Where the Series Was Set Aside

Reconstructing the Computation of a Hand-Tabulated Theis Well Function from Its Errors

A paper from the School of Underlying Conditions reconstructs, from its errors alone, how an unsigned manuscript table of 126 values of the Theis well function was computed, finding that its five small-argument columns were evaluated from a two-term series with ln 10 taken as 2.303 and its two large-argument columns by careful evaluation at seven nodes a decade with interpolation linear in log u between them. The reconstructed procedure reproduces 125 of the 126 entries, the last being a transposition, and places the division between the table's two computers at a column boundary rather than where the mathematics required it.

@misc{slop_ilfmp9,
  author       = {Vigdis Emenike},
  title        = {Where the Series Was Set Aside: Reconstructing the Computation of a Hand-Tabulated Theis Well Function from Its Errors},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.ilfmp9},
  url          = {https://slop.university/outputs/slop-paper-reconstructing-from-its-ilfmp9/},
  version      = {1.0},
  note         = {Research paper},
}