my great-grand father & family had a lumber/mill work business on the Beaverkill - roughly turn of the century. unfortunately I don't have essentially any info on it other than that was their business and they built a number of larger homes/structures/fishing lodges in the area - all but one is gone.
some historical background tho - water mills are limited in how much horse power they generate. a 20 diameter water wheel running 3,000 gallons per minute produces on the order of 10 horse power. and 3,000 gpm is a lot of water -
Watt's early steam engines did not produce huge horsepower either, on the order of 10 hp. and their initial mechanical designs did not lend it to rotary motions (i.e. reciprocating saws yes, circular saws not so easy)
the Corliss steam engine produced more horsepower - 100 hp models appeared in the last quarter - 1875 and later. the mechanics to go from reciprocating steam pistons to rotary motion was well developed by then.
the amount of hp needed for circular saw - single blade, gang saws not considered - varies by species, wet/dry, thickness, etc - but generally in the range of 75-100 hp for "large diameter" blades.
fuel consumption for the mid-century high hp steam engines was huge. this was problematic where fuel was transported by horse&wagon / hand - fuel consumption was obviously much less a problem at a sawmill - just burn the scraps.....
the other thing to consider for that area - logging was big, and logs were rafted down the rivers. they would not likely raft rough sawn lumber down the rivers.... local mills supplied local needs - after the railroads came into the area it would have been more economical to mill onsite and transport rough sawn lumber to market. the railroad arrived in the later half of the 1800's.
the answers likely depend on whether you're looking at early or late 19th century - 1860-ish is about when the railroads came into the area and that would have spurred higher production at saw mills leading to higher hp circular saws.