670. 60 |
86 |
00 |
84.01 |
26 |
15 |
1068. 40 |
56 |
15 |
666. 29 |
85 |
46 |
89.35 |
|
26 |
30 |
1066. 14 |
56 |
30 |
661.97 |
86 |
30 |
73.52 |
26 |
45 |
1063. 86 |
56 |
45 |
657.64 |
86 |
15 |
78.76 |
|
27 |
00 |
1061. 56 |
57 |
00 |
653. 29 |
87 |
TO |
63.03 |
27 |
15 |
1059. 24 |
57 |
15 |
648.93 |
86 |
45 |
68.37 |
|
27 |
30 |
1056. 90 |
57 |
30 |
644.55 |
87 |
30 |
52.53 |
27 |
45 |
1054. 54 |
57 |
45 |
640. 17 |
87 |
15 |
57.78 |
|
28 |
00 |
1052. 16 |
58 |
00 |
635. 77 |
88 |
00 |
42.03 |
28 |
15 |
1049. 76 |
58 |
15 |
631. 36 |
87 |
45 |
47.28 |
|
28 |
30 |
1047.34 |
58 |
30 |
626. 93 |
88 |
30 |
31.53 |
28 |
45 |
1044. 90 |
58 |
45 |
622.49 |
88 |
15 |
36.78 |
|
29 |
00 |
1U42. 44 |
59 |
00 |
618. 05 |
89 |
00 |
21.02 |
29 |
15 |
1039. 97 |
59 |
15 |
613. 59 |
88 |
45 |
26.27 |
|
29 |
30 |
1037. 47 |
59 |
30 |
609. 11 |
89 |
30 |
10.51 |
29 |
45 |
1034. 95 |
59 |
45 |
604. 62 |
89 |
15 |
16.76 |
|
30 |
00 |
1032. 41 |
60 |
00 |
600. 13 |
90 |
00 |
00.00 |
30 |
15 |
1039. 85 |
60 |
15 |
595. 62 |
89 |
45 |
5.26 |
188
A MANUAL OF TOPOGEAPHIG METHODS.
Table XXVI. — Areas of quadrilaterals of Earth's surface of 16' extent in latitme and longitude. [Prepared by K. S. "Woodward.]
|
Middle latitude of quadri- lateral. |
A.rea in |
Middle latitude |
Area in |
MidcUe latitude |
Area in |
Middle latitude |
Area in |
Middle latitude |
\roa in |
Middle latitude |
Area in |
|
square miles. |
of quadri- lateral. |
square miles. |
of quadri- lateral. |
square mues. |
of quadri- lateral. |
square miles. |
of quadri- lateral. |
square miles. |
of quadri- lateral. |
square miles. |
|
|
0 07 30 |
297.02 |
8 15 00 |
294. 03 |
16 22 30 |
285. 28 |
24 30 00 |
270. 91 |
32 37 30 |
251. 15 |
40 45 00 . |
226. 32 |
|
0 15 00 |
297.02 |
8 22 30 |
293. 94 |
16 30 00 |
285. 10 |
24 37 30 |
270. 65 |
32 45 00 |
250.80 |
40 52 30 |
225. 90 |
|
0 22 30 |
297. 02 |
8 30 00 |
293.85 |
16 37 30 |
284. 92 |
24 45 00 |
270. 38 |
32 52 30 |
250. 45 |
41 00 00 |
225. 48 |
|
0 30 00 |
297. 01 |
8 37 30 |
293. 75 |
16 45 00 |
284. 74 |
24 53 30 |
270.11 |
33 00 00 |
250. 11 |
41 07 30 |
225. 06 |
|
0 37 30 |
297.01 |
8 45 00 |
293. 66 |
16 52 30 |
284. 56 |
25 00 00 , |
269. 85 |
33 07 30 |
249. 76 |
41 15 00 |
224.64 |
|
0 45 00 |
297. 00 |
8 52 30 |
293. 56 |
17 00 00 |
284. 38 |
25 07 30 |
269. 58 |
33 15 00 |
249.41 |
41 22 30 |
224. 21 |
|
0 52 30 |
296. 99 |
9 00 00 |
293.47 |
17 07 30 |
284. 19 |
25 15 00 |
269. 31 |
33 22 30 |
249. 06 |
41 30 00 |
223. 79 |
|
1 00 00 |
296. 98 |
9 07 30 |
293. 37 |
17 15 00 |
284. 00 |
25 22 30 |
269. 04 |
33 30 00 |
248. 71 |
41 37 30 |
223. 36 |
|
1 07 30 |
290. 97 |
9 15 00 |
293. 27 |
17 22 30 |
283. 81 |
25 30 00 |
268. 76 |
33 37 30 |
248. 36 |
41 45 00 |
222. 93 |
|
1 15 00 |
296. 96 |
9 22 30 |
293. 16 |
17 30 00 |
283. 62 |
25 37 30 |
268. 49 |
33 45 00 |
248. 00 |
41 52 30 |
222. 50 |
|
1 22 30 |
296. 94 |
9 30 00 |
293. 06 |
17 37 30 |
283. 43 |
25 45 00 |
268. 21 |
33 52 30 |
247. 65 |
42 00 00 |
222. 08 |
|
1 30 00 |
296. 93 |
9 37 30 |
292.95 |
17 45 00 |
283. 24 |
25 52 30 |
267. 94 |
34 00 00 |
247. 29 |
42 07 30 |
221. 65 |
|
1 37 30 |
296. 91 |
9 45 00 |
292.85 |
17 52 30 |
2S3. 05 |
26 00 00 |
267. 66 |
34 07 30 |
246. 93 |
42 15 00 |
221. 21 |
|
1 45 00 |
296. 89 |
9 52 30 |
292.74 |
18 00 00 |
282. 86 |
26 07 30 |
267. 38 |
34 15 00 |
246. 57 |
42 22 30 |
220. 78 |
|
1 52 30 |
296.87 |
10 00 00 |
292. 63 |
18 07 30 |
282. 66 |
20 15 00 |
267. 10 |
34 22 30 |
246. 21 |
42 30 00 |
220. 35 |
|
2 00 00 |
296. 85 |
10 07 30 |
292. 52 |
18 15 00 |
282. 46 |
26 22 30 |
266.82 |
34 30 00 |
245. 85 |
42 37 30 |
219. 91 |
|
2 07 30 |
296. 82 |
10 15 00 |
292.41 |
18 22 30 |
282. 26 |
26 30 00 |
266. 54 |
34 37 30 |
245. 49 |
42 45 00 |
219. 48 |
|
2 15 00 |
296. 80 |
10 22 30 |
292. 30 |
18 30 00 |
282. 06 |
26 37 30 |
266. 25 |
34 45 00 |
245. 13 |
42 52 30 |
219. 04 |
|
2 22 30 |
296. 77 |
10 30 00 |
292. 19 |
18 37 30 |
281. 86 |
26 45 00 |
265. 97 |
34 -52 30 |
244.76 |
43 00 00 |
218. 60 |
|
2 30 00 |
296. 75 |
10 37 30 |
292. 07 |
18 45 00 |
281.66 |
26 52 30 |
265. 68 |
35 00 00 |
244. 40 |
43 07 30 |
218. 10 |
|
2 37 30 |
296. 72 |
10 45 00 |
291. 95 |
18 52 30 |
281.45 |
27 00 00 ' 265. 39 |
35 07 30 |
244.03 |
43 15 00 |
217. 73 |
|
|
2 45 00 |
296. 69 |
10 52 30 |
291. 83 |
19 00 00 |
281. 25 |
27 07 30 |
265. 10 |
35 15 00 |
243. 06 |
43 22 30 |
217. 28 |
|
2 52 30 |
296. 66 |
11 00 00 |
291. 71 |
19 07 30 |
281. 04 |
27 15 00 |
264. 81 |
35 22 30 |
243. 29 |
43 30 00 |
216.84 |
|
3 00 00 |
296. 63 |
11 07 30 |
291.59 |
19 15 00 |
280. 83 |
27 22 30 |
264.52 |
35 30 00 |
242. 92 |
43 37 30 |
216. 40 |
|
3 07 30 |
296. 60 |
U 15 00 |
291.47 |
19 22 30 |
280. 62 |
27 30 00 |
264. 23 |
35 37 30 |
242.55 |
43 45 00 |
215. 96 |
|
3 15 00 |
296. 56 |
11 22 30 |
291. 34 |
19 30 00 |
280. 41 |
27 37 30 |
263. 93 |
35 45 00 |
242.18 |
43 52 30 |
215. 51 |
|
3 22 30 |
296. 53 |
11 30 00 |
291. 22 |
19 37 30 |
280. 20 |
27 45 00 |
263. 64 |
35 52 30 |
241. 80 |
44 00 00 |
215. 06 |
|
3 30 00 |
296.49 |
11 37 30 |
291. 09 |
19 45 00 |
279. 99 |
27 52 30 |
263. 34 |
36 00 00 |
241.43 |
44 07 30 |
214. 61 |
|
3 37 30 |
296.45 |
11 45 00 |
290. 96 |
19 52 30 |
279. 77 |
28 00 00 |
263. 04 |
36 07 30 |
241. 05 |
44 15 00 |
214. 17 |
|
3 45 00 |
296,41 |
11 52 30 |
290. 83 |
20 00 00 |
279. 55 |
28 07 30 |
262. 74 |
36 15 00 |
240. 67 |
44 22 30 |
213. 72 |
|
3 52 30 |
296. 36 |
12 00 00 |
290. 70 |
20 07 30 |
279. 34 |
28 15 00 ' 262. 44 |
36 22 30 |
240. 29 |
44 30 00 |
213. 27 |
|
|
4 00 00 |
296. 32 |
12 07 30 |
290.57 |
20 15 00 |
279. 12 |
28 22 30 262. 14 |
36 30 00 |
239. 91 |
44 37 30 |
212. 82 |
|
|
4 07 30 296. 28 |
12 15 00 |
290.44 |
20 22 30 |
278. OQ |
28 30 00 1 261. 84 |
36 37 30 |
239. 53 |
44 45 00 |
212. 37 |
||
|
4 15 00 |
296. 23 |
12 22 30 |
290. 30 |
20 30 00 |
278. 68 |
28 37 30 |
261. 53 |
36 45 00 |
239. 15 |
44 52 30 |
211.91 |
|
4 22 30 |
296. 18 |
12 30 00 |
290. 17 |
20 37 30 |
278. 46 |
28 45 00 |
261. 23 |
36 52 30 |
238. 77 |
45 00 00 |
211. 46 |
|
4 30 00 |
296. 13 |
12 37 30 |
290. 03 |
20 45 00 |
278. 23 |
28 52 30 |
260. 92 |
37 00 00 |
238. 38 |
45 07 30 |
211.00 |
|
4 37 30 |
296. 08 |
12 45 00 |
289. 89 |
20 52 30 |
278.00 |
29 00 00 |
260. 01 |
37 07 30 |
237. 99 |
45 15 00 |
210. 55 |
|
4 45 00 |
296. 03 |
12 52 30 |
289. 75 |
21 00 00 |
277. 78 |
29 07 30 |
260. 30 |
37 15 00 |
237. 61 |
45 22 30 |
210. 09 |
|
4 52 30 |
295. 98 |
13 00 00 |
289. 61 |
21 07 30 |
277. 55 |
29 15 00 |
259. 99 |
37 22 30 |
237. 22 |
45 30 00 |
209. 63 |
|
5 00 00 |
295. 93 |
13 07 30 |
289.47 |
21 15 00 |
277. 32 |
29 22 30 |
259. 68 |
37 30 00 |
236. 83 |
45 37 30 |
209. 17 |
|
5 07 30 |
295. 87 |
13 15 00 |
289. 33 |
21 22 30 |
277. 09 |
29 3i) 00 |
259. 37 |
37 37 30 |
236. 44 |
45 45 00 |
208. 71 |
|
5 15 00 |
295. 81 |
13 22 30 |
289. 18 |
21 30 00 |
276. 86 |
29 37 30 |
259. 05 |
37 45 00 |
236. 05 |
45 52 30 |
208. 25 |
|
5 22 30 |
295.75 |
13 30 00 |
289. 03 |
21 37 30 |
276. 63 |
29 45 00 |
258. 74 |
37 52 30 |
235. 60 |
46 00 00 |
207. 78 |
|
5 30 00 |
295. 69 |
13 37 30 |
288. 88 |
21 45 00 |
276. 39 |
29 52 30 |
258. 42 |
38 00 00 |
235. 26 |
46 07 30 |
207. 32 |
|
5 37 30 |
295. 63 |
13 45 00 |
288. 73 |
21 52 30 |
276. 16 |
30 00 00 |
258. 10 |
38 07 30 |
234. 87 |
46 15 00 |
206. 86 |
|
5 45 00 |
295. 57 |
13 52 30 |
288. 58 |
22 00 00 |
275. 92 |
30 07 30 |
257. 78 |
38 15 00 |
234.47' |
46 22 30 |
206. 39 |
|
5 52 30 |
295. 51 |
14 00 00 |
288. 43 |
22 07 30 |
275. 68 |
30 15 OO |
257. 46 |
38 22 30 |
234. 07 |
46 30 00 |
205. 92 |
|
6 00 00 |
295.44 |
14 07 30 |
288. 28 |
22 15 00 |
275.44 |
30 22 30 |
257. 14 |
38 30 00 |
233. 68 |
46 37 30 |
205. 45 |
|
6 07 30 |
295. 37 |
14 15 00 |
288. 12 |
22 22 30 |
275. 20 |
30 30 00 |
256. 82 |
38 37 30 |
233. 28 |
46 45 00 |
204. 99 |
|
6 15 00 |
295. 31 |
14 22 30 |
287.96 |
22 30 00 |
274. 96 |
30 37 30 |
256. 49 |
38 45 00 |
232. 88 |
46 52 30 |
204. 52 |
|
6 22 30 |
295.24 |
14 32 CO |
287. 81 |
22 37 30 |
274. 72 |
30 45 00 |
256. 17 |
38 52 30 |
232. 48 |
47 00 00 |
204. 05 |
|
6 30 00 |
295. 17 |
14 37 30 |
287. 65 |
22 45 00 |
247.47 |
30 52 30 |
255. 84 |
39 00 00 ; 232. 07 |
47 07 30 |
203. 57 |
|
|
6 37 30 |
295. 09 |
14 45 00 |
287. 49 |
22 52 30 |
274. 22 |
31 00 00 |
255. 52 |
39 07 30 |
231. 67 |
47 15 00 |
203. 10 |
|
6 45 00 |
295. 02 |
14 52 30 |
287. 33 |
23 00 00 |
273. 98 |
31 07 30 |
255. 19 |
39 15 00 |
231. 27 |
47 22 30 |
202. 63 |
|
6 52 30 |
294. 95 |
15 00 00 |
287. 17 |
23 07 30 |
273. 73 |
31 15 00 |
254. 86 |
39 22 30 |
230. 86 |
47 30 00 |
202. 15 |
|
7 00 00 |
294. 87 |
15 07 30 |
287. 00 |
23 15 00 |
273.48 |
31 22 30 |
254. 53 |
39 30 00 |
230.45 |
47 37 30 |
201. 67 |
|
7 07 30 |
294. 79 |
15 15 00 |
286. 83 |
23 22 30 |
273. 23 |
31 30 00 |
254. 19 |
39 37 30 |
230. 04 |
47 45 00 |
201. 20 |
|
7 15 00 |
294. 71 |
15 22 30 |
286. 67 |
23 30 00 |
2T2. 98 |
31 37 30 |
253. 86 |
39 45 00 |
229. 03 |
47 52 30 |
200. 72 |
|
7 22 30 |
294. 63 |
15 30 00 |
286. 50 |
23 37 30 |
272. 72 |
31 45 00 |
253. 53 |
39 52 30 |
229. 22 |
48 00 00 |
200. 24 |
|
7 30 00 |
294. 55 |
15 37 30 |
286. 33 |
23 45 00 |
272.47 |
31 52 30 |
253. 19 |
40 00 00 |
228. 81 |
48 07 30 |
199. 76 |
|
7 37 30 |
294. 47 |
15 45 00 |
286. 16 |
23 52 30 |
272. 21 |
32 00 00 |
252. 85 |
40 07 30 |
228. 40 |
48 15 00 |
199. 28 |
|
7 45 00 |
294. 39 |
15 52 30 |
285. 99 |
24 00 00 |
271. 95 |
32 07 30 |
252. 51 |
40 15 00 |
227. 99 |
48 22 30 |
198.80 |
|
7 52 30 |
294. 30 |
10 00 00 |
285. 82 |
24 07 30 |
271.69 |
32 15 00 |
252. 17 |
40 22 30 |
227. 57 |
48 30 00 |
198. 32 |
|
8 00 00 |
294. 21 |
16 07 30 |
285. 64 |
24 15 00 |
271. 44 |
32 22 30 |
251. 83 |
40 30 00 |
227. 15 |
48 37 30 |
197. 83 |
|
8 07 30 |
294. 12 |
16 15 00 |
285. 46 |
24 22 30 |
271. 17 |
32 30 00 |
251. 49 |
40 37 30 |
226. 73 |
48 45 00 |
197. 35 |
AEEAS OF QUADRILATERALS.
189
Table XSVI. Areas of qitadrilaterals of Earth's surface of 15' extent in latitude and longitude — Cont'd.
[Prepared by E. S. "Woodward.]
|
Middle latitude of quadri- lateral. |
ireain square) milea. |
Middle latitude of quadri- lateral. |
A.rea in square miles. |
MidiUe latitude of quadri- lateral. |
Alreaiu square miles. |
Middle Latitude of quadri- lateral. |
Arcaiu square miles. |
Middle latitudi' of ciuadri- latfral. |
A.rea in square miles. |
Middle latitude of quadri- lateral. |
Area in square miles. 35.38 |
|
|
48 52 30 |
196. 86 |
55 45 00 |
168. 72 |
62 37 30 |
138.04 |
69 30 00 |
105. 27 |
76 22 30 |
70.87 |
83 15 00 |
||
|
49 00 00 |
196. 38 |
55 52 30 |
153. 19 |
62 45 00 |
137. 47 |
69 37 30 |
104. 65 |
76 30 00 |
70.24 |
83 23 30 |
34.73 |
|
|
49 07 30 |
195. 89 |
56 00 00 |
167. 65 |
63 52 30 |
136. 89 |
69 45 00 |
104. 04 |
76 37 30 |
69.60 |
83 30 00 |
34.08 |
|
|
49 15 00 |
195. 40 |
56 07 30 |
167. 11 |
63 on 00 |
136. 31 |
69 52 30 |
103. 43 |
76 46 00 |
68.96 |
83 37 30 |
33.42 |
|
|
49 22 30 |
194. 91 |
56 15 00 |
166. 57 |
03 07 30 |
136. 73 |
70 00 00 |
102. 81 |
76 52 30 |
68.32 |
83 45 00 |
32.77 |
|
|
49 30 00 |
194. 42 |
56 23 30 |
106. 03 |
63 15 00 |
135. 15 |
70 07 30 |
102. 20 |
77 00 00 |
67.68 |
83 52 30 |
33.12 |
|
|
49 37 30 |
193. 93 |
56 30 00 |
165. 49 |
63 22 30 |
134. 66 |
70 15 00 |
101. 59 |
77 07 30 |
67.04 |
84 00 00 |
31.47 |
|
|
49 45 00 |
193. 44 |
56 37 30 |
164.95 |
63 30 00 |
133. 98 |
70 22 30 |
100. 97 |
77 15 00 |
66.41 |
84 07 30 |
30.81 |
|
|
49 52 30 |
192. 94 |
56 45 00 |
164. 41 |
63 37 30 |
133. 40 |
70 30 00 |
100. 35 |
77 22 30 |
65.77 |
84 15 00 |
30.16 |
|
|
50 00 00 |
192. 45 |
56 52 30 |
163. 87 |
63 45 00 |
132. 81 |
70 37 30 |
99.74 |
77 30 00 |
65.13 |
84 23 30 |
29.51 |
|
|
50 07 30 |
191.95 |
57 00 00 |
163. 32 |
63 52 30 |
132.33 |
70 45 00 |
99.13 |
77 37 30 |
64.49 |
84 30 00 |
28.86 |
|
|
50 15 00 |
191.46 |
57 07 30 |
162. 78 |
64 00 00 |
131. 64 |
70 52 30 |
98.50 |
77 45 00 |
63.86 |
84 37 30 |
28.20 |
|
|
50 22 30 |
190. 96 |
57 15 00 |
162. 23 |
64 07 30 |
131. 06 |
71 00 00 |
97.88 |
77 52 30 |
63.20 |
84 46 00 |
37.54 |
|
|
50 30 00 |
190. 46 |
57 22 30 |
161. 68 |
64 15-00 |
130. 47 |
71 07 30 |
97.36 |
78 00 00 |
62.56 |
84 52 30 |
36.89 |
|
|
60 37 30 |
1S9. 96 |
57 30 00 |
161. 14 |
64 22 30 |
129. 88 |
71 15 00 |
96.65 |
78 07 30 |
61.92 |
85 00 00 |
26.24 |
|
|
50 45 00 |
189. 46 |
57 37 30 |
160. 59 |
64 30 00 |
129. 29 |
71 22 30 |
96.03 |
78 15 00 |
61.28 |
85 07 30 |
25.58 |
|
|
50 52 30 |
188. nii |
57 45 00 |
160. 04 |
64 37 30 |
128. 70 |
71 30 00 |
95.41 |
78 22 30 |
60.64 |
85 15 00 |
24.93 |
|
|
51 00 00 |
188.40 |
■ 57 52 30 |
159.49 |
64 45 00 |
128. 12 |
71 37 30 |
94.78 |
78 30 00 |
60.00 |
85 22 30 |
34.37 |
|
|
51 07 30 |
187. 96 |
58 00 00 |
158. 94 |
64 52 30 |
137. 53 |
71 46 00 |
94.16 |
78 37 30 |
59.35 |
85 30 00 |
23.62 |
|
|
51 15 00 |
187. 46 |
58 07 30 |
158. 39 |
65 00 00 |
126. 94 |
71 52 30 |
93.54 |
78 45 00 |
68.71 |
85 37 30 |
22.97 |
|
|
51 22 30 |
186. 95 |
58 15 00 |
157. 84 |
65 07 30 |
126. 34 |
72 00 00 |
92.92 |
78 62 30 |
58.06 |
85 45 00 |
22.31 |
|
|
51 30 00 |
186. 45 |
58 22 30 |
157. 29 |
65 16 00 |
125. 75 |
72 07 30 |
93.30 |
79 00 00 |
57.43 |
85 52 30 |
21.66 |
|
|
51 37 30 |
185. 94 |
58 30 00 |
156. 73 |
65 23 30 |
125. 16 |
72 15 00 |
91.68 |
79 07 30 |
56.78 |
86 00 00 |
21.00 |
|
|
51 45 00 |
185, 43 |
58 37 30 |
156. 18 |
65 30 00 |
124. 57 |
72 32 30 |
91.05 |
•79 15 00 |
56.13 |
86 07 30 |
20.35 |
|
|
51 52 30 |
184. 92 |
58 45 00 |
155. 63 |
65 37 30 |
123. 97 |
72 30 00 |
90.43 |
79 22 20 |
55.49 |
86 15 00 |
19.69 |
|
|
52 00 00 |
184. 41 |
58 52 30 |
155. 07 |
65 45 00 |
123. 38 |
72 37 30 |
89.80 |
79 30 00 |
54.84 |
86 22 30 |
19.04 |
|
|
52 07 30 |
183. 90 |
59 00 00 |
154. 51 |
65 52 30 |
123, 78 |
73 46 00 |
89.18 |
79 37 30 |
54.20 |
86 30 00 |
18.38 |
|
|
52 15 00 |
183. 39 |
69 07 30 |
153. 96 |
66 00 00 |
122. 19 |
72 52 30 |
88.55 |
79 45 00 |
63.55 |
86 37 30 |
17.73 |
|
|
52 22 30 |
182 88 |
59 15 00 |
153. 41 |
66 07 30 |
121. 59 |
73 00 00 |
87.93 |
79 52 30 |
52.91 |
86 45 00 |
17.07 |
|
|
52 30 00 |
182.37 |
59 22 30 |
152. 84 |
66 15 00 |
120. 99 |
73 07 30 |
87.30 |
80 00 00 |
52.26 |
86 52 30 |
16.41 |
|
|
52 37 30 |
181. 85 |
59 30 00 |
152. 28 |
66 22 30 |
120. 40 |
73 16 00 |
86.67 |
80 07 30 |
51.63 |
87 00 00 |
15.76 |
|
|
52 45 00 |
181. 34 |
59 37 30 |
151. 72 |
66 30 00 |
U9.80 |
73 22 30 |
86.05 |
80 15 00 |
50.97 |
87 07 30 |
16.10 |
|
|
52 52 30 |
180. S2 |
59 45 00 |
151. 16 |
66 37 30 |
119. 20 |
'73 30 00 |
85.43 |
80 22 30 |
50.32 |
87 15 00 |
14.44 |
|
|
53 00 00 |
180. 31 |
59 52 30 |
150. 60 |
66 45 00 |
118. 60 |
73 37 30 |
84.79 |
80 30 00 |
49.68 |
87 22 30 |
13.79 |
|
|
53 07 30 |
179. 79 |
60 00 00 |
150. 03 |
66 52 30 |
118. 00 |
73 45 00 |
84.16 |
80 37 30 |
49.03 |
87 30 00 |
13.13 |
|
|
53 15 00 |
179. 27 |
60 07 30 |
149. 47 |
67 00 00 |
117. 40 |
73 52 30 |
83.53 |
80 46 00 |
48.38 |
87 37 30 |
12.48 |
|
|
53 22 30 |
178. 75 |
60 15 00 |
148. 91 |
67 07 30 |
116.80 |
74 00 00 |
82.91 |
80 52 30 |
47.73 |
87 45 00 |
11.82 |
|
|
53 30 00 |
178. 23 |
60 23 30 |
148. 34 |
67 15 00 |
116.20 |
74 07 30 |
83.38 |
81 00 00 |
47.08 |
87 52 30 |
11.16 |
|
|
53 37 30 |
177.71 |
60 30 00 |
147. 77 |
67 22 30 |
115. 59 |
74 16 00 |
81.65 |
81 07 30 |
46.44 |
88 00 00 |
10.51 |
|
|
53 45 00 |
177. 19 |
60 37 30 |
147. 21 |
67 30 00 |
114. 99 |
74 22 30 |
81.01 |
81 15 00 |
45.79 |
88 07 30 |
9.85 |
|
|
53 52 30 |
176. 67 |
60 45 00 |
146. 64 |
67 37 30 |
114. 39 |
74 30 00 |
80.38 |
81 22 30 |
45.14 |
88 15 00 |
9.20 |
|
|
54 00 00 |
176. 14 |
60 52 30 |
146. 07 |
67 45 00 |
113. 78 |
74 37 30 |
79.75 |
81 30 00 |
44.49 |
88 22 30 |
8.54 |
|
|
54 07 30 |
175. 62 |
61 00 00 |
145. 50 |
67 52 30 |
113.18 |
74 45 00 |
79.12 |
81 37 30 |
43.84 |
88 30 00 |
7.88 |
|
|
54 15 00 |
175. 10 |
61 07 30 |
144.93 |
68 00 00 |
112.57 |
74 53 30 |
78.49 |
81 45 00 |
43.19 |
88 37 30 |
7.22 |
|
|
54 22 30 |
174. 57 |
61 15 00 |
144. 36 |
68 07 30 |
111. 97 |
75 00 00 |
77.86 |
81 53 30 |
42.64 |
88 45 00 |
6.57 |
|
|
54 30 00 |
174. 04 |
61 22 30 |
143. 79 |
68 15 00 |
111.36 |
76 07 30 |
77.22 |
82 00 00 |
41.89 |
88 53 30 |
5.91 |
|
|
54 37 30 |
173. 51 |
61 30 00 |
143. 22 |
68 22 30 |
110. 76 |
75 16 00 |
76.59 |
82 07 30 |
41.24 |
89 00 00 |
6.36 |
|
|
54 45 00 |
172. 99 |
' 61 37 30 |
142. 65 |
68 30 00 |
110. 15 |
76 22 30 |
75.95 |
82 15 00 |
40.59 |
89 07 30 |
4.60 |
|
|
54 52 30 |
172. 46 |
61 47 00 |
142. 08 |
63 37 30 |
109. 54 |
75 30 00 |
75.33 |
82 22 30 |
39.94 |
89 15 00 |
3.94 |
|
|
55 00 00 |
171. 93 |
61 52 30 |
141. 50 |
68 45 00 |
108. 93 |
75 37 30 |
74.69 |
83 30 00 |
39.29 |
89 22 30 |
8.28 |
|
|
55 07 30 |
171. 39 |
i 62 00 00 |
140. 93 |
68 52 30 |
108. 32 |
75 45 00 |
74.05 |
83 37 30 |
38.64 |
89 30 00 |
2.63 |
|
|
55 15 00 |
170. 86 |
63 07 30 |
140. 35 |
69 00 00 |
107. 71 |
75 52 30 |
73.42 |
83 45 00 |
37.99 |
89 37 30 |
1.97 |
|
|
55 22 30 |
170. 33 |
62 15 00 |
139. 78 |
69 07 30 |
107. 10 |
76 00 00 |
72.78 |
82 52 30 |
37.34 |
89 45 00 |
1.31 |
|
|
55 30 00 |
169. 79 |
1 62 22 30 |
139. 20 |
69 15 00 |
106. 49 |
76 07 30 |
72.14 |
83 00 00 |
36.69 |
89 52 30 |
0.66 |
|
|
55 37 30 |
169. 26 |
1 62 30 00 |
138. 62 |
69 22 30 |
105. 88 |
76 15 00 |
71.61 |
83 07 30 |
36.03 |
190 A MANUAL OF TOPOGEAPHIC METHODS.
TA.BLE XXVII.— fitf/ofs /or the compuiation of (jeodetic latitudes, longittides, and azimuths.
[From Appendix No. 7, Kcport U. S. Crast and Geodetic Survey, 1884.]
LATITUDE 25^.
log. A
log. B
Iditt. 1" = — 0.06 diff.l" = — 0.16
log.C diff.l" = + 0.54
log. D log. E
diff. 1" = +0.03 diff. 1" = + 0.04
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 191
Table XXVXI. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 26°.
|
log. A |
log. B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
(liflF.l" = -0.06 |
diff. 1"— — 0.17 |
diff. 1"= +0.53 |
diff. l" = +0.03 |
diff. 1"= +0.04 |
|
|
26 00 |
8. 509 4439 |
8. 511 8283 |
1. 09400 |
2.2885 |
5. 8458 |
|
1 |
36 |
72 |
432 |
87 |
61 |
|
33 |
62 |
464 |
89 |
63 |
|
|
3 |
29 |
52 |
496 |
91 |
66 |
|
4 |
26 |
42 |
527 |
93 |
69 |
|
05 |
22 |
32 |
559 |
95 |
71 |
|
6 |
19 |
32 |
691 |
97 |
74 |
|
7 |
IG |
12 |
633 |
99 |
77 |
|
8 |
12 |
01 |
655 |
2. 2901 |
79 |
|
9 |
09 |
8. 5U 8191 |
687 |
03 |
82 |
|
10 |
8. 509 4406 |
8.511 818! |
1.09718 |
2. 2905 |
6.8485 |
|
11 |
02 |
71 |
750 |
07 |
88 |
|
12 |
8. 509 4399 |
61 |
782 |
09 |
90 |
|
la |
95 |
51 |
814 |
11 |
93 |
|
14 |
92 |
40 |
845 |
13 |
96 |
|
15 |
88 |
30 |
877 |
15 |
98 |
|
16 |
85 |
20 |
909 |
17 |
5. 8501 |
|
17 |
82 |
10 |
940 |
19 |
04 |
|
18 |
78 |
00 |
972 |
20 |
06 |
|
19 |
8. 511 8089 |
1. 10004 |
22 |
09 |
|
|
20 |
8. 509 4372 |
8. 511 8079 |
1. 10036 |
2. 2924 |
6. 8512 |
|
21 |
08 |
69 |
067 |
26 |
14 |
|
22 |
65 |
59 |
099 |
28 |
17 |
|
23 |
61 |
48 |
130 |
30 |
20 |
|
24 |
58 |
38 |
162 |
32 |
22 |
|
25 |
54 |
28 |
194 |
34 |
25 |
|
26 |
51 |
18 |
225 |
36 |
28 |
|
27 |
48 |
08 |
257 |
38 |
30 |
|
28 |
44 |
8. 611 7997 |
288 |
40 |
33 |
|
29 |
41 |
87 |
820 |
42 |
36 |
|
30 |
8. 609 4337 |
8. 611 7977 |
1. 10351 |
2.2944 |
5. 8539 |
|
31 |
34 |
67 |
383 |
46 |
41 |
|
32 |
31 |
56 |
• 414 |
47 |
44 |
|
33 |
27 |
46 |
446 |
49 |
47 |
|
34 |
24 |
36 |
477 |
51 |
49 |
|
35 |
20 |
25 |
609 |
53 |
52 |
|
36 |
17 |
15 |
540 |
55 |
55 |
|
37 |
13 |
05 |
571 |
57 |
57 |
|
38 |
10 |
8. 511 7895 |
603 |
69 |
60 |
|
39 |
07 |
84 |
634 |
61 |
63 |
|
40 |
8. 509 4303 |
8. 511 7874 |
1. 10666 |
2. 2963 |
5. 8566 |
|
41 |
00 |
64 |
697 |
65 |
68 |
|
42 |
8. 509 4296 |
53 |
728 |
66 |
71 |
|
43 |
93 |
43 |
760 |
68 |
74 |
|
44 |
89 |
33 |
791 |
70 |
76 |
|
45 |
86 |
22 |
832 |
72 |
79 |
|
46 |
83 |
12 |
854 |
74 |
82 |
|
47 |
79 |
02 |
885 |
76 |
85 |
|
48 |
76 |
8. 511 7791 |
9J6 |
78 |
87 |
|
49 |
73 |
81 |
947 |
80 |
90 |
|
50 |
8. 609 4269 |
8. 511 7771 |
1. 10979 |
2.3981 |
5. 8593 |
|
51 |
05 |
60 |
1. 11010 |
83 |
95 |
|
52 |
62 |
50 |
041 |
85 |
98 |
|
53 |
5S |
40 |
073 |
87 |
5.8601 |
|
54 |
66 |
29 |
103 |
89 |
04 |
|
55 |
52 |
19 |
134 |
91 |
06 |
|
56 |
48 |
09 |
166 |
93 |
09 |
|
57 |
46 |
8.511 7698 |
197 |
94 |
12 |
|
58 |
41 |
88 |
228 |
96 |
14 |
|
59 |
38 |
77 |
259 |
98 |
17 |
|
60 |
8. 509 4234 |
8. 511 7667 |
1. 11290 |
2.3000 |
5. 8630 |
192
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic lalituclcs, longitudes, and azimuths — Coutinued,
LATITUDE 27°.
|
log. A |
log. B |
log. C |
log. D |
log. E |
||
|
latitude. |
||||||
|
difl'. 1"=— 0.06 |
diir.l"=-0.18 |
diff. 1"=+0.51 |
diff.l"=+0.03 |
diff. 1"= +0.05 |
||
|
27 00 |
8. 509 4234 |
8.511 7667 |
1. 11290 |
2. 3000 |
5. 8620 |
|
|
1 |
31 |
57 |
321 |
02 |
23 |
|
|
2 |
27 |
46 |
352 |
04 |
25 |
|
|
3 |
24 |
36 |
383 |
06 |
28 |
|
|
4 |
20 |
25 |
414 |
07 |
31 |
|
|
5 |
17 |
15 |
445 |
09 |
34 |
|
|
6 |
13 |
05 |
476 |
11 |
36 |
|
|
7 |
10 |
8. 511 7594 |
507 |
13 |
39 |
|
|
8 |
06 |
84 |
538 |
15 |
42 |
|
|
9 |
03 |
73 |
569 |
17 |
44 |
|
|
10 |
8. 509 4200 |
8. 511 7563 |
1. 11600 |
2.3018 |
5. 8647 |
|
|
11 |
8. 509 4196 |
53 |
631 |
20 |
50 |
|
|
12 |
93 |
42 |
662 |
22 |
53 |
|
|
13 |
89 |
32 |
693 |
24 |
55 |
|
|
14 |
86 |
21 |
724 |
26 |
58 |
|
|
15 |
82 |
11 |
755 |
27 |
01 |
|
|
36 |
79 |
00 |
786 |
29 |
64 |
|
|
17 |
75 |
8. 511 7490 |
817 |
31 |
66 |
|
|
18 |
79 |
848 |
33 |
69 |
||
|
19 |
68 |
69 |
878 |
35 |
72 |
|
|
20 |
8.509 4165 |
8. 511 7458 |
1. 11909 |
2. 3037 |
5. 8675 |
|
|
21 |
61 |
48 |
940 |
38 |
77 |
|
|
22 |
58 |
37 |
971 |
40 |
80 |
|
|
23 |
54 |
27 |
1. 12002 |
42 |
83 |
|
|
24 |
51 |
16 |
032 |
44 |
86 |
|
|
25 |
47 |
06 |
063 |
45 |
88 |
|
|
26 |
44 |
8. 511 7395 |
094 |
47 |
91 |
|
|
27 |
40 |
85 |
125 |
49 |
94 |
|
|
28 |
37 |
74 |
156 |
51 |
97 |
|
|
29 |
33 |
64 |
186 |
63 |
99 |
|
|
30 |
8. 509 4130 |
8. 511 7353 |
1. 12217 |
2. 3054 |
5. 8702 |
|
|
31 |
26 |
43 |
248 |
66 |
05 |
|
|
32 |
23 |
32 |
278 |
58 |
08 |
|
|
33 |
19 |
22 |
' 309 |
60 . |
10 |
|
|
34 |
16 |
11 |
340 |
61 |
13 |
|
|
35 |
12 |
01 |
370 |
63 |
16 |
|
|
36 |
08 |
8. 511 7290 |
401 |
65 |
19 |
|
|
37 |
05 |
80 |
482 |
67 |
22 |
|
|
38 |
01 |
69 |
462 |
69 |
24 |
|
|
39 |
8. 509 4098 |
58 |
493 |
70 |
27 |
|
|
40 |
8.509 4094 |
8. 511 7248 |
1.12523 |
2. 3072 |
5. 8730 |
|
|
41 |
91 |
37 |
554 |
74 |
33 |
|
|
42 |
87 |
27 |
584 |
76 |
35 |
|
|
43 |
84 |
16 |
615 |
77 |
38 |
|
|
44 |
80 |
06 |
646 |
79 |
41 |
|
|
45 |
77 |
8. 511 7195 |
676 |
81 |
44 |
|
|
46 |
73 |
84 |
707 |
83 |
46 |
|
|
47 |
70 |
74 |
737 |
84 |
49 |
|
|
48 |
66 |
63 |
768 |
86 |
52 |
|
|
49 |
63 |
53 |
798 |
88 |
55 |
|
|
50 |
8. 509 4059 |
8. 511 7142 |
1.12829 |
2. 3090 |
5. 8757 |
|
|
51 |
56 |
31 |
859 |
91 |
60 |
|
|
.52 |
52 |
21 |
889 |
93 |
63 |
|
|
53 |
49 |
10 |
920 |
95 |
66 |
|
|
54 |
45 |
00 |
950 |
96 |
69 |
|
|
55 |
41 |
8.511 7089 |
981 |
98 |
72 |
|
|
56 |
38 |
78 |
1. 13011 |
2. 3100 |
74 |
|
|
57 |
34 |
68 |
■ 041 |
02 |
77 |
|
|
58 |
31 |
57 |
072 |
03 |
80 |
|
|
59 |
27 |
46 |
102 |
05 |
83 |
|
|
60 |
8. 509 4024 |
8. 511 7036 |
1. 13132 |
2.3107 |
5. 8785 |
FACTORS FOE COMPUTATION OF GEODETIC POSITIONS. 193
Table XXVII. — Factors for ilie computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 28°.
|
log. A |
log. B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.06 |
difif. l"=-0.1if |
diflf. l"=+0.50 |
diff. l"=+0.03 |
diff. l"=+0.05 |
|
|
28 00 |
8. 509 4024 |
8. 511 7036 |
1. 13132 |
2. 3107 |
5. 8785 |
|
1 |
20 |
25 |
163 |
09 |
88 |
|
2 |
17 |
14 |
193 |
10 |
91 |
|
3 |
13 |
04 |
223 |
12 |
94 |
|
4 |
10 |
8. 511 6993 |
254 |
14 |
97 |
|
05 |
06 |
82 |
284 |
15 |
99 |
|
6 |
02 |
72 . |
314 |
17 |
5. 8802 |
|
7 |
8.509 3999 |
61 |
345 |
19 |
05 |
|
8 |
95 |
50 |
375 |
20 |
08 |
|
9 |
92 |
40 |
405 |
22 |
11 |
|
10 |
8. 509 3988 |
8. 511 6929 |
1. 13435 |
2. 3124 |
5. 8813 |
|
11 |
85 |
18 |
465 |
26 |
16 |
|
12 |
81 |
08 |
496 |
27 |
19 |
|
13 |
78 |
8. 511 6897 |
526 |
29 |
22 |
|
14 |
74 |
86 |
556 |
31 |
25 |
|
15 |
70 |
75 |
586 |
32 |
27 |
|
16 |
67 |
65 |
616 |
34 |
30 |
|
17 |
63 |
54 |
646 |
36 |
33 |
|
18 |
60 |
43 |
677 |
37 |
36 |
|
19 |
56 |
33 |
707 |
39 |
39 |
|
20 |
8.509 3952 |
8.511 6822 |
1. 13737 |
2.3141 |
5.8841 |
|
21 |
49 |
11 |
767 |
42 |
44 |
|
22 |
45 |
00 |
797 |
44 |
47 |
|
23 |
42 |
8.511 6790 |
827 . |
46 |
50 |
|
24 |
38 |
79 |
857 |
47 |
53 |
|
25 |
35 |
68 |
887 |
49 |
55 |
|
26 |
31 |
57 |
917 |
51 |
58 |
|
27 |
27 |
47 |
947 |
52 |
61 |
|
28 |
24 |
36 |
977 |
54 |
64 |
|
29 |
20 |
25 |
1. 14007 |
56 |
67 |
|
30 |
8.509 3917 |
8.511 6714 |
1. 14037 |
2. 3157 |
5.8870 |
|
31 |
13 |
04 |
067 |
69 |
72 |
|
32 |
09 |
8. 511 6693 |
097 |
61 |
75 |
|
33 |
06 |
82 |
127 |
62 |
78 |
|
34 |
02 |
71 |
157. |
64 |
81 |
|
35 |
8.509 3899 |
61 |
187 |
66 |
84 |
|
36 |
95 |
50 |
217 |
67 |
87 |
|
37 |
92 |
39 |
247 |
69 |
89 |
|
38 |
83 |
28 |
277 |
70 |
92 |
|
39 |
84 |
17 |
307 |
72 |
95 |
|
40 |
8. 509 3881 |
8. 511 6607 |
1. 14337 |
2. 3174 |
5. 8898 |
|
41 |
77 |
8. 511 6596 |
366 |
75 |
5.8901 |
|
42 |
73 |
85 |
396 |
77 |
04 , |
|
43 |
70 |
74 |
426 |
79 |
06 |
|
44 |
66 |
63 |
456 |
80 |
09 |
|
45 |
63 |
52 |
486 |
82 |
12 |
|
46 |
59 |
42 |
516 |
83 |
15 |
|
47 |
55 |
31 |
545 |
85 |
18 |
|
48 |
52 |
20 |
575 |
87 |
21 |
|
49 |
48 |
09 |
605 |
88 |
23 |
|
50 |
8. 509 3845 |
8. 511 6498 |
1. 14635 |
2. 3190 |
5.8926 |
|
51 |
41 |
87 |
664 |
92 |
29 |
|
52 |
37 |
76 |
694 |
93 |
32 |
|
63 |
34 |
66 |
724 |
95 |
35 |
|
54 |
30 |
55 |
754 |
96 |
38 |
|
55 |
26 |
a |
783 |
98 |
40 |
|
56 |
23 |
33 |
813 |
2. 3200 |
43 |
|
57 |
19 |
22 |
843 |
01 |
46 |
|
58 |
16 |
11 |
872 |
03 |
49 |
|
59 |
12 |
00 |
902 |
04 |
52 |
|
60 |
8.509 3808 |
8.511 6389 |
1. 14932 |
2. 3206 |
5.8955 |
MON SXII-
-13
194
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the compatation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 29°.
|
Latitude. |
log. A |
log. B |
log.C |
log.D |
log.E |
|
difif. 1"=— 0. 06 |
difl.l"=— 0.18 |
diff.l"=+0.49 |
diff. l"=+0. 03 |
diff.l"=+0.05 |
|
|
29 00 |
8. 509 3808 |
8. 511 6389 |
1.14932 |
2.3206 |
5.8955 |
|
1 |
05 |
78 |
961 |
08 |
58 |
|
01 |
68 |
991 |
09 |
60 |
|
|
3 |
8.509 3797 |
57 |
1.15021 |
11 |
63 |
|
4 |
94 |
46 |
050 |
12 |
66 |
|
05 |
90 |
35 |
080 |
14 |
69 |
|
6 |
86 |
24 |
109 |
15 |
72 |
|
7 |
83 |
13 |
139 |
17 |
75 |
|
8 |
79 |
02 |
168 |
19 |
78 |
|
9 |
76 |
8. 511 6291 |
198 |
20 |
80 |
|
10 |
8. 509 3772 |
8.511 6280 |
1. 15228 |
2.3222 |
5.8983 |
|
11 |
68 |
69 |
257 |
23 |
86 |
|
12 |
65 |
58 |
287 |
25 |
89 |
|
13 |
61 |
47 |
316 |
26 |
92 |
|
14 |
57 |
36 |
346 |
28 |
95 |
|
15 |
54 |
26 |
375 |
30 |
98 |
|
16 |
50 |
15 |
405 |
31 |
5. 9000 |
|
17 |
46 |
04 |
434 |
33 |
03 |
|
18 |
43 |
8. 511 6193 |
464 |
34 |
06 |
|
19 |
39 |
82 |
493 |
36 |
09 |
|
20 |
8. 509 3735 |
8. 511 6171 |
1.15522 |
2.3237 |
5.9012 |
|
21 |
32 |
60 |
552 |
39 |
15 |
|
22 |
28 |
49 |
581 |
40 |
18 |
|
23 |
24 |
38 |
611 |
42 |
21 |
|
24 |
21 |
27 |
640 |
43 |
23 |
|
25 |
17 |
16 |
670 |
45 |
26 |
|
26 |
13 |
05 |
699 |
47 |
29 |
|
27 |
10 |
8.511 6094 |
728 |
48 |
32 |
|
28 |
06 |
83 |
758 |
50 |
35 |
|
29 |
02 |
72 |
787 |
51 |
38 |
|
30 |
8. 509 3699 |
8. 511 6061 |
1.15816 |
2.3253 |
5. 9041 |
|
31 |
95 |
50 |
846 |
54 |
43 |
|
32 |
91 |
39 |
875 |
56 |
46 |
|
33 |
88 |
28 |
904 |
57 |
49 |
|
34 |
84 |
17 |
934 |
59 |
52 |
|
35 |
80 |
06 |
963 |
60 |
55 |
|
36 |
77 |
8. 511 5995 |
992 |
62 |
58 |
|
37 |
73 |
84 |
1. 16021 |
63 |
61 |
|
38 |
69 |
73 |
051 |
65 |
64 |
|
39 |
66 |
61 |
080 |
66 |
67 |
|
40 |
8. 509 3662 |
8. 511 5950 |
1. 16109 |
2. 3268 |
5. 9069 |
|
41 |
58 |
39 |
138 |
69 |
72 |
|
42 |
55 |
28 |
167 |
71 |
75 |
|
43 |
51 |
17 |
197 |
72 |
78 |
|
44 |
47 |
06 |
226 |
74 |
81 |
|
45 |
44 |
8. 511 5895 |
255 |
75 |
84 |
|
46 |
40 |
84 |
284 |
77 |
87 |
|
47 |
36 |
73 |
313 |
78 |
90 |
|
48 |
33 |
62 |
343 |
80 |
93 |
|
49 |
29 |
51 |
372 |
81 |
96 |
|
50 |
8. 509 3625 |
8. 511 5840 |
1. 16401 |
2. 3283 |
5. 9098 |
|
51 |
21 |
29 |
430 |
84 |
5. 9101 |
|
52 |
18 |
18 |
459 |
86 |
04 |
|
53 |
14 |
06 |
488 |
87 |
07 |
|
54 |
10 |
8. 511 5795 |
517 |
89 |
10 |
|
55 |
07 |
84 |
546 |
90 |
13 |
|
56 |
03 |
73 |
575 |
92 |
16 |
|
57 |
8. 509 3599 |
62 |
604 |
93 |
19 |
|
58 |
96 |
51 |
633 |
95 |
22 |
|
59 |
92 |
40 |
663 |
96 |
25 |
|
60 |
8. 509 3588 |
8.511 5729 |
1. 16692 |
2. 3298 |
5. 9127 |
FACTORS FOR COMPUTATIOlSr OF GEODETIC POSITIONS. 195
Table XXVIl. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 30°.
|
log. A |
log. B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
dlff.l" = — 0.06 |
diff.l"=— 0.19 |
diff.l"= + 0.48 |
diff.l" = +0.02 |
diff. l" = +0.05 |
|
|
30 00 |
8. 509 3588 |
8. 511 5729 |
1. 16692 |
2, 3298 |
5. 9127 |
|
1 |
84 |
18 |
721 |
99 |
30 |
|
2 |
81 |
06 |
750 |
2. 3301 |
33 |
|
3 |
77 |
8.511 5695 |
778 |
02 |
36 |
|
4 |
73 |
84 |
807 |
04 |
39 |
|
05 |
69 |
73 |
836 |
05 |
42 |
|
6 |
66 |
62 |
865 |
06 |
45 |
|
7 |
62 |
51 |
894 |
08 |
48 |
|
8 |
58 |
40 |
923 |
09 |
51 |
|
9 |
55 |
28 |
952 |
11 |
54 |
|
30 |
8. 509 3551 |
8.511 5617 |
1. 16981 |
2. 3312 |
5. 9157 |
|
11 |
47 |
06 |
1. 17010 |
14 |
59 |
|
12 |
43 |
8.511 5595 |
039 |
15 |
62 |
|
13 |
40 |
84 |
068 |
17 |
65 |
|
14 |
36 |
73 |
097 |
18 |
68 |
|
15 |
32 |
61 |
126 |
19 |
71 |
|
16 |
29 |
50 |
155 |
21 |
74 |
|
17 |
25 |
39 |
184 |
22 |
77 |
|
18 |
21 |
28 |
212 |
24 |
80 |
|
19 |
17 |
17 |
241 |
25 |
83 |
|
20 |
8. 509 3514 |
8.511 5505 |
1. 17270 |
2. 3327 |
5. 9186 |
|
21 |
10 |
8. 511 5494 |
299 |
28 |
89 |
|
22 |
06 |
83 |
328 |
30 |
92 |
|
23 |
02 |
72 |
357 |
31 |
95 |
|
24 |
8. 509 3499 |
61 |
385 |
32 |
98 |
|
25 |
95 |
49 |
414 |
34 |
5. 9200 |
|
26 |
91 |
38 |
443 |
35 |
03 |
|
27 |
88 |
27 |
472 |
37 |
06 |
|
28 |
84 |
16 |
500 |
38 |
09 |
|
29 |
80 |
04 |
529 |
39 |
12 |
|
30 |
8. 509 3476 |
8.511 5393 |
1. 17558 |
2.3341 |
5. 9215 |
|
31 |
72 |
82 |
587 |
42 |
18 |
|
32 |
69 |
71 |
615 |
44 |
21 |
|
33 |
65 |
59 |
644 |
45 |
24 |
|
34 |
61 |
48 |
673 |
47 |
27 |
|
35 |
57 |
37' |
701 |
48 |
30 |
|
36 |
54 |
26 |
730 |
49 |
33 |
|
37 |
50 |
14 |
759 |
51 |
36 |
|
38 |
46 |
03 |
788 |
52 |
39 |
|
39 |
42 |
8. 511 5292 |
816 |
54 |
42 |
|
40 |
8. 509 3439 |
8. 511 5281 |
1. 17845 |
2. 3355 |
5.9245 |
|
41 |
35 |
69 |
874 |
56 |
'48 |
|
42 |
31 |
58 |
902 |
58 |
51 |
|
43 |
27 |
47 |
931 |
59 |
53 |
|
44 |
24 |
35 |
959 |
60 |
56 |
|
45 |
20 |
24 |
988 |
62 |
59 |
|
46 |
16 |
13 |
1. 18017 |
63 |
62 |
|
47 |
12 |
02 |
045 |
65 |
65 |
|
48 |
09 |
8.511 5190 |
074 |
66 |
68 |
|
49 |
05 |
79 |
102 |
67 |
71 |
|
50 |
8. 509 3401 |
8.511 5168 |
1. 18131 |
2.3368 |
5. 9274 |
|
51 |
8. 509 3397 |
56 |
160 |
70 |
77 |
|
52 |
94 |
45 |
188 |
71 |
80 |
|
53 |
90 |
34 |
217 |
73 |
83 |
|
54 |
86 |
22 |
245 |
74 |
86 |
|
55 |
.82 |
11 |
274 |
76 |
89 |
|
56 |
78 |
00 |
302 |
77 |
92 |
|
57 |
75 |
8.511 5088 |
331 |
78 |
95 |
|
58 |
71 |
77 |
359 |
80 |
98 |
|
59 |
67 |
66 |
388 |
81 |
5. 9301 |
|
60 |
8. 509 3363 |
8.511 5054 |
1. 18416 |
2.3382 |
5. 9304 |
196
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimufhs — Coutiuued.
LATITUDE 31°.
|
log. A |
log.B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.06 |
diff. 1"=— 0.19 |
diff.l"=+0.47 |
diff.l"=+0.02 |
diff.l"=+0.05 |
|
|
31 00 |
8. 509 3363 |
8. 511 5054 |
1. 18416 |
2. 3382 |
5.9304 |
|
1 |
60 |
43 |
445 |
84 |
07 |
|
2 |
66 |
32 |
473 |
85 |
10 |
|
3 |
52 |
20 |
501 |
86 |
13 |
|
4 |
48 |
09 |
530 |
88 |
16 |
|
05 |
44 |
8. 511 4998 |
558 |
89 |
19 |
|
6 |
41 |
86 |
587 |
90 |
22 |
|
7 |
37 |
75 |
615 |
92 |
26 |
|
8 |
33 |
61 |
643 |
93 |
28 |
|
9 |
29 |
52 |
672 |
95 |
31 |
|
10 |
8. 509 3325 |
8. 5U 4941 |
1. 18700 |
2. 3396 |
5.9334 |
|
11 |
22 |
29 |
729 |
97 |
37 |
|
12 |
18 |
18 |
757 |
99 |
39 |
|
13 |
14 |
07 |
785 |
2. 3400 |
42 |
|
14 |
10 |
8. 511 4895 |
813 |
01 |
45 |
|
15 |
06 |
84 |
842 |
02 |
48 |
|
16 |
03 |
72 |
870 |
04 |
61 |
|
17 |
8. 509 3299 |
61 |
898 |
06 |
54 |
|
18 |
95 |
50 |
927 |
06 |
67 |
|
19 |
91 |
38 |
955 |
08 |
60 |
|
20 |
8.509 3287 |
8. 511 4827 |
1. 18983 |
2. 3409 |
5. 9363 |
|
21 |
84 |
15 |
1. 19012 |
10 |
66 |
|
22 |
80 |
04 |
040 |
12 |
69 |
|
23 |
76 |
8. 611 4793 |
068 |
13 |
72 |
|
24 |
81 |
096 |
14 |
75 |
|
|
25 |
68 |
70 |
125 |
16 |
78 |
|
26 |
65 |
58 |
153 . |
17 |
81 |
|
27 |
61 |
47 |
181 |
18 |
84 |
|
28 |
57 |
35 |
209 |
20 |
87 |
|
29 |
53 |
24 |
238 |
21 |
90 |
|
30 |
8. 509 3249 |
8. 511 4713 |
1. 19266 |
2. 3422 |
5.9393 |
|
31 |
46 |
01 |
294 |
23 |
96 |
|
32 |
42 |
8. 511 4690 |
322 |
25 |
99 |
|
32 |
38 |
78 |
351 |
26 |
5. 9402 |
|
34 |
34 |
67 |
379 |
27 |
05 |
|
35 |
30 |
55 |
407 |
29 |
08 |
|
36 |
26 |
44 |
435 |
30 |
11 |
|
37 |
23 |
32 |
463 |
31 |
14 |
|
38 |
19 |
21 |
491 |
33 |
17 |
|
39 |
15 |
09 |
520 |
34 |
20 |
|
40 |
8.509 3211 |
8. 511 4598 |
1. 19548 |
2.3435 |
6. 9423 |
|
41 |
07 |
86 |
576 |
36 |
26 |
|
42 |
03 |
75 |
604 |
38 |
29 |
|
43 |
00 |
63 |
632 |
39 |
32 |
|
44 |
8. 509 3196 |
52 |
660 |
40 |
35 |
|
45 |
92 |
40 |
688 |
41 |
38 |
|
46 |
83 |
29 |
716 |
43 |
41 |
|
47 |
84 |
17 |
744 |
44 |
44 |
|
48 |
81 |
06 |
772 |
45 |
47 |
|
49 |
77 |
8. 511 4494 |
800 |
47 |
50 |
|
50 |
8. 509 3173 |
8. 511 4483 |
1. 19828 |
2.3448 |
6.9453 |
|
51 |
09 |
71 |
856 |
49 |
56 |
|
52 |
65 |
60 |
884 |
50 |
69 |
|
53 |
61 |
48 |
912 |
52 |
62 |
|
54 |
67 |
37 |
940 |
53 |
65 |
|
55 |
54 |
26 |
968 |
54 |
68 |
|
56 |
50 |
14 |
996 |
55 |
72 |
|
57 |
46 |
02 |
1. 20024 |
57 |
75 |
|
68 |
42 |
8.511 4391 |
052 |
58 |
78 |
|
59 |
38 |
79 |
080 |
59 |
81 |
|
60 |
8. 509 3134 |
8.5U 4368 |
1.20108 |
2.3460 |
5.9484 |
FACTORS FOE COMPUTATION" OP GEODETIC POSITIONS.
197
Table XXVll.— Factors for
; compiitaUoii of geodetic latitudes. Ion LATITUDE 321
\id azimuths — Continued.
|
log. A |
log.B |
log.C |
log.D |
log.E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.06 |
diff. 1"=— 0.19 |
diff. l"=+0.46 |
dift'. l"=+0.02 |
diff. l"=+0.05 |
|
|
32 00 |
8.509 3134 |
8. 511 4368 |
1.20108 |
2.3460 |
6. 9484 |
|
1 |
31 |
56 |
136 |
62 |
87 |
|
27 |
44 |
164 |
63 |
90 |
|
|
3 |
23 |
S3 |
192 |
64 |
93 |
|
4 |
19 |
21 |
220 |
66 |
96 |
|
05 |
15 |
10 |
243 |
67 |
99 |
|
6 |
11 |
8.511 4298 |
276 |
68 |
6. 9502 |
|
7 |
07 |
87 |
304 |
69 |
05 |
|
8 |
04 |
75 |
332 |
70 |
08 |
|
9 |
00 |
63 |
360 |
71 |
11 |
|
10 |
8. 509 3096 |
8. 511 4252 |
1. 20337 |
2. 3473 |
5. 9514 |
|
11 |
92 |
40 |
415 |
74 |
17 |
|
12 |
38 |
29 |
443 |
76 |
20 |
|
13 |
84 |
17 |
471 |
76 |
23 |
|
14 |
80 |
05 |
499 |
78 |
26 |
|
15 |
76 |
8.511 4194 |
627 |
79 |
29 |
|
16 |
73 |
82 |
655 |
80 |
32 |
|
17 |
67 |
71 |
682 |
.81 |
36 |
|
18 |
65 |
59 |
610 |
82 |
38 |
|
19 |
61 |
47 |
638 |
84 |
41 |
|
20 |
8.509 3057 |
8. 511 4136 |
1. 20666 |
2. 3485 |
5. 9644 |
|
21 |
53 |
24 |
694 |
36 |
47 |
|
22 |
49 |
13 |
722 |
87 |
50 |
|
23 |
46 |
01 |
749 |
88 |
53 |
|
24 |
42 |
8.511 4089 |
777 |
90 |
66 |
|
25 |
38 |
78 |
805 |
91 |
60 |
|
26 |
34 |
66 |
833 |
92 |
63 |
|
27 |
30 |
54 |
860 |
93 |
06 |
|
28 |
26 |
43 |
888 |
94 |
69 |
|
29 |
22 |
31 |
916 |
96 |
72 |
|
30 |
8. 509 3018 |
8. 611 4020 |
1. 20944 |
2. 3497 |
5. 9575 |
|
31 |
15 |
03 |
971 |
98 |
78 |
|
32 |
11 |
3. 511 3996 |
999 |
99 |
81 |
|
33 |
07 |
35 |
1. 21027 |
2. 3500 |
84 |
|
34 |
03 |
73 |
054 |
02 |
87 |
|
35 |
8.509 2999 |
61 |
032 |
03 |
90 |
|
36 |
95 |
50 |
110 |
04 |
93 |
|
37 |
91 |
33 |
137 |
05 |
96 |
|
33 |
87 |
26 |
165 |
06 |
99 |
|
39 |
83 |
15 |
193 |
07 |
5. 9602 |
|
40 |
8. 509 2930 |
3. 511 3903 |
1. 21220 |
2. 3509 |
5. 9605 |
|
41 |
76 |
8. 511 3391 |
248 |
10 |
08 |
|
42 |
72 |
79 |
276 |
11 |
U |
|
43 |
68 |
63 |
303 |
12 |
16 |
|
44 |
64 |
56 |
331 |
13 |
18 |
|
45 |
60 |
44 |
368 |
14 |
21 |
|
46 |
66 |
33 |
386 |
16 |
24 |
|
47 |
62 |
21 |
414 |
17 |
27 |
|
43 |
43 |
09 |
441 |
18 |
30 |
|
49 |
44 |
8. 511 3798 |
469 |
19 |
33 |
|
50 |
8. 509 2940 |
8. 611 3786 |
1. 21496 |
2. 3620 |
6.9636 |
|
51 |
37 |
74 |
524 |
21 |
39 |
|
52 |
33 |
63 |
551 |
23 |
42 |
|
53 |
29 |
61 |
579 |
24 |
46 |
|
54 |
25 |
39 |
607 |
25 |
48 |
|
55 |
21 |
27 |
634 |
26 |
51 |
|
56 |
17 |
16 |
662 |
27 |
64 |
|
57 |
13 |
04 |
689 |
28 |
68 |
|
68 |
09 |
8. 511 3692 |
717 |
29 |
61 |
|
59 |
06 |
80 |
744 |
31 |
64 |
|
60 |
8. 509 2901 |
8. 611 3669 |
1. 21772 |
2. 3532 |
6. 9667 |
15:18
A MAXUAL OF TOPOGEAPHIO METHODS.
Table XX^'II. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 38°,
|
log. A |
log.B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
diff.l"= — 0.07 |
di£f.l"= — 0.20 |
diff.l"=+0.45 |
AiS. l"=+0.02 |
diff.l"=+0.05 |
|
|
33 00 |
8.509 2901 |
8.511 3669 |
1.21772 |
2. 3532 |
5. 9667 |
|
1 |
8.509 2897 |
57 |
799 |
33 |
70 |
|
2 |
94 |
45 |
827 |
34 |
73 |
|
3 |
90 |
33 |
854 |
35 |
76 |
|
i |
86 |
22 |
882 |
36 |
79 |
|
05 |
82 |
10 |
909 |
37 |
82 |
|
6 |
78 |
8. 511 3598 |
937 |
38 |
85 |
|
7 |
74 |
86 |
964 |
40 |
88 |
|
8 |
70 |
75 |
992 |
41 |
92 |
|
9 |
66 |
63 |
1.22019 |
42 |
95 |
|
10 |
8.509 2862 |
8. 511 3551 |
1. 22047 |
2. 3643 |
6. 9698 |
|
11 |
58 |
39 |
074 |
44 |
5. 9701 |
|
12 |
54 |
28 |
101 |
45 |
04 |
|
13 |
51 |
16 |
129 |
46 |
07 |
|
14 |
47 |
04 |
156 |
47 |
10 |
|
15 |
43 |
8.611 3492 |
184 |
49 |
13 |
|
16 |
39 |
80 |
211 |
50 |
16 |
|
17 |
35 |
69 |
238 |
51 |
19 |
|
18 |
31 |
57 |
266 |
52 |
22 |
|
19 |
27 |
45 |
293 |
53 |
26 |
|
20 |
8. 509 2823 |
8. 511 3433 |
1. 22321 |
2. 3554 |
6. 9729 |
|
21 |
19 |
21 |
348 |
65 |
32 |
|
22 |
15 |
10 |
375 |
56 |
35 |
|
23 |
11 |
8.511 3398 |
403 |
57 |
38 • |
|
24 |
07 |
86 |
430 |
58 |
41 |
|
25 |
03 |
74 |
457 |
60 |
44 |
|
26 |
8. 509 2799 |
62 |
485 |
61 |
47 |
|
27 |
95 |
51 |
512 |
62 |
50 |
|
28 |
91 |
39 |
539 |
63 |
53 |
|
29 |
88 |
27 |
567 |
64 |
57 |
|
30 |
8. 509 2784 |
8. 511 3315 |
1. 22594 |
2. 3565 |
5.9760 |
|
31 |
80 |
03 |
621 |
66 |
63 |
|
82 |
76 |
8.511 3291 |
648 |
67 |
66 |
|
33 |
72 |
80 |
676 |
68 |
69 |
|
34 |
68 |
68 |
703 |
69 |
72 |
|
35 |
64 |
58 |
730 |
70 |
75 |
|
36 |
60 |
44 |
757 |
71 |
78 |
|
37 |
56 |
32 |
785 |
73 |
81 |
|
38 |
52 |
20 |
812 |
74 |
85 |
|
39 |
43 |
09 |
839 |
75 |
88 |
|
40 |
8. 509 2744 |
8. 511 3197 |
1.22866 |
2. 3576 |
5. 9791 |
|
41 |
40 |
85 |
893 |
77 |
94 |
|
42 |
36 |
73 |
921 |
78 |
97 |
|
43 |
32 |
61 |
948 |
79 |
5.9800 |
|
44 |
28 |
49 |
975 |
80 |
03 |
|
45 |
24 |
37 |
1. 23002 |
81 |
06 |
|
40 |
20 |
25 |
029 |
82 |
10 |
|
47 |
16 |
13 |
057 |
83 |
13 |
|
48 |
12 |
02 |
084 |
84 |
16 |
|
49 |
08 |
8.511 3090 |
111 |
85 |
19 |
|
50 |
8. 509 2704 |
8. 511 3078 |
1. 23138 |
2.3586 |
6.9822 |
|
51 |
01 |
66 |
165 |
87 |
26 |
|
52 |
8.509 2697 |
54 |
192 |
88 |
28 |
|
53 |
93 |
42 |
220 |
89 |
31 |
|
54 |
89 |
30 |
247 |
91 |
35 |
|
55 |
85 |
18 |
274 |
92 |
38 |
|
56 |
81 |
06 |
301 |
93 |
41 |
|
57 |
77 |
8. 511 2995 |
328 |
94 |
44 |
|
68 |
73 |
83 |
355 |
95 |
47 |
|
59 |
69 |
71 |
382 |
96 |
50 |
|
60 |
8. 509 2665 |
8. 511 2959 |
1.23409 |
2. 3597 |
6.9853 |
FAOTOES FOE COMPUTATION OF GEODETIC POSITIONS.
199
Table XXVII. — Factors for the computation of geodetic latitudes, longitades, and azimuths — Continued.
LATITUDE 340.
|
log. A |
log.B |
lug.C |
log.B |
log.E |
|
|
Latitude |
|||||
|
diff. 1"=— 0.07 |
diff.l"=_0.20 |
diff, 1" = + 0.45 |
difi'. l"=+0.02 |
diff. 1" = + 0.05 |
|
|
34 00 |
8. 509 2665 |
8. 511 2959 |
1. 23409 |
2. 3697 |
5. 9853 |
|
1 |
61 |
47 |
437 |
98 |
57 |
|
2 |
57 |
35 |
464 |
99 |
60 |
|
3 |
53 |
23 |
491 |
2. 3600 |
63 |
|
4 |
49 |
11 |
518 |
01 |
66 |
|
05 |
45 |
8.511 2899 |
546 |
02 |
69 |
|
6 |
41 |
87 |
572 |
03 |
72 |
|
7 |
37 |
76 |
699 |
04 |
76 |
|
8 |
33 |
63 |
626 |
05 |
79 |
|
9 |
30 |
51 |
653 |
06 |
82 |
|
10 |
8. 609 2625 |
8.511 2840 |
1. 23680 |
2, 3607 |
5. 9886 |
|
11 |
21 |
28 |
707 |
08 |
88 |
|
12 |
17 |
16 |
734 |
09 |
91 |
|
13 |
13 |
04 |
761 |
10 |
94 |
|
14 |
09 |
8. 511 2792 |
788 |
11 |
97 |
|
15 |
05 |
80 |
815 |
12 |
6. 9901 |
|
16 |
01 |
68 |
842 |
13 |
04 |
|
17 |
8. 609 2597 |
56 |
869 |
14 |
07 |
|
18 |
93 |
44 |
896 |
16 |
10 |
|
19 |
89 |
32 |
923 |
16 |
13 |
|
20 |
8. 609 2685 |
8. 611 2720 |
1. 23950 |
2. 3617 |
5. 9916 |
|
21 |
81 |
08 |
977 |
18 |
19 |
|
22 |
77 |
8. 511 2696 |
1. 24004 |
19 |
23 |
|
23 |
73 |
84 |
031 |
20 |
26 |
|
24 |
69 |
72 |
068 |
21 |
29 |
|
25 |
65 |
60 |
085 |
22 |
32 |
|
26 |
61 |
48 |
112 |
23 |
35 |
|
27 |
57 |
36 |
139 |
24 |
38 |
|
28 |
63 |
24 |
166 |
25 |
42 |
|
29 |
49 |
12 |
192 |
26 |
45 |
|
30 |
8. 509 2545 |
8. 611 2600 |
1. 24219 |
2. 3627 |
5. 9948 |
|
31 |
41 |
8. 611 2688 |
246 |
28 |
61 |
|
32 |
37 |
76 |
273 |
29 |
64 |
|
33 |
33 |
64 |
300 |
30 |
57 |
|
34 |
29 |
62 |
327 |
31 |
61 |
|
35 |
25 |
40 |
354 |
32 |
64 |
|
36 |
21 |
28 |
381 |
33 |
67 |
|
37 |
17 |
16 |
408 |
34 |
70 |
|
38 |
13 |
04 |
434 |
36 |
73 |
|
39 |
09 |
8. 511 2492 |
461 |
36 |
76 |
|
40 |
8. 509 2506 |
8. 511 2480 |
1.24488 |
2. 3637 |
5. 9980 |
|
41 |
0] |
68 |
515 |
38 |
83 |
|
42 |
8.509 2497 |
56 |
542 |
39 |
86 |
|
43 |
93 |
44 |
569 |
40 |
89 |
|
44 |
89 |
32 |
595 |
41 |
92 |
|
45 |
85 |
20 |
622 |
42 |
96 |
|
46 |
81 |
08 |
649 |
43 |
99 |
|
47 |
77 |
8.511 2396 |
676 |
44 |
6. 0002 |
|
48 |
73 |
84 |
703 |
44 |
06 |
|
49 |
69 |
72 |
729 |
45 |
08 |
|
50 |
8.509 2465 |
8.511 2360 |
1. 24756 |
2. 3646 |
6. 0011 |
|
51 |
61 |
48 |
783 |
47 |
15 |
|
52 |
67 |
35 |
810 |
48 |
18 |
|
53 |
53 |
23 |
837 |
49 |
21 |
|
54 |
49 |
11 |
863 |
50 |
24 |
|
55 |
45 |
8. 511 2299 |
890 |
51 |
27 |
|
5S |
41 |
87 |
917 |
52 |
31 |
|
67 |
37 |
76 |
944 |
63 |
34 |
|
58 |
33 |
63 |
970 |
64 |
37 |
|
59 |
29 |
51 |
997 |
66 |
40 |
|
60 |
8. 509 2425 |
2.511 2239 |
1. 26024 |
2. 3666 |
6. 0043 |
200
A MANUAL OP TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the comjyutation of geodetic latitudes, longitudes, and azimuths — Coutinued.
LATITtTDE S5°.
|
log. A |
log.B |
log.C |
log.D |
log.E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.07 |
diff. 1"=— 0.20 |
diff. 1"= + 0.44 |
difl',l"= + 0.01 |
diff. 1"= + 0.05 |
|
|
35 00 |
8.509 2425 |
8. 511 2239 |
1. 25024 |
2. 3656 |
6, 0043 |
|
1 |
21 |
27 |
050 |
57 |
47 |
|
2 |
17 |
15 |
077 |
68 |
50 |
|
3 |
13 |
03 |
104 |
59 |
53 |
|
4 |
09 |
8.5112191 |
131 |
59 |
56 |
|
05 |
05 |
78 |
157 |
60 |
59 |
|
6 |
01 |
66 |
184 |
61 |
63 |
|
7 |
8..=;09 2396 |
54 |
211 |
62 |
66 |
|
8 |
93 |
42 |
237 |
63 |
69 |
|
9 |
88 |
30 |
264 |
64 |
72 |
|
10 |
8.509 2384 |
8. 511 2118 |
1.25291 |
2.3665 |
6. 0075 |
|
11 |
80 |
06 |
317 |
66 |
79 |
|
12 |
76 |
8. 511 2094 |
344 |
67 |
82 |
|
13 |
72 |
82 |
371 |
68 |
85 |
|
14 |
68 |
70 |
397 |
69 |
88 |
|
15 |
64 |
57 |
424 |
70 |
91 |
|
16 |
60 |
45 |
461 |
70 |
96 |
|
17 |
56 |
33 |
477 |
71 |
98 |
|
18 |
52 |
21 |
504 |
72 |
6. 0101 |
|
19 |
48 |
09 |
531 |
73 |
04 |
|
20 |
8.509 2344 |
8.511 1997 |
1. 25557 |
2.3674 |
6. 0107 |
|
21 |
40 |
85 |
584 |
76 |
11 |
|
22 |
36 |
72 |
610 |
76 |
14 |
|
23 |
32 |
60 |
637 |
77 |
17 |
|
24 |
28 |
48 |
664 |
78 |
20 |
|
25 |
24 |
36 |
690 |
79 |
23 |
|
26 |
20 |
24 |
717 |
79 |
27 |
|
27 |
16 |
12 |
743 |
80 |
30 |
|
28 |
12 |
00 |
770 |
81 |
33 |
|
29 |
08 |
8. 611 1887 |
796 |
82 |
36 |
|
30 |
8.509 2304 |
8. 511 1875 |
1. 25823 |
2.3683 |
6. 0140 |
|
31 |
00 |
63 |
850 |
84 |
43 |
|
32 |
8. 609 2296 |
51 |
876 |
85 |
46 |
|
33 |
92 |
39 |
903 |
86 |
49 |
|
34 |
87 |
27 |
929 |
86 |
52 |
|
35 |
83 |
15 |
956 |
87 |
56 |
|
36 |
79 |
02 |
982 |
88 |
59 |
|
37 |
75 |
8.511 1790 |
1.26009 |
89 |
62 |
|
38 |
71 |
78 |
036 |
90 |
65 |
|
39 |
67 |
66 |
062 |
91 |
69 |
|
40 |
8.609 2263 |
8. 511 1754 |
1. 26088 |
2. 3692 |
6. 0172 |
|
41 |
59 |
41 |
115 |
93 |
75 |
|
42 |
65 |
29 |
141 |
93 |
78 |
|
43 |
51 |
17 |
168 |
94 |
81 |
|
44 |
47 |
05 |
194 |
95 |
85 |
|
45 |
43 |
8. 511 1693 |
221 |
96 |
88 |
|
46 |
39 |
80 |
247 |
97 |
91 |
|
47 |
35 |
68 |
274 |
98 |
94 |
|
48 |
31 |
56 |
300 |
99 |
98 |
|
49 |
27 |
44 |
327 |
99 |
6. 0201 |
|
50 |
8. 509 2222 |
8. 511 1632 |
1. 26353 |
2. 3700 |
6.0204 |
|
51 |
18 |
20 |
380 |
01 |
07 |
|
52 |
14 |
07 |
406 |
02 |
11 |
|
53 |
10 |
8.511 1596 |
432 |
03 |
14 |
|
54 |
06 |
83 |
469 |
04 |
17 |
|
55 |
02 |
71 |
485 |
05 |
20 |
|
56 |
8. 509 2198 |
58 |
512 |
05 |
24 |
|
57 |
94 |
46 |
538 |
06 |
27 |
|
58 |
90 |
34 |
665 |
07 |
30 |
|
59 |
86 |
22 |
591 |
08 |
33 |
|
60 |
8. 509 2182 |
8. 511 1510 |
1.26617 |
3. 3709 |
6. 0237 |
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 201
Table XXVII. — Factors for the computation of geodetic latitudes, Jongitudes, and azimuths — Continued.
LATITUDE 36°
|
log. A |
log. B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
dlflf.l" = -0.07 |
diff. 1"=— 0.20 |
diff. l"=+0.44 |
diff. J"=+0.01 |
diff. ] "=+0.05 |
|
|
36 00 |
8. 509 2182 |
8. 511 1510 |
1. 26617 |
. 2.3709 |
6.0237 |
|
1- |
78 |
8.511 1497 |
644 |
10 |
40 |
|
2 |
74 |
85 |
670 |
10 |
43 |
|
3 |
70 |
73 |
697 |
11 |
46 |
|
4 |
65 |
61 |
723 |
12 |
60 |
|
05 |
61 |
48 |
749 |
13 |
53 |
|
6 |
57 |
36 |
776 |
14 |
56 |
|
7 |
53 |
24 |
802 |
14 |
59 |
|
8 |
49 |
12 |
828 |
15 |
63 |
|
9 |
45 |
8.511 1399 |
855 |
16 |
66 |
|
10 |
8. 509 2141 |
8. 511 1387 |
1. 26881 |
2. 3717 |
6.0269 |
|
11 |
37 |
75 |
908 |
18 |
72 |
|
12 |
33 |
63 |
934 |
19 |
76 |
|
13 |
29 |
50 |
960 |
19 |
79 |
|
14 |
25 |
38 |
987 |
20 |
82 |
|
15 |
21 |
26 |
1. 27013 |
21 |
85 |
|
16 |
16 |
14 |
039 |
22 |
89 |
|
17 |
12 |
01 |
066 |
23 |
92 |
|
18 |
08 |
8.511 1289 |
092 |
23 |
95 |
|
19 |
04 |
77 |
118 |
24 |
99 |
|
20 |
8. 509 2100 |
8. 511 1265 |
1. 27145 |
2. 3725 |
6. 0302 |
|
21 |
8. 509 2096 |
52 |
171 |
26 |
05 |
|
22 |
92 |
40 |
197 |
27 |
08 |
|
23 |
88 |
28 |
223 |
27 |
12 |
|
24 |
84 |
15 |
250 |
28 |
15 |
|
25 |
80 |
03 |
276 |
29 |
18 |
|
26 |
75 |
8.511 1191 |
302 |
30 |
21 |
|
27 |
71 |
79 |
329 |
31 |
25 |
|
28 |
67 |
66 |
355 |
31 |
28 |
|
29 |
63 |
54 |
381 |
32 |
31 |
|
30 |
8. 509 2059 |
8.511 1142 |
1. 27407 |
2. 3733 |
6. 0334 |
|
31 |
55 |
29 |
434 |
34 |
38 |
|
32 |
51 |
17 |
460 |
35 |
41 |
|
33 |
47 |
05 |
486 |
35 |
44 |
|
34 |
43 |
8. 511 1092 |
512 |
36 |
48 |
|
35 |
39 |
80 |
639 |
37 |
51 |
|
36 |
35 |
68 |
565 |
38 |
64 |
|
37 |
30 |
56 |
591 |
38 |
57 |
|
38 |
26 |
43 |
617 |
39 |
61 |
|
39 |
22 |
31 |
644 |
40 |
64 |
|
40 |
8. 509 2018 |
8. 511 1019 |
1. 27670 |
2. 3741 |
6. 0367 |
|
41 |
14 |
06 |
696 |
41 |
71 |
|
42 |
10 |
8. 511 0994 |
722 |
42 |
74 |
|
43 |
06 |
82 |
748 |
43 |
77 |
|
44 |
02 |
69 |
775 |
44 |
80 |
|
46 |
8.509 1998 |
57 |
801 |
45 |
84 |
|
46 |
93 |
45 |
827 |
45 |
87 |
|
47 |
89 |
32 |
853 |
46 |
90 |
|
48 |
85 |
20 |
879 |
47 |
94 |
|
49 |
81 |
08 |
905 |
48 |
97 |
|
50 |
8. 509 1977 |
8. 511 0895 |
1. 27932 |
2. 3748 |
6. 0400 |
|
51 |
73 |
83 |
958 |
49 |
03 |
|
52 |
69 |
71 |
984 |
50 |
07 |
|
53 |
65 |
58 |
1. 28010 |
51 |
10 |
|
54 |
61 |
46 |
036 |
51 |
13 |
|
55 |
56 |
34 |
062 |
52 |
17 |
|
56 |
52 |
21 |
088 |
63 |
20 |
|
57 |
48 |
09 |
114 |
54 |
23 |
|
58 |
44 |
8. 611 0797 |
141 |
54 |
27 |
|
59 |
40 |
84 |
167 |
55 |
30 |
|
60 |
8. 509 1936 |
8. 511 0772 |
1. 28193 |
2. 3756 |
6. 0433 |
202
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and a^iniulhn — Continued.
LATITUDE 87°.
|
log. A |
log. B |
log. C |
log. D |
log.E |
|
|
Latitude. |
|||||
|
dUi".l"=— 0.07 |
diff.l"= — 0.21 |
diir.l"= + 0.43 |
diff. 1"— + 0. 01 |
diff. 1"= + 0.06 |
|
|
37 00 |
8.509 1936 |
8. 511 0772 |
1.28193 |
2. 3756 |
6. 0433 |
|
1 |
32 |
60 |
219 |
56 |
. 37 |
|
28 |
47 |
245 |
57 |
40 |
|
|
3 |
23 |
35 |
271 |
58 |
43 |
|
i |
19 |
22 |
297 |
69 |
46 |
|
05 |
15 |
10 |
324 |
69 |
50 |
|
6 |
11 |
8. .511 0698 |
350 |
60 |
53 |
|
07 |
85 |
376 |
61 |
56 |
|
|
8 |
03 |
73 |
402 |
62 |
60 |
|
9 |
8. 509 1899 |
61 |
428 |
62 |
63 |
|
10 |
8. 509 1895 |
8.611 0648 |
1.28454 |
2. 3763 |
6, 0466 |
|
11 |
90 |
36 |
480 |
64 |
70 |
|
12 |
86 |
23 |
506 |
65 |
73 |
|
13 |
82 |
11 |
532 |
65 |
76 |
|
14 |
78 |
8.511 0599 |
558 |
66 |
80 |
|
15 |
74 |
86 |
584 |
67 |
83 |
|
16 |
70 |
74 |
610 |
67 |
86 |
|
17 |
66 |
61 |
636 |
68 |
89 |
|
18 |
62 |
49 |
662 |
69 |
93 |
|
19 |
57 |
37 |
638 |
69 |
96 |
|
20 |
8.509 1853 |
8.511 0524 |
1. 28715 |
2. 3770 |
6. 0499 |
|
21 |
49 |
12 |
741 |
71 |
6. 0503 |
|
22 |
45 |
00 |
767 |
72 |
06 |
|
23 |
a |
8.511 0487 |
793 |
72 |
09 |
|
24 |
37 |
75 |
819 |
73 |
13 |
|
25 |
33 |
62 |
. 845 |
74 |
16 |
|
26 |
28 |
50 |
871 |
74 |
19 |
|
27 |
24 |
37 |
897 |
75 |
23 |
|
28 |
20 |
25 |
923 |
76 |
26 |
|
29 |
16 |
13 |
949 |
76 |
29 |
|
30 |
8.509 1812 |
8. 511 0400 |
1. 28975 |
2.377/ |
6. 0533 |
|
31 |
08 |
8. 511 0388 |
1. 29001 |
78 |
36 |
|
32 |
04 |
75 |
027 |
79 |
39 |
|
33 |
00 |
63 |
053 |
79 |
43 |
|
34 |
8. 509 1795 |
51 |
079 |
80 |
46 |
|
35 |
91 |
38 |
104 |
81 |
49 |
|
36 |
87 |
26 |
130 |
81 |
53 |
|
37 |
83 |
13 |
166 |
82 |
56 |
|
38 |
79 |
01 |
182 |
83 |
59 |
|
39 |
75 |
8.511 0288 |
208 |
83 |
63 |
|
40 |
8. 509 1771 |
8.511 0276 |
1. 29234 |
2. 3784 |
6. 0566 |
|
41 |
66 |
64 |
260 |
85 |
69 |
|
42 |
62 |
51 |
286 |
86 |
73 |
|
43 |
58 |
39 |
312 |
86 |
76 |
|
44 |
54 |
26 |
338 |
87 |
79 |
|
45 |
50 |
14 |
364 |
87 |
83 |
|
46 |
46 |
01 |
390 |
88 |
86 |
|
47 |
41 |
8. 511 0189 |
416 |
89 |
89 |
|
48 |
37 |
76 |
442 |
89 |
93 |
|
49 |
33 |
64 |
468 |
90 |
96 |
|
50 |
8. 509 1729 |
8. 511 0151 |
1.29494 |
2, 3791 |
6. 0600 |
|
51 |
25 |
39 |
620 |
91 |
03 |
|
52 |
21 |
26 |
546 |
•i 92 |
06 |
|
53 |
16 |
14 |
571 |
93 |
10 |
|
54 |
12 |
02 |
697 |
93 |
13 |
|
55 |
08 |
8. 511 0089 |
623 |
94 |
16 |
|
56 |
04 |
77 |
649 |
95 |
20 |
|
57 |
00 |
64 |
675 |
95 |
23 |
|
58 |
8.509 1696 |
52 |
701 |
96 |
26 |
|
59 |
92 |
39 |
727 |
96 |
30 |
|
60 |
8. 509 1687 |
8. 511 0027 |
1. 29753 |
2. 3797 |
6. 0633 |
FAOTOES FOli COMPUTATION OF GEODETIC POSITIONS. 203
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 38°.
|
log. A |
log. B |
log. C |
log. D |
log. E |
|
|
Latitude. |
|||||
|
difl.l"=— 0.07 |
aiff.l"=— 0.21 |
diff.l"= + 0.43. |
diff.l" = + 0.01 |
diff.l"= + 0.06 |
|
|
38 00 |
8.509 1687 |
8. 511 0027 |
1. 29753 |
2. 3797 |
6. 0633 |
|
1 |
83 |
14 |
778 |
98 |
36 |
|
2 |
79 |
02 |
804 |
98 |
40 |
|
3 |
75 |
8. 510 9989 |
830 |
99 |
43 |
|
4 |
71 |
77 |
856 |
2. 3800 |
47 |
|
05 |
67 |
64 |
882 |
00 |
50 |
|
6 |
62 |
52 |
908 |
01 |
53 |
|
7 |
58 |
39 |
934 |
02 |
57 |
|
8 ■ |
54 |
27 |
959 |
02 |
60 |
|
9 |
50 |
14 |
985 |
03 |
63 |
|
.0 |
8. 509 1646 |
8. 510 9902 |
1. 30011 |
2. 3803 |
6. 0667 |
|
11 |
42 |
8. 510 9889 |
037 |
04 |
70 |
|
12 |
37 |
77 |
063 |
05 |
73 |
|
13 |
33 |
64 |
089 |
05 |
77 |
|
14 |
29 |
52 |
114 |
06 |
80 |
|
16 |
25 |
39 |
140 |
07 |
84 |
|
16 |
21 |
27 |
166 |
07 |
87 |
|
17 |
17 |
14 |
192 |
08 |
90 |
|
18 |
12 |
02 |
218 |
08 |
94 |
|
19 |
08 |
8.510 9789 |
243 |
09 |
97 |
|
20 |
8.509 1604 |
8. 510 9777 |
1. 30269 |
2. 3810 |
6. 0701 |
|
21 |
00 |
64 |
295 |
10 |
04 |
|
22 |
8. 509 1596 |
52 |
321 |
U |
07 |
|
23 |
92 |
39 |
347 |
12 |
11 |
|
24 |
87 |
- 27 |
372 |
12 |
14 |
|
25 |
83 |
14 |
398 |
13 |
17 |
|
26 |
79 |
01 |
424 |
13 |
21 |
|
27 |
75 |
8. 510 9689 |
450 |
14 |
24 |
|
28 |
71 |
77 |
476 |
16 |
28 |
|
29 |
66 |
64 |
501 |
15 |
31 |
|
30 |
8.509 1562 |
8. 510 9652 |
1.30527 |
2. 3816 |
6. 0734 |
|
31 |
58 |
39 |
553 |
16 |
38 |
|
32 |
54 |
27 |
579 |
17 |
41 |
|
33 |
50 |
14 |
604 |
17 |
44 |
|
34 |
46 |
01 |
630 |
18 |
48 |
|
35 |
41 |
8.510 9589 |
656 |
19 |
51 |
|
36 |
37 |
76 |
682 |
19 |
66 |
|
37 |
33 |
64 |
707 |
20 |
58 |
|
38 |
29 |
51 |
733 |
20 |
61 |
|
39 |
25 |
39 |
769 |
21 |
65 |
|
40 |
8. 509 1521 |
8. 510 9526 |
1. 30785 |
2. 3822 |
6. 0768 |
|
41 |
16 |
14 |
810 |
22 |
72 |
|
42 |
12 |
01 |
836 |
23 |
75 |
|
43 |
08 |
8. 510 9488 |
862 |
23 |
78 |
|
44 |
04 |
76 |
88T |
24 |
82 |
|
45 |
00 |
63 |
913 |
24 |
85 |
|
46 |
8. 509 1495 |
61 |
939 |
25 |
89 |
|
47 |
91 |
38 |
965 |
26 |
92 |
|
48 |
87 |
26 |
990 |
26 |
95 |
|
49 |
83 |
13 |
1. 31016 |
27 |
99 |
|
50 |
8. 509 1479 |
8. 510 9401 |
1. 31042 |
2. 3827 |
6. 0802 |
|
51 |
75 |
8. 510 9388 |
067 |
28 |
06 |
|
52 |
70 |
76 |
093 |
28 |
09 |
|
53 |
66 |
63 |
119 |
29 |
13 |
|
54 |
62 |
50 |
144 |
30 |
16 |
|
55 |
58 |
38 |
170 |
30 |
19 |
|
56 |
53 |
25 |
196 |
31 |
23 |
|
57 |
49 |
13 |
221 |
31 |
26 |
|
58 |
45 |
00 |
247 |
32 |
30 |
|
59 |
41 |
8.510 9287 |
273 |
32 |
33 |
|
60 |
8. 509 1437 |
8. 510 9275 |
1. 31299 |
2.3833 |
6. 0836 |
•204
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for the compntaiion of geodetic latitudes, longitudes, and azimuths — Contiuvied.
LATITUDE S90.
|
log A |
logB |
log C |
log I) |
logE |
|
|
Latitude. |
|||||
|
difif. 1"=— 0.07 |
diff. 1"=— 0.21 |
diff. I"=+0.43 |
diff. 1"=+0.01 |
ditt. l"=+0.06 |
|
|
39 00 |
8. 509 1437 |
8. 510 9275 |
1. 31299 |
2. 3833 |
6. 0836 |
|
1 |
33 |
62 |
324 |
33 |
40 |
|
2 |
28 |
50 |
350 |
34 |
43 |
|
3 |
24 |
37 |
375 |
35 |
47 |
|
4 |
20 |
25 |
401 |
35 |
50 |
|
05 |
16 |
12 |
427 |
36 |
53 |
|
6 |
12 |
8. 510 9199 |
452 |
36 |
57 |
|
7 |
07 |
87 |
478 |
37 |
60 |
|
8 |
03 |
74 |
504 |
37 |
- 64 |
|
9 |
8.509 1399 |
62 |
529 |
38 |
67 |
|
10 |
8. 509 1395 |
8. 510 9149 |
1. 31555 |
2.3838 |
6.0871 |
|
U |
91 |
36 |
581 |
39 |
74 |
|
12 |
86 |
24 |
606 |
39 |
77 |
|
13 |
82 |
11 |
632 |
2.3840 |
81 |
|
U |
78 |
8. 510 9098 |
658 |
40 |
84 |
|
15 |
74 |
86 |
683 |
41 |
88 |
|
16 |
70 |
73 |
709 |
41 |
91 |
|
17 |
65 |
61 |
734 |
42 |
95 |
|
18 |
61 |
48 |
760 |
43 |
98 |
|
19 |
57 |
36 |
786. |
43 |
6. 0902 |
|
20 |
8. 509 1353 |
8. 510 9023 |
1.31811 ■ |
2. 3844 |
6. 0905 |
|
21 |
49 |
10 |
837 |
44 |
08 |
|
22 |
44 |
8. 510 8998 |
862 |
45 |
12 |
|
23 |
40 |
85 |
888 |
45 |
15 |
|
2i |
36 |
73 |
913 |
46 |
19 |
|
25 |
32 |
60 |
939 |
46 |
22 |
|
26 |
28 |
47 |
965 |
47 |
26 |
|
27 |
23 |
35 |
990 |
47 |
29 |
|
28 |
19 |
23 |
1.32016 |
48 |
32 |
|
29 |
15 |
09 |
041 |
48 |
38 |
|
30 |
8. 509 1311 |
8. 510 8897 |
1. 32067 |
2. 3849 |
6.0939 |
|
31 |
07 |
84 |
092 |
49 |
43 |
|
32 |
02 |
72 |
118 |
2.3850 |
46 |
|
33 |
8. 509 1298 |
59 |
144 |
50 |
50 |
|
34 |
S4 |
46 |
169 |
51 |
53 |
|
35 |
90 |
34 |
195 |
51 |
57 |
|
36 |
86 |
21 |
220 |
52 |
60 |
|
37 |
81 |
08 |
246 |
52 |
63 |
|
38 |
77 |
8.510 8796 |
271 |
53 |
67 |
|
39 |
73 |
83 |
297 |
53 |
70 |
|
40 |
8.509 1269 |
8.510 8771 |
1. 32323 |
2. 3854 |
6.0974 |
|
41 |
64 |
58 |
348 |
54 |
77 |
|
42 |
60 |
45 |
374 |
55 |
81 |
|
43 |
56 |
33 |
399 |
55 |
84 |
|
44 |
52 |
20 |
425 |
56 |
83 |
|
45 |
48 |
07 |
450 |
56 |
91 |
|
46 |
43 |
8. 510 8695 |
476 |
57 |
95 |
|
47 |
39 |
82 |
501 |
57 |
98 |
|
48 |
35 |
69 |
527 |
57 |
6. 1002 |
|
49 |
31 |
57 |
552 |
58 |
05 |
|
50 |
8. 509 1227 |
8.510 8644 |
1. 32578 |
2.3858 |
6. 1008 |
|
51 |
22 |
31 |
603 |
59 |
12 |
|
52 |
18 |
19 |
629 |
59 |
15 |
|
53 |
14 |
06 |
654 |
2.3860 |
19 |
|
54 |
10 |
8. 510 8593 |
680 |
60 |
22 |
|
55 |
06 |
81 |
705 |
61 |
26 |
|
56 |
01 |
68 |
731 |
61 |
29 |
|
57 |
8.509 1197 |
55 |
756 |
62 |
33 |
|
58 |
93 |
43 |
782 |
62 |
36 |
|
59 |
89 |
30 |
807 |
63 |
40 |
|
60 |
8.509 1184 |
8. 510 8517 |
1. 32833 |
2. 3863 |
6. 1043 |
FACTOES FOE COMPUTATION OF GEODETIC POSITIOE^S. 205
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and aaimutlis — Continued.
LATITUDE 40°.
|
log A |
log B |
log C |
log D |
log E |
|
|
Latitude. |
|||||
|
diff.l"=— 0.07 |
diff.l"=— 0.2'l |
diff.l"=+0.42 |
diff.l"= + 0.01 |
diff. 1"= + 0.06 |
|
|
40 00 |
8. 509 1184 |
8.510 8517 |
1. 32833 |
2. 3863 |
6.1043 |
|
1 |
80 |
05 |
858 |
64 |
47 |
|
2 |
76 |
8. 510 8492 |
884 |
64 |
50 |
|
3 |
72 |
79 |
909 |
64 |
54 |
|
4 |
67 |
67 |
935 |
65 |
57 |
|
05 |
63 |
54 |
960 |
65 |
61 |
|
6 |
59 |
41 |
986 |
66 |
64 |
|
7 |
55 |
29 |
1. 33011 |
66 |
67 |
|
8 |
60 |
16 |
037 |
67 |
71 |
|
9 |
46 |
03 |
062 |
67 |
74 |
|
10 |
8. 509 1142 |
8. 510 8391 |
1. 33688 |
2. 3868 |
6. 1078 |
|
11 |
38 |
78 |
113 |
68 |
81 |
|
12 |
34 |
65 |
139 |
68 |
85 |
|
13 |
29 |
53 |
164 |
69 |
88 |
|
14 |
25 |
40 |
189 |
69 |
92 |
|
15 |
21 |
27 |
215 |
2. 3870 |
95 |
|
16 |
17 |
15 |
240 |
70 |
99 |
|
17 |
12 |
02 |
266 |
71 |
6. 1102 |
|
18 |
OS |
8. 510 8289 |
291 |
71 |
06 |
|
19 |
04 |
77 |
317 |
72 |
09 |
|
20 |
8.509 1100 |
8. 510 8264 |
1. 33342 |
2. 3872 |
6.1113 |
|
21 |
8. 509 1096 |
51 |
363 |
72 |
16 |
|
22 |
91 |
38 |
393 |
73 |
20 |
|
23 |
87 |
26 |
418 |
73 |
23 |
|
24 |
83 |
13 |
444 |
74 |
27 |
|
25 |
79 |
00 |
469 |
74 |
30 |
|
26 |
74 |
8.510 8188 |
495 |
74 |
34 |
|
27 |
70 |
75 |
520 |
75 |
37 |
|
28 |
66 |
62 |
546 |
75 |
41 |
|
29 |
62 |
50 |
571 |
76 |
44 |
|
30 |
8.509 1057 |
8. 510 8137 |
1.33596 |
2. 3876 |
6. 1148 |
|
31 |
53 |
24 |
622 |
77 |
51 |
|
32 |
49 |
11 |
■ 647 |
77 |
55 |
|
33 |
45 |
8. 510 8099 |
673 |
77 |
58 |
|
34 |
41 |
86 |
698 |
78 |
62 |
|
35 |
36 |
73 |
723 |
78 |
65 |
|
36 |
32 |
61 |
749 |
79 |
69 |
|
37 |
28 |
48 |
774 |
79 |
72 |
|
38 |
24 |
35 |
800 |
79 |
76 |
|
39 |
19 |
23 |
825 |
2. 3880 |
79 |
|
40 |
8. 509 1015 |
8. 510 8010 |
1. 33850 |
2.3880 |
6. 1183 |
|
41 |
11 |
8.510 7997 |
876 |
81 |
86 |
|
42 |
07 |
84 |
901 |
81 |
90 |
|
43 |
02 |
72 |
926 |
81 |
93 |
|
44 |
8.509 0998 |
59 |
952 |
82 |
97 |
|
45 |
94 |
46 |
977 |
82 |
6. 1200 |
|
46 |
90 |
33 |
1. 34003 |
83 |
04 |
|
47 |
85 |
21 |
028 |
83 |
07 |
|
48 |
81 |
08 |
053 |
83 |
11 |
|
49 |
77 |
8. 510 7895 |
079 |
84 |
15 |
|
50 |
8. 509 0973 |
8. 510 7883 |
1. 34104 |
2.3884 |
6. 1218 |
|
51 |
68 |
70 |
129 |
84 |
22 |
|
52 |
64 |
57 |
155 |
85 |
25 |
|
53 |
60 |
44 |
180 |
85 |
29 |
|
54 |
56 |
32 |
206 |
86 |
32 |
|
55 |
52 |
19 |
231 |
86 |
36 |
|
56 |
47 |
06 |
256 |
86 |
39 |
|
57 |
43 |
8. 510 7793 |
282 |
87 |
43 |
|
58 |
39 |
81 |
307 |
87 |
46 |
|
59 |
34 |
68 |
332 |
87 |
50 |
|
60 |
8.509 0930 |
8. 510 7755 |
1. 34358 |
2. 3888 |
6. 1253 |
206
A MANUAL OP TOPOGEAPHIO METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 41°.
|
log. A |
log.B |
log.C |
log.D |
log.E |
|
|
latitude. |
|||||
|
difF.l"=— 0.07 |
diff.l" = — 0.21 |
diff. 1" = + 0.42 |
diff. 1"= + 0.01 |
diff. 1"= + 0.06 |
|
|
41 00 |
8. 509 0930 |
8.510 7755 |
1. 34358 |
2. 3888 |
6. 1253 |
|
1 |
26 |
42 |
383 |
88 |
57 |
|
2 |
22 |
30 |
408 |
89 |
60 |
|
3 |
18 |
17 |
434 |
89 |
64 |
|
4 |
13 |
04 |
459 |
89 |
67 |
|
05 |
09 |
8. 510 7691 |
484 |
90 |
71 |
|
6 |
05 |
79 |
510 |
90 |
75 |
|
7 |
00 |
66 |
535 |
90 |
78 |
|
8 |
8.509 0896 |
53 |
560 |
91 |
82 |
|
9 |
92 |
40 |
586 |
91 |
85 |
|
10 |
8.509 0888 |
8. 510 7628 |
1.34611 |
2. 3891 |
6. 1289 |
|
11 |
83 |
15 |
636 |
92 |
92 |
|
12 |
79 |
02 |
662 |
92 |
96 |
|
13 |
75 |
8. 510 7590 |
687 |
93 |
99 |
|
14 |
71 |
77 |
712 |
93 |
6. 1303 |
|
15 |
67 |
64 |
738 |
93 |
06 |
|
16 |
62 |
51 |
763 |
94 |
10 |
|
17 |
58 |
39 |
788 |
94 |
14 |
|
18 |
54 |
26 |
814 |
94 |
17 |
|
19 |
49 |
13 |
839 |
95 |
21 |
|
211 |
8. 509 0845 |
8. 510 7500 |
1.34864 |
2.3895 |
6. 1324 |
|
21 |
41 |
8. 510 7488 |
890 |
95 |
28 |
|
23 |
37 |
75 |
915 |
96 |
31 |
|
23 |
32 |
62 |
940 |
96 |
35 |
|
24 |
28 |
49 |
965 |
96 |
38 |
|
25 |
24 |
36 |
991 |
97 |
42 |
|
26 |
20 |
24 |
1. 35016 |
97 |
46 |
|
27 |
15 |
11 |
041 |
97 |
49 |
|
28 |
11 |
8.510 7398 |
066 |
98 |
53 |
|
29 |
07 |
85 |
092 |
98 |
56 |
|
30 |
8. 509 0803 |
8. 510 7373 |
1. 35117 |
2. 3898 |
6. 1360 |
|
31 |
8.509 0798 |
60 |
142 |
99 |
63 - |
|
32 |
94 |
■ 47 |
168 |
99 |
67 |
|
33 |
90 |
34 |
193 |
99 |
70 |
|
34 |
86 |
22 |
218 |
2.3900 |
74 |
|
35 |
81 |
09 |
243 |
00 |
78 |
|
36 |
77 |
8. 510 7296 |
269 |
00 |
81 |
|
37 |
73 |
83 ■ |
294 |
00 |
85 |
|
38 |
69 |
70 |
319 |
01 |
88 |
|
39 |
64 |
58 |
345 |
01 |
92 |
|
40 |
». 509 0760 |
8.510 7245 |
1.35370 |
2. 3901 |
6. 1395 |
|
41 |
56 |
32 |
395 |
02 |
99 |
|
42 |
52 |
19 |
420 |
02 |
6. 1403 |
|
43 |
47 |
07 |
446 |
02 |
06 |
|
44 |
43 |
8. 510 7194 |
471 |
03 |
10 |
|
45 |
39 |
81 |
496 |
03 |
13 |
|
46 |
35 |
68 |
522 |
03 |
17 |
|
47 |
30 |
55 |
547 |
03 |
20 |
|
48 |
26 |
43 |
572 |
04 |
24 |
|
49 |
22 |
30 |
597 |
04 |
28 |
|
50 |
8. 509 0738 |
8. 510 7117 |
1. 35623 |
2.3904 |
6. 1431 |
|
51 |
13 |
04 |
648 |
05 |
35 |
|
52 |
09 |
8. 510 7091 |
673 |
OS |
38 |
|
53 |
05 |
79 |
698 |
05 |
42 |
|
51 |
00 |
66 |
723 |
05 |
46 |
|
55 |
8. 509 0696 |
53 |
749 |
06 |
49 |
|
56 |
92 |
40 |
774 |
06 |
53 |
|
57 |
88 |
27 |
799 |
06 |
56 |
|
58 |
83 |
15 |
824 |
07 |
60 |
|
59 |
79 |
02 |
850 |
07 |
63 |
|
60 |
8. 509 0675 |
8. 510 6989 |
1.35875 |
2. 3907 |
6. 1467 |
FACTOES FOE COMPUTATION OF GEODETIC POSITIONS. 2()7
Table XXVIT. — Factors for the compntaUon of ffcodelic latitudes, longitudes, and azimuths — Contimied.
LATITUDE 42°
|
log. A |
log. B |
Ing.C |
logD. |
log. E |
|
|
Latitude. |
|||||
|
diff.l"=— 0.07 |
:difl'. 1"=— 0.21 |
ditf. l"=+0.42 |
diff. l"=+0.00 |
diff. 1" =+0.06 |
|
|
42 00 |
8. 509 0675 |
8. 510 6989 |
1. 35875 |
2.3907 |
6. 1467 • |
|
1 |
71 |
76 |
900 |
08 |
71 |
|
2 |
66 |
64 |
925 |
08 |
74 |
|
3 |
62 |
51 |
951 |
08 |
78 |
|
4 |
58 |
38 |
976 |
08 |
81 |
|
05 |
54 |
25 |
1. 36001 |
09 |
85 |
|
6 |
49 |
12 |
026 |
09 |
89 |
|
7 |
45 |
00 |
052 |
09 |
92 |
|
8 |
41 |
8. 510 6887 |
077 |
09 |
96 |
|
9 |
36 |
74 |
102 |
10 |
99 |
|
10 |
8. 509 0632 |
8.510 6861 |
1. 36127 |
2. 3910 |
6. 1503 |
|
11 |
28 |
48 |
152 |
10 |
07 |
|
12 |
24 |
36 |
178 |
10 |
10 |
|
13 |
19 |
23 |
203 |
11 |
14 |
|
14 |
15 |
10 |
228 |
11 |
17 |
|
15 |
11 |
8. 510 6797 |
253 |
11 |
21 |
|
16 |
07 |
84 |
278 |
12 |
25 |
|
17 |
02 |
72 |
304 |
12 |
28 |
|
18 |
8. 509 0598 |
59 |
329 |
12 |
32 |
|
19 |
94 |
46 |
354 |
12 |
35 |
|
20 |
8.509 6590 |
8.510 6733 |
1. 36379 |
2. 3913 |
6. 1539 |
|
21 |
85 |
20 |
404 |
13 |
43 |
|
22 |
81 |
07 |
430 |
13 |
46 |
|
23 |
77 |
8. 510 6695 |
455 |
13 |
50 |
|
24 |
72 |
82 |
480 |
13 |
54 |
|
25 |
68 |
69 |
505 |
14 |
57 |
|
26 |
64 |
56 |
530 |
14 |
61 |
|
27 |
60 |
43 |
556 |
14 |
64 |
|
28- |
55 |
31 |
681 |
14 |
68 |
|
29 |
51 |
18 |
606 |
15 |
72 |
|
30 |
8.509 0547 |
8.530 6605 |
1.36631 |
2. 3915 |
6. 1575 |
|
31 |
43 |
8. 510 6592 |
056 |
15 |
79 |
|
32 |
38 |
79 |
682 |
15 |
83 |
|
33 |
34 |
66 |
707 |
16 |
86 |
|
84 |
30 |
54 |
732 |
16 |
90 |
|
35 |
25 |
41 |
757 |
16 |
93 |
|
36 |
21 |
28 |
782 |
16 |
97 |
|
37 |
17 |
15 |
808 |
17 |
6. 1601 |
|
38 |
13 |
02 |
833 |
17 |
04 |
|
39 |
08 |
8. 510 6490 |
858 |
17 |
08 |
|
40 |
8. 509 0504 |
8, 510 6477 |
1. 36883 |
2. 3917 |
6. 1612 |
|
41 |
00 |
64 |
908 |
17 |
15 |
|
42 |
8. 509 0496 |
51 |
934 |
18 |
19 |
|
43 |
91 |
38 |
959 |
18 |
22 |
|
44 |
87 |
25 |
984 |
18 |
26 |
|
45 |
83 |
13 |
1. 37009 |
18 |
30 |
|
46 |
78 |
00 |
034 |
19 |
33 |
|
47 |
74 |
8.510 6387 |
0.59 |
19 |
37 |
|
48 |
70 |
74 |
085 |
19 |
41 |
|
49 |
66 |
61 |
110 |
19 |
44 |
|
50 |
8. 609 0461 |
8.510 6348 |
1. 37135 |
2. 3919 |
6. 1648 |
|
51 |
57 |
36 |
160 |
20 |
52 |
|
52 |
53 |
23 |
185 |
20 |
55 |
|
53 |
48 |
10 |
210 |
20 |
59 |
|
54 |
44 |
8. 610 6297 |
235 |
20 |
63 |
|
55 |
40 |
84 |
261 |
20 |
66 |
|
56 |
36 |
71 |
286 |
21 |
70 |
|
57 |
31 |
59 |
311 |
21 |
73 |
|
68 |
27 |
46 |
336 |
21 |
77 |
|
59 |
23 |
33 |
361 |
21 |
81 |
|
60 |
8. 509 0419 |
8. 510 6220 |
1. 37386 |
2. 3921 |
6. 1084 |
208
A MANUAL OP TOPOGEAPHIO METHODS.
Table XXVII. — Factors for the computation of geodetic latitiides, longitudes, and azimuths — Contiuued.
LATITDDE 43°.
|
log. A |
log.B |
log.C |
log.D |
log.E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.07 |
diff. 1"«=— 0.21 |
diff'. 1"= + 0.42 |
diff. 1"= + 0.00 |
diff. 1"=+ 0.06 |
|
|
43 00 |
8. 509 0419 |
8. 510 6220 |
1.37386 |
2. 3921 |
6. 1684 |
|
1 |
14 |
07 |
412 |
22 |
88 |
|
2 |
10 |
8. 510 6195 |
437 |
22 |
92 |
|
3 |
06 |
82 |
462 |
22 |
95 |
|
i |
01 |
69 |
487 |
22 |
99 |
|
05 |
8. 509 0397 |
56 |
512 |
22 |
6, 1703 |
|
6 |
93 |
43 |
537 |
22 |
06 |
|
7 |
89 |
30 |
663 ■ |
23 |
10 |
|
8 |
84 |
17 |
588 |
23 |
14 |
|
9 |
80 |
05 |
613 |
23 |
17 |
|
10 |
8. 509 0376 |
8. 510 G092 |
1. 37638 |
2.3923 |
6. 1721 |
|
11 |
71 |
79 |
663 |
23 |
25 |
|
12 |
67 |
66 |
688 |
24 |
28 |
|
13 |
63 |
53 |
713 |
24 |
32 |
|
14 |
59 |
40 |
739 |
24 |
36 |
|
15 |
54 |
28 |
764 |
24 |
39 |
|
16 |
50 |
15 |
789 |
24 |
43 |
|
17 |
46 |
02 |
814 |
24 |
47 |
|
18 |
41 |
8. 510 5989 |
839 |
25 |
50 |
|
19 |
37 |
76 |
864 |
25 |
54 |
|
20 |
8. 509 0333 |
8. 510 5963 |
1. 37889 |
2. 3925 |
6. 1758 |
|
21 |
29 |
50 |
915 |
25 |
61 |
|
22 |
24 |
38 |
940 |
25 |
65 |
|
23 |
20 |
25 |
965 |
25 |
69 |
|
24 |
16 |
12 |
990 |
25 |
72 |
|
25 |
12 |
8.510 5899 |
1. 38015 |
26 |
76 |
|
26 |
07 |
86 |
040 |
26 |
80 |
|
27 |
03 |
73 |
065 |
26 |
83 |
|
28 |
8. 509 0299 |
60 |
091 |
26 |
• 87 |
|
29 |
94 |
48 |
116 |
26 |
91 |
|
30 |
8. 509 0290 |
8. 510 5835 |
1. 38141 |
2. 3926 |
6. 1795 |
|
31 |
86 |
22 |
166 |
27 |
98 |
|
32 |
82 |
09 |
191 |
27 |
6. 1802 |
|
33 |
77 |
8.510 6796 |
216 |
27 |
06 |
|
34 |
73 |
83 |
241 |
27 |
09 |
|
35 |
69 |
71 |
266 |
27 |
13 |
|
36 |
64 |
58 |
292 |
27 |
17 |
|
37 |
60 |
45 |
317 |
27 |
20 |
|
38 |
56 |
32 |
342 |
27 |
24 |
|
39 |
52 |
19 |
367 |
28 |
23 |
|
40 |
8. 509 0247 |
8. 510 .5706 |
1. 38392 |
2.3928 |
6. 183] |
|
41 |
43 |
8.510 5693 |
417 |
28 |
35 |
|
42 |
39 |
81 |
442 |
28 |
39 |
|
43 |
34 |
68 |
467 |
28 |
42 |
|
44 |
30 |
55 |
492 |
28 |
46 |
|
45 |
26 |
42 |
518 |
28 |
50 |
|
46 |
22 |
29 |
543 |
28 |
53 |
|
47 |
17 |
16 |
568 |
29 |
57 |
|
48 |
13 |
03 |
593 |
29 |
61 |
|
49 |
09 |
8.510 5591 |
618 |
29 |
65 |
|
50 |
8.609 0204 |
8. 510 5578 |
1. 38643 |
2. 3929 |
6. 1868 |
|
51 |
00 |
65 |
668 |
29 |
72 |
|
52 |
8. 509 0196 |
52 |
693 |
29 |
76 |
|
53 |
92 |
39 |
719 |
29 |
79 |
|
54 |
87 |
26 |
744 |
29 |
83 |
|
55 |
83 |
13 |
769 |
30 |
87 |
|
56 |
79 |
01 |
794 |
30 |
91 |
|
57 |
74 |
8.510 6488 |
819 |
30 |
94 |
|
58 |
70 |
75 |
844 |
30 |
98 |
|
59 |
66 |
02 |
869 |
30 |
6. 1902 |
|
60 |
8. 509 0162 |
8. 510 5449 |
1. 38894 |
2. 3930 |
6. 1905 |
FACTOES FOR OOMPUTATIOS^ OF GEODETIC POSITIONS. 209
Table XXVII. — Factors for the compulation of yeodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 44°.
|
log. A |
log.B |
log.C |
log. D |
log.E |
|
|
Latitude. |
|||||
|
diff. 1"=— 0.07 |
diff. 1"=— 0.21 |
difl-. l"=+0.42 |
diff. l"=+0.00 |
diff. l"=+0.06 |
|
|
44 00 |
8. 509 0162 |
8.510 5449 |
1. 38894 |
2. 3930 |
6. 1905 |
|
1 |
57 |
36 |
919 |
30 |
09 |
|
2 |
53 |
23 |
945 |
30 |
13 |
|
3 |
49 |
01 |
970 |
30 |
17 |
|
4 |
44 |
8. 510 5388 |
995 |
30 |
20 |
|
05 |
40 |
75 |
1. 39020 |
31 |
24 |
|
6 |
36 |
62 |
045 |
31 |
28 |
|
7 |
31 |
49 |
070 |
31 |
31 |
|
8 |
27 |
36 |
095 |
31 |
35 |
|
9 |
23 |
23 |
120 |
31 |
39 |
|
10 |
3. 509 0119 |
8. 510 5311 |
1. 39145 |
2. 3931 |
6. 1943 |
|
11 |
14 |
07 |
171 |
31 |
46 |
|
12 |
10 |
8. 510 5295 |
196 |
fl |
50 |
|
13 |
06 |
82 |
221 |
31 |
54 • |
|
14 |
02 |
09 |
246 |
31 |
58 |
|
15 |
8. 509 0097 |
56 |
271 |
31 |
61 |
|
16 |
93 |
43 |
296 |
31 |
6b |
|
17 |
89 |
30 |
321 |
32 |
69 |
|
18 |
84 |
18 |
346 |
32 |
72 |
|
19 |
80 |
05 |
371 |
32 |
76 |
|
20 |
8. 509 0076 |
9. 510 5192 |
1. 39396 |
2. 3932 |
6. 1980 |
|
21 |
72 |
79 |
422 |
32 |
84 |
|
22 |
67 |
66 |
447 |
32 |
87 |
|
23 |
63 |
53 |
472 |
32 |
91 |
|
24 |
59 |
40 |
497 |
52 |
95 |
|
25 |
54 |
28 |
622 |
32 |
99 |
|
26 |
50 |
15 |
547 |
32 |
6. 2002 |
|
27 . |
46 |
02 |
572 |
32 |
06 |
|
28 |
42 |
8. 510 5089 |
697 |
32 |
10 |
|
29 |
37 |
76 |
623 |
32 |
14 |
|
30 |
8. 509 0033 |
8. 510 5063 |
1.39648 |
2. 3932 |
6. 2017 |
|
31 |
29 |
50 |
673 |
32 |
21 |
|
32 |
24 |
37 |
698 |
H2 |
25 |
|
- 33 |
20 |
25 |
723 |
33 |
29 |
|
34 |
16 |
12 |
748 |
33 |
32 |
|
35 |
11 |
8.510 4999 |
773 |
33 |
36 |
|
36 |
07 |
86 |
79S |
33 |
40 |
|
37 |
03 |
73 |
823 |
33 |
44 |
|
38 |
8. 508 9999 |
60 |
848 |
33 |
47 |
|
39 |
94 |
47 |
873 |
33 |
51 |
|
40 |
8. 508 9990 |
8. 510 4935 |
1.39898 |
2. 3933 . |
6. 2055 |
|
41 |
86 |
22 |
924 |
33 |
59 |
|
42 |
81 |
09 |
949 |
33 |
62 |
|
43 |
77 |
8. 510 4896 |
974 |
33 |
66 |
|
44 |
73 |
83 |
999 |
33 |
70 |
|
45 |
69 |
70 |
1. 40024 |
33 |
74 |
|
46 |
64 |
57 |
049 |
33 |
77 |
|
47 |
60 |
44 |
074 |
33 |
81 |
|
48 |
56 |
32 |
099 |
33 |
85 |
|
49 |
51 |
19 |
124 |
33 |
89 |
|
50 |
8. 508 9947 |
8. 510 4806 |
1. 40149 |
2. 3933 |
6.2092 |
|
51 |
43 |
8. 510 4793 |
174 |
33 |
96 |
|
52 |
39 |
80 |
200 |
33 |
6. 2100 |
|
53 |
34 |
67 |
225 |
33 |
04 |
|
54 |
30 |
54 |
250 |
33 |
08 |
|
55 |
26 |
41 |
275 |
33 |
11 |
|
56 |
21 |
29 |
300 |
33 |
15 |
|
57 |
17 |
16 |
325 |
33 |
19 |
|
58 |
13 |
03 |
350 |
33 |
23 |
|
59 |
09 |
8. 510 4690 |
375 |
33 |
27 |
|
60 |
8. 508 9904 |
8. 510 4677 |
1. 40400 |
2. 3933 |
6. 2130 |
-14
210
A MANUAL OF TOPOGEAPHIO METHODS.
Table XXVII.— Fne/ors for Ihe c<>m}>ittalioii of geodetic latitudes, longitudes, and azimuths— Contimied.
LATITUDE -ISO.
log. A !.liff.l"=-0.07
log. B <litt'.l" = — 0.21
log. C
iliir.l" = H-0.42
log. D
dlff.l"=±0.00
log. E cliff. 1" = +0.06
FACTORS FOR COMPUTATION OF GEODETIC POSITIONS. 211
Table XXVII.— Factors for the computation of geodetic latitudes, longitudes, and asmui^tg— Continued.
LATITUDE 46°.
|
log. A |
log.B |
log.C |
log.D |
log.E |
||
|
Latitude |
||||||
|
(liff. ]"=— 0.07 |
diff. 1"=— 0.21 |
diff. 1"= +0.42 |
difif. 1"=— 0.00 |
diff. 1"= +0.06 |
||
|
46 00 |
8. 508 9647 |
8. 510 3905 |
1. 41906 |
2. 3932 |
6. 2359 |
|
|
1 |
43 |
8. 510 3892 |
931 |
32 |
63 |
|
|
2 |
38 |
79 |
957 |
31 |
67 |
|
|
3 |
34 |
67 |
982 |
31 |
71 |
|
|
4 |
30 |
54 |
1. 42007 |
31 |
75 |
|
|
05 |
25 |
41 |
032 |
31 |
79 |
|
|
6 |
21 |
28 |
057 |
31 |
82 |
|
|
7 |
17 |
15 |
082 |
31 |
86 |
|
|
8 |
13 |
02 |
107 |
31 |
90 |
|
|
9 |
08 |
8.510 3739 |
132 |
31 |
94 |
|
|
10 |
8. 508 9604 |
8.510 3776 |
1.42157 |
2.3931 |
6. 2398 |
|
|
11 |
00 |
64 |
183 |
31 |
6. 2402 |
|
|
12 |
8. 508 959S |
51 |
208 |
31 |
06 |
|
|
13 |
91 |
38 |
233 • |
30 |
09 |
|
|
14 |
87 |
25 |
268 |
30 |
13 |
|
|
15 |
83 |
12 |
283 |
30 |
17 |
|
|
16 |
78 |
8. 510 3699 |
308 |
30 |
21 |
|
|
17 |
74 |
86 |
333 |
30 |
25 |
|
|
18 |
70 |
74 |
358 |
30 |
29 |
|
|
19 |
65 |
61 |
. 384 |
30 |
33 |
|
|
20 |
8. 508 9561 |
8. 510 3648 |
1. 42409 |
2. 3930 |
6. 2436 |
|
|
21 |
57 |
35 |
434 |
30 |
40 |
|
|
22 |
53 |
22 |
459 |
30 |
44 |
|
|
23 |
'48 |
09 |
484 |
29 |
48 |
|
|
24 |
44 |
8. 510 3596 |
509 |
29 |
52 |
|
|
25 |
40 |
84 |
534 |
29 |
56 |
|
|
26 |
35 |
71 |
559 |
29 |
60 |
|
|
27 |
31 |
58 |
584 |
29 |
64 |
|
|
28 |
27 |
45 |
610 |
29 |
67 |
|
|
29 |
23 |
32 |
635 |
39 |
71 |
|
|
30 |
8. 508 9518 |
8. 510 3519 |
1.42660 |
2. 3929 |
6. 2475 |
|
|
31 |
14 |
06 |
685 |
29 |
79 |
|
|
32 |
10 |
8. 510 3494 |
710 |
28 |
83 |
|
|
33 |
05 |
81 |
735 |
28 |
87 |
|
|
34 |
01 |
68 |
760 |
28 |
91 |
|
|
35 |
8. 508 9497 |
55 |
786 |
28 |
95 |
|
|
36 |
93 |
42 |
811 |
28 |
99 |
|
|
37 |
88 |
29 |
836 |
28 |
8, 2502 |
|
|
38 |
84 |
17 |
861 |
28 |
06 |
|
|
39 |
80 |
04 |
886 |
28 |
10 |
|
|
40 |
8. 508 9475 |
8. 510 3391 |
1. 42911 |
2. 3927 |
6. 2514 |
|
|
41 |
71 |
78 |
936 |
27 |
18 |
|
|
42 |
67 |
65 |
961 |
27 |
22 |
|
|
43 |
63 |
52 |
987 |
27 |
26 |
|
|
44 |
58 |
39 |
1. 43012 |
27 |
30 |
|
|
45 |
54 |
27 |
037 |
27 |
34 |
|
|
46 |
50 |
14 |
062 |
27 |
38 |
|
|
47 |
45 |
01 |
087 |
26 |
41 |
|
|
48 |
41 |
8. 510 3288 |
112 |
26 |
45 |
|
|
49 |
37 |
75 |
137 |
26 |
49 |
|
|
50 |
8.508 9433 |
8. 510 3262 |
1.43163 |
2.3926 |
6. 2553 |
|
|
51 |
28 |
49 |
188 |
26 |
57 |
|
|
52 |
24 |
37 |
213 |
26 |
61 |
|
|
53 |
20 |
24 |
238 |
26 |
65 |
|
|
54 |
16 |
11 |
263 |
25 |
69 |
|
|
55 |
11 |
8.510 3198 |
288 |
25 |
73 |
|
|
56 |
07 |
85 |
314 |
25 |
77 |
|
|
57 |
03 |
72 |
339 |
25 |
81 |
|
|
58 |
8.508 9398 |
60 |
364 |
25 |
84 |
|
|
59 |
94 |
47 |
389 |
25 |
88 |
|
|
60 |
8.508 9390 |
8. 510 3134 |
1. 43414 |
2. 3924 |
6. 2592 |
212
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVII. — Factors for ike oompulallon of geodetic latitudes, longitudes, and azimuths— Continued.
LATITUDE 47°.
|
log. A |
log.B |
log.C |
log.D |
log.E |
|
|
Latitude. |
|||||
|
(liff. l"=.-0.07 |
<litt-. 1"=— 0.21 |
diB'. l"=+0.42 |
dift'. 1"=— 0.00 |
ditl'. l"=+0.07 |
|
|
47 00 |
8. 508 9390 |
8.510 3134 |
1.43414 |
2. 3924 |
6.2592 |
|
1 |
86 |
21 |
439 |
24 |
96 |
|
2 |
81 |
08 |
465 |
24 |
6. 2600 |
|
3 |
77 |
8.510 3095 |
490 |
24 |
04 |
|
4, |
73 |
82 |
515 |
24 |
08 |
|
05 |
08 |
70 |
540 |
24 |
12 |
|
6 |
64 |
57 |
565 |
23 |
16 |
|
7 |
00 |
44 |
590 |
23 |
20 |
|
8 |
56 |
31 |
615 |
23 |
24 |
|
9 |
51 |
18 |
641 |
23 |
28 |
|
10 |
8. 508 9347 |
8. 510 3005 |
1.43666 |
2. 3923 |
6. 2632 |
|
11 |
43 |
8. 510 2993 |
691 |
23 |
35 |
|
12 |
' 38 |
SO ■ |
716 |
22 |
39 |
|
13 |
34 |
• 67 |
741 |
22 |
43 |
|
14 |
30 |
54 |
760 |
22 |
47 |
|
15 |
26 |
41 |
792 |
22 |
51 |
|
16 |
21 |
28 |
817 |
22 |
55 |
|
17 |
17 |
16 |
842 |
21 |
59 |
|
18 |
13 |
03 |
867 |
21 |
63 |
|
19 |
09 |
8. 510 2890 |
892 |
21 |
67 |
|
20 |
8, 508 9304 |
8. 510 2877 |
1.43917 |
2. 3921 |
6. 2671 |
|
21 |
00 |
64 |
943 |
21 |
75 |
|
22 |
8. 508 9296 |
51 |
968 |
20 |
79 |
|
23 |
91 |
39 |
993 |
20 |
83 |
|
24 |
87 |
26 |
1.44018 |
20 |
87 |
|
25 |
83 |
13 |
043 |
20 |
91 |
|
26 |
79 |
00 |
069 |
20 |
95 |
|
74 |
8. 510 2787 |
094 |
19 |
99 |
|
|
28 |
70 |
74 |
119. |
19 |
6. 2702 |
|
29 |
66 |
62 |
144 |
19 |
00 |
|
30 |
8.508 9261 |
8. 510 2749 |
1.44169 |
2. 3919 |
6.2710 |
|
31 |
57 |
36 |
195 |
19 |
14 |
|
32 |
53 |
23 |
220 |
18 |
18 |
|
33 |
49 |
10 |
245 |
18 |
22 |
|
34 |
44 |
8. 510 2698 |
270 |
18 |
26 |
|
35 |
40 |
85 |
295 |
18 |
30 |
|
36 |
36 |
72 |
321 |
18 |
34 |
|
37 |
32 |
59 |
346 |
17 |
38 |
|
38 |
27 |
46 |
371 |
17 |
42 |
|
39 |
23 |
33 |
,396 |
17 |
a |
|
40 |
8. 508 9219 |
8. 510 2621 |
1.44421 |
2. 3917 |
6. 2750 |
|
41 |
14 |
08 |
447 |
16 |
54 |
|
42 |
10 |
8. 510 2595 |
472 |
16 |
68 |
|
43 |
06 |
82 |
497 |
16 |
62 |
|
44 |
02 |
69 |
522 |
16 |
66 |
|
45 |
8.508 9197 |
57 |
547 |
16 |
70 |
|
46 |
93 |
44 |
573 |
15 |
74 |
|
47 |
89 |
31 |
598 |
15 |
78 |
|
48 |
84 |
18 |
623 |
15 |
82 |
|
49 |
80 |
05 |
648 |
15 |
86 |
|
50 |
8. 508 9176 |
8. 510 2493 |
1. 44673 |
2. 3914 |
6. 2790 |
|
51 |
72 |
80 |
699 |
14 |
94 |
|
52 |
67 |
67 |
724 |
14 |
98 |
|
53 |
63 |
54 |
749 |
14 |
6. 2802 |
|
54 |
59 |
41 |
774 |
13 |
06 |
|
55 |
55 |
28 |
800 |
13 |
10 |
|
50 |
50 |
16 |
825 |
13 |
14 |
|
57 |
46 |
03 |
850 |
13 |
18 |
|
58 |
42 |
8. 510 2390 |
875 |
12 |
22 |
|
59 |
38 |
77 |
900 |
12 |
26 |
|
60 |
8. 508 9133 |
8. 510 2364 |
1.44926 |
2. 3912 |
6. 2830 |
FACTORS FOE COMPUTATION OF GEODETIC POSITIONS. 213
Table XXVIl.^Factors for the computation of geodetic latitudes, lougitttdes, and azimuths — Continued.
LATITUDE 48°.
|
loj;. A |
log. B |
log. C |
log. h |
log. E |
|
|
Lalitiule. |
|||||
|
(liff.l" =— 0.07 |
cliflf.l"=— 0.21 |
lUff. l"=+0.42 |
diflU"=— 0.00 |
(lifif. l" = +0.07 |
|
|
48 00 |
8. 508 91B3 |
8. 510 2364 |
1. 44926 |
2. 3912 |
6. 2830 |
|
1 |
29 |
52 |
951 |
12 |
34 |
|
2 |
25 |
39 |
976 |
11 |
38 |
|
3 |
20 |
26 |
1.45001 |
11 |
42 |
|
i |
16 |
13 |
027' |
n |
46 |
|
05 |
12 |
00 |
052 |
11 |
50 |
|
6 |
08 |
8.510 2288 |
077 |
10 |
54 |
|
7 |
03 |
75 |
102 |
10 |
58 |
|
8 |
8. 5118 9099 |
62 |
128 |
10 |
62 |
|
9 |
95 |
49 |
153 |
10 |
66 |
|
10 |
8. 508 9091 |
8. 510 2236 |
■ 1.45178 |
2. 3909 |
6.2870 |
|
11 |
86 |
24 |
203 |
0!) |
74 |
|
12 |
82 |
11 |
229 |
09 |
78 |
|
13 |
78 |
8. 510 2198 |
254 |
08 |
82 |
|
14 |
74 |
85 |
279 |
08 |
86 |
|
15 |
69 |
72 |
304 |
08 |
90 |
|
16 |
65 |
60 |
330 |
08 |
94 |
|
17 |
61 |
47 |
355 |
07 |
98 |
|
18 |
57 |
34 |
380 |
07 |
6.2902 |
|
19 |
52 |
21 |
406 |
07 |
06 |
|
20 |
8. 508 9048 |
8. 510 2108 |
1.45431 |
2.3907 |
6. 2910 |
|
21 |
44 |
8.510 2096 |
456 |
06 |
14 |
|
22 |
39 |
83 |
481 |
06 |
18 |
|
23 |
35 |
70 |
507 |
06 |
22 |
|
?i |
31 |
57 |
532 |
05 |
26 |
|
25 |
27 |
45 |
557 |
05 |
30 |
|
26 |
22 |
32 |
582 |
05 |
34 |
|
27 |
18 |
19 |
608 |
05 |
38 |
|
28 |
14 |
06 |
633 |
04 |
42 |
|
29 |
10 |
8. 510 1993 |
658 |
04 |
46 |
|
30 |
8. 508 9005 |
8. 510 1981 |
1.45683 |
2. 3904 |
6. 2950 |
|
31 |
01 |
68 |
709 |
03 |
54 |
|
32 |
8. 508 8997 |
55 |
734 |
03 |
58 |
|
33 |
93 |
42 |
759 |
03 |
62 |
|
34 |
88 |
30 |
785 |
02 |
«6 |
|
35 |
84 |
17 |
810 |
02 |
70 |
|
36 |
80 |
04 |
835 |
02 |
74 |
|
37 |
76 |
8. 510 1891 |
861 |
02 |
78 |
|
38 |
71 |
78 |
886 |
01 |
82 |
|
39 |
67 |
66 |
911 |
01 |
86 |
|
40 |
8. 508 896i |
8. 510 1853 |
1. 45937 |
2. 3901 |
6. 2990 |
|
41 |
59 |
40 |
962 |
00 |
94 |
|
42 |
54 |
27 |
987 |
00 |
98 |
|
43 |
50 |
15 |
1.46012 |
00 |
6. 3002 |
|
44 |
46 |
02 |
038 |
2. 3899 |
06 |
|
45 |
41 |
8. 510 1789 |
063 |
99 |
10 |
|
46 |
37 |
76 |
088 |
99 |
15 |
|
47 |
33 |
64 |
114 |
98 |
19 |
|
48 |
29 |
51 |
139 |
98 |
23 |
|
49 |
24 |
38 |
164 |
98 |
27 |
|
50 |
8. 508 8920 |
8.510 1725 |
1.46190 |
2. 3897 |
6. 3031 |
|
51 |
16 |
13 |
215 |
97 |
35 |
|
52 |
12 |
00 |
240 |
97 |
39 |
|
53 |
08 |
8. 510 1687 |
266 |
96 |
43 |
|
54 |
03 |
74 |
291 |
96 |
47 |
|
55 |
8. 508 8899 |
62 |
316 |
96 |
51 |
|
56 |
95 |
49 |
342 |
95 |
55 |
|
57 |
90 |
36 |
367 |
95 |
59 |
|
58 |
86 |
23 |
392 |
95 |
63 |
|
59 |
82 |
10 |
418 |
94 |
67 |
|
60 |
8. 508 8878 |
8.510 1598 |
1.46443 |
2. 3894 |
6. 3071 |
214
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXVU.— Factors for the comimtation of geodetic latitudes, longitudes, and azimuths— ContinneA.
LATITUDE 49°.
log. A diff.l"=— 0.07
log.B diff.l"=— 0.21
log. 0 fliff.l"=:+0.42
log.D diff. 1"=— 0. 01
1. 508 8708 04 00
1.508 8695
FACTOES FOR COMPUTATION OF GEODETIC POSITIONS. 215
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued.
LATITUDE 30°.
|
Latitude. |
log. A |
log. B |
log. C |
log. D |
log. E |
|
dift'. 1"=— 0.07 |
dlfif. 1"=_0.21 |
diff. 1"=X0.43 |
diff. 1"=— 0.01 |
diir. l"=+0.07 |
|
|
60 0 |
8. 608 8623 |
8. 510 0835 |
L 47968 |
2. 3871 |
6. 3318 |
|
1 |
19 |
22 |
993 |
70 |
22 |
|
2 |
15 |
09 |
1. 48019 |
70 |
26 |
|
3 |
11 |
8. 510 0797 |
044 |
70 |
30 |
|
4 |
06 |
84 |
070 |
69 |
34 |
|
05 |
02 |
71 |
096 |
69 |
39 |
|
6 |
8. 508 8598 |
.59 |
121 |
68 |
43 |
|
7 |
94 |
46 |
146 |
68 |
47 |
|
8 |
90 |
33 |
172 |
67 |
51 |
|
9 |
85 |
21 |
197 |
67 |
55 |
|
10 |
8. 508 8581 |
8. 510 0708 |
1.48223 |
2. 3866 |
6. 3369 |
|
11 |
77 |
8. 510 0695 |
248 |
66 |
63 |
|
12 |
73 |
83 |
274 |
66 |
68 |
|
13 |
68 |
70 |
299 |
66 |
72 |
|
14 |
64 |
57 |
325 |
65 |
76 |
|
15 |
60 |
45 |
350 |
64 |
80 |
|
16 |
56 |
32 |
376 |
64 |
84 |
|
17 |
52 |
19 |
401 |
63 |
88 |
|
18 |
47 |
07 |
427 |
63 |
93 |
|
19 |
43 |
8. 510 0594 |
452 |
62 |
97 |
|
20 |
8. 508 8539 |
8. 510 0581 |
1. 43478 |
2.3862 . |
6. 3401 |
|
21 |
35 |
69 |
504 |
61 |
06 |
|
22 |
30 |
56 |
529 |
61 |
09 |
|
23 |
26 |
43 |
655 |
60 |
14 |
|
24 |
22 |
31 |
580 |
60 |
18 |
|
25 |
18 |
18 |
606 |
60 |
22 |
|
26 |
14 |
06 |
631 |
59 |
26 |
|
27 |
09 |
8. 510 0493 |
657 |
69 |
30 |
|
28 |
05 |
80 |
682 |
58 |
34 |
|
' 29 |
01 |
67 |
708 |
58 |
39 |
|
30 |
8. 508 8497 |
8. 510 0455 |
1.48734 |
2. 3857 |
6. 3443 |
|
31 |
93 |
42 |
759 |
67 |
47 |
|
32 |
88 |
29 |
785 |
56 |
61 |
|
33 |
84 |
17 |
810 |
66 |
55 |
|
34 |
80 |
04 |
836 |
65 |
60 |
|
35 |
76 |
8. 510 0392 |
861 |
55 |
64 |
|
36 |
71 |
79 |
887 |
54 |
68 |
|
87 |
07 |
66 |
913 |
54 |
72 |
|
38 |
63 |
54 |
938 |
53 |
76 |
|
39 |
59 |
41 |
964 |
53 |
81 |
|
40 |
8. 508 8455 |
8. 510 0328 |
1. 48989 |
2. 3852 |
6. 3485 |
|
41 |
50 |
16 |
1.49015 |
52 |
89 |
|
42 |
46 |
03 |
041 |
51 |
93 |
|
43 |
42 |
8.5W0291 |
066 |
51 |
97 |
|
44 |
38 |
78 |
092 |
50 |
6. 3502 |
|
45 |
34 |
65 |
117 |
50 |
06 |
|
46 |
29 |
53 |
143 |
49 |
10 |
|
47 |
26 |
40 |
169 |
49 |
14 |
|
48 |
21 |
27 |
194 |
48 |
18 |
|
49 |
17 |
16 |
220 |
48 |
23 |
|
50 |
8. 508 8413 |
8. 510 0202 |
1. 49246 |
2. 3847 |
6. 3527 |
|
51 |
08 |
8. 510 0190 |
271 |
47 |
31 |
|
52 |
04 |
77 |
297 |
46 |
35 |
|
63 |
00 |
64 |
322 |
46 |
40 |
|
54 |
8. 508 8396 |
62 |
348 |
45 |
44 |
|
55 |
92 |
39 |
374 |
45 |
48 |
|
56 |
87 |
27 |
399 |
44 |
52 |
|
57 |
83 |
14 |
425 |
44 |
56 |
|
58 |
79 |
01 |
451 |
43 |
61 |
|
59 |
75 |
8. 510 0089 |
476 |
43 |
65 |
|
60 |
8. 508 8371 |
8.510 0076 |
1.49502 |
2. 3842 |
6.3569 |
216
A MAifUAL OF TOPOGEAPHIC METHODS.
Table XXVII. — Factors for the computation of geodetic latitudes, longitudes, and azimuths — Continued. COEEEOTIOXS TO LONGITUDE FOR DIFFERENCE IN ARC AND SINE.
|
Log. K (-) |
Log. difference. |
Log. d M (+) |
Log. K (-) |
Log. difference. |
Log.dM (+) |
Log.K |
Log. difference. |
Log.dM (+) |
|
3.876 |
0.000 0001 |
2.385 |
4.813 |
0. 000 0075 |
3.322 |
5.114 |
0. 000 0300 |
3.623 |
|
4.026 |
02 |
2. 535 |
4.825 |
080 |
3.334 |
5.120 |
309 |
3.629 |
|
4.114 |
03 |
2.623 |
4.834 |
084 |
3.343 |
5.126 |
318 |
3.635 |
|
4.177 |
04 |
2.686 |
4.849 |
089 |
3.358 |
5.132 |
327 |
3.641 |
|
4.225 |
05 |
2.734 |
4.860 |
094 |
3.369 |
5.138 |
336 |
3.647 |
|
4.265 |
06 |
2.774 |
4.871 |
098 |
3.380 |
5.144 |
345 |
3.653 |
|
4.298 |
07 |
2.807 |
4.882 |
103 |
3.391 |
5.150 |
354 |
3.659 |
|
4.327 |
08 |
2.836 |
4.892 |
108 |
3.401 |
5.156 |
364 |
3.665 |
|
4.353 |
09 |
2.862 |
4.903 |
114 |
3.412 |
5.161 |
373 |
3.670 |
|
4.376 |
10 |
2.885 |
4.913 |
119 |
3.422 |
5.167 |
383 |
3.676 |
|
4.396 |
11 |
2.905 |
4.922 |
124 |
3.431 |
5.172 |
392 |
3.681 |
|
4.415 |
12 |
2.924 |
4.932 |
130 |
3.441 |
5.178 |
402 |
3.687 |
|
4.433 |
. 13 |
2.942 |
4.941 |
136 |
3.450 |
5.183 |
412 |
3.692 |
|
4.449 |
14 |
2.958 |
4.950 |
142 |
3.459 |
5.188 |
422 |
3.697 |
|
4.464 |
15 |
2.973 |
4.959 |
147 |
3.463 |
5.193 |
433 |
3.702 |
|
4.478 |
16 |
2.987 |
4.968 |
153 |
'3.477 |
5.199 |
443 |
3.708 |
|
4.491 |
17 |
3.000 |
4.976 |
160 |
3.485 |
5.204 |
453 |
3.713 |
|
4.503 |
18 |
3.012 |
4.985 |
166 |
3.494 |
5.209 |
464 |
3.718 |
|
4.526 |
20 |
3.035 |
4.993 |
172 |
3.502 |
5.214 |
474 |
3.723 |
|
4.548 |
23 |
3.057 |
5.002 |
179 |
3.511 |
5.219 |
486 |
3.728 |
|
4.570 |
25 |
3.079 |
5.010 |
186 |
3.519 |
5.223 |
497 |
3.732 |
|
4.591 |
27 |
3.100 |
5. 017 |
192 |
3.526 |
5. 228 |
508 |
3.737 |
|
4.612 |
30 |
3.121 |
5.025 |
199 |
3.534 |
5.233 |
519 |
3.742 |
|
4.631 |
33 |
3.140 |
1 5.033 |
206 |
3.542 |
5.238 |
530 |
3.747 |
|
4.649 |
36 |
3.158 |
5.040 |
213 |
3.549 |
5.242 |
541 |
3.761 |
|
4.667 |
39 |
3.176 |
5.047 |
221 |
3. 556 |
5.247 |
553 |
3.756 |
|
4.684 |
.42 |
3.193 |
5.054 |
228 |
3.563 |
5.251 |
565 |
3.760 |
|
4.701 |
45 |
3.210 |
5.062 |
236 |
3.571 |
5.256 |
577 |
3.765 |
|
4.716 |
48 |
3.225 |
5.068 |
243 |
3.577 |
5.260 |
588 |
3.769 |
|
4.732 |
52 |
3.241 |
5.075 |
251 |
3.584 |
5.265 |
600 |
3.774 |
|
4.746 |
56 |
3.255 |
5. 082 |
259 |
3.591 |
5.269 |
613 |
3.778 |
|
4.761 |
59 |
3. 270 |
5.088 |
267 |
3.597 |
5.273 |
625 |
3.782 |
|
4.774 |
63 |
3.283 |
5. 095 |
275 |
3.604 |
5.278 |
637 |
3.787 |
|
4.788 |
67 |
3.297 |
5. 102 |
284 |
3.611 |
5.282 |
650 |
3.791 |
|
4. 801 |
71 |
3. 310 |
5. 108 |
292 |
3.617 |
5.286 |
663 |
3.795 |
FACTOES FOE EEDUGTION OF TEANSIT OBSEEVATIONS. 217
Table XXVIII. — Factors for reduction of transit ohservations.
[Extracted from Appendix 14, U. S. Coast and Geodetic Survey Report for 1880.]
To find A enter left-hand column -with, tlie zenith ^^distance; its intersection "with declination column gives azimuth factor.
To find B enter ri^ht-liand column with tlie zenith distance ; its intersection with declination column gives level factor. C is given on laat line of each section of the table.
Azimuth, factor A=sin, ^ sec. 6. Star's declination :
Inclination factor B^cos ^ sec. A.
|
i |
0° |
10° |
15^ |
20° |
22° |
24° |
26° |
28° |
30° |
32° |
34° |
36° |
38° |
40° 41° |
42° |
430 |
'44° |
45° |
46° |
47° |
48° |
490 |
50° |
i |
|
|
1° |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.03 |
.02 |
.02 |
i .02: .02 |
.02 |
.02 |
.02 |
.02 |
.02 |
.03 |
.03 |
.03 |
.03 |
89° |
|
|
2 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.04 |
.05 |
.06 |
.05 |
.05 |
.05 |
.05 |
.05 |
.05 |
.05 |
.05 |
.05 |
88 |
|
3 |
.05 |
.05 |
.05 |
.06 |
.06 |
.06 |
.00 |
.06 |
.06 |
.06 |
.06 |
.00 |
.07 |
.07 |
.07 |
.07 |
.07 |
.07 |
.07 |
.07 |
.08 |
.08 |
.08 |
.08 |
87 |
|
4 |
.07 |
.07 |
.07 |
.07 |
.08 |
.08 |
.08 |
.08 |
.08 |
.08 |
.08 |
.09 |
.09 |
.09 |
.09 |
.09 |
.10 |
.10 |
.10 |
.10 |
.10 |
.10 |
.11 |
.11 |
86 |
|
5 |
.09 |
.09 |
.09 |
.09 |
.09 |
.10 |
.10 |
.10 |
.10 |
.10 |
.10 |
.11 |
.11 |
.11 |
.11 |
.12 |
.12 |
.12 |
.;2 |
.13 |
.13 |
.13 |
.13 |
.13 |
85 |
|
6 |
.11 |
.11 |
.111 |
.11 |
.11 |
.11 |
.12 |
:i4 |
.12 |
.12 |
.13 |
.13 |
.13 |
.14 |
.14 |
.14 |
.14 |
.16 |
.15 |
.15 |
.15 |
.16 |
.16 |
.16 |
84 |
|
7 |
.12 |
.12 |
.131 |
.13 |
.13 |
.13 |
.11 |
.14 |
.14 |
.15 |
.15 |
.15 |
.16 |
.16 |
.16 |
.17 |
.17 |
.17 |
.18 |
.18 |
.18 |
.19 |
.19 |
83 |
|
|
8 |
.14 |
.14 |
.14 |
.15 |
.15 |
.15 |
.16 |
.16 |
.16 |
.16 |
.17 |
.17 |
.18 |
.18 |
.18 |
.19 |
.19 |
.19 |
.20 |
.20 |
.20 |
.21 |
.21 |
.22 |
82 |
|
9 |
.16 |
.16 |
.16 |
.17 |
.17 |
.17 |
.17 |
.18 |
.18 |
.18 |
.19 |
.19 |
.20 |
.20 |
.21 |
.21 |
.21 |
.22 |
.22 |
.22 |
.23 |
.23 |
.24 |
.24 |
81 |
|
lo- |
.17 |
.18 |
.18 |
.19 |
.19 |
.19 |
.19 |
.20 |
.20 |
.21 |
.21 |
.21 |
.22 |
.23 |
.23 |
.23 |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
.26 |
.27 |
SO |
|
ll |
.19 |
.19 |
.20' |
.20 |
.21 |
.21 |
.21 |
.22 |
.22 |
.23 |
.23 |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
.27 |
.27 |
.28 |
.28 |
.28 |
.29 |
.30 |
79 |
|
12 |
.21 |
.21 |
.22 |
.22 |
. 22 |
.23 |
.23 |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
.27 |
.27 |
,28 |
.28 |
.29 |
.29 |
.30 |
.30 |
.31 |
.32 |
.32 |
78- |
|
13 |
. 22 |
.23 |
.23' |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
.27 |
.27 |
.28 |
.29 |
.29 |
.30 |
.30 |
.31 |
.31 |
.32 |
.32 |
.33 |
.34 |
.34 |
.35 |
77 |
|
14 |
.2+ |
.25 |
.251 |
.26 |
.26 |
.27 |
.27 |
.27 |
.28 |
.29 |
.29 |
.30 |
.31 |
.32 |
.32 |
.33 |
.33 |
.34 |
.34 |
.35 |
..36 |
.36 |
.37 |
.38 |
76 |
|
15 |
.26 |
.26 |
.271 |
.28 |
.28 |
.28 |
.29 |
.29 |
.30 |
.31 |
.31 |
.32 |
.33 |
.34 |
.34 |
.36 |
.35 |
.36 |
.37 |
.37 |
.38 |
.39 |
.39 |
.40 |
76 |
|
10 |
.28 |
.28 |
.29, |
.29 |
.30 |
.30 |
.31 |
.31 |
.32 |
.33 |
.33 |
.34 |
.35 |
.36 |
.37 |
.37 |
.38 |
.38 |
.39 |
.40 |
.40 |
.41 |
.42 |
.43 |
.74 |
|
17 |
.29 |
.30 |
.30 |
.31 |
.31 |
.32 |
.33 |
.33 |
.34 |
.34 |
.35 |
.36 |
.87 |
.38 |
.39 |
.39 |
.40 |
.41 |
.41 |
'.42 |
.43 |
.44 |
.45 |
.45 |
73 |
|
IS |
.3; |
.31 |
.32 |
.33 |
.33 |
.3a |
.34 |
.35 |
.36 |
.36 |
.37 |
.38 |
.39 |
.40 |
.41 |
.42 |
.42 |
.43 |
.44 |
.44 |
.45 |
.46 |
.47 |
.48 |
72 |
|
19 |
.33 |
.33 |
.34 |
.35 |
.35 |
.36 |
.36 |
.37 |
.38 |
.38 |
.39 |
.40 |
.41 |
.42 |
.43 |
.44 |
.45 |
.45 |
.40 |
.47 |
.48 |
.49 |
.50 |
.51 |
71 |
|
20 |
.34 |
.35 |
.35 |
.36 |
.37 |
.37 |
.38 |
.39 |
.40 |
.40 |
.41 |
.42 |
.43 |
.45 |
.45 |
.46 |
.47 |
.48 |
.48 |
.49 |
.50 |
.51 |
.62 |
.53 |
JO |
|
21 |
.36 |
.36 |
.37 |
.38 |
.39 |
.39 |
.40 |
.41 |
.41 |
.42' .43 |
.44 |
.45 |
.47 |
.47 |
.48 |
.49 |
.50 |
.51 |
.52 |
..52 |
.54 |
.55 |
.66 |
69 |
|
|
22 |
.37 |
.38 |
.39 |
.40 |
.40 |
.41 |
.42 |
.42 |
.43 |
.44' .45 |
.46 |
.48 |
.49 |
.50 |
.50 |
.61 |
..52 |
. 53 |
.54 |
.55 |
.56 |
.67 |
.58 |
68 |
|
|
23 |
.39 |
.40 |
.41 |
.42 |
.42 |
.43 |
.44 |
.44 |
.45 |
.46| .47 |
.48 |
.50 |
.51 |
.52 |
.53 |
.53 |
.51 |
. 5ii |
.56 |
. 57 |
.58 |
.60 |
.61 |
67 |
|
|
24 |
.41 |
.41 |
.42 |
.43 |
.44 |
.45 |
.45 |
.46 |
.47 |
.48 |
.49 |
.60 |
.52 |
.53 |
.54 |
.55' .56 |
.67 |
.58 |
.59 |
.00 |
.61 |
.62 |
.63 |
66 |
|
|
25 |
.42 |
.43 |
.44 |
.45 |
.46 |
.46 |
.47 |
.48 |
.49 |
.60 |
.51 |
.52 |
.64 |
.55 |
.56 |
.57 |
.58 |
.59 |
.60 |
.61 |
.62 |
.63 |
.64 |
.66 |
66 |
|
26 |
.44 |
.45 |
.45 |
.47 |
.47 |
.48 |
.49 |
.50 |
.51 |
.62 |
.53 |
.54 |
.56 |
.67 |
.58 |
.69 |
.60 |
.61 |
.62 |
.63 |
.64 |
.65 |
.67 |
.68 |
64 |
|
27 |
.45 |
.46 |
.47 |
.48 |
.49 |
.50 |
.51 |
.51 |
.62 |
.54 |
.55 |
.66 |
.58 |
.59 |
.60 |
.61 |
.62 |
.63 |
.64 |
.66 |
.67 |
.68 |
.69 |
.71 |
63 |
|
28 |
.47 |
.48 |
.49 |
.50 |
.51 |
.51 |
.52 |
.53 |
.54 |
.56 |
.67 |
.58 |
.60 |
.61 |
.62 |
.63 |
.64 |
.65 |
.66 |
.68 |
.69 |
.70 |
.72 |
.73 |
02 |
|
29 |
.48 |
.49 |
.50 |
.52 |
.52 |
.53 |
.54 |
.55 |
.56 |
.57 |
.58 |
.60 |
.61 |
.63 |
.64 |
.66 |
.66 |
.67 |
.69 |
.70 |
.71 |
.72 |
.74 |
.75 |
61 |
|
30 |
.50 |
.51 |
.62 |
.53 |
.64 |
.55 |
.56 |
.57 |
.68 |
.59 |
.60 |
.62 |
.63 |
.65 |
.66 |
.67 |
.68 |
.69 |
.71 |
.72 |
.73 |
.75 |
.76 |
.78 |
(iO |
|
31 |
.52 |
.52 |
.53 |
.55 |
.56 |
.56 |
.67 |
.58 |
.59 |
.61 |
.62 |
.64 |
.65 |
.67 |
.68 |
.69 |
.70 |
.72 |
.73 |
.74 |
.75 |
.77 |
.78 |
.80 |
59 |
|
32 |
.63 |
.54 |
.56 |
..56 |
.57 |
.58 |
.69 |
.60 |
.61 |
.63 |
.64 |
.66 |
.67 |
.69 |
.70 |
.71 |
.72 |
.74 |
.75 |
.76 |
.78 |
.79 |
.81 |
.82 |
58 |
|
33 |
.54 |
.55 |
56 |
.58 |
.69 |
.60 |
.61 |
.62 |
.63 |
.64 |
.66 |
.67 |
.69 |
.71 |
.72 |
.73 |
.74 |
.76 |
.77 |
.78 |
.80 |
.81 |
.83 |
.85 |
57 |
|
34 |
.56 |
.57 |
.58 |
.159 |
.60 |
.61 |
.62 |
.63 |
.65 |
.66 |
.67 |
.69 |
.71 |
.73 |
.74 |
.75 |
.70 |
.78 |
.79 |
.80 |
.82 |
.84 |
.85 |
.87 |
66 |
|
35 |
.57 |
.58 |
.59 |
.61 |
.62 |
.63 |
.64 |
.65 |
.66 |
.68 |
.69 |
.7) |
.73 |
.75 |
.76 |
.77 |
.78 |
.80 |
.81 |
.83 |
.84 |
.86 |
.87 |
.89 |
55 |
|
36 |
.59 |
.60 |
,61 |
.63 |
.63 |
.64 |
.65 |
.67 |
.68 |
.69 |
.71 |
.73 |
.75 |
.77 |
.78 |
.79 |
.80 |
.82 |
.83 |
.85 |
.86 |
.88 |
.90 |
.91 |
54 |
|
37 |
.60 .61 |
.62 |
.64 |
.65 |
.65 |
.67 |
.68 |
.70 |
.71 |
.73 |
.74 |
.76 |
.79 |
.80 |
.81 |
.82 |
.84 |
.85 |
.87 |
.88 |
.90 |
.92 |
.94 |
63 |
|
|
38 |
.62 .63 |
.64 |
.66 |
.66 |
.67 |
.69 |
.70 |
.71 |
.73 |
.74 |
.76 |
.78 |
.80 |
.82 |
.83 |
.84 |
.86 |
.87 |
.89 |
.90 |
.92 |
.94 |
.96 |
52 |
|
|
39 |
.63 .64 |
.65 |
.67 |
.68 |
.69 |
.70 |
.71 |
.73 |
.74 |
.76 |
.78 |
.80 |
.82 |
.83 |
.85 |
.86 |
.87 |
.89 |
.91 |
.92 |
.94 |
.96 |
.98 |
51 |
|
|
10 |
.64 |
.65 |
.66 |
.68 |
.69 |
.70 |
.72 |
.73 |
.74 |
.76 |
..77 |
.79 |
.82 |
.84 |
.85 |
.86 |
.88 |
.89 |
.91 |
.93 |
.94 |
.96 |
.98 |
1.00 |
50 |
|
41 |
.66 |
.67 |
.68 |
.70 |
.71 |
.72 |
.73 |
.74 |
.76 |
.77 |
.79 |
.81 |
.83 |
.86 |
.87 |
.88 |
.90 |
.91 |
.93 |
.94 |
.90 |
.98 |
1.00 |
1.02 |
49 |
|
42 |
.67 |
.68 |
.69 |
.71 |
.72 |
.73 |
.74 |
.76 |
.77 |
.79 |
.81 |
.83 |
.85 |
.87 |
.89 |
.90 |
.91 |
.93 |
.95 |
.96 |
.9S |
1.00 |
1. 02 |
1.04 |
48 |
|
43 |
.68 |
.69 |
.71 |
.73 |
.74 |
.75 |
.76 |
.77 |
.79 |
.80 |
.82 |
.84 |
.86 |
.89 |
.90 |
.92 |
.93 |
.95 |
.96 |
.98 |
1.00 |
1.02 |
1.04 |
1.06 |
47 |
|
44 |
.69 |
.71 |
.72 |
.74 |
.75 |
.76 |
.77 |
.79 |
.80 |
.82 |
.84 |
.86 |
.89 |
.90 |
.92 |
.93 |
.96 |
.96 |
.98 |
1.00 |
1.02 |
1.04 |
1.06 |
1.08 |
46 |
|
45 |
.71 |
.72 |
.73 |
.75 |
.76 |
.77 |
.79 |
.80 |
.82 |
.83 |
.85 |
.87 |
.90 |
.92 |
.94 |
.95 |
.97 |
.98 |
1.00 |
1.02 |
1.04 |
1.06 |
1.08 |
1.10 |
46 |
|
46 |
.72 |
.73 |
.74' |
.77 |
.78 |
.79 |
.80 |
.82 |
.83 |
.85 |
.87 |
.89 |
.91 |
.94 |
.95 |
.971 .98 |
1.00 |
1. 02 |
1.04 |
1.06 |
1.07 |
1.10 |
1.12 |
44 |
|
|
47 |
.73 |
.74 |
.76 |
.78 |
.79 |
.80 |
.81 |
.83 |
.84 |
.86 |
,88 |
.90 |
.93 |
.95 |
.97 |
.98,1.00 |
1.02 |
1.03 |
1.05 |
1.07 |
1.09 |
1.11 |
1.14 |
43 |
|
|
48 |
.74 |
.76 |
.77 |
.79 |
.80 |
.81 |
.83 |
.84 |
.86 |
.88 |
.90 |
.92 |
.94 |
.97 |
.98 1.00:1. 02 |
1.03 |
1. 05 |
1.07 |
1.09 |
1.11 |
1.13 |
1.16 |
42 |
||
|
49 |
.75 |
.77 |
.78 |
.80 |
.81 |
.83 |
.84 |
.86 |
.87 |
.89 |
.91 |
.93 |
.96 |
.99 |
1.001.02;!. 03 |
1.05 |
1. 07 |
1.09 |
1.11 |
1.13 |
1.15 |
1.17 |
41 |
||
|
60 |
.77 |
.78 |
.79 |
.82 |
.83 |
.84 |
.85 |
.87 |
.89 |
.90 |
.92 |
.95 |
.97 |
1.00 |
1.011.031.05 |
1.06 |
1. 08 |
1.10 |
1.12 |
1.14 |
1.17 |
1.19 |
40 |
||
|
51 |
.78 |
.79 |
.80 |
.83 |
.84 |
.85 |
.87 |
.88 |
.90 |
.92 |
.94 |
,96 |
.99 |
1.01 |
1.031.051.06 |
1. 08 |
1. 10 |
1.12 |
1.14 |
1.16 |
1.18 |
1.21 |
39 |
||
|
52 |
.79 |
.80 |
.82 |
.84 |
.85 |
.86 |
.88 |
.89 |
.91 |
.93 |
.95 |
.97 |
1.00 |
1.03 |
1.041.0611.08 |
1.10 |
1. 11 |
1.13 |
1.15 |
1.18 |
1.20 |
1.23 |
33 |
||
|
53 |
.80 |
.81 |
.83 |
.85 |
.86 |
.87 |
.89 |
.91 |
.92 |
.94 |
.96 |
.99 |
1.01 |
1.04 |
1.061.071.09 |
1. 11 |
1. 13 |
1.15 |
1.17 |
1.19 |
1. 22 |
1.24 |
37 |
||
|
54 |
.81 |
.82 |
.84 |
.86 .87 |
.89 |
.90 |
.92 |
.93 |
.95 |
.98 |
1.00 |
1.03 |
1.06 |
1.07 1.091.11 |
1. 12 |
1. 14 |
1.16 |
1.11 |
1.21 |
1.23 |
1.26 |
36 |
|||
|
55 |
.82 |
.83 |
.85 |
.87, .88 |
.90 |
.91 |
.93 |
.95 |
.97 |
.99 |
1.01 |
1.01 |
1.0- |
1. 08 1. 10 1. 12 |
1.14 |
1.16 |
1.18 |
1.20 |
1.22 |
1.25 |
.1.27 |
35 |
|||
|
56 |
.83 |
.84 |
.86 |
.88 .89 |
.91 |
.92 |
.94 |
.06 |
.98 |
1.00 |
1.02 |
1.05 |
1.08 |
1. 10 1. 12 1. 13 |
1.16 |
1.17 |
1.19 |
1.22' 1.24 |
1.26 |
1.29 |
34 |
||||
|
57 |
.84 |
.85 |
.87 |
.89 .90 |
.92 |
.93 |
.95 |
.97 |
.991.01 |
1.04 |
1.06 |
1.09 |
1. 11 1. 13 1. 15 |
1.17 |
1.19 |
1.21 |
1.23 1.25 |
1.28 |
1.31 |
33 |
|||||
|
58 |
.85 |
.86 |
.88 |
.90 .91 |
.93 |
.94 |
.96 |
.98 |
1. 00 1. 02 |
1.05 |
1.08 |
1. 11 |
1. 12 1. 14 1. 16 |
1.18 |
1.20 |
1.22 |
1.24 1.27 |
1.29 |
1.32 |
32 |
|||||
|
59 |
.86 |
.87 |
.89 |
.91 .92 |
.94 |
.95 |
.97 |
.99 |
1.011.03 |
1-.06 |
1. 09 |
1.12 |
1. 14 1. 15 1. 17 |
1.19 |
1.21 |
1.23 |
1. 26 1. 28 |
1.31 |
1.33 |
31 |
|||||
|
60 |
.87 |
.88 |
.90 |
.92 .93 |
.96 |
.96 |
.98 |
1.00 |
1. 02 1. 04 |
1.07 |
1.10 |
1.13 |
1.161.1711.18 |
1.20 |
1.22 |
1.25 |
1.27 1.29 |
1.32 |
1.35 |
SO |
218
A MA]!fUAL OP TOPOGRAPHIC METHODS.
Table XXVIII. — Factors for reduction of transit oiservations — Continued. Azimuth factor A:=sia C sec. 6. Star's declination + i. Inclination factor B=coa ^ sec. 6.
0°! 10° 15° 20° 22° ■ 24°i 26° 28° 30° 32° 34° 36° 88° 40° 41° 42° 43° 44° 45° 46° 47° ' 48° 49° 50°
.% .97 .9!) 11.01,1. 03
. 98 1. 00 .98] .991.01 .98 1.110 1.02 . 99I1. 01 1. 03
1. 02 1. 04 1.0311.05 I.O1I1.O6 1.05,1.07
.95 1 .97' .991. .95/ .98 .9'.! 1. .96l .9!) l.UO I. .97 .99 L. Ill 1. .971 l.OOjl. Olll.
.98,i.01il.02'l. .98 1.01il.0:l|l. .99 1.02'l.03!l.i .OOjl. 02 1.041.
.ooii.oaii.w'i.
1.05,1.08ll.H:i. 141. 16 1.06 1.09:1.12 1.151.17 1. 07JHO 1.13,11.16 1.18 1. OS 1. 111. 14 1. 17 1. 19 1. 09 1. I3I1. 15 1.18,1.20
05 1. 07
06 1, 08
06 1. 08
07 1. 09
08 1. 0!)
1.091. 1. 10 1. 1. 10 1. 1. 11 1. 1. 12 1.
.OSl. . 09 1.
.ooli. . 10 1. : .111.:
121.; 12 1. : 131.: 13 1. : 141.:
. 13 1. 16
.141. 17 . 15 1. 1.^ .15 1. 18 .161. 10;
.17:1.20' .171.31 . 18 1. 21I .191.22 .191.23;'
M9'I.2I 1. 23 1.25,1,
1.2011.22 1. 21 1. 23 1.22 1.24 1.23J1. 25 1.241. 26 1.28
1. 25 1. 1.26,1. 1. 27 1. 1. 27 1. 1. 28 1.
.29 1. . 30 1. .811. . 31 1. .321.
1.26 1.27 1.28 1.20 1.30
29 1. 32
30 1
31 1. 33
32 1. 34
33 1. 35 i
341.36
34 1. 37
35 1. 38
36 1. 38
37 1. 39
. 97 . 99 I. 00 1. 0;l 1. 05 1. 06 1. 08 1. HI I. 12 1. 14 1. IT 1. 20 1. 2:1 1. 27 I. 29 1. 31
.97 .9:11.01 1.04 1.11,1 l.iiT l.llil. 10 il. 1:5 1. IS 1.17 1.20 1.24 1.27 1.29 1. 31
.98 .OOU.III 1,04 1.0.'. 1.07 1.110 1. 11 1.13 1.151. IS 1.21 1.24 1.28 1.30 1.32
. 98 1. 00 1. 02 1. 04 1. 00 1. 08 1. 0;l 1. 11 1. 13 1. 16 1. IS 1. 21 1. 25 1. 281. 30 1. :f2
1.331.35 1.371.40 1.331.35 1.381.40 1.341. 36 1.381.41 1.34 1. 36 1.391.41
i 1.001. 02 1.05 1.06,1. OSl. 10 1.12 11.14 1.16 1.19 1.221.25, 1. 29'1. 30 1. 331.351. 37 1.391.42
! ■ ' I !■ : i ' i ' '':■■! ■ I I
81 ' .991.0Qtl.03' 1.051. 07|1. 08 1.101. 12 ,1. 14 1. 17 1. 19 1. 22 1. 25 1. 39 1. 31 1. 33 1. 351. 37 1.401.42
82 I .991.01;!. 03, 1. 05 1. 07il. 03 1. 10 1. 12 1. Ul- 17 1. 19 1. 23 1. 26 ,1.29 1. 31 1. 33 1. 35 1. 38 1.401.43
83 1 . 99 1. Olll. 03' 1. 06 1. 07:1. 09 1. 10 1. 12 1. 15 1. 17 1. 20,1. 23 1. 26 1. 30 1. 32 1. 34 1. 36 1, 38 1. 40 1. 43
84 I . 9911. Olll. 031:1. 06il. 07ll. 09 1. 11 1. 13 il. 15 1. 17 1. 20il, 33 1. 26 1. 30|l. 32 1. 34|1. 36 1. 38 1. 41 1. 43
85 1. 00 1. 01 1. 03 1. 06 1. 07 1. 09 1. 11 1. 13 11. 15 1. 17 1. 20 1. 33 1. 26 1. 3oll. 3211. 34 1. 36 1. 38 1. 4lll. 43
1.28 1.31 1. 29 1, 32
1.31 1.33
1.32 1.34 1. 33 1. 35
1.34 1.371
1.35 1.38 1.30! 1.
1. 37, 1. 40
1.38 1.40
1.39 1.41 1. 39 1. 42 1.40;i.43 1.41 1.44 1. 42 1. 44
1.42' 1.45 1.43; 1.46
1.43 1.46
1.44 1.4'i 1.44 1.47
1.49 1.49 1.50
1.51 1.52 1.53 1.53
1.50 1.53
1.51 1.54 1.51; 1.54 1.51' 1.54
1.52 1.55
1.53 1,55
88 1. 00 1. 01.1. 03' 1. 06 1. 08 1. 09,1. 111.13 1.15 1. 18 1. 20
89 1. 00 1. 02 1. 04' 1. 06 1. 08 1. 09: 1. 11 1. 13 1. 15 1. 18,1. 21
90 1. ODJl. 02,1. 04 1. 06,1. 08|l. 09 1. llll. 13 1. 15|l. 18,1. 21
1.231.27 1.30 1.321. 3 I 1.37 1.30 1.41 1,44 1.40 1.49' 1.52 1.55 1.241.27 1.31 I.:i2,l.:i5,l. :i71. 39, 1.411. 44,1. 47 1.49 1.52 1.56 1. 24:1. 27|il. 31,1. 32 1. 35,1. 37,1. 39 ,1. 41|1. 44 1. 47 1. 49, 1. 52; 1. 56|
r-r-T-r
FACTOES FOE REDUCTION OF TRANSIT OBSEUVATIONS. 219
Table XXVIII. — Factors for reduction of transit observations — Continued. Azimath factor A = sin ^ sec. 6. Star's declination ± 5. Inclination factor B = cos i sec. i.
|
i |
51° .03 |
52° .03 |
53° .03 |
54° .03 |
55° .03 |
56° .03 |
57° |
58° |
59° .03 |
60° .03 |
60J° .01 |
61° .04 |
6U° .04 |
62° .04 |
621° .04 |
63° .04 |
63i° |
64° |
64i° .04 |
65° .04 |
65J .04 |
66° .04 |
66i° .04 |
67° .04 |
i |
|
1° |
1 . 03 . 03 |
.04 .04 |
89° |
||||||||||||||||||||||
|
2 |
.06 |
.06 |
.06 |
.06 |
.06 |
.06 |
.06 .07 |
.07 |
.07 |
.07 |
.07 |
.07 |
.07 |
.08 |
.08 |
.08' .08 |
.08 |
.08 |
.08 |
.09 |
.09 |
.09 |
88 |
||
|
3 |
.08 |
.08 |
.09 |
.09 |
.09 |
.08 |
. 10| . 10 |
.10 |
.10 |
.11 |
.11 |
.11 |
.11 |
.11 |
.12 |
.13' .13 |
.12 |
.13 |
.13 |
.13 |
.13 |
.13 |
87 |
||
|
4 |
.11 |
.11 |
.12 |
.12 |
.12 |
.12 |
.13 |
.13 |
.14 |
.14 |
.14 |
.14 |
.15 |
.15 |
.15 |
.15 |
.16, .16 |
.16 |
.17 |
.17 |
.17 |
.18 |
.18 |
86 |
|
|
5 |
.14 |
.14 |
.14 |
.15 |
.15 |
.16 |
.16 |
.16 |
.17 |
.17 |
.18 |
.18 |
.18 |
.19 |
.19 |
.19 |
.19 |
.30 |
.20 |
.21 |
.21 |
.31 |
.22 |
.22 |
85 |
|
6 |
.17 |
.17 |
.17 |
.18 |
.18 |
.19 |
.19 |
.20 |
.20 |
.21 |
.21 |
.22 |
.22 |
.22 |
.23 |
.23 |
.23 |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
.27 |
84 |
|
7 |
.19 |
.20 |
.20 |
.21 |
.21 |
.22 |
.22 |
.23 |
.24 |
.24 |
.25 |
. 35 |
.26 |
.26 |
.26 |
.27 |
.27 |
.38 |
.28 |
.29 |
.29 |
.30 |
.31 |
.31 |
83 |
|
8 |
.22 |
.23 |
.23 |
.24 |
.24 |
.25 |
.26 |
.26 |
.27 |
.28 |
.28 |
.39 |
.29 |
.30 |
.30 |
.31 |
.31 |
.32 |
.32 |
.33 |
.34 |
.34 |
.35 |
.36 |
82 |
|
9 |
.25 |
.25 |
.26 |
.26 |
.27 |
.28 |
.29 |
.29 |
.30 |
.31 |
.32 |
.32 |
.33 |
.33 |
.34 |
.35 |
.35 |
.36 |
.36 |
.37 |
.38 |
.39 |
.39 |
.40 |
81 |
|
10 |
.28 |
.28 |
.29 |
.30 |
.30 |
.31 |
.32 |
.33 |
.34 |
.35 |
.35 |
.36 |
.36 |
.37 |
.38 |
.38 |
.39 |
.40 |
.40 |
.41 |
.42 |
.43 |
.43 |
.44 |
80 |
|
11 |
.30 |
.31 |
.32 |
.32 |
.33 |
.34 |
.35 |
.36 |
.37 |
.38 |
.39 |
.39 |
.40 |
.41 |
.41 |
.43 |
.43 |
.44 |
.44 |
.45 |
.46 |
.47 |
.48 |
.49 |
77 |
|
12 |
.33 |
..34 |
.35 |
.35 |
.36 |
.37 |
.38 |
.39 |
.40 |
.42 |
.42 |
.43 |
.44 |
.44 |
.45 |
.46 |
.47 |
.47 |
.48 |
.49 |
.50 |
.51 |
.53 |
78 |
|
|
13 |
.36 |
.36 |
.37 |
.38 |
.39 |
.40 |
.41 |
.42 |
.44 |
.45 |
.46 |
.46 |
.47 |
.48 |
.49 |
.50 |
.50 |
.51 |
.52 |
.53 |
.54 |
.55 |
!56 |
.58 |
77 |
|
14 |
.38 |
.39 |
.40 |
.41 |
.42 |
.43 |
.44 |
.46 |
.47 |
.48 |
.49 |
.50 |
.51 |
.52 |
.52 |
.53 |
.54 |
55 |
.56 |
.57 |
.58 |
.59 |
.61 |
.62 |
76 |
|
15 |
.41 |
.42 |
.43 |
.44 |
.45 |
.46 |
.48 |
.49 |
.50 |
.52 |
.53 |
.53 |
.54 |
.55 |
.56 |
.57 |
.58 |
.59 |
.60 |
.61 |
.62 |
.64 |
.65 |
.66 |
75 |
|
16 |
.44 |
.45 |
.46 |
.47 |
.48 |
.49 |
.51 |
.52 |
.54 |
.55 |
.56 |
.57 |
.58 |
.59 |
.60 |
.61 |
.62 |
.63 |
.64 |
.65 |
.66 |
.68 |
.69 |
.71 |
74 |
|
17 |
.46 |
.47 |
.49 |
.50 |
.51 |
.52 |
.54 |
.55 |
.57 |
.58 |
.59 |
.60 |
.61 |
.62 |
.63 |
.64 |
.66! .67 |
.68 |
.69 |
.70 |
.72 |
.73 |
.75 |
73 |
|
|
18 |
.49 |
.50 |
.51 |
.53 |
.54 |
.55 |
.57 |
.58 |
.60 |
.62 |
.63 |
.04 |
.65 |
.66 |
.67 |
.68 |
.69 .70 |
.72 |
.73 |
.74 |
.76 |
.77 |
.79 |
72 |
|
|
19 |
.52 |
.53 |
.54 |
.5.'> |
.57 |
.58 |
.60 |
.61 |
.63 |
.65 |
.66! .67 |
.68 |
.69 |
.70 |
.72 |
.73 |
.74 |
.76 |
.77 |
.78 |
.80 |
.82 |
.83 |
71 |
|
|
20 |
.54 |
.50 |
.57 |
.58 |
.60 |
.61 |
.63 |
.04 |
.66 |
.68 |
.69 |
.70 |
.72 |
.73 |
.74 |
.75 |
.77 |
.79 |
.79 |
.81 |
.83 |
.84 |
.86 |
.88 |
70 |
|
21 |
.57 |
.58 |
.59 |
.61 |
.62 |
.64 |
.66 |
.68 |
.70 |
.72 |
.73 |
.74 |
.75 |
.76 |
.78 |
.79 |
.80 |
.83 |
.83 |
.85 |
.86 |
.88 |
.90 |
.92 |
69 |
|
22 |
.60 |
.61 |
.62 |
.64 |
.65 |
.67 |
.69 |
.71 |
.73 |
.75 |
.76 |
.77 |
.78 |
.80 |
.81 |
.82 |
.84 |
.85 |
.87 |
.89 |
.90 |
.92 |
.94 |
.96 |
68 |
|
23 |
.62 |
.63 |
.65 |
.66 |
.68 |
.70 |
.72 |
.74 |
.76 |
.78 |
.79 |
.81 |
.83 |
.83 |
.85 |
.86 |
.88 |
.89 |
.91 |
.92 |
.94 |
.96 |
.98 |
1.00 |
67 |
|
24 |
.65 |
.66 |
.68 |
.69 |
.71 |
.73 |
.75 |
.77 |
.79 |
.81 |
.83 |
.84 |
.85 |
.87 |
.88 |
.90 |
.91 |
.93 |
.94 |
.96 |
.98 |
1.00 |
1.03 |
1.04 |
66 |
|
25 |
.67 |
.69 |
.70 |
.72 |
.74 |
.76 |
.78 |
.80 |
.83 |
.85 |
.86 |
.87 |
.89 |
.90 |
.92 |
.93 |
.95 .96 |
.08 |
1.00 |
1.02 |
1.04 |
1.06 |
1.08 |
65 |
|
|
2G |
.70 |
.71 |
.73 |
.75 |
.76 |
.78 |
.80 |
.83 |
.85 |
.88 |
.89 |
.90 |
.92 |
.93 |
.95 |
.97 |
.98'l.00 |
1.03 |
1.04 |
1.06 |
1.08 |
1.10 |
1.12 |
64 |
|
|
27 |
.72 |
.74 |
.75 |
.77 |
.79 |
.81 |
.83 |
.86 |
.88 |
.91 |
.92 |
.94 |
.95 .97 |
.98 |
1.00 |
1.021.04 |
1.05 |
1.07 |
1.09 |
1.13 |
1.14 |
1.16 |
03 |
||
|
28 |
.75 |
.76 |
.78 |
.80 |
.82 |
.84 |
.86 |
.89 |
.91 |
.94 |
.95 |
.97 |
. 98 1. 00 |
1.02 |
1.03 |
1.05,1.07 |
1.09 |
1.11 |
1.13 |
1.15 |
1.18 |
1.20 |
62 |
||
|
29 |
.77 |
.79 |
.81 |
.82 |
.84 |
.87 |
.89 |
.91 |
.94 |
.97 |
.98 |
1.00 |
1. 02 1. 03 |
1.05 |
1.07 |
l.OO'l. 11 |
1.13 |
1.15 |
1.17 |
1.19 |
1.22 |
1.24 |
61 |
||
|
30 |
.79 |
.81 |
.83 |
.85 |
.87 |
.89 |
.92 |
.94 |
.97 |
1.00 |
1.01 |
1.03 |
1.05 1.07 |
1.08 |
1.10 |
1.121.141.16 |
1.18 |
1.21 |
1.23 |
1.25 |
1.28 |
60 |
|||
|
31 |
.82 |
.84 |
.86 |
.88 |
.90 |
.93 |
.95 |
.97 |
1.00 |
1.03 |
1.05 |
1.06 |
1. 08,1. 10 |
1.11 |
1.13 |
1.151.17 |
1.20 |
1.22 |
1.24 |
1.27 |
1.29 |
1.32 |
59 |
||
|
32 |
.84 |
.80 |
.88 |
.90 |
.92 |
.95 |
.97 |
1.00 |
1.03 |
1.06 |
1.08 |
1.09 |
1.111.13 |
1.15 |
1.17 |
1.19)1.21 |
1.23 |
1.25 |
1.28 |
1.30 |
1.33 |
1.36 |
58 |
||
|
33 |
.87 |
.88 |
.91 |
.93 |
.95 |
.97 |
1.00 |
1.03 |
1.00 |
1.09 |
1. U |
1.12 |
1. 14 1. 16 |
1.18 |
1.20 |
1. 22 1. 21 |
1.26 |
1.29 |
1.31 |
1.34 |
1.37 |
1.39 |
57 |
||
|
34 |
.89 |
.91 |
.93 |
.95 |
.97 |
1.00 |
1.03 |
1.05 |
1.09 |
1.13 |
1.14 |
1.15 |
1. 17 1. 19 |
1.21 |
1.23 |
1. 251. 27 |
1.30 |
1.32 |
1.35 |
1.37 |
1.40 |
1.43 |
56 |
||
|
35 |
.91 |
.93 |
.95 |
.98 |
1.00 |
1.03 |
1.05 |
1.08 |
1.11 |
1.15 |
1.16 |
1.18 |
1.201.22 |
1.24 |
1.30 |
1.291.31 |
1.33 |
1.36 |
1.38 |
1.41 |
1.44 |
1.47 |
55 |
||
|
36 |
.93 |
.95 |
.98 |
1.00 |
1.03 |
1.05 |
1.08 |
1.11 |
1.14 |
1.18 |
1.19,1.21 |
1.231.25 |
1.27 |
1.30 |
1.321.34 |
1.37 |
1.39 |
1.42 |
1.45 |
1.47 |
1.51 |
54 |
|||
|
37 |
.96 |
.98 |
1.00 |
1.02 |
1.05 |
1.08 |
1.10 |
1.14 |
1.17 |
1.20 |
1.221.24 |
1.261.28 |
1.30 |
1.33 |
1.351.37 |
1.40 |
1.42 |
1.45 |
1.48 |
1.51 |
1.54 |
53 |
|||
|
38 |
.98 |
1.00 |
1.02 |
1.05 |
1.07 |
1.10 |
1.13 |
1.16 |
1.20 |
1.33 |
1.251.27 |
1.291.31 |
1.33 |
1.36 |
1.38'l.40 |
1.43 |
1.46 |
1.48 |
1.51 |
1.54 |
1.58 |
52 |
|||
|
39 |
1.00 |
1.02 |
1.05 |
1.07 |
1.10 |
1.12 |
1.15 |
1.19 |
1.22 |
1.26 |
1.281.30 |
1.321.34 |
1.36 |
1.39 |
1.411.43 |
1.46 |
1.49 |
1.52 |
1.55 |
1.58 |
1.61 |
51 |
|||
|
10 |
1.02 |
1.04 |
1.07 |
1.09 |
1.12 |
1.15 |
1.18 |
1.21 |
1.25 |
1.29 |
1.311.33 |
1.351.37 |
1.39 |
1.42 |
1.44 1.47 |
1.49 |
1.52 |
1.55 |
1.58 |
1.61 |
1.65 |
50 |
|||
|
41 |
1.04 |
1.07 |
1.09 |
1.12 |
1.14 |
1.17 |
1.20 |
1.24 |
1.27 |
1.3l!l.331.35 |
1.37 |
1.40 |
1.42 |
1.45 |
1.47 |
1.50 |
1.53 |
1;55 |
1.58 |
1.61 |
1.64 |
1.68 |
49 |
||
|
42 |
1.06 |
1.09 |
1.11 |
1.14 |
1.17 |
1.20 |
1.23 |
1.26 |
1.30 |
1. 34jl. 361. 38 |
1.40 |
1.42 |
1.45 |
1.47 |
1.50 |
1.53 |
1.55 |
1.58 |
1.61 |
1.64 |
1.68 |
1.71 |
48 |
||
|
43 |
1.08 |
1.11 |
1.13 |
1.16 |
1.19 |
1.22 |
1.25 |
1.29 |
1.32 |
1.361.391.41 |
1.43 |
1.45 |
1.48 |
1.50 |
1.53 |
1.56 |
1.58 |
1.61 |
1.64 |
1.68 |
1.71 |
1.75 |
47 |
||
|
44 |
1.10 |
1.13 |
1.15 |
1.18 |
1.21 |
1.24 |
1.28 |
1.31 |
1.35 |
1.391.41,1.43 |
1.46 |
1.48 |
1..50 |
1.53 |
1.56 |
1.581.61 |
1.64 |
1.67 |
1.71 |
1.74 |
1.78 |
46 |
|||
|
45 |
1.12 |
1^ |
1.17 |
1.20 |
1.23 |
1.26 |
1.30 |
1.33 |
1.37 |
1.411.441.46 |
1.48 |
1.51 |
1.53 |
1.56 |
1.58 |
1.611.64 |
1.67 |
1.70 |
1.74 |
1.77 |
1.81 |
45 |
220
A MAXUAL OF TOPOGRAPHIC METHODS.
Table XXVIII. — Factors fur reduction- of transit ohserimtions — Continued.
Aziiniith factor A = sill sec, 5. Star's declination ± 5. Inclination factor B = cos ^ sec. 5.
i2° 53° c
i 51° 52° ! 53° 54° 55° 50= 57° 58° 59° ' 60° 60^° 61° 61^° 02° 63|o 63° 63Jo 04° 64J° 05°
46° 1. 14|1. 17 1. 19 1. 22 1.251.29
47 |1. lull. 19 1.211. 24 1.27J1.31
48 1 1. \&'y. 21 1. 23 1. 26 1 1. 30 1. 33
49 1 1. 20| 1. 23 1. 25 1. 28 1. 32 1. 35
50 1.221.24 1. 27 I.30I1.34I1. 3'
1. 36 1. 40 1. 44il. 461 1. 48 1. 51| 1. 53 1. 56 1 58|1. 611. 64 1. O'i 1. 70 1. 74 1. 77 1. 38 1. 42!! I. 40 1. 4911. 51 1. 53 1. 56 1. 58 1. 61,1. 61 1. 67 1'. 7ol 1. 73 1. 70 1. 80 1. 40 1. 44,il. 48 1. 50,1. 53 1,55 1. 58 1. 60 1. 03 1. 66 1. 69 1. 72 1. 75 1. 79 1. 82 1. 42 1, 47)1. 51 1. 53|1. 56 1. 58 11. 01 1. 63 1, 66 1. 60 1. 72 I. 75 .\. 79,1. 82 1. 86 1. 44 1. 49; 1. 53 1. 5611. 58 1. 60 1. 03 1. 66 I. 69 1. 721. 75 1. 78|!1. 8111. 85 1. 88
51 1. J; l.LM l.-".i l::- 1.:;.""' l.:i ij.4'; 1-47 l.r.l I. .".". 1. .IS 1. 00 1. 63 1. 66 1. 08 1.
52 l.•-'^ 1. J- I ::i 1 ;; I, :: I. (1 1. -t:. I 4:i 1. :>:; i.r,s i.C'i 1. 11:; 1.65 1.68 1.71 1. 5;i 1.27 1.:; ' 1 . : 1. :Vi I.:::M. I.: I. 47 1..M 1. '.' l.i'.nl. t:2 1. ns 1. 07 |l. 70 1. 73 1.
54 1.2:l l.:;U.:U l.::~ 1. 41 1 4.'> 1. 4'i 1. .) : 1. ,'.7 1. 1)2 1. 04 1. 67 1. 09 1.72 1.75 1.
55 1.30:1.33 1.36 1.30 1.4311.461.50 1.55 1.59 1.011.661.69 1.72 1.741.77 1.
1.71 1.77 l.,-<i) 1..S4 1.871.91
1.77 l.,sn l..s:: I. so 1.90 1.94
1.70 l..-<2 l.s", 1. so 1.93 1.96
l.sl l.S,-. l.S.S 1.911.951.99
1.84 1.87 1.90 1.94 1.98 2.01
63 ,1,
04 1
05 II,
35 1.381.41
36 1. 39 1. 43 381.41 1.44
39 1.421.40
41 1.441.47 I.
42 1.4.'"' 1.40 1. 4:j I. 47 1.. 'ill 1. 45 1.40 1.52 1.
40 1. 40 1. 5:;" 1. 47 1.51 1.54 1.
1. 45 I. 48 1.46; 1.50
1.48 1.52
1.49 1.53
! 1.50 1.61 1.661.081.711.74 581.63 1.681.70|l. 731. 76 60 1.65 1.701.7211.751.78 02 1.66 1.711.7411.771.80 631. 6.1' 1. 73 1. 76'1. 79 1. 81 tl. 84 1. 88 1. 911. 94 1. 97 2. 01 2. 05'2. 09 2. 13
1. 77 1. 8.1 1. 83 1. 80 1. 89 1. 93 1. 90 2. 00 2. 04 1. 79 1. 82 1. 85 1. 88 1. 91 1. 95 ll. 98 2. 02 2. 06 1. 81 1. 84 1. 87 1. 90 1. 93 1. 97 |2. 01 2. 05 2. 08 1. 83 1. 86 1. 89:1. 92 1. 95 1. 99 l2. 03'2. 07 2. 11
.6411. .65 1. .66 1.
18 1.73 1.781.81 1.84 LS7 l.liii l.:i:; l.'.i' - ' J '0,1. 75 ,1.80 1. 83 1. 85 1. Ss 1. Ill 1. 'X, i. 0,-: 2. U2 2. " J ■1,1. 76 1 1. 81 1. 84]l. 87 1. 90 1. 93,1. 96 2. 00 2. OJ 2. 07
2. 11 2.15 2.19 2. 13 2. 17 2. 21 2. 14 2. 19 2. 23
Oej° 67°
1.87 1.90 1.93
2.02 2.04 2.07 2.10
2.15 2.17 2.19 2.22
2.27
. 20 2. 25 1 2. 29 . 22 2. 20 ■ 2. 31 .24 2.28 2.32 . 25 2. 30 , 2. 34 . 27 2. 31 I 2, 36
71 'l. 50 1. 54 1. 57 1. 61 1. 65 1.69 1. 74 1. 78 1. 84 1. 80 1. 92 1. 95 1. 9S| 2. 01 2. 05 2. 08 2. 12 2. 10 2, 20 i2. 24 2. 28 2. 32 2. 37
72 1 1.51 1.54 1.581.62 1.00 1.70 1.75 1.80 1.85 1.90 1.93 1.961.991
73 !l. 52 I. 55 1. .59 1. 63 1. 07 1. 71 1. 70 1. SO 1. 86 1.91 1. 94 1. 97 2. 00; 2. 04 2. 07 2. 112. 14 2. IS 2. 22 ;2. 26 2. 31 2. 35 2. 40
74 1.53 1.56 1.60 1.63 1.081.72,1.701.811.87 1.92 1. 95 1. 98 2. Oil 2.05 2.08 2. 12|2. 15 2. 19 2. 23
75 11. 53 1. 57 1. 60 1. 64 1. 63 1. 73:1. 77:1. 82 1. 88 1. 93 1. 96 1. 99 2. 02l 2. 06 2. 09 2. 13i2. 16,2. 20 2. 24||2. 29|2. 33i2. 37 i 2. 42
66 ! 1. 45,1. 48 1. 52 1. 55 1. .59 1. 03 1. 68 1. 721. 77 1. 83'l. 85' 1. 88 1. Oil 1. 951. 98 2. 01'2. 05'2. 08 2. 12 I
67 1. 46 1. 50 1. 53 1. ,57 1.60 1.651.69 1.74 1.79 1. S4 1.87 1.90 1.9:! 1. 9i; 1. 99 2. 0:i 2. 0(i 2. 10 2. 14 03 1.47 1.511 54 1. .58 1.621.06 1.70 1.75 1.8;; 1.S5 1.SS1.91 1.'.14 l.|i7 2.nl j, iin' os j. 11 j, ]3 69 1.481.521.551.59 1.63 1.071.711.701.81 1.87 1.9111.03 1.0:; 1. Oil 2. il2 J. "n 2. n:i j. ]:; -. 17 JO .1.49 1.53 1.50 1.00 1.041.68 1.73 1.771.82 1. .SS 1.91 1.94 1.07 2. OU 2. u:; 2. u7 2. 11 -. 14 2. is
2.32
«2.34 2.36 2.37 2.39 2.40
2.42 2.43 2.45 2.46 2.47
76 1.54 1.58 1.611.05 1. 69 1. 73 1.781. 83;1. SS 1.04 1.97 2.00 2.03'
77 ll. 55 1.58 1.62 1.60 1. 70 1. 74 1. 79' 1. 84:1. 89 1.051,0- 2111 2 D |
78 ;l..55 !.. 59 1.621.66 1.701. 75I1.SO 1.85 1.90 1.06 1.: . :_ -j,.j-jj -_
79 1.. 56 1.591. 631.67 1.71 1.701.80 1.S5 1.91 1.96 1.:: _ . J : _ . 8D 1.561.60 1.641.67 1.721.761.81,1.86 1.91 1.972.11 ■ J. II -" 2 'J :.:j iT-:
81 1.57|l.60'l. 64 1.68 1.72 1.77 1.81 1.80 1,02 1. 98 2. 111 j. 1:4 2. "7 2.1:12.142 ls2.:
jl.eill. 64 1.68 1.73 1.77 1.82 1.87 1.92 1.98 2. "1 l."4 2. us -. 11 -J. 151,'. IS 2.;
I. 58 I.61I1. 65 1.69 1.73 1.77 1. 82 1.87 1.93 1. 90 2. 02 2. 05 2. lis -. v^-l. Vrl. Iil2.:
1.58ll.62 1.65l.69 1. 73 1. 78 1. 83!!. 88 1. 93 1.90 2.02 2.05 2.08 2.12 2,15 2,19 2,;
1. 58 1. 62 1, 65 1, 69 11, 74 1, 78 1, 83 1, 83 1, 93 1, 99 2, 02 2, 0512, 091 2, 12,2, 16.2. 19|2. 1
1.59 1.621,601,70 1,74 1,73 )..s:;l.
1, .59 1. 62 1. 66 1.70 1. 74 1. 7;i 1 - : i
1.59 1.62 1.06 1.70 1.74 1 '
1.591.62 1.66 1,70 1, 74 ; ^
1.591.621,661,70 1,74 i T:' 1 ■, ;
n.94
, 30'2. 34'2. 39 ' 2. 43
. :n 2. 3r, 2. 40 2
.. .. ;;,;- 41) ■_.
_ _ :7 -.41 2
:, 34 2, 38 2, 43 i 2. 48 , 34(2, 39 2, 43 : 2, 48 , 3512, 39 2, 44 , 35|2, 40 2, 45 . 3612. 40 2. 45
,36 2,41,2,45
2.49
. II 2. 40 2. 50 2, 50
I I 2 40 2.51 2,50
I 2.40 2.51 2,;
112, 40 2, 51 2, 56
FACTOES FOE EEDUCTION OF TEAifSlT OBSEKVATIONS. 221
Table XXYJIl.—Faeiors for reduction of transit ohservations— Continued. Azimuth factor A = siu i sec. S, Star's doclination ± S. Inclination factor B = cos i sec. 5.
|
i |
67J° .05 |
68° .05 |
68^0 .05 |
69° ,05 |
69io .05 |
70° .05 |
7040 ,05 |
70J° .05 |
.05 |
71° .05 |
... .05 |
71i° .05 |
711° .05 |
72° .06 |
72J° .06 |
72i° .06 |
72JO .06 |
73° .06 |
73i° .06 |
73i° .06 |
73i° .06 |
740 .06 |
74i° .06 |
i |
|
89° |
||||||||||||||||||||||||
|
1° |
||||||||||||||||||||||||
|
2 |
.09 |
.09 |
.10 |
,10 |
.10 |
.10 |
,10 |
.10 |
.11 |
.11 |
.11 |
.11 |
.11 |
.11 |
.11 |
.12 |
.12 |
.12 |
.12 |
.12 |
.12 |
.13 |
.13 |
88 |
|
3 |
. 14 |
.14 |
. 14| . 15 . 15 |
.15 |
,15 |
.16 |
.16 |
.16 |
.16 |
.16 |
.17 |
.17 |
.17 |
.17 |
.18 |
.18 |
.18 |
.18 |
.19 |
. 19 |
.19 |
87 |
||
|
l |
.18 |
.19 |
.19 .20 .20 |
.20 |
.21 |
.21 |
.21 |
.21 |
.22 |
.22 |
.22 |
.23 |
.23 |
.23 |
.23 |
.24 |
.24 |
.24 |
.25 |
.25 |
.26 |
86 |
||
|
5 |
.23 |
.23 |
.24 .24 |
.25 |
.25 |
.26 |
.26 |
.26 |
.27 |
.27 |
.27 |
.28 |
.28 |
.29 |
.29 |
.29 |
.30 |
.30 |
.31 |
.31 |
.32 |
.32 |
85 |
|
|
6 |
,27 |
.28 |
.28 .29 |
.30 |
.31 |
.31 |
.31 |
.32 |
.32 |
.33 |
.33 |
.33 |
.34 |
.34 |
.35 |
.35 |
.36 |
.36 |
.37 |
.37 |
.38 |
.39 |
84 |
|
|
7 |
.32 |
.33 |
.33! .34 |
.35 |
.36 |
.36 |
.37 |
.37 |
.37 |
.38 |
.38 |
.39 |
.39 |
.40 |
.41 |
.41 |
.42 |
.42 |
.43 |
.44 |
.44 |
.45 |
83 |
|
|
8 |
.36 |
.37 |
.38 .39 |
.40 |
.41 |
.41 |
.42 |
.42 |
.43 |
.43 |
.44 |
.44 |
.45 |
.46 |
.46 |
.47 |
.48 |
.48 |
.49 |
.50 |
.50 |
.51 |
82 |
|
|
g |
.41 |
.42 |
.43 .44 |
.45 |
.46 |
.46 .47 |
.47 |
.48 |
.49 |
.49 |
.50 |
.51 |
.51 |
.52 |
.53 |
.53 |
.54 |
.55 |
.56 |
.57 |
.58 |
81 |
||
|
10 |
.45 |
.46 |
.47| .49 |
.50 |
.51 |
.61 .52 |
.53 |
.53 |
.54 |
.55 |
.55 |
.56 |
.57 |
.58 |
.59 |
.60 |
.60 |
.61 |
.02 |
.63 |
.64 |
80 |
||
|
11 |
.50 |
.51 |
.52' ..53 |
.54 |
.56 |
.56 .57 |
.58 |
.59 |
.59 |
.60 |
.61 |
.62 |
.63 |
.63 |
.64 |
.65 |
.66 |
.67 |
.68 |
.69 |
.70 |
79 |
||
|
12 |
.54 |
.56 |
.57 |
,58 |
.59 |
.61 |
.62 .62 |
.63 |
.64 |
.65 |
.63 |
.66 |
.67 |
.68 |
.69 |
.70 |
■.71 |
. 72 |
.73 |
.74 |
.75 |
.77 |
78 |
|
|
13 |
.59 |
.60 |
.61 |
,63 |
.64 |
.66 |
.67 |
.67 |
.68 |
.69 |
.70 |
.71 |
.72 |
.73 |
.74 |
.75 |
.76 |
.77 |
.78 |
.79 |
.80 |
.82 |
.83 |
77 |
|
14 |
.63 |
.65 |
.66 |
.68 |
.69 |
.71 |
.72 |
.72 |
.73 |
.74 |
.75 |
.76 |
.77 |
.78 |
.79 |
.80 |
.82 |
.83 |
.84 |
.85 |
.87 |
.88 |
.89 |
76 |
|
15 |
.68 |
.69 |
.71 |
.72 |
.74 |
.76 |
.77 |
.78 |
.78 |
.79 |
.80 |
.81 |
.83 |
.84 |
.85 |
.86 |
.87 |
.89 |
.90 |
.91 |
.93 |
.94 |
.95 |
75 |
|
16 |
.72 |
.74 |
.75 |
.77 |
.79 |
.81 |
.82 |
.83 |
.84 |
.85 |
.86 |
.87 |
.88 |
.89 |
.91 |
.92 |
.93 |
.94 |
.96 |
.97 |
.99; 1.00 |
1.02 |
74 |
|
|
17 |
.76 - 7S |
. 80' . HI |
.83 |
.85 |
.86' .88 |
.89 |
.90 |
.91 |
.92 .93 |
.95 |
.96 |
.97 |
.99 |
1.00 1.01 |
1.03 |
1.05! 1.06 |
1.08 |
73 |
||||||
|
18 |
.81 |
.83 |
.84| .86! .88 |
.90 |
.911 .93 |
.94 |
.95 |
.96 |
.97 .991.00 1.01 |
}-??o |
1.04 |
1.06 |
1.07 |
1.09 |
1. 10 1. 12 |
1.14 |
72 |
|||||||
|
19 |
.85 |
.87 |
.89' .91 .93 |
.95 |
.96i .98 |
.99 |
i.oo!i.oi |
1. 03 1. 04 1. 05 |
1.07 |
1.08 |
1.10 |
1.11 |
1.13 |
1.15 |
1. 16i 1.18 |
1.20 |
71 |
|||||||
|
20 |
.89 |
.91 |
.93 .95 .98 |
1.00 |
1.011.02 |
1.04 |
1.05:1.06 |
1.081.091.11 |
1.12 |
1.14 |
1.15 |
1.17 |
1.19 |
1.20 |
1.22j 1.24 |
1.26 |
70 |
|||||||
|
21 |
.94 |
gii |
. 98 1. 00 1. 02 |
1. 05 |
1.06:1.07 |
1.09 |
1,10 1,11 l,13 1,14'l,16 |
1.17 |
1.19 |
1.21 |
1.22 |
1.24 |
1.26 |
1.28 1.30 |
1.32 |
69 |
||||||||
|
22 |
.981.00 |
1.021.051.07 |
l.OO.l.ll'l. 12 |
1.14 |
1,15 1,17 1, LSI, 20 1.2111, 23 |
1.25 |
1.26 |
1.28 |
1.30 |
1.32 |
1.34; 1.36 |
1.38 |
68 |
|||||||||||
|
23 |
1.021.04 |
1.07 1.091.12 |
1, 14!l,161,17 |
1.19 |
1,2(11 21 1,2:; 1,25 1,26 1,28 |
1.30 |
1.32 |
1.34 |
1.36 |
1.38 |
1.40' 1.42 |
1.44 |
67 |
|||||||||||
|
24 |
1. Oe'l. 09 |
1. 11 1. 14 1. Ifi |
1. 19 1. 20 1, 22 |
1, 23 1, li.'. 1. 27 1 , i.l 1, 30 1, 32 1, 33|1, 35 |
1.37 |
1.39 1.41 |
1.43 |
1.45 1.48 |
1.50 |
66 |
||||||||||||||
|
25 |
l!l0|l.l3 |
1.1,-. 1,1s 1,21 |
1,241,251,27 |
1.28 |
l.i'.ii 1,31 1,:;:! 1. 3,' 1,37 1,39,1,41 |
1.42 |
1.45, 1.47 |
1.49 |
1.51 |
1.53 |
1.56 |
65 |
||||||||||||
|
26 27 28 29 30 |
1. 15 1. 17 |
,1,1 ,1,1 .ir, |
1, 28 1, 30' 1,31 |
1, Sj |
1.:;,-. l.:;ii 1. :i,-< 1.411 1,421, ll'l, 46 |
1.48 |
1.51 |
1.52 |
1.54 |
1.57 |
1.59 |
1.61 |
64 |
|||||||||||
|
l!l9l'-Jl |
1. •_*-! 1. 'JT 1, :!0 |
1. :!;i'l, 34 1, 31 |
1. :;.^ |
l.:;:i 1, 11 1, 1:; 1. 4.' 1. 47 1, 49 1. r.l |
1.53 |
1. 55 |
1.58 |
1.60 |
1.62 |
1.65 |
1.67 |
63 |
||||||||||||
|
1. ■j,'^ 1, ;ii 1 . ,14 |
1, :;7 1, :;'.i !. 11 |
1, IL |
1, .|.| 1. Ill 1.4^ 1. .'Hi 1. .■•2 1, Til 1. -'1' |
1.58 |
1.00 |
1.63 |
1.65 |
1.68 |
1.70 |
1.73 |
62 |
|||||||||||||
|
1 '"^~ 1 ■"'! |
1. 41; 1, l:M . r |
1. 47 |
1 .j'l 1 .■. 1 I :■:] ) .'.', 1. ,",7 1, .''11 1 111 |
1.63 |
1.661 1.68 |
1.71 |
1.73 |
1.76 |
1.79 |
61 |
||||||||||||||
|
L3u'..5:; |
l,:j(il,:;9 1,4:1 |
1,40 L4,S L.-'l |
1. nil.. -.11 l..-,s 1,111) 1.112 1,114 1,110 |
1.69 |
1.71 1.73 |
1.76 |
1.79 |
1.81 |
1.84 |
60 |
||||||||||||||
|
31 |
1.35 |
1.38 |
1.40'l.44'l,47 |
'1.51 1,52 1,54 |
1,56 |
1, 58 1. 60 1, 62 1, 64 1, 67 1, 69|1, 71 |
1.74 |
f.iel 1.79 |
1.81 |
1.84 |
1.87 |
1.90 |
59 |
|||||||||||
|
32 |
1.39 |
1.421.451.481.51 |
1. 55!l. 57 -I. 59 |
1,61 |
1,03 1.65' 11.67 1,691,711,74 |
1.7b |
1.79 |
1.81 1.84 |
1.87 |
1.89 |
1.92 |
1.95 |
58 |
|||||||||||
|
33 |
1.42 |
1.451.49 1.521.55 |
'1.59;l,0i:i,63 |
1,65 |
1,67,1,69 |
!l.721.741.761.7£ |
1.81 |
1.84 |
1.86 1.89 |
1.92 |
1.95; 1.98 |
2.01 |
57 |
|||||||||||
|
34 |
1.46 |
1 . 49 1 . 53 1 . 56 1 . 60 |
1, 63]l, 65 1. 6S |
1,70 |
1. 72il. 74 |
'l.7G1.791.811.8r |
l.Sb |
1.80 |
1.91] 1.94 |
1.97 |
2.00 2.03 |
2.06 |
56 |
|||||||||||
|
35 |
1. 50|1. 53 |
1,56,1.601,64 |
|1, 681,701,72 |
1,74 |
,1.761.78 |
1.81|1.831. 861.8f |
1.91 |
1.93 |
1.961 1.99 |
2.02 |
2.05 2.08 |
2.11 |
55 |
|||||||||||
|
36 |
1.54 |
1.57 |
1, 60 1. 64 1, 68 |
1 1 1.721.74 1.76 |
1,78 |
1.80 1.83 |
11.851.881.901.9 |
1.95 |
1.98 |
2.01 2.04 |
2.07 |
2.10 |
2.13 |
2.16 |
54 |
|||||||||
|
37 |
1.57 |
1. 61 |
1, 64 1, 68 1, 72 |
1,761, 78 1,80 |
1,83 |
'1.851.87 |
1 90 1. 92 1. 95 1. 97i2. 00 |
2.03 |
2.06 2.09 |
2.12 |
2.15 |
2.18 |
2.22 |
53 |
||||||||||
|
38 |
1.61 |
1. 64 |
1. 681.721,76 |
1, 80 1, 82 1. 84 |
1,87 |
1.891.91 |
1.941.971.99 2.02 2.05 |
2.08 |
! 2.11 2.14 |
2.17 |
2.20 |
l^i |
2.27 |
52 |
||||||||||
|
39 |
1 65 |
1 68 |
1.721,751,80 |
1,84 1,861,88 |
1,91 |
1.931.96 |
1.98 2.012.04:2.06 2.09 |
2.12 |
, 2.15 2. IE |
2.22 |
2.25 |
2.28 |
2.32 |
51 50 |
||||||||||
|
40 |
1.68 |
1.72 |
1,751,791,84 |
1,881,901,93 |
1.95 |
1.97 2.00 |
2. 03 2. 05 2. 08 2. 11 2. 14 |
2.17 |
2.20 2.23 |
2.26 |
2.3C |
2.83 |
2.37 |
|||||||||||
|
41 |
1.71 |
1.75 |
1.79 1.83 1,87 |
l,92'l,94 1.9f |
i.or |
2. 01 2. 04 |
2. 07 2. 09!2. 12 2. 15!2.18 |
2.21 |
2.24 2.2E |
2.31 |
2. 84 |
2.38 |
2.42 |
49 |
||||||||||
|
42 |
1.75 |
1.79 |
1, S3 1, 87 1, 91 |
1,96,1, 9H2, 01 |
2. 0: |
2. 05 2. 118, 2. 11 2. 14'2. 16 2. 19!2. 22 |
2.26 |
2.2 |
2.31 |
2.3e |
2.3£ |
2.43 |
2.46 |
48 |
||||||||||
|
43 |
1. 7f |
1.82 |
1, 86 1, 90 1, 95 |
1,99 2,02 2,04 |
2. 0" |
2. 09 2. 1-. |
2. 15 2.182. 212. 24!2. 27 |
2.30 |
2.3 |
2.3'" |
2.4t |
2.41 |
2.47 |
2.51 |
47 |
|||||||||
|
44 |
1 82 |
1 85 |
1, 90 1. 94 1 98 |
2, 03:2, 06 2. 08 |
2,1 |
i2. 13 2. 16 |
2. 19 2. 22 2. 25 2. 28!2. 31 |
2.34 |
2.3 |
2.41 |
2.4E |
2.4f |
2.52 |
2.5e |
46 |
|||||||||
|
45 |
1.85 |
1.89 |
1.931,97 2,02 |
2, 07 2. 09 2. 12,2, 1 1 1 |
;2.17i2.20 1 |
2.23 2.26 2.29,2.32 2.36 1 ! 1 |
2. 88 |
2.4 |
2.4> |
2.4E |
2.5 |
2.5* |
2. 6C |
45 |
222
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXVIII. — Factors for reduction of transit oiservations — Continued. Azimuth factor A = sin J sec. S, Star's declination ± 8. Inclination factor B=co3 i sec. i.
|
i |
67S° l.SS |
68° 1.92 |
68io 1.96 |
69° 2.01 |
69io 2.05 |
70° 2.10 |
70J° 2.13 |
704° 2.15 |
703° 2.18 |
71° 71J' |
71J° |
71P 2.30 |
72° 2.33 |
72J° 2.36 |
72i° 2.39 |
72J° 2.42 |
73° 2.46 |
731° 2.49 |
73JO 2.53 |
73i° 2.57 |
74° 2.61 |
7^140 2.65 |
? |
|
46° |
2.212.24 |
44° |
|||||||||||||||||||||
|
47 |
i.iiiii.ti:. |
2. no -J. (14 |
2. Oil |
2.14 |
' 111 ■' I'.i " ■ :. ■' ", ■' :;n |
3.33 |
2.37 |
2.40 |
2.43 |
2.47 |
2.50 |
2.54 |
2.57 |
2.61 |
2.65 |
2.69 |
43 |
||||||
|
48 |
l-'.l-l L'. us |
2. I'2 2. 07 |
2. 12 |
2. 17 |
2,111 J -J.' L- . -■-■ :i - :12.37 |
2.40 |
2.44 |
2.47 |
2.51 |
2.54 |
2.58 |
2.62 |
2.66 |
2.70 |
2.74 |
42 |
|||||||
|
49 |
l.L'T -. "1 |
2. (Hi 2. ] 1 |
2. 11; |
2.21 |
'■'::■■ :. ;s ■"* 41 |
2.44 |
2.48 |
2.51 |
2.55i |
2.58 |
2.62 |
2.66 |
2.70 |
2.74 |
2.78 |
41 |
|||||||
|
50 |
1. (JO 2. Ul |
2. US 2. 14 |
2.1a |
2.24 |
2. 27,2. 2. 2. .2, 2. .3,2..., 11,2.45 |
2.48 |
2.51 |
2.55 |
2.58 |
2.62 |
2.66 |
2.70 |
2.74 |
2.78 |
2.82 |
40 |
|||||||
|
51 |
2.03 |
2.07 |
2. 12 2. 17 |
2.22 |
2.27 |
2.30 2.33 |
2.36 |
2.39 |
2.42 |
2.45 |
2.48 |
2.51 |
2.55 |
2.58 |
2.62' |
2.66 |
2.70 |
2.74 |
2.78 |
2.82 |
2.86 |
39 |
|
|
52 |
2.06 |
2.10 |
2.15 |
2.20 |
2.25 |
2.30 |
2.33 2.36 |
2.39 |
2.42 |
2.45 |
2.48 |
2.52 |
2.55 |
2.58 |
2.62 |
2.66, |
2.69 |
2.73 |
2.77 |
2.82 |
2.86 |
2.90 |
38 |
|
53 |
2.09 |
2.13 |
2.18 |
2.23 |
2.28 |
2.33 |
2. 36 2. 39 |
2.42 |
2.45 |
2.48 |
2.52 |
2.55 |
2.58 |
2. 62 2. 66 |
2.69 |
2.73 |
2.77 |
2.81 |
2.85 |
2.90 |
2.94 |
37 |
|
|
54 |
2.11 |
2.16 |
2.21 |
2.26 |
2.31 |
2.37 |
2.39 2.42 |
2.45 |
2.48 |
2.52 |
2.55 |
2.58 |
2.62 |
2. 65 2. 69 |
2.73 |
2.77 |
2.81 |
2.85 |
2.89 |
2.94 |
2.98 |
36 |
|
|
55 |
2.14 |
2.19 |
2.23 |
2.29 |
2.34 |
2.40 |
2.42 2.45 |
2.48 |
2.52 |
2.55 |
2.58 |
2.62 |
2.65 |
2.69 2.72 |
2.76 |
2. SO |
2.84 |
2.88 |
2.93 |
2.97 |
3.02 |
35 |
|
|
56 |
:.i7-:.2i |
2 ^7 |
2 42 |
2.15 2 1 = |
2 51 2 55 2 5«'2 01 |
2 fi5'2, m |
2. 72 2. 76 |
2.80 2.83 2.86 |
2.84 2.87 2.90 |
2.88 2.91 2.94 |
2.92 2.95 2.99 |
2.96 3.00 3.03 |
3.01 3.04 3.08 |
3.05 3.09 3.12 |
34 33 32 |
||||||||
|
57 |
- '" ' -' |
'- ■, _ :., - ■: 'J : - ' : ; i -^ :i I 742:78|2!82 |
|||||||||||||||||||||
|
58 |
|||||||||||||||||||||||
|
59 50 |
I... .11 42 |
2.47 |
2w.j |
^ 7, J 77 _ . .. _ . .. ..-r. „ 7.._, ; , ..77 2.8ll2.85 |
2.89 2.92^ |
2.93 2,96 |
2.97 3.01 |
3.02 3.05 |
3.06 3.09 |
3.11 3.14 |
3.16 3.19 |
31 30 |
|||||||||||
|
liioli.Jl |
-..Jl,-.obl2.0., 2.(jU2.(,i)2. ,o2. ,0 |
2.80 |
2.84 2.88 |
||||||||||||||||||||
|
61 |
2. 2912. .33 |
2. 39 12. 44 |
2.50 |
2.56 |
2.59 2.62 2.65 2.69 2.72 2.76 |
2 79 |
2.83 |
2.8712.91 |
2.95 |
2.99 |
3.04 |
3.08 |
3.13 |
3.17 |
3.22 |
29 |
|||||||
|
62 |
2.312.36 |
2.41:2.46 |
2.52 |
2.58 |
2.612.64 2.68 12.712.75 2.78 |
2 82 |
2.86 |
2.90 2.94 |
2.98 |
3.02 |
3.06 |
3.11 |
3.16 |
3.20 |
3.25 |
28 |
|||||||
|
63 |
2.33;2.38 |
2.43 2.49 |
2.54 |
2.6(1 |
2. 64 2. 67 2. 70' 2. 74 2. 77 2. 81 |
2.84 |
2.88 |
2.92I2.96 |
3.00 |
3.05 |
3.09 |
3.14 |
3.18 |
3.23 |
3.28 |
27 |
|||||||
|
64 |
2.35|2.40 |
2.45 2. SI |
2. rt~ |
2. C3 |
2. 66 2. 69 2. 73 2. 76 2. 80i2. 83 |
2.87 |
2.91 |
2.9512.99 |
3.03 |
3.07 |
3.12 |
3.16 |
3.21 |
3.26 |
3.31 |
26 |
|||||||
|
65 |
2.37 2.42 |
2. 47 2. 52 |
2.59 |
2.65 |
2.88 2.71,2.75,2.78,2.82 |
2.86 |
2.89 |
2.93 |
2. 97j3. 01 |
3.06 |
3.10 |
3.14 |
3.19 |
3.24 |
3.29 |
3.34 |
25 |
||||||
|
66 |
2, I'l |
2 1-- |
2,7"2. 74 2, 77 2,1-12.84 |
2.88 |
2.92 |
2.96 |
3.00 3.04 |
3.08 |
3.13 |
3.17 |
3.22 |
3.27 |
3.31 |
3.37 |
24 |
||||||||
|
67 |
-!_-■. -:■ . -12.86 |
2.90 |
2.94 |
2.98 3.02,3.06 |
3.10 |
3.15 |
3.20 |
3.24 |
3.29 |
3.34 |
3.39 |
23 |
|||||||||||
|
68 |
7 7- -: _ --iL7 8Si2.92 |
2.96 |
3.0ol3.04i3.08 |
3.13 |
3.17 |
3.22 |
3.26 |
3.31 |
3.36 |
3.42 |
22 |
||||||||||||
|
69 |
J . -U '^ . 4 |
J 7', J -ii J - 1 ll,,-7 2.90]2.94 |
2.98 |
3.0213.06 3.10 |
3.15 |
3.19 |
3.24 |
3.29 |
3.34 |
3.39 |
3.44 |
21 |
|||||||||||
|
70 |
.'. 4U ■.;. 51 |
2. oli 2. Ui; |
2. US |
2. iS 2. 81 2. 8.5 2. 89,2. 92,2. 96 |
3.00 |
3.04(3.08 3.12 |
3.17 |
3.21 |
3.26 |
3.31 |
3.36 |
3.41 |
3.46 |
20 |
|||||||||
|
71 |
2.47 |
2.52 |
2.58 |
2.64 |
2.70 |
2.77 |
2.8o'2.83'2.87'2.90 2,94 2.98 |
3.02 |
3. 06^3. 103. 14 |
3.19 |
3.24 |
3.28 |
3.33 |
3.38 |
3.43 |
3.48 |
19 |
||||||
|
72 |
2.49 |
2.54 |
2.59 |
2.65 |
2.72 |
2.78 |
2. 8Ij2. 85j2. 88 :2. 92:2. 96'3. 00i3. 04 |
3. 08,3. 12,3. 16 |
3.21 |
3.25 |
3.30 |
3.35 |
3.40 |
3.45 |
3.50 |
18 |
|||||||
|
73 |
2.50 |
2.55 |
2.61 |
2.67 |
2.73 |
2.80 |
2. 83(2. 8612. 90l 2. 94 2. 97 3. 0l|3. 05 |
3.09 3.14 3.18 |
3.22 |
3.27 |
3.32 |
3.37 |
3.42 |
3.47 |
3.52 |
17 |
|||||||
|
74 |
2.51 |
2.57 |
2.62 |
2.68 |
2.74 |
2.81 |
2. 84,2. 88 2. 92; 2. 95 2. 99 3. 03,3. 07 |
3.ir3.]5 3.20 |
3.24 |
3.29 |
3.33 |
.3.38 |
3.44 |
3.49 |
3.54 |
16 |
|||||||
|
75 |
2.52 |
2.58 |
2.64 |
,2.70 |
2.76 |
2.82 |
2. 86|2. 89l2. 93| 2. 97,3. 00,3. 04 |
3.08 |
3.13 3.17 3.21 |
3.26 |
3.30 |
3.35 |
3.40 |
3.45 |
3.50 |
3.56 |
15 |
||||||
|
76 |
J..MJ. -;- |
2. i:-'2. 71 |
2. -1 |
2 -7 11 111 -M7 J nil 11. 02:3. 06 |
3.10 |
3.15,3.18:3.23 |
3.28 |
3.32 |
3.37 |
3.42 |
3.47 |
3.53 |
3.58 |
14 |
|||||||||
|
- -■ - - " - I'l'::. 0313.07 |
3.11 |
3. 1513.19 8. 24 |
3.29 |
3.33 |
3.38 |
3.43 |
3.48 |
3.54 |
3.59 |
13 |
|||||||||||||
|
78 |
. J . , - "11. 04'3.08 |
3.12 |
3.16,3.213.25 |
3.30 |
3.34 |
3.39 |
3.44 |
3.49 |
3.55 |
3.60 |
12 |
||||||||||||
|
79 |
-■' i;^ ■' 7-1 |
J, 111 -.iMu,'K :i..i-:i (1513.09 |
3. 13|3. 18l3. 22 |
3.26 |
3.31 |
3.36 |
3.41 |
3.46 |
3.51 |
3.56 |
3.62 |
11 |
|||||||||||
|
80 |
2. 57 2. 63 |
2! 69 2. ::, |
2. 81 |
2^88 |
2. 91 2. 95 2. 99 3. 02 3. 06 3. 10 |
3.14 |
3. 19 3. 23 |
3.27 |
3.32 |
3.37 |
3.42 |
3.47 |
3.52 |
3.57 |
3.63 |
10 |
|||||||
|
81 |
2. 58' 2. 64 |
2. 69 2. 76 |
2.82 |
2.89 |
2. 92 2. 9613.0013. 03 3.07:3.11 |
3.15 |
3. 20 3. 24 |
3.28 |
3.33 |
3.38 |
3.43 |
3.48 |
3.53 |
3.58 |
3.64 |
9 |
|||||||
|
82 |
2.59,2.64 |
2.70 2.76 |
2.83 |
2.90 |
2. 93 2. 97 3. 00 3. 04 3. 08 3. 1213. 16 |
3. 20 3. 25i3. 29 |
3.34 |
3.39 |
3.44 |
2.49 |
3.54 |
3.59 |
3.65 |
8 |
|||||||||
|
83 |
2.59 2.65 |
2.71 2.77 |
2.83 |
2.90 |
2. 94 2. 97 :;. Ill 2. 0,5 3. 0913. 13'3. 17 |
3.21,3.2613.30 |
3.35 |
3.40 |
3.45 |
3.49 |
3. 55 |
3.60 |
3.66 |
7 |
|||||||||
|
84 |
2. 60 2. 66 |
2.71:2.78 |
2.84 |
2.91 |
2.94 2.11,-11.112 li, ml n. 09'3. 13 3. 18 |
3.22 3.263.31 |
3.35 |
3.40 |
3.45 |
3.50 |
3.55 |
3.61 |
3.66 |
6 |
|||||||||
|
85 |
2. 60 2. 66 |
2.72i2.78 |
2.84 |
2.91 |
2. 95 2, 98 IJ. U2 11. Ui; 3. 1013. 14:3. 18 |
3. 22 3. 27(3. 31 |
3.36 |
3.41 |
3.46 |
3.51 |
3.56 |
3.61 |
3.67 |
5 |
|||||||||
|
86 |
2. 61 2. l-J |
2.92 |
2.95 |
2.99,3.03 |
.3. 06|3. 10 |
3. 14 3. 19 |
3. 23 3. 27 |
3.32 |
3.36 |
3.41 |
3.46 |
3.51 |
3.57 |
3.62 |
3.68 |
4 |
|||||||
|
87 |
2.612.1' |
2.92 |
2.95 |
2.99 |
3.03 |
3.07 |
3.11 |
3. 15 3. 19 |
3. 23 3. 28 |
3.32 |
3.37 |
3.42 |
3.47 |
3.52 |
3.57 |
3.62 |
3.68 |
3 |
|||||
|
88 |
2.61 2. i;: |
2.92 |
2.96 |
2.-99 |
3.03 |
3.07 |
3.11 |
3.15 3.19 |
3.23 3.28 |
3.32 |
3.37 |
3.42 |
3.47 |
3.52 |
3.57 |
3.62 |
3.68 |
2 |
|||||
|
89 |
2. 6112. u: |
2. 71>||2. 71) |
2.80 |
2.92 |
2.96 |
3.00 |
3.03 |
3.07 |
3.11 |
3.15 3.19 |
3. 24 3. 28 |
3.33 |
3.37 |
3.42 |
3.47 |
3.52 |
3.57 |
3.63 |
3.68 |
1 |
|||
|
90 |
2.612.67 |
2. 73|J2. 79 |
:f |
2.92 |
2.96 |
3.00 |
3.03 |
3.07 |
3.11 |
3. 15 3. 19 |
3.24 3.28 |
3.33 |
3.37 |
3.42 |
3.47 |
3.52 |
3.57 |
3.63 |
3.68 |
0 |
FACTOES FOE EEDUCTION OF TEANSIT OBSERVATIOifS. 223
Table XXVIII. — Factors for reduction of transit observations — Continued. Azimuthfactor A=:8inisec. 6. Star's tleclination ± S. Inclination factor B = cos ^ sec. S.
|
i 1^ |
74i° .06 |
74,o .07 |
75° .07 |
751^ .07 |
7=S° .07 |
75,0 |
76° |
76,° .07 |
76,° .07 |
76»° .08 |
77° .08 |
77,° .08 |
77i° .08 |
77i° .08 |
78° .08 |
78i° .09 |
78J° |
78J° |
, 79° |
79i° .09 |
79J° .10 |
79J° .10 |
80° .IC |
i |
|
.07 |
.07 |
.09 |
. 09: • 09 |
'89 |
||||||||||||||||||||
|
2 |
.13 |
.13 |
.13 |
.14 |
.14 |
.14 |
.14 |
.15 |
.15 |
.15 |
.16 |
.16 |
.16 |
.16 |
.17 |
.17 |
■ .18 |
. 18' . 16 |
.19 |
.19 |
.20 |
.2C |
88 |
|
|
3 |
.20 |
.20 |
.20 |
.21 |
.21 |
.21 |
.22 |
.22 |
.22 |
.23 |
.23 |
.24 |
.24 |
.25 |
.25 |
.26 |
.26 |
. 271 . 27 |
.28 |
.29 |
.29 |
.31 |
87 |
|
|
4 |
.26 |
.27 |
.27 |
.27 |
.28 |
.28 |
.29 |
.29 |
.30 |
.30 |
.31 |
.32 |
.32 |
.33 |
.34 |
.34 |
.35 |
. 36: . 37 |
.37 |
.38 |
.39 |
.41 |
86 |
|
|
5 |
.33 |
.33 |
.34 |
.34 |
.35 |
.35 |
.36 |
.37 |
.37 |
.38 |
.39 |
.40 |
.40 |
.41 |
.42 |
.43 |
.44 |
.45 |
.46 |
.47 |
.48 |
.49 |
.50 |
85 |
|
6 |
.39 |
.40 |
.40 |
.41 |
.42 |
.42 |
.43 |
.44 |
.45 |
.46 |
.46 |
.47 |
.49 |
.49 |
.51 |
.51 |
.52 |
.54 |
.55 |
.56 |
.57 |
.59 |
.60 |
84 |
|
7 |
.46 |
.46 |
.47 |
.48 |
.49 |
.50 |
.50 |
.51 |
.52 |
.53 |
.64 |
.55 |
.56 |
.57 |
.59 |
.60 |
.61 |
.62 |
.64 |
.65 |
.67 |
.69 |
.70 |
83 |
|
8 |
.52 |
.53 |
.54 |
.55 |
.56 |
.57 |
.58 |
.59 |
.60 |
.61 |
.62 |
.63 |
.64 |
.66 |
.67 |
.68 |
.70 |
.71 |
.73 |
.75 |
.76 |
.78 |
.80 |
82 |
|
9 |
.58 |
.59 |
.60 |
.61 |
.62 |
.64 |
.65 |
.66 |
.67 |
.68 |
.70 |
.71 |
.72 |
.74 |
.75 |
.77 |
.78 |
.80 |
.82 |
.84 |
.86 |
.88 |
.90 |
81 |
|
10 |
.65 |
.66 |
.67 |
.68 |
.69 |
.71 |
.72 |
.73 |
.74 |
.76 |
.77 |
.79 |
.80 |
.82 |
.84 |
.85 |
.87 |
.89 |
.91 |
.93 |
.95 |
.98 |
1.00 |
80 |
|
11 |
.71 |
.73 |
.74 |
.75 |
.76 |
.77 |
.79 |
.80 |
.82 |
.83 |
.85 |
.86 |
.88 |
.91) |
.92 |
.94 |
.96 |
.98 |
1.00 |
1.02 |
1.05 |
1.07 |
1.10 |
79 |
|
12 |
.78 |
.70 |
.80 |
.82 |
.83 |
.85 |
.86 |
.88 |
.89 |
.91 |
.92 |
.94 |
.96 |
.98 |
1.00 |
1.02 |
1.04 |
1.07 |
1.09 |
1.11 |
1.14 |
1.17 |
1.20 |
78 |
|
13 |
.84 |
.86 |
.87 |
.88 |
.90 |
.91 |
,93 |
.95 |
.96 |
.981.00 1.02 |
1.04 |
1.06 |
1.08 |
1.10 |
1.13 |
1.15 |
1.18 |
1.21 |
1.23 |
1.26 |
1.30 |
77 |
||
|
11 |
.91 |
.92 |
.94 |
.95 |
.97 |
.98 |
1.00 |
1.02 |
1.01 |
1.061.08 1,10 |
1.12 |
1.14 |
1.16 |
1.19 |
1.21 |
1.24 |
1.27 |
1.30 |
1.33 |
1.36 |
1.39 |
76 |
||
|
15 |
.97 |
.98 |
1. Oil |
1.02 |
1.03 |
1.05 |
1.07 |
1.09 |
1.11 |
1.13 1.15 1,17 |
1,20 |
1.22 |
1.25 |
1.27 |
1.30 |
1,33 |
1.36 |
1.39 |
1.42 |
1.46 |
1,49 |
75 |
||
|
16 |
1.03 |
1.05 |
1.06 |
1.08 |
1.10 |
1.12 |
1.14 |
1, 16 1. 18'i,2o'l,2:i 1.25 |
1.28 |
1.30 |
1.33 |
1.35 |
1.38 |
1.41 |
1.44 |
1,48 |
1.51 |
1,55 |
1,59 |
74 |
||||
|
17 |
1. 09 |
1,11 |
1.13 |
1.15 |
1.17 |
1.19 |
1.21 |
1, 2:l!l, 25 1. 28 1, 30 1. 32 |
1.35 |
1,38 |
1.40 |
1.44 |
1.47 |
1.50 |
1.53 |
1.57 |
1.60 |
1,64 |
1.68 |
73 |
||||
|
19 |
1.16 |
1.17 |
1.19 |
1.21 |
1.23 |
1. 25 ;i. 2S 1. 3U|1, 32 1. 35 1. 37 1, 411 |
1.43 |
1.46:i.49 |
1.52 |
1.55 |
1.58 |
1.62 |
1.66 |
1.70 |
1.74 |
1.78 |
72 |
|||||||
|
10 |
1.22 |
1.24 |
1.20 |
1.28 |
1.30 |
1.32 |
1. .35 |
1.37 1, 39|1, 42:1,45 1.47 |
1.51 |
1. 53 |
1.57 |
1.60 |
1.63 |
1.67 |
1.71 |
1.75 |
1.79 |
1.83 |
1.87 |
71 |
||||
|
20 |
1.28 |
1.30 |
1.32 |
1.34 |
1.37 |
1.30 |
1.41 |
1. 44ll,461, 49 1,50 1.55 |
1.58 |
1.61 |
1.65 |
1.68 |
1,73 |
1.75 |
1.79 |
1.83 |
1.88 |
1.93 |
1.97 |
70 |
||||
|
21 |
1.34 |
1.36 |
1.3R |
1.41 |
1.43 |
1.46 |
1.48 |
1,51 1,541, 56 1.591 1.62 |
1.65 |
1.69 |
1,72 |
1.76 |
1.80 |
1.84 |
1.88 |
1.92 |
1.97 |
2.01 |
2.06 |
69 |
||||
|
22 |
1.40 |
1.42 |
1.45 |
1.47 |
1.50 |
1.52 |
1. 55 |
1. 58 1, 60 1, 63 1. 66' 1. ■Jo |
1,73 |
1.77 |
1,80 |
1.84 |
1.88 |
1.92 |
1.96 |
2.01 |
2.06 |
2.11 |
2.16 |
68 |
||||
|
23 |
1.46 |
1.49 |
1.51 |
1.54 |
1.56 |
1.59 |
1.62 |
1. 04 1. 67 1. 70 1. 74[ 1. 77 |
1,81 |
1, 84il.88 |
1.92 |
1.96 |
2.00 |
2.05 |
2,09 |
2.14 |
2.20 |
2.25 |
67 |
|||||
|
24 |
1, .52 |
1.55 |
1.57 |
1.60 |
1.63 |
1.65 |
1.68 |
1,711, 74jl, 771. 8ll|l, 84 |
1,88 |
1. 92 1. 96 |
2.00 |
2.04 |
2.08 |
2.13 |
2.18 |
2.23 |
2.29 |
2.34 |
66 |
|||||
|
25 |
1.58 |
1.61 |
1.63 |
1.66 |
1.69 |
1.72 |
1.75 1.781,811,84 1.88 1,91 |
1.95 |
1,99 2.03 |
2.07 |
2.12 |
2.17 |
2.22 |
3.27 |
3.32 |
2.38 |
2.43 |
65 |
||||||
|
26 |
1.64 |
1.67 |
1.69 |
1.72 |
1.75 |
1.78 |
1.811.841,881,911,9.-1 1,9!) |
2. 02 |
2, 07:2. 11 |
2.15 |
2.20 |
2.25 |
2.31 |
2.35 |
2.41 |
2.46 |
2,52 |
64 |
||||||
|
27 |
1.70 |
1.73 |
1.75 |
1.78 |
1.81 |
1.85 |
1, 88ll.911.951.98 2, (12 2, 111! |
2, 10 |
2,14'2.18 |
2.23 |
2,28 |
2.33 |
2.38 |
2,43 |
2.49 |
2.55 |
2,61 |
63 |
||||||
|
28 |
1.70 |
1.78 |
1.81 |
1.84 |
1.87 |
1.91 |
I. 94 1. 97 2. 0i;2. 05 2, 119 2. 13 |
2,17 |
2, 21 '2, 26 |
2.31 |
2.36 |
2,41 |
2.46 |
2,52 |
2'. 58 |
2.64 |
2.70 |
62 |
||||||
|
29 |
1.81 |
1.84 |
1.87 |
1.90 |
1.94 |
1.97 |
2. 002.04 2. 08.2. 112. 15i!2. 20 |
2.24 |
2, 28 2. 33 |
2.38 |
2.43 |
2,48 |
2.54 |
2.60 |
2.66 |
2.73 |
2.79 |
61 |
||||||
|
30 |
1.87 |
1.90 |
1.93 |
1.96 |
2.00 |
2.03 |
2.07:2. 10 2. 14:2. 18 2. 22!i2. 27 |
3.31 |
2.36 2.40 |
2.46 |
2.51 |
2.56 |
3.62 |
2.68 |
2.74 |
2.81 |
2.88 |
60 |
||||||
|
31 |
1.93 |
1.96 |
1.99 |
2.02 |
2.06 |
2.09 |
2. 13 2. 17 2. 2rj J.V-J. -J'.i J. :::; |
2,38 |
2. 43 2 48 |
2.53 |
2.58 |
3.64 |
2.70 |
2.76 |
2.83 |
2.89 |
2.97 |
59 |
||||||
|
32 |
1.98 |
2.01 |
2.05 |
2.08 |
2.12 |
2.15 |
2, 19 2, 23 2, -j: : - ' : ,1 |
2,45 |
2.50 2.55 |
2.60 |
2.66 |
2.72 |
2.78 |
2.84 |
2.91 |
2.98 |
3.05 |
58 |
||||||
|
33 |
2.04 |
2.07 |
2.10 |
2.14 |
2.18 |
2.21 |
2.25 2.29 2,:::;- - - i : |
2,52 |
2.57i2.62 |
2.67 |
2.73 |
2.79 |
2.85 |
2.93 |
2.99 |
3.06 |
3.14 |
57 |
||||||
|
34 |
3.09 |
2.13 |
2.16 |
2.20 |
2.23 |
2. 27 |
2.312,35 2,4111' 1 ' : I ' J.:.:: |
2,58 |
2. 64'2. 69 |
2.75 |
2.80 |
2.87 |
2.93 |
3.00 |
3.07 |
3,14 |
3,23 |
56 |
||||||
|
35 |
2.15 |
2.18 |
2.22 |
2.25 |
2.29 |
2.33 |
2,37 2.412,40 J. riij, l.'i J.r.n |
2,65 |
2. 70 2. 76 |
2.82 |
2.88 |
2.94 |
3.01 |
3.08 |
3,15 3.28 |
3.30 |
55 |
|||||||
|
36 |
2.20 |
2.24 |
2.27 |
2.31 |
2,35 |
2.39 |
2.432.472,,52-J.,-i;2.i;l 2. CO |
2, 77 2. 83 |
2.89 |
2.95 |
3.01 |
3.08 |
3.15 |
3.23 3.30 |
3.38 |
54 |
||||||||
|
37 |
2.25 |
2.29 |
2.33 |
2.36 |
2.40 |
2.44 |
2, 49 2, 53 2. 58 2. O:.: 2, 07 2, ''J |
2:7s |
2. 84 2. 90 |
2.95 |
3.02' |
3.08 |
3.15 |
3.23 |
3.30 3.38 |
3.47i 63 |
||||||||
|
38 |
2.30 |
2.34 |
2.38 |
2.42 |
2. 46 2. 50 |
2,55 2,59 2.64,2.69 |
2.74i2.79 |
2,85 |
2. 90 2, 96 |
3,02 |
3.09: |
3,16 |
3.23 |
3.30 |
3.38 3.46 |
3.551 52 |
||||||||
|
39 |
2.35 |
2.39 |
2.43 |
2.47 |
2.512,56 |
2.60 2.65 2.70 2.75 |
2. 80 '2. 85 |
2,91 |
2. 97 3, 03 |
.3.09 |
3.161 |
3,23 |
3.30 |
3.37 |
3.45 3.53 |
3. 62 51 |
||||||||
|
40 |
2.40 |
2.44 |
2.48 |
2.52 |
2. 57 2. 61 |
2.66 2.70 2.75 2.80 |
2. 86,, 2, 91 |
3.97 |
3.03 |
3,09 |
3.16 |
3.22 |
3.29 |
3.37 |
3.45 |
3.53 3.61 |
3. 70j 50 |
|||||||
|
41 |
2.45 |
2.49 |
2.53 |
2.58 |
2. 62 2. 66 |
2.7l'2.76 2.812.86 |
2,92:2,97 |
3.03 |
3.09 |
3.16 |
3,22 |
3,29 |
3.36: 3.44 |
3.52 |
3.60 3.69 |
3.78 |
40 |
|||||||
|
42 |
2.50 |
2.54 |
2.58 |
2.63 |
2. 67 2. 72 |
2. 77 2. 81 2. 87|2. 92 2. 97, |
3.03 |
3.09 |
3.15 |
3,22 |
3,29 |
3.36 |
3.43; 3.51 |
3.59 |
3. 67 1 3. 76 |
3.85 |
48 |
|||||||
|
43 |
2.55 |
2.59 |
2.63 |
2.68 |
2. 72 2. 77 |
2.82 2.87,2.922.98 3,03 |
3.09 |
3,15 |
3.21 |
3.28 |
3.35 |
3.42 |
3.50] 3.57 |
3.66 |
3.74 3.83 |
3.93 |
47 |
|||||||
|
44 |
2.60 |
2.64 |
2.68 |
2.73 |
2. 77 2. 82 |
2.87,2.92 2.98,3.03 3.09 |
3.15 |
3.21 |
3.27 |
3.34 |
3.41 |
3.48 |
3.56: 3.64 |
3.72 |
3.81 3.91 |
4.00 |
46 |
|||||||
|
45 |
2.65 |
2.69 |
2.73 |
2.78 |
2. 82 2. 87 |
2. 92|2. 97 3. 03 3. 08 3. 14 |
8.20 |
3.27 |
3.33 |
3.40 |
3.47 |
3.55 |
3.62 3.71 |
3.79 3.88 3.97| |
4.07 |
45 |
224
A ma:n^ual of topogeaphic methods.
Table XXVIII. — Factors for reduction of transit ohservations — Continued. Azimuth factor A=sm C sec. 5. Star's decliuation ± 6. Inclmation factor B = cos i sec. 6.
|
460 |
74J= 2. 6n |
74r |
75° |
75io |
75J= 2.S7 |
75r 2.92 |
76° 2.97 |
76i0 76io 3. 03 3. OS |
76J° |
770 |
77i° 3.20 |
77J° 3.32 |
77i° 3.39 |
78° 3.46 |
78i° 3.53 |
78J° 3.01 |
78i° 3.69 |
79° |
79i° 3.86 |
79J° 3.95 |
79J° 4.04 |
80° 4.14 |
i |
|
2.7s'2.S2 |
3. 14'3. 20 |
3.77 |
44° |
||||||||||||||||||||
|
47 |
^ 7 |
■J. 1-17 |
_\ |i'^ |
■J, 117 |
11. li"J |
:i, 08 :i. i: |
11 IP 11, 2," 11 "1 |
11, 118 |
11, 4," |
3.52' 3.59 |
3. 67i 3.75 |
3.83 |
3.92 |
4.01 |
4.11 |
4.21 |
43 |
||||||
|
48 |
11, '57 |
3.05 |
3.73 |
3.81 |
3.89 |
3.98 |
4.08 |
4.18 |
4.28 |
42 |
|||||||||||||
|
49 |
,1,03 |
3.71 |
3.79 |
3.87 |
3.96 |
4.05 |
4.14 |
4.24 |
4.35 |
41 |
|||||||||||||
|
50 |
J ;il |
"'■'-'' |
■■!"■ |
.1. 11 |
.1,1: |
■■■ ■-' ■'■ -;:" |
11, 114. 1,41 : ,:; |
1, -■! |
1 ill |
11, 08 |
3.76 |
3.84 |
3.93 |
4.02 |
4.11 |
4.20 |
4.30 |
4.41 |
40 |
||||
|
51 |
2.91 |
2.95 |
3.00 |
3.05 |
3.10 |
3.16 |
3.21 |
3. 27 3. 33 |
3.39 |
3.45 11,5. |
11.00 |
11.74 |
3.82 |
3.90 |
3.98 |
4.07 |
4.17 |
4.26 |
4.37 |
4.48 |
39 |
||
|
52 |
2.95 |
3.00 |
3.04 |
3.09 |
3.15 |
3.20 |
3.26 |
3.313.38 |
3.44 |
3. .10 11, ,-.7 |
11. 114 |
11, 71 |
3.79 |
3.87 |
3.95 |
4.04 |
4.13 |
4.22 |
4.32 |
4.43 |
4.54 |
38 |
|
|
63 |
2.99 |
3.04 |
3.09 |
3.14 |
3.19 |
3.24 |
3.30 |
3.36 3.42 |
3.48 |
3. 35 3. 02 |
11, 00 |
3, 77 |
11.84 |
3.92 |
4.01 |
4.09 |
4.19 |
4.28 |
4.3b |
4.49 |
4.60 |
37 |
|
|
54 |
3.03 |
3.08 |
3.13 |
3.18 |
3.23 |
3.29 |
3.34 |
3.40 3.47 |
3.53 |
3. 60 3. 67 |
3.74 |
3. 81 |
3.89 |
3.97 |
4.00 |
4.15 |
4.24 |
4.34 |
4.44 |
4.55 |
4.66 |
36 |
|
|
55 |
3.07 |
3.11 |
3.16 |
3.22 |
3.27 |
3.33 |
3.39 |
3.45 3.51 |
3.57 |
3. 64 3. 71 |
3.78 |
3.86 |
8.94 |
4.02 |
4.11 |
4.20 |
4.29 |
4.39 |
4.50 |
4.60 |
4.72 |
35 |
|
|
56 |
3.10 |
3. 15 |
3.20 |
3.26 |
3.31 |
3.37 |
3. 43 |
3. 49 3. 55 |
3,62 |
3. OS 3. 70 |
3. Sll |
3.91 |
3.99 |
4.07 |
4.16 |
4.25 |
4.34 |
4.44 |
4.55 |
4.66 |
4.77 |
•34 |
|
|
57 |
::. 11 |
; l:i |
1. -11 |
1, 17 |
1, Til 11 81' |
1, 8- |
11, 0,' |
4,04 |
4.12 |
4.21 |
4.30 |
4.39 |
4.50 |
4.60 |
4.72 |
4.83 |
33 |
||||||
|
58 |
1.08 |
4.16 |
4.25 |
4.35 |
4.44 |
4.55 |
4.65 |
4.77 |
4.88 |
32 |
|||||||||||||
|
59 |
> ,11 ; i 1 7 |
4.12 |
4.21 |
4.30 |
4.39 |
4.49 |
4.60 |
4.70 |
4.82 |
4.94 |
31 |
||||||||||||
|
(iO |
.:.-,! |
;,-h |
'■-i'' |
1 ,-.s |
1 <i.;:i 71 |
I, .11 |
.1, |
4, 17 |
4.25 |
4.34 |
4.44 |
4.54 |
4.64 |
4.75 |
4.87 |
4.99 |
SO |
||||||
|
61 |
3.27 |
3.33 |
3.38 |
3.44 |
3.49 |
3.55 |
3.62 |
3. 683. 75 |
3. 82 |
3.^93.96 |
4.04 |
4.12 |
4.21 |
4.29 |
4.39 |
4.48 |
4.58 |
4.69 |
4.80 |
4.92 |
5.04 |
29 |
|
|
62 |
3.30 |
3.36 |
3.41 |
3.47 |
3.53 |
3.59 |
3.65 |
3. 72 3. 78 |
3! 85 |
3. 92 4. 00 |
4.08 |
4.10 |
4.25 |
4.34 |
4.43 |
4.53 |
4.63 |
4.73 |
4.85 |
4.96 |
5.08 |
28 |
|
|
63 |
3.33 |
3.39 |
3.44 |
3.50 |
3.56 |
3.62 |
3.68 |
3. 75 3. 82 |
3.89 |
3. 96 4. 04 |
4.12 |
4.20 |
4.29 |
4.38 |
4.47 |
4.57 |
4.67 |
4.78 |
4.89 |
5.01 |
5.13 |
27 |
|
|
64 |
3.36 |
3.42 |
3.47 |
3.53 |
3.59 |
3.65 |
3.72 |
3. 78,3. 85 |
3.92 |
4. 00 4. 07 |
4.15 |
4.24 |
4.32 |
4.41 |
4.51 |
4.61 |
4.71 |
4.82 |
4.93 |
5.05 |
5.18 |
26 |
|
|
65 |
3.39 |
3.45 |
3.50 |
3.56 |
3.62 |
3.68 |
2.75 |
3. 8113. 88 |
3.95 |
4. 03 4. 11 |
4.19 |
4.27 |
4.36 |
4.45 |
4.55 |
4.65 |
4.75 |
4.86 |
4.97 |
5.09 |
5.22 |
25 |
|
|
66 |
3, J2 |
:?. 47 |
_ |
■5, 50 |
l.fi.T |
3 71 |
?, 7S |
!. 84 3, 91 |
3, 99 |
4. 004. 14 |
4,22 |
4.31 |
4.40 |
i.49 |
4.58 |
4.68 |
4.79 |
4.90 |
5.01 |
5.14 |
5.26 |
24 |
|
|
67 |
:. 4-1 |
; il- |
: . 1 |
; ^i |
1 -T : 04 |
4, I'L' |
1, 0:14, 17 |
t, 20 |
4, 1-14 |
4.43 |
4.52 |
4.62 |
4.72 |
4.82 |
4.94 |
5.05 |
5.18 |
5.30 |
23 |
||||
|
68 |
1. 1 1 ■, |
1- 1;; 1, 20 |
1, 2.^ |
4, 117 |
4.46 |
4.55 |
4.65 |
4.75 |
4.86 |
4.97 |
5.09 |
5.21 |
5.34 |
22 |
|||||||||
|
69 |
4, 11, |
4. 1,", 1, 2,1 |
1.112 |
4,40 |
4.49 |
4.58 |
4.68 |
4.79 |
4.89 |
5.00 |
5.12 |
5.25 |
5.38 |
21 |
|||||||||
|
JO |
J.i: |
... i; |
o.GJ |
;.GJ |
J. t; |
,.j: |
.. Ml |
.1. Li.j 4. u;; |
4. lu |
4. 18 4.25 |
4.34 |
4.43 |
4.52 |
4.61 |
4.71 |
4.82 |
4.93 |
5.04 |
5.16 |
5.28 |
5.41 |
20 |
|
|
71 |
3.54 |
3.60 |
3.65 |
3.71 |
3.78 |
3.84 |
3.91 |
3. 98*4. 05 |
4.13 |
4. 20 4. 28 |
4.37 |
4.40 |
4.55 |
4.64 |
4.74 |
4.85 |
4.96 |
5.07 |
5.19 |
5.32 |
5.45 |
19 |
|
|
72 |
3.56 |
3.63 |
3.67 |
3.74 |
3.80 |
3.86 |
3.93 |
4. 00 4. 07 |
4.15 |
4. 23!4. 31 |
4.39 |
4.48 |
4.57 |
4.67 |
4.77 |
4.88 |
4.98 |
5.10 |
5.22 |
5.34 |
5.48 |
18 |
|
|
73 |
3.58 |
3.64 |
3.69 |
3.76 |
3.82 |
3.89 |
3.95 |
4. 02 4. 10 |
4.17 |
4.25:4.33 |
4.42 |
4.51 |
4.60 |
4.70 |
4.80 |
4.90 |
5.01 |
5.13 |
5.25 |
5.37 |
5.51 |
17 |
|
|
74 |
3.60 |
3.65 |
3.71 |
3.78 |
3.84 |
3.91 |
3.97 |
4. 04;4. 12 |
4.19 |
4. 2714. 36 |
4.44 |
4 53 |
4.62 |
4.72 |
4.82 |
4.93 |
5.04 |
5.15 |
5.27 |
5.40 |
5.53 |
16 |
|
|
75 |
3.61 |
3.67 |
3.73 |
3.79 |
3.86 |
3-92 |
3.99 |
4.06 4.14 |
4.21 |
4. 29 4. 38 |
4.46 |
4.55 |
4; 65 |
4.74 |
4.84 |
4.95 |
5.06 |
5.18 |
5.30 |
5.43 |
5.56 |
15 |
|
|
76 |
3.64 |
3. on |
'. "-■ |
, 5, |
.94 |
4. 01 |
4. OS 4. ir. |
4, 2'_1 |
4. .11 '4. 40 |
4,4s |
4. .57 |
4.07 |
4.76 |
4.87 |
4.97 |
5.09 |
5.20 |
5.32 |
5.45 |
5.59 |
14 |
||
|
77 |
3.65 |
3.711 |
-.1 |
'. 'Mi |
4. 03 |
1.10 4,17 |
1, 11114.41 |
4. ,'iO |
1, ,'.0 |
4.68 |
4.78 |
4.89 |
4.90 |
5.11 |
5.22 |
5.35 |
5.47 |
5.61 |
13 |
||||
|
78 |
3,66 |
3.7: |
'. 07 |
4. 04 |
4.11 4.111 |
4. 27 |
4, 11,'. 4,411 |
1, ,'.2 |
4,01 |
4.70 |
4.80 |
4.9] |
5.01 |
5.13 |
5.24 |
5.37 |
5.50 |
5.63 |
12 |
||||
|
79 |
3.67 |
3.7.1 |
1.119 |
4. OlJ |
4.1114.21 |
4, 1;,^ |
4, 110 4.4,'. |
1. ,'.4 |
I, OH |
4.72 |
4.82 |
4.92 |
5.03 |
5.14 |
5.26 |
5.39 |
5.52 |
5.65 |
11 |
||||
|
SO |
3.68 |
3.74 |
i.sl |
i.bl |
0. 113 |
4.00 |
4.07 |
4.144.22 |
4. 3U |
4. 38 4. 40 |
4.55 |
4.04 |
4.74 |
4.84 |
4.94 |
5.05 |
5.16 |
5.28 |
5.40 |
5.54 |
5.67 |
10 |
|
|
81 |
3.70 |
3.75 |
3.82 |
3.88 |
3.94 |
4.01 |
4.08 |
4.16 4.23 |
4.31 |
4. 39 4. 48 |
4. .56 |
4.65 |
4.75 |
4.85 |
4.95 |
5.06 |
5.18 |
5.30 |
5.42 |
5.55 |
5.69 |
9 |
|
|
82 |
3.71 |
3.76 |
3.83 |
^.89 |
3.96 |
4.02 |
4.09 |
4. 17 4. 24 |
4. 32 |
4. 40 4. 49 |
4.57 |
4.67 |
4.76 |
4.86 |
4.97 |
5.08 |
5.19 |
5.31 |
5.43 |
5.56 |
5.70 |
S |
|
|
83 |
3.72 |
3.77 |
3.84 |
3.90 |
3.96 |
4.03 |
4.10 |
4. 18 4, i,". |
4. 414. .io |
4. :'.9 |
4. 08 |
4.78 |
4.87 |
4.98 |
5.09 |
5.20 |
5.32 |
5.45 |
5.58 |
5.72 |
7 |
||
|
84 |
3.72 |
3.78 |
3.84 |
3.91 |
3.97 |
4.04 |
4.11 |
4, 18 4,20 |
4.34 |
4. 42 4. 51 |
4.00 |
4.09 |
4.79 |
4.88 |
4.99 |
5.10 |
5.21 |
5.33 |
5.46 |
5.59 |
5.73 |
6 |
|
|
85 |
3.73 |
3.79 |
3.85 |
3.91 |
3.98 |
4.05 |
4.12 4. 1114 27 |
4. 115 |
4,4114.51 |
4.60 |
4.09 |
4.79 |
4.89 |
5.00 |
5.11 |
5.22 |
5.34 |
5.47 |
5.60 |
5.74 |
5 |
||
|
86 |
3.73 |
3.711 |
4. ;i.' |
1, l-jli.^M L-27 |
4.35 |
4.43 4,52 |
4. 01 |
4.70 |
4.80 |
4.90 |
5.00 |
5.11 |
5.23 |
5.35 |
5.47 |
5.61 |
5.74 |
4 |
|||||
|
87 |
3.74 |
3.71. |
4. 30 4. 44 4. 52 |
4.02 |
4.714.81 |
4.90 |
5.01 |
5.12 |
5.23 |
5.35 |
5.48 |
5.61 |
5.75 |
3 |
|||||||||
|
88 |
3.74 |
3,8' |
4,36 4.44 4.51! |
4.02 |
4. 71 4. 81 |
4.91 |
5.01 |
5.12 |
5.24 |
5.36 |
5.48 |
5.61 |
5.75 |
2 |
|||||||||
|
89 |
3.74 |
S.Su |
1. ,m1 |
1 M,; |
. ll'.i |
1. ml |
1. 1:1 -I. -Jl 4. 1.8 4.30 4.44 4.53 |
4.62 |
4. 71 4. 81 |
4.91 |
5.01 |
5.12 |
5.24 |
5.36 |
5.49 |
5.62 |
5.76 |
1 |
|||||
|
90 |
3.74 |
3.80 |
J. Sli |
3! 93 |
3.99 |
4.06 |
4. 1314. 21 4. 28,4. 36J4. 44l4. 53 4. 62 |
4. 7114. 81 |
4.91 |
5.02 |
5.13 |
5.24 |
5.36 |
5.49 |
5.62 |
5.76 |
0 |
Table XXIX. — For reducing observations for latitude hy Talcotfs metliod.
[Extracted from Appendix 14. TJnited States Coast and Geodetic Survey, Eeport for 1880.]
Correction for differential refraction. — The difference of refraction for any pair of stars ia so small that we can uegieet the variation in the state of the atmosphere at the time of the observation from that mean state supposed in the refraction tables. The refraction being nearly proportional to the tangent of the zenith-distance, the differ- ence of refraction for the two stars will be given by — r— r'=57".7 sin [z—z') sec.-s;
and since the difference of zenith-distances is measured by the micrometer, the follow- in £; table of correction to the latitude for differential refraction has been prepared
EEDUCTION OF LATITUDE OBSEEVATIONS.
225
for the argument ^difference of zenith-distance, or J difference of micrometer-reading on the side, and the argument "Zenith-distance" on the top. The sign of the cor- rection is the same as that of the micrometer difference.
|
i diff. in |
Zenith-distance |
i dift-. in |
|||||||||||
|
zenith- distance. |
|||||||||||||
|
0° |
lOo |
20°- |
25° |
30° |
35° |
distance. |
0° |
10° 20° |
25° |
30° |
35° |
||
|
0 |
.00 |
.00 |
.00 |
.00 |
.00 |
.00 |
6.5 |
11 |
.11 |
K |
.13 |
.14 |
.16 |
|
0.5 |
.01 |
.01 |
.01 |
.01 |
.01 |
.01 |
7 |
IX |
.12 |
13 |
.14 |
.15 |
.18 |
|
1 |
.02 |
.02 |
.02 |
.02 |
.02 |
.02 |
7.5 |
13 |
.13 |
14 |
.15 |
.16 |
.19 |
|
1.5 |
.02 |
.03 |
.03 |
.03 |
.03 |
.03 |
8 |
13 |
.14 |
15 |
.16 |
.18 |
.21 |
|
2 |
.03 |
.03 |
.04 |
.04 |
.04 |
.05 |
8.5 |
14 |
.15 |
16 |
.17 |
.19 |
.22 |
|
2.5 |
.04 |
.04 |
.05 |
. .05 |
.05 |
.06 |
9 |
15 |
.16 |
17 |
.18 |
.20 |
.23 |
|
3 |
.05 |
.05 |
.06 |
.06 |
.07 |
.08 |
9.5 |
IB |
.17 |
18 |
.20 |
.21 |
.24 |
|
3.5 |
.06 |
.06 |
.07 |
.07 |
.08 |
.09 |
10 |
17 |
.18 |
19 |
.21 |
.23 |
.26 |
|
4 |
.07 |
.07 |
.08 |
.08 |
.09 |
.10 |
10.5 |
IK |
.19 |
W |
.22 |
.24 |
.27 |
|
4.5 |
.08 |
.08 |
.09 |
.09 |
.10 |
.11 |
11 |
IK |
.19 |
21 |
.23 |
.25 |
.28 |
|
5 |
.08 |
.09 |
.10 |
.10 |
.11 |
.13 |
11.5 |
1» |
.20 |
•>v. |
.24 |
.26 |
.30 |
|
5.5 |
.09 |
.10 |
.10 |
.11 |
.12 |
.14 |
12 |
2() |
.21 |
23 |
.25 |
.27 |
.31 |
|
6 |
.10 |
.10 |
.11 |
.12 |
.13 |
.15 |
Reduction to the meridian. — First, when the line of collimation of the telescope is off the meridian, the instrument having been revolved in azimuth and the star observed at the hour-angle t, near the middle thread, then
2 sin^ hr cos a cos d m= — ^ — -—. 4--= —
sm 1" sm C
and the correction to the latitude, if the two stars are observed off the meridian = ^ (m'—m). The value of
2 sin^ ^T t sin 1"
for every second of time up to two minutes (a star being rarely observed at a greater distance than this from the meridian in zenith-telescope observations'! is given in the following table :
|
- |
Term. |
- |
Term. |
^ |
Term. |
- |
Term. |
- |
Term. |
Term. |
|
|
1 |
0.00 |
21 |
0.24 |
41 |
0.91 |
61 |
2.03 |
s. 81 |
3.58 |
101 |
6.56 |
|
'2 |
0.00 |
22 |
0.26 |
42 |
0.96 |
62 |
2.10 |
82 |
3.67 |
102 |
5.67 |
|
3 |
0.00 |
23 |
0.28 |
43 |
1.01 |
63 |
2.16 |
83 |
3.76 |
103 |
6.78 |
|
4 |
0.01 |
24 |
0.31 |
44 |
1.06 |
64 |
2.23 |
84 |
3.85 |
104 |
5.90 |
|
5 |
0.01 |
25 |
0.34 |
45 |
1.10 |
65 |
2.31 |
85 |
3.94 |
105 |
6.01 |
|
6 |
0.02 |
26 |
0.37 |
46 |
1.15 |
66 |
2.38 |
86 |
4.03 |
106 |
6.13 |
|
7 |
0.02 |
27 |
0.40 |
47 |
1.20 |
67 |
2.45 |
87 |
4.12 |
107 |
6.24 |
|
8 |
0.03 |
28 |
0.43 |
48 |
.1.26 |
■ 68 |
2.52 |
88 |
4.22 |
108 |
6.36 |
|
9 |
0.04 |
29 |
0.46 |
49 |
1.31 |
69 |
2.60 |
89 |
4.32 |
109 |
6.48 |
|
10 |
0.05 |
30 |
0.49 |
50 |
1.36 |
70 |
2.67 |
90 |
4.42 |
110 |
6.60 |
|
11 |
0.06 |
31 |
0.52 |
51 |
1.42 |
71 |
2.75 |
91 |
4.52 |
111 |
6.72 |
|
12 |
0.08 |
32 |
0.56 |
52 |
1.48 |
72 |
2.83 |
92 |
4.62 |
112 |
6.84 |
|
13 |
0.09 |
33 |
0.59 |
53 |
1.53 |
73 |
2.91 |
93 |
4.72 |
113 |
6.06 |
|
14 |
0.11 |
34 |
0.63 |
54 |
1.59 |
74 |
2.99 |
94 |
4:82 |
114 |
7.09 |
|
15 |
0.12 |
35 |
0.67 |
65 |
1.65 |
75 » |
3.07 |
95 |
4.92 |
115 |
7.21 |
|
16 |
0.14 |
36 |
0.71 |
56 |
1.71 |
76 |
3.15 |
90 |
5.03 |
116 |
7.34 |
|
17 |
0.16 |
37 |
0.75 |
57 |
1.77 |
77 |
3.23 |
97 |
5.13 |
117 |
7.46 |
|
18 |
0.18 |
38 |
0.80 |
58 |
1.83 |
78 |
3.32 |
98 |
5.24 |
118 |
7.60 |
|
.19 |
0.20 |
39 |
0.83 |
59 |
1.89 |
79 |
3.40. |
99 |
5.34 |
119 |
7.72 |
|
20 |
0.22 |
40 |
0.87 |
60 |
1.96 |
80 |
3.49 |
100 |
5.45 |
120 |
7.85 |
MON XXII-
-15
226
A MANUAL OF TOPOGEAPHIC METHODS.
Seco7ully, when the star is observed oft' the liue of coUimatioii, the instrumeut remaining in the plane of the meridian, then
m— — -. — zrvr- sin 0 cos o sm 1"
2 sin^ iT_ sin 1"
i siu2(J
and the correction to the latitude is half of this quantity, whether the star be north or south, and if the two stars forming a pair are observed off the line of collimation, two such corrections, separately computed, must be added to the latitude. If the stars should be south, of the equator, the essential sign of the correction is negative. The value of m for every. 5° of declination is given in the following table:
|
IDs. |
15. |
205. |
25s. |
30s. |
35s. |
405. |
45s. |
50s. |
55s. |
60s. |
||
|
6 |
„ |
„ |
„ |
„ |
„ |
„ |
„ |
„ |
„ |
S |
||
|
5° |
.00 |
.01 |
.02 |
.03 |
.04 |
.06 |
.08 |
.10 |
.12 |
.14 |
.17 |
85° |
|
10 |
.01 |
.02 |
.04 |
.06 |
.08 |
.11 |
.15 |
.19 |
.23 |
.28 |
.34 |
80 |
|
15 |
.01 |
-.03 |
.05 |
.09 |
.12 |
.17 |
.22 |
.28 |
.34 |
.41 |
.49 |
75 |
|
20 |
.02 |
.04 |
.07 |
.11 |
.16 |
.22 |
.28 |
.36 |
.44 |
.53 |
.63 |
70 |
|
25 |
.02 |
.05 |
.08 |
.13 |
.19 |
.26 |
.34 |
.42 |
.52 |
.63 |
.75 |
65 |
|
30 |
.02 |
.05 |
.09 |
.15 |
.21 |
.29 |
.38 |
.48 |
.59 |
.71 |
.85 |
60 |
|
35 |
.03 |
.06 |
.10 |
.16 |
.23 |
.31 |
.41 |
.53 |
.64 |
.77 |
.92 |
55 |
|
40 |
.03 |
.06 |
.11 |
.17 |
.24 |
.33 |
.43 |
.54 |
.67 |
.81 |
.97 |
50 |
|
43 |
.03 |
.06 |
.11 |
.17 |
.25 |
.33 |
.44 |
.55 |
.68 |
.82 |
.98 |
45 |
Table XXX. — For facilitathifi the reduction of observatio7is, on close circumpolar stars^ made in determining the value of a revolution of the micrometer.
[Extmcted from Appeudix 14. TJ. S. Coast and Geodetic Surve;Vi Keport for 1880.]
Let ?=difference of time of observation and elongation of the star, and «"=num- ber of seconds of arc in the direction of the vertical from elongation, then
cos S sin t sin 1"
for which we can write
"z=15coS(y] *-i(L5sinl")'*=
where t is expressed in seconds of time. It is convenient to apply the term ^ (15 siu l")^^' to the observed time of noting, additive to the observed time before, and sub- tractive after, either elongation. The following table gives the value of i(15 sin vyf, also of the additional term
—120 (15 sin 1")^ f when sensible, for every minute of time from elongation to QS"".
|
t j Term. |
1 t 1 Term. 1 |
t |
Term. |
t |
Term. |
t |
Term. |
t |
Term. |
||
|
m |
J |
m. |
s. |
m |
s. |
m. |
«. |
m. |
s. |
m. |
s. |
|
6 |
0.0 |
16 |
0.8 |
26 |
3. .3 |
36 |
8.9 |
46 |
18.5 |
56 |
33.3 |
|
0.1 |
17 |
0.9 |
27 |
3.7 |
37 |
9.6 |
47 |
19.7 |
57 |
35.1 |
|
|
8 |
0.1 |
18 |
1.1 |
28 |
-'4.2 |
38 |
10. t |
48 |
21.0 |
58 |
37.0 |
|
9 |
0.1 |
19 |
1.3 |
29 |
4.6 |
39 |
11.3 |
49 |
22.3 |
59 |
39.0 |
|
10 |
0.2 |
20 |
1.5 |
30 |
5.1 |
40 |
12.2 |
50 |
23.7 |
60 |
41.0 |
|
11 |
0.3 |
21 |
1.8 |
31 |
5.7 |
41 |
13.1 |
51 |
25.2 |
61 |
43.1 |
|
12 |
0.3 |
22 |
2.0 |
■32 |
6.2 |
42 |
14.1 |
52 |
26.7 |
62 |
45.2 |
|
13 |
0.4 |
23 |
2.3 |
33 |
6.8 |
43 |
15.1 |
53 |
28.3 |
63 |
47.4 |
|
14 |
0.5 |
24 |
2.6 |
34 |
7.5 |
44 |
16.2 |
54 |
29.9 |
64 |
49.7 |
|
15 |
0.6 |
25 |
3.0 |
35 |
8.2 |
45 |
17.3 |
55 |
31.6 |
65 |
52.1 |
COirV^EESION OF SIDEEAL INTO MEAN TIME.
227
Table XXXI. — For converting intervals of sidej'eal mto coi'responding intervals of mean solar time, [Extracted from Lee'a Tables.]
|
Hours. |
Minutes. |
Seconds. |
|||||||
|
ft. |
m s |
m |
s. |
m |
J |
J |
, |
J |
J |
|
1 |
0 ' 09. 830 |
1 |
0.164 |
31 |
5.079 |
i |
o.'6o3 |
31 |
0.085 |
|
2 |
0 19. 659 |
2 |
0.328 |
32 |
5.242 |
2 |
0.005 |
32 |
0.087 |
|
3 |
0 29.489 |
3 |
0.491 |
33 |
5.406 |
3 |
0.008 |
33 |
0.090 |
|
4 |
0 39. 318 |
4 |
0.655 |
34 |
5.570 |
4 |
0.011 |
34 |
0.093 |
|
5 |
0 49.148 |
5 |
0.819 |
35 |
5.734 |
5 |
0.014 |
35 |
0.096 |
|
6 |
0 58.977 |
6 |
0,983 |
36 |
5.89S |
6 |
0.016 |
36 |
0.098 |
|
7 |
1 08. 807 |
7 |
1.147 |
37 |
6.062 |
7 |
0.019 |
37 |
0.101 |
|
8 |
1 18. 636 |
8 |
1.311 |
38 |
6.225 |
8 |
0.022 |
38 |
0.104 |
|
9 |
1 28.466 |
9 |
•1.474 |
39 |
6.389 |
9 |
0.025 |
39 |
0.106 |
|
10 |
1 38.296 |
10 |
1.638 |
40 |
6.553 |
10 |
0.027 |
40 |
0.109 |
|
11 |
1 48.125 |
11 |
1.802 |
41 |
6.717 |
11 |
0.030 |
41 |
0.112 |
|
12 |
1 57.955 |
12 |
1.966 |
42 |
6.881 |
12 |
0.033 |
42 |
0.115 |
|
13 |
2 07.784 |
13 |
2.130 |
43 |
7.044 |
13 |
0.036 |
43 |
0.118 |
|
14 |
2 17.614 |
14 |
2. 294 |
44 |
7.208 |
14 |
0.038 |
44 |
0.120 |
|
15 |
2 27.443 |
15 |
2.457 |
45 |
7.372 |
15 |
0.041 |
45 |
0.123 |
|
16 |
2 37. 273 , |
16 |
2.621 |
46 |
7.536 |
16 |
0.044 |
46 |
0.126 |
|
17 |
2 47.103 |
17 |
2.785 |
47 |
7.700 |
17 |
0.047 |
47 |
0.128 |
|
18 |
2 56.932 |
18 |
2.949 |
48 |
7.864 |
18 |
0.049 |
48 |
0.131 |
|
19 |
3 06. 762 |
19 |
3.113 |
49 |
8.027 |
19 |
0.052 |
49 |
0.134 |
|
20 |
3 16.591 |
20 ' |
3.277 |
50 |
8.191 |
20 |
0.055 |
50 |
0.137 |
|
21 |
3 26.421 |
21 |
3.440 |
51 |
8.355 |
21 |
0.057 |
51 |
0.140 |
|
22 |
3 36. 250 |
22 |
3.604 |
52 |
8.519 |
22 |
0.060 |
52 |
0.142 |
|
23 |
3 46.080 |
23 |
3. 768 |
53 |
8.083 |
23 |
0.063 |
53 |
0.145 |
|
24 |
3 55.909 |
24 |
3.932 |
54 |
8.847 |
24 |
0.066 |
54 |
0.148 |
|
25 |
4.096 |
55 |
9.010 |
25 |
0.068 |
55 |
0.150 |
||
|
26 |
4.259 |
56 |
9.174 |
26 |
0.071 |
50 |
0.153 |
||
|
27 |
4.423 |
57 |
9.338 |
27 |
0.074 |
57 |
0.156 |
||
|
28 |
4.587 |
58 |
9.502 |
28 |
0.076 |
58 |
0.159 |
||
|
29 |
4.751 |
59 |
9.666 |
29 |
0.079 |
59 |
0.161 |
||
|
30 |
4.915 |
60 |
9.830 |
30 |
0.082 |
60 |
0.164 |
228.
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXII. — For converting intervals of mean solar time into corresponding intervals of sidereal time.
[Extracted from Lee's Tables.]
|
Hours. |
Minutes. |
Seconds. |
||||||||
|
h. |
m |
J |
m. |
c. |
m. |
s. |
». |
s. |
, |
s. |
|
1 |
0 |
09. 850 |
1 |
0.164 |
31 |
5'.092 |
i |
0.' 003 |
3i |
0.085 |
|
0 |
19. 713 |
0.329 |
32 |
5.257 |
2 |
0.005 |
32 |
0.0S8 |
||
|
3 |
0 |
29. 669 |
3 |
0.493 |
33 |
5.421 |
3 |
0.008 |
33 |
0.090 |
|
4 |
0 |
39.426 |
4 |
0.657 |
34 |
5.585 |
4 |
0.011 |
34 |
0.093 |
|
g |
0 |
49.282 |
5 |
0.821 |
35 |
5.750 |
5 |
0.014 |
35 |
0.096 |
|
6 |
0 |
59. 139 |
6 |
0.986 |
36 |
5.914 |
6 |
0.016 |
36 |
0.098 |
|
7 |
08.995 |
7 |
1.150 |
37 |
6.078 |
7 |
0.019 |
37 |
0.101 |
|
|
8 |
18. 852 |
8 |
1.314 |
38 |
6.242 |
8 |
0.022 |
38 |
0. 104 |
|
|
0 |
28. 708 |
9 |
1.478 |
39 |
6.407 |
9. |
0.025 |
39 |
0.106 |
|
|
10 |
38. 565 |
10 |
1.643 |
40 |
6.571 |
10 |
0.027 |
40 |
0.109 |
|
|
11 |
48.421 |
11 |
1.807 |
41 |
6.735 |
11 |
0.030 |
41 |
0.112 |
|
|
12 |
58.278 |
12 |
1.971 |
42 |
6.900 |
12 |
0.033 |
.42 |
0. 116 |
|
|
13 |
US. 134 |
13 |
■ 2. 136 |
43 |
7.064 |
13 |
0.036 |
43 |
0.118 |
|
|
14 |
2 |
17.991 |
14 |
2.300 |
44 |
7.228 |
14 |
0.038 |
44 |
0.120 |
|
16 |
2 |
27. 847 |
15 |
2.464 |
45 |
7.392 |
15 |
0.041 |
45 |
0.123 |
|
16 |
2 |
37. 704 |
16 |
2.628 |
46 |
7.557 |
16 |
0. 044 |
46 |
0.126 |
|
17 |
2 |
47. 560 |
17 |
2,793 |
47 |
7.721 |
17 |
0.047 |
47 |
0.129 |
|
18 |
2 |
57. 416 |
18 |
2.957 |
48 |
7.885 |
18 |
0.049 |
48 |
0.131 |
|
19 |
3 |
07. 273 |
19 |
3.121 |
49 |
8.050 |
19 |
0.052 |
49 |
0.134 |
|
20 |
3 |
17. 129 |
20 |
3.285 |
50 |
8.214 |
20 |
0.055 |
50 |
0. 137 |
|
21 |
3 |
26. 986 |
21 |
3.450 |
51 |
8.378 |
21 |
0.057 |
51 |
0.140 |
|
22 |
3 |
36. 842 |
22 |
3.614 |
52 |
8.542 |
22 |
0.060 |
52 |
0.142 |
|
23 |
3 |
46. 699 |
23 |
3.778 |
53 |
8.707 |
23 |
0.063 |
53 |
0.145 |
|
24 |
3 |
56.555 |
24 |
3.943 |
54 |
8.871 |
24 |
0.066 |
54 |
0.148 |
|
25 |
4.107 |
55 |
9. 035 |
25 |
0.068 |
5S |
0.151 |
|||
|
26 |
4.271 |
56 |
9.199 |
26 |
0.071 |
56 |
0.153 |
|||
|
27 |
4.436 |
57 |
9.364 |
27 |
0.074 |
57 |
0.156 |
|||
|
28 |
4.600 |
58 |
9.528 |
28 |
0.077 |
58 |
0.159 |
|||
|
29 |
4.764 |
59 |
9.692 |
29 |
0.079 |
59 |
0.161 |
|||
|
30 |
4.928 |
60 |
9.856 |
30 |
0.082 |
60 |
0.164 |
The quantities taken from this table mnat be added to a i real time.
Qterval to obtain the correeponding interval in side-
CONYEESION OF AEG INTO TIME.
•229
Table XXXIII. — To comet-t parts of the equator in arc into sidereal time, or to convert terrestrial longitude
in arc into time.
[Extracted from Lee's Tables.] *
|
Degrees. |
De |
grees |
De |
grees |
De |
grees. |
Degrees. |
Degrees. |
|||||
|
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
||
|
1 2 3 4 5 |
ft. m. 0 4 0 8 0 12 0 16 0 20 |
61 62 63 64 65 |
h. 4 4 4 4 4 |
m. 4 8 12 16 20 |
121 122 123 124 125 |
ft. 8 8 8 8 8 |
4 8 12 16 20 |
181 182 183 181 185 |
ft. m. 12 4 12 8 12 12 12 16 12 20 |
241 242 243 244 245 |
ft. -m. 16 4 16 8 16 12 16 16 16 20 |
301 302 303 304 305 |
ft. m. 20 4 20 8 20 12 20 16 20 20 |
|
6 7 8 9 10 |
0 24 0 28 0 32 0 36 0 40 |
66 67 68 69 70 |
4 4 4 4 4 |
24 28 32 36 40 |
126 127 128 129 130 |
8 8 8 8 8 |
24 28 32 36 40 |
186 187 188 189 190 |
12 24 12 28 12 32 12 36 12 40 |
246 247 248 249 250 |
16 24 16 28 16 32 16 36 16 40 |
306 307 308 309 310 |
20 24 20 28 20 32 20 36 20 40 |
|
11 12 13 14 15 |
0 44 0 48 0 52 0 56 1 0 |
71 72 73 74 75 |
4 4 4 4 5 |
44 48 .52 56 0 |
131 132 133 134 135 |
8 8 8 8 9 |
44 48 52 66 0 |
191 192 193 194 195 |
12 44 12 48 12 52 12 66 13 0 |
261 252 253 254 255 |
16 44 16 48 16 52 16 56 17 0 |
311 312 313 314 315 |
20 44 20 48 20 62 20 56 21 0 |
|
16 17 . 18 19 20 |
1 4 1 8 1 12 1 16 1 20 |
76 77 78 79 80 |
. 5 5 5 5 5 |
4 8 12 16 20 |
136 137 138 139 140 |
9 9 9 9 9 |
4 8 12 16 20 |
196 197 198 199 200 |
13 4 13 8 13 12 13 16 13 20 |
256 257 258 259 260 |
17 4 17 8 17 12 17 16 17 20 |
316 317 318 319 320 |
21 4 21 8 21 12 21 16 21 20 |
|
21 22 23 24 25 |
1 24 1 28 1 32 1 36 1 40 |
81 82 83 84 85 |
5 5 5 5 5 |
24 28 32 36 40 |
141 142 143 144 145 |
9 9 9 9 9 |
24 28 32 36 40 |
201 202 203 204 205 |
13 21 13 28 13 32 13 36 13 40 |
261 262 263 264 265 |
17 24 17 28 17 32 17 36 17 40 |
321 323 323 324 325 |
21 24 21 28 21 32 21 36 21 40 |
|
26 27 28 29 30 |
1 4-1 1 48 1 52 1 56 2 0 |
86 87 88 89 90 |
5 5 5 5 6 |
44 48 52 56 0 |
146 147 148 149 150 |
9 9 9 9 10 |
44 48 52 56 0 |
206 207 208 209 210 |
13 44 13 48 13 52 13 56 14 0 |
266 267 268 269 270 |
17 44 17 48 ■ 17 ,52 17 56 18 0 |
326 327 328 329 330 |
21 44 21 48 21 52 21 66 22 0 |
|
31 32 33 34 35 |
2 4 2 8 2 12 2 16 2 20 |
91 92 93 94 95 |
6 6 6 6 6 |
4 8 12 16 20 |
151 152 153 154 155 |
10 10 10 10 10 |
4 8 12 16 20 |
211 212 213 214 216 |
14 4 14 8 14 12 14 16 14 20 |
271 272 273 274 275 |
18 4 18 8 18 12 18 16 18 20 |
331 332 333 334 335 |
22 4 22 8 22 12 22 16 22 20 |
|
36 37 38 39 40 |
2 24 2 28 2 32 2 36 2 40 |
96 97 98 99 loo " |
6 6 6 6 6 |
24 28 32 36 40 |
156 157 168 159 160 |
10 10 10 10 10 |
24 28 32 36 40 |
216 217 218 219 220 |
14 24 14 28 14 32 14 36 14 40 |
276 277 278 279 280 |
18 24 18 28 18 32 18 36 18 40 |
336 337 338 339 340 |
22 24 22 28 22 32 22 36 22 40 |
|
41 42 43 44 45 |
2 44 2 48 2 52 2 66 3 0 |
lOl l02 l03 l04 l05 |
6 6 6 6 7 |
44 48 52 56 0 |
161 162 163 164 165 |
10 10 10 10 11 |
44 48 52 56 0 |
221 222 223 224 225 |
14 44 14 48 14 52 14 56 15 0 |
281 282 283 284 285 |
18 44 18 48 18 62 18 56 19 0 |
341 342 343 344 345 |
22 44 22 48 22 52 22 56 23 0 |
|
46 47 48 49 50 |
3 4 3 8 3 12 3 16 3 20 |
l06 107 108 . 109 no |
7 7 7 7 7 |
4 8 12 ■6 20 |
166 167 168 169 170 |
11 11 11 11 11 |
4 8 12 16 20 |
226 227 228 229 230 |
15 4 15 8 15 12 15 16 15 20 |
286 287 288 •289 290 |
19 4 19 8 19 12 19 16 19 20- |
346 347 348 349 350 |
23 4 23 8 23 12 23 16 23 20 |
|
51 52 53 54 55 |
3 24 3 28 3 32 3 36 3 40 |
111 112 113 114 115 |
7 7 7 7 7 |
24 28 32 36 40 |
171 172 173 174 175 |
11 11 11 11 11 |
24 28 32 36 40 |
231 232 233 234 235 |
15 24 15 28 15 32 15 36 15 40 |
291 292 293 294 295 |
19 24 19 28 19 32 19 36 19 40 |
351 352 363 354 355 |
23 24 23 28 23 32 23 36 23 40 |
|
56 57 58 59 60 |
3 44 3 48 3 52 3 56 4 0 |
116 117 118 119 120 |
7 7 7 8 |
44 48 52 56 0 |
176 177 178 179 180 |
11 11 11 11 12 |
44 48 52 56 0 |
236 237 238 239 240 |
15 44 15 48 15 62 15 56 16 0 |
296 297 398 299 300 |
19 44 19 48 19 62 19 56 20 0 |
356 367 358 369 360 |
23 44 33 48 28 52 23 66 24 0 |
230
A MANUAL OF TOPOGEAPHIC METHODS.
Taule XXXIII. — To coni'ert parts of the equator in arc into sidereal time, or to eonvert teirestrial longitude in arc into time — Continued.
[Extracted from Lee's Tables.]
|
1 Minutes. |
Minutes. |
Minutes. |
Seconds. |
Seconds. |
Seconds. |
||||||
|
Arc* |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
|
m s |
, |
m s. |
m. s. |
„ |
J |
J |
|||||
|
1 1 |
0 4 |
21 |
1 24 |
41 |
2 44 |
1 |
0.067 |
21 |
1.400 |
41 |
2.733 |
|
( 2 |
0 8 |
22 |
1 28 |
42 |
2 48 |
2 |
0.133 |
22 |
1.467 |
42 |
2.800 |
|
3 |
0 12 |
23 |
1 32 |
43 |
2 52 |
3 |
0.200 |
23 |
1.533 |
43 |
2.867 |
|
* |
0 16 |
24 |
1 86 |
44 |
2 56 |
4 |
0.267 |
24 |
1.600 |
44 |
2.933 |
|
5 |
0 20 |
25 |
1 40 |
45 |
3 0 |
5 |
0.333 |
25 |
1.667 |
45 |
3.000 |
|
6 |
0 24 |
26 |
1 44 |
, 46 3 4 |
6 |
0.400 |
26 |
1.733 |
46 |
3.067 |
|
|
7 |
0 28 |
27 |
1 48 |
47 1 3 8 |
• 7 |
0.467 |
27 |
1.800 |
47 |
3.133 |
|
|
8 |
0 32 |
28 |
1 52 |
48 ; B 12 |
8 |
n.533 |
28 |
1.867 |
48 |
3.200 |
|
|
9 1 0 36 |
29 |
1 56 |
49 1 3 16 |
9 |
0.600 |
29 |
1.933 |
49 |
3.267 |
||
|
10 I 0 40 |
30 |
2 0 |
50 3 20 |
10 |
0.667 |
30 |
2.000 |
50 |
3.333 |
||
|
11 |
0 44 |
31 |
2 4 |
51 3 24 |
11 |
0.733 |
31 |
2.067 |
51 |
3.400 |
|
|
12 |
0- 48 |
32 |
2 8 |
52 3 28 |
12 |
0.800 |
32 |
2.133 |
52 |
3.467 |
|
|
13 |
0 52 |
33 |
2 12 |
53 3 32 |
13 |
0.867 |
33 |
2.200 |
53 |
3. 533 |
|
|
14 |
0 56 |
34 |
2 16 |
54 3 36 |
14 |
0.933 |
34 |
2.267 |
54 |
3.600 1 |
|
|
15 |
1 0 |
35 |
2 20 |
55 3 40 |
15 |
1.000 |
35 |
2.333 |
55 |
3.667 < |
|
|
16 , 1 4 |
36 |
2 24 |
56 3 44 |
16 |
1.067 |
36 |
2.400 |
56 |
3. 733 |
||
|
17 1 1 8 |
37 2 28 |
57 3 48 |
17 |
1.133 |
37 |
2.467 |
57 |
3. 800 |
|||
|
18 1 12 |
38 2 32 |
58 3 52 ' |
18 |
1.200 |
38 |
2.633 |
58 |
3.867 |
|||
|
19 1 16 |
39 2 36 |
59 , 3 56 |
19 |
1.267 |
39 |
2.600 |
59 |
3.933 1 |
|||
|
20 1 20 |
40 2 40 |
60 1 4 0 |
20 |
1.333 |
40 |
2.667 |
60 |
4.000 1 1 |
T.\Bi.E XXXIV. — To convert sidereal time into parts of the equator in arc, or to convert time into terrestrial
longitude in arc.
[Extracted from Lee'.^ Tables.]
|
Hours. |
Minutes. |
Seconds. |
|||||||
|
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
|
h. |
0 |
m |
o - |
m |
o , |
s. |
s. |
, // |
|
|
1 |
15 |
1 |
0 15 |
31 |
7 45 |
1 |
0 15 |
31 |
7 45 |
|
2 |
30 |
2 |
b 30 |
32 |
8 00 |
2 |
0 30 |
32 |
8 00 |
|
3 |
45 |
3 |
0 45 |
33 |
8 15 |
3 |
0 45 |
33 |
8 15 |
|
4 |
60 |
4 |
1 00 |
34 |
8 30 |
4 |
1 00 |
34 |
8 30 |
|
5 |
75 |
5 |
1 15 |
35 |
8 45 |
5 |
1 15 |
35 |
8 45 |
|
6 |
90 |
6 |
1 30 |
36 |
9 00 |
6 |
1 30 |
36 |
9 00 |
|
7 |
105 |
7 |
1 45 |
37 |
9 15 |
7 |
1 45 |
37 |
9 15 |
|
8 |
120 |
8 |
2 00 |
38 |
9 30 |
8 |
2 00 |
38 " |
9 30 |
|
9 |
135 |
9 |
2 15 |
39 |
9 45 |
9 |
2 15 |
39 |
9 45 |
|
10 |
150 |
10 |
2 30 |
40 |
10 00 |
10 |
2 30 |
40 |
10 00 |
|
11 |
165 |
11 |
2 46 |
41 |
10 15 |
11 |
2 45 |
41 |
10 15 |
|
12 |
180 |
12 |
3 00 |
42 |
10 30 |
12 |
3 00 |
42 |
10 30 |
|
13 |
195 |
13 |
3 15 |
43 |
10 45 |
13 |
3 15 |
43 |
10 45 |
|
14 |
210 |
14 |
3 30 |
44 |
11 00 |
14 |
3 30 |
44 |
11 00 |
|
15 |
225 |
.15 |
3 45 |
45 |
11 15 |
15 |
3 45 |
45 |
11 15 |
|
16 |
240 |
16 |
4 00 |
46 |
11 30 |
16 |
4 00 |
46 |
11 30 |
|
17 |
255 |
17 |
4 15 |
47 |
11 45 |
17 |
4 15 |
47 |
11 45 |
|
18 |
270 |
18 |
4 30 |
48 |
12 00 |
18 |
4 30 |
48 |
12 00 |
|
19 |
285 |
19 |
4 45 |
49 |
12 15 |
19 |
4 45 |
49 |
12 15 |
|
1 20 |
300 |
20 |
5 00 |
50 |
12 30 |
20 |
5 00 |
50 |
12 30 |
|
21 |
315 |
21 |
5 15 |
51 |
12.45 |
21 |
5 15 |
51 |
12 45 |
|
22 |
330 |
22 |
5 30 |
52 |
13 00 |
22 |
5 30 |
52 |
13 00 |
|
23 |
345 |
23 |
5 45 |
53 |
13 15 |
23 |
5 45 |
63 |
13 15 |
|
24 |
360 |
24 |
6 00 |
54- |
13 30 |
24 |
6 00 |
54 |
13 30 |
|
25 |
6 15 |
55 |
13 45 |
25 |
6 15 |
55 |
13 45 |
||
|
26 |
6 30 |
56 |
14 00 |
26 |
6 30 |
56 |
14 00 |
||
|
27 |
6 45 |
57 |
14 15 |
27 |
6 45 |
57 |
14 15 |
||
|
28 |
7 00 |
58 |
14 30 |
28 |
7 00 |
58 |
14 30 |
||
|
29 |
7 15 |
59 |
14 45 |
29 |
7 15 |
59 |
14 45 |
||
|
30 |
7 30 |
60 |
15 00, |
30 |
7 30 |
60 |
15 00 |
CONVERSION OF TIME INTO AEG. 231
Table XXXIV.— To covrert sidereal lime into j)«)'(s of the equator in arc, eic,— Coutinued. [Extracted from Lee's Tables.]
|
Tenths o: |
seconds |
Thou- sandths |
|||||||||
|
of sec- |
Arc. |
||||||||||
|
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
Time. |
Arc. |
onds of time. |
|
|
s. 0.21 |
3.15 |
s. 0.41 |
6.15 |
s. 0.61 |
9.15 |
0.81 |
12. 15 |
0.061 |
0.015 |
||
|
0.30 |
0.22 |
3.30 |
0.42 |
6,30 |
0.62 |
9.30 |
0.82 |
12.30 |
0.002 |
||
|
0.03 |
0.45 |
0.23 |
3.45 |
0.43 |
6.45 |
0.63 |
9.45 |
0.83 |
12.45 |
||
|
0.60 |
0.24 |
3.60 |
0.44 |
6.60 |
0.64 |
9.60 |
0.84 |
0.004 |
|||
|
0.05 |
0.75 |
0.25 |
3.75 |
0.45 |
6.75 |
0.65 |
9.75 |
0.85 |
12.75 |
0.005 |
0.075 |
|
0.90 |
0.26 |
3,90 |
0.40 |
6.90 |
0.66 |
9.90 |
0.86 |
12.90 |
0.006 |
0.090 |
|
|
0.07 |
1.05 |
0.27 |
4.U5 |
0.47 |
7.05 |
0.67 |
10.05 |
0.87 |
13.05 |
0.007 |
0.105 |
|
0.08 |
1.20 |
0.28 |
4.20 |
0.48 |
7.20 |
0.68 |
10.20 |
0.88 |
13.20 |
0.008 |
0,120 |
|
1.35 |
0.29 |
4.35 |
0.49 |
7.35 |
0.69 |
10.35 |
0.89 |
0.009 |
|||
|
0.10 |
1.50 |
0.30 |
4.50 |
0.50 |
7.50 |
0.70 |
10.50 |
0.90 |
13.50 |
0,010 |
0,150 |
|
0.11 |
1.65 |
0.31 |
4.65 |
0.51 |
7.65 |
0.71 |
10.65 |
0.91 |
13.65 |
||
|
1.80 |
0.32 |
4.80 |
0.52 |
7.80 |
0.72 |
10. 80 |
0.92 |
13.80 |
|||
|
0.13 |
1.95 |
0.33 |
4.95 |
0.53 |
7.95 |
0.73 |
10.95 |
0.93 |
13.95 |
||
|
2.10 |
0.34 |
5.10 |
0.54 |
8.10 |
0.74 |
11.10 |
0.94 |
||||
|
0.15 |
2.25 |
0.35 |
5.25 |
0.55 |
8.25 |
0.75 |
11.25 |
0.95 |
14.25 |
||
|
0.16 |
2.40 |
0.36 |
5.40 |
0.56 |
8.40 |
0.76* |
11:40 |
0.96 |
14.40 |
||
|
0.17 |
2.55 |
0.37 |
5.55 |
0.57 |
8.55 |
0.77 |
11.65 |
0.97 |
14.55 |
||
|
0.18 |
2.70 |
0.38 |
5.70 |
0.58 |
8.70 |
0.78 |
11.70 |
0.98 |
|||
|
2.85 |
0.39 |
5.85 |
0.59 |
8.85 |
0.70 |
11.85 |
0.99 |
||||
|
0.20 |
3.00 |
0.40 |
6.00 |
0.60 |
9.00 |
0.80 |
12.00 |
1.00 |
15.00 |
Table XXXV. — Containiiuj logarithms of nnmliers from 1 to 11,000. [Extracted froin Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
Log. |
N. |
Log. |
N. |
Log. |
N. |
Log. |
N. |
Log. |
|
0 |
_ |
20 |
1. 30 103 |
40 |
L60 206 |
60 |
1. 77 815 |
80 |
1.90 309 |
|
1 |
0.00 000 |
21 |
1. 32 222 |
41 |
1.61 278 |
61 |
1. 78 533 |
81 |
1. 90 849 |
|
2 |
0.30 103 |
22 |
1. 34 242 |
42 |
1. 62 325 |
62 |
1. 79 239 |
82 |
1. 91 381 |
|
3 |
0. 47 712 |
23 |
1. 36 173 |
43 |
1.63 347 |
63 |
1. 79 934 |
83 |
1. 91 908 |
|
4 |
0. 60 206 |
24 |
1. 38 021 |
44 |
1. 64 345 |
64 |
1.80 618 |
84 |
1.92 428 |
|
5 |
0. 69 897 |
25 |
1. 39 79'J |
45 |
L65 321 |
65 |
1. 81 291 |
85 |
1. 92 942 |
|
6 |
0. 77 815 |
26 |
L41 497 |
46 |
1. 66 276 |
66 |
1.81 954 |
86 |
1. 93 450 |
|
7 |
0.84 510 |
27 |
1.43 130 |
47 |
1.67 210 |
67 |
1. 82- 607 |
87 |
|
|
8 |
0.90 309 |
28 |
1.44 716 |
48 |
1. 68 124 |
68 |
1. 83 251 |
88 |
1.94 448 |
|
9 |
0. 95 424 |
29 |
1.46 240 |
49 |
1.69 020 |
69 |
1.83 885 |
89 |
1. 94 939 |
|
10 |
1. 00 000 |
30 |
\. 47 712 |
50 |
1, 69 897 |
70 |
1. 84 510 |
90 |
1. 95 424 |
|
11 |
1.04 139 |
31 |
1.49 136 |
51 |
1. 70 757 |
71 |
1.85 126 |
91 |
1. 95 004 |
|
12 |
1.07 918 |
32 |
1.50 515 |
52 |
1.71 600 |
72 |
1.85 733 |
. 92 |
1.96 379 |
|
13 |
1.11 394 |
33 |
1, 51 851 |
53 |
1. 72 428 |
73 |
L86 332 |
93 |
1. 96 848 |
|
14 |
1. 14 613 |
34 |
1.53 148 |
54 |
1. 73 239 |
74 |
1.86 923 |
||
|
15 |
L17 609 |
35 |
1. 54 407 |
55 |
1. 74 036 |
75 |
L87 506 |
95 |
1. 97 772 |
|
16 |
1.20 412 |
36 |
1. 55 630 |
56 |
1.74 819 |
76 |
1.88 08 L |
96 |
1. 98 227 |
|
17 |
1. 23 045 |
37 |
1. 56 820 |
57 |
1.75 587 |
77 |
1.88 649 |
||
|
18 |
1. 25 527 |
33 |
1. 57 978 |
58 |
1. 76 343 |
78 |
1. 89 209 |
98 |
1.99 123 |
|
1. 27 875 |
39 |
1.59 106 |
59 |
1. 77 085 |
79 |
1. 89 763 |
99 |
1. 99 564 |
|
|
20 |
1. 30 103 |
40 |
1. 60 200 |
60 |
1. 77 815 |
80 |
1. 90 309 |
100 |
2. 00 000 |
232
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing Jogariihms of «itw6e7's from 1 to 11,000- [Extracted trom GauSs' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
0 |
00 000 |
30 103 |
47 712 |
60 206 |
69 897 |
77 815 |
84 510 |
90 309 |
95 424 |
|
|
1 |
00 000 |
04 139 |
07 918 |
11 394 |
14 613 |
17 609 |
20 412 |
23 045 |
25 527 |
27 875 |
|
2 |
30 103 |
32 222 |
34 242 |
36 173 |
38 021 |
39 794 |
41 497 |
43 136 |
44 716 |
46 240 |
|
3 |
47 712 |
49 136 |
50 515 |
51 851 |
53 148 |
54 407 |
55 630 |
56 820 |
57 978 |
59 106 |
|
4 |
60 206 |
61 278 |
62 325 |
63 347 |
64 345 |
65 321 |
60 276 |
67 210 |
68 124 |
69 020 |
|
5 |
69 897 |
70 757 |
71 600 |
72 428 |
73 239 |
74 036 |
74 819 |
75 587 |
70 343 |
77 085 |
|
6 |
77 815 |
78 533 |
79 239 |
79 934 |
80 018 |
81 291 |
81 954 |
82 607 |
83 251 |
83 885 |
|
84 510 |
85 126 |
85 733 |
86 332 |
.86 923 |
87 506 |
88 081 |
88 649 |
89 209 |
89 763 |
|
|
8 |
90 309 |
90 849 |
91 381 |
91 908 |
92 428 |
92 942 |
93 430 |
93 952 |
94 448 |
94 939 |
|
9 |
95 424 |
95 904 |
96 379 |
96 848 |
97 313 |
97 772 |
98 227 |
98 677 |
99 123 |
99 564 |
|
10 |
00 OOO |
00 432 |
00 860 |
01 284 |
01 703 |
02 119 |
02 531 |
02 938 |
03 342 |
03 743 |
|
11 |
04 139 |
04 532 |
04 922 |
05 308 |
05 690 |
00 070 |
06 446 |
06 819 |
07 188 |
07 555 |
|
12 |
07 918 |
08 279 |
08 636 |
08 991 |
09 342 |
09 691 |
10 037 |
10 380 |
10 721 |
11 039 |
|
13 |
11 394 |
11 727 |
12 057 |
12 385 |
12 710 |
13 033 |
13 354 |
13 672 |
13 983 |
14 301 |
|
14 |
14 613 |
14 925 |
15 229 |
15 534 |
15 836 |
10 137 |
16 435 |
16 732 |
17 020 |
17 319 |
|
15 |
17 609 |
17 898 |
18 184 |
18 469 |
18 752 |
19 033 |
19 312 |
19 590 |
19 866 |
20 140 |
|
16 |
20 412 |
20 683 |
20 952 |
21 219 |
21 484 |
21 748 |
22 Oil |
22 272 |
22 631 |
22 789 |
|
17 |
23 045 |
23 300 |
23 553 |
23 805 |
24 055 |
24 304 |
24 551 |
24 797 |
25 042 |
25 285 |
|
18 |
25 527 |
25 768 |
26 007 |
26 245 |
26 482 |
26 717 |
26 951 |
27 184 |
27 416 |
27 646 |
|
19 |
27 875 |
28 103 |
28 330 |
28 55(1 |
28 780 |
29 003 |
29 226 |
29 447 |
29 667 |
29 885 |
|
20 |
30 103 |
30 320 |
30 535 |
30 750 |
30 963 |
31 175 |
31 387 |
31 597 |
31 806 |
32 015 |
|
21 ■ |
32 222 |
32 428 |
32 634 |
32. 838 |
33 041 |
33 244 |
33 445 |
33 646 |
33 846 |
34 044 |
|
22 |
34 242 |
34 439 |
34 035 |
34 830 |
35 025 |
35 218 |
35 411 |
35 603 |
35 793 |
35 984 |
|
23 |
36 173 |
36 361 |
30 549 |
36 736 |
36 922 |
37 107 |
37 291 |
37 175 |
37 058 |
37 840 |
|
24 |
38 021 |
38 202 |
38 382 |
38 561 |
38 739 |
38 917 |
39 094 |
39 270 |
39 446 |
39 620 |
|
25 |
39 794 |
39 907 |
40 140 |
40 312 |
40 483 |
40 654 |
40 824 |
40 993 |
41 162 |
41 330 |
|
26 |
41 497 |
41 064 |
41 830 |
41 996 |
42 160 |
42 325 |
42 488 |
42 651 |
42 813 |
42 976 |
|
27 |
43 136 |
43 297 |
43 457 |
43 616 |
43 775 |
43 933 |
44 091 |
44 248 |
44 404 |
44 660 |
|
28 |
• 44 716 |
44 871 |
45 025 |
45 179 |
45 332 |
45 484 |
45 637 |
45 788 |
45 939 |
46 090 |
|
29 |
46 240 |
46 389 |
40 538 |
46 687 |
46 835 |
46 982 |
47 129 |
47 276 |
47 422 |
47 667 |
|
30 |
47 712 |
47 857 |
48 001 |
48 144 |
48 287 |
48 430 |
48 572 |
48 714 |
48 855 |
48 996 |
|
31 |
49 136 |
49 276 |
49 415 |
49 554 |
49 693 |
49 831 |
49 969 |
50 106 |
50 243 |
50 379 |
|
32 |
50 515 |
50 651 |
50 786 |
50 920 |
51 055 |
51 188 |
51 322 |
51 455 |
51 587 |
51 720 |
|
33 |
51 851 |
51 983 |
52 114 |
52 244 |
52 375 |
52 504 |
52 634 |
52 763 |
52 892 |
53 020 |
|
34 |
53 148 |
53 275 |
53 403 |
53 529 |
53 656 |
53 782 |
53 908 |
54 033 |
54 158 |
54 283 |
|
35 |
54 407 |
54 531 |
54 654 |
54 777 |
54 900 |
55 023 |
55 145 |
55 267 |
53 388 |
55 509 |
|
36 |
55 630 |
55 751 |
55 871 |
55 991 |
56 110 |
56 229 |
56 348 |
56 467 |
60 585 |
56 703 |
|
87 |
56 820 |
56 937 |
57 054 |
57 171 |
57 287 |
67 403 |
57 519 |
57 634 |
57 749 |
57 864 |
|
38 |
57 978 |
58 092 |
58 206 |
58 320 |
58 433 |
58 546 |
58 059 |
58 771 |
58 883 |
58 995 |
|
39 |
59 106 |
59 218 |
59 329 |
59 439 |
59 550 |
59 660 |
59 770 |
59 879 |
59 988 |
60 097 |
|
40 |
60 206 |
60 314 |
60 423 |
60 531 |
60 638 |
60 746 |
60 853 |
60 959 |
61 066 |
61 172 |
|
41 |
61 278 |
61 384 |
61 490 |
61 595 |
61 700 |
61 805 |
61 909 |
62 014 |
62 118 |
62 221 |
|
42 |
62 325 |
62 428 |
62 531 |
62 634 |
62 737 |
62 839 |
62 941 |
63 043 |
63 144 |
63 246 |
|
43 |
63 347 |
63 448 |
63 548 |
63 649 |
63 749 |
63 849 |
63 949 |
64 048 |
64 147 |
64 246. |
|
44 |
64 345 |
64 444 |
64 542 |
64 640 |
64 738 |
64 836 |
64 933 |
65 031 |
65 128 |
65 225 |
|
45 |
65 321 |
65 418 |
65 514 |
65 610 |
65 706 |
65 801 |
65 896 |
65 992 |
60 087 |
66 181 |
|
46 |
66 276 |
66 370 |
66 464 |
66 558 |
66 652 |
66 745 |
66 839 |
66 932 |
67 025 |
67 117 |
|
47 |
67 210 |
67 302 |
67 394 |
67 486 |
67 578 |
67 069 |
67 701 |
67 852 |
67 943 |
68 034 |
|
48 |
68 124 |
68 215 |
68 305 |
68 395 |
68 485 |
68 574 |
68 664 |
68 753 |
68 842 |
68 931 |
|
49 |
69 020 |
69 108 |
69 197 |
69 285 |
69 373 |
09 461 |
69 548 |
69 636 |
69 723 |
69 810 |
|
50 |
69 897 |
69 SJ84 |
70 070 |
70 157 |
70 243 |
70 329 |
70 415 |
70 501 |
70 586 |
70 672 |
|
N". |
L. 0 |
1 |
2 |
3 |
4 |
5, |
6 |
7 |
8 |
9 |
LOGARITHMS OF NUMBEES.
233
Table XXXV. — Containing_ logarithms of numhers from 1 to 11,000 — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
• 1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
60 |
69 897 |
69 984 |
70 070 |
70 157 |
70 243 |
70 329 |
70 415 |
70 501 |
70 586 |
70 672 |
|
51 |
70 757 |
70 842 |
70 927 |
71 012 |
71 096 |
71 181 |
71 265 |
71 349 |
71 433 |
71 517 |
|
52 |
71 600 |
71 684 |
71 767 |
71 850 |
71 933 |
72 016 |
72 099 |
72 181 |
72 263 |
72 346 |
|
53 |
72 428 |
72 509 |
72 591 |
72 673 |
72 754 |
72 835 |
72 916 |
72 997 |
73 078 |
73 159 |
|
54 |
73 239 |
73 320 |
73 400 |
73 480 |
73 560 |
73 640 |
73 719 |
73 799 |
73 878 |
73 957 |
|
55 |
74 036 |
74 115 |
74 194 |
74 273 |
74 351 |
74 429 |
74 607 |
74 586 |
74 663 |
74 741 |
|
56 |
74 819 |
74 896 |
74 974 |
75 051 |
75 128 |
75 205 |
75 282 |
75 358 |
75 436 |
75 511 |
|
67 |
. 75 587 |
75 004 |
75 740 |
75 815 |
75 891 |
75 967 |
76 042 |
76 118 |
76 193 |
76 268 |
|
58 |
76 343 |
76 418 |
76 492 |
76 567 |
76 641 |
76 716 |
76 790 |
76 864 |
76 938 |
77 012 |
|
59 |
77 085 |
77 159 |
77 232 |
77 305 |
77 379 |
77 452 |
77 525 |
77 597 |
77 670 |
77 743 |
|
60 |
77 815 |
77 887 |
77 960 |
78 032 |
78 104 |
78 176 |
78 247 |
78 319 |
78 390 |
78 462 |
|
61 |
78 533 |
78 604 |
78 675 |
78 746 |
78 817 |
78 888 |
78 958 |
79 029 |
79 099 |
79 169 |
|
62 |
79 239 |
79 309 |
79 379 |
79 449 |
79 518 |
79 588 |
79 667 |
79 727 |
79 796 |
79 865 |
|
63 |
79 934 |
80 003 |
80 072 |
80 140 |
80 209 |
80 277 |
80 346 |
80 414 |
80 482 |
80 650 |
|
64 |
80 618 |
80 686 |
80 754 |
80 82X |
80 889 |
80 956 |
81 023 |
81 090 |
81 158 |
81 224 |
|
65 |
81 291 |
81 358 |
81 425 |
81 491 |
81 558 |
81 624 |
81 690 |
81 757 |
81 823 |
81 889 |
|
66 |
81 954 |
82 020 |
82 086 |
82 151 |
82 217 |
82 282 |
82 347 |
82 413 |
82 478 |
82 543 |
|
67 |
82 607 |
82 672 |
82 737 |
82 802 |
82 866 |
82 930 |
82 995 |
83 059 |
83 123 |
83 187 |
|
68 |
83 251 |
83 315 |
83 378 |
83 442 |
83 506 |
83 569 |
83 632 |
83 696 |
83 759 |
83 833 |
|
69 |
83 885 |
83 948 |
84 Oil |
84 073 |
84 136 |
84 198 |
84 261 |
84 323 |
84 386 |
84 448 |
|
70 |
84 510 |
84 572 |
84 634 |
84 696 |
84 757 |
84 819 |
84 880 |
84 942 |
85 003 |
85 065 |
|
71 |
85 126 |
85 187 |
85 248 |
85 309 |
85 370 |
85 431 |
85 491 |
85 552 |
85 612 |
85 673 |
|
72 |
85 733 |
85 794 |
85 854 |
85 914 |
85 974 |
86 034 |
86 094 |
86 153 |
86 213 |
86 273 |
|
73 |
86 332 |
86 392 |
86 451 |
86 510 |
86 570 |
86 629 |
86 688 |
86 747 |
86 806 |
86 864 |
|
74 |
86 923 |
86 982 |
87 040 |
87 099 |
87 157 |
87 216 |
87 274 |
87 332 |
87 390 |
87 448 |
|
75 |
87 506 |
87 564 |
87 622 |
87 679 |
87 737 |
87 795 |
87 852 |
87 910 |
87 967 |
83 024 |
|
76 |
8< 081 |
88 138 |
88 195 |
88 252 |
88 309 |
88 366 |
88 423 |
88 480 |
88 636 |
88 593 |
|
77 |
88 649 |
88 705 |
88 762 |
88 818 |
88 874 |
88 930 |
88 986 |
89 042 |
89 098 |
89 154 |
|
78 |
89 209 |
89 205 |
89 321 |
89 376 |
89 432 |
89 487 |
89 542 |
89 597 |
89 653 |
89 708 |
|
79 |
89 763 |
89 818 |
89 873 |
89 927 |
89 982 |
90 037 |
90 091 |
90 146 |
90 200 |
90 256 |
|
80 |
90 309 |
90 363 |
90 417 |
90 472 |
90 526 |
90 580 |
90 634 |
90 687 |
90 741 |
90 795 |
|
81 |
90 849 |
90 902 |
90 956 |
91 009 |
91 062 |
91 116 |
91 169 |
91 222 |
91 276 |
91 328 |
|
83 |
91 381 |
91 434 |
91 487 |
91 540 |
91 593 |
91 645 |
91 698 |
91 751 |
91 803 |
91 855 |
|
S3 |
91 908 |
91 960 |
92 012 |
92 065 |
92 117 |
92 169 |
92 221 |
92 273 |
92 324 |
93 376 |
|
84 |
92 428 |
92 480 |
92 531 |
92 583 |
92 634 |
92 686 |
92 737 |
92 788 |
92 840 |
92 891 |
|
85 |
92 942 |
92 993 |
93 044 |
93 095 |
93 146 |
93 197 |
93 247 |
93 298 |
93 349 |
93 399 |
|
86 |
93 450 |
93 500 |
93 551 |
93 601 |
93 651 |
93 702 |
93 752 |
93 802 |
93 852 |
93 902 |
|
87 |
93 952 |
94 002 |
94 052 |
94 101 |
94 151 |
94 201 |
94 250 |
94 300 |
94 349 |
94 399 |
|
88 |
94 448 |
94 498 |
94 547 |
94 596 |
94 645 |
94 694 |
94 743 |
94 792 |
94 841 |
94 890 |
|
89 |
94 939 |
94 988 |
95 036 |
95 085 |
95 134 |
95 182 |
95 231 |
95 279 |
95 328 |
95 376 |
|
90 |
95 424 |
95 472 |
95 521 |
95 569 |
95 617 |
95 665 |
95 713 |
95 761 |
96 809 |
95 856 |
|
91 |
95 904 |
95 952 |
95 999 |
96 047 |
96 095 |
96 142 |
96 190 |
96 237 |
■ 96 284 |
96 333 |
|
92 |
96 379 |
96 426 |
96 473 |
96 520 |
96 567 |
96 614 |
96 661 |
96 708 |
96 755 |
96 802 |
|
93 |
96 848 |
96 895 |
96 942 |
96 088 |
97 035 |
97 081 |
97 128 |
97 174 |
97 230 |
97 267 |
|
94 |
97 313 |
97 359 |
97 405 |
97 451 |
97 497 |
97 643 |
97 589 |
97 035 |
97 681 |
97 727 |
|
95 |
97 772 |
97 818 |
97 864 |
97 909 |
97 955 |
98 000 |
98 046 |
98 091 |
98 137 |
98 182 |
|
96 |
98 227 |
98 272 |
98 318 |
98 363 |
98 408 |
98 453 |
98 498 |
98 543 |
98 588 |
98 632 |
|
97 |
98 677 |
98 722 |
98 767 |
98 811 |
98 856 |
98 900 |
98 945 |
98 989 |
99 034 |
99 078 |
|
98 |
99 123 |
99 167 |
99 211 |
99 255 |
99 300 |
99 344 |
99 388 |
99 432 |
99 476 |
99 520 |
|
99 |
99 564 |
99 607 |
99 651 |
99 695 |
99 739 |
99 782 |
99 826 |
99 870 |
99 913 |
99 957 |
|
100 |
00 000 |
00 043 |
00 087 |
00 130 |
00 173 |
00 217 |
00 260 |
00 303 |
00 346 |
00 389 |
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
234
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXY. — Containing Jogariihms of numbers from 1 to 11,000 — Continued. [Extracted from Ciauss' Logaritluuic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P |
P. |
||
|
100 |
00 000 |
043 |
087 |
130 |
173 |
217 |
260 |
303 |
346 |
389 |
||||
|
101 |
432 |
475 |
518 |
561 |
604 |
647 |
689 |
732 |
775 |
817 |
44 |
43 |
42 |
|
|
102 |
860 |
903 |
945 |
988 |
,030 |
,072 |
,115 |
,157 |
,199 |
,242 |
1 |
4,4 |
4,3 |
4,2 |
|
1.13 |
01 284 |
326 |
368 |
410 |
452 |
494 |
536 |
578 |
620 |
662 |
2 |
8,8 |
8,6 |
8,4 |
|
104 |
703 |
745 |
787 |
828 |
870 |
912 |
953 |
995 |
,036 |
.078 |
3 |
13,2 |
12,9 |
12'6 |
|
105 |
02 119 |
100 |
202 |
243 |
284 |
325 |
366 |
407 |
449 |
490 |
4 |
17,6 |
17,2 |
16,8 |
|
106 |
531 |
572 |
612 |
653 |
694 |
735 |
776 |
816 |
857 |
808 |
5 |
22,0 |
21,5 |
21,0 |
|
107 |
938 |
979 |
,019 |
,060 |
,100 |
,141 |
.181 |
,222 |
,262 |
,302 |
6 |
26,4 |
25,8 |
25,2 |
|
108 |
03 342 |
383 |
423 |
463 |
503 |
543 |
583 |
623 |
603 |
703 |
7 |
30,8 |
30,1 |
29,4 |
|
109 |
743 |
782 |
822 |
802 |
902 |
941 |
981 |
,021 |
,060 |
,100 |
8 |
35,2 |
34,4 |
33,6 |
|
110 |
04 139 |
179 |
218 |
258 |
297 |
336 |
376 |
415 |
454 |
493 |
9 |
39,6 |
38,7 |
37,8 |
|
111 |
532 |
571 |
610 |
650 |
689 |
727 |
766 |
805 |
844 |
883 |
41 |
40 |
39 |
|
|
112 |
922 |
961 |
999 |
,038 |
,077 |
,115 |
,154 |
,192 |
,231 |
,269 |
1 |
4,1 |
4,0 |
3,9 |
|
113 |
05 308 |
346 |
385 |
423 |
461 |
500 |
538 |
576 |
614 |
■652 |
2 |
8,2 |
8,0 |
7,8 |
|
114 |
690 |
729 |
767 |
805 |
843 |
881 |
918 |
956 |
994 |
,032 |
3 |
12,3 |
12,0 |
11,7 |
|
115 |
06 070 |
108 |
145 |
183 |
221 |
258 |
296 |
333 |
371 |
'408 |
4 |
16,4 |
16,0 |
15,6 |
|
116 |
446 |
«3 |
521 |
558 |
695 |
633 |
670 |
707 |
744 |
781 |
5 |
20,5 |
20,0 |
19,5 |
|
117 |
819 |
856 |
893 |
930 |
967 |
,004 |
,041 |
,078 |
,115 |
,151 |
6 |
24,6 |
24,0 |
23,4 |
|
118 |
07 ISS |
225 |
262 |
298 |
335 |
372 |
408 |
445 |
482 |
518 |
7 |
28,7 |
28,0 |
27,3 |
|
119 |
555 |
591 |
628 |
664 |
700 |
737 |
773 |
809 |
846 |
882 |
8 |
32,8 |
32,0 |
31,2 |
|
120 |
918 |
954 |
990 |
,027 |
,063 |
,099 |
,135 |
,171 |
,207 |
,243 |
9 |
36,9 |
36,0 |
35,1 |
|
121 |
08 279 |
314 |
350 |
386 |
422 |
458 |
493 |
529 |
565 |
600 |
88 |
37 |
36 |
|
|
122 |
636 |
672 |
707 |
743 |
778 |
814 |
849 |
884 |
920 |
955 |
1 |
3,8 |
3,7 |
3,6 |
|
123 |
991 |
,026 |
,061 |
,096 |
,132 |
,167 |
,202 |
,237 |
,272 |
,307 |
2 |
7,6 |
TA |
7,2 |
|
124 |
09 342 |
377 |
412 |
447 |
482 |
517 |
552 |
587 |
621 |
656 |
3 |
11,4 |
11,1 |
10,8 |
|
125 |
691 |
728 |
760 |
795 |
830 |
864 |
899 |
934 |
968 |
,003 |
4 |
15,2 |
14,8 |
14,4 |
|
120 |
10 037 |
072 |
106 |
140 |
175 |
209 |
243 |
278 |
312 |
346 |
5 |
19,0 |
18,5 |
18,0 |
|
127 |
380 |
415 |
449 |
483 |
517 |
551 |
585 |
619 |
653 |
687 |
6 |
22,8 |
22,2 |
21,6 |
|
128 |
721 |
755 |
789 |
823 |
857 |
890 |
924 |
958 |
992 |
,025 |
7 |
26,6 |
25,9 |
25,2 |
|
129 |
11 059 |
093 |
126 |
160 |
193 |
227 |
261 |
294 |
327 |
361 |
8 |
30,4 |
29,6 |
28,8 |
|
130 |
394 |
428 |
461 |
494 |
528 |
561 |
594 |
628 |
661 |
694 |
9 |
34,2 |
33,3 |
32,4 |
|
131 |
727 |
760 |
793 |
826 |
860 |
893 |
926 |
959 |
992 |
,024 |
35 |
34 |
33 |
|
|
132 |
12 057 |
090 |
123 |
156 |
189 |
222 |
254 |
287 |
320 |
352 |
1 |
3,5 |
3,4 |
3,3 |
|
133 |
385 |
418 |
450 |
483 |
516 |
548 |
581 |
613 |
646 |
678 |
2 |
7,0 |
6,8 |
6,6 |
|
134 |
710 |
743 |
775 |
808 |
840 |
872 |
905 |
937 |
969 |
,001 |
3 |
10,5 |
10,2 |
9,9 |
|
135 |
13 033 |
066 |
■ 098 |
130 |
162 |
194 |
226 |
258 |
290 |
322" |
4 |
14,0 |
13,6 |
13,2 |
|
136 |
354 |
386 |
418 |
450 |
. 481 |
513 |
545 |
577 |
609 |
640 |
5 |
17,5 |
17,0 |
16,5 |
|
137 |
672 |
704 |
735 |
707 |
799 |
830 |
862 |
893 |
925 |
956 |
6 |
21,0 |
20,4 |
19,8 |
|
138 |
988 |
,019 |
,051 |
,082 |
,114 |
,145 |
,176 |
,208 |
,239 |
,270 |
7 |
24,5 |
23,8 |
23,1 |
|
139 |
14 301 |
333 |
364 |
395 |
426 |
457 |
489 |
520 |
551 |
582 |
8 |
28,0 |
27,2 |
26,4 |
|
140 |
613 |
644 |
675 |
706 |
737 |
768 |
799 |
829 |
860 |
891 |
9 |
31,5 |
30,6 |
29,7 |
|
141 |
922 |
953 |
983 |
,014 |
,045 |
,076 |
,106 |
,137 |
,168 |
,198 |
33 |
31 |
30 |
|
|
142 |
15 229 |
259 |
290 |
320 |
351 |
381 |
412 |
442 |
473 |
503 |
1 |
3,2 |
3,1 |
3,0 |
|
143 |
534 |
564 |
594 |
625 |
655 |
685 |
715 |
746 |
776 |
806 |
2 |
6,4 |
6,2 |
6,0 |
|
144 |
836 |
866 |
897 |
927 |
957 |
987 |
,017 |
,047 |
,077 |
,107 |
3 |
9,6 |
9,3 |
9'0 |
|
145 |
16 137 |
167 |
197 |
227 |
256 |
286 |
316 |
346 |
376 |
406 |
4 |
12,8 |
12,4 |
12,0 |
|
146 |
435 |
465 |
. 495 |
524 |
554 |
584 |
613 |
643 |
673 |
702 |
5 |
16,0 |
15,5 |
15,0 |
|
147 |
732 |
761 |
791 |
820 |
850 |
879 |
909 |
938 |
967 |
997 |
6 |
19,2 |
18,6 |
18,0 |
|
148 |
17 026 |
056 |
085 |
114 |
143 |
173 |
202 |
231 |
260 |
289 |
7 |
22,4 |
21,7 |
21,0 |
|
149 |
319 |
348 |
377 |
406 |
435 |
464 |
493 |
522 |
551 |
580 |
8 |
25,6 |
24,8 |
24,0 |
|
150 |
609 |
638 |
667 |
696 |
725 |
754 |
782 |
811 |
840 |
869 |
9 |
28,8 |
27,9 |
27,0 |
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P |
P. |
logaeithms of numbees.
235
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Continued. [Extracted from Graass' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
||
|
ISO |
17 609 |
638 |
667 |
696 |
725 |
754 |
782 |
811 |
840 |
869 |
|||
|
151 |
898 |
926 |
955 |
984 |
,013 |
,041 |
,070 |
,099 |
,127 |
.156 |
29 |
28 |
|
|
152 |
18 184 |
213 |
241 |
270 |
298 |
327 |
355 |
384 |
412 |
441 |
1 |
2,9 |
2,8 |
|
153 |
469 |
498 |
526 |
554 |
583 |
611 |
639 |
667 |
696 |
724 |
2 |
5,8 |
5,6 |
|
154 |
752 |
780 |
808 |
837 |
865 |
893 |
921 |
949 |
977 |
,005 |
3 |
8,7 |
8,4 |
|
155 |
19 033 |
061 |
089 |
117 |
145 |
173 |
201 |
229 |
257 |
285 |
4 |
11,6 |
11,2 |
|
156 |
312 |
340 |
368 |
396 |
424 |
451 |
479 |
507 |
535 |
562 |
5 |
14,5 |
14,0 |
|
157 |
590 |
618 |
645 |
673 |
700 |
728 |
756 |
783 |
811 |
838 |
6 |
17,4 |
16,8 |
|
158 |
866 |
893 |
921 |
948 |
976 |
,003 |
,030 |
,058 |
,085 |
,112 |
7 |
20,3 |
19,6 |
|
159 |
20 140 |
167 |
194 |
232 |
249 |
276 |
303 |
330 |
368 |
385 |
8 |
23,2 |
22,4 |
|
160 |
412 |
439 |
466 |
493 |
520 |
548 |
575 |
602 |
629 |
656 |
9 |
26,1 |
25,2 |
|
161 |
683 |
710 |
737 |
763 |
790 |
817 |
844 |
871 |
898 |
925 |
27 |
2e |
|
|
162 |
952 |
978- |
..005 |
,032 |
,059 |
,085 |
,112 |
.139 |
,165 |
,192 |
1 |
2,7 |
2,6 |
|
163 |
21 219 |
245 |
272 |
299 |
325 |
352 |
378 |
405 |
431 |
458 |
2 |
5,4 |
6,2 |
|
164 |
4S4 |
511 |
537 |
564 |
590 |
617 |
643 |
669 |
696 |
722 |
3 |
8,1 |
7,8 |
|
165 |
748 |
775 |
801 |
827 |
854 |
880 |
906 |
932 |
958 |
985 |
4 |
10,8 |
10,4 |
|
166 |
22 on |
037 |
063 |
089 |
115 |
141 |
167 |
194 |
220 |
246 |
5 |
13,5 |
13,0 |
|
167 |
272 |
298 |
324 |
350 |
376 |
401 |
427 |
453 |
479 |
505 |
6 |
16,2 |
15,6 |
|
168 |
531 |
557 |
583 |
608 |
634 |
660 |
686 |
712 |
737 |
763 |
7 |
18,9 |
18,2 |
|
169 |
789 |
814 |
840 |
866 |
891 |
917 |
943 |
968 |
994 |
,019 |
8 |
21,6 |
20,8 |
|
170 |
23 045 |
070 |
096 |
121 |
147 |
172 |
198 |
223 |
249 |
274 |
9 |
24,3 |
23,4 |
|
171 |
300 |
325 |
350 |
376 |
401 |
426 |
452 |
477 |
502 |
528 |
25 1 |
||
|
172 |
553 |
578 |
603 |
629 |
654 |
679 |
704 |
729 |
754 |
779 |
1 |
2,5 |
|
|
173 |
805 |
830 |
855 |
880 |
905 |
930 |
955 |
980 |
,005 |
,030 |
2 |
5,0 |
|
|
174 |
24 055 |
080 |
105 |
130 |
155 |
180 |
204 |
229 |
254 |
279 |
3 |
7,5 |
|
|
175 |
304 |
329 |
353 |
378 |
403 |
428 |
452 |
477 |
502 |
527 |
4 |
10,0 |
|
|
176 |
551 |
576 |
601 |
625 |
650 |
674 |
699 |
724 |
748 |
773 |
5 |
12,5 |
|
|
177 |
797 |
822 |
846 |
871 |
895 |
920 |
944 |
969 |
993 |
,018 |
6 |
15,0 |
|
|
178 |
25 042 |
066 |
091 |
115 |
139 |
164 |
188 |
212 |
237 |
261 |
7 |
17,5 |
|
|
179 |
285 |
310 |
331 |
358 |
382 |
406 |
431 |
455 |
479 |
503 |
8 |
20,0 |
|
|
ISO |
527 |
551 |
575 |
600 |
624 |
648 |
672 |
696 |
720 |
744 |
9 |
22,5 |
|
|
181 |
768 |
792 |
816 |
840 |
864 |
888 |
912 |
935 |
959 |
983 |
24 |
2S |
|
|
182 |
26 007 |
031 |
055 |
079 |
102 |
120 |
150 |
174 |
198 |
221 |
1 |
2,4 |
2,3 |
|
183 |
245 |
269 |
293 |
316 |
340 |
364 |
387 |
411 |
435 |
458 |
2 |
4,8 |
4,6 |
|
184 |
482 |
505 |
529 |
553 |
576 |
600 |
623 |
647 |
670 |
694 |
3 |
7,2 |
6,9 |
|
185 |
717 |
741 |
764 |
788 |
811 |
834 |
858 |
881 |
905 |
928 |
4 |
9,6 |
9,2 |
|
186 |
951 |
975 |
998 |
,021 |
,045 |
,068 |
,091 |
,114 |
,138 |
,161 |
5 |
12,0 |
11,6 |
|
187 |
27 184 |
207 |
231 |
254 |
277 |
300 |
323 |
346 |
370 |
393 |
6 |
14,4 |
13,8 |
|
188 |
416 |
439 |
462 |
485 |
508 |
531 |
554 |
577 |
600 |
623 |
7 |
16,8 |
16,1 |
|
189 |
646 |
669 |
692 |
715 |
738 |
761 |
784 |
807 |
830 |
852 |
8 |
19,2 |
]8,4 |
|
190 |
875 |
898 |
921 |
944 |
967 |
989 |
,012 |
,035 |
*058 |
,081 |
9 |
21,6 |
20,7 |
|
191 |
28 103 |
126 |
149 |
171 |
194 |
217 |
240 |
262 |
285 |
307 |
22 |
21 |
|
|
192 |
330 |
353 |
375 |
398 |
421 |
443 |
466 |
488 |
511 |
533 |
1 |
2,2 |
2,1 |
|
193 |
556 |
578 |
601 |
623 |
646 |
668 |
691 |
713 |
735 |
758 |
2 |
4,4 |
4,2 |
|
194 |
780 |
803 |
825 |
847 |
870 |
892 |
914 |
937 |
959 |
981 |
3 |
6,6 |
6,3 |
|
195 |
29 003 |
026 |
048 |
070 |
092 |
115 |
137 |
159 |
181 |
203 |
4 |
8,8 |
8,4 |
|
196 |
226 |
248 |
270 |
.292 |
314 |
336 |
358 |
380 |
403 |
425 |
5 |
11,0 |
10,5 |
|
197 |
447 |
469 |
491 |
513 |
535 |
557 |
579 |
601 |
623 |
645 |
6 |
13,2 |
12,6 |
|
198 |
667 |
688 |
710 |
732 |
754. |
776 |
798 |
820 |
842 |
863 |
7 |
15,4 |
14,7 |
|
199 |
885 |
907 |
929 |
951 |
973 |
994 |
,016 |
,038 |
,060 |
*081 |
8 |
17,6 |
16,S |
|
200 |
30 103 |
125 |
146 |
168 |
190 |
211 |
233 |
255 |
276 |
298 |
9 |
.19,8 |
18,9 |
|
N. |
L.O |
1 |
2 |
3 |
* |
5 |
6 |
7 |
8 |
^ |
P.P. |
236
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logariihms of numbers from 1 to 11,000- [Estractetl from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
||
|
200 |
30 103 |
125 |
146 |
168 |
190 |
211 |
233 |
255 |
276 |
298 |
|||
|
201 |
320 |
341 |
363 |
384 |
406 |
428 |
449 |
471 |
492 |
514 |
22 |
21 |
|
|
202 |
535 |
557 |
578 |
600 |
621 |
643 |
664 |
685 |
707 |
728 |
1 |
2,2 |
2,1 |
|
203 |
750 |
771 |
792 |
814 |
835 |
856 |
878 |
899 |
920 |
942 |
2 |
4,4 |
4,2 |
|
204 |
963 |
984 |
,006 |
,027 |
,048 |
,069 |
,091 |
,112 |
,133 |
,154 |
3 |
6,6 |
6,3 |
|
205 |
31 175 |
197 |
218 |
239 |
260 |
281 |
302 |
323 |
345 |
366 |
4 |
8,8 |
8,4 |
|
206 |
387 |
408 |
429 |
450 |
471 |
492 |
513 |
534 |
555 |
576 |
5 |
11,0 |
10,5 |
|
207 |
597 |
618 |
639 |
660 |
681 |
703 |
723 |
744 |
765 |
785 |
6 |
13,2 |
12,6 |
|
208 |
806 |
827 |
848 |
869 |
890 |
911 |
931 |
952 |
973 |
994 |
7 |
15,4 |
14,7 |
|
209 |
32 015 |
035 |
. 056 |
077 |
098 |
118 |
139 |
160 |
181 |
201 |
8 |
17,6 |
16,8 |
|
210 |
222 |
243 |
263 |
284 |
305 |
325 |
346 |
366 |
387 |
408 |
9 |
19,8 |
18,9 |
|
2U |
428 |
449 |
469 |
490 |
610 |
531 |
552 |
572 |
593 |
613 |
20 1 |
||
|
212 |
634 |
654 |
675 |
695 |
715 |
736 |
756 |
777 |
797 |
818 |
1 |
2,0 |
|
|
213 |
838 |
858 |
879 |
899 |
919 |
940 |
960 |
980 |
,001 |
,021 |
2 |
4,0 |
|
|
214 |
33 041 |
062 |
082 |
102 |
122 |
143 |
163 |
183 |
203 |
224 |
3 |
6,0 |
|
|
215 |
244 |
264 |
284 |
304 |
325 |
345 |
365 |
385 |
405 |
425 |
4 |
8,0 |
|
|
216 |
445 |
465 |
486 |
506 |
526 |
546 |
566 |
586 |
606 |
626 |
5 |
10,0 |
|
|
217 |
646 |
666 |
686 |
706 |
726 |
746 |
766 |
786 |
806 |
826 |
6 |
12,0 |
|
|
218 |
846 |
866 |
885 |
905 |
925 |
945 |
965 |
985 |
,005 |
,025 |
7 |
14,0 |
|
|
219 |
3i 044 |
061 |
084 |
104 |
124 |
143 |
163 |
183 |
203 |
223 |
8 |
16,0 |
|
|
220 |
242 |
262 |
282 |
301 |
321 |
341 |
361 |
380 |
400 |
420 |
9 |
18,0 |
|
|
221 |
439 |
459 |
479 |
498 |
518 |
%m |
557 |
577 |
596 |
616 |
19 1 |
||
|
222 |
635 |
655 |
674 |
694 |
713 |
733 |
753 |
772 |
792 |
811 |
1 |
1,9 |
|
|
323 |
830 |
850 |
869 |
889 |
908 |
928 |
947 |
967 |
986 |
,005 |
2 |
3,8 |
|
|
224 |
35 025 |
044 |
064 |
083 |
102 |
122 |
141 |
160 |
180 |
199 |
3 |
5,7 |
|
|
225 |
218 |
238 |
257 |
276 |
295 |
315 |
334 |
353 |
372 |
392 |
4 |
7,6 |
|
|
226 |
411 |
430 |
449 |
468 |
488 |
507 |
526 |
545 |
564 |
583 |
5 |
9,5 |
|
|
227 |
603 |
622 |
641 |
660 |
679 |
698 |
717 |
736 |
755 |
774 |
6 |
11,4 |
|
|
228 |
793 |
813 |
832 |
851 |
870 |
889 |
908 |
927 |
946 |
965 |
7 |
13,3 |
|
|
"29 |
984 |
,003 |
,021 |
,040 |
,059 |
,078 |
,097 |
,116 |
,135 |
,154 |
8 |
15,2 |
|
|
230 |
36 173 |
192 |
211 |
229 |
248 |
267 |
286 |
305 |
324 |
'342 |
9 |
17,1 |
|
|
231 |
361 |
380 |
399 |
418 |
436 |
455 |
474 |
493 |
511 |
530 |
18 |
||
|
232 |
549 |
568 |
586 |
605 |
624 |
642 |
661 |
680 |
698 |
717 |
1 |
1,8 |
|
|
233 |
736 |
754 |
773 |
791 |
810 |
829 |
847 |
866 |
884 |
903 |
2 |
3,6 |
|
|
234 |
922 |
940 |
959 |
977 |
996 |
,014 |
,033 |
,051 |
,070 |
,088 |
3 |
5,4 |
|
|
235 |
37 107 |
125 |
144 |
162 |
181 |
199 |
218 |
236 |
254 |
'273 |
, 4 |
7,2 |
|
|
236 |
291 |
310 |
328 |
346 |
365 |
383 |
401 |
420 |
438 |
457 |
5 |
9,0 |
|
|
237 |
475 |
493 |
511 |
530 |
548 |
566 |
585 |
603 |
621 |
639 |
6 |
10,8 |
|
|
238 |
658 |
676 |
694 |
712 |
731 |
749 |
767 |
785 |
803 |
822 |
7 |
12,6 |
|
|
239 |
840 |
858 |
876 |
894 |
912 |
931 |
949 |
967 |
985 |
003 |
8 |
14,4 |
|
|
240 |
38 021 |
039 |
057 |
075 |
093 |
112 |
130 |
148 |
166 |
184 |
9 |
16,2 |
|
|
2a |
202 |
220 |
238 |
256 |
274 |
292 |
310 |
328 |
346 |
364 |
17 1 |
||
|
242 |
382 |
399 |
417 |
435 |
453 |
471 |
489 |
507 |
525 |
543 |
1 |
1,7 |
|
|
243 |
561 |
578 |
596 |
614 |
632 |
650 |
668 |
686 |
703 |
721 |
2 |
3,4 |
|
|
244 |
739 |
757 |
775 |
792 |
810 |
828 |
846 |
863 |
881 |
890 |
3 |
5,1 |
|
|
245 |
917 |
034 |
952 |
970 |
987 |
,005 |
,023 |
,041 |
,058 |
,076 |
4 |
?»* |
|
|
246 |
39 094 |
111 |
129 |
146 |
164 |
182 |
199 |
217 |
235 |
252 |
5 |
8,5 |
|
|
247 |
270 |
287 |
305 |
322 |
340 |
358 |
375 |
393 |
410 |
428 |
6 |
10,2 |
|
|
248 |
445 |
463 |
480 |
498 |
515 |
533 |
550 |
568 |
685 |
602 |
7 |
11,9 |
|
|
249 |
620 |
637 |
655 |
072 |
690 |
707 |
724 |
742 |
759 |
777 |
8 |
13,6 |
|
|
250 |
794 |
811 |
829 |
846 |
863 |
881 |
898 |
915 |
933 |
950 |
9 |
15,3 ■ |
|
|
K. |
L. 0. |
1 |
2 |
3 |
4 |
5 |
6 |
■ 7 |
8 |
9 |
P.P. |
LOGAEITHMS OF NUMBERS.
237
Table XXXV. — Containimj logarithms of mimhers from I to 11,000 — Continued. [Extracted from Gauss' Loo;arithmic ami Trigonometric Tablef&.J
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
|
|
250 |
39 794 |
811 |
829 |
846 |
863' |
881 |
898 |
915 |
933 |
950 |
||
|
251 |
967 |
985 |
,002 |
,019 |
,037 |
,054 |
.071 |
,088 |
,106 |
,123 |
1 |
1,8 |
|
252 |
40140 |
157 |
175 |
192 |
209 |
220 |
243 |
261 |
278 |
295 |
2 |
3,6 |
|
253 |
312 |
329 |
346 |
364 |
381 |
398 |
415 |
432 |
449- |
466 |
3 |
6,4 |
|
254 |
483 |
500 |
518 |
535 |
552 |
509 |
586 |
603 |
620 |
637 |
4 |
7,2 |
|
265 |
654 |
671 |
688 |
705 |
722 |
739 |
756 |
773 |
790 |
807 |
5 |
9,0 |
|
256 |
824 |
841 |
858 |
875 |
892 |
909 |
926 |
943 |
960 |
•976 |
6 |
10,8 |
|
257 |
993 |
,010 |
.027 |
,044 |
,061 |
,078 |
,095 |
,111 |
,128 |
,145 |
7 |
12,6 |
|
258 |
41 162 |
179 |
196 |
212 |
229 |
246 |
263 |
280 |
296 |
313 |
8 |
14,4 |
|
259 |
330 |
347 |
363 |
380 |
397 |
414 |
430 |
447 |
464 |
481 |
9 |
16,2 |
|
260 |
497 |
514 |
531 |
547 |
564 |
581 |
597 |
614 |
631 |
647 |
„ 1 |
|
|
261 |
664 |
681 |
697 |
714 |
731 |
747 |
764 |
780 |
797 |
814 |
1 |
1/7 |
|
262 |
83"0 |
847 |
863 |
880 |
896 |
913 |
929 |
946 |
963 |
979 |
2 |
3,4 |
|
263 |
996 |
,012 |
,029 |
.,045 |
,062 |
,078 |
,095 |
.,111 |
,127 |
,144 |
3 |
5,1 |
|
264 |
42160 |
177 |
193 |
210 |
220 |
243 |
259 |
275 |
292 |
308 |
4 |
6,8 |
|
265 |
325 |
341 |
357 |
374 |
390 |
406 |
423 |
439 |
455 |
472 |
5 |
8,5 |
|
266 |
488 |
504 |
521 |
537 |
553 |
570 |
586 |
602 |
619 |
635 |
6 |
10,2 |
|
267 |
651 |
667 |
684 |
700 |
716 |
732 |
749 |
765 |
781 |
797 |
7 |
11,9 |
|
268 |
813 |
830 |
846 |
862 |
. 878 |
894 |
911 |
927 |
943 |
959 |
8 |
13,6 |
|
269 |
975 |
991 |
,008 |
,024 |
,040 |
,056 |
,072 |
,088 |
,104 |
,120 |
9 |
15,3 |
|
270 |
43136 |
152 |
169 |
185 |
201 |
217 |
233 |
249 |
265 |
281 |
,/ |
|
|
271 |
297 |
313 |
329 |
345 |
361 |
.' 377 |
393 |
409 |
425 |
441 |
1 |
1,6 |
|
272 |
457 |
473 |
489 |
505 |
521 |
537 |
553 |
569 |
584 |
■ 600 |
2 |
3,2 |
|
273 |
616 |
632 |
048 |
664 |
680 |
696 |
712 |
727 |
743 |
759 |
2 |
4,8 |
|
274 |
775 |
791 |
807 |
823 |
838 |
854 |
870 |
886 |
902 |
917 |
4 |
6,4 |
|
275 |
933 |
949 |
965 |
981 |
996 |
,012 |
,028 |
.,044 |
,059 |
,075 |
5 |
8,0 |
|
276 |
44 091 |
107 |
122 |
138 |
154 |
170 |
186 |
'201 |
217 |
232 |
6 |
9,6 |
|
277 |
248 |
264 |
279 |
295 |
311 |
326 |
342 |
358 |
373 |
389 |
7 |
11,2 |
|
278 |
404 |
420 |
436 |
451 |
467 |
483 |
498 |
514 |
529 |
545 |
8 |
12,8 |
|
279 |
560 |
576 |
592 |
607 |
623 |
638 |
654 |
669 |
686 |
■ 700 |
9 |
14,4 |
|
280 |
716 |
731 |
747 |
762 |
778 |
793 |
809 |
824 |
840 |
855 |
,. 1 |
|
|
281 |
871 |
886 |
902 |
917 |
932 |
948 |
963 |
979 |
994 |
,010 |
1 |
1,5 |
|
i82 |
45 025 |
040 |
056 |
071 |
086 |
102 |
117 |
133 |
148 |
163 |
2 |
3,0 |
|
283 |
179 |
194 |
209 |
225 |
240 |
255 |
271 |
286 |
301 |
317 |
3 |
4,5 |
|
284 |
332 |
347 |
362 |
378 |
393 |
408 |
423 |
439 |
454 |
469 |
4 |
6,0 |
|
285 |
484 |
500 |
515 |
530 |
545 |
561 |
576 |
591 |
606 |
621 |
5 |
7,5 |
|
286 |
637 |
652 |
667 |
682 |
697 |
712 |
728 |
743 |
758 |
773 |
0 |
9,0 |
|
287 |
788 |
803 |
818 |
834 |
849 |
864 |
879 |
894 |
009 |
924 |
7 |
10,5 |
|
288 |
939 |
954 |
969 |
984 |
.,000 |
,016 |
,030 |
,045 |
,060 |
.,075 |
8 |
12,0 |
|
289 |
46 090 |
105 |
120 |
135 |
150 |
165 |
180 |
195 |
210 |
225 |
9 |
13,5 |
|
290 |
240 |
255 |
270 |
286 |
300 |
315 |
330 |
345 |
359 |
374 |
,, 1 |
|
|
291 |
389 |
404 |
419 |
434 |
449 |
464 |
479 |
494 |
509 |
523 |
1 |
1,4 |
|
292 |
538 |
553 |
668 |
583 |
598 |
613 |
627 |
642 |
657 |
672 |
2 |
2,8 |
|
293 |
687 |
702 |
716 |
731 |
746 |
761 |
776 |
790 |
805 |
820 |
3 |
4,2 |
|
294 |
■835 |
850 |
864 |
879 |
894 |
909 |
923 |
938 |
953 |
967 |
4 |
5,6 |
|
295 |
982 |
997 |
,012 |
.,026 |
..041 |
,056 |
,070 |
,085 |
,100 |
,114 |
5 |
7,0 |
|
296 |
47129 |
144 |
159 |
173 |
188 |
202 |
217 |
232 |
246 |
261 |
6 |
8,4 |
|
297 |
276 |
290 |
305 |
319 |
334 |
349 |
363 |
378 |
392 |
407 |
7 |
9,8 |
|
298 |
422 |
436 |
451 |
465 |
480 |
494 |
509 |
524 |
538 |
553 |
8 |
11,2 |
|
299 |
567 |
582 |
596 |
611 |
625 |
640 |
654 |
669 |
683 |
698 |
9 |
12,6 |
|
300 |
712 |
727 |
741 |
756 |
770 |
784 |
799 |
813 |
828 |
842 |
||
|
M". |
.L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
238
A MANUAL OF TOPOGEAPHIC METHODS.
Table XX.XV. — Containing logarithms of iiamiers from 1 to 11,000 — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. 300 |
L. 0 47 712 |
1 |
2 |
3 ■ |
4 |
= |
6 |
7 |
8 |
9 |
P.P. |
|
|
727 |
741 |
756 |
770 |
784 |
799 |
813 |
828 |
842 |
||||
|
301 |
857 |
871 |
885 |
900 |
914 |
929 |
943 |
958 |
972 |
986 |
||
|
302 |
48 001 |
015 |
029 |
044 |
058 |
073 |
087 |
101 |
116 |
130 |
||
|
303 |
144 |
159 |
173 |
187 |
202 |
216 |
230 |
244 |
259 |
273 |
15 |
|
|
30 1 |
287 |
302 |
316 |
330 |
344 |
359 |
373 |
387 |
401 |
416 |
1 |
1,5 |
|
305 |
430 |
444 |
458 |
473 |
487 |
501 |
515 |
530 |
544 |
558 |
o |
3,0 |
|
306 |
572 |
■ 586 |
601 |
615 |
629 |
643 |
657 |
671 |
686 |
700 |
3 |
4,5 |
|
307 |
714 |
728 |
742 |
756 |
770 |
785 |
799 |
813 |
827 |
841 |
4 |
6,0 |
|
308 |
855 |
869 |
883 |
897 |
911 |
926 |
940 |
954 |
963 |
982 |
5 |
7,5 |
|
309 |
996 |
,010 |
,024 |
,038 |
,052 |
,066 |
,080 |
,094 |
,108 |
,122 |
6 |
9,0 |
|
310 |
49 136 |
150 |
164 |
178 |
192 |
206 |
220 |
234 |
248 |
262 |
7 8 |
10,5 12,0 |
|
311 |
276 |
290 |
304 |
318 |
332 |
346 |
360 |
374 |
388 |
402 |
9 |
13,5 |
|
312 |
415 |
429 |
443 |
457 |
471 |
485 |
499 |
513 |
527 |
541 |
||
|
313 |
554 |
568 |
582 |
596 |
610 |
624 |
638 |
651 |
665 |
679 |
||
|
314 |
693 |
707 |
721 |
734 |
748 |
762 |
776 |
790 |
803 |
817 |
||
|
315 |
831 |
845 |
859 |
872 |
886 |
900 |
914 |
927 |
941 |
955 |
11 |
|
|
316 |
969 |
982 |
996 |
,010 |
,024 |
,037 |
,051 |
,065 |
,079 |
,092 |
1 |
1,4 |
|
317 |
50 106 |
120 |
133 |
147 |
101 |
174 |
188 |
202. |
215 |
229 |
2 |
2,8 |
|
318 |
243 |
256 |
270 |
284 |
297 |
311 |
325 |
338 |
352 |
365 |
3 |
4,2 |
|
319 |
379 |
393 |
406 |
420 |
433 |
447 |
461 |
474 |
488 |
501 |
4 |
5,6 |
|
320 |
515 |
529 |
542 |
556 |
569 |
583 |
596 |
610 |
623 |
637 |
5 6 |
7,0 8,4 |
|
321 |
651 |
664 |
678 |
691 |
705 |
718 |
732 |
745 |
759 |
772 |
7 |
9,8 |
|
322 |
786 |
799 |
813 |
826 |
840 |
853 |
866 |
880 |
893 |
907 |
8 |
11,2 |
|
323 |
920 |
934 |
947 |
961 |
974 |
987 |
,001 |
,014 |
,028 |
,041 |
9 |
12,6 |
|
324 |
51 055 |
068 |
081 |
095 |
108 |
121 |
135 |
148 |
162 |
175 |
||
|
325 |
188 |
202 |
215 |
228 |
242 |
255 |
268 |
282 |
295 |
308 |
||
|
326 |
322 |
335 |
348 |
362 |
375 |
388 |
402 |
415 |
428 |
441 |
13 |
|
|
327 |
455 |
468 |
481 |
495 |
508 |
521 |
534 |
548 |
561 |
574 |
1 |
1,3 |
|
328 |
587 |
601 |
614 |
627 |
640 |
654 |
667 |
680 |
693 |
706 |
2 |
2,6 |
|
329 |
720 |
733 |
746 |
759 |
772 |
786 |
799 |
812 |
825 |
838 |
3 |
3,9 |
|
330 |
851 |
865 |
878 |
891 |
904 |
917 |
930 |
943 |
957 |
970 |
4 5 |
5,2 6,5 |
|
331 |
983 |
996 |
,009 |
jm |
,035 |
,048 |
4)61 |
,075 |
,088 |
,101 |
6 |
7,8 |
|
332 |
52 114 |
127 |
140 |
153 |
166 |
179 |
192 |
205 |
218 |
231 |
7 |
9,1 |
|
333 |
244 |
257 |
270 |
284 |
297 |
310 |
• 323 |
336 |
349 |
362 |
8 |
10,4 |
|
334 |
375 |
388 |
401 |
414 |
427 |
440 |
453 |
466 |
479 |
492 |
9 |
11,7 |
|
335 |
504 |
517 |
530 |
543 |
556 |
569 |
582 |
595 |
608 |
621 |
1 |
|
|
336 |
634 |
647 |
660 |
673 |
686 |
699 |
711 |
724 |
737 |
750 |
12 1 |
|
|
337 |
763 |
776 |
789 |
802 |
815 |
827 |
840 |
853 |
866 |
879 |
1 |
1,2 |
|
338 |
892 |
905 |
917 |
930 |
943 |
956 |
969 |
982 |
994 |
,007 |
2 |
2,4 |
|
339 |
53 020 |
033 |
046 |
058 |
071 |
084 |
097 |
110 |
122 |
135 |
3 |
3,6 |
|
340 |
148 |
161 |
173 |
186 |
199 |
212 |
224 |
237 |
250 |
263 |
4 5 |
4,8 6,0 |
|
341 |
275 |
288 |
301 |
314 |
326 |
339 |
352 |
364 |
377 |
390 |
6 |
7,2 |
|
342 |
403 |
415 |
428 |
441 |
453 |
466 |
479 |
491 |
504 |
517 |
7 |
8,4 |
|
343 |
529 |
542 |
555 |
567 |
580 |
593 |
605 |
618 |
631 |
643 |
8 |
9,6 |
|
344 |
656 |
668 |
681 |
694 |
706 |
719 |
732 |
744 |
757 |
769 |
. 9 |
10,8 |
|
345 |
782 |
794 |
807 |
820 |
832 |
845 |
857 |
870 |
882 |
895 |
||
|
346 |
908 |
920 |
933 |
945 |
958 |
970 |
983 |
995 |
,008 |
,020 |
||
|
347 |
54 033 |
045 |
058 |
070 |
083 |
095 |
108 |
120 |
133 |
145 |
||
|
348 |
158 |
170 |
183 |
195 |
208 |
220 |
233 |
245 |
238 |
270 |
||
|
349 |
283 |
295 |
307 |
820 |
332 |
345 |
357 |
370 |
382 |
394 |
||
|
350 |
407 |
419 |
432 |
444 |
456 |
469 |
481 |
494 |
506 |
518 |
||
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
LOGARITHMS OF NUMBEES.
239
Table XXXV". — Containing logarithms of numbers from 1 to 11,000 — Coutiuued. [Extracted from G-ausa' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
|
|
350 |
51 407 |
419 |
432 |
444 |
456 |
469 |
481 |
494 |
506 |
518 |
||
|
351 |
531 |
643 |
656 |
568 |
580 |
693 |
605 |
617 |
630 |
642 |
||
|
352 |
654 |
667 |
679 |
691 |
704 |
716 |
728 |
741 |
753 |
765 |
13 |
|
|
353 |
777 |
790 |
802 |
814 |
827 |
839 |
851 |
864 |
876 |
888 |
||
|
354 |
900 |
913 |
926 |
937 |
949 |
962 |
974 |
986 |
998 |
,011 |
1 |
1,3 |
|
355 |
55 023 |
035 |
047 |
060 |
072 |
084 |
096 |
108 |
121 |
133 |
2 |
2,6 |
|
356 |
145 |
167 |
169 |
182 |
194 |
206 |
218 |
230 |
2J2 |
255 |
3 |
3,9 |
|
357 |
267 |
279 |
291 |
303 |
315 |
328 |
340 |
362 |
364 |
376 |
4 |
5,2 |
|
358 |
388 |
40O |
413 |
■425 |
437 |
449 |
461 |
473 |
486 |
497 |
5 |
6,5 |
|
359. |
509 |
522 |
534 |
546 |
558 |
570 |
582 |
594 |
606 |
618 |
6 |
7,8 |
|
360 |
630 |
642 |
654 |
666 |
678 |
691 |
703 |
715 |
727 |
739 |
7 8 |
9,1 10,4 |
|
361 |
751 |
763 |
775 |
787 |
799 |
811 |
823 |
836 |
847 |
859 |
9 |
11,7 |
|
362 |
871 |
883 |
895 |
907 |
919 |
931 |
943 |
955 |
967 |
979 |
||
|
363 |
991 |
,003 |
,016 |
,027 |
,038 |
.050 |
,062 |
,074 |
,086 |
,098 |
||
|
364 |
56 110 |
122 |
134 |
146 |
158 |
170 |
182 |
194 |
205 |
217 |
12 |
|
|
305 |
229 |
241 |
253 |
265 |
277 |
289 |
301 |
312 |
321 |
336 |
||
|
366 |
348 |
360 |
372 |
384 |
396 |
407 |
419 |
431 |
443 |
455 |
1 |
1,2 |
|
367 |
467 |
478 |
490 |
502 |
514 |
526 |
538 |
549 |
561 |
573 |
2 |
2,4 |
|
368 |
585 |
597 |
608 |
620 |
632 |
644 |
656 |
667 |
679 |
691 |
3 |
3,6 |
|
369 |
703 |
714 |
726 |
738 |
750 |
761 |
773 |
785 |
797 |
808 |
4 |
4,8 |
|
370 |
820 |
832 |
844 |
856 |
867 |
879 |
891 |
902 |
914 |
926 |
5 6 |
6,0 7,2 |
|
371 |
937 |
949 |
961 |
972 |
984 |
996 |
,008 |
,019 |
,031 |
,043 |
7 |
8,4 |
|
372 |
67 054 |
066 |
078 |
089 |
101 |
113 |
124 |
136 |
148 |
159 |
8 |
9,6 |
|
373 |
171 |
183 |
194 |
206 |
217 |
229 |
241 |
252 |
264 |
276 |
9 |
10,8 |
|
374 |
287 |
299 |
310 |
322 |
334 |
345 |
357 |
368 |
380 |
392 |
||
|
375 |
403 |
415 |
426 |
438 |
449 |
461 |
473 |
434 |
496 |
507 |
||
|
376 |
619 |
630 |
642 |
553 |
665 |
576 |
688 |
600 |
611 |
623 |
11 |
|
|
377 |
634 |
646 |
657 |
669 |
630 |
692 |
703 |
715 |
726 |
738 |
||
|
378 |
749 |
761 |
772 |
784 |
795 |
807 |
818 |
830 |
841 |
852 |
1 |
1,1 |
|
379 |
864 |
875 |
887 |
898 |
910 |
921 |
933 |
944 |
955 |
967 |
2 |
2,2 |
|
380 |
978 |
990 |
,001 |
,013 |
,024 |
,035 |
,047 |
,058 |
,070 |
,081 |
3 4 |
3,3 4,4 |
|
381 |
58 092 |
104 |
116 |
127 |
138 |
149 |
161 |
172 |
184 |
196 |
5 |
6,5 |
|
382 |
206 |
218 |
229 |
240 |
252 |
263 |
274 |
286 |
297 |
309 |
6 |
6,6 |
|
383 |
320 |
331 |
343 |
354 |
365 |
377 |
388 |
399 |
410 |
422 |
7 |
7,7 |
|
384 |
433 |
444 |
456 |
467 |
478 |
490 |
501 |
512 |
624 |
535 |
8 |
8,8 |
|
385 |
646 |
657 |
569 |
580 |
591 |
602 |
614 |
625 |
636 |
647 |
9 |
9,9 |
|
386 |
659 |
670 |
681 |
692 |
704 |
715 |
726 |
737 |
749 |
760 |
||
|
387 |
771 |
782 |
794 |
805 |
816 |
827 |
838 |
850 |
861 |
872 |
||
|
388 |
883 |
894 |
906 |
917 |
928 |
939 |
960 |
961 |
973 |
984 |
10 |
|
|
389 |
995 |
»ao6 |
,017 |
,028 |
,040 |
,051 |
,062 |
,073 |
,084 |
,095 |
||
|
390 |
59 106 |
118 |
129 |
140 |
151 |
162 |
173 |
184 |
195 |
207 |
1 2 |
1,0 2,0 |
|
391 |
218 |
229 |
240 |
251 |
262 |
273 |
284 |
295 |
306 |
318 |
3 |
3,0 |
|
392 |
329 |
340 |
351 |
362 |
373 |
384 |
395 |
406 |
417 |
428 |
4 |
4,0 |
|
393 |
439 |
450 |
461 |
472 |
483 |
494 |
506 |
517 |
528 |
539 |
5 |
5,0 |
|
394 |
550 |
661 |
572 |
683 |
694 |
6C5 |
616 |
627 |
638 |
649 |
6 |
6,0 |
|
395 |
660 |
671 |
682 |
693 |
704 |
715 |
726 |
737 |
748 |
759 |
7 |
7,0 |
|
396 |
770 |
780 |
701 |
802 |
813 |
824 |
835 |
846 |
857 |
868 |
8 |
8,0 |
|
397 |
879 |
800 |
901 |
912 |
923 |
934 |
946 |
956 |
966 |
977 |
9 |
9,0 |
|
398 |
988 |
999 |
,010 |
,021 |
,032 |
,043 |
,054 |
,065 |
,076 |
,086 |
||
|
399 |
60 097 |
108 |
119 |
130 |
141 |
152 |
163 |
173 |
184 |
195 |
||
|
400 |
206 |
217 |
228 |
239 |
249 |
260 |
271 |
282 |
293 |
304 |
||
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
240
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXY.— Containing logarithms of mimbers from 1 to i^OW— Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
3,0 4,0 5,0 6,0 7,0 8,0 9,0
LOGAEITHMS OF NUMBEES.
241
Table XXXV. — Containing logarithms of numhera from 1 to 11,000 — Continued. [Extracted from Gauss' Logaritlimic and Triganometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
|
|
450 |
65 321. |
331 |
341 |
350 |
360 |
369 |
379 |
389 |
398 |
408 |
||
|
451 |
418 |
427 |
437 |
447 |
456 |
466 |
475 |
485 |
495 |
504 |
||
|
452 |
514 |
523 |
533 |
543 |
552 |
562 |
571 |
581 |
591 |
600 |
||
|
453 |
610 |
619 |
629 |
639 |
648 |
658 |
667 |
677 |
686 |
696 |
||
|
454 |
70G |
715 |
725 |
734 |
744 |
753 |
763 |
772 |
782 |
792 |
||
|
455 |
801 |
811 |
820 |
830 |
839 |
849 |
858 |
868 |
877 |
887 |
||
|
456 |
896 |
906 |
916 |
925 |
935 |
944 |
954 |
903 |
973 |
982 |
10 |
|
|
457 |
992 |
,001 |
*011 |
,020 |
,030 |
,039 |
,049 |
,058 |
,068 |
,077 |
1 |
1,0 |
|
458 |
66 087 |
096 |
106 |
115 |
124 |
134 |
143 |
153 |
162 |
172 |
2 |
2,0 |
|
459 |
181 |
191 |
200 |
. 210 |
219 |
229 |
238 |
247 |
257 |
266 |
3 |
3,0 |
|
460 |
276 |
285 |
295 |
304 |
314 |
323 |
332 |
342 |
351 |
361 |
4 5 |
4,0 5,0 |
|
461 |
370 |
380 |
389 |
398 |
408 |
417 |
427 |
436 |
445 |
455 |
6 |
6,0 |
|
462 |
464 |
474 |
483 |
492 |
502 |
511 |
521 |
530 |
539 |
549 |
7 |
7,0 |
|
463 |
558 |
507 |
577 |
586 |
596 |
605 |
614 |
624 |
633 |
642 |
8 |
8,0 |
|
464 |
■ 652 |
661 |
671 |
680 |
689 |
699 |
708 |
717 |
727 |
736 |
9 |
9,0 |
|
465 |
745 |
755 |
764 |
773 |
783 |
792 |
801 |
811 |
820 |
829 |
||
|
466 |
839 |
848 |
857 |
867 |
876 |
885 |
894 |
904 |
913 |
922 |
||
|
467 |
932 |
941 |
950 |
960 |
969 |
978 |
987 |
997 |
,006 |
,015 |
||
|
468 |
67 025 |
014 |
043 |
052 |
062 |
071 |
080 |
089 |
099 |
108 |
||
|
469 |
117 |
127 |
136 |
145 |
154 |
164 |
173 |
182 |
191 |
201 |
||
|
470 |
210 |
219 |
228 |
237 |
247 |
• 25G |
265 |
274 |
284 |
293 |
„ |
|
|
471 |
302 |
311 |
321 |
330 |
339 |
348 |
357 |
367 |
376 |
385 |
1 |
0,9 |
|
472 |
394 |
403 |
413 |
422 |
431 |
440 |
449 |
459 |
468 |
477 |
2 |
1,8 |
|
473 |
486 |
495 |
504 |
514 |
523 |
532 |
541 |
550 |
560 |
569 |
3 |
2,7 |
|
474 |
578 |
687 |
596 |
605 |
614 |
624 |
633 |
642 |
651 |
660 |
4 |
3,6 |
|
475 |
669 |
679 |
688 |
697 |
706 |
715 |
724 |
733 |
742 |
752 |
5 |
4,5 |
|
476 |
761 |
770 |
779 |
788 |
797 |
806 |
815 |
825 |
834 |
843 |
6 |
5,4 |
|
477 |
852 |
861 |
870 |
879 |
888 |
897 |
906 |
916 |
925 |
934 |
7 |
6,3 |
|
478 |
943 |
952 |
961 |
970 |
979 |
988 |
997 |
,006 |
,015 |
,024 |
8 |
7,2 |
|
479 |
68 034 |
043 |
052 |
061 |
070 |
079 |
088 |
097 |
106 |
115 |
9 |
8,1 |
|
480 |
124 |
133 |
142 |
151 |
160 |
169 |
178 |
187 |
196 |
205 |
||
|
481 |
215 |
224 |
233 |
242 |
251 |
260 |
269 |
278 |
287 |
296 |
||
|
482 |
305 |
314 |
323 |
332 |
341 |
350 |
3')9 |
368 |
377 |
386 |
||
|
483 |
395 |
404 |
413 |
422 |
431 |
440 |
449 |
458 |
467 |
476 |
||
|
484 |
485 |
494 |
502 |
511 |
520 |
529 |
538 |
547 |
556 |
565 |
||
|
485 |
574 |
583 |
592- |
601 |
010 |
619 |
628 |
637 |
646 |
655 |
S |
|
|
486 |
664 |
673 |
681 |
690 |
699 |
708 |
717 |
726 |
735 |
744 |
1 |
0,8 |
|
487 |
753 |
762 |
771 |
780 |
789 |
797 |
806 |
815 |
824 |
833 |
2 |
1,0 |
|
488 |
842 |
851 |
860 |
869 |
878 |
886 |
895 |
904 |
913 |
922 |
3 |
2,4 |
|
489 |
931 |
940 |
949 |
958 |
966 |
975 |
984 |
993 |
,002 |
,011 |
4 |
3,2 |
|
490 |
69 020 |
028 |
037 |
046 |
055 |
064 |
078 |
082 |
090 |
099 |
5 6 |
4,0 4,8 5,6 |
|
491 |
108 |
117 |
126 |
135 |
144 |
152 |
161 |
170 |
179 |
188 |
7 |
|
|
492 |
197 |
205 |
214 |
223 |
232 |
241 |
249 |
258 |
267 |
276 |
8 |
6,4 |
|
493 |
285 |
294 |
302 |
311 |
320 |
329 |
338 |
346 |
355 |
364 |
9 |
7,2 |
|
494 |
373 |
381 |
390 |
399 |
408 |
417 |
425 |
434 |
443 |
452 |
||
|
495 |
461 |
469 |
478 |
487 |
496 |
504 |
513 |
522 |
531 |
539 |
||
|
496 |
548 |
557 |
566 |
574 |
583 |
592 |
601 |
609 |
618 |
627 |
||
|
497 |
636 |
644 |
653 |
062 |
671 |
679 |
°688 |
697 |
705 |
714 |
||
|
498 |
723 |
732 |
740 |
749 |
758 |
767 |
775 |
784 |
793 |
801 |
||
|
499 |
810 |
819 |
827 |
836 |
845 |
854 |
862 |
871 |
880 |
888 |
||
|
500 |
897 |
906 |
914 |
923 |
932 |
940 |
949 |
958 |
966 |
975 |
||
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
MON XXII-
-16
242
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXV. — Containiiifj logarithms of numbers from 1 to 11,000 — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
|
|
600 |
69, 897 |
906 |
914 |
923 |
932 |
940 |
949 |
958 |
906 |
975 |
||
|
501 |
984 |
992 |
,001 |
,010 |
,018 |
,027 |
,036 |
,044 |
,053 |
,062 |
||
|
502 |
70, 070 |
079 |
088 |
096 |
105 |
114 |
122 |
131 |
140 |
148 |
||
|
503 |
157 |
165 |
174 |
183 |
191 |
200 |
209 |
217 |
226 |
234 |
||
|
504 |
243 |
252 |
260 |
269 |
278 |
286 |
295 |
303 |
312 |
321 |
||
|
505 |
329 |
338 |
346 |
355 |
364 |
372 |
381 |
389 |
398 |
406 |
||
|
506 |
415 |
424 |
432 |
441 |
449 |
458 |
467 |
475 |
484 |
492 |
||
|
507 |
501 |
509 |
518 |
526 |
535 |
544 |
552 |
561 |
569 |
578 |
9 |
|
|
508 |
586 |
595 |
603 |
612 |
621 |
629 |
638 |
646 |
655 |
663 |
1 |
0,9 |
|
509 |
672 |
680 |
689 |
697 |
706 |
714 |
723 |
731 |
740 |
749 |
2 |
1,8 |
|
510 |
757 |
766 |
774 |
783 |
791 |
800 |
808 |
817 |
825 |
834 |
3 4 |
2,7 3,6 |
|
511 |
842 |
851 |
859 |
868 |
876 |
885 |
893 |
902 |
910 |
919 |
5 |
4,5 |
|
512 |
927 |
935 |
944 |
952 |
901 |
969 |
978 |
980 |
995 |
,003 |
6 |
5,4 |
|
513 |
71,012 |
020 |
029 |
037 |
046 |
054 |
063 |
071 |
079 |
088 |
7 |
6,3 |
|
514 |
096 |
105 |
113 |
122 |
130 |
139 |
147 |
155 |
164 |
172 |
8 |
7,2 |
|
51-5 |
181 |
189 |
198 |
206 |
214 |
223 |
231 |
240 |
248 |
257 |
9 |
8,1 |
|
516 |
265 |
273 |
282 |
29U |
299 |
307 |
315 |
324 |
332 |
341 |
||
|
517 |
349 |
357 |
366 |
374 |
383 |
391 |
399 |
408 |
416 |
425 |
||
|
518 |
433 |
441 |
450 |
458 |
466 |
475 |
483 |
492 |
500 |
508 |
||
|
519 |
517 |
525 |
533 |
542 |
550 |
559 |
567 |
575 |
584 |
592 |
||
|
620 |
600 |
609 |
617 |
625 |
634 |
642 |
650 |
659 |
667 |
675 |
||
|
521 |
684 |
692 |
700 |
709 |
717 |
725 |
734 |
742 |
750 |
759 |
8 |
|
|
522 |
767 |
775 |
784 |
792 |
800 |
809 |
817 |
825 |
834 |
842 |
1 |
0,8 |
|
523 |
850 |
858 |
867 |
875 |
883 |
892 |
900 |
908 |
917 |
926 |
2 |
1,6 |
|
524 |
933 |
941 |
950 |
958 |
966 |
975 |
983 |
991 |
999 |
,008 |
3 |
2,4 |
|
525 |
72, 016 |
024 |
032 |
041 |
049 |
957 |
066 |
074 |
082 |
090 |
4 |
3,2 |
|
526 |
099 |
107 |
115 |
123 |
132 |
140 |
148 |
156 |
165 |
173 |
5 |
4,0 |
|
527 |
181 |
189 |
198 |
206 |
214 |
222 |
230 |
239 |
247 |
255 |
6 |
4,8 |
|
528 |
263 |
272 |
280 |
288 |
296 |
304 |
313 |
321 |
329 |
337 |
7 |
5,6 |
|
529 |
346 |
354 |
362 |
370 |
378 |
387 |
395 |
403 |
411 |
419 |
8 |
6,4 |
|
530 |
428 |
436 |
444 |
452 |
460 |
469 |
477 |
485 |
493 |
601 |
9 |
7,'. |
|
531 |
509 |
518 |
526 |
534 |
542 |
550 |
558 |
567 |
575 |
583 |
||
|
532 |
591 |
599 |
607 |
616 |
624 |
632 |
640 |
648 |
656 |
665 |
||
|
533 |
673 |
681 |
689 |
697 |
705 |
713 |
722 |
730 |
738 |
746 |
||
|
534 |
754 |
762 |
770 |
779 |
787 |
795 |
803 |
811 |
819 |
827 |
||
|
535 |
835 |
843 |
852 |
860 |
869 |
876 |
884 |
892 |
900 |
908 |
||
|
536 |
916 |
925 |
933 |
941 |
949 |
957 |
965 |
973 |
981 |
989 |
J |
|
|
537 |
997 |
,006 |
,014 |
,022 |
,030 |
,038 |
,046 |
,054 |
,062 |
,070 |
1 |
0,7 |
|
538 |
73, 078 |
■ 086 |
094 |
102 |
111 |
119 |
127 |
135 |
143 |
151 |
2 |
1,4 |
|
639 |
159 |
167 |
175 |
183 |
191 |
199 |
207 |
215 |
223 |
231 |
3 |
2,1 |
|
640 |
239 |
247 |
255 |
263 |
272 |
280 |
288 |
296 |
304 |
312 |
4 5 |
2,8 3,5 |
|
541 |
320 |
328 |
336 |
344 |
352 |
360 |
368 |
376 |
384 |
392 |
6 |
4,2 |
|
542 |
400 |
408 |
416 |
424 |
432 |
440 |
448 |
456 |
464 |
472 |
7 |
4,9 |
|
543 |
480 |
488 |
496 |
504 |
512 |
520 |
528 |
536 |
644 |
552 |
8 |
5,6 |
|
544 |
560 |
568 |
576 |
584 |
592 |
600 |
608 |
616 |
624 |
632 |
9 |
6,3 |
|
545 |
640 |
648 |
656 |
664 |
673 |
679 |
687 |
695 |
703 |
711 |
||
|
546 |
719 |
727 |
735 |
743 |
751 |
759 |
767 |
775 |
783 |
791 |
||
|
547 |
799 |
807 |
815 |
823 |
■630 |
838 |
846 |
854 |
862 |
870 |
||
|
548 |
87S |
886 |
894 |
902 |
910 |
918 |
926 |
933 |
941 |
949 |
||
|
549 |
957 |
965 |
973 |
981 |
989 |
997 |
*005 |
*013 |
*020 |
*028 |
||
|
650 |
74, 036 |
044 |
052 |
060 |
068 |
076 |
084 |
092 |
099 |
107 |
||
|
K. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
, 8 |
9 |
P.P. |
LOGARITHMS OF IvTUMBBRS.
243
Table XXXY. — Containing logarithms of numbers from 1 to ll,00t [Extracted from Gauss' Logarithmic and Trigonometric Tables."
|
N. |
L. 0. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
|
|
550 |
74 036 |
044 |
052 |
060 |
068 |
076 |
084 |
092 |
099 |
107 |
||
|
551 |
115 |
123 |
131 |
139 |
147 |
155 |
162 |
170 |
178 |
186 |
||
|
552 |
194 |
202 |
210 |
218 |
225 |
233 |
241 |
249 |
257 |
265 |
||
|
553 |
273 |
280 |
288 |
296 |
304 |
312 |
320 |
327 |
335 |
343 |
||
|
554 |
351 |
359 |
367 |
374 |
382 |
390 |
398 |
406 |
414 |
421 |
||
|
555 |
429 |
437 |
445 |
453 |
461 |
468 |
476 |
484 |
492 |
500 |
||
|
556 |
507 |
515 |
523 |
531 |
539 |
547 |
554 |
562 |
570 |
578 |
||
|
557 |
586 |
593 |
601 |
609 |
617 |
624 |
632 |
640 |
648 |
656 |
||
|
553 |
663 |
671 |
679 |
687 |
695 |
702 |
710 |
718 |
726 |
733 |
||
|
559 |
741 |
749 |
757 |
764 |
772 |
780 |
788 |
796 |
803 |
811 |
||
|
560 |
819 |
827 |
834 |
842 |
850 |
858 |
865 |
873 |
881 |
889 |
||
|
561 |
896 |
904 |
912 |
920 |
927 |
935 |
943 |
950 |
958 |
966 |
R |
|
|
562 |
974 |
981 |
989 |
997 |
,005 |
^012 |
,020 |
.028 |
,035 |
.043 |
1 |
0,8 |
|
563 |
75 051 |
059 |
066 |
074 |
082 |
089 |
097 |
105 |
113 |
120 |
2 |
1,6 |
|
564 |
128 |
136 |
143 |
151 |
159 |
166 |
174 |
■ 182 |
189 |
197 |
3 |
2,4 3,2 |
|
565 |
205 |
213 |
220 |
228 |
230 |
243 |
261 |
259 |
266 |
274 |
4 |
|
|
566 |
282 |
289 |
297 |
305 |
312 |
320 |
328 |
335 |
343 |
351 |
5 |
4,0 |
|
567 |
358 |
366 |
374 |
381 |
389 |
397 |
404 |
412 |
420 |
427 |
6 |
4,8 |
|
568 |
435 |
442 |
450 |
458 |
465 |
473 |
481 |
488 |
496 |
504 |
7 |
5,6 |
|
569 |
511 |
519 |
526 |
534 |
542 |
549 |
557 |
565 |
572 |
580 |
8 |
6,4 |
|
570 |
587 |
595 |
603 |
610 |
618 |
626 |
633 |
641 |
648 |
656 |
9 |
7,2 |
|
571 |
664 |
671 |
679 |
686 |
694 |
702 |
709 |
717 |
724 |
732 |
||
|
572 |
740 |
747 |
755 |
762 |
770 |
778 |
785 |
793 |
800 |
808 |
||
|
563 |
815 |
823 |
831 |
838 |
846 |
853 |
861 |
868 |
876 |
884 |
||
|
574 |
891 |
899 |
906 |
914 |
921 |
929 |
937 |
944 |
952 |
959 |
||
|
575 |
967 |
974 |
982 |
989 |
997 |
,005 |
,012 |
.020 |
.027 |
,035 |
||
|
576 |
76 042 |
050 |
057 |
065 |
072 |
080 |
087 |
095 |
103 |
110 |
||
|
577 |
118 |
125 |
133 |
140 |
148 |
155 |
163 |
170 |
178 |
185 |
||
|
578 |
193 |
200 |
208 |
215 |
223 |
230 |
238 |
245 |
253 |
260 |
||
|
579 |
268 |
275 |
283 |
290 |
298 |
305 |
313 |
320 |
328 |
335 |
||
|
580 |
343 |
350 |
358 |
365 |
373 |
380 |
388 |
395 |
403 |
410 |
7 1 0,7 |
|
|
581 |
418 |
425 |
433 |
440 |
448 |
455 |
462 |
470 |
477 |
485 |
||
|
582 |
492 |
500 |
507 |
515 |
522 |
530 |
537 |
545 |
552 |
559 |
2 |
1,4 |
|
683 |
567 |
574 |
582 |
589 |
597 |
604 |
612 |
619 |
626 |
634 |
3 |
2,1 |
|
584 |
641 |
649 |
656 |
664 |
671 |
678 |
686 |
693 |
701 |
708 |
4 |
2,8 |
|
585 |
716 |
723 |
730 |
738 |
745 |
753 |
760 |
768 |
775 |
782 |
5 |
3,5 |
|
586 |
790 |
797 |
805 |
812 |
819 |
827 |
834 |
842 |
849 |
856 |
6 |
4,2 |
|
587 |
864 |
871 |
879 |
886 |
893 |
901 |
908 |
916 |
923 |
930 |
7 |
4,9 |
|
588 |
938 |
945 |
953 |
960 |
967 |
975 |
982 |
989 |
997 |
,004 |
8 |
5,6 |
|
589 |
77 012 |
019 |
026 |
034 |
041 |
048 |
056 |
063 |
070 |
078 |
9 |
6,3 |
|
690 |
086 |
093 |
100 |
107 |
115 |
122 |
129 |
137 |
144 |
151 |
||
|
591 |
159 |
166 |
173 |
181 |
188 |
195 |
203 |
210 |
217 |
225 |
||
|
592 |
232 |
240 |
247 |
254 |
262 |
269 |
276 |
283 |
291 |
298 |
||
|
593 |
305 |
313 |
320 |
327 |
335 |
342 |
349 |
357 |
364 |
371 |
||
|
594 |
379 |
386 |
393 |
401 |
408 |
415 |
422 |
430 |
437 |
444 |
||
|
595 |
452 |
459 |
466 |
474 |
481 |
488 |
495 |
503 |
510 |
517 |
||
|
596 |
525 |
532 |
539 |
646 |
554 |
561 |
568 |
576 |
583 |
590 |
||
|
597 |
597 |
605 |
612 |
619 |
627 |
634 |
641 |
648 |
656 |
663 |
||
|
598 |
670 |
677 |
685 |
692 |
699 |
706 |
714 |
721 |
728 |
735 |
||
|
599 |
743 |
750 |
757 |
764 |
772 |
779 |
786 |
793 |
801 |
808 |
||
|
600 |
815 |
822 |
830 |
837 |
844 |
851 |
859 |
866 |
873 |
880 |
||
|
S. |
L. 0. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
244
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Coutinned. [Extracted from G.iuss' Log.arithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
|
|
600 |
77 815 |
822 |
830 |
837 |
844 |
851 |
859 |
866 |
873 |
880 |
||
|
601 |
887 |
895 |
902 |
909 |
916 |
924 |
931 |
938 |
945 |
952 |
||
|
602 |
960 |
967 |
974 |
981 |
988 |
^96 |
,003 |
,010 |
,017 |
,025 |
||
|
603 |
78 032 |
039 |
046 |
053 |
061 |
068 |
075 |
082 |
089 |
097 |
||
|
604 |
104 |
111 |
118 |
125 |
132 |
140 |
147 |
154 |
161 |
168 |
||
|
605 |
176 |
183 |
190 |
197 |
204 |
211 |
219 |
226 |
233 |
240 |
||
|
606 |
247 |
254 |
262 |
269 |
276 |
283 |
290 |
297 |
305 |
312 |
8 |
|
|
607 |
319 |
326 |
333 |
340 |
347 |
355 |
362 |
369 |
376 |
383 |
||
|
608 |
390 |
398 |
405 |
412 |
419 |
426 |
433 |
440 |
447 |
455 |
1 |
0,8 |
|
6oa |
462 |
469 |
470 |
483 |
490 |
497 |
504 |
512 |
519 |
526 |
2 |
1,6 |
|
610 |
533 |
540 |
547 |
554 |
561 |
669 |
576 |
583 |
590 |
597 |
3 4 |
2,4 3,2 |
|
611 |
604 |
611 |
618 |
625 |
633 |
640 |
647 |
654 |
661 |
668 |
6 |
4,0 |
|
612 |
675 |
682 |
689 |
696 |
704 |
711 |
718 |
725 |
732 |
739 |
6 |
4,8 |
|
era |
746 |
753 |
760 |
767 |
774 |
781 |
789 |
796 |
803 |
810 |
7 |
5,6 |
|
614 |
817 |
824 |
831 |
888 |
845 |
852 |
859 |
866 |
873 |
880 |
8 |
6,4 |
|
615 |
888 |
895 |
902 |
909 |
916 |
923 |
930 |
937 |
944 |
951 |
9 |
7,2 |
|
616 |
958 |
965 |
072 |
979 |
986 |
993 |
,000 |
,007 |
,014 |
,021 |
||
|
617 |
79 029 |
036 |
043 |
050 |
057 |
064 |
071 |
078 |
085 |
092 |
||
|
618 |
099 |
106 |
113 |
120 |
127 |
134 |
141 |
148 |
155 |
163 |
||
|
6in |
169 |
176 |
183 |
190 |
197 |
204 |
211 |
218 |
225 |
232 |
||
|
620 |
239 |
246 |
253 |
260 |
267 |
274 |
281 |
288 |
295 |
302 |
||
|
621 |
309 |
316 |
323 |
330 |
337 |
344 |
351 |
358 |
360 |
372 |
7 |
|
|
822 |
379 |
386 |
393 |
4U0 |
407 |
414 |
421 |
428 |
435 |
442 |
1 |
0,7 |
|
623 |
449 |
456 |
463 |
470 |
477 |
484 |
491 |
498 |
505 |
511 |
2 |
l,* |
|
624 |
518 |
525 |
532 |
539 |
546 |
553 |
560 |
567 |
574 |
581 |
3 |
2,1 |
|
625 |
588 |
595 |
602 |
609 |
616 |
623 |
630 |
637 |
644 |
650 |
4 |
2,8 |
|
626 |
657 |
664 |
. 671 |
678 |
685 |
692 |
699 |
706 |
713 |
720 |
5 |
3,5 |
|
627 |
727 |
734 |
741 |
748 |
754 |
761 |
768 |
775 |
782 |
780 |
6 |
4,2 |
|
628 |
796 |
803 |
810 |
817 |
824 |
831 |
837 |
844 |
851 |
858 |
7 |
4,9 |
|
629 |
865 |
872 |
879 |
886 |
893 |
900 |
906 |
913 |
920 |
927 |
8 |
6'6 |
|
030 |
934 |
941 |
948 |
955 |
962 |
969 |
976 |
982 |
989 |
996 |
9 |
6,3 |
|
631 |
80 003 |
010 |
017 |
024 |
030 |
037 |
044 |
051 |
058 |
065 |
||
|
632 |
072 |
079 |
085 |
092 |
099 |
106 |
113 |
120 |
127 |
134 |
||
|
633 |
140 |
147 |
154 |
161 |
168 |
175 |
182 |
188 |
195 |
202 |
||
|
634 |
209 |
216 |
223 |
229 |
236 |
243 |
250 |
257 |
264 |
271 |
6 |
|
|
635 |
277 |
284 |
291 |
298 |
305 |
312 |
318 |
325 |
332 |
339 |
||
|
636 |
346 |
353 |
359 |
366 |
373 |
380 |
387 |
393 |
400 |
407 |
1 |
0,6 |
|
637 |
414 |
421 |
428 |
434 |
441 |
448 |
455 |
462 |
468 |
475 |
2 |
1,2 |
|
638 |
482 |
489 |
496 |
502 |
509 |
516 |
623 |
530 |
536 |
543 |
3 |
1,8 |
|
639 |
550 |
557 |
564 |
570 |
577 |
584 |
591 |
698 |
604 |
611 |
4 |
2,4 |
|
640 |
618 |
625 |
632 |
638 |
645 |
652 |
659 |
665 |
672 |
679 |
5 6 |
3,0 3,6 |
|
641 |
686 |
693 |
699 |
706 |
713 |
720 |
726 |
733 |
740 |
747 |
7 |
4,2 |
|
642 |
754 |
760 |
767 |
774 |
781 |
787 |
794 |
801 |
808 |
814 |
8 |
4,8 |
|
643 |
821 |
828 |
835 |
841 |
848 |
855 |
862 |
868 |
875 |
882 |
9 |
5,4 |
|
644 |
889 |
895 |
902 |
909 |
916 |
■922 |
929 |
936 |
943 |
949 |
||
|
645 |
956 |
903 |
069 |
976 |
983 |
990 |
996 |
,003 |
,010 |
,017 |
||
|
646 |
81 023 |
030 |
037 |
043 |
050 |
057 |
064 |
070 |
077 |
084 |
||
|
647 |
090 |
097 |
104 |
111 |
117 |
124 |
131 |
137 |
144 |
151 |
||
|
648 |
138 |
164 |
171 |
178 |
184 |
191 |
198 |
204 |
211 |
218 |
||
|
649 |
224 |
231 |
238 |
245 |
251 |
258 |
265 |
271 |
278 |
285 |
||
|
650 |
291 |
298 |
305 |
311 |
318 |
325 |
331 |
338 |
345 |
351 |
||
|
N. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
LOGARITHMS OF NUMBEES.
245
Table XXXY.— Containing logarithms of niimbcrx from 1 to 11,000— Continued. [Extracted from Gauss' Logaritlimic and Trigouometric Tables.]
|
8 |
9 |
|
315 |
351 |
|
411 |
418 |
|
4V8 |
485 |
|
bU |
551 |
|
611 |
617 |
|
till |
681 |
|
743 |
750 |
|
809 |
816 |
|
8Vb |
883 |
|
941 |
948 |
|
,007 |
,014 |
|
073 |
079 |
|
138 |
145 |
|
204 |
210 |
|
269 |
276 |
|
334 400 |
341 inR |
246
A MANUAL OF TOPOGEAPHIC.METHODS.
Table XXXV. — Containing logarithms of numbers from 1 to 11,000 — Contmued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 . |
6 |
7 |
8 |
9 |
P. P. |
|
|
•sm |
84 510 |
516 |
522 |
528 |
535 |
541 |
547 |
553 |
559 |
566 |
||
|
701 |
572 |
578 |
584 |
590 |
597 |
603 |
609 |
615 |
621 |
628 |
||
|
702 |
634 |
640 |
646 |
052 |
658 |
665 |
671 |
677 |
683 |
689 |
||
|
703 |
696 |
702 |
708 |
714 |
720 |
726 |
733 |
739 |
745 |
751 |
||
|
704 |
757 |
763 |
770 |
776 |
782 |
788 |
794 |
800 |
807 |
813 |
f ' |
|
|
705 |
819 |
825 |
831 |
837 |
844 |
850 |
856 |
862 |
868 |
874 |
1 |
|
|
706 |
■ 880 |
887 |
893 |
899 |
905 |
911 |
917 |
924 |
930 |
936 |
1 |
0,7 |
|
707 |
942 |
948 |
934 |
960 |
967 |
973 |
979 |
985 |
991 |
997 |
2 |
1,4 |
|
708 |
85 003 |
009 |
016 |
022 |
028 |
034 |
040 |
046 |
052 |
058 |
3 |
2,1 |
|
709 |
065 |
071 |
077 |
083 |
089 |
095 |
101 |
107 |
114 |
120 |
4 |
2,8 |
|
710 |
126 |
132 |
138 |
144 |
150 |
156 |
163 |
169 |
175 |
181 |
5 6 |
3,5 4,2 |
|
711 |
187 |
193 |
199 |
205 |
211 |
217 |
224 |
230 |
236 |
242 |
7 |
4,9 |
|
712 |
248 |
254 |
260 |
266 |
272 |
278 |
285 |
291 |
297 |
303 |
8 |
5,6 |
|
713 |
309 |
315 |
321 |
327 |
333 |
339 |
345 |
352 |
358 |
364 |
9 |
6,3 |
|
714 |
370 |
376 |
382 . |
388 |
394 |
400 |
406 |
412 |
418 |
425 |
||
|
715- |
431 |
437 |
443 |
449 |
455 |
461 |
467 |
473 |
479 |
485 |
||
|
716 |
491 |
497 |
503 |
509 |
516 |
522 |
528 |
534 |
540 |
546 |
||
|
717 |
552 |
558 |
564 |
570 |
576 |
582 |
588 |
594 |
600 |
606 |
||
|
718 |
612 |
618 |
625 |
631 |
637 |
643 |
649 |
655 |
601 |
667 |
||
|
719 |
673 |
679 |
685 |
691 |
697 |
703 |
709 |
715 |
721 |
727 |
||
|
720 |
733 |
739 |
745 |
751 |
757 |
763 |
769 |
775 |
781 |
788 |
e |
|
|
721 |
794 |
800 |
806 |
812 |
818 |
824 |
830 |
836 |
842 |
848 |
1 |
0,6 |
|
722 |
854 |
860 |
866 |
872 |
878 |
884 |
890 |
896 |
902 |
908 |
2 |
1,2 |
|
723 |
914 |
920 |
926 |
932 |
938 |
944 |
950 |
956 |
962 |
968 |
3 |
1,8 |
|
724 |
974 |
980 |
986 |
992 |
998 |
,004 |
,010 |
,.016 |
,022 |
,028 |
4 |
2,4 |
|
725 |
86 034 |
040 |
046 |
052 |
058 |
064 |
070 |
076 |
082 |
088 |
5 |
3,0 |
|
726 |
094 |
100 |
106 |
112 |
118 |
124 |
130 |
136 |
141 |
147 |
6 |
3,6 |
|
727 |
153 |
159 |
165 |
171 |
177 |
183 |
189 |
195 |
201 |
207 |
7 |
4,2 |
|
728 |
213 |
219 |
225 |
231 |
237 |
243 |
249 |
255 |
261 |
267 |
8 |
4,8 |
|
729 |
273 |
279 |
285 |
291 |
297 |
303 |
308 |
314 |
320 |
326 |
9 |
5,4 |
|
730 |
332 |
338 |
344 |
350 |
356 |
362 |
368 |
374 |
380 |
386 |
||
|
731 |
392 |
398 |
404 |
410 |
415 |
421 |
427 |
433 |
439 |
445 |
||
|
732 |
451 |
457 |
463 |
469 |
475 |
481 |
487 |
493 |
499 |
604 |
||
|
733 |
510 |
516 |
522 |
528 |
534 |
540 |
546 |
552 |
658 |
664 |
||
|
734 |
570 |
576 |
581 |
587 |
593 |
599 |
605 |
611 |
617 |
622 |
||
|
735 |
629 |
635 |
641 |
646 |
652 |
658 |
664 |
670 |
676 |
682 |
||
|
736 |
688 |
694 |
700 |
705 |
711 |
717 |
723 |
729 |
735 |
741 |
5 |
|
|
737 |
747 |
753 |
759 |
764 |
770 |
776 |
782 |
788 |
794 |
800 |
||
|
738 |
806 |
812 |
817 |
82a |
829 |
835 |
841 |
847 |
853 |
859 |
1 |
0,5 |
|
739 |
864 |
870 |
876 |
882 |
888 |
894 |
900 |
906 |
911 |
917 |
2 |
1,0 |
|
740 |
923 |
929 |
935 |
941 |
947 |
953 |
958 |
964 |
970 |
976 |
3 4 |
1,5 2,0 |
|
741 |
982 |
988 |
994 |
999 |
,,005 |
,011 |
»017 |
,023 |
,029 |
,035 |
5 |
2,5 |
|
742 |
87 040 |
046 |
052 |
058 |
064 |
070 |
075 |
081 |
087 |
093 |
6 |
3,0 |
|
743 |
099 |
105 |
111 |
116 |
122 |
128 |
134 |
140 |
146 |
151 |
7 |
3,5 |
|
744 |
157 |
163 |
169 |
175 |
181 |
186 |
192 |
198 |
204 |
210 |
8 |
4,0 |
|
745 |
216 |
221 |
227 |
233 |
239 |
245 |
251 |
256 |
262 |
268 |
9 |
4,5 |
|
746 |
274 |
280 |
286 |
291 |
297 |
303 |
309 |
315 |
320 |
326 |
||
|
747 |
332 |
338 |
344 |
349 |
355 |
361 |
367 |
373 |
379 |
384 |
||
|
748 |
390 |
396 |
402 |
408 |
413 |
419 |
425 |
431 |
437 |
442 |
||
|
749 |
448 |
454 |
460 |
466 |
471 |
477 |
483 |
489 |
495 |
500 |
||
|
750 |
506 |
512 |
518 |
523 |
529 |
535 |
541 |
547 |
552 |
558 |
||
|
If. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P. P. |
LOGAEITHMS OF NUMBEES.
247
Table XXXV. — Containing logarithms of nunibers from 1 to llfiOO — Continued.
[Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
|
|
750 |
87 506 |
512 |
518 |
523 |
529 |
535 |
541 |
547 |
552 |
558 |
||
|
751 |
564 |
570 |
576 |
581 |
587 |
593 |
599 |
604 |
610 |
616 |
||
|
752 |
622 |
628 |
633 |
639 |
645 |
651 |
656 |
662 |
668 |
674 |
||
|
753 |
679 |
685 |
691 |
697 |
703 |
708 |
714 |
720 |
726 |
731 |
||
|
754 |
737 |
743 |
749 |
754 |
760 |
766 |
772 |
777 |
783 |
789 |
||
|
755 |
795 |
800 |
806 |
812 |
818 |
823 |
829 |
835 |
841 |
846 |
^ |
|
|
756 |
852 |
858 |
864 |
869 |
875 |
881 |
887 |
892 |
898 |
904 |
||
|
757 |
910 |
915 |
921 |
927 |
933 |
938 |
944 |
950 |
955 |
961 |
||
|
758 |
967 |
973 |
978 |
984 |
990 |
996 |
,001 |
,007 |
,013 |
,018 |
||
|
759 |
88 024 |
030 |
036 |
041 |
047 |
053 |
058 |
064 |
070 |
076 |
||
|
760 |
081 |
087 |
093 |
098 |
104 |
110 |
116 |
121 |
127 |
133 |
||
|
761 |
138 |
144 |
150 |
156 |
161 |
167 |
173 |
178 |
184 |
190 |
6 |
|
|
762 |
195 |
201 |
207 |
213 |
218 |
224 |
230 |
235 |
241 |
247 |
1 |
0,6 |
|
763 |
252 |
258 |
264 |
270 |
275 |
281 |
287 |
292 |
298 |
304 |
2 |
1,2 |
|
764 |
309 |
315 |
321 |
326 |
332 |
338 |
343 |
349 |
355 |
360 |
3 |
1,8 |
|
765 |
366 |
372 |
377 |
383 |
389 |
395 |
400 |
406 |
412 |
417 |
4 |
2,4 |
|
766 |
423 |
429 |
434 |
440 |
446 |
451 |
457 |
463 |
468 |
474 |
5 |
3,0 |
|
767 |
480 |
485 |
491 |
497 |
502 |
508 |
513 |
619 |
525 |
530 |
6 |
3,6 |
|
768 |
536 |
542 |
547 |
553 |
659 |
564 |
570 |
676 |
581 |
537 |
7 |
4,2 |
|
769 |
593 |
598 |
604 |
610 |
615 |
621 |
627 |
632 |
638 |
643 |
8 |
4,8 |
|
770 |
«e49 |
655 |
660 |
666 |
672 |
677 |
■ 683 |
689 |
694 |
700 |
9 |
6'4 |
|
771 |
705 |
711 |
717 |
722 |
728 |
734 |
739 |
745 |
750 |
756 |
||
|
772 |
762 |
767 |
773 |
779 |
784 |
790 |
795 |
801 |
807 |
812 |
||
|
773 |
818 |
824 |
829 |
835 |
840 |
846 |
852 |
857 |
863 |
868 |
||
|
774 |
874 |
880 |
885 |
891 |
897 |
902 |
908 |
913 |
919 |
925 |
||
|
775 |
930 |
936 |
941 |
947 |
953 |
958 |
964 |
969 |
975 |
981 |
||
|
776 |
986 |
992 |
997 |
,003 |
,009 |
,014 |
,020 |
,025 |
,031 |
,037 |
||
|
777 |
89 042 |
048 |
053 |
059 |
064 |
070 |
076 |
081 |
087 |
092 |
||
|
778 |
098 |
104 |
109 |
115 |
120 |
126 |
131 |
137 |
143 |
143 |
||
|
779 |
154 |
159 |
165 |
170 |
176 |
182 |
187 |
193 |
198 |
204 |
||
|
780 |
209 |
215 |
221 |
226 |
232 |
237 |
243 |
248 |
254 |
260 |
||
|
781 |
265 |
271 |
276 |
282 |
287' |
293 |
298 |
304 |
310 |
315 |
5 |
|
|
782 |
321 |
326 |
332 |
337 |
343 |
348 |
354 |
360 |
365 |
371 |
1 |
0,5 |
|
783 |
376 |
382 |
387 |
393 |
398 |
404 |
409 |
415 |
421 |
426 |
2 |
I'O |
|
784 |
432 |
437 |
443 |
448 |
454 |
459 |
465 |
470 |
476 |
481 |
3 |
1,5 |
|
785 |
487 |
492 |
498 |
504 |
509 |
515 |
520 |
626 |
531 |
537 |
4 |
2,0 |
|
786 |
542 |
648 |
553 |
559 |
564 |
570 |
575 |
. 581 |
586 |
592 |
5 |
2,5 |
|
787 |
597 |
603 |
609 |
614 |
620 |
625 |
631 |
638 |
642 |
647 |
6 |
3,0 |
|
788 |
653 |
658 |
664 |
669 |
675 |
680 |
686 |
691 |
697 |
702 |
7 |
3,5 |
|
789 |
708 |
713 |
719 |
724 |
730 |
735 |
741 |
746 |
752 |
757 |
8 |
4,0 |
|
790 |
763 |
768 |
774 |
779 |
785 |
790 |
796 |
801 |
807 |
812 |
9 |
4,5 |
|
791 |
818 |
823 |
829 |
834 |
840 |
845 |
851 |
856 |
862 |
867 |
||
|
792 |
873 |
878 |
883 |
889 |
894 |
900 |
905 |
911 |
916 |
922 |
||
|
793 |
927 |
933 |
938 |
944 |
949 |
955 |
960 |
966 |
971 |
977 |
||
|
794 |
982 |
988 |
993 |
998 |
,004 |
,009 |
,015 |
,020 |
«026 |
,031 |
||
|
795 |
90 037 |
042 |
048 |
053 |
059 |
064 |
069 |
075 |
080 |
086 |
||
|
796 |
091 |
097 |
102 |
108 |
113 |
119 |
124 |
129 |
135 |
140 |
||
|
797 |
146 |
151 |
157 |
162 |
168 |
173 |
179 |
184 |
189 |
195 |
||
|
798 |
200 |
206 |
211 |
217 |
222 |
227 |
233 |
238 |
244 |
249 |
||
|
799 |
255 |
260 |
266 |
271 |
276 |
282 |
287 |
293 |
298 |
304 |
||
|
800 |
309 |
314 |
320 |
325 |
331 |
336 |
342 |
347 |
352 |
358 |
||
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
248
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logarithms of numiers from 1 to il,000— Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 1 1 |
'■•,:'. |
4 |
_ |
6 |
' |
8 |
9 |
r. P. |
|||
|
800 |
90 309 |
314 |
320 |
325 |
331 |
336 |
342 |
347 |
352 |
358 |
||
|
801 |
" 363 |
369 |
374 |
380 |
385 |
390 |
396 |
401 |
407 |
412 |
||
|
802 |
417 |
423 |
428 |
434 |
439 |
445 |
450 |
455 |
461 |
466 |
||
|
803 |
472 |
477 |
482 |
488 |
493 |
499 |
504 |
509 |
515 |
620 |
||
|
804 |
526 |
531 |
536 |
542 |
547 |
553 |
558 |
563 |
569 |
574 |
||
|
805 |
580 |
585 |
590 |
596 |
601 |
607 |
612 |
617 |
623 |
628 |
||
|
806 |
634 |
639 |
644 |
650 |
655 |
660 |
666 |
671 |
677 |
682 |
||
|
807 |
* 687 |
693 |
698 |
703 |
709 |
714 |
720 |
725 |
730 |
736 |
||
|
808 |
741 |
747 |
752 |
757 |
763 |
768 |
773 |
779 |
784 |
789 |
||
|
809 |
795 |
800 |
806 |
811 |
816 |
822 |
827 |
832 |
838 |
843 |
||
|
810 |
849 |
854 |
859 |
865 |
870 |
875 |
881 |
886 |
891 |
897 |
||
|
811 |
902 |
907 |
913 |
918 |
924 |
929 |
934 |
940 |
945 |
950 |
6 |
|
|
813 |
956 |
961 |
966 |
972 |
977 |
982 |
988 |
993 |
998 |
,004 |
1 |
0,6 |
|
813 |
91 009 |
014 |
020 |
025 |
030 |
036 |
041 |
046 |
052 |
057 |
2 |
1,2 |
|
814. |
062 |
068 |
073.,- |
078 |
084 |
089 |
094 |
100 |
105 |
110 |
3 |
1,8 |
|
815 |
116 |
121 |
126 |
132 |
137 |
142 |
148 |
153 |
158 |
164 |
4 |
2,4 |
|
816 |
169 |
174 |
180 |
185 |
190 |
196 |
201 |
206 |
212 |
217 |
5 |
3,0 |
|
817 |
222 |
228 |
233 |
238 |
243 |
249 |
254 |
259 |
265 |
270 |
6 |
3,6 |
|
818 |
275 |
281 |
286 |
291 |
297 |
302 |
307 |
312 |
318 |
323 |
7 |
4,2 |
|
819 |
328 |
334 |
339 |
344 |
350 |
355- |
360 |
365 |
371 |
376 |
8 |
4,8 |
|
820 |
381 |
387 |
392 |
397 |
403 |
408 |
413 |
418 |
424 |
429 |
9 |
5,4 |
|
821 |
434 |
440 |
445 |
450 |
455 |
461 |
466 |
471 |
477 |
482 |
» |
|
|
822 |
487 |
492 |
498 |
503 |
508 |
514 |
519 |
624 |
529 |
535 |
||
|
823 |
540 |
545 |
551 |
556 |
561 |
S66 |
572 |
577 |
582 |
587 |
||
|
824 |
593 |
598 |
603 |
609 |
614 |
619 |
624 |
030 |
635 |
640 |
||
|
825 |
645 |
651 |
656 |
661 |
666 |
672 |
677 |
682 |
687 |
693 |
||
|
826 |
698 |
703 |
709 |
714 |
719 |
724 |
730 |
735 |
740 |
745 |
||
|
827 |
751 |
756 |
761 |
766 |
772 |
777 |
782 |
787 |
793 |
798 |
||
|
828 |
803 |
808 |
814 |
819 |
824 |
829 |
934 |
840 |
845 |
850 |
||
|
829 |
855 |
861 |
866 |
871 |
876 |
882 |
887 |
892 |
897 |
903 |
||
|
sso |
908 |
913 |
918 |
924 |
929 |
934 |
939 |
944 |
950 |
955 |
||
|
831 |
960 |
965 |
971 |
976 |
981 |
986 |
991 |
997 |
,002 |
,007 |
6 |
|
|
832 |
92 012 |
018 |
023 |
028 |
033 |
038 |
044 |
049 |
054 |
059 |
1 |
0,5 |
|
833 |
065 |
070 |
075 |
080 |
085 |
091 |
096 |
101 |
106 |
111 |
2 |
1,0 |
|
834 |
117 |
122 |
127 |
132 |
137 |
143 |
148 |
153 |
158 |
163 |
3 |
1,5 |
|
835 |
169 |
174 |
179 |
184 |
189 |
195 |
200 |
205 |
210 |
215 |
4 |
2,0 |
|
83<> |
221 |
226 |
231 |
236 |
241 |
247 |
252 |
257 |
262 |
267 |
5 |
2,5 |
|
837 |
273 |
278 |
283 |
288 |
293 |
298 |
304 |
309 |
314 |
319 |
6 |
3,0 |
|
838 |
324 |
330 |
835 |
340 |
345 |
350 |
355 |
361 |
366 |
371 |
7 |
3,5 |
|
839 |
376 |
381 |
387 |
392 |
397 |
402 |
407 |
412 |
418 |
423 |
8 |
4,0 |
|
840 |
428 |
433 |
438 |
443 |
449 |
454 |
459 |
464 |
469 |
474 |
9 |
4,5 |
|
841 |
480 |
485 |
490 |
495 |
500 |
505 |
511 |
516 |
521 |
526 |
||
|
842 |
531 |
536 |
542 |
547 |
552 |
557 |
562 |
567 |
572 |
578 |
||
|
843 |
583 |
588 |
593 |
598 |
603 |
609 |
614 |
619 |
624 |
629 |
||
|
844 |
634 |
639 |
145 |
650 |
655 |
660 |
665 |
670 |
675 |
681 |
||
|
845 |
686 |
691 |
696 |
701 |
706 |
711 |
716 |
722 |
727 |
782 |
||
|
846 |
737 |
742 |
747 |
752 |
758 |
763 |
768 |
773 |
778 |
783 |
||
|
847 |
788 |
793 |
799 |
804 |
809 |
814 |
819 |
824 |
829 |
834 |
||
|
848 |
840 |
845 |
850 |
855 |
860 |
865 |
870 |
875 |
881 |
886 |
||
|
849 |
891 |
896 |
901 |
906 |
911 |
916 |
921 |
927 |
932 |
937 |
||
|
850 |
942 |
947 |
952 |
957 |
962 |
967 |
973 |
978 |
983 |
988 |
||
|
IJ". |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P.. |
LOGAEITHMS OF NUMBEES.
249
Table XXXV. — Containing logarithms of numbers from 1 to lljOOO — Continued. [Extracted from Gauss' Logarithmic and. Trigonometric Tables.]
|
N. |
L. 0 |
1 |
3 |
4 |
5 |
6 |
' ! ' |
9 |
I |
.P. |
||
|
850 |
92 942 |
947 |
952 |
957 |
962 |
967 |
973 |
978 |
983 |
988 |
||
|
851 |
993 |
998 |
,003 |
,008 |
,013 |
.018 |
,024 |
,029 |
,034 |
,039 |
||
|
852 |
93 044 |
049 |
054 |
059 |
064 |
069 |
075 |
080 |
085 |
090 |
||
|
853 |
095 |
100 |
105 |
110 |
115 |
120 |
125 |
131 |
136 |
141 |
||
|
854 |
146 |
151 |
156 |
161 |
166 |
171 |
176 |
181 |
186 |
192 |
||
|
855 |
197 |
202 |
207 |
212 |
217 |
222 |
227 |
232 |
237 |
242 |
||
|
856 |
247 |
252 |
258 |
263 |
268 |
273 |
278 |
283 |
288 |
293 |
||
|
857 |
298 |
303 |
308 |
313 |
318 |
323 |
328 |
334 |
339 |
344 |
6 |
|
|
858 |
349 |
. 354 |
359 |
364 |
369 |
374 |
379 |
384 |
389 |
394 |
1 |
0,6 |
|
859 |
399 |
404 |
409 |
414 |
420 |
425 |
430 |
435 |
440 |
445 |
2 |
1,2 |
|
8G0 |
450 |
455 |
460 |
465 |
470 |
475 |
480 |
485 |
490 |
495 |
3 4 |
1,8 2,4 |
|
861 |
500 |
505 |
510 |
515 |
520 |
526 |
531 |
536 |
541 |
546 |
5 |
3,0 |
|
862 |
551 |
556 |
561 |
566 |
571 |
576 |
581 |
586 |
591 |
596 |
6 |
3,6 |
|
863 |
601 |
606 |
611 |
616 |
621 |
626 |
631 |
636 |
641 |
646 |
7 |
4,2 |
|
864 |
651 |
656 |
661 |
666 |
671 |
676 |
682 |
687 |
092 |
697 |
8 |
4,8 |
|
865 |
702 |
707 |
713 |
717 |
722 |
727 |
732 |
737 |
742 |
747 |
9 |
5,4 |
|
866 |
752 |
757 |
762 |
767 |
772 |
777 |
782 |
787 |
792 |
797 |
||
|
867 |
802 |
807 |
812 |
817 |
822 |
827 |
832 |
837 |
842 |
847 |
||
|
868 |
852 |
857 |
862 |
867 |
872 |
877 |
882 |
887 |
892 |
897 |
||
|
869- |
902 |
907 |
912 |
917 |
922 . |
927 |
932 |
937 |
942 |
947 |
||
|
870 |
952 |
957 |
962 |
967 |
972 |
977 |
982 |
987 |
992 |
997 |
||
|
871 |
94 002 |
007 |
012 |
017 |
022 |
027 |
032 |
037 |
042 |
047 |
5 |
|
|
872 |
052 |
057 |
062 |
067 |
072 |
077 |
082 |
086 |
091 |
096 |
1 |
0,5 |
|
873 |
101 |
106 |
111 |
116 |
121 |
126 |
131 |
136 |
141 |
146 |
2 |
1,0 |
|
874 |
151 |
156 |
161 |
166 |
171 |
176 |
181 |
186 |
191 |
196 |
3 |
1,5 |
|
875 |
201 |
206 |
211 |
216 |
221 |
226 |
231 |
236 |
240 |
245 |
4 |
2,0 |
|
876 |
250 |
255 |
260 |
265 |
270 |
275 |
280 |
285 |
290 |
295 |
5 |
2,5 |
|
877 |
300 |
305 |
310 |
315 |
320 |
325 |
330 |
335 |
340 |
345 |
6 |
3,0 |
|
878 |
349 |
354 |
359 |
364 |
369 |
374 |
379 |
384 |
389 |
394 |
7 |
3,5 |
|
879 |
399 |
404 |
409 |
414 |
419 |
424 |
429 |
433 |
438 |
443 |
8 |
4,0 |
|
SSO |
448 |
453 |
458 |
463 |
468 |
473 |
478 |
483 |
488 |
493 |
9 |
4,5 |
|
881 |
498 |
503 |
507 |
512 |
517 |
522 |
527 |
532 |
537 |
542 |
||
|
882 |
547 |
552 |
557 |
562 |
567 |
571 |
576 |
581 |
586 |
591 |
||
|
883 |
596 |
601 |
606 |
611 |
616 |
621 |
626 |
630 |
635 |
640 |
||
|
884 |
645 |
650 |
655 |
660 |
665 |
670 |
675 |
680 |
685 |
689 |
||
|
885 |
694 |
699 |
704 |
709 |
714 |
719 |
724 |
729 |
734 |
738 |
||
|
886 |
743 |
748 |
753 |
758 |
763 |
768 |
773 |
778 |
783 |
787 |
4 |
|
|
887 |
792 |
797 |
802 |
807 |
812 |
817 |
822 |
827 |
832 |
836 |
1 |
0,4 |
|
888 |
841 |
846 |
851 |
856 |
861 |
866 |
871 |
876 |
880 |
885 |
2 |
0,8 |
|
889 |
890 |
895 |
900 |
905 |
910 |
915 |
919 |
924 |
929 |
934 |
3 |
1,2 |
|
890 |
939 |
944 |
949 |
954 |
959 |
963 |
968 |
973 |
978 |
983 |
4 5 |
1,6 2,0 |
|
891 |
988 |
993 |
998 |
,002 |
,007 |
,012 |
,017 |
,022 |
,027 |
,032 |
6 |
2,4 |
|
892 |
95 036 |
041 |
046 |
051 |
056 |
061 |
066 |
071 |
075 |
080 |
7 |
2,8 |
|
893 |
085 |
090 |
095 |
100 |
105 |
109 |
114 |
119 |
124 |
129 |
8 |
3,2 |
|
894 |
134 |
139 |
143 |
148 |
153 |
158 |
163 |
168 |
173 |
177 |
9 |
3,6 |
|
895 |
182 |
187 |
192 |
197 |
202 |
207 |
211 |
216 |
221 |
226 |
||
|
896 |
231 |
236 |
240 |
245 |
250 |
255 |
260 |
265 |
270 |
274 |
||
|
897 |
279 |
284 |
289 |
294 |
299 |
303 |
308 |
313 |
318 |
323 |
||
|
898 |
328 |
332 |
337 |
342 |
347 |
352 |
357 |
361 |
366 |
371 |
||
|
899 |
376 |
381 |
386 |
390 |
395 |
400 |
405 |
410 |
415 |
419 |
||
|
900 |
424 |
429 |
434 |
439 |
444 |
448 |
453 |
458 |
463 |
468 |
||
|
!«-. |
L. 0 |
1 |
2 |
3 |
4 |
3 |
0 |
7 |
8 |
9 |
P |
.P. |
250
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containing logaritlims of numbers from 1 to 11,000. — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
P.P. |
|
|
900 |
95 424 |
429 |
434 |
439 |
- 444 |
448 |
453 |
458 |
463 |
468 |
||
|
901 |
472 |
477 |
482 |
487 |
492 |
497 |
501 |
506 |
511 |
616 |
||
|
902 |
521 |
525 |
530 |
635 |
640 |
545 |
550 |
554 |
559 |
564 |
||
|
903 |
669 |
574 |
578 |
583 |
588 |
693 |
598 |
602 |
607 |
612 |
||
|
904 |
617 |
622 |
626 |
631 |
636 |
641 |
646 |
650 |
655 |
660 |
||
|
905 |
665 |
670 |
674 |
679 |
684 |
689 |
694 |
698 |
703 |
708 |
||
|
906 |
713 |
718 |
722 |
727 |
732 |
737 |
742 |
746 |
751 |
756 |
||
|
907 |
761 |
766 |
770 |
775 |
780 |
785 |
789 |
794 |
799 |
804 |
||
|
91p8 |
809 |
813 |
818 |
823 |
828 |
832 |
837 |
842 |
847 |
852 |
||
|
909 |
856 |
861 |
866 |
871 |
875 |
880 |
885 |
890 |
895 |
899 |
||
|
910 |
904 |
909 |
914 |
918 |
923 |
928 |
933 |
938 |
942 |
947 |
||
|
911 |
952 |
957 |
961 |
966 |
971 |
976 |
980 |
985 |
990 |
995 |
6 |
|
|
912 |
999 |
»004 |
,009 |
«014 |
,019 |
,023 |
,028 |
,033 |
,038 |
,042 |
1 |
0,5 1 |
|
913 |
96 047 |
052 |
057 |
061 |
066 |
071 |
076 |
080 |
085 |
090 |
2 |
1,0 i |
|
914 |
095 |
099 |
104 |
109 |
114 |
118 |
123 |
128 |
133 |
137 |
3 |
1,5 1 |
|
915 |
142 |
147 |
152 |
156 |
161 |
166 |
171 |
175 |
180 |
185 |
4 |
2,0 |
|
916 |
190 |
194 |
199 |
204 |
209 |
213 |
218 |
223 |
227 |
232 |
5 |
2,5 |
|
917 |
237 |
242 |
246 |
251 |
256 |
261 |
265 |
270 |
275 |
280 |
6 |
3,0 |
|
918 |
284 |
289 |
294 |
298 |
303 |
308 |
313 |
817 |
322 |
327 |
7 |
3,5 |
|
919 |
332 |
336 |
341 |
346 |
350 |
355 |
360 |
365 |
369 |
374 |
8 |
4,« |
|
920 |
379 |
384 |
388 |
393 |
398 |
402 |
407 |
412 |
417 |
421 |
9 |
4,5 |
|
921 |
426 |
431 |
435 |
440 |
445 |
450 |
454 |
459 |
464 |
468 |
||
|
922 |
473 |
478 |
483 |
487 |
492 |
497 |
501 |
506 |
611 |
615 |
||
|
923 |
520 |
525 |
530 |
534 |
539 |
544 |
648 |
553 |
558 |
562 |
||
|
924 |
567 |
572 |
577 |
581 |
586 |
591 |
595 |
600 |
605 |
609 |
||
|
925 |
614 |
619 |
624 |
628 |
633 |
638 |
642 |
647 |
662 |
656 |
||
|
926 |
661 |
006 |
670 |
675 |
630 |
685 |
689 |
694 |
699 |
703 |
||
|
927 |
708 |
713 |
717 |
722 |
727 |
731 |
736 |
741 |
745 |
750 |
||
|
928 |
755 |
759 |
704 |
769 |
774 |
778 |
783 |
788 |
792 |
797 |
||
|
929 |
802 |
806 |
811 |
816 |
820 |
825 |
830 |
834 |
839 |
844 |
||
|
330 |
848 |
853 |
858 |
862 |
867 |
872 |
876 |
881 |
886 |
890 |
||
|
931 |
895 |
900 |
904 |
909 |
914 |
918 |
923 |
928 |
932 |
937 |
4 |
|
|
932 |
942 |
946 |
951 |
956 |
960 |
965 |
970 |
974 |
979 |
984 |
1 |
0,4 |
|
933 |
988 |
993 |
997 |
,002 |
,007 |
.011 |
,016 |
,021 |
,025 |
,030 |
2 |
0,8 |
|
934 |
97 035 |
039 |
044 |
049 |
053 |
058 |
063 |
067 |
072 |
077 |
3 |
1,2 |
|
935 |
081 |
0S6 |
090 |
095 |
100 |
104 |
109 |
114 |
118 |
123 |
4 |
1,6 |
|
936 |
128 |
132 |
137 |
142 |
146 |
151 |
155 |
160 |
165 |
169 |
5 |
2,0 |
|
937 |
174 |
179 |
183 |
188 |
192 |
197 |
202 |
206 |
211 |
216 |
6 |
2,4 |
|
938 |
220 |
225 |
230 |
234 |
239 |
243 |
248 |
253 |
257 |
262 |
7 |
2,8 |
|
939 |
267 |
271 |
276 |
280 |
285 |
290 |
294 |
299 |
304 |
308 |
8 |
3,2 |
|
910 |
313 |
317 |
322 |
327 |
331 |
336 |
340 |
345 |
350 |
354 |
9 |
3,6 |
|
941 |
359 |
364 |
368 |
373 |
377 |
382 |
387 |
391 |
396 |
400 |
||
|
942 |
405 |
410 |
414 |
419 |
424 |
42,S |
433 |
437 |
442 |
447 |
||
|
943 |
451 |
456 |
460 |
465 |
470 |
474 |
479 |
483 |
488 |
493 |
||
|
944 |
497 |
502 |
506 |
511 |
516 |
520 |
525 |
529 |
534 |
539 |
||
|
945 |
543 |
548 |
552 |
667 |
662 |
566 |
571 |
675 |
580 |
585 |
||
|
946 |
589 |
594 |
598 |
603 |
607 |
612 |
617 |
621 |
626 |
630 |
||
|
947 |
635 |
640 |
644 |
649 |
663 |
658 |
663 |
667 |
672 |
676 |
||
|
948 |
681 |
685 |
690 |
693 |
699 |
704 |
708 |
713 |
717 |
722 |
||
|
949 |
727 |
731 |
736 |
740 |
745 |
749 |
754 |
759 |
763 |
768 |
||
|
950 |
772 |
777 |
782 |
786 |
791 |
795 |
800 |
804 |
809 |
813 |
||
|
N. |
X. 0 |
1 |
2 |
3 |
4 |
6 |
6 |
7 |
8 |
9 |
P.P. |
LOGARITHMS OF i^UMBEES.
251
Table XXXV. — Containing logarithms of mmibers from 1 to 11,000,- [Estracted fi'oiu Gauss' Logarithmic aud Trigonoroetric Tables.]
|
0 |
1 |
2 |
3 |
|
7 772 |
777 |
782 |
786 |
|
818 |
823 |
827 |
832 |
|
864 |
868 |
873 |
877 |
|
909 |
914 |
918 |
923 |
|
955 |
959 |
964 |
968 |
|
8 000 |
005 |
009 |
014 |
|
046 |
050 |
055 |
059 |
|
091 |
096 |
100 |
105 |
|
137 |
141 |
146 |
150 |
|
182 |
186 |
191 |
195 |
|
227 |
232 |
236 |
241 |
|
272 |
277 |
281 |
286 |
|
318 |
322 |
327 |
331 |
|
363 |
367 |
372 |
376 |
|
408 |
412 |
417 |
421 |
|
453 |
457 |
462 |
466 |
|
498 |
502 |
507 |
511 |
|
543 |
547 |
552 |
556 |
|
588 |
692 |
597 |
601 |
|
632 |
637 |
641 |
640 |
|
677 |
682 |
686 |
691 |
|
722 |
726 |
731 |
735 |
|
767 |
771 |
776 |
780 |
|
811 |
816 |
820 |
825 |
|
856 |
860 |
865 |
869 |
|
900 |
905 |
909 |
914 |
|
945 |
949 |
954 |
958 |
|
989 |
994 |
998 |
,003 |
|
99 034 |
038 |
043 |
047 |
|
078 |
083 |
087 |
092 |
|
123 |
127 |
131 |
136 |
|
167 |
171 |
176 |
180 |
|
211 |
216 |
220 |
224 |
|
255 |
260 |
264 |
269 |
|
300 |
304 |
308 |
313 |
|
844 |
348 |
352 |
357 |
|
388 |
392 |
396 |
401 |
|
432 |
436 |
441 |
415 |
252
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXV. — Containinfi Ingarithms of numhers from 1 to ii,00fl.— Coutinuecl. [Extracted from Gauss' Logarithmic and Trigouometric Ta"bles-]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
d. |
|
louo |
000 ouoo |
0434 |
0869 |
1303 |
1737 |
2171 |
2605 |
3039 |
3472 |
3907 |
434 |
|
1001 |
4341 |
4775 |
5208 |
5642 1 |
6076 |
6510 |
6943 |
7377 |
7810 |
8244 |
434 |
|
1002 |
8677 |
9111 |
9544 |
9977 |
.0411 |
,0844 |
,1277 |
,1710 |
,2143 |
,2576 |
433 |
|
1003 |
001 3009 |
3442 |
3875 |
4308 |
4741 |
5174 |
5607 |
6039 |
0472 |
6905 |
433 |
|
1004 |
7337 |
7770 |
8202 |
8C35 |
9067 |
9499 |
9932 |
,0364 |
,0796 |
.1228 |
432 |
|
1(106 |
002 1601 |
2093 |
2525 |
2957 |
3389 |
3821 |
4253 |
4685 |
5116 |
5548 |
432 |
|
1006 |
5980 |
6411 |
6843 |
7275 |
7706 |
8138 |
8569 |
9001 |
9432 |
9863 |
431 |
|
1007 |
003 0295 |
0726 |
1157 |
1588 |
2019 |
2451 |
2882 |
3313 |
3744 |
4174 |
431 |
|
lOOS |
4605 |
5U36 |
5467 |
5898 |
6328 |
6759 |
7190 |
7620 |
8051 |
8481 |
431 |
|
10U9 |
8912 |
9342 |
9773 |
,0203 |
,0633 |
,1063 |
,1493 |
,1924 |
,2354 |
,2784 |
430 |
|
1010 |
004 3214 |
3644 |
4074 |
4504 |
4933 |
'5363 |
5793 |
6223 |
6652 |
7082 |
430 |
|
1011 |
7512 |
7941 |
8371 |
8800 |
9229 |
9659 |
,0088 |
,0517 |
,0947 |
,1376 |
429 |
|
1012 |
005 1805 |
2234 |
2663 |
3092 |
3521 |
3950 |
4379 |
4808 |
5237 |
5666 |
429 |
|
1013 |
6094 |
6523 |
6952 |
7380 |
7809 |
8238 |
8666 |
9094 |
9523 |
9951 |
429 |
|
1014 |
006 03S0 |
0808 |
1236 |
1664 |
2092 |
2521 |
2949 |
3377 |
3805 |
4233 |
428 |
|
1015 |
4660 |
5088 |
5516 |
5944 |
6372 |
6799 |
7227 |
7655 |
8082 |
8510 |
428 |
|
1010 |
8937 |
9365 |
9792 |
,0219 |
,0647 |
,1074 |
,1501 |
,1928 |
,2355 |
,2782 |
427 |
|
1017 |
007 3210 |
3637 |
4064 |
4490 |
4917 |
5344 |
5771 |
6198 |
6624 |
7051 |
427 |
|
1018 |
7478 |
7904 |
8331 |
8757 |
9184 |
9610 |
,0037 |
,0463 |
,0889 |
,1316 |
426 |
|
1019 |
008 1742 |
2168 |
2594 |
3020 |
3446 |
3872 |
4298 |
4724 |
'5150 |
5576 |
426 |
|
1020 |
6002 |
6427 |
6853 |
7279 |
7704 |
8130 |
8556 |
8981 |
9407 |
9832 |
426 |
|
1021 |
009 0257 |
0683 |
1108 |
1533 |
1959 |
2384 |
2809 |
3234 |
3659 |
4084 |
425 |
|
1022 |
4509 |
4934 |
5359 |
5784 |
6208 |
6633 |
7058 |
7483 |
7907 |
8332 |
425 |
|
102:1 |
8756 |
9181 |
9605 |
.0030 |
.0454 |
,0878 |
,1303 |
,1727 |
,2151 |
,2575 |
424 |
|
1024 |
010 3000 |
3424 |
3848 |
4272 |
4696 |
5120 |
5544 |
5967 |
6391 |
6815 |
424 |
|
1025 |
7239 |
7662 |
8086 |
8510 |
8933 |
9357 |
9780 |
,0204 |
,0627 |
,1050 |
424 |
|
1026 |
Oil 1474 |
1897 |
2320 |
2743 |
3166 |
3590 |
4013 |
4436 |
4859 |
5282 |
423 |
|
1027 |
5704 |
6127 |
6550 |
6973 |
7396 |
7818 |
8241 |
8664 |
9086 |
9509 |
423 |
|
1028 |
9931 |
.0854 |
.,0776 |
,1198 |
,1621 |
,2043 |
,2465 |
.2887 |
,3310 |
,3732 |
422 |
|
1029 |
012 4154 |
4576 |
4998 |
5420 |
'5842 |
6264 |
6685 |
7107 |
7529 |
7951 |
422 |
|
1030 |
8372 |
8794 |
9215 |
9637 |
,0059 |
,0480 |
,0901 |
,1323 |
,1744 |
,2165 |
422 |
|
1031 |
013 2587 |
3008 |
3429 |
3850 |
4271 |
4692 |
5113 |
5534 |
5955 |
6376 |
421 |
|
1032 |
6797 |
7218 |
7639 |
8059 |
8480 |
8901 |
9321 |
9742 |
,0162 |
,0583 |
421 |
|
1033 |
014 1003 |
1424 |
1844 |
2264 |
2685 |
3105 |
3525 |
3945 |
4365 |
4785 |
420 |
|
1034 |
5205 |
5625 |
6045 |
6465 |
6885 |
7305 |
7725 |
8144 |
8564 |
8984 |
420 |
|
1035 |
9403 |
9823 |
,0243 |
„l.662 |
,1082 |
,1501 |
,1920 |
,2340 |
,2759 |
,3178 |
420 |
|
1036 |
015 3598 |
4017 |
4436 |
4855 |
5274 |
5693 |
6112 |
6531 |
6950 |
7369 |
419 |
|
1037 |
7788 |
8206 |
8625 |
9044 |
9462 |
9881 |
,0300 |
,0718 |
,1137 |
,1555 |
419 |
|
1038 |
016 1974 |
2392 |
2810 |
3229 |
3647 |
4065 |
4483 |
4901 |
5319 |
5737 |
418 |
|
1039 |
6155 |
6573 |
6991 |
7409 |
7827 |
8245 |
8663 |
9080 |
9498 |
9916 |
418 |
|
1040 |
017 0333 |
0751 |
1168 |
1586 |
2003 |
2421 |
2838 |
3256 |
3673 |
4090 |
417 |
|
1041 |
4507 |
4924 |
5342 |
5759 |
6176 |
6593 |
7010 |
7427 |
7844 |
8260 |
417 |
|
1042 |
8677 |
9094 |
9511 |
9927 |
,0344 |
,0761 |
,1177 |
,1594 |
,2010 |
,2427 |
417 |
|
1043 |
018 2843 |
3259 |
3676 |
4092 |
4508 |
4925 |
5341 |
'5757 |
'6173 |
6589 |
416 |
|
1044 |
7005 |
7421 |
7837 |
8253 |
8669 |
9084 |
9500 |
9916 |
,0332 |
,0747 |
416 |
|
1045 |
019 1163 |
1578 |
1994 |
2410 |
2825 |
3240 |
3656 |
4071 |
4486 |
4902 |
415 |
|
1046 |
5317 |
5732 |
6147 |
6562 |
6977 |
7392 |
7807 |
8222 |
8637 |
9052 |
415 1 |
|
1047 |
9467 |
9882 |
»0296 |
,0711 |
,1126 |
,1540 |
,1955 |
,2369 |
,2784 |
,3198 |
415 |
|
1048 |
020 3613 |
4027 |
4442 |
4856 |
'5270 |
5684 |
6099 |
6513 |
6927 |
7341 |
414 |
|
1049 |
7755 |
8169 |
8583 |
8997 |
9411 |
9824 |
,0238 |
,0652 |
,1066 |
,1479 |
414 |
|
1050 |
021 1893 |
2307 |
2720 |
3134 |
3547 |
3961 |
4374 |
4787 |
■5201 |
5614 |
413 |
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
» |
' |
7 8 |
9 |
d. |
LOGAEITHMS OP NUMBEKS.
253
Table XXXV, — Containing hxjariihms of numbv.vti from 1 to J1,000. — Continued. [Extracted from. Gauas' Logarithmic and Trigonometric Tables.]
|
N. |
L. 0 |
1 |
2 |
3 |
4 |
5 |
6 |
8 |
9 |
d. |
|
|
1050 |
021 1893 |
2307 |
2720 |
3134 |
3547 |
3961 |
4374 |
4787 |
5301 |
5614 |
413 |
|
1051 |
6027 |
6440 |
6854 |
7267 |
7680 |
8093 |
8506 |
8919 |
9333 |
9745 |
413 |
|
1052 |
022 0157 |
0570 |
0983 |
1396 |
1808 |
2231 |
2634 |
3046 |
3459 |
3871 |
413 |
|
1053 |
4284 |
4696 |
5109 |
5521 |
5933 |
6345 |
6758 |
' 7170 |
7583 |
7994 |
412 |
|
1054 |
8406 |
8818 |
9230 |
9643 |
,0054 |
,0466 |
,0878 |
,1289 |
,1701 |
,2113 |
412 |
|
1055 |
023 2525 |
2930 |
3348 |
3759 |
4171 |
4583 |
4994 |
5405 |
5817 |
6228 |
411 |
|
1056 |
6639 |
7050 |
7462 |
7873 |
8284 |
8095 |
9106 |
9517 |
9928 |
,0339 |
411 |
|
1057 |
024 0750 |
1161 |
1572 |
1982 |
2393 |
2804 |
3214 |
3025 |
4036 |
4446 |
411 |
|
1058 |
4857 |
5267 |
5678 |
6088 |
6498 |
6909 |
7319 |
7729 |
8139 |
8549 |
410 |
|
1059 |
8960 |
9370 |
9780 |
,0l90 |
,0600 |
,1010 |
,1419 |
,1829 |
,2239 |
,2649 |
410 |
|
1060 |
025 3059 |
3468 |
3878 |
4288 |
4697 |
5107 |
5516 |
5926 |
6335 |
6744 |
410 |
|
1061 |
7154 |
7563 |
7972 |
8382 |
8791 |
9300 |
9609 |
,0018 |
,0427 |
,0836 |
409 |
|
1062 |
026 1245 |
1654 |
2063 |
2472 |
2881 |
3289 |
3698 |
4107 |
4515 |
4924 |
409 |
|
1063 |
5333 |
5741 |
6350 |
6558 |
6967 |
7375 |
7783 |
8192 |
8600 |
9008 |
408 |
|
1064 |
9416 |
9824 |
,0233 |
,0641 |
,1049 |
,1457 |
,1865 |
,3373 |
,2680 |
,3088 |
408 |
|
1065 |
027 3496 |
3904 |
4312 |
4719 |
5127 |
5535 |
5942 |
6350 |
6757 |
7165 |
408 1 |
|
1006 |
7572 |
7979 |
8387 |
8794 |
9201 |
9609 |
,0016 |
,0423 |
,0830 |
,1237 |
407 |
|
1067 |
028 1644 |
2051 |
2458 |
2865 |
3272 |
3679 |
4086 |
4492 |
4899 |
5306 |
407 |
|
1068 |
5713 |
6119 |
6526 |
6932 |
73S9 |
7745 |
8152 |
8558 |
8964 |
9371 |
406 |
|
1069 |
9777 |
,0183 |
,0590 |
,0996 |
,1402 |
,1808 |
,2214 |
,2620 |
,3026 |
,3433 |
406 |
|
1070 |
029 3838 |
4244 |
4649 |
5055 |
5461 |
5867 |
6272 |
6678 |
7084 |
7489 |
406 |
|
1071 |
7895 |
8300 |
8706 |
9111 |
9516 |
9922 |
,0327 |
,0732 |
,1138 |
,1543 |
405 |
|
1072 |
030 1948 |
2353 |
2758 |
3163 |
3568 |
3973 |
4378 |
4783 |
5188 |
5592 |
405 |
|
1073 |
5997 |
6402 |
6807 |
7211 |
7616 |
8020 |
8425 |
8830 |
9234 |
9638 |
405 |
|
1074 |
031 0043 |
0447 |
0851 |
1256 |
1660 |
2064 |
2468 |
2872 |
3277 |
3681 |
404 |
|
1075 |
4085 |
4469 |
4893 |
5396 |
5700 |
6104 |
6508 |
,0Sl7 |
7315 |
7719 |
404 |
|
1076 |
8133 |
8526 |
8930 |
9333 |
9737 |
,0140 |
,0544 |
,1350 |
,1754 |
403 |
|
|
1077 |
032 2157 |
2560 |
2963 |
3367 |
3770 |
4173 |
4576 |
4979 |
5382 |
5785 |
403 |
|
1078 |
6188 |
6590 |
6993 |
7396 |
7799 |
8201 |
8604 |
9007 |
9409 |
9812 |
403 |
|
1079 |
033 0214 |
0617 |
1019 |
1422 |
1824 |
2336 |
2629 |
3031 |
3433 |
3835 |
402 |
|
1080 |
4238 |
4640 |
5042 |
5444 |
5846 |
62 J 8 |
6650 |
7052 |
7453 |
7855 |
402 |
|
1081 |
8257 |
8659 |
9060 |
9462 |
9864 |
,0265 |
,0667 |
,1068 |
,1470 5482 |
,1871 |
402 |
|
1082 |
034 2273 |
2674 |
3075 |
3477 |
3878 |
4279 |
4680 |
5081 |
5884 |
401 |
|
|
1083 |
6285 |
6686 |
7087 |
7487 |
7888 |
8289 |
8690 |
9091 |
9491 |
9893 |
401 |
|
1084 |
035 0293 |
0693 |
1094 |
1495 |
1895 |
2296 |
2696 |
3096 |
3497 |
3897 |
400 |
|
1085 |
4297 |
4698 |
5098 |
5498 |
5898 |
6298 |
6698 |
7098 |
7498 |
7898 |
400 |
|
1086 |
8298 |
8698 |
9098 |
9498 |
9898 |
,0297 |
,0697 |
,1097 |
,^496 |
,1896 |
400 |
|
1087 |
036 2295 |
2695 |
3094 |
3494 |
3893 |
4393 |
4692 |
5091 |
5491 |
5890 |
399 |
|
1088 |
6289 |
6688 |
7087 |
7486 |
7885 |
8284 |
8683 |
9082 |
9481 |
9880 |
399 |
|
1089 |
037 0279 |
0678 |
1076 |
1476 |
1874 |
2272 |
2671 |
3070 |
3468 |
3867 |
399 |
|
1090 |
4265 |
4663 |
5062 |
5460 |
5858 |
6357 |
6655 |
7053 |
7451 |
7849 |
398 |
|
1091 |
8248 |
8646 |
9044 |
9442 |
9839 |
,0237 |
,0635 |
,1033 |
,1431 |
,1829 |
398 |
|
1092 |
038 2226 |
2624 |
3022 |
3419 |
3817 |
4214 |
4612 |
5009 |
5407 |
5804 |
398 |
|
1093 |
6202 |
6599 |
6996 |
7393 |
7791 |
8188 |
8585 |
8982 |
9379 |
9776 |
397 |
|
1094 |
039 0173 |
0570 |
0067 |
1364 |
1761 |
2158 |
2554 |
2951 |
3348 |
3745 |
397 |
|
1095 |
4141 |
4538 |
4934 |
5331 |
5727 |
6124 |
6520 |
6917 |
7313 |
7709 |
397 |
|
1096 |
8106 |
8502 |
8898 |
9294 |
9690 |
,0086 |
,0482 |
,0878 |
.1274 |
,1670 |
396 |
|
1097 |
040 2066 |
2462 |
2858 |
3354 |
3650 |
4045 |
4441 |
4837 |
'5232 |
5638 |
396 |
|
1098 |
6023 |
6419 |
6814 |
7310 |
7605 |
8001 |
8396 |
8791 |
9187 |
9582 |
395 |
|
1099 |
9977 |
,0372 |
,0767 |
,1162 |
,1557 |
,1953 |
,2347 |
,3742 |
,3137 |
,3532 |
395 |
|
1100 N. |
041 3927 L. 0 |
4322 |
4716 |
5111 |
5506 |
5900 |
6295 |
6690 |
7084 8 |
7479 |
395 |
|
1 |
2 3 |
4 |
5 |
6 |
9 |
d. |
254
A MANUAL OF TOPOGRArHIC METHODS.
Tablic XXXVI. — Logarithmic sines, cosines, tangents, and cotangents. [Extracted from Oaiiss' Logarithmic anil Tiigouomctrio Tables,]
0°
|
' |
L. Sin. |
(1. |
L. Tang. 1 1 |
d. 0. |
L. Cotg. |
L. Cos. |
|
|
0 |
1 |
0. 00 000 0. 00 oon |
60 59 |
||||
|
6. 46 373 |
0.46 373 |
3.53 627 |
|||||
|
6. 76 476 |
30103 |
6.76 476 |
30103 3.23 524 |
0.00 000 |
58 |
||
|
17609 |
6.94 085 |
17609 3.05 915 |
0. 00 000 |
57 |
|||
|
4 |
7. 06 579 |
12494 9691 |
7. 06 579 |
12494 9691 |
2.93 421 |
0. 00 000 |
66 |
|
5 |
7.16 270 |
7. 16 270 |
2.83 730 |
0.00 000 |
55 |
||
|
6 |
7. 24 188 |
7918 |
7.24 188 |
2.75 812 |
0.00 000 |
||
|
7.30 S82 |
6691 |
7. 30 882 |
2.69 118 |
0.00 000 |
|||
|
7.36 682 |
5800 |
7.36 682 |
2.63 318 |
0.00 000 |
52 |
||
|
11 10 ^ |
7.41 797 |
5115 4576 |
7.41 797 |
4576 |
2. 58 203 |
0. 00 000 |
51 |
|
7. 46 373 |
7. 46 373 |
2.53 627 |
0.00 000 |
50 |
|||
|
4139 |
7. 50 512 |
2.49 488 |
0.00 000 |
49 |
|||
|
7 54 291 |
3779 |
7.54 291 |
2.45 709 |
0. 00 000 |
48 |
||
|
7 57 767 |
3476 |
7. 57 767 |
2.42 233 |
0.00 000 |
47 |
||
|
14 |
7. 60 985 |
3218 2997 |
7. 60 986 7.63 982 |
2996 |
2.39 014 |
0.00 000 |
46 |
|
7.63 982 |
2.36 018 |
0.00 000 |
45 |
||||
|
2802 |
7. 66 785 |
2. 33 215 |
0.00 000 |
44 |
|||
|
17 |
7.69 417 |
2633 |
7. 69 418 |
2482 |
2. 30 582 |
9.99 999 |
43 |
|
7.71 900 |
2483 |
7. 71 900 |
2.28 100 |
9.99 999 |
|||
|
19 20 |
7.74 248 |
2348 2227 |
7.74 248 |
. 2228 |
2. 25 752 |
9.99 999 |
41 |
|
7 76 475 |
7. 76 476 |
2. 23 524 |
9.99 999 |
40 |
|||
|
2119 |
7.78 595 |
2.21 405 |
9.99 999 |
39 |
|||
|
22 |
7.80 615 |
2021 |
7.80 615 |
2. 19 385 |
9.99 999 |
38 |
|
|
7.82 545 |
1930 |
7.82 546 |
2. 17 454 |
9.99 999 |
|||
|
24 |
7. 84 393 |
1848 1773 |
7, 84 394 |
1773 |
2.15 606 |
9.99 999 |
36 |
|
7.86,166 |
7.86 167 |
2. 13 833 |
9.99 999 |
35 |
|||
|
1704 |
7. 87 871 |
2.12 129 |
9.99 999 |
34 |
|||
|
27 |
7.89 509 |
1639 |
7. 89 510 |
1639 |
2. 10 490 |
9.99 999 |
33 |
|
'S |
7.91 088 |
7.91 089 |
2. 08 911 |
9.99 999 |
|||
|
29 |
7.92 612 |
1472 |
7. 92 613 7. 94 086 |
1473 |
2.07 387 |
9.99 998 |
|
|
30 |
7.94 084 |
2. 05 914 |
9.99 998 |
30 |
|||
|
7.95 508 |
7.95 510 |
2. 04 490 |
9.99 998 |
||||
|
32 |
7.96 887 |
1379 |
7.96 889 |
2.03 111 |
9.99 998 |
28 |
|
|
33 |
7.98 223 |
1336 |
7.98 225 |
2.01 775 |
9.99 998 |
27 |
|
|
34 |
7.99 520 |
1259 |
7.99 522 |
1259 |
2. 00 478 |
9.99 998 |
|
|
8.08 781 |
1.99 219 |
9. 99 998 |
25 |
||||
|
« 8. 02 0U2 8.03 192 |
1223 |
8. 02 004 |
1223 |
1.97 996 |
9.99 998 |
24 |
|
|
1190 |
8.03 194 |
1.96 806 |
9.99 997 |
23 |
|||
|
38 |
8.04 350 |
1158 |
8. 04 353 |
1.95 647 |
9.99 997 |
22 |
|
|
39 |
8.05 478 |
1100 |
8. 05 481 8. 06 581 |
1100 |
1.94 519 |
9.99 997 |
|
|
40 |
8.06 578 |
1.93 419 |
9.99 997 |
20 |
|||
|
1072 |
8.07 653 |
1.92 347 |
9.99 997 |
||||
|
8.08 696 |
1046 |
8. 08 700 |
1.91 300 |
9.99 997 |
18 |
||
|
8. 09 718 |
1022 |
8.09 722 |
1. 90 278 |
9.99 997 |
17 |
||
|
44 45 |
8. 10 717 8.11 693 |
999 976 |
8. 10 720 |
976 |
1. 89 280 |
9.99 996 |
16 |
|
8. 11 696 |
1.88 304 |
9. 99 996 |
15 |
||||
|
8. 12 651 |
1.87 349 |
9. 99 996 |
14 |
||||
|
8.13 581 |
934 |
8. 13 585 |
934 |
1.86 415 |
9. 99 996 |
13 |
|
|
48 |
8.14 495 |
914 |
8. 14 500 |
915 |
1.85 300 |
9. 99 996 |
12 |
|
49 SO |
8.15 391 |
896 877 |
8. 15 395 |
895 878 |
1.84 605 |
9. 99 996 |
11 |
|
8. 16 268 |
8. 16 273 |
1.83 727 |
9. 99 995 |
10 |
|||
|
51 |
8.17 128 |
8.17 133 |
1.82 867 |
9. 99 995 |
9 |
||
|
8. 17 971 |
8.17 976 |
1, 82 024 |
9.99 995 |
||||
|
53 |
8. 18 798 |
827 |
8. 18 804 |
828 |
1.81 196 |
9. 99 995 |
7 |
|
54 |
8. 19 610 |
797 |
8. 19 616 |
797 |
1.80 384 |
9.99 895 |
|
|
55 |
8. 20 407 |
8. 20 413 |
1. 79 587 |
9. 99 994 |
5 |
||
|
50 |
8.21 189 |
782 |
8. 21 195 |
1.78 805 |
9. 99 994 |
4 |
|
|
57 |
8.21 958 |
769 |
8. 21 964 |
1.78 036 |
9. 99 994 |
3 |
|
|
58 |
8.22 713 |
8. 22 720 |
1.77 280 |
9.99 994 |
|||
|
59 |
8. 23 456 |
730 |
8. 23 462 8. 24 192 |
730 |
1.76 538 1. 75 808' |
9.99 994 |
|
|
60 |
8. 24 186 |
9. 99 993 |
0 |
||||
|
L. Cob. |
d. |
L. Cotg. |
d.c. |
L. Tang. |
L. Sin. |
' |
89=
LOGAEITHMS OF CIECULAE FUNCTIONS.
255
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents. — Continued.
[Extracted from Gauss' Logarithmic and Trigonometric Tables.]
1°
|
' |
L. Sin. |
d. |
L. Tang. |
d. 0. |
L. Cotg. |
L. Cos. |
|
|
0 |
8. 24 186 |
717 706 695 684 673 |
8. 24 192 |
718 706 696 684 673 |
1. 75 808 |
9. 99 993 |
60 |
|
1 |
8.24 903 |
8. 24 910 |
1. 75 090 |
9. 99 993 |
59 |
||
|
2 |
8. 25 609 |
8.25 616 |
1. 74 384 |
9.99 993 |
58 |
||
|
3 |
8. 26 304 |
8. 26 312 |
1. 73 688 |
9. 99 993 |
57 |
||
|
4' |
8. 26 988 |
8. 26 S96 |
1.73 004 |
9. 99 992 |
56 |
||
|
5 |
8.27 661 |
8.27 669 |
1.72 331 |
y.99 992 |
55 |
||
|
6 |
8. 28 324 |
8. 28 332 |
1.71 668 |
9.99 992 |
54 |
||
|
8. 28 977 |
8. 28 986 |
1. 71 014 |
9. 99 992 |
53 |
|||
|
8. 29 021 |
8. 29 629 |
1.70 371 |
9. 99 992 |
52 |
|||
|
9 |
8. 30 255 |
624 |
8.30 263 |
625 |
1. 69 737 |
9. 99 991 |
51 |
|
10 |
8.30 879 |
8. 30 888 |
1. 69 112 |
9. 9'J 991 |
50 |
||
|
11 |
8. 31 495 |
8. 31 505 |
1. 63 495 |
9. 99 991 |
49 |
||
|
8.32 103 |
8. 32 112 |
1. 67 S88 |
9. 99 990 |
48 |
|||
|
13 |
8. 32 702 |
8.32 711 |
1. 67 289 |
9. 99 990 |
47 |
||
|
14 |
8.33 292 |
583 |
8.33 302 |
584 |
1. 66 698 |
9. 99 990 |
46 |
|
15 |
8. 33 875 |
8.33 886 |
1.-66 114 |
9.99 990 |
45 |
||
|
8. 34 450 |
8. 34 461 |
1. 65 539 |
9.99 989 |
44 |
|||
|
17 |
8.35 018 |
568 |
8. 35 029 |
568 |
1. 64 971 |
9.99 989 |
43 |
|
8. 35 590 |
1.64 410 |
9. 99 989 |
42 |
||||
|
19 |
8.36 131 8. 36 678 |
553 547 |
8. 36 143 |
553 546 |
1, 63 857 |
9.99 989 |
41 |
|
20 |
8. 36 689 |
1.63 311 |
9.99 988 |
40 |
|||
|
8.37 217 |
8. 37 229 |
1. 62 771 |
9. 99 988 |
39 |
|||
|
2j |
8.37 750 |
533 |
8. 37 762 |
1. 62 238 |
9.99 988 |
38 |
|
|
8. 38 289 |
1. 61 711 |
9. 99 987 |
37 |
||||
|
24 |
8.38 796 |
520 514 |
8. 38 809 |
520 514 |
1.61 191 |
9.99 987 |
36 |
|
25 |
8.39 310 |
8. 39 323 |
1. 60 677 |
9. 99 987 |
35 |
||
|
8.39 818 |
8. 39 832 |
1. 60 168 |
9.99 986 |
34 |
|||
|
8.40 320 |
8. 40 334 |
1. 59 660 |
9. 99 986 |
33 |
|||
|
28 |
8.40 816 |
8. 40 830 |
1. 59 170 |
9. 99 986 |
32 |
||
|
29 |
8.41 307 |
485 |
8.41 321 |
486 |
1.58 679 |
9. 99 985 |
31 |
|
30 |
8.41 792 |
8.41 807 |
1.58 193 |
9. 99 985 |
30 |
||
|
8.42 272 |
8.42 287 |
1. 57 713 |
9. 99 985 |
||||
|
32 |
8.42 746 |
8. 42 762 |
475 |
1.57 238 |
9. 99 984 |
28 |
|
|
33 |
8.43 216 |
8.43 232 |
1. 56 768 |
9.99 984 |
27 |
||
|
34 |
8.43 680 |
459 |
8.43 696 |
460 |
1. 56 304 |
9. 99 984 |
26 |
|
8.44 156 |
1.65 844 |
9.99 983 |
25 |
||||
|
36 |
8,44 594 |
8.44 611 |
455 |
1.55 389 |
9.99 983 |
24 |
|
|
37 |
8.45 044 |
8. 45 061 |
1.54 939 |
9. 99 983 |
23 |
||
|
8. 45 489 |
8. 45 507 |
1. 54 493 |
9.99 982 |
22 |
|||
|
39 |
8.45 930 |
436 |
8. 45 948 |
441 437 |
1. 54 052 |
9. 99 982 |
21 |
|
40 |
8. 46 366 |
8. 46 385 |
1.53 615 |
9. 99 982 |
20 |
||
|
41 |
8.46 799 |
8.46 817 |
1.53 183 |
9. 99 981 |
19 |
||
|
8.47 226 |
8.47 245 |
1. 52 755 |
9.99 981 |
18 |
|||
|
8.47 650 |
424 |
8. 47 669 |
1.52 331 |
9. 99 981 |
17 |
||
|
44 |
8.48 069 |
419 416 |
8.48 089 |
416 |
1.51 911 |
9. 99 980 |
16 |
|
8.48 485 |
8.48 505 |
1.51 495 |
9. 99 980 |
15 |
|||
|
46 |
8.48 896 |
8.48 917 |
1.51 083 |
9. 99 979 |
14 |
||
|
8.49 304 |
8.49 325 |
1. 50 675 |
9. 99 979 |
13 |
|||
|
48 |
8.49 708 |
404 |
8.49 729 |
1.50 271 |
9. 99 979 |
12 |
|
|
49 |
8. 50 108 |
396 |
8.50 130 |
397 |
1.49 870 |
9. 99 978 |
11 |
|
30 |
8.50 504 |
8.50 527 |
1.49 473 |
9. 99 978 |
10 |
||
|
51 |
8. 50 897 |
8.50 920 |
1.49 08U |
9. 99 977 |
9 |
||
|
52 |
8.51 287 |
8.51 310 |
1.48 690 |
9.99 977 |
8 |
||
|
53 |
8.51 673 |
386 |
8.51 696 |
1.48 304 |
9. 99 977 |
7 |
|
|
54 |
8. 52 055 |
379 |
8.52 079 |
380 |
1. 47 921 |
9. 99 976 |
6 |
|
8.52 459 |
1.47 541 |
9. 99 976 |
5 |
||||
|
8. 52 810 |
376 |
8. 52 835 |
1.47 165 |
9.99 975 |
4 |
||
|
57 |
8.53 183 |
373 |
8. 53 208 |
1.46 792 |
9. 99 975 |
3 |
|
|
58 |
8. 53 552 |
369 |
8.53 578 |
1.46 422 |
9. 99 974 |
2 |
|
|
59 |
8. 53 919 |
363 |
8. 53 945 8. 54 308 |
363 |
1.46 055 |
9. 99 974 |
1 |
|
60 |
8. 54 282 |
1.45 692 |
9.99 974 |
0 |
|||
|
L. Cos. |
d. |
L. Cotg. |
d. c. |
L. Tang. |
L. Sin. |
' |
880
256
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Lofiarithmic sines, cosines, tangents, and cotangents. — Coutmued. [Erfraottd from Gauss' Logarithmic and Trigonometric Tables.]
|
L. Sin. |
|
|
0 |
8. 54 282 |
|
8. 54 042 |
|
|
8. 54 99D |
|
|
8. 55 354 |
|
|
8.55 705 |
|
|
8.56 054 |
|
|
8. 56 400 |
|
|
8. 56 743 |
|
|
8. 57 084 |
|
|
8. o7 421 |
|
|
10 |
8. 57 757 |
|
11 |
8. 58 089 |
|
12 |
8. 58 419 |
|
13 |
8. 58 747 |
|
14 |
8. 59 072 |
|
15 |
8. 59 395 |
|
16 |
8. .59 715 |
|
17 |
8. 60 033 |
|
18 |
8.6U 349 |
|
19 |
8. 60 662 |
|
20 |
8. 60 973 |
|
21 |
6. 61 282 |
|
22 |
8.61 589 |
|
23 |
8.61 894 |
|
24 |
8. 62 196 |
|
25 |
8. 62 497 |
|
26 |
8. 62 795 |
|
27 |
8. 63 091 |
|
28 |
8. 63 385 |
|
29 80 |
8.63 678 |
|
8. 63 968 |
|
|
31 |
8. 64 256 |
|
32 |
8. 64 543 |
|
33 |
8. 64 827 |
|
34 |
8.65 110 |
8. 66 497
8.66 769 8. 67 039
8.67 308 8. 67 575
8.67 841
8. 68 104 8. 68 367 8. 68 627
8. 68 886
8.69 144 8.69 400 8. 69 654
8.69 907
8. 70 159 8. 70 409 8. 70 658
8.70 905
8.71 151 8.71 395 8. 71 638 8.71 880
87=
LOGARITHMS OF CIRCULAR FU:srCTIO:SS.
257
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Contiuued. [Extracted from Gauss' Logaritttraic and Trigonometric Tables.]
30
MON XXII
258
A MxVNUAL OF TOPOGEArHIG METHODS.
Table XXXVI. — Logaritltmic sines, cosines, tanncnts, and cotangents — Contiuuod. [Bxtractea from Gauss' Losaritlimic ami Trigouometric Tables.]
4°
8. 84 358 S. 84 539 S. 8i 718 S. 81 897 8. 85^075 8.85^252 8. 85 429 8.85 605 8. 85 780
8.85 955 87 86 128 8. 86 301
8. 86 474
8.87 661
8. 87 829 8. 87 995
8. 88 161 8.88 326 8. 88 490 8. 88 654 8. 88 817
8.89 142 8.89 304 8. 89 464 8.89 625 8. 89 784
8.89 943
8.90 102
8.91 807 8. 91 959
8.92 110 8. 92 261 8. 92 411
8. 92 561 8.92 710
8.92 859 8. 93 007 8. 93 154
8. 93 3DT 8. 93 448 8. 93 594 8.93 740 8.93 885 a. 94 030
8. 84 464 8. 84 04C
8. 84 826
8. 85 006 8^85 185
"8.85 363" 8. 85 540 8.85 717
8.85 893
8.86 069
8. 86 243 8. 86 417 8. 86 591 8. 86 763
8. 87 953 8. 88 120
8. 88 287 8. 88 453 8^88_618^
" 8. 88 783 8. 88 948
8.89 111 8. 89 274
_ 8^9^432 8. 89 598
8.91 185 8.91 340 8.91 495 8.91 6.50 8.91 803
1. 15 536 1.15 354 1. 15 174 1. 14 994 L14 815 1. 14 637" 1. 14 460 1. 14 283 1.14 107 1. 13 931
1. 13 757 1. 13 583 1.13 409 1.13 237 1.13 065 1.12 894 1. 12 723 1.12 553 1.12 384 1. 12 215
1.11 880 1. 11 713 1. 11 547 1.11 382
8. 93 462 8.93 609 8.93 756 8. 93 903 8. 94 049 "8.94 195
L. Cotg. d. c.
1.11 217 1. 11 052 1. 10 889 1.10 726 1. 10 563 1. 10 402 1. 10 240 1. 10 080 1.09 920 1,09 760
1. 09 601 1.09 443 1. 09 285 1.09 128 1. 08 971 1. 08 815" 1. 08 060 1. 08 505 1. 08 350 J. 08 197 f. 08 043" 1. 07 890 1.07 738 1. 07 586 1. 07 435
9. 99 894 9. 99 893 9.99 892 9.90 891 9.99 891 I 9. 99 990" 9. 99 889 9. 99 888 9. 99 887
9. 99 880 9. 99 879 9.99 879 9. 99 878
9. 99 874 9. 99 873 9.99 872 9. 99" 871 9. 99 870 9. 99 869 9. 99 868
.99 ;
9.99 861 9.99 860 9. 99 859
9. 99 856 9. 99 855 9. 99 854 9. 99 853 9. 99 852
1. 07 284 1.07 134
1.06 835 1.06 687
1,06 538 1.06 391 1. 06 244 1. 06 097 JJ)5J)51 1, 05 805
9, 99 851 9, 99 850 9,99 848 9, 99 847 9, 99 846 9, 99 845 9, 99 844 9, 99 Si3 9. 99 842 9. 99 841
9. 99 840 9.99 839
9.99 836 9. 99 834
|
182 |
ISl |
1V9 |
17S |
|
3,0 |
3,0 |
3,0 |
3,0 |
|
6,1 |
6,0 |
6,0 |
5,9 |
|
9,1 |
9,0 |
9,0 |
8,9 |
|
12,1 |
12,1 |
11,9 |
11,9 |
|
15,2 |
15,1 |
14,9 |
14,8 |
|
18,2 |
18,1 |
17,9 |
17,8 |
|
21,2 |
21,1 |
20,9 |
20,8 |
|
24,3 |
24,1 |
23,9 |
23,7 |
|
27,3 |
27,2 |
26,8 |
26,7 |
|
17G |
175 |
174 |
17S |
|
2,9 |
2,9 |
2,9 |
2,9 |
|
5,9 |
5,8 |
5,8 |
5,8 |
|
8,8 |
8,8 |
8,7 |
8,6 |
|
11,7 |
11,7 |
11,6 |
11,5 |
|
14,7 |
14,6 |
14,5 |
14,4 |
|
17,6 |
17,5 |
17,4 |
17,3 |
|
20,5 |
20,4 |
20,3 |
20,2 |
|
23,5 |
23,3 |
23,2 |
23,1 |
|
26,4 |
26,2 |
26,1 |
26,0 |
|
171 |
170 |
169 |
168 ; |
|
2'8 |
2,8 |
2,3 |
2,8 |
|
5,7 |
5,7 |
5,6 |
5,6 |
|
8,6 |
8,5 |
8,4 |
8,4 |
|
11,4 |
U,3 |
11,3 |
11,2 |
|
14,2 |
14,2 |
14,1 |
14,0 |
|
17,1 |
17,0 |
16,9 |
16,8 |
|
20,0 |
19,8 |
19,7 |
19,6 |
|
22,7 |
22,5 |
22,4 |
|
|
25,6 |
52'5 |
25,4 |
25,2 |
|
166 |
165 |
1G4 |
163 |
|
2,8 |
2,8 |
2,7 |
2,7 |
|
5,5 |
5,5 |
5,5 |
6,4 |
|
8,3 |
8,2 |
8,2 |
8,2 |
|
11,1 |
11,0 |
10,9 |
10,9 |
|
13,8 |
13,8 |
13,7 |
13,6 |
|
16,6 |
16,5 |
16,4 |
16,3 |
|
19,4 |
19,2 |
19,1 |
19,0 |
|
22,1 |
22,0 |
21,9 |
21,7 |
|
24,9 |
24,8 |
24,6 |
24,4 |
|
161 |
160 |
150 |
168 |
|
2,7 |
2,7 |
2,6 |
2,6 |
|
5,4 |
5,3 |
5,3 |
6,3 |
|
8,0 |
8,0 |
8,0 |
7,9 |
|
10,7 |
10,7 |
10,6 |
10,5 |
|
13,4 |
13,3 |
13,2 |
13,2 |
|
16,1 |
16,0 |
15^9 |
15,8 |
|
18,8 |
18,7 |
18,6 |
18,4 |
|
21,5 |
21,3 |
21,2 |
21,1 |
|
24,2 |
24,0 |
23,8 |
23,7 |
|
156 |
155 |
154 |
153 |
|
2,6 |
2,6 |
2,6 |
2,0 |
|
5,2 |
5,2 |
5,1 |
5,1 |
|
7,8 |
7,8 |
7,7 |
7,6 |
|
10,4 |
10,3 |
10,3 |
10,2 |
|
13,0 |
12,9 |
12,8 |
12,8 |
|
16,6 |
16,5 |
15,4 |
16,3 |
|
18,2 |
18,1 |
18'0 |
17,8 |
|
20,8 |
20,7 |
20,5 |
20,4 |
|
23,4 |
23,2 |
23,1 |
23,0 |
177
3,0 6,9 8,8 11,8 14,8 17,7 20,6 23,6 26,6
172
2,9 6,7 8,6 11,5 14,3 17,2 20,1 22,9
8,4 11,1 13,9 16,7 19,5 22,3 25,0
8,1 10,8 13,5 16,3 18,9 21,6 24,3
157
2,6 6,2 7,8 10,5 13,1 15,7 18,3 20,9 23,6
152
2,5 5,1 7,6 10,1 12,7 15,2 17,7 20,3 22,8
85°
LOGARITHMS OF CIECULAE FUNCTIONS.
259
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
91 030 94 174 94 317 94 461 94 603
94 746
94 887
95 029 95 170 95 310
95 450 95 589 95 728
97 095 97 229 97 363
97 496 97 629 97 762
97 894
98 026
98 157 98 288 98 419 98 549 98 679
98 937
99 066 99 194 99 332
99 450 99 577 99 704
00 704 00 838
00 951
01 074 01 196 01 318 01 440 01 561 01 682 01 803
8.94 195 S. 94 340 8. 94 485 8. 94 630 8. 94 773
8.94 917
8.95 060 8. 95 202 8. 95 344 8. 95 486
8.95 627 8. 95 767
8. 95 908
8.96 047 8. 90 187
8. 96 325 8. 96 464 8.96 603 8.96 739 8. 96 877
8. 97 013 8.97 150 8. 97 285 8. 97 421 8. 97 556
8.97 691 8. 97 825 8. 97 959 8. 98 092
8.98 358 8. 98 490 8. 98 622 8. 98 763
9. 00 301 9. 00 427 9.00 553
9.00 679 9. 00 805 9. 00 930
9.01 055 9.01 179 9. 01 303 9. 01 427 9.01 550
9.01 673 9. 01 796 9. 01 918
9.02 040 9.02 162
140 138
1. 05 805 1. 05 660 1.05 515 1.05 370 1. 05 227
1. 05 083 1.04 940 1.04 798 1.04 650 1. 04 514
1. 04 373 1. 04 233 1.04 092 1. 03 953 1.03 813
1.03 675 1. 03 536 1. 03 398 1. 03 261 1.03 123
1. 02 987 1.02 850 1. 02 715 1. 02 579 1. 02 444
1.02 309 1.02 175 1. 02 041 1.01 908 1. 01 775
1.01 642 1.01 510 1.0] 378 1.01 247 1. 01 116
1. 00 985- 1. 00 855 1. 00 723 1. 00 595 1. 00 466
1.00 338 1. 00 209 1.00 081 0.99 954 0 99 826
99 699 99 573 99 447
98 697 98 573 98 450 98 327 98 204 98 C82 97 960
824
9.99 823 9. 99 822 9. 99 821 0. 99 820 9. 99 819
9.99 806 9. 99 81)4 9. 99 803 9. 99 802 9.99 801
9. 99 800 9.99 798 9. 99 797 9. 99 796 9. 99 795
9.99 793 9. 99 792 9. 99 791 9. 99 790 9. 99 788
0.99 787 9. 99 786 9.99 785
9. 99 778 9. 99 777 9.99 776
9. 99 771 :1. 99 769 9.99 708 9. 99 767 9.99 765 9.99 764 9. 99 763 9. 99 761
L. Cotg. d.c. L. Tang. I L. Sin.
|
149 |
148 |
|
2,5 |
2,5 |
|
6,0 |
4,9 |
|
V,4 |
7,4 |
|
9,9 |
9,9 |
|
13,4 |
12,3 |
|
14,9 |
14,8 |
|
r/,4 |
17,3 |
|
19,9 |
19,7 |
|
22,4 |
22,2 |
|
T4+ |
US |
|
2,4 |
2,4 |
|
4,8 |
4,8 |
|
V,3 |
7,2 |
|
9,6 |
9,5 |
|
12,0 |
11,9 |
|
14,4 |
14,3 |
|
16,8 |
16,7 |
|
19,2 |
19,1 |
|
31,6 |
21,4 |
|
11,2 |
11,1" |
|
13,4 |
13,3 |
|
15,6 |
15,5 |
|
17,9 |
17,7 |
|
30,1 |
20,0 |
|
129 |
138 |
|
2,2 |
2,1 |
|
4,3 |
4,3 |
|
6,4 |
6,4 |
|
8,6 |
8,5 |
|
10,8 |
10,7 |
|
12,9 |
12,8 |
|
l.'l.O |
14,9 |
|
17,2 |
17,1 |
|
19,4 |
19,2 |
|
124 |
123 |
|
2,1 |
2,0 |
|
4,i |
•t,l |
|
6,2 |
6,2 |
|
8,3 |
8,2 |
|
10,3 |
10,2 |
|
13,4 |
12,3 |
|
14„'> |
14,4 |
|
16,5 |
16,4 |
|
18,6 |
18,4 |
4,1 6,1 8,1 10,2 12,2 14,2 16,3 18,3
146
2,4 4,9 7,3 9,7 12,2 14,6 17,0 19,5 21,9 141 2,4 4,7 7,0 9,4 11,8 14,1 16,4 18,8 21,2 136 2,3 4,5 6,8 9,1 11,3 13,6 15,9 18,1 20,4
131
2,2
8,7 10,9 13,1 15,3 17,5 19,6
126
2,1 4,2 6,3 8,4 10,5 13,6 14,7 16,8 18,9 121
10,1 12,1 14,1 16,1 18,2
84=
2(30
A MA]S^UAL OF TOPOGEAPUIC METHODS.
Taulk XXXVI. — Logarithmic sines, cosines, tangents, and cottingenls — Contiuued. [Extractu<Uro:n Gauss' Logarithmic anil Trigouometric Tables.]
|
121 |
120 |
119 |
|
2,0 |
2,0 |
2,0 |
|
4,(1 |
4,0 |
4,0 |
|
(i,0 |
0,0 |
6,0 |
|
8,1 |
8,0 |
7,9 |
|
10,1 |
10,0 |
9,9 |
|
12,1 |
12,0 |
11,9 |
|
14,1 |
14,0 |
13,9 |
|
1li,l |
16,0 |
15,9 |
|
1H,2 |
18,0 |
17,8 |
|
20,2 |
20,0 |
19,8 |
|
4o,;i |
40,0 |
39,7 |
|
60,5 |
G0,0 |
59,5 |
|
80,7 |
80,0 |
79,3 |
|
100,8 |
100,0 |
99,2 |
|
117 |
110 |
115 |
|
2,0 |
1,9 |
1,9 |
|
a,9 |
3,9 |
3,8 |
|
5,8 |
6'8 |
5,8 |
|
V,8 |
7,7 |
7,7 |
|
9,8 |
9,7 |
9,6 |
|
11,7 |
11,6 |
11,5 |
|
13,6 |
13,5 |
13,4 |
|
lo,B |
15,5 |
15,3 |
|
IV, (i |
17,4 |
17,2. |
|
19,5 |
19,3 |
19,2 |
|
39,0 |
38,7 |
38,3 |
|
i)8,b |
58,0 |
57,5 |
|
V8,0 |
77,3 |
76,7 |
|
9V,o |
96,7 |
95,8 |
|
lis |
112 |
111 |
|
|
1 |
1,9 |
1,9 |
1,8 |
|
2 |
3,8 |
3,7 |
3,7 |
|
3 |
5,6 |
5,6 |
5,6 |
|
4 |
7,5 |
7,5 |
7,4 |
|
.■i |
9,4 |
9,3 |
9,2 |
|
(i |
11,3 |
11,2 |
11,1 |
|
V |
13,2 |
13,1 |
13,0 |
|
8 |
15,1 |
14,9 |
14,8 |
|
9 |
17,0 |
16,8 |
16,6 |
|
10 |
18,8 |
18,7 |
18,5 |
|
20 |
37,7 |
.37,8 |
37,0 |
|
30 |
56,5 |
56,0 |
55,5 |
|
40 |
75,3 |
74,7 |
74,0 |
|
60 |
94,2 |
93,3 |
92,5 |
|
109 |
108 |
107 |
|
1,8 |
1,8 |
1,8 |
|
3,6 |
3,6 |
3,6 |
|
5,4 |
5,4 |
5,4 |
|
7,3. |
7,2 |
7,1 |
|
9,1 |
9,0 |
8,9 |
|
10,9 |
10,8 |
10,7 |
|
12,7 |
12,6 |
12,5 |
|
14,5 |
14,4 |
14,3 |
|
16,4 |
16,2 |
16,0 |
|
18,2 |
18,0 |
17,8 |
|
36,3 |
36,0 |
35,7 |
|
54,5 |
54,0 |
53,5 |
|
72,7 |
72,0 |
71,3 |
|
90,8 |
90,0 |
89,2 |
118
2,0
15,7 17,7 19,7 39,3
114
1,9
9,5 11,4 13,3 15,2 17,1 19,0 38,0 57,0 76,0 95,0
110
1,8 3,7 5,5 7,3 9,2 11,0 12,8 14,7 16,5 18,3 36,7 55,0 73,3 91,7
106
1,8 3,5 5,3
10,6 12,4 14,1 15,9 17,7 35,3 53,0 70,7
LOGARITHMS OF OIRCULAE FUNCTIONS.
261
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued. [Extracted froniGanss' Logarithmic aiul Trigonometric Tables.]
1. L. Tang.
I 999
9.09 101 9.09 202 9. 09 304, 9. 09 405 9. 09 506
9.09 606 9. 09 707 9.09 807 9. 09 907 0. 10 000
9. 10 106 9. 10 20.5 9. 10 304 9.10 402 9. 10 501
9.10 599 9. 10 697 9.10 795 9. 10 893 9. 10 990
9.11 087 9. 11 184 9.11 281 9. 11 377 9. 11 474 9. H 570 9. 11 666 9.11 761 9.11 857
9.11 953 S. 12 047
9. 12 142 9. 12 236 9. 12 331 9. 12 425 9. 12 519 9. 12 012 9.12 706 9. 12 799 9.12 892
9. 12 985
9.13 078 9.13 171 9. 13 263 9. 13 355 9. 13 447 9.13 539 9.13 630 9. 13 722 9. 13 813 9. 13 904
9.13 994
9. 14 085 9. 14 175 9. 14 266 9. 14 856
92 91
9. 08 914 9. 09 019 9.09 123 9.09 227 9. 09 330
n. 09 434 9. 09 537 9.09 640 9. 09 742 9.09 845
9. 09 947
9.10 049 9.10 150 9.10 253 9. 10 353
9.10 J54 9.10 5.55 9. 10 056 9. 10 756 9.10 850
9.10 956
9.11 O.iO 9.11 155 9. 11 254 9.11 353
9.11 452 9.11 551 9. 11 G49 9. 11 747 9. 11 845
9. 11 943
9. 12 040 9. 12 138 9. 12 235 9. 12 332 9. 12 428 9. 12 625 9. 12 621 9. 12 717 9. 12 813
9. 12 909 9. 13 004
9. 13 099 9.13 194 9. 13 289 9.13 384 9. 13 478 9. 13 573 9. 13 667 9. 13 761 9. 13 854
9. 13 948
9. 14 041 9. 14 134 9. 14 227 9. 14 320 9. 14 412 9. 14 504 9. 14 597 9. 14 688 9. 14 780
0.91 080 0. 90 981 0.90 877 0. 90 773 0.90 670
0.90 053 0. 89 951 0. 89 850 0. 89 748
9. 99 675 9. 99 674 9. 99 672 9. 99 670 9. 99 669
9.99 667 9. 99 666 9. 99 664 9. 99 663 9.99 661
9.99 659 9.99 658 9. 99 656 9.99 655 9.99 653
0.89 244
0.1
144
9.99 651 9. 99 650 9.99 64S 9. 99 647 9, 99 645
0.69 044 0. 88 944 0. 88 845 0. 88 746 0. 88 647
9.99 643 9. 99 642 9.99 640 9. 99 638 9.99 637
0.83 548 0. 88 449 0.88 351 0. 83 253 0. 88 155 0. 88 057 I 0.87 960 0. 87 862 0. 87 765 0. 87 068 I 0. 87 572 0. 87 475 0. 87 379 0.87 283 0. 87 187 0.87 U9l 0.86 I 0. 86 901 0.86 80G 0.86 711 0.86 016 0.86 522 0. 86 427 0. 86 333 0. 86 239 0.86 146 0.86 052 0. 85 959 0.85 866 0. 85 773 0.85 680 0.1 0. 85 496 0.85 403 0. 85 312
9. 99 635 9. 99 633 9.99 632 9. 99 630 9. 99 629 9.99 627 9. 99 625 9.99 624 9. 99 622 9. 99 620 9. 99 618 I 9. 99 617 9.99 615 9. 99 613 9.99 r ' 9.99 610 1 9. 99 608 9. 99 607 9. 99 605
9. 99 603 I
9799 601 1 15
9.!
I 600
9. 99 586 9. 99 584 9. 99 582 9.99 581 9. 99 579 9. 99 577 9. 99 575
|
10.1 |
104 |
103 |
102 |
|
1,8 |
1,7 |
1,7 |
1,7 |
|
3,5 |
3,5 |
3,4 |
3,4 |
|
5,2 |
5,3 |
5,3 |
5,1 |
|
V,0 |
6,9 |
6,9 |
0,8 |
|
K,K |
8,7 |
8,6 |
8,5 |
|
10,5 |
10,4 |
10,3 |
10,2 |
|
12,3 |
13,1 |
12,0 |
11,9 |
|
14,0 |
13,9 |
13,7 |
13,0 |
|
15,8 |
15,6 |
15,4 |
15,3 |
|
17,5 |
17,3 |
17,3 |
17,0 |
|
35,0 |
34,7 |
34,3 |
34,0 |
|
52,5 |
53,0 |
51,5 |
51,0 |
|
70,0 |
69,3 |
68,7 |
68,0 |
|
8V,b |
86,7 |
85,8 |
85,0 |
|
101 |
100 |
99 |
98 |
|
1,V |
1,7 |
1,6 |
1,6 |
|
3,4 |
3,3 |
3,3 |
3,3 |
|
5,0 |
5,0 |
5,0 |
4,9 |
|
6,7 |
6,7 |
6,6 |
6,5 |
|
8,4 |
8,3 |
8,2 |
8,2 |
|
10,1 |
10,0 |
9,9 |
9,8 |
|
11,8 |
11,7 |
11,6 |
11,4 |
|
13, b |
13,3 |
13,2 |
13,1 |
|
15,2 |
15,0 |
14,8 |
14,7 |
|
16,8 |
16,7 |
16,5 |
16,3 |
|
3H,V |
33,3 |
33,0 |
32,7 |
|
bO,b |
50,0 |
49,5 |
49,0 |
|
BV,3 |
■66,7 |
66,0 |
65,3 |
|
84,2 |
83,3 |
83,5 |
81,7 |
|
97 |
96 |
95 |
94 |
|
1,6 |
1,6 |
1,6 |
1,6 |
|
3,2 |
3,2 |
3,2 |
3,1 |
|
4,8 |
4,8 |
. 4,8 |
4,7 |
|
6,5 |
6,4 |
6,3 |
6,3 |
|
8,1 |
8,0 |
7,9 |
7,8 |
|
9,7 |
9,6 |
9,5 |
9,4 |
|
11,3 |
11,2 |
11,1 |
11,0 |
|
13,9 |
12,8 |
12,7 |
12,5 |
|
14,6 |
14,4 |
14,2 |
14,1 |
|
16,2 |
16,0 |
15,8 |
15,7 |
|
33,3 |
32,0 |
31,7 |
31,3 |
|
48,b |
48,0 |
47,5 |
47,0 |
|
64,7 |
64,0 |
63,3 |
62,7 |
|
80,8 |
80,0 |
79,2 |
78,3 |
|
OS |
92 |
91 |
90 |
|
1,6 |
1,5 |
1,5 |
1,5 |
|
3,1 |
3,1 |
3,0 |
3,0 |
|
4,6 |
4,6 |
4,6 |
4,5 |
|
6,2 |
6,1 |
6,1 |
6,0 |
|
7,8 |
7,7 |
7,6 |
7,5 |
|
9,3 |
9,2 |
9,1 |
9,0 |
|
10,8 |
10,7 |
10,6 |
10,5 |
|
12,4 |
13,3 |
12,1 |
12,0 |
|
14,0 |
13,8 |
, 13,6 |
13,5 |
|
ib,b |
15,3 |
15,2 |
15,0 |
|
31,0 |
30,7 |
30,3 |
30,0 |
|
46,5 |
46,0 |
45,5 |
45,0 |
|
62,0 |
61,3 |
60,7 |
60,0 |
|
7V,6 |
76,7 |
75,8 |
75,0 |
83=
262
A MANUAL OF TOPOaKAPHIC METHODS.
Table XXXVI. — Logarithmic shies, cosines, tangents, and cotangents — Contiuned. [Extracted from Gauss' Logaritlimic and Trigonometvic. Tables.]
9. 14 356 9.U 445 9. 14 535 9. 14 624 9. 14 714
9. 14 8U3 9. 14 891
9. 14 980
9. 15 069 9. 15 157
9. 15 245
9. 15 333
9. 15 421
9.15 508
9. 15 596
9.16 116 9. 16 203 9. 16 289 9. 16 374 9. 16 460
9. 16 545 9. 16 631 9. 16 716 9. 16 801 9. 16 886
9. 16 970 I
9. 17 055 1 9. 17 139 9. 17 223 9. 17 307 6. 17 391 9. 17 474 9.17 ,558 9. 17 641
9. 17 973
9. 18 055 9. 18 137 9. 18 220 9. 18 302 9. 18 383 ! 9. 18 465 i 9. 18 547 { 9.18 628 9.18 709 9.18 790 9.18 871
9. 18 952
9. 19 033 9.19 113 9.19 193 9. 19 273 9. 19 353 9.19 433
9. 14 780 9. 14 872
9. 14 963
9. 15 054 9.15 145
9. 15 236 9. 15 327 9.15 417 9. 15 508 9. 15 598
9. 17 965
9.18 051 9.18 136 9. 18 221 9. 18 306 9.18 391 9. 18 475 9.18 560 9. 18 644 9.18 728 9. 18 812 9. 18 896
9. 18 979
9. 19 063 9. 19 146 9.19 229 9.19 312 9.19 395 9. 19 478 9. 19 561 9.19 643 9. 19 725 9.19 807 9. 19 889 9. 19 971
0. 85 220 0.85 128 0.85 037 0.84 946 0.84 855
0.84 764 0.84 673 0.S4 583 0. 84 492 0.84 402
0.84 312 0.84 223 0. 84 133 0.84 044 0. 83 954
0. 83 865 0. 83 776 0.83 688 0.83 599 0.83 511
0.83 423 0.83 335 0. 83 247 0.83 159 0.83 072
0. 82 984 0.82 897 0.82 810 0. 82 723 0. 82 637
0.82 550 0. 82 464 0.82 378 0. 82 292 0.82 201; 0. 82 120 0.82 035 0.81 949 Q.81 864 0.81 779 0.81 694 0.81 609 0.81 525 0. 81 440 0. 81 356 I 0. 81 272 I 0. 81 188 0. 81 104 0.81 021 0. 80 937
9.99 572 9.99 570 9.99 568
9. 99 566 9.99 565 9.99 563 9.99 561 9.99 559
9.99 557 9. 90 556 9.99 554 9.99 5.52 9.99 550
9. 99 548 9. 99 546 9.99 545 9. 99 543 9.99 541
9.99 528 9.99 526 9.99 524 9.99 522
9.99 520 9. 99 518 9. 99 517 9.99 515 9.99 513 9.99 511 9.99 509 9.99 507 9.99 505 9.99 503 9.99 501 9.99 499 9.99 497 9.99 495 9.99 494 9.99 492 9.99 490 9.99 488 9. 99 486 9.99 484 9.99 482 9.99 480 9.99 478 9. 99 476 9.99 474 9. 99 472 9.99 470 9.99 468 9. 99 466 9.99 464 9. 99 462
L. Tang.
|
92 |
91 |
90 |
|
1,5 |
1,5 |
1,5 |
|
3,1 |
3,0 |
3,0 |
|
4,6 |
4,6 |
4,5 |
|
• 6'1 |
6,1 |
6,0 |
|
7/7 |
7,6 |
7,5 |
|
9,2 |
9,1 |
9,0 |
|
10,7 |
10,6 |
10,5 |
|
12,3 |
12,1 |
12,0 |
|
13,8 |
13,6 |
13,5 |
|
15,3 |
15,2 |
15,0 |
|
30,7 |
30,3 |
30,0 |
|
46,0 |
45,5 |
45,0 |
|
61,3 |
60,7 |
60,0 |
|
76,7 |
75,8 |
75,0 |
|
S9 |
88 |
8J |
|
1,5 |
1,5 |
1,4 |
|
3,0 |
2,9 |
2,9 |
|
4,4 |
4,4 |
4,4 |
|
5,9 |
5,8 |
|
|
7,4 |
7,3 |
7,2 |
|
8,9 |
8,8 |
8,7 |
|
10,4 |
10,3 |
10,2 |
|
11,7 |
.11,6 |
|
|
13,4 |
13,2 |
13,0 |
|
14,8 |
14,7 |
14,5 |
|
29,3 |
29,0 |
|
|
44,0 |
43,5 |
|
|
59,3 |
58,7 |
58,0 |
|
V4,2 |
73,3 |
72,5 |
|
86 |
85 |
84 |
|
1,4 |
1,4 |
1,4 |
|
2,8 |
2,8 |
|
|
4,3 |
4,2 |
4,2 |
|
0,1 |
5,7 |
5,6 |
|
'1,'i |
7,1 |
7,0 |
|
8,b |
8,5 |
«8,4 |
|
10,0 |
9,9 |
9,8 |
|
ll,b |
11,3 |
11,2 |
|
12,9 |
12,8 |
12,6 |
|
14,3 |
14,2 |
14,0 |
|
28,7 |
28,3 |
28,0 |
|
43,0 |
42,5 |
42,0 |
|
57,3 |
56,7 |
56,0 |
|
71,7 |
70,8 |
70,0 |
|
■S» |
82 |
81 |
|
1,4 |
1,4 |
1,4 |
|
2,7 |
2,7 |
|
|
4,2 |
4,1 |
4,0 |
|
5,5 |
6,5 |
5,1 |
|
6,9 |
6,8 |
6,8 |
|
8,3 |
8,2 |
8,1 |
|
9,6 |
9,4 |
|
|
11,1 |
10,9 |
10,8 |
|
12,4 |
12,3 |
12,2 |
|
13,8 |
13,7 |
13,5 |
|
27,7 |
27,3 |
27,0 |
|
41,5 |
41,0 |
40,5 |
|
55,3 |
54,7 |
54,0 |
|
69,2 |
68,3 |
67,5 |
81^
LOGAEITHMS OF CIRCULAR FUNCTIONS.
263
Table XXXVI. — Loganthmic [Extracted ftom Gai
sines, cosines, tangents, and cotangents — Continued, iss' Logaritlunic and Trigonometric Tables.]
9.19 433 9. 19 613 9.19 592 9. 19 672 9. 19 751
9.19 830 9.19 909
9. 19 988 9. 20 067
9.20 145
9.20 223 9. 20 302 9.20 380 9.20 458 9. 20 535
9.20 768 9. 20 846 9^20 922^
9.20 999 9. 21 076
9.21 153 9.21 229 9.21 306
9.21 382 9.21 468 9.21 534 9.21 610 9^21_685^ 9.21 761 9.21 836 9.21 912 9. 21 987 9. 22 002
9. 22 137 9. 22 211 9. 22 286 9.22 361 9. 22 435
9. 22 509 9, 22 583 9. 22 657 9.22 731 9.22 805
9.22 952
9.23 025 9.23 098 9.23 171 9. 23 244 9.23 317 9.23 390 9. 23 463 9.23 535 9.23 607 9.23 679 9.23 752 9.23 823 9. 23 895 9. 23 967
9. 19 971 9. 20 053 9. 20 134
9.20 216 9.20 297
9.20 378 9.20 469 9. 20 540 9. 20 021 9. 20 701
9. 22 747 9.22 824 9.22 901
9.22 977
9.23 054 9.23 130 9.23 206 9.23 283 9. 23 359 9. 23 435
9. 23 510 6.23 586 9.23 661 9.23 737 9. 23 812 9.23 887
9. 23 962
9.24 037 9.24 112 9.24 186 9. 24 261 9.24 335 9. 24 410 9. 24 484 9. 24 558 9. 24 632
0. 79 947 0. 79 866 0.79 784 0.79 703
0. 79 622 0. 79 541 0.79 460 0. 79 379 0. 79 299
0. 79 218 0.79 138 0.79 058 0. 78 978
0. 78 739 0. 78 659 0.78 580 0. 78 501
0. 78 422 0. 78 343 0.78 264 0.78 186 0.78 107
0.78 029 0. 77 951 0. 77 873 0.77 795 0.77 717
9. 99 462 9. 99 460 9.99 458 9.99 456 9. 99 454
9.99 442 9. 99 440 9.99 438 9.99 436 9. 99 434
9, 99 432 9.99 429 9. 99 427 9.99 425 9. 99 423
9.99 421 9.99 419 9. 99 417 9.99 415 9.99 413
9.99 411 9.99 409 9. 99 407 9.99 404 9. 99 402
9.99 396 9. 99 394 9. 99 392
0. 76 113 0. 76 038 0.75 963 0. 75 888 0. 75 814 0. 75 739 I 0.75 665 0.75 590 0.75 516 0.75 442 0.751
L. Tang.
9. 99 390 9. 99 388 9. 99 385 9.99 383 9. 99 381 9. 99 379 9. 99 377 9. 99 375 9. 99 372 9. 99 370 9.99 368 9.99 366 9. 99 364 9.99 363 9. 99 359 9. 99 357 9. 99 355 9. 99 353 9. 99 351 9. 99 348 9. 99 346 9.99 344 9. 99 342 9. 99 340 9. 99 337 9. 99 335
|
80 |
79 |
78 |
|
1,3 |
1,3 |
1,3 |
|
2,7 |
2,6 |
2,6 |
|
4,0 |
4,0 |
3,9 |
|
5,3 |
5,3 |
5,2 |
|
6,7 |
6,6 |
6,5 |
|
8,0 |
7,9 |
7,8 |
|
9,3 |
9,2 |
9,1 |
|
10,7 |
10,5 |
10,4 |
|
12,0 |
11,8 |
11,7 |
|
13,3 |
13,2 |
13,0 |
|
26,7 |
26,3 |
26,0 |
|
40,0 |
39,5 |
39,0 |
|
53,3 |
52,7 |
52,0 |
|
66,7 |
65,8 |
65,0 |
|
76 |
75 |
74 |
|
1,3 |
1,2 |
1,2 |
|
2,5 |
2,5 |
2,5 |
|
3,8 |
3,8 |
3,7 |
|
5,1 |
5,0 |
4,9 |
|
6,3 |
6,2 |
6,2 |
|
7,6 |
7,5 |
7,4 |
|
8,9 |
8,8 |
8,6 |
|
10,1 |
10,0 |
9,9 |
|
11,4 |
11,2 |
11,1 |
|
12,7 |
12,5 |
12,3 |
|
25,3 |
35,0 |
24,7 |
|
38,0 |
37,5 |
37,0 |
|
50,7 |
50,0 |
49,3 |
|
63,3 |
62,5 |
61,7 |
|
72 |
71 |
S |
|
1,2 |
1,2 |
0,0 |
|
0,1 |
||
|
3,6 |
3,6 |
0,2 |
|
4,8 |
4,7 |
0,2 |
|
6,0 |
5,9 |
0,2 |
|
7,2 |
7,1 |
0,3 |
|
8,4 |
8,3 |
0,4 |
|
9,6 |
9,5 |
0,4 |
|
10,8 |
10,6 |
0,4 |
|
12,0 |
11,8 |
0,5 |
|
24,0 |
23,7 |
1,0 |
|
36,0 |
35,5 |
1,5 |
|
48,0 |
47,3 |
2,0 |
|
60,0 |
59,2 |
2,5 |
|
3 79 |
3 78 |
|
13,2 39,5 65,8 |
13,0 39,0 65,0 |
12,5 37,5 62,5
12,8 38,5 64,3
13,3 37,0 61,7
9,7 11,0 13,2 24,3
80°
264
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXVI. — Logaritnmic sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
10°
9. 23 967
9.24 039 9. 24 110 9.24 181 9.24 253
9. 24 324 9.24 395 9. 24 466 9.24 536 9. 24 607
9.25 098 9.25 168 9. 25 237 9.25 307
9.25 721 9. 25 790 9. 25 858 9.25 927 9. 25 995
9. 26 063 9. -6 131 9.26 199 9. 26 267 9.26 335
9. 26 403 9. 26 470 9. 26 538 9. 26 605 9. 26 672
9. 26 739 9. 26 806 9. 26 873 9. 26 940 9.27 207
9. 27 073 9.27 140 9. 27 206 9. 27 273 9. 27 339
9. 27 405 9. 27 471 9. 27 537 9. 27 602 9. 27 668
9. 27 734 9. 27 799 9. 27 864 9. 27 930 9. 27 995
9. 24 632 9. 24 706 9. 24 779 9. 24 853 9. 24 926
I. 25 000 '.25 073
9.25 365 9.25 437 9.25 510 9. 25 582 9.25 655
9.25 727 9. 25 799 9. 25 871 9. 25 943 9. 26 015
9. 26 086 9.26 158 9. 26 229 9. 26 301 9. 20 372
9.20 443 9. 26 514 9. 26 585 9.26 655 9. 26 726
9. 26 797 9. 26 867
9. 26 937
9.27 008 9. 27 078
9.27 148 9.27 218 9. 27 288 9.27 357 9. 27 427
9. 27 496 9. 27 566 9. 27 635 9.27 704
9.28 254 9.28 323 9. 28 391 9. 28 459
9. 28 527 9. 28 595 9.28 662 9. 28 730 9.28 798 9.28 865
0. 74 635 0. 74 563 0. 74 490 0.74 418 0. 74 345
0. 74 273 0. 74 201 0. 74 129 0. 74 057 0. 73 985
0.73 914 0.73 842 0. 73 771 0.73 699 0. 73 628
0. 73 657 0. 73 486 0. 73 415 0. 73 345 0 73 274
0. 73 203 0.73 133 0. 73 063 0. 72 992 0. 72 922
0. '
I 852
0.72 0.72 712 0. 72 643 0. 72 573
0. 72 504 0. 72 434 0. 72 365 0.72 296 0. 72 227 0.72T5¥ 0. 72 089 0. 72 020 0.7] 951 0. 71 883
0. 71 814 0. 71 746 0. 71 677 0. 71 609 0. 71 541
L. Tang.
9.99 331 9. 99 328 9. 99 326
9. 99 324 9. 99 322 9.99 319 9.99 317 9. 99 315
9. 99 301 9. 99 299 9.99 297 9. 99 294 9. 99 292
9.99 290 9. 99 2S8 9.99 285 9.99 283 9.99 281
9.99 270 9. 99 274 9. 99 271 9.99 269 9. 99 267 9. 99 264 9. 99 202 9. 99 260 9. 99 257
9. 99 219 9. 99 217 9. 99 214
9. 99 200 9. 99 197 9. 99 195
|
74 |
73 |
|
1,2 |
1,2 |
|
2,5 |
2,4 |
|
3,7 |
3,6 |
|
4,9 |
4,9 |
|
6,2 |
0,1 |
|
7,4 |
7,3 |
|
8,6 |
8,5 |
|
9,9 |
9,7 |
|
11,1 |
11,0 |
|
12,3 |
12,2 |
|
24,7 |
24,3 |
|
37,0 |
36,5 |
|
49,3 |
48,7 |
|
61,7 |
60,8 |
|
71 1,2 |
70 1,2 |
|
2,4 |
2,3 |
|
3'6 |
3,5 |
|
4,7 |
4,7 |
|
5,9 |
5'8 |
|
7,1 |
7,0 |
|
8,3 |
8,2 |
|
9,5 |
9,3 |
|
10,6 |
10,5 |
|
11,8 |
11,7 |
|
23,7 |
23,3 |
|
35,5 |
35,0 |
|
47,3 |
46,7 |
|
59,2 |
58,3 |
|
08 |
67 |
|
1/1 |
1,1 |
|
2,3 |
2,2 |
|
3,4 |
3,4 |
|
4,5 |
4,5 |
|
5,7 |
5,6 |
|
6,8 |
6,7 |
|
7,9 |
7,8 |
|
9,1 |
8,9 |
|
10,2 |
10,0 |
|
11,3 |
11,2 |
|
22,7 |
22,3 |
|
34,0 |
33,5 |
|
45,3 |
44,7 |
|
56,7 |
55,8 |
9,0
10,8 12,0 24,0 30,0 48,0 00,0
3,4 4,6 5,8 6,9 8,0 9,2 10,4 11,5 33,0 34,5 46,0 E.7,5
66
1,1 2,2 3,3 4,4 5,5 6,6
9,9 11,0 22,0 33,0 44,0 53,0
12,3 12,2 12,0 .37,0 36,5 36,0 61,7 i 60,8 60,0
|
3 71 |
3 JO |
3 69 |
|
11,8 35,5 59,2 |
11,7 35,0 58,3 |
11,5 34,5 57,5 |
11,3 34,0 56,7
79°
LOGAEITHMS OF CmCULAR FUNCTIONS.
265
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents- [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
11°
9.28 060 9.28 125 9. 28 190 I 9.28 254 9.28 319
9 28 705 9.28 769 9.28 833 9.28 896 9.28 960
9.29 024 9.29 087 9.29 150 9.29 214 9.29 277
9.29 340 9. 29 403 9.29 466 9.29 .529 9.29 591
9.29 054 9.29 716 9,29 779 9.29 841 9.29 903
9.29 966
9.30 028 9.30 090 9. 30 151 9. 30 213
9.30 887
9.30 947
9.31 008 9.31 068 9.31 129 9.31 i89 9.31 250 9.31 310 9.31 370 9. 31 430 i). 31 490 9.31 549 9.31 609 9.31 069 9.31 728 9:31 788
9.28 384 9.28 448 i 9.28 512 9.28 577 9.28 641 I
9.28 865 9. 28 933
9.29 000 9.29 067 9.29 134
9.29 201 9.29 268 9.29 335 9.29 402 9. 29 468
9.29 535 9.29 601 9.29 668 9.29 734 9.29 800
9. 39 932
9.29 998
9.30 064 9.30 130 9.30 195 9.30 261 9.30 326 9.30 391 9. 30 457
9.30 522 9.30 587 9.30 652 9.30 717 9.30 782
9. 30 846 9.30 911
9.30 975
9.31 040 9.31 104
9.31 168 9.31 233 9.31 297 9.31 361 9. 31 425 9.31 489^ 9.31 552 9.31 616 9.31 679 9.31 743 9. 31 806 9.31 870 9.31 933
9.31 996
9.32 059
9. 32 436 9.32 498 9. 32 561 9.32 623 9.32 685 9. 32 747
L. Cotg.
L. Cotg.
0.71 135 0.71 067 0.71 000 0.70 933 0, 70 866 0.70 799 0.70 732 0.70 005 0.70 598 0. 70 532
0. 70 465 0. 70 399 0.70 332 0.70 266 0.70 200
0.70 134 0.70 068 0.70 002 0.69 936 0.69 870 0. 69^80"5~l 0. 09 739 I 0. 69 674
9.99 190 9.99 187 9.99 185
9.99 170 9.99 167 9.99 165 9.99 162 9.99 160
9.99 157 9.99 155 9.99 152 9.99 150 9. 99 147 9. 99 145 9.99 142 9.99 140
0. 69 413 0.69 348 0, 69 283 0. 69 218
0.68 767 0.68 703 0.68 639
0^68 2J)7 0. 68 194
JUi7 941_ 0.67 878 0. 67 815 0. 67 7.52 I 0. 67 689
_a W 627^ 0. 67 564 0. 67 502 1 0. 67 439 0.67 37 0. 07 315
9.99 112 9.99 109
9.99 106 9.99 104 9.99 101 9.99 099 9.09 096 9. 99 093 9.99 091 9.99 088 9.99 086 9.99 083
9. 99 062 9.99 059 9.99 056 9.99 054 9.99 051 9.99 048 9.99 046 9.99 043 9. 99 040
|
65 |
Gi |
|
1/1 |
1,1 |
|
2,2 |
2,1 |
|
3,2 |
3,2 |
|
4,3 |
4,3 |
|
5,4 |
5,3 |
|
6,5 |
0,4 |
|
7,6 |
7,5 |
|
8,7 |
8,5 |
|
9,8 |
9,6 |
|
10,8 |
10,7 |
|
21,7 |
21,3 |
|
32,5 |
32,0 |
|
43,3 |
42,7 |
|
54,2 |
53,3 |
|
62 |
61 |
|
1,0 |
1,0 |
|
2,1 |
2,0 |
|
3,1 |
3,0 |
|
4,1 |
4,1 |
|
5,2 |
5,1 |
|
6,2 |
6,1 |
|
7,2 |
7,1 |
|
8,3 |
8,1 |
|
9,3 |
9,2 |
|
10,3 |
10,2 |
|
2C,7 |
20,3 |
|
31,0 |
30,5 |
|
41,3 |
40,7 |
|
51,7 |
50,8 |
|
59 1,0 |
3 0,0 |
|
2,0 |
0,1 |
|
3,0 |
0,2 |
|
3,9 |
0,2 |
|
4,8 |
0,2 |
|
5,9 |
a 0,3 |
|
6,9 |
0,4 |
|
7,9 |
0,4 |
|
8,8 |
0,4 |
|
9,8 |
0,5 |
|
19,7 |
1,0 |
|
29,5 |
1,5 |
|
39,3 |
2,0 |
|
49,2 |
2,5 |
10,7 32,0 53,3
11,0 33,0 56,0
10,5 31,5 52,5
1,0 2,1 3,2 4,2
6^3 7,4 8,4 9,4 10,5 21,0 31,5 42,0 52,5
10,0 20,0 30,0 40,0 50,0
10,8 32,5 54,2
78^
266
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXyi.—Loijayithmic [Extractocl fnim Giii
incs, cosines, tangents, and cotangents — Continued. as' Logarithmic and Trigouomotric Tables.]
9.31 788 9.31 847 9.31 907 9.31 9CC
9.32 202 9.32 2G1 9.32 319
9.32 437 9.32 49.5 9.32 553
9.32 S44 9.32 902
9.32 960
9.33 018 9.33 075 9.33 133 9.33 190
9.33 248 9.33 305 9.33 362 9.33 420 9.33 477
9.33 761
9.33 818 9.33 874 9.33 831
9.33 987
9.34 043
•55
9.34 100 9.34 156 9.34 212 9.34 268 9.34 324
9.34 380 9.34 436 9.34 491 9.34 547 9.34 602
9.34 058 9.34 713 9.34 769 9.34 824 9.34 879
9.34 934
9.34 989
9.35 044
9.32 933 9.32 995
9.33 057 9.33 119 9.33 180 9.33 242 9.33 303 "9.33 365 9.33 426 9.33 487
9.33 670 9.33 731 0.33 792 9.33 853 9.33 913
9.33 974
9.34 034 9.34 095 9.34 155 9Ji4 215 9.34 276 9.34 336 9.34 396 9.34 456 9.34 516
9.34 576 9.34 635 9.34 695 9.34 755 9.34 814
9.34 874 9.34 933
9.34 992
9.35 051 9.35 111
9.35 170 9.35 229 9.35 288 9.35 347 9.35 405 9.35 464" 9.35 523 9.35 581 9.35 640 9.35 698
9.35 757 9.35 815 9.35 873 9.35 931 9.35 989
L. Cotg.
L. Cotg
0. 67 253 0.67 190 0.67 128 0.67 067 0.67 005
0.66 943 0.66 881 0.66 820 0.66 758 0.66 697
0. 66 635 0.66 574 0.66 513 0.66 452 0.66 391
0.66 330 0.66 269 0.66 208 0.66 147 0. 66 q87_ 0.66 026 0.65 966 0.65 905 0.65 845 0.65 785
L. Cos.
9.99 040 9. 99 038 9.99 035 9.99 032 9.99 030
9.99 027 9.99 024 9.99 022 9.99 019 9.99 016
9.99 013 9.99 Oil 9.99 008 9.99 006 9.99 002
9.98 983 9.98 980 9.98 978 9.98 975
0.65 724 0.65 664 0.65 604 0.65 544 0.65 484
0.65 424 0.65 365 0.65 305 0.65 245 0.65 ISO
0.65 126 0.65 067 0.65 008 0.64 949 0. 64 889 0. 64 830 0.64 771 0.64 712 0.64 653 0.64 595
0.64 536 0.64 477 0.64 419 0.64 360 0.64 302
0.64 243 0.64 185 0.64 127 0.64 069 0.64 Oil
0.63 953 0.63 895 0.63 837 0.03 779 0.63 721 0.63.664
9.98 953 9.98 950 9.98 947
9.98 916 9.98 913 9.98 910
|
C3 |
62 |
|
1,0 |
1,0 |
|
2,1 |
2,0 |
|
3,2 |
3,1 |
|
4,2 |
4,1 |
|
5,2 |
5,2 |
|
6,8 |
6,2 |
|
7,4 |
7,2 |
|
8,4 |
8,3 |
|
9,4 |
9,3 |
|
10,5 |
10,3 |
|
21,0 |
20,7 |
|
31,5 |
31,0 |
|
42,0 |
41,3 |
|
52,5 |
51,7 |
|
60 |
59 |
|
1,0 |
1,0 |
|
2,0 |
2,0 |
|
3,0 |
8,0 |
|
4,0 |
3,9 |
|
5,0 |
4,9 |
|
6,0 |
5,9 |
|
7,0 |
6,9 |
|
8,0 |
7,9 |
|
9,0 |
8,8 |
|
10,0 |
9,8 |
|
20,0 |
19,7 |
|
30,0 |
29,5 |
|
40,0 |
39'3 |
|
50,0 |
49'2 |
|
57 |
56 |
|
1,0 |
0,9 |
|
1,9 |
1,9 |
|
2,8 |
2,8 |
|
3,8 |
3,7 |
|
4'8 |
4,7 |
|
5,7 |
5,6 |
|
6,6 |
6,5 |
|
7,6 |
7,5 |
|
8,6 |
8,4 |
|
9,5 |
9,3 |
|
19,0 |
18,7 |
|
28,5 |
28,0 |
|
38,0 |
37,3 |
|
47,5 |
46,7 |
10,3 31,0 51,7
|
3 |
S 1 |
|
59 |
oS |
|
9,8 29,5 49,2 |
9,7 29,0 48,3 |
1,0 2,0 3,0 4,1 5,1 6,1 7,1 8,1 9,2 10,2 20,3 30'5 40,7 50,8
3,9 4;8 5,8 6,8 7,7 8,7 9,7 19'3 29'0 38'7 48'3
0,9 1,8 2,8 3,7 4,6 5,5 6,4 7,3 8,2 9,2 18,3 27,5 36,7 45,8
10,0 30,0 50,0
9,5
28'5 47'5
77c
LOGAEITHMS OF CIECULAR FUIJGTIONS.
267
Table XXXVI — Loganthmio sines, cosines, tangents, and cotangents — Continued. [Extracted from Gaa33' Logaritlunio and Trigonometric Tables.]
13°
9. 35 209 9. 35 263 9. 35 318 9. 35 373 9. 35 427
9. 35 481 9.35 536 9. 35 590 9. 35 644 9. 35 698
9.35 752 9.35 806 9. 35 860 9. 35 914 9. 35 968
9. 36 022 9. 36 075 9.36 129 9.36 182 9. 36 236
9. 36 289 9. 36 342 9. 36 395 9. 36 449
9. 37 081 9. 37 133 9, 37 185 9. 37 237 9. 37 289
9. 37 341 9. 37 393 9. 37 445 9. 37 497 9. 37 549
9. 37 600 9. 37 652 9. 37 703 9. 37 755 9. 37 806
9.37 858 9. 37 909 9. 37 960 9. 38 Oil 9. 38 062
L. Tang.
9. 36 336 9. 36 394 9. 36 453 9,36 509 9. 36 566
9. 36 624 9. 36 681 9. 36 738 9. 36 795 9.36 852
9. 36 909 9. 36 966 9. 37 023 9. 37 080 9. 37 137
9. 37 193 9.37 250 9. 37 306 9. 37 363 9. 37 419
9. 37 476 9. 37 533 9. 37 588 9. 37 644 9. 37 700
9. 37 756 9.37 813 9. 37 868 9. 37 924
9. 38 918 9. 38 972 9. 39 027 9. 39 082
9. 39 136 9. 39 190 9. 39 245 9. 39 299 9. 39 353
9. 39 407 9. 39 461 9. 39 515 9. 39 569 9. 39 623 9. 39 677
L. Cotg.
0. 63 664 0. 63 606 0. 63 548 0. 63 491 0. 33 434
0.
376
0. 63 319 0. 63 262 0.63 205 0.63 148
0.63 091 0. 63 034 0. 62 977 0. 02 920 0. 62 863
0. 62 807 0.62 750 0. 62 694 0. 62 637 0. 62 581
0. 63 524 0. 63 468 0. 62 413 0. 63 356 0. 63 300
0.63 244 0.62 188 0.63 133 5. 62 076 0. 62 020
0. 61 965 0.61 909 0. 61 853 0. 61 798 0. 61 743
0. 61 687 0. 61 632 0. 61 577 0. 61 521 0. 61 466
0.61 411 0. 61 356 0. 61 301 0. 61 246 0. 61 192
0. 61 137 0. 61 082 0. 61 028 0.60 973 0. 00 918
0. 60 864 0. 60 810 0. 60 755 0. 60 701 0. 60 647
0.60 593 0. 60 539 0. 60 485 0.60 431 0. 60 377 0.60 323
9. 98 858 9.93 855 9. 98 852
9. 98 843 9. 98 840 9. 98 837 9. 98 834 9. 98 831
9. 98 828 9. 98 825 9. 98 822 9. 98 819 9. 98 816
9. 98 813 9. 98 810 9. 98 807 9. 98 804 9.98 801
9.98 798 9. 98 795 9. 98 792 9. 98 789 9. 98 786
9. 98 783 9, 98 780 9. 98 777 9. 98 774 9. 98 771
9. 98 768 9. 98 765 9. 98 763 9. 98 759 9. 98 756
9.98 753 9. 98 750 9. 98 746 9. 98 743 9. 98 740
9. 98 737 9. 98 734 9. 98 731 9. 98 728 9. 98 725
9. 98 722 9. 98 719 9. 98 715 9.98 712 9. 08 709
9. 98 706 9. 98 703 9. 98 700
|
S7 |
36 |
|
1,0 |
0,9 |
|
1,9 |
1,9 |
|
2,8 |
2,8 |
|
3,8 |
3,7 |
|
4,8 |
4,7 |
|
5,7 |
5,6 |
|
6,6 |
6,5 |
|
7,6 |
7,5 |
|
8,6 |
8,4 |
|
9,5 |
9,3 |
|
19,0 |
18,7 |
|
28,6 |
28,0 |
|
33,0 |
37,3 |
|
47,5 |
46,7 |
|
Si |
53 |
|
0,9 |
0,9 |
|
1,8 |
1,8 |
|
2,7 |
2,6 |
|
3,6 |
3,5 |
|
4,5 |
4,4 |
|
5,4 |
5,3 |
|
6,3 |
6,2 |
|
7,2 |
7,1 |
|
, 8,1 |
8,0 |
|
9,0 |
8,8 |
|
18,0 |
17,7 |
|
27,0 |
26,5 |
|
36,0 |
35,3 |
|
45,0 |
44,2 |
|
51 |
4 |
3 |
|
0,8 |
0,1 |
0,0 |
|
1,7 |
0,1 |
0,1 |
|
2,6 |
0,2 |
0,2 |
|
3,4 |
0,3 |
0,2 |
|
4,2 |
0,3 |
0,2 |
|
5,1 |
0,4 |
0,3 |
|
6,0 |
0,5 |
0,4 |
|
6,8 |
0,5 |
0,4 |
|
7,6 |
0,6 |
0,4 |
|
8,5 |
0,7 |
0,5 |
|
17,0 |
1,3 |
1,0 ' |
|
35,5 |
2,0 |
1,5 |
|
34,0 |
2,7 |
2,0 1 |
|
42,5 |
3,3 |
2,5 I |
|
3^ S6 |
3 53 |
|
9,3 28,0 46,7 |
9,2 27,5 45,8 |
2,8 3,7 4,6 5,5 6,4 7,3 8,2 9,2 18,3 27,5 36,7 45,8
6,9 7,8 8,7 17,3 26,0 34,7 43,3
|
4 |
4 |
3 |
|
53 |
34 |
58 |
|
6,9 |
6,8 |
9,7 |
|
20,6 |
20,2 |
29,0 |
|
34,4 |
33,8 |
48,3 |
|
48,1 |
47,2 |
— |
9,0 27,0 45,0
76=
268
A MANUAL OJ? TOPOGEAPHIO METHODS.
Table XXXVI. — Logarithmic sines, cosinen, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.)
|
51 |
53 |
|
0,9 |
0,9 |
|
1,8 |
1,8 |
|
3,7 |
2,6 |
|
3,6 |
3,5 |
|
4,5 |
4,4 |
|
5,4 |
5,3 |
|
6,3 |
8,2 |
|
7,2 |
7,1 |
|
8,1 |
8,0 |
|
9,0 |
8,8 |
|
18,0 |
17,7 |
|
27,0 |
20,5 |
|
36,0 |
35,3 |
|
45,0 |
44,2 |
|
51 |
50 |
|
0,8 |
0,8 |
|
1,7 |
1/7 |
|
2,6 |
2,5 |
|
3,4 |
3,3 |
|
4,2 |
4,2 |
|
5,1 |
5,0 |
|
6,0 |
5,8 |
|
6,8 |
6,7 |
|
7,6 |
7,5 |
|
8,5 |
8,3 |
|
17,0 |
16,7 |
|
25,5 |
25,0 |
|
34,0 |
33,3 |
|
42,5 |
41,7 |
|
48 0,8 |
47 0,8 |
i 0,1 |
|
1,6 |
1,6 |
0,1 |
|
2,4 |
214 |
0,2 |
|
3,2 |
3,1 |
0,3 |
|
4,0 |
3,9 |
0,3 |
|
4,8 |
4,V |
0,4 |
|
5,6 |
5,5 |
0,5 |
|
6,4 |
6,3 |
0,5 |
|
7,2 |
7,0 |
0,6 |
|
H,0 |
7,8 |
0,7 |
|
16,0 |
15,7 |
1,3 |
|
24,11 |
i;:),5 |
2,0 |
|
32,U |
■■UrI |
'■^,7 |
|
4U,ll |
:jo,2 |
3,3 |
3,5 4,3 5,2 6,1 6,9 7,8 8,7 17,3 26,0 34,7 43,3
1,6 2,4 3,3 4/1 4,9 5,7 6,5 7,4 8,2 16,3 24,5 32,7 40,8
3
0,0 0,1 0,2 0,2 0,2 0,3 0,4 0,4 0,4 0,5 1,0 1,5 2,0 2,5
|
4 |
4 |
4 |
|
1 ^* |
.53 |
52 |
|
6,8 |
6,6 |
6,5 |
|
20,2 |
19,9 |
19,5 |
|
33,8 |
33,1 |
32,5 |
|
! 47,2 |
46,4 |
45,5 |
|
3 |
3 |
3 |
|
54 |
53 |
52 |
|
i 9,0 ! 27,0 45,0 |
8,8 26,5 44,2 |
8,7 26,0 43,3 |
6,4 19,1 31,9 44,6
8,5 25,5 42,5
75=
LOGARITHMS OF OlECULAK ru:NGTIO:tfS.
269
Table XXXVI. — LogarUhniie sines, cosines, tangentSj and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
15°
9. 41 300 9. 41 347 9.41 394 9.41 441 9.41 488
9.41 635 9.41 582 9.41 628 9.41 675 9.41 722
9.41 768 9.41 815 9.41 861 9.41 908 9.41 954
9.42 001 9.42 047 9.42 093 9.42 140 9.42 186
9.42 232 9.42 278 9.42 324 9.42 370 9. 42 416
9. 42 461 9.42 507 9.42 553 9.42 599 9.42 644
9.42 690 9. 42 735 9. 42 781 9. 42 826 9. 42 872
9. 42 917
9.42 962
9. 43 008 9.43 053 9. 43 098
9.43 143 9.43 188 9. 43 233 9.43 278 9.43 323
9.43 367 9.43 412 9.43 457 9.43 502 9.43 546
9.43 591 9.43 635 9.43 680 9.43 724 9.43 769
9.43 813 9.43 857 9.43 901 9.43 946
9.43 990
9. 44 034
9.43 U57 9. 43 108 9.43 1.58 9.43 208 9.43 258 9.43 308 9. 43 358 9. 43 408 9.43 458 9.43 508
9.43 658 9.43 607 9.43 657 9.43 707 9.43 756
9.44 787 9. 44 836 9. 44 884 9. 44 933 9. 44 981
9. 45 029 9.45 078 9.45 126 9. 45 174 9.45 222
9.45 271 9.45 319 9.45 367 9.45 415 9.45 463
9. 45 511 9.45 559 9.45 gu6 9.45 654 9.45 702 9.45 IW
L. Cotg.
0. 57 195 0. 57 144 0. 57 094 0. 57 043 0.56 993
0. 56 943 0. 56 892 0. 56 842 0. 56 792 0. 56 742
0. 56 692 0. 56 042 0. 56 592 0.50 542 0. 56 492
0. .56 442 0. 56 393 0. 56 343 0. 56 293 0. 56 244 0. 56 194 0.56 145 0.56 095 0. 56 040
0.55 947 0. 55 898 0.55 849 0. .55 799 0^5^750 6. 55 701 0. 55 652
0.;
603
0. 55 456 0. 55 408 0. 55 359 0. 55 310
0. 55 164 0.55 116 0. 55 067 0. 55 019
0. 54 971 0. 54 922 0. 54 874 0. 54 826 0. 54 778
0. 54 729 0.54 681 0. 54 633 0. 54 585 0. 54 537
0. 54 489 0. 54 441 0.54 394 0.54 346 0. 54 298 0. 54 250
9. 98 494 9. 9,S 491 9.98 488 9. 98 484 9. 98 481
9. 98 477 9. 98 474 9. 98 471 9.98 467 9. 98 464
9. 98 373 9. 98 370 9. 98 366 9. f 8 363 9. 98 359
9. 98 356 9. 98 352 9. 98 349 9. 98 345 9. 98 342
9.98 338 9. 98 334 9.98 331 9. 98 327 9. 98 324
9. 98 320 9.98 317 9. 98 313 9. 98 309 9. 98 306
9.98 302 9. 98 299 9.98 295 9.98 291 9.98 288 I
L. Tang. L. Sin. I d.
740
|
51 |
50 |
|
0,8 |
0,8 |
|
1,7 |
1,7 |
|
2,6 |
2,5 |
|
3,4 |
3,3 |
|
4,2 |
4,2 |
|
5,1 |
5,0 |
|
6,0 |
5,8 |
|
6,8 |
6,7 |
|
7,6 |
7,5 |
|
8,5 |
8,3 |
|
17,0 |
16,7 |
|
25,5 |
25,0 |
|
34,0 |
- 33,3 |
|
42,5 |
41,7 |
|
48 0,8 |
47 0,8 |
|
1,6 |
1,6 |
|
2,4 |
2,4 |
|
3,2 |
3,1 |
|
4,0 |
3,9 |
|
4,8 |
4,7 |
|
5,6 |
5,5 |
|
6,4 |
6,3 |
|
7,2 |
7,0 |
|
8,0 |
7,8 |
|
16,0 |
15,7 |
|
24,0 |
23,5 |
|
32j0 |
31,3 |
|
40,0 |
39,2 |
|
45 0,8 |
44 0,7 |
4 0,1 |
|
1,5 |
1,5 |
0,1 |
|
2,2 |
2'2 |
0,2 |
|
3,0 |
2,9 |
0,3 |
|
3,8 |
3,7 |
0,3 |
|
4,5 |
4,4 |
0,4 |
|
5,2 |
5,1 |
0,5 |
|
6,0 |
5,9 |
0,5 |
|
6,8 |
6,6 |
0,6 |
|
7,5 |
7,3 |
0,7 |
|
15,0 |
14,7 |
1,3 |
|
22,5 |
22,0 |
2,0 |
|
30,0 |
29,3 |
2,7 |
|
37,5 |
36,7 |
3,3 |
16,3 24,5 32,7 40,8
7,7 15,3 23,0 30,7 38,3
3
0,0 0,1 0,2 0,2 0,2 0,3 0,4
|
4 |
1 |
4 |
|
50 |
49 |
48 |
|
6,2 18,8 31,2 43;8 |
6,1 18,4 30,6 42,9 |
6,0 18,0 30,0 42,0 |
|
51 |
50 |
49 |
|
8,5 1 25,5 42,5 |
8,3 25,0 41,7 |
8,2 24,5 40,8 |
5,9 17,0 29,4 41,1
8,0 24,0 40,0
270
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — C'ontiuueil. IBxtracted from Gauss' Logaritlmiic ami Trigonometric Tables.]
16°
|
48 |
47 |
|
0,8 |
0,8 |
|
1,6 |
1,6 |
|
2,4 |
2,4 |
|
3,2 |
3,1 |
|
4,0 |
3,9 |
|
4,8 |
4,7 |
|
5,6 |
5,5 |
|
6,4 |
'6,3 |
|
7,2 |
7,0 |
|
8,0 |
7,8 |
|
16,0 |
15,7 |
|
24,0 |
23,5 |
|
32,0 |
31,3 |
|
40,0 |
39,2 |
|
45 |
44 |
|
0,8 |
0,7 |
|
1,5 |
1,5 |
|
2,2 |
2,2 |
|
3,0 |
2,9 |
|
3,8 |
3,7 |
|
4,5 |
4,4 |
|
5,2 |
5,1 |
|
6,0 |
5,9 |
|
6,8 |
6,6 |
|
7,5 |
7,3 |
|
15,0 |
14,7 |
|
22,5 |
22,0 |
|
30,0 |
29,3 |
|
37,5 |
36,7 |
|
42 |
41 |
4 |
|
0,7 |
0,7 |
0,1 |
|
1,4 |
1,4 |
o,u |
|
2,1 |
2,0 |
0,2 |
|
2,8 |
2,7 |
0,3 |
|
3,5 |
3,4 |
0,3 |
|
4,2 |
4,1 |
0,4 |
|
4,9 |
4,8 |
0,5 |
|
5,6 |
5,5 |
0,5 |
|
6,3 |
0,2 |
0,6 |
|
7,0 |
6,8 |
0,7 |
|
14,0 |
13,7 |
1,3 |
|
21,0 |
20,5 |
2,0 |
|
28,0 |
27,3 |
2,7 |
|
35,0 |
34,2 |
0,8 1,5 2,3 3,1 3,8 4,6 5,4 6,1 6,9 7,7 15,3 23,0 30,7
0,7 1,4 2,2 2,9 3,6 4,3 5,0 5,7 6,4 7,2 14,3 21,5 28,7 35,8
|
4 |
4 |
|
48 |
47 |
|
6,0 18,0 30,0 42,0 |
5,9 17,6 29,4 41,1 |
|
.•5 48 |
3 47 |
|
8,0 24,0 40,0 |
7,8 23,5 39,2 |
5,6 16,9 28,1 39,4
7,7 7,5 23,0 22,5 38,3 37,5
73°
LOGAEITHMS OF CIECULAR FUNCTIONS.
271
Table liXXYl,~~Loganthmic sinesy cosineSj tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometiic Tablea.]
17°
9. 46 670 9. 46 717 9.46 758 9.46 800 9. 46 841 9. 46 882 9. 46 923 9. 46 964
9.47 045 9. 47 086 9. 47 127 9.47 168
9. 47 209 9.47 249 9. 47 290 9. 47 330 9. 47 371
9. 47 411 9. 47 432 9. 47 492 9.47 533 _9^47_57£ 9. 47 6i3 9. 47 654 9.47 694
9.47 814 9. 47 854 9. 47 894 9. 47 934 9^ 47 974
9.48 014 9. 48 054 9. 48 094 9.48 133 9. 48 173
9.48 213 9.48 252 9. 48 292 9.48 332 9. 48 371
9. 48 411 9. 43 450 9. 48 490 9.48 529
9.48 803 9. 48 842 9. 48 881 9. 48 920 9. 48 959
1.48 534 1.48 579 i. 48 624 i. 48 669 I. 48 714 I. 48 759 I. 48 804 :. 48 849 1.48 894 1.48 939
1.48 984
1.49 029 I. 49 073 1.49 118 1.49 163
'. 49 207 I. 49 252 '.49 296 .49 341 '. 49 385
'. 49 430 1. 49 474 '. 49 519 .49 563 . 49 607
9. 49 652 9. 49 696 9.49 740 9. 49 784 9. 49 828
i. 50 180 I. 50 223 1. 50 267 '. 50 311 . 50 355 . 50 398 . 50 442 . 50 485
I. 50 529 1.50 572 1. 50 616 I. 50 659 I. 50 703 I. 50 746 I. 50 789 I. 50 833 I. 50 876 I. 50 919
1. 50 962
1.51 005 '. 51 048 I. 51 092 .51 135
0.51 466 0.51 421 0. 51 376 0. 51 331 0. 51 286
9, 98 056 9. 98 052 9. 98 048 9. 98 044
0.51 241 0. 51 196 0.51 151 0. 51 106 0. 51 061
0. 51 016 0.50 971 0. 50 927 0. 50 882 _0.J0_837 0. 50 793 0. 50 748 0. 50 704 0. 50 659 0.50 615
9. 98 036 9.98 032 9.98 029 9.98 025^ 9. 98 021 9. 98 017 9. 98 013 : 9. 98 009 9. 98 005
0.50 570 0. 50 526 0. 50 481 0. 50 437 0. 50 393
0. 50 348 0. 50 304 0. 50 260 0. 50 216 0. 50 172
0.50 128 0. 50 084 0.50 040 0.49 996 0.49 952
0.49 908 0.49 804 0.49 820 0.49 777 0. 49 733
0.49 689 0.49 645 0. 49 602 0. 49 558 0.49 515
0. 49 471 0. 49 428 0.49 384 0. 49 341 0. 49 297
0. 49 254 0.49 211 0.49 167 0.49 124 0. 49 081 6.49 038 0. 48 995 0.48 952 0. 48 908 0. 48 865 0. 48 822
9.98 001 I 9. 97 997 1 9. 97 993 i 9. 97 989 9. 97 986
9. 97 982 9.97 978 9. 97 974 ■
9.97
70
9. 97 966_ 9. 97 962 9. 97 958 9. 97 954 9. 37 950 9.97 946
9.97 942 9. 97 938 9.97 934 ! 9. 97 930 9. 97 926 '
9. 97 910 9. 97 906
9. 97 902 9. 97 898 9. 97 894 9. 97 890 I 9. 97 886
9. 97 861 9. 97 857 9. 97 8.53 9. 97 849 9. 97 845
9. 97 841 9. 97 837 9. 97 833 9. 97 829 9. 97 825
L. Tang. I L. Sin.
|
45 |
44 |
|
0,8 |
0,7 |
|
1,5 |
1,5 |
|
2,2 |
2,2 |
|
3,0 |
2,9 |
|
3,8 |
3,7 |
|
4,5 |
4,4 |
|
5,2 |
5,1 |
|
5,9 |
|
|
6,8 |
6,6 |
|
7,5 |
7,8 |
|
15,0 |
14,7 |
|
22,5 |
22,0 |
|
30,0 |
29,3 |
|
37,5 |
36,7 |
|
42 |
41 |
|
0,7 |
0,7 |
|
1,4 |
1,4 |
|
2,1 |
2,0 |
|
2,8 |
2,7 |
|
3,5 |
3,4 |
|
4,2 |
4,1 |
|
4,9 |
4,8 |
|
5,6 |
5,5 |
|
6,3 |
6,2 |
|
7,0 |
6,8 |
|
14,0 |
13,7 |
|
21,0 |
20,5 |
|
28,0 |
27,3 |
|
3b,0 |
34,2 |
|
39 |
5 |
4 |
|
0,6 |
0,1 |
0,1 |
|
1,3 |
0,2 |
0,1 |
|
2,0 |
0,2 |
0,2 |
|
2,6 |
0,3 |
0,3 |
|
3,2 |
0,4 |
0,3 |
|
3,9 |
0,5 |
0,4 |
|
4,6 |
0,6 |
0,5 |
|
5,2 |
0,7 |
0,5 |
|
5,8 |
0,8 |
0,6 |
|
6,5 |
0,8 |
0,7 |
|
13,0 |
1,7 |
1,3 |
|
19,5 |
2,5 |
2,0 |
|
26,0 |
3,3 |
2,7 ! |
|
32,5 |
4,2 |
3,3 |
|
5 |
4 |
|
43 |
45 |
|
4,3 |
5,6 |
|
12,9 |
16,9 |
|
21,5 |
28,1 |
|
30,1 |
39,4 |
|
38,7 |
- |
0,7 1,4 2,2 2,9 3,6 4'3 5,0 5,7 6,4 7,2 14,3 21,5 28,7 35,8
4,0 4,7 5,3 6,0 6,7 13,3 20,0 26,7 33,3
0,0 !
0,1 I
0,2
0,2
0,2
0,3
0,4
0,4
0,4
0,5
1,0
1,5
2,0
2,5
5,5 16,5 27,5
|
4 |
3 |
3 |
|
4S |
45 |
44 |
|
5,4 |
7,5 |
7,3 |
|
16,1 |
22,5 |
|
|
26,9 |
37,5 |
36,7 |
|
37,6 |
|
■ |
|
P |
P. |
72^
272
A MANUAL OF TOrOGKAPHIO METHODS.
Table XXXVl.^ Lof/anthmic !<'ntes, cosines, lanfjentH, and cotangents — Contiuued, [Extraotod Iroui Gauss" Loi^iirithmic ami Trigonometric Tables.]
18°
9.48 998
9.49 037 9. 49 07(i 9.49 115 9.49 153
9. 49 192 9.49 231 9.49 269 9.49 308 9.49 347
9. 49 385 9. 49 424 9. 49 462 9. 49 500 9.49 539
9.49 577 9.49 615 9.49 654 9.49 692 9.49 7J0
9. 49 76S 9. 49 806 9.49 844 9. 49 882 9. 49 920
9.49 958
9.49 996
9.50 034 9. 50 072 9.50 110
9. 50 148 9. 50 185 9. 50 223 9.50 261 9. 50 298
9. 50 336 9. .50 374 9.50 411 9. 50 449 9.50 480
9. 50 523 9.50 561 9. 50 598 9. 50 635 9. 50 673
9.50 710 9.50 747 9.50 784 9.50 821 9.50 8.58
9. 50 890 9. 50 933
9.50 970
9.51 007 9. 51 043
9.51 080 9.51 117 9.51 154 9.51 191 9.51 227 9. 51 264
L. Tang.
9. 51 606 9,51 648 9.51 691 9.51 734 9. 51 776
9.51 819 9.51 861 9.51 903 9.51 946 9.51 988
9. 52 031 9. 52 073 9.52 115 9.52 157 9.^2 200 9.52 242 9. 52 284 9.52 326 9. 52 368 9^52 410 9. 52 452 9. 52 494 9. 52 536 9.52 578 9. 52 620
9. 52 661 9. 52 703 9. 52 745 9.52 787 9.52 829
9.53 078 9.53 120 9.53 161 9.53 202 9.53 244
9.53 492 9.53 533 9.53 574 9.53 615 9. 53 656 9. 53 697
L. Cotg.
L. Cotg.
0. 48 822 0, 48 779 0. 48 736 0.48 694 0. 48 651
0.48 008 0.48 505 0.48 ,522 0.48 480 0.48 437
0. 48 394 0. 48 352 0.48 309 0. 48 266 0.48 224
0.48 181 0.48 139 0.48 097 0.48 0.54 0.48 012
0.47 069 0.47 927 U.47 885 0.47 343 0.47 800
0. 47 716 0.47 674 0. 47 632 0. 47 590
0. 47 548 0. 47 506 0.47 464 0.47 422 0.47 380
0.47 339 0.47 297 0.47 255 0.47 213 0.47 171
0. 47 130 j 0, 47 088 0. 47 047 0. 47 005 0. 46 963
0. 46 922
0. 46 880
0. 46 839
0. 46 798
0. 46 7.56
0.46 715 0. 46 673 0. 46 632 0. 46 591 0. 46 550 !
9. 97 821 9.97 817 9.97 812
9.97 767 9.97 763
9.97 759 9.97 7.54 9.97 750 9. 97 746 9.97 742
9. 97 738 9.97 734 9.97 729 9.97 725 9^7 731 9. 97 717 9. 97 713 9.97 708 9. 97 704 9.97 700
9. 97 696 9. 97 691 9. 97 687 9.97 683 9.97 679
9.97 674 9.97 670 9.97 666 9.97 662 9. 97 657
9.97 653 9.97 649 9.97 645 9.97 640 9.97 636
9.97 632 9.97 628 9.97 623 9.97 619 9.97 615
9.97 610 9. 97 606 9 97 602 9.97 .597 9.97 593
1.97 589
0.46 508 I 0. 46 467 0. 46 426 0. 46 385 0. 46 344 I 0. 46 303 i
L. Tang. I L. Sin.
|
43 0,7 |
42 0,7 |
|
1,4 |
1,4 |
|
2,2 |
2,1 |
|
2,9 |
2,8 |
|
3,6 |
3,5 |
|
4,3 |
4,2 |
|
5,0 |
4,9 |
|
. 5,7 |
5,6 |
|
6,4 |
6,3 |
|
7,2 |
7,0 |
|
14,3 |
14,0 |
|
21,5 |
21,0 |
|
28,7 |
28,0 |
|
35,8 |
35,0 |
|
.S9 |
88 |
|
0,6 |
0,6 |
|
1,3 |
1,3 |
|
2,0 |
1,9 |
|
2,6 |
2,5 |
|
3,2 |
3,2 |
|
3,9 |
3,8 |
|
4,0 |
4,4 |
|
5,2 |
5,1 |
|
5,8 |
5,7 |
|
6,5 |
6,3 |
|
13,0 |
12,7 |
|
19,5 |
19,0 |
|
26,0 |
25,3 |
|
32,5 |
31,7 |
|
30 |
5 |
|
0,6 |
0,1 |
|
1,2 |
0,2 |
|
1,8 |
0,2 |
|
2,4 |
0,3 |
|
3,0 |
0!4 |
|
3,6 |
0,5 |
|
4,2 |
0,6 |
|
4,8 |
.0,7 |
|
5,4 |
0,8 |
|
6,0 |
0,8 |
|
12,0 |
1,7 |
|
18,0 |
2,5 |
|
24,0 |
3,3 |
|
30,0 |
4,2 |
|
5 |
.5 |
|
43 |
43 |
|
4,3 ; |
4,2 |
|
12,9 ; |
12,0 |
|
21,5 1 |
21,0 |
|
30,1 |
29,4 |
|
38,7 |
37,8 |
0,7 1,4 2,0 2,7 3,4 4,1 4,8 5,5 6,2 6,8 13,7 20,5 27,3 34,2
4,1 12,3 20,5 28,7 36,9
|
5,4 |
5,2 |
5,1 |
|
16,1 |
15,8 |
15,4 |
|
26'9 |
26,2 |
25,6 |
|
37,6 |
36,8 ; |
35,9 |
71^
LOGAEITHMS OF CIECULAR FUifCTIONS.
273
Table XXXVI. — Logarithmic sines, cosines, iangentSj and cotangents — Contiaiued. [Extracted from Gauss' Logaritbmic and Trigonometric Tables.]
19°
9. 51 264 9.51 301 9.51 338 9.51 374 9.51 411
9.51 447 9.51 484 9.51 520 9.51 557 9. 51 593 9.'51 629 9.51 666 9. 51 702 9.51 738 9.51 774 9.51 811 9.51 847 9.51 883 9.51 919 9.51 955
9. 52 527 9. 52 563 9. 52 598 9. 52 634 9. 52 669
9.52 705 9. 52 740 9.52 775 9. 52 811 9. 52 846
9. 58 021
9. 53 056 9.53 092 9.53 126 9.53 161 9.53 196
9. 53 231 9.53 266 9. 53 301 9.53 336 9. 53 370 9. 53 405
d. c. ! L. Cotg.
9. 53 697 9. 53 738 9.53 779 9.53 820 9.53 861 9. 53 902 9.53 943 9. 53 981 9. 54 025 9. 51 0C5
9.54 106 9.54 147 9. .54 187 9. 54 228 9.54 269
9.54 309 9. .54 350 9.54 390 9.54 431 9. 54 471
9.54 915 9.51 955 9.54 995 9. 55 035 9. 55 075
9.55 115 9.55 155 9.55 195 9. 55 235 9. 55 275
9.55 315 9.55 355 9.55 395 9. 55 434 9.-55 474 9. 55 514 9. 55 554 9.55 593 9. 55 633 9.55 673
9. 55 712 9.55 752 9.55 791 9.55 831 9.55 870
L. Cotg.
0.46 303 0.46 262 0.46 221 0.46 180 0.46 139
0.46 098 0. 46 057 0.46 016 0.45 975 0. 45 935
0.45 894 0.45 853 0.45 813
0.45 010 0. 45 569 0.45 .529
0.45 488 0.45 448 0. 45 407 0.45 367 0.45 327
0.45 286 0.45 246 0,45 206 0. 45 165 0.45 125
0.45 085 0.45 045 0.45 005 0.44 965 0.44 925
0.44 885 0.44 845 0. 44 805 0.44 765 0.44 725
0.44 685 0.44 645 0.44 6115 0.44 566 0. 44 526
0. 44 486 0. 44 446 0,44 407 0. 44 367 0.44 327
0.44 288 0.44 248 0. 44 209 0.44 169 0.44 130
0.44 090 0,44 051 0.44 Oil 0.43 972 0.43 933 0. 43 893
d. c. L. Tang.
9.97 435 9.97 430 9.97 426 9. 97 421 9. 97 417
9. 97 412 9. 97 408 9. 97 403 9. 97 399 9.97 394
9. 97 390 9.97 385 9.97 .381 9.97 376 9. 97 372 9.97 367 9.97 363 9. 97 358 9.97 353 9.97 349
9.97 340 9.97 335 9.97 331 9.97 326
9.97 322 9.97 317 9.97 312 9.97 308 9.97 303 9. 97 299
|
41 |
40 |
|
0,7 |
0,7 |
|
1,4 |
1,3 |
|
2,0 |
2,0 |
|
2,7 |
2,7 |
|
3,4 |
3,3 |
|
4,1 |
4,0 |
|
4,8 |
4,7 |
|
5,5 |
5,3 |
|
6,2 |
6,0 |
|
6,8 |
6,7 |
|
13,7 |
13,3 |
|
20,5 |
20,0 |
|
27,3 |
26,7 |
|
34,2 |
33,3 |
|
37 |
36 |
|
0,6 |
0,6 |
|
1,3 |
1,2 |
|
1,8 |
1,8 |
|
2,5 |
2,4 |
|
3,1 |
3,0 |
|
3,7 |
3,6 |
|
4,3 |
4,2 |
|
4,9 |
4,8 |
|
5'6 |
5,4 |
|
6,2 |
6,0 |
|
12,3 |
12,0 |
|
18,5 |
18,0 |
|
24'? |
24,0 |
|
30,8 |
30,0 |
|
34 |
5 |
|
0,6 |
0,1 |
|
1,1 |
0,2 |
|
1,7 |
0,2 |
|
2,3 |
0,3 |
|
2,8 |
0,4 |
|
3,4 |
0,5 |
|
4,0 |
0,6 |
|
4,5 |
0,7 |
|
5,1 |
0,8 |
|
5,7 |
0,8 |
|
11,3 |
1,7 |
|
17,0 |
2,5 |
|
22,7 |
|
|
28,3 |
4,2 |
|
5 |
5 |
|
41 |
40 |
|
4,1 |
4,0 |
|
12,3 |
12,0 |
|
20,5 |
20,0 |
|
28,7 |
28,0 |
|
36,9 |
36,0 |
|
41 |
40 |
|
5,1 |
5,0 |
|
15,4 |
15,0 |
|
25,6 |
25,0 |
|
35,9 |
35,0 |
6,5 13,0 19,5 26,0 32,5
5,2 5,8 11,7 17,5 23'3 29,2
11,7 19,5 27,3 35,1
4,9 14,6 24,4 34,1
MON XXII-
-18
70=
274
A MAXUAL OF TOPOGRAPHIC METHODS.
Taiu.k WWl.—Lundrithmic shies, roslnes, taHi/euts, mid mlaiii/cnts—Contiuned. tExtractfil from lliiuss' Logarithmic iim\ Trigouomctric Tables.]
20°
|
L. Sin. |
rt. |
L. Tang. |
(I.C. |
L. Cotg. |
L. Cos. |
a. |
P. |
P. |
||||
|
0 |
9. 53 405 |
9. 56 107 |
0. 43 893 |
9. 97 299 |
5 5 4 5 4 5 5 4 |
60 |
40 |
39 0,6 1,3 2,e |
38 0,6 |
|||
|
I |
9.53 440 |
35 |
. 9. 56 146 |
0. 43 854 |
9. 97 294 |
59 |
1,3 2,0 •2,7 |
1,3 1,9 2,5 3,2 3,8 |
||||
|
9.53 475 |
35 |
9. 56 185 |
0.43 815 |
9. 97 289 |
58 |
|||||||
|
3 |
9. 53 509 |
9.56 224 |
0.43 776 |
9. 97 285 |
2,6. 3,2 3,9 |
|||||||
|
4 |
9. 53 544 9. 53 578 |
34 |
9. 56 264 |
39 |
0. 43 736 |
9.97 276 |
5 6 |
3,3 4,0 |
||||
|
5 |
9. 56 303 |
0. 43 697 |
55 |
|||||||||
|
6 |
9. 53 613 |
35 |
9.56 342 |
0.43 658 |
9. 97 271 |
54 |
7 |
4,7 |
4,6 |
4,4 |
||
|
9.53 647 |
34 |
9. 50 381 |
0. 43 619 |
9. 97 266 |
53 |
8 |
5,3 |
5,2 |
. 5,1 |
|||
|
S |
9.53 682 |
35 |
9.56 420 |
0.43 580 |
9. 97 262 |
52 |
9 |
6,0 |
5,8 |
5,7 |
||
|
9 |
9, 53 716 |
34 35 |
9. 56 459 9.56 498 |
39 |
0.43 541 |
5 |
10 20 |
6,7 13,3 |
6,5 13,0 |
6,3 12,7 |
||
|
10 |
e. 43 502 |
9. 97 252 |
50 |
|||||||||
|
11 |
9 53 785 |
34 |
9. 56 537 |
0.-43 463 |
9. 97 248 |
49 |
30 |
20,0 |
19,5 |
19,0 |
||
|
12 |
9. 53 819 |
34 |
9.56 576 |
0.43 424 |
9. 97 243 |
5 4 |
48 |
40 |
26,7 |
|||
|
13 |
9.53 854 |
35 |
9. 50 615 |
0.43 385 |
9. 97 238 |
47 |
50 |
|||||
|
14 |
9.53 888 0. 53 922 |
34 34 |
9. 56 654 |
39 |
0. 43 346 |
9.97 234 |
46 |
1 |
37 0,6 |
35 0,6 |
34 0,0 |
|
|
15 |
9.56 693 |
0. 43 307 |
9. 97 229 |
45 |
||||||||
|
16 |
9.53 957 |
35 |
9. 5B 732 |
0.43 268 |
9.97 224 |
4 5 5 4 |
44 |
2 |
1,2 |
1,2 |
1,1 |
|
|
17 |
9.53 991 |
34 |
9. 56 771 |
0. 43 229 |
9. 97 220 |
43 |
3 |
1,8 |
1,8 |
1,7 |
||
|
18 |
9. 54 025 |
34 |
9. 56 ,S10 |
0.43 190 |
9.97 215 |
42 |
4 |
2,5 |
2,3 |
2,3 |
||
|
19 |
9. 54 059 |
34 34 |
9. 56 849 |
38 |
0.43 151 |
■9.97 210 9. 97 206 |
41 |
5 6 |
8,1 3,7 |
2,9 3,5 |
2,8 3,4 |
|
|
20 |
9.56 887 |
0.43 113 |
40 |
|||||||||
|
9.54 127 |
34 |
9.56 926 |
39 |
0. 43 074 |
9. 97 201 |
5 4 5 |
39 |
7 |
f'? |
*,1 |
4,0 |
|
|
22 |
9.54 161 |
34 |
9. .56 965 |
39 |
0.43 035 |
9. 97 196 |
38 |
8 |
4,9 |
4,7 |
||
|
23 |
9.54 195 |
34 |
9. 57 004 |
0. 42 996 |
9.97 192 |
37 |
||||||
|
24 |
9. 54 229 |
34 |
9.57 042 |
39 39 38 39 |
0. 42 958 |
9.97 187 |
36 |
20 30 40 50 |
12,3 18,5 24,7 30,8 |
11,7 17,5 23,3 . 29,2 |
11,3 17,0 22,7 28,3 |
|
|
26 28 |
9. .54 203 9. 54 297 9. 54 331 9. 54 365 |
34 34 34 34 |
9. 57 081 9. 57 120 9.57 158 9.57 197 |
0.42 919 0.42 880 0. 42 842 0. 42 803 |
9.97 182 9.97 178 9. 97 173 9.97 168 |
4 5 5 |
35 34 33 32 |
|||||
|
29 |
9. 54 399 |
34 34 |
9. 57 235 9.57 274 |
39 |
0.42 765 0.42 726 |
9.97 163 9. 97" 1.59 |
4 |
1 |
33 0,6 |
5 0,1 |
i 0,1 |
|
|
30 |
9.54 433 |
SO |
||||||||||
|
31 |
9.54 466 |
33 |
9. 57 312 |
0. 42 688 |
9. 97 154 |
^ |
29 |
|||||
|
32 |
34 |
9.57 351 |
0. 42 649 |
9.97 149 |
4 5 5 |
28 |
||||||
|
33 |
9.54 534 |
34 |
9.57 389 |
0. 42 611 |
9. 97 145 |
27 |
||||||
|
34 |
9. 54 567 |
33 34 |
9.57 428 |
38 |
0. 42 572 |
9.97 140 |
26 |
5 6 7 8 9 10 20 30 |
2,8 3,3 3,8 4,4 5,0 5,5 11,0 16,5 |
0,4 0,5 0,6 0,7 0,8 0,8 1,7 2,5 |
0,4 0,5 0,5 0,6 0,7 1,3 2,0 |
|
|
35 |
9.54 6U1 |
9. 57 466 |
0.42 534 |
9.97 135 |
25 |
|||||||
|
36 |
9.54 635 |
34 |
9. 57 504 |
0.42 496 |
9.97 130 |
4 |
||||||
|
37 |
0. 54 668 |
33 |
9. 57 543 |
0. 42 457 |
9.97 126 |
|||||||
|
38 |
9.54 702 |
34 |
9. 57 581 |
0.42 419 |
9.97 121 |
^ |
22 |
|||||
|
39 |
9. 54 735 |
33 34 |
9.57 619 |
39 |
0.42 381 |
9.97 116 |
5 |
|||||
|
40 |
9. 54 769 |
9.57 658 |
0. 42 342 |
9.97 111 |
ao |
|||||||
|
41 |
9. 54 802 |
33 |
9.57 696 |
0. 42 304 |
40 |
22,0 |
3,3 |
2,7 |
||||
|
42 |
9.54 836 |
34 |
9. 57 734 |
0. 42 266 |
9.97 102 |
18 |
50 |
27,5 |
4,2 |
3,3 |
||
|
33 |
9.57 772 |
0.42 228 |
5 5 4 5 5 |
|||||||||
|
44 |
9.54 903 |
34 33 |
9. .57 810 |
38 39 |
0.42 190 |
9.97 092 |
16 |
5 |
5 |
^ |
||
|
45 |
9.54 930 |
9.57 849 |
0.42 151 |
9.97 087 |
15 |
|||||||
|
46 |
9.54 969 |
33 |
9.57 887 |
0.42 113 |
9.97 083 |
14 |
||||||
|
47 |
9. 55 003 |
34 |
9.57 925 |
0.42 075 |
9. 97 078 |
13 |
3,9 |
3,8 |
||||
|
48 |
9.55 036 |
33 |
9. 57 963 |
0.42 037 |
9. 97 073 |
12 |
12,0 |
11,7 |
11,4 |
|||
|
49 |
9.55 069 |
33 33 |
9. 58 001 9. 58 039 |
38 |
0.41 999 |
5 4 5 5 |
3 4 5 |
•20,0 28,0 |
19,5 27,3 |
19,0 26,6 |
||
|
50 |
9.55 102 |
0.41 961 |
9. 97 063 |
10 |
||||||||
|
51 |
9.55 136 |
34 |
9. 58 077 |
0.41 923 |
9.97 059 |
36,0 |
35,1 |
34,2 |
||||
|
9. 55 169 |
33 |
9.58 115 |
38 |
0.4L 885 |
9. 97 054 |
8 |
||||||
|
53 |
9.55 202 |
33 |
9.58 153 |
0.41 847 |
9.97 049 |
7 |
5 |
4 |
4 |
|||
|
54 |
9. 55 235 |
33 33 |
9.58 191 |
38 |
0.41 809 |
9. 97 044 |
5 4 |
6 |
37. |
39 |
3S |
|
|
55 |
9. 55 263 |
9. 58 229 |
0.41 771 |
9. 97 039 |
5 |
|||||||
|
56 |
9. 55 301 |
33 |
9. 58 267 |
38 |
0.41 733 |
9.97 035 |
4 |
0 |
3,7 |
4,9 |
4,8 |
|
|
57 |
9.55 334 |
33 |
9.58 304 |
0.41 696 |
9.97 030 |
3 |
11,1 |
14,6 |
14,2 |
|||
|
58 |
9.55 367 |
33 |
9. 58 342 |
0.41 658 |
18,5 |
24,4 |
23,8 |
|||||
|
59 |
9. 55 400 |
33 33 |
9.58 380 9. 58 418 |
38 |
0.41 620 |
5 |
4 5 |
25,9 33,3 |
34,1 |
33,2 |
||
|
60 |
9. 55 433 |
0.41 582 |
9. 97 015 |
0 |
||||||||
|
1. Cos. |
(1. |
L. Cotg. |
a.c. |
L. Tang. |
L. Sin. |
d. |
' |
P |
.P. |
69<^
LOGARITHMS OF CIEOITLAR FUNCTIONS.
275
Table XXXVI. — Lorjarithmio sines, cosines, tangents, and cotanrjents- [Estracted from Gauss' Logaritlimic .aud Trigonometric Tables.]
21°
|
L. Sin. |
d. |
L. Tang. |
d. c. |
L. Cotg. |
L, Cos. |
|
|
0 |
9.55 433 |
9. 58 418 |
0. 41 582 |
9. 97 015 |
||
|
1 |
9. 55 466 |
9. 58 455 |
0.41 545 |
9. 97 010 |
||
|
9. 55 499 |
9. 58 493 |
0. 41 507 |
9. 97 005 |
|||
|
3 |
9. 55 532 |
9. 58 531 |
0. 41 469 |
9. 97 001 |
||
|
4 |
9. .55 564 |
33 |
9. 58 569 |
37 |
0.41 431 |
•9. 96 996 |
|
5 |
9.55 597 |
9.58 606 |
0.41 394 |
9. 96 991 |
||
|
6 |
9. 55 630 |
9. .58 644 |
0.41 356 |
9. 90 980 |
||
|
7 |
9.55 663 |
9. 58 081 |
0. 41 319 |
9. 90 981 |
||
|
8 |
9.55 695 |
9.58 719 |
0.41 281 |
9. 90 976 |
||
|
9 |
9. 55 728 |
33 |
9. 58 757 |
37 |
0. 41 243 |
9. 96 971 |
|
10 |
9.55 761 |
9. 58 794 |
• 0. 41 206 |
9. 96 966 |
||
|
11 |
9.55 793 |
9. 58 832 |
0.41 168 |
9. 96 962 |
||
|
12 |
9. 55 826 |
9. 58 809 |
0.41 131 |
9. 96 957 |
||
|
13 |
9.55 858 |
9. 58 907 |
0.41 093 |
9. 96 952 |
||
|
14 |
9.55 891 |
32 |
9. 58 944 |
37 |
0.41 056 |
9. 90 947 |
|
15 |
9. 55 923 |
9. 58 981 |
0.41 019 |
9. 96 942 |
||
|
16 |
9. 55 956 |
9. 59 019 |
0.40 981 |
9. 96 937 |
||
|
17 |
9. 55 988 |
9. 59 056 |
0. 40 944 |
9. 96 932 |
||
|
18 |
■ 9.56 021 |
9. 59 094 |
0.40 906 |
9. 96 927 |
||
|
19 20 |
9. 56 053 |
32 |
9.59 131 |
37 |
0.40 869 |
9. 96 922 |
|
9.56 085 |
9. .59 168 |
0. 40 832 |
9. 90 917 |
|||
|
21 |
9.56 118 |
9.59 205 |
0. 40 795 |
9, 90 912 |
||
|
22 |
9.56 1.50 |
9. .59 243 |
0.40 757 |
9. 90 907 |
||
|
23 |
9. 56 182 |
9.50 280 |
0. 40 720 |
9. 96 903 |
||
|
24 |
9.56 215 9.56 247 |
32 |
9. 59 317 |
37 |
0.40 683 |
9. 96 898 |
|
25 |
9. 59 354 |
0. 40 646 |
9. 96 893 |
|||
|
26 |
9.56 279 |
9.59 391 |
0. 40 009 |
9. 90 888 |
||
|
27 |
9.56 311 |
9. 59 429 |
0. 40 571 |
9. 96 883 |
||
|
28 |
9.60 343 |
9. 59 466 |
0.40 534 |
9. 96 878 |
||
|
29 |
9.66 375 |
33 |
9. 59 503 |
37 |
0. 40 497 |
9.96 873 |
|
30 |
9. 56 -408 |
9.59 540 |
0. 40 460 |
9. 90 868 |
||
|
31 |
9.56 440 |
9. 59 577 |
0.40 423 |
9. 96 863 |
||
|
32 |
9. 56 472 |
9. 59 614 |
0. 40 386 |
9. 96 858 |
||
|
33 |
9. 56 504 |
9. 59 651 |
0. 40 349 |
9. 90 853 |
||
|
34 |
9. 56 630 |
32 |
9. 59 688 |
37 |
0,40 312 |
9. 96 848 |
|
35 |
9.56 568 |
9. 59 725 |
0. 40 275 |
9. 96 843 |
||
|
36 |
9.56 599 |
9. 59 762 |
0.40 238 |
9.96 838 |
||
|
37 |
9.56 631 |
9. 69 799 |
0.40 201 |
9. 90 833 |
||
|
38 |
9.56 663 |
9. 59 835 |
0. 40 165 |
9. 96 828 |
||
|
39 |
9.56 695 |
32 |
9. 69 872 |
:i7 |
0. 40 128 |
9. 96 823 |
|
10 |
9. 56 727 |
9.59 909 |
0. 40 091 |
9. 96 818 |
||
|
41 |
9. 56 759 |
9. 59 946 |
0.40 054 |
9. 96 813 |
||
|
42 |
9.56 790 |
9. 59 983 |
0. 40 017 |
9.96 808 |
||
|
43 |
9.56 822 |
9.60 019 |
0.39 981 |
9. 90 803 |
||
|
44 |
9. 56 854 |
32 |
9. 60 056 |
37 |
0. 39 944 |
9. 96 798 |
|
45 |
9. 56 886 |
9. 60 093 |
0. 39 907 |
9. 96 793 |
||
|
46 |
9.56 917 |
9. 60 130 |
0. 39 870 |
9. 96 788 |
||
|
47 |
9.56 949 |
9.60 166 |
0. 39 834 |
9. 90 783 |
||
|
48 |
9. 56 980 |
9.60 203 |
0. 39 797 |
9. 90 778 |
||
|
49 |
9. 57 012 |
32 |
9. 60 24U |
36 |
0. 39 760 |
9. 90 772 |
|
50 |
9. 57 044 |
9. 60 276 |
0. 39 724 |
9.96 767 |
||
|
51 |
9. 57 075 |
9.00 313 |
0. 39 687 |
9. 96 762 |
||
|
52 |
" 9. 57 107 |
32 |
9. 60 349 |
0. 39 651 |
9.96 757 |
|
|
53 |
9. 57 138 |
9. 60 386 |
0. 39 614 |
9. 96 762 |
||
|
54 |
9.57 169 |
32 |
9. 60 422 |
37 |
0. 39 578 |
9, 96 747 |
|
55 |
9.57 201 |
9. 60 459 |
0.39 541 |
9. 96 742 |
||
|
56 |
9.57 232 |
31 |
9. 00 495 |
0. 39 505 |
9. 96 737 |
|
|
57 |
9. 57 264 |
9. 60 532 |
0. 39 468 |
9. 96 732 |
||
|
58 |
9. 57 295 |
9.60 508 |
0. 39 432 |
9. 96 727 |
||
|
59 |
9. 57 326 |
31 |
9. 60 005 |
30 |
0. 39 395 |
9,90 722 9, 90 717 |
|
60 |
9. 57 358 |
9. 00 041 |
0. 39 359 |
|||
|
L. Cos. |
d. |
L. Cotg. |
d. c. |
L. Tang. |
L. Sin. |
|
38 0,0 |
37 0,0 |
|
1,3 |
1,2 |
|
1,9 |
1,8 |
|
2,5 |
2,5 |
|
3,2 |
3,1 |
|
3,8 |
3,7 |
|
4,4 |
4,3 |
|
5,1 |
4,9 |
|
6,7 |
5,0 |
|
6,3 |
0,2 |
|
12,7 |
12,3 |
|
19,0 |
18,5 |
|
25,3 |
24,7 |
|
31,7 |
30,8 |
|
33 |
33 |
|
0,6 |
0,5 |
|
1,1 |
1,1 |
|
1,0 |
1,0 |
|
2,8 |
2,7 |
|
3,3 |
3,2 |
|
3,8 |
3,7 |
|
4,4 |
4,3 |
|
5,0 |
4,8 |
|
5,5 |
5,3 |
|
11,0 |
10,7 |
|
10,5 |
10,0 |
|
22,0 |
21,3 |
|
2- ,5 |
20,7 |
|
0 0,1 |
0,1 |
|
0,2 |
0,2 |
|
0,3 |
0,2 |
|
0,4 |
0,3 |
|
0,5 |
0,4 |
|
0,6 |
0,5 |
|
0,7 |
0,6 |
|
0,8 |
0,7 |
|
0,9 |
0,8 |
|
1,0 |
0,8 |
|
2,0 |
1,7 |
|
3,0 |
2,5 |
|
4,0 |
3,3 |
|
5,0 |
|
6 |
» |
|
37 |
38 |
|
3,1 |
3,8 |
|
9,2 |
11,4 |
|
15,4 |
19,0 |
|
21,6 |
26,6 |
|
27,8 |
34,2 |
|
33,9 |
|
|
5 |
4 |
|
36 |
88 |
|
3,6 |
4,8 |
|
10,8 |
14,2 |
|
18,0 |
23,8 |
|
25,2 |
33,2 |
|
32,4 |
3,0 3,6 4,2 4,8 5,4 6,0 12,0 18,0 24,0 30,0
2,1 2,6 3,1 3,6 4,1 4,6 5,2 10,3 15,6 20,7 25,8
11,1
18,5 26,9
13,9 23,1 32,4
68<:
276
A MANUAL OF TOrOGEAPHIC METHODS.
'1\UJLE XXXVI.— io.'/"»'i'/""'(- xine.f!, cosines, langciits, ami cu'tiiiflCH/.s— Coutiuiicd. [Extractwl tVmii Gauss' Ldsaritliniii' and Triaiiuomotric Tables.]
22°
LOGAEITHMS OF CIRCULAE FUNCTIONS.
277
Table XXXVI. — Logarithmic sinesj cosines^ tangents, and cotangents — Continued. [Extracted from Gauss' liOgarithmic and Trigonometric Tables.]
23°
L.Sm.
9.59 188 9. 59 218 9. 59 247 9. 59 277 9. 59 307
9. 59 330 9. 59 366 9. 59 396 9. 59 425 9. 59 455
9. 59 484 9. 59 614 9. 59 543 9. 59 573 9. 59 602
9. 59 632 9. 59 661 9.59 690 9. 59 720 9. 59 749
9. 59 778 9. 59 808 9. 59 837 9. 59 866 9. 59 895
9. 59 924 9. 59 954 9.59 983 9. 60 012 9. 60 041
9. 60 215 9. 60 244 9. 60 273 9. 60 302 9.60 331
9.60 359 9.60 388 9. 60 417 9. 60 446 9.60 474
9. 60 503 9. 60 532 9. CO 561 9. 60 589 9. 60 618
9. 60 646 9. 60 675 9. 60 704 9. 60 732 9. 60 761
9. 60 789 9. 60 818 9. 60 846 9.60 875 9. 60 903 9.60 931
9. 62 785 9. 62 820 9. 62 855 9. 62 890 9. 62 926
9. 62 961 9. 62 996 9.63 031 9. 63 066 9. 63 101
9. 63 135 9. 63 170 9.63 205 9. 63 240 9. 63 275
9. 63 310 9. 63 .345 9.63 379 9. 63 414 9. 63 449
9.63 484 9. 63 519 9. 63 553
9. 63 726 9.63 761 9. 63 796
9. 64 003 9. 64 037 9. 64 072 9. 64 106 9. 64 140
9. 64 175 9. 64 209 9. 64 243 9.64 278 9.64 312
9. 64 346 9. 64 381 9. 64 415 9. 64 449 9. 64 483
9. 64 517 9. 64 552 9. 64 586 9. 64 620 9.64 654
9. 64 688 9. 64 722 9. 6i 756 9. 64 790 9. 64 824 9. 64 858
L. Cotg. a. c.
L. Cotg.
0. 37 215 0.37 180 0. 37 145 0.37 110 0. 37 074
0. 37 039 0. 37 004 0. 36 969 0. 36 934 0. 36 899
0.36 865 0.30 8.30 0.36 795 0. 36 760 0. 36 725
0.36 690 0, ,36 655 0. 36 621 0. 36 586 0.30 551
0. 36 516 0. 36 481 0. 36 447 0.36 412 0. 36 377
0. 36 343 0. 36 308 0. 36 274 0. 36 239 0. 36 204
0. 36 170 0. 36 135 0. 36 101 0. 36 066 0. 36 032
0. 35 997 0.35 963 0. 35 928 0. 35 894 0. 35 860
0. 35 825 0.35 791 0. 35 757 0. 35 722 0.35 688
0.35 654 0.35 619 0. 35 585 0.35 551 0.35 517
0. 35 483 0. 35 448 0. 35 414 0. 35 380 0. 35 346
0. 35 312 0. 35 278 0. 35 244 0. 35 210 0. 35 176 0. 35 142
9. 96 403 9.96 397 9. 96 392 9. 96 387 9. 96 381
9.96 376 9. 96 370 9.96 365 9. 96 360 9. 96 354
9. 96 349 9.96 343 9.90 338 9.96 333 9.96 327^ 9.96 322 9. 96 316 9.96 311 9.96 305
9. 96 284 9. 96 278 9.96 273
9.90 207 9. 96 262 9. 96 256 9. 96 251 9. 96 245
9.96 207 9. 96 201 9.96 196 9.96 190
9.96 185 9.96 179 9. 96 174 9. 96 168 9.96 162
9.96 157 9. 96 151 9 96 146 9.96 140 9.96 135
9. 90 129 9.96 123 9.96 lis 9.96 112 9.96 107
9.96 101 9. 96 095 9. 96 090 9. 96 084 9.96 079 9. 96 073
|
36 0,6 |
35 0,6 |
|
1/2 |
1,2 |
|
1,8 |
1,8 |
|
2,4 |
2,3 |
|
3,0 |
2,9 |
|
3,6 |
3,5 |
|
4,2 |
4,1 |
|
4,8 |
4,7 |
|
5,4 |
5,2 |
|
6,0 |
5,8 |
|
12,0 |
11,7 |
|
18,0 |
17,5 |
|
24,0 |
23,3 |
|
30,0 |
29,2 |
|
30 |
29 |
|
0,5 |
0,5 |
|
1,0 |
1,0 |
|
1,5 |
1,4 |
|
2,0 |
1,9 |
|
2,5 |
2,4 |
|
3,0 |
2,9 |
|
3,5 |
3,4 |
|
4,0 |
3,9 |
|
4,5 |
4,4 |
|
5,0 |
4,8 |
|
10,0 |
9,7 |
|
15,0 |
14,5 |
|
20,0 |
19,3 |
|
25,0 |
24,2 |
3,4 4,0 4,5 5,1 5,7 11,3 17,0 22,7 28,3
1,9 2,3 2,8 3,3 3,7 4,2 4,7 9,3 14,0 18,7 23,3
|
G |
6 |
|
36 |
35 |
|
3,0 |
2,9 |
|
9,0 |
8,8 |
|
15,0 |
14,6 |
|
21,0 |
20,4 |
|
27,0 |
26,2 |
|
33,0 |
32,1 |
8,5 14,2 19,8 25,5 31,2
|
3,5 |
3,4 |
|
10,b |
10,2 |
|
IV, b |
17,0 |
|
24,5 |
23,8 |
|
31,0 |
30,6 |
66=
278
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXXVI. — Logarithmic sines, cosines, tatigcnts, and cotanyenis — Contimied.
[Exti-actecl from Gauss' Logaritlimic and Trigonometric Tables.)
24°
9. 60 960 9. 60 988 9. 61 QIC
9.61 045
9. 61 073 9. 61 101 9.61 129 9.61 loS 9.61 186
9.61 214 9. 01 242 9.61 270 9.61 298 9.61 326
9.61 354 9.61 382 9.61 411 9.61 438 9. 61 466
9. 61 494 9. 61 522 9.61 550 9.61 578 9.61 606
9.61 634 9.61 662 9.6] 689 9. 61 717 9. 61 745
9.61 773 9.61 800 9. 61 828 9. 61 856 9.61 883
9. 61 911 9.61 939 9.61 966 9. 61 994 9. 62 021
9. 02 049 9. 62 076 9. 62 104 9. 62 131 9. 62 159
9.62 186 9. 62 214 9. 62 241 9. 62 268 9. 62 296
9. 62 323 9. 62 350 9. 62 377 9. 62 405 9. 62 432
9. 62 459 9. 62 486 9. 62 513 9. 62 541 9. 62 568 9. 62 595
9. 64 858 9. 04 892 9. 64 026 9. 64 960 9. 64 994
9. 65 028 9. 65 062
9.65 197 9. 65 231 9. 65 265 9. 65 299 9. 65 333
9. 65 366 9. 65 400 9. 65 434 9. 63 467 9. 65 501
9. 65 535 9. 65 568 9. 65 602 9. 65 636 9. 65 669
9. 65 703 9. 65 736 9. 65 770 9. 65 803 9. 65 837
9. 65 870 9. 65 904 9. 65 937 9. 65 971 9. 66 004
9. 66 038 9. 66 071 9. 06 104 9. 66 138 9. 66 171
9. 66 204 9-. 66 238 9. 66 271 9.66 304 9. 66 337
9. 66 371 9. 66 404 9. 66 437 9. 66 470 9. 66 503
9. 66 .537 9. 66 570 9. 66 603 9. 66 636 9. 66 669
9. 66 702 9. 66 735 9. 66 768 9. 66 801 . 9. 66 834 9. 66 867
L. Cotg.
0. 35 142 0.35 108 0. 35 074 0. 35 040
0. 35 oon
0. 34 972 0. 34 938 0. 34 904 0. 34 870 0. 34 836
0. 34 803 0.34 769 0. 34 735 0. 34 701 0.34 667
0.34 634 0.34 600 0. 34 566 0. 34 533 0. 34 499
0. 34 465 0. 34 432 0. 34 398 0. 34 364 0. 34 331
0. 34 297 0. 34 264 0. 34 230 0. 34 197 0.34 163
9. 96 073 9. 96 067 9. 96 062 n. 96 056 9. 96 050
9. 96 045 9. 96 039 9. 96 034 9. 96 023 9.96 022
9. 96 017 9.96 Oil 9. 96 005 9. 96 000 9. 95 994
9. 95 988 9. 95 982 9. 95 977 9. 95 971 9. 95 965
9. 95 960 I 9. 95 954 9. 95 948 9. 95 942 9. 96 937
0. 34 130 0. 34 096 0. 34 063 0. 34 029 0.33 996
0.33 962 0.33 929 0.33 896 0.33 802 0. 33 829
9. 95 931 9. 95 925 9. 95 920 9.95 914 9.95 908
9.95 902 9.95 897 9. 95 891 9. 95 885 9. 95 879
0. 33 796 0. 33 762 0. 33 729 0. 33 696 0. 33 663
0.1
629
9. 95 873 9. 95 868 9. 95 862 9. 95 856 9. 95 850
9. 95 844 9. 95 839 9. 95 833
0.33 596 0. 33 563 I
0. 33 463 0. 33 430 0. 33 397 0. 33 364 0.33 331
0. 33 298 0. 33 265 0. 33 232 0. 33 199 0. 33 166 0. 33 133
9. 95 810 9.95 804 9. 95 798 9. 95 792
9. 95 757 9.-95 751 9. 95 745 9, 95 739 9.95 733 9. 95 728
|
0,6 |
0,6 |
|
1,1 |
1,1 |
|
i,v |
1,6 |
|
2,3 |
2,2 |
|
2,8 |
2,8 |
|
3,4 |
3,3 |
|
4,0 |
3,8 |
|
4,b |
4,4 |
|
5,1 |
0,0 |
|
5,V |
b,6 |
|
11,3 |
11,0 |
|
17,0 |
16,b |
|
22,7 |
22,0 |
|
28,3 |
2V,b |
|
29 |
28 |
|
0,5 |
0,5 |
|
1,0 |
0,9 |
|
1,4 |
1,4 |
|
1,9 |
1,9 |
|
2'4 |
2,3 |
|
2,9 |
2,8 |
|
3,4 |
3,3 |
|
3,9- |
3,7 |
|
4,4 |
4,2 |
|
4,8 |
4,7 |
|
9,7 |
9,3 |
|
14,5 |
14,0 |
|
19,3 |
18,7 |
|
24,2 |
23,3 |
|
G |
6 |
|
34 |
S3 |
|
2,8 |
2,8 |
|
8,5 |
8,2 |
|
14,2 |
13,8 |
|
19,8 |
19,2 |
|
25,5 |
24,8 |
|
31,2 |
30,2 |
0,4 0,9
1;4:
1,8 2,2 2,7 3,2 3,6 4,0 4,5 9,0. 13,5 18,0 22,5
10,2 17,0 23,8 30,6
63"^
LOGARITHMS OF CIRCULAR FUNCTIONS.
279
Tablk XXXVI. — Logarithmic Hnes, cosi^ies, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometrii; Tables.]
950
9. 62 595 9. 62 622 9. 62 649 9. 62 676 9. 62 703
9.62 7TO 9. 62 757 9. 62 784 9.62 811 9. 62 838
9.62 865 9. 62 892 9.62 918 9.62 945 9.62 072
9. 62 999 9. 63 026 9. 63 052 9. 03 079 9. 63 106
9.03 133 9. 63 159 9.63 180 9. 63 213 9. 63 239
9. 63 266 9.63 292 9. 63 319 9.63 345 9. 63 372
9. 63 398 9. 63 425 9. 63 451 9. 63 478 9. 63 304
9. 63 .531 9. 63 557 9.63 583 9. 63 610 9. 63 636
9. 63 662 9. (i3 689 9.63 715 9. 63 741 9.63 767
9. 63 794 9.63 820 9. 63 846 9. 63 872 9. 63 898
9.63 924 9. 63 950
9. 63 976 9. 64 002
9. 64 028 9. 64 054 9. 64 080 9. 64 106 9. 64 132 9. §4 158 9. 64 184
9. 66 867 9. 66 900 9. 66 933 9. 66 966 9. 66 999
9.07 032 9.67 065 9. 67 098 9. 67 131 9. 67 163
9.67 196 9. 67 229 9. 67 262 9. 67 293 9. 67 327
9. 67 360 9. 67 393 9. 67 426 9. 67 458 9. 67 491
9. 67 524 9. 67 556 9.67 589 9.67 622 9. 67 654
9.67 687 9. 67 719 9. 67 752 9. 67 785 9.67 817
9. 67 850 9. 67 882 9. 67 915 9. 67 947 9. 67 980
9. 68 012 9. 68 044 9. 68 077 9.68 109 9. 68 142
9. 68 497 9. 68 529 9. 68 561 9. 68 593 9. 68 626
L. Cotg.
L. Cotg.
0.33 133 0.33 100 0.33 067 0.33 014 0.33 001
0. 32 968 0. 32 935 0. 32 902 0. 32 869 0. 32 837
0. 32 804 0. 32 771 0. 32 738 0. 32 705 0. 32 673
0. 32 640 0. 32 607 0. 32 574 0. 32 542 0. 32 509
0. 32 476 f 0. 32 444 0.32 411 0. 32 378 0. 32 346
0.32 313 0. 32 281 0. 32 248 0. 32 215 0.32 183
0. 32 150 0. 32 118 0. 32 085 0. 32 053 0. 32 020
0. 31 988 0.31 9.56 0.31 923 0.31 891 0.31 858
0.31 826 0. 31 794 0.31 761 0. 31 729 0.31 697
0.31 664 0.31 632 0.31 600 0.31 568 0.31 535
0. 31 503 0. 31 471 0.31 439 0.31 407 0.31 374
0.31 342 0.31 310 0. 31 278 0. 31 246 0.31 214 0. 31 182
9.95 728 9. 95 722 9.95 716 9. 95 710 9. 95 704 9795^8" 9.95 692 9. 95 686 9. 95 680 9. 95 674
9. 95 668 9. 95 663 9.95 657 9.95 65] 9. 95 645
9. 95 639 9.95 633 9.95 627' 9. 95 621 9.95 615
9. 95 603 9. 95 597 9. 95 591 9.95 585
9. 95 679 9. 95 573 9.95 567 9. 95 661 9. 95 555
9. 95 549 9. 95 543 9. 95 537 9. 95 531 9. 95 525
9. 95 519 9. 95 513 9. 95 507 9. 95 500 9. 95 494
9. 95 488 9. 95 482 9. 95 476 9. 95 470 9. 95 464
9.95 4.58 9. 95 453 9. 95 446 9. 95 440 9. 95 434
9. 95 427 9. 95 421 9.95 415 9. 95 409 9.95 403
9. 95 397 9. 95 391 9. 95 384 9. 95 378 I 9. 95 372 9. 95 366
|
5,0 |
4,8 |
|
5,0 |
5,3 |
|
11,0 |
10,7 |
|
16,b |
16,0 |
|
22,0 |
21,3 |
|
2V,b |
26,7 |
|
27 |
26 |
|
0,4 |
0,4 |
|
0,9 |
0,9 |
|
1,4 |
1,3 |
|
1,8 |
1,7 |
|
2,2 |
2,2 |
|
2,7 |
2,0 |
|
3,2 |
3,0 |
|
3,6 |
3,5 |
|
4-0 |
3,9 |
|
4,b |
4'3 |
|
9,0 |
8,7 |
|
13,5 |
13,0 |
|
18,0 |
17,3 |
|
22,5 |
21,7 |
|
0,1 |
6 0,1 |
|
0,2 |
0,2 |
|
0,4 |
0,3 |
|
0,5 |
0,4 |
|
0,6 |
0,5 |
|
0,7 |
0,6 |
|
0,8 |
0,7 |
|
0,9 |
0,8 |
|
1,0 |
0,9 |
|
1,2 |
1,0 |
|
2,3 |
2,0 |
|
3,5 |
3,0 |
|
^,^ |
4,0 |
|
5,8 |
5,0 |
|
' |
G |
|
32 |
32 |
|
2,3 |
2,7 |
|
6,9 |
8,0 |
|
11,4 |
13,3 |
|
16,0 |
18,7 |
|
20,6 |
24,0 |
|
25,1 |
29,3 |
|
29,7 |
9,9 16,5 23,1 29,7
64^^
280
A MANUAL OF TOrOGEAPHIC METHODS.
Table XXXVI. — Loijariihmic shies, cosi-nes, tmufenis, and cotangents — Contin;ied. [Extracted I'rom Gauss' Logarithmic and Trigonometric Tables.]
26°
9.64 184 9. 64 210 9. 64 236 9. 64 262 9. 64 288
9. 64 313 9.64 339 9. 64 365 9.C4 391 9. 64 417
9. 64 442 1 9. 64 468 9. 64 494 1 9. 64 519 9. 64 545
9. 64 571 9.64 596 9. 64 622 9. 64 647 9. 64 673
9. 64 698 9. 61 724 9. 64 749 9. 64 775 9. 64 800
9. 64 826 9. 64 851 9. 64 877 9. 64 902 9. 64 927 9. 64 953
9.64 978 9. 65 003
9. 65 029 9. 65 054
9.65 331 9.65 356 9. 65 381 9.65 406 9. 65 431
9.65 456 9. 65 481 9.65 506 9. 65 531 9.65 556
9. 65 580 9. 65 605 9. 65 630 9. 65 655 9.65 680 9. 65 705
9. 68 850 9.68 882 9. 68 914 9.68 946
9. 68 '978 9.69 010 9.09 042 9.69 074 9.69 106
9. 69 138 9.69 170 9.69 202 9.69 234 9.69 266
9. 69 298 9. 09 329 9. 69 361 9. 69 393 9. 69 425
9.70 089 9.70 121 9. 70 152 9.70 184 9.70 215
• 9. 70 247 9.70 278 9. 70 309 9. 70 341 9.70 372
9. 70 404 9. 70 435 9. 70 466 9. 70 498 9. 70 529
L. Cotg.
0. 31 182 0.31 150 0.31 118 0.31 086 0.31 054
0.31 022 0.30 990 0.30 958 0.30 926 0. 30 894
0.30 S62 0.30 830 0. 30 798 0.30 766 0.30 7.34
0.30 702 0.30 671 0. 30 639 0. 30 607 0. 30 575
0. 30 385 0. 30 353 0. 30 321 0. 30 290 0. 30 258
0. 30 226 0. 30 195 0.30 163 0. 30 132 0. 30 100
0. 30 (168 0. 30 037 0. 30 005 0. 29 974 0, 29 942
0.29 911 0. 29 879 0. 29 848 0. 29 816 0. 29 785
0.29 753 0. 29 722 0. 29 691 0. 29 659 0. 29 628
0. 29 596 0.29 565 0. 29 534 0. 29 502 0. 29 471
0. 29 440 0.29 408 0. 29 377 0. 29 346 0. 29 315 0. 29 283
9.95 360 9. 95 360 9.95 354 9.95 348 9.95 341 9.95 335 9.95 329 9.95 323 9.95 317 9.95 310
9.05 304 9.95 298 9. 95 292 9.95 286 9.95 279
9.95 273 9. 95 267 9. 95 261 9.95 254 9. 95 248
9.95 242 9.95 236 9. 95 229 9. 95 223 9. 95 217
9. 95 211 9. 95 204 9. 95 198 9. 95 192 9.95 185
9.95 179 9.95 173 9. 95 167 9. 95 160 9.95 154
9. 95 148 9.95 141 9.95 135 9.95 129 9.95 122 9. 95 lie 9.95 110 9. 95 103 9. 95 097 9.95 090
9. 95 084 9. 95 078 9. 95 071 9.95 065 9.95 059
9. 95 052 9.95 046 9. 95 039 9. 95 033 9.95 027
9. 95 020 9. 95 014 9. 95 007 9.05 001 9 94 995 9. 94 988
|
d. |
||
|
«0 |
||
|
6 |
59 |
|
|
58 |
||
|
57 |
||
|
V |
56 |
|
|
6 |
55 |
|
|
54 |
||
|
53 |
||
|
52 |
||
|
7 |
51 |
|
|
6 |
50 |
|
|
6 |
49 |
|
|
48 |
||
|
6 |
47 |
|
|
6 |
46 |
|
|
45 |
||
|
44 |
||
|
43 |
||
|
42 |
||
|
41 |
||
|
6 |
||
|
40 |
||
|
39 |
||
|
V |
38 |
|
|
37 |
||
|
36 |
||
|
6 |
"35 |
|
|
34 |
||
|
6 |
33 |
|
|
32 |
||
|
31 |
||
|
6 |
||
|
SO |
||
|
29 |
||
|
28 |
||
|
6 |
26 |
|
|
6 |
||
|
25 |
||
|
24 |
||
|
6 |
23 |
|
|
B |
22 |
|
|
21 |
||
|
6 |
||
|
2(1 |
||
|
19 |
||
|
V |
18 |
|
|
6 |
17 |
|
|
V 6 |
16 |
|
|
15 |
||
|
14 |
||
|
13 |
||
|
b |
12 |
|
|
7 6 |
11 |
|
|
10 9 |
||
|
8 |
||
|
7 |
||
|
6 |
||
|
5 |
||
|
6 |
4 |
|
|
3 |
||
|
2 |
||
|
6 |
1 |
|
|
V |
0 |
|
|
(1. |
' |
|
32 |
|
|
1 |
0,5 |
|
2 |
1,1 |
|
3 |
1,6 |
|
4 |
2,1 |
|
5 |
2,7 |
|
6 |
3,2 |
|
7 |
3,7 |
|
8 |
4,3 |
|
9 |
4,8 |
|
1» |
5,3 |
|
^(1 |
10,7 |
|
30 |
16,0 |
|
40 |
21,3 |
|
i>0 |
26,7 |
10,3 15,5 20,7 25,8
|
20 |
25 |
|
0,4 |
0,4 |
|
0,9 |
0,8 |
|
1,3 |
1,2 |
|
1,7 |
1,7 |
|
2,2 |
2,1 |
|
2,6 |
2,5 |
|
3,0 |
2,9 |
|
8,5 |
3,3 |
|
3,9 |
3,8 |
|
4,3 |
4,2 |
|
8,7 |
, 8,3 |
|
13,0 |
12,5 |
|
17,3 |
16,7 |
|
21,7 |
20,8 |
0,8 1,2 1,6 2,0 2,4 2,8 3,2 3,0 4,0 8,0 12,0 16,0 20,0
|
_ |
|
|
33 |
31 |
|
2,3 |
2,2 |
|
6,9 |
6,0 |
|
11,4 |
11,1 |
|
16,0 |
15,5 |
|
-20,6 |
19'9 |
|
25,1 |
24,4 |
|
29,7 |
.28,8 |
2,7 8,0 13,3 18,7 24,0
63°
LOGAEITHMS OF CIECULAE FUNCTIONS.
281
Table XXXVI. — Lofiarithmic sines, cosines, tangents, and cotangents — Continued.
fExtracted from Gauss' Logaritlimic anil Trifcononietric Tables.]
27°
9. 65 705 9. 65 729 9. 65 754 9. 65 779 9. 65 804
9. 65 828 9. 65 853 9. 65 878 9. 65 902 9. 65 927 9.65 952 9. 65 976 9. 66 001 9. 66 025 9. 66 050
■ 9. 66 U75 9. 66 099 9. 66 124 9.66 148 9.66 173
9.66 197 9. 66 221 9.66 246 9. 66 270 9. 66 295
9.66 319 9. 66 343 9. 66 368 9. 66 392 9, 66 416
9. 66 441 9. 66 465 9. 66 489 9.66 513 9.66 537
9.66 562 9. 66 586 9. 66 610 9.66 634 9. 66 658
9.66 I
1 706
9. 66 S03 9. 66 827 9. 66 851 9. 66 875 9. 66 899
9. 66 922 9. 66 946 9.66 970 9. 66 994 9. 67 018
9.70 779 9.70 810 9.70 841 9. 70 873 9. 70 904 9.70 935 9. 70 966 9. 70 997
9.71 028 9.71 059 9.71 090 9.71 121 9.71 153
9.71 493 9. 71 524 9.71 555 9. 71 586 9.71 617
9.71 648 9.71 679 9. 71 709
9. 72 262 9. 72 293 9.72 323 9.72 354 9. 72 384 9. 72 415 9.72 445 9. 72 476 9. 72 506 9. 72 537 9. 72 567
L. Cotg.
L. Cotg.
0. 29 283 0. 29 252 0.29 221 0.29 190 0.29 159
0.29 127 0.29 096 0. 29 065 0. 29 034 0. 29 003
0.28 972 0. 28 941 0.28 910 0.28 879 0.28 847
0.28 816 0. 28 785 0. 28 754 0.28 723 J)^28 692 0. 28 601 0.28 630 0. 28 599 0.28 569 0. 28 538
0.28 507 0. 28 476 0. 28 445 0. 28 414 0. 28 383
0. 28 352 0. 28 321 0. 28 291 0. 28 260 0. 28 229
0.28 198 0.28 167 0. 28 137 0. 28 106 0.28 075
0. 28 045 0. 28 014 0. 27 983 0.27 952 0.27 922
0. 27 891 0. 27 860 0. 27 830
0. 27 707 0.27 677 0. 27 646 0. 27 616 0. 27 585 0. 27 555 0. 27 524 0. 27 494
9. 94 988 9. 94 982 9.94 975 9.94 969 9.94 962
9. 94 956 9.94 949 9.94 943 9. 94 936 9. 94 930
9. 94 923 9. 94 917 9. 94 911 9. 94 904 9. 94 898
9.94 891 9.94 885 9. 94 878 9. 94 871 9.94 865
9.94 858 9. 94 852 9. 94 845 9.94 839 9. 94 832
9.94 826 9. 94 819 9.94 813 9.94 806 9. 94 799
9. 94 793 9. 94 786 9. 94 780 9. 94 773 9. 94 767
9.94 760 9. 94 763 9. 94 747 9. 94 740 9.94 734
9. 94 727 9. 94 720 9. 94 714 9. 94 707 9. 94 700
9. 94 660 9. 94 654 9. 94 647 9. 94 640 9. 94 634 9. 94 627 9. 91 620 9. 94 614 9. 94 607 9. 94 600 9. 94 593
|
32 |
31 |
|
0,5 |
0,5 |
|
1,1 |
1,0 |
|
1,6 |
1,6 |
|
2,1 |
2,1 |
|
2,7 |
2,6 |
|
3,2 |
3,1 |
|
3,7 |
3,6 |
|
4,3 |
4,1 |
|
4,8 |
4,6 |
|
5,3 |
5,2 |
|
ig,7 |
10,3 |
|
16,0 |
15,5 |
|
21,3 |
20,7 |
|
26,7 |
25,8 |
|
25 |
24 |
|
0,4 |
0,4 |
|
0,8 |
0,8 |
|
1,2 |
1,2 |
|
1,7 |
1,6 |
|
2,1 |
2,0 |
|
2,5 |
2,4 |
|
2,9 |
2,8 |
|
3,3 |
3,2 |
|
3,8 |
3,6 |
|
4,2 |
4,0 |
|
8,3 |
8,0 |
|
12,5 |
12,0 |
|
16,7 |
16,0 |
|
20,8 |
20,0 |
10,0 15,0 20,0 25,0
2,3 2,7 3,1 3,4 3,8 7,7 11,5 15,3 19,2
|
' |
G |
|
30 |
31 |
|
2,1 |
2,6 |
|
6,4 |
7,8 |
|
10,7 |
12,9 |
|
15,0 |
18,1 |
|
19,3 |
23,2 |
|
23,6 |
28,4 |
|
27,9 |
2,5 7,5 12,5 17,5 22,5 27,5
62=
282
A MANUAL OF TOPOGKAPHIC METHODS.
Table XXKri.— Logarithmic sines, cosines, tangents, and coinngents—ContiaueA.
[Extracted from Gauss' Logai-ithmic and Trigonometric Tables.]
S8°
|
SI •0,5 |
30 0,5 |
|
1,0 |
1,0 |
|
1,0 |
1,5 |
|
2,1 |
2,0 |
|
2,6 |
2,5 |
|
3,1 |
3,0 |
|
3,6 |
3,5 |
|
4,1 |
4,0 |
|
4,6 |
4,5 |
|
5,2 |
5,0 |
|
10,3 |
10,0 |
|
15,5 |
15,0 |
|
20,7 |
20,0 |
|
25,8 |
25,0 |
|
24 |
2S |
|
0,4 |
0,4 |
|
0,8 |
0,8 |
|
1,2 |
1,2 |
|
■ 1,6 |
|
|
2,0 |
1,9 |
|
2,4 |
2,3 |
|
2,8 |
2,7 |
|
3,2 |
3,1 |
|
3,6 |
3,4 |
|
4,0 |
3,8 |
|
8,0 |
7,7- |
|
12,0 |
11,5 |
|
10,0 |
15,3 |
|
20,0 |
19,2 |
1,4 1,9 2,4 2,9 3,4 3;9 4,4 4,8 9,7 14,5 19,3 24,2
11,0 14,7 18,3
|
6 |
|
|
SI |
31 |
|
2,2 |
2,6 |
|
6,6 |
7,8 |
|
11,1 |
12,9 |
|
15,5 |
18,1 |
|
19,9 |
23,2 |
|
24,4 |
28,4 |
|
28,8 |
2,5 7,5 12,5 17,5 23,5 27,5
61°
LOGARITHMS OF CIRCULAE FUNCTIONS.
283
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
39°
L. Tang.
9. 68 G71 9. 68 694 9.68 716 9. 68 739 9^68 762 9. 68 784 9. 68 807 9. 68 829 9.68 852 9.68 875 '9. 68 897" 9. 68 920 9. 68 942 9. 08 965 9.68 987
9. egliiir
9. 69 032 9. 69 055 9. 69 077 9. 69 100 9. 69 122
9. 69 345 9. 69 368 9 69 390 9. 69 412
9.69 611 9. 69 633 9. 69 655
9. 74 375 9. 74 405 9. 74 435 9. 74 465 9. 74 494
9. 74 524 9. 74 554 9. 74 583 9. 74 613 9. 74 643
9. 74 969 9. 74 998
9.75 028 9. 75 058 9.75 087
9.75 205 9. 75 235
9. 75 264 9. 75 294 9. 75 323 9. 75 353 9.75 382
9.75 411 9. 75 441 9. 75 470 9.75 500 9. 75 529
9.75 558 -9. 75 588 9.75 617 9. 75 647 9. 75 676
9.75 764 9. 75 793 9. 75 822
9. 75 852 9.75 881 9. 75 910 9. 75 939 9. 75 969
9.75 998 9. 76 027 9. 76 056
L. Cotg.
0.24 736 0. 24 706 0. 24 677 0. 24 647 0. 24 618
0. 24 589 0. 24 559 0. 24 530 0. 24 500 0. 24 471
9.93 934 9.93 927 9. 93 920 9.93 912 9. 93 905
|
30 0,5 |
29 0,5 |
|
1,0 |
1,0 |
|
1,5 |
lA |
|
2,0 |
1,9 |
|
2,5 |
2,4 |
|
3,0 |
2,9 |
|
3,5 |
3,4 |
|
4,0 |
3,9 1 |
|
4,5 |
4,4 |
|
5,0 |
4,8 |
|
10,0 |
9,7 |
|
15,0 |
14,5 |
|
20,0 |
19,3 |
|
25,0 |
24,2 |
|
2*2 |
8 |
|
0,4 |
0,1 ' |
|
0,7 |
0,3 |
|
1,1 |
0,4 |
|
1,5 |
n,5 |
|
1,8 |
0,7 |
|
2,2 |
0,8 |
|
2,6 |
0,9 |
|
2,9 |
1,1 |
|
3,3 |
1,2 |
|
3,7 |
1,3 |
|
7,3 |
2,7 |
|
11,0 |
4,0 |
|
14,7 |
5,3 |
|
18,3 |
6,7 |
|
8 |
S |
|
30 |
29 |
|
1,9 |
1,8 |
|
5,6 |
5,4 |
|
9,4 |
9,1 |
|
13,1 |
12,7 |
|
16,9 |
16,3 |
|
20,6 |
19,9 |
|
24,4 |
23,6 |
|
28,1 |
27,2 |
|
2,1 |
2,1 |
|
6,4 |
0,2 |
|
10// |
10,4 |
|
15,0 |
14,5 |
|
19,3 |
18j6 |
|
23.6 |
22,8 |
|
27,'J |
26,9 |
11,5 15,3 19,2
60=
284
A MANUAL OF TOrOGKAPHlO METHODS.
Table XXXVI. — Lognrifhmic sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
30°
9. 09 919 9. 69 941 9. 69 963 9. 69 984
9.70 OUO 9. 70 02S 9. 70 050 9. 70 072 9.70 093
9.70 115 9. 70 137 9.70 159 9.70 189 9. 70 202 9. 70 22T 9. 70 245 9. 70 267 9. 70 288 9. 70 310
9. 70 332 9. 70 353 9. 70 375 9. 70 396 9. 70 418
9.70 654 9. 70 675 9. 70 697 9. 70 718
9. 70 909 9. 70 931 9.70 952
9. 76 144 9. 76 173 9. 76 202 9. 76 231 9.76 261
9. 76 290 9.76 319 9.76 348 9. 76 377 9.76 406
9.76 435 9. 76 464 9. 76 493 9. 76 522 9. 76 551
9.77 159 9.77 188 9.77 217 9.77 240 9. 77 274
9.77 303 9. 77 332 9.77 361 9. 77 390 •9.77 418
9. 77 447 9. 77 476 9. 77 505 9. 77 533 9. 77 562
9. 77 591 9. 77 619 9.77 648 9. 77 677 9.77 706
9.77 734 9. 77 763
L. Cotg.
0. 23 856 0. 23 827 0. 23 798 0.23 769 0.23 739
9. 93 753 9. 93 746 9. 93 738 9.93 731 9.93 724
0. 23 710 0.23 681 0.23 652 0.23 623 0.23 594
0, 23 565 0.23 536 0.23 .507 0.23 478 0. 23 449
9.93 717 9. 93 709 9.93 702 9.93 695 J)^93 687 9.93 680 9.93 673 9.93 065 9.93 058 9.93 050
0. 23 420 0.23 391 0. 23 361 0.23 332 0.23 303
9.93 643 9.93 636 9.93 628 9.93 621 9. 93 614
0. 23 275 0.23 246 0. 23 217 0.23 188 0.23 159
9.93 606 9.93 599 9.93 591 9.93 584 9.93 577
0.23 130 0.23 101 0.23 072 0.23 043 0.23 014
9.93 569 9. 93 562 9.93 554 9.93 547 9.93 539
9.93 532 9.93 525 9. 93 517 9. 93 510 9.93 50£ 9. 93 495 9. 93 487 9. 93 480 9.93 472 9.93 465
0. 22 097 0. 22 668 0.22 639 0.22 610 0.22 582
9.93 457 9.93 450 9. 93 442 9.93 435 9.93 427
0.22 653 0. 22 524 0. 22 495 0. 22 467 0. 22 438
9. 93 420 9.93 412 9.93 405 9. 93 397 9.93 390
0. 22 409 0.22 381 0.22 352 0. 22 323 e. 22 294
9. 93 382 9.93 375 9.93 367 9. 93 360 9. 93 352
0. 22 266 0. 22 237 0.22 209 0. 22 180
L. Tang.
9.93 344 9. 93 337 9. 93 329 9. 93 322 9. 93 314 9. 93 li07"
|
80 |
29 |
|
0,5 |
0,5 |
|
1,0 |
1,0 |
|
1,5 |
14 |
|
2,0 |
1,9 |
|
2,5 |
2,4 |
|
3,0 |
2,9 |
|
3,5 |
3,4 |
|
4,0 |
3,9 |
|
4,5 |
4,4 |
|
5,0 |
4,8 |
|
io;o |
9,7 |
|
15,0 |
14,5 |
|
20,0 |
19,3 |
|
25,0 |
24,2 |
2,8 3,3 3,7 4,2' *,7 9,3 14,0 18,7 23,3
1,0 1,4 1,8 2,1 2,4 2,8 3,2 3,5 7,0 10,5 14,0 17,5
|
; |
J |
|
30 |
29 |
|
2,1 |
2,1 |
|
6,4 |
6,2 |
|
10,7 |
10,4 |
|
15,0 |
14,5 |
|
19,3 |
18,6 |
|
23,6 |
22,8 |
|
27,9 |
26,9 |
10,0 14,0 18,0 22,0 26,0
59°
LOGAEITHMS OF GIRCULAE FUNCTIONS.
285
Taule XXXVI. — Logarithmic sineSj cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
31°
9.71 184 9.71 205 0. Tl 2a6 9. 71 247 9.71 268
9.71 289 9. 71 310 9.71 331 9. 71 352 9. 71 373
9.71 393 9. 71 414 9. 71 435 9. 71 456 9. 71 477
9. 71 498 9.71 519 9. 71 539 9. 71 560 9. 71 581
9. 71 602 9. 71 622 fl.71 643 9. 71 664 9.71 685
9. 71 705 9.71 726 9.71 747 9.71 767 9. 71 788
9. 71 809 9. 71 829 9.71 850 9.71 870
9.71 911 9.71 932 9.71 952 9,71 973
9. 72 014 9. 72 034 9.72 055 9. 72 075 9. 72 096
9. 72 238 9. 72 259 9. 72 279 9. 72 299
•8 249
'& 277
9. 78 306 9.: 8 334 9. 78 363 9. 78 391 9. 78 419
8 448 8 476 9. 78 505 9.78 533 9. 78 562
9.78 590 9.78 018 9. 78 647 9.78 675 9. 78 704
9. 78 732
9.7
760
9. 78 817 9. 78 845
9. 78 874 9. 78 902 9. 78 930 9.78 959 9. 78 987
9.79 015 9.79 043 9. 79 072 9. 79 100 9.79 128
9. 79 156 9. 79 185 9. 79 213 9. 79 241 9. 79 269
9. 79 297 9. 79 326 9. 79 354 9.79 382 9. 79 410
L. Cotg.
0.22 123 0. 22 094 0. 22 065 0, 22 037 0. 22 008
0.21 980
0. 21 951
0.21 923
0.21 894
0.21 865
0. 21 837 0,21 808 0. 21 780 0.21 751 0.21 723
U. 21 694 0. 21 666 0. 21 637 0. 21 609 0. 21 581
0.21 552 0. 21 524 0. 21 495 0. 21 467 0. 21 438
0.21 410 0.21 382 0.21 353 0. 21 325 0. 21 -296
0. 21 268 0. 21 240 0.21 211 0.21 183 0.21 155
0.21 126 0.21 098 0. 21 070 0. 21 041 0.21 013
0. 20 985 0. 20 957 0. 20 928 0.20 900 0. 20 873
0. 20 844 0. 20 815 0. 20 787 0.20 759 0. 20 731
0.20 703 0. 20 674 0. 20 646 0. 20 618 0. 20 590
0. 20 562 0. 20 534 0.20 505 0. 20 477 0. 20 449 0. 20 421
9. 93 307 9.93 299 9. 93 291 9. 93 284 9.93 276
9. 93 230 9. 93 223 9.93 215 9. 93 207 9. 93 200
9.93 192 9. 93 184 9.93 177 9.93 169 9, 93 161
9.93 154 9.93 146 9.93 138 9.93 131 9. 93 123
9. 93 115 9.93 108 9.93 100 9. 93 092 9.93 084 9. 93 077' 9. 93 069 9.93 061 9.93 053 9. 93 046
9.93 038 9.93 030 9. 93 022 9.93 014 9. 93 007
9. 92 999 9. 92 991 9. 92 983 9. 92 976 9. 93 968
9.92 960 9. 92 953 9. 92 944 9. 92 936
9. 93 929
9.92 921 9. 92 913 9. 92 905 9. 92 897 9. 92 889
9. 92 881 9. 92 874 9. 92 866 9. 92 858 9. 92 850 9. 92 842
|
29 |
|
|
1 |
0,5 |
|
2 |
1,0 |
|
3 |
1,4 |
|
4 |
1,9 |
|
5 |
2,4 |
|
6 |
2,9 |
|
7 |
3,4 |
|
8 |
3,9 |
|
9 |
4,4 |
|
10 |
4,8 |
|
20 |
9,7 |
|
30 |
14,5 |
|
40 |
19,3 |
|
50 |
24,2 |
1,4 1,9 2,3 2,8 3,3 3,7 4,2 4,7 9,3 14,0 18,7 23,3
|
10,5 |
10,0 |
|
14,0 |
13,3 |
|
17,5 |
16,7 |
|
S |
J |
|
0,1 |
0,1 |
|
0,3 |
0,2 |
|
0,4 |
0,4 |
|
0,5 |
0,5 |
|
»;i |
0,6 |
|
0,8 |
0,7 |
|
0,9 |
0,8 |
|
1,1 |
0,9 |
|
1,2 |
1,0 |
|
1,3 |
1,2 |
|
2,/ |
2,3 |
|
4,0 |
3,5 |
|
b,3 |
4,7 |
|
6,7 |
5,8 |
|
S |
8 |
|
30 |
29 |
|
1,9 |
1,8 |
|
5,6 |
5,4 |
|
9,4 |
9,1 |
|
13,1 |
12,7 |
|
16,9 |
16,3 |
|
20,6 |
19,9 |
|
24,4 |
23,6 |
|
28,1 |
27,2 |
]2,2 15,8 19,2 22,8 26,2
58°
286
A MANUAL OF TOPOGRAPHIC METHODS.
Table XXXVl.—Loganthmio sines, cosines, tantfents, and cotaugenis—Contmauii.. [Extracted from Gauss' Logaritlimic and Trigonometric Tables.]
32°
|
29 |
•2S |
|
0,5 |
0,5 |
|
1,1) |
0,0 |
|
1,4 |
1,4 |
|
1,9 |
1,0 |
|
2,4 |
2,3 |
|
2,9 |
2,8 |
|
3,4 |
3,3 |
|
3,9 |
3,7 |
|
4,4 |
4,2 |
|
4,8 |
4,7 |
|
9,7 |
9,3 |
|
14,5 |
14,0 |
|
19,3 |
18,7 |
|
■24,2 |
23,3 |
|
21 |
20 |
|
0,4 |
0,3 |
|
0,7 |
0,7 |
|
1,0 |
1,0 |
|
1,4 |
1,3 |
|
1,8 |
1,7 |
|
2,1 |
2,0 |
|
2,4 |
2,3 |
|
2,8 |
2,7 |
|
3,2 |
3,0 |
|
3,5 |
3,3 |
|
7,0 |
6,7 |
|
10,5 |
10,0 |
|
14,0 |
13,3 |
|
17,5 |
16,7 |
|
8 |
8 |
|
29 |
28 |
|
1,8 |
1,8 |
|
.5,4 |
5,2 |
|
9,1 |
8,8 |
|
12,7 |
12,2 |
|
10,3 |
15,8 |
|
19,0 |
19,2 |
|
23,6 |
22,8 |
|
27,2 |
26,2 |
0,0 1,4 1,8 2,2 2,7 3,2 3,6 4,0 4,5 9,0 13,5 18,0 22,5
0,5 0,6 0,7 0,8 0,9 1,0 1,2 2,3 3,5 4,7 5,8
2,0 6,0 10,0 14,0 18,0 22,0 26,0
S7=
LOGARITHMS OF CIEOULAE FUNCTIONS.
287
Table XXXVI. — Logariilimic sin&s, cosives, tangents, and cotangents — Coutinued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
33^
9.73 901 9.73 921 9.73 940 9.73 959 9.73 978
9. 73 997 9. 74 017 9. 74 036 9.74 055 9. 74 074
9.74 093 9.74 113 9. 74 132 9.74 151 9.74 170
9. 74 189 a. 74 208 9.74 227 9.74 246 9.74 265
9.74 284 9.74 303 9. 74 322 9.74 341 9.74 360
9.74 379 9. 74 398 9. 74 417 9.74 436 9. 74 455
9. 74 474 9. 74 493 9.74 512 9. 74 531 9. 74 549
9. 74 568 9. 74 587 9.74 606 9. 74 625 9. 74 644
9. 74 662 9. 74 681 9. 74 700 9.74 719 9.74 737 9. 74 756
81 252 81 279 81 307 81 335 SI 362
81 39U 81 418 81 445 81 473 81 500j 81 528 81 556 81 583 ! 81 611 I 81 638 i
81 666 81 693 81 721 81 748 81 776
81 941 81 968
81 996
82 023 82 051
82 078 82 106 82 133 82 161 82 188 82 21.5 82 243 82 270 82 298, 82 325 82 352 82 380 82 407 82 435 82 462
82 544 82 571 82 599
82 626 82 653 82 681
82 762 82 790 82 817
L. Cotg. a. c,
0. 18 74S 0. 18 721 0. 18 693 0. 18 665 0.18 638
0. 18 010 0. 18 582 0. 18 .555 0. 18 527 0. 18 5110
0. 18 472 0. 18 441 0. 18 417 0. 18 389 0. 18 362
0. 18 334 0.18 307 0. 18 279 0. 18 252 0.18 224
0. 18 197 0.18 169 0. 18 142 0.18 114
0.18 087
0. 18 059 0. 18 032 0. 18 004 0. 17 977 0. 17 949 0^ 17 922 0.17 894 0. 17 867 0. 17 839 0.17 812 0. 17 785 0. 17 757 0. 17 730 0.17 702 0.17 675 0. 17 648 0.17 620 0. 17 593 0.17 565 0.17 538
0. 17 511 0. 17 483 0. 17 456 0. 17 429 0. 17 401
9. 92 359 9.92 351 9.02 343 9. 92 335
_9^92 326 9. 92 3i8"
. 9.92 310 9. 92 .302 9.92 293 9.92 285
9.92 277 9.92 269 9.92 260 9. 92 252 9. 92 24!
9.92 111 9. 92 102 9. 92 094 9. 92 086 9. 92 077 9. 92 069 9. 92 060 9. 92 052 9. 92 044 9. 92 035
9. 92 027 9. 92 018 9. 92 010 9. 92 002 0. 91 993
9.91 985 9.91 976 9.91 968 9.91 959 9. 91 951
9. 91 942 9. 91 934 9.91 925 9.91 917 9. 91 908 9.91 900 9. 91 891 I 9.91 883 9.91 874 9.91 866 9. 91 857
14,0 18,7 23,3
0,4 0,9 1,4 1,8. 2,2 2,7 3,2 3,6 4,0 4,5 9,0 13,5 18,0 22,5
|
20 |
19 |
|
0'3 |
0,3 |
|
0,7 |
06 |
|
1,0 |
1,0 |
|
1,3 |
1,3 |
|
1,7 |
1,6 |
|
2,0 |
1,9 |
|
2,3 |
2,2 |
|
2,7 |
2,5 |
|
3,0 |
2,8 |
|
3,3 |
3,2 |
|
6,7 |
6,3 |
|
10,0 |
9,5 |
|
13,3 |
12,7 |
|
16,7 |
15,8 |
3,0 6,0 9,0 12,0 15,0
|
9 |
9 |
|
2S |
27 |
|
1,6 |
1,5 j |
|
4,7 |
4,5 |
|
7,8 |
7,5 |
|
10,9 |
10,5 |
|
14,0 |
13,5 |
|
17,1 |
16,5 |
|
20,2 |
19,5 |
|
23,3 |
- 22,5 |
|
26,4 |
25,5 |
15,2 18,6 21,9 25,3
5G''
288
A MANUAL OF TOrOGEAPHIO METHODS.
Table XXXVI. — LogarUlimic sines, cosines, tantjents, and cotangents— ContinnaA, [Extractcil from Gauss' Logaritlimic aud Trigouometric Tables.]
34°
9. 74 756 9. 74 775 9. 74 794 9.74 812 9.74 831
9.74 850 9. 74 863 9.74 887 9.74 906 9.74 024
9. 74 943 9.74 901 9.74 9S0
9.74 999
9.75 017
9.75 036 9.75 054 9. 75 073 9.75 091 9. 75 110
9.75 V>i 9.75 147 9.75 165 9.75 184 9.75 202
9. 75 221 9.75 239 9. 75 258 9. 75 276 9.75 294
9.75 313 9.75 331 9,75 350 9.75 368 9. 75 386
9.75 405 9. 75 423 9, 75 441 9.75 459 9.75 478 9.75 496 9.75 514 9. 75 533 9.75 551 9.75 569 9.75 .587 9. 75 605 9.75 624 9.75 64 2 9.75 660 9.75 678 9.75 696 9. 75 714 9.75 733 9. 75 751 9.75 769 9.75 787 9. 75 805 9. 75 823 9.75 841 9.75 859
L. Tang. il. o,
9. 82 899 9. 82 926 9.82 953
9.82 980
9.83 008
9.83 171 9.83 198 9. 83 225 9. 83 252 9.83 280
9.83 307 9.83 334
9. 83 415
9. 83 442 9. 83 470 9. 83 497 9.83 524 9. 83 551
9. 84 119 9.84 146 9.84 173 9.84 200 9. 84 227 9. 84 254 9.84 280 9. 84 307 9. 84 334 9. 84 361 9. 84 388 9. 84 415 9. 84 442 9.84 469 9. 84 496 9. 84 523
L. Cotg. d. I
0. 17 047 0. 17 020 0.16 992
0. 16 965 0. 16 938 0. 16 911 0. 10 883 0. 16 856
0. 16 829 0.16 822 0.10 775 0. 10 748 0. 16 720
0, 16 093 0. 16 666 0. 16 639
9.91 857 9.91 849 9.91 840 9,91 832 9.91 823
9.91 815 9,91 806 9.91 798 9,91 789 9,91 781
9,91 7' 9.91 7 9.91 7: 9,91 7 9,91 7
0. 16 558 0. 16 530 0.16 503 0, 16 476 0, 16 449
0, 16 422 0. 16 395 0, 16 368 0. 16 341 0. 16 314
0. 16 287 0. 16 260 0. 16 232 0, 16 205 0. 16 178
0,16 151 0, 16 124 0.16 097 0.16 070 0. 10 043
0.10 016 0, 15 989 0, 15 902 0. 15 935 0, 15 908 0, 15 881 0. 15 854 0, 15 827 0. 15 800 0. 15 773 0. 15 746 0. 15 720 0. 15 693 0, 15 666 0. 15 639 0.15 612 0, 15 585 0. 15 5.58 0.15 531 0. 15 504 0. 15 477
9.91 729 9.91 720 9.91 712 9.91 703 9,91 695
9.91 686 9,91 677 9,91 069 9.91 660 9,91 651
9,91 643 9,91 634 9.91 625 9.91 017 9,91 608
9,91 599 9,91 .591 9.91 582 9.91 ,573 9.91 565
9,91 556 9,91 547 9.91 538 9.91 530 9.91 521
9.91 512 9,91 504 9.91 495 9.91 486 9,91 477 9.91 409 9.91 460 9. 91 451 9.91 442 9,91 433 9,91 425 9,91 416 9,91 407
9! 91 389 9,91 381 9.91 372 9.91 363 9.91 354 9,91 345 9, 91 336
|
28 0,5 |
27 0,4 |
|
0,9 |
0,9 |
|
1,4 |
1,4 |
|
1,9 |
1,8 |
|
2,3 |
2,2 |
|
2,8 |
2,7 |
|
3,3 |
3,2 |
|
3,7 |
3,6 |
|
4,2 |
4,0 |
|
4,7 |
4,5 |
|
9,3 |
9,0 |
|
14,0 |
13,5 |
|
18,7 |
18,0 |
|
23,3 |
22,5 |
1,6 4,7 7,8 10,9 14,0 17,1 20,2 23,3 26,4
0,4 0,9 1,3 1,7 2,2 2,6 3,0 3,5- 3,9 4,3 8,7 13.0 17,3 21,7
18 0,3 0,6 0,9 1,2 1,5 1,8 2,1 2,4 2,7 3,0 6,0 9,0 12,0 15,0
|
0,2 |
0,1 |
|
0,3 |
0,3 |
|
0,4 |
0,4 |
|
(1,6 |
0,5 |
|
0,8 |
0,7 |
|
0,9 |
0,8 |
|
1,0 |
0,9 |
|
1,2 |
1,1 |
|
1,4 |
1,2 |
|
1,5 |
1,3 |
|
3,0 |
2,7 |
|
4,5 |
4,0 |
|
6,0 |
5,3 |
12,2 15,8 19,2 22,8 26,2
8,4 11,8 15,2 18,6 21,9 25,3
55^
LOGAEITHMS OP CIRCULAE FUNCTIONS.
289
Table XXXVI. — LogarWwiie sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauas' Logarithmic and Trigonometric Tables.]
35°
9. 75 859 9. 75 877 9. 75 895 9.75 913 9. 75 931
9. 75 949 9.75 967 9. 75 985 9. 76 003 9. 76 021
9.76 039 9. 76 057 9. 76 075 9.70 093 9. 76 111
9. 76 129 9. 76 146 9.76 164 9.76 182 9. 76 200
9. 76 218 9. 76 236 9. 76 253 9. 76 271 9. 76 289
9. 76 307 9. 76 324 9. 76 342 9. 76 360 9.76 378
9. 76 395 9. 76 413 9. 76 431 9. 76 448 9. 76 466
9. 76 484 9. 76 501 9. 76 519 9. 76 537 9. 76 554
9. 76 572 9. 76 590 9. 76 607 9. 76 625 9: 76 642
9. 76 660 9. 76 677 9. 76 695 9. 76 712 9. 76 730
9. 76 747 9. 76 765 9.76 782 9.76 800 9. 76 817
9.76 835 9. 76 852 9.76 870 9.76 887 9. 76 904
9. 76 922
L. Tang. d. c.
84 523 84 550 84 576 84 603 84 630
84 657 84 684 84 711 84 738 84 764
84 791 84 818 84 845 81 872 84 899
84 935 84 952
84 979
85 006 85 033
85 140 85 166
85 193 85 220 85 247 85 273 85 300
85 487 85 514 85 540 85 567
85 594 85 620 85 647 85 674 85 700
85 727 85 754 85 780 85 807 85 834
85 860 85 887 85 913 85 940 85 967
85 993
86 020 86 046 86 073 86 100 86 126
0. 15 477 0. 15 450 0. 15 424 0. 15 397 0. 15 370
0. ]5 343 0.15 316 0. 15 289 0. 15 262 0. 15 236
0. 15 209 0. 15 182 0. 15 155 0. 15 128 0. 15 101
0. 15 075 0. 15 048 0. 15 021 0. 14 994 0. 14 967
0. 14 941 0. 14 914 0. 14 887 0. 14 860 0. 14 834
0. 14 807 0. 14 780 0. 14 753 0. 14 727 0.14 700
0. 14 673 0. 14 646 0. 14 620 0.14 593 0. 14 566
0.14 540 0.14 513 0. 14 486 0. 14 460 0. 14 433
0. 14 406 0. 14 380 0. 14 353 0. 14 326 0. 14 300
0. 14 273 0. 14 246 0. 14 220. 0. 14 193 0. 14 166
9. 91 336 9.91 328 9.91 319 9. 91 310 9. 91 301
9. 91 292 9.91 283 9.91 274 9.91 266 ■9.91 257
9. 91 248 9. 91 239 9.91 230 9.91 221 9.91 212
9. 91 203 9.91 194 9.91 185 9.91 176 9.91 167
9.91 158 9.91 149 9.91 141 9.91 132 9.91 123
9.91 114 9.91 105 9.91 096 9.91 087 9.91 078
9.91 069 9.91 060 9.91 051 9. 91 042 9.91 033
9. 91 023 9.91 014 9.91 005 9. 90 996 9.90 987
9.90 978 9. 90 969 9. 90 960 9.90 951 9.90 942
0. 14 140 0. 14 113 0. 14 087 0. 14 060 0. 14 033
0. 14 007 0. 13 980 0. 13 964 0. 13 927 0. 13 900
0. 13 874
L. Cotg. d. c. L. Tang. L. Siu. d
9.90 887 9.90 878 9.90 869
9. 90 823 9. 90 814 9. 90 805
|
27 |
2« |
|
0,4. |
0,4 |
|
0,9 |
0,9 |
|
1,* |
1,3 |
|
1,8 |
1,7 |
|
2,2 |
2,2 |
|
2,7 |
2,6 |
|
3,2 |
3,0 |
|
3,6 |
3,5 |
|
4,0 |
3,9 |
|
4,5 |
4,3 |
|
9,0 |
8,7 |
|
13,5 |
13,0 |
|
18,0 |
17,3 |
|
22,5 |
21,7 |
|
17 |
10 |
9 |
|
0,3 |
0,2 |
0,2 |
|
0,6 |
0,3 |
0,3 |
|
0,8 |
0,5 |
0,4 |
|
1,1 |
0,7 |
0,6 |
|
1,4 |
0,8 |
0,8 |
|
1,7 |
1,0 |
0,9 |
|
2,0 |
1,2 |
1,0 |
|
2,3 |
1,3 |
1,2 |
|
2,6 |
1,5 |
1,4 |
|
2,8 |
1,7 |
1,5 |
|
5,7 |
3,3 |
3,0 |
|
8,5 |
.5,0 |
4,5 |
|
11,3 |
e,7 |
0,0 |
|
14,2 |
8,3 |
7,5 |
9,0 12,0 15,0
-19
54°
290
A MANUAL OP TOPOGEAPHIC METHODS.
Table XXXVI. — Logarillimic sines, cosines, tangents, and' cotiingenis — Continued. [Extracted from Gauss' Logaritlimic anil Trigonometric Tables.]
36°
9.76 922 9.76 939 9.76 957 9. 76 974 9. 76 991
9.77 009 9. 77 026 9. 77 043 9. 77 061 9. 77 078
9.
9.77 164
095
147
9.77 181 9.77 199 9. 77 216 9. 77 233 9. 77 250
9. 77 268 9.77 285 9.77 302 9.77 319 9. 77 336
9. 77 353 9.77 370 9.77 387 9. 77 405 9. 77 432
9. 77 456 9. 77 473 9. 77 490 9.77 507
9. 77 524 9. 77 541 9. 77 558 9. 77 575 9. 77 592
9.77 609 9.77 626 9. 77 G43 9. 77 660 9. 77 677
9. 77 694 9. 77 711 9.77 728 9. 77 744 £. 77 761
9.77 778 9.77 795 9.77 812 9.77 829 9.77 846
L. Tang. d. c
9. 86 126 9. 86 153 9.86 179 9. 86 206 9. 86 232
9. 86 269 9. 86 285 9.86 312 9. 86 338 9. 86 365
9. 86 392 9. 86 418 9. 86 445 9. 86 471 9. 86 498
9.86 656 9. 86 683 9. 86 709 9. 86 736
9. 86 815 9. 86 842 9. 86 868 9. 86 894
9. 86 921 9. 86 947 9. 86 974 9.87 000 9. 87 027
9. 87 053 9. 87 079 9.87 106 9. 87 132 9.87 158
9.87 185 9. 87 211 9. 87 238 9.87 264 9. 87 290
9.87 317 9. 87 343 9. 87 369 9. 87 396 9. 87 422
9.87 448 9. 87 475 9.87 501 9.87 527 9. 87 554
9.87 580 9.87 606 9.87 633 9.87 659 9.87 685 I 9. 87 711 I
L. Cotg. ' d.
L. Cotg.
0. 13 874 0. 13 847 0. 13 821 0. 13 794 0. 13 768
0. 13 741
0. 13 715
0. 13 688
0. 13 662
0. 13 635
0. J 3 608
0. 13 582
0. 13 555
0. 13 529
0. 13 502
0. 13 476 0. 13 449 0. 13 423 0. 13 397 0.13 370
0. 13 344 0.13 317 0. 13 291 0. 13 264 0. 13 238
0. 13 211 0. 13 185 0.13 158 0.13 132 0. 13 106
0. 13 079 0. 13 053 0. 13 026 0.13 000 0. 12 973
0. 12 947 0. 12 921 0. 12 894 0. 12 868 0. 12 842
0. 12 815 0. 12 789 0. 12 762 0. 12 736 0.12 710
0. 12 683 0. 12 657 0. 12 631 0.12 604 0.12 578
0. 12 552 0. 12 525 0. 12 499 0. 12 473 0. 12 446
0. 12 420 0. 12 394 0.12 367 0. 12 341 0. 12 315 0. 12 289
9. 90 796 9. 90 787 9. 90 777 9. 90 768 9. 90 759
9.90 750 9. 90 741 9.90 731 9. 90 722 9.90 713
9. 90 657 9.90 648 9. 90 639 9.90 630 9.90 620
9.90 611 9.90 602 9. 90 692
9. 90 565 9. 90 555 9. 90 546
9.90 424 9. 90 415 9. 90 406 9. 90 396
9. 90 311 9.90 301 9.90 292
9.90 263 9. 90 264 9. 90 244
0,9 1/4 1,8 2,2 2,7 3,2 3,6 4,0 4,5 9,0 13,5 18'0 22,5
0,4 0,9 1,3 1,7 2,2 2,6
8,7 13,0 17,3 21,7
|
18 |
17 |
|
0,3 |
0,3 |
|
0,6 |
0,6 |
|
0,9 |
0,8 |
|
1,2 |
1/1 |
|
1,5 |
M |
|
1,8 |
1/7 |
|
2,1 |
2,0 |
|
2,4 |
2,3 |
|
2,7 |
2,6 |
|
3,0 |
2,8 |
|
6,0 |
5,7 |
|
9,0 |
8'5 |
|
12,0 |
11,3 |
|
15,0 |
14,2 |
0,4 0,6 0,8 0,9 1,0 1,2 1/4 1,5 3,0 4,5
|
4,5 |
4'3 |
|
V,b |
7,2 |
|
l(),.'i |
10,1 |
|
13,5 |
13,0 |
|
I6„S |
15,9 |
|
19,6 |
18,8 |
|
22,5 |
21,7 |
|
2b,b |
24,6 |
53°
LOGARITHMS OF CIECULAE FUNCTI02fS.
291
Table XXXVI. — Logarithmic sines, cosines, tangents, and cotangents — Continued. [Extraoted from Ganss' Logarithmic and Trigonometric Tables.]
37°
9. 77 946 9. 77 963 9.77 980 9.77 997 9. 78 013
9. 78 030 9. 78 047 9. 78 063
9. 78 130 9.78 147 9. 78 163 9. 78 180
9. 78 197 9. 78 213 9. 78 230 9. 78 246 9. 78 263 9. 78 280 9. 78 296 9. 78 313 9. 78 329 9. 78 346
9. 78 395 9. 78 412 9. 78 428
9. 78 445 9. 78 461 9. 78 478 9. 78 494 9. 78 510
9. 78 527 9.78 543 9. 78 560 9. 78 576 9. 78 592
9. 78 609 9. 78 625 9. 78 642 9. 78 658 9. 78 674
9. 78 691 9. 78 707 9. 78 723 9. 78 739 9. 78 756
9.78 772 9. 78 788 9. 78 805 9. 78 821 9. 78 837
L. Tang, d
87 764 87 790 87 817
87 843 87 869 87 895 87 922
; 071
88 105 88 131 88 158 88 184 88 210
88 629 88 655 88 681
89 125
89 151 89 177 89 203 89 229 89 255 89 281
L. Cotg. d. c.
0.12 289 0. 12 262 0. 12 236
0. 12 105 0. 12 078 0. 12 052
0. 12 026 0. 12 000 0. 11 973 0.11 947 0. 11 921
0. 11 895 0. 11 869 0. 11 842 0.11 816 0. 11 790
0. 11 764 0. 11 738 0. 11 711 0.11 685 0. 11 659
0.11 633 0. 11 007 0. 11 580 0. 11 554 0.11 528
0. 11 502 0. 11 476 0. 11 450 0. 11 423 0. 11 397
0. 11 371 0. 11 345 0. 11 319 0. 11 293 0. 11 267
0. 11 241 0. 11 214 0.11 188 0. 11 162 0. 11 136
0.11 110 0. 11 084 0. 11 058 0. 11 032 0.11 006
0. 10 980 0. 10 954 0. 10 927 0. 10 901 0. 10 875
0. 10 849 0. 10 823 0. 10 797 0.10 771 0. 10 745 0. 10 719
L. Tang.
90 235 90 225 90 216 90 206 90 197
90 187 90 178 90 168 90 159 90 149
90 120 90 111 90 101
89 947 89 937 89 927 89 918
89 702 89 693 89 683 89 673
|
0,4 |
0,4 |
|
0,9 |
0,9 |
|
1,4 |
1,3 |
|
1,« |
1,7 |
|
2,2 |
2,2 |
|
2,7 |
2,6 |
|
3,2 |
3,0 |
|
3,6 |
3,5 |
|
4,0 |
3'9 |
|
4,6 |
4,3 |
|
9,0 |
8,7 |
|
13,5 |
13,0 |
|
18,0 |
17,3 |
|
22,5 |
21,7 |
|
17 |
16 |
|
0,3 |
0,3 |
|
0,6 |
0,5 |
|
0,8 |
0,8 |
|
1,1 |
1,1 |
|
l,i |
1,3 |
|
I'V |
1,6 |
|
2'() |
1,9 |
|
2,3 |
2,1 |
|
2'6 |
2,4 |
|
2,8 |
2,7 |
|
5,7 |
5,3 |
|
K,5 |
8,0 |
|
11,3 |
10,7 |
|
14,2 |
13,3 |
|
10 |
9 |
|
0,2 |
0,2 |
|
0,3 |
0,3 |
|
0,5 |
0,4 |
|
0,7 |
0,6 |
|
0,8 |
0,8 |
|
1,0 |
0,9 |
|
1,2 |
1,0 |
|
1,3 |
1,2 |
|
1,5 |
1,4 |
|
1,7 |
1,5 |
|
3,3 |
3,0 |
|
5,0 |
4,5 |
|
6,V |
6,0 |
|
8,3 |
7,5 |
|
1,4 |
1,3 |
|
4,1 |
3,9 |
|
6,8 |
6,5 |
|
9,4 |
9,1 |
|
12,2 |
11,7 |
|
14,8 |
14,3 |
|
17,6 |
16,9 |
|
20,2 |
19,5 |
|
22,9 |
22,1 |
|
2b,6 |
24,7 |
52=
292
A IMANUAL OF TOPOGKAPlilO METUODS.
Table XXXVI. — Loiiayillimic [Extracted from Gai
/«(«, cosines, laiigents, and cotangents — Coutinued. .s' Lojiarithmic aud Trigonometric Tables.]
38°
«50 967
9. 78 nS3 _9.7S_0!)9
9.79 015" 9. 79 031 9. 79 047 9. 79 063 9. 79 079
"977Dl)9T 9. 79 111 9. 79 128 9. 79 144 9. 79 160 9. 79 176 9. 79 192 9. 79 208 9. 79 224 9. 79 240
■9 256
9. 79 383 9^9^399 9. 79 415 9. 79 431 9. 79 447 9. 79 463 9. 79 478 9. 79 494 9. 79 510 9.79 526 9. 79 542 9.79 558
9. 79 573 9. 79 589 9. 79 605 9. 79 621 9. 79 636
9.79 652 9. 79 668 9. 79 684 9.79 699 9.79 715
9.79 731 9. 79 746 9.79 762 9. 79 778
9. 79 825 9.79 840 9. 79 856 9. 79 872
L. Tang. d. c.
9. 89 801 9.89 827 9.89 853
9.90 112 9. 90 138 9.90 164
9. 90 190 9. 90 216 9. 90 242 9. 90 268 9. 90 294
.9.90 ;
346
9. 90 449 9. 90 475 9. 90 501 9. 90 527 9. 90 553
9.90 578 9.90 604 9.90 630 9. 90 656 9.90 682 9. 90 708 9. 90 734 9.90 759
L. Cotg.
0. 10 719 0. 10 693 0. 10 667 0. 10 641 0^10_615 0. 10 589 0. 10 563 0. 10 537 O 10 511 0. 10 485
0. 10 459 0.10 4« 0. 10 407 0. 10 381 0. 10 355 0. 10 329 0. 10 303 0.10 277 0. 10 251 0. 10 225
0. 10 199 0. 10 173 0.10 147 0. 10 121 0. 10 095
0. 10 069 0.10 043 0.10 017 0. 09 99] 0. 09 965
0.09 939 0. 09 914 0.09 888 0. 09 862 0. 09 836
0. 09 810 0. 09 784 0.09 758 0. 09 732 0. 09 706
0. 09 551 0. 09 525 0. 09 499 0. 09 473 0. 09 447
0. 09 422 0. 09 396 0.09 370 0. 09 344 0.09 318 0.09 292 0.09 266 0. 09 241 0. 09 215 0.09 189
L. Cos.
9. 89 633
9.89 624
J)JS9 61£ 9. 89' 004
9.89 594
9. 89 584
9. 89 574
9. 89 564
9.89 524 9. 89 514 9.89 504 9.89 495 9. 89 485 9. 89 475 J3^89 465 9. .89 455" 9. 89 445 9. 89 435 9. 89 425 9. 89 415
9.89 405 9. H9 395 9. 89 385 9. 89 375 9. 89 364
9. 89 354 9. 89 344 9. 89 334 9. 89 324 9. 89 314
9. 89 304 9. 89 294 9.89 284 9.89 274 9.89 264 9:89 254 9.89 244 9.89 233
9. 89 152 9.89 142 9.89 132 9.89 122
9. 89 091 9.89 081 9.89 071 9.89 060
P.P.
4,3 8,7 13,0 17,3 21,7
0,4 0,8 1,2 1,7 2,1 2,5 2,9 3,3 3,8 4,2 8,3 12,5 16,7 20,8
|
17 0,3 |
16 0,3 |
|
0,6 |
0,5 |
|
0,8 |
0,8 |
|
1,1 |
1,1 |
|
1,4 |
1,3 |
|
1/7 |
1,6 |
|
2,0 |
1,9 |
|
2,3 |
2,1 |
|
2,6 |
2,4 |
|
2,8 |
2,7 |
|
5,7 |
.5,3 |
|
8,5 |
8,0 |
|
11,3 |
10,7 |
|
14,2 |
13,3 |
|
11 |
10 |
|
0,2 |
0,2 |
|
0,4 |
0,3 |
|
0,6 |
0,5 |
|
0,7 |
0,7 |
|
0,9 |
0,8 |
|
1/1 |
1,0 |
|
1,3 |
1,2 |
|
1,5 |
1,3 |
|
1,6 |
1,5 |
|
1,8 |
1,7 |
|
3,7 |
3,3 |
|
5,5 |
5,0 |
|
7,3 |
6,7 |
|
9,2 |
8,3 |
|
10 |
10 |
|
26 |
25 |
|
1,3 |
1/2 |
|
3,9 |
3,8 |
|
6,5 |
6,2 |
|
9,1 |
8,8 |
|
11,7 |
11,2 |
|
14,3 |
13,8 |
|
16,9 |
16,2 |
|
19,5 |
18,8 |
|
22,1 |
21,2 |
|
24,7 |
23,8 |
1,2 1,5 1,8 2,0 2,2 2,5 5,0 7,5 10,0 12,5
1/4 4,3 7,2 10,1 13,0 15,9 18,8 21,7 24,6
31'
LOGAEITHMS OF CIRCULAR FUNCTIONS.
293
Table XXXVI. — Logarithmic s'mes, cosines, tangents^ and cotangents — Continued, [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
39°
9. 79 903 9.79 918 9. 79 934 9.79 950
9.79 905 9.79 981
9.79 990
9.80 012 9 80 027
9.80 043 9.80 058 9. 80 074 9. 80 C89 9.80 105
9.80 120 9.80 136 9.80 151 9. 80 160 9.80 182
9.80 197 9. 80 213
9. 80 274 9. 80 290 9.80 305 9. 80 320
9.80 428 9. 80 443 9. 80 458 9. 80 473 9. 80 489
9.80 504 9. 80 519 9. 80 534 9. 80 550 9.80 565
9.80 580 9. 80 595 9. 80 610 9. 80 625 9. 80 641
9. 80 656 9. 80 671 9. 80 686 9. 80 701 9. 80 716
90 837 90 863 90 889 90 914 90 940
90 906
90 992
91 018 91 043 91 009
91 095 91 121 91 147 91 172 91 198
91 224 91 250 91 276 91 301 91 327
91 353 91 379 91 404 91 430 91 456 91 482 91 507 91 533 91 559 91 585
91 610 91 636 91 662 91 688 91 713
91 739 91 765 91 791 91 816 91 842
91 868 91 893 91 919 91 945 91 971
91 996
92 022 92 048 92 073 92 099
92 125 92 150 92 176 92 202 92 227
92 253 92 279 92 304 92 330 92 356 92 381
0. 09 163 0.09 137 0.09 111 0. 09 086
0.08 879 0. 08 853 0. 08 828 0.08 802
0. 08 750 0. 08 724 0. 08 099 0. 08 673
0. 08 617 0. 08 621 0. 08 596 0. 08 570 0. 08 544
0. 08 518
0.1
415
0.08 390 0.08 364 0.08 338 0. 08 312 0. 08 287
0. 08 261 0. 08 235 0. 08 209 0.08 184 0.08 158
0. 08 132 0. 08 107 0. 08 081 0. 08 055 0. 08 029
0. 08 004 0. 07 978 0. 07 952 0. 07 927 0. 07 901
0. 07 875 0. 07 850 O: 07 824 0. 07 798 0.07 773
0. 07 747 0. 07 721 0. 07 696 0. 07 670 0. 07 644 0.07 619
L. Tang.
88 793 88 782 88 772 88 761
88 678 88 668 88 657 88 647
88 636 88 626 88 615 88 605 88 594
88 573 88 563 88 552 88 542
|
n,4 |
0,4 |
|
0,9 |
0,8 |
|
1,3 |
1,2 |
|
1,V |
1,7 |
|
2,2 |
2,1 |
|
2,6 |
2,,') |
|
3,0 |
2,9 |
|
3,!> |
3,3 |
|
3'9 |
3,8 |
|
4,3 |
4,2 |
|
8,3 |
|
|
13,0 |
12,5 |
|
ri,3 |
16,7 |
|
21,7 |
20,8 |
|
1 |
16 0,3 |
|
2 |
0,5 |
|
3 |
0,8 |
|
4 |
1/1 |
|
5 |
1,3 |
|
6 |
1,6 |
|
V |
1,9 |
|
H |
2,1 |
|
9 |
2,4 |
|
10 |
2,7 |
|
20 |
5,3 |
|
30 |
8'0 |
|
40 |
10,7 |
|
50 |
13'3 |
|
1,2 |
1,J |
|
3,6 |
3,4 |
|
b,9 |
5,7 |
|
8,3 |
7,9 |
|
10,6 |
10,2 |
|
13,0 |
12,5 |
|
lb,4 |
14,8 |
|
1V,V |
17,1 |
|
20,1 |
19,3 |
|
22,5 |
21,6 |
|
24,8 |
23,9 |
50=
294
A MANUAL OF TOPOGEAPHIC METHODS.
Table XXXVI. — Locjaritiimic sines, cosines, tangents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables.]
40°
9.80 837 9. 80 852 9. 80 867
9. 80 987 9.81 002 9.81 017
9. 81 032 i 9.81 047 '9.81 061 9. 81 076 , 9.8] 091
9. 81 106 9.81 121 9.81 136 9.81 151 9.81 166
9. SI 180 9.81 195 9. 81 210 9.81 225 9.81 240
9. 81 254 9.81 269 9. 81 284 9.81 299 9.81 314
9.81 328 9.81 343 9.81 358 9. 81 372 9. 81 387
9. 81 402 9.81 417 9.81 431 9. 81 446 9.81 461
9. 81 475 9. 81 490 9.81 505 9. 81 519 9. 81 534
9. 81 549 9.81 563 9. 81 578 9. 81 592 9.81 607 9. 81 622 9.81 636 9.81 651 9.81 665 9. 81 680 9. 81 694
9.92 381 9. 92 407 9. 92 433 9. 92 458 9. 92 484
9. 92 510 9. 92 535 9. 92 561 9. 92 587 9. 92 612
9. 92 638 9.92 663 9. 92 689 9. 92 715 9. 92 740
9. 92 766 9. 92 792 9. 92 817 9. 92 843 9. 92 868
9. 92 894 9. 92 920 9. 92 945 9. 92 971 9. 92 996
9.93 022 9. 93 048 9.93 073 9.93 099 9.93 124
9.93 150 9. 93 175 9.93 201 9. 93 227 9.93 252
9. 93 406 9. 93 431 9. 93 457 9. 93 482 9.93 508
9.93 533 9.93 559 9.93 584 9. 93 610 9.93 636
9.93 661 9. 93 687 9.93 712 9. 93 738 9.93 763 9.93 789 9. 93 814 9. 93 840
0. 07 619 0. 07 593 0.07 667 0.07 542 0.07 516
0. 07 490 0.07 465 0. 07 439 0. 07 413 0.07 388
0.U7 362 0. 07 337 0.07 311 0. 07 285 0. 07 260
0. 07 234 0.07 208 0.07 183 0. 07 157 0.07 132
O.07 106 0.07 080 0. 07 055 0.07 029 0.07 004
0. 06 978 0.06 952 0. 06 927 0.06 901 0. 06 876
0.06 850 0. 06 825 0. 06 799 0.06 773 0. 06 748
0.1
: 722
0.06 697 0.06 671 0. 06 646 0. 06 620
0. 06 594 0. 06 569 0. 06 543 0. 06 518 0. 06 492
0.06 467 0. 06 441 0. 06 416 0. 06 390 0. 06 364
0.06 339 0. 06 313 0.06 288 0. 06 262
0.1
0.06 211 0.06 186 0.06 160 0.06 135 0. 06 109 0. 06 084
d. c. L. Tang.
88 372 88 362 88 351 88 340
88 201 88 191 88 180 88 169
88 105 88 094 88 083
88 040 88 029 88 018 88 007
87 985 87 975 87 964 87 953
87 942 87 931 87 920 87 909 87 898
87 887 87 877 87 866 87 855 87 844 87 833 87 822 87 811
|
0,4 |
0,4 |
|
0,9 |
0,8 |
|
1,3 |
1,2 |
|
1/' |
i:i |
|
2,2 |
2,1 |
|
2,6 |
2,b |
|
3,0 |
2,9 |
|
3,5 |
3,3 |
|
3,9 |
3,8 |
|
4,3 |
4,2 |
|
8,V |
8,3 |
4,7 7,0 9,3 11,7 10 0,2 0,3 0,5
|
n |
10 1 |
|
26 |
26 |
|
1,2 |
1,3 |
|
3,5 |
3,9 |
|
5,9 |
6,5 |
|
8,3 |
9,1 |
|
10,6 |
11,7 |
|
13,0 |
14,3 |
|
15,4 |
16,9 |
|
17,7 |
19,5 |
|
20,1 |
22,1 |
|
22,5 |
24,7 |
|
24,8 |
1,2 3,8 6,2 8,8 11,2 13,8 16,2 18,8 21,2 23,8
49=
LOGAEITHMS OF CIEOULAE FUNCTIONS.
295
Table XXXVI. — Logarithmic sines, cosines, tangents^ and cotangents — Continued.
[Extractetl from Gauss' Logarithmic and Trigonometric Tables.]
410
L. Tang.
L. Cotg.
81 694 81 709 81 723 81 738 81 752
81 767 81 781 81 796 81 810 81 825
81 9U 81 926 81 940 81 955 81 969
81 983
81 998
82 012 82 026 82 041
82 055 82 069 82 084 82 098 82 112
82 126 82 141 82 155 82 169 82 184
82 198 82 212 82 226 82 240 82 255
82 269 82 283 82 297 82 311 82 326
82 340 82 354 82 368 82 382
82 410 82 424 82 439 82 453 82 467
9. 93 916 9. 93 942 9. 93 967
9. 93 993
9.94 018
9.94 044 9. 94 069 9. 94 095 9. 94 120 9. 94 146
9. 94 171 9. 94 197 9. 94 222 9.94 248 9. 94 273
9.94 299 9.94 324 9. 94 350 9.94 375 9. 94 401 9. 94 426 9. 94 452 9. 94 477 9. 94 503 9. 94 .528
9. 94 554 9. 94 579 9. 94 604 9.94 630 9. 94 655
9. 94 681 9. 94 706 9.94 732 9. 94 757 9. 94 783
9. 95 062 9. 95 088 9.95 113 9. 95 139 9.95 164
9.95 190 9.95 215 9. 95 240 9. 95 266 9. 95 291 9. 95 317 9. 95 342 9. 95 368 9. 95 393 9. 95 418 9.95 444
0. 06 084 0. 06 058 0. 06 033 0.06 007 0. 05 982
0.05 956 0. 05 93] 0. 05 905 0. 05 880 0. 05 854
0. 05 829 0. 05 803 0.05 778 0. 05 752 0. 05 727
0. 05 701 0. 05 676 0.05 650 0. 05 625 0. 05 599
0. 05 574 0. 05 548 0. 05 523 0. 05 497 0.05 472
0.05 446 0. 05 421 0. 05 396 0. 05 370 0. 05 345
0. 05 319 0. 05 294 0. 05 268 0. 05 243 0. 05 217
0.05 192 0.05 166 0.05 141 0.05 116 0. 05 090
0. 05 065 0.05 039 0.05 014 0. 04 988 0. 04 963
0. 04 938 0. 04 912 0. 04 887 0. 04 861 0. 04 836
0.04 810 0. 04 785 0.04 760 0. 04 734 0. 04 709 0.04 683 0. 04 658 0. 04 632 0. 04 607 0.04 582 0. 04 556
87 778 87 767 87 756 87 745 87 734
87 723 87 712
87 668 87 657 87 646 87 635 87 624
87 613 87 601 87 590
87 546 87 535 87 524 87 513
87 501 87 490 87 479
87 446 87 434 87 423 87 412 87 401
87 390 87 378 87 367 87 356 87 345
87 334 87 322 87 311 87 300
87 288
9.87 277 9.87 266 9.87 255 9.87 243 9.87 232
221 9. 87 209
9.87 141 9.87 130 9.87 119
|
0,4 |
0,4 |
|
0,9 |
0,8 |
|
1,3 |
1,2 |
|
1;7 |
1,7 |
|
2,2 |
2,1 |
|
2,6 |
2,5 |
|
3,0 |
2,9 |
|
3,5 |
3,3 |
|
3,9 |
3,8 |
|
4,3 |
4,2 |
|
«,v |
8,3 |
|
13,0 |
12,5 |
|
17,3 |
16,7 |
|
21,7 |
20,8 |
|
15 |
14 |
|
0,2 |
0,2 |
|
0,5 |
0,5 |
|
0,8 |
0,7 |
|
1,0 |
0,9 |
|
lr2 |
1,2 |
|
l,c |
1,4 |
|
1,8 |
1,6 |
|
2,0 |
1,9 |
|
2,2 |
2,1 |
|
2,5 |
2,3 |
|
5,0 |
4,7 |
|
V,5 |
7,0 |
|
10,0 |
9,3 |
|
12,b |
11,7 |
|
12 |
11 |
|
0,2 |
0,2 |
|
0,4 |
0,4 |
|
0,6 |
0,6 |
|
0,8 |
0,7 |
|
1,0 |
0,9 |
|
1,2 |
1,1 |
|
1,4 |
1,3 |
|
1,6 |
15 |
|
1,8 |
1,6 |
|
2,0 |
1,8 |
|
4,0 |
3,7 |
|
6,0 |
5,5 |
|
8,0 |
7,3 |
|
10,0 |
9,2 |
|
12 |
12 |
|
26 |
25 |
|
1,1 |
1,1 |
|
8,2 |
3,1 |
|
5,4 |
5,2 |
|
7,6 |
7,3 |
|
9,8. |
9,4 |
|
11,9 |
11,5 |
|
14,1 |
13,5 |
|
16,2 |
15,6 |
|
18,4 |
17,7 |
|
20,6 |
19,8 |
|
22,8 |
21,9 |
|
24,9 |
23,9 |
1,1
3,4 5,7 7,9 10,2 12,5 14,8 17,1 19,3 21,6 23,9
48°
296
A MxiNUAL OF TOPOGKAPHIC METHODS.
Table XXXVI. — Loiiarillimic siiics, cosines, tangenis, and coteH(/e»/s— Continued. [Extraotocl Iroin Gausa' Logarithmic and Trigonometric TivViles.)
42°
47c
LOGAEITHMS OF CIEGULAR FUNCTIONS.
297
Table XXXVI. — Logarithmic sines, cosines, tanffents, and cotangents — Continued. [Extracted from Gauss' Logarithmic and Trigonometric Tables-]
430
83 378 83 392 83 405 83 419 83 432
83 441)
83 513 83 527 83 540
83 661 83 674 83 688 83 701 83 715 83 728 83 741 83 755
83 901 83 914 83 927 83 940 83 954 83 967 S3 980
83 993
84 006 84 020 84 033 84 046 84 059 84 072 84 085 84 098 84 112 84 125 84 138 84 151 84 164 84 177
9. 97 016 9. 97 042 9. 97 067
9. 97 345 9. 97 371 9. 97 396 9. 97 421
9. 97 447
9. 97 472 9.97 497 9. 97 523 9. 97 548 9.97 573 9.97 698 9. 97 624 9.97 649 9. 97 674 9.97 700 9.97 725 9. 97 750 9. 97 776 9. 97 801 9.97 826 9. 97 851 9. 97 877 9.97 902 9.97 927 9.97 953
9.98 180 9.98 206 9. 98 231 9. 98 256 9. 98 281 9. 98 307 9. 98 332 9. 98 357
L. Cotg. d. c.
0. 03 034 0. 03 009 0. 02 984 0. 02 958 0. 02 933
0. 02 908 0. 02 882 0.02 857 0. 02 832 0. 02 807
0. 02 781 0.02 756 0. 02 731 0. 02 705 0. 02 6fi0
0.02 655 0.02 629 0. 02 604* 0. 02 579 0. 02 553
0. 02 528 0. 02 503 0. 02 477 0. 02 452 0. 02 427 0. 03 402 0. 02 376 0. 02 351 0. 02 326 0.02 300 0. 02 275 0.02 250 0, 02 224 0.02 199 0. 02 174 0.02 149 0. 02 123 0. 02 098 0. 02 073 0.02 047 0.02 022 0. 01 997 0.01 971 0.01 946 0. 01 921 0.01 896 0.01 870 0.01 845 0.01 820 0.01 794 0. 01 769 0.01 744 ■ 0. 01 719 0.01 693 0. 01 668 0. 01 643 0. 01 617 0.01 592 0. 01 567 0. 01 542 0.01 516
1 200
86 176 86 164 86 152 86 140 86 128 86 116 86 104 86 092 86 080 86 068
85 900 85 888 85 876 85 864 85 851 83 839 85 827 85 815 85 803 85 791 85 779 85 766 85 754 85 742 85 730 85 718 85 706 85 693
9,0 11,0 13,0 10,0. 17,0 19,0 21,0 23,0 25,0
|
0,4 |
0,4 |
|
0,9 |
0,8 |
|
1,3 |
1,2 |
|
1,Y |
1,7 |
|
2,2 |
2,1 |
|
2,6 |
2,5 |
|
3,0 |
2,9 |
|
3,5 |
3,3 |
|
3,9 |
3,8 |
|
4,3 |
4,2 |
|
8,7 |
8,3 |
|
13,0 |
12,.T |
|
l/,3 |
16,7 |
|
21,7 |
20,8 |
|
14 |
IS |
|
0,2 |
0,2 |
|
0,5 |
0,4 |
|
0,7 |
0,6 |
|
0,9 |
0,9 |
|
1,2 |
1,1 |
|
1,4 |
1,3 |
|
1,6 |
1,5 |
|
1,9 |
1,7 |
|
2,1 |
2,0 |
|
2,3 |
2,2 |
|
4,V |
4,3 |
|
7,0 |
6,,') |
|
9,3 |
8,V |
|
11,V |
10,8 |
|
12 |
11 |
|
0,2 |
0,2 |
|
0,4 |
0,4 |
|
(1,6 |
0,6 |
|
0,8 |
0,7 |
|
1,0 |
0,9 |
|
1,2 |
i,l |
|
1,4 |
1,3 |
|
1,6 |
l,.*) |
|
1,8 |
1,6 |
|
2,0 |
1,8 |
|
4,0 |
3,V |
|
6,0 |
b,5 |
|
8,0 |
7,3 |
|
1U,0 |
9,2 |
8,7 10,6 12,5 14,4 16,3 18,3 20,2 22,1 24,1
1,1 3,1 5,2 7,3 9,4 11,5 13,5 15,6 17,7 19,8 21,9 23,9
46°
298
A MANUAL OF TOPOGRAPHIC METHODS.
Ta^le XXXVI. — Loijarithmic sines, cosmesj tangents, and cotangents — Continued.
[Extracted, from Crauss' LogiU'itlimic and Trigonometric Tables.]
440
9. 84 177 9. 84 190 9. 84 203 9.84 216 9.84 229
9. 84 308 9. 84 321 9. 84 334 9. 84 347 9.84 360
9. 84 373 9. 84 385 9. 84 308 9. 84 411 9. 84 424
9. 84 437 9. 84 450 9. 84 463 9. 84 476 9. 84 489 9. 84 502 9.84 515 9.84 528 9. 84 540 9. 84 553 9. 84 566 9.84 579 9. 84 592 9.84 605 9. 84 618 9. 84 630 9.84 643 9. 84 656 9. 84 669
9. 84 707 9. 84 720 9. 84 733 9. 84 745 9.84 75S 9. 84 771 9. 84 784 9. 84 796 9. 84 809 9.84 822 9.84 835 9.84 847 9. 84 860 9.84 873 9. 84 885 9. 84 898 9. 84 911 9. 84 923 9.84 936 9. 84 949
9.98 509 9.98 534 9. 98 560 9. 98 585
9. 98 610 9. 98 635 9. 98 681 9.98 686
9. 98 863 9. 98 888 9.98 913 9. 98 939 9. 98 964
9. 98 989 9.99 015 9. 99 040 9.99 065 9.99 090 9.99 116 9.99 141 9.99 166 9.99 191 9.99 217 9. 99 242 9.99 267 9.99 293 9. 99 318 9.99 343 9.99 368 9.99 394 9. 99 419 9. 99 444 9. 99 460 9. 99 495 9.99 520 9. 99 545 9. 99 570 9.99 596 9. 99 621 9. 99 646 9.99 672 9. 99 697 9. 99 722 9.99 747 9.99 773 9. 99 798 9.99 823 9. 99 848 9. 99 874 9. 99 899 9.99 924 9. 99 949 9. 99 975
L. Cotg.
0. 01 516 0. 01 491 0. 01 460 0. 01 440 0.01 415
0.01 390 0. 01 365 0.01 339 0. 01 314 0. 01 289
0. 01 263 0.01 238 0.01 213 0. 01 188 0. 01 162
0.01 137 0.01 112 0. 01 087 0. 01 061 0. 01 036
0.01 Oil 0.00 985 0.00 960 0.00 935 0. 00 910 0. 00 884 0.00 859 0. 00 834 0.00 809 0. 00 783 0.00 758 0.00 733 0. GO 707 0.00 682
0. (
657
0. 00 632 0. 00 606 0. 00 581 0.00 556 0. 00 .531 0. 00 505 0. 00 480 0. 00 455 0.00 430 0. 00 404 0. 00 379 0. 00 354 0. 00 328 0.00 303 0. 00 278 0, 00 253 0. 00 227 0. 00 202 0. 00 177 0.00 152 0. 00 126 0.00 101 0. 00 076 0. 00 051 0.00 025 0. 00 000
9.85 669 9. 85 657 9.85 645^ 9. 85 632 9.85 620 9. 85 608 3.85 596 9.85 583
9. 85 571 9.85 559 9. 85 547 9.85 534 9. 85 522
9. 85 510 9.85 497 9. 85 485 9. 85 473 9. 85 460
9. 85 448 9.85 436 9. 85 423 9.85 411 9.85 399 9. 85 386 9. 85 374 9.85 361 9.85 349 9.85 337 9.85 324 9. 85 312 9.85 299 9.85 287 9. 85 274 9.85 262 9.85 2.50 9. 85 237 9. 85 225 9. 85 212 9.85 200 9.85 187 9.85 175 9. 85 162 9.85 150 9.85 137 9. 85 125 9.85 112 9.85 100 9.85 087 9. 85 074 9.85 062 9. 85 049 9.85 037 9. 85 024
0,4 0,9 1,3 h^ 2,2 2,6 3,0 3,5 3,9 4,3 8,7 13,0 17,3 21,7
1,7 2,1 2,5 2,9 3,3 3,8 4,2 8,3 12,5 16,7 20,8
|
14 |
13 |
|
0,2 |
0,2 |
|
0,5 |
0,4 |
|
0,7 |
0,6 |
|
0,9 |
0,9 |
|
1,2 |
1,1 |
|
1,4 |
1,3 |
|
1,6 |
1,5 |
|
1,9 |
1,7 |
|
2,1 |
•2,0 |
|
2,3 |
2,2 |
|
4,7 |
4,3 |
|
7,0 |
6,5 |
|
9,3 |
8,7 |
|
11,7 |
10,8 |
3,0 5,0 7,0 9,0 11,0 13,0 15,0 17,0 19,0 21,0 23,0 25,0
1,1 3,2 5,4 7,6 9,8 11,9 14,1 16,2 18,4 20,6 22,8 24,9
0,9 2,9 4,8 6,7 8,7 10,6 12,5 14,4 16,3 18,3 20,2 23,1 24,1
1,0 3,1 5,2 7,3 9,4 11,5 13,5 15,6 17,7 19,8 21,9 23,9
45=
INDEX
Acciiracy of control
Adirondack survey
Alidade
for traversing
Altitudes, measurement of, in connection with traverse
linea
"witli plane table
Amount of control
Amphitheaters
Aneroid
Apparent time
Aqueous agencies
Arid region, erosion in
Astronomic determination of position
Astronomical station, selection of
transit and zenith telescope
A zimuth, correction for deviation in
observations, example of record
example of reduction
tor
on Polaris at elongation
reduction of
summary of results
Baldwin device for stretching tape in base line meas- urement
Barometric observations, reduction of
tables, use of
Base level
line, alignment of.
measurement
example of reduction of
instruments used in
personnel of party
reduction of
tension of tape in
selection of site
Batteries in use
Canyons, formation of
in strata, alternating hard and soft
Chronograph
Chronometer, break circuit
Cistern barometer
filling of tubes
method of use
Classification of work
Coast and Geodetic Survey, United States
Collimation, correction for error of
Colors used on original maps
Comparison of time
Contour interval
Conventions
Corrasion
Declination
Declinations, apparent, computationof
Deposition from volcanic action
water
the atmosphere
Disintegration
Distances, computation of
Diurnal aberration, correction for
Douglas odometer
Erosion
European maps, scales of
Features represented
Field work of astronomical determination
scale of
Figure adjustment
Fortieth parallel survey
Greneralization of maps
Geodetic coordinates
Geological and Geographical Survey of Territories
Geometric control
Glacial deposition
Heliotrope, Coast Survey form
Steinheil
Horizontal angles, errors incident to measurement of . .
form of record
instructions for measurement of
order of readings
location
Inequality of pivots, correction for
Inspection
Introduction
Johnson plane table
Lake survey, United States
Land OflBce plats
surveys
Latitude determination, form of record of
how determined
observations
list of stars for
reduction of
Least squares in figure adjustment
station adjustment
Legencls upon maps
Level, corrections for error of
division, measurement of
Longitude determination, example of reduction
how determined -
Massachusetts, Borden survey of
Mean time -
Method of adjusting transit in meridian -
control
Micrometer screw, measurement of division of head of
New Jersey State survey
299
300
INDEX.
Page.
New York State survey ^
Nortliern trauscontiueutnl survey 3
Odometers ^^
Offloework 128
Organization of parties *1
Pennsylvania State survey 5
Personal equation 35
Piracy H^
Plan of map of United States 6
Plane table ^
sheets 82
Primary elevations ''''
triangulation -IS
prosecution of work 63
selection of stations 49
Private surveys 5
Profiles of streams 112
Projections 129
Public land surveys, plan of 101
utilization of 101
Eailroad profiles 6
surveys 5
Eeduction to center 65
Reports 125
Eight ascension 17
Eocky Mountain region, survey of 3
Scaleof United States map 7
Secondary triangulation 79
Sidereal time 17
Signals and observing towers in triangulation 51
in triangulation 50
Sinks, origin of 115
Size of sheets 10
Sketching U-106
Solar time 17
Spherical excess 65
Stadia measurement ^ 92
Station error 35
Station adjustment 66
Support for astronomical transit 21
Surveys under United States Government 2
Talcott's method 17
Theodolites for triangulation 5i
Three-point problem 83
Time determination, example of record 32
observations for 28
reduction of 29
Titles of maps 130
Topographic features, origin of 108
forms, influence of structure upon 117
parties, distribution of work in 91
Transportation HI
Traversing 12, 13
Traverse lines for primary control 75
work 85
plane tables for 86
Triangulation 12
Uplift 108
Water gaps 116
Weathering HI
Wind gaps 116
Zenith distance 17
telescope and asti'!>uomical transit - - 18
\
\
k
y.^}^^
/.
LEGEND
1 I NorOuSTi I'naAc Ttaiui. Survey.
^^m^p I'-^.t'otttit anil Oeodetiv Sut^fty.
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siioinxn I'lioGUKSS OFTKLVNT.i-LVTiox Tomciui'in-
ASTRONOMIC LOC.ATKIX.
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