Though the foregoing information merely embraces a few general principles and facts, the reader will have no difficulty in understanding that refraction exercises a very inconvenient disturbing influence on observations which relate to the exact places of celestial objects. No such observations are available for mutual comparison, however great the skill of the observer, or the perfection of his instrument, unless, and until certain corrections are applied to the observed positions in order to neutralise the disturbing effects of refraction. In practice this is usually done by means of tables of corrections, those in most general use being Bessel’s. Inasmuch as refraction depends upon the aqueous vapour in the atmosphere, its amount at any given moment is affected by the height of the barometer and the temperature of the air. Accordingly when, for any purpose, the utmost precision is required, it is necessary to take into account the height of the barometer and the position of the mercury in the thermometer at the moment in question. At the zenith there is no refraction whatever, objects appearing projected on the background of the sky exactly in the position they would occupy were the earth altogether destitute of an atmosphere at all. The amount of the refraction increases gradually, but in accordance with a very complex law, from the zenith to the horizon. Thus the displacement due to refraction which at the zenith is nothing and at an altitude of 45° is only 57″ becomes at the horizon more than ½°. One very curious consequence is involved in the fact that the displacement due to refraction is at the horizon what it is; the diameter both of the Sun and Moon may be said to be ½°, more or less, so that when we see the lower edge of either of these luminaries just _touching_ the horizon _in reality_ the whole disc is completely _below_ it, and would be altogether hidden by the convexity of the earth were it not for the existence of the earth’s atmosphere and the consequent refraction of the rays of light passing through it from the Sun (or Moon) to the observer.