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Difference Engine

Eight columns of figure wheels, after Babbage's No. 2 design. It tabulates a polynomial by addition alone: each column is added into the one before it, so the table never needs a multiplication.

Table to compute

Speed

The columns

Printed table

n	printed	checked

What's checked

✓Every printed value is compared with the polynomial computed directly, as it prints.
✓Wheel addition (all digits at once, then carries rippling up) matches integer addition on 5,000 random pairs.
✓200 random polynomials up to degree 7 tabulate correctly. Textbook starting differences don't on a two-phase engine, which the test also confirms.
✓When a value no longer fits on eight wheels, the check says so instead of printing a wrong number.

A simplified model: real No. 2 has 31 digits per column, and its carry and locking mechanisms are drawn here as plain levers. The two half-cycles and the arithmetic are faithful.