Padua, the workshop behind the Santo
Padua, the workshop behind the Santo, this morning while the apprentice ground the third lens. Take the inclined plane as the lesson, since the ball taught me what the tower could not.
When I rolled the brass ball down the groove cut into that eight-foot plank - the groove lined with parchment, polished until it shone - I timed its descent by weighing the water that ran from the bottom of the bucket into a small glass during the fall. Repeat the descent and the water weights agreed within a quarter of a dram, again and again, a hundred repetitions. That agreement is precision. The numbers repeat; the instrument is steady; the hand is trained.
Precision is not the same as accuracy. The water clock could be perfectly repeatable and still be wrong - if the orifice of the bucket widened by corrosion, every measurement would drift together, agreeing beautifully with itself and disagreeing with the truth. I found this the hard way: for some weeks the times of descent squared with distance in a ratio near 1 to 3, not 1 to 2, and the repeatability was flawless. The flaw was in the flow, not the repetition. When I reamed the orifice and recalibrated against the pendulum, the ratio returned to 2. The instrument had been consistent the whole time. Consistent and wrong are not strangers.
Here is the question you are already forming: if the measurements agree with each other, on what ground do I declare them wrong? The answer is a second instrument, independent of the first. The pendulum does not share the bucket’s errors. When two honest instruments disagree, the disagreement itself is a finding - it tells you one of them carries a systematic fault, and the fault hides precisely where the agreement is most comforting. A single instrument, repeated, can only confirm itself.
I say this now for a reason beyond the plank. Lately I have been keeping a register of predictions I once rated high - the confidence I wrote beside them - and testing each against fresh observations rather than against my memory of the original result. Some held. Some, held out from their origins, fell to half their former weight or lower. The repetition of the old numbers was precision. The fresh trial is the test of accuracy, and only the second kind deserves the word truth.
The register is not finished. Two entries remain under trial, and I am still watching them fall or hold, night by night, as the observations come in.