There are slides devoted to this topic: Lecture 3, pp. 10-33.
For a detailed history and purpose of the Difference Engine, read “The Differential Engine of Charles Babbage” on the History of Computers site. The article discusses the historical significance of numerical tables, and the development, design, and function of the Engine itself.
The Computer History Museum’s short documentary, “False Dawn: The Babbage Engine,” discusses Babbage’s first and second Difference Engines, and the construction of Difference Engine No. 2 a century later.
If you really want to get into the nitty-gritty of the Difference Engine, take an hour and a half to watch Doron Swade’s discussion of “Babbage’s Calculating Engine.” Swade is an engineer and historian – he is, in fact, the world’s preeminent scholar on Babbage and his work – who was the head of the team that constructed Difference Engine No. 2 from Babbage’s designs. Why did Babbage fail to create the Difference Engine? Perceptions of limitations of technology in Babbage’s day are false, Swade says; instead, scientific perceptions of the day, Babbage’s personal hostilities, costs of constructions, and other factors affected the fate of the engines. But could the machines have been built, and would they have worked? Swade provides an overview of Babbage’s character and intellectual activities before expanding on the motivations behind the Difference Engine and the mechanical calculators that preceded it. He explains the exact functions of the Engine and the mechanics within it, comparing its structure to that of modern-day computers. He then discusses the 20th-century construction of the machine and the complications that his team encountered in constructing the Engine.
Can’t get enough of Doron Swade? Then come and celebrate with Swade and Nathan Myhrvold as Difference Engine No. 2 visits the Computer History Museum. First, starting six minutes in, Swade talks about Babbage’s life and his place in Industrial Revolution; Babbage’s vision behind, plans for, and computing innovations in the design of the Difference Engine; and the Science Museum in London’s construction of the Difference Engine No. 2. At around the 33 minute mark, Myhrvold – who sponsored the Science Museum’s construction of the Difference Engine’s printer – speaks on the project’s relevance to modern computing and to his own interests. Afterwards, watch the Q & A with both men and learn more about the challenges in constructing the machine, speculation on why Babbage never succeeded in constructing the machine, why the machine is called the “Difference Engine,” the range of Babbage’s accomplishments (fun fact: Babbage invented the first tic-tac-toe device), the “real” story of Ada Lovelace, and more!
Watch the 15-minute dramatic short film “Babbage.” It provides a pleasurable recap of the inventor’s life and work in the form of a dinner party filled with Babbage’s family and friends – but there’s a sobering twist.