This is the type of book that comes along all too infrequently. It is good. In fact, it is very good.

Anyone familiar with the subject of difference engines will immediately recognize the names of Charles Babbage, Georg and Edvard Scheutz, and Johann Müller. This book takes a careful look at the difference engines that were either proposed or actually constructed by each of these people and then discusses the background to their construction efforts, the influences each had on the others, and the reasons behind their individual successes and failures. In the process, an incredible wealth of detail is presented, particularly about the Scheutz team. This indicates that a major research effort has gone into the gathering, analysis, and presentation of this story.

The book starts with a short history of tables and table makers. The information mainly comes from the famous 1785 publication of Mathematical Tables by Charles Hutton. This is useful because the original publication is now difficult to locate in any form. I have a slight criticism with some of this material. Hutton made a few errors that Lindgren neither corrects nor comments on. Lindgren also attributes the invention of the slide rule to Edmund Gunter when it might have been more accurate to qualify the term as either “Gunter’s line of numbers” or “The Sliding Gunter.” These small quibbles aside, the introduction is readable. The entire book is heavily annotated, with extensive notes printed at the end. These notes not only give complete references for the statements made in the main text but provide much in the way of extra information or asides about individual topics.

A section on the life of Charles Babbage follows the introduction. It contains one of the best descriptions of the circumstances surrounding the construction of Babbage’s difference engine that I have ever seen--highly detailed, yet easily read. It is noteworthy in that, like most other works on this topic, it discusses the famous dispute between Babbage and his chief mechanic, Joseph Clement; however, unlike all the other works, it actually gives Clement’s side of the story and explains his business and legal responsibilities in such a way as to show that he was anything but the villain that he is often made out to be.

The second chapter concentrates on the main topic of the book, the Scheutz team and the Swedish difference engines. It contains a wealth of detail that is simply not available from any other source. A major topic is an excellent discussion of how the elder Scheutz, during his career as a printer, first learned of the concept of a difference engine. This influenced both the design and construction of the final product. The discussion clearly illustrates that, because of his background knowledge of the printing industry, he was able to short-circuit the many wasteful experiments that Babbage was forced to make. This was one of the major factors that led to the successful completion of their difference engines.

After describing the history and technology of the major difference engines, as well as the inventors themselves, Lindgren goes on to analyze the basic information in an attempt to answer the questions of why Babbage failed in the technical production of a difference engine and why the Scheutz team, while producing three functional engines, failed in an attempt to gain any commercial advantage from this effort.

As a social and technical history, this book is a great success. It not only provides a superb introduction to the whole subject of difference engines by surveying the existing literature but also contains enormous amounts of new historical information and a fine analysis of the influences on the major projects and participants. This book will become a classic and should be on the bookshelf of anyone interested in history.