BLM - Manual of Instructions - 1973

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CHAPTER 1The General Plan

THE MANUALPurpose and Scope of the Manual

1-1. The Manual of Surveying Instructionsdescribes how cadastral surveys of the publiclands are made in conformance to sta tutory lawand its judicial interpretation. This chaptersummarizes the various Acts and the generalplan of surveying based on them. Previous edi-tions of the Manual were issued in 1855 (re-printed as the Manual of 1871), 1881, 1890,1894, 1902, 1930, and 1947.1-2. Surveying, in general, is the art ofmeasuring and locating lines, angles, and eleva-tions on the surface of the earth, within under-ground workings, and on the beds of bodies ofwater. A cadastral survey creates (o r re-

surveying. The applications of photogramme-try and electronic instrumentation to public landsurveying are covered for the first time in thisedition of the Manual.1-4. Extended treatment is given to sub-division of sections, restoration of lost o r oblit-erated corners, resurveys, and special surveysof many kinds. These now make up the majorpart of the surveying program of t he Bureauof Land Management. Stress is placed on thor-oughness in the identification and perpetuationof t he surveys already completed.Development of the Manual

1-5. The surveys of public lands have beenconducted since 1785, when a beginning point


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THE ENERAL PLAN 3ship was changed to that practiced today. Sub-sequent laws called for additional subdivision,and the system of surveys was gradually re-fined to its present form. In the early periodadvice and general instructions were given theSurveyor General by th e Secretary of the1Treasury, then in charge of land sales, and laterby th e Commissioner of the General Land Of-fice. Instructions to deputy surveyors were is-sued by the Surveyor General. A Surveyor ofth e Lands of the United Sta tes South of Ten-nessee was appointed in 1803 with the sameduties as the Surveyor General, and eventuallya surveyor general was appointed for each ofmany public-land States and Territories.1-7. In 1831 the Commissioner of t he Gen-eral Land Office issued detailed instructions tothe surveyors general concerning surveys andplats. The applicable parts were incorporatedby individual surveyors general in bound vol-umes of instructions suitable fo r use in the fieldby deputy surveyors. From these directionsevolved th e Manual of Surveying Instructions.The .Act of July 4, 1836, placed the overall direc-tion of th e public land surveys under the princi-pal clerk of surveys in t he General Land Office.The immediate forerunner of the Manual series

Data for the sun ar e given in terms of Green-wich apparent noon fo r ready use with the solartransit. Data for all stellar positions are givenin terms of th e Greenwich meridian, m e a n t i m eand m e a n time in tervals . The data a re preparedby the Nautical Almanac Office of the UnitedStates Naval Observatory.(3) Restorat ion of Los t OVT Obliterated Cor-ners and Subdivis ion o f Sect ions , a Guide f o rSurveyors . Paper cover, 6 x 9, 40 pages, illus.The subject matter under this title first ap-peared in the decisions of the Department ofthe Interior, 1 L.D. 339; 2d ed., 1 L.D. 671(1883). There have been several revisions andextensions, the latest in 1973. Providing an in-troduction to the rectangular system of publicland surveying and resurveying, with a com-pendium of basic laws relating t o the system, itanswers many common questions arising inpractical work. Although intended especiallyfor surveyors outside th e Bureau of LandManagement, it is also of interest to attorneys,title insurance company personnel, and otherswho have professional interests in former orpresent public lands.


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4 MANUAL O F SURVEYING INSTRUCTIONSfore they were acquired are in the first instanceth e exclusive property of the United States,t o be administered, o r for disposal to such per-sons, at such time, in such modes, and by suchtitles as the Government may deem most advan-tageous to the public. Congress alone has thepower, derived from Article IV, Section 3, ofthe Constitution, of disposing of the publicdomain and making all needful rules and regula-tions in respect thereto.

1-11. It is within the province of the Direc-tor of the Bureau of Land Management to deter-mine what are public lands, what lands havebeen surveyed, what are to be surveyed, whathave been disposed of, what remains to bedisposed of, and what are reserved. By a wellsettled principle of law the United States,through the Department of the Interior, hasthe authority and duty to extend the surveys asmay be necessary to include lands erroneouslyomitted from earlier surveys.Navigable Waters

1-12. Beds of navigable bodies of water arenot public domain and are not subject to sur-vey and disposal by the United States. Sover-eignty is in the individual states. Under the

1-14. The Act of March 2, 1849 (9 Stat.352), granted to th e State of Louisiana all itsswamp and overflowed lands fo r the purpose ofaiding in their reclamation. The Act of Septem-ber 28 , 1850 (9 Stat. 519), extended the grantto other public land States then in the Union.The grant was also extended to Minnesota andOregon by the Act of March 12, 1860 (12 Stat.3). These various grants were carried over intoR.S. 2479 (43 U.S.C. 982). A notable exceptionto the swamp land laws is found in the ArkansasCompromise Act of April 29, 1898 (30 Stat.367; 43 U.S.C. 991), by which all right, title,and interest to the remaining unappropriatedswamp and overflowed lands reverted to theUnited States.

1-15. The provisions of the grants apply toelevations below the uplands where, without theconstruction of levees or drainage canals, theareas would be unfit for agriculture. The grantsapply to all swamp and overflowed lands unap-propriated at the dates of th e granting acts,whose character at that time would bring themwithin the provisions of the grant. Discussionof swamp and overflowed lands in connectionwith field examinations and surveys is found inchapter VII on Special Surveys.


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THE GENERAL PLAN 5were made as the surveys progressed westwarduntil the general plan was complete.

Adoption of the rectangular system markedan important transition from the surveyingpractice th at generally prevailed in the ColonialStates where lands were described by irregularmetes and bounds, each parcel depending moreor less on the description of its neighbors.Revised Statutes and United States Code

1-18. The surveying system developed un-der the early laws was incorporated in the Re-vised Statutes and the United States Code:

Duties of Director. Tke Secretary of the In-terior, or such officer as he may designate, shallperform all executive duties appertaining tothe surveying and sale of t he public lands of theUnited States, or in any wise respecting suchpublic lands, and, also, such as relate to privateclaims of land, and the issuing of patents forall grants of land under the authority of theGovernment. (R.S. 453; 3 U.S.C. 2.)

The Secretary of the Interior, or such officeras he may designate, is authorized to enforceand carry into execution, by appropriate regula-tions, every pa rt of the provisions of th is title

one milel from each other, and marking cor-ners at th e distance of each half mile. The sec-tions shall be numbered, respectively, begin-ning with the number one in the northeastsection and proceeding west and east alternatelythrough the township with progressive num-bers, until the thirty-six be completed.

Fourth. The deputy surveyors, respectively,shall cause to be marked on a tree near eachcorner established in the manner described, andwithin the section, the number of such section,and over i t the number of the township withinwhich such section may be; and the deputysurveyors shall carefully note, in their respec-tive field books, the names of the corner treesmarked and th e numbers so made.

Fifth. Where the exterior lines of th e town-ships which may be subdivided into sections orhalf-sections exceed, or do not extend six miles,the excess or deficiency shall be specially noted,and added to or deducted from the western andnorthern ranges of sections or half-sections insuch township, according as the error may bein running the lines from east to west, or fromnorth to south ; he sections and half-sectionsbounded on the northern and western lines ofsuch townships shall be sold as containing only


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6 MANUAL O F SURVEYING INSTRUCTIONSlicks, salt springs, and mill seats which cometo his knowledge ; all watercourses over whichthe line he runs may pass ; and also the qualityof the lands.Eighth. These field books shall be returned tothe Secretary of the Interior or such officer ashe may designate, who shall cause therefroma description of the whole lands surveyed t o bemade out and transmitted to the officers whomay superintend the sales. He shall also cause afair plat to be made of the townships and frac-tional parts of townships contained in the lands,describing the subdivisions thereof, and themarks of the corners. This plat shall be recordedin books to be kept fo r that purpose ; and a copythereof shall be kept open at the office of theSecretary of th e Interior or of such agency ashe may designate for public information, andother copies shall be sent to the places of thesale, and to the Bureau of Land Management.(R.S. 2395; March 3, 1925, 43 Stat. 1144; 43U.S.C. 751.)

Boundaries and Contents of Public Lands;How Ascertained. The boundaries and contentsof t he several sections, half-sections, and quar-ter-sections of the public lands shall be ascer-tained in conformity with the following princi-

where no such opposite corresponding cornershave been or can be fixed, the boundary linesshall be ascertained by running from the estab-lished corners due north and south or east andwest lines, as the case may be, to the water-course, Indian boundary line, o r other externalboundary of such fractional township.

Third. Each section or subdivision of sec-tion, the contents whereof have been returnedby the Secretary of the Interior or such agencyas he may designate, shall be held and con-sidered as containing the exact quantity ex-pressed in such return; and the half-sectionsand quarter-sections, the contents whereof shallnot have been thus returned, shall be held andconsidered as containing the one-half or theone-f our th part , respectively, of the returnedcontents of the section of which they may makepart. (R.S. 2396; March 3, 1925, 43 Stat. 1144;43 U.S.C. 752) .Lines of Division of H alf-Qua rter Sections,H o w Run. In every case of the division of aquarter-section the line for the division thereofshall run north and south, and the corners andcontents of half-quarter sections which maythereafter be sold shall be ascertained inthe manner and on the principles directed


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THE GENERAL PLA N 7lands, shall remain and be deemed public high-ways ; nd, in all cases where the opposite banksof any stream not navigable belong to differentpersons, the stream and the bed thereof shallbecome common to both. (R.S. 2476; 43 U.S.C.931).

E x t e n s i o n of P u b l i c S u r v e y s O v e r M in e r a lLands . The public surveys shall extend over allmineral lands ; and all subdividing of surveyedlands into lots less than one hundred and sixtyacres may be done by county and local surveyorsat the expense of claimants ; but nothing in thissection contained shall require the survey ofwaste or useless lands. (R.S. 2406; 43 U.S.C.766).

S u r v e y o f Priv a te Land C la ims. The Secre-tary of the Interior or such officer as he may des-ignate shall cause to be surveyed all privateland claims after they have been confirmed byauthority of Congress, so fa r as may be neces-sary to complete the survey of the public lands.(R.S. 2223; March 3, 1925, 43 Stat. 1144; 43U.S.C. 52).

Pena l ty f o r I n t e r r u p t in g S u r v e y s . Whoever,by threats or force, interrupts, hinders, or pre-vents the surveying of the public lands, or ofany private land claim which has been or may

SUBSEQUENT LEGISLATION ANDESTABLISHMENT O F THEBUREAU OF LAND MANAGEMENT

1-19. Additional legislation and orders per-tinent to the survey of th e public lands:

Purchase of Meta l Monumen ts . The Act ofMay 27, 1908 (35 Stat. 347) provided for thepurchase of metal monuments to be used forpublic land survey corners wherever practi-cable.P e n a l t y f o r the Des truc t ion o f S u r v e y M o n u-m e n t s . Section 57 of the Criminal Code of 1909provided a penalty for the unauthorized altera-tion or removal of any Government surveymonument or marked trees. The wording wasslightly modified June 25, 1948, in ch. 645,62 Stat. 789; 18 U.S.C. 1858, to read: Who-ever willfully destroys, defaces, changes, or

removes to another place any section corner,quarter-section corner, or meander post, on anyGovernment line of survey, or willfully cutsdown any witness tree or any tree blazed tomark the line of a Government survey, or will-fully defaces, changes, or removes any monu-ment or bench mark of any Government survey,shall be fined not more than $250 or imprisoned


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8 MANUAL OF SURVEYING INSTRUCTIONSThis provision of law brought to a close thepractice of letting contracts for the making ofsurveys of public lands.

Further Author i t y f o r Resurveys. The Act ofSeptember 21, 1918 (40 Stat. 965; 43 U.S.C.773), provides authority for the resurvey, bythe Government, of townships in which thedisposals exceed 50 percent of the total area.Such resurveys will be undertaken only uponapplication of the owners of at least three-fourths of the privately owned land in thetownship, and upon deposit of the estimatedcosts of the resurvey.Acceptance of Contributions o r Surveys. TheAct of July 14, 1960 (74 Stat. 506; 43 U.S.C.13641, provides that the Secretary of the In-terior may accept contributions for cadastralsurveying performed on federally controlled o rintermingled lands.The Nat ional Environmental Pol icy Act o f1969. The Act effective January 1, 1970 (83Stat. 852; 42 U.S.C. 43211, states in part th atThe purposes of this chapter are: To declarea national policy which will encourage pro-ductive and enjoyable harmony between manand his environment; to promote efforts whichwill prevent o r eliminate damage to the en-

In the organization of the Bureau of LandManagement, the Division of Cadastral Surveyis located in the headquarters office. This divi-sion has technical supervision, through stateand service center directors, of surveying thepublic lands. The chief of the division acts asconsultant to th e Director in the formulation ofpolicies, programs, standards, and proceduresof cadastral surveys.

GENERAL RULES1-20. From the foregoing synopsis of con-gressional legislation it is evident:First. That the boundaries and subdivisionsof the public lands as surveyed under approvedinstructions by the duly appointed surveyors,the physical evidence of which survey consistsof monuments established upon the ground, and

the record evidence of which consists of fieldnotes and plats duly approved by the authori-ties constituted by law, are unchangeable af terthe passing of the title by the United States.Second. That the original township, section,quarter-section, and other monuments as physi-cally evidenced must stand as th e tr ue cornersof the subdivisions which they were intended to


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THE GENERAL PLAN 9other boundary of such fractional section, asdue parallelism with section lines will permit.Sixth. That lost or obliterated corners of theapproved surveys must be restored to their orig-inal locations whenever thi s is possible.1-21. The basic provisions require that thepublic lands shall be divided by north andsouth lines run according to the tr ue meridian,and by others crossing them at right angles,so as to form townships six miles square ; tha tthe townships shall be subdivided into sec-tions, containing as nearly as may be, sixhundred and forty acres each; and that theexcess o r deficiency shall be specially noted, andadded to or deducted from the western andnorthern ranges of sections o r half-sections insuch townships, according as the error maybe in running the lines from east to west, orfrom south to north. The system of rectangu-lar surveys fits the basic requirements to thecurved surface of th e globe.In this rectangular plan the townshipboundaries are intended to be due north andsouth o r due east and west. The boundariesrunning north and south are termed rangelines. The boundaries running east and westar e called township lines.

vergency is taken up at intervals by the run-ning of standard parallels, on which the meas-urements are again made full. On the standardparallels (first named correction lines) thereare offsets in the range lines and two sets ofcorners, standard corners for the lines to thenorth and closing corners for lines to the south.The usual interval between t he standard paral-lels is 24 miles, but there were many excep-tions in th e older surveys.

In order to make the sections representsquare miles as nearly as may be, the merid-ional lines are run from south t o north andparallel to the east boundary of th e townshipfor a distance of five miles from th e southboundary. These are run and monumented astr ue lines. The remainder of t he section linesare all run by random and true between theestablished section corners. This produces therectangular sections, 25 of which contain 64 0acres each, within allowable limit. The sectionsalong the north and west boundaries are sub-divided on a plan for certain lottings to absorbth e convergency and the excess o r deficiency inthe measurements. These sections provide amaximum number of aliquot parts (160-, 80-,and 40-acre units) or regular subdivisions of a


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10 MANUAL OF SURVEYING INSTRUCTIONSNevada State Office at Reno, Nevada.New Mexico State Office at Santa Fe, NewMexico. (Administers public lands in New

Mexico and Oklahoma.)Oregon State Office at Portland, Oregon. (Ad-ministers public lands in Oregon and Wash-ington.)U t a h State Officeat Salt Lake City, Utah.W y o m i n g State Officeat Cheyenne, Wyoming.(Administers public lands in Wyoming,Kansas, and Nebraska.)Headquarters for surveys in the remainingStates are at the Eastern States Office,Silver Spring, Maryland.

THE PUBLIC LAND STATES1-23. Thirty States have been created out

of the public domain. In those where th e publicland surveys have been substantially com-pleted, excepting Oklahoma, the original rec-ords have been transferred to the States. Inmost cases duplicate copies are on file in Wash-ington, D.C. The Director of the Bureau ofLand Management has administrative authorityin questions relating to the remaining public

Arkansas . Acquired under the Louisiana Pur-chase in 1803 and admitted into the Union June15, 1836 (5 Stat. 50) ; ecords with the Depart-ment of State Lands at Little Rock.California. Ceded by Mexico in 1848 and ad-mitted into the Union September 9, 1850 (9Stat. 452) ; records in the State Office of theBureau of Land Management in Sacramento.

Colorado. Acquired largely under the Louisi-ana Purchase in 1803, but including additionalland, title to which was quieted through treatywith Spain, in 1819, with other lands annexedwith Texas in 1845, and lands ceded by Mexicoin 1848; admitted into the Union August 1,1876 (18 Stat. 474; 19 Stat. 665) ; records inthe State Office of the Bureau of Land Manage-ment in Denver.

Florida. Ceded by Spain in 1819 and admit-ted into the Union March 3, 1845 (5 Stat.742)) ; records with the Board of Trustees ofthe Internal Improvement Trust Fund at Tal-lahassee.

Idaho. Acquired with the Oregon Territory,title to which was established in 1846, and ad-mitted into the Union July 3, 1890 (26 Stat.215) ; records in the State Ofice of the Bureau


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THE GENERAL PLAN a 1additional lands, title to which was quietedthrough treaty with Spain in 1819; admittedinto the Union April 30, 1812 (2 Stat. 701) ;records with the Register, State Land Office, a tBaton Rouge,Mich ig a n . Included in the territory of theoriginal 13 States and admitted into the UnionJanuary 26, 1837 (5 Stat. 144) ; records withthe State Department of Treasury a t Lansing.

Min n eso ta . Included in the territory of theoriginal 13 States (additional lands acquiredunder the Louisiana Purchase in 1803); ad-mitted into the Union May 11, 1858 (11 Stat.285) records with the Department of Conserva-tion at Saint Paul.Mississ ipp i . Included in the territory of theoriginal 13 States and admitted into the UnionDecember 10, 1817 (3 Stat. 472) ; ecords withthe State Land Commissioner at Jackson.

Misso u r i . Acquired under the Louisiana Pur-chase in 1803 and admitted into the UnionAugust 10, 1821 (3 Stat. 645, 3 Stat. Appendix11) ; records with the State Land Survey Au-thority at Rolla.Mo n ta n a . Acquired under the bouisiana Pur-chase in 1803 and with the Oregon Territory,title to which was established in 1846 ;admitted

O k l a h o m a . Acquired under the LouisianaPurchase in 1803 and with lands annexed withTexas in 1845; admitted into the Union No-vember 16, 1907 (34 Stat. 267; 35 Stat. 2160) ;records in the New Mexico State Office of theBureau of Land Management at Santa Fe, NewMexico.Ohio. Included in the territory of the original13 States and admitted into the Union Novem-ber 29, 1802 (2 Stat. 173) ; records with theAuditor of State at Columbus.

Oreg o n . Included in the Oregon Territory,title to which was established in 1846 :admittedinto the Union February 14, 1859 (11 Stat.383) ; records in the State Office of the Bureauof Land Management a t Portland.S o u t h D a k o t a . Included in the territory ofthe original 13 States and with lands acquiredunder the Louisiana Purchase in 1803; admit-ted into the Union November 2, 1889 (25 Stat.676; 26 Stat. 1549) ; records with the Commis-sioner of Schools and Public Lands at Pierre.The plats of mineral patent surveys of SouthDakota are filed in the Montana State Office ofthe Bureau of Land Management at Billings,Montana, and the necessary mineral surveys aredirected from that office.


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CHAPTER I1Methods of Survey

The methods described in this chapter com-prise the specifications for determining thelength and direction of lines.

DISTANCE MEASUREMENTUnits

2-1. The law prescribes the chain as theunit of linear measure for the survey of thepublic lands. All returns of measurements inthe rectangular system are made in the truehorizontal distance in miles, chains, and links.(Exceptions are special requirements for meas-urement in feet in townsite surveys, chapterVII, and mineral surveys, chapter X.)

in arpents. The arpent is a unit of area, but theside of a square arpent came to be used forlinear description. The Spanish crown and theMexican Government granted lands which wereusually described in linear varas. Both thearpent and the vara have slightly differentvalues in different States. The conversions mostoften needed are shown in the Standard FieldTables.Tapes

2-2. Use of the steel tape is the commonlyaccepted method of measurement. The tapesused vary in length from one to eight chains,th e appropriate length depending upon the top-ography and the nature of the survey. Gradua-


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14 MANUAL OF SURVEYING INSTRUCTIONSurements are found in the Standard FieldTables.

Suhtense BarThe subtense bar may be used providedthat no measurement is over ten chains andthat the instrument used in connection with itis capable of measuring in single seconds.

2-4.

Traversing2-5. Traverses may be run where the ter-rain is too precipitous for chaining and theintervisible points required for triangulationcannot be practicably obtained. Traversingshould be kept to a minimum.

Triangulation2-6. Triangulation may be used in measur-

ing distances across water or over precipitousslopes. The measured base should be laid out soas to adopt the best possible geometric propor-tions of the sides and angles of the triangle. Ifi t is necessary to determine the value of anangle with a precision of less than the leastreading of the vernier, the method of repetitionshould be employed.

ments for accuracy. Determining factors in itsuse are the terrain, ground cover, and avail-ability of t he proper instruments. Some typesar e adapted to the measurement of long dis-tances, others to measurement of intermediatedistances. Transport and maintenance must beconsidered in determining whether the use oftelemetry will expedite a particular survey.Provision must be made for measuring distancesto important items of topography.

The variety of electronic distance-measuringdevices, the rapid development of combinationswith optical theodolites, and modifications ofthe instruments make it impracticable to de-scribe the methods of use in this manual. Thesurveyor should consult the manufacturer'soperating manual for calibration, use, care, andadjustments.

A special kind of triangulation is used whenit is desired to locate on the ground a point forwhich the geographic position has been deter-mined in advance. Two intervisible triangulationstations are occupied simultaneously with opti-cal theodolites and electronic measuring devices.A mobile party sets a temporary point at theapproximate position of t he desired point by


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METHODSOF SURVEY 15PHOTOGRAMMETRYl

2-8. The earliest uses of aerial photographyby the cadastral surveyor were for terrain stud-ies, locating himself on the ground, and as anaid in the search for corners. As methodologyimproved, simple photogrammetric processesenabled the surveyor to delineate topographicfeatures , determine th e meanders of water bod-ies, compute areas of erroneously omitted lands,and lay out townsites as they actually exist.Photogrammetric projects involving both dis-tance measurements and the dfrection of lineshave been completed f o r both original surveysand resurveys of extensive areas of public lands.Aerial Camera

The aerial camera is a high-precisioninstrument designed for making photographson which reliable measurements can be madeafter resolvable errors have been analyzed andremoved. The camera must be maintained incalibration at all times. To insure this the cali-bration should be checked periodically by acompetent testing agency such as the BurezJ ofStandards. The aerial camera used for cadas-tral surveys should include the following fea-

2-9.

tortion, and til t of the camera preclude its hav-ing a uniform scale.Topographic maps may be compiled either bythe use of stereoplotting instruments or bymaking measurements directly upon the photo-graph. Elements which may affect the accuracyare camera calibration, height of the aircraftabove the terrain being mapped, the density andaccuracy of ground control, the tip o r tilt of thecamera at the moment of exposure, filmdistortion, and the instruments used in makingthe measurements.An approximate scale for a vertical aerialphotograph is stated by the equation S =-where :f = the focal length of t he cameraH = th e flying height above sea levelh = th e average elevation of th e terrain above

Stereophotogrammetry utilizes a stereoscopicplotting instrument (optical-mechanical de-vice) to compile data from aerial photographs.These data, usually in the form of a map, varyin accuracy according to the design of theinstrument. Often the instrument embodies a

fH-h

sea level


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16 MANUAL O F SURVEYING INSTRUCTIONStrast of the subject, vibration, size of the sub-ject, and the processing of the film afterexposure.Field Control

2-11. A network of control points of knownposition is used as a reference to fix the detailof aerial photographs by photogrammetricprocesses. The density and distribution of fieldcontrol points to be photo-identified are de-termined primarily by the characteristics of thephotography, the type of photogrammetricequipment and computer programs to be used,and the accuracy required. Ground control sur-veys a re usually necessary to identify the exist-ing basic control and to provide additionalcontrol points.

The basic control into which the supplementalsurveys are tied, the supplemental surveysthemselves, and the photo-identification ofpoints must in toto provide the degree ofaccuracy required of the resultant cadastralsurvey. The survey methods used in the controlsurvey have to be of equal o r higher order ac-curacy than is specified for the results. Theclassification and standards of accuracy of

have been made of the basic network, the mostrecent in 1929.Basic vertical control bench marks withinor adjacent to a photogrammetric project shouldbe used to expand the vertical control over theproject area. When there is no basic verticalcontrol near the project area, an arbitrarydatum may be assumed and expanded to controlthe project.Sta te Plane Coordinates . State plane coordi-nate systems are used extensively for photo-grammetric plotting. (section 2-83.) Formuhsand tables for computing values for these sys-tems have been prepared by the United StatesCoast and Geodetic Survey (now the NationalGeodetic Survey) fo r each individual State. Thecomputations involve corrections for gridlengths, sea level factors, and grid azimuths.Horizontal Control. Basic horizontal controlis that which has been established by theNational Geodetic Survey to form th e NationalNetwork; this should be the origin for all sup-plemental control on each photogrammetricproject.The supplemental control should be of suffi-cient density to permit an efficient control ofall the photographs at the time of the analytical


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METHODS OF SURVEY 17points ar e normally targeted prior to the aerialphotography. The targets ar e centered over therespective stations and have a symmetricaldesign easily identified on the photography.Care should be taken when selecting the size,shape, color, and material to be used for thetargets.In cases where targeted points have beendestroyed prior to photography i t may be neces-sary to substitute natural targets to supple-ment the control. Such points are selected inthe field and referenced into the control scheme.The identification should be made only whileviewing the photography stereoscopically andat the site of the feature. A photograph showingthe feature and its relationship with the de-stroyed station should be furnished the operatorof the comparator at the time of the analyticalphototriangulation.Mechanical Phototriangulation

2-12. The mechanical (known also as ana-logue or instrumental) method of phototrian-gulation establishes positions and elevationsby use of an instrument viewing a spatial model.Precise connections are made between suc-cessive models which in turn are tied to vertical

advent of the electronic computer made itpracticable to use analytical methods in photo-triangulation. The basic foundation for analy-tical photogrammetry had been established bySebastian Finsterwalder about 1900.The accuracy of the data obtained by use ofthe analytical process is usually of a higherorder than that obtained by the mechanicalmethods. The Bureau of Land Management hastherefore adopted it for use in photogrammetriccadastral surveys.Photogrammetry in Original Surveysand Resurveys

2-14. Pilot projects employing photogram-metric methods for making original surveys andresurveys have led to standardization ofmethods and equipment. As new equipment andrefinements in methods are developed they willbe tested and employed as warranted.ProtractionDiagrams. A diagram represent-ing th e plan for the extension of the rec-tangular system over unsurveyed public lands,based upon computed values for the corner posi-tions, is termed a protraction diagram. Suchdiagrams have been prepared for substantiallyall unsurveyed areas of public lands except the


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18 MANUAL OF SURVEYING INSTRUCTIONSControl . The plan of geodetic control depends

on the number of flight lines and the numberof models in each flight line. It should be basedon triangulation or traverse stations establishedto second-order accuracy. It is advisable thatelectronic distance-measuring instruments andtheodolites be used in establishing new stations.Final values for such stations should be givenas state plane coordinates.

Panels . m e heoretical position of each cor-ner, as plotted on maps or existing photographs,as well as each original o r new control station,is marked on the ground by a systematicallydesigned panel. Care should be taken to centerthe panel over the monument o r survey stake.

The panels should be of such a design and sizeas to be conspicuous in the subsequent aerialphotographs. The photography is undertakenimmediately following the control and panelingoperation in order to assure the least disturb-ance to panelled points. If a panel is destroyedbefore the photography can be accomplished,the photogrammetrist should select a naturalobject near the destroyed panel to serve as asubstitute during the remaining operations.

Aer i a l Pho t ography . Complete stereoscopiccoverage of the area to be surveyed is essen-tial. The photography should have a minimum

work closely with the photogrammetrist toassure that the necessary ties to such items aremade.Once the corners are monumented at the pro-tracted positions, the cadastral surveyor pre-pares his plats in the normal manner, prefac-ing his notes with a statement concerning themethod of procedure. i

Execution of ResurvegsAs in the making of original surveys, plan-

ning and cooperation between the cadastral sur-veyor and the photogrammetrist are essentialto success,Corner P os i t ions . From the original surveynotes and plats the theoretical position of eachpreviously established corner is plotted uponexisting aerial photography. Where suitablemaps do not exist, a cursory search for the ex-terior boundaries of the townships to be resur-veyed should be made. Any corners found areidentified upon existing aerial photography andthe interior corners plotted in accordance withthe record of the original survey.A careful search is made for the corners inthe positions plotted on the photographs. Whena corner i s recovered, i t i s rehabilitated or re-

I


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METHODS OF SURVEY 19the precision with which the sinuosities of theshoreline are drawn, and the correctness of scal-ing from the manuscript.

In areas of little relief single photographscan be used as the displacement of features isat a minimum. Distortion caused by camera tiltis small enough to be removed by adjustment.Either contact prints projected by a reflectingprojector and enlarged to convenient scale or en-largements made from the original film may beused.Whether the stereoplotting instrument o r the

single print is used, it is desirable t ha t the fieldman verify the shoreline and perhaps delineateit on the photographs with colored ink.Accuracy Checks

In both the original survey and theresurvey it is advisable to establish the co-ordinate position for a number of cornersselected at random, being sure that there areseveral check positions in each flight line. It ispreferable tha t these check positions fall in theoverlap area between flight lines, this beingone of th e weak points in a photogrammetricbridge.

The values of the check points should be

2-15.

ments will vary inversely as the length of thecourse.Accuracy

2-16. The accuracy obtainable in photo-grammetric surveys depends on the scale andtype of photography, the instruments used, theskill of th e compiler, the density of ground con-trol, the amount of relief, and the nature ofthe vegetative cover. These factors relate tothe data taken from t he photographs. If mark-ers are positioned by relationship to nearbyphoto-identifiable objects, the precision of thefield methods used also affects the final ac-curacy. If meanders ar e recorded, the reliabilityof their delineation on the photography is afactor in the accuracy of the work.It is axiomatic that the greater the ac-curacy, the greater the cost. The scale of th ephotography for each project, therefore, should

be commensurate with the accuracy required.The amount of topographic relief may affectthe choice of methods. In flat terrain, withphotography nearly vertical, measurements forsome purposes may be made on a photographicprint. As th e relief o r the til t increases, rectifica-tion and adjustment are necessary.If precision is not required, a tube magnifier,


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20 MANUAL O F SURVEYING INSTRUCTIONSManual of 1894 required that all classes of linesbe surveyed with reference to the t rue meridianindependent of the magnetic needle.

A field note record is required of the averagemagnetic declination over the area of each sur-vey. The value is shown on the plat and in thefield notes. The principal purpose of this recordis to provide an approximate value for use inlocal surveys and retracements, where a startis to be made by the angular value of themagnetic north in relation to the true north.Methods of Establishing Directionazimuth by one of the following methods :o r other star s

2-19. Current practice is to determine true(1) Direct observations of the sun, Polaris,(2) Observations with a solar attachment(3) The turning of angles from triangula-

tion stations of the horizontal control network.At remote locations, if these methods aremade impracticable for long periods by thickcloud cover, angles may be turned from identi-fiable lines of an adjacent Bureau of LandManagement survey. Use may also be madeof a gyro-theodolite, properly calibrated and

The showing of latitude and longitude on th eplat of the cadastral survey should be extendedto seconds if ties t o a geodetic station warrantth at refinement.2-22. Precision of Observat ions . Themethods that are set out in the Manual for awell balanced observing program are good forresults within +6 seconds of time and t15"in latitude and azimuth, when estimated vernierreadings are made to the nearest 30".

2-23. A s t r o n o m y in the Manual . The basicastronomy needed for understanding of theobservations described in the Manual is wellcovered in college courses in applied astronomy.The theory relating to the observations and th ederivation of formulas is riot repeated in theManual. The subjects are treated with a viewto securing the most direct practical results. Themethods are not difficult when coupled withpractice in making the observations. Until thesteps become familiar i t is helpful to record foran experienced observer and to assist in makingthe reductions.The methods applied principally in observa-tions upon Polaris and the sun are arrangedto facilitate the work under most conditions en-countered in the field. The tables and formulas


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METHODSOF SURVEY 21

FIGURE .-The pole-zenith-sun triangle as viewedfrom outside the celestial sphere.ing direct and reversed observations on the op-posite limbs of the sun. The mean observedvertical angle to the suns center is designatedv in the notation. In single observations the ver-tical reduction to the suns center = 16. A re-

2-25. Refraction. Tables of mean refrac-tions both in zenith and polar distance appearin the Standard Field Tables, arranged to meetthe requirements of field use, Another tablelists coefficients to apply to mean refractionsin zenith o r polar distance for variations inatmospheric pressure and temperature. Lack-ing a barometer to determine atmospheric pres-sure, the argument approximate elevationabove sea level may be substituted. The dif-ferences between the true and the tabulatedrefractions are generally small and negligibleexcepting for the combined effect of low ver-tical angle with high elevation o r extreme tem-perature. The following example shows themethod to be used in reductions from the tabu-lated refractions :Tabulated refraction = 646or 6.76Elevation above sea level = 10,000 feet, coefficient forTemperature at time of observation = 82 F., oefficientTrue refraction = 0.70 X 0.94 x 6.76 = 4l.44 or 426

which is 0.70for which is 0.94

Time2-26. Because the earth revolves around thesun, a point on the earths surface faces thesun one less time each year than it does the


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22 MANUAL O F SURVEYING INSTRUCTIONSlocal mean time, one hour for 15 difference inlongitude.

2-30. The equation of time is the amount tobe added to, o r subtracted from apparent timeto convert over into local mean time. The equa-tion of time is changing constantly. Its valuefor apparent noon each day, on the Greenwichmeridian, is tabulated in the Ephemeris. Theequation of time reaches a maximum of about16 minutes early in November.

2-31. Standard time is identical with localmean time on th e central meridian of each timebelt, as Eastern Standard Time on the 75thmeridian; Central Standard Time on the 90thmeridian; Mountain Standard Time on the105th meridian; Pacific Standard Time on the120th meridian; Yukon Standard Time on the135th meridian; Alaska Standard Time onthe 150th meridian; Bering Standard Time onthe 165th meridian of longitude. Correction forlongitude is all that is required for convertingover into local mean time, additive when eastof the central meridian, subtractive when west.An additional correction of one hour is neces-sary when daylight saving time is in effect.

2-32. If an observation is to be made ofPolaris on a different meridian than that of

minutes 4.091 seconds in mean solar time. Thereare 366% sidereal 24-hour periods in the solaryear of 365% days.The mathematical equations that are em-ployed in the observations upon the equatorialstars, for time and altitudes, and for the azi-muths and altitudes of Polaris at various hourangles, are based upon the sidereal time rate.The same equations are applicable in thereduction of observations upon the sun fo r time,the moment of the observation being expressedin apparent time.Assume that a star and mean sun cross theGreenwich meridian at the same instant. Thestar would cross each succeeding meridianahead of the sun by an increasing time inter-val proportionate to the longitude west ofGreenwich. These time intervals, called side-real conversions,ar e listed for increasing longi-tudes in both the Ephemeris and the StandardField Tables. Sidereal conversions are appliedto the mean solar time to obtain sidereal timeand vice versa.Sidereal time is not employed directly in theManual methods. It is avoided through the planof the tabulations that are published in theEphemeris for the upper culmination and


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METHODS OF SURVEY 23find it convenient to change over to local meantime, or to carry a substitute watch set to localmean time. On solar transit orientation, thetime circle reads apparent time. If t he solar unitis being used constantly, as is nearly alwaysthe case where the line runs through heavyforest cover or dense undergrowth, many sur-veyors like to use a watch set to apparent time.

The record entry should therefore be explicit(1) as to the setting of th e watch to approxi-mate standard, local mean, or apparent time;(2) the conversion, if from standard to localmean time; and (3) the method of ascertainingth e watch error in terms of local mean time inevery case when making an hour angle observa-tion on Polaris. Many Polaris observations aremade during the season, sometimes daily. It isfor this purpose that the Manual devotes somuch attention to the practical field observa-tions for time.

2-34. The element of time enters into allazimuth determinations, apparent time for allobservations upon the sun, local mean time forall observations on Polaris and other stars. Thesun's declination varies with t he apparent timeand the longitude west from Greenwich. Thedeclination enters into all observations on thesun for azimuth. Thus the apparent time andlongitude should be known to a degree of ac-curacy commensurate with the refinement nec-

f orrection for longitude. The correction f o rlongitude is additive east and subtractive westof the standard meridian of the time belt. Theconversion table, "degrees to time," StandardField Tables, is convenient in this reduction.For example, in longitude 77'01'37.5" W. :Watch time of observation ~ ~ ~ ~ ~ ~ . . ~ ~ ~ . ~ . .6"26"40' p. m.Watch slow of 76th meridian stand-

ard time by comparison with astandard clock = +1"22s

Correction for longitude of station(77"01'37.6"W. or 6"08"06.6') ~~~~.~~~-8"06"

Local mean time of observation _ _ _ _ _ = 6h19"56~ m.2-37. Apparent time into local mean time:Apparent time of observation -t- the equation oftime. The equation of t ime is taken from the

Ephemeris fo r the date of observation and cor-rected for the longitude and time of observa-tion, conveniently interpolated as the intervalfrom Greenwich noon to the time of observa-tion. The watch er ror in local mean time is thenfound by taking the difference between thewatch reading a t the instant of the observationand the reduced mean time of observation. Forexample, in longitude 77'01'37.5'' W. :Mar. 18, 1970, apparent time of al-Equation of time,

titude observation upon sun .~~~~~~~..... = 3h42"11' p. m.Greenwich apparent


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24 MANUAL OF SURVEYING INSTRUCTIONSPolaris2-38. Polaris, the North Star, occupies aposition in the northern heavens about 1 roma line defined by t he axis of th e earths rotation.

Being a star of the second magnitude and nearthe polar axis, it ranks as the most useful cir-cumpolar star. It will be assumed that t he sur-veyor has learned how to identify Polaris in theclear night sky by reference to the pointersin th e constellation of th e Great Bear, popu-larly called the Dipper. Polaris, CY Ursae Mi-noris, is nearly on a line (or great circle) deter-mined by the pole and the star 6 Cassiopeiae.Both stars are located in the same directionfrom .the pole. The same line, or great circle,passes near the star 6 Ursae Majoris, anotherstar of the Dipper. The latter star is locatedon the opposite side of the pole. The relativeposition of the three stars gives an immediateindication of the approximate position of Po-laris in i ts diurnal circle at th at time. The threestars ar e all of about the same brightness. In-structions will follow regarding the identifica-tion of Polaris by instrumental methods duringthe twilight period, before the star is visible tothe naked eye. The same method may be used forverification of a night observation if the neigh-boring constellations are obscured by clouds.

An experienced surveyor ca;n readily observePolaris d t sunriseor sunset, reading the meas-

Star Magnitudes% % t i

2 3 4 5 d* 1*\ >k--*J

K X I \/ I *c

Star Magnitudes% % t i

2 3 4 5 d* 1*\ >k--*J

K X I \/ I *c

III

II

I ,I ,I \I !I \

I \I \

FIGURE.-Naked-eye identification of Polaris.About noon March 23d .About 6 a.m. June 22d.About midnight September 22d.


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METHODS OF SURVEY 25time of an observation, he may set the intersec-tion of the telescope cross-wires exactly on thestar, then, without moving the instrument, notethe direction of the stars motion and comparewith the diagram.The motion of Polaris at western elongationis vertically downward ; at eastern elongationthe motion is vertically upward. At western oreastern elongation the motion in azimuth iszero.At the equator, if Polaris could be observed,the hour angle of Polaris at elongation would be900O or 6hOm0s idereal hour angle o r 5h59m-1.02s mean time hour angle, but as stations ofobservation are occupied in the higher latitudesthe hour angle of Polaris at elongation decreasesprogressively. The reason fo r this is that all ver-tical planes intersect at the zenith, and the pointof tangency of a vertical plane with the diurnalcircle of Polaris occurs at points correspondingto decreasing hour angles with the higherlatitudes. The spread of the two vertical planesintersecting Polaris at eastern and westernelongation increases with higher latitudes, giv-ing increasing azimuths at elongation with themore northern latitudes.

2-39. The position of Polaris in it s diurnalcircle at any time may be determined by refer-ence to the mean time interval from upperculmination to any observed position west of

Zenith

HorizonFIGURE.-The meridian and vertical planes tangent tothe diurnal circle of Polaris as viewed from inside

the celestial sphere.

the local mean time of upper culmination ofPolaris, longitude 11115 W. :Aug. 16, 1972, Gr. U. C. of Polaris... ..._ 427.3 a.m.Red. to long, 11116W., 1 9 3.........._.._-1.2


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26 MANUAL O F SURVEYING INSTRUCTIONSLocal mea n time of elongation of Polaris: themean time of elongation of Polaris, Greenwichmeridian, latitude 40, is taken from theEphemeris fo r the date of observation. Theamount subtracted from the mean time ofelongation of Polaris, Greenwich meridian,latitude 40, o obtain th e mean time of elonga-tion of Polaris, local meridian, latitude 40", nwhich the argument is the longitude west fromGreenwich, is obtained from the table of side-real conversions, Standard Field Tables, with-out computation. The amount to apply to the

local mean time of elongation of Polaris latitude40" to obtain the local mean time of elongationof Polaris at the latitude of observation is tabu-lated in the Ephemeris in connection with thetable of azimuths of Polaris at elongation.

Examples of reduction from the Greenwichmean time of elongation of Polaris, latitude40, to the local mean time of elongation ofPolaris, latitude 64'30' N., and longitude 146"30' W. :

Eastern Elongat ionlat. 40 " = 8h33.8m .m.Sept. 14, 1972, Gr. E. E. f Polaris,Red. to long. 146'30,' W., l"36" _..._.......-..--1.6Red. to lat. 64"30' N. ............. ~ ~ ~ . . ~ . ~ ~ ~ ~....... = +4.3

L. M. T. of E. E. of Polaris ..........~~...~....8h36.5mp.m.

val, to obtain th e equivalent. The conversion isrequired in the reduction of an alt itude ob-servation upon a star fo r time, as the observedhour angle is in the sidereal interval.Conversion of a mean time interval into asidereal time interval, or vice versa: Theamount to apply to one time interval to obtainthe other time interval is found in the table ofsidereal conversions without computation.Example of conversion of a mean time inter-val into a sidereal time interval:Mean time hour angle of Polaris for anassumed observation in Alaska= 7h32.6m = 7"32"36"Conversion into equivalent siderealhour angle ~ ~ ~ . .+1 14Sidereal hour angle = 7"33"50'

7h = 105"33" = 8'15'6OS = 12'30"

113"27'30"idereal hour angle converted to degrees ..The conversion from a mean time intervalto the equivalent sidereal hour angle is requiredin the analytical reduction of the hour angleobservation upon Polaris for azimuth o r lati-tude, whenever the reduction is made by theequations in place of, or as a check upon, taking


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METHODS OF SURVEY 27of the meridian have been referred to the lastpreceding upper culmination, those east of themeridian have been referred to the next suc-ceeding upper culmination, thus avoiding anyhour angles exceeding 11h58m028.Hour angles of Polaris: verification b y thestar chart: a simple check on the approximatevalue of the hour angle at any moment, anydate, and of the position west or east of themeridian, may be secured by use of the starchart in the Ephemeris. First, scale a line forthe date, then place the overlay scale on thechart making the date line agree with the scalefor the time of observation, a.m. or p.m., lowerse t of figures. In this position, note where Fo-laris will be found with respect t o the meridianline of the overlay scale. Finally, read the scalefor hour angle, upper set of figures, star west orstar east of the meridian. The reduction values

should of course be taken from the tabulateddaily position of Polaris.The tables of the azimuths of Polaris a t allhour angles, that are published in the Ephem-eris, are tabulated with the argument in meantime hour angle, counting from upper culmina-tion. Therefore, for an observation west of themeridian the hour angle is referred to the pre-ceding upper culmination; for one east of themeridian the reference is to the next succeed-ing upper cumination. The hour angle at lowerculmination is the half ( l l h 58m ) of the side-real day (23"56.1m). mat position is a goodone for a latitude observation. It should be un-derstood that hour angle observations for azi-muth are not referred t o the point of lowerculmination. The equations for the azimuth andaltitude observations count strictly from upperculmination.

Examples of computing hour angles of Polaris, all for long. 117'15' W.:I h P 7 8 m

West o f the meridian, p.m. observation, U.C. in p.m.Feb. 23, 1972,)1.m.t. of observation = Sh20.1" p.m.Gr. U.C., same date... = 3'63.6" p.m.


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28 MANUAL O F SURVEYING INSTRUCTIONS

West of the meridian, a.m. Observation,U.C. n a.m.Aug. 15, 1972,1.m.t. of observation....... = Sh05.9" .m.Gr. U.C., same date............................................................ = 4'31.2" a.m.Red. for long. .................................................................... = -1.3 = 4 9.9 a.m.Hour angle, west = 0'36.0"

East of the meridian, p.m. observation, U.C. in p.m.Gr. U.C., Dec. 22, 1972 = 8"00.8" p.m.Red. for long. . .....................= -1.3L.m.t. of U.C.,Dec. 22, = 7 59.5 p.m.L.m.t. of observation, same date ...................................................................... = 4 36.1 p.m.Hour angle, east .......................... 3'24.4"

East o f the meridian, p.m. observation, U. C . in a.m.2 +$ % Gr. U.C., Sept. 6, 1972 = 3'06.2" a.m.

= 5 3 1.33.9 a.m.a ed. for long. ..................

2 +I2.m.t. of U.C., Sept. 6 ................................................................................ =3'0%q L.m.t. of observation, Sept. 6 .= 6 34.0 p.m.


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METHODS O F SURVEY 292-43. Mean time hour angle o f Polaris atelongation: t = he sidereal hour angle in angu-lar measure. This is converted first into thesidereal time interval and then into the meantime interval, which is the mean time hourangle of Polaris a t elongation.

Cos t = cotan S tan 4Example of computing the mean time hourangle of Polaris at elongation, ~ ~ ~ i l, 1970, in

latitude 48000' N., on which date the declina-tion of polaris is 89007'50.3" N. :+ = 48"OO';6 = 89"07'60.3"; tan + = . i i o 6 icotan 6 = 0.01618cos t = (0.01618) (1.11061) = 0.01686Sidereal hour ang le = 89'02'02"89" = 6'66"2' = P 0 8 "2" = (negligible)

2-44. Altitudeupper culmination

6h66m08'Mean time hour angle at elongation = Sh5Srnl0"Reduction to mean time hour angle = - 0 68 (sidereal conversion)

observation of Polaris atfor latitude:4 = h + 6 - 90"Altitude observation of Polaris at lower cul-

mination f o r latitude: The mean time hourangle of Polaris at lower culmination is 11hours58 minutes 2 seconds:+= +90" -The settings for the approximate altitudeof Polaris at upper and lower culminations,respectively, are :v = + + - (goo-6)

ture 60" F., and approximate altitude above sea level3,600 ft., I make an alt itude observation of Polaris atupper culmination for latitude, making four observa-tions, two each with the telescope in direct and reversedpositions.Summary of resultsWatch correct for 106th meridiantime by comparison with radiosignals.Mean watch time of observation..........= 3'16"31" a.m.Mean observed vertical angle................= 34"16'23"Reduced latitude .................................... = 33'23'22" N.

Field notationSetting: 90'00'


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30 MANUAL O F SURVEYING INSTRUCTIONSHour Angle Observation ofPolaris f o r Latitude

2-45. The latitude may be determined by analtitude observation of Polaris at any hourangle. By this method the vertical angles areread in pairs, or double pairs, with reversals ofthe position of the telescope, and watch timenoted at each setting. A watch correction isrequired, which will be applied to the mean (oraverage) of the watch readings to obtain thecorrect local mean time of observation for thepair or double pair of settings. The mean timehour angle of Polaris at the epoch of observa-tion is then taken o u t as in observations for azi-muth, and the declination of Polaris for thedate $s ascertained in the Ephemeris.

With the two values, mean time hour angleand declination, the latitude may be computedor there may be derived from the table in theEphemeris the vertical angle equivalent for theposition of Polaris above or below the earth'spolar axis at the epoch of observation. The lat-ter value is applied to the observed verticalangle, corrected for refraction, to secure thetrue elevation of the pole, or the latitude of thestation. The method may be combined with the

The latitude may then be derived from theequation: . Sin a sin h

sin 6os ( + - a ! ) =Example of hour angle observation of Polarisfor latitude, making use of the table given inthe Ephemeris :June 28, 1972, in approximate latitude 41'20' N., andlongitude 111"37' W., a t approximate temperature50 " F., and elevation above sea level 6,800 ft., I makean hour angle observation of Polaris for latitude, mak-ing four observations, two each with the telescope indirect and reversed positions.

Summaru of resultsMean observed vertical angle .Mean watch time of observation..........= 4h46m388 .m.Watch fast of local mean time, by

= 41"55'00"comparison with radio time signalcorrected for longitude = 26"28"

Reduced latitude . _........................... = 41 "20'37"N.Field notation

Telescope Vertical anale Watch timeDirect .............................. 41"53'OOt' 4'44"45" a.m.Reversed . 41 54 00 4 45 50Reversed ........................ 41 66 00 4 4 7 20Direct .............................. 41 57 00 4 48 37

Mean .......................... 41"55'00" 4'46"38* a.m.


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METHODS OF SURVEY 31Polaris at Elongation

2-46. Of the various methods of observa-tion to establish the t rue meridian, t he simplestis the observation upon Polaris at eastern orwestern elongation.Azimuth of Polaris at elongation :cos sSin A = -os qhExample of computing the azimuth of Polarisat elongation, October 20, 1970, in latitude46'20' N., on which date the declination ofPolaris is 89'07'54" N.: cos 6 = 0.015156CQS q5 = 0.690462sin A = 0.015155 + 0.690462 = 0.021949A = Azimuth of Polaris at elongation =1"15'28''.A table of azimuths of Polaris at elongationfor latitudes from 10" to 70" N. appears in the

Ephemeris, arguments : declination of Polarisand latitude of station.Example in th e use of t he table of azimuths

of Polaris at elongation, same date and stationas above, showing the method of interpolation :Declination

Latitude 89"07'60" 89'07'64'' 89'08'00"Azimuths elongation

46'00' ...... 1' 5'06" 1"15'00'' 1' 4'62''46"20'--.... .. l"15'28"47"OW....... . l"16'3Q" 1O 16'N" l"16'16"By interpolation in the table the requiredazimuth of Polaris at elongation is thereforefound to be 1'15'28".

Azimuth of Polaris at Ang Hour Angle2-47. While there is no better method forthe establishment of the true meridian thanthe observation upon Polaris at elongation, formost of the year this requires nighttime ob-servations. Moreover, should Polaris be obscured

by clouds at th e time of elongation, the observa-tion must fail.The "hour angle" method admits of observa-


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32 MANUAL OF SURVEYING INSTRUCTIONStion upon Polaris for azimuth at any time thatthe star is visible; the precise watch error inlocal mean time must be known, but if this hasbeen determined, the hour angle method be-comes at once the most convenient. The possibleaccuracy of the result compares favorably inevery way with the refinement obtained in anobservation at elongation.2-48. Azimuth of Polaris at any hour angle:t = sidereal hour angle in angular measure ; nhour angles exceeding 90" the function "- in4 cos t" becomes positive by virtue of the cosineof an angle between 90' and 270' being treatedas negative in analytical reductions :sin tTan A = co s 4 tan 6 - in 4 cos tA table of azimuths of Polaris at all hourangles, f o r latitudes from 10' to 65" N., ap-pears in the Ephemeris, arguments : declina-tion of Polaris, mean time hour angle, andlatitude of station. For other than the latitudesgiven in th e table, and for greater accuracy interms of seconds of azimuth, the surveyor willbe required to solve the above equation.

Example of computing the azimuth of Po-laris, February 21, 1972, at a mean time hourangle of 2h37.4m,n latitude 33'20' N., on which

Azimuth of Polaris CorrectionMean Mean declination + 89"08'30" subtractivetime forhour Latitude declinationangle + 89"08'40"32" 3 3 2 0 ' 34"2'29.6" ....- 37.2' 37.8' 38.1' 0.1'37.4 ............. 39.4 0.139.6 39.3 39.9 40.2 0.1

By interpolation in the table th e required azi-muth of Polaris is therefore found to be 0'39.4'- .1' = 0'39.3' or O"39'18".Polaris at Sunset or Sunrise

2-49. If the sky is clear Polaris may be mostconveniently observed by t he hour angle methodat sunset o r sunrise without artificial illumina-tion. The preparation for the observation con-sists in computing in advance the approximatesettings in azimuth and altitude in order tofind Polaris. The plan contemplates an approxi-mate reference meridian. With the time ofsunset o r sunrise assumed as the time of ob-servation, the hour angle 't" and azimuth "A"are ascertained in order to find the position ofPolaris in azimuth. The vertical angle will beequal to the latitude of the station plus the pri-mary adjustment when Polaris is above the


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METHODS OF SURVEY 33Polaris at sunset, May 6, 1972, at a station inlatitude 47'20' N., and longitude 102'40' W. :

From the Ephemeris the declination of the sun ad-justed to approximate sunset is found t o be 16"48' N.;the equation of time 3", to be subtracted from apparenttime; upper culmination of Polaris, Greenwich meridianl lh06.2" a.m.; the declinat ion of Polaris + 89O08'16".From the Standard Field Tables, the apparent time ofsunset is found to be 7"17" p.m.May 6 ,1 9 7 2 :Sunset .. = 7h17m .m., app. t.Equation of time .......... = - 3

Anticipated time ofobservation = 7"14" p.m., 1.m.t.+12Gr. U.C. f

Red. t o long.Hour angle of Polaris, westLatitude of station = 47'20'Vertical angle adjustment,

Polaris ......= l lh06.2" a.m.1 0 2 " 4 0 ~_.._._-1.1 11 06 a.m., 1.m.t.of meridian .... # 8h09mA # 1'03' W.

Polaris below the pole ........= -2 8 v # 46"52"Example of the computation of the positionof Polaris at sunset, November 6, 1972, samestation :Declination of the sun adjusted to approximate sun-set 16"14' s.;equation of time 16" to be subtracted from

__

November 7, 1972:Sunrise = 7'15" a.m., app. t.Equation of time ..................=Anticipated time of

-1 6~

observation = 6'59" a.m., 1.m.t.-I-12Upper culmination ofPolaris, November 6 . = 11 01 p.m., 1.m.t.Hour angle of Polaris, westLatitude of station = 47'20'Vertical angle adjustment,

. .of meridian ..................... # 7"58" A # 1'05' W.-Polaris below the pole ........ = -2 6 v # 46"54'

Stellar Observations, Equatorial BeltThere ar e two customary methods ofstar identification, First, the brighter starsmay be found individually by naked eye duringstarlight, each by means of its position withinit s own constellation and with th e aid of a chart

th at shows the outline of t hat and the neighbor-ing constellations ; second, using the transit,any s ta r may be found by reference to verticalangle and horizontal angle from the meridian,both values related to an anticipated time ofobservation, and to an approximate north andsouth line. The second method is frequently

2-50.


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34 MANUAL OF SURVEYING INSTRUCTIONSHaving selected the star to be observed andthe anticipated time of observation, th e time ofthe meridian passage of the star for tha t dateis then taken from the Ephemeris. The hour

angle for the position is the t ime interval be-tween the anticipated time of observation andth e time of the meridian passage.Use the following equation to find the verti-cal angle of the star at the anticipated momentof observation :sin h = cos t cos 4 cos 6 + sin 4 sin 6(If sin h is negative the star is below the

horizon.)Then use the companion equation to find thehorizontal angle from t he meridian, as follows :sin 6C O SA = - tan C tan hcos 4 cos hThe product sin 4 sin 8 and the fractionsin 6

cos 4 cos h ar e negative for south declinations.The product cos t cos 4 60s 6 is negative forhour angles exceeding 6 hours or 90.If the result for cos A is ) he

north.{south.ngle counts from theThe vertical angle setting (v fo r this pur-

second magnitude 2.0; etc. Brighter than firstmagnitude is rated, as Capella, 0.2; slightlybrighter, as Vega, 0.1 ; much brighter, as Cano-pus, -0.9; r still brighter, as Sirius, -1.6 n thisscale a magnitude of 2.1 is rated for Polaris.This detail is an important feature of identifica-tion.As an additional aid in star identification, itis helpful to note the positions of the brightplanets Venus, Mars, Jupiter, and Saturn. Thetimes of their transits, and their approximatedeclinations, are tabulated in the Ephemerisfor the first and sixteenth day of each month.The planets are wanderers (very changeablein position) so that the interpolations betweenthe tabulated dates will be rough, althoughclose enough or identification, and th e varyingpositions will become more readily noted oncontinued acquaintance. The proximities of theplanets to the selected stars, up to about 40minutes in time of transit and 1 0 difference indeclination, are shown in the tabulations byfootnote-ref erence.

The planets appear different in the telescope,Venus very bright and slightly crescent whenfarthest from the sun, and not so bright,but decidedly crescent when near t he sun. Mars


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METHODS OF SURVEY 352-52. The stellar observation is useful anytime of year, particularly when the sun reachesa meridian altitude exceeding 60" o r 65".There is no difficulty in picking up the merid-

ian passage of a star when the conditions forvisibility are good. Most of the selected starsare brighter than Polaris; ome of them can beobserved throughout any day that is clear andfre e from haze.After th e initial preparations have been madefor a Polaris observation, including the mark-ing of a meridian reference by solar transitorientation, o r by reference to lines previouslydetermined, it is good practice to include themeridian passage of a star in the observingprogram. In this manner the watch correctionfo r local mean time is obtained just when neededand on the most direct plan under the usual fieldconditions.The Greenwich mean times of the meridiantransi t of t he selected bright stars of t he equa-torial belt are tabulated in the Ephemeris forthe 1st and 16th day each month; the reduc-tions to the other days of the month a re in-dicated on each page of th e stellar tabulations.This data must be converted to the local meantime of transit.Example of the computation of the finding

sin 6cos $ cos hos A = - an + tan hsin 6 = 0.2097

C O S $ = 0.7402 tan + == 0.9083cash = 0.8997 tan h = 0.4852sin 6cos+ cos h 0.3149 tan + tan h = 0.4407-0.4407

cos A = -0.1258 (Negative indicates horizontalangle counts from south.)A = S. 82'46'E.

Using the finding positions of the star (h =25"53', A = S . 82'46' E.), four observations aremade, two each with the telescope in direct andreversed positions. The t rue values for timeand azimuth are obtained by a more precisereduction of the observations by use of the aboveformulas. Keep in mind that in all stellar ob-servations the true vertical angle (h) is equal tothe observed vertical angle (v) minus the re-fraction (r) in zenith distance. There is no cor-rection for parallax. In solving for time, thehour angle (t) obtained by use of the formula isin terms of the sidereal rate. A subtraction of 10seconds per hour (sidereal conversion) will giveth e equivalent mean time hour angle.Direct Solar Observations


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36 MANUAL OF SURVEYING INSTRUCTIONS2-54. Meridian Observation o f the Sun f o rApparent Noon. With the telescope on themeridian elevated to the sun's altitude, thewatch times of tr ansi t of th e sun's west and east

limbs are noted, the mean of which is the watchtime of apparent noon. If the observation failsfo r either limb the reduction to the sun's centeris accomplished by adding o r subtracting 68seconds; a refinement in the amount of thisinterval is had by referring to the Ephemerisfo r th e time of the sun's semi-diameter passingthe meridian fo r th e date of observation.The setting for the approximate altitude ofthe sun's center is:

v#9O0-rp+6OBSERVINGPROGRAM

Determine the meridian by the best means athand and compute the vertical angle setting f o rthe sun.Level the transit, align the instrument on themeridian, and elevate the telescope to the alti-tude of th e sun's center.Note the watch time of the sun's west limbtangent to the vertical wire.Note the watch time of the sun's east limb

4 Watch time of transit, W. limb.....~..llb54m481+ Watch time of transit, E. limb..........= 11 56 56Watch time of apparent noon_........... 11"55m525Apparent noon_____.._12"00m00"Eq. of time ad-justed to timeof observation _._. -2 37Local mean time of apparent noon-.-.= 11 57 23Watch slow of local mean time___..... 1"3lS

2-55. Meridian Altitude Observation o f theSun fo r Latitude.-Reverse the sign of 6 forsouth declinations :+ = 0" + 6 - hThe following observing program is recom-mended :Thoroughly level the transit and place thetelescope in t he meridian elevated t o the sun'sapproximate altitude at noon.Observe the altitude of th e sun's lower limbwith the sun slightly east of the meridian.Reverse the transit.Observe the altitude of the sun's upper limbwith the sun slightly west of the meridian.Take the mean observed vertical angle forthe altitude of the sun's center at apparentnoon.


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METHODS OF SURVEY 37Settings : 90"OO'

$ # (-)48"10' N.6 # (-) O"49'S.v # 41'01'

40'45'41 O 17'Sun's semi-diameter # 16'Upper limb (41"Ol' + 16')Lower limb (41"Ol' - 6') ................+ Observed alt., lower limb,+ Observed alt., upper limb,telescope dir. .............................. = 40"46'30~"telescope rev. .............................. = 41"18'30"

Mean observed altitude, v = 41"02'30"Refraction .... = -0 69Parallax .............................. = +O 06h = 41"01'37"Declination, Gr.

Red. t o longitudeapp. noon ........= O"42'01.0" S.1 0 9 " lO ~w.,7.278 X 58.46" = 7'06.4" S.O~"49'06.4"S.

S = O~"49'06"S.$ = 90 " - - h. = 48'09'17'' N.Example of meridian observation of the sunfor time and latitude:September 10, 1969, in approximate latitude 41'85' N.,and longitude 109"68' W., at temperature 50 " F., andelevation above sea level 6,600 ft., I make a meridian

Watch time of apparent noon........................ = 11"57"22"Apparent noon .......................... = 12h00m00"Equation of time,Gr. noon sub-tractive fromapp. t ......................= 3"Ol"Red. to long.109"68'W............... = 7

3"08"Local mean time of apparentnoon ........................................Watch fas t of local mean time

-3 08l lh56m52s= 11 56 6 2

30'.................--The accuracy of the reduced latitude is di-rectly related to the refinement of t he value ofthe observed vertical angle. A better determina-tion of th e latitude by this method is possibleonly by making a series of observations on suc-cessive days, o r the observation may be dupli-cated by vertical angle readings on stars withinthe equatorial belt at meridian passage, and

by combining the result with Polaris observa-tions for latitude.Altitude Observation of the Sun for Azimuth

2-56. While observations of Polaris for azi-muth are used extensively, there are situationswhere a direct altitude observation on the sun


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38 MANUAL OF SURVEYING INSTRUCTIONSnoon observation for time and latitude. In thenorthern States, from late October until lateFebruary, t he sun is too low fo r the best observ-ing for time and azimuth. The bright northdeclination stars are especially helpful for theobserving in Alaska, the southern declinationstars for t he meridian time-and-latitude ob-servations in Florida.The trigonometric elements of the altitudeobservation for time and azimuth are verticalangle, latitude, and declination of t he sun o rthe star.Accuracy in latitude is essential to good ob-serving for azimuth by the altitude method.If the latitude has not been well determinedpreviously, an azimuth observation on the sunsoutheasterly should be balanced by one south-westerly at about the same vertical angle. Aver-aging the results will eliminate the effect of anunknown discrepancy in latitude.

The precision with which the azimuth may bedetermined by the altitude observation of t hesun or a star is dependent on the correctnessof the vertical angle. The error in azimuth th atresults from a discrepancy in vertical angle in-creases rapidly when the angular elevation islarge, when the hour angle is small, o r with

ment, but with an error in the readings of ver-tical angles, the error in azimuth is multipliedone, two, or three times, depending on thesun's position in altitude, hour angle, anddeclination. The effect is shown graphically infigure 8. By balancing an observation south-easterly with one southwesterly at about thesame vertical angle, the error in azimuth will becompensated.The altitude observation calls for accuracy inthe instrumental adjustments and for goodjudgment in t he selection of a well formed pole-zenith-sun triangle. Vertical angles from 20"to 50" are to be preferred, not less than threehours from meridian passage, and north declina-tion. A bright star in north declination is muchbetter than the sun when the south declinationof t he sun exceeds 10".In order to balance the altitude observation

fo r azimuth, to compensate fo r uncertainties invertical angle, the sun may be observed south-eas te r ly and sou thwes te r l y ; o r the sun in oneposition and a star in the companion position;or two north declination stars may be selected,especially when the sun is in southerly declina-tion ; etc. ; th e purpose being to balance the ob-


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METHODS OF SURVEY 39The solar transit is equipped with a full ver-tical circle, a neutral-tint colored glass in thedust shutter of the eyepiece, a removable pris-

matic eyepiece, and a removable reflector forilluminating the cross wires. These ar e essentialto rapid and accurate altitude observations, andfor the night observing. The latest model fea-tures a solar circle on the reticle of th e tr an si ttelescope ; his gives the horizontal and verticalangle sightings to the suns center (instead ofto th e limbs). Double lines are provided fo rhalf of each the vertical and horizontal crosswires; this spacing is to improve the stellarobservation for exact centering, avoiding thecomplete covering of the star by the wire (asthe lat ter may obscure the star in the daylightobservation). See section 2-64.There are a number of equations for solvingthe altitude observation for azimuth, in whichthe elements are vertical angle, latitude, anddeclination of the sun o r the star. These arecompanion equations to those employed in solv-ing the altitude observation for time, using thesame elements. Some of the equations areadapted to the use of natural trigonometricfunctions and the computing machine; thesame equations may be employed by logarithmic

separate results will vary somewhat, much thesame as separate orientations of the solar unit.When desired, in order to guard against error,or to check a discrepancy, any of the sightingsmay be reduced to the suns center and solvedseparately.

For the stellar altitude observation foursightings are required, two each with the tele-scope in direct and reversed position, to bereduced as one observation. The number of theobservations may be increased if desirable, al-though it is good practice to limit the numberof sightings to not over six in any one series.Any of them may be reduced separately if de-sired to check against an error in the reading ofthe angles. As each sighting is centered onthe star, the differences in the rate of travelin time, horizontal angle, and vertical angle,will be uniform.

It is emphasized that none of the reducedaltitude observations for azimuth, in terms ofthe indicated bearing of the reference mark,standing alone as one observation, can be re-garded as within the attainable limit of accu-racy of th e one-minute transit until duly verifiedby a completely independent method, such asthe Polaris observation to check the altitude ob-


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METHODS OF SURVEY 41


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This order, A. M.Pel.1 Dir. Upper-right .6 Rev. Lower-left ............................

This order, P. M.I Watch Hor. Ang. Vert. Ane.time~~~ ~ ~ ~Lower-rightUpper-left

2 Dir. Upper-right..........................6 RRV Lower-left ...Mean *_ A A ALower-right ...Upper-left ......

3 Dir. Upper-right4 Rev. Lower-leftMean . B B BLower-right ............................................Upper-left ....Mean C C (3

Mean of all ................ A-B-C A-B-C A-B-Cprovided the time spacing is nearly uniformfrom 1 o 2, 2 o 3, 4 o 5,and 5 o 6.Any largediscrepancy in the means will indicate a mis-reading at some point. If th e means ar e slightlyirregular, the differences from 1 to 2, 2 to 3,4 o 5,and 5 o 6,which should be proportional,may be checked by slide rule method.

An equivalent observing plan, thought bymany surveyors to be a simpler tangent-motionmanipulation, may be substituted if desired, asfollows :A . M .

2-63. Example of direct al titude observa-tion of t he sun for azimuth and time, sun northdeclination :The altitude observations are made of th esun, each with the telescope in direct and re-versed positions, observing opposite limbs ofthe sun. The horizontal angle is read from a flagon line to the east, southward to the sun. Theknown position of t he instrument sta tion is inlatitude 412240 N., and longitude 1114640W. Observation is begun at 9:15 a.m., 1. m. t. ,with watch set to approximate local mean time.The declination of th e sun fo r the mean period


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42 MANUAL O F SURVEYING INSTRUCTIONS~

vertical ans,e Horizontal angle.Telescope Sun Watch time flag to sunbservation

1st se t .

!&Iet .................... -3d se t ......................

Direct $- 9" 15" 05" 46" 34' 00" 21" OW 00"Reversed p 9 15 59 46 10 00 20 29 00Mean 9" 15" 32* 46" 2% 00" 20" 44' 30"Direct .......................... $- 9" 17" 02" 46" 54' 00" 21" 28' 00"

....................

Reversed .................... p 9 17 36 46 26 00 20 49 00Mean . gh 17" 19" 46" 40' 00" 21" 08' 30"

Direct . $- 9" 18" 41" 47" 12' 00" 21" 52' 00''Reversed p 9 19 2#0 46 45 00 21 16 00...................Mean .. 9" 19" OO * 46" 58' 30" 21" 34' 00"

By 1st obsn. flag bears ........................ N. 89'59'10'' E.By 2nd obsn. flagbears ....................... N. 89 59 23 E.By 3rd obsn. flag bears ........................ N. 89 59 08 E.Mean true bearing of flag ................N. 89'59'14'' E.Watch slow of 1. m. t., 1st obsn. = 25"2nd " ..........= 203rd ' I .........= 25Mean watch time slow of 1. m. t. .......= 23"

i' I ( I i i II ( I ( I i I' I

1st obsn. 2nd obsn. 3rd obsn......................................... 46" 8'30"u 46"22'00" 46" 0'00"Refraction....................................................................................... -65" -55" - 4"Parallax_............................................... ............................... +06" +06" $06''

h 46'21'11'' 46 39'11" 46 57'42"



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2d set:log cos $ 9.876274log cos h 9.836686

log 9.711860

3d set:log cos $ 9.876274log cos h 9.834096

log sin S 9.469842

log 9.711860log 9.767982nat+ 57277

log sin 6 9.469842

log ta n $ 9.944941log tan h 0.025074log 9.970015nat- .93328nat+ 57277

Cos A .36061True bearing of sun S.686207 E.Angle, flag to sun +210830S.900037 E.True bearing of flag N.896923 E.

log ta n qj 9.944941log tan h 0.029762log 9.709369 log 9.709369

log 9.760473nat+ 57607log 9.974703nat- .94342nat+ .67607

COSA - .36736True bearing of sun S.682662 E.Angle, flag to sun +213400S.900062 E.True bearing of flag N.896908 E.

The above observations are reduced for time by the equation:sin - an 4 tan scos dl cos 6os t=1st obsn. :log cos qj = 9.876274 log sin h = 9.869603 logtan$ = 9.944941

44 MANUAL OF SURVEYING INSTRUCTIONS


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3d obsn: log sin hlog cos $4 cos 6lognat ( + Inat tan + tan 6 (-)cos tt = 41'3'7'54" = 846"32# _.......__Equation of time ..................._-...--

= 9.863866= 9.856502= 0.008354= 1.01942= .27199= .74743= 9"13"28" a.m.= + 6 67

L.m.t. of observation..........~ ___.....9hlP'25' a. m.Watch time of observation__..__._9 19 00 a.m.Watch slow of local mean time....= 25#

The Solar Circle2-64. The design of t he reticle of the transittelescope to include a circle tha t is equal to theimage of the sun's diameter adds a desirableimprovement to th e technique of the altitudeobservation for azimuth. There are two advan-tages, first, all sightings for vertical angle andhorizontal angle read to the sun's center; sec-ond, the manipulation of the vertical and hori-zontal tangent-motions to the position of con-centric fitting of the circle to th e sun's imagemay be accomplished with utmost certaintythat the values for the vertical and horizontalangles are exactly simultaneous. Any single

observations by using both the vertical andhorizontal rod, on the ratio of 1:132.The double cross wires in the left and in thelower halves (direct position of the telescope)ar e spaced at 40"; this is t o improve the day-light stellar observation. The double lines avoidthe covering of the star by the cross wire(which may easily obscure the star). The cen-tering and the manipulation of the tangent mo-tions is indicated in the following diagrams :

Direct Reversed



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Obaw- Apparent Verticalvation T ~ W W P ~ time angleDirect 8h13m25" 39"57'00"Direct . 40"02'00"Direct 40"07'00"4-...--..-... Reversed .. .. 40"20'30"Reversed ... 40'25'30"6. Reversed ......8 16 25 40'32!00''

Horizontalangle fromreferenceto sun34"38'00"34'33'00''34"29'00"34"18'00"34'14'00"34'09'00"

Mean . 8h14m56s

Equal Altitude Observations of the Sunf o r Meridian2-65. The tr ue meridian may be establishedby the method of equal altitude observations ofth e sun. The observation is not well adapted toline work, but i t possesses a certain usefulnessin camp, in that the surveyor may thus deter-mine the true meridian by the sun with mereapproximations as to time and latitude.The fixation of the true meridian by thismethod depends upon the theory that the sun'scenter at equal altitudes occupies symmetricalpositions in azimuth east and west of th e merid-ian in the morning and in the afternoon exceptfor the correction necessary to be applied dueto th e change in the sun's declination in the

46 MANUAL O F SURVEYING INSTRUCTIONS


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great circle that passes through the pole andth e sun. The suns hour angle at th at moment isth e angle measured along the plane of th e Equa-tor, intercepted between the plane of the merid-ian and the plane of the great circle thatpasses through the pole and the sun. This anglereads apparent time on the hour circle of thesolar unit.The vertical angle inclination of t he polar axisequals the latitude of the station; this angle isset on the latitude arc. The angle on the planeof t he great circle tha t passes through t he poleand the sun, counting between them equals 90

minus the suns north declination, or 90 plusthe suns south declination, corrected by anincrement equivalent to the refraction in polardistance. The settings for this angle are com-puted for each day in advance; it is set on thedeclination arc to agree with the apparent timeof observation. The correct position of th e sunszenith distance measured on the vertical planeof the great circle that passes through the sunis secured by the careful leveling of the transit.

After setup and careful leveling, the solartransit may be instrumentally oriented by anexperienced surveyor in less than two minutes.The accuracy or acceptable tolerance is equalto that of any single, unverified, average directaltitude observation on the sun.

Use of the solar unit avoids the cumulativeerror normally encountered in long back-and-foresight lines and in traverse lines wherethere are many turns. A traverse line may beru n by occupying each alternate station, cuttingin half the time required for the instrumentalwork. Heavy winds or insecure ground, wind-falls, timber, undergrowth, and obstructionsthat require offset are not in themselves anypreventative to rapid and accurate solar ori-entation.2-67. The instrumental orientation of th esolar unit is made possible through five elements

in th e construction, as follows:(1) A telescope whose line of collimation isthe polar axis ; he polar axis corresponds to anelement of the more elaborate observatoryequatorial instrument mounting, which isdesigned for the telescope to follow a starstravel in diurnal circle. The solar telescope ismounted in collar bearings whose bases are at-tached to a vertical limb; the telescope may berevolved o r turned 12 hours in hour angle.

(2) The vertical limb is an arc th at is gradu-ated to read in latitude; a vernier mounted onthe base frame gives the reading in latitude;the center of t he limb is called the latitude axis,and is horizontal.

___



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BLM - Manual of Instructions - 1973

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