On the other hand, given no letter prefix to that serial number, it would appear you have a "38 Hand Ejector Military & Police Model of 1902 (First Change, if you want to get picky about it). Those were produced from 1903 to 1905, from number 33804 to 62449.

A dead giveaway to the accuracy of this guess will be the absence of a screw going into the frame (bottom side---in front of the trigger guard).

And just in case it should come up in casual conversation, I wouldn't recommend using "+P" ammunition in it.

Ralph Tremaine

And on yet another hand, given the presence of that screw, we have a whole new ball game, and you may have a 38/44 Hand Ejector---a k a a 38/44 Heavy Duty. They hail from 1930 to 1941, and you can shoot +P ammo in it all day long----+++P too---if there is such a thing.