On fixing the ship's position at sea, three or more position lines are necessary to avoid an inaccurate position due to accidental errors. Though an error ellipse of astro-fix is defined only cut angles of the lines, we usually reject position lines because of their large error, if the cocked hats are too large. What is the criterion of the rejection. The author goes steps further and introduces a statistical test for the criterion and the least square method for the estimation of accidental errors. Under this treatment the confidential area of the fixed position can be calculated by hand or a digital computer.