The theoretical determination of a fix from a number of simultaneous, or near simultaneous, positional data has attracted considerable attention during the last five years. A problem is presented whenever the amount of information obtained is more than sufficient to determine the fix, the most common case being when a set of three position lines is obtained. In this instance the size of the triangle of intersection can be used to estimate whether or not the position lines are likely to be consistent with each other; if they are, some central point inside the triangle is accepted as the fix. In doing this the influence of the position provided by the vessel's past history (the dead reckoning position) is ignored; once the fix is decided on, however, a comparison between the two estimates of position may be of value either in enabling a blunder to be detected or, possibly, in selecting some intermediate point as a position from which subsequent navigation should be based. Although the determination of a position from a number of data is, mathematically, a single problem whether these data include the dead reckoning estimates or not, it is usual navigational procedure to consider first the latest positional information. It is the study of this problem that is the object of this article.