Uh... the secondary loops.
Separate but concentric secondary loops Faraday via Maxwell: "The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop." With concentric secondaries the rate of change is equal on all sectors. Gibbs's red circles will each have the same induced emf because all sectors of these loops are normal to the changing magnetic flux. On the rectangular secondary there is a decrease in induced emf, not because the area of the loop has changed but because not all of the secondary conductor is normal to the changing magnetic flux. If you distort that rectangular secondary into a nice round loop, the same amount of emf will be induced as each of the above two red circles. Here is where we get into trouble by considering 'potential differences' between any two points around the secondary'. AND  Where we run into the contradiction That is my take on it!

"As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality."  Einstein
"What we observe is not nature itself, but nature exposed to our method of questioning."  Werner Heisenberg
