Difference Engine No. 2

8 COLUMNS31 DIGITSⓘ

Evidence boundary248 wheel states · corrected interfaces · positional interlocks. Not a complete, historically certified replica.

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designed 1847–1849 · Computing

Babbage Difference Engine No. 2

Crank eight columns of decimal wheels that tabulate polynomials, carry digit by digit and print their own results.

Charles Babbage designed Difference Engine No. 2 to tabulate polynomial functions by the method of finite differences. For a polynomial of degree n, the n-th difference is constant, so successive values follow from repeated addition alone. This exhibit models the calculating unit at full capacity—eight columns of 31 decimal figure wheels, one tabular value and seven differences—together with a 30-channel output train, an inked checking copy and two stereotype banks.

The numerical core uses exact integer arithmetic on individual wheel states. Every control—Run, a single tooth or event, a phase, a whole cycle or the hand crank—drives the same forward-only kernel: odd and even differences give off tooth by tooth into their neighbours, warned levers carry from the lowest digit upward, and sectors restore what they transferred. Positional interlocks refuse displaced or disconnected parts. Geometry, tooth profiles, cam timing and the part inventory are provisional research reconstructions; this is not a dimensional or dynamically complete replica, and its fidelity ledger lists what remains unverified.

Babbage designed No. 2 between 1847 and 1849 but did not build it. The Science Museum in London completed an engine from his drawings in 1991 and added the printing and stereotyping apparatus in 2002; that completed assembly is the model’s selected baseline. The nominal 4:1 crank reduction, the page format and the quick-setting controls are educational conventions, as the source ledger records.

Specifications

Method: Finite differences; odd and even columns add alternately
Model registers: 8 columns × 31 figure wheels × 40 teeth
Output: 30 channels to an inked copy and two stereotype banks
Scope: Research reconstruction; provisional geometry and timing

All exhibits

Difference Engine No. 2

Ready at home

Fidelity ledger

This is not a complete replica.

Completed Science Museum assembly baseline

Eight columns, 31 wheels each

All museum components and hidden parts

Successive carry and alternating additions

Verified dimensions and tooth engagements

31-digit exact numerical behavior

Printing and both stereotype banks

Manual/run/step shared state

Crank and camshaft relation

Section, X-ray, select, isolate

All internal save state

Museum mechanical fidelity certification

R2 repairs

Source access and unresolved evidence

Important distinctions

Operate & inspect

1. Initialize at home

2. Drive the same mechanism

3. Follow the transfer

4. Inspect the geometry

5. Save an interrupted operation

6. Know the limits

In the current issue