Work

Difference Engine

project · 1822

Computing Mechanical Engineering Mathematics

The Difference Engine was an automatic mechanical calculator designed by Charles Babbage starting in 1822. It was the first successful automatic calculator and a precursor to the more ambitious Analytical Engine. While never completed in Babbage’s lifetime, it established the fundamental concepts of mechanical computation.

Origins

The idea was born from frustration. In 1821, while checking astronomical tables with John Herschel, Babbage was exasperated by the numerous calculation errors and exclaimed, “I wish to God these calculations had been executed by steam!”[1]

Mathematical tables were essential for navigation, engineering, and science, but they were computed by human “computers” and riddled with errors. Babbage conceived of a machine that could calculate and print tables automatically, eliminating human error.

The Method of Differences

The engine derives its name from the mathematical technique it employed: the method of finite differences. This method can evaluate polynomial functions through simple addition, avoiding the more complex operations of multiplication and division[2].

For example, to calculate successive values of x², one only needs to add increasing odd numbers (1, 3, 5, 7…). This made mechanical implementation feasible with 19th-century technology.

Design and Construction

Babbage designed two versions:

Difference Engine No. 1 (1822-1833):

Difference Engine No. 2 (1847-1849):

Modern Reconstruction

In 1991, the London Science Museum built a complete Difference Engine No. 2 using only materials and tolerances available in Babbage’s era. It worked perfectly, proving the design was sound and could have been built in the 19th century[3].

Legacy

Though the Difference Engine was never completed, it:


Sources

  1. Computer History Museum. “The Engines.” Documents Babbage’s famous exclamation.
  2. Wikipedia. “Difference engine.” Explains the mathematical method of finite differences.
  3. Science Museum. “Charles Babbage’s Difference Engines.” Details the 1991 reconstruction.