Worn Eyelet No Bite

To John Herschel, at Slough

The card lacing in the second difference column keeps slipping its knot, and I have spent the morning watching the carry propagate wrong from the seventh figure onward. The lacing is not the fault. The fault is the lace itself: a strip of hide I cut in ‘22, worn smooth now at the eyelets so that it draws through with no bite, and the cards shift a half-thousandth before the pin engages. A fresh lace would hold. The fresh lace would also hide the fault, because a fresh lace holds so well that the half-thousandth never shows, and you would run the engine for a year believing the seventh column sound.

At step 4,102 the expected state of the seventh wheel was a carry of one. The actual state was zero, and the zero propagated forward through every subsequent addition. The mill did not err. The mill was given a card displaced by a worn lace, and it executed the displacement faithfully. Trace the carry backward: the error entered where the card was read, not where the sum was struck.

Here is what the worn tool teaches. It has been operated so long against the same brass that its failure is legible. The new lace will fail too, but at a place I have not yet learned to look, and its failure will be silent because the tool is unproven. The worn lace is a record of every operation it has survived, and that record is the audit.

I began this letter believing the worn part should be replaced before it corrupts the computation. I now believe it should be kept and its wear read as data, and the new lace broken in beside it under observation, not trusted on the strength of being new.