Alfred Cornell had some sort of working relationship with F.Davidson. I have never come across an extant example of a Cornell instrument but there are patent drawings in existence showing both Cornell and Davidson's names on them, that picture the same instrument as mine. The one pictured in the 1912 patent is a more modern version. It seems that while Cornell may have been a designer, that F. Davidson was the maker. The design in the 1912 patent link , may never have been made. The Davon #2 is a field instrument and is unlike either.
The # 1, had actually 5 different telescope attachments of differing focal lengths. It seems you continued to use the same microscope objective lens with them. The patent is 13251/12, so carries the same # as the 1912 patent above but various versions of the instrument exist, some of them appearing to be at least to the turn of the century, so the design had been in existence for some time.
F.Davidson made a number of microscopes, and seems to have had a preoccupation with stretching the boundaries of what had become the base microscope principle. They had the Micro-camera, that incorporated a 4 x 5 camera back and bellows in place of the microscope tube and eyepiece of the Micro-telescope. https://www.antiq-photo.com/en/collecti ... ography-2/
They had a folding portable micro-telescope, and a super microscope https://americanhistory.si.edu/collecti ... ah_1349425
. The latter, appears to have an extra set of focusers in the optical tube, presumably to focus a set of lenses on the objective image; something akin to an image multiplier, used on various modern scopes.
Getting back to the original post. John Browning was a respected optician and manufacturer, making instruments on The Strand, as early as 1872. The original instrument in the thread, has appearances of having been made earlier than the Davon instruments. Since Browning made most of his reputation with spectrometers and nautical instrumentation, it's possible that he either made the base instrument for or sold the design of his early microscope to F. Davidson, upon which they based a few of their oddities and sought to improve upon them.
As far as a price for your Browning Instrument. I would start at about 150 sterling , in an auction style format and see how it goes. It is cased and is in nice condition but no accessories. Small instruments with no accessories often aren't that interesting to collectors, unless there is a specific interest.