Page 865 miscellaneous 9442 



To make the computation, starting with a buoy whose position is fixed, known as 

 the initial buoy, the buoy stations are tabulated in the order they are to be computed, 

 with the azimuth and the distance between each pair of stations properly entered. 

 Each distance multiplied by the cosine of the respective azimuth gives the plane lati- 

 tude difference, and multiplied by the sine of the azimuth gives the plane longitude 

 difference (departure). The progressive algebraic sums of latitude difference and 

 longitude difference are next determined for each buoy station; differences of north 

 latitude and west longitude are additive, and those of south latitude and east longi- 

 tude are subtractive. The resulting sums are the values in meters, uncorrected for 

 curvature, to be applied to the position of the initial station. They can be corrected 

 by the simple methods described below with sufficient accuracy for the usual conditions. 



The plane longitude differences must be corrected for convergence of the meridians. 

 This correction must be computed for each pair of adjacent buoy stations and applied 

 as a progessive algebraic sum to the progressive sums of longitude differences. The 

 ccrrection is zero on north-south lines, and so far as azimuth only is concerned, is a 

 maximum on east-west lines. Special Publication No. 5 can be used in determining 

 this correction. For the mean latitude of the line of buoys, take from the left-hand 

 page the value (in hundredths of meters) of the change in length of 1 minute of longi- 

 tude per minute of latitude. Multiply this value by the difference in longitude (in 

 minutes) between the pairs of buoys, and then multiply this product by the difference 

 in latitude (in minutes) between the forward buoy of the pair and the terminal buoy of 

 the traverse. Or, the difference in length (in meters) of 1 minute of longitude at the 

 latitudes of the forward buoy of the pan and the terminal buoy can be taken directly 

 from the tables by subtraction, and multiplied by the difference in longitude (in min- 

 utes) between the pan* of buoys. In the northern hemisphere the correction increases 

 the longitude difference where the terminal buoy is south of the buoy to which the 

 correction applies, and vice versa. The approximate latitudes and longitudes of the 

 buoy stations as determined by dead reckoning are sufficiently accurate for use in 

 determining the corrections. 



There is also a latitude correction, which is applicable where the differences in 

 longitude between successive buoys are large enough to warrant it. It varies with the 

 latitude and is in proportion to the square of the difference in longitude. In latitude 

 40°, the correction is less than 3 meters for a longitude difference of 6,000 meters. For 

 an ordinary traverse whose whole length is in the same general direction and with 

 buoys approximately equally spaced, this correction will be satisfactorily taken care of 

 in the adjustment of the closure error. Where it needs to be applied, the correction 

 can be taken from Special Publication No. 5 under the appropriate latitude, and from 

 the last column on the right-hand page, using the difference in longitude between suc- 

 cessive pairs of buoys. The correction increases the latitude difference where the for- 

 ward buoy of a pair is south of the preceding one, and vice versa. The correction is a 

 progressive one, being applied to the plane latitude differences in the same manner as. 

 described above for the longitude corrections. 



To find the closure error of a traverse computed by this method, convert the total 

 corrected traverse values for the terminal buoy into minutes and meters and apply this 

 to the geographic position of the initial buoy. Compare the results with the fixed 

 position of the terminal buoy. The differences in latitude and longitude (in meters) 

 are the closure error, which should be distributed through the traverse according tO' 

 distance from the initial buoy. 



