This document details Alan Turing's application for grant support from the Royal Society for the engineering of a special machine to calculate approximate values for the Riemann zeta-function on its critical line. The calculation required summation of a trigonometrical series, and Turing knew of the Liverpool tide predicting machine which performed the summation of a somewhat similar series.
Turing was assisted by Donald MacPhail, a Canadian student engineer then at King's College. They prepared a blueprint which can be seen in the Turing Digital archive. The machine was partially constructed but abandoned on the outbreak of war and never completed. No parts survive.Other links:
The document was quoted in chapter 3 of Alan Turing: the enigma.