Why is a "fountain pen" so called?

I was accused of using a fountain pen the other day (guilty as charged). Does anyone know why it is called so? The mess of ink I get on the page, the table, my person, etc when refilling it is certainly voluminous but can scarcely be described as a fountain.

The earliest meaning for fountain shown by the OED is:

A spring or source of water issuing from the earth and collecting in a basin, natural or artificial; also, the head-spring or source of a stream or river. Now arch. or poet.

and a later meaning is "reservoir". When fountain pens began to be used, most pens were a quill only and had to be dipped into an inkwell every few words in order to replenish the ink. Hence, the new style of pen was called a fountain pen since it included a reservoir.

Last time, the pens were what is called, a "dip pen". You had to dip in the ink periodically (messier than your fountain pen) in order to write. With the invention of a nib pen, people called it a fountain pen because you no longer had to dip, it just came out as if had a fountain of ink as its source within the pen, hence the expression, "fountain pen".