I live in a old house, built in 1867, and have a 100-AMP main breaker that was put in in 1978. Recently I have had an issue with the electricity. One of the two service lines coming into the house will read 10-volts with my multi-meter when the main BUSE fuses are in, but when the fuses are removed the service line reads 120-volts. I have tried shutting off every breaker in the box, one by one, to see which breaker hold the issue, but none of them make the multi-meter read 120-volts. Amazingly enough, the only thing that seems to make the voltage jump back up to 12-volts is when the pump for the well turns on. I did check the connections there, and found the ground wire was carrying the volts and fixed that issue, but was still wondering if there were any other reasons for the low voltage reading. I am not an electrician but I am a willing DIYer.

Try turning off all the breakers and check voltage. Should have 120 between each leg and the ground and 240 between the two legs. Then turn on breakers one at a time, checking voltage again. Not sure why but think you will find something to do with pump breaker.
If that doesn't narrow things down, turn off all breakers then turn one on and check voltage. Turn that breaker off and turn next one on.

Is pump 120 or 240?

Let me add something to my other post. The pump breaker goes to a small box with two fuses before going to the pump, which I believe is typical for most pumps. When I held my multimeter to either of the hot lines and touched my ground it gave me a reading of 120.

The pump is 240. I will try turning off all the breakers and turn them on one by one to see if I get a different reading. In addition just to be proactive I plan on re-wiring any portion of the house that I haven't already since purchasing it three years ago.

Hopefully you got 240 when checking voltage between the two hots.

Okay so I tried turning off all the breakers and then turning them on one by one. I found that the double breaker that feeds the sub-panel in my garage caused a trip. I found the spot where it leaves my house and goes under-ground, with no conduit to the garage. I also found that before it leaves my house, the wires are split and the lines feed an unused out building located at the back of my property. I went there and there was no power getting to the building. I figured the line was cut somewhere and so, I cut the lines at the house, taped them off and pulled them into the house (in my crawl space) and above ground. Turned the power back on and everything was fine, for a couple of days. Still have issues, only now the voltage doesn't drop to 10 volts, it drops to 40 volts. There doesn't seem to be any definite combination that will make the power trip, and when it does trip, the same combinations doesn't always make the power jump. As of the writing of this post, all the breakers except the garage are on, and still have full power to the box. I will next be changing out all of the lines that leave the subpanels that are old, and hope that in doing so I fix the problem without really knowing I did.