239 q (yi.iki.i) -I- (91.2ai.2) ~l~ (yi.s«1.3) -T (<pi.»-i 1 n 1 where <px.! is the bearing at station I to orientation point x 91.2 is the bearing at station I to orientation point 2 etc. ai,4 the observed direction at station I to the orientation point i n is the total number of observed directions at I, the direction to P inclusive. The bearing 91.P then becomes <pi.p «I .p 0\. This bearing is to be used for the adjustment of the coordinates of P. The other bearings 911,p, 9111.P etc. are determined in a similar way. Correlation exists between the coordinates of all stations and consequently also between the orienting bearings not only at the station I but also at the other occupied stations e.g. 91.,- and 911.4. Therefore theoretically the adjustment of taking the mean 01 of all orienting angles <pi.i au of equal weights is a (very convenient) practical simplification of an adjustment which should be one of correlated observations with weight coefficients derived from the weight coefficients of the coordinates. The proper weight coefficients of the orientation bearings will be derived and submitted to an investigation as to the conditions under which they may be replaced by new weight coefficients expressing equal variances and zero covariances. Only if these conditions are satisfied the simple adjustment of 01 by taking the mean of all observed orienting angles would be the most accurate indeed. The bearing 91^ can be written as Yi—Yi t 91.» arc tan x._Xj- (2) After the expansion of this equation into a Taylor series the following correction equation can be derived <j>U an\Y\ -f- b\.iAX\ - auAYi b\,iAXj au vH i Öi (3) where a and b are the so called direction coefficients p" cos <t>U j p" sin <j>u «(.i «I.» -~jand b,.i =—bu r- »I.i dl.i d\,{ being the distance from station I to point i. Similar equations can be derived for the stations II etc. Putting Vi i «uAYi bj.iAXj T" ai.iAYi bnAXi -\- (4) in (3) gives: V\.i au <|>i.»- (5)

Digitale Tijdschriftenarchief Stichting De Hollandse Cirkel en Geo Informatie Nederland

Tijdschrift voor Kadaster en Landmeetkunde (KenL) | 1963 | | pagina 7