Based on the age of the dwelling, it would be my guess the basement is what we call a Michigan basement. It was hand dug and either large stones or non-watertight block were used, could also be joint failure. If that is the case, the cause of the dampness could be seeping thru the floor or the walls. As BRCJR stated it could be a water flow control issue, it could be a high-water table, it could be lack of air circulation or some combination thereof.
Without knowing the source and extent of the moisture, it is difficult suggest a correction.