My house was built in 1950. I just found out it is not grounded. I'm a little scared about that, especially when I see my wife with a hairdryer in her hand.
By ungrounded I mean that most outlets only have 2 holes, and there is no ground going into the, well, ground. The electrician said "see those outlets with three holes? Those 3rd holes aren't connected to anything".
You have a black hot wire and a neutral ground as the white wire. If you measure the potential from the white wire to ground it should be zero. I ran a short jumper from the white wire to the neutral tab on the outlets and now you have ground to the ground tab of the outlet. The key to this trick is outside at the meter loop the white and neutral should be bonded together. If you check your circuit, the white and neutral should be bonded in several places, even on the light company pole. They should never be separated.
If the white wire ever goes open, of course the outlet would quit working, but you would be in danger because electricity is always looking for a path to ground and the white wire was it until it became open. Then the 3rd wire would serve as protection to keep the juice from flowing through you. If you don't have a 3rd wire to ground, you are in danger. In real life, however, the white wire will work. Adding a 3rd wire would be prohibitive just for this slight chance you need it. The bond outside is the key. It MUST be ZERO ohms.
I worked as a phone installer/repairman for 30 years and we bonded to the light company neutral for our ground. I disagreed with this practice, but was forced to by the company. I have seen the light company neutral become hot and smoke our stuff. The protection is outside with a ground rod bonded to the company neutral. That gives a path to ground BEFORE entering the house.
The 3rd wire is just another path to ground, but if things go wrong, ( corrosion, ants, damage to the wire, etc), the 3rd wire is still useless. It is just a redundant safety requirement that helps, but isn't fool proof.