You may have to take it to a gun smith to find out the caliber. 38 Factory Engraved with Mother of Pearl Stocks. The police Positive came out around 1908 and was made up into the 1970's I think. It falls between the above rounds in length and is the same diameter as the 38 Special. Usually when a Colt is marked DA38 it is a 38 Long Colt. It is also a few thousandths bigger in diameter.
Measure you cylinder and see how long it is. The overall length of a 38 Special is about 1.45".
The frame is longer and also the cylinder to accommodate the 38 Special. Colt also made a Police Positive Special. The trigger guard on your has an elliptical shape that was part of D frame revolvers. That was Colt's version of the 38 S&W, and they are interchangeable. They were marked in a weird manner Colt then Police over Positive, with the bottom of the Police touching the.top of the Positive, then 38 I believe the caliber is 38NP (New Police). That is what would be on the barrel left side.
Colt police positive 38 special serial number serial number#
I believe your gun is a Colt Police Positive 38. is a refined version of the Army Special, which it replaced in 1928 at about serial number 520,000.