The figure 9 refused to carry

The trial wheels for the seventh column were cut and fitted this afternoon at Dorset Street, and the engine computed two hundred differences without a fault until the third hour, when the figure 9 refused to carry. The wheel showed 9. The wheel beside it showed the old value. Ten revolutions of the test crank produced the same pair: a correct digit standing beside an incorrect one, both true to their own positions, both wrong together.

Herschel’s old objection came back to me across the dinner table at Turin, the question he put to the whole enterprise: how shall you know the figures are right? The answer then was the same as now. The engine prints its result, and the impression is taken directly from the wheels, with no copying hand between. But today’s failure was not a printing failure. The wheels themselves disagreed. Precision is the machine keeping its own counsel faithfully; accuracy is the counsel being true to the numbers the machine was meant to serve. The wheel achieved the first and betrayed the second, and it did so because a single tooth on the intermediate pinion had been cut one-hundredth of an inch shallow. The mechanism performed its wrong operation with perfect regularity. Two hundred trials, two hundred identical wrong answers. A consistent error is the more dangerous error, because it wears the costume of a law.

The specification said: when the wheel passes 9, advance the wheel above. The mechanism said: when the tooth engages, advance the wheel above. The plan was silent about the case where the tooth failed to engage. Find the step where the specification assumed the engagement rather than requiring it. That is where the divergence was licensed.

I had the tooth re-cut by four o’clock and ran the same two hundred differences again. Agreement throughout, to the last figure, verified against the printed sheet. The lesson costs nothing to state and a fortnight to learn: an instrument can be exactly wrong. The shallow tooth cut every figure one-hundredth of an inch from truth, with no drift, no variation, no signature of error at all.

The re-cut pinion engaged on trial 201. The two hundred prior computations are wrong.