For a modern presentation, see https://topex.ucsd.edu/geodynamics/HW3_2010_presentations/C_...
Autographic notes might be found in the vicinity of https://gallica.bnf.fr/ark:/12148/btv1b9061905f/f9.image.r=f...
The closest to a cellar discussion I find in his 1822 book is: https://gallica.bnf.fr/ark:/12148/bpt6k1045508v/f43.item but in this book I only find him working out the zero variation depth, not the depth for six-month temperature lag. Anyone have a title for the cellar paper? (just before giving up I found Mémoire sur la température du globe terrestre et des espaces planétaires, which mentions that one would need a good sampling of local reflectivity and plenty of computation to derive global heating due to insolation.)
related: https://en.wikipedia.org/wiki/Age_of_Earth#Radiometric_datin...
An underground home needs substantial strength to resist the weight of the soil all around it. Concrete is strong and cheap but porus --- not watertight. To make it water tight, you need a sealed membrane that extends all the way under the foundation. Otherwise, water/moisture will be seep up through the floor. Saturated soil surrounding your home will exhibit water pressure from gravity trying to force it into your home. The required moisture membrane is subject to being broken during construction or afterwards from settlement.
Personally, if I was sold on the concept, I would look at the possibility of building up --- not down. Think of a tube open on the ends or a box open on one side but otherwise covered by a mound of soil. The foundation could rest on one big French drain system and this could be extended up the sides as well. This way, the force of gravity can pull water away from the home, not into it.
If you want a waterproof container I'd look into used plastic or fiberglass industrial process tanks (preferably ones that held something not too nasty, so likely from the food industry), dig a hole, do proper compaction and gravel base then plop the tanks in (fill them with water or something so they don't float away) and then pour concrete around them for strength (leaving holes for your vents and doors and whatnot). You're going to have to become well versed in chemistry and construction to prevent all your "rooms" from leaking at the doorways where you have cut holes to join them together.
Checking google maps, it appears that they've finally remediated these structures, but they were in fine condition up until then.