A confusing subject at best, but I want to give it one more try. Reading RR corner articles, Eueberal/Singer, Winslow bulletin articles, and checking the Ohio corp database with Tom Brown's help, I think it may go something like this.

Whitcomb Metten Ball early 1879
Whitcomb Ball later 1879
Ball's Jewelry 1880-6/85 bankrupt
Webb C Ball 1885 thru 1902?
Ball and Co 1892 thru 1902
The Ball Standard Railroad Watch Co 1897 thru 1914
Railroad watch co 1897 thru ?
Ball Watch Co 1894 thru ?
Norris Alister-Ball Bridges 1902 thru 1930?
Norris Alister-Ball Co 1902 thru 1927?
Norris Alister-Ball Watch Co 1902 thru 1913
The Ball Co 1913? thru 1962?

Official Bureau of Railroad Time service is listed as the prior name for the Ball railroad time service which was listed from 1918 to 1963

adding to the confusion seems to be that many of these companies seem to never have been incorporated and many of the entities were just allowed to expire as they were folded into other partnerships or no longer used.

I think the RR watch co and the Stnd RR watch co were two seperate entities. the one was inc and I don't think it was an accident that the one run is only marked RRWCO without any Ball markings in the 20k serial range and then later in the 90K the mvmts are marked Ball and co.

Note that all the RRWCO and STD RRWCO were all sold to Webb C Ball. I believe that entity acted as the wholesaler to the other entities.

Interesting stuff and fun to research! Not claiming that I am absolutely correct and future information might clarify or contradict.