> "Androcles believes that it was impossible for Urbain Le Verrier
> to observe that the precession of Mercury was 566 arcsec per century"

Correct,  Urbain Le Verrier (1811-1877) didn't observe for a century,
 he was dead after 66 years. Therefore it was impossible. I doubt
he did any serious observing until after the age of 16 at the earliest,
so he might have observed for half a century and wrote it up on his=20
deathbead.