Thanks for your response! It looks more like the first one (it has a really short barrel) but the grip is like the 2nd one.
Okay, sounds like you have a "J" frame Centennial (model 40). The Standard Catalog of S&W only list the serial numbers as 1 thru 30160 from 1952 till 1971.
To narrow it any further (short of getting the letter from S&W) you'll need to look for clues on the gun itself.
1. On the right side of the gun, there are screws holding in the side plate. If there are 4 of them then it was made 1952 - 1955. If only 3 screws then 1955 on. The one that was eliminated was up near the hammer.
2. In 1957 S&W started stamping the model numbers on the forward inside of the frame behind the yoke assembly. It's only visable when the cylinder is opened. If yours has "MOD 40" stamped there then it was made from 1957 on. If not then prior to 1957. There are usually some assembly numbers stamped there as well the serial number on later guns.
3. In 1966 S&W changed from the flat thumbpiece (to release the cylinder) to a more rounded one.
The model 36 in this picture has a flat thumbpiece (also called a "flat latch").
4. In 1968 the diamond shape in the center on the wood grips was eliminated. Of course, that doesn't apply to your pearl grips.
5. In 1971 the serial numbers received a 'L' prefix and in 1974 the Model 40 (Centennial) was discontinued. However, S&W has recently started producing them again.
Hope this helps,