Problem, find the logarithm of 581.1
Place the Vernier Cursor at 581 and ease it right a bit, until the 1st vernier line is over a number (in this case 581)
Observe that the spiral line this number is on sits between coils 7 and 8, so the first digit of the mantissa is 7. This is the first digit of the mantissa
On the logarithm scale, read the mantissa as .7 642 and the vernier in my case reads 2, which is .1 of a tick. Add that to the end of the mantissa .76421.
The characteristic is log 100 = 2, and the complete result is 2.76421. The correct value should be: 2.76425. I attribute the reading error to a problem with alignment of the vernier in my homebuilt version.