"The Barrier Moment"

Poul Anderson, "The Barrier Moment" IN Anderson, The Collected Short Works Of Poul Anderson, Volume 4: Admiralty (NESFA Press, Framington, MA, USA, 2011), pp. 307-312. See also here.

The time machine, called the Tempotron, is a "...fifty-foot cylinder..." (p.307). The time projector in "The Little Monster" is also cylindrical. Such details are necessary at the start of a story although the reader hurries on to learn what the author is going to do with the familiar premise this time and soon forget this scene-setting stuff.

The Tempotron is another "time machine" that does not carry a traveler through a period of time but sends, projects or transmits him to a particular other time. A cage of mice appears beside itself. A few hours later, the experimenters strap the original cage to the projector board, throw the switch and are left with a single cage. Once, they tried the experiment of not sending the original cage back - until someone, testing a new hookup, absent-mindedly did project it back.

I said before (see the above link) that this time machine answers a previously unanswerable philosophical question. When I reread the previous post, I had forgotten what that question was so I have reread the story and now remember.