I’m interested in knowing what “jack looms” are. As you can tell, I’m a beginning weaver.
You might be a new weaver, but your question is a good one. Jack looms are sometimes mis-named “rising-shed” looms (a shed doesn’t rise; a shed opens). Jack looms open sheds by making some of the shafts go up. Counterbalance and countermarch looms open sheds by making some shafts go up while the others go down.
The difference is in the shed mechanism. Jack looms have “jacks,” or pivoting levers, a pair at the side of each shaft (either below to push it up or above to pull it up). When you step on a treadle tied to raise a shaft, the levers are pulled down on one side, the other side goes up to push or pull the shaft up.
There are advantages to jack looms (you only tie up the shafts that rise; you can tie up any combination; you can step on more than one treadle at a time) and disadvantages (the shafts usually place greater tension on the raised threads than on the threads left down; and the shafts can be heavy to treadle, especially on wide jack looms).
As far as we know, jack looms are a recent invention. I’ve heard credit for the invention given to both Mary M. Atwater and E. Everett Gilmore, she the advisor and he the inventor, sometime in the 1930s, but this invites further research.