Based on my SN list 902xx likely shipped sometime in late 1906. The dual-caliber barrel stamping ended in the 1907-08 period, so the marking on your barrel is correct. The "U. S. Service Cartridge" is the .38 Long Colt, and indeed at that time it was the official revolver cartridge of the U. S. military. It is slightly shorter and less powerful than the later .38 S&W Special cartridge, so both .38 Special and .38 Long Colt can be used in any .38 Special revolver. You are not likely to see any boxes of .38 Long Colt ammunition on any dealers' shelves as it is essentially obsolete. Almost certainly, your revolver was not in official use or issued by the U. S. military. At that time they used Colt revolvers.