What kind of spring ( shape, size, strength, ... ) goes at the bottom of the battery case of a Graflex mod 37 synchronizer anno 1940 to help batteries make contact with the circuit ?

I would salvage the spring from any hand flashlight (torch) that takes size "D" batteries-that should do the trick nicely

Commonly known as "phosphor bronze," the stuff that metal weatherstripping for exterior doors is made from, is an excellent conductor and has enough "springiness" to make good electrical contact, and it's durable. I renewed a contact in my wall oven (220 V) with the stuff, so it should withstand anything that small batteries can produce. Buy a roll of it at the hardware store and you'll have a lifetime supply, and enough of it to play around with different shapes to get the best configuration for your purposes.

Thanks Gentlemen !