Many texts stress the need for marine sextants to be held precisely vertical at the instant that the altitude of a heavenly body is measured. Several authors lay particular emphasis on the technique of ‘rocking’ the instrument in a small arc about the horizontal axis to obtain a good sight. Nobody, to the author's knowledge, however, has attempted to quantify the errors involved, so as to compare them with other errors inherent in determining celestial position lines. This paper sets out to address these issues and to pose the question: what level of accuracy of vertical alignment can reasonably be expected during marine sextant work at sea ?

When a heavenly body is brought to tangency with the visible horizon it is particularly important to ensure that the sextant is held in a truly vertical position. To this end the instrument is rocked gently about the horizontal so that the image of the body describes a small arc in the observer's field of vision. As Bruce Bauer points out, tangency with the horizon must be achieved during the process of rocking and not a second or so after rocking has been discontinued. The altitude is recorded for the instant that the body kisses the visible horizon at the lowest point of the rocking arc, as in Fig. 2. The only other visual clue as to whether the sextant is vertical is provided by the right angle made by the vertical edge of the horizon glass mirror with the horizon. There may also be some input from the observer's sense of balance and his hand orientation.