The Back Story

Much is left to inference, but as I understand it the alternative-history backstory of the events in The Difference Engine is this:

In our world, the "primary world" as we'll call it, Lord Byron died in Missolonghi, during the Greek war for independence. In the world of this novel, though, Byron survived his illness there and returned to Britain, where he became the key figure in a revolution, leader of the winning side in Britain's "Time of Troubles." He was on the victorious side of that conflict and became Prime Minister in the 1830s, lived on into the 1850s, ruling until his death.

The losing side in the Time of Troubles consisted of old-order Tories, led by Wellington, allied with Luddites, who were both equally discomfitted by capitalist technologies. The Byronic revolution was a pro-steam engine, pro-technology revolution. It raised to prominence Byron's daughter, Ada, known in primary-world history books as Ada Lovelace, and often described as the author of history's first computer program. But presumably the revolution led her life in an alternative path, so she never wed William King, 1st Earl of Lovelace. She is Ada Byron throughout the novel. (She, too, lives longer in this novel than she did in the primary world.)

Another consequence of the rise of the Byrons and the defeat of the Luddites is the prominence of Charles Babbage, fom whom we get a snippet of interior monologue near the book's end. Babbage  became a crucial figure in the government. Here is the inspiration for the novel and its title. In the primary world, Babbage planned workable computers. He called his earlier plans  "difference engines" and his later plans "analytic engines," but the novel for convenience used the term "difference engine" generically. Ada Lovelace's "program" was designed to run on one of Babbage's engines. If they had had the resources of the whole Empire available to them, and had really been able to create such things -- databanks, credit cards, and a hacker subculture would have gotten a much earlier start.

Mathematicians might even have achieved an understanding of Godel's theorem, and thus the limits of algorithmic achievement, sooner than they did.

The authors have also implied changes from the primary-world timeline in events outside of the British isles. Notably, the US seems to have had its civil war a lot earlier -- apparently during the Andrew Jackson administration. The south won the war, so that by the 1850s there are five sovereigns claiming chunks of what in the primary world is The United States. There is the Northern Union, the Southern Confederacy, the Republic of Texas, French Mexico, and the Republic of California. There is also a large chunk of wild terrain in the northern plains and Rockies, where some key paleontological digs have taken place, once the paleontologists have made the necessary bargains with the Cheyenne.

One critical character in the book is a British paleontologist who discovered the bones of the brontosaurus there, and who has acquired the nickname "Leviathan Mallory" as a consequence.

There is also, blocking off the mouth of the Hudson from control of the Northern Union, the Commune of Manhattan, a conceit that the authors borrow from events in primary-world Paris in 1871. But these are the 1850s, remember, and presumably the forward push give to technology by the Time of Troubles in Britain has sped up a lot of related historical developments.