Since the vast majority of Burlington watches were made by the Illinois Watch Co., information about them is contained in "American Pocket Watches Vol. 2, Illinois Watch Co., Encyclopedia and Price Guide," William Meggers, Jr. & Roy Ehrhardt, Heart of America Press, Kansas City, MO, 1985. In seeking information about a watch, it is the serial number on the movement (the "works") that is important.
In addition to printed references, and Russell W Snyder's Data Base CD on Illinois there are Oldwatch.com's Illinois Production Date Chart and the PocketWatchSite's Illinois Date Table which are an online means for determining the very approximate production date of Illinois pocket watches. In general, we think of serial number lists (not just for Illinois, but for other watch manufacturers as well) to only be accurate within a year or two at best, and recognize that there are numerous exceptions wherein which the dates may be off as much as 3 years or more.
Burlington seems to have started up around 1908-1910 and lasted until about 1923-1924. For about the first ten years, Burlington sold mostly 19-jewel watches, a lot of which were marketed as the "Burlington Special." The 1912 ad at the first link shows the classic open-face "Burlington Special" while the hunting-case model is shown in the second link: elginwatches.org/scans/non_elgin_ads/1912/m_05_burlington_special.html
To view, go to the Elgin Watch Collectors Site Home Pageatelginwatches.org, then copy and paste the address in your browser's address bar and click on 'Go'.
Its difficult to know whether to call these watches Burlington Special's or just plain Burlington's. Burlington marketed their 19-jewel watch as the Burlington Special watch, but the only place that the "Burlington Special" marking appeared was on the dial. Thus the question arises, is a "Burlington Special" fitted with a different dial still a "Burlington Special"?
There were several models of 16-size "Burlington Special" made by the Illinois Watch Co.: 21-Jewel Model 5 Sangamo Grade Movement & Its Dial (courtesy of John Cote & his Interstatetime Co.), which, being adjusted to temperature and 6 positions, was widely accepted for railroad service. 19-Jewel Model 5 19-Jewel Model 9 (Please note that the movement in the Model 9's picture is missing its regulator whipspring with its associated mounting and adjusting screws.)
Thank you Fred and Kent for this information about the Burlington Special watch. The watch is away being repaired so I can't give you the S/N at this time. I will post it when the watch comes back.