The most probable position is accompanied with an error ellipse--two-dimensional joint probability density. This theme has been treated geometrically in many reports, and some nomographs are given for two or three observations. In this report it is treated analytically, therefore, the calculation and display of an ellipse on account of many position lines can be done by a digital computer and a plotter. And besides, here is explained astro-fix efficiencies due to azimuths of celestial bodies ; and a new method to estimate observation error from the distance between two positions determined independently or by different persons.