Babbage Difference Engine No. 2

Babbage's Difference Engine No. 2 tabulates polynomials by the method of finite differences: for a degree-n polynomial the n-th difference is constant, so each new value f(0), f(1), … needs only additions — no multiplication. Eight columns (y and the seven differences Δ¹…Δ⁷) of 31 decimal figure wheels each compute degree-7 polynomials to 31 digits, with negatives held in tens-complement — exactly as the brass machine does.

One turn of the crank = one tabulated value, in four mechanical phases:

① ADD the even columns into the odd ones (Δ¹+=Δ², Δ³+=Δ⁴, Δ⁵+=Δ⁶). ② CARRY ripples through the odd columns. ③ ADD the odd columns into the even ones (y+=Δ¹, …). ④ CARRY ripples through the even columns. Babbage split the adds into two parallel groups to halve the cranking — at the cost of staggering the higher differences in time, which the loader prepares for you. Watch a carry climb a column late in each phase: a wheel rolls past 9, trips its warning lever, and kicks the next wheel one tooth.

Hit X-ray to dissolve the cast iron and watch the inner drive — meshing pinions, the adding racks, and the camshaft the crank turns. Columns glow amber when they receive, blue when they give.

Drag to orbit · pinch or scroll to zoom · X toggles X-ray.