This report deals with two aspects of the problem of fixing the co-ordinates of points situated on lines which together form the idealized mathematical position pattern, resulting from the erection of the Decca transmitters in the Netherlands for the Delta works. Firstly, the basis and the derivation of the formulae used are discussed; and secondly, attention is given to the sequence of calculations and the way in which they are carried out, with the help of the electronic computer known as Stantec-Zebra. Decca patterns on sea-charts - involving much greater areas than covered by the Delta chain - are always calculated directly in geographical co-ordinates on the ellipsoid and mapped in respect of the network of parallels and meridians appearing on such charts; by this means any desired degree of calculating accuracy can be obtained, although great accuracy is usually not required for the purpose contemplated. For mapping purposes - and thus also for the Delta chain - it is desirable, also in view of the possibilities of comparison with conventional terrestrial position fixing, to make the Decca calculations in rectangular co-ordinates; for the Delta chain these should of course be the rectangular co-ordinates on the stereographic map projection used in land triangulation (R.D.co-ordinates). Direct conversion of geographical co-ordinates of a number of points on Decca lines into rectangular R.D. co-ordinates leads to formulae which are difficult to handle. It is for this reason that the indirect method making use of flat hyperbolae has been followed for the Delta chain, as described in this study; it leads to simple formulae which are very suitable for working out with the help of an electronic computer. When, as a result of the accuracy of drawing and the map scale used, the differences between Decca lines and flat hyperbolae are sufficiently small, the flat hyperbolic pattern is justified and the map pattern is then constructed from confocal flat hyperbolae. This pattern is discussed in Chapter 3 and can be considered as the approximated pattern for the more accurate Decca pattern. By using fairly simple formulae, based on the distances between a point on the approximated pattern and Master, Slave and the central point situated in Amersfoort, plus several pattern constants and a map projection constant, the approximated pattern is corrected point by point and the Decca pattern is thus obtained. Fig. 8 gives a survey of the size of these corrections, which makes it clear that the corrections should be taken into account for the map scales which are fixed at 1 : 5000 and 1 : 10.000. However, the problem was whether the pattern to be mapped could not be the flat hyperbolic pattern, so that corrections for map projection could also be included in the correction graph given in Chapter 6; by means of this graph decometer readings are corrected for variations occurring in the uniform propagation speeds of the radio waves which are used in the mathematical pattern. In order to make sure that deviations from the mathematical pattern which occured in practice are attributed only to physical conditions concerning the pattern actually emitted and to the inaccuracy of the reading devices and not to neglecting the map projection, this solution was not chosen. The investigation of such deviations is consequently simplified. In addition, the fact that the Decca lines should preferably connect with the accurate map content of the land area is also an argument for preferring the Decca pattern to the approximated pattern.