Euclid's C-Finder location
You can locate the field "gun" for the ARCHIMEDES weapon by entering the Freeside's East Gate and locating the two children chasing each other (not chasing the mutated rat) during daylight. Talk to the one possessing what appears to be a toy gun. You can purchase the gun for 1,000 caps or 20 caps with Barter at level 45 or greater. To use the weapon you must supply the power to ARCHIMEDES II during the "That Lucky Old Sun" mission.