Tom Frederick, your Police Positive probably takes 32 Smith & Wesson Long, which at one time was also known as 32 Colt New Police, mainly because Colt did not want to put S&W's name on a Colt revolver. See how the barrel is marked. (Also, see my PPS below. If your gun is a Police Positive Special, there is some chance it is chambered for .32-20 WCF [Winchester Center Fire], which is a whole different ball game.)
Older Colt revolvers used 32 Long Colt, which is long out of production and hard to find. To me, the hard rubber grips combined with the shape of the cylinder release suggest your gun was made in the 1920's, and that is too late for it to be 32 Long Colt, fortunately.
As for value, it all depends on whether the bluing on your gun is the original factory finish. If it is, you have a fairly valuable gun there, because it seems to be in very good shape. A close up of any stamped markings, like the caliber on the barrel or the Colt trademark on the frame, would help people here tell whether the finish is original or not.
I can't give you a dollar figure myself, because I am not familiar enough with current values. And all the rest of the above is just my $.02 as well, of course.
PS - If your gun is 32 S&W Long / 32 Colt New Police, then 32 Smith & Wesson (the short version of the Long cartridge) will also fit and fire safely, but it is extremely low-powered, so there is little point to it, IMO.
Also, thanks for putting up good pictures! It's a handsome gun, and a pleasure to see.
PPS - I almost forgot. There are really 3 different types of Colt Police Positive: the Police Positive 32, the Police Positive 38, and the Police Positive Special. Confusingly, both the 38 and the Special were made in 32 S&W Long, and the Special was also made in a non-interchangeable caliber called .32-20 Winchester Center Fire. What are the barrel model and caliber stampings?
If you get the model nailed down, you can try to look up the year of manufacture at this website:
http://proofhouse.com/colt/
Sorry to have made things confusing!