The story I'm looking for is probably late-50's to mid-60's, and may well have occurred in an SF magazine.
"Brooklyn Project" by William Tenn (pseudonym of Philip Klass) was first published in Planet Stories, Fall 1948, available at the Internet Archive (click here for download options).
A professor is demonstrating his new time machine to a scientific audience.
Sort of. Not exactly a professor, not exactly a scientific audience:
Twelve reporters of both sexes exhaled very loudly as he sauntered to the front of the booth and turned his back to the semi-opaque screen stretching across it. Then they all rose in deference to the cheerful custom of standing whenever a Security official of the government was in the room.
He smiled pleasantly, waved at them, and scratched his nose with a wad of mimeographed papers. His nose was large and it seemed to give added presence to his person. "Sit down, ladies and gentlemen, do sit down. We have no official fol-de-rol in the Brooklyn Project. I am your guide, as you might say, for the duration of this experiment—the acting secretary to the executive assistant on press relations. My name is not important. Please pass these among you."
The machine looks like two large spheres touching each other. In operation, one is sent back into deep time (let's say, although my memory has dropped this particular datum, 10 billion years). It will then return to the present, then bounce off its twin and jump back half that temporal distance (5 billion years), return, bounce half again (2.5 billion years), etc. Each trip will take half the time (in present-day units) as the previous, so the whole thing will be over in a finite time.
"That is why you see two spheres on the floor. Only one of them, the ball on the right, is equipped with chronar. The other is a dummy, matching the other's mass perfectly and serving as a counterbalance. When the chronar is excited, it will plunge four billion years into our past and take photographs of an earth that was still a half-liquid, partly gaseous mass, solidifying rapidly in a somewhat inchoate solar system.
"At the same time, the dummy will be propelled four billion years into the future, from whence it will return much changed but for reasons we don't completely understand. They will strike each other at what to us is now and bounce off again to approximately half the chronological distance of the first trip, where our chronar apparatus will record data of an almost solid planet, plagued by earthquakes and possibly holding forms of sublife in the manner of certain complex molecules.
And when the final (Boi-Bo-B-B-Boing!) fades away
XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. Bong--bong--bong
bongbongbongongongngngngggg . . .
he raises his tentacles in triumph and cries, "See? Nothing has changed!"
"See," cried the thing that had been the acting secretary to the executive assistant on public relations. "See, no matter how subtly! Those who billow were wrong: we haven't changed." He extended fifteen purple blobs triumphantly. "Nothing has changed!"
