It was long ago that I first read H. Beam Piper's 1948 story with the above title, I've read it from time to time over the years, and I read it again with enjoyment recently. It was one of his first published stories, but he was already 44 at the time, and it seems to me higher in quality than much of his other output, although it takes the unusual form of an exchange of correspondence, rather than a conventional narrative.
It considers the well-known mysterious disappearance in 1809 of Benjamin Bathurst, a British diplomat passing through Prussia, who disappeared during a coach stop and wasn't seen again. This is a genuine event known to history, although the real Bathurst was 25 years old and was probably murdered and robbed, at a time and place when this wouldn't have been surprising or unusual.
Piper's Bathurst is in late middle age, for reasons known only to Piper, and finds himself transported to an alternative world, in which the American and French Revolutions both failed. The interaction between him and his new world is then described by means of letters between Prussian and British officials.
The point at which the alternative history diverged from our own occurred during the American Revolution, when Benedict Arnold was shot dead near Quebec, and was therefore not present at the Battle of Saratoga, where the British forces under Burgoyne went "through Gates' army like a hot knife through butter", and then went down the Hudson to join Howe.
I'm not a student of the American Revolution and have never before bothered to look up the Battle of Saratoga. Doing so now, I'm rather disappointed. There were probably tipping points in the American Revolution at which something small could have made a difference, but it seems to me that this battle wasn't one of them.
Burgoyne was simply too ambitious. He had already taken casualties and was facing a superior force in difficult terrain, but he decided to attack that superior force in a prepared defensive position. This is something that you just don't do, unless you have a death wish. I don't think it mattered whether Arnold was there or not, Burgoyne was doomed to lose. I don't know whether he was gravely misinformed about the opposing force, or just insane. As it happened, he survived the battle (unlike many of his officers, who were picked off by American riflemen), but his career was dead, and likewise British hopes of retaining control of the colonies.
Sadly, I think Piper's alternative history is a non-starter as given, although one could surely find more plausible ways for the American Revolution to fail. As for the French Revolution, I know even less about that, and couldn't say whether it might have been easily stopped.
In the alternative history, there's another Benjamin Bathurst who is the King's lieutenant governor for the Crown Colony of Georgia. Napoleon Bonaparte is a Colonel of Artillery and a brilliant military theoretician, whose loyalty to the French monarchy has never been questioned. Cardinal Talleyrand is regarded by Sir Arthur Wellesley as being "the sort of fellow who would land on his feet on top of any heap". I'm fond of alternative history; though I do like to see a well-chosen, elegant, and plausible point of divergence.