Electrical – extend cloth cable with romex

The wires themselves don't have polarity, that only exists within an outlet based on it being wired correctly, or reversed (hot/neutral reversed).

So essentially you just need to identify the hot wires and the neutral wires, and if you maintain this correctly throughout all of the wiring and correctly wire up your outlets, then polarity will be correct.

Non-contact testers are good for determining if there is any power on, but not perfect for finding the hot wire - sometimes neutral wires will give false positives if there is a hot wire in close proximity.

The best tool to use is a multi-meter. The neutral and ground should read 0 (or a very low number), and hot to neutral or hot to ground should give you 120V (assuming your are in North America).

A standard outlet tester will tell you whether the polarity is correct or reversed. If it's reversed, then you just swap the hot/neutral wires.

My house had a fair bit of that wiring. It was apparently available both with and without ground but the ungrounded type is all I have ever seen.

If you arent doing any work on it its probably fine to just leave it alone. If you start doing significant rewiring, adding outlets, or any of the cloth is damaged, its probably time to run new cable back to the electrical panel. In my case, the cloth on most of it had become very brittle and started to flake off if it was moved too much, so if rewiring things I would replace it.

I have slowly replaced most of it in my house when convenient - when we were renovating and had the walls opened up anyways, mostly to get proper grounds everywhere.