Hello Tony
Though by no means an expert on Railroad Grade Watches, I have done some extensive reading about them in a few watch oriented reference books. What I gather from my reading is that a serious railroad wreck in 1891 near Cleveland, Ohio causing loss of life and a high property loss cost in goods and most especially in mail, caused the creation of a committee to address the issues of shared trackage rights, scheduling and time keeping. This committee issued its report in 1893, which was universally adopted by all Class A railroads in the country, and many of the lessor railroads as well, not to mention eventual acceptance, at least in parts, by railroads around the world. Established by this committee was the critical need of precision time keeping, along with a series of recommendations concerning how this could be achieved.
Fortunately, the American watch making industry had well matured before this point in time, so that their Horological science & technology was already well up to meeting the requirements newly being imposed. In fact, the best-known brands of American watch makers had been making watches capable of meeting these new standards for decades already, though they only made watches of that quality in their highest grades, at their highest prices, and so the run of the mill pocket watch of the day was not generally up to those standards. With the issuance and adoption of that report, the primary watch manufacturers started specifically identifying those grades of watches that would meet the new standards and thus was born the Railroad Grade Pocket Watch.
The new requirements imposed by the committee's report needed a size 16 or 18 watch that was open face with Arabic numerals every five minutes at least, lever set with a twelve o'clock stem, temperature and five position adjusted to within 30 seconds a week, with a minimum of 17 jewels, along with several lessor technical specifications that needed to be met. Perhaps of greatest importance was the establishment of the position of "Time Inspector" with each railroad to come into compliance with the new standards. The time inspector was charges with making sure all the individual time pieces in use by the railroad were within the specifications of the requirements and properly set.
For most of the railroads in America, the Engineer's and Conductor's time pieces were not company owned but rather were required to be purchased by the employee themselves from the various approved manufacturers and grades available. But the railroad was required to assure that those time pieces were in proper adjustment, and when they were not, have them sent out to authorized watch repairmen (some railroads employed their own) for adjustment or repair. When this occurred, the railroad did own a few such time pieces that were then loaned to the employee until their own time piece was returned in proper order.
The watch companies themselves continued offering these same higher grade watch mechanisms to the general public, sometimes promoting them as being accurate enough to meet the stringent railroad requirements to help justify their higher prices. Thus, any individual could purchase a "Railroad Grade" watch. The norm at that time was for the customer to purchase the mechanism and the case separately, so as to best meet their own needs and desires. So, a watch found in a lighter and possibly fancier case was likely sold to a "civilian" while one found in a much sturdier and probably plainer case would very likely have actually been used on a railroad by an engineer or conductor.
Apparently, the last known sale of an American Railroad Grade Pocket Watch was a Hamilton in 1969?!?!
As an aside, your Waltham "Premier" is a very high grade "top of the line" watch .... NICE!!!