I raise the issue myself in my principles classes, because I think the reversal of the
axes is one of the things that throws students off balance (unconsciously perhaps) when
they're trying to assimilate an unfamiliar mode of thinking. Best to get it out on the
table and talk about it up front.
   
I go through the business of Marshall's Principles locking in the reversal and I talk
about how he approached the construction of the demand function: Instead of asking, as
modern economicsts do, "how much can be sold at such & such a price?" he came at it by
asking "if I wish to sell such & such an output, what price can I charge?", which makes
quantity the independent variable. I also make the point that there's not much difference
in the two ways of posing the question.
   
But I've wondered a little bit about WHY Marshall came at the problem from this particular
direction. My own, purely speculative, hypothesis is that the answer reflects a line of
continuity between his work and the classical literature, particularly Ricardo. The
classicals explained price as regulated by long-period cost of production. Where
production is subject to diminishing or increasing returns, cost and hence price will vary
with output. The classicals (at least before Mill) didn't think in terms of a continuous
function linking unit cost to output, but when Marshall, who was trained in mathematics,
tried to put Ricardo into a formal model, the idea of a continuous cost function must have
appeared to be a natural way to proceed. And since he was starting from Ricardo, quantity
would have been the independent variable. Then when he introduced the other blade of the
scissors, he stuck to that perspective.
   
Marshall studies isn't really my area, so I'm not really sure how his thinking evolved,
but I don't think any of the other responses to Avi's query nail the answer down. The
passages from Knight that were quoted at the start of the discussion rightly emphasize the
cost side without tracing the issue back to the classicals, which I suspect is necessary
to solve the puzzle.
   
Nobody here mentioned Whewell (unless I missed it), who modeled demand as a function of
price.
   
Gary Mongiovi