Umm. Here's a 38 Special that shipped in April 1900.Scale would make it more of a good guessing game. No way to decipher the overall length, etc. But, you named the image file "M&P 3rd change #2" so I will go with an M&P, probably .32 since you state it is over 100 years old. .38 started in 1948 I believe, which is less than 100 years old.
Was the 1900 an M&P, or just a .38 special? I glanced at the S&W 4th edition and thought it was stating that the .38 caliber of M&P started up n 1948, but might have read that wrong.Umm. Here's a 38 Special that shipped in April 1900.
And No Peeking at the file name!!!