Hi Stephen,
Part II - the Rayleigh & Dawes criteria vs what you can actually see, and optical quality.
The Rayleigh & Dawes criteria concern the closest pair of stars - of equal brightness - that can be discerned visually as not a single star, assuming ostensibly perfect optics. It turns out - with the help of optical theory - that this depends solely on the aperture of the telescope, and the wavelength of the light. See
https://www.telescope-optics.net/tel...resolution.htm In essence, the two central Airy disks overlap and resemble a dog-biscuit, just enough that an observer can say with confidence it is not a circular disk (ie single star). Note there is NO black gap visible between the stars.
Conversely, armed with a list of close bright double stars of similar magnitudes - and there are several - you can test the quality of the optics of your scope in the harsh real world if you are blessed with a night of excellent seeing. I guarantee you will find it very very difficult to split double stars at double the Rayleigh limit for your scope, never mind close to the Rayleigh limit. This also says something about the quality of the refractors available in the 19th century - some of them clearly did have exquisite optics despite the simple eyepieces of that era.
Note however that these resolution limits only apply in the context of two close bright stars of equal magnitude. In other contexts the limits to what you can see will differ - particularly double stars of unequal magnitude - a dimmer star is much harder to see and the minimum separation that can be clearly resolved will be greater than the Dawes limit.
Similarly the moment the subjects cease to be point objects (stars) the Dawes/Rayleigh criteria do not apply - eg observing Jupiter and its moons, or Saturn/Mars/Venus/Neptune/Uranus which can all be resolved in amateur scopes.
With excellent optics it is also possible to see features smaller than the Dawes limit, such as a dark linear feature against a bright background, for example a slender shadow on the moon cast by a crater rim or rille, or Cassini's division and Encke's division in the rings of Saturn.
Optical theory suggests - using somewhat simplistic maths - that a scope producing a wavefront error not exceeding quarter of the wavelength of light will resolve stars at the Rayleigh limit. For a reflector this means the surfaces of mirrors must conform to the required shape with 1/eighth of the wavelength as a defect in a mirror produces a wavefront defect twice as high.
A few telescope manufacturers will guarantee their products meet a specific criterion in terms of wavefront error - many do not.