buckit: When you say under the shroud, I assume you mean under the barrel? The number under the yoke is probably an assembly number, used to track parts in the factory. The serial number should be under the barrel, on the cylinder and on the bottom of the grip frame.
Assuming 387xxx is the serial number, you have a .32 Hand Ejector Third Model, a six shot gun built on the small I frame & manufactured between 1917 & 1942 in the serial number range 263001 to 536684.
Heat treating of barrels began at serial number 321000 in 1921, so I would place your gun in the early 1920s.