Eleven Seconds of Arc

Berlin, 14 May, in the observatory at the Academy - spent the day mounting a new mural quadrant and then did something foolish with it: measured the same star twice, an hour apart, without moving the instrument.

The star was Regulus. First transit gave 148° 12′ 40″. Second gave 148° 12′ 51″. Eleven seconds of arc, from a fixed quadrant, a fixed star, and a fixed observer. The instrument did not change. The star did not change. Therefore the error lives in the edge between them - in the act of reading itself.

This is the Königsberg problem wearing different clothes. Strip away the geography: forget that the thing measured is a star, that the measurer is a man with a tired eye, that the brass is imperfect. What remains is a graph with three nodes - instrument, object, observer - and the question is which node carries the odd degree. A traversal that visits every edge exactly once demands even degree everywhere. Eleven seconds of arc is the signature of an odd node. Count the in-degree and out-degree at each vertex: the instrument contributes refraction and flexure, the observer contributes parallax and the tremor of judgment, the star contributes only its light. Two of the three nodes are suspect, and the second reading cannot tell them apart, because the second reading shares its structure with the first. Two structurally identical problems will produce structurally identical errors, and identical errors look like truth.

The escape is to break the identity. Tobius Mayer’s lunar tables, which I have been correcting all spring, fail for the same reason: every determination of the moon’s position was made through the same chain of edges, so the errors of the chain were folded into the moon. Vary the observer, vary the hour, vary the instrument - add a new edge to the graph - and the odd degree announces itself by refusing to cancel.

Tomorrow I will have the apprentice take the third reading, and I will take the fourth, so that the two chains can be compared at the junction. The discrepancy did not close by evening. Regulus stands where it stood, the quadrant holds its division, and the eleven seconds sit between the readings still, unexplained, and I am still watching them.