There are members much more knowledgeable than I am, but as none have freplied to yr query as yet, I'll try to help. Beginning in 1899, all K-frames were round butt till s/n 58,000 ca November 1904, when the first square butts appeared. Older posts on this section of the forum have included catalog pages showing round butts available in various barrel lengths up thru 1911-'13 or so. The round butt frames may have been made during the first decade of the 20th Century but not assembled into complete revolvers & sold until some years later.
After the factory was returned to S&W control once WWI production of 1917 Army .45 revolvers had ended, production of K-frames resumed but mostly as square butts. Some of the books and other threads on this forum mention certain engineering changes that were adopted on round butts at different times than square butts from approx 1915 to sometime in the mid-20s, but round butts had faded from popularity by the 1930s, until the 2" M&P revived the round butt during that decade.
The 32-20s had their own number series and they also were available in square butts till that caliber was dropped (I think during the Depression). I have no idea on the proportion of frame types in that caliber. In the 38s, we know that the original number series reached 999,999 ca 1942, followed by over 800,000 Victory models. My GUESS would be roughly 200,000 (could be less, or perhaps a few more) could have been round butts out of that 1,800,000+ total. After WW2, the 2" M&P was available in round butt, but I think any postwar RB with a longer bbl would have been a custom order. My opinion is that RBs were made in very small numbers until the SB style was phased out.
Of course, beginning sometime in the 1980s (I think--someone else will know the extat date, I'm sure--I'm not looking at any of the books while typing this), S&W standardized on the round butt style for most production. (One type of frame forging reduces production cost & time.) So the pendulum has swung back to either 1899 or November 1904, depending on how one chooses to look at it.
I hope the above may be of some use to you.
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