The Cogwheel Brain by Doron Swade is the story of Charles Babbage and his quest to build the first computer. The book also details how Doron Swade built a Babbage Difference Engine for the 200th anniversary of Babbage's birth in 1991.
Charles Babbage designed 3 machines. His started with the Difference Engine that would use the method of finite differences to generate tables such as logarithms and navigation tables. The computing section of his first design was built although it did not have a printer. Next he conceived and designed an Analytic Engine, which was a fully functioning computer that was programmed by the same kind of punched cards that were used to run a Jacquard weaving loom. In the course of designing the Analytic Engine he realized that he could improve the design of the Difference Engine to make it faster and use less parts. This resulted in the design of Difference Engine 2. Only small demonstration parts of the Analytic Engine were built and the Difference Engine 2 existed only as a set of plans.
I expected the story to be similar to several other computing projects that I have seen and worked with. You know the projects, the ones where the architect keeps jumping to a new idea while the overall project goals get lost and the project overruns for years before it is abandoned. Building the Difference Engine was a lot more disciplined. The core of the first difference machine was built and worked even although it used orders of magnitude more machined parts than any other machine built up to that time. While it did take a long time, given the engineering practices of the day, all the parts had to be made by a single craftsman in a single workshop.
One thing from the book that surprised me is that during the 19th century other difference engines were built by other engineers. Although these machines were completed, they were never successfully used for any purpose. I think this goes to show that the 19th century was not ready for mechanical computing. The book is easy to read and highly recommended.