If the aëroplane or airship were not moving, then two successive observations of the sun, with an interval of an hour or more between them, would give the intersecting circles and fix the position. But the aircraft being in motion, it is necessary to combine the method of "Dead Reckoning" with the use of the Sumner circles, as found by observation of the sun's altitude. In order to avoid drawing the entire circle, a small portion only of it is shown on the chart--so small that it may be regarded as a straight line. Such a small section of the Sumner circle is known as a "position line." The desired track is laid out on the chart, and the "Dead Reckoning" position for the time of the solar observation is indicated on it. The track should be intersected at this point by the position line, the observation thus forming a check upon the "Dead Reckoning." The altitude of the sun or of a star is measured by the sextant. For such an observation to be exact, it is necessary that not only should the sun or stars be viewed clearly, but that a clear horizon, formed either by the ocean or by suitable clouds, should be visible. Corrections must be applied to the observed altitude for the aircraft's height above the horizon, for refraction, and for the diameter of the body under observation--the latter two corrections being given in the nautical almanac. There may be, also, an error inherent in the sextant itself. For extremely refined navigation, corrections are applied in accordance with the direction and velocity of the aëroplane or airship; but these are not really necessary, since navigation of aircraft does not require such close calculation. When the sun or star observed is directly south of the aërial navigator in the northern hemisphere, or north of him in the southern hemisphere, the altitude, corrected for declination of the body under observation, gives the aircraft's latitude. When the navigator is directly east or west, the altitude, corrected for the time of observation, gives its longitude. If the horizon is invisible, owing to fogs or unsuitable clouds, it may be replaced by means of a spirit level; but great care should be taken in making such observations, since a spirit level on an aëroplane or airship is not wholly reliable, unless the craft is proceeding in an absolutely straight direction, and without sway of any kind. All methods of navigation by Astronomical Observation fail when the sky is obscured by clouds and the heavenly bodies cannot be seen. As a general rule this drawback does not hamper air navigation to any great extent, since aircraft should be able to climb above most of the obscuring clouds. Yet it may happen, as it did in the case of our transatlantic flight, that the clouds are too high for such a maneuver.