The barrel serial number is usually stamped on the bottom of the barrel assembly right where it mates up to the frame. And the frame number is typically right across the joint from that.
If it is not there, it is most likely a replacement barrel that someone had cut down to make a "Sheriff Model" out of it.
Regarding Three Hawks above response, I wonder why he doesn't want to recognize that the high officials also have retarded daughters that need gainful employment. Come on now, this is the age of equal rights regardless of age, gender, IQ or number of legitimate parents. Please be Politically Correct, else the ACLU might get after your case. If they don't some other alphabet group might.