Johann Helfrich von Müller Builds a Calculator and Plans, But Does Not Build, a Difference Engine

In 1784 Johann Helfrich von Müller issued from Frankfurt a 50-page instruction manual for a beautiful calculating machine that he designed and built: Beschreibung seiner neu erfundenen Rechenmaschine, nach ihrer Gesalt, ihrem Gebrauch und Nutzen. Herausgegeben und mit einer Vorrede begleitet von Ph. E. Klipstein. Müller's calculating machine was based on the principles of Leibniz's stepped reckoner, and could do addition, subtraction, multiplication and division. To this work Müller added a two-page appendix which can be translated as "Further Inventions of Superior Calculating Machines and an Arithmetical Printing Machine." In this he stated that he intended to build a difference engine that could calculate and print mathematical tables by the method of differences. Müller estimated that his device would be capable of one addition per second, and that a table of the cubes of the integers from 1 to 100,000 could be produced by 'a common laborer' in about 10.5 days. 

Charles Babbage, who collected extensively on mathematical tables and calculating machines, owned a copy of Müllers book that John Herschel found on a trip to the Continent.

Muller's original calculator is preserved in the Grossherz Hessichen Museum at Darmstadt.