Observations from the Earth's surface have to be made through the atmosphere. Although the air is tenuous, it has a refractive index which is significantly greater than 1, the value for a vacuum. When we observe a celestial object at an angle from the vertical the rays are bent slightly away from the path they would have followed if the atmosphere had not been present. The atmosphere clings to the curve of the Earth and it acts rather like a weak lens, making stars appear to be nearer to the vertical than they really are. The largest effect is seen at rising and setting where the horizontal refraction is about 34 minutes of arc. Since the effect is always to increase the Sun's apparent altitude, the length of the day is increased because of it.

Subroutine REFRACT assumes a model atmosphere whose refractive properties depend only on pressure, PR</b.>, and temperature, TR, at the place of observation. The amount of refraction actually observed depends on the detailed disposition of the atmosphere along the line of sight to the celestial object in question, and significant deviations from the values calculated here must be expected in some instances, especially near the horizon. Nevertheless, REFRACT will provide a very good approximation which will be more than adequate in most circumstances.

The altitude of the object is input via the parameter Y, corrected by the routine, and returned via the parameter Q. The direction of correction is indicated by the switch SW(6).