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Steve

The vernier is marked in 1 minute increments.  The scale is marked in 20 minute increments

It is therefore impossible to obtain 15°39.9', as the vernier is not marked in tenths of a minute.

The nonius of the vernier aligns very nicely with 15°40'.  When reading the vernier, we find the line which is most closely in alignment with the scale and add the vernier reading to the scale reading.  The nonius line is the zero line.

So we have

15°40' + 0' = 15°40'  <--  this is the right value

Now if you look closely, you will find that the 20' line of the vernier is also aligned with the scale.  So you might think to add 20' to 15°40' yielding 16°, but that would be an error.  It will be easy to convince you otherwise.  Suppose for a moment, that we nudge the nonius 1' back such that it was in between 15°20' and 15°40'.  In that case, you would use 15°20' as the base value and the vernier value of 19'  as the offset, yielding 15°39'.  A one minute rotation of the index arm should not result in a 21 minute change in reading the scale.

This provides us with the basic rule.  Should the nonius align perfectly with the scale, the vernier value is to be zero.  

Brad