Assuming this watch has been handed down in your family, you have a nice heirloom!
To add to the good information posted by Rob:
Please excuse me if I repeat some of what you already know, it's easier for me this way. Checking the references listed in the Waltham Watches Encyclopedia article (and to be confirmed upon seeing your picture of the movemwnt - see "How To Open A Pocket Watch Case - Hunting Case"), Waltham movement serial number 8,503,473 can be seen to be
an 0-size Ladies, model 1891,
Seaside grade, unadjusted, pendant-set, open-face movement (placed in a hunting case),
having 7 jewels,
and a Plain Regulator.
The movement is fitted with a single-sunk, Fancy Arabic dial and gilt fancy hands.
It was built in about 1899, give or take a year or so. This was a popular movement of which well over 250,000 of this variation were made from about 1897 to 1907.
Having gathered and printed out information about a family watch, it is a wise idea to write out as much as you know about the family member to whom the watch originally belonged - or as far back as you can go, including (and clearly identifying) what you can guess. Then, add the names and relationships of the family members who passed it down to the current holder. Make up a booklet with this and all of the watch information and try to keep it with the watch. You might even include a CD or, better yet, a USB thumb drive with copies of the pictures or information, in addition to the printouts. Even though they may not be readable 100 years from now, some more recent descendent may transfer the files to the then current format and media. This way, the watch has real family heritage instead of it just being an old family watch, the identity and relationship of the original owner having been lost in the distant past.
Unfortunately, many of the links in our Encyclopedia articles were disrupted when we changed to the current version of our Message Board and its been a long process getting them all reinstated. So, if you come across a broken link, please report it here.
Please feel free to ask about anything that isn't clear to you.