I have an older house with a mixture of grounded and ungrounded outlets. Every room has at least one grounded outlet in it, except one. I've long wanted to run a new cable to that room and at least put a single outlet in it, so that I can stop running an extension cord across the hall. There are no nearby grounded outlets, so I've never figured out a way to do it, until now.
There are three rooms in a row - the dining room, a bathroom, and my wife's office. The office is the room without the grounded outlet. There is a grouded outlet on the wall between the dining room and the bathroom.
Would it be legal / advisable to run a cable from the grounded outlet in the dining room into the hollow of the bathtub, and through the wall into the office? I assume that some sort of extra waterproofing would be necessary, and maybe even putting a GFI into the dining room outlet. The floor joists (inaccessible from below without ripping the drywall off the basement ceiling) run crossways to how I want to run the wire, so running under the floor is difficult, and I have a very short attic (maybe three feet tall), so running it up and over is also difficult. Going through the tub hollow is probably the best bet, if I can do so legally and safely.
I'm in the United States.