Here we survey results on 20×20 and larger squares. As for the 12 × 12 and 16 × 16 cases we show the tours graphically, leaving the reader to put in the numbers and check the magic totals if desired. The numbering starts at the cell marked with a black square and ends at the cell marked with an arrowhead. The cells with black circles mark the other ends of the quarters of the tour. The positions of these eight cells usually help to indicate of the structure of the tour.
The Fairy Chess Review vol.9 no.5 August 1955 p.44 gave a brief obituary of H. J. R. Murray who died on 16th May that year aged 86. The next issue, vol.9 no.6 October 1955 pp.46-47 reported work by H. E. de Vasa who had applied Murray's 16 × 16 method to construct magic tours on boards of side 24, 32, 48 and 64, though space prevented publication of diagrams.
Here is a diagonally magic open tour 20×20 by T.H.Willcocks from Journal of Recreational Mathematics (1968). Both diagonals add to 4010.
Further maerial to be added in due course.