Babbage's Difference Engine
Babbage's book, On the Economy of Machinery and Manufacturies (1832) was the single most important book in the field of economics between Adam Smith's The Wealth of Nations (1776) and Principles of Political Economy (1848) or Karl Marx's Das Kapital (1867). Both Mill and Marx read and commented on On the Economy of Machinery and Manufacturies. Babbage discussed a wide range of subjects there, ranging from the need for worker ownership (Babbage recommended what we would now call profit-sharing plans), through the need for public regulation of industries where there was a natural monopoly (his example was a water distribution utility), to discussions of the impact of automation on industrial jobs.
We remember Babbage for his work on computing machinery, and in fact, it was his interest in mechanical computing that led him to send his machinists on tours of England and Europe to take jobs in various industries and report back to him on any innovations they observed. It was these reports, apparently, that led Babbage to write his book on economics. He was also Lucasian Professor of Mathematics at Cambridge (a title he shared with Isaac Newton and Stephen Hawking) and a founder of the British Actuarial Society.
In On the Economy of Machinery and Manufacturies. Babbage writes at length about the division of mental labor, and then, deep in this chapter full of digressions, he gives an algorithm that he calls "the method of differences" for computing polynomial interpolating functions, all the while not using that term. This is the foundation for Babbage's difference engines. The challenge reading Babbage is to find the computer science hidden in a river of very wordy Victorian English.
Difference engines based on Babbage's work were built commercially during Babbage's lifetime by George Scheutz, a craftsman in Stockholm, Sweden. One of his engines is now in the Smithsonian (origianally sold to the Dudley Observatory in Albany). Another was sold to the British government and is now in the Science Museum in London.
You can see a brief writeup on the Scheutz difference engines at the Georg & Edvard Scheutz web page maintained by The Computer History Museum.
More detail is availabel in The differential engine of Pehr-Georg and Edvard Scheutz at http://history-computer.com/.