...and why would Kirk need to jettison it in (the excellent episode) "Court Martial?"
As many times as I've seen this, while I was watching the blu ray today at lunch, it occurred to me that I don't really know what one does or why Finney would get caught in it.
The September 26, 1966 Final Draft script for "Court Martial" has a brief comment that explains this a bit--a comment which never made it into the final cut of the episode:
Weatherscan indicated an ion
storm, dead ahead. I sent
Finney into the pod.
That's outside the ship.
It's attached to the skin. One
of our missions is to get
electron readings in abnormal
conditions, such as ion storms.
This can only be done by direct
exposure on ion-sensitive plates.
For what it's worth, there is slightly more exposition in the old novelization for "Court Martial" by James Blish in the book Star Trek 2
. Blish worked from slightly earlier versions of the scripts, so his adaptations sometimes have some content that differs a bit from the final episode. In this case, there's a tiny bit more explanation about ion pods--although I don't know if it was from an earlier version of the script or if it was just Blish's fertile imagination:
"The pod is outside the ship, attached to the skin. One of our missions is to get radiation readings in abnormal
conditions, including ion storms. This can only be done by direct exposure of the necessary instruments in a plastic pod. However, in a major storm, the pod rapidly picks up a charge of its own that becomes a danger to the rest of the ship, and we have to get rid of it."