I found a website from Oregon State University on wood ash...can't post a link to it, but it said that the first patent issued in USA was for an improved method of making fertilizer from wood ash. It had the following information that ties to earlier discussions about wood ash...
The fertilizer value of wood ash depends on the type of wood you burn. As a general rule, hardwoods such as oak weigh more per cord and yield more ash per pound of wood burned. Hardwood ash contains a higher percentage of nutrients than ash from softwoods such as Douglas-fir or pine.
"Hardwoods produce approximately three times as much ash per cord and five times as many nutrients per cord as softwoods," said Sullivan.
Ash from a cord of oak meets the potassium needs of a garden 60 by 70 feet, he said. A cord of Douglas-fir ash supplies enough potassium for a garden 30 by 30 feet. Both types of ash contain enough calcium and magnesium to reduce soil acidity (increase soil pH) slightly.