While working at a piano dealer in Manhattan, one of my co-workers
(a tuner/refinisher), told me of a book he had come across, from the
turn of the century (late 1800s to early 1900s).  In it were formulas
for various everyday solutions and mixtures used in manufacturing
products for industry and the home.

One of those mixtures he had come across was for furniture refinishing.
I can't recall what the mixture contained for sure, but it most likely
contained denatured alcohol along with an agent that slowed down its
evaporation rate.  He in turn approached the Ford Piano Supply House
with the formula, and they in turn went about having it made and
subsequently added it to their product line.  It was marketed as
"Check-Eradicator".

The liquid was applied judiciously to the alligatored/checkered piece
of furniture (care being taken to have the piece of furniture laying
flat, or otherwise as the finish became reconstituted, it would melt
and run) and as the finish softened up, you could take a brush and even
out the finish.  If there were any noticeable uneven areas after the
finish had re-hardened, it could be evened out by rubbing and polishing
as you would a new finish.

Checking or alligatoring  was and is a problem with mainly shellac or
varnish finishes, where over time the oils within the finish have
evaporated causing the finish to shrivel or check.  Hope this helps.

Sincerely,
Dale F. Rowe
Bronx, New York