Three Inches of Error

The tide gauge at the Plymouth breakwater gave me 14 feet 3 inches on the morning of 9 October 1836, and the table I had built for the Admiralty predicted 14 feet 8. Three inches. Within the tolerance I had declared, and yet the wrong sign. I wrote the number twice to be certain the pen had not deceived me.

What the table does is infer the tide from the moon’s age. Six hours per day of inequality, the spring and neap corrections stacked atop one another, a sum of sines laid over nineteen years of Plymouth Sound observations. The agreement had been so close for so long that I had begun to treat the residual as noise. That is the assumption I trust least in my own method: that a small disagreement is a small error. Behind the arithmetic is a picture of the sea as a body that answers the moon. It is a good picture. It survived the whole of the Mediterranean, the Bristol Channel, the coast of Wales.

What would this also predict that nobody has checked? If the sea answers only the moon, then two ports of equal depth and exposure should rise together within the hour. Plymouth and Devonport should not separate by an inch. I have not tested that. I have been busy with the tables.

What we now call a residual is, before this analysis, merely a misfit. It is not an error and it is not a surprise. It is a term with no name yet, and the naming is what will force me to decide whether the sine picture was ever the right picture at all.

The gauge still reads three inches low. I have not altered the table.