Calculating the date and year when a lunar eclipse will fall on the Winter Solstice
A university library in 1947 might have a copy of T. von Oppolzer,
Canon der Finsternisse (1887),
which lists those lunar eclipses on pages 368 and 374.
A reader with a working knowledge of astronomy could make sense of the tables even if not proficient in mathematics or German.

If that reference were not available, a text such as R. Buchanan,
The Mathematical Theory of Eclipses (1904),
would equip the professor to work it out from scratch.
As lunar eclipses are visible from the entire night hemisphere,
they are simpler to compute than solar eclipses,
which are total only along a narrow path.

Eclipses recur in
saros cycles
of 18 years and 11.3 days.
Given dates of some contemporary eclipses,
one could trace
saros 119
back: 1945-06-25, 1927-06-15, ..., 1638-12-21; or trace
saros 125
forward: 1938-11-07, 1956-11-18, ..., 2010-12-21.
The saros numbers were not assigned until 1955,
but the cycles were known to ancient astronomers.