M. Da Pieve:
As mentioned previously specific units records can be found at the National Archives and other locations but there is no overarching serial number database.
For the Trapdoor the serial number indicates that it was made at the end of 1893. Many of these weapons were issued to Volunteer Guard units for the Spanish American War.
On the Colt Navy, the Colt website has a serial number look up:Colt's Manufacturing LLC
This is the information for your revolver:
Year of Manufacture
1851 NAVY (.36 CALIBER WITH NAVAL ENGAGEMENT ON CYLINDER, OCTAGONAL BARREL)
It was made about mid 1863, Here is a interesting article on the use of the Colt Navy over time: Colt’s ‘Old Model Navy’ Revolvers Found a Ready Market in the West (navytimes.com)
Texas Military Forces Museum