When I was in college, I had an instructor who taught me that the turning errors in a magnetic compass were due to a counter-weight installed on the south side of the compass that was intended to counter the magnetic dip on the northern side.
This makes sense for both acceleration and turning errors.
For example, flying east the weight would be on the right, south-facing side, of the compass, which is the side labeled as 'N'. Now imagine a straight line acceleration...
The heavier, right side, would move rearward in relation to the aircraft due to its inertial lag, bringing the, weighted, southern side of the compass (which reads north) closer to the compass window causing the viewed indication be a number closer to north, making the "accelerate north" error, true.
This same idea also holds true for the north and south (Lead North, Lag South) turning errors because the weighted side of the compass would basically fall to the direction of bank.
Edit: (This is false, and the weighted side would not 'fall')
For example, flying due north, the south side of the dial, marked north, is facing you and is weighted to counteract the downward pull of the north pole on the north-facing side of the dial. If you turn right, the side facing the pilot would fall to the right, making the dial spin counter-clockwise, and a right turn would ultimately make the dial spin in that direction anyway to indicate east causing the "lead north" phenomenon because the weight made it swing around premature to the actual turn of the aircraft.
The thing is, I have never seen this explanation on paper, just that it is "magnetic dip" error. Is it true, and can you find a source that says so, or was my instructor wrong?