It is difficult to get satisfactory noon observations when the zenith distance is very small, because the Sun is rapidly changing in azimuth, the sextant must be swung through a wide arc of the horizon, and the Sun only dwells at the highest altitude for a very short period. To avoid these difficulties it is suggested that, instead of trying to measure the altitude of the Sun, one should measure its distance from a point on the horizon in a known azimuth. To make this measurement the Sun is brought down to the required point on the horizon, tilting the sextant as necessary; we shall distinguish this type of observation from the normal one, made with the sextant vertical, by calling the angle so obtained the horizon distance. At normal altitudes this method, however sound in theory, breaks down because one cannot measure the azimuth with sufficient accuracy. However, at very high altitudes the rate of change of horizon distance with change of azimuth of the point from which the distance is measured becomes so small that it is not necessary to know the azimuth with such precision. In fact, at a zenith distance of 1°, the largest we shall consider here, the greatest error caused by an error of 1° in the azimuth is l″, and for smaller zenith distances the maximum error is proportionately less.