This is new pictures to make viewing easier.
http://www.durgan.org/URL/?ZFZLX
http://www.durgan.org/URL/?QHBIN 21 August 2009 How a Potato Plant Grows
There is a great deal of information on the Internet about growing potatoes in tires, boxes and indicating that large quantities of new tubers can be produced with high vertical hilling. The view propagated is that potatoes grow from branches all along the main stalk. This is utter nonsense, as the pictures indicate. New tubers are formed around the seed potato and always slightly above it.

My potato growing test box was opened today. The pictures speak for themselves. Clearly there is no advantage in carrying out excessive hilling when growing potatoes. The purpose of hilling is to insure the tubers are covered, since light affects potatoes producing a green appearance, which is an indication of solanine, which is harmful if ingested in large quantities.. For comparison one Pontiac Red was dug in the same row, which was almost identical to the test box potato in appearance.