This first example is a 3 digit computation, ignoring the vernier for now. The way that Macdonald assumed you'd use this calculator is that you'd be holding onto the (rigid) vernier casing in one hand, and spinning the disk and managing the index with the other hand. I follow his algorithm in these examples.
ZERO the disk; also line up the index with origin on disk
CONNECT the index
Rotate disk left until 9504 is under the vernier ( the 4th line on the vernier lines up with the tick at 954). Record 1 in the characteristic dial, 9.5 on the mantissa dials.
LOCK the index
ZERO the disk
CONNECT the index
Rotate disk left until 7512 is under the vernier (the 2nd vernier line is on 753); Add 1 in the characteristic dial, add 8.5 on the mantissa dial s (9.5 + 8.5 = 18. 18 - 10 = 8 is recorded)
LOCK the index,
ZERO the disk ,
CONNECT the index
Rotate disk left until .8701 is under the vernier (vernier line 1 is over 871, the coil is 9 add 9 to the mantissa dials, 8 + 9 = 17, 17-10 = 7; add 1-1 to characteristic)
LOCK the index
Rotate the index back to 1000; read the answer on the vernier 622.3, on coil 7 (stored in mantissa dials). I obtained 622.1 which I suppose is within tolerance, given how sloppy my ow careless my SR handling is.
NOTES: Here you see how the index is used to accumulate interim results of a computation.