The advice my family once got from an electrician on this question was that if you have low amperage service and NEVER touch it, you're probably okay. If you have regular electrical service or touch the circuits at all, remove ALL of it. His basic theory was that if you keep the wires cool, and they haven't caused you trouble yet, it's unlikely to cause a problem. Granted that advice was about 15 years ago and none of that wiring is improving with age.
Once you touch the lines at all, rip it all out. It's very likely that you will introduce a problem between the coating and the wire. The house we were dealing with went another 10 years before we needed to rewire one of the old circuits. Once that happened we rewired the entire house all at once.
If you're concerned at all, turn off the affected circuits, and get rid of it. Better safe than sorry on this one.
The answer changes depending on location.
Because of a complete lack of actual fire incidents, four Western USA States: CA, OR, WA and ID petitioned for an exception to NEC 394.12 and permit insulating over Knob & Tube Wiring. In some places you must first file a Knob-and-Tube Wiring Safety Report, and everywhere else it's a good idea.
It is a complete myth that Knob & Tube must be air cooled. Instead measure the gauge of the wire and put in an appropriate AFCI breaker for the gauge, and you're done. 100 year old copper is just as good as modern copper, in regards to household use. You should remove from the K&T any high load devices. What's left, especially in the era of CFL's and LED's, won't draw enough current to cause a problem.
The insulation of the era was not all that good, and perhaps for that reason K&T does not depend on it. Ceramic tubes will outlast civilizations, and hold the wires apart even if the insulation is damaged.
You can even add an extra margin of safety by underrating the K&T (the opposite of depending on air cooling). For example if you find 12 gauge wire, put a 15 amp AFCI in place, and you're more than done. For 14 gauge wire, a 10 amp breaker might do nicely, even if they look at you funny at Home Depot. Home Depot probably won't have the right breaker, but you can brave DIY scorn at Grainger, or just order online.
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You should, however, replace any fuses. Those are dangerous, even with Type S fuse bases.
Best Answer
Knob and tube wiring uses two separate copper conductors, each isolated by cotton cloth or soft rubber. The conductors are strung tightly through the cavities of your walls and floors, and depend on being separated by air in order to avoid overheating. When going through joists, the wires pass through porcelain tubes. In the wall and floor cavities, they are attached intermittently by porcelain knobs.
Knob and tube wiring was commonly used in North America from the 1880s through the 1930s.