Dawes' Limit

It is often said that the Dawes Limit was derived from observations using a 1" refractor. This is untrue, but I often find myself contradicted when I assert that the observations were carried out with a variety of apertures. Dawes' own words on the subject should serve to answer any questions on this score. The following quotation is taken from Vol. 35 of the Memoirs of the Royal Astronomical Society.

It is a point of considerable interest to determine the separating power of any given telescopic aperture. Having ascertained about five and thirty years ago, by comparisons of the performance of several telescopes of very different apertures, that the diameters of star-disks varied inversely as the diameter of the aperture, I examined with a great variety of apertures a vast number of double stars, whose distances seemed to be well determined, and not liable to rapid change, in order to ascertain the separating powers of those apertures, as expressed in inches of aperture and seconds of distance. I thus determined as a constant, that a one-inch aperture would just separate a double star composed of two stars of the sixth magnitude, if their central distances was 4.56 seconds; - the atmospheric circumstances being moderately favourable. Hence, the separating power of any given aperture, a, will be expressed by the fraction of 4.56"/a.