Re: C R Smith & Son Philadelphia age??
I suggest that you start a new thread for your Elgin watch, repeating the pictures. It would be helpful if you could post pictures of the movement (the "works") and markings stamped inside of the watch case (you can ignore any "hand-scratched" characters, they're watch repairers' marks), the clearer and sharper, the better. Clearness and sharpness is important as differences in make or grade can be subtle. Other pictures will help a little, but these are the most important. We may be able to identify it by the shape of the plates. In trying to open the watch, you might find the information in the Encyclopedia article entitled "How To Open A Pocket Watch Case" useful.
Your C R Smith & Son watch looks like a Longines caliber 19/70, a 16-size, hunting-case movement. Checking the references in the linked-to Encyclopedia article, serial number 1600299 was built in about 1905.
Insofar as the C R Smith & Son movement is Swiss, this thread should be moved (by the moderator) to the European & Other Pocket Watches Forum. Once there you may receive so more information from people more experienced with Swiss watches.
If you tell us the markings stamped inside the back of the watch case (or post a picture of them), we may be able to tell you something about it. You can ignore any "hand-scratched" characters, they're watch repairers' marks.
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. 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.
Unless you know that it has been cleaned and oiled within the last few years, you should have the watch serviced before running it very much. It may be helpful for you to read the Encyclopedia article on Watch Service and its related links, especially the one to the message board thread on the subject. The Encyclopedia article on Choosing a Pocket Watch Repair Person may be useful as well.
Please feel free to ask about anything that isn't clear to you.
That guy down in Georgia