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The Determination of Longitude in Landsurveying.” by ROBERTHENRY BURNSIDE DOWSES, Assoc

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The Determination of Longitude in Landsurveying.” by ROBERTHENRY BURNSIDE DOWSES, Assoc 316 DOWNES ON LONGITUDE IN LAXD SUIWETISG. [Selected (Paper No. 3027.) The Determination of Longitude in LandSurveying.” By ROBERTHENRY BURNSIDE DOWSES, Assoc. M. Inst. C.E. THISPaper is presented as a sequel tothe Author’s former communication on “Practical Astronomy as applied inLand Surveying.”’ It is not generally possible for a surveyor in the field to obtain accurate determinationsof longitude unless furnished with more powerful instruments than is usually the case, except in geodetic camps; still, by the methods here given, he may with care obtain results near the truth, the error being only instrumental. There are threesuch methods for obtaining longitudes. Method 1. By Telrgrcrph or by Chronometer.-In either case it is necessary to obtain the truemean time of the place with accuracy, by means of an observation of the sun or z star; then, if fitted with a field telegraph connected with some knownlongitude, the true mean time of that place is obtained by telegraph and carefully compared withthe observed true mean time atthe observer’s place, andthe difference between thesetimes is the difference of longitude required. With a reliable chronometer set totrue Greenwich mean time, or that of anyother known observatory, the difference between the times of the place and the time of the chronometer must be noted, when the difference of longitude is directly deduced. Thisis the simplest method where a camp is furnisl~ed with eitherof these appliances, which is comparatively rarely the case. Method 2. By Lunar Distances.-This observation is one requiring great care, accurately adjusted instruments, and some littleskill to obtain good results;and the calculations are somewhat laborious. The observation consists of measuringthe angular distance between the moon and certain tabulated celestial bodies (given in the Ephemeris of the Nautical Almanack for the month), and also the altitude of one or both of the bodies, or, in the case of the true mean time a.t. the observer’s place being Minutes of Proceedings ht.C.E., vol. cviii. p. 230. Minutes of the Proceedings of the Institution of Civil Engineers 1898.133:316-330. Pnper3.1 DOWNESLOXGITUDEON IN LANDSURVEYING. 317 known, of the distanceonly. Inthe first case two or three instrumental observers are required, but in the second only one. That one is, however, dependent on thetrue time in amuch greater degree, and much extralabour isinvolved inthe computation. Next, by comparing the distance so obtained, after reduction to true distance with the tabulated lunar distances for the meridian of Greenwich, as given in the Nautical Almanack (whence the Greenwich time of theinstant of observation is computed, andby comparison withthe true mean time of the observer’s station),the longitude of the place is found.Hence, if the true mean time of the place is not known, it is necessary that the Iatitude should be known, or that a true azimuth should be observed, the latter course beingunusual and inconvenient. The usual conditions are that the latitude is known, and one or both altitudes or the true mean time are observed. The accuracy of the observationdepends upon the exact measurement of the lunar distance; a smallerror in the observed altitude will not much affect the calculation, but an error of l’in the distance will cause an error of nearly 30’ in arc of longitude. For this measure- ment it isnecessary to have a good and accurately adjusted sextant, which should be used with the long telescope. It is best when possible to observe at least one altitude-that of the moon by pre- ference, if its position admits of it, because the correction for the moon’s parallax in altitude and the moon’s semi-diameter depend upon the apparent altitude-for an error of 1”in time represents a in arc, which is theprincipal trouble when no altitudeis observed. The observation is easier when the altitude of the moon is less than that of the sun, or greater than that of a star or a planet.The moon’s enlightenedlimb should bebrought into contact with the nearer limb of the sun or with the centre of a star or planet. In taking the altitude of the moon with a sextant, the upper or lower limb must be brought down to the horizon. In the computation the corrections necessary to all the data to be used, both from observation and the NauticalAlmanack, depend- ing upon the features observed, are first applied. The moon’s semi-diameter is obtained as follows:-Take the semi-diameter for Greenwich mean noon or midnight (Ephemeris, pp. 111 of the Nautical Almanack) and apply to it the correction for the assumed difference of longitude; next apply the positive correction for augmentation (Chambers’ Tables, p. 432), and the result is the moon’s augmented semi-diameter. The correction for augmentation is dependant upon apparentaltitude, but it is practicallythe same whetherthe altitude be true or apparent, Minutes of the Proceedings of the Institution of Civil Engineers 1898.133:316-330. 318 DOWNES ON LONGITUDE IN LAND SURVEYING. [Sclocted still, in thecase of no altitude being observed, it may be left until after the apparent altitudehas been calculated. The correction for the moon’s parallax in altitude is dependant upon apparent altitude; hence, if no altitude be observed, it will be necessary to defer the reduction until after the apparent altitude has beencalculated. To thehorizontal parallax obtained from the Nautical Almanack (Ephemeris, pp. 111) apply the correction for the assumed difference of longitude; the equatorial horizontal parallax is a negative quantity dependant on latitude (Chambers’ Tables, p. 427), and theresult is reduced horizontal parallax, which must be reduced to seconds and multiplied by the cosine of the moon’s apparent altitude (corrected for refraction) when, after reduction tominutes and seconds, it is theparallax in altitude. To obtain the true altitudeof the moon’s centre, if the altitude of a limb of the moonbe observed, from this observed altitude subtract the “dip” (if the sextant is used for this part of the observation), also theindex error ( T), if any,and apply the moon’s augmented semi-diameter(as above), andthe result is the moon’s apparent altitude; from this subtract the refraction (Chambers’ Tables, p. 428) and add the parallax in altitude (as above). If no altitude be observed, thisquantity must be computed, as explained below. In determining the apparent distance, to the observed distance, after correctingfor index error, if auy, apply themoon’s augmented semi-diameter (previously obtained), and, if the sun be the com- panion body observed, the sun’s semi-diameter (Nautical Almanack, Ephemeris, pp. 111). If the altitude of the second body, sun or star, be observed, the apparent altitude and true altitude are deduced in the ordinary manner. If a planet be used, toits observed altitudemust be applied a correction for parallax in altitude,for which is required a Table that does not appear in the books usually in the hands of a surveyor. If one or more altitudes have to be calculated owing to their not having been observed, the moon’s right ascension and declina- tion must be taken from the NauticalAlmanack (Ephemeris, pp. V) and corrected for the assumed difference of longitude. Also the right ascension and declination of the companion body must be taken from the Almanack,and, if necessary, corrected for the assumed difference of longitude. Having now right ascension of the moon and of the companion body, subtract the less from the greater and the difference is the Minutes of the Proceedings of the Institution of Civil Engineers 1898.133:316-330. Pfbpe15.l DOWNEB ON LONGITUDE IN LAND SUBVEYIIG. 319 hour angle between them. Next, having the latitude of the place, the true altitude (if the moon’s altitude has been observed) and declination of the moon, the hour angle between that body and the meridian of the place can be computed by the extra meridian computation for time. Thehour angle thus obtained, on being applied to the hour angle between the meridians sf the bodies, will give the hour angle between the meridian of the place and that of the companion body. Then with the hour angle, latitude and declination of the companion body, its true altitude can be computed, and from thisresult the apparent altitude must be deduced by theconverse of the usual correction. In the eventof no altitude havingbeen obtained byobservation, both altitudes must be calculated from the true mean time at the place, which must be very accurately known. The procedure is as follows :-From the true mean time of the place at the instant of observation must be deduced the siderealtime, or right ascension of the meridian of the place by the conversion of the interval of mean time sinceprevious mean noon, intothe corresponding interval of sidereal time, and to this must be applied the sidereal time at previous mean noon, the result being the right ascension of the meridian of the place. Having the right ascension of the . place, and that of each of the bodies observed, the hour angle of each of the bodies may be readily deduced, and then the true and apparentaltitudes canbe obtained (as related above) for the companion body. This method of computing the altitudes shows the meaning of‘ eachstep, butthe following concise tabulated form for the computation, given in Norie’s epitome,’ which is mathematically the same, may be noted :-Having obtained the hour angle (HA) of the body, as mentioned above, then cos HA X cot lat ( -10.0 in logs) = tan Arc I. Arc IN polar distance = Arc 11, if HA be less than 90°, or Arc I + polar distance = Arc 11, if HA be greater than 90°, that is, whenthe hour angle is less than G hours, takethe difference between Arc I and the polar distance to obtain Arc 11, but if greater take the sum sine true alt = sin lat X sec ( - 10.0 in logs) Arc I X cos Arc 11, and then the apparent altitude isdeduced as before.
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