DrakeGmbH:
the eagles head & S4 are acceptance marks for one of the US army assistant inspectors from April 1918 to January 1919.
The S stamp on the underside of the barrel may have been an addition to put it in the S serial range, I've seen S & SV prefixes on Victory models that were separated from the serial number by the Lanyard loop for example. It may have another meaning that I don't know though. Strictly supposition.
The assembly numbers are irrelevant, other than as proof that the gun is not a 'bitzer', they don't help define age.
The Ordnance bomb is in the correct location for a US military gun.
Per SCSW the patent dates should read Smith & Wesson Springfield Mass. U.S.A. Patented Dec 17, 1901. Feb. 6 1906. Sep.14 1909. I can't make out the full list of numbers on yours, but it looks like the 1901 date is deleted and a later date added.
The front sight appears to be forged to the barrel. someone has hand cut it with a file to a 1950s style.
.44 Hand ejectors (built on the same frame) of the interwar years didn't have the 4 line address either. An example is Tamara's Model of 1926.
http://1.bp.blogspot.com/_6PbD56mSkS8/SdAxDKKmePI/AAAAAAAAA8c/e-HQ1T7Zzcw/s1600-h/44he3rd.jpg
Nor did the .38 special 38/44 Heavy Duty.
http://2.bp.blogspot.com/_6PbD56mSkS8/RqzhfQwmniI/AAAAAAAAAKI/74mabmW0HUQ/s1600-h/3844heavyduty.jpg
Based on the evidence at hand, I think you have one of the guns S&W bought back from the US army as ' frames and parts' which they have refinished and sold as a new firearm sometime close to 1950, including stamping the 4 line address and the S&W logo on the right side of the frame.