Brass wheel failed the vernier test

My dear Herschel,

The brass wheel for the second order of differences, cast in London on the fourteenth of July, 1823, failed the vernier test this morning. Joseph Clement finished the teeth to a tolerance of one two-thousandth of an inch. The instrument is precise. Every tooth matches its neighbor within the breadth of a human hair. The metal is uniform. The polishing is exquisite. Yet, when mounted in the frame, the wheel consistently registered a value three arc-minutes wide of the calculated position.

Precision is the repeatability of the stroke. The lathe produced exactly what was commanded. Accuracy is the truth of the position. The lathe produced a perfect replica of a flawed measurement. I spent four hours tracing the carry mechanism backward. I examined the store of parts. I audited the specification for the mounting pins. The error did not originate in the grinding of the teeth or the movement of the mill.

The fault lay in the thermal expansion of the gauge used to set the zero-point. The shop was ten degrees warmer than the drafting room. The gauge elongated. The workman followed the gauge with absolute precision. He achieved a precise result that was entirely inaccurate. The machine functioned perfectly upon a lie. We have built a system capable of repeating a disaster to the tenth decimal place.

I previously argued that the primary risk to the Engine was the friction of the parts. I now believe the primary risk is the fidelity of the initial constants. A machine that is perfectly precise but slightly inaccurate is more dangerous than a machine that is clunky but true. I shall recalibrate the master gauges at a fixed temperature of sixty-two degrees and discard the July castings.