For a circular contour, which is one of the methods for indicating an error boundary, the author has studied the conditions for the probability of a ship's position (fixed by two position lines) lying within a 95 per cent circle by probability integration. In this case, the coefficient in the equation to indicate the radius is a function of an intersecting angle and an accuracy ratio between two position lines. The author has examined several accuracy ratios and applied the system to the error boundary of a ship's position fixed by three equally accurate position lines. However, as interpolation involves both angle of cut and accuracy ratio, the process is somewhat troublesome.

In this paper it is shown that the accuracy contour for a fix is an ellipse, whether the accuracies of the position lines are the same or not, and a method is developed to replace an error ellipse for two position lines of unequal accuracy with an ellipse formed by two equal-accuracy position lines. The method is extended to three position lines of unequal accuracy. It then becomes possible to indicate an error boundary by a 95 per cent probability circle.