This is the land snail species Thomas Say described twice under different names, the first time as Helix lineata and the second time as a freshwater snail with the name Planorbis parallelus. I already discussed this in a previous post.
Here is a live Helicodiscus parallelus I found in Belt Woods recently. The diameter of this snail's shell was 3 mm. As Pilsbry, citing E.S. Morse, noted in Land Mollusca of North America (1948), H. parallelus is "blind" in that it doesn't have visible eye spots at the tips of its upper tentacles.
Say didn't give figures of his specimens. I don't know if anyone published figures of this species before Amos Binney did, as Helix lineata, in 1857 in volume 3 of his Terrestrial Air-Breathing Mollusks of the United States etc. However, Binney's drawing showing the shell from the side doesn't look like a typical H. parallelus. The spire is too high and the aperture is too descending. Compare Binney's drawing, reproduced below, with my photographs of shells here and in my previous post.