I encountered this story a couple of times when I was younger (back in the '70s or '80s), but I can't find it now. My impression is that the story is pretty old, written in sort of a Lovecraftian style and dripping with atmosphere.
A scientist is invited to visit another scientist who has dropped out of society for several years at the recluse's home, a moldy old mansion in the (New?) England countryside. After a creepy dinner where the food tastes funny, the recluse shows the scientist a machine which the recluse invented.
The machine mainly consists of a chamber with floor, ceiling, and a wide open window in one side. When the machine is turned on, the floor and ceiling of the chamber disappear, replaced with what seem to be repeating copies of the chamber, forming sort of a tube. The upper and lower parts of the tube bend away as if forming a giant ring.
The recluse demonstrates the machine by throwing let's say a right-hand glove into the chamber. It slowly sinks into the lower tube and disappears around the bend, then eventually reappears from above. Only now it's a left-hand glove.
The recluse goes on to explain that sending the glove around the tube again would turn it inside out, and if sent around a third time, it wouldn't come back.
We learn that the recluse accidentally made a trip through the machine several years ago, and can't leave home because all of his food has to be sent through the machine. He reveals a crazy plan to send the other scientist through the tube, then join him in studying the phenomenon. There's a struggle, the recluse falls into the machine again, and we're treated to a graphic description of his final one and a half trips through the machine.
In searching for this story, I came across this website listing fiction stories with mathematical themes. The site has entries for other stories about people being turned into a mirror image (such as Clarke's Technical Error), but I couldn't find an entry for the story that I remember.
