Many authorities "of the time" assert that yarn spun with "the new method" (ie with a DFW of the Mager type) has a much, much better quality - as if consistent grist and twist come automatically with the wheel type. (Maybe it does... after all, I haven't got mine operational yet)
To let you all know as much as I now do, I took a stab at translating the first part of the Book with the Hopeless Title - the part that should instruct us all how to use this famous wheel.
(It can be that you, too, become a bit disappointed with the contents. But I assure you: this is all there is!)
The first part, same as the other, is now available in .pdf-form, the translated variant here with text in both Swedish and (my attempt to translate it into) English. The plate is on the very last page. (Comments on the translation(s) are most welcome!)
There is also the "original" (transcribed, some sort of Swedish) - found here. The drawing is on the last page.
For my local-ish Swedish friends: do you know anything about the Gårdsby Lin-Institut, at Gårdsby outside Växjö, that was in existence 1811-1827 (or -28)? There is a rumour that they used double flyer wheels there, too, but as the Mager type was not known until 1843, I would be very interested to know what kind of DFWs they were using.