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Does anybody recognize this story? A man fiddles with a time machine, and meets another man. As the story progresses, the man is now the second man, meeting the earlier incarnation of himself.
The story progresses such that from the first person point of view the protagonist is sequentially one of three or four characters he meets.
I recall that when he manipulated the time controls he referred to the "vernier dial."
"By His Bootstraps", a novella by Robert A. Heinlein; first published (as by "Anson MacDonald") in Astounding Science-Fiction, October 1941, available at the Internet Archive. Any of these covers look familiar?
Here's the part about the "vernier dial":
It was a long chore. The further the time button was displaced from the center, the poorer the control became. It took patient practice to be able to stop the image within a century or so of the period he wanted. It was in the course of this experimentation that he discovered what he had once looked for, a fractional control — a vernier, in effect. It was as simple as the primary control, but twist the bead instead of moving it directly.
Plot summary from Wikipedia:
Bob Wilson locks himself in his room to finish his graduate thesis on a mathematical aspect of metaphysics, using the concept of time travel as a case in point. Someone says, "Don't bother with it. It's a lot of utter hogwash anyhow." The interloper, who looks strangely familiar, calls himself "Joe" and explains that he has come from the future through a Time Gate, a circle about 6 ft (1.8 m) in diameter in the air behind Joe. Joe tells Bob that great opportunities await him through the Gate and thousands of years in his future. By way of demonstration, Joe tosses Bob's hat into the Gate. It disappears.
Bob is reluctant. Joe plies him with drink, which Joe (a stranger, from Bob's point of view) inexplicably retrieves from its hiding place in Bob's apartment, and Bob becomes intoxicated. Finally, Joe is about to manhandle Bob through the Gate when another man appears, one who looks very much like Joe. The newcomer does not want Bob to go. During the ensuing fight, Bob gets punched, sending him through the Gate.
He recovers his senses in a strange place. A somewhat older-looking, bearded man explains that he is 30,000 years in the future. The man, calling himself Diktor, treats Bob to a sumptuous breakfast served by beautiful women. Diktor explains that humans in the future are handsome, cultured in a primitive fashion, but have none of the spunk of their ancestors. An alien race built the Gate and refashioned humanity into compliant slaves, but the aliens are gone now, leaving a world where a 20th-century go-getter can make himself king.
Diktor asks him to go back through the Gate and bring back the man he finds on the other side. Bob agrees. Stepping through, he finds himself back in his own room, watching himself typing his thesis. Without much memory of what happened before, he reenacts the scene, this time from the other point of view, and calling himself "Joe" so as not to confuse his earlier self. Just as he is about to shove Bob through the Gate, another version of himself shows up. The fight happens as before, and Bob goes through the Gate.
His future self claims that Diktor is just trying to tangle them up so badly that they can never get untangled, but Joe goes through and meets Diktor again. Diktor gives him a list of things to buy in his own time and bring back. A little annoyed by Diktor's manner, Bob argues with him, but eventually returns to the past, back in his room once again.
He lives through the same scene for the third time, then realizes that he is now free. He collects the items on Diktor's list, which seem to be things a 20th-century man could find useful in making himself king in the future. After returning to the future, he adjusts the Gate to send himself back to a point ten years earlier, to give himself time to establish himself as the local chieftain. Thus he hopes to preempt Diktor's influence, charting his own course instead. While setting the Gate, he finds two things beside the controls: his hat, and a notebook containing translations between English words and the language of Diktor's slaves.
He sets himself up as chief, taking precautions against the arrival of Diktor. He adopts the name, which is simply the local word for "chief" (the etymology is not explained - "Diktor" might be derived from "doctor", "director" and/or "dictator"). He experiments with the Time Gate, hoping to see its makers. Once, he does catch a glimpse of one and has a brief mental contact with it. The experience is so traumatizing that he runs away screaming. He forces himself to return long enough to shut down the Gate, then stays away from it for more than two years. He does not notice that his hair has begun to whiten prematurely, as a result of the stress and shock. Having worn out the notebook through long use, he copies its text into a new, identical, one.
One day, upon setting the Gate to view his old room in the past, he sees three versions of himself in a familiar arrangement. Shortly, his earliest self comes through. The circle has closed. He is Diktor—the only Diktor there ever was. Wondering who actually compiled the notebook, Diktor prepares to brief Bob, who has to orchestrate events to ensure his own future.
Almost certainly Robert Heinlein's By His Bootstraps. The hero experiences exactly what you describe and about halfway through there is the following passage.
He wondered in great exasperation why whoever had built the double-damned gadget had failed to provide it with graduations or some sort of delicate control mechanism - a Vernier or the like.
He ends by promising his earlier self exactly what his later self had said to him at the beginning
"There is a great future in store for you and me, my boy - a great future".
