Astronomical refraction: Computational method for all zenith angles

It is shown that the problem of computing astronomical refraction for any v alue of the zenith angle may be reduced to a simple, nonsingular, numerical quadrature when the proper choice is made for the independent variable of integration. The angle between the radius vector and the light ray is such a choice. The implementation of the quadrature method is discussed in its g eneral form and illustrated by means of an application to a piecewise polyt ropic atmosphere. The flexibility, simplicity, and computational efficiency of the method are evident.