Re3iever:
If you look at some of the old literature, Ballard came up with their .38-55 in 1884, {which, due to conflicting histories, was either just a lengthened version of their 1876 .38-50, or was the same but just made with their "Everlasting" brass (so essentially it was still just a .38-50, but because of MIBS [More Is Better Syndrome] even way back then, the name made for better copy}, because it had less recoil than the .40 target cartridges which were then popular (.44-75, .44-100, both introduced in 1876 & the .40-63, .40-70, .40-85, .40-90, all introduced in 1881), which were introduced because of their having less recoil than the .45's, which were brought out because they had less recoil than the .50's, although in Ballard's case, they never, as far as I know, made any Big 50's.
It's also interesting to note that Ballard's original .38-50 came about a scant year after Stevens' introduction of their .38-35 & .38-45 cartridges in 1875.
A short time after introduction of the .38-55 in 1884, they introduced their .32-40 for the exact same reason and eventually Stevens got into the act with their .25-25 in 1895, .25-21 in 1897, and taking that line of thought to the extreme, they came out with their .22-15-60 in 1896. To my mind, this was done due to the lack of strength in their 44 series (not their 44 1/2 series) rifles.
While the above relates only to Ballard and Stevens cartridges, Remington, Bullard & Maynard all went through the same shrinking process, as did the shirt-maker.