## 1 Introduction  
The Earth's atmosphere imparts a prismatic effect on incident starlight, producing a spectral angular spread that increases with the tangent of the zenith angle at which the star is observed. At large zenith distances the effect can lead to several arc seconds elongation in the visible band. Figure 1 depicts atmospheric dispersion as a function of Zenith Distance in degrees. Since [PERSON]'s description [1, 2] of difficulties arising from atmospheric dispersion during measurements of the transits of Venus and Mercury, astronomers have been investigating means of correcting it. [PERSON] and his assistant [PERSON] attempted to correct atmospheric dispersion by first introducing various prisms between the eyepiece and the eye, then later by arranging for the planar surface of the plano-convex field lens of a [PERSON] eyepiece to be tilted by rotating the lens about the centre of curvature of its convex spherical surface. The resultant tilted plane surface introduced variable compensating dispersion and as the plane was at the telescope image, where marginal ray heights are zero, the tilted plane did not significantly degrade the telescope image. In modern telescopes, spectrograph slits, fibres, and/or electronic detectors have replaced the eye. Additionally, the angular resolution of telescope images has improved to at least the seeing limit of excellent sites. In the case of telescopes incorporating adaptive optics systems, image quality has improved to near the theoretical diffraction limit imposed by the telescope aperture. There is also, in general, pressure to develop systems with increased bandwidth. The concomitant demand for improved correction of atmospheric dispersion correctors can be seen to have led to the development of three basic types. The first type produces the desired tuneable dispersion in the \"zenith-pointing\" (zero parallactic angle) direction by counter-rotating pairs of Amici prisms. Each Amici prism has glasses selected to match in refractive index at a \"stationary wavelength\" but to have different dispersions. The prisms can be counter-rotated about the telescope's optical axis so that their dispersion directions are aligned, giving a maximum dispersion, or counter-aligned, cancelling the dispersion. The former case is the setting when the telescope is at its maximum observing zenith-distance. The latter case occurs when the telescope points at zenith, and no correction is required. For intermediate pointing angles, the prisms are rotated in opposite directions by equal magnitudes through the range of 0 to \(\pm\)90 degrees, with the bisector of the dispersion direction of the prisms kept parallel to the zenith direction. This arrangement provides a resultant dispersion in a fixed orientation matching the atmosphere and an adjustable magnitude. The prism's angles are determined by the dispersion difference of the materials employed over the observed wavelength range. For the purposes of this discussion this type shall be referred to here as the \"Rotating ADC\" (R-ADC). These systems introduce no monochromatic aberrations if used in collimated light, but if used in converging light, such as f8/-f/15 pencils commonly occurring at Cassegrain foci, or the faster convergence at prime focus, the plane surfaces of these prisms at normal incidence to the optical axis introduce spherical aberration and the tilted surfaces introduce asymmetric aberration. [PERSON] [3] gives a comprehensive summary of the development of such correctors, in both collimated and in converging light, and describes the evolution of design of R-ADCs as they were used in shorter convergence of telescopes at Cassegrain and Prime Focus, which led to the incorporation of prismatic components in curved corrector elements. [PERSON] [4] and [PERSON] [5] give some of the earliest published examples of such correcting R-ADCs for telescopes.