The running fix or sight-run-sight fix is a classic problem in celestial navigation. Methods employed to obtain the fix traditionally involve advancing a Line of Position (LoP) taken at an earlier time and crossing it with one obtained later. Attempts to generalise the operation of advancing an LoP when the Earth's surface is represented by a plane to the case of the sphere have resulted in proposals that contain poorly constrained approximations or are otherwise fundamentally flawed. A simple rapidly-convergent iterative procedure to obtain a running fix is described that avoids the notion of advanced LoPs and is readily applicable to both the sphere and ellipsoid.

K. H. Zevering has recently proposed a way to calculate the position of a moving observer, from the intersection of position circles, that differs from the methods hitherto accepted by mariners1. Zevering concludes, from discrepancies between his own results and that of other methods, that those others are in error. However, the discrepancies result from incorrect assumptions in his proposed method, which give rise to erroneous answers. My comments will be restricted to the simplest case of two observations only, and will assume that the Earth is, for our purposes, spherical.