You said it's not knob & tube, but it's old. I have only seen knob & tube, BX cable or sheathed electrical cable. Was there a type of wiring used between K&T & BX? Seems as if you would only need a third wire if you had knob & tube. (with BX you can ground to the box.) What type of wiring do you have? What is it sheathed in?
I'm not an electrician (obviously) - but I've remodeled a lot of houses. (nothing from after the 50's though) I suggest you find an electrician forum or ask a professional.
I'm not endorsing your plan to add an earth ground because I don't know the answer - but Ron & bc did not explain why you CAN'T do it. If you look into an electrical panel, you see that a sheathed electrical cable ground ties directly into the Earth Ground. You sometimes also see a ground tied into copper plumbing (e.g. disposals, furnaces, jacuzzis) That doesn't seem any different than what you're proposing.
Ron & bc are probably right that it wouldn't pass code - but that doesn't mean it's not going to work. Code is written not only for everyday safety, but also as a standard. This would definitely not be standard - however, that doesn't mean it isn't safe. (I'm not saying it IS safe, either.)