[glenc (Glen)]

I have been trying to establish working magnitude limits (WML) for the southern deep sky catalogs produced by Lacaille in 1751-52, Dunlop in 1826 and John Herschel (JH) in 1834-38. I defined the WML as the magnitude where they saw half the objects in a modern catalog and missed half of them.
For example JH saw half the galaxies in the Principle Galaxy Catalog (PGC) brighter than magnitude 12.7 and he missed half the galaxies brighter than 12.7. Dunlop's WML using the PGC is 10.9. Lacaille only saw one galaxy (M83 = mag 7.1) so I used globular clusters to find his WML = 6.4.

It turns out that the WML is about 85% of their magnitude limits for stars.
Their star mag limits are L=7.6, D=13.1 and JH=15.2.

This suggests that we can comfortably (or easily) see deep sky objects to magnitude [9.1 + 5log(D)] x 85% where D is the aperture in inches.
The WML for a 12" is 12.3. We can see fainter objects but they are not obvious when sweeping.
(Some more WML are 8" = 11.6, 10" = 12.0, 16" = 12.9 and 20" = 13.3)

Does anyone have any suggests or comments on how to define or find a WML? Does the above sound reasonable?